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Vol. 43 No. I MARCH 1996


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CONTENTS

Vol. 43 No. I March 1996

The Peace Dividend: Military Spending Cuts and Economic Growth

MALCOLM KNIGHT. NORMAN LOA YZA. and DELANO VILLANUEVA• I

Saving Behavior in Low- and Middle-Income Developing Countries: A Comparison

MASAO OGAKI, JONATHAN D. OSTRY, and

CARMEN M. REINHART • 38

Are Exchange Rates Excessively Volatile? And What Does "Excessively Volatile" Mean, Anyway?

LEONARDO BARTOLINI and GORDON M. BODNAR • 72

Relative Price Convergence in Russia

PAULA DE MASI and VINCENT KOEN • 97

Internal Migration, Center-State Grants, and Economic Growth in the States of India

PAUL CASHIN and RATNA SAHAY • 123

The Costs of Taxation and the Marginal Efficiency Cost of Funds

JOEL SLEMROD and SHLOMO YITZHAKl • 172

Nonlinear Effects of Inflation on Economic Growth

MICHAEL SAREL • 199

Asymmetry in the U.S. Output-Inflation Nexus

PETER CLARK, DOUGLAS LAXTON, and DAVID ROSE • 216

Corrigendum • 252

IMF Working Papers • 254

IMF Papers on Policy Analysis and Assessment • 257

iii


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IMF Staff Papers Vol. 43. No. I (March 1996) © 1996 International Monetary Fund

The Peace Dividend:

Military Spending Cuts

and Economic Growth

MALCOLM KNIGHT, NORMAN LOAYZA, and DELANO VILLANUEVA*

Although conventional wisdom suggests thar reducing military spending may improve a country's economic growth performance, empirical studies have produced ambiguous results. This paper extends a standard growth model and obJains consistent panel data estimates of the growth retarding effects of militcny spending via its adverse impact on capital formation and resource allocation. Simulation experiments suggest that a substantial long-run "peace dividend"-in the form of higher capacity output-may result from markedly lower military expenditure levels achieved in most regions during the late 1980s, and the further military spending cuts that would be possible if global peace could be secured. [JEL 041, 04 7]

THERE IS A WIDELY HELD view that political tensions and associated high levels of military spending are likely to detract from a country's long

run economic growth performance. In an insecure region, so the argument goes, each country must devote a disproportionate share of its endowment of scarce economic resources to "unproductive" military spending. In the absence of international cooperation to reduce political tensions, military

* Malcolm Knight, Deputy Director of the IMF's Middle Eastern Department. holds a Ph.D. from the London School of Economics and Political Science. Norman Loayza is an Economist in the Macroeconomics and Growth Division of the World Bank's Policy Research Department. He received his doctorate from Harvard University. Delano Villanueva, who holds a doctorate from the University of Wisconsin, was Assistant to the Director of the TMF s Middle Eastern Department when this article was written. He is currently on a year's sabbatical leave at the University of Hawaii. The authors are indebted to Paul Cashin, Daniel Hewitt, Mohsin Khan, Anne McGuirk, Peter Montiel, and Michael Sarel for comments. Daniel Hewitt also provided data and advice on interpreting available statistics on militruy expenditures. Peter Kunze) assisted with the empirical research.


2 MALCOLM KNIGHT, NORMAN LOAYZA, and DELANO VILLA UEVA

spending may be ratcheted up throughout a region as each country tries to outspend its neighbors to ensure its own security, resulting in higher levels of military expenditure but no increase-or even a decrease-in the secutity of the region. While political tensions themselves can weaken various aspects of economic perfom1ance, there are two direct and interrelated avenues by which higher military spending may adversely affect long-run output growth. First, increases in military spending may reduce the total stock of resources that is avai !able for alternative domestic uses such as investment in productive capital, education, and market-oriented technological innovation. Second, high spending on the military may aggravate distortions that reduce the efficiency of resource allocation, thereby lowering total factor productivity.

If these effects turn out to be empirically significant. then a converse proposition is also likely to be valid: the sustained military spending cuts that would become feasible as a result of improved international security should yield a "peace dividend" in the form of higher long-run levels of capacity output. It would then follow that forms of international cooperation that succeeded in reducing tensions, and thus in lowering military spending, would be to the long-run economic benefit of all countries. Interest in the potential size of this peace dividend has risen considerably in recent years with the improvements in international security that have become evident for both industrial and developing countries with the end of the Cold War and the more recent initiatives aimed at achieving a comprehensive peace in the Middle East.

The view that low levels of military spending are associated with strong growth performance is usually argued by recourse to casual empiricism. For example, the post-World War II experiences of the Federal Republic of Germany and Japan fend support to the notion that there are substantial economic benefits from sustaining low rates of military expenditure over long periods of time. The st1ict postwar limits on defense spending in these countries-combined with the Allies' effective guarantee of their securitywere factors that allowed the Federal Republic of Germany and Japan to devote relatively large proportions of their total factor endowments to productive capital formation, thereby contributing to their impressive economic growth performance during the succeeding five decades. Such general but striking observations have left most economists with a strong presumption that, on average, a country that has a relatively low ratio of military expenditure to GOP is likely to display relatively strong long-run growth performance.

Yet not all military spending is unambiguously counterproductive, or even unproductive, in an economic sense. It is often argued, for example, that expenditure on military training in developing countties may contribute to improving the educational level and disci pi ine of the labor force and may act


THE PEACE DIVIDEND 3

as a stabilizing influence in the society. Likewise, it has been argued (see, for example, Thompson ( 1974)) that military expenditure can be economically productive to the extent that it enhances the state of national security and improves the enforcement of property rights, thereby encouraging private investment and growth. Capital expenditure on the military can also have productive uses: many developing countries still benefit from transport and communications networks that were originally constructed for military purposes. These counterexamples suggest that the question of whether, and to what extent, military spending is economically unproductive cannot be resolved by recourse to anecdotal evidence and historical generalizations, but instead requires rigorous theoretical and empirical analysis.

The analysis must also be able to confront formidable estimation problems. Even if cuts in military spending do improve growth performance substantially, these effects are likely to occur with a long lag. Thus, even in cases where military spending cuts are large, the ultimate beneficial effects may be hard to disentangle empirically from other factors that also influence economic growth. Given these considerations, i t is not surprising that the existing empirical literature yields ambiguous results, not only on the magnitude of the impact of military expenditure on long-term economic growth, but even on whether the effect is positive or negative. Nevertheless, if national governments are to be convinced that it is to their economic advantage to stockpile fewer guns in order to make room for more investment in productive capital, they need to be presented with robust quantified estimates of the costs that military spending imposes on the economic welfare of their citizens and to have convincing evidence of the improvements in living standards that can result over the long run from military spending cuts.

Such a quantification is attempted in this paper. We address several questions. Is there a peace dividend from military spending cuts? If so, how large might it eventually be? More specifically. how much is productive investment likely to increase in response to military spending cuts. and how strongly will the associated improvements in the efficiency of resource allocation increase long-run capacity output, relative to the level it would have attained if the fraction of GDP absorbed by military spending had remained unchanged?

This paper extends a standard neoclassical growth model to take account of important linkages between military spending, productive investment, and the long-run growth of per capita capacity output. It implements an econometric technique for obtaining empirical estimates of the model from a panel of time-series and cross-sectional data for a large sample of developed and developing countries. We then use the estimated model in simulation experiments designed to gauge the size of the peace dividend-that is, the impact of cuts in military spending on economic growth performance-in a number of major geographic regions. Our estimation and sim-


4 MALCOLM KNIGHT, NORMAN LOA YZA, and DELANO VILLANUEVA

ulation analyses suggest that these peace dividend effects would take some time to emerge, but would eventually be large, especially for countries in regions-such as Eastern Europe, North Africa, and the Middle Eastwhere levels of military spending have traditionally been high.

The paper is organized as follows. Section I summarizes trends in military expenditures since the early I 970s and reviews the empirical literature on the relationship between military spending and economic growth. Section II outlines our extension of a standard neoclassical growth model and the estimation technique used. Section III first presents standard crosssectional estimates of the effect of military spending on investment and economic growth, and then contrasts them with the results of our panel data estimation. Section IV describes two simulation experiments that help to indicate the rough order of magnitude of the peace dividend from military spending cuts. We first simulate the long-run growth effects of the developments in mjJitary spending that have already taken place in various geographic regions during the latter half of the I 980s. We then simulate the potential effects of further declines in military spending that might occur in various regions in the future if a lasting global peace could be secured. Section V concludes.

I. Data and Empirical Research on Military Spending

Throughout this paper we define the military spending rcuio, m, as the ratio of total military expenditure (M) to GDP; the data used here are those published by the Stockholm International Peace Research Institute (SIPRI). 1 We define the peace dividend natTowly as the percentage difference between the level of real capacity output per capita that would result from a given sustained reduction in the military spending ratio, and the baseline path of capacity output that would have prevailed in the absence of such a reductjon.

Trends in Military Spending, 1972-1990

The descriptive literature on trends in military expenditures (see Hewitt ( 1993) and the primary data sources cited there) indicates the large extent

1 Appendix I provides definitions and sources for all data used in this study. A detailed discussion and analysis of the SIPRI data on military spending, as well as that provided by other sources, is given in Hewitt ( 1992 and 1993). Based on his detailed analysis, Hewitt concludes that the SIPRI data are to be preferred to other sources for empirical work of the sort we undertake here.



Table I. Ratios of Milital)' Spending 10 GOP for Various Coumrv Groups and Time Periods•

Full sample Industrial countries Developing countries

Regional groupings: Asia Eastern Europe Middle East North Africa Sub-Saharan Africa Western Hemisphere

Source: Hewitt (I 992).

Period weighted averages. in percemh

Full period Period I Period II ( 1972-90) ( 1972-85) ( 1986-90)

5. 10

3.90

5.20

5.70 1 2.40 10.00 7.20 3.20 2 . 10

5 . 19

3.97

5.54

6.35 1 1 .75 10.36 8.12 3.12 2. 16

4.84 3.70

4.26

3.88 14.22 9.06 4.60 3.42 1 .94

" See Appendix I for lists of countries included in each grouping for Hewitt's sample.

h The weights are each country's share in the group GDP measured in U.S. dollars using official exchange rates.

to which the world's productive resources have been devoted to the military throughout the petiod since World War J£.2 Hewitt's data show important differences in military spending across country groupings as well as over time. On average during the period 1972-90. for example, over 5 percent of world resources, as measured by the combined GOP of the countries considered by Hewitt. was devoted to military spending. Table I sununarizes the main patterns of military expenditure for industrial countries and for developing countries i n various geographic regions. The entries in this table are weighted averages of national military spending ratios, where the weights are each country's share of the regional total GOP level measured in U.S. dollars using official exchange rates.

Table I presents these averages for nine country groupings: the full sample of 124 countries; a group of 22 industrial countries; and I 02 developing countries subdivided into six regional groups-Asia, Eastern Europe, Middle East, North Africa, sub-Saharan Africa, and Western Hemisphere. This table also regroups these regional data into two time periods. Period I

extends over 1972-85; it covers roughly the years when the Cold War was still at its height and when initiatives toward improved security in the

�Our paper makes use of the data on military expenditures presented in Hewitt ( 1992 and 1993), which are based mainly on statistics published by SIPRI. Hewitt's data cover 124 industrial and developing countries.



Middle East had not yet borne fruit. Period II covers 1986-90, which can be characterized as a period of diminishing tensions associated with the gradual end of the Cold War and somewhat improved security conditions in Asia, the Middle East, and North Africa.

The data in Table l yield several broad observations. First, in both periods military spending ratios varied widely between the industrial and developing country groups, and among developing countries in different geographic regions. For example, among the developing country groups during Period I regional average military spending ratios ranged from a high of over I I percent of GDP for countries in Eastern Europe to only just over 2 percent for the Western Hemisphere. These differences correspond broadly to what one would expect given the different levels of security across regions. For example, in both periods countries in Eastern Europe and the Middle East had the highest military spending ratios, reflecting the failure to achieve comprehensive improvements in security in those regions. Next in ranking were Asia and North Africa, followed by subSaharan Africa. Finally, the very low ratio for Western Hemisphere developing countries in both periods reflects the low incidence of major armed conflicts in this region.

A second striking feature of the data is that world military spending has been declining in recent years. When Hewitt compares the ratios for the midl980s with those for 1990, he finds that total military expenditures of all countries i n his sample fell sharply, from 5.6 percent of combined GOP in 1985 to 4.3 percent five years later. Table I shows that this feature i s the most striking in North Africa and Asia. For the group of Middle East countries, where military spending absorbed over 10 percent of GOP during 1972-85, the weighted average ratio also fell markedly in the latter half of the 1980s. The industrial countries had a modest decline in military spending during the late 1980s associated with the end of the Cold Wm·. Developing countries in the Western Hemisphere region, which already had very low levels relative to other developing regions, experienced only very small further reductions. An unfortunate contrast with these trends is evident in Eastern Europe and sub-Saharan Africa, where ongoing internal and regional tensions caused weighted average military spending ratios to rise by 2.5 and 0.3 percentage points, respectively, in 1986-90. While these averages were higher for 1986-90 than for Period I, a year-by-year analysis shows that military spending ratios were on a declining trend in both regions after 1987.3

J It is noteworthy that the weighted average military spending ratio for the whole group of developing countries fell by considerably more than it did in the industrial countries. Whereas the weighted average ratio of developing countries had been nearly 1.6 percentage points higher than that of the industrial countries in Period I, in Period II it fell to a level only 0.6 percentage points higher.



The Relationship Between Military Spending and Growth

The relationship between military spending and output growth is complicated by the fact that it has both short-run and long-run components, which may act in opposite directions. In the short run. as with increases in other types of government expenditure, a rise in military spending on final goods and services may increase aggregate domestic demand, thereby exerting a stimulative Keynesian impact on the growth rate by inducing a rise in capacity utilization-that is, it raises the growth of current output relative to that of capacity output.4 However, these short-run stimulative effects do not necessarily lead to higher levels of capital formation and capacity output. Indeed, over the longer term increases in military spending are likely to exert a negative effect on capacity output.

There are at least two channels by which a sustained increase in military expenditure might depress a country's secular growth performance. The first results from the likelihood that, other things equal, a rise in military spending exerts a negative impact on the rate of investment in (public and private) productive fixed capital. This occurs because of well-known crowding-out effects: an increase in military spending may be financed either by raising current taxes or by borrowing (future taxes). In either case. it will lower the expected after-tax return on productive fixed capital. while simultaneously reducing the flow of (domestic plus foreign) savings that is available to finance productive fixed capital formation in the domestic economy. Alternatively, the rise in military spending may be accomodated by a fall i n public sector investment. These channels are likely to be particularly important in net-debtor developing countries. Since such countries are faced with external financing constraints, a rise in military spending-to the extent that it is not associated with larger net capital inflows to finance a higher external current account deficit-can be expected to crowd out capital investment and/or private consumption.�

� Hewitt ( 1 992) hypothesizes that military expendiwres can have a net positive or negative impact on economic growth depending on the alternative use of rhe funds. He argues that military expenditures on general-use public infrastrucrure and promotion of research, as well as demobilization of trained personnel, contribute to economic growth; however, military spending is an inefficient way to enhance growth compared with private investment expenditure or government expenditure on social infrastructure and education. In the context of developing countries, Hewitt contends that the justification for military expenditures must be on national security grounds, since the economic benefits are limited.

5 Hewitt ( 1992) notes that increases in military spending may be financed through higher external borrowing, lower private consumption. lower private investment, and lower expenditures on other government programs, including productive ones such as education and health services, pub I ic infrastructure, and the police and judicial systems. In general. the likely consequences would be lower current consumption and investment levels and lower future growth. the exact mix being dependent on the particular financing channel.


8 MALCOLM KNIGHT, NORMAN LOAYZA, and DELANO VILLANUEVA

A second channel by which military expenditures may affect the growth path of capacity output is through their direct impact on the efficiency of resource allocation. Since military spending is not governed by market processes, it tends to create distortions in relative prices that result in a deadweight loss to total productive capacity. In addition, it may exert negative externalities on capacity output. There are several ways in which these inefficiencies directly affect the growth rate. A higher deadweight loss to domestic production results from either an increase in contemporaneous taxes or heavier borrowing to finance higher military spending. In developing countries this financing often involves increased government borrowing from the domestic banking system, which raises inflation and distorts resource allocation.6 Furthermore, research and development activities may concentrate on military progress at the expense of technological advances in economically productive areas. Policies implemented to support a military program are often detrimental to efficient resource allocation and market growth: examples are trade restrictions, nationalization of military equipment producers, military procurement preferences for certain firms and industries, and compulsory mjlitary service. Finally, rent-seeking activities grow around the military because of its noncompetitive allocation of resources. In this way, over and above their depressing effect on the level of investment, military expenditures may exert a direct adverse impact on the economy's productive efficiency.

These considerations suggest that the net effect of a rise in military expenditure on a country's growth rate and its steady-state level of capacity output is likely to be negative. Therefore, one would expect to find evidence of this negative impact in longer-run economic data both across countries and over time. However, it is obviously difficult to disentangle empirically the potential positive short-run effect of the demand stimulus associated with an increase in military spending from the depressing effect of high military spending on the longer-run growth path of capacity output, particularly if the estimation work fails to exploit both the time-series and cross-sectional dimensions of the data. The striking ambiguity of past econometric results in the face of strong anecdotal evidence on the long-run economic benefits of lowering military expenditure suggests that weaknesses in the econometric techniques used to test these hypotheses may be a problem.

Thus it is not surprising that a number of past attempts to subject the relation between military spending and growth to empirical testing-Benoit ( 1973 and 1978) and Frederiksen and Looney ( 1982)-find apparent empir-

b See Tommasi ( 1993) and de Gregorio ( 1993).



ical support for the thesis that military expenditures are not detrimental to growth. Benoit ( 1978), using data for 44 developing countries over 1950-65, finds a positive association between military spending and growth of civilian per capita output. In contrast, Rothschild ( 1977), on the basis of rank correlations on growth, exports, and military spending for 14 OECD countries during 1956-69, concludes that higher military spending is associated with lower exports and lower economic growth. Deger and Smith ( 1983) find that the direct impact of military expenditures on growth is positive, while the effect on savings is negative; in their view the net impact of military expenditures on growth is adverse because the negative indirect effect on savings outweighs the positive direct impact. Biswas and Ram ( 1 986) conclude that military expenditures neither help nor hinder economic growth. Aschauer ( 1989) finds that government expenditure on infrastructure in the United States has a positive effect on growth, while military capital expenditures have virtually no impact. Using data for 7 1 countries over the period 1969-89, Landau ( 1 993) concludes that military expenditure is not associated with lower rates of economic growth, capital formation, or government social and infrastructure spending. Some other studies have obtained a negative, but weak empirical relationship between military spending and economic growth.7 Both the model we specify in the next section and the technique we suggest for estimating it are intended to address the limitations of past empirical research on this relationship.

II. Model and Empirical Methodology

We now extend the standard neoclassical growth model of Solow ( 1956) and Swan ( 1956) to incorporate the linkages between military spending, productive investment, and the growth of capacity output. We do this by expanding the empirical analysis of this model that we undertook in Knight, Loayza, and Villanueva ( 1 993) to allow for the possible effects of military spending on the growth path of per capita capacity output. First, we expand the basic neoclassical growth equation: in addition to the investment ratio and other factors considered in our earlier paper, it now includes the military spending ratio as a determinant of capacity output. Second, we specify an explicit investment function in which the ratio of investment to GDP is determined by several standard factors, and also by the fraction ofGDP that is devoted to military spending.

Our equation for the rate of economic growth is based on the Mankiw, Romer, and Wei I ( 1992) version of the Solow-Swan model. It is derived by

7 See Chan ( 1985) for a selected bibliography.


1 0 MALCOLM KNIGHT, NORMAN LOAYZA. and DELANO VILLANUEVA

linearizing the transition path of output per capita around irs steady-state level.x The resulting equation specifies output growth as a function of initial output and variables that condition for the economy's steady state. The conditioning variables that we include are the ratio of investment to GOP; the rate of population growth; a proxy for the degree of restrictiveness of the country's international trade regime (i.e., a weighted average of its tariff rates on intermediate and capital goods); the Barro-Lee ( 1993) proxy for the incidence of wars;9 the ratio of military spending to GOP; and a dummy variable that catches any otherwise unspecified country-specific effects. In accordance with the Solow-Swan model we assume that the conditioning variables are exogenous with respect to output growth; in particular, the ratio of military expenditures to GDP is assumed to be unaffected by the rate of output growth. 10

Equation ( I ) specifies the per capita output growth rate, Z;.,- Z;.1-1, where z is the natural logarithm of output per capita:

z;,, -zu_1 =911 ln(n;,, +g+8)+9k ln(sk;,,)+9111 ln(m;, )

+911 lnsh; + 9 I ln f,. + ew ln w; +yzi.t-l +�, + J.l; +�u; (l)

a natural logarithm is indicated by In; the indices i and t represent the country and time period, respectively; n i s the average population growth rate; g is the rate of technical progress, 8 is the rate of depreciation of the stock of physical capital, and g + 8 is assumed to be equal to 0.05:1 1 sk is the ratio of physical capital investment to GDP; m is the ratio of military expenditures to GOP; sh is a proxy for the ratio of human capital investment to GOP;f is a proxy for the degree of restrictiveness of the economy's international trade system; w is the proxy for the incidence of wars; s, represents time-specific factors; J.l, represents country-specific factors; and e is a whitenoise error term.

8 For details of this derivation, see Knight, Loayza, and Villanueva ( 1993). The growth effects that we discuss in the current paper apply to the transition to the steady state.

9 The Barro-Lee proxy variable for the incidence of wars is defined for each country as the number of war years as a frac1ion of total years in the period 1960-85. See Barro and Lee ( 1993). 111 There are three differences between the growth equation specified in this paper and the one used in our 1993 paper. First, in this paper we do not include the ratio of government fixed investment to GOP as an explanatory variable, since we found it to be statistically insignificant in our previous study. Second, and more important, we now include as a regressor the ratio of military expenditures to GOP. Finally, to isolate the effect of military expenditures on the allocation of productive resources, we control for the incidence of wars on economic growth by including the above-mentioned Barro-Lee proxy.

11 The assumption that g + o = 0.05 follows Mankiw. Romer, and Weil ( 1 992). We find that although changes in this number affect the estimated 6., they do not significantly affect the other estimated coefficients.


THE PEACE DIVIDEND I I

In order to allow for the indirect effect of military spending on growth via its impact on productive investment, we extend the model of our earlier paper to include a second equation that specifies the ratio of real investment to real GDP as a function of the rate of investment in human capital, sh; the restrictiveness of the trade system,/; the proxy for the incidence of wars, w; and the military spending ratio, m. The investment equation is

In sk;., = 11, ln(n;., + g + 0) + TJ111 In m;_, + 1l1r Jnsh;

+TJ1 In _t; + 11,. In w; + s, + ).!; + e;_,. (2) As already noted, we use Hewitt's annual data on the ratios of military

expenditure for all the countries in our sample. However, owing to limitations on the availability of data for some countries on the other variables that enter into equations ( I) and (2), our estimation sample is a subset of the countries covered by Hewitt.12

The basic estimation sample covers 79 countries over the period from 1971 to 1985. The countries included, together with the simple and weighted means and standard deviations for their ratios of military spending to GDP over 1971-85 and 1986-90, are presented in Table 2. A comparison of the weighted averages for each of the country groups in our sample with those for the full group of 124 countries discussed by Hewitt shows thar, for the regions we include, our sample has features that are quite close to those highlighted by Hewitt. In particular, the declines in the weighted average military spending ratios in each region are about the same size in the two samples.L1 This broad correspondence gives us a degree of confidence that although the sample we use to estimate the model has a less comprehensive country coverage than Hewitt's, it nevertheless retains broadly simi lar characteristics.

Since available statistics indicate that the fraction of GDP devoted to the military varies widely both across countries and over time, our empirical

12 The countries excluded from our sample are those in Eastern Europe (including the countries of the former Soviet Union and the former Democratic Republic of Germany), and other countries for which complete data were not available for other variables in the model. The latter include several developing countries in Asia, sub-Saharan Africa, and the Western Hemisphere. Consistent with other empirical studies of long-term economic growth, we also exclude from the estimation sample a few countries-mostly in the Middle East and North Africa-whose main source of GDP comes from the extraction of petroleum resources. The list of countries and the data sources for the variables used to estimate our model are presented in Appendix I.

.. , The exception is sub-Saharan Africa, where the country coverage of our sample is much less comprehensive than Hewitt's owing to the unavailability of data on the other variables in equations (I) and (2). As a result of these differences in coverage, our data show a small decline in the weighted average military spending ratio for these countries, while Hewin's more comprehensive data show a small rise.

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methodology is designed to exploit these two dimensions of the data to overcome some of the shortcomings of past empirical work and obtain consistent estimates of the effect of military expenditures on investment and economic growthY Specifically, we employ the econometric technique proposed in our earlier paper (Knight, Loayza. and Villanueva ( 1993)) to deal with time-series cross-sectional data.

To construct the panel data set we work with non-overlapping intervals of five years each. We have cross-sectional data covering output growth and several other variables in three separate five-year periods: 197 1-75, 1976-80, and 198 1-85. Since data for all variables are available for 79 countries, this gives us a relatively large panel data sample of 79 X 3 = 237 observations on the dependent variables in equations ( I ) and (2). We measure the growth of per capita output over a five-year interval. rather than a single year. This procedure provides a simple means of smoothing out shortrun cyclical variations in the rate of capacity utilization, thereby helping to ensure that this variable approximates output growth at the average rate of capacity utilization in each five-year time period for each country in the sample. 15 Similarly, the data for the investment ratio sk are averaged over the same five-year intervals. The variables for which panel data are available are indexed by both time, t, and country, i; these variables are z, h, sk, m, and sh. The remaining variables, f and w, for which we have only cross-sectional data, are indexed only by country. The observations for the level of per capita output that are used to obtain the growth rate for each five-year interval correspond exactly to the years 1970, 1975, 1980, and 1985. For the rest of the panel variables-n, sh, m-observations correspond to the averages over the five-year intervals 1971-75, 1976-80, 1981-85. For the crosssectional variables-sh,f, w-observations for each country correspond to averages over the whole 15-year period ( 1971-85) under consideration or, in a few cases, that portion of it for which data are available.

The fact that panel data are available for most of the variables of interest allows us to account for both country-specific and time-specific effects. Country-specific effects are especially important irn the present analysis. There are a host of factors that are peculiar to each country-government policies, resource endowments, social institutions, geographic location, and cultural traits-and these may well be correlated with the regressors considered in the model. Failure to account for them would lead to inconsistent estimates of the parameters. To account for country-specific effects, we use

14 In this paper the term investment, used alone. refers t<> investment in physical capital. When we refer to human capital investment, we say so explicitly.

15 This follows the technique used by Phillips ( 1958) to ensure that his estimated relation between the rate of change of nominal wages and the level of the unemployment rate was approximately a phase line.


THE PF.ACE DIVIDEND 1 5

the methodology proposed by Chamberlain ( 1982 and 1 984), commonly known as the 0-matrix technique. We control for the time-specific effects by removing the time means from each variable. Given that the growth regression contains a lagged dependent variable. the fixed-effects "within'' estimator that is commonly used to control for specific effects would yield inconsistent estimates.

A detailed exposition on the application of the 0-matrix technique to growth regressions estimated using panel data is presented in our earlier paper. Basically the application has two steps. First, we replace the countryspecific factor J.l;.� by its linear predictor E•(J.l;_,) plus an error term in the regression equation for each time period. The linear predictor is a linear function of the regressors for all time periods. This yields a system of reduced-form regression equations. with one equation for each time period. Second, we estimate the reduced-form parameters in the system and, from them, obtain the structural parameter estimates through a minimum-distance estimation procedure. Chamberlain ( 1 982) shows that this procedure resull'> in consistent and asymptotically efficient estimates.

III. Estimation Results

We now present the estimation results for our two-equation growth model. To illustrate the difficulties (discussed in Section I) that may have arisen in past empirical work on the impact of military spending on growth, we first employ a standard estimation procedure that is widely in use in empirical research in growth economics. Specifically, we obtain standard crosssectional estimates of equations ( I ) and (2) using the data on output growth and the investment ratio for each country in our sample averaged over the whole period 1971-85 and average levels for each country of the values of the right-hand-side variables over the same period. This approach will show us what the parameter estimates for our model would look like if they were obtained without taking full advantage of the time-series dimension of the data set. Next, we re-estimate the model on our sample of panel data observations using our proposed econometric approach, and compare the parameter estimates obtained using the two alternative estimation methods.

Standard Cross-Sectional Estimation

Table 3 reports standard cross-sectional estimates of the growth equation (equation ( I )). To account for geopolitical and developmental differences across regions we consider two regional dummy variables in our crosscountry regressions, one for Africa (AFR) and the other for the developing



Table 3. Standard Cross-Sectional Regressions for the Growth Rate•

Coefficient Coefficient Coefficient Variable (t-ratio) (t-ratio) ( t-ratio)

z,_ , -0.0057 -0.0055 -0.0057 ( - 1 . 1 7 ) ( - 1 . 17) ( - 1 . 19)

In (n + 0.05) 0.01 03 0.0091 0.0088 ( 1 .5 1 ) ( 1.37) ( 1.28)

In sk 0.0 1 12 0.01 10 0.0107 (2.73) (2.68) (2.57)

In sh 0.0013 0.0012 0.0012 (0.86) (0.87) (0.89)

In/ -0.0189 -0.0 1 8 1 -0.0184 ( -2. 1 2) (-2.12) (-2. 1 1 )

In m 0.0023 0.0026 (0.69) (0.72)

w -0.0043 (-0.50)

constant 0.0537 0.0471 0.0489 ( 1 .79) ( 1 .70) ( 1 .74)

AFRh -0.0079 -0.0072 -0.0070 ( - 1 .09) ( -2.98) (-0.95)

WH -0.0139 -0.0128 -0.0 125 ( -2.78) (-2.48) ( -2.30)

Adjusted R2 0.244 0.241 0.231 • Number of countries = 79 .

h ··Africa'· is defined as countries in the North and sub-Saharan African regions.

countries in the Western Hemisphere (WH). We find that only the investment ratio, the proxy variable for international trade restrictions, and the dummy variable for the developing countries in the Western Hemisphere enter significantly with the expected signs. Indeed, in line with the results of several of the empirical studies cited in Section I above, in the crosssectional regression for the growth rate the estimated coefficient of military spending is positive but statistically insignificant. Note also that when the military spending ratio is included in the regression, the estimated coefficients of the other variables change very little. The same results are obtained when the proxy for the incidence of wars is included. We believe that these rather inconclusive cross-sectional results help to illustrate why the past empirical work cited in Section I has been affected by the application of estimation procedures that do not take advantage of all the information available in the data set.

Table 4 reports the estimation results for a standard cross-sectional regression of the investment equation (equation (2)). Only the proxy for investment in human capital and the dummy variable for Africa exert positive and statistically significant effects on investment in physical capital.


THE PEACE DIVIDEND

Table 4. Standard Cross-Sectional Regressions for the Ratio of Investment to GDP•

17

Variable Coefficient ( t-ratio) Coefficient (!-ratio)

In (n + 0.05) -0.1400 -0.1478 ( -0.79) (-0.89)

In sh 0.0702 0.0664 (3.47) (3.43)

In/ -0.0895 -0.0985 ( -0.36) (-0.41)

In m 0.0401 0.0809 (0.54) ( 1 .0 I )

w -0.5190 ( - 1 .5 1 )

constant 2.1726 2. 1620 (4.16) (4.3 1 )

AFR" -0.4054 0.3723 (-2.10) ( - 1 .89)

WH -0.1736 -0.1362 ( - 1 .37) (- 1 .05)

Adjusted R2 0.463 0.483 • Number of countries = 79. b "Africa" is defined as countries in the North and sub-Saharan African regions.

In particular, the cross-sectional regression cannot identify a significant relationship, whether positive or negative, running from the level of military spending to the rate of capital investment When the proxy for the incidence of wars is added to the regression equation the parameter estimates change only slightly; as expected, the proxy exerts a negative effect on investment that is statistically significant at the 10 percent level.

Panel Data Estimation

We now contrast these standard results with our panel data estimates of the investment and growth equations. Table 5 reports estimates of the growth equation (equation ( I )) using our panel data and estimation technique. First, consider the results when military expenditure is not included in the regression. The lagged value of per capita output is significant and negatively related to the growth rate. This is the standard result in the empirical growth literature, known as ·'conditional convergence." Our results imply that the growth rate of population is not a significant determinant of per capita output growth. This is somewhat surprising in the light of previous studies, which find a negative relationship on the basis of data from 1960 to 1985. Investments in physical capital and human capital both exert a positive effect on growth, and trade restrictions have a negative influence.



Table 5. Panel Regressions for the Growth Rare·'

Coefficient Coefficient Coefficient Variable (r-ratio) (r-ratio) (r-ratio)

z,_, -0.0989 -0.6656 -0.0262 (-3.83) ( -2.96) ( - 1 .27 )

In (n + 0.05) 0.00003 0.0064 -0.0004 (0.003) (0.48) (-0.03)

In sk 0.0227 0.0225 0.0165 (3.65) (3.94) (2.92)

In sh 0.0603 0.0404 0.0158 (3.73) (2.99) ( 1 .32)

lnf -0.0286 -0.0204 -0.0091 ( - 4.35) ( -3.39) (- 1 .63)

In m -0.0081 -0.0060 (-2.67) ( -2.06)

w -0.0132 (- 1 .5 1 )

Wald test for uncorrelated 28.19 5 1 .61 55.59 effects (p-value) (0.0000) (0.0000) (0.0000)

" Number of countries = 79.

When we include the military spending ratio as an explanatory variable in our panel data regression. we find that it has a negative and significant effect on growth. It implies that, in addition to crowding out physical investment (as analyzed below and reported in Table 6), a rise in military spending also exerts an independent negative impact on economic growth. This is true even though we are additionally controlling for human capital investment, population growth, and trade restrictions. The panel data estimation results of the growth equation that are reported in Table 5 are therefore consistent with the view that a rise in military spending adversely affects the growth performance of the economy.

A further important result of our empirical work is that inclusion of the military spending ratio reduces the absolute size of the estimated coefficients of physical investment, human investment, and trade restrictions in the growth equation. This follows from the fact that military expenditures are generally negatively correlated with both types of investment, and positively correlated with the intensity of trade restrictions.'" Given that both

16 As expected, the proxy for the incidence of wars exerts a direct negative and significant effect on economic growth. The inclusion of this variable in the panel estimates also alters the magnitude of the estimated coefficients of the other regressors. In fact, all such coefficients decrease in absolute size, reflecting the fact that levels of both physical and human capital are negatively correlated with the incidence of military conflict, whereas the incidence of military conflict is positively correlated with intensification of trade restrictions and with increases in military expenditures.


THE PEACE DIVIDEND 1 9

Table 6. Panel Regressions for the lnvestmelll to GDP Ratio•

Coefficient Coefficient Coefficient Variable (t-ratio) ( t-ratio) (t-ratio)

In (n + 0.05) 0.5081 0.6506 0.6950 (3.37) (4.65) (4.74)

In sh 0.2707 0.25 1 1 0.2294 (2.99) (2.99) (2.99)

lnf -0.1225 -0.0947 -0.0766 (-2.03) ( - 1 .69) ( - 1 .52)

ln m -0.0742 -0.0754 ( - 1 .98) (-2.14)

w - 1 .3232 ( - 6.78)

Wald test for uncorrelated 5.46 38.57 65.85 effects ( p-value) (0.1410) (0.0000) (0.0000) a Number of countries = 79.

human capital investment and the openness of the trade system have a significant positive impact on output growth, their negative correlation with military expenditures indicates the possibility of other channels through which military spending adversely affects growth; namely, through crowding out human capital investment and fostering the adoption of various types of trade restrictions. 17 Owing to the lack of panel data on the proxies for human capital investment and trade restrictions, we cannot run separate regressions explaining the variables sh and J, and thus we are unable to quantify such effects. However, as explained below, we do estimate the effect of military spending on physical capital investment.

Table 6 reports the panel data estimates for the investment equation. In contrast to the standard cross-sectional results, in our panel regressions of this equation all the variables now enter with the expected sign and all but one are significant at the 5 percent level; the effect of jis significant at about the 20 percent level. The inclusion of the proxy for the incidence of wars does not importantly modify the parameter estimates but, as expected, it affects investment in a negative and significant way. Population growth and human capital investment have positive effects on physical capital investment, while a more restrictive trade system has a negative impact. Most interesting for our purposes-and consistent with our priors-the panel data

17 The positive correlation between military spending and trade restrictions is particularly strong in developing nations. Given that most of these countries import military armaments from industrial countries, they are more exposed to balance of payments difficulties when these purchases are made. This may be one of the reasons why developing countries also tend to operate more restrictive trade regimes.



estimates reveal that a rise in the ratio of military spending has a statistically significant negative impact on investment. Thus our results for equation (2) are consistent with the hypothesis that higher military spending does indeed lead to crowding out of investment in productive fixed capital.

IV. The Peace Dividend: Simulation Experiments

As mentioned in Section I , the ending of the Cold War in Europe and the other improvements in international security that occurred in the latter half of the 1980s were associated with significant reductions in military spending in a number of mqjor geographic regions. ln addition, the ongoing peace process in the Middle East raises the prospect that substantial further cuts in military spending could take place in that region in future years. Thus it is interesting to use the panel data estimates of the quantitative impact of military expenditures on investment and growth obtained in the preceding section to assess the timing and rough order of magnitude of the peace dividend effects that might occur in each region.

Simulated Long-Run Effects of the Changes in Military Spending in the Late 1 980s

As a first step, we run simulations to see what our model has to say about the likely long-run effects of the major changes in military spending ratios that took place in a number of regions during the late 1980s. As the data in Table 1 above make clear, the improvements in international security that became evident during the 1 980s permitted governments in all but two geographic regions to achieve reductions in their military spending ratios.

While our empirical results indicate that the effects of these changes may eventually be substantial, the estimated lags also suggest that they will take time to appear. The simulation experiments provide a useful gauge of the timing and size of these effects. We undertake these simulations for the industrial countries and the six regional groups of developing countries analyzed by Hewitt and described in Section 1: Asia, Eastern Europe, the Middle East, North Africa, sub-Saharan Africa, and the Western Hemisphere. The exogenous development that generates each simulation is the change in the military spending ratio that took place in each region during the second half of the 1980s. Specifically, we take the difference between Hewitt's weighted average military spending ratio for Period 1 ( 1972-85) and the corresponding ratio for Period II ( 1986-90) for each country group in Table I . The levels and the resulting changes are reprinted in the first three lines of Table 7.



In these simulation experiments we assume for simplicity that the change in the average military spending ratio in each region is spread over the whole period 1986-90, '8 and that after reaching its new level in 1990 the mjlitary ratio remajns constant. The stylized paths of the changes in military spending ratios that occurred in each region during the late 1980s are illustrated by the solid lines in the top panels of Figure I . The numerical parameters of the model are our panel estimates from Tables 5 and 6. 19

Table 7 and Figure l (solid lines) summarize the simulation results for each of the seven regions. Line 4 indicates the change in the investment ratio that results from the shift in the military spending ratio in each region. For example, in the Asian developing and North African countries, which had the biggest cuts in their military spending ratios over 1986-90, the resulting increase in investment is nearly 0.7 percent of GOP: in the Middle East investment rises by 0.25 percent of GOP; in the industrial countries and the developing countries of the Western Hemisphere the rise is about 0.15 percentage points.

The middle panel in Table 7 shows the difference between the simulated growth rate of capacity output per capita and its baseline path that will eventually result from the changes in military spending levels that actually occurred in each region in the late 1980s. The bottom panel shows the percentage difference in the level of capacity output per capita in each region relative to its baseline path.

In our model, a one-shot increase in the military spending ratio causes a permanent rise in the level of GOP as a result of a transitory rise in the growth rate: since our first set of simulations assumes that military spending ratios are held constant at their new levels from 1990 onward, the growth rates of per capita output in each region gradually decelerate again until they return to the baseline rates. As a result, the percentage deviation in the levels of per capita GOP (shown in the bottom panel of Table 7 and the solid lines in the lower panel of Figure 1 ) continue to rise at decreasing rates until the new steady states are reached in each region.

18 Specifically, we assume that the natural logarithm of the military spending ratio declines linearly over this period. 19 To implement the simulation we first substitute equation (2) into equation ( I ) to obtain the reduced-form relationship between the military spending ratio and the growth path. From this reduced-form equation we obtain the deviation of the simulated growth path for each region owing to the change in the military spending ratio from the path that would have prevailed if this exogenous change had not occurred (for a detailed explanation see Appendix II). Note that since ours is a longrun model the simulations trace the dynamic effects of this change on regional levels of capaciry output. We are not interested in the short-run Keynesian multiplier effects of military spending cuts, since these affect actual output relative to capacity output.

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26 MALCOLM KNIGHT, NORMAN LOA YZA. and DELANO VILLANUEVA

Obviously, the geographic regions that experienced the largest reductions in military spending ratios in the late 1 980s are the ones that will eventually benefit from the largest gains in capacity output per worker. As indicated in the middle panel of Table 7, these past cuts are projected to result in modest but persistent gains in annual growth rates. For example, in the cases of Asia and North Africa, where military spending cuts were largest. the gains in annual growth rates reach a maximum that is about 0.3-0.4 percent per year higher than the baseline growth rate during years 5-1 0; the effects are of course smaller for other country groups, particularly the industrial countries and the developing countries in the Western Hemisphere.

Owing to the dynamic properties of our estimated growth model (relatively slow conditional convergence), these modest deviations in growth rates persist for a long time, and as a result their ultimate effects on the levels of capacity output per worker are noteworthy. For example, our simulations indicate that over the long run the changes in military spending ratios of the late 1980s would-if sustained-result in a gain in the capacity level of per capita output in North Africa of nearly 16 percent relative to the baseline level that would have prevailed in the absence of such cuts; for Asia. output would eventually be nearly 14 percent higher; and for the Middle East it would be 3.6 percent higher.

These results suggest that the long-run peace dividend from the military spending cuts that have already taken place in several regions during the late 1980s will eventually cumulate to substantial effects on the levels of capacity output. 20 By contrast, because of the rise in mi I itary spending ratios that occurred in Eastern Europe and sub-Saharan Africa during the latter half of the 1980s, per capita GDP in these regions would be lower by some 5.3 percent and 2.3 percent, respectively, in the long run.

Simulated Effects of a Generalized Peace i n All Regions

Our second set of simulation experiments looks at the long-run gains in capacity output that could result from jillure large military spending cuts that might be associated with the achievement of a generalized peace in all geographic regions of the world. Specifically, we pose the following questions. If global peace were achieved, by how much might military spending

2u Even for the industrial countries and Western Hemisphere developing countries, where initial military spending levels were low and where the cuts during the latter half of the 1980s were modest. per capita output levels would eventually be 2.0 percent and 2.9 percent, respectively, above the baseline paths.



ratios decline? What might be the size of the stimulus to productive investment? How soon might the resulting peace dividend exert discernible effects on the growth paths of capacity output in various regions? How large might these effects ultimately be? These are. of course, highly speculative questions. Even if there were a sustained improvement in global security, it is not clear how large the resulting cuts in military spending ratios would actually be, since most countries would probably still wish to maintain at least some minimal level of military preparedness.

We have already emphasized that-reflecting the differing levels of political tensions and risks of military conflict in different parts of the world-there has been a wide regional variation in ratios of military spending to GOP throughout the period for which comparable data are available. In particular, as seen in Table I , developing countries in the Western Hemisphere have maintained the lowest average military spending ratios of any region (about 2 percent) over a long period of time. Since the Western Hemisphere developing countries have avoided major armed conflicts throughout this period, it is plausible to assume that the average military spending ratio already observed for this region can be taken as a simple approximation of the minimum level that could be attained in other regions if a lasting world peace were achieved.

Our second set of simulations assumes that the military spending ratio in each region declines steadily over a ten-year period from its regional average level over 1 986-90 to the average level observed for the Western Hemisphere developing countries over the same period-that is, just under 2 percent of GOP. We then simulate the effects of these reductions in military spending on the growth paths of per capita capacity output for each of the regions, and compare them to the baseline paths that would have been traced out if military spending ratios had remained at the average levels observed over 1972-85. Thus these simulations include both the effects of the changes in military spending that occurred in 1 986-90 (relative to the average levels for 1972-85) and the additional effects that would eventually result from a generalized international peace. The results are summarizedin Table 8 and Figure I (dotted lines).

In our model, these large further reductions in military spending ratios would act as a strong stimulus to productive investment in all regions. The fourth line of Table 8 shows that the resulting increases in investment ratios would be especially striking for Eastern Europe (a rise equivalent to 4.9 percent of GOP) and the Middle East (a rise of 3.3 percent of GOP), the regions that-since they currently have high levels of military spending-stand to gain the most from reducing military spending to the minimum level associated with a generalized peace.

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30 MALCOLM KNIGHT. NORMAN LOA YZA. and DELANO VILLANUEVA

The dotted lines in the upper panels in Figure I show the hypothetical downward paths of military spending for each region over the next ten years. The dotted lines in the lower panels represent the percentage deviation of each region's per capita capacity output from the baseline path over a 50-year period starting from 1986. As the simulations indicate, the further gradual declines in military spending in all regions that might be associated with a lasting improvemenr in international security would exert very marked stimulative effects on the growth paths of per capita output in all regions (except Western Hemisphere, where there is assumed to be no further fall in military spending after 1990).

The simulated transitory effects on growth rates are much larger than in the first simulation. For example. in Eastern Europe where-on our assumptions-the total decline in the military spending ratio would be the largest (on the order of 9.8 percent of GOP), the rate of growth of per capita GOP would rise to a maximum during years I 0 to 25. when it would be 0.9 percenr per annum higher than the baseline. In the Middle East, Asia, and North Africa, growth rates would reach a maximum that would be more than 0.6 percent a year higher.

As a result of these differences in growth rates, the ultimate long-run effects on the levels of capacity output would differ widely across regions. but they would eventually be very large indeed. When all lagged effects had worked their way through after more than 50 years, capacity output levels in Eastern Europe and the Middle East would be 50 percenr and 46 percent higher, respectively, than they would have been if the permanent reductions in military spending ratios had not occurred. In the developing countries of Asia and North Africa the long-run gain would be 30 to 40 percent, and in sub-Saharan Africa, over I 0 percent. For industrial countries, capacity output per capita would eventually be higher by 20 percent. This second set of simulations, therefore, suggests that military spending cuts of a size that could be expected to occur in each region if a comprehensive global peace were achieved would exert large positive peace dividend effects on capacity output in most geographic regions.

V. Summary and Conclusion

There are a number of good reasons to expect that military spending cuts associated with improved international security would be likely to enhance long-run economic growth performance. Thus it is surprising that the empirical literature, taken as a whole, yields an ambiguous answer to the question whether military spending cuts have a positive impact on growth. This paper was motivated by our suspicion that the ambiguous results of past studies may reflect weaknesses in estimation methodology, particularly



the failure to exploit both the cross-sectional and time-series dimensions of available data using appropriate econometric techniques.

To unravel the contradictory empirical findings, we estimate an extension of a standard growth model that includes an output growth equation and an investment equation, both of which are functions of the military spending ratio as well as other determinants. We estimate the model on panel data for a large sample of industrial and developing countries.

In contrast to standard cross-sectional estimates, which give no clear empirical results, the panel estimates of both the investment and the growth equations are robust in the sense that all variables enter significantly with the expected sign. The empirical results provide a clear answer to the question whether military expenditure is economically unproductive. Our answer is in the affirmative. When the military spending ratio is added to a growth equation that already includes the determinants suggested by standard theory, the direct effect of higher military spending on per capita output growth is unambiguously negative and large. The indirect impact of military spending on economic growth, through its negative impact on productive investment, is also found to be statistically significant. Thus our empirical estimates clearly indicate that high levels of military expenditure detract from economic growth both because they reduce productive fixed capital formation and because they act more generally to distort resource allocation.

Using simulations with the estimated model, we quantify the likely size of the peace dividend that would result over the long run from sustained cuts in military spending ratios. We find that the improved security conditions and associated military spending cuts in most regions in d1e late 1 980s will lead-provided they are sustained-to substantial gains in capacity output over the long run.

Deeper cuts in military spending that would be made possible by a generalized peace would result in an even larger peace dividend. Specifically, we find that a generalized improvement in security that allowed military spending ratios in all regions to fall to the levels actually observed in the Western Hemisphere in recent years would result in very large long-run gains in capacity output in most regions. For example, in Eastern Europe and the Middle East-where military spending ratios have been high in the past-the salutary effects of military spending cuts on investment and growth could increase capacity output in the very long run by nearly 50 percent over the levels that would have prevailed if military spending ratios had remained fixed at the high average levels that were prevalent in these regions over 1972-85. The long-run peace dividend effects for other regions, though less spectacular than in these cases, are still very large.

It is also relevant to note that these simulation results may actually tend to understate the positive output-growth effects of enhanced international



security. First, a sustained global peace might eventually reduce the world military spending ratio by more than our simulations assume. Universal peace, after all, would be a classic example of a public good. Furthermore, although our simulations explicitly assume that all determinants of investment and growth other than military spending would remain unchanged even if a generalized peace were achieved, it is likely that there would be positive synergies in the evolution of productive technology. Since improved security would allow a greater proportion of research and development expenditures to be devoted to nonmilitary goals, it would stimulate market-oriented technological innovation, thus enhancing the growth of total factor productivity.

Over the long run, improvements in international security would almost certainly result in improvements in the other economic variables that are significant determinants of economjc growth. As political tensions subsided, more and more countries would be able to concentrate on improving economic performance by dismantling barriers to free international exchange of goods, services. and financial assets. In this way, a generalized peace would foster more open trading systems, increased global economic integration, and associated specialization gains. For analogous reasons, a better international security situation would also allow national education programs to concentrate on productive skills, and participation in the educational systems could rise markedly in a number of populous countries where political insecurity has long limited educational opportunities.

Given these considerations, the key policy implication of this study is straightforward. Although the effects of military spending cuts may cumulate gradually over many years, the peace dividend is likely to be very substantial in the long term. Thus, for policymakers who can exercise sufficient patience, reductions in military spending should be attractive structural policy elements of economic reform programs designed to enhance economic growth performance.

APPENDIX I

Data Sources and Definitions, and Sample of Countries

Data Sources and Definitions

The basic data used in this study are annual observations. The following variables were obtained from Summers and Heston's ( 1991) Penn World Tables:


THE PEACE DIVIDEND

z : natural logarithm of real GOP per capita;

sk: ratio of real investment to real GOP (five-year average);

n : population growth rate (five-year average).

33

The following variable was obtained from Mankiw, Romer. and Wei I ( 1992):

sh: percent of working-age population enrolled in secondary schools (average for the period 1960-85).

Data on tariffs were obtained from Lee ( 1993 ):

f : import-share-weighted average of tariffs on intermediate and capital goods (from various years in the early 1980s).

Data on military expenditures were provided by Daniel Hewitt, who collected the data from the 1992 Yearbook of the Stockholm International Peace Research Institute (SIPRI):

m : ratio of SIPRI military expenditures to GDP (data are annual for 1971-1990).

Data on the incidence of wars were obtained from Barra and Lee ( 1993):

w : ratio of years spent in international wars to the total number of years in the period 1960-1985.

List of Countries Included in Hewitt's 124-Country Sample, and Used for Estimation in Our 79-Country Panel Data Set

(Countries from Hewitt's sample that are included in our panel data estimation are marked with an asterisk).

Industrial Countries

Australia* Austria* Belgium* Canada* Denmark*

Finland* France* Germany, Federal Republic of* Greece* Ireland* Japan*

Developing Countries

Algeria* Angola Argentina* Bahrain Bangladesh*

Benin* Bolivia*

Italy* Luxembourg Netherlands* Norway* Portugal*

Singapore* Spain* Sweden* Switzerland* United Kingdom* United States*

Bulgaria Burkina Faso* Burundi* Cameroon* Central African Republic*

Chad China



Botswana Brazil* Congo* Costa Rica* Cote d'Jvoire Cuba Cyprus

Czechoslovakia Dominican Republic Ecuador* Egypt* El Salvador*

Ethiopia* Fiji Gabon German Democratic Republic Ghana*

Guatemala* Guinea-Bissau Guyana Haiti* Honduras

Hungary India* Indonesia* Iran Iraq

Israel Jamaica* Jordan* Kenya* Korea*

Kuwait Lebanon Liberia Libya Madagascar*

Malawi* Malaysia* Mali Mauritania Mauritius* Mexico* Morocco*

Chile* Colombia Mozambique Myanmar Nepal* Nicaragua* Niger

Nigeria* Oman Pakistan* Panama Paraguay*

Peru* Philippines* Poland Romania Rwanda*

Saudi Arabia Senegal* Sierra Leone* Somalia* South Africa

Sri Lanka* Sudan* Swaziland Syrian Arab Republic* Taiwan Province of China

Tanzania* Thailand* Togo Trinidad and Tobago* Tunisia*

Turkey* Uganda* United Arab Emirates USSR Uruguay*

Venezuela* Yemen Arab Republic Yemen People's Democratic Republic Yugoslavia Za'ire* Zambia* Zimbabwe*



APPENDIX II

Simulation Exercise

There are three elements that determine the gains in GDP over time for a given reduction in the ratio of military spending to GDP (M!GDP = m). First, the effect of m on the ratio of investmem to GDP. and the laner's effect on per capita GDP growth; second. the direct effect of m on per capita GDP growth: and third, the effect of the current per capita GDP on its growth rate (the convergence effect.) From equations ( I ) and (2). the percemage gain in per capita GDP (�z,) for a given percentage change in the military spending ratio (�In m) is given by

tlz, = (9m + 9k 11m )!l in 171,

tlz,+1 = rc I + y) + 1 ] (911, + 9k 11m )!lin m,

tlzr+j = [t ( l + y );l(9m +9k11m)tl lnm, t=O

(for - I < y < 0).

The estimates for e,., 6t. and -y are taken from Table 5. column 4; and the estimate for TJ,, from Table 6. column 4.

The change in the lePel of the investment ratio produced by a given percentage change in the military spending ratio can be approximated as follows:

tlsk1 = (11111tl lnm)sk1_ 1 •

�In m for each group of countries is computed as follows:

tlln m = In (Average MIGDP( 1 986-1990)] - In [Average M/GDP( I972-1985)]

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Benoit, Emile, Defense and Economic Growth in Developing Countries (Lexington, Massachusetts: Lexington Books, 1 973).

---, "Growth and Defense in Developing Countries, .. Economic Development and Cultural Change, Vol. 26 (January 1978), pp. 271-80.



Biswas, Basudeb, and Rati Ram, "Military Expenditures and Economic Growth in Less Developed Countries: An Augmented Model and Further Evidence," Economic Development and Cultural Change, Vol. 34 (January 1986), pp. 362-72.

Chamberlain, Gary. ·'Multivariate Regression Models for Panel Data:· Journal of Econometrics, Vol. 1 8 (January 1982), pp. 5-46.

---, "Panel Data," in Handbook of Econometrics, Vol. II, ed. by Zvi Griliches and Michael D. lntriligator (New York: North-Holland, 1984). pp. 1248-1318.

Chan, Steve, "The Impact of Defense Spending on Economic Performance: A Survey of Evidence and Problems," Orbis, Vol. 29 (Summer 1985), pp. 403-34.

Deger, Saadet. and Ron Smith, "Military Expenditure and Growth in Less Developed Countries," Journal of Conflict Resolution, Vol. 27 (June 1983), pp. 335-53.

De Gregorio, Jose, ''Inflation. Taxation, and Long-Run Growth,'' Journal of Monetary Economics, Vol. 3 1 (June 1993), pp. 271-98.

Frederiksen, P., and R. Looney, "Defense Expenditures and Economic Growth in Developing Countries: Some Further Empirical Evidence," Journal of Economic Development, Vol. 7 (July 1982), pp. 1 13-25.

Hewitt, Daniel, "Military Expenditures Worldwide: Determinants and Trends. 1972-1988." Journal of Public Policy. Vol. 12 ( 1992), pp. I 05-52.

---, "Military Expenditures 1972-1 990: The Reasons Behind the Post-1985 Fall in World Military Spending,'' IMF Working Paper 93118 (Washington: International Monetary Fund. March 1993).

Knight, Malcolm. Norman Loayza, and Delano Villanueva. ''Testing the Neoclassical Theory of Economic Growth: A Panel Data Approach,'' Staff Papers, International Monetary Fund, Vol. 40 (September 1993), pp. 512-41.

Landau, Daniel, "The Economic Impact of Military Expenditures;· World Bank Policy Research Working Paper No. 1 1 38 (Washington: World Bank. May 1993).

Lee, Jong-Wha. "International Trade. DistOrtions. and Long-Run Economic Growth," Staff Papers, International Monetary Fund, Vol. 40 (June 1993), pp. 299-328.

Mankiw. N. Gregory, David Romer, and David N. Wei!. ''A Contribution to the Empirics of Economic Growth,'' Quarterly Journal of Economics, Vol. I 07 (May 1992), pp. 407-37.

Phillips, A.W .. "The Relation Between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom, 1861-1957.'' Economica (November 1958), pp. 283-99.

Rothschild, Kurt W., "Military Expenditure, Exports and Growth,'' Kyklos, Vol. 26,

No. 4 ( 1977), pp. 804-14.

Solow, Robert M., "A Contribution to the Theory of Economic Growth," Quarterly Journal of Economics, Vol. 50 (February 1956), pp. 65-94.

Summers, Robert, and Alan Heston, "The Penn World Table (Mark 5): An Expanded Set of International Comparisons, 1950-1 988," Quarterly Joumal of Economics, Vol. 106 (May 1991), pp. 327-68.



Swan, T.W., "Economic Growth and Capital Accumulation,"' Economic Record. Vol. 32 (November 1956), pp. 334-61.

Thompson, Earl A .. "Taxation and National Defense," Journal of Polilical Economy. Vol. 82 (July/August 1974), pp. 755-82.

Tommasi, Mariano, ''High Inflation: Resource Misallocations and Growth Effects;· University of Los Angeles Department of Economics Working Paper No. 704 (Los Angeles, California: University of California, Department of Economics. November 1993).


IMF Staff Papers Vol. 43, No. I (March 1996) © 1996 International Monetary Fund

Saving Behavior in Low- and

Middle-Income Developing Countries

A Comparison

MASAO OGAKI, JONATHAN D. OSTRY, and CARMEN M. REINHART*

The relationship between real interest rates, saving, and growth is a central issue in development economics. Using macroeconomic data for a cross-section of countries, we estimate a model in which the intertemporal elasticity of substitution varies with the level of wealth. The estimated parameters are used to calculate, in the context of a simple endogenous growth model, the responsiveness of saving to real interest rate changes for countries at differing stages of development. The hypothesis that the saving rate, and its sensitivity to the interest rate, are a rising .fimction of income

.finds strong empirical support. [JEL E2 1 , F41 , F43, 0 I I , 016, 057]

THE IMPACT OF CHANGES in real interest rates on saving, investment, and economic growth is a central issue in development economics. Ac

cording to one familiar view (see, for example, McKinnon ( 1973) and Shaw ( 1973)), an increase in real interest rates in developing countries should encourage saving and expand the supply of credit available to domestic investors, thereby enabling the economy to grow more quickly. Indeed, a number of liberalization programs supported by the international financial institutions over the years have had as their explicit objective to increase interest rates from levels that in many cases were substantially negative in real

* Masao Ogaki, Associate Professor of Economics at Ohio State University, holds a doctorate from the University of Chicago; Jonathan D. Ostry is a Senior Economist in the Southeast Asia and Paci fie Department and holds a doctorate from the University of Chicago; and Carmen M. Reinhart, an Economist in the Western Hemisphere Department, holds a doctorate from Columbia University. The authors wish to thank seminar participants at the IMF and Ohio State University, as well as Sergio Rebelo, Michael Sarel, Miguel Savastano. and Peter Wickham, for helpful comments and suggestions. and Jared Romey for excellent research assistance.

38


SAVING BEHAVIOR IN DEVELOPING COUNTRIES 39

terms. While increases in real interest rates have often been the outcome of such liberalization episodes (see, for example, Galbis ( 1 993)), their impact on domestic saving and invesunent has been unclear.'

There is little consensus in the empirical literature on the interaction between saving and the real rate of interest (see, for instance, Savastano ( 1995) and Schmidt-Hebbel and others ( 1 992) for a review of this literature). Some researchers have been unable to detect much of an effect of changes in real interest rates on domestic saving in developing countries. For example, Giovannini ( 1985) finds that in only 5 of the 1 8 developing countries in his sample are consumption and saving sensitive to changes in the real interest rate. He concludes that, for the majority of cases, "the response of consumption growth to the real rate of interest is insignificantly different from zero" (p. 215) and that one should therefore expect "negligible responses of aggregate saving to the real rate of interest [in developing countries]" (p. 1 97). Rossi ( 1988) also finds that "increases in the real rate of return are not likely to elicit substantial increases in savings, especially in low-income developing countries" (p. I 04). In a model with a single consumption good, Ostry and Reinhart ( 1992) confirm these findings but when a disaggregated commodity structure that allows for traded and nontraded goods is assumed, these authors find higher and statistically significant estimates of the intertemporal elasticity of substitution. However, regional differences emerge, with Asian countries showing a greater responsiveness to real interest rate changes.2

The finding of a zero or near-zero interest rate sensitivity of saving in a number of developing countries has led researchers to consider a number of alternative hypotheses that could help to explain this result. One such hypothesis is that consumption in developing countries may be more related to subsistence considerations-particularly in the case of low-income countries-than to intertemporal consumption smoothing.3 If households must first achieve a subsistence consumption level, letting intertemporal considerations guide their decisions only for that portion of their budget left after subsistence has been satisfied, then the intertemporal elasticity of substitution and the interest-rate sensitivity of private saving will be close to zero for countries at or near subsistence consumption levels, and will rise thereafter.

1 For a view running contrary to the McKinnon-Shaw hypothesis, see van Wijnbergen ( 1983). For an analysis of the Uruguayan experience with financial liberalization, see de Melo and Tybout ( 1986).

1 Ostry and Reinhart ( 1992) attributed these differences to the presence of more binding liquidity constraints in Africa and Latin America than in Asia. Using a reduced form approach, similar regional differences in the interest-rate sensitivity of saving were found by Gupta ( 1987).

•1 For models that stress the role played by subsistence considerations in consumption/saving decisions, see Rebelo ( 1992) and Easterly ( 1994).


40 MASAO OGAKI, JONATHAN D. OSTRY. and CARMEN M. REINHART

A second reason why the intertemporal elasticity of substitution may be lower for low-income countries concerns the relative share of necessities in the budgets of relatively poor households. If necessities (for example, food) are less substitutable through time than other goods, then the intertemporal elasticity of substitution will be lower for households with a larger proportion of necessities in their budgets than for households in which such goods are less important. The implication is that for relatively poor countries, where budget shares of food are relatively high, the interest-rate elasticity of saving would be relatively low.�

It is indeed a well-established empirical regularity that food consumption accounts for a markedly lower share of total expenditure in high-income than in low-income countries (see Mitchell and I ngco ( 1993) and Putnan and Allshouse ( 1993)). As shown in Table I , food consumption accounts for less than 20 percent of total expenditure in most industrial countries and for only 8 percent of total consumption in the United States. For middle-income countries such as Mexico and Thailand, the share is often 30-40 percent, while for the poorer countries the share of food approaches 60-70 percent.

Empirical support for these hypotheses is found in Atkeson and Ogaki ( 1993). Specifically, using a panel of data on Indian households, they find that the intertemporal elasticity of substitution of the richest six households in their data set is approximately 1.6 times that of the poorest six households. Thus, from their results, the effects of the level of income on the intertemporal elasticity of substitution would indeed appear to be economically significant.

There are, however, additional reasons why saving may be less responsive to changes in real interest rates in low-income than in middle-income countries. Rossi ( 1 988), for example, argues that low-income developing countries are characterized by pervasive liquidity constraints that imply that consumption growth in such countries is more likely to follow income growth than changes in expected rates of return.5 The empirical evidence appears to point to the presence of liquidity constraints in many developing countries; however, Haque and Montiel ( 1 989) highlight that the severity of these constraints varies considerably across countries. More recently,

" On the basis of a similar argument, Rebelo ( 1992) argues that financial liberalization in low-income developing countries is unlikely to produce large effects on saving and economic growth. For a discussion of the effects of financial market deregulation in developing countries, see Galbis ( 1993). For an analysis that highlights stylized facts conceming the differences in saving behavior between low- and middle-income developing countries, see two recent World Bank volumes (World Bank ( 1993 and 1994a)), dealing, respectively, with the performance of the economies of East Asia and Africa.

5 Deaton ( 1989) has also emphasized the importance of liquidity constraints in explaining consumption/saving behavior in developing countries.


SAVING BEHAVIOR IN DEVELOPING COUNTRIES

Table I . Food as a Percem of Total Personal Expenditure for Selected Countries ( 1990)

Country Percent

Low-income countries Honduras India Sierra Leone Sri Lanka Sudan

Average for group Lower middle-income countries

Colombia Ecuador Fiji Jamaica Jordan Philippines Thailand

Average for group Upper middle-income countries

Greece Malaysia Mexico South Africa Venezuela

Average for group High-income countries

44.5 50.6 68.0 51.3 63.5 55.6

29.5 32.4 25.8 15.0 39.8 55.2 27.3 32.1

32.4 25.8 37.0 28.6 28.6 30.5

Australia 14.8 Belgium 16.1 Canada 1 1 .8 Sweden 15.4 United Kingdom I 1 .8 United States 8.0

Average for group 13.0 Sources: Putnam and Allshouse ( 1993); and Mitchell and lngco ( 1993).

4 1

Note: For classification of economies by income level see World Bank ( 1 994b).

Vaidyanathan ( 1 993) shows that the incidence of liquidity constraints among households is inversely related to the degree of economic development, which would imply-following Rossi ( 1988)-that saving in poorer countries should be less responsive to interest rate changes.6

6 Vaidyanathan ( 1993) also finds that financial liberalization in developing countries reduced the severity of borrowing constraints. Although no direct tests were undertaken, the implication would be that financial liberalization, by reducing the fraction of households for which liquidity constraints are binding, should increase the interest-rate sensitivity of private saving. For a direct test of this hypOLhesis, see Bayoumi ( 1993) for the case of the United Kingdom, and Ostry and Levy ( 1995) for the case of France.


42 MASAO OGAKI, JONATHAN D. OSTRY, and CARMEN M. REINHART

Lastly, it could be argued that failure to detect a systematic relationship between saving and real interest rates across countries and across time may also be due to considerable variation in the economic significance and information content of the real rates of return themselves. Lack of sophistication and depth in domestic financial markets or direct regulation may result in nominal interest rates that do not adequately reflect expectations about the underlying economic fundamentals. This problem may be particularly severe for some of the poorer countries. In addition, lack of information on inflation expectations is a problem that may, as the literature on the peso problem has shown. be especially relevant for high-inflation countries and/or episodes.

While a number of hypotheses have been put forward to suggest that saving behavior in developing countries is affected by the level of development, there has been little systematic empirical investigation of this issue at the macroeconomic level in the literature. Yet from a policy perspective, the issue is of central importance since, for example, the effects on investment and growth of a number of policy actions frequently undertaken by developing countries-including financial liberalization, the reduction of capital controls, and the transmission of fiscal and commercial policy changes to the current account-will all be governed to some degree by the responsiveness of saving to interest rate changes.7

With this in mind, the purpose of this paper is to quantify empirically the response of consumption/saving to changes in the real rate of interest. We proceed in two steps. First, we use macroeconomic data for a sample of countries with diverse income levels to estimate a model that allows the intertemporal elasticity of substitution to vary with the level of wealth. We then use the estimated parameters to calculate, in the context of a simple endogenous growth model, the elasticity of saving with respect to changes in the real rate of interest.

7 In addition to policy-induced shocks, the transmission of a temporary terms of trade disturbance, through its effect on the consumption rate of interest, depends crucially on the sensitivity of saving to intenemporal relative prices (see. for example, Svensson and Razin ( 1983) and Ostry ( 1988)). In the area of commercial policies, noncredible liberalizations will also generate changes in consumption rates of interest as households may view the reduction in import prices (associated with tariff reduct-ions) as a temporary phenomenon (see, for example, Razin and Svensson ( 1983), Calvo ( 1987, 1988, and 1989), Edwards and Ostry ( 1990), and Ostry ( 1991a and 1991 b)). The extent to which such noncredible liberalizations will induce a consumption boom (and a current account deterioration) therefore depends on the intertemporal elasticity of substitution in consumption. The finding that this parameter is low in a number of countries may help to rationalize the empirical findings of Ostry and Rose ( 1992) that tariffs have little systematic effect on saving and current account behavior. Finally, the transmission of fiscal policy changes (which engender movements in domestic interest rates) to the current account will be governed in part by the responsiveness of private saving to real interest rates (see, for example, Frenkel and Razin ( 1992) and Ostry ( 1994)).



The remainder of the paper is organized as follows. Section I presents some stylized facts on saving behavior and income levels and focuses on the differences between low- and middle-income developing countries. Section II describes the analytical framework, while Section Ill discusses the empirical methodology and summarizes the estimation results. The response of saving to changes in real interest rates is examined in the context of a simple endogenous growth model in Section IV. The implications for policy and future research are taken up in the final section.

I. Stylized Facts

A model, such as the one developed in this paper, that emphasizes the role of subsistence consumption has two main predictions about saving behavior. First, saving rates should increase with the level of wealth at the initial stages of development, with the largest increases in the saving rate occurring as a country moves from low- to middle-income levels.8 Second, saving should become more responsive to changes in real interest rates as countries become richer. The first prediction follows directly from the role of subsistence consumption in the low-income developing countries, and the fact that the share of subsistence in total consumption declines with income.9 The second prediction may also be related to subsistence considerations, since intertemporal incentives should only affect that portion of the budget left over after subsistence has been achieved, that is, discretionary income.

With regard to saving rates, a model that stresses the role of liquidity constraints offers a different prediction; if poor consumers cannot borrow but face an uncertain income stream, the demand for precautionary saving rises (see, for instance, Deaton ( I 989)). 10 Hence, it may be the poorest liquidity-constrained consumers that have relatively high saving rates. However, as with the subsistence model, the responsiveness of saving to changes in interest rates rises with the level of wealth as liquidity constraints become less binding.

Among countries in various income groups, the patterns of saving rates that emerge are broadly consistent with the predictions of the subsEstence model. As Table 2 highlights for selected countries, private saving is, on average, considerably lower for the poorest developing countries, where the

� In fact, in such models (see Rebelo ( 1 992) and Sarel ( 1996)), the saving rate need not increase in the transition from middle- to high-income levels.

9 See, for example, Rebelo ( 1992). 10 This precautionary motive, without explicitly modeling liquidity constraints. is empirically investigated in Ghosh and Ostry ( 1994).



Table 2. Personal Saving Rates for Selected Countries•

( 1985-1993 averages, unless otherwise noted)

GNP per equivalent adult Personal savings in 1985 $ as a percent

Country 1980-87 average ofGDP

Low-income countries Tanzaniab 639.5 - 1 .0 Burkina Fasob 644.6 1.0 Bangladesh 889.2 13.5 Madagascar 916.8 4.3 Togo 937.9 14.0 Somalia 1 . 1 46.4 6.2 Ghana 1, 164.1 6. 1 Haiti 1 ,210.4 4.5 Kenya 1 , 197.9 18.2 Sierra Leone I ,341.0 8.1 Nigeria 1 .603.5 9.5 Pakistan 1 ,672.0 23.0 Honduras" 1,679.9 7.5 Guyana< 1 ,833.0 14.3 Sri Lanka 2,156.1 19.8 Egypt 2,158.3 29.8

Average for group I ,324.4 I 1.2 Lower middle-income countries

Bolivia 2,047.9 12.2 Cote d'lvoire" 2,057.6 12.7 Cameroon 2,170.4 1 1 .0 El Salvador 2,203.0 15.0 Philippines< 2,432.0 16.2 Morocco" 2,472.4 20.9 Dominican Republic 2,8 1 1 .4 14.8 Thailand 2,901.4 22.8 Paraguay 3,082.4 14.6 Tunisia< 3,773.4 14.5 Peru 3,786.5 24.4 Turkey 3,93 1.6 21 .4 Iran 3,962.5 20.0 Colombia 4,164.0 12.7 Poland< 4,360.6 26.8 Chile 4,587.8 12.8

Average for group 2,805.8 17. 1 Upper middle-income countries

Mauritius 4,406.6 24.2 Korea 4,409.5 25.4 Argentina 4,994.5 18.5 Brazil< 5,099.8 17.4 Portugal 5,280.9 2 1 .3 South Africa 5,770.9 22.8



Table 2. (concluded)

( 1 985-1993 averages. unless otherwise noted)

45

Country

GNP per equivalent adult in 1985 $

1980-87 average

Personal savings as a percent

ofGDP Upper middle-income countries

(continued) Malaysia Greece Mexico Venezuela< Trinidad and Tobagoc

Average for group High-income countries

5,824.4 6,232.5 6,968.8 7,672.1

I I , 1 6 1 .0 6,165.5

18.6 25.8 13.8 1 1 .4 15 . 1 19.5

Ireland 7, 170.9 22.0 Spain 7,477.8 20.7 Israel 10,572.9 16.9 Austria 1 1 , 147.3 23.3 United Kingdom 1 1 ,462.6 15.2 Italy I I ,613.1 25.7 Belgium I I ,675. 1 23.2 Japan 1 1 ,8 19.9 25.5 Netherlands 12,013.8 24.9 Finland 12,019.5 19.4 France 1 2,775.6 19.1 Australia 13,841.5 18.8 Switzerland 16,079. 1 23.5 Canada 16,529.3 21 .5 United States 18, 194.5 16.4

Average for group 1 2,292.9 2 1 . 1 Sources: TMF, World Economic Outlook; Savastano ( 1994); World Bank ( 1994a). • For classification of economies by income level, see World Bank ( 1994b). h Average for 1987-91 from World Bank ( 1994a). c Average for 1985-92 from Savastano ( 1995).

saving rate is about one half that of the high-income group. 1 1 In fact, such differences also appear within regions. According to the World Bank ( l994a), median gross domestic saving as a percentage of GOP ( 1987-91 average) was 5.6 percent for the low-income African countries and 19.0 percent for the middle-income African countries (the average was 7.7 percent).

As predicted, the relationship between the level of income and the saving rate appears to be nonlinear for the countries in our sample (see Rebelo

1 1 We adopt the World Bank ( 1 994b) classification of economies. See also Aghevli and others ( 1990).



( 1992)); the largest increases in the saving rates occur in the transition from low- to lower middle-income, where the average personal saving rate rises by 5.9 percentage points (Table 2). The average for the upper middleincome countries is still 2.4 percentage points above that of the lower middle-income group. but there appears to be less of a difference ( 1 .6 percentage points) between the average saving rates in the high-income and upper middle-income countries in our sample.

StiJl, there appear to be sharp differences in saving rates that cannot be accounted for by the subsistence model. For example, saving rates in Latin America are well below those observed in many Asian countries, despite similar income levels. 12 As pointed out in World Bank ( 1993), gross domestic saving as a percentage of GDP was nearly 40 percent for the highperforming (middle-income) Asian economies in 1990; it is argued that these relatively high saving rates were an engine of growth in many of these countries, since they financed higher rates of investment as well.

The role of real interest rates in saving behavior is more difficult to gauge. One problem-which is particularly important in Africa-is that financial markets remain thin and governments set interest rates, frequently at nonmarket levels. As pointed out in a recent World Bank study on Africa (World Bank ( 1994a)). "most countries [in Africa] have few banks, and . . . there is little scope for 'true' market-determination of interest rates" (p. 1 14). This feature of credit markets in low-income countries may itself make saving less responsive to interest rates.

Nevertheless, there is some evidence that financial savings increased as a result of the increase in real interest rates associated with liberalization of financial markets, both in Africa and elsewhere among developing countries. For example, among the Asian countries, the increase in real interest rates in Taiwan Province of China in 1949 contributed to a sharp increase in savings. Similar results were achieved by Indonesia and Korea and, more recently. by Argentina, Chile, Mexico, and Pakistan (see World Bank ( 1993) and the references therein). There is also some evidence that reform programs in Africa have succeeded in raising domestic savings. For example, as documented in World Bank ( 1994a), median gross domestic saving rates climbed 3.3 percentage points for the six African countries with a large improvement in macroeconomic policies (which consisted of five main indicators, one of which was interest rate policy), compared with a decline of

12 Income distribution within a country is often argued to exert an independem influence on saving behavior, but we are unaware of any systematic empirical investigation of this hypothesis. Kaminsky and Pereira (forthcoming) do find evidence that social indicators. which reflect the skewness of income distribution, he I p explain the downward rigidity of consumption in Latin American countries relative tc the Asian countries in their sample.



3.3 percentage points for countries with policy deterioration. In general, moving real interest rates from sharply negative to mildly positive levels seems to be a positive factor in mobilizing domestic savings, although there is no particular evidence that the effectiveness of such policies rises with the level of development, as the subsistence model would suggest. An investigation of this issue is undertaken in the following three sections.

II. Analytical Framework

We begin by describing the maximization problem faced by a representative household in a given country. Since our ultimate purpose is to examine cross-country differences in saving behavior, we do not assume that representative households in different countries have identical preferences. As in Ostry and Reinhart ( 1 992), we adopt a two-good framework that distinguishes between traded and nontraded goods. As argued in that paper, it is important to estimate the intertemporal elasticity of substitution allowing for two goods in order to avoid biases arising from changes in the relative price of traded and nontraded goods (the real exchange rate). We allow for cross-country variation in both the intratemporal elasticity of substitution between traded and non traded goods and the intertemporal elasticity of substitution. The assumption is that the latter varies systematically with the level of real income. We begin by describing, in equations ( I )-(7) below. the optimization problem at the national level. 13

Consider then an economy with an infinite-lived representative household whose objective is to choose a consumption stream that maximizes

� 1-llcr _cr_ E � rv ( . 1-1 /e + 1-1/r ) l-I te O.L.J f-1 am, n, , (cr- 1 ) t=O

subject to the series of budget constraints

CI,�,£,<J>0, � < J.

p,m, + q,n, = p,iii, + q,n, + x, + B, -( 1 / R,*_ 1 )8,_ 1 , and the transversality condition

,��rr �=o (l l Rns, = o.

( I )

(2)

(3)

where £0 is the expectations operator conditional on information available at time 0; B, denotes the real level of debt carried from period t to period

IJ For a fuller discussion of the underlying model at the national level, see Ostry and Reinhart ( 1992).



t + I with 8_ 1 given; ( 1 /Rf) - 1 = rf is the real interest rate (in terms of the numeraire) on the debt so Rt is the associated world real discount factor; m (n) denotes consumption of importables (nontradables) and p (q) denotes the relative price of m (n) in terms of the numeraire; i3 is the subjective discount factor; and e (a") denotes the intratemporal (intertemporal) elasticity of substitution.14 An intratemporal elasticity of substitution greater (less) than one implies gross substitutability (complementarity) between traded and nontraded goods; a value of unity cotTesponds to the logarithmic utility case. The intertemporal elasticity of substitution reflects the sensitivity of consumption (and therefore saving) to changes in intertemporal prices (i.e., the consumption rates of interest), with higher values indicating greater sensitivity.

The problem of the representative consumer in a given country is to choose an optimal sequence { m,, n,, B,} that maximizes equation ( I ) subject to equations (2) and (3). The first-order necessary conditions for an optimum are

and

I cr-t 1

I 1-11£ 1-1/t cr<e-l) -;

E _P_,_[amt+ 1 + n,+1 ] [mt+1 ] = -'-, • 1-1/t 1-lle A ' R, Pt+ l am, + n, m, 1-'

I cr-t I

I _q_,_ [ am]; ,llt + n];,l lt ]cr!t-ll [nt+l

]-; = _I_ £, * l-Ilt 1-11£ A ' R, q,-t-1 am, + n, n, 1-'

a(n, I m, )1 1£ = p, I q,.

(4)

(5)

(6) Equation (4) is the intertemporal Euler equation associated with importables consumption in two consecutive periods; it states that the marginal utility cost of giving up one unit of m at time t should be equated to the expected utility gain from consuming one more unit of m at 1 + I . Equation (5) is the analogous condition relating the marginal rate of substitution between consumption of good n at 1 and t + 1 to the relevant intertemporal relative price. Finally, equation (6) is the nonstochastic first-order condition equating the intratemporal marginal rate of substitution between importables and nontradables to the corresponding relative price ratio. l t can be verified that equations (4)-(6) are not independent. Specifically, combining

14 Following the discussion in Section I, we allow for cross-country differences in the elasticities of substitution in the estimation.



equation (6) with either of the two remaining equations yields the third. Therefore, given that the nonstochastic first-order condition holds. equations (4) and (5) do not provide independent restrictions on the evolution of consumplion through time.

The main difference between the model described above and standard Euler-equation models that have been applied previously to developing countries (for exampl·e. Giovannini ( 1 985) and Rossi ( 1988)) relates to the goods structure. In the above model, we allow for consumption of tradables and nontradables si nee the latter appear to account for a large fraction of the consumption basket in many developing countries. Moreover, imposing a one-good structure can seriously bias the resulting estimates of preference parameters. If the real exchange rate (the relative price of traded and nontraded goods) varies over time, as is the case in most developed and developing countries. aggregate consumption will respond to those price changes. This is because a change in the real exchange rate alters the consumption rate of interest. As such channels are ignored in a one-good structure, the empirical results from such models may be biased. 15 For example, the finding that intertemporal elasticities of substitution are insignificantly different from zero in the majority of developing countries was found by Ostry and Reinhart ( 1992) not to be robust to a relaxation of the one-good assumption.

Given time-series data on importables and nontradables consumption, and on interest rates, and import, export, and nontradables prices, it is possible to estimate the system consisting of equations (4)-(6) and recover the main parameters of interest. Since equation (6) must hold identically (in the absence of measurement error), and si nee equations ( 4) and (5) are not independent given that equation (6) holds, we can eliminate equation (4) or (5) from the estimation. The restrictions on the joint behavior of consumption of importables and nontradables, the terms of trade, and the relevant rate of return, implied by the maximization of the expected utility function given by equation ( I ) subject to the constraints given in equations (2) and (3), are summarized in equation (4). In addition, given the assumption of rational expectations, we can use equation (4) to define the disturbance

(7)

where u, must be uncon·elated with any variable that is in the information set of agents at time t.

15 For a discussion of the bias issue, see Ostry and Reinhart ( 1992) and Ogaki and Reinhart ( 1995).



Now that we have fully described the optimization problem of a representative household in a given country, we must specify how intertemporal parameters governing saving behavior vary systematically across countries. In what follows, we take a particularly simple approach motivated by a Stone-Geary preference specification (as described, for example. by Rebelo ( 1 992)). We adopt a specification in which the intertemporal elasticity of substitution is an increasing function of the gap between permanent income and the subsistence level of consumption, namely,

a. = a( t -l) I {1 ' Y;

(8)

where u; denotes the intertemporal elasticity of substitution in country i; "' is a constant that reAects subsistence consumption, and yf'is a measure of permanent income in country i. Clearly, equation (8) is similar to the StoneGeary preference specification, with permanent income replacing consumption. Conceptually, we focus 0111 income rather than consumption in order to make transparent the connection between the intertemporal elasticity of substitution and the level of development (i.e., income per capita). Equation (8) shows that the interest-rate sensitivity of aggregate consumption (as well as the level of saving itself) will be lower as the ratio, "{lyi, approaches unity and wealth is only sufficient to support a subsistence level of consumption.

III. Estimation Strategy and Empirical Results

We begin by describing our data set, before moving to a description of the econometric methodology.

Data Issues

The parameters of the representative household's utility function outlined in the previous section are estimated using annual time-series data for thirteen countries. The low-income countries in the sample are Egypt, Ghana, India, Pakistan, and Sri Lanka; the low-middle-income countries consist of Colombia, Costa Rica, Cote d'lvoire, Morocco, and the Philippines; and three upper middle-income countries-Brazil. Korea, and Mexico-are also included in the analysis. Data coverage for each country begins in I 968 and ends anywhere between I 983 and 1992.

As equations (7) and (8) highlight, estimation of the intertemporal and intratemporal elasticities of substitution requires data on household con-


SAVING BEHAVIOR IN DEVELOPING COUNTRIES 5 1

sumption of traded and non traded goods, on the terms of trade, and on permanent income or wealth. While time series on the terms of trade are readily available, consumption data are generally not disaggregated into traded and non traded goods, and estimates of wealth are scarce. The methodology applied to disaggregate consumption is described in detail in Ostry and Reinhart ( 1992). Basically, we assume that the non traded goods sector of the economy consists of public and private services while traded goods production emanates from the agriculture, mining, and industrial sectors. Consumption of importables can then be constructed using the supply-side data and data on exports and imports of consumer goods. Consumption of nontraded goods is calculated residually as total private consumption less consumption of importables. The relevant price deflators for the consumption of traded and nontraded goods are price indices for imports and services. respectively. Deposit rates of interest were used when available: in their absence, a money market rate was employed. Finally, as a proxy for pennanent income, an average of real income per equivalent adult for the period 1980-87 was used Y•

Methodology and Results

In this subsection, we apply Cooley and Ogaki's (forthcoming) two-step procedure to obtain estimates of the intratemporal elasticity of substitution between traded and nontraded goods and of the intertemporal elasticity of substitution. An alternative procedure described in Ostry and Reinhart ( l 992) uses a cointegration approach to obtain first-stage estimates of the intratemporal parameter and Hansen and Singleton's ( 1 982) Generalized Method of Moments (GMM) approach to obtain (second-step) estimates of the intertemporal parameters.

The First Step: Estimating the lntratemporal Elasticity of Substitution

Many economic time series can be modeled as being difference stationary with drift. Under such conditions, the notions of stochastic and deterministic cointegration are useful in examining the interaction between two or more variables of interest. 17 Suppose that the components of a vector series X(t) are I( I ) processes with drift; if a linear combination of X(t), say A.'X(t), is trend stationary, the components of X(t) are said to be (stochas-

16 All series are available from the authors upon request. 17 Stochastic cointegration and the deterministic cointegration restrictions were

defined by Ogaki and Park ( 1989) and Campbell and Perron ( 1991 ). Efficiency gains from estimating the cointegrating vectors by imposing the deterministic cointegration restriction were discussed by West ( 1988) for the one-regressor case and by Hansen ( 1992) and Park ( 1992) for the multiple-regressor case.



ticaJiy) cointegrated with a cointegrating vector A. Consider an additional restriction that the cointegrating vector eliminates the deterministic trend as well as the stochastic trend, so that A'X(r) is stationary. This restriction is called the deterministic cointegration restriction.

Standard unit root tests suggest that it is reasonable to model the relative price of traded and nontraded goods and the consumption ratio (of nontraded to traded goods) as I( I ) processes.1H We now focus on the relationship between these two variables. The intratemporal first-order condition (equation 6) implies that the log of the relative price and the log of the consumption ratio are cointegrated with the deterministic cointegration resrriction. 19 If cointegration obtains, we can recover a consistent estimate of the intratemporal elasticity of substitution, E.20To test for cointegration, we employ Park's ( 1992) Canonical Cointegrating Regression (CCR) procedure.21

There are several advantages associated with CCR. First, the estimated parameters, a and E in this case, are not only consistent (as is OLS), but also asymptotically efficient and median unbiased. Second, unlike OLS, the asymptotic distributions of CCR estimators are nuisance-parameter free and normal conditioned on the regressors. This feature allows for the usual interpretation of the standard enors and therefore for hypothesis testing. Third, as Monte Carlo experiments show (see Park and Ogaki ( 1991 )), CCR estimators have better small-sample properties than Johansen's estimators. This makes CCR particularly attractive for the present application, where the data are annual and the sample size is limited.

Rearranging terms, taking logs, and introducing a disturbance term (to allow, for example, for measurement enor) equation (6) becomes

ln(n, I m,) = e ln(a) + e ln(p, I q,) + u,. (9)

Equation (9) is likely to suffer from simultaneity bias, since relative prices are determined endogenously, and the error term may be serially correlated.22 To correct for the potential presence of such nuisance parameters, long-run covariances are estimated and used to transform the data. As

1� The results of the Dickey-Fuller (DF) and augmented Dickey-Fuller (ADF) unit root tests for a l i the series of interest are not reponed but are available from the authors upon request.

19 As shown by Hall ( 1 978), consumption is a random walk when the real interest rate is assumed to be constant. Since we allow the real interest rate to vary over time, the first difference of the log of consumption can be serially correlated. 20 This will also yield a point estimate for the parameter a, which is related to the consumption share.

21 See Ogaki ( 1 993a) for a more detailed explanation of CCR-based estumation and testing. 22 Note that the OLS estimator is consistent but not efficient because of long-run simultaneity bias.



shown in Park ( 1992). the transformed data will be cointegrated with the same parameter vector as the original data.

Under the null of cointegration, an important property of the CCR procedure is that linear restrictions can be tested by x2 testsY These x2 tests are used in a regression with spurious deterministic trends added to test for deterministic and stochastic cointegration. For this purpose, the CCR procedure is applied to a regression of the form

(/ ln(n, I m, ) = e ln a +I., ll; r; + e ln(p, I q,) + u, .

i=l (10)

We let H(p,q) denote the standard Wald statistic to test the hypothesis TJ11 + 1 = TJ11 + 2 == . . . TJ<1 = 0, where the variance of u, has been replaced with elements of the long-run covariance matrix (see Park ( 1990)). Under the null of co integration H(p,q) converges to a x�-w In particular, the H(O, 1 ) statistic tests the deterministic cointegrating restriction, which i s suggested by the intratemporal first-order condition. On the other hand, the H( I ,q) tests for stochastic cointegration.

Table 3 reports the CCR results.24 As shown in column ( I ), with the exception of Korea, the intratemporal elasticity of substitution, E, is estimated to be positive, consistent with our theoretical priors. I n the case of Korea, where the estimate of E is significantly negative, the H(O, I ) test statistic presented in column (2) also rejects the specification implied by the model at the 0.1 percent level. It is possible that the assumption of homothetic preferences implied by the CES utility function is causing problems in this case.25 For the remaining countries, the point estimates for E range from a low of 0.38 to a high of 2.16: for 8 of the 1 3 countries the intratemporal elasticity of substitution exceeds unity, implying gross substitutability between traded and nontraded goods. For the Philippines, the point estimate of E is positive but is not significantly so, and the H(O, I ) test is significant

23 This is in contrast to other cointegration tests, which have a null of no coinregrarion.

2� We used Ogaki's ( 1993b) GAUSS CCR package for the CCR estimations. The CCR procedure requires an estimate of the long-run covariance of the disturbances in the system. We used Park and Ogaki's ( 1 99 1 ) method with Andrews and Monahan·s ( 1992) prewhitened HAC estimator with the QS kernel. A first-order VAR was used for prewhitening. We followed Andrews and Monahan ( 1992) with the maximum absolute value of the elements oft. (their notation) set to 0.99. Andrews' (199 J ) automatic bandwidth estimator, Sr. was constructed by fitting an AR( I ) to each disturbance.

25 See, for example, Atkeson and Ogaki ( 1993), for an attempt to model nonhomothetic preferences with an extended addilog utility function. These authors assume time separability of preferences over two goods, in order to use an aggregation result over households. Finally, the failure to obtain cointegration could also arise from measurement error.



Table 3. Canonical Cointegrating Regression Results

Country £ £ ln(a) 1-1(0, I ) 1-1( 1.2) H(l,3) H(l,4) ( I ) (2) (3) (4) (5) (6) (7)

Brazil 2.156 -0.224 3.599 3.971 4. 1 17 4.128 (0.148) (0.069) (0.058) (0.046) (0.128) (0.248)

Colombia 0.678 -0.512 5.363 0.687 0.836 1.207 (0.214) (0.037) (0.021 ) (0.407) (0.658) (0.75 1 )

Costa Rica 1 . 132 -0.5 1 3 0.474 1 .087 1 .934 3.878 (0.179) (0.049) (0.491 ) (0.297) (0.37 1 ) (0.275)

Cote d'lvoire 1 .749 - 1 .424 1 . 147 3.078 3.730 3.884 (0.208) (0.219) (0.284) (0.079) (0.155) (0.274)

Egypt 0.440 -0.457 0.221 3.752 3.877 4.707 (0.240) (0.244) (0.638) (0.053) (0.144) (0.195)

Ghana 0.634 0.867 0. 1 15 0.710 1 .280 1 .599 (0.33 1 ) (0.295) (0.734) (0.400) (0.527) (0.660)

India 1 .547 1 .666 1 .828 1 .227 1 .637 2.339 (0.410) (0.109) (0.176) (0.268) (0.441 ) (0.505)

Korea - 5.257 - 1 .650 15.877 3.957 5.168 14.481 ( 1 .022) (0.190) (0.000) (0.047) (0.075) (0.002)

Mexico 1 .707 -0.914 0.005 0.000 2.670 3.009 (0.414) (0. 1 3 1 ) (0.946) (0.992) (9.263) (9.390)

Morocco 1 .070 - 0.735 0.263 4.051 4.054 4. 1 19 (0. 1 8 1 ) (0.092) (0.608) (0.044) (0.132) (0.249)

Pakistan 2.075 0.054 0.558 2.256 3.942 4.2 1 5 (0.267) (0.08 1 ) (0.455) (0.133) (0. 1 39) (0.239)

Philippines 0.382 0. 142 7.989 0.695 2.040 2.304 (0.333) (0.088) (0.005) (0.404) (0.36 1 ) (0.5 12)

Sri Lanka 1 .587 -0.421 0.669 0.674 1 .737 1 .887 (0.157) (0.088) (0.414) (0.419) (0.419) (0.596)

Note: Park and Ogaki's ( 1991) method with Andrews's ( 1991) automatic hand-width parameter estimator was used to estimate long-run correlation.

at the I percent level, implying that the null of deterministic cointegration is rejected; however, the null of stochastic cointegration cannot be rejected (columns (3) and (4)) at standard significance levels. For the other coun-tries, none of the H(O, I ) test statistics are significant at the I percent level and only a few of them are significant at the 5 percent level, indicating that the null hypothesis of deterministic cointegration cannot be rejected.

To summarize, we find evidence that the CES specification of prefer-ences is not rejected by the data for all the sample countries except Korea and, possibly, the Philippines. On this basis, we proceed with this specifi-cation when estimating the intertemporal elasticity of substitution.



The Second S1ep: Estimating the lntertemporal Parameters

1 n the first step, consistent estimates of the i ntratemporal parameters were obtained via a cointegration regression. In the second step, we impose the country-specific estimated values of e and a and apply GMM to the Euler equation defined by equation (7) in order to obtain estimates of the intertemporal parameters. This two-step procedure does not alter the asymptotic disnibution of the GMM estimators or test statistics because our coinregrating regression estimator is super-consistent and converges at a rate faster than T1n, where T is the sample size.

As discussed previously. we assume that the intertemporal elasticity of substitution of country i satisfies the Stone-Geary condition given in equation (8), reproduced below

cr. = cr( I -.l) I v!' • . I ( I I )

where y/'is a measure of permanent income of country i, and 'Y is a constant that reflects the subsistence level. In the GMM estimation, we fix 'Y and estimate cr. Since it is difficult to assess the real dollar value of the subsistence basket (i.e., "{). we allow 'Y to vary across a fairly broad range of values. Its minimum level of 100 is slightly below the value of US$123 ( 1985 prices) found for lndia by Atkeson and Ogaki ( 1993) and its upper level of 400 was determined by the income level of the poorest countries since, for equation (9) to make sense, it must be that ( 1 - "{lyf') ;::: 0. In any case, the sensitivity of the results with respect to the choice of 'Y is reported.

We apply GMM to the Euler equation defined by equation (7) in a panel data set of countries, imposing equation ( 1 1 ) as a cross-country restriction.2(• For each country, a and E are set at the values obtained in the first step cointegrating regression for the country in question. We restrict the discount factor, �. to be the same across countries in order to obtain more precise estimates of a, which is the main parameter governing the responsiveness of saving to changes in the real rate of interest. Hence. in the second step, we estimate two parameters, a and 13. Because the sample size is not the same for all countries, we use the panel data estimation method described in Ogaki ( l993d). Since there are many moment restrictions from many countries, we use only constants as instruments and avoid the use of lagged variables as instruments. Because lagged instrumental variables are not used, our method is robust to the time aggregation problem.

26 Hansen!Heaton/Ogaki's GAUSS GMM package (see Ogaki ( 1993c)) is used for the GMM estimations in this paper.



Table 4 presents the second-step GMM results. We report results for twelve of the developing countries in our sample (all except Korea) for different values of -y. The panel excludes Korea because the CES specification is rejected by the data in this case. Our point estimates of (J' are positive and significant while the point estimates of 13 are greater than one. Hansen's J-test statistics do not reject the overidentifying restrictions implied by the model at conventional levels. An attractive feature of the results is that they are not very sensitive to the choice of 'Y for the broad range used.

We recover the country-specific value of the intertemporal elasticity of substitution, (J';. by employing the Stone-Geary specification given in equation ( I I ). Figure I plots, for the sample countries, the intertemporal elasticity of substitution against the ratio of the country' permanent income to U.S. income, for the case of 'Y = 400. The intertemporal elasticity of substitution rises markedly with the level of income when low- to middleincome countries are compared: the change from middle- to high-income levels makes less of a difference. The nonlinearities that were evident in the relationship between the saving rate and income are also present here.

To examine the implications of our results for a broader set of countries, we use the estimated value of 0' and measure permanent income in the same way as for "within-sample'' countries. I.n column (4) of Table 5, we provide the estimate of each country's 0'; for the case where 'Y = 400. In addition, we report (in columns (3) and (5)) the range of values that result from adding and subtracting one standard error from the point estimate. As Table 5 makes clear, the range of variation of (J'; is wide, from a low value of about 0.05 for Uganda and Ethiopia, the poorest countries in our sample, to a high of about

Table 4. The lmenempomf Parwneiers: Generalized Me I hod l�{ Momems Resufis

'Y (T � lr Degrees of freedom Panel size ( I ) (2) (3) (4) (5) 12 countries 100 0.596 1 .051 14.600 10

(0.208) (0.015) (0.147) I 2 countries 250 0.606 I .055 13.531 10

(0.20 1 ) (0.020) (0. I 95) I 2 countries 300 0.615 1 .056 13.312 10

(0.20 I ) (0.015) (0.207) I 2 countries 350 0.628 J .057 13 . 180 10

(0.202) (0.020) (0.214) J 2 countries 400 0.646 I .057 1 3 . 1 5 1 10

(0.204) (0.020) (0.215) Notes: In columns (2) and (3). the standard errors are in parentheses. Column (4)

reports Hansen· s J-test and the corresponding asymptotic ?-values are given in parentheses. The last column gives the degrees of freedom for Hansen's J-statistic.



Figure I . The lntenempora/ Elasticity ofSubstirutionfor Sample Countries

Intertemporai eia.�ticity or substitution

Colombia 0.65 - £ 1. 1 \ Brazil 8. P Morocm � • 0·60 - Cote d'lvoire , \ / Cosw��:::' 0.55 - . _��Philippines

PakiSittll • Sri Lanka 0.50 -

0.45 -

0.40 -

• c1u,w

0.35 - • India 0.30

0 0.05 0.10 0. 1 5 0.20 0.25 0.30 Income level as a share of U.S. income

0.35

• Mexico -

------

0.40 0.45

Notes: The point estimates for the intertemporal elasticity of substitution and the income level and as a share of U.S. income are taken from columns (4) and (2), respectively. of Table 5.

57

0.64 for the United States and several other high-income countries. These estimates are in line with several earlier studies: Atkeson and Ogaki ( 1993), who examjne Indian panel data; Ostry and Reinhart ( 1 992), who focus on regional patterns; and Reinhart and V egh ( 1995), who apply a monetary model to several chronic-inflation countries. The implications for saving behavjor of these cross-country differences are taken up in the next section.

IV. Saving and the Rate of Interest

Having estimated the key parameters that characterize household consumption and saving behavior, we now turn to the implications of our estimates for the interaction between saving and the real rate of return. As noted earlier, the attempt to encourage saving by raising real interest rates is at the heart of adjustment programs in a number of low- and middle-income developing countlies. Higher saving, it is argued, can finance higher investment and lead to faster growth. In addition, the external current account effects of fiscal policy changes that alter domestic interest rates will be sensitive to the elasticity of plivate saving with respect to changes in the rate of return. To examine the interactions between interest rates, saving, investment, and growth, it is necessary to have some model in which these variables are determined endogenously. Rebelo's ( 1991) endogenous



Table 5. The lntertemporaf Elastici(r of Substitution: Low- and Lower Middle-Income Countries

GNP per equivalent adult in 1985$ lmcncmporal elasticity

( 1980-87 average) of substitution As a share

of U.S. Lower Point Upper Level level bound estimate bound

Country ( I ) (2) (3) (4) (5) Low-income countries

Uganda·' 430.8 0.024 0.032 0.047 0.061 Ethiopiah 435.1 0.024 0.036 0.052 0.069 ZMre 448.4 0.025 0.049 0.070 0.092 Chad·' 593.0 0.033 0.146 0.2 1 2 0.277 Tanzania 639.5 0.035 0.169 0.243 0.318 Guinea" 640.3 0.035 0.169 0.244 0.319 Burkina Faso 644.6 0.035 0.171 0.247 0.323 Mali 644.8 O.Cl35 0. 1 7 1 0.247 0.323 Burundi 671.3 0.037 0.182 0.263 0.343 Malawi 727.9 0.040 0.203 0.293 0.383 Myanmar·• 768.2 0.042 0.2 1 6 0.3 1 2 0.407 India* 829.1 0.046 0.233 0.336 0.440 Bangladesh" 889.2 0.049 0.248 0.358 0.468 Niger 897.6 0.049 0.249 0.360 0.47 I Central African Republic 898.1 0.049 0.250 0.361 0.471 Afghanistan• 907.8 0.050 0.252 0.364 0.475 Nepal• 909.2 0.050 0.252 0.364 0.476 Madagascar 9 16.8 0.050 0.254 0.366 0.479 Togo 937.9 0.052 0.258 0.373 0.487 Gambia" 940.0 0.052 0.259 0.373 0.488 Rwanda 962.3 0.053 0.263 0.380 0.497 Zambia 1 ,054.0 0.058 0.279 0.403 0.527 Somalia 1 , 1 46.4 0.063 0.293 0.423 0.553 Ghana* 1 , 164.1 0.064 0.295 0.427 0.558 Kenya 1 , 1 97.9 0.066 0.300 0.433 0.566 Haiti 1 .2 10.4 0.067 0.301 0.435 0.569 Sudan 1 .300.8 0.071 0 .312 0.450 0.589 Mozambique 1 .342.3 0.074 0.316 0.456 0.597 Pakistan* I ,672.0 0.092 0.342 0.494 0.647 Sri Lanka* 2,156.1 0. 1 1 9 0.367 0.529 0.692 Egypt* 2,158.3 0. 1 19 0.367 0.530 0.692

Average for group 972.1 ().()53 0.233 0.337 0.441 Average for the ten

poorest countries 587.6 0.032 0.133 0.192 0.251 Lower middle-income

countries Cote d' lvoire* 2,057.6 0. 1 1 3 0.363 0.524 0.685 Philippines* 2,432.0 0.134 0.376 0.543 0.710 Morocco* 2,472.4 0.136 0.377 0.545 0.712



Table 5. (cominued)

GNP per equivalent adult in 1985$ I ntenemporal elasticity

( 1980-87 average ) of substitution As a share

of U.S. Lower Point Upper Level level bound estimate bound

Country ( I ) (2) (3) (4) (5)

Dominican Republic 2,8 1 1 .4 0.155 0.386 0.558 0.729 Congoh 2,860.7 0.157 0.387 0.559 0.731 Thailand 2.901.4 0.159 0.388 0.560 0.733 Paraguay 3.082.4 0.169 0.392 0.566 0.740 Jordan 3,600.5 0.198 0.400 0.578 0.756 Ecuador 3,666.8 0.202 0.401 0.579 0.757 Tunisia 3,773.4 0.207 0.402 0.581 0.760 Peru 3,786.5 0.208 0.402 0.581 0.760 Turkey 3.93 1 .6 0.216 0.404 0.584 0.764 Iran• 3,962.5 0.218 0.405 0.584 0.764 Algeria 3.993.5 0.219 0.405 0.585 0.765 Colombia* 4,164.0 0.229 0.407 0.588 0.768 Poland 4.360.6 0.240 0.409 0.590 0.772 Panamab 4,422.9 0.243 0.409 0.591 0.773 Costa Rica* 4,487.9 0.247 0.410 0.592 0.774 Chile 4,587.8 0.252 0.4 1 1 0.593 0.776 Fiji 4,605.4 0.253 0.4 1 1 0.594 0.776 Iraq" 5,092.5 0.280 0.41 5 0.599 0.783

Average for group 3,669.2 0.202 0.398 0.575 0.752

Upper middle-income countries Gabon" 4,990.5 0.274 0.414 0.598 0.782 Argentina 4,994.5 0.275 0.414 0.598 0.782 Brazil* 5.099.8 0.280 0.41 5 0.599 0.783 Taiwan 5.166.1 0.284 0.415 0.600 0.784 Yugoslavia 5,207.6 0.286 0.415 0.600 0.785 Portugal 5,Q80.9 0.290 0.416 0.601 0.786 South Africa 5,770.9 0.317 0.419 0.605 0.791 Malaysia 5.824.4 0.320 0.419 0.605 0.792 Hungary 5,883.3 0.323 0.419 0.606 0.792 Uruguay 5,926.6 0.326 0.420 0.606 0.793 Greece 6,232.5 0.343 0.421 0.608 0.795 Malta 6,282.9 0.345 0.421 0.609 0.796 Syria 6,667.8 0.366 0.423 0.61 I 0.799 Mexico* 6,968.8 0.383 0.424 0.613 0.801 Venezuela 7,672.1 0.422 0.427 0.616 0.806

Average for group 5.864.6 0.322 0.419 0.605 0.791

High-income countries Ireland 7,170.9 0.394 0.425 0.614 0.803 Israel 10.572.9 0.581 0.433 0.625 0.818 Singapore• 10,966.2 0.603 0.434 0.626 0.819 United Kingdom 1 1 .462.6 0.630 0.434 0.627 0.820


60 MASAO OGAKl, JONATHAN D. OSTRY, and CARMEN M. REINHART

Country Hong Kong Italy Japan Denmark France Sweden Australia Iceland Norway Switzerland Canada United States* Kuwait� United Arab Emirates"

Average for group ·'Average for 1980-85. � Average for 1980-86.

Table 5. (concluded)

GNP per equivalent adult in 1985 $

( 1 980-87 average )

Level ( I )

1 1 ,474.9 1 1 ,6 1 3 . 1 1 1 ,8 1 9.9 12,406.6 1 2,775.6 12,940.9 13,841.5 14,087.9 14,408.3 1 6,079. 1 1 6,529.3 1 8 , 1 94.5 20,033.0 30,904.5 14,712.4

As a share of U.S.

level (2)

0.631 0.638 0.650 0.682 0.702 0.7 1 1 0.761 0.774 0.792 0.884 0.908 1 .000 1 . 1 0 1 1 .699 0.786

lntertemporal elasticity of substitution

Lower bound

(3)

0.434 0.435 0.435 0.435 0.436 0.436 0.437 0.437 0.438 0.439 0.439 0.440 0.441 0.444 0.436

Point estimate

(4) 0.627 0.628 0.628 0.629 0.630 0.630 0.631 0.632 0.632 0.634 0.634 0.636 0.637 0.642 0.63 1

Upper bound

(5) 0.820 0.821 0.821 0.823 0.823 0.824 0.825 0.826 0.826 0.829 0.829 0.831 0.833 0.839 0.825

Notes: The lower (upper) bounds are constructed by subtracting (adding) one standard error to the point estimate. An asterisk denotes that the country was included i n the sample.

growth model is particularly well suited to the issue at hand because it allows us to calculate the effects of different values of the intertemporal elasticity of substitution on saving rates very easily.

A Simple Model of Endogenous Growth

Since the aim is illustrative, we make a series of simplifying assumptions and focus on a linearized, continuous-time version of Rebelo's ( 1991)

model. The reader is referred to these papers for further details. The household problem is outlined in equations ( I )-(7), except that now

we focus on a continuous-time version of the model and assume that the technology is such that the traded good can be transformed into the nontraded good at a constant rate, so that the equilibrium relative price of these goods is constant.27 Hence, total consumption is given by

27 For estimation purposes this simplifying assumption turns out to be too restrictive and is rejected by the data (see Ostry and Reinhart ( 1992)). However, the aim here is to describe the interaction between saving and real rates under the simplest of settings.



c, = m1 +n1• (12)

Production takes place under a linear technology and employs a single type of capital good that is a composite of physical and human capital

y, = Az,. (13)

where A represents the technology level andy, (z,) is output (capital). The linear technology, which is a common feature of a class of endogenous growth models (see Romer ( 1989)), ensures that the rate of return to capital does not decline as the capital stock increases. Finally, output is either consumed or used for capital accumulation, namely.

y, = c, + z,. ( 14)

Production efficiency equates the marginal product of capital to the rate of return

A = l + r, (15) where r is the real rate of interest.

The standard equations of motion for consumption and the accumulation of capital that arise from the optimization problem are given by

and

i: -L = cr,-(r-o) c,

(16)

(17)

where 8, which is greater than zero, represents the constant rate of time preference and o-,. is, as before, the intertemporal elasticity of substitution for country f.28 Hence, in this economy all real variables grow at the same constant rate.

Saving is defined as

s, = y, - c, = cr,.(r- o)z,

and the saving rate, s,, is given by

s, = cr,.[t-( I + o)]

· ( l + r)

28 Note that 13 = l/(1 + 5).

(18)

(19)



To determine the response of the saving rate to changes in the real rate of interest, we differentiate equation ( 19) with respect to r and obtain

ds 1 + 8 - = cr; ---? . dr ( I + rt

(20)

Equation (20) highlights the key role that the intertemporal elasticity of substitution plays in determining how saving rates react to changes in real interest rates.29 Specifically, as <r; approaches zero, saving declines, growth declines, and saving ceases to respond to real interest rates altogether. In the remainder of this section, the estimated parameters are used to calculate-under the assumption that these economies share a common technology and thus face a common interest rate-the response of saving to real interest rate changes for a broad spectrum of countries with very different income levels.

Results

Using equation (20), the point estimates of <r; reported in Table 5, and a variety of plausible values for the real rate of interest and the subjective discount factor, we can calculate the implied response of saving to changes in the real rate of interest under various scenarios.

There are several features of the results presented i n Table 6 that are worth noting. First, as implied by this simple analytical framework, the intertemporal elasticity of substitution plays a central role in determining how much (or how little) saving rates respond to changes in the real rate of interest. Indeed, the saving elasticities presented in Table 6 closely resemble the <r; reported earlier (Table 5). Second, it follows from the previous observation that the cross-country variation is wide. For the poorest countries, a one percentage point rise in the real rate of interest should elicit a rise in the saving rate of only about one tenth of one percentage point;30 for the wealthiest countries, the rise i n the saving rate in response to a similar change in the real interest rate is about two thirds of a percentage point.31

29 In our context, these reactions should be thought of as steady-state effects. 30 These results are consistent with the result that regressions of the saving rate

against the real interest rate in low-income developing countries fail to find evidence of a significant coefficient on the rate of return variable: see, for example, Savastano ( 1 994 ).

31 Although the model used here ignores a number of important determinants of household behavior, it is interesting to note that in the context of a more complicated model that included, inter alia, the effects of financial deregulation on household saving behavior (see Ostry and Levy ( 1995)), the rna�nitude of the implied elasticities for the case of France is broadly similar to what IS reported here.

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SAViNG BEHAVIOR IN DEVELOPING COUNTRIES 67

Third, as columns (2) and (3) of Table 6 highlight, the saving elasticity is not very sensitive to the level of the real rate of interest assumed nor to the subjective discount factor (columns (4) and (5)).

V. Conclusions

This paper has sought to investigate the effect of the level of development on household saving behavior. The main issue with which we were concerned was the responsiveness of saving to interest rate changes, and whether there were any economically significant behavioral differences within a sample of countries at different stages of development. This issue was argued to be of relevance to policymakers because the investment and growth effects of, for example, financial liberalization, will depend on how responsive consumption/saving is to changes in real rates of return. Other policy questions-for example, the relationship between government deficits and the current account-will also depend on the responsiveness of private saving to real interest rates to the extent that changes in public (dis)saving alter domestic rates of return.

The main conclusion that emerged from our analysis was that much of the considerable cross-country variation in both the level of saving and the responsiveness of saving to the real rate of interest could be systematically explained by the country's income level. Specifically, the hypothesis that the saving rate and its sensitivity to interest rate changes were a rising function of income found strong empirical support. There is, of course, an often wide variation in saving behavior across countries with similar income levels that remains unaccounted for by the simple framework presented here. With these Limitations in mind, however, our results may help to explain why the rising real interest rates that typically accompany financial liberalization have often failed to elicit an appreciable rise in private saving.32 They may also shed some light on the wide cross-country variation in the response of the current account to fiscal policy changes that alter domestic interest rates.

The results presented here suggest that higher saving rates may not be forthcoming, even with relatively large increases in real interest rates, if the country in question is at the lower end of the income spectrum. In addition, the simple endogenous growth model presented in Section IV suggested that the growth effects of higher interest rates would also tend to be relatively small for relatively poor countries.

32 Nonetheless, even among the low-income countries, a move from negative to positive real interest rates, even if it has little impact on saving, may still be desirable from the point of view of macroeconomic stabilization and improving the efficiency of investment.



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IMF Staff Papers Vol. 43, No. I (March 1996) © 1996 International Monetary Fund

Are Exchange Rates Excessively

Volatile? And What Does "Excessively

Volatile" Mean, Anyway?

LEONARDO BARTOLINI and GORDON M. BODNAR*

We apply recent asset price volatility tests to re-examine whether exchange rates have been "excessively" volatile over the post-Bretton Woods period relative to the predictions of the monetary model of the exchange rate and of standard extensions with sticky prices, sluggish money adjustment, and risk premiums. Our tests reject most of the models that we examine. In general, however, we find that exchange rates have not been excessively volatile, relative to the predictions of even the most restrictive versions of the model. Alternative measures of volatility, however, may disguise the cause of rejection as excessive exchange rate volatility. [JEL F31, E44]

ARE EXCHANGE RATE FLUCTUATIONS justified by changes in their "fundamental" determinants? In an efficient market with rational investors,

exchange rates are forward-looking prices that reflect anticipated changes of the relative demand and supply of two moneys. Hence, their volatility should reflect investors' expectations of changes in the determinants of money stocks, such as incomes and interest rates. Given a model of exchange rate determination, market efficiency places restrictions on the relative volatility of exchange rates and of their determinants, which can be tested to yield insight on the validity of the underlying model. We apply a

* Research for this paper was conducted when Leonardo Bartolini was an Economist in, and Gordon Bodnar was visiting, the Research Department of the IMF. Leonardo Bartolini is now in the Research Department of the Federal Reserve Bank of New York. Gordon Bodnar is at the Wharton School of the University of Pennsylvania. Both authors hold a Ph.D. from Princeton University. They thank Eswar Prasad for providing them a Gauss code of the Hodrick-Prescott filter, Peter lsard, Peter Clark, Carol Osler, and participants in seminars at the fMF and at the Federal Reserve Bank of New York for comments, and Susanna Mursula for technical assistance.

72


ARE EXCHANGE RATES EXCESSIVELY VOLATILE? 73

family of such tests i n this paper, to assess whether some popular exchange rate models are capable of matching observed patterns of exchange rate volatilities over the post-Bretton Woods period.

Our interest in exchange rate volatility is motivated by both analytical and policy concerns. Exhibit A in policy discussions of exchange rate volatility is often represented by a chart such as Figure I , pointing to the dramatic increase in exchange rate volatility for major currencies since the breakdown of the Bretton Woods system. This evidence is often accompanied by an expression of concern that "private markets may not always anchor their behavior to economic fundamentals, thus making their responses susceptible to contagion and bandwagon effects that may be disruptive and detrimental to economic performance" (Mussa and others ( 1994), p. 18). Excessive exchange rate volatility is also often advocated as grounds for throwing sand in the wheels of currency markets (see, for instance, Eichengreen, Tobin, and Wyplosz ( 1995)).

Before policies to inhibit market response can be advocated, however, one ought to verify that the volatility of exchange rates does not simply reflect that of their underlying determinants. Also, as these tests are typically joint tests of market efficiency and of a specific exchange rate model, the results must be conditioned on the particular model that they are based on.

Giv,en the prominence in research on exchange rates of the monetary model and of its variants, early studies of exchange rate volatility, including Huang (1981), Vander Kraats and Booth ( I 983), and Wadhwani ( 1 987), followed Shiller's ( 198 I ) work on stock price volatility to construct "variance bounds" tests of the monetary model of the exchange rate. Invariably, these studies found the volatility of exchange rates since the breakdown of the Bretton Woods system to exceed the model's predictions, leading their authors and several conunentators (see, for instance, Levich ( 1 985)), to asset1 either the inefficiency of foreign exchange markets or the invalidity of the underlying model, or both.

Later studies, however, questioned those results. Diba ( 1 987), for instance, showed that the tests of Huang ( 1981) and Vander Kraats and Booth ( 1983) were vitiated by an erroneous transformation of annual semielasticities of money demand to interest rates into thei.r high-frequency counterparts. When correctly calibrated, those tests failed to reject the monetary model's predictions, although that failure was likely to reflect the weak restrictions placed by those tests on the model. Early volatility tests of asset price models were also shown to suffer from serious statistical biases, leading them to reject the underlying model too often in finite samples (see, for instance, Kleidon ( 1986) and Marsh and Merton ( I 986)). To address some of these concerns, Gros ( 1989) used improved volatility inequalities to present new evidence of excessive exchange rate volatility. His analysis, how-


74 LEONARDO BARTOLINI and GORDON M. BODNAR

Figure I . Gem1.any, Japan. and I he United Stales: Volatilily of Nominal Exchange Ra1es

(Percent changes from previous month)

Japanese yen/U.S. dollar

10 10

5 5

-5 -5

-10 -10 -15 '----'----'---'--'---'----'----'---'---'--' 1 5 1962 66 70 74 66 82 86 90 94 -

Deutsche mark/U.S. dollar

Deutsche mark/Japanese yen 1 5 .--------.----------------· 15

- ) 519L6-2 --6.l.6 __ __.70---'-7L4 ___ 6.l.6 __ __,82---8L6 __ ___,_9() __ __,94-' -15

Dotted line indicates approximate date of breakdown of the Bretton Woods System. Source: IMF, International Financial Statistics.



ever, was not based on a formal statistical test, was subject to the same calibration problems pointed out by Diba ( 1987), and involved measuring exchange rate volatility in a way that was likely to overstate his finding of excessive volatility. In summary, after 15 years of research, evidence on the ability of the most popular exchange rate models to match the observed variability of exchange rates rests largely on rills-specified and weak statistical tests. Not surprisingly, several authors have expressed a perception of futility when reviewing the inconclusive state of research on exchange rate volatility (see, for instance, Frankel and Meese ( 1 987), pp. 1 34-6).

I n this paper we use recent volatility-based tests of asset price models to provide new, clearer evidence on the ability of some popular exchange rate models to match observed patterns of exchange rate volatilities over the post-Bretton Woods period. We apply the methodology developed by Mankiw, Romer, and Shapiro ( 1991) i n the context of stock price models, and use data for the eight major currencies from 1973 to 1994 to test the textbook flex -price version of the monetary model as well as more general models with sticky prices, sluggish adjustment of money stocks, and time-varying risk premiums.

Our tests show that these models are broadly rejected by the data, but that this rejection can-in general-be attributed not to excessive exchange rate volatility, but rather to the inconsistency of these models with the assumed efficiency of currency markets. Hence, our tests confinn the wisdom from standard regression-based tests of these models (see Hod rick ( 1987) for a survey). However, since our tests possess better statistical properties than previous regression-based tests (in particular, they are unbiased in small samples), they provide even stronger evidence against the joint hypotheses of the monetary model (or of its extensions) and of market efficiency. Furthermore, because they are explicitly constructed as volatility tests, our tests help clarify the role played by exchange rate volatility in the models' rejection.

Specifically, our tests point to the importance of choosing an economically meaningful definition of exchange rate volatility as a basis for the tests, so as to avoid disguising a model's rejection as evidence of excessive volatility. The tests show that when exchange rate volatility is defined-traditionally-as the average of conditional or unanticipated exchange rate changes, then there is no evidence that exchange rates may have been excessively volatile with respect to the predictions of even the most restrictive version of the monetary model. Evidence of excessive exchange rate volatility, however, may emerge on the basis of alternative definitions of volatility.

Our findings, we hope, will contribute to future research on exchange rate volatility being more clearly defined in its scope and perhaps encourage greater caution i n making claims of "excessive" exchange rate volatility.



Our imposition on the data of a monetary model straitjacket should strengthen our conclusions: if exchange rates do not appear to be excessively volatile even with respect to a framework predicting their close movement with money and income alone, the likelihood that evidence of excess volatility would be uncovered based on more flexible models appears even more remote.

I. Volatility Tests of the Monetary Model

It is easiest to introduce our volatility tests based on a standard specification of the monetary model with flexible prices and instantaneous adjustment of money stocks. We outline the general testing methodology in this section and apply it to more general models in the next section.

The Monetary Model of the Exchange Rate

The standard specification of the monetary model includes two equations describing domestic and foreign money demands, a purchasing power parity equation, and an uncovered interest parity equation. Assuming, as is standard, that the domestic and foreign money demand parameters are the same, the model can be written as

m, - p, = �y, - CJ.i1 ,

p, =s, + P1,

i, - it = E, [s,+1 -s,] ,

(I)

(2)

(3)

(4)

where m,, p,, and y, denote (log) domestic money supply, prices, and real income, respectively, and i, denotes the interest rate at time r on deposits matUJing at time t + I . Foreign variables are denoted with an asterisk. The (Jog) exchange rate, defined as the domestic price of a unit of foreign currency, is denoted by s,, while £,[.] denotes the rational expectation operator conditional on information available at time r. The exogenous terms y, and m, may incorporate a stochastic component; alternatively, a stochastic ("velocity") term can be added to introduce unce1tainty in the right-hand side of equation ( I ). For ease of exposition, we shall adhere to the convention that m, already incorporates an exogenous stochastic shock.

Equations ( 1)-(4) can be collapsed into

(5)


ARE EXCHANGE RATES EXCESSIVELY VOLATILE') 77

where

!, = (m, -m;)-13( y, - l). (6)

Equations (5) and (6) express the exchange rate as the sum of current "fundamentals," J,, plus a linear function of its own value at time 1 + I . Solving equation (5) forward up to time r + h, yields

I

(

,_ , ( ); l ( )" s, = l + a � I :a E, [!,+; ] +

I :a E, [s,+,]. (7)

It is standard in the literature to assume the absence of exchange rate

bubbles, that is, that .lim(�); £, [.!,+;) = 0 , and to solve equation (7) for,�� I + <X

ward solely i n terms of fundamentals:

s, = -1 f(�)i£,[!,+; ]. J + <X i=O l +<X (8)

The tests considered in this paper, however, are robust to the presence of bubbles, and can be performed directly on equation (7): if s,+ll incorporates a bubble term (i.e., a capital gain that reflects solely the anticipation of a future currency transaction), so does s,, and equation (7) remains valid. In most of our tests, the investment's holding period, h, is set at 3, as forward markets tend to be most liquid for 3-month maturities, and the power of our tests falls when h increases much above 3. Tests for different values of h are discussed below.

Volatility Tests of the Monetary Model

Let us now define the perfect-foresight (or "fundamental") exchange rate,

s�, as the value that the exchange rate would take if investors could predict with certainty future fundamentals, as well as the exchange rate at t + h. The fundamental exchange rate s1 is obtained from equation (7) by dropping the expectation operator

I ( ,_, ( ); l ( )" s; = I + <X � I :a !,+; +

I :a 5'+1" (9)

so that, by definition. s, = E, [s;"] under the assumptions of the monetary model.



We must now choose a "benchmark" exchange rate, denoted by s;•, around which to measure the volatility of both market and fundamental exchange rates. The need for a benchmark rate reflects analytical and statistical considerations. First, there is simply no unique way to define exchange rates' volatility, except with respect to a reference benchmark (be it its sample mean or other variables). Second, the notorious nonstationarity of exchange rates requires measuring their movements with respect to a specific stochastic trend.

There are two main requirements for the choice of s r that it be known to investors at time t, and that the differences s, - s;' and s;� - sf' be stationary. There are many alternative ways to chooses;', however, so as to satisfy these requirements. For instance, st could be defined as the model's prediction at time t - I of the exchange rate at time t, which can be obtained by lagging equation (5) once and solving for £,_1(s,] :

o _ £ [ J - ( I +cx ) h-1 s, = ,_1 s, - � s,_1 -� . (I 0)

When s," is chosen in this fashion, the series s,* - s(' and s, - s;' describe fundamental and actual exchange rate surprises, based on the predictions of the monetary model.

Alternatively, exchange rate volati�ity could be measured by setting s," = St-t.• where L is a suitable lag. For instance, it is customary to focus on conditional volatilities, defined (with L = 1 ) as the volatility of the first difference of exchange rates, s, - s,-1 • Our task, in this case, would be to assess the consistency of the model's predictions of market and "fundamental" exchange rate changes from the last known realization of the exchange rate.

Yet another possibility would be to choose st as some "naive" exchange rate forecast, for instance, as the value that the exchange rate would take if investors expected fundamentals to evolve as a random walk. Under this assumption (and, in this case, under the no-bubble condition that

lim (�); E,[fr+;] = 0 ), equation (7) can be solved forward with ��- I + ex

EJf,+;] = f,, as implied by the random walk hypothesis, to obtain s, = J,: the exchange rate itself should follow a random walk under the assumptions of the monetary model. Note that this naive forecast need not be a rational one (although there is, indeed, a considerable amount of evidence that exchange rates may be well approximated by random walks): as long as s, = f, is known to investors at time t, and s, - s;' and sf - s;' are stationary, then s ;' = f, is an acceptable benchmark for our volatility tests. Indeed, Mankiw, Romer, and Shapiro ( 1 985 and 1991) have suggested a very sim-



ilar benchmark when testing for excess stock price volatility, by assuming that stock dividends follow a random walk. Gros ( 1989) followed their lead, measuring exchange rates with respect to a random walk benchmark. These issues, and their implications for the volatility tests performed in this paper, are further discussed in Section Til.

With rational expectations, the forecast error s�' - E,[si"] = s1' - s, should be uncorrelated with variables known at time 1, including s, and s;'. This implies that

( I I )

Therefore, squaring both sides of the identity

( 1 2 )

taking expectations, and using equation ( I I) , yields

( 13)

or

(14)

Therefore, the monetary model implies the testable restriction q, = 0. and hence the restriction E[q,] = 0: the sample mean of the q, s, q, should be close to zero if the model correctly describes the dynamjcs of exchange rates. As noted above, this test is robust to the presence of exchange rate bubbles: if the market exchange rate s, incorporates a bubble term, so do s;'�< ands;', and equation (14) remains valid.

Thus, we can construct a test of the monetary model as follows. First, we can compute the fundamental exchange rate, st, and the benchmark exchange rate, s ;•, from equations (9) and ( I 0), after calibrating the money demand parameters a and j3. Then we can use an asymptotic distribution of the sample mean q and reject the model when q differs significantly from zero. A Generalized Method of Moments (GMM) distribution of q (see Bollerslev and Hodrick (1 995)) is a normal distribution

( 15)

whose variance is estimated by V = C(O) + 2 I1�1 C(j), with C(j) =



h - j ( q,+ ,qt + !J- ) -- "VT h Lt=i+l T , which is robust to heteroscedasticity and serial

correlation in the eiTOr terms.' Equation ( 1 3) also implies that

£[ ( si - s, r] � £[ ( s� - sir l E[(s, - s;'f] � E[(s;' - s,* rJ

(16A)

(16B)

where the expectations are now taken unconditionally. Should either one of these inequalities be violated, then E,[q,] < 0 (although the opposite is not necessarily true), thus suggesting the use of inequalities ( 1 6A) and ( l6B) as diagnostics for the model. Inequality ( 1 6A), in particular, states that the market exchange rate, s,, should forecast the behavior of the fundamental rate, s�. better than the benchmark rate, s(', in terms of the usual meansquare error criterion. Inequality ( 16B) states that the market exchange rate should be less volatile around the benchmark rate than the fundamental rate. This latter inequality provides an "excess volatility" test of the model, and its intuition is simple: the fundamental exchange rate should deviate from the benchmark rate by as much as the market rate does, plus a forecast error sf - s/" If markets are efficient and the monetary model correctly describes exchange rate dynamics, this forecast error should not be systematically related to information available to investors. The volatility of the fundamental exchange rate around the benchmark rate, therefore, should exceed that of the market rate.

Relation to Alternative Tests of the Model

Two points should be noted about the test procedure just outlined. First, there is a close relationship between the volatility-based tests presented here and previous regression-based tests (see Hodrick ( 1987) for a survey). Recall that the starting point of our analysis is the condition that sf - s, and s, - s� should be uncorrelated if exchange rates reflect information available to market participants and if the monetary model correctly describes the dynamics of exchange rates. Using regression analysis, the natural test of this hypothesis would be to regress sf - s, on s, - sf', and test if the

1 Serial correlation is often a problem when using overlapping observations. In our case, in particular, observations overlap over the holding period h.


ARE EXCHANGE RATES EXCESSIVELY VOLATILE? 8 1

regression coefficient is zero. A nonzero 7T 1 implies that the prediction error s,* - s, can be forecast at time t. This, among other things, implies that

s,+ 1 - £,[s,+1] is forecastable, since sf - s, = 1 �ex (s,+ 1-£,[s,+ 1]), i.e.,

that there is a systematic bias between exchange rate predictions and realizations.

In comparison with ( 17), the volatility tests implemented in this paper reject the model when the mean of the q,s is zero. Now, since q can be written as

q = �I(s, -s�)(s;- s,)·2, (18) I

a link between the regression-based and the volatility-based methods is

apparent. Both methods involve testing whether � t<s, - s :')(sf-s,), suit

ably standardized, is significantly different from zero, and both tests provide (when statistically significant) evidence of excess returns' forecastability, namely, that markets are inefficient, or the assumed exchange rate model is invalid, or both. There are two main differences between the two methods, however.

The first difference is that the test used in this paper is directly linked to measures of exchange rate volatility and to conesponding volatility inequalities. These inequalities allow testing whether "excessive" volatility (suitably defined) is indeed a cause of failure of the model.

The second difference is more technical: the volatility-based tests used here have been shown to exhibit better statistical properties than the conespending regression-based tests. Specifically, Mankiw and Shapiro ( 1 986) and Mankiw, Romer, and Shapiro ( 1991) present Monte Carlo simulations showing that the finite-sample distribution of a sample-mean q is well approximated by its asymptotic distribution, namely, that the volatility-based test tends to reject the underlying model on average the right number of times. In contrast, the finite-sample distribution of the regression coefficient 7T 1 is poorly approximated by its asymptotic distribution. In particular, if the dependent and the independent variables are conelated, and the independent variable is itself serially conelated-which is certainly the case in our tests, where the same "fundamentals" drive both the dependent and independent variables-then regression-based tests are systematically biased, tending to reject the underlying model too often in finite samples.

Next, the ability of the test to reject the model, as well as the interpretation of the test results, depend crucially on the particular choice of s;'. The



usefulness of the rejection of the model, in particular, depends on s:· being a useful benchmark for the measurement of exchange rate volatility. Establishing the best benchmark is a task well beyond the scope of this paper, particularly since different benchmarks are bound to be useful in different contexts. In welfare analysis, for instance, the appropriate definition of exchange rate volatility depends on agents' attitudes toward risk, the nature of adjustment costs, and other such factors. Nevertheless, it is clear that the usefulness of a particular benchmark is likely to depend on whether exchange rates tend to gravitate, in some loose sense, around it. For similar reasons, few scientists seem to find useful a description of stars' and planets' positions in space with respect to the moon, nor do they find useful the (formally correct) statement that the sun is more volatile than is the earth with respect to the moon.

As the issue of choosing a suitable benchmark cannot be resolved in a statistical context-only on the basis of a well-specified economic model-we follow an eclectic approach in our statistical analysis. We present results for a variety of choices of sj', drawing from common usage in research and policy analysis, in order to highlight the implications of alternative definitions of exchange rate volatility. We focus, in particular, on the conditional volatility of exchange rates and on the volatility of their unanticipated movements. We present tests that use the model's one-period-ahead prediction of the exchange rate as a benchmark (see equation ( I 0)) to test whether unanticipated changes in exchange rates are consistent with movements in their determinants. We also present tests that use the lagged exchange rate as a benchmark, to test whether total changes in exchange rates are justified by movements in their determinants. Finally, we present tests in which the benchmark rate is set at the value that the exchange rate would take if investors believed that fundamentals behave as random walks. The tests can be applied in a straightforward way to other definitions of s {'.

Though our tests' dependence on the benchmark s{' may seem unfortunate, this dependence simply reftects the intrinsic ambiguity of the concept of exchange rate volatility: there is simply no unique way to measure exchange rates' volatility-just as there is no unique way to measure planets' movements-except with respect to a specific benchmark. This is the main point we wish to emphasize in this paper: that this ambiguity should be explicitly recognized.

ll. More General Specifications of the Model

The test procedure described in the previous section can be applied to a variety of exchange rate models. We discuss here some extensions of the



monetary model that allow for slow adjustment of prices and money holdings. and for violations of the interest parity condition. The point here is not to insist on the empirical accuracy of these specifications, although we draw from the empirical literature in calibrating our models. Rather, the aim is to illustrate the flexibility of the testing procedure, and to provide preliminary evidence of the robustness of our results. Our qualitative findings turn out to be rather robust, suggesting that greater effort to incorporate empirically accurate models, while welcome, is unlikely to overturn our main results.

Sticky Prices

Following Mussa ( 1 985) and Gros ( 1989), we adopt a sticky-price version of purchasing power parity (PPP), much along the lines of the standard Dornbusch model. In this model, the real exchange rates, + p '! - p, moves toward its ppp value at the rate e, as in

(19)

In equation ( 19), when 6 = 0 the real exchange rate follows a rantlom walk with no tendency to revert to PPP. When e = 1 the exchange rate is expected to converge to PPP in a single period.

Replacing equation (3) with equation ( 19) in the model, some tedious but straightforward algebra yields the "fundamental" sticky-price exchange rate, solved forward up to time t + h:

* - "' (1 -y")(l -e) * s, = s,· - e (p,_1 - p,_1 - s,_1 ), l + a (20)

where -y = <;�a;:, and s,* denotes the fundamental exchange rate for the

flex-price model (see equation (9)). The expectation at t - I of the market exchange rate at time t is

o _ _ fr-1 + Pt-1 -P:-1 . s, - s,_ 1 rt. rt (21)

For 6= I, the sticky-price model degenerates into the flex-price model; for smaller values of e, the sticky-price model predicts greater volatility of exchange rates in response to changes in their determinants. Except for this redefinition of variables, the test procedure remains the same as described in the previous section.



Sluggish Money Adjustment

We can also relax the assumption that real money balances adjust instantaneously to their long-run equilibrium value. Partial adjustment equations of the form

mr -Pr = A.(PYr -air )+ (1 - A.)(mr-1 -Pr ),

m; -p; = A.<Pl -ai1* ) + ( 1 - A.)(m1*_ 1 -p;),

(22)

(23)

have been widely used in the literature on money demand functions. The terms (I - A.)(m1_ 1 - Pt) and (I - A)(mr- 1 - pn include lagged money terms and contemporaneous price terms, reflecting an adjustment process of money balances specified in nominal terms. Alternatively, the adjustment term could have been specified as ( I - A)(m1_ 1 -p1_ 1) (and similarly for the foreign equation), if the assumed slow response were of real money balances. We use the former specification because it allows the familiar forward solution of the exchange rate in terms of fundamentals, and because of its superior empirical performance (see Fair ( 1 987)).2

Thus, the coefficients (3 and a in equations (22) and (23) describe the long-run income elasticity and long-run interest semi-elasticity of money demand, respectively; A measures the speed of adjustment of real money balances to their steady state, and takes values between zero and one: when A = 1 , real money balances adjust immediately to their steady state; when A = 0, money demand does not respond to interest rates and income, and the model has no steady-state solution.

Replacing equations ( 1 ) and (2) with equations (22) and (23) yields

r = (mr -m;) - (1- A.)(mr-1 -mr*_, ) A( ' - * ) J I - A }J ) t Yt • (24)

Except for this redefinition, the test procedure remains the same as described above.

2 We limited our exploration of money demand equations to specifications with instantaneous or partial adjustment of money stocks. Recent literature has considered buffer-stock and error-correction models that imply even greater departure from the standard specification of the monetary model (see Boughton ( 1992) for a survey). These specifications arc difficult to integrate in equilibrium exchange rate models because of their data-dependent parameterization and their tendency to involve lags of interest rates at different maturities and to predict long-run price nonhomogeneity.


ARE EXCHANGE RATES EXCESSIVELY VOLATILE·) 85

Time-Varying Risk Premiums

Finally, we can allow for a time-varying residual, x, in the interest parity equation (4):

(25)

For our purposes, an ex post estimate of the residual x, can be obtained by de-trending i, - if - (s,+ 1 - s,). that is, ( 1 + a)s, - as,+ 1 - (m, - m,*) + !3( y, - y,*) with a Hedrick-Prescott filter. The test procedure then remains the same as that described above, with "fundamentals" redefined as

!, = (m, -m;) -PCy, -y;) + x,. (26)

One possible interpretation of x, is as a risk premium and, for simplicity, we shall use this label in our discussion. Nevertheless, our simple treatment must be viewed only as an ad hoc way to relax the interest parity equation, not as a structural model of a risk premium. Our aim, once again, is not to provide a satisfactory exchange rate model, but only to verify the robustness of our results to relaxation of the basic assumptions of the monetary modeP Hence, in our tests we have used a variety of values for the Hodrick-Prescott smoothing coefficient, p, summarized by the choices p = 14,400 (which, following the literature, equals l 00 times the square of the sample frequency), and p = l ,600, a lower value that allows the model to better fit the data.

III. Empirical Results

Data and Calibration of the Tests

The full sample covers data for Canada, France, Germany, Italy, Japan, Switzerland, the United Kingdom, and the United States between January 1973 and September 1994. We use the same proxies for the monetary model's va1iables used in previous studies: monthly data for narrow and broad money supply, GDP, industrial production, consumer price indices, and exchange rates against the U.S. dollar (end-of-period data). All data are from the IMF's International Financial Statistics, except for a few series

' In particular, since we use all the model's equations to obtain an ex post estimate of x , , the model would be identically satisfied (i.e., s,* = s,) if we set the Hedrick-Prescott smoothing coefficient, p, at zero. The model specified with equation (25) imposes restrictions on the data only to the extent that the filtered residual is required to be smooth over time.



that were incomplete in the International Financial Statistics, which were obtained from the JMF's Current Economic Indicators database.

We calibrated our tests using parameters estimated in previous empirical studies, choosing wide ranges to encompass both estimated and plausible values for each parameter.

Most estimates of the annualized semi-elasticity of money demand to short-term interest rates, for money demand functions with instantaneous adjustment, fall i n the range of I to 4 (see, for instance, Laidler ( 1 993)). Estimated exchange rate models tend to yield smaller values of a (see, for instance, Flood, Rose, and Mathieson ( 1991 )), while money demand equations with partial adjustment tend to yield somewhat higher values of a (see, for instance, Fair ( 1987) and Goldfeld and Sichel ( 1 990)). We took the values a = 0 . 1 and a = 6 (to be multiplied by 12 in monthly tests) as spanning the plausible range of a, using a = 1 as a baseline.

Most estimates of the income elasticity of money demand, 13. range from about 0.5 to about 1.5, independent of the assumed speed of money adjustment (see, for instance, Fair ( 1 987) and Goldfeld and Sichel ( 1990)). We begin by considering the values 13 = 0.2 and 13 = 2, and then fix 13 at unity for the rest of the analysis.

The speed of adjustment of money stocks to their steady state, A., is more difficult to calibrate. Annual'ized estimates of A. from pre-1974 (quarterly) data typically range around 0.3-0.5, suggesting a half-life of money shocks between 6 and 1 8 months, already a surptisingly slow response. In fact, estimates from post- 1 974 data typically yield near-zero estimates of A., implying no response of money demand to changes in its determinants, and a breakdown of the steady-state solution of the model. It is now well understood that the estimated unstable behavior of money balances from post- 1974 data reflects more the difficulty of capturing with simple dynamic specifications the financial innovations and institutional changes that occurred since 1 974, than an implausibly low speed of portfolio adjustment (see Goldfeld and Sichel ( 1990) and Boughton ( 1 992) for a discussion). We report results for the baseline case of instantaneous adjustment, 'A = I , and for the cases oft.. = 0.5 and A. = 0.1 (corresponding to monthly values of about A. = 0.06 and A. = 0.01 ). We also present results of tests conducted over split samples, as a preliminary check of robustness of our inference to structural breaks.

Estimated half-lives of price shocks in PPP equations range anywhere from one to six years, depending on currency and sample (see, for instance, Hakkio ( 1992) and Lothian and Taylor ( 1 993)). Hence, (annualized) values of e should range between 0. 1 and 0.5. We report tests with e set at 0.3; results for tests calibrated with e = 0.1 and e = 0.5 were very similar.

Finally, "fundamental" data for output, money, and prices must be normalized. First, data are reported only in index number form. Second, econo-



metricians can only guess which macro-aggregates best capture the theoretical concepts of "output," "money," and "prices," suggesting allowance for a degree of freedom in scaling raw data. After allowing for a multiplicative factor in raw data (i.e., for an additive constant in log-transformed data), the model suggests a logical way to normalize the series: by scaling raw data so that the model holds on average over the sample (that is, so that s,* = s,).

Results

Tables 1-3 report a sample of the volatility tests that we implemented.� Table I reports results of tests of the textbook flex-price instantaneous

money-adjustment version of the monetary model, for different values of the elasticities 13 and a. Several important features are apparent from these results.

First, the model is strongly rejected in almost all cases. with test statistics often exceeding their 99 percent critical values of ::!::2.57. The rejection is strong when s:' = £,_ 1 [s,] is used as a benchmark, and is due to the occurrence of a positive test statistic. This positive sign reflects a positive correlation between the forecast error, s'j' - s,, and the exchange rate surprise at time 1, s, - £,_ 1 [s,]. That is, on average, either s'j' - s, > s, > £1-1 [s,] or s, < s, < £,_ 1[s,] . Hence, these tests indicate that market exchange rates tend to stay closer to their one-period-ahead forecasts than predicted by the monetary model, confirming evidence from regression-based tests that the joint hypothesis of the monetary model and that of market efficiency are mutually exclusive, as systematic profit opportunities would have persisted in the major currency markets over the sample period. The tests also show, however, that excessive exchange rate volatility is not a cause of rejection, as inequality ( 16B) (a violation of which is marked "B" in Tables 1-3) is never violated when s:' = £,_ 1 [s,] is used as a benchmark: the sample volatility of market exchange rates around the model's prediction at time 1 - I , E[(s, - s ;')2], i s smaller than that of fundamental rates around the same benchmark, E[(s;;' - s{')2]. Market exchange rates at time 1 also appear to forecast fundamental rates better than the model's predictions at time t - I , as required by inequality ( 16A) (a violation of which is marked "A" in the tables). Thus, both inequalities ( 16A) and ( 16B) are satisfied. These inequalities are only necessary-not sufficient-conditions for model acceptance, however, and their fulfillment does not prevent the model from being rejected on grounds of forecastability of excess returns.

4 A more complete set of tests is available from the authors, together with the data and a copy of the GAUSS program used for the tests.

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ARE EXCHANGE RATES EXCESSIVELY VOLATILE? 9 1

There i s also n o evidence o f excessive exchange rate volatility when the lagged exchange rate is used as a benchmark (sf' = s,_ 1): conditional volatilities of major exchange rates do not exceed the predictions of even the most restrictive version of the monetary model over the post-Bretton Woods period. Inequality ( 16A) is violated for the Japanese yen at low values of a, and for the Italian lira at low values of a and large values of 13. Interestingly, it is much more difficult to reject the model when sf' = s,_, than when s, - s{' = £,_ 1 (s,]: exchange rate innovations, s, - s,_" appear as largely random in the data (particularly at short horizons) and only for high values of a is the model rejected with confidence. These are intuitive results: as a falls, the discount rate implicit in the model rises, so that the weights attached by the test to events in the near future rise. As exchange rates are usually difficult to distinguish from random walks at very short horizons, the test cannot reject the hypothesis that s, - s,_, is pure noise.

Setting s [' = f, causes inequality ( 1 68) to be violated for all currencies and parameter values, and q to be significantly negative: market exchange rates are too volatile around s ;· = f, to be consistent with the predictions of the monetary model. Inequality ( 16A) is also violated, though only for very low values of a. Violation of ( 168) is consistent with the evidence presented by Gros ( 1989) who, following Mankiw, Romer, and Shapiro's ( 1985) work on stock prices, measured exchange rates as deviations from a random walk benchmark. Indeed, it is visually apparent from plots of market, fundamental, and benchmark exchange rates (available upon request from the authors), that s? tracks s, more closely than st when s;' = £,_ 1[s,] or s:' = s,_,. In contrast, s;• tracks st more closely than s, when s;' = f,. As a result, s, is not excessively volatile when s;' = £,_1 [s,) or s;' = s,_ ., but is

excessively volatile when s;' = f,, for all currencies and acceptable parameter values. Evidence of excessive volatility when measuring exchange rates as deviations from a "random walk" benchmark is therefore formally correct, though most researchers (including ourselves) would argue this to be a finding of little use. Loosely speaking, what would be viewed as "excessively volatile," for most purposes, would be the benchmark itself, not the exchange rate. Indeed, when exchange rates are measured with respect to common benchmarks (the value predicted by the underlying model based on last period's information, or the last value in the public's information), then there is no evidence that major exchange rates may have been too volatile i n the post-Bretton Woods period with respect to the predictions of even the most restrictive version of the monetary model.

Tables 2 and 3 confirm the previous discussion for alternative specifications of the model. Table 2 presents results for the baseline set of parameters (a = 13 = A = e = I), for the model with partial adjustment of money stocks (A = 0.5 and A = O.l), and for the sticky price model. Predictably,



the models with sluggish money and price adjustment can be rejected with somewhat less confidence than the baseline model.5 More careful modeling of the money and price processes is likely to weaken the evidence against the model even further. For the purpose of the present study, however, it suffices to note that these extensions tend to make the model's rejection marginally less significant, while not affecting the volatility inequalities: there is no evidence of excess volatility when exchange rates are measured with respect to their lagged values or with respect to the trends anticipated by the model: there is evidence of excess volatility, however, when exchange rates are measured with respect to a random walk benchmark.

Table 3 presents test results for the model with time-varying risk premiums and for the baseline model over two half-samples. Allowing for violations of the interest parity condition sharply weakens the overall evidence against the model, particularly when the Hodrick-Prescott parameter p is set to such a low value (p = I ,600) that much of the interest parity residuals are incorporated into fundamentals. While these tests are clearly skewed in favor of the model (little structure is imposed on the premiums x, except that they should be smooth over time), our previous discussion of the volatility inequalities ( l 6A-B) requires little change. Indeed, these results suggest that more accurate modeling of the interest parity condition is likely to weaken the evidence of excess volatility even based on a random walk benchmark.

Finally, overall evidence against the model remains strong when the tests are performed over split samples, and the qualitative aspects of the excess volatility tests are also unchanged.

A variety of alternative specifications of the tests, for which results are available upon request, gave very similar results. We relaxed the assumption of long-run PPP by allowing for a time-varying trend in the real exchange rate (estimated, as in the case of a time-varying risk premium, by passing S1 + p1* - p1 through a Hodrick-Prescott filter); we performed tests with narrow money instead of broad money as the monetary variable, using moving averages rather than the Hodrick-Prescott filter to filter the data, using quarterly (instead of monthly) data and. in this case. using real GDP instead of industrial production data: we measured exchange rates with respect to the deutsche mark rather than the dollar; and we considered different holding periods, h, in the definition of the fundamental exchange rate, and different lags, L, in the definition of the benchmark exchange rate. Our volatilitybased tests continued to provide evidence against the model as a whole

5 Given the existing econometric evidence on money demand equations, it is also not surprising that the data favor an extremely low value of A. See the discussion of the calibration of A above.



(more precisely: evidence of excess returns forecastability), but no evidence of excess volatility-except with respect to a random walk benchmark.6

IV. Concluding Remarks

The volatile behavior of exchange rates since the breakdown of the Bretton Woods system has led scholars and policymakers to question the consistency of exchange rate fluctuations with movements in their underlying determinants, with complaints of unjustified (or irrational) market turbulence rising loud during episodes of exchange rate instability. Several previous studies have presented evidence that exchange rates since 1973 have been excessively volatile with respect to the predictions of a variety of popular exchange rate models. However, for reasons ranging from calibration errors, small-sample biases, and lack of a proper testing procedure, these studies failed to present convincing evidence of the inability of these models to match the observed pattem of exchange rate volatilities over the postBretton Woods period.

We have tried in this paper to provide more solid evidence on the ability of a popular family of exchange rate models to match observed patterns of exchange rate changes, by applying recent tests of asset price volatility. Two main points have emerged from the analysis.

First, consistent with previous regression-based tests of the monetary model, our volatility-based tests strongly reject the monetary model in its textbook flex-price format and in more general versions that allow for sluggish price and money adjustments: excess returns in currency markets appear to be too forecastable for these markets to be efficient and exchange rates to be governed by the rules of the monetary model. As the volatilitybased tests that we employ have been shown to possess better statistical properties. than previous regression-based tests, our evidence against the monetary model should be viewed as stronger than that previously available in the literature. Nevertheless, rejection of the monetary model is hardly a novelty, and this negative outcome would be, on its own account, of secondary interest.

Second, and more interesting, our tests highlight the ambiguity of the concept of exchange rate volatility, and the implications of this ambiguity for claims of "excess" exchange rate volatility. Measuring exchange rate

6 Exceptions included moving to quarterly data, which caused most tests to become insignificant, likely as a result of a drastic fal l in the degrees of freedom; and increasing the holding period beyond six months and the lag L in sr = Sr-L beyond three months, which also caused many of the tests to become insignificant. Replacing broad money with narrow money tended to increase the confidence of rejection.



deviations with respect to different benchmarks leads to different conclusions on whether major currencies' exchange rates have been excessively volatile over the post-Bretton Woods period. While we have made no attempt to resolve this ambiguity, we have showed that based on certain (odd, in our view) definitions of exchange rate volatility, claims that major exchange rates may have been too volatile over the post-Bretton Woods period may be formally justified. However, based on definitions of exchange rate volatility common in the exchange rate literature (which focus on the volatility of exchange rate surprises, and on the conditional volatility of exchange rates), major exchange rates over the post-Bretton Woods period do not appear to violate the predictions of even the most restrictive version of the monetary model: their volatility is consistent with the anticipated volatility of their determinants.

Our results should lead to greater skepticism of future claims of "excessive" exchange rate volatility, and our focus on a model as restrictive as the monetary model should reinforce this skepticism: models that do not tie down exchange rate movements to those of such a narrow set of macroeconomic variables (for instance, portfolio balance models with imperfect substitutability, asset-price models with variable rates of discount, etc.) should provide even less evidence of excess volatility. (Formally, for a perfectly-fitting model, s,* = s,, q = 0, and both ( 16A) and ( 16B) would be satisfied.) The technique applied in this paper to test for excess exchange rate volatility is simple and general, and future research is bound to subject this conjecture to a direct test.

REFERENCES

Bollerslev, Tim, and Robert J. Hodrick, "Financial Market Efficiency Tests," in Handbook of Applied Econometrics. ed. by M. Hashem Pesaran and Michael R. Wickens (Cambridge: Blackwell, 1995), pp. 4 15-58.

Boughton, James M., "International Comparisons of Money Demand,'' Open Economies Review, Vol. 3 ( 1992), pp. 323-43.

Cochrane, John H., "Volatility Tests and Efficient Markets: A Review Essay," Journal ofMonetaly Economics, Vol. 27 (June 1991), pp. 463-85.

Diba, Behzad T., "A Critique of Variance Bounds Tests for Monetary Exchange Rate Models," Journal of Money, Credit. and Banking, Vol. 1 9 (February 1987), pp. 104- 1 1 .

Eichengreen, Barry, James Tobin, and Charles Wyplosz, "Two Cases for Sand in the Wheels of International Finance," Economic Journal, Vol. 105 (January 1995), pp. 162-72.

Fair, Ray C., "International Evidence on the Demand for Money," Review of Economics and Statistics, Vol. 69 (August 1987), pp. 473-80.


ARE EXCHANGE RATES EXCESSIVELY VOLATILE') 95

Fama, Eugene, "Forward and Spot Exchange Rates," Journal of Monetary Economics, Vol. 14 (November 1984), pp. 3 19-38.

Flood, Robert, Andrew K. Rose, and Donald J. Mathieson, "An Empirical Exploration of Exchange Rate Target Zones," Carnegie-Rochester Conference Series on Public Policy, Vol. 35 (Autumn 1991), pp. 7-66.

Frankel, Jeffrey A., and Richard Meese, "Are Exchange Rates Excessively Variable?" NBER Macroeconomics Annua/ 1987 (New York: National Bureau of Economic Research, 1987), pp. 1 1 7-53.

Goldfeld, Stephen M .. and Daniel E. Sichel, "The Demand for Money," in Handbook of Monetary Economics, Vol. I , ed. by Benjamin M. Friedman and Frank H. Hahn (New York: North-Holland, 1990), pp. 299-356.

Gros, Daniel, "On the Volatility of Exchange Rates: Tests of Monetary and Portfolio Balance Models of Exchange Rate Determination," We/twirtschaftliches Archiv, Vol. 125, No. 2 ( 1 989), pp. 273-95.

Hakkio, Craig S., "Is Purchasing Power Parity a Useful Guide to the Dollar?" Federal Reserve Bank of Kansas City Economic Review, Vol. 77, No. 3 (Third Quarter 1992), pp. 37-51 .

Hodrick, Robert, The Empi rica/ Evidence on the Efficiency ofF orward and Futures Foreign Exchange Markets, Vol. 24 in Fundamentals of Pure and Applied Economics (New York: Harwood, 1987).

Huang, Roger D., ''The Monetary Approach to Exchange Rate in an Efficient Foreign Exchange Market: Tests Based on Volatility," Journal of Finance, Vol. 36 (March 1981), pp. 31-41.

Kleidon, Allan W., "Variance Bounds Tests and Stock Price Valuation Models," Journal of Political Economy, Vol. 94 (October 1986), pp. 953-100 I .

Laidler, David E.W., The Demand for Money: Theories, Evidence, and Problems (New York: HarperCollins, 4th ed., 1993).

Levich. Richard M., "Empirical Studies of Exchange Rates: Price Behavior, Rate Determination and Market Efficiency," in Handbook of International Economics, ed. by Ronald W. Jones and Peter B. Kenen (New York: NorthHolland, 1985), pp. 979-1040.

Lothian, James R .• and Mark P. Taylor, "Real Exchange Rate Behavior: The Recent Float from the Perspective of the Past Two Centuries" (unpublished; Washington, International Monetary Fund, 1993); and forthcoming in the Journal of Political Economy.

Mankiw, N. Gregory, David Romer, and Matthew D. Shapiro, "An Unbiased Reexamination of Stock Market Volatility," Joumal of Finance, Vol. 40 (July 1985). pp. 677-87.

---. "Stock Market Forecastability and Volatility: A Statistical Appraisal," Review of Economic Studies, Vol. 58 (May 1991 ), pp. 455-77.

Mankiw, N. Gregory, and Matthew D. Shapiro, "Do We Reject Too Often? Small Sample Bias in Tests of Rational Expectations Models," Economics Letters, Vol. 20, No. 2 ( 1 986), pp. 139-45.

Marsh, Terry A., and Robert C. Merton, "Dividend Variability and Variance Bounds Tests for the Rationality of Stock Market Prices," American Economic Review, Vol. 76 (June 1986), pp. 483-98.



Mussa, Michael. "Official Intervention and Exchange Rate Dynamics," in Exchange Rate Management Under Uncertainty, ed. by Jagdeep Bhandari (Cambridge: MIT Press. 1985), pp. 1-30.

---. and others, Improving the lmernational Monetary System: Constraints and Possibilities, IMF Occasional Paper No. 1 16 (Washington: International Monetary Fund, December 1994 ).

Shiller, Robert J., "Do Stock Prices Move Too Much to Be Justified by Subsequent Changes in Dividends?'' American Economic Review, Vol. 7 I (June 1981). pp. 421-36.

Vander Kraats. Ronald H., and Lawrence D. Booth, ''Empirical Tests of the Monetary Approach to Exchange Rate Determination;· Journal of International Money and Finance, Vol. 2 (December 1983). pp. 255-78.

Wadhwani, Sushi I B., "Are Exchange Rates 'Excessively' Volatile?" Journal ojlnrernational Economics, Vol. 22 (May 1987), pp. 339-48.


lMF Staff Papers Vol. 43. No. I (March 1996) © 1996 International Monetary Fund

Relative Price Convergence in Russia

PAULA DE MASI and VINCENT KOEN*

Following price and exchange rate liberalization, domestic consumer prices in Russia moved closer to market levels. This paper quantifies the magnitude of the associated relative price changes. It also shows that relative price variability has been positively correlated with inflation. It isfurther established that convergence toward international relative and absolute price levels is Jar from complete, and that geographical price dispersion within Russia has declined since early 1992 but remains fairly high. [JEL E3 1 , P22, R32]

HIGH OPEN INFLATION appeared in 1991 in Russia as a result of partial price reforms and the de facto loosening of price controls.1 Following

the January 2, 1 992, comprehensive price liberalization and the associated price jump, monthly inflation rates remained in the double digits during most of the next three years.2 By the end of 1994. consumer prices had increased by almost 2,000 times compared to December 1990 (Figure I , top panel).

Eliminating controls allowed prices to become market determined. ft is commonly accepted that relative prices were highly distorted under central planning and that liberalization prompted major shifts in the price structure. Supportive evidence typically consists of selected examples of goods (and more rarely services) for which the relative price change has been particularly conspicuous. However, to our best knowledge, no systematic empirical analysis of the realignment of relative prices has yet been undertaken

* Paula De Masi is an Economist in the Research Department. She holds a Ph.D. from Harvard University. Vincent Koen is a Principal Administrator at the OECD. At the time of writing, he was an Economist in the IMF's Research Department. He holds a Ph.D. from MIT. Suggestions and other inputs from Gerard Belanger, Andrew Berg, Ales Bulfi', David T. Coe, Fran9ois Lequiller, Bogdan Lissovolic, Anthony Richards, and Bryan Roberts are gratefully acknowledged.

1 Previous episodes include the hyperinflation of the early 1920s and a period of chronic high inflation in the 1930s and 1940s.

2 For details, see Koen and Phillips ( 1993).

97


98

100,000

50,000

10.000

5.000

1.000

500

400

200

100

80

60

40

30 1990

PAULA DE MASI and VINCENT KOEN

Figure I. Price Levels and Relative Prices (December 1990=100. log scale)

:April 1991 :price ;reform

1991

1991

Overall Price Levels"

: January 1992 : price ; liberalization

RelaLive Prices•

Paid services

- - -.... _ _ Foodh

1993 1994

Sources: Goskomstat of the Russian Federation; and authors· calculations. •Relative to the overall CPI, linking the hybrid CPI ( 1991-92) and the

expanded CPI ( 1993-94). bExcluding alcohol and wbacco.


RELATIVE PRICE CONVERGENCE IN RUSSIA 99

showing to what extent and how fast prices in Russia have converged to some market economy benchmark.

This paper explores this question for consumer prices, using several large data sets ranging from 1 980 to 1994.3 Price convergence can be thought of along several dimensions. Section I examines the realignment of average nationwide domestic relative prices in the wake of the freeing of prices and the associated removal of subsidies; it also documents the increasing synchronization of price-setting as agents adapt to a high inflation environment. Section II offers alternative measures of the movement of the overall price level in Russia toward international heights. Section III discusses the evolution of regional price disparities within Russia as a way to assess market integration. Section IV summarizes the main findings of the paper and outlines areas for further research.

I. Realignment of Domestic Relative Prices

At any level of disaggregation of the overall consumer price index (CPI) and at any frequency. it is immediately apparent that inflation rates varied a lot across items or groups of items, implying that relative domestic consumer prices changed considerably over time. This section analyzes the timing, direction, and permanence of these shifts in the structure of relative prices, and identities a number of long-nm changes and trends. In addition, some insights are offered on the short-run dynamics of open inflation.

Pre- Versus Post-Liberalization Prices

The evolution of individual relative prices suggests that during the 1980s-i.e., even before prices were liberalized-the structure of domestic administered prices was not completely frozen. For example, the relative price of vodka surged between 1985 and 1990 in connection with the antialcohol campaign launched in the early stages of perestroika. The April l991 retail price adjustments translated into large increases in the relative price of a number of items (e.g., meat and meat products, butter, sugar, bread, potatoes, and many electrical appliances) and large drops in the relative price of others (e.g., vodka and construction materials). The January 1992 liberalization led to very significant changes, including large increases for some items (such as meat, canned fish, butter, cheese, sugar, refrigerators, washing machines, and construction materials), and large declines for others (such as eggs, bread, vodka, many electronic entertainment goods, watches, sewing machines, and bicycles). As a result, by 1992, the relative price of many goods had changed considerably compared with 1980 (Figure 2).

3 The data are presented in De Masi and Koen ( 1995).


100 PAULA DE MAS! and VINCENT KOEN

Figure 2. Relative Price Change for Selected Goods in Stores, 1992 versus 1980 (Percent)

25Qr---------------------------------------------�

200 -

150 -

100 -

50 1"-Mear

• Fislr

Cheese •

• Burrer

• Pot a roes

• Sugc1r

Color 7V

Refrigeraror •

-

-

-

-

() 1----------------------------�--------------�__, Rooji11g s\re

\ • \ Eggs •

Bread Bicycle • Radio •

• • Vodka Warclr -�0 �--------------------------------------------�

Sources: Goskomstat of the Russian Federation; and authors' calculations.

During the 1 980s and even more so in 1991, food prices in city markets, which had been free all along, typically increased faster than prices in stores for those items that were sold through both channels, reflecting repressed inflation. [n 1992, following price liberalization, food prices rose much less in city markets than in stores. While by 1991 prices in city markets were typically two to four times higher than in stores, prices in the two types of outlets broadly converged in 1992.4

4 The remaining spread may reflect quality differences or local price controls.



Table I . Cross-Correlations of Price Structures

Prices in Stores

All goods 1985 1990 1991 1992 Dec. 1992 June 1993

1980 0.98 0.99 0.98 0.96 0.62 0.63 1985 1 .00 0.99 0.95 0.94 0.55 0.55 1990 1 .00 0.98 0.95 0.61 0.61 1991 1 .00 0.96 0.68 0.68 1992 1 .00 0.75 0.75

Dec. 1992 1 .00 0.99

Foodstuffs 1985 1990 1991 1992 Dec. 1992 June 1993

1980 0.99 0.98 0.99 0.95 0.94 0.82 1985 1 .00 0.99 0.99 0.95 0.93 0.79 1990 1 .00 0.97 0.91 0.88 0.74 1991 1 .00 0.95 0.94 0.79 1992 1 .00 0.98 0.90

Dec. 1992 1 .00 0.87

Nonfood goods 1985 1990 1991 1992 Dec. 1992 June 1993

1980 0.98 0.99 0.97 0.94 0.59 0.59 1985 1 .00 0.99 0.93 0.9 1 0.50 0.51 1990 1.00 0.97 0.92 0.56 0.57 1991 1 .00 0.94 0.63 0.64 1992 1 .00 0.74 0.74

Dec. 1992 1 .00 0.99

Prices in City Markets

Foodstuffs 1985 1990 1991 1992 Dec. 1992 June 1993

1980 0.97 0.95 0.93 0.93 0.92 0.96 1985 1 .00 0.98 0.98 0.98 0.96 0.94 1990 1 .00 0.99 0.97 0.98 0.92 1991 1 .00 0.99 0.99 0.88 1992 1 .00 0.97 0.86

Dec. 1992 1 .00 0.88 Sources: Goskomstat of the Russian Federation; and authors' calculations.

It is difficult, however, to compare the overall magnitude of relative price shifts without some summary measure. One such indicator is the correla-tion between price structures over time (or space).5 The cross-period corre-lation coefficients shown in Table I confirm that relative prices changed moderately during the 1980s, that they shifted more significantly in 1 99 1 , and that the largest changes took place in 1992. The cross-correlations also

5 Berg ( 1994) computes such a measure for Poland.


102 PAULA DE MASI and VINCENT KOEN

suggest that the structure of relative prices in city markets was much less affected by price liberalization than that of prices in stores.6

As already noted, seasonality may distort comparisons involving a given month and a yearly average. Using end-1 990, end- 1 99 1 , end- 1 992, and end-1993 prices for a similar (albeit slightly different) set of goods, analogous cross-correlations controlling for potential seasonal biases corroborated the above conclusions. 7 Furthermore, the correlations suggest that the bulk of the relative price changes had taken place by end-1992, especially for nonfood goods. They also highlight continuing changes in the structure of food prices in 1 993, probably as a result of adjustments in the structure of subsidies.

Although the above correlations between price structures are informative global measures of relative price changes, they suffer from two shortcomings. First, the sample under consideration excludes services, the prices of which behaved very differently from that of goods. Second, the sample is fairly small and items are unweighted, which might produce misleading results.8

At the most aggregate level, the prices of "paid services" increased much less than that of goods in April 1991 and January 1992 (Figure I , bottom panel).9 However, a very rapid catch-up began after the early 1 992 jump in the overall price level. By late 1992, the relative price of services had returned to its December I 990 level, and by late 1994, it had surged to about five times that level. In part, this process reflected the commercialization of a number of services such as child and health care that were previously provided for a nominal fee. It also reflected the adjustment of cost recovery ratios from a very low basis, for example in the case of housing, with rents rising by almost 500 times between end-1 992 and end-1994, compared to a 30-fold increase in the overall CPT. A similar U-curve pattern for the relative price of services has been observed in many other countries of the former Soviet Union.10 It is also reflected in the evolution of the share of

6 The relative price stlructure in city markets was nevertheless affected because some of the items sold in city markets were also sold in stores, and because of nonzero cross-product demand elasticities.

7 The raw data appear in Goskornstat ( 1994). For the sake of brevity, the correlations are not reported here.

3 The weights of individual items in the CPI vary considerably. Vodka by far carries the largest weight (9.34 percent, almost twice as much as the second largest element, sugar). A number of items for which no household budget survey information is available, but which are presumably a small proportion of the CPI, are given the minimal weight of 0.0 I percent.

9 Many services are (or were) public "goods"' and therefore do not (or did not) apftear in the CPI, hence the qualifier "paid."

° For example, in the Baltic countries, Kazakstan, Ukraine, Armenia, Azerbaijan, and Tajikistan. See De Masi and Koen (forthcomjng).



services in household expenditures, which fell through 1992 but then rebounded, although by 1994 it was still extremely low compared to market economy standards (Figure 3). 1 1

Whereas the trends i n service prices are invariant to the choice of the price index, the evolution of food prices depends on which measure of consumer prices is selected. Based on the "hybrid CPI," the price of food relative to the overall CPI declined rapidly after a spike associated with the January 1992 price jump and hovered around 85 percent of its December 1990 reference level between mid-1992 and end-1994 (Figure I , bottom panel); based on the "urban CPI," however, the relative price of food fell less after January I 992 and remained at about I 20 percent of its December I 990 level through 1994. 12

Further insights into the shifts in relative prices emerge from a more disaggregated analysis. Data for the full decomposition of the CPI were obtained for July 1993 and July I 994, 13 and prices covering a bit more than half of the CPI were reconstructed for January and July 1992.14 The trends described above are reflected in the evolution of individual prices. 15

The magnitude of the relative price changes confirms that the broadbased liberalization that took effect on January 2, 1992, did not instantaneously bring about a new stable relative price structure, not least because a large number of prices temporarily remained subject to federal or local price controls before they were freed. Specifically, the relative price of those items that were free of controls early on changed little from mid- 1992 onward: for example, the prices of potatoes, apples, and eggs moved broadly in line with the overall CPI.16 The prices of some food items and of some medicines rose substantially more than the overall CPI once subsidies were cut. For example, the relative price of milk rose a lot during the first half of 1992 as subsidization was reduced, and grew further between mid-1993 and mid-1994 for the same reason. The relative price of bread doubled between mid-1 993 and mid-1994, reflecting the sharp reduction in subsidies in the fall of 1993. At the same time, the relative price of aspirin

1 1 The price of services typically also rises more rapidly than the overall CPI in market economies, but not that much faster. Ln the United States, for instance, it rose by 15.7 percent between end-1990 and end-1994, compared to an 1 1 .9 percent increase for the overall CPl.

12 The differences between the "hybrid" and "urban" CPls are described by Koen and Phillips ( 1992).

13 The numbers were directly provided by Goskomstat. The complete list of items appears in Russian in Goskomstat ( 1993) and in English in Granville and Shapiro ( 1994).

14 Based on Goskomstat price tables published weekly by Delovoy Mir and on data provided directly by the Center for Economic Analysis.

15 See Table A3 in De Masi and Koen ( 1995). 16 The comparison with January 1992 is difficult because of seasonality.


104 PAULA DE MAS! and VINCENT KOE.N

Figure 3. Structure of Household Consumption: lnrernational Comparison (Percent)

0 Housing" 0 Services [] Food • Nonfood goods 60r-------------------------------------------------�

Russia

1989

1989 Poland

1990 1991

1989/90 Ponugal

1992

1993 France

1993 1994

1993 United States

Sources: Goskomstat (Russia); GUS (Poland); National Statistical Institute (Portugal): INSEE (France); Bureau of Economic Analysis (United States); and authors' calculations.

aJncludin!! utilities.


RELATIVE PRICE CONVERGENCE IN RUSSIA 1 05

and other analgesics rose tremendously as a result of import subsidy cuts, termination of humanitarian aid in kind, and decontrol measures. The price of electricity rose much less than the overall CPI through mid-1993 but much faster thereafter, reflecting a deliberate policy to raise cost recovery ratios. 17 A similar price path was registered for many other services.

Other reasons underlying the instability of relative prices after January 1992 include sheer uncertainty (see below) and sectoral or aggregate demand and supply shocks causing shifts in the equilibrium relative price structure. For example, the ten-fold real exchange rate appreciation between January 1992 and mid-1 994 heightened import competition and contributed to the significant relative price declines recorded for some foodstuffs (such as sugar, vegetable oil, vodka, and tea) and some nonfood items (including a number of consumer durables).

Short-Run Open Inflation Dynamics

Although inflation declined in the first half of 1992 following the price jump associated with generalized decontrol, macroeconomic stabilization failed and a regime of chronic high inflation set in. One way to analyze the trajectory of the price level in this context would be to relate inflation to the evolution of the potentially relevant monetary and credit aggregates, as done by Koen and Marrese ( 1995). A somewhat different and less conventional perspective on the dynamics of inflation involves the analysis of the link between relative price variability and overall inflation. In principle, these variables could be positively or negatively correlated, or display no stable relationship whatsoever. 18 In practice, the results offered by the empirical literature on this subject vary depending on the country, the period, and the level of disaggregation.

For Russia, monthly inflation rates for 66 food items and 87 nonfood goods have been published by Goskomstat ( 1994) for the period 1992-93. Based on 1993 weights, these items cover 75 percent of the overall CPI (88 percent of the food, beverages, and tobacco component and 66 percent of the nonfood goods component).

The measure of relative price variability used here is analogous to the indices that are traditionally used in the literature, and can be described as a weighted variance:

with 17 See IMF ( 1995). 18 See Fischer ( 1 982), Goel and Ram ( 1993), and the references therein.

( I )



where w; and 7T; denote the weight and monthly percent change in price associated with item i. The weights used come from the 1993 CPI, thus reflecting 1992 expenditure patterns, and are normalized to sum to unity.'9

Figure 4 illustrates the evolution of relative price variability for all goods as well as for food and nonfood goods separately. The inflation rates shown are the weighted arithmetic averages of the inflation rates for the individual items. January 1992 is excluded because the price changes associated with the one-time jump are orders of magnitude larger and inherently different from subsequent ones.20 The underlying distributions of the inflation rates across all goods in February 1992 and December I 993 for Russia are shown in the top half of Figure 5; for comparative purposes, analogous distributions for France and the United States are presented in the bottom half. Several lessons can be drawn from Figures 4 and 5.

First, while relative price variability subsided in the course of the first half of I 992, it remained very high throughout the period under consideration in comparison with market economies. Specifically, it was more than 20 times larger on average in 1993 than in the United States and France.21 Even the minimum value of relative price variability in the Russian sample (reached for nonfood goods in July 1992) was more than three times higher than the corresponding measure in the United States and France.

Second, relative price variability for food from mid-1992 onward was almost constantly higher than for nonfood goods, the only exceptions being October and November 1992. In 1993, relative price variabil ity for food was on average more than two times larger than for nonfood goods. One plausible explanation for this apparent regularity is that seasonality affects food prices more than nonfood goods prices.22 In this regard, it is worth

19 An analogous measure based on geometric rather than arithmetic averaging of item-specific price changes was also computed, but none of the results reported below was qualitatively affected.

20 Relative price variability for all goods was 86 times larger in January than in February 1992, and the average January jump in the price level for goods amounted to 347 percent versus a 24 percent increase in February.

21 Monthly values for vartability measures analogous to those computed for Russia were calculated for the United States, based on a set of 60 food items and 60 nonfood goods (using 1994 price indices from the monthly CPI Derailed Report and 1993 weights from the bulletin on the Relative Importance of Components in the Consumer Price Index, both published by the U.S. Bureau of Labor Statistics), and for France, based on a set of79 food items and 123 nonfood goods (using 1994 observations and weights as published in the INSEE's Bulletin Mensuel de Statistique). 22 Chart 3 in Koen ( 1994) suggests that seasonal variations are very Iaroe for food prices on city markets. The behavior of the price of some individual food items (e.g., apples, carrots, and beets) also points to strong seasonal variability. Some nonfood goods prices are also subject to large seasonal swings (e.g., some clothing items).


RELATIVE PRICE CONVERGENCE IN RUSSIA

Figure 4. Relative Price Variability and Inflation for Goods (Monthly inflmion rates in percent)

107

12oor---------------------------------------------------. 4o

1000

800

600

400

200

All goods

,,

35

30

25

20

15

10 / \ Variability

1 '- _ (left scale) ; ..... 5 / - - - - / ' � / ' ' - � _ _ _ ./ ....... 0 '---'--'--'--'---'--�......._.......__.__,___.___.__.___.___.___.____._----'-----'-----'----'-'-''---J O 1992 1993

1200 ,----------------------------------------------------, 40 Food

1000

800

600

400

200

1992 1993

35

30

25

20

1200 ,----------------------------------------------------, 40 Nonfood

1000

800

600

400

200

0 1992

35

30

25

20

1 5

10 Variability 5

, , - ...... ...... ...... _ _ I - - 0 1993

Sources: Goskomstat of the Russian Federation ( 1994); and authors' calculations.



Figure 5. Distribution of Inflation Rates for Goods (Percent)

Proportion of goods sor-----�--------------� Russia

February 1992

40 153 items Mean = 34.9 Median = 28.0 Standard deviation = 31.5

0 W � W W IOO IW I� IW Monthly innation

Proportion of goods 50 .---------------------�

40

30

20

1 0

France December 1993

202 items Mean =-0.03 Median = 0.00 Standard

o��UL�� -1.4 - 1 .0-o.6 -0.2 0.2 0.6 1.0 1.4 1.8

Monthly inllation

Proportion of goods r

---�----------�----� 50

I

Russia December 1993

153 items 40 Mean = 13.2 Median = 12.0 Standard deviation = 6.3

30

20

1 0

��t�·��o -20 0 20 40 60 80 100 120 140 160

Monthly innmion

Proportion of goods -----------------------, 50

120 items

United States December 1993

Mean =-0.17 Median = -0.06 Standard deviation = 3.37

deviation = 1.09

-4.6-3.8-3.0-2.2- 1 .4-0.6 0.2 1.0 1.8 2.6 Monthly innation

40

30

Sources: Goskomstat of the Russian Federation (Russia); Bureau of Labor Statistics (United States); TNSEE (France); and authors' calculations.



Table 2. Inflation and Relative Price Variability: Regression Results"

(/-statistics in parentheses)

Dependent Regressors

variable: Change in Durbin-variabilityb Constant Inflation inflation Dummy< J?z Watson

All goods 264.7 9.2 -33 1 . 1 0.85 1.64 (5.4) (4.1) ( - 1 0.5)

328.5 5 . 1 8.2 -316.0 0.89 2.35 (8.4) (2.8) (3.9) ( - 1 2 .8)

Food 182.2 7.4 -22 1 .9 0.62 2.27 (3.2) (2.8) (-5.9)

241.7 4.3 5.9 -216.2 0.65 2.00 (3.9) ( 1 .4) ( 1 .9) (-5.4)

Nonfood goods 271.3 15.0 -428.7 0.50 2.41 ( 1.8) (2.6) ( -3.8)

465.9 10.6 16 . 1 -554.7 0.43 2.66 (2.6) ( 1 .5) ( 1.9) ( -4.0)

Sources: Goskomstat of the Russian Federation ( 1994); and authors' calculations.

• Based on monthly observations for February 1992-December 1993, and using ordinary least squares.

b As defined in equation (I) . c Dummy equals zero prior to July 1992 and I from July 1992 onward.

noting that in the United States and France as well, relative price variability is typically two to three times higher for food than for nonfood goods.

Third, the average level of relative price variability was much lower in 1993 than in 1992. This is consistent with the earlier finding that most of the relative price changes for goods had taken place by the end of I 992. It is also consistent with the presumption that as agents became more familiar with chronic high inflation, price setting became increasingly synchronized across goods.23

Fourth, relative price variability and inflation display a strong positive correlation, as suggested by Figure 4 and confirmed by the regressions in Table 2.24 For nonfood goods, the April-May I 992 spike in variability, which accounts for the poor correlation of variability and inflation during

2� An extension of the analysis to 1994 if and when the necessary data become available would allow a more confident confirmation or refutation of this conjecture.

24 It could be argued that the regression equation should be specified differently as greater relative price variability may cause greater inflation. for instance because of asymmetric price responses to disturbances (in the form of downward inflexibility). However, the purpose of the regressions in Table 2 is to establish a correlation more than to test for causality.


1 10 PAULA DE MASI and VINCENT KOEN

the first half of the year, is overwhelmingly caused by very large increases in the price of gasoline.25 Apart from this episode, variability and inflation move closely together. Adding the change in inflation among the independent variables suggests that an acceleration in the overall price level is accompanied by greater relative price variability, and vice versa.

The dummy variable introduced in the regressions captures the shift in the relationship between variability and inflation that occurred around mid-1 992, and which can be thought of as a regime switch. In the immediate aftermath of the initjal price jump, some prices were adjusted downward and others increased substantially as price setters developed a perception of new overall and relative price levels. Some confusion about their true values persisted for several months and entailed significant further relative price adjustments.26 By midyear, however, much of this uncertainty had abated and a new regime of high, chronic inflation set in.

In the longer run, the positive correlation between relative variability and inflation may weaken. Indeed, one would expect agents to compete away an increasing portion of relative price variability as high inflation becomes entrenched, and more vigorously so as inflation rises. Ultimately, price setters are likely to coordinate price adjustments by responding to a visible and unambiguous high-frequency signal such as the exchange rate, and virtually all domestic prices will be moving in line with the latterY In the extreme case of a hyperinflation, the variability of relative prices may thus turn out to be quite small.

Among the potential extensions of the regression analysis conducted here would be to relate relative price variability separately to anticipated and unanticipated inflation.28 One hypothesis worth testing in such a framework would be that relative price variability is more closely linked to inflation surprises than to the expected component of inflation.29

25 ln April 1992, gasoline alone accounted for 67 percent of the variability of relative nonfood goods prices and in May, for 90 percent.

26 This confusion is reflected in the widely different estimates for the size of the price jump and for inflation in the early months of 1992 associated with alternative retail/consumer price indices, see Koen and Phillips ( 1993), Table 2.

27 Symptomatic is the following description of the foreign exchange market in early 1995: "Only about half an hour will pass after the beginning of tenders and thousands of pagers wi II beep and thousands of telephones will ring announcing the news about the new exchange rate of the dollar. A little more time will pass and the money-changing offices will post new figures on their doors and the announcers on practically all the television and radio stations will interrupt themselves in order to expressively read a couple of four-digit figures . . . " (Kommersant Daily, February 3, 1995, p. 5). 28 One way to distinguish between the two components of inflation would be to identify them with the fined value and the residual respectively from a regression of inflation on lagged money or credit.

29 Goel and Ram ( 1 993) find that this is indeed the case in the United States.


RELATIVE PRJCE CONVERGENCE IN RUSSIA I l l

II. International Convergence of the Overall Price Level

The previous section analyzed the movements of domestic relative prices following price liberalization. This section examines the extent to which domestic price levels have converged to international levels after the freeing of prices. No attempt is made to compare the gap between domestic and foreign prices before and after January 1992 because information on pre-1992 prices is relatively scanty,30 and because the complex system of multiple exchange rates in place unti I the end of 1991 would render such a comparison extremely difficult. Exchange rate unification only occurred in mid-1 992,31 implying that even the price level comparisons presented below for the first half of 1992 and based on the interbank exchange rate are somewhat perilous and tend to understate the Russian price level.

The Price of Staples

One indicator occasionally referred to in Russia to evaluate the gap between domestic and international prices is the price of a basket of 19 staples considered as a minimum food consumption standard. This basket covers about one half of the food component of the Russian CPI at 1993 weights (excluding alcoholic drinks).32 If the U.S. price of this basket is taken as a benchmark, this measure suggests that Russian prices rose from 4 percent of "international levels" in January 1992 to one fourth in December 1993, and to almost one third in December 1994 (Figure 6, bottom panel). If the price in France is used instead, the measure implies that Russian prices rose from 3 percent of "international levels" in January 1992 to close to one fifth in December 1993 and slightly above one fifth in December 1994.33

Since a number of the staples included in the basket are often subsidized by local governments in Russia, it may seem that the price level ratio derived from this basket should be viewed as a lower bound for the overall price level. While this is a plausible conjecture as far as goods prices are concerned, it is not clear a priori whether it would sti II hold if service prices are taken into account. As discussed above, the relative price of a number

30 Particularly on black market prices and volumes. 31 See Koen and Meyem1ans ( l994) for details. 32 The basket reflects the minimum food consumption required for a 45-year-old,

able-bodied worker as defined by the former USSR State Committee for Labor and Social Problems.

33 The two measures differ because the price of the basket is higher in France and because of changes in the franc/dollar exchange rate over the period under consideration.


1 1 2 PAULA DE MAS! and VINCENT KOEN

Figure 6. International Comparison of Price LeveJsa

Consumer prices of goods in Russia in percent of French pricesb

50 .---�----------�------.

20

1 0

Nonfood goods : P :.· L

.. .. .. ' / L .. • ·: p . .

Consumer prices of goods and services in Russia in percent of French pricesh

Goods L p

Goods and sen,ices

;�

50

40

30

20

10

O L-----------------------� L---�-�-�-�-�-�-�----------� 0 Jan. July July July 1992 1992 1993 1994

July July 1992 1993

July 1994

Price of staples in Russia t so .-----------------------�----------------------�

. . .

/11 percem of French price

. . .

Sources: Goskomstal of the Russian Federation; Center for Economic Analysis; IN SEE; U.S. Bureau of Labor Statistics; and authors' calculations.

•Using the exchange rate quoted on the MICEX. bp denotes a Paasche, Russian-weighted index, and L, a Laspeyres. French·

weighted index. cBasket of 19 staples.


RELATIVE PRICE CONVERGENCE IN RUSSIA 1 1 3

of important services remained extremely low throughout 1992-94, meaning that the overall consumer price level in Russia was lower than what goods prices alone would indicate.

Broader Price Measures

In order to cover a more representative sample of consumer goods and services, a systematjc comparison with contemporaneous French prices was attempted for all the items of the Russian CPJ.34 Whenever applicable, the lowest quality variety appearing in the French nomenclature was used so as to account for the likely quality differentials. Not surprisingly, matching fillled for many items, mostly because of insufficiently precise specifications or absence of a counterpart. Nevertheless, the coverage was extended significantly compared with the basket of staples.

The Russian data set for January 1992 was more limited than for subsequent dates, mainly because no service prices were available for that month. Two separate comparisons were therefore conducted. The first was for goods only, starting in January 1992, with matches achieved for 74 percent of foodstuffs and 25 percent of nonfood goods, jointly representing 5 1 percent of the overall CPI (all at 1993 Russian weights). The second comparison pertained to a broader set of goods and services, starting in July 1992, with matches achieved for the same 74 percent of food goods, 29 percent of nonfood goods, and 29 percent of services, altogether covering 54 percent of the overall CPT (also at 1993 Russian weights).

Cross-country price level ratios can be computed in several ways. Since the weights of the milln groups of items in household expenditures are dramatically different in Russia from what they are in France (Figure 3), and since domestic relative price structures also differ enormously, one would expect the results to be sensitive to the formula that is selected. One way to measure the distance between Russian and French price levels is to define a Paasche-type index, P, based on Russian weights:

p = i - _ _.!.i-.,,.---- , F R - F '

where

£..J P; q; ' EL 00� . £..J R I I i P;

(2)

3" Average prices in France are published in the lNSEE's Bulletin Mensuel de Staristique. France was selected as the comparator country because of the availability of fairly detailed price level data and the familiarity of one of the authors with the empirical content of this information.


1 14

R R R P· q .

PAULA DE MASI and VINCENT KOEN

(J) - J J J - "'\;' R R ' £.,. Pi qi

with i indexing the items for which matches were achieved, and R denoting Russia and F, France.

An alternative approach involves the use of French rather than Russian weights, and the computation of a Laspeyres-type index, denoted L:

(3)

where

There is no compelling reason to prefer domestic or foreign weights in a bilateral price level comparison. If a single point-estimate were to be sought, a measure such as a Fisher-type index (i.e., an equi-weighted geometric average of L and P) would be an agnostic compromise. However, given the data limitations, it may be preferable to think of the Paasche and Laspeyres indices as delineating an estimated range for the price level ratio.

The results of the first comparison, shown in the top left panel of Figure 6, are broadly in line with those obtained above for the basket of 19 staples. The Paasche index for food prices increased from less than 2 percent in January 1992 to 8 percent in mid-1992, l 0 percent in mid-1993, and 2 1 percent by mid-1 994.35 It also appeared that the domestic price of nonfood goods relative to France was consistently higher than for foodstuffs but followed a similar path, rising from less than 3 percent in January 1992 to 13 percent in mid-1992, 1 7 percent in mid-1993, and 35 percent by mid-1994. The use of the corresponding Laspeyres indices produced very similar results.

The results of the second comparison appear i n the top right panel of Figure 6. The point estimates of the level of service prices are much more sensitive to the choice of the weights than those for goods. Nevertheless, both

35 Richards and Tersman ( 1995) find that food prices in Latvia in March 1994 were about 37 percent of the Swedish level.



the Paasche and the Laspeyres measures indicate that the domestic price of services compared to France started from an extremely low level in mid-1992, and that although it rose faster than that of goods, it remained well below the latter by mid- 1 994. The inclusion of services into an overall consumer price level comparison therefore brings down the ratio of Russian to French prices. Broadly speaking, consumer prices in Russia rose from about 6-7 percent of the French level i n July 1992 (immediately foJJowing exchange rate unification) to 20-22 percent in July 1994. This is almost exactly in line with the estimates derived based on the basket of 19 staples, reflecting the offsetting effects of higher relative prices for nonfood goods and of lower relative prices for services.

The gap between domestic and foreign prices thus narrowed between 1992 and I 994, but remained very wide in mid- I 994. The relatively swift movement toward international price levels in the early phase of the transition is consistent with the pattern described by Halpern and Wyplosz ( 1995) in their cross-country study. The persistence of a chasm between the price level in Russia and that in market economies is consistent with the wellknown positive correlation between per capita income and price levels.3C• The law of one price clearly does not apply to nontradables such as services. but it also fails for tradables insofar as the latter are subject to import or export tariffs or quotas. Even when no restrictions or taxes come into play, the price of highly tradable items embodies a nontradable component in the form of distribution costs. Given the very low dollar wage levels prevailing in Russia, one would expect prices in Russia to be well below those in comparator market economies.

III. Regional Disparities

Geographical price and nominal income dispersion has traditionally been very pronounced in Russia, not least owing to the vastness of the country and the harshness of its climate, which implied substantial distribution costs. Unfortunately, the available data do not allow us to judge whether prices across regions converged or diverged as a result of the transitionY It is nevertheless possible to examine the evolution of price dispersion mea-

>6 Rationalized by Balassa ( 1964) and Samuelson ( 1964), among others. In this respect, the selection of France influences the point estimates presemed above but given the order of magnitude of the price level gap, the same qualitative results would have been obtained using other market economies as a benchmark.

37 Regional inflation rates have been published but in the absence of information on regional price levels for some base period, it cannot be established whether differential price increases entailed convergence or divergence of price levels across regions.


1 16 PAULA DE MAS! and VINCENT KOEN

Table 3. Geographical Price Dispersion for Food and Nonfood Goods•

(average coefficient of variation, in percent)b

Foodstuffs<

March 1992 37 July 1993 25 June l994 1 7 Memorandum item: Canada 1991 < 1 3

Nonfood goodsd

28 25 1 7

Sources: Statistical Bulletin of the Statistical Committee of the Commonwealth of Independent States (various issues); Center for Economic Analysis; Statistics Canada, Consumer Prices and Price Indexes, various issues; and authors' calculations.

" The statistics shown pertain to a sample of9 cities (Moscow. Chelyabinsk, Ekaterinburg, Kazan, Nizhni Novgorod, Novosibirk, Saint Petersburg, Volgograd, and Voronezh). For March 1992, information was available for an extra I 0 cities (Arkhangelsk, Krasnodar, Kemerovo, Pskov, Ryazan. Samara, Smolensk, Stavropol, Tambov, and Yologda) and the dispersion coefficients are 38 percent for foodstuffs and 28 percent for nonfood goods.

b For Russia, weighted average of item-specific coefficients of variation, with weights reflecting the share of the items in the CPl.

< Representing about half of the weight of food items in the CPl. d Representing about one sixth of the weight of nonfood goods in the CPl. e For Canada, equi-weighted average of item-specific coefficients of variation,

based on retail prices for 60 food goods for the first week of January, April, July, and October, 1991, and covering a sample of 25 cities (St. John's, Charlottetown, Sydney, Halifax, Moncton, Saint John, Chicoutimi, Quebec, Trois Rivieres, Sherbrooke, Montreal, Hut!, Ottawa, Toronto, Hamilton, London, Sudbury, Thunder Bay, Winnipeg, Regina, Saskatoon, Edmonton, Calgary, Vancouver, and Victoria).

sures following the January 1992 price liberalization in order to assess the evolution of market integration.

Falling Geographical Dispersion

There are reasons to expect geographical price dispersion to have been high in early 1992 and to have declined thereafter. Uncertainty about actual new relative prices was probably more pronounced in the immediate aftermath of the price jump than one or two years later and may have contributed to price dispersion. I n addition, remaining local subsidization or other controls differed across regions depending inter alia on their wealth and on local politics, but presumably declined over time.

The average coefficients of variation presented in Table 3 point to a reduction i n cross-regional dispersion both for food and nonfood goods prices.38 Also noteworthy is the fact that the dispersion was initially larger

Js The data sources and coverage are described in Table 3. The subset of foodstuffs is very similar to the one constituting the basket of 19 staples. No information on local services prices was available.


RELATIVE PRICE CONVERGENCE lN RUSSiA 1 17

for food than for nonfood goods. probably because of more extensive residual subsidization and trade barriers for the former, but that by mid-1 993, the dispersion was of the same order of magnitude for the two categories of goods.

Even by mid-1 994, the level of geographic price dispersion remained on the high side compared to market economy standards.39 In Canada-which among industrialized countries comes closest to Russia as far as climate and distances are concerned-the average coefficient of variation for food items was on the order of 1 3 percent, that is, somewhat lower than the estimate for Russia as of mid-1 994.

Residual Subsidization

While information on regional price disparities in general is limited, data have been published on the price of the aforementioned 19 staples basket across a large number of cities from early 1992 onward. The coverage of outlets, however, changed in the second half of 1992, when it was extended to include city markets alongside stores. The impact of this modification on the price dispersion measures shown in Table 4 (coefficient of variation, maxjmum over minimum ratio, and decile ratio) is a priori ambiguous. Thus, the only relevant comparisons over time pertain to June versus February 1992 on the one hand, and to end-1992, end-1993, and end-1994 on the other.-to

In contrast to the result derived above for a set of broadly similar individual food items, the dispersion indicators point to a significant increase i n geographical variation from end-1992 to end-1993, possibly owing to an increasing divergence in local subsidization levels. Consistent with the earlier results, however, they show a slight decline between end-1 993 and end-1994.41 To a large extent, the discrepancy between the results displayed in Tables 3 and 4 is due to the fact that the sample used in Table 3 was much smaller and did not include cities of the far east or the far north. Controlling for the difference in geographical coverage, as is done in the bottom line of Table 4, helps reconcile the results and suggests that after price liberalization at the federal level in early J 992, local subsidies became relatively more important in the colder and more remote parts of the country.42

39 Some dispersion is observable even in market economies, as noted long ago by Mills ( 1 927) for the United States.

40 Apart from the change in coverage, seasonality would also render the comparison with February and June 1992 hazardous.

41 The max/min ratio rises a little but is a less relevant measure of dispersion than the decile ratio, which clearly drops.

42 Another difference between Tables 3 and 4 is that Table 3 was for midyear rather than end-year data, and was based on averages of individual coefficients of variation rather than coefficients of variation for the price of a basket.


1 1 8 PAULA DE MASI and VINCENT KOEN

Table 4. Geographical Price Dispersion for a Baske1 of Swples"

Coefficient of variation (in percent)

Maximum/minimum Top decile/bouom decile Number of observations Memorandum ilem: Coefficient of variation

for 9 cities<

18.5

2.4 1 .8

99

39.4

1992

Juneb

18.7

2.7 2.0

9 1

18.7

Dec."

22.0

3.8 2. 1

97

18.7

1993 1994

Dec."

34.1

5.0 2.8

62

18.6

Dec.<

30.1

5 . 1 2.4

98

17.3

Memorandum ilem:

Canada 1991 d 6.5

1 .3 1.3

25

Sources: Goskomstat data published in Delovoy Mir and in the quarterly reports of the Center for Economic Analysis; Statistics Canada, Consumer Prices and Price Indexes, various issues; and authors' calculations.

• The sample of cities includes Abakan, Angarsk, Arkhangelsk. Arzamas. Astrakhan, Barnaul, Belgorod, Berdsk, Birobidzhan, Bryansk, Cherkessk, Chita, Divnogorsk, Dzerzhinsk, Gorno-Altaysk, lshimbay, Izhevsk, Kaliningrad, Kaluga, Kamyshin, Kazan, Kemerovo, Kirov, Kirovo-Chepetsk. Kopeysk, Kostroma. Krasnodar, Krasnoyarsk, Kurgan, Kursk, Lipetsk, Magadan, Makhachkala, Maykop, Miass, Moscow, Murmansk, Naberezhnyye Chelny, Nalchik, Neftekamsk, Nizhni Novgorod, Nizhni Tagil, Norilsk, Novocheboksarsk, Novosibirsk, Novokuznetsk, Novorossiysk, Novyy Urengoy, Obninsk, Omsk, Orel, Orenburg, Orsk, Penza, Perm, Petropavlosk-Kamchatskiy, Petrozavodsk, Prokolyevsk, Pskov, Rostov-on-Don, Rubtsovsk, Ryazan, Rybinsk, Samara, Severodvinsk. Saint Petersburg, Salekhard, Saransk, Shakhty, Shebekino, Sovetsk, Syktyvkar. Syzran, Taganrog, Tambov, Tayshet, Tolyaui, Tomsk, Tuapse, Tula, Tver, Tyumen, Ufa, Ukhta, Ulyanovsk, Vladikavkaz, Vladimir, Vlagoveshchensk, Volgograd. Vologda, Volgodonsk, Vorkuta, Voronezh, Yaroslav, Yekaterinburg, Yakutsk, Yelets, Yoshkar-Ola, and Yuzhno-Sakhalinsk, but for some dates several observations were missing. The exact dates are February 18, 1992; June 23. 1992; December 8. I 992; December 28, 1993; and December 13, 1994.

b Excluding city markets. < Including city markets. d A Canadian basket was constructed replicating the Russian basket of staples.

The statistics shown are the averages of the statistics computed for the first week of January, April, July, and October, 1991 . The geographical coverage is the same as in Table 3.

< Moscow, Chelyabinsk, Yekaterinburg, Kazan, Nizhni Novgorod, Novosibirsk, Saint Petersburg, Volgograd, and Voronezh (same cities as in Table 3).

Looking at the ranking of specific cities, certain patterns emerge. The highest prices were consistently registered in areas such as the Far East (e.g., Magadan and Yuzhno-Sakhalinsk), and the lowest ones in areas such as the Volga region (Ulyanovsk and Kazan), partly reflecting differences in climate and transportation costs, but also local price policies.43 Notwith-

•·1 As denoted by its name, Ulyanovsk is Lenin's birth place. The local authorities took steps to limit exports of agricultural products to other regions in order to ensure local supply at low, controlled prices.



Table 5. Geographical Price Cross-Correlations for a Basket of Staples

Feb. 1992 June 1992 Dec. 1992 Dec. 1993

Feb. 1992

1.00

Sources: as for Table 4.

June 1992

0.51 J.OO

Dec. 1992

0.47 0.72 1 .00

Dec. 1993

0.35 0.61 0.67 1 .00

Dec. 1994

0.29 0.62 0.72 0.89

standing the relative ordinal stability of the extrema, the overall cardinal ranking of cities changed substantially over time, particularly during the first half of 1992 (Table 5). In the course of 1993, significant further shifts occurred, which, as evident from Table 4, resulted in higher geographical price dispersion. During the third year following price liberalization, the ranking changed much less. as attested by the high correlation coefficient between end- 1993 and end-1 994 prices. The evolution over time of the relative price of staples across regions is presumably largely determined by changes i n relative subsidization and administrative control levels, which in turn are conditioned by local policies and budgetary resources.

IV. Conclusions

The empirical investigation conducted in this paper confirms that after their decontrol, prices in Russia moved closer to market levels. For goods, most of the permanent realignment in domestic relative prices had taken place by the end of 1992, even though some further shifts occurred in 1993-94. For services, convergence to market levels appears to be a more protracted process; by mid- 1994, notwithstanding sharp increases in relative domestic terms, the prices of many important services remained far below advanced market economy levels.

Because of major discontinuities in the exchange rate regime, it remains difficult to pass judgment on the impact of the transition on the gap between the domestic overall price level and the level prevailing abroad. However, it is clear that this gap, which was huge in January 1992, has narrowed substantially. Similarly, while the effect of the transition on geographical price dispersion within Russia cannot be assessed, it was possible to establish that the degree of integration of the domestic goods market, particularly for nonfood items, seems to have increased since early 1992.

It would be hazardous, however, to view these results as more than early, indicative ones. While some of the trends identified in this paper are probably robust to the use of alternative indices and superior samples, others are ambiguous and need further substantiation. In particular, the comparison of



international price levels carried out here is extremely tentative,-1-1 as is the analysis of geographical price dispersion.45

Several promising areas for further research can be identified. The first is to expand the samples used in this paper in order to assess the robustness of its main results. In particular, the inclusion of more recent data would reveal whether the incipient trend toward greater synchronization in price setting uncovered looking at 1992-93 inflation rates continues in 1994 and beyond. Longer time series would also permit a potentially interesting investigation of the impact of seasonality on relative price variability.46 Furthermore, it would be worthwhile to examine to what extent the results obtained for Russia can be generalized to other economies in transitionY

A second area for further work would involve extending the analysis to producer prices. Highly disaggregated industrial producer price data exist and could be exploited, albeit taking into account the complication of arrears. The latter have not played a large role for cash-based, retail transactions but have been ubiquitous at the noncash, wholesale level. Based on producer prices, convergence toward international levels may well be more advanced than for consumer prices because of the larger share of nontradables in the CPI than in the PPI.48 Indeed, the speed of convergence has been more rapid for producer prices, which rose almost twice as much as consumer prices in Russia between December 1 990 and December 1994, with the bulk of the faster growth occurring in 1991-92. But in the absence of level estimates, this evidence is not sufficient to confirm that the gap between domestic and international prices is narrower for producer prices.

A third set of issues worthy of further research pertains to the pathology of inflation, as opposed to the morphological approach adopted in this paper. As longer time series become available, quantitative work could be carried out on the dynamic interaction of money and credit, arrears, relative consumer and producer prices, and the overall price level. In this context, the neutrality or influence of market structures could also be examined.

4.t The European Comparison Program results for 1993, due to be released in 1996, should shed some further light on this comparison.

45 Far more comprehensive data than those we had access to seem to exist at Goskomstat and would permit a more thorough investigation.

46 In the United States and France, seasonality probably accounts for a quarter or more of the total relative price variability for goods at a I 00-200-item level of disaggregation.

47 Such an investigation is currently under way, see De Broeck, De Masi, and Koen ( 1995) and De Masi and Koen (forthcoming).

4s As noted by Froot and Rogoff ( 1994), this point was made by Keynes in his 1925 pamphlet on The Economic Consequences ofMr. Churchill.


RELATIVE PRICE CONVERGENCE IN RUSSIA 1 2 1

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Berg, Andrew, ''Does Macroeconomic Reform Cause Structural Adjustment? Lessons from Poland,'' Journal of Comparative Economics, Vol. 1 8 (June 1994). pp. 376-409.

De Broeck, Mark, Paula De Masi, and Vincent Koen, ''Inflation Dynamics in Kazakstan," IMF Working Paper 95/140 (Washington: International Monetary Fund, December 1995).

De Masi, Paula, and Vincent Koen. ''Relative Price Convergence in Russia.'' IMF Working Paper 95/54 (Washington: International Monetary Fund, May 1995).

---. "Price Convergence in Transition Economies:· IMF Working Paper (forthcoming).

Fischer, Stanley, "Relative Price Variability and Inflation in the United States and Germany,'' European Economic Review, Vol. 18 (June 1982), pp. 17 1-96.

Froot, Kenneth A., and Kenneth Rogoff, ·'Perspectives on PPP and Long-Run Real Exchange Rates,'' NBER Working Paper No. 4952 (Cambridge: National Bureau of Economic Research. December 1994).

Goel, Rajeev K., and Rati Ram, "Inflation and Relative-Price Variability: The Effect of Commodity Aggregation,'' Applied Economics. Vol. 25 (May 1993). pp. 703-9.

Goskomstat, "Regulations on the Procedure for Monitoring Changes in Prices and Fees for Goods and Services and Determining the Consumer Price Index" (in Russian), Goskomstat of the Russian Federation. Bulletin of the Sciemijic and Methodological Council, No. I ( 1993), pp. 58-76.

---, Prices in the Russian Federation ( in Russian) (Moscow: Goskomstat of the Russian Federation, 1994 ).

Granville, Brigitte, and Judith Shapiro. ''Russian Inflation, A Statistical Pandora's Box," RIIA Discussion Paper No. 53 (London: Royal Institute of International Affairs, 1994).

Halpern, Laszl6 and Charles Wyplosz, "Equilibrium Real Exchange Rates in Transition." CEPR Discussion Paper No. 1 145 (London: Centre for Economic Policies Research, April 1995).

International Monetary Fund, Russian Federation, 1994 IMF Economic Review No. 1 6 (Washington: IMF, March 1995).

Koen. Vincent. "Measuring the Transition: A User's View of National Accounts in Russia," IMF Working Paper 94/6 (Washington: International Monetary Fund, January 1994).

---, and Michael Marrese, "Stabilization and Structural Change in Russia, 1992-94,'' IMF Working Paper 95/13 (Washington: International Monetary Fund, January 1995).

Koen, Vincent. and Eric Meyermans, "Exchange Rate Determinants in Russia: 1992-93," IMF Working Paper 94/66 (Washington: International Monetary Fund. June 1994).



Koen, Vincent, and Steven Phillips, "Price Liberalization in Russia: The Early Record," lMF Working Paper 92/92 (Washington: International Monetary Fund, November 1992).

---, Price Liberalization in Russia: Behavior of Prices. Household Incomes and Consumption During the First Year, IMF Occasional Paper No. 104 (Washington: International Monetary Fund, June 1993).

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Richards, Anthony, and Gunnar Tersman, �'Growth, Nontradables, and Price Convergence in the Baltics," IMF Working Paper 95/45 (Washington: International Monetary Fund, April 1995).

Samuelson, Paul A., ''Theoretical Notes on Trade Problems,'' Review of Economics and Statistics, Vol. 46 (May 1964), pp. 145-54.



Internal Migration, Center-State

Grants, and Economic Growth

in the States of India

PAUL CASHIN and RATNA SAHAY*

This paper examines the growth experience of 20 states of India during 1961-91, using cross-sectional estimation and the analytical framework of the Solow-Swan neoclassical growth model. We find evidence of absolute convergence-initially poor states grew faster than their initially rich counterparts. Also, the dispersion of real per capita state incomes widened over the period 1961-91. However, relatively more grants were transferred from the central government to the poor states than to their rich counterparts. Significant barriers to population flows also exist, as net migration from poor to rich states responded only weakly to cross-state income differentials. [JEL 041, 047, 053, R l l ]

ASTRIKING FEATURE of India's economic development since it became independent i n 1947 is its low rate of per capita income growth, partic

ularly in comparison with most other Asian countries. This is all the more noticeable given the favorable preconditions in the late 1940s of a welldiversified resource base, the world's fourth largest pool of skilled (scientific and technical) manpower, a sizable group of entrepreneurs, a long experience with public administration, and a relatively stable political system.

* Paul Cashin was an Economist in the IMFs Research Department when this paper was written, and holds a Ph.D. in economics from Yale University. He is now Lecturer in economics at the University of Melbourne and Principal Economist at the Victorian Department of Agriculture, Energy and Minerals, Australia. Ratna Sahay, who has a doctorate from New York University, is an Economist in the IMF's Research Department. The authors are grateful to Ajai Chopra, Charles Collyns, Nadeem Haque, Mohsin Khan, Neeraj Prasad, Arvinder Singh Sachdeva, Michael Sarel, and Sunil Sharma for their invaluable input. Brooks Dana Calvo provided excellent research assistance.

123


124 PAUL CASHIN and RATNA SAHAY

India's growth process since the I 950s has largely been influenced by the economic policies of the Congress Party and the country's first Prime Minister, Jawaharlal Nehru. The Congress Party embraced the "socialist pattern of development" whereby central planning guided public and private sector activities, with emphasis placed on import substitution policies and heavy industry: Industrial licensing was an integral part of government intervention in the economy, as it directed investment flows both across sectors and across states. In addition, the "commanding height" industries (defense, heavy industry, mining, air and rail transport, communications, and power) were exclusively the purview of the public sector. India's planners also sought to influence interregional investment flows so as to engender balanced regional development, which is particularly important in the context of this paper. The process of public sector expansion and nationalization continued through the 1970s with several new public financial institutions being set up or nationalized during the period. Thus, until the mid-1 980s, India essentially operated as a closed economy, with the public sector dominating economic activity. Macroeconomic crises were typically resolved through the imposition of quantitative and price controls that contributed, in part, to India's relatively low inflation rates, in comparison with other developing countries.

In common with many of the developed world's federal countries (Germany, Switzerland, Australia, Canada, and the United States), there have been concerns within India since independence about regional disparities in national economic development. In addition, the efficiency costs of using income-equalizing center-state grants to promote objectives such as national economic equity have been an important related theme in the economics of fiscal federalism.•

Early work by Myrdal ( 1 957), Hirschman ( 1958), and Kaldor ( 1970) gave rise to the hypothesis of an inverted U-shaped curve relationship between the extent of regional income disparity and a nation's level of income. Some of the first empirical tests of the validity of 1ising, and then falling, cross-regional disparities in income were conducted by Kuznets ( 1958) and Williamson ( 1 965) for regions of developed countries. This body of work sparked much interest in India, the developing world's most populous federal country (see Section IV).

1 A key early discussion of the efficiency-equity aspects occurred between Buchanan ( 1950 and 1952) and Scott ( 1950). The efficiency case against centerstate grants is that they result in a misallocation of national resources, because the consequent expansion of state and local public services acts to slow the movement of labor out of regions where it has a low marginal product to regions where its marginal product is high. Balogh ( 1962) and Gupta ( 1973) make similar points in discussing India's programs designed to reduce disparities in regional incomes.


ECONOMIC GROWTH IN THE STATES OF INDIA 1 25

While there are many studies of the international processes of growth and convergence across countries (see Baumol ( 1986), DeLong ( 1988),. Dowrick and Nguyen ( 1989), and Barro ( 1991 ), among others), there are relatively few that examine regional growth patterns within any given country. Exceptions have been Easterlin ( 1960a and 1960b), Williamson ( 1 965), and Barro and Sala-i-Martin ( I 992a) for the states of the United States of America; Williamson ( 1 965) and Barro and Sala-i-Martin ( 1991) for the regions of Europe; Coulombe and Lee ( 1993) for the provinces of Canada; Cashin ( 1995) for the regions of Australasia; De Gregorio ( 1992) for several South American nations; and Barro and Sala-i-Martin ( 1992b) and Shioji ( 1993) for the prefectures of Japan. This paper represents one of the first formal econometric analyses of the neoclassical growth model's predictions for the process of income growth and convergence across the regions of a developing country.

By undertaking an analysis of the 20 Indian states, we hope to minimize the problems that would arise if the various economies exhibited different steady-state real per capita incomes.2 Assuming that all regions within a given country possess similar levels of technology and similar preferences, and that there are no institutional barriers to the flow of either capital or labor across regional borders, then the neoclassical growth model would predict all regions to have similar levels of real per capita income in the steady state. Accordingly, absolute convergence should then be closely approximated by conditional convergence.3

It is important to note that, given the neoclassical growth model's assumption of closed economies, such a model of the convergence process obviously cannot be applied literally to the Indian states because, for given technologies, convergence in both per capita income and capital stocks will

2 In this paper the term "state" wil I be used to describe the 20 regional economies of India, although for the period of analysis Delhi was a union territory and not a state of India. The key difference between a state and a union territory is that the taxing and spending powers of the latter are severely circumscribed; their budget is essentially derived from the central government. The acronyms used for the 20 Indian regions we study are: Andhra Pradesh (AP), Assam (A), Bihar (B), Delhi (D), Gujarat (G), Haryana (H), Himachal Pradesh (HP), Jammu and Kashmir (JK), Karnataka (KA), Kerala (KE), Madhya Pradesh (MP), Maharashtra (MH), Manipur (MN), Orissa (0), Punjab (P), Rajasthan (R), Tamil Nadu (TN), Tripura (T), Uttar Pradesh (UP), and West Bengal (WB).

In 1991 India comprised 25 states and 7 union territories; in 1961 there were 1 5 states and 12 union territories. The 20 regions studied in this paper accounted for 93.1 percent of India's net national product (at factor cost) and 99.0 percent of India's population in 1991; the corresponding figures for 196 I were 90. 1 and 99.3 percent, respectively (Government oflndia (1991 a and 1995)).

3 If the states vary in their savings rates and technologies, then the neoclassical growth model predicts conditional convergence-state per capita incomes still converge, but this convergence is conditional on each economy's own steady state.



occur faster in open than in closed economies. However, as shown by Barro, Mankiw, and Sala-i-Martin ( 1995), in the presence of imperfect capital markets that constrain only a fraction of physical capital to serve as collateral for investment by governments and/or individuals, aggregate income exhibits very similar behavior to that which would be predicted by a closed economy model. That is, partial capital mobility in an openeconomy version of the neoclassical growth model can explain the gradual incidence of cross-state income convergence. Undoubtedly, these constraints on the role of capital for collateral were present in India over the period 1961-9 1 .

Across regions of a given country, which share a common steady state, convergence of per capita incomes in the neoclassical growth model is driven by diminishing returns to capital. Each addition to the capital stock of a region generates large (small) increases in output when the regional stock of capital is small (large). Accordingly, if the only difference between regional economies lies in the level of their initial stock of capital, the neoclassical growth model predicts that poor regions will grow faster than rich ones; regions with lower starting values of the capital-labor ratio will have higher per capita income growth rates. Two other channels by which convergence can occur are the redistribution of incomes from relatively rich regions to relatively poor regions of a federal country by its central government, and flows of labor from poor to rich regions. We examine these last two channels in this paper. These issues are relevant from a policy perspective in that this study evaluates whether, in the Indian context, fiscal federalism and the flow of labor across states have contributed to the equalization of state per capita incomes.

Accordingly, answers to the following questions wiU be explored in this paper. First, did the initially poor states of India subsequently grow faster than the initially rich states? Second, has the cross-sectional dispersion of per capita incomes across the states widened or narrowed over the period of analysis? Third, did cross-state migration from poor to rich states respond to differentials in per capita incomes across the states? Evidence is found that supports the conjectures of the neoclassical growth model of Solow ( 1956) and Swan ( 1956): the relatively poor states did indeed grow faster, with 1.5 percent of the gap between per capita incomes in initially poor and initially rich states being closed every year. There has also been a widening in the cross-sectional dispersion of real per capita state incomes over the period 1961-9 1 . However, center-state grants ensured that the dispersion of real per capita state disposable incomes remained relatively constant over the period. Finally, net migration across states does not appear to be greatly influenced by differentials in state per capita incomes, which indicates that there are sizable barriers to labor flows across the states of


ECONOMIC GROWTH IN THE STATES OF INDIA 127

India. There is also little evidence that cross-state migration is an important cause of the convergence of real state per capita incomes in India.

I. Overview of the Indian State Economies

Before rule by the British crown was officially validated in the Indian subcontinent in 1858, it is perhaps fair to say, the region as a whole had been united only twice in recorded history. The first unification was by the Mauryan emperor, Ashoka, during the third century B.C., and the second by Akbar during the Mughal empire during the 16th century A.D. (Wolpert ( 1 993)).4 Even at the time of India's independence from Britain in 1947, the Indian states remained fairly diverse in their ethnic and linguistic background.

Center-State Relations

The need to maintain a strong sense of national unity was clearly recognized during 194 7-50, when the Indian constitution was drafted. Consequently, within the confines of a federal system, the constitution gave strong political and economic powers to the center, in particular, the power to allocate financial resources between itself and the states. One of the notable exceptions is in the area of agriculture, where the states have primary control; this includes the taxation of land and agricultural income and the implementation of land reforms (Joshi and Little ( 1994)).5 The constitution also provides for the establishment every five years of a Finance Commission, to review the distribution of tax revenues both between the central and state governments and across state governments.

The relative financial stTength of the center vis-a-vis the states can be ascertained from the following facts: most taxes are levied and accrue to the center (the vast majority accounted for by income, excise, and custom taxes);6 the relatively elastic sources of tax revenues have also been the purview of the center; and the center can borrow from domestic and inter-

• An interesting observation is that the capital city of Pataliputra (now Patna) under Ashoka is today the capital of the poorest state, Bihar, while Delhi, the capital city under Akbar and of Jndia today, is the richest (measured in per capita income terms; see Table 2).

5 Along with agriculture, the responsibilities of state governments extend to power generation, education, health, sanitation, small industries, and road transport.

6 During 1951-85, on average, the center accounted for more than 70 percent of the total resources raised by the center and the states, of which only 3 1 .4 percent was transferred to the states (Sarkari a Commission ( 1988)).


128 PAUL CASHIN and RA TNA SAHA Y

national markets while the states cannot bOITOW abroad and need the center's permission, de facto, to borrow domestically.7 In case of a conRict on overlapping governmental responsibilities, the center's decision (through legislation) dominates. BroadJy speaking, taxes on income and production (with some exceptions) are levied by the center and those on sales and purchases are levied by the states. It is interesting to note that while the states could potentiaJJy have tapped their own resources by levying taxes on agriculture and land, they have shown little inclination to do so. Indeed, the share of such taxes in total state tax revenue has been barely I percent (Sury (1992)).

Given the vertical imbalance between the resource raising powers and expenditure needs of the center and the states, the constitution has provided for a complex mechanism of transfers from the center to the states.� Essentially, there are three direct channels: statutory transfers (comprising tax sharing and "grants-in-aid") through the Finance Commission mechanism;9 plan grants through the Planning Commission mechanism; and "discretionary" grants through central ministries, primarily for centrally sponsored schemes. There also exist indirect channels such as loans from the central government and the aJJocation of credit by financial institutions controlled by the central government. 1o

The purpose of examining transfers in this paper is to determine whether they served their intended purpose of reducing regional income disparities, by the central government allocating relatively greater grants to lowincome states. Since not all transfers defined in the Indian context are intended to reduce such disparities, for estimation purposes we use data published in state budgets that can best be singled out as outright intended

7 The center's consent is needed either if a loan from the center to the states remains outstanding or if the center has guaranteed an outstanding loan to the states. Since all states have typically been indebted to the center from the very beginning, the center's permission has de facto been sought for raising all fresh loans.

8 See Toye ( 1973) for an early analysis of the structure of both states' receipts (revenues plus transfers) and states' expenditures.

9 Willie the constitution provides for financial transfers from the center, it does not specify the criteria for dividing the divisible pool of taxes between the center and the states and among the states. Finance Commissions, which determine these shares, have often recommended grants to fill gaps between projected current revenues and expenditures of states. This may have discouraged states from increasing public savings, because of the resultant loss in grants. Although the Finance Commission's recommendations are not binding on the Government of India, the center has generally accepted its major recommendations (Sury ( 1992)).

10 Of total gross transfers from the center to the states in 1961, some 24 percent comprised the sharing of taxes; 30 percent, grants; and 46 percent, gross loans. The equivalent shares for 1971 were 32, 26, and 42 percent; for 1981 the shares were 39, 29, and 32 percent; and for 1991 the shares were 34, 32, and 34 percent, respectively (Reserve Bank of India ( 1993) and Government of Jndia ( 1994)).



grants. Specifically, these include statutory "grants-in-aid," as specified by the Finance Commission; grants for plan purposes as assessed by the Planning Commission; and grants for centrally sponsored schemes. 1 1 Thus we exclude from the typical Indian definition of transfers those designed for center-state tax sharing, and indirect transfers through loans. The justification for excluding the tax-sharing transfers is primarily the tack of transparency in determining the magnitude of the income equalizing component. 12 Loans are clearly distinct from grants in that they have to be repaid. Accordingly, to the extent that we exclude those center-state taxsharing transfers designed explicitly to reduce regional disparities, and exclude loans (including external assistance) that may have been subsequently forgiven, 13 our estimate of what we will henceforth call "grants" understates the role played by the center in reducing regional disparities.

Economic Features of Indian States and Regional Disparities

Although the Indian states have long shared conunon political institutions and national economic policies, there is wide diversity in geographic, demographic, and economic features (Tables 1 and 2). While the states in central India-Madhya Pradesh, Rajasthan, and Maharashtra-are the largest in land area, the eastern states-Uttar Pradesh and Bihar-have the highest population levels. The highest population density (persons per square kilometer) is observed at extreme geographical ends, the highest in Delhi in the north, followed by Kerala in the south and West Bengal in the east. The states that lag far behind the others in literacy rates (total as well as female) and in reducing death rates are Uttar Pradesh, Bihar, Madhya Pradesh, and Rajasthan; these four regions also have the highest birthrates.

Of the six initially poor states (Manipur, Bihar, Orissa, Tripura, Uttar Pradesh, and Madhya Pradesh) in 196 1 , five remained among the six poorest (in per capita income) in 1991. 14 The exception was Madhya Pradesh, which had moved up three notches by 1991, and was replaced by Jammu and Kashmir (Table 2). Delhi, the richest region in 1961 as well as in 1991,

1 1 See Bhat ( 1993) for an analysis of the determinants of Lhe level of grants to Indian states, and Sastry and Nag ( 1990) for a discussion of the influence of such center-state transfers on states' economic growth.

12 The formula that determines the states' shares in the center's revenue has, over time, depended to varying degrees on collections by states, state population, and several indicators of per capita income.

13 The Seventh ( 1979-84) and Eighth ( 1984-89) Finance Commissions provided limited amounts of debt relief in the form of debt rescheduling and/or write-offs.

14Unless otherwise denoted, state "income" refers to the value of state net domestic product at factor cost (NDP)-see Section l l l and the Appendix for details.

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is clearly an outlier in that its per capita income in both years was more than double the average of the remaining states. Apart from Delhi, six other states (Maharashtra, West Bengal, Punjab, Gujarat, Tamil Nadu, and Haryana) had above average per capita income in 1961 and all, with the exception of West Bengal, remained above average in 1991 .

While, in general, the richer states in 1991 were more industrialized than others (for example, Tamil Nadu, Maharashtra, Delhi, and Gujarat), Punjab and Haryana, primarily agricultural states, had the second and third highest per capita income in 1991 (Table 2). The success story of Punjab and Haryana is mainly accounted for by the "green revolution" during the 1960s, when the productivity of agricultural output (mainly wheat) rose sharply; their agricultural productivity has remained high compared with that of other agrarian states. Also, Punjab has invested heavily in irrigation and flood control measures, both of which have helped to reduce its susceptibility to weather-induced output shocks. West Bengal stands out as a highly industrialized state that was among the richest in 1961, but fell below average in 1991. Supply shocks in the form of power shortages and labor unrest have frequently beset industry in West Bengal; it also saw a rapid decline in one of its significant export industries-jute-as artificial fibers flooded international markets. In some states (Assam, Bihar, and Manipur) the share of manufacturing in state NDP actually declined substantially between 1961 and I 98 l .

Figures 1-3 illustrate the variations i n per capita output for the 20 states in our sample over the period 1961-91. Among the six initially poor states in 1961 (Figure I), Manipur has recorded the highest per capita annual growth rate between 1961 and 1991 at 3.3 percent, despite having the third highest population growth rate in the whole sample. Manipur and Tripura (with the second highest population growth rate) also clearly benefited the most from center-state grants in the post- 1 970 period (Table 2). Several northeastern states, including Tripura, have faced a large influx of refugees from Bangladesh, following that country's creation in 1971 . At the other extreme, Bihar has grown at a very slow pace, recording the second lowest growth in per capita NDP during 1961-9 1 . This dismal performance, despite net out-migration over the period of analysis, appears to be closely related to low agiicultural productivity in a largely agrarian state, poor infrastructure, and disincentives to invest because of political uncertainty, industrial unrest, and the steady erosion of law and order.

Among the nine initially middle-income states (Figure 2), Haryana, Himachal Pradesh, Andhra Pradesh, and Kerala grew at a faster pace in annual per capita terms during 1961-9 J than the country-wide average of 1.82 percent a year (Table 2). Moreover, both Himachal Pradesh and Jammu and Kashmir benefited greatly from center-state grants (Table 2).


ECONOMIC GROWTH IN THE STATES OF INDIA

Figure l . Real Per Capiw NDP ( 1990 mpees) Six lnilially Poor Slates, 1961-91

Log of real per capital NDP

135

8.6 r---------------------------, 8.4

7.8

7.4

7.2 1961 1964 1967 1970 1973 1976 1 979 1 982 1985 1988 1991

Log of real per capital NOP 8.6

8.4

8.2

8.0

7.8

7.6 I I

7.4 ,. /

_.._/

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Log of real per capital NDP 8.6

8.4

8.2

8.0

7.8

7.6

7.4

7.2 1961 1964 1967 1970 1973 1 976 1979 1982 1985 1988 1991



Figure 2. Real Per Capita NDP ( 1990 rupees) Nine Initially Middle-Income States. 1961-91


9.0

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1973 1976 1 979

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Himachal Pradesh

1982 1985 1988

1982 1985 1988

Andhra Pradesh • · •

1982 1985 1988

1991

1991

1991



Figure 3. Real Per Capita NDP ( 1990 rupees) Five Initially Rich States. 1961-91

Log of real per capital NDP

137

9.4r--------------------------------------------------.

9.2 / - � - · /

9.0

8.8

8.6

8.4

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Andhra Pradesh and Kerala were among the main exporters of labor to the Middle East during the 1970s and the early 1980s; remittances to these states through the late 1980s may also have been a significant factor contributing to their relatively high rates of income growth during 1961-91 .

Of the five initially rich states (Delhi, Punjab, Maharashtra, Gujarat, and West Bengal), Punjab and Maharashtra have grown at the highest rates (Table 2 and Figure 3) during 1961-91. Punjab's success has already been accounted for above, while Maharashtra appears to have made inroads into expanding indust1ial production (compare the declining share of agriculture and the rising share of manufacturing in state NDP during 1961-81 in Table 2) and exports.

A common feature shared by virtually all the 20 states is large intertemporaJ variations in output. The main factors accounting for these variations include terms of trade shocks (particularly movements in the price of oil and other commodities), border conAicts and civil disturbances, variations in weather conditions, and other supply-side constraints. Nor only is agricultural output in many states dependent on the timeliness and extent of rainfall (the monsoons), but weather conditions also affect agriculturebased industries (such as food and textiles) and infrastructure (water sup-



ply and hydro-based power plants). Finally. rigidities in state-based product and factor markets have also precluded more rapEd adjustment by states to unforeseen macroeconomic shocks.

II. Concepts of Convergence

This section lays out the concepts of convergence that are used in this study. Barro and Sala-i-Martin ( 1992a) derive an equation in discrete time for the average growth rate of per capita output, y, over the interval between t - T and t:

( I )

where i indexes the economy; T is the length of the observation intervaJ; 1 is time; Yi.r-T is real per capita net domestic product (NDP) for each economy at time 1 - T, the beginning of the subperiod; 15 y;, is real per capita NDP at time t; 13 is the convergence coefficient; 16 e i s the exponential constant; E;, is an independent error term; and C is the constant term, which is common across states. In the neoclassicaJ growth model of Solow ( 1956) and Swan ( 1956), convergence is conditional, because 13 is driven by the level of per capita income for each economy relative to its own steady-state per capita income and steady-state growth rate, which need not be homogeneous across economies. The probability of such homogeneity is, however, greater for regions of a given country, which are more likely to share common levels of technology, common preferences, and common political institutions. Here we follow Barro and Sala-i-Martin ( 1992a) and assume that all 20 state economies have the same steady-state levels of real per capita NDP and steady-state growth rates. and so equation ( I ) implies absolute convergence if 13 > 0.1 7

Two measures of convergence follow from equation ( I ). The first, known as 13-convergence, asks whether initiaJiy poor economies tend to grow faster than initiaHy rich ones (that is, whether there is mean reversion in the level of real per capita NDP across economies.). Another concept is

15 The concept of state net domestic product is discussed in detail in Section Ill. 16 For a Cobb-Douglas production function in intensive form. and assuming a

constant saving rate (as do Solow ( 1956) and Swan ( 1956)), there is a closed-form solution for the convergence coefficient: 13 = ( I - a)(g + n + o), where a is the share of capital in output, n is the rate of population growth, g is the exogenous rate of labor-augmenting technical progress, and o is the depreciation rate.

17 This assumption is tested (and could not be rejected) empirically in Section lV below.



<r-convergence, which considers the decline of the cross-sectional dispersion of real per capita NDP over time. That is, it asks whether the standard deviation of the logarithm of per capita NDP (the coefficient of variation) is shrinking across economies over time. Barra and Sala-i-Martin ( l992a) note that 13-convergence is a necessary but not a sufficient condition for <r-convergence, as a positive 13 will tend to reduce <r, (the dispersion of In y;, in equation ( I)) for a given distribution of E;,, but new exogenous shocks to E;, will tend to raise <r,.

An aggregate shock such as a large relative fall in the price of agricultural commodities would reduce the value of real output (akin to an income effect) in agriculture-based states. Conversely, it would raise the value of real output for those states that did not have a relatively large agricultural sector. Such disturbances alter the disttibution of the error term, E;,, so that E;, is no longer distributed independently of Ej, for states i and j, thus tending to raise <r, temporarily above its steady-state value, <r. However, given that the steady-state distribution of E;, does not change, for any given temporary shock, <r, approaches <r over time.

Omitted variable bias can result if we do not control for these shocks. For example, such an aggregate shock to agricultural prices would differentially affect the more rural-based Indian states. If such states were initially poor, then an adverse price shock would induce underestimation of the subsequent speed of convergence, as the omitted (shock) variable would be positively correlated with initial income, Yu-r-18 Moreover, the main sectoral shift of employment in the Indian states over this petiod was from agriculture to other sectors, principally manufacturing and services. As economies develop, workers generally shift out of agriculture, and if these other sectors have higher labor productivity than agriculture, then this shift alone in the pattern of the workforce would generate growth in those states with initially high shares of their economy in agriculture (Kuznets ( 1966)). 19 Hence the share of each state's NDP derived from agriculture in the initial year of each subperiod (AGR;,.r). and the share derived from manufacturing in the initial year of each subperiod (MAN;,-r) are added as explanatory variables in the estimation of equation ( I ), to control for the sectoral composition of state production.

18 I t i s assumed here that y;, represents real per capita income from the production of goods and services in economy i, and so changes in relative prices appear as changes in y;,. That is, assuming no quantities change, a fall in agricultural (or manufacturing) prices generates a lower growth rate of y1, in economies that are large agricultural (manufacturing) producers.

19 See Mitra ( 1 988) for an analysis of Kuznets' hypothesis in the context of the states of India.



III. Data

In this paper we consider the period 1961-91, using data on 20 states of India.20 The output data used are per capita state net domestic product (PCNDP) in constant ( 1990 rupees) prices, derived from current price data on state and union territory NDP and per capita NDP at factor cost (Government of India (1986 and 1995)), deflated by the national GDP deflator (DEF), base year 1990 (International Monetary Fund (1 994)). The state-based measures of NDP are analogs of national net domestic productthey measure income originating from factors of production physically located within the boundaries of each state, and represent the value of goods and services produced within a state. The NDP and per capita NDP series are prepared on the basis of a uniform methodology as prescribed by the Central Statistical Organization (CSO), which is discussed in detail by Dholakia ( 1985), Government of lndia ( 1986), and Choudhury ( 1993).21

Two additional points should be made regarding the output data. First, at the regional level there could be important differences between the mcome originating within the boundaries of any given state and the income accruing to the residents of that state, due to flows of factor incomes across state borders. However, data on income accruing to residents by state in India do not exist. Second, the relative standard of living of the residents of any given state may not be accurately reflected in per capita income, to the extent that state-based per capita consumption expenditure diverges from per capita income. Choudhury ( 1993) found that between 1967 and 1987 the divergence was small for most states, except for Rajasthan and Uttar Pradesh where consumption exceeded income (as both states were large net exporters of goods and services to other states), and for Tamil Nadu and Karnataka where income exceeded consumption.

The state population estimates (POP) are derived from census figures for 1961, 1971, 1981 , and 1991, and midyear population estimates are used for all other years (Government of India ( 199 I a and I 991 b); Registrar General and Census Commissioner (1991 )). Data on the share of manufacturing

20 The data are taken from official Government of India sources, to ensure consistency in definition and compilation and to aid the comparability of data across states and through time. All income, price, and fiscal data are for years ending March. See the Appendix for further details.

21 The CSO-consolidated series for state NDP uses the same methodology and source material as those for the national estimates of NDP. However, to the extent that minor revisions called for by the availability of new source material are not retrospectively incorporated for earlier years, the state NDP estimates are not strictly comparable over time. Similarly, differences in the source material used, data availability, and the extent of statistical development mean that the quality of income measures may vary across states at any given point in time (Government of India ( 1 986)).



(MAN) and agriculture, forestry and fishing (AGR) in state NDP at factor cost are taken from Government of India ( 1986).

As a measure of internal population mobility, census data on migration during the 1 960s and 1970s are used to calculate the intercensal annual average net migration into each state as a share of that state's population at the beginning of each intercensal period (MIG). Net migration figures for the subperiod 1981-91 are derived from state-based vital statistics (population growth and crude birth- and death rates) due to the unavailability of 1991 census data (Government of India (1991 a and 1991 b); Registrar General and Census Commissioner for India ( 1977 and 1988)).22

Estimates of state per capita disposable income (SOl) are derived by adding the grant component of transfers (TR) from the central government to state governments to NDP, then dividing by POP and applying the appropriate DEF. As noted in Section I, TR comp1ises statutory grants-in-aid, grants from state and central plan schemes, and grants from centrally sponsored schemes. State disposable income (SOl) is the state-based analog of national disposable income, in that it represents the total income available to residents of a given state for consumption and saving. As mentioned above, in the Indian context this concept will not be a perfect state-based analog of the national accounts definition of national disposable income, as our measure of SOl excludes net factor incomes flowing across state borders to residents of a state.

To examine whether there are regional differences in the steady-state level of per capita income to which the states of India are converging, each of the 20 states is allocated into one of four geographic regions; these dummy variables were east (six states), north (six states), south (four states), and west (four states). Further details on the definition, derivation, and sources of all the variables used in this study can be found in the Appendix. Tables 1 , 2, and A I present summary statistics of the above data for each of the 20 state economies.

IV. Did the Initially Poor States Grow Faster than the Initially Rich Ones?

The analysis of disparities in per capita incomes and growth rates across the states of India has been a popular theme for research on the Indian union, with key contributions by Chaudhry ( 1 966), Mukherjee ( 1969), Nair (1971), Majumdar ( 1976), Majumdar and Kapoor ( 1980), Choudhury ( 1980), Dholakia ( 1985), Nair ( 1985), Rao (1 985), Singh (1985), Sastry and

22 Unless otherwise denoted, net migration in this paper is synonymous wiLh net immigration.



Nag ( 1 990), Singh ( 1 992). Choudhury ( 1993), and Ghuman and Kaur ( 1993). However, apart from the important work of Dholakia ( 1985), most of these papers did not move beyond analyses of trend movements in NDP and per capita NDP. or the ranking of states by per capita income, or they focused more narrowly on determining the causes of sectoral-based shocks to income or consumption in particular states. The task of this empirical section is to analyze formally whether the initially poor states grew faster than the initially rich ones between 1961 and 199 1 , using equation ( I ) and real per capita NDP as the measure of income.

Column ( I ) of Table 3 reports the regression estimates of the convergence coefficient (13) in equation ( I ), where the onJy explanatory variables are a constant term (not reported) and the logarithm of initial subperiod income (In Yu-r). Note that a positive coefficient on initial income can be translated as initially poor states growing faster than initially rich ones. The first row of column (1) in Table 3 reports the results for a single regression on the period 1961-91, and it is found that � = 0.0027 (s.e. = 0.0057) is the result, with a coefficient of determination of 0.654 and standard error of the regression of 0.207. However, while this estimate of 13 is not statistically different from zero, the simple correlation between In y1961 and the 1961-91 growth rate of -0. 1 16 reflects 13-convergence (Figure 4 ). As expected, both Manipur (MN) and Himachal Pradesh (HP) had below-average per capita incomes in 1961, and relatively high rates of growth of per capita incomes in the 30 years thereafter. While Delhi (D) clearly had the highest per capita income in 1961, its 1961-91 growth rate was close to that which would be predicted given its initial level of per capita NDP.

Rows two to four of column ( I ) in Table 3 divide the 1961-91 period into three intercensal subperiods: 1961-71 , 1971-81, and 1981-91. Nonlinear least squares estimates of equation ( I ) find that the estimated convergence coefficients for 1961-71 , 1971-81, and 1981-91 have the appropriate (positive) sign, indicating 13-convergence, but are not statistically significant.

Figures 5-7 depict the negative correlation between initial income and the subsequent growth rate for these subperiods, which is clearly strongest for the subperiod 1961-7 1 . The relatively strong growth performance in the 1961-71 subperiod of initially poor Manipur (MN), Kerala (KE), and Himachal Pradesh (HP), and the relatively poor performance of initially rich Delhi (D), is clear from Figure 5. Accordingly, there is quite rapid 13-convergence in the 1960s as the initially poor states grew faster than their initially rich counterparts, which barely grew at all in per capita terms-the simple correlation of In y1961 with the growth rate for 1961-71 is -0.237.

The relatively good growth performance of initially rich Delhi (D), Punjab (P), Haryana (H), Maharashtra (MH), and Gujarat (G) in the 1971-81 and 1981-91 subperiods stands out in Figures 6 and 7. The correlation of

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Figure 4. Convergence of Real Per Capita NDP Across 20 Indian States: 1961 NDP and 1961-91 NDP Growth

Annual growth rate. 1961-91 0.050,.------------------------,

0.045 -

0.040 -

0.035 -0.030 -0.025 -0.020

0.015 f-0.010 r-0.005

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8.0 8.5 Log of 1961 real per capita NDP

Figure 5. Convergence of Real Per Capita NDP Across 20 Indian States: 1961 NDP and 1961-71 NDP Growth

Annual growth rate. 1961-71 0.05

0.04 MN

0.03 I

0.02

0.01

0

-0.01 7.0 7.5

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8.0 Log of 1961 real per capita NDP

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Figure 6. Convergence of Real Per Capita NDP Across 20 Indian Slates: 1971 NDP and 1971-81 NDP Grow1h

Annual growth rate, 1971-81 0.06

0.04 -

0.02 -

0

-0.02 -

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Figure 7. Convergence of Real Per Capiia NDP Across 20 Indian Suaes: 1981 NDP and 1981-91 NDP Grow1h

Annual growth rate. 1981-91 0.05

004 �

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0.01 �

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In y1971 with the 1971-81 growth rate is much lower at -0.065; and the correlation of In y1981 with the 1981-91 growth rate is also low at -0.064. Accordingly, there is only slight [3-convergence in these intercensal periods.23 A multivariate regression on the three-equation system yields a restricted estimate of f3 = -0.001 2, which is not statistically significant, and a Wald test of the hypothesis of the same [3-coefficient in all three subperiods indicates that this hypothesis is rejected.

The apparent instability of the convergence coefficients in the three subperiods could reflect aggregate disturbances that differentially affected state NDP (as mentioned in Section I I above).24 Accordingly, in column (2) of Table 3 the share of NDP derived from the agricultural sector of each state (AGRi.t-r) is added to the basic regression to control for aggregate shocks. As a result, the estimated coefficient for the subperiod 1971-81 is raised considerably (from � = 0.0034 to � = 0.0220), and that for the subperiod 1961-71 is lowered considerably (from � = 0.0125 to � = 0.0010). The restricted coefficient in the multivariate regression (row five, column (2)) now has a value of � = 0.0052, which is not statistically significant, and a Wald test of the hypothesis of equality of the estimated [3-coefficients across the three subperiods indicates that this hypothesis is again rejected. It appears that AGRi.t-T is unable to fully capture the influence of aggregate shocks on the growth process, although it does provide information on the sectoral pattern of state growth across the three subperiods.

Accordingly, in column (3) of Table 3 the share ofNDP derived from the manufacturing sector of each state (MANi.t-r) is added to the basic regression to further control for aggregate shocks. This variable is likely to be particularly important in the Indian context, given the industrialization strategy pursued in lndi.a from the early 1960s until the mid-1980s. Its absence from the growth regression would thus be expected to result in omitted variable bias. The result is that the estimated coefficient for the subperiod

23 States in which real per capita NOP declined were Assam, Delhi, and Tamil Nadu in the 1960s; Assam, West Bengal, and Rajasthan in the 1970s; and Jammu and Kashmir in the 1980s. However, it is important to recognize that, while decennial rates of growth of real NOP were positive in all these cases, they did not keep pace with intercensal population growth rates. 24 A further cause of potential bias is our use of a national deflator to adjust nominal state NOP figures for the change in prices. That is, where PINolA (the level of India's national GOP deflator) is used rather than P; (state-based deflators) to derive real NOP for each state from nominal state NOP, if prices differ across states at points in time, the correlation between PINolA and the error term will induce bias in the estimated coefficients. However, the use of a common (national) deflator for each state at each point in time in a cross-sectional analysis will affect only the constant term in each regression. Moreover, work by Oholakia ( 1985) confirms that for the 1960s, the series of real per capita state NDP at local and at national prices were statistically identical. Bhattacharyay ( 1982) also finds that there was little cross-state variation in the purchasing power of a rupee between 1964 and 1978.



1971-81 remains much the same as in column (2) (from � = 0.0220 to � = 0.0223); that for the subperiod 1981-91 is raised (from � = 0.0029 to � = 0.0075); and that for the subperiod 1961-71 is lowered (from � = 0.0010 to � = -0.0077). The restricted coefficient in the multivariate regression (row five, column (3)) now has a statistically significant value of � = 0.0153, and a Wald test of the hypothesis of equality of the estimated 13-coefficients across the three subperiods indicates that this hypothesis is not rejected. Such a value for 13 implies a half-life of the logarithm of per capita income (the time it takes to close half of the gap between any state's initial level of per capita income and the common steady-state level of per capita income) of 45 years.25

The agricultural variable (reported as e in column (2) of Table 3) is negative for the 1971-81 and 1981-91 subperiods and positive for the 1961-71 subperiod. This indicates that, for example, those states where the agricultural sector was a large contributor to NDP had relatively lower levels of final per capita income in the 1971-81 subperiod. That is, they enjoyed relatively lower rates of growth of per capita income over that subperiod (0 = -0. 1736). Note that in row three of column (2) it is the period 1971-81 that exhibits the largest convergence coefficient (� = 0.0220). The relative decline in agricultural commodity prices over the decade hurt those economies specializing in such products. In 1971 Bihar, Orissa, Tripura, and Uttar Pradesh had below-average per capita incomes, yet each had a relatively large share of its 1971 NDP derived from agriculture: the correlation of In y1971 with AGR1971 is - 0.534. Consequently, because of the positive correlation between the aggregate shock and initial income, � is underestimated in row three of column ( I ): i t reflects the tendency of the poorer states to be agricultural and hence to experience relatively slow growth during this subperiod (Table 3). For the 1961-71 subperiod, again agriculture-based states tended to be relatively poor (the correlation of In y1961 with AGR1961 is -0.766), yet the positive shock to agriculture means that in row two of column (I) , � is overestimated: controlling for the aggregate shock lowered � in row two of column (2), because of the negative correlation between the agricultural shock and initial income (Table 3).

Similarly, the manufacturing variable (reported as 1- in column (3) of Table 3) is positive for the 1971-81 and 1981-91 subperiods and negative for the 1961-71 subperiod. This indicates, for example, that those states where the manufacturing sector was a large contributor to NDP had relatively higher levels of final per capita income in the 1981-91 subperiod. That is, they enjoyed relatively higher rates of growth of per capita income over that subperiod ( f = 0. 1283). Note that in row two of column (3) it is

25 The formula for the '·half-life" (HL) in years is HL = log(2)/j3.


148 PAUL CASHIN and RATNA SAHA Y

the period I 961-71 that exhibits the greatest shift in its convergence coefficient (from � = 0.00 10 to � = -0.0077). The relative decline in manufacturing prices over that decade hurt those economies specializing in such products. In 196 I Delhi, Maharashtra, West Bengal, Gujarat, Tamil Nadu, and Assam had above-average per capita incomes, yet for each a relatively large share of its 1961 NDP was derived from manufacturing: the con-elation of In Yr961 with MANr96r is 0. 7 1 8. Consequently, because of the negative conelation between the aggregate shock and initial income, � was overestimated in row two of column (2): it reflected the tendency of richer states to be manufacturing-based and hence to experience relatively slow growth during this subperiod (Table 3). For the I 981-91 subperiod, again manufacturing-based states tended to be relatively rich (the con-elation of In y19KJ with MAN1981 was 0.504), yet the positive shock to manufacturing meant that � in row four of column (2) was underestimated: controlling for the aggregate shock raised � in row four of column (3) because of the positive correlation between the manufacturing shock and initial income (Table 3).

The estimated speed of convergence for the Indian states between 1961 and 1991 (� = 0.0 153) is slower than that found in most earlier studies of regional economies of developed countries: the states of the United States ([3 = 0.0249) between 1880 and 1988 by Barro and Sala-i-Martin ( I992a); the regions of European OECD countries ([3 = 0.0 178) between 1950 and 1985 by Bano and Sala-i-Martin ( 1991 ); the provinces of Canada ([3 = 0.024) between 1961 and 1991 by Coulombe and Lee ( 1 993); the regional economies of Australasia ([3 = 0.0 1 2 1 ) between 1861 and 199 I by Cashin ( 1995); 98 (OECD and non-OECD) countries ([3 = 0.0 I I I ) between 1 960 and 1985 by Barro ( 1991 ); the prefectures of Japan ([3 = 0.034) between 1930 and 1987 by Barro and Sala-i-Martin ( 1 992b); the prefectures of Japan ([3 = 0.033) between 1 960 and I 988 by Shioji ( 1993); and the developed and developing island economies of the South Pacific ([3 = 0.0432) between 1971 and 1 993 by Cashin and Loayza ( 1 995).26 Barro and Sala-iMartin ( 1991 ) hypothesized that the more heterogeneous the steady states to which a group of economies are converging, the slower the speed of con-

26 As noted in Section II, using the Cobb-Douglas-based closed-form solution for the speed of convergence from the Sol ow-Swan ( 1956) model yields 13 = ( I - a) (n + g + 5). Assuming that (g + 5) = 0.04 (reflecting the slow rate of exogenous technical change in developing countries); letting n = 0.03 (replicating India's rapid rate of population growth}, then 13 = 0.015 can only be approximated with a value for a of about 0.75. As argued by Barro and Sala-i-Martin ( 1995), such a capital share is too high for a narrow concept of physical capital, but would be consistent with a broad concept of capital that also includes human capital.

A speed of convergence of about 1 .5 percent a year is also close to that obtained for a sample of 95 developing countries (13 = 0.014) between 1970 and 1990 by Khan and Kumar ( 1 993).



vergence, even after controlling for the disparate steady states. That is, regions of a given country (such as the United States, Canada, Japan, India, and Australasia) should exhibit the fastest convergence, followed by similar national economies (such as the OECD), followed by all national economies. While for some subperiods the present findings fit into this hierarchy of convergence speeds, over the full sample period this does not appear to be the case for the Indian states. However, the fact that f3-convergence is observed in India without controlling for differences in steadystate growth rates or steady-stare levels of per capita incomes is indicative of homogeneous steady states across the states of India but heterogeneous initial levels of per capita state incomes.27 Hence, absolute and conditional convergence in the Indian states do appear to be almost synonymous.2s

V. Did the Cross-State Dispersion of Per Capita Incomes Widen or Narrow?

To determine the extent of the dispersion of per capita incomes across the 20 Indian states, the unweighted cross-sectional standard deviation of In )';, eyNDP,, was calculated for the period 1961-91 .29 Figure 8 shows that over this period there has been an increase in the dispersion of real per capita incomes (cYNDP,) across the Indian states. except for the subperiods 1962-68. 1972-75, 1977-78, and 1980-84. The dispersion fell from 0.292 in 1961 and 0.328 in 1 962 to 0.268 in 1975, then increased to reach 0.339 in 1980, fell to 0.297 in 1984, and then rose to 0.333 by 1991.30

27 Moreover, a formal test of the null hypothesis that the coefficients on the regional dummy variables are all equal ro zero found that the hypothesis could not be rejected. A test of this restriction, run by adding the dummies to the three intercensal regressions of Table 3, yielded a Like! ihood Ratio test statistic of 8.1 12; the corresponding x2 value with 9 degrees of freedom at the 0.05 percent level is 16.919. 28 In future work the authors will examine the robustness of this result, using alternative models of the growth process.

29 The aNDP, calculations exclude certain states for certain years, due to the unavailability of data on state per capita NDP. These are Assam, Haryana, Himachal Pradesh, and Punjab for 1962-65; Himachal Pradesh for 1966; Assam and Himachal Pradesh for 1967; and Assam for 1968.

30 A least squares regression of aNDP, on a time trend and a constant term revealed that for the 1961-91 subperiod the coefficient on the time trend (�) was small yet significantly positive (� = 0.0015 [s.e.= 0.0004]). This indicates that aNDP, increased at the small trend rate of growth of 0. I 5 percent a year over the period 1961-91.

As noted in Section I and by both Barro and Sala-i-Martin ( 1992a) and Quah ( 1993), even if absolute 13-convergence holds (as it does for the states of India), the dispersion of per capita incomes across economies need not decline.



Figure 8. Dispersion o.lRect! Per Capira Incomes: 20 Indian Srares. 1961-91

Standard deviation of log of real per capita income

0.36.---------------------------,

I I I I I I

'.,, "' I '�

0. 22 L....I---'---'-_J__J___L....I__J_--'-_J__J___J__l__J_--'-_J__J___J__l__J_--'-_J__J___J__l__J___L_J__J___L...J 1961 1964 1967 1970 1973 1976 1979 1982 1985 1988 1991

The dispersion of real per capita NDP across the states narrowed between 1961 and 1971 because of robust growth rates in initially poor states (Manipur, Kerala, and Himachal Pradesh) and slow growth rates in initially rich states (Delhi, West Bengal, and Maharashtra). However, in the 1971-81 and 1981-91 subperiods the initially poor states (Manipur, Bihar, and Orissa in 1 97 1 ; Bihar, Assam, and Orissa in 198 1 ) and the initially rich stares (Delhi, Punjab, and Haryana in 1971 ; Delhi, Punjab, and Maharashtra in 198 1 ) had similar rates of economic growth (Figures 6 and 7). 31

This process of a widening in the cross-sectional dispersion of real per capita NDP for the Indian states contrasts with the pattern exhibited by developed countries (the states of Australia, the prefectures of Japan, and the states of the United States), where the minimum value of a, was found to be 0.12, 0.12, and 0.14, respectively (Cashin ( 1 995) and Barro and Salai-Martin ( 1992b)). One explanation for the observed pattern of aNDP, for India is that the steady-state value for a is about 0.32, and that aNDP, should remain close to this level until there is an aggregate shock that differentially affects the states. Interestingly, India's steady-state value of a is over twice the level of those for the regional economies of Australia, Japan, and the United States, and most likely reflects higher barriers to the free

.lt Evidence of increasing regional disparities in the 1980s was also found in the work of Majumdar and Kapoor ( 1980), Nair ( 1985), Singh ( 1985). and Rao ( 1985) on the cross-state dispersion of per capita incomes.



flow of capital and labor across the Indian states than those existing in these developed economies.

In Figure 8 is also plotted a measure of the dispersion of state per capita disposable incomes, fiSDI, where SDI is defined as state NDP plus centerstate grants.32 Given d1e presence of center-state grants, which are allocated more to relatively poor states than to relatively rich ones, it would be expected a priori that the dispersion of per capita income would be greater for (JNDP, than (JSDI,. This is indeed the case, as (JNDP, > fiSDI, for all t (Figure 8). Accordingly, center-state grants have been operating to equalize per capita incomes across the 20 states-the poor states are the relative beneficiaries of this aspect of Indian fiscal federal ism, at the expense of their relatively rich counterparts. For state disposable income there is only slight fi-divergence over the 1961-91 period: fiSDI, rose from 0.290 in 1961 and a period high of0.326 in 1 962 to reach 0.324 in 1 980, fell to 0.284 in 1984, and then rose to 0.306 by 199 1 .

The gap between fiSDI, and fiNDP, widened considerably after the mid-1 960s, which reveals the much greater role played by center-state grants after this date (Figure 8). That is, while the dispersion of per capita NDP has widened, there has also been an increase in grants to relatively poor states over the 1961-91 period. This has resulted in relatively little change in the dispersion of per capita SDI across the states of India during this period, as grants have compensated for the widening dispersion of the per capita NDP component of per capita SDI. In particular, after J 975 the value of fJSDI, has fluctuated around 0.30, while that of (JNDP, has fluctuated around 0.32; between 1966 and 1975 the fi, values fluctuated around 0.26 and 0.27, respectively.

A useful disaggregation of the data is to examine whether the initially rich economies in 1961 (Delhi, Maharashtra, West Bengal, Gujarat, and Punjab) experienced (J-convergence as a subgroup, and whether the initially poor economies (Manipur, Bihar, Orissa, Tripura, Madhya Pradesh, and Uttar Pradesh) and initially middle-income economies (Andhra Pradesh, Assam, Haryana, Himachal Pradesh, Jammu and Kashmir, Karnataka, Kerala, Rajasthan, and Tamil Nadu) did likewise. The results are depicted in Figures 9-1 I .

The gap between fiNDP, and fiSD!, is small for the five initially rich states, indicating that grants have had little effect on the dispersion of per capita incomes across these states (Figure 9). However, even among these rich states fiNDP, is greater than fiSDI, for all t, indicating that the poor members of this subgroup benefited from center-state grants rela-

32Data on grants from the central government to the Union Territo•y of Delhi over the period 1961-91 are unavailable. Accordingly, our measure of uSDI, does not include center-state grants to Delhi.



Figure 9. Dispersion of Real Per Capita Incomes: Five Initially Rich Indian States. 1961-91

Standard deviation of log of real per capita income 0.32

O . J6 1�9-6

�1��

� 9�

M��

I 9-6�

7�-1

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9-73��

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19-7�

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�9�85��

[-98�

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Figure I 0. Dispersion of Real Per Capita Incomes: Nine Initially Middle-Income Indian States. /96/-91


0.20

0.15

0.10

0.05 L....L--'......L....l._L....L--'......L....l._L....L__t__L_..l._L....I.--'--'-.L...JL....l......L....L...L...JL....L.....L-L-.L...J� 1961 19M 1967 1970 1973 1976 1979 1982 1985 1988 1991



Figure II. Dispersion of Real Per Capita Incomes: Six Initially Poor Indian SICites, 1961-91


0.25

0.20

0.15

0.10

0·05 1961

_, ;\ / v \ / \ ;\ r ' ./ I I

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1964 1967 1970 1973 1976 1979 1982 1985 1988 1991

tively more than their richer counterparts. Overall, there is 0'-di vergence for both measures of income; O'NOP, rises from 0.229 in 1961 to 0.271 in 1991, and 0'501, rises from 0.226 in 1961 to 0.263 i n 1991. This result can be largely attributed to the relatively rapid growth of rich Delhi, and the relatively slow growth of poor West Bengal.

Interestingly, while O'NDP, is greater than 0'501, from 1961 to 1975 for the nine initially middle-income states, O'NOP, is less than 0'501, between 1976 and 1988 (Figure l 0). While the poor members of this subgroup were relative beneficiaries of center-state grants in the former subperiod, the reverse occurred in the latter subperiod. From 1990 onward, O'NDP, is again greater than 0'501,. Overall, there is clear 0'-divergence for both measures of income; O'NOP, rises from 0.089 in 1961 to 0.188 in 199 1 , and 0'501, rises from 0.087 in J 96l to 0. 1 7 1 in 199 1 . This result can be largely attributed to the relatively rapid growth of rich Haryana, and the relatively weak growth performance of poor Jammu and Kashmir.

For the six initially poor states there is little difference between O'NOP, and 0'501, until 1970-center-state grants played a minor role in influencing the dispersion of per capita income across the initially poor states in these early years (Figure 1 1 ). However, beginning in 1970 0'501, exhibits erratic behavior-oNOP1970 is less than 0'5011970, then the dispersion of per capita NDP jumps so that O'NOP1971 is greater than 0'50/1971 , and then the dispersion of per capita disposable income jumps so that O'NDP1912 is less



than O"SD/1972. This erratic behavior can be largely attributed to the beginning of payments of grants to Manipur (in 197 1 ) and Tripura (in 1972). However, between 1972 and 1991 O"NDP, is clearly smaller than O"SD/" indicating that the rich members of this subgroup were relative beneficiaries of center-state grants. That is, the grants acted to exacerbate inequalities in per capita incomes across the six poor states, especially after 1974. The high level of per capita grants received by both Manipur and Tripura, combined with the relatively low level of per capita grants received by Bihar and Uttar Pradesh, resulted in O"-divergence for O"SDJ, between 1974 and 1985, and slight O"-convergence for O"SDI, after this period.33 The value of O"SDI, for the six initially poor states rises from 0. 176 in 1961 to 0.214 in 1991, after reaching a period high of 0.253 in 1985 and a period low of 0.075 in 1971. Indeed, there is u-convergence for the six initially poor states with respect to CJNDP, which declined from 0.173 in 1961 to 0.147 in 1991; per capita incomes in the poorest Indian states became more similar over this period. This was largely due to the relatively rapid growth of initially poor Manipur, and the relatively weak growth performance of initially rich Tripura and Uttar Pradesh.

VI. How Strongly Does Net Migration Respond to Cross-State Differentials in Per Capita Incomes?

One important mechanism by which differences in cross-regional per capita incomes can be equalized within national economies is by population movements from relatively poor to relatively rich regions. Interstate migration in India is of particular interest, because of the strong heterogeneity across states in their levels of per capita income and demographic characteristics (see Tables I and 2). In this section we examine the strength of the interrelationship between net in-migration and initial per capita incomes for the 20 states of India.

In terms of total volume, rural-to-rural migration dominates over other streams of migration (such as rural-to-urban) in India. Moreover, there is a clear preponderance of women in rural-to-rural migration, due to the system of patrilocal migration after marriage. For example, intercensal migration across the states between 1971 and 1981 resulted in 70 male rural-torural migrants per I 00 females; for rural-to-urban migrants the ratio was

�� An examination of the dispersion of per capita state disposable incomes for four of the six initially poor states, excluding Manipur and Tripura, yields aNDP, approximately equal to aSDI, between 1961 and 1988, while aNDP, was clearly greater than aSDI, after 1989. Accordingly, it appears that in comparison with Manipur and Tripura, the states of Bihar, Orissa, Uttar Pradesh, and Madhya Pradesh benefited much less from center-state grants prior to the late 1980s.



142 males per 100 females (Skeldon ( 1 986)). However, this marriage-based migration is mainly across district boundaries separating neighboring settlements of a given state; most of this type of population movement is eliminated from census data on cross-state migration (Datta ( 1985)). Urban-tourban and rural-to-urban migration are the dominant components of interstate migration in India; each comprised about 32 percent of all intercensal cross-state migranrs between 1971 and 1981 (Skeldon ( 1986)). As with most other developing countries, long-distance migration in India is male dominated and overwhelmingly urban oriented.

Table 4 sets out the volume of interstate migration between 1 961 and 1991, on an intercensal basis, taken from official migration data from the Registrar General and Census Commissioner for India ( 1977 and 1988) for cross-state migration in the 1960s and 1970s, and implied net migration (derived from vital statistics) for cross-state migration in the I980s.3� Our intercensal cross-state migration calculations closely approximate those of Datta ( I 985) for the 1971 census and Skeldon ( I 986) for the 1981 census. Gross intercensal migration across states between I 96 I and 1971 was 2.07 percent of the all-India population in 1961; gross interstate migration between 1971 and 1981 was 1 .96 percent of the 1971 all-India population; and gross interstate migration between 1981 and 1991 was 1 .97 percent of the 1981 all-India population (Table 4).

The strong (and increasing) attraction of Delhi for the rest of India stands out in the data, with the aggregate of net migration during the decade as a share of its initial census year population being 0.215 for the 1960s, 0.234 for the 1970s, and 0.293 for the 1 980s. Other relatively large net immigration states over the 1961-91 period were Manipur, Maharashtra, Madhya Pradesh, and Tripura, while Punjab, Himachal Pradesh, Kerala, and Bihar were net emigration states over the 1961-91 sample period.35 In general, the states of northern [ndia (paJticularly Punjab and Himachal Pradesh) and Bihar in the east can be characterized as net out-migration regions; the western states (particularly Maharashtra) as net in-migration regions; and the southern states exhibit close to zero net migration. Moreover, net in-migration across the states of India is highly persistent-the simple correlation between M/G1961 and MIG1971 is 0.974; that between M1Gr97r and M/G19s1 is 0.817; and that between M/G1961 and M/G1981 is 0.825.

34 Mukerji ( 1982) also uses crude birth- and death rates in estimating net migration to the eastern states of India in the 1970s. 35 Care needs to be taken in interpreting the figure for net migration to the eastern states of India, in particular to Tripura. This is because the derivation of the large figure for migration in the 1980s is based on vital statistics that, unlike those taken directly from the census data for the 1960s and 1970s, also include international migrants.

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1 58 PAUL CASHIN and RATNA SAHA Y

In explaining migration we follow Braun ( 1993) and use a reduced form expression for MIG;, the annual rate of in-migration to state i as a share of the population of state i in the initial year of each intercensal period:

MIG;, = 1J.. + v ln(y;,1-r) + �'TT;.1-r + w TI7.1-r + E;, (2)

where Yi.t·T is real (constant 1 990 rupees) per capita NDP of state i at the beginning of the intercensal period; 'TTi.f.r is the population density (persons per square kilometer) of state i at the beginning of the intercensal period; and E;, is an independent error term. The equation also includes the square of the population density, which captures nonlinearities in the relation between migration and density. We expect initial income, population density, and the square of population density to have, respectively, positive, negative. and positive effects on net in-migration to state i.36 The empirical relationship is tested using iterative, weighted (by initial state populations) least squares.

Figure 1 2 reveals the relationship between the annual average migration rate between 1961 and 199 J and the logarithm of real per capita income in 1961 Y The relationship is clearly positive (with simple correlation 0.574), which supports the proposition that net in-migration is positively affected by cross-state differentials in per capita incomes.

The extremely strong attraction of Delhi (Figure 12) to the rest of India is indicated by much higher net migration rates than would be predicted by its initial level of per capita NDP. While the slope of the regression line would still be positive in the absence of Delhi, the relationship of migration to initial income would have been much weaker. Delhi has successfully attracted migrants for several reasons. First, the differential in per capita incomes between Delhi and all other states has been substantial. This is likely to induce large-scale in-migration, even if the prospects for employment in Delhi are limited (Harris and Todaro ( 1 970)). Second, the private sector (industry and services) has expanded rapidly between 1961 and 199 1 . In India's highly regulated economic environment during 1961-91, physical proximity to a strong central government was a key to success in lobbying efforts. Finally, the central government itself, along with other public sector companies, has expanded and absorbed a growing labor force.

Figures 13-15 present the net migration and income relationship for the three subperiods ( 1 961-71, 1971-81, and 1981-91). The results are simi-

36 The marginal effect of Yu-r on MIG11 is positive if v > 0; the marginal effect ofTI1.1-r On MIG11 is negative if� + 2w < 0. 37 The variable on the vertical axis of Figure 12 is the annual average of inmigration to each state during 1961-91 (the numerator), expressed as a share of the population of each stale in 1961 (the denominator).



Figure 12. Migration and Initial State Income - 20 Indian States: 1961-91

Annual migration rme. 1961-91 0.05 .------=---------------------------,

D 1

-0.01 7.0 7 5 8.0 8.5 9.0 Log of 1961 real per capita NDP

Figure 13. Migration and Initial State Income - 20 Indian States: /961-71

Annual migration rate. 1961-71 O.o25 ,------------------------�

8.0 8.5 9.0 Log of 1961 real per capita NDP



Figure 14. Migrarion and Initial State Income - 20 Indian Stmes: 1971-81

Annual migration rate, 1971-81 0.025 ,--_:::_ __ ___:_ ___________________ _, ol

Log of I 97 I real per capita NDP

Figure 15. Migration and Initial State Income - 20 Indian States: 1981-91

Annual migration rate, I 98 I -9 I 0.04 .----=-----------------------,

�.01 L--L�L-��--��--��--��--�-L--L--L--L--L--L-� 7.4 7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.0 9.2

Log of I 981 real per capita NDP



Jar to those depicted in Figure 1 2-the positive outlier is again Delhi, and apart from Assam in the 1970s and Tripura and Manipur in the 1980s, most states are bunched close to the zero net migration line.

Table 5 presents the results of the regressions on equation (2). The regression on the migration rate for the full period 1961-91 results in a positive coefficient on initial income, yet it is not statistically significant, while the coefficients on density and the square of density are significantly negative and positive, respectively. The next three regressions break up this period into the three intercensal subperiods analyzed i n Section IV (1961-7 1 , 1971-81, and 1981-91 ). The values for v are positive for two of the three subperiods, and statistically signi ficant only for the 197 L -81

Table 5. Regressions for Net Migration into Indian States, 1961-91•

Square of Personal Population population

Period income density density R2[sJ

1961-91 0.0030 -0.15E-04 0.16E-07 0.857 (0.0029) (0.31E-05) (0.21 E-08) [0.0017 ]

1961-71 0.0016 -0.83E-05 0. 1 1 E-07 0.839 (0.0017) (0.24E-05) (0.19E-08) [0.00 I 0]

1971-81 0.0014 - 0.88E-05 0.58E-08 0.854 (0.0006) (0.27E-05) (0. 1 1 E-08) [0.00 1 1 ]

1981-91 -0.0010 -O . IOE-04 0.39E-08 0.660 (0.0028) (0.34E-05) (0.88E-09) [0.0025]

Restrictedb 0.0012 (0.0009)

Sources: Authors' calculations, derived from Government of India ( 1977 and 1988); Government of India ( 1 995) and earlier issues; Government of India ( 1991 a) and earlier issues.

" All regressions are for 1 9 states of India, and the Union Territory of Delhi. The regressions use iterative, weighted (by initial state populations) least squares to estimate equations of the form: MIG;, = f.1 + vln( Y;.,-r) + �7T,.r-r + w(7T;.,-r)2 + other variables, where MIG;, is the average annual net migration into state i between years t - T and t, expressed as a share of the state's population in year t - T; Y•.r-r is real per capita NDP at the beginning of the subperiod t - T, as described in Table 3; 7Tu-r is the population density (thousands of people per square kilometer) of state i at the beginning of the subperiod t - T; Tis the length of each subperiod; and "other variables" (unreported) are the share of agriculture in each state's NDP at time t - T, AGR;.,-r. and the share of manufacturing in each state's NDP at time t - T, MAN�.r-r· R2 is the coefficient of determination. All regressions contain a constant term (unreported). Heteroscedastic-consistent standard errors are in parentheses. The standard errors of the regression, s , are in brackets.

• The restricted regression requires the values of v to be the same across all three subperiods, and the restricted v are estimated using iterative, weighted seemingly unrelated regression, which allows for the correlation of error terms across subperiods. The Wald test statistic for equal values for v is 3.231 and the p-value is 0.199. The 0.05 X2 value with two degrees of freedom is 5.9915.



subperiod. Moreover, the values for � and w are all statistically significant and have the appropriate signs, in each of the three regressions. A multivariate regression on the three-equation system yields in row five a restricted estimate of v = 0.0012, which is not statistically significant. However, a Wald test of the hypothesis of the same v-coefficient in all three subperiods indicates that this hypothesis cannot be rejected. Everything else held constant, a 10 percent differential in initial per capita income would raise net in-migration to the richer state by a very small 0.012 percentage points per year.

This result can be contrasted with those for the states of the United States between 1900 and 1987 and the prefectures of Japan between 1955 and 1985 of Barro and Sala-i-Martin ( 1992b), who find that, everything else held constant, a I 0 percent differential in initial per capita income would raise net in-migration to the richer region by a relatively large 0.26 and 0.27 percentage points per year, respectively. However, Braun ( 1 993) finds that migration across 80 regions of the five largest European countries (Germany, the United Kingdom, Italy, France, and Spain) between 1950 and 1990 responds only weakly to initial income-everything else held constant, a 10 percent differential in initial per capita income would raise net in-mjgration to the richer region by only 0.064 percentage points per year. Accordingly, it appears that while the migration rate for the states of India is positively related to initial per capita income, it is not statistically different from zero. In that sense, the income elasticity of migration across the states of India more closely resembles the relatively weak responsiveness of population movements to income differentials in the regions of Europe than the relatively stronger responsiveness to differentials in the states of the United States or the prefectures of Japan. Implicitly, the costs of crossregional labor mobility are high in India and Europe-they are relatively low in Japan and the United States. This anemic Indian response of crossstate migration to income differentials is most likely due to a combination of several barriers to the mobility of labor: strong local workers' unions that act to keep out competing potential employees; rigidities in nominal wages (Joshi and Little ( 1 994)); Jack of housing in fast-growing urban areas; and most important, social, cultural, and linguistic barriers to the cross-regional substitutability of labor.

VII. Is Cross-State Migration a Likely Cause of the Convergence of State Per Capita Incomes in India?

As argued above, migration from poor states to rich states should accelerate the speed of convergence of per capita incomes across the 20 states of



India. If so, then the estimated convergence coefficients of Table 3 also embody the contribut]on of migration to the convergence process. Accordingly, the expectation is that in-migration should have a negative effect on the rate of growth of per capita incomes, and that the introduction of migration as an explanatory variable in the growth regressions should lead to a reduction in the estimated �·

The inclusion of migration (MIG;) in the growth regression of column (3) of Table 3 results in a statistically significant restricted estimate of� for the three subperiods of � = 0.0244. For two of the three subperiods, the coefficient on MIG1, is negative, yet only one is statistically significant. This restricted estimate of � (with migration) is larger than that calculated in the absence of migration (� = 0.0 153), and most likely reflects the endogeneity of migration and the growth of state per capita incomes-fast-growing states are more likely to attract migrants.

Accordingly, the growth regression was estimated by generalized instrumental variables, using fitted values from reduced form estimation of MIG as instruments for actual MIG in the structural growth regression (White ( 1982)).38 The restricted coefficient on initial income is now � = 0.0168 and is statisticaUy significant, yet the coefficients on MIG;, for two of the three subperiods are positive, which is the opposite of what would be expected if migration is the cause of cross-state income convergence. If we then restrict the coefficients on MIG1, to be the same for all three subperiods, the estimated coefficient on MJG1, is positive and statistically insignificant, while the restricted estimate of� is statistically significant at 0.0157.39 This speed of convergence is very close to that calculated in the absence of migration (� = 0.0 153). These results suggest that the process of migration has little effect on the convergence of per capita incomes in the states of India. Holding net migration rates constant, the speed of convergence of per capita incomes in poor states to those in rich states is very close to that estimated in the absence of controls for cross-state migration.

VIII. Conclusions

Have the initially poor economies of India grown faster than their initially rich counterparts? A key conclusion of this paper is that there has

38 The fitted values of MJG1, were obtained using the following set of independent variables (the exogenous variables from the structural and reduced form regressions): In Yu-r. 1T;,1-r, 1T1u-r. In AGR1,,.r. In MAN;,-r· The R2 statistic on the reduced form regressions for MJG1961 , MIG197r. and MIG1981 are 0.839, 0.854, and 0.660, res�ectively (Table 5).

3 A Wald test did not reject the hypothesis that the coefficient on MIG, is the same for each of the three subperiods.



indeed been convergence in real per capita incomes across the states of India during the period 1961-9 1 . The convergence found is absolute because it occurs when no explanatory variables other than the initial level of per capita income are held constant. That is, the 20 states of India displayed homogeneity across states with respect to the steady-state level of per capita income, yet exhibited heterogeneous initial levels of per capita income. However, while convergence has occurred, the speed at which the initially poor states have caught up to the initially rich states, with I .5 percent of the gap between them being closed each year, is slower than that obtained in analyses of regional convergence in developed countries, which generally center on 2 percent per year. Accordingly, while a typical Indian state would take about 45 years to close one half of the gap between its initial per capita income and the steady-state per capita income, the typical region of a developed country would take only about 35 years to complete the same task.

There has also been a widening in the dispersion of real state per capita incomes in India during the period I 961-91 . . However, grants from the central government to the states did ensure that the dispersion of state real per capita disposable incomes was narrower than the dispersion of state real per capita incomes, as relatively more grants were transferred to poor states than to their rich counterparts.

The extent to which population movements occurred in response to differential state incomes was rather weak, indicating that significant economic, social, and cultural barriers to the free migration of labor across the states of India continue to exist. I n that sense the labor markets of Indian states resemble more closely the relatively closed regional labor markets of Europe than the relatively open regional labor markets of the United States and Japan. Finally, as for the above developed countries, there is Little evidence that population movements are an important factor in the convergence of state real per capita incomes in India.



Registrar General and Census Commissioner for India, Census of India, for census years I961. 1 97 1 , 1981, and 1991 (COl);

Government of India, Central Statistical Organization, Estimates of Stare Domestic Product 1960-6/ to 1983-84 (ESOP);

Reserve Bank of India. Reserve Bank of India Bulletin, various issues (RBI);

Government of India, Basic Statistics Relating to the Indian Economy. various issues (STAT); and

Government of India, Statistical Pocket Book: India, various issues (BOOK).

Table A I contains a detailed listing of the mean and standard deviation of the key variables used in the cross-sectional growth regressions. The derivation and description of the data used in the paper are as follows:

AGR-The logarithm of the share of agriculture, forestry, logging, and fishing in net state domestic product at factor cost at current prices; taken from ESOP. The figure for Assam in 196I is for its present boundaries (excludes Meghalaya, Nagaland, and Mizoram). The I96I figure for Himachal Pradesh is the 1968 share, because in 1961 it was part of Punjab State. The figures for Punjab and Haryana for 1961 are both for their present boundaries. In the growth regressions, AGR enters in logarithmic form.

AREA-Geographic area (in thousands of square kilometers) of each state in each census year; taken from the same sources as POP. For 1961 : Himachal Pradesh has the area it had as a Union Territory in 1961; and Haryana is assumed to have the area it had upon the granting of its statehood in 1966.

CBR-Crude birthrate per 1,000 persons in the rural areas of each state; taken from STAT.

CDR-Crude death rate per I ,000 persons in the rural areas of each state; taken from STAT.

DEF-NDP deflator for India; taken from IMF line 99b, base 1990 = 100.

DEN-The density of each state's population, defined as the number of persons per square kilometer; derived as (AREA/POP)* 1 .000, and taken from the same sources as POP.

DENSQ-The square of DEN; taken from the same sources as POP.

DUM-Regional dummies for the four regions of India; the 19 states and the Union Territory of Delhi have been allocated as follows: East (Assam, Bihar, Manipur, Orissa, Tripura, West Bengal); North (Haryana, Himachal Pradesh, Jammu and Kashmir, Punjab, Uttar Pradesh, Delhi); South (Andhra Pradesh, Karnataka, Kerala, Tamil Nadu); West (Gujarat, Madhya Pradesh, Maharashu·a, Rajasthan).

FLIT -State-specific literacy rates, indicating the number of literate females per 1,000 females at each census year; taken from Government of India ( 1 983). Data for Assam for 1981 are not available, as the 1981 census was not conducted in that state because of civil disturbances. The 1961 data exclude that part of each state's female population aged between 0 and 4 years.

LIT-State-specific literacy rates, indicating the number of literates per 1,000 persons at each census year; taken from Government of India ( 1983). Data for



Table A I . Dara.for lndian Srares. 1961-91

Variable Year(s)

Logarithm of NDP" 1961 1971 1981 1991

Growth of NOPb 1961-91

Share of agriculture

1961-71 1971-81 1981-91

in state NDP< 1961

Share of manufacturing

1971 1981

in state NO?' 1961

Regional dummies East North South Wes1

Net migration rate"

Population density

Square of population density

1971 1981

1961-91 1961-71 1971-81 1981-91 1961 1971 1981

1961 1971 1981

Mean

7.918 8.066 8.187 8.458 0.0180 0.0148 0.0121 0.0270

0.534 0.525 0.440

0. 1 18 0. 1 13 0.134

0.300 0.300 0.200 0.200 0.0032 0.00 1 1 0.0014 0.0034

236.483 323.538 447.543

192.107£+03 424. 1 85E +03 947.21 1 E+03

Standard deviation

0.292 0.294 0.322 0.333 0.0066 0.0145 0.0151 0.01 1 1

0.128 0.141 0.127

0.057 0.056 0.076

0.458 0.458 0.400 0.400 0.0093 0.0048 0.0052 0.0072

369.031 565.251 864.243

678.712£+03 1590.375£ +03 3729.197£+03

Sources: Authors' calculations; see Appendix text for sources and definitions. " The logarithm of income is the logarithm of real (constant 1990 rupees) per

carita NDP in state i at time 1, In y,. The growth of income is the annual average growth rate of real (constant 1990

rupees) per capita NDP in state i between years 1 - Tand 1: ( l/7)ln (y,, ly;,-r). < The share of agriculture is the share of NDP derived from the agriculture,

forestry, and fishing sectors of state i at time 1, AGR;,. d The share of manufacturing i s the share of NDP derived from the manufactur

ing sector of state i at time r, MAN,. • The net migration rate is the annual average rate of net in-migration (on an

intercensal basis) as a share of the population of state i at the initial year of each intercensal period, MIG;,. Indian census years were 1961, 1971, 1981, and 1991.



Assam for 1981 are not available, as the 1981 census was not conducted in that state because of civil disturbances. The 1961 data exclude that pan of each state's population aged between 0 and 4 years.

MAN-The logarithm of the share of manufacturing in net state domestic product at factor cost at current prices; taken from ESOP. Additional details are as for AGR. In the growth regressions, MAN enters in logarithmic form.

M/G-Intercensal annual net migration as a share of the state's population in the initial year of the intercensal period; the net migration data are taken from the COl Migration Tables for 1971 (Series l , Part 11-D(i)) and 1981 (Series l , Part V. A and B). The migration data for the 1980s are an implied net immigration rate and are derived as the difference between the annual rate of population growth and the rate of natural increase (crude birthrates less crude death rates) and are taken from STAT for all states. Where census data were unavailable (Himachal Pradesh for 1971 and Assam for 1981) the implied net immigration rate was calculated, based on data taken from STAT.

NDP-State net domestic product at factor cost, in current Rs. million; taken from the same sources as PCNDP. Additional details are as for PCNDP.

PCNDP-Per capita state net domestic product at factor cost, in current rupees; taken from ESOP for 1961 tO 1980. and ES for 1981 to 1991. The figures for Delhi for 1982-84 are taken from BOOK. The figure for Himachal Pradesh for 1961 (based on its present boundary) is taken from La! ( 1985). The figure for Assam in 1961 is for its present boundaries (excludes Meghalaya. Nagaland, and Mizoram).

The figures for Punjab and Haryana for 1961 are both for their present boundaries. Figures for the following states (based on their present boundaries) and years are not available: Assam ( 1962-65, 1967-68), Haryana ( 1962-65), Himachal Pradesh ( 1962-67), and Punjab ( 1962-65).

POP-State population (in millions) at census dates; taken from STAT for 1961. 1971, and 1981, and from COl for 1991. As no census was carried out in Assam in 1981 , the official statistics interpolate its population using the 1971 and 1991 census results. Similarly, the 1991 census has yet to be conducted in Jammu and Kashmir; the figure in COl is an official projection.

TR-The grant component of transfers from the central government to state governments, in currelll Rs. million; taken from RBI. This measure comprises statutory grants-in-aid, grants on account of state and central plan schemes, and grants on account of centrally sponsored schemes.

URB-Urban share of state populations in each census year: taken from the same sources as POP.

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lMF Staff Papers Vol. 43. No. I (March 1996) © 1996 International Mone tary Fund

The Costs of Taxation and the

Marginal Efficiency Cost of Funds

JOEL SLEMROD and SHLOMO YITZHAKI*

It is argued that taxation causes deadweight losses-from substitution, evasion, and avoidance activities-and direct, administrative and compliance, costs. Some of these social costs tend to be discontinuous and/or nonconvex. Because most models of taxation ignore some components of the social costs of taxation, their conclusions cannot be considered all-encompassing. An alternative approach to policy evaluation is to rely on a marginal efficiency cost of funds rule that can indicate appropriate directions of reforms. The paper discusses the merits, applicability, and limitation of this rule, as well as its relationship to other concepts. [JEL H20, H21, H26]

ACASUAL SURVEY of the public finance literature reveals an interesting pattern. Until the mid-1 950s, almost all textbooks devoted a consider

able amount of space to the problems of tax administration, compliance, and enforcement.' Beginning in the 1 960s, though, administration and compliance issues almost disappeared from the literature, excluding that on developing countries.2 The interest of economists shifted to deadweight losses and formal normative models, known generally as optimal taxation. I n the early 1970s, before optimal taxation literature reached its peak,

* Joel Slemrod graduated from Harvard University. He is a Professor of Business Economics and Public Policy and Director of the Office of Tax Policy Research at the University of Michigan Business School. This paper was written while Shlomo Yitzhaki was a visiting scholar in the IMF's Fiscal Affairs Department. He is now Director of the Falk Institute for Economic Research in Israel and a Professor of Economics at Hebrew Universi ty of Jerusalem. He received his Ph.D. from Hebrew University. The authors thank Vito Tanzi, Howell Zee, and Louis Kaplow for many helpful discussions and comments; the FAD staff for providing a stimulating environment; and the FAD librarians for their help.

1 See, for example, Blough ( I 952); Shoup, Blough, and Newcomer ( 1937). 2 Musgrave ( 1959) does not mention the terms. Atkinson and Stiglitz ( 1980) do

mention tax administration as an important subject, but no analysis is offered. In contrast, Bird and Casanegra de Jantscher ( 1992) stress the importance of tax administration.

172


THE MARGINAL EFFICIENCY COST OF FUNDS 173

Allingham and Sandmo ( 1 972) marked a turning point with their choicebased model of tax evasion; a large theoretical and empirical literature followed. In the mid-1980s, the problem of tax administration regained some attention, but mainly in verbal as opposed to technical presentations.3 However, little effort has been made to integrate these aspects of tax analysis into a coherent normative framework.

We begin this integrative task in this paper. We argue that excess burdens, administrative costs, and compliance costs are all components of what we shall refer to as the social costs of taxation: the costs incurred by society in the process of transferring purchasing power from the taxpayers to the government. The social costs include the cost of enacting and administering the law, involuntary compliance cost, and the deadweight losses and expenditures caused by taxpayer activities undertaken to reduce the tax burden, such as evasion, avoidance, and switching to more lightly taxed, but otherwise less attractive, consumption. All these components of social cost should be included in a proper model of the costs of taxation, and they should affect the design of an optimal tax system. Hence, it is a bit puzzling that the interest of economists has tended to focus on only one or two components of the costs.4

One possible interpretation of this stylized fact is that the focus of the literature reflects the issues that economists are able to solve at a given time. Until the introduction of the concept of excess burden in the 1 960s, the public finance literature was mainly verbal and descriptive. Hence, the range of issues was not limited to what could be solved by tractable mathematical models. With the emergence of mathematical models, however, the literature began to emphasize those elements of the social cost that could be easily modeled and analyzed, that is, the excess burden. This led to the optimal taxation literature, i n which the main target was to find optimal rates of tax, and tax administration issues were set aside as technical matters that had no substantial bearing on the problem at hand.5

3 Rosen ( 1985) devotes four pages (pp. 3 19-22) to the subject. � Among the few exceptions are Cremer and Gahvari ( 1 994), Fortin and Lacroix

( 1994 ), Mayshar ( 1991 ), Sandmo ( 1981 ), Slemrod ( 1990 and 1994 ), and Usher ( 1991) .

s Administrative costs of taxation are fundamentally different from market transaction costs. In a market transaction, both parties willingly engage in the transaction. Hence, in a market transaction, the demand price exceeds the price received by the seller by the amount of transaction costs. Such costs can be viewed as being embodied in the utility or production functions, and they do not affect the stability of the equilibrium. In the case of taxation, one party may not be interested in participating in the deal and one role of the administration is to force the other party to part.icipate. Since one partner may be trying to escape from the deal, tax transactions, unlike market transactions, are not stable. The administrator's ability to


174 JOEL SLEMROD and SHLOMO YITZHAKI

The pathbreaking paper by Allingham and Sandmo ( 1972) added another dimension that could be analyzed by mathematical models-the issue of tax evasion. Following the Allingham and Sandmo paper, hundreds of papers dealing with different aspects of evasion, most of them theoretical, were published.6 Relatively fewer books and papers have attempted to estimate empirically the magnitude and determinanrs of evasion.

The realization that tax evasion is a serious problem faced by many industrial countries has led economists to raise the issue of tax administration; the mere fact that tax evasion exists often implies administrative inability to enforce tax laws. However, relatively little analytical work incorporating tax administration has been done, mainly because administrative issues are hard to analyze with continuous differentiable functions and, therefore, they require complex modeling.

In this paper, we argue that the problem of designing a tax system is much broader than that presented in the optimal taxation problem, although the target is still to maximize social welfare or, alternatively, to minimize social costs subject to given targets. The most important component missing from models of optimal taxation is the administration of the tax law, which includes not only the process by which tax bases are determined, but also the tax process itself-the procedure that determines and transfers tax revenue from the individuals to the government.

Enacting a tax law does not by itself raise revenue. It is the enforcement of the tax law by the administration that transfers the tax from the individuals to the government. This was already well understood 50 years ago. Note the following quote from Blough ( ( 1952), p. 146):

It is tax policy in action, not simply the wording of the statute, that determines how much the taxpayer must pay, and the effects of the payment. Knowledge of the statute is only a start in knowing a tax system. The interpretations placed on language by administrators and courts, the simplicity and understandability of tax forms, the competence and completeness of audit, the vigor and impartiality of enforcement, and the promptness and finality of action all influence the amount of revenue collected. the distribution of the tax load, and the economic effects of the tax. One expert has even declared that in developing countries "tax adminis

tration is tax policy" (Casanegra de Jantscher ( 1990), p. 1 79). Although one may judge such a statement to be too extreme, most public finance experts

gather information and exert his power on the taxpayer depends on the amount of resources budgeted for the administrator's activities. The more public the information, the lower the administrative costs needed to retrieve it. One of the targets of compliance costs is to force parties that are engaged in market transactions to reveal the information to the tax authorities. This would reduce administrative costs.

6 See the survey by Cowell ( 1990), and Tanzi and Shome ( 1993).



would probably agree that the way the laws and regulations are administered affects the economic implications of the tax laws.7 Therefore, administrative issues should not be ignored.

The aim of this paper is to present the social cost of taxation in a broad context that includes administration, evasion, and optimal taxation issues so that one can fit the various components of the tax problem into one framework. One theme of the paper is that the problem of taxation may be too complicated to be solved in the generaJ case. so that one has to rely on models that cover only certain parts of the problem. But if an essential part of the problem is overlooked, partial models may give incorrect answers. We explore an alternative approach that is limited to identifying desirable marginal changes, without a claim of optimality. The less ambitious objective enables us to use the concept of the marginal efficiency cost of funds. This methodology is less demanding than alternative methods in terms of data, as its application revolves around forecasts of marginal tax revenue.

The paper proceeds as follows. In Section I we identify the major actors of the tax system, and in Section I I we discuss the costs associated with each actor. In Section III we derive the marginal efficiency cost of funds concept in a simpJe model. In Section IV we extend the analysis to include distributional issues, and in Section V we discuss the problems that arise in analyzing nonmarginal changes. Some conclusions are offered in Section VI.

I. The Cast of Characters

We begin this task by laying out a stylized framework of the important actors in a tax system. The simplest framework has a social planner and two sets of agents-the tax administrators and the taxpayers. The social planner, which encompasses the legislative branch, the spending branch, and the judicial system, aims to maximize social welfare. The tax administrator acts as an agent on behalf of the social planner, while the taxpayers pay taxes.8 It is important to distinguish the tax administrator from the social planner because the tax administrator is only an agent, and the planner must therefore take into account the possibility of self-serving behavior by the administrator, including rent seeking, corruption, abuse of power, and disloyalty. Hence, it must limit the power delegated to the administrator, for example by requiring a lengthy and detailed prosecution process, including tax courts and provisions to allow the taxpayer to appeal. These hurdles

7 Note that whether a tax is feasible is determined only by administrative issues. 8 One way to interpret tax withholding is to view it as drafting some taxpayers

(e.g., employe rs) into the tax administration. They are not empowered to act fully as tax administrators but this kind of hierarchy is typical of any bureaucracy.


176 JOEL SLEMROD and SHLOMO YlTZHAKI

increase the administrative cost (see Virmani ( 1987), Chander and Wilde ( 1 992), and Tanzi ( 1994) on corruption)Y

The Social Planner

For our purposes, the only objective of the social planner is to raise a given amount of revenue while keeping the social cost of raising revenue at a minimum level. Provision of public goods and any other services provided will be ignored. Also ignored are the motives of the social planner in governing, which could be the maximization of a social welfare function, the maximization of the tax revenue (Levi ( 1 988)), rent seeking, or acting " . . . like a discriminating monopolist, separating each group of constituents and devising property rights for each so as to maximize state revenue" (North ( 1981 ) , p. 23). All those targets are consistent with the aim of keeping the social cost of taxation as low as possible. At this stage, we do not consider other targets of (or constraints on) taxation, such as horizontal equity and redistribution of income. We will return to these issues in Section IV. However, some equity issues could be perceived as enhancing cost minimization, and therefore could be included in the analysis, for example, because it is easier to collect taxes when they are viewed by the taxpayers as fair, or when the tax law is simple and unambiguous. 10 In this case, the value attached to fairness is the reduction in cost that it causes.

9 There are many instances in which one has to resort to a wider classification of actors. For example, the assumption of one social planner implicitly assumes that the social planner is interested in collecting the tax revenue. But whenever the planner is composed of several agents, as is the case in a democratic society, they may hold different opinions or represent different interest groups. In order to reach a decision about the tax system, compromises must be made. The result may be a blurred tax law that is hard to administer or to comply with. We refrain from extending the problem of taxation in this direction, not because it is an unimportant issue, but because it is difficult to analyze a tax law with a social planner who, in effect, undermines his own proposals.

Another case that is not captured in this framework is one in which the social planner, that is, the government itself, undermines the implementation and administration of the tax law. When the government consists of several branches, if some of the spending branches are relatively strong, they may use their influence to increase their budget by allowing contractors to evade taxes. Such a situation undermines the ability of the tax administrator to collect taxes. As we will argue later, these kinds of issues, which are country specific, are difficult to model. On the other hand, they are captured by the marginal efficiency cost of funds.

10 The term "simple" is not well defined. Slemrod (( 1985), p. 7 1 ) defines complexity in terms of the amount of resources needed to operate the law. Blough (( 1952), pp. 430-1 ) makes a direct attempt to define i t by arguing:

Tax simplification has been a loudly demanded objective. A good deal of discussion of simplification reflects a misunderstanding of what makes a tax complex. Emphasis is often placed on cumbersome and complicated language. The most important quality of a well-drafted statute is that it shall not be open to



Since the tax administrator and the social planner are different entities, the social planner must set not only the tax law, but also the rules of the game being played by the administrator and the taxpayers. It determines the rights and the duties of each party, including possibly the duties of the taxpayers to collect information or taxes on behalf of the tax administrator.

The Tax Administrator

Roy Blough (( 1952), pp. 388-9) defines the target of the administration as "to collect every dollar due the government-and no more." He continues: "In tax administration the problem of equity or equal treatment is whether everyone is being required to pay the amount of tax due under the law . . . . But a more important source of inequity is the failure of administrators to collect taxes from those who owe them. Such taxpayers receive a financial subsidy, while the tax loads of other taxpayers must be increased to make up the resulting revenue deficiency."

Definitions of the target of tax administration used in modern analytical models focus almost entirely on revenue maximization. (See, for example, Reinganum and Wilde ( 1 985).) Such a target, if taken seriously, implies ignoring overpayment by taxpayers and any other activity whose objective is not to raise short-term revenue. On the other hand, tax administrations, like any other bureaucracy, are not subject to competition and can set their own agendas, which have nothing to do with the intentions of the social planner.1 1 Two issues arise here: what should be the targets of tax administration, and how does one devise a framework so that the administration adheres to those targets, which include both cost minimization and equity?12

The first target can be defined quantitatively, and requires simply that administrative effort, like any other economic activity, be subject to cost considerations. The other target, equity, can be interpreted as pursuing jus-

more than one interpretation. The ordinary taxpayer does not need to read the tax statute. More simple statements are available for his use. The language of the law is for administrators and courts. Wherever possible, the language should be simple rather than complex, but the matter is relatively unimportant. Lack of clarity, on the other hand, is of very great importance. Simple language, which proves to be ambiguous, may result in great complexity and uncertainty. 1 1 Note the following statement: "Unfortunately. tax administrations do not func

tion optimally. In some cases, they can be so inefficient as to distort completely the intention expressed by the tax laws" (Tanzi and Pellechio ( 1995), p. 2). See also Bird (1989).

12 Tanzi and Pellechio ( 1995) differentiate between "effectiveness" and "cost minimization," where effectiveness is defined as attaining a high level of compliance among citizens and cost minimization for a given revenue is identical to revenue maximization for a given cost. Interpreting "high'' as "equal" would make their target similar to the targets referred to in this paper.


1 7 8 JOEL SLEMROD and SHLOMO YITZHAKI

tice regardless of its cost implications. We return in Section IV to the issue of how to combine justice and efficiency in an analytical model.13

The Taxpayer

Taxpayers can minimize the impact of the tax system by engaging in three kinds of activities, all of which involve a substitution effect: 14

l . A shift to other activities. Taxation makes the tax base more expensive, so one way to avoid its impact is to divert the derivation of utility to other, cheaper sources. The importance of this factor depends on the substitutability and/or complementarity between the tax base and the untaxed commodities. The distortion that results from this activity is measured by the standard deadweight loss.

2. The taxpayer may try to avoid the tax by investing time and other resources into finding legal ways not to pay the tax. This activity is usually referred to as avoidance, and is considered a component of compliance costs. However, as will be argued later, one has to differentiate between two kinds of compliance costs-those that are imposed on the taxpayer by the social planner or the tax administrator, and those that the taxpayer voluntarily makes in order to reduce the tax paid. I n this paper, the term avoidance will be restricted to voluntary compliance costs that are intended to reduce the tax paid.

3. The taxpayer may evade tax liability illegally. By imposing a tax with evasion opportunities, the relative price of being honest is increased. The substitution effect that is causing evasion is the change in relative price of honesty and the increase in the return to 1isk bearing through tax evasion.

All in all, we have encountered five components of the cost of taxation: administrative costs-the cost of establishing and/or maintaining a tax administration; compliance costs-the costs imposed on the taxpayer to comply with the law; the regular deadweight loss-the inefficiency caused by the reallocation of activities by taxpayers who switch to nontaxed activities; the excess burden of tax evasion-the risk borne by taxpayers who are evading; and avoidance costs-the cost incurred by a taxpayer who searches for legal means to reduce tax liability.

In some cases the classification of a particular activity into one category of cost or another is arbitrary, and may depend on one's interpretation of the

13 One can argue thai activities that are directed toward equity establish confidence between taxpayers and administration. which may lead to a long-run increase in revenue.

14 We consider ·a one-period model. In a multiperiod model one would have accounted for such taxpayer behavior as deferral of taxable income to future periods.


THE MARGINAL EFFICIENCY COST OF FUNDS 1 79

agents' intentions. Taxpayers can spend money to conceal the tax base or they can spend it to comply; similarly, they may try to avoid taxes but end up evading them. Because of this overlap, some investigators use the term "aversion" to refer to both avoidance and evasion (Cross and Shaw ( 1 982)). The separation of the costs borne directly by taxpayers into avoidance costs and involuntary com pi iance costs requires know ledge of the intentions of the taxpayers. However, as demonstrated below, this classification is important in avoiding double counting of social costs. These distinctions present a challenge when constructing optimal models of a tax system.

II. The Components of the Cost of Taxation: Properties and Modeling Problems

In this section we describe the five components of the social cost of taxation and basic problems in modeling systems.

Administrative Costs

Tax administrations deal, among other things, with information gathering. But this is a difficult element to model because information varies in quality. There is a qualitative difference between an auditor "knowing'' that a given taxpayer is evading and having sufficient evidence to sustain a court finding to that effect. Also, the cost of gathering information depends on how accessible the information is, and whether it can be easily hidden. The advantages of taxing a market transaction relative to taxing an activity of the individual such as self-consumption result from several properties. First, in any market transaction there are two parties with conflicting interests. Hence, any transaction has the potential of being reported to the authorities by one unsatisfied party. A second property is that the more documented the transaction, the lower the cost of gathering information on it. For this reason it is easier to tax a transaction that involves a large company, which needs the documentation for its own purposes, than to tax a small business, which may not require the same level of documentation. Administrative cost may also be a function of the physical size and the mobility of the tax base {it is harder to tax diamonds than windows), whether there is a registration of the tax base (e.g., owners of cars; holders of driver's licenses), the number of taxpayer units, and information sharing with other agencies. 15 It is also an increasing function of the complexity and lack of clarity of the tax law.

15 A good description of the properties of administrative cost can be found in Shoup. Blough. and Newcomer ( 1937), pp. 337-51 .



Administrative costs possess two additional properties that complicate the modeling of tax administration issues: they tend to be discontinuous and to have decreasing average costs with respect to the tax rate. To see the first property, consider two commodity tax rates, denoted by 11 and r2• If t1 = t2, then only the total sales of the two commodities need be reported and monitored. If, however, the two rates differ even slightly, then the sales of the two commodities must be reported separately, doubling the required flow of information. There are decreasing average costs because the cost of inspecting a tax base does not depend on the tax rate (except to the extent that people are more inclined to cheat with a higher tax rate). Hence, a higher tax rate reduces the administrative cost per dollar of revenue collected (see Sandford ( 1973)). Administrative cost may also be a function of the combination of taxes employed and their rates, because the collection of information concerning one tax may facilitate the collection of another tax (e.g., inspection of value-added tax (VAT) receipts may aid the collection of income tax). Because of these properties of administrative costs, it is not surprising that economic modeling, which more easily handles continuous and differentiable variables, tends to be scarce in this area.

Compliance Costs

As far as we know, there is only one formal normative model that addresses compliance costs (Mayshar (1991)), although one can find estimates of its magnitude (Sandford ( 1973); Sandford, Godwin, and Hardwick (1989); Slernrod and Sorum ( 1 984 ); Blumenthal and Slernrod ( 1 992)). As an example of the modeling difficulties this topic poses, consider the following problem: when is it optimal to delegate to employers the authority to collect taxes and convey information about employees, thus requiring the administration to audit both the taxpayer agent and the taxpayer himself, and when is it optimal to deal only with the employee? Clearly, given that the employer already has the necessary information, it would save administrative costs to require him to pass it along to the tax· administrator. This might also reduce total social costs if the cost of gathering information by the administration is higher than the increase in cost caused by imposing a two-stage gathering system. J6

However, the potential efficiency of involving taxpayers in the administrative process must be tempered with a practical consideration. Adminis-

16 Note that a withholding system requires two information gathering systems and creates an opportunity for the withholding agency to evade the taxes it collects (Yaniv ( 1988 and 1992)). In a period of rapid inflation, the gain to the agenL from withholding may exceed the cost.


THE MARGINAL EFFICIENCY COST OF FUNDS 1 8 1

trative costs must pass through a budgeting process, while compliance costs are hidden. Hence, there may be a tendency to view a decrease in administrative cost accompanied by an equal (or greater) increase in compliance costs as a decrease i n social cost, because it results in a decrease in government expenditures. We return to this point later.

Regular Deadweight Loss

Any tax that creates a wedge between the relative prices that any two taxpayers face entails an efficiency loss. The deadweight loss created is an increasing and continuous function of the tax rates, but it is also a function of the combination of taxes employed. If one abandons the assumption that the set of taxed commodities is given, one cannot assume that the deadweight loss is a continuous function.

Excess Burden of Tax Evasion

In the Allingham and Sandmo model of a taxpayer who maximizes his expected utility, tax evasion occurs only if the taxpayer expects to increase his expected income by evading taxes, including the expected fines that he would have to pay if he were caught. Hence, a taxpayer who evades taxes increases both his exposure to risk and his expected income. This additional exposure to risk is a deadweight loss to society. In principle, the taxpayer could be better off under an agreement whereby the taxpayer pays at least as much as the government currently collects, while the government ceases to audit. Assuming a risk-neutral government, the excess burden of tax evasion is equal to the risk premium that the taxpayer would be ready to pay in order to eliminate the exposure to risk (Yitzhaki ( 1 987)). Depending on the other assumptions about the probability of detection, the penalty structure, and risk aversion, the excess burden of evasion may be a continuous function that increases with the tax rates.

A voidance Costs

We distinguish between compliance costs, which are imposed on the taxpayer by the tax agency, and avoidance costs, which result from voluntary action carried out by taxpayers whose intention is to reduce tax payments. Clearly, any activity to reduce the tax is a pure loss from the social point of view, and therefore creates a deadweight loss. In practice it is hard to distinguish between avoidance and compliance costs because the distinction



between the two depends on the intentions of the taxpayer. It will be made evident later in the paper that it is important to distinguish who controls each activity. The taxpayer controls activities that produce excess burden (including avoidance), while the tax administrator controls compliance and administrative costs.

Basic Problems in Modeling Tax Systems

Slemrod ( 1990) distinguishes between the theory of optimal taxation and optimal tax systems. Optimal taxation is usually restricted to the optimal setting of a given set of tax rates, ignoring administrative costs, compliance costs, avoidance, and evasion. When optimizing tax systems one has to consider all the elements of the problem. Clearly, any general solution that ignores components of the problem is doomed to fai l if the omitted part of the problem is an important issue. For example, minimizing the classical excess burden requires (in the general case) unequal commodity tax rates, and the finer the classification of commodities, the lower the excess burden. But this solution ignores the administrative costs of differential commodity taxes. 17

Another example concerns normative models of enforcement of tax evasion, which, with a few exceptions, imply that it is optimal to impose a penalty severe enough to abolish all evasion. 1s The main idea is simple. A rational taxpayer will never evade if the costs to him are too high, and tbe tax administrator can make the private cost as high as he wishes by increasing the penalty to infinity. l n this case no one will evade and it will be possible to reduce costly monitoring almost to zero. But this kind of model ignores the possibility of a corrupt tax administrator who abuses the system or, alternatively, harshly punishes someone who commits an honest mistake. The harsher the penalty, the more damage that can be inflicted by a corrupt administrator or, in the case of an honest mistake, the more cruel and unfair the system is. Hence, the harsher the penalty, the more detailed and cautious the prosecution process should be, although this may increase its administrative costs. In the absence of modeling the interaction between the penalty rate and administrative costs, analytical models usually assume a ceiling on the penalty rate.

A final example is that optimal tax models, which ignore administrative costs, if taken literally, generally imply that lump-sum taxation is the first-

17 For additional examples, see Tanzi ( 1992). 18 For example, Christiansen ( 1980) argues that a large fine and a small chance

of detection are the most powerful deterrent in the case of tax evasion. This result is due to Becker ( 1968).



best solution. However, in real life lump-sum taxes rarely exist and when they do, they are for the most part connected with military service (i.e., the draft, reserve duty, national service): an exception is jury duty. 19 The main reason that lump-sum taxes do not exist is the cost of their administration. The problem in enforcing a lump-sum tax is how to proceed if the taxpayer declares he is unable to pay it. If the administrator has to prove that the taxpayer can afford to pay the tax, it is not a lump-sum tax. The advantage of taxing a market transaction is that the transaction itself reveals an indication of both the ability to pay the tax and the liquidity that enables the taxpayer to pay without excessive damage.

lll. Marginal Efficiency Cost of Funds

Listing the basic components of social costs in a taxation problem, together with their unfriendly nature, is a reminder that the quest for an optimal tax system is far from being complete. No model can both cover all the important issues and provide important insights. Nor can we provide such a model here. Instead, in what follows, we offer a tractable methodology that can evaluate marginal changes in tax systems and take account of all five components of the cost of tax systems. The methodology is based on the concept of the marginal cost of public funds.

Marginal Efficiency Cost of Funds with Only Regular Deadweight Loss

The concept of marginal cost of public funds that we will be using is based on Mayshar ( 1990) and Wildasin ( 1984), as refined by Mayshar and Yitzhaki ( 1995) to distinguish between distributional issues and efficiency issues. We first discuss the concept in the absence of administrative costs, evasion, or avoidance, and extend the application to these issues in later sections. We will show that being able to forecast the revenue from each tax allows us to calculate the relevant marginal excess burdens. Furthermore, knowing these marginal excess burdens allows us to identify a revenue neutral marginal change that will improve the tax system by lowering its total social cost.

Consider a representative taxpayer with a well-behaved utility function u( ), and an observed allocation of its budget that satisfies y = L; q; X;, where

19 See Hahn ( 1973) for existence of lump-sum taxes during the U.S. civi I war.



q; is the price of the ith commodity the household faces, X; is the quantity consumed, and y is given income.20 Assume that the vector of producers' prices, p, is given and that t; = q; - p; are the tax rates. Then, the marginal burden of a marginal tax reform on the household is2 1

MB = 2:; X; dq;. ( I )

The marginal burden i s the income equivalent of the effect of the reform. Equation ( 1 ) shows that MB is a function of the quantities (tax bases) consumed and the changes in prices.

Tax revenue is

R(t, p, y) = 2-, t;X; ( p + t, y), (2)

where X; (q, y) is the demand for commodity i, y is income, and consumer prices are q = p + t, where t is a vector of specific taxes. Revenue neutrality requires that

MR = 2.,MR;dt; = 0, (3)

where MR; = aR/at; is the change in total tax revenue due to a small change in the tax rate on commodity i.

It will turn out to be convenient to work with dollars of revenues rather than with tax parameters. Denote by 8, the change, measured in dollars of tax revenue, that results from a change i n the tax rate on commodity i, dt;, so that

(4)

Then the marginal tax reform, dt, can also be characterized by the vector of tax receipts 8, and the change in tax revenue would then be MR = 2.,8,.

Substituting expression (4) into ( I ), while taking into account that dt; = dq;, yields

MB = 2., (X;/MR;) 8,, (5)

subject to the constraint 2.;8; = 0.

20 The "commodities" may include factors of production such as labor. In this case the quantity of the commodity is non positive.

21 One can derive this relationship under two alternative sets of assumptions: ( I ) That the taxpayer is a utility maximizer and by Roy's identity ov( ) I at; =

- X. X, where vis the indirect utility function and X. is the marginal utility of income. The marginal burden is the income equivalent of the change caused by the reform.

(2) No optimization is carried out by the taxpayer and we are only interested in a Slutsky compensation to the household. That is, the question asked is what compensation would enable the taxpayer to continue to consume the basket he consumed before the reform.



The term in the parentheses is the marginal efficiency cost of public funds (henceforth MECF),22 interpreted as the cost to the society of increasing tax revenue by a dollar, through a change i n the ith tax rate or other fiscal instrument. 23

Let us illustrate the implications of equation (5) by concentrating on a revenue neutral tax reform that involves only two taxes, i n which case, because o1 = -o2,

As long as MECF1 does not equal MECF2, a tax reform can reduce the burden of taxation and therefore increase the welfare of the representative taxpayer. If MECF2 > MECF�o the reform must feature 01 > 0, that is shifting revenue toward t1; if MECF2 < MECF1, a welfare-improving reform should decrease reliance on t1 to raise revenue. Thus, promising directions for tax reform are indicated by comparing the MECFs. To estimate the MECFs, one has to be able to estimate only two parameters for each instrumentthe marginal change in revenue, MR;, and the tax base, X;, equal to the expected change in tax revenue if the tax base is inelastic.24 X; is the burden imposed on the taxpayer at the margin.

Note that the above interpretation is not limited to reforms involving tax rates. One may define the marginal cost of funds with respect to any parameter of the tax system (e.g., income brackets, exemption levels, penalties for tax evasion, etc.). Nor does its application rely on an assumption that tax policy has been set optimally. The only assumption is that the taxpayer is a utility maximizer.

Having established the relevance of the MECF in a simple setting, we next discuss how it can be extended to other issues involving evasion and avoidance.

Extensions of the Marginal Efficiency Cost of Public Funds to Include Other Cost Components

The concept of marginal efficiency cost of public funds presented above was derived in a model that ignored administrative and compliance costs as

22 The term MECF is slightly different from marginal cost of funds because efficiency considerations are separated from distributional issues. We will return to this poim later. 23 This cost does not net out any benefits that arise because of the expenditure of the funds collected.

24 In many practical estimations, X; is also used as an estimate of MR, (see Sutherland (1991 )). The imerpretation in those cases is that all MECFs are assumed to equal one or, alternatively, that all taxes are lump-sum taxes.



well as evasion and avoidance. It can, however, be applied and used in a tax system framework. To see that, let us start with an intuitive explanation of the concept.

Recall that the potential change in tax revenue (assuming an inelastic base) is X,. but, because of taxpayers' response, the government collects only MR,.. We can divide the potential tax X,. into two components as follows:

X; = (X,. - MR,-) + MR,-, (7)

where M R,. dollars are collected and (X,. - M R;) "leaks., outside the tax system. The critical question is how to evaluate. from a social point of view, the leaked dollars. To do this one must ask how much a taxpayer is ready to expend (on the margin) to save a dollar of taxes or, alternatively, how much utility loss he is willing to suffer to save a dollar of taxes. The answer is that a rational taxpayer will be ready to sacrifice up to, but no more than, one dollar in order to save a dollar of taxes. Hence, on the margin the private cost, which is equal to "leaked" dollars multiplied by their cost per dollar, is X,. - MR,.. Hence, the collection of MR,. dollars results in a loss of (X; - MR,.) to the taxpayer over and above the taxes paid. If we assume that the private marginal cost of the leaked tax revenue is also a social cost, then the cost to society of transferring a dollar to the government is (X, - MR,.)IMR,. = X;IMR, - l . The total marginal cost to the individual taxpayer, including the taxes paid, is X;IMR,..

Consider now a taxpayer who also has the option to .evade part of the additional tax. On the margin, he would be ready to sacrifice the value of one dollar (in additional risk bearing due to evasion and/or due to substitution to cheaper but less rewarding activities) in order to save a dollar of taxes. Hence, we do not have to know whether the ''leak" was through evasion or substitution to evaluate the costs to society.

The same rule applies to avoidance activity and, in fact, to any activity under taxpayer control, including substitution and evasion. Therefore, all one needs to know is the potential tax (i.e., assuming an inelastic tax base) that will be collected from a change of a parameter of the tax system, and the actual change (taking into account all behavioral responses) in order to evaluate the marginal efficiency cost of raising revenue.

In constructing the MECF we have made use of two critical assumptions that deserve further attention. The first of these is that the taxpayer is not constrained. (That is. he is not at a corner solution. An example of such a taxpayer is one who is unable to evade additional taxes simply because he has evaded all the tax due.) If there are corner solutions, it is not appropriate to presume that at the margin the taxpayer is giving up a dollar's worth of utility to save a dollar of taxes; thus the "leak" in tax revenue may have



a private cost that is less than the revenue cost. As an example, consider the MECF of raising the tax rate on labor income in a situation where. in an economy with two taxpayers, one taxpayer reports no labor income at all and, at that corner, is bearing risk valued at 20 cents to evade one dollar; the other taxpayer, with identical labor income, reports all of it. Assuming no substitution or avoidance response and zero compliance and administrative costs, the economy MECF with respect to an increased tax rate is 1 .2, even though the potential tax base is exactly twice the revenue collected.

To take account of the possibility of the taxpayer being at such corner solutions, we generalize the expression for the MECF by introducing a parameter -y, the marginal value to the taxpayer of a dollar of tax saved is multiplied by X; - MR;, the leaked revenue. Introducing 'Y reduces the simplicity of the MECF expression because its value varies depending on the situation under study. Empirical investigation is required to determine whether it is reasonable to assume that 'Y = I .

The second critical assumption i s that the cost borne by taxpayers in the process of reducing tax liability is equivalent to the social cost. This is certainly true in many situations, such as when the private cost takes the form of a distorted consumption basket. But in some cases the private cost is not identical to the social cost. A straightforward example is when the taxpayer hires an accountant to search for legal reductions in taxable income, and these costs are deductible from taxable income. In this case the social cost is 1/(1 - L) higher than the private cost, where t is the taxpayer's marginal tax rate.

Fines (but not imprisonment) for tax evasion bring up a more subtle example of divergence between the private and social costs of tax-reducing activities. The possibility of a fine for detected tax evasion is certainly viewed as a cost by the taxpayer, but from the society's point of view it is merely a transfer. Thus the leak of revenue resulting from evasion has a lower social value than the private value: in the extended MECF below, we subsume this issue into the 'Y parameter. Note that if the fine itself is the ith policy instrument, this argument implies that its MECF could be close to zero, and almost certainly less than one, making an increase in fines look like an attractive policy option indeed. As discussed above, there are reasons unrelated to cost minimization for which increasing fines for tax evasion without limit is not desirable.25

We turn now to application of the MECF rule to administrative and compliance issues. Earlier normative models of taxation that address adminis-

�5 This result is due to the fact that we did not distinguish between the administrator and the social planner. Raising fines increases the possibility of corruption on behalf of the administrator.


188 JOEL SLEMROD and SHLOMO YITZHAKJ

trative costs have formed the problem as follows.26 There are two ways to raise revenue. One way is to increase a set of tax rates, and by so doing to increase excess burden. The alternative involves increasing administrative costs (e.g., by broadening the tax base as in Yitzhaki ( 1 979), or by increasing the probability of a tax audit, as in Slemrod and Yitzhaki ( 1 987)). On the margin, it is optimal to equalize the marginal costs of raising revenue under the two alternatives. Hence, in order to incorporate administrative cost all we have to do is to define the costs of taxation as deadweight loss plus administrative costs. At an optimum, the MECF of each tax rate should be equal to the MECF of administrative improvements that raise revenue. In calculating the MECF of administrative improvement, it is important to account for the fact that these expenses come out of funds that were presumably raised with tax instruments that have a MECF in excess of one.H In other words, administrative improvements that raise net revenue decrease the excess burden; hence, on the margin and for given revenue, the saving in excess burden should be equal to the increase in administrative costs. In this way, the MECF criterion can be applied to tax administration, too.2s

Compliance costs are additional costs imposed on the taxpayer. Therefore, they should be added to the burden imposed on the taxpayer. They serve as a substitute to administrative costs, but the expenses are borne directly by the taxpayer rather than through the government budget.

Having described all the components of the MECF, we have to define what are the relevant MECFs for society. Clearly, one has to sum the excess burden of the tax to compliance and administrative costs to reach the total cost to society. But should we sum the marginal costs of substitution, compliance, and administration to come up with the social marginal costs to society of raising revenue? First, note that if optimal policy prevails, all policy instruments yield the same MECF, and hence it is sufficient to calculate one MECF to know them all. In reality, the MECF of different instruments

26 Most of the models that incorporate administrative costs restrict the analysis to a subset of the types of cost related to taxation. For example, Yitzhaki ( 1979) and Wilson ( 1989) deal with excess burden and administrative cost, while Sandmo ( 1981 ), Slemrod and Yitzhaki ( 1987), and Mayshar ( 1991) deal with evasion, administrative costs, and labor supply. The main drawback of the first type of model is that it relies on specific utility functions (Cobb-Douglas in Yitzhaki ( 1 979); CES utility in Wilson ( 1989)) to overcome the discontinuity created by having different commodities. The latter set of models do not allow for more than one tax in the system. 27 This means that it is not optimal for a tax administration to behave like a tax farmer, that is, setting marginal revenue equal to marginal costs, ignoring the fact that it spends tax dollars. Hence, privatization of tax collection may lead to overenforcement. See Slemrod and Yitzhaki ( 1987) and Mayshar ( 1991 ).

28 Yitzhaki and Yakneen ( 1989) use the term "the shadow price of a tax inspector," which is the revenue collected by adding another tax inspector. Note that the MECF is actually the reciprocal of the shadow price of a tax inspector.



can differ, and it is feasible to raise revenue utilizing only those policy instruments with a relatively low MECF.29 In either case. one should not add the MECF of administrative costs to the MECF of the other costs (excess burden and compliance costs) to get the overall MECF, because administrative costs are "factors of production" in the process of taxation and their role is to reduce the excess burden of the tax system.

The revised MECF that includes all components is

MECF; = y(X; - MR; ) + C; + MR;

, MR; - A;

(8)

where -y is the value that the taxpayer is sacrificing at the margin in order to save a dollar of tax, C; is the marginal compliance cost associated with the ith instrument, A; is the marginal administrative cost, and M R; - A; is the net revenue collected at the margin. The intuitive interpretation of the expression is the same as before, with some qualifications. The potential tax is X;. X; - MR; is Ieake� at a social cost of -y per dollar, MR; is collected by the government, and C, is the additional involuntary compliance cost. Hence, the total burden on society is the sum of those components. Of the MR; collected by the government, A; is spent on administration, leaving MR; - A; in the coffers. The MECF is the burden on society divided by what is collected after subtracting the cost of doing business. This yields the marginal costs of a dollar collected.

Because in equation (8) C; is added in the numerator and A; is subtracted in the denominator, the key conceptual difference between the two is explicit-only the latter uses revenue raised from taxpayers. To illustrate this difference, consider that a tax for which C; = MR, (with A; and X; -MR; = 0) might conceivably be part of an optimal tax regime (if the MECFs of other instruments exceed 2), it would never be optimal to have A; = MR;, for at the margin this instrument has social cost but raises no revenue.30

IV. Distributional Issues

In this section we introduce distributional considerations into the analysis. Distributional issues can be divided into two separate issues: vertical equity and horizontal equity. Vertical equity deals with the treatment of

�9 MECFs may differ even in an optimal taxation model if one includes other targets in addition to cost minimization. We return to this point in the next section.

30 To formally see the point, assume that MECF > 1 and ask what would be the changes in compliance costs and administrative costs that will keep MECF constant. It is easy to see that - dC,IdA, = MECF, which means that C; should increase more than A, decreases while keeping MECF constant.


190 JOEL SLEMROD and SHLOMO YlTZHAKI

individuals that are identical in all properties except income. Horizontal equity deals with the treatment of individuals with different characteristics.

Vertical Equity

The MECF concept ignores differences in the distributional patterns of different taxes. When distribution matters one cannot continue to treat all dollars alike, but instead each dollar of potential marginal revenue (whether collected or leaked) should be weighted by the social evaluation of the marginal utility of income of the taxpayers. l n other words, one should take into account what Feldstei n ( 1972) calls the distributional characteristics of the burden on the taxpayers. There are three different approaches to incorporating distributional concerns: an explicit assumption of a social welfare function; an implicit assumption of a social welfare function; and an assumption of a broad class of social welfare functions.

Using an explicit social welfare function, one should weight the X (the burden on the taxpayer) by the social evaluation of the marginal utility of income. For example, using an Atkinson-type (Atkinson ( 1970)) social welfare function implies that the marginal burden is weighted by the marginal utility of income Y�r-•, so that instead of X/MR; as the basic expression of the MECF (in the simple model) we get the marginal cost of funds (MCF) as

I., xi/, y;;• I., y;;•

MR; MCFj = (9)

where xu, is the marginal burden of the tax on taxpayer h. Optimal tax theory implies that one should equate all the MCF;.31 For a sophisticated application of this approach, see Ahmad and Stern ( 1984 and 1991 ).

The main problem with assuming a specific social welfare function is that it is difficult to defend such a strong assumption. Hence, Ahmad and Stern consider whether a reform is suitable under a range of social welfare functions. An alternative approach is based on inequality measures (or a poverty index) such as the Gini coefficient. Then the investigator implicitly assumes a social welfare function. In some cases one can recover the (implicit) social evaluation of the marginal utility of income. Those marginal utilities can be used to estimate a weighted income elasticity that summarizes the distributional characteristics of the tax base. For example, Yitzhaki ( 1994) uses IJ( I - G), where IJ is the mean income (e.g., consumption per capita) and

31 Note that we use MCF; rather than MECF; when we take into account both distributional and efficiency issues.


THE MARGINAL EFFICIENCY COST OF FUNDS 1 9 1

C i s the Gini index of income inequality, as a social welfare function. In this case. MCF1 becomes

MCF, = X;( l - ll;C)

= MECF ( l - 11-C) I MR; I I , (10)

where TJ; is the Gini income elasticity of the tax base.32 l n essence, equation ( I 0) adjusts the MECF by the appropriate income elasticity to take distributional issues into account. Note that, other things being equal, the higher the income elasticity of the tax base, the lower will be the MCF of raising a given amount of revenue. The attractiveness of this kind of methodology is that it separates the estimation of the income elasticity from the estimation of the MECF. Hence, it can be useful for first-order approximations, where one can rely on a conjecture concerning the income elasticity and the Gini measure of income inequality.

Implicitly assuming a social welfare function does not, however, eliminate the need to defend it. Hence. an attractive alternative is to investigate whether an assumption of a specific social welfare function is really needed to determine the direction of a tax reform. Under certain conditions one may find a refonn that improves upon a large set of social welfare functions. For an illustration, see Mayshar and Yitzhaki ( 1995).

Horizontal Equity, Fairness, and Justice

Objectives related to horizontal equity or the fairness of the tax process itself are more difficult to incorporate into the analysis, and we do not attempt that task here. Yet we believe that these issues are fundamental to understanding the design of tax systems. Because the interpretation of fairness is influenced by cultural setting. ideology, prejudice, and propaganda. it cannot be generalized over time or across countries. For example, one's view of whether the rich accumulated their wealth by theft or by hard work, and whether the poor are poor because of lack of opportunities or because of laziness, leads to different interpretations of fair taxes. However, it seems to us that there are some widely accepted characteristics of fair taxes. Among them are that ( I ) taxes should not be arbitrary, that is, they must be imposed either on a tax base that indicates an ability to pay or on benefits derived from the provision of public goods;33 (2) taxes should not be

31 The (Gini) income elasticity is a weighted average of the income elasticities of the potential marginal tax, weighted by the (implicit) weighting scheme of the Gini index. The term in parentheses is always positive (provided that the tax base is always positive) .

.1.' One can point out that random taxes. such as a draft lottery or random auditing, do exist but, in practice, random taxes arc often imposed in the presence of indivisibilitics or increasing returns to scale.



imposed retroactively, that is, the taxpayer should be given advance notice, so that he has a chance to adjust his activities to the tax; and (3) the tax should not serve the specific interest of any person and should be general in the sense that equal taxpayers are treated equally.3�

These arguments were contained in the four canons of taxation of Adam Smith. Bastable ( 1 895), in his interpretation of Smith's canons, points out that others have considered those rules as "partly ethical . . . and partly economical" and recommends that one "regard them nor as economic, ethical, or constitutional, bur as essentially financial; they therefore rightly combine the different elements that must enter into problems connected with that subject" (pp. 385-86).

If these important objectives cannot be quantified, all one can do is calculate the cost to society of adhering to those targets, and then discuss whether it is worthwhile to pay this price in the name of fairness. Alternatively, changes in the tax law that do not conform with constraints related to these objectives may simply be discarded.

V. Evaluating Nonmarginal Changes

Although marginal analysis can be helpful for evaluating small changes in the tax system, it cannot handle the grand design of the tax system. Because of the nature of the system-namely, the noncontinuity of administrative costs, nonconcaviry of the revenue constraint, nonconcavity of deadweight loss, and increasing returns to scale in rax administrationchanges to it cannot be evaluated by deriving marginal conditions in a wellbehaved optimization problem. In order ro compare the actual level of the social welfare function under different tax regimes, one may have to resort to simulation models.

Presumptive Taxes

One interesting example, which involves both non-cost-related targets and nonmarginal changes, is presumptive taxation. Presumptive taxes involve tax bases, or indicators, that can serve as proxies for ideal tax bases, but which are less easily manipulated and more easily monitored than the otherwise ideal tax base. Although the main motivation of presumptive taxes is to save administrative and compliance costs, the use of a proxy means that achievement of other targets will likely be adversely affected. The use of the term presumptive can be interpreted as including an apology for the

3• See the discussion in Lambert and Yitzhaki ( 1995) on horizontal inequity.



fact that other targets (such as faimess) are sacrificed. In the sense that all taxes make design sacrifices for administrative reasons, all taxes are presumptive; after all, i f there were no information gathering costs, an ability tax would arguably be optimal.

Consider the following tax design issues in the context of presumptive taxation. Most economists would agree that the household, and not the family, is the appropriate unit for capturing economies of scale in measuring economic well-being. However, actual income taxes and transfer payments are related to the family, where individuals are connected by relationships that cannot be manipulated easily. The choice of the family as the appropriate unit of taxation can be explained by administrative costs. One may be able to evaluate the cost saving in taxing the family instead of the household, but a proper evaluation of this issue requires the knowledge of the harm done-in terms of mismeasuring ability to pay-by not taxing the household.

Presumptive taxation is usually applied to income taxation. Most economists recognize that ability to pay is a function of full income, which includes the value of leisure. However, it is difficult to value leisure and therefore all tax systems are based on income and not on full income or the return to ability. Thus, taxes based on income are in a sense presumptive taxes on full income. Furthermore, one can interpret the provision existing in many countries allowing spouses to file separately as a presumptive recognition of the fact that two working spouses have less leisure than one working spouse. Whether this is a reasonable approximation depends on the value attached to the deviation from horizontal equity caused by separate filing.

One can add to the list of presumptive taxes depreciation schedules, the standard deduction, and a long list of what are explicitly labeled as presumptive taxes (see Tanzi and Casanegra de Jantscher ( 1987), Sadka and Tanzi ( 1 992), and Slemrod and Yitzhaki ( 1 994)). In our· opinion, the issues involved in presumptive taxes cannot be easily handled by the MECF concept nor by simple optimization, because they involve cost saving at the expense of another target (horizontal equity) that is analytically intractable. Numerical simulation combined with evaluation of the cost attached to deviations from justice principles may be necessary (see, for example, Stern ( 1982)).

VI. Conclusions

In this paper, we explore the usefulness of the marginal efficiency cost of funds (MECF) as a guiding principle in the formation of tax policy recommendations. We argue that the MECF concept is useful for analyzing



minor tax reforms. For any change in the tax system that is considered.35 one has to evaluate the expected tax revenue and the expected leaked tax revenue. In the simplest case, the sum of the two, divided by the former, is the MECF. One can calculate the MECF for alternative ways of raising revenue. and other things being equal, the one with the lowest MECF is the one that should be recommended.

How relevant is the concept of MECF to the International Monetary Fund? Our argument is that policy recommendations that are derived from abstract models (or, in some cases, experience) tend to be almost idenrical for all countries, simply because differences in culture. ethics, technological development, market structure, or any other country-speci fie difference, such as the level of income, are missing in those models. To overcome the complexity of the tax problem, there is a tendency to concentrate on one component of the problem, which leads to policy guidelines that are only correct under certain conditions, and those conditions tend to be forgotten. For example, the aims of "tax neutrality'' and "optimal tax rates" are correct conclusions from disparate models, but they contradict each other. Careful application of the MECF concept can begin to sort out which component of the tax problem is most relevant to a particular country because country-specific properties, such as corruption, administrative capabilities, and an inability to enact simple tax laws. are all captured in the MECF.·16

Consider the following example. The effectiveness of a VAT depends, among other things, on the validity of bookkeeping records in the country, which in turn depends on whether taxpayers need the records for running their own businesses. Excluding multinational corporations, it seems safe to assume that the larger the business, the higher the reliance on records for in-house management, and the more costly manipulations would be. Hence, one can expect the efficiency of a VAT to increase with the size of the business. Therefore, we should expect a crucial level of development that is required for a VAT to be efficient. We do not know what this crucial "level of development" is and how to measure it. But clearly, the MECF of having a VAT may differ among countries, and comparing the MECF of a VAT to the MECF of other taxes within a country may shed some light on

35 It is argued by Bird and Casanegra de Jantscher ( 1992, p. 3) that "it seldom makes sense to try to reform tax administration without simultaneously reforming the tax structure."' One can generalize the argument by saying that it is rarely ideal to change only one tax parameter. Rather, an optimized combination is necessary. 36 Morag ( 1965) ar�ued that taxes should be changed from time to time simply because it takes lime tor the taxpayers to learn how to "adjust" themselves to a new tax. This argument means that one cannot expect the same tax to be "the"' appropriate tax for a long period of time. Recalculations of MECFs can indicate when to abolish a tax.



whether a VAT is the appropriate tax for a country. The challenge, then, is to measure the MECF. Calculations similar to those performed by Silvani and Brondolo ( 1 993) can be viewed as a first step toward doing soY

We are not offering the MECF concept as a replacement for traditional analysis of efficiency of tax systems, nor as a substitute for an expert's analysis of the weaknesses of a tax system. We do suggest, though, that it can be useful in making the choice between competing alternative approaches.

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Feldstein, Martin S., "Distributional Equity and the Optimal Structure of Public Prices," American Economic Review, Vol. 62 (March 1972), pp. 32-6.

Fortin, Bernard, and Guy Lacroix, '"Labor Supply, Tax Evasion and the Marginal Cost of Public Funds: An Empirical Investigation;· Journal of Public Economics, Vol. 55 (November 1994), pp. 407-3 1 .

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---, and Milka Casanegra de Jantscher, ·'Presumptive Income Taxation: Administrative Efficiency and Equity Aspects," IMF Working Paper 87/54 (Washington: International Monetary Fund, August 1987); also published as "The Use of Presumptive Income Taxation in Modern Tax Systems: Administrative Efficiency and Equity Aspects." in Changes in Revenue STrucTure. Proceedings of The 42nd Congress of The InTernational InsTiTute of Public Finance, Athens. 1986, ed. by Aldo Chiancone and Ken Messere (Detroit, Michigan: Wayne State University Press, 1989), pp. 37-5 1 .

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fM F Staff Papers Vol. 43. No. I (March 1996) © 1996 International Monewry Fund

Nonlinear Effects of Inflation

on Economic Growth

MICHAEL SAREL *

This paper examines the possibility o.f nonlinear e.f{ects of i1�{1ation on economic growth. It finds evidence of a significant structural break in the.fimction that relates economic growth to inflation. The break is estimated to occur when the inflation rate is 8 percent. Below that rate, i1�{1ation does not have any effect on growth, or it may even have a slightly positive effect. When the inflation rare is above 8 percent, however, the estimated effect of inflation on growth rates is significant, robust, and extremely powelful. The paper also demonstrates that when the existence of the structural break is ignored, the estimated effect of inflation on growth is biased by a factor of three. [JEL E3 1 , 040]

IT IS NOW WIDELY ACCEPTED that in Ration has a negative effect on economic growth. This negative effect, however, was not detected in data

from the 1950s and the 1960s. Based on those data, the view that prevailed in the economic profession was that the effect of inRation on growth was not particularly important. Until the 1970s, many studies found this effect to be nonsignificant, and in fact some found it to be positive. In general, the empirical evidence was, at best, mixed. 1 The change in view came only after

* Michael Sarel is an Economist in the Southeast Asia and Pacific Department. He graduated from the Hebrew University of Jerusalem and received a Ph.D. from Harvard University. This paper was written while the author was in the IMF's Research Deprutment. He would like to thank Cru·men Reinhart and Peter Wickham for helpful discussions and comments.

1 This is documented, for example, by Bruno and Easterly ( 1995). They write (p. 4): " . . . Johnson in 1967 suggested that there was no conclusive empirical evidence one way or the other-as a series of studies in the IMF Staff Papers around that time bear witness (Wai 1959, Dorrance 1963, 1966 and Bhatia I 960). Even for Latin America, where higher double-digit rates of inflation were experienced during that period, the evidence well into the 1970s was ambiguous (Pazos, 1972; Galbis, 1979)."

199


200 MICHAEL SAREL

many countries experienced severe episodes of high and persistent inflation in the 1970s and the 1980s. These high-inflation episodes were usually associated with a general decline in the macroeconomic performance and with balance of payments crisis. As more data became available on these episodes, studies repeatedly confirmed that inflation had a negative effect on economic growth.2 This effect was shown to be statistically significant, albeit of a small magnitude, and it was one of the very few variables influenced by macroeconomic policy found to affect growth rates. As a result of these new conclusions, the dominant view regarding the effects of inflation changed radically. Currently, many economjsts are convinced that inflation is undesirable and that it should be avoided completely. They propose policy measures and institutional changes to guarantee low inflation. One favorite suggestion is to establish independent central banks with a clear mandate to keep inflation levels within a specific range, usually defined as consistent with price stability. Such proposals have been adopted in New Zealand and in Canada, and are being discussed in many other countries.

The abrupt change in the view regarding the effects of inflation on growth raises three important questions: ( I ) Why did it take so long and so many studies to uncover such an obvious link between two of the most important and most closely watched macroeconomic variables? (2) As the estimated effect of inflation on growth is relatively small, should the results of these studies affect policy priorities and institutional arrangements? (3) If a specific range for inflation is to be adopted as a policy target and included in legislative measures, what should this range be?

Motivated by these questions, this paper explores the possibility of nonlinear effects of inflation on economic growth, and finds evidence of a structural break in the function that relates growth rates to inflation. When inflation is low, it has no significant negative effect on economic growth; the effect may even be slightly positive. But when inflation is high, i t has a powerful negative effect on growth. The structural break is estimated to occur where the average annual rate of inflation is 8 percent.

The existence of such a structural break can explain why the negative effect of inflation on economic growth was not detected for such a long time: before the 1970s, there had been few episodes of high (i.e., beyond the structural break) inflation. It also suggests a specific target for policy: keep inflation below the structural break. Most important, the existence of a structural break implies that previous studies seriously underestimated the negative effects of higher rates of inflation on economic growth. This paper

2 There are many studies that found support for this view. Some of the latest are Smyth ( 1994), Sbordone and Kuttner ( 1994), De Gregorio ( 1993), Fischer ( 1993), and De Gregorio ( 1992).


NONLINEAR EFFECTS OF INFLATION ON ECONOMIC GROWTH 201

demonstrates that if the existence of the structural break is ignored, the estimated effect of higher rates of inflation on economic growth decreases by a factor of three. Taking the structural break into account. the paper finds evidence that the negative effects of high inflation on growth are much more powerful than previous studies had estimated.

The paper is organized as follows: Section I presents the data that are used in the empirical tests. A preliminary test is performed in Section II to uncover the general shape of the function that relates growth rates to inflation. This test involves estimating the effects of twelve inflation groups on growth. The results of this preliminary test raise the possibility that the function contains a structural break. In Section III we perform the main test, which estimates the point of the structural break, its level of significance, and the two inflation effects, below and above the structural break. Additional tests are performed in Section IV as variations to the main test. Section V presents concluding remarks and policy implications.

I. The Data

This paper uses data on population, GDP, consumer price indices, terms of trade, real exchan.ge rates, government expenditures, and investment rates. Two databases are used as inputs for this study, the "Penn World Table 5.5

" database and the "World Tables" database.3 The CPI and the terms of trade data are used to reduce the problem of

negative correlation between inflation and growth rates, which is not directly caused by inflation effects on growth. It is better to use CPI data than implicit GDP deflators in this type of study because changes in GDP deflators are, by construction, negatively correlated with the growth rates.�

' The "PWT 5.5" is an NBER update to "PWT 5.0," a database described by Summers and Heston ( L 991 ). The ··world Tables'' database is an on-line database of the World Bank (World Bank ( 1995)). Most of the variables used in this paper are from the first daLabase: annual data on population. output per person. govemment expenditures as percent of GOP, and investment as percent of GOP, all measured in PPP 1985 dollars. Annual data on consumer prices and on terms of trade indices are extracted from the second database.

4 Suppose, for example, that there are two periods and a measurement error overestimates the output volume in the second period. In this case. the growth rate between the two periods will be overestimated, while the change in the implicit GOP deRator between the two periods will be underestimated. lf the output volume is underestimated in the second period, the growth rate between the two periods will be underestimated, while the change in the implicit GOP deRator between the two periods will be overestimated. In both cases, the measurement error will induce a negative correlation between real growth rates and GOP deRators. Because CPI indices are calculated independently of output volume, their use should prevent this problem.


202 MICHAEL SAREL

The terms of trade data are used to eliminate the negative correlation between growth and inflation that is caused by external supply shocks.5

Combining the two databases, a joint panel database is produced. This database contains continuous annual information for 87 countries, during the period J 970-90.6 The 20-year sample period is divided into four equal periods of 5 years each, obtaining a total of 248 observations.' For each 5-

year period, between the year 1 and the year 1 + 5, the growth rates of output per person, population growth rates. inflation rates, and rates of change in the terms of trade are defined as th·e average logarithmic annual changes during the period:8

and

. _ log(y,+5 I y,) 810Wth(T.T+5) -5

,

log( pop,+5 I pop, ) N(/.1+5> = 5

t..TOT = log(TOT,+51TOT,) (f./+5) 5

( I )

(2)

(3)

(4)

5 Negative external supply shocks, such as an increase in oil prices in the case of industrialized countries, tend to increase inflation and to reduce growth, inducing a negative correlation between the two variables. Positive shocks increase growth and reduce inflation, again inducing a negative correlation between the two variables. Fischer ( 1993) recognizes this problem. He writes: "The inclusion of changes in the terms of trade as a regressor goes a long way towards dealing with this problem." This study follows his advice and always controls for changes in the terms of trade.

c. The complete list of countries is presented in the Appendix. For some of the countries, the PWT 5.5 database does not contain observations for the year 1990; the last year of observations for these countries was I 989. In these cases, data on GOP, GOP deflators and population for the years 1989 and I 990 are extracted from the World Tables database. Then, these data are used to calculate the growth rates of real income per person and of population between 1989 and 1990. These rates are used to extend the PWT 5.5 database to I 990. This procedure is applied for the following 12 countries: Barbados, Ghana, Haiti, Iran, Jamaica, Korea, Malta, M�anmar, Niger, Seychelles, Sri Lanka, and Suriname.

Dividing the sample period into smaller periods has two advantages. First. it increases the number of observations. Second, it introduces a time dimension, making it possible to estimate country-speci fie effects. Making the subperiods too short, however, may cause problems related to business cycles and their effects on inflation. The division to five-year periods is chosen as a compromise and it also follows a standard practice in the empirical literature on economic growth.

8 When inflation is low, a logarithmic (continuous) rate is very similar to a discrete rate. But the two differ when inflation is high. A logarithmic rate of 50 percent, for example, corresponds to a cumulative discrete rate of 65 percent from one year to the next. All the rates discussed in this paper are annual averages of logarithmic rates.



An interesting (but not so important) question is how to treat the observations with a negative inflation rate. One possibility is to argue that the effect of inflation around zero is monotonic. and therefore to leave these observations as they are. Another option is to argue that what rea II y matters for growth is price stability, and therefore the relevant variable is the absolute value of inflation (or some monotonic transformation of that value). A third possibility is to ignore these observations altogether. Finally, the fourth possibility is to treat these observations just as being close to zero, as a compromise between the first two approaches. This study chooses to take this last approach and substitutes an inflation rate of 0. 1 percent for the negative observations.9

A less interesting (but more important) question is whether it is better to use a transformation of the inflation rate than simply to use the rate itself. Figures I and 2 present, respectively, the histograms of the distribution of the inflation rate and of its logarithmic transformation. As these figures make clear, the rate of inflation has a very asymmetric distribution (the lowest tenth of its range contains 88 percent of the observations). Using this variable would place an enormous weight on the very few observations with the highest inflation rate. The logarithm of inflation, on the other hand, has a much more balanced distribution. In the remainder of this paper, therefore, the logarithmic transformation of the inflation rate will be used.

II. A Preliminary Test

This section makes a first attempt to uncover nonlinear features i n the function that relates economic growth to inflation. In order to find the general shape of this function, the 348 inflation observations are divided into 1 2 equal groups of 29 observations each. The groups contain increasingly higher inflation observations. 10 Each inflation group except Group 6 is assigned a dummy variable.

Then, an OLS regression is estimated for the growth rate on the inflation dummies, on country dummies (except the first country, Algeria), on period dummies (except the first period, 1970-75), and on the other explanatory variables that are usually used in growth regressions, such as the log of initial income per person (LY), the population growth rate (N), government

'1 The reason this problem is not very important is that the sample used in this study contains only two observations of negative inflation. Both observations occur in the period 1985-90: Burkina Faso ( -0.5 percent) and Niger ( -3.1 percent). The chosen corrective value of 0.1 percent corresponds to the smallest positive inflation observation in the sample.

10 Group I , for example, contains inflation rates of less than 3.8 percent, while Group 12 contains inflation rates in excess of 39.3 percent.


204 MICHAEL SAREL

Figure l . The Distribwion of Inflation

Number of observations 350r----------------------------------------------.

300

250

200

150

100

5 0

Inflation rate (decilcs)

Figure 2. The Distribution rlthe Log of ln.flation

Number of observations 150

120

90

60

30

Log of inflation (deciles)


NONLINEAR EFFECTS OF INFLATION ON ECONOMIC GROWTH 2()5

expenditures as a percent of GOP ( GOV), and the rate of change in the terms Of trade (!;:,.ron. I I

The results of the regression (except the estimated coefficients for the country and the period dummies) are presented in Table I , Regression I . An F-test rejects at the I percent confidence level the hypothesis that the 86

country dummies are equal to zero. This rejection implies that countryspecific effects are important in explaining the growth rates. The same is true about an F-test for the three period dummies. Nevertheless, Regression 2 in Table I presents the results of a regression that includes neither country dummies nor period dummies. The estimated coefficients of the different inflation groups represent the effect on growth of each group relative to Group 6, which is used as a reference. 1 2

Figure 3 describes the estimated coefficient and the corresponding standard error for each inflation group, as reported by Regression I . An important feature of the data emerges in the results presented in Table I and in Figure 3: the effects of inflation on economic growth may contain a structural break. When inflation is low, there are no significant differences in the coefficients of different inflation groups. In other words, it does not make a significant difference to the growth rates if inflation is low, very low. or zero. When inflation is high, on the other hand, moving to a higher inflation group has a dramatic impact on the growth rates. For example, the difference in the effect on growth rates between the highest inflation group and Group 6 is estimated to be close to 4 percentage points-more than twice the sample's average growth rate.

III. The Main Test

The previous section presented evidence that the function that relates economic growth to inflation may contain a structural break. This finding raises at least three questions:

1 1 The regressions in this section. as well as the regressions in the rest of this paper. basically confirm the stylized facts about the determinants of economic growth, as documented by many other studies, such as Barro ( 1991 ). The growth rate of income per person depends negatively on initial income, on the population growth rate, and on government expenditures and depends positively on changes in the terms of trade. Because this study concentrates on the effects of inflation on growth. the results concerning the other variables will not be further discussed. 1 2 A word of caution: here, as well as in the other sections of this paper, the results of the regressions are interpreted as measuring the marginal effects of inflation on economic growth. This interpretation has a long tradition, and has strong and direct policy implications, but is certainly not the only possible one. Levine and Zervos ( 1993), among others, raise important questions about this kind of interpretation.


206 MICHAEL SAREL

Table I . The Estimated Coefficients of the inflation Groups

Regression 2

Country and year dummies yes no Adjusted R1 0.493 0.148

c 0.504 0.0943 (7.09) (3.95)

LY -0.0641 -0.00556 (-6.95) (-2.33)

N -0. 1 13 -0.700 ( -0.306) (-3.5 1 )

GOV -0.00103 -0.000755 ( - 1 .47) ( -3.03)

t::.TOT 0.0841 0.0822 (3.27) (2.77)

GRJ 0.00554 0.00265 (0.708) (0.335)

GR2 0.0071 8 0.000122 (0.986) (0.0155)

GR3 -0.00 1 1 5 -0.00609 (-0. 16 1 ) ( -0.775)

GR4 -0.00101 -0.00610 (-0.144) (-0.777)

GR5 0.00401 -0.002 13 (0.547) (0.27 1 )

GR7 0.00872 0.0 1 1 0 ( 1 .26) ( 1 .41)

GR8 -0.00270 -0.000605 (-0.376) (-0.0772)

GR9 -0.0142 -0.0102 (-2.01) (- 1 .30)

GR10 -0,0300 -0.0239 ( -4.05) (-3.04)

GRI I -0.0298 -0.0147 ( - 3.73) (- 1 .87)

GR12 -0.0390 -0.0252 (-4.14) (-3.21)

Notes: ( I ) The dependent variable is the average growth rate of output per person. (2) The number of observations is 348. (3) The method of estimation is OLS. (4) /-statistics are reported in parentheses. (5) Regression I does not report 86 country dummies and 3 period dummies.


NONLINEAR F.FFECTS OF INFLATION ON ECONOMIC GROWTH 207

Figure 3. Effects of Different h(flation Croups 011 Crou·th

Effecl on 1he growlh rale (+I- I s.e.) 0.02

0.01

-0.01

-0.02

-0.03

-0.04

-0.05

-0.06 2 4 6 8 10 1 2

lnOmion group

( I ) At what level of inflation does the structural break occur? (2) Is the break significant?D (3) What is the estimated value of the inflation effect on growth on either

side of the structural break? This section answers these three central questions, using a simple

estimation technique. First, it defines

and

IT* = the rate of inflation at which the structural break occurs.

DD = I if IT > IT*, 0 otherwise,

EXTRA = DD [log (IT) - log (IT*) ] .

Then, an OLS regression is estimated for the growth rate on the two variables log n and EXTRA, in addition to the usual explanatory Valiables. When inflation is low (IT < IT*), EXTRA = 0 (by construction) and the effect of inflation on growth is estimated by the coefficient of log IT. However, when inflation is high (IT > IT*), the relevant estimator is the sum of two coefficients: the coefficient of log IT and the coefficient of EXTRA. The coefficient of EXTRA estimates the difference in the i nflation effect on

._1 In other words, is the effect of inflation on growth significantly different above the structural break from what it is below the structural break?


208 MICHAEL SAREL

Figure 4. Goodness-or Fit for Different Structural Breoks

0.6286

0.6284

0.6282

0.6280

0.6278 0.075 0.08 0.085 Point of structural break

0.09

growth between the two sides of the structural break, and its t-statistic value tests whether or not the structural break is significant}�

We are now in a position to answer the second and the third questions raised at the beginning of this section, but we still have to answer the firstat what level of inflation does the structural break occur? Assuming that the error variance is equal for the entire inflation range, we can estimate the regression for different values of ll* and choose as the breakpoint the value of 11* that minimizes the sum-of-squared residuals from the regression. This is equivalent to picking the TI* that maximizes R2• Figure 4 presents the results of iterating the regression for different values of Il*. 1t shows that the value of R2 is maximized when Il* = 8.0 percent.

Regression I in Table 2 assumes a value of 8 percent for Il*. The last row of the table calculates the implied effect of inflation when ll > Il*. Using the variance-covariance matrix of the regression's coefficients, we also calculate the standard error of this effect and report its t-statistic. The results of Regression I confirm that there is indeed a significant structural break at an inflation level of 8 percent. The t-statistic for EXTRA makes possible to reject at the I percent confidence level the hypothesis of equal effects of

1• A similar spline function was estimated by Fischer ( 1993). Fischer divides his observations into three arbitrary groups (Table 8 in his paper). His variables are defined differently than the ones used in this study, and the technique he uses is also different. Using his specific division, he did not find signi ficant effects of inflation on growth for any of the inflation groups, although he found evidence of negative effects in the whole sample.



Table 2. Regressions for the Main Test

Regression 2 3

Country and year dummies yes yes no Assumes a structural break yes no yes Estimated point of the

structural break 0.080 0. 101 Adjusted R2 0.491 0.435 0.148 c 0.551 0.467 0.0910

(7.81) (6.44) (3.79) LY -0.0672 -0.0595 -0.00487

(-7.39) (-6.29) ( -2.07) N -0.516 -0.560 -0.675

(- 1 .44) ( - 1 .48) (-3.44) GOV -0.000936 -0.000887 -0.000730

( - 1 .38) ( - 1 .24) (-2.93) l:iTOT 0.0853 0.0778 0.0835

(3.37) (2.92) (2.87) log rr 0.00277 -0.0082 1 0.00160

(0.964) (- 3.87) (0.6 1 1 ) EXTRA -0.0276 -0.0176

(-5.38) (-4.02) Estimated coefficient of

log IT for high Lnfiation -0.0248 -0.00821 -0.0160 ( -3.33) ( - 3.87) ( - 2.42)

Notes: ( I ) The dependent variable is the average growth rate of output per per-son. (2) The number of observations is 348. (3) The method of estimation is OLS. (4) t-statistics are reported in parentheses. (5) Regressions I and 2 do not report 86 country dummies and 3 period dummies.

inflation (below and above 8 percent). When the inflation rate is less than 8 percent, its effect is positive, but very weak and statistically insignificant. On the other hand, the effect of inflation when it is greater than 8 percent is not only significant at the 1 percent confidence level, but also extremely powerful. The coefficient of -0.0248 for log D can be interpreted to mean that the annual growth rate decreases by 1 .7 percentage points (the equivalent of the average growth rate in the sample) when the inflation rate doubles. The results of the regression also confirm our prior expectations about the other included variables.

Regression 2 reports, for comparison, the results in the case in which the EXTRA variable is not included. It demonstrates how ignoring the existence of the structural break makes a huge impact on the estimated effect of inflation on economic growth. By not including the variable EXTRA as a regressor, Regression 2 estimates the effect of inflation on economic growth, con-


2 1 0 MICHAEL SAREL

ditional on this effect being the same throughout the inflation spectrum. In the case of high inflation CIT > IT*), the estimated effect of inflation in Regression 2 is only one third of the effect estimated by Regression I . Another look at Figure 3 provides a simple intuition for this important result: when IT > IT*, Regression 1 estimates the slope of the function that relates economic growth to inflation, but only for the range of inflation where this slope is steep. Regression 2, on the other hand, estimates an average slope over the whole inflation spectrum, including the range where the slope of the function is close to zero or even slightly positive. Therefore, a large bias occurs in the estimated effect of inflation in Regression 2, as well as in all the other studies that ignore the existence of the structural break.

The country dummies group and the period dummies group are both significant at the 1 percent confidence level. However, we also look at the case in which these dummies are not included. In this case, the IT* that maximizes R2 is 10.1 percent. Regression 3 does not include dummies and assumes that IT* = I 0.1 percent. It reports results that are very similar to the results of Regression I . The main difference is that the negative effect of inflation above IT* is about 35 percent weaker than in Regression I (but still twice the estimate of Regression 2).

IV. Additional Tests

This section performs additional tests as variations to the main test. One reason for these additional tests is to increase our understanding of the effects of inflation on economic growth. A second reason is to use changes in the specifications of the regression to check the robustness of the earlier results regarding the nonlinear effects of inflation on economic growth.

Table 3 presents results of regressions that use only observations from the last 3 periods ( 1975-90). These regressions assume that the structural break occurs when the rate of inflation is 8 percent. Regression I , which presents the basic results, is the equivalent of Regression I in Table 2. The results here confirm our previous conclusions. The main difference is that the estimated effect of inflation when rr is greater than 8 percent is weaker than before (although the structural break remains significant). Regressions 2 and 3 in Table 3 include, respectively, log IT lagged for one period, and first-differences in log fl. The estimated coefficients of these variables are not significant. Changes in the inflation rate, at least between the five-year periods used in this study, do not appear to have any effect on growth. Also, including these additional variables has no significant effect on the estimated coefficients of the other variables in the regression.

Table 4 again uses all four periods. and includes additional explanatory variables. Regression I presents the basic results (reported previously in Table 2, Regression I ). Regression 2 includes the investment rate (as per-


NONLINEAR EFFECTS OF INFLATION ON ECONOMIC GROWTH 2 1 1

Table 3. Regressions with l£1gged Inflation

Regression I 2

Adjusted R2 0.553 0.551

c 0.664 0.666 (7.56) (7 .4 7)

LY -0.0782 -0.0786 (-7.01) ( -6.83)

N - l . l 9 - 1 . 1 9 ( -2.69) ( -2.69)

GOV -0.000910 -0.000919 ( - 1.07) (- 1.08)

!::.TOT 0.0787 0.0781 (2.25) (2.21)

log O 0.00397 0.00405 ( 1.25) ( 1 .24)

EXTRA -0.02 12 -0.02 12 (-3.49) ( -3.47)

log fL 1 -0.00051 9 ( -0. 136)

log n - log n_ l

Estimated coefficient of log n for high inflation -0.0172 -0.0 1 7 1

( - 2.02) ( - 2.00)

3

0.551 0.666

(7.47) -0.0786

( -6.83) - 1 . 1 9

( - 2.69) -0.000919

( - 1 .08) 0.0781

(2.21) 0.00354

(0.782) -0.0212

( -3.47)

0.00051 9 (0.136)

-0.0177 ( - 1.93)

Notes: ( I ) The dependent variable is the average growth rate of output per per-son. (2) The number of observations is 261. (3) The method of estimation is OLS. (4) /-statistics are reported in parentheses. (5) 86 country dummies and 2 period dummies are not reported.

cent of GDP, measured in PPP 1985 dollars). Including the investment rate may help identify how inflation affects growth. If inflation reduces growth only indirectly, by reducing capital accumulation, we would expect to find a much weaker direct inflation effect once the investmem rate is included as an explanatory variable. But the results of Regression 2 demonstrate that, even controlling for the investment rate, the inflation coefficient remains strong and significant, and it retains about 88 percent of its previous value. One possible interpretation of this result is that inflation affects growth mainly through its harmful effect on efficiency and productivity. Regression 3 includes the real exchange rate, defined as the average deviation from PPP in the dollar price ofGDP, compared to the United States (based on the data in PWT 5.5). The real exchange rate has no significant effect on growth and its inclusion does not change in any way the estimated effect of inflation on growth.


2 1 2 MICHAEL SAREL

Table 4. Regressions with Additional Variables

Regression 2 3

Adjusted R2 0.491 0.525 0.489 c 0.551 0.597 0.545

(7.81) (8.67) (7.51) LY - 0.0672 -0.0788 -0.0666

( -7.39) ( -8.59) ( -7.21) N -0.516 -0.659 -0.513

( - 1 .44) ( - 1 .89) ( - 1 .43)

GOV -0.000936 -0.000879 -0.0009 16 ( - 1 .38) ( - 1 .34) ( - 1 .34)

t.TOT 0.0853 0.0936 0.0858 (3.37) (3.81) (3.38)

log n 0.00277 0.00199 0.00250 (0.964) (0.716) (0.848)

EXTRA -0.0276 - 0.0239 -0.0273 ( - 5.38) (-4.78) ( - 5.28)

/NV 0.00170 (4.41 )

RER - 0.00355 (-0.39 1 )

Estimated coefficient of log IT for high inflation -0.0248 -0.0219 -0.0248

( -3.33) ( -3.03 ) ( -3.28) Notes: ( I ) The dependent variable is the average growth rate of output per per

son. (2) The number of observations is 348. (3) The method of estimation is OLS. (4) /-statistics are reported in parentheses. (5) The regressions do not repon 86 country dummies and 3 period dummies.

Table 5 repeats the procedure from Table 2, using the same raw data, but dividing the observations differently. Now, instead of four periods of five years each, the data are divided into five periods of four years each, for a total of 435 observations.

The results reported in the three regressions of Table 5 should be compared with the results reported in Table 2, for the case of five-year periods. The results of Table 5 confirm all the previous conclusions. I n particular, they confirm the existence of a significant structural break. Also, the estimated point of the break in Regression I (7.9 percent) is very close to the previous estimate (8.0 percent). The results of Table 5 also reinforce the conclusion that ignoring the existence of the structural break has a huge effect on the estimated effect of inflation; the estimated effect based on Regression 2 is one fifth of that predicted by Regression I ! There is one notable exception, however: now the positive effect of inflation at low levels of inflation is statistically significant.


NONLINEAR EFFECTS OF INFLATION ON ECONOMIC GROWTH 2 1 3

Table 5. Regressions with Four- Year Periods

Regression 2 3

Country and year dummies yes yes no Assumes a structural break yes rno yes Estimated point of the

structural break 0.079 0.063

Adjusted R1 0.454 0.364 0.160

c 0.574 0.473 0. 1 1 3 (8.53) (6.64) (4.94)

LY -0.0660 -0.0566 -0.005 1 I (-7.51) (-6.03) ( - 2.35)

N -0.850 -0.87 1 -0.642 (- 2.60) ( - 2.47) ( -3.57)

cov -0.00 1 7 1 -0.00 1 5 1 -0.000803 (-2.7 1 ) (-2.22) ( -3.48)

11TOT 0.0415 0.0334 0.0420 (2.33) ( I . 74) (2.02)

log n 0.00546 -0.00589 0.00645 (2.43) (-3.25) (2.66)

EXTRA -0.0335 -0.0224 ( -7.57) ( -6.03)

Estimated coefficient of log n for high inflation -0.0280 -0.00589 -0.0160

( - 4.55) ( - 3.25) ( - 2.72)

Notes: ( I ) The dependent variable is the average growth rate of output per person. (2) The number of observations is 435. (3) The method of estimation is OLS. (4) /-statistics are reported in parentheses. (5) Regression I does not report 86 country dummies and 4 period dummies.

V. Conclusions and Policy Implications

This paper has explored the possibility of nonlinear effects of inflation on economic growth. It found that the function that relates growth rates to inflation contains a structural break. When inflation is low, it has no significant negative effect on economic growth, and the effect may even be slightly positive. But when inflation is high, it has a negative effect on growth. This negative effect is robust, statistically significant, and very powetful. The point of the structural break was estimated to occur when the average annual rate of inflation is 8 percent.

If a structural break exists, failing to take it into account introduces a significant bias in the estimated effect of inflation. This paper has demonstrated that when the structural break is taken into account, the estimated effect of inflation on economic growth increases by a factor of three. The existence of such a structural break also suggests a specific numerical target for policy: always keep inflation below the structural break.


214 MICHAEL SAREL

One possible interpretation of the empirical results of this paper is that when the inflation rate doubles (for example, a relatively moderate increase in inflation from 20 percent to 40 percent), the growth rate decreases by 1.7 percentage points. This difference of 1 .7 percentage points is much higher than previous studies have estimated, and is exactly equal to the average worldwide growth rate of per capita income in the last two decades. In other words, it is the difference between sustained growth and stagnation. This interpretation implies that a macroeconomic policy to avoid high inflation is one of the best recommendations economists can make.

Country

I . Algeria 2. Argentina 3. Australia 4. Austria 5. Bangladesh

6. Barbados 7. Bolivia 8. Brazil 9. Burkina Faso

10. Burundi

I I . Canada 12. Chile 13. China 14. Colombia 15 . Congo

16. Costa Rica 17. Cote d'Ivoire 18. Cyprus 19. Denmark

APPENDIX

Table A I . Complere Lisr of Counrries

Country

30. Guatemala 3 1 . Guyana 32. Haiti 33. Honduras 34. Hong Kong

35. Iceland 36. India 37. Indonesia 38. Iran, Islamic Republic of 39. Ireland

40. Israel 4 1 . Italy 42. Jamaica 43. Japan 44. Jordan

45. Kenya 46. Korea, Republic of 47. Madagascar 48. Malaysia

Country

59. Pakistan 60. Panama 6 1 . Paraguay 62. Peru 63. Philippines

64. Poland 65. Portugal 66. Senegal 67. Seychelles 68. Sierra Leone

69. Singapore 70. South Africa 7 1 . Spain 72. Sri Lanka 73. Suriname

74. Sweden 75. Switzerland 76. Syria 77. Thailand

20. Dominican Republic 49. Malta 78. Togo

2 1 . Ecuador 50. Mauritius 79. Trinidad and Tobago 22. Egypt 5 1 . Mexico 80. Tunisia 23. Fiji 52. Morocco 8 1 . Turkey 24. Finland 53. Myanmar 82. United Kingdom 25. France 54. Netherlands 83. United States

26. Gambia 55. New Zealand 84. Uruguay 27. Germany, West 56. Niger 85. Venezuela 28. Ghana 57. Nigeria 86. Zambia 29. Greece 58. Norway 87. Zimbabwe



REFERENCES

Barro, Robert J., "Economic Growth in a Cross Section of Countries;· Quar1erly Journal of Economics, Vol. I 06 (May 1991 ), pp. 407-43.

Bhatia, Rattan J., "Inflation, Deflation, and Economic Development,'' Swff Papers. International Monetary Fund, Vol. 8 (November 1960), pp. 101-14.

Bruno, Michael, and William Easterly. "Inflation Crises and Long-Run Growth ...

World Bank Policy Research Working Paper No. 15 17 (Washington: World Bank, September 1995).

De Gregorio, Jose, "The Effects of Inflation on Economic Growth-Lessons from Latin America,'' European Economic Review, Vol. 36 (April 1992), pp. 4 17-25.

---. "Inflation, Taxation and Long-Run Growth." Journal of Monerary Economics, Vol. 3 1 (June 1993). pp. 271-98.

Dorrance, Graeme S., "The Effect of Inflation on Economic Development,'' Swff

Papers. International Monetary Fund. Vol. 10 (March 1963), pp. 1-47. ---, "Inflation and Growth," Swff Papers, International Monetary Fund, Vol.

1 3 (March 1966), pp. 82-102. Fischer. Stanley, ''The Role of Macroeconomic Factors in Growth," Journal of

Monerwy Economics, Vol. 32 (December 1993), pp. 485-5 12. Galbis, Vicente, "Money, Investment and Growth in Latin America. 1961-73,''

Economic Developmenl and Culrural Change, Vol. 27 (April 1979), pp. 423-43.

Johnson, Harry G., "Is Inflation a Retarding Factor in Economic Growth?" in Fiscal and Mone/C/1)' Problems in Developing Slaies, Proceedings of the Third Rehoroth Conference. ed. by David Krivine (New York: Praeger, 1967), pp. 1 2 1-30.

Levine, Ross, and Sara J. Zervos, "What We Have Learned About Policy and Growth from Cross-Country Regressions," American Economic Revieu·. Papers and Proceedings, Vol. 83 (May 1993), pp. 426-30.

Pazos. Felipe. Chronic lnjlarion in Larin America (New York: Praeger, 1972).

Sbordone, Argia, and Kenneth Kuttner, "Does Inflation Reduce Productivity?" Economic Perspec1ives. Vol. 18 (November-December 1994), pp. 2-14.

Smyth, David J., "Inflation and Growth." Journal of Macroeconomics, Vol. 16 (Spring 1994). pp. 26 1-70.

Summers, Robert, and Alan Heston, ·'The Penn World Table (Mark 5): An Expanded Set of International Comparisons, 1950-1988,'' Quanerly Journal of Economics, Vol. 106 (May 1991), pp. 327-68.

Wai, U Tun. ''The Relation Between Inflation and Economic Development: A Statistical Inductive Study," Swjf Papers, International Monetary Fund, Vol. 7 (October 1959), p. 302-17.

World Bank, World Tables, on-line database (February 1995).


IMF Staff Papers Vol. 43. No. I (March 1996) © 1996 lmernational Monetary Fund

Asymmetry in the

U.S. Output-Inflation Nexus

PETER CLARK, DOUGLAS LAXTON, and DAVID ROSE*

This paper presents empirical evidence supporting the proposition that there is a significant asymmetry in the U.S. output-inflation process. The important policy implicalion o.fthis asymmetry is that it can he very costly (f the economy overheats because this will necessitate a severe tightening in monetary condilions in order to re-establish inflation control. The empirical results presented in the paper show that the conclusions regarding asymmetry are robust to a number of tests for sensitivity to changes in the method used to estimate potential output and in the specification of the Phillips curve. [JEL CS I , E3 1 , E52]

THIS PAPER PRESENTS empirical evidence supporting the proposition that there is a statistically significant and large asymmetry in the U.S. Phillips

curve, namely, that excess demand conditions are much more inflationary than excess supply conditions are disinflationary. This asymmetry implies that potential output-defined as the level of output that can be attained, on average, in an asymmet1ic stochastic economy-lies below what could be attained in the same economy without shocks. The measure of excess demand that is appropriate for an asymmetric Phillips curve, therefore, cannot have a zero mean; rather, this mean must be negative if inflation is to be stationary. The proper measure of excess demand needs to be taken into account in estimation in order to obtain unbiased tests of a restriction to lin-

* Peter Clark is currently on leave from the IMF at the London School of Economics. Douglas Laxton is an Economist in the IMFs Research Department, and David Rose is a Research Adviser at the Bank of Canada. Peter Clark received a doctorate from MIT and David Rose received his Ph.D. from the University of Manchester. Douglas Laxton did his graduate studies at the University of Western Ontario. This paper has benefited from discussions with several individuaJs who attended seminars at the U.S. Federal Reserve Board of Governors, the Bank of Canada, and the International Monetary Fund.

2 1 6


ASYMMETRY IN THE U.S. OUTPUT-INFLATION NEXUS 2 1 7

earity. Failure to do so can explain why some other researchers may have been misled into falsely accepting the linear model. The conclusions regarding the presence of asymmetry in the U.S. Phillips curve are shown to be robust to a number of tests for sensitivity to changes in the specification.

The paper sketches some of the implications of this asymmetry for monetary policy, using a small macro model calibrated ro reflect the properties of the U.S. data. Simulations of this model contrast the effects of delaying the monetary response to a demand shock obtained from a linear model with those from a model with the estimated asymmetric Phillips curve. The simulations show that if the output-inflation process is linear, then there is no strong case for a speedy monetary policy response to a shock that creates excess demand. Dramatically different results emerge if the economy features the type of asymmetry revealed in the estimation results, namely, delaying the response results in higher inflation and necessitates a significantly stronger monetary tightening to bring inflation back under control. This model thus predicts that the seeds of large contractions are sown when the monetary authority temporizes in dealing with rising inflation and allows conditions of excess demand to become entrenched.

A key policy insight from the analysis is that the degree to which potential output in a stochastic asymmetric economy lies below that obtainable without shocks depends on the variability of output, and hence on the degree of success of the monetary authority in stabilizing the output cycle. Indeed, the results reported in the paper show that policies that allow the economy to overheat periodically can have very significant and deleterious effects on the level of potential output. Moreover. as linear models of the output-inflation process predict that there are small costs from overheating. these results suggest that there could be significant output costs associated with basing monetary policy on the predictions of a linear model.

I. Introduction

In modern economies owpur levels may nor be so rigidly constrained in rhe short run as they used to be when large segmems of output were governed by facilities such as the old hearth steel furnaces that had rated capacities that could not be exceededfor long without breakdown. Rather. the appropriate analogy is a flexible ceiling that can be stretched when pressed, bw as the degree of pressure increases. the exrenr ofjfexibility diminishes.

Allan Greenspan ( 1995}, p. 257

The decision to tighten the stance of U.S. monetary policy in 1994 was based on a view that there could be large costs associated with allowing the U.S. economy to overheat. In several statements to Congress, Federal Reserve Chairman Greenspan presented a strong case that if U.S. monetary


2 1 8 PETER CLARK, DOUGLAS LAXTON, and DAVID ROSE

policy were not tightened, the inflationary risks associated with exceeding potential output would be large, and the process of containing these inflationary forces would then require a much more severe tightening of monetary conditions in the future.

This view appears to be based on a model with an asymmetric outputinflation nexus in which inflation responds more to positive output gaps than it does to negative gaps. 1 If this view of the world is correct, then allowing the economy to produce in excess of its potential will be costly because monetary tightening and large negative output gaps will be required later to rein in inflationary pressures. Lndeed, as Clark, Laxton, and Rose ( 1995a) show, policy rules that fail to guard against overheating will result in significantly larger monetary business cycles and permanent losses in output. Moreover, policy rules that guard against the emergence of excess demand will reduce the variance of aggregate demand and raise the mean level of output.

This view of the business cycle is significantly different from that embodied in linear models of the output-inflation process. Indeed, linear models suggest that there are small costs or perhaps even some benefits from delaying interest rate hikes in the face of positive aggregate demand shocks (Laxton, Meredith. and Rose ( 1 995)).

Despite the obvious importance of this issue for the conduct of monetary policy, there is little econometric evidence available for the United States that supports the view that capacity constraints imply that there is an important nonlinearity in the output-inflation nexus.2 Indeed, Braun ( 1 984) and Gordon ( 1994), for example, claim that there is no evidence of nonlinearity in the U.S. data, while Eisner ( 1994) presents evidence that inflation may respond more to negative gaps than to positive gaps.3 The linear models estimated by Braun and Gordon imply that the average level of output will be independent of the parameters in the monetary policy rule, while Eisner's model predicts that policies that increase the variance of output will actually raise the average level of output.

In this paper, we present evidence of significant asymmetry in the U.S. output-inflation nexus. We argue that the contrary empirical work noted

1 We measure output gaps such that positive values are associated with excess demand and upward pressure on inflation. Some researchers follow Arthur Okun's convention and define gaps the other way around.

1 There is, however, a growing literature that provides examples of how asymmetric aggregate properties can arise from agent behavior. See, for example, Ball and Mankiw ( 1 994) and Tsiddon ( 1991 and 1993).

> Eisner's model uses unemployment gaps. He finds that a reduction in unemployment is less inflationary if the economy is booming and unemployment is initially below the natural rate than if unemployment is initially above the natural rate. The statement in the text assumes that there is a direct relationship between excess demand conditions in the goods market and excess demand conditions in the labor market.

-


ASYMMETRY IN THE U.S. OUTPUT-INFLATION NEXUS 2 1 9

above has been biased against finding evidence of asymmetry, in part because of the way that researchers have measured the output gap and specified how it should enter the Phillips curve. As the basic notion behind the Phillips curve is that inflation is driven by an unobservable output gap, it is not surprising that the econometric results and policy conclusions of different studies have been sensitive to the methods that were used to identify these output gaps.4 As we shall argue, however, it is not so much the measurement of the gaps that causes the problem as the specification of how those measures should enter the Phillips curve. In a stochastic economy with an asymmetric Phillips curve, the gaps that enter the Phillips curve cannot have zero means, as generated by standard detrending techniques. We show that taking this into account is crucial for identifying the outputinflation nexus and for avoiding bias in econometric tests for the presence of asymmetry.

The econometric identification problem is especially problematic in small samples, where '·small" refers to the number of observations of cycles. Moreover, if policymakers became more successful in preventing their economies from overheating, and thereby reduced the frequency of sharp outbreaks of inflation followed by painful corrections, identifying the existence or importance of capacity constraints, at least from the relationship between output and inflation, would become correspondingly more difficult. In fact, it is episodes with major policy errors that give the econometrician the clearest information.5

Given the limited U.S. experience with inflationary surges, one obvious empirical strategy is to draw on a much larger set of monetary policy errors by using data from different countries. In this vein, Laxton, Meredith, and Rose ( 1 995) show that if one assumes that the Phillips curve is identical in each of the G-7 economies, then there is fairly strong evidence of asymmetry. In a recent paper, Turner ( 1995) relaxes this identification restriction and finds that there is some evidence of asymmetry in the Phillips curves of three of the seven major industrialized countries, including the United States.6

This paper builds on Turner's work using U.S. data. One advantage of focusing on the U.S. data is that survey measures of inflation expectations are available and have been found to have significant predictive content for

• Laxton, Rose, and Tetlow ( 1993a) present Monte Carlo evidence that reliance on traditional detrending techniques to measure gaps can explain why some researchers may have falsely rejected asymmetries.

5 Of course, asymmeu·y in the output-inflation nexus will have implications for other endogenous macro variables, such as interest rates. Indeed, one of the concerns voiced by U.S. Federal Reserve Chairman Greenspan is that bumping into capacity limits increases the uncertainty about future inflation and creates more volatility in financial markets.

6 The other countries for which Turner finds significant asymmetry are Canada and Japan. Laxton, Rose, and Tetlow ( 1993b) also provide evidence for asymmetry in the Canadian Phillips curve.


220 PETER CLARK, DOUGLAS LAXTON, and DAVID ROSE

inflation-see Roberts ( 1994b and 1 994c). The availability of such measures is important for two reasons. First, it makes it easier to distinguish between intrinsic dynamics and expectational dynamics. This separation is important for models that are constructed for policy experiments because, as is now well understood from the literature on the "Lucas critique," it can be seriously misleading to assume that expectations formation will remain the same in the face of a change in monetary policy. It is also important for econometric work; recent evidence by Evans and Wachtel ( 1993), Laxton, Ricketts, and Rose ( 1 994), and Ricketts and Rose ( 1995) suggests that traditional fixed-parameter reduced-form models may inaccurately characterize inflation expectations. Second, the use of survey measures of inflation expectations eliminates the econometric problems associated with using instrumental variables in models with forward-looking behavior and aUows one to focus more clearly on issues concerning the role of the output gap in inflation dynamics.

The remainder of this paper is organized as follows. In Section II we provide some empirical evidence that (unlike the earlier studies by Braun and by Gordon) confirms Turner's finding that there is significant evidence of asymmetry in the U.S. data. Section In contains a simple macroeconomic model of the U.S. output-inflation process. We compare some predictions of a linear version of this model with those of our asymmetric version. In Section IV, we provide some further tests of the robustness of our conclusions, discuss some of the implications of our results for policy analysis, and explore several important methodological issues in the specification and estimation of Phillips curves. Finally, Section V provides a brief summary of our conclusions.

II. The U.S. Phillips Curve

The Basic Linear Model

The essential notion of the Phillips curve is that inflation is driven by inflation expectations and the output gap. The simplest form of the model can be written as

( l )

where 1r is inflation, 'IT" is expected inflation, gap is the output gap (or the unemployment gap), and E" represents a stochastic disturbance term.7 The

7 We focus on modeling price dynamics in this paper and our empirical work uses the output gap. This is not to deny that there are interesting issues in linking labor and output markets in macro models and discussions of inflation. However, we have chosen to keep our macro model as simple as possible and do not include a separate treatment of the labor market.


ASYMMETRY IN THE U.S. OUTPUT-INFLATION NEXUS 221

disturbance term also includes special factors (other than aggregate excess demand conditions and expectations) that can affect the inflation process from time to time. This could include, for example, cost-push factors such as an exogenous increase in wage demands or a change in the price of crude oil.

Equation ( 1 ) is often motivated by appealing to costly price level adjustment, as in the models of Calvo ( 1 983) or Rotemberg ( 1987), for example. Strictly speaking, however, these models consider price levels and not inflation rates. The simple theoretical framework has been extended by some authors (e.g., Cozier ( 1989)) by assuming that the change in prices is costly to adjust. In our view, however, Buiter and Miller ( 1 985) and Roberts ( I994c) describe this appropriately when they refer to it as "slipping a derivative" into the firm's optimization problem.

The simple form of the model in equation ( 1 ) implies that the main source of inertia in inflation dynamics is rigidities in expectations. If combined with an assumption of model-consistent or rational expectations, the model implies that inflation can, in principle, be adjusted without cost. In other words, an announced reduction in the target inflation rate can be achieved without any output costs, as long as the expected inflation term in equation (I) moves one-for-one with the announced change in the target. For this to be so, however, one needs more than simple consistency with the predictions of a dynamic model; full credibility of the announced policy change is necessary.

Experience suggests that it is impossible to reduce inflation without creating a negative output gap. This can be rationalized through either one of two simple extensions to the above discussion. One extension adds the notion of intrinsic dynamics to equation ( I ), as would be suggested by a model with costly price adjustment. The sources of intrinsic dynamics could also take the form of overlapping wage contracts (e.g., Taylor ( 1980)). In either case, this would imply that an additional term in the lag(s) of inflation would have to be added to equation ( I ). The second extension focuses on how expectations are formed. If there is a backward-looking element to expectations formation, and we reinterpret expectations in equation ( 1 ) as the model-consistent component of overall expectations, then another rationalization of additional lags emerges. In other words, additional lags in equation ( 1 ) can arise either from intrinsic elements of inflation dynamics, which are independent of expectations, or from inertia in expectations formation itself (a backward-looking component), or both.8

Although there are differing interpretations of precisely why, there seems to be reasonably broad agreement among researchers working in this area

8 See Suiter and Miller ( 1985) or Fuhrer and Moore ( 1995) for further discussion of these issues.



that the simple model must be extended to account for inertia over and above what is possible in equation ( I ).9 The resulting model is often referred to as the "backward- and forward-looking components" model (Buiter and Miller ( 1985)). In this model, inflation in any time period is tied down, at least partially, by historical conditions (the backward-looking component), while the forward-looking component responds to new information about the future in a model-consistent fashion. The extended dynamic model can be written as

(2)

This version of the linear model provides the start·ing point for our extension to include asymmetry and the null hypothesis in tests of restriction to linearity of the asymmetric alternative. 10

Extending the Model for Asymmetric Effects

The most straightforward test of state-dependent asymmetry is to add positive output gaps to the model and test if the estimated parameter(s) on the additional term(s) can help explain inflation. Robert Gordon ( 1994) provides some econometric evidence of this nature by augmenting his simple, backward-looking, inflation-unemployment model with positive unemployment gaps. Although Gordon focuses his attention on Eisner's version of asymmetry-that inflation falls more when the economy is in a recession than it rises when the economy is booming-his statistical evidence can be easily reinterpreted as a test for asymmetry arising from capacity constraints. Gordon's results reveal no statistical evidence in favor of either form of asymmetry.

These results stand in sharp contrast with some recent empirical results reported by Laxton, Meredith, and Rose ( 1995), who found strong empirical evidence for the major industrial countries that positive output gaps have more powerful effects on inflation than negative output gaps. One possible reconciliation of these results could be insufficient business cycle variation in the U.S. data for researchers to be able to say anything with confidence about the role of capacity constraints on the basis of U.S. experience alone. However, since Turner ( 1995) finds evidence of significant asymmetry in the U.S. data, and we report corroborating evidence in this paper,

9 Taylor ( 1 980) was an important contribution to this literature. 10 In the simulations presented in Section Ill, we adopt the pure intrinsic dynamics interpretation of equation (2). That is, we simulate under the assumption of model-consistent expectations and treat the backward-looking component of the equation as coming entirely from intrinsic rigidities and not from expectations.



it appears that the explanation must be found in another element of the methodology.

One of the points argued by Laxton, Meredith, and Rose is that it is critical for econometricians to recognize the implications of asymmetry for the measurement of the output gaps that enter the Phillips curve in order to identify properly the asymmetric model. In particular, the mean value of the gap that enters the Phillips curve will be negative under the assumption of conve!lity and positive under the assumption of concavity in the functional form.11 Laxton, Meredith, and Rose demonstrate, in the context of the pooled G-7 data, that failing to recognize this point will bias test results toward not rejecting a restriction to linearity. Turner takes this into account in his specification and tests, and we show below that the Laxton, Meredith, and Rose conclusions regarding tests for linearity carry over to applications with the U.S. data.

With this issue in mind, we specify an asymmetric Phillips curve as follows:

1r, = A(L)TI,_ I + B(L)1Tf+l + 13 gapf + 'Y gapposr + e-;r, (3)

where gap* = y - y + a and gappos* represents the positive values of these adjusted gaps. The variable y is the log of output and we define y to be potential output, that is, the level of output that is attainable on average in an economy subject to continual shocks.12 Thus, the gap measured as y - y will have a mean of zero in large samples. In an economy with a linear symmetric Phillips curve, this would also be an appropriate property for the gap measure used in the Phillips curve. However, with asymmetry where positive gaps have larger effe.cts than negative gaps-if 'Y > 0 in equation (3)-and assuming that there is some variance in aggregate demand conditions, a must be less than zero for inAation to be bounded. In other words, the gap that enters a convex asymmetric Phillips curve must have a negative mean.

Equation (3) embodies the simplest empirical form of asymmetry-a piecewise linear function with the possibility of a kink at the point where gap* begins to exert upward pressure on inflation. We think of this representation as an approximation of any convex functional form. Its advantage is that we can test for asynunetry in a very simple and direct manner. Laxton, Meredith, and Rose ( 1995) argue that there are advantages to more complicated functions with marginal convexity. We do not dispute this but, with the limited data available to identify the nature of the function, we pre-

1 1 A formal proof of this can be found in Section IV .2 of Clark, Laxton, and Rose (1995b). 12 Output is measured in logarithms so that in a growing economy gaps constructed with a symmetric two-sided filter will have a zero mean in large samples.



fer to keep the empirical exercise as simple as possible. Equation (3) allows us to test for the presence of asymmetry, which is our prime objective here. Although we go on to use this particular model for some policy experiments, both here and in an earlier paper (Clark, Laxton, and Rose ( 1995a)), we consider this work illustrative. For policy analysis, it may be appropriate to assume alternative functional forms.

So far, we have not taken a stand on how one should measure potential output in practice. In any study of the Phillips curve, the choice of a measure of the output gap is very important. We shall show, however, that for the issues addressed here, it becomes less important once proper care has been taken to specify the functional form of the Phillips curve to be consistent with the hypothesis being tested. We report results using a variety of methodologies. To begin, however, we follow Laxton, Meredith, and Rose ( 1 994) and measure the trend level of output using a simple two-sided moving average filter of actual output. In their study with annual data, they measure trend output as a five-year, centered-moving average of actual output (a two-year horizon, forward and backward). In this paper, we use the same approach but report results for a range of alternative horizons (the parameter k in equation (4) below) in the two-sided filter. We later test the sensitivity of our conclusions to this methodology by repeating the estimation with a number of alternative measures of the output gap.

y = 2k 1+ 1 [y, + t (y,+i + y,_;)] (4)

I= I With this filter, a small value of k implies that potential output is highly

correlated with actual output and, at the limit, when k = 0, potential output is equal to actual output at all points in time. This calibration would be consistent with an extreme real-business-cycle view of the world, where prices adjust instantaneously to changes in excess demand. In such a world, it obviously makes no sense to estimate a Phillips curve. At the other extreme, a large value of k would be consistent with a view that most of the variation in observed output at business cycle frequencies is associated with movements in the output gap and not with potential output. Because there is considerable uncertainty about the role of demand and supply shocks in the economy and because imposing a false restriction can result in invalid statistical inferences, one way to proceed is to report results, and hypothesis tests, for a wide range of values of k. 13 This is the strategy we adopt.

As emphasized above, this (or any mean zero) measure of the output gap may be a seriously biased proxy for the gap that is appropriate for use in the Phillips curve. It is to correct for this potential bias that we introduce the

13 See Eichenbaum ( 1 99 1 ) for an excellent discussion of why econometric techniques cannot provide reliable estimates of the relative variance of demand and supply shocks. We pursue this issue in Section IV.



level shift to the filter measures of the output gap for use in the identification of the Phillips curve. This level shift is assumed to be fixed over our sample period and is estimated as the parameter a.14 If short-run capacity constraints are truly a feature of the U.S. economy, imposing a zero value on a will bias -y toward zero and bias standard tests for the presence of asymmetry toward false rejection. 15 We will show that this point is of the utmost importance in assessing the empirical evidence.

Is There Asymmetry in the U.S. Phillips Curve?

In this subsection, we report estimates of the U.S. Phillips curve and tests for whether it has significant asymmetry. We begin with our specification and tests and then turn to supporting evidence in the form of documentation of what happens when the logical implications of asymmetry are not taken into account in the estimation and testing.

Unbiased Tests for Asymmetry in the U.S. Phillips Curve

Table 1 reports the results of estimating our model with a determined simultaneously along with the other parameters. We report estimates for values of k ranging from 2 to 16 (quarters). Because we want to hold the estimation period fixed to see how alternative gap measures perform in explaining the same data on inflation, the sample for the dependent variable (for all regressions) must end in 1 990:4. (The two-sided filter with k = 16, requires data on actual output for the years 1991 to 1 994.)

The details of the model to be estimated are provided at the top of Table 1 . We wanted to keep the model parsimonious, because in such a small sample it is difficult to identify more than a few key parameters with any precision. This led us, for example, to limit the output gap effects to contemporaneous measures. Second, we use the Michigan Survey measure of inflation expectations. We knew from the work of Roberts ( 1 994b and I 994c) that this measure is useful in explaining movements in actual inflation, but the most important reason for using a survey measure is, we think, that having a forward-looking element to expectations is important in estimation as well as in policy analysis. The use of the survey measure allows

14 We have noted already and will argue more formally later in the paper that the extent of this shift will depend on the nature of the monetary reaction function and the consequent cyclical properties of the economy. There may be good reason to doubt that the same monetary reaction function has been operating throughout our estimation sample. However, we leave this complication to future research and interpret the estimated shift parameter as reflecting average historical behavior. 15 See Section IV for a discussion of the statistical properties of asymmetric models when researchers fail to account for their logical implications.



Table I . A Simple Asymmetric Model of the U.S. Oulpul-fnjiarion Nexus

(r-statistics in parentheses)

Estimated equation: 1r, = o 'if�+• + ( I - o)1rt- 1 + 13 gapf + 'Y gapposf + E;'.

where gap* = y - y* = y - y + a, gappos* = positive values of gap* iff+4 = .2(,'Tff+4 + t- 17Tf+J + r-1'1T�+2 + r-)"'T�+I + t--l'lTn

1r = percent change in the CPI at annual rates 1Tf+J = Michigan Survey measure of inflation expectations [ k

y = 2k � I y, + ?, v,+, + y,_,] t=l

and SL = significance level.

Data: U.S. quarterly data, 1964: 1-1990:4.

Wald test: k a 'Y 13 0 R2 (J SL(a, 'Y = 0)

5 -0.354 0.878 0.458 0.566 .7776 1 .6445 0.087 (0.99) ( 1 .83) (2.59) (4.65)

6 -0.441 0.873 0.384 0.576 .7816 1 .6296 0.032 ( 1.23) (2.19) (2.64) (4.9 1 )

7 -0.547 0.813 0.337 0.582 .7821 1 .6275 0.022 ( 1 .44) (2.36) (2.55) (5.01)

8 -0.670 0.780 0.308 0.585 .7844 1.6192 O.Ql5 ( 1 .73) (2.64) (2.6 1 ) (5.20)

9 -0.770 0.758 0.282 0.586 .7850 1.6168 0.004 (2.09) (3.21) (2.60) (5.48)

1 0 -0.893 0.772 0.254 0.587 .7851 1 .6164 0.010 (2.72) (3.00) (2.52) (5.87)

1 1 - 1 . 149 0.918 0.218 0.591 .7873 1 .6081 0.004 (3.27) (2.99) (2.4 7) (6.07)

1 2 - 1 .256 0.925 0.202 0.593 .7892 1 .6010 0.001 (3.66) (3.16) (2.43) (6.13)

1 3 - 1 .369 0.916 0.189 0.600 .7890 1.6017 0.001 (3.67) (3. 1 3) (2.47) (5.99)

1 4 - 1 .478 0.896 0.177 0.595 .7879 1 .6058 0.007 (3. 1 3) (2.72) (2.43) (5.88)

15 - 1 .661 0.919 0.166 0.593 .7862 1.6123 0.002 (3.38) (2.69) (2.47) (5.79)

1 6 - 1 .712 0.866 0. 1 6 1 0.587 .7834 1 .6229 0.010 (3 .02) (2.56) (2.49) (5.58)



us to avoid the difficult econometric issues implied by explicit modelconsistent expectations (e.g., the use of instTumental va1iables, as in Laxton, Meredith, and Rose ( 1 995)). We chose a specification that includes the contemporaneous value of one-year-ahead inflation expectations as well as four lags, where each lag is assumed to have the same weight. In addition, a lagged inflation term was added to allow for intrinsic inertia in inflation dynamjcs. 16

The results in Table I were obtained using nonlinear least squares in RATS. The value of k that minimizes the standard error of the inflation equation is 1 2 quarters. This estimate suggests that variation in the output gap, as opposed to potential output, is the dominant source of variation in output at business cycle frequencies. Based on this preferred model, there is clear evidence that positive gaps have larger effects on inflation than do negative gaps. Indeed, the estimated total coefficient on the positive gaps (� + -y) is l . l or about five times greater than the coefficient on the negative gaps (� alone). This is a very similar finding to that reponed in Laxton, Meredith, and Rose ( 1995).

The estimated value of ex is - 1 .3; this implies that the gap* measures that are used in the Phillips curve are 1 .3 percentage points smaller than the gaps based on our simple filter. Figure 1 illustrates the results for the asymmetric model. In this case, "potential" output in the top panel is raised by 0.0 1 3,

relative to the trend measure from the filter, so that we can illustrate the "gaps" that enter the Phillips curve. It is important to remember that this level of output is not attainable in the stochastic economy.

The estimated value of 8 is just under 0.6, leaving a weight of just over 0.4 on the lagged value of inflation. Regardless of how one chooses to interpret these coefficients (see the discussion in the previous subsection), the results suggest that there is important inertia (a backward-looking component) in inflation dynamjcs. There is also, however, an important forwardlooking component that enters through the expectations.

Examination of the residuals from the preferred estimation indicated that there was some minor autocorrelation, primarily at the third lag. For this reason we have used the robust standard errors option in RATS to obtain the t-tests reported in parentheses. Note that the t-test for -y indicates that the simple restriction to linearity (-y = 0) is strongly rejected and that this result is robust over a wide range of values of k. Note, further, that ex is strongly and significantly different from zero, a result that is also robust to substantial variation in k. Finally, we report a Wald test of the joint restric-

16 This choice of lag structure does not affect our conclusions. We obtain basically the same results if we estimate an unrestricted model with four lags on inflation and inflation expectations or impose a triangular distribution on lagged inflation expectations.



Figure I . lnrerpreting U.S. Inflation with an Asymmetric Model

Real GOP (har) and Adjust�d Potential GOP (solid line) (25-quaner centered moving average plus .0 13. in logs)

CPI In nation (bar) and In nation Expectations (solid line) 20r---------------�----------�------------------�

-5 ��7-�� 1964 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94

7t1- .597t� + 4 - .41 7t1_1 (bar) .20gap1 + .93gappos1 (solid line) 6r-----------------------------------------------�

4

2

-2

-4

-61964 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94



tion, a, -y = 0, which imposes the full conditions of the linear null hypothesis. This test is performed on the condition that � is strictly positive, a hypothesis that is not rejected by a direct test. 17 It indicates that the joint restriction is rejected at the 99.9 percent confidence level for our preferred result.

Biased Tests for Asymmetry in the U.S. Phillips Curve

In discussing the motivation for including the shift effect captured by the parameter a in our model, we argued that this was essential in order to obtain unbiased tests for the presence of asymmetry. We now return to this important issue. Table 2 reports some econometric estimates of the same model under the assumption that a = 0, again for a range of values of k. The standard errors for the r-statistics (reported in parentheses) are again computed using the robust errors option of RATS.

In this case, the value of k that minimizes the standard error of the inflation equation is 8. This still has substantial smoothing of the data in the implied profile of trend output, but less than in the model of Table I . The relative weight estimated on the forward- and backward-looking components of the dynamics is not much affected by the restriction on a. However, the preferred model here has two noteworthy features that are very different. First, the econometrician would reject the hypothesis that -y > 0 at the usual confidence levels and conclude that there was no compelling evidence of asymmetry in the U.S. Phillips curve. Second, the coefficient on the output gap is statistically significant, so there is evidence that inflation is related to the output gap-a Phillips curve exists. Again, these results are robust over a substantial range of values of k.

Figure 2 provides a graphical representation of the linear Phillips curve when we impose a, -y = 0 and choose the model that maximizes the fit of the inflation equation. The regression results are shown in the second line of Table 2 with k = 9, which gives the best fit under these restrictions. The top panel of the chart plots our filter measure of potential output. The middle panel presents the percent change in the CPI measured at annual rates along with the Michigan Survey measure of one-year-ahead CPI inflation expectations. The bottom panel presents the difference between inflation and its backward- and forward-looking components, 1r, - 81Tf - ( I - 8 )1T,_ 1 , and the contribution of the output gap, as measured by the coefficient times the output gap, �gap,. As can be seen in the chart, there is a tendency for the lin-

17 The notional restriction on f3 is necessary so that a is identified under the null hypothesis. This avoids the necessity to compute a more complicated test of the restriction when there is a nuisance parameter. See, for example, Andrews and Ploberger ( 1994 ).



Table 2. Some Biased Tests of Asymmetry

(!-statistics in parentheses)

Estimated equation: TI, = 8 'ff�+4 + ( I - O)TI,_ 1 + f3 gapf + 'Y gappos1 + E�. where gap* = y - y* = y - y + ex, gappos* = positive values of gap*

7fr+..s = .2(,if�·+4 + t-J1T�·+.' + ,_]'iT�·+2 + 1-.t"iT�+J + 1-.(IT;') 1r = percent change in the CPI at annual rates

1T�+J = Michigan Survey measure of inflation expectations [ k Y = 2k � I y, + � Yt+• + Yt-1 t � l .

Data: U.S. quarterly data. 1964: 1-1990:4.

k ()( 'Y f3 0 R! 11

5 0.00 0.285 0.593 0.547 .7739 1.6499 (0.96) (3.34) (4. 73)

6 0.00 0.302 0.497 0.556 .7761 1.6296 ( 1.20) (3.32) (4.9 1 )

7 0.00 0.28 1 0.435 0.562 .7769 1 .6387 ( 1 .27) (3. 1 0) (5 .02)

8 0.00 0.23 1 0.414 0.564 .7787 1 .6321 ( 1 . 12) (3.13) (5.07)

9 0.00 0. 1 92 0.391 0.564 .7785 1.6331 (0.99) (3. 15) (5.14)

9 0.00 0.00 0.484 0.552 .7765 1 .6328 (4.54) (4.61)

1 0 0.00 0.174 0.362 0.563 .7774 1 .637 1 (0.93) (3. 1 2) (5.25)

I I 0.00 0.154 0.341 0.560 .7765 1 .6403 (0.86) (3.09) (5.3 1 )

1 2 0.00 0.134 0.326 0.557 .7761 1 .642 1 (0.79) (3.14) ( 5.33 )

13 0.00 0. 1 1 0 0.316 0.555 .7747 1 .6469 (0.67) (3.22) (5.28)

14 0.00 0.907 0.308 0.552 .7736 1 .6510 (0.57) (3.29) (5 .21)

15 0.00 0.745 0.301 0.549 .7725 1 .6548 (0.48) (3.39) (5. 13)

1 6 0.00 0.059 0.296 0.545 .7713 1.6594 (0.39) (3.48) (5.04)


ASYMMETRY IN THE U.S. OUTPUT-INFLATION NEXUS 23]

Figure 2. lnrerprering U.S. ir!flarion wirh an Linear Model

R�al GDP (bar) and Adjusred l'orenrial GOP (�olid line) (I 9-quaner ccrucred moving average, in Jogs)

8.75.-----------------------------,

8.25

8.00

7.75

7.50 t964 66 68 10 n 74 76 78 so s2 84 86 ss 90 92 94

CPI lnnarion (bar) and lnllarion Expec 1a1ions (solid line) 20 ,---------------------------�-------------------,

-5��L-��-i�� 1964 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94

rr,- .56n� + 4 - .44n, _1 (bar) .39gap, (solid line) 6.-------------------------------------------------,

-61964 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94



ear model to underpredict inflation during the two inflationary episodes in the 1970s when there was large and persistent excess demand.

I n conclusion, we find evidence of significant asymmetry in the U.S Phillips curve, confirming the result in Turner ( 1995) (and the result in Lax· ton, Meredith, and Rose ( 1995) for the pooled G-7 data). A major distinguishing feature of this work, which sets it apart from other work that finds no such evidence for the U.S. data, is the explicit attention to the implications of asymmetry for the manner in which the gaps must enter the estimated Phillips curve. It is clear that procedures that do not allow for the logical implications of the alternative hypothesis can produce biased results in tests of restriction(s) to the null hypothesis. We maintain that the failure of some researchers to account for how the output gap should enter the Phillips curve i n an asymmetric world has biased their test results toward false rejection of the presence of asymmetry. We have shown that the results of tests for asymmetry in the U.S. Phillips curve are changed dramatically toward not rejecting the linear null hypothesis if ex is suppressed, echoing a similar result shown by Laxton, Meredith, and Rose ( 1 995) for the major industrialized countries. We return to this issue in Section IV.

III. Asymmetric Versus Linear Models of the Inflation Process

This section provides a brief discussion of some properties of the estimated linear and asymmetric models of inflation dynamics described in Section II. In particular, we compare the trade-offs faced by a monetary authority in dealing with a shock to aggregate demand, using deterministic simulations of a small model of the macroeconomy and the policy control process. The model, which is essentially the same as that used in Clark, Laxton, and Rose ( 1995a), is sketched out below.

As the simulations embody model-consistent expectations, the monetary policy reaction function plays a key role in conditioning the overall dynamics of the economy. Indeed, the essential task of the monetary authority in the model is to act so that inflation and inflation expectations are eventually anchored to the target rate of inflation.

The simulations compare the consequences of delaying the monetary response to a demand shock in the two versions of the model. They show that, in contrast to the linear case, where delay is relatively costless, in a world with asymmetric inflation dynamics, delaying interest rate hikes in the face of excess demand results in a substantial cumulative output loss because the monetary authority is then forced to impose a more severe monetary reaction in order to reign in the higher inflationary pressures. Indeed, an important prediction of the asymmetric model is that large recessions are



caused by policy errors that allow the economy to overheat and that the eventual tightening in monetary conditions is only a proximate cause.

A Simple Model of the U.S. Output-Inflation Process

The equations of the model are listed in Table 3. In addition to the two versions of the Phillips curve and some definitions, the model has two equations: one that describes the dynamics of the output gap and the mechanism by which monetary policy influences aggregate demand, and another that describes a policy reaction function designed to keep inflation in the neighborhood of a chosen target level.

The equation for output dynamics has two features that are important for these experiments. First, there are lags in the effect of the monetary control variable. Second, there is an autoregressive propagation structure that, all else being equal, initially amplifies the effects of shocks to aggregate demand and then sustains them for some time. The monetary control vari-

Table 3. A Small Simulation Model of the U.S. Output-Inflation Process

Asymmetric Phillips curve:

'IT, = .593'ffr .... + ( I - .593)'TT,-1 + .202 gapf + .925 gapposf + E� 'ffr+4 = .2(,'1Tf+4 + ,_.'JTf+J + 1-21rr ... 2 + ,_J'TTr .... + ,_4'JTn

Linear Phillips curve:

'IT, = .548'fff+4 + ( I - .548)1T,_1 + .524 gap, + Ei' Real interest rate:

rr, = rs, - 'Ti�H

Inflation and inflation expectations:

'IT, = [(P,/P,_.)4 - I ] * IOO, 'TTr+4 = (?, ... 4/P,- I ) * 100

Aggregate demand equation:

gap, = 1 .074 gap,_1 - .290 gap,_2 - . 158 rr,_2 + ef"P Policy reaction function:

rs, - 'TifH = 2(1i, .... , - 'IT*) + gap,

'IT = CPJ inflation at annual rates gap = output gap (y - )i)

gap* = (y - y + ex) = (y - y*) rr = real interest rate rs = Federal Reserve funds rate

r.r ... 4 = one-year-ahead inflation expectations 'Ti* = inflation target P, = price level



able in the model, i.e., the variable that provides the transmission mechanism for monetary policy, is a short-term real interest rate. We treat the Federal Reserve funds rate as the policy instrument, but it is an ex ante real interest rate that enters the demand equation. The model is specified with a two-quarter delay before changes in the real interest rate begin to have an influence on aggregate demand. Thereafter, the effect builds such that after five to six quarters, a persistent real interest rate hike of 100 basis points that is sustained for four quarters would reduce the output gap by 0.4 percentage points. The propagation of demand shocks is represented by a second-order autoregressive structure. All else being equal, the effects of a shock are amplified in the second period and then die out slowly. These properties are roughly consistent with the evidence from both reduced-form models of the transmission mechanism (e.g., Roberts ( 1 994a)) and more structural models (e.g., Mauskopf ( 1 990)).

These properties of output dynamics and the monetary policy transmission mechanism have an important implication for the design of monetary policy mles-monetary policy cannot offset completely the effects of shocks. There will be cycles in economic activity and there will be temporary deviations of inflation from its target level. This makes it especially important for the monetary authority to be forward-looking in its actions. The particular forward-looking policy reaction function that we use is a variant of the rule considered by Bryant, Hooper, and Mann ( 1993). In setting the short-term interest rate, the monetary authority acts to raise the real rate that enters the output equation when inflation is expected to be above the target level three quarters ahead or there is excess demand in the economy. The particular calibration adopted is designed to ensure that inflation remains in the region of the target level and returns to the target level within a reasonably short period (two years) following a shock to aggregate demand.

The Effects of Delaying Monetary Response to a Demand Shock

The simulations show what happens when there is an impulse shock of I percent to aggregate demand, i.e., when a I percentage point output gap opens on impact and there are no further shocks.'� We compare the consequences of delaying the monetary policy response by just one quarter for the two versions of the model. The delay is implemented by simply holding the U.S. Federal Reserve funds rate at its control value for one quarter

18 The simulations reported here are deterministic. Although these types of experiments are useful for developing the basic intuition behind the model, they do not do justice to the full policy implications. See Clark, Laxton, and Rose ( 1 995a) for a more extensive analysis of the policy implications of asymmetry in inflation dynamics in a stochastic environment.



(i.e., the normal reaction function is turned off for one quarter and then operates normally). 19 The results from the model with a linear Phillips curve are shown in Figures 3 (no delay) and 4 (delay). Figures 5 and 6 show the comparable results from the model with asymmetry.

If the economy is linear, the effects of delay are relatively innocuous. With an immediate response amounting to a 270 basis point increase in the short-term interest rate in the first quarter, inflation peaks at about 1 percentage point above control, and there is a cumulative gain of output of about 2 percent. With a delayed monetary response, there is a larger hike in short-term interest rates, and inflation edges slightly higher, peaking at about 1 .3 percentage points above control, but the cumulative gain in output is even larger, amounting to about 2.5 percent by the end of the simulation. These results show that if the world is linear, there is no strong case for aggressive monetary resistance to inflationary demand shocks. While the monetary authority may be concerned to see inflation rise above the target by more and for a longer period of time, it would be difficult to argue that there are any real costs to delaying interest rate hikes when output exceeds potential output.

The picture looks quite different if there are capacity constraints that result in asymmetry in inflation dynamics. Despite a much stronger policy response in the no-delay scenario, with short-term interest rates up by over 400 basis points in the first quarter, inflation peaks at about 2 percentage points above control. While the course of output is roughly similar over the first few quarters, the task of reining in the higher inflationary consequences of the same shock in this model requires a much deeper secondary contraction and the elimination of any cumulative gain in output. In fact. there is a small cumulative loss of output

The consequences of delaying the monetary response to the shock are much more dramatic in this case. Short-term interest rates must be raised substantially higher to combat the cumulating inflationary pressures, as expectations respond to the more sustained excess demand and rising inflation. Inflation now peaks at 3 percentage points above control. To bring inflation back under control in this environment requires a much more severe contraction. Indeed, the cumulative change in output is now substantially negative because a large contraction is needed to counteract the inflationary effects that are caused by the initial temporary boom.

The model with asymmetry has many of the predictions that most central bankers highlight when discussing the fundamental role of monetary policy. It provides a clear and compelling reason for forward-looking action by the

19 Thes-; simulations were carried out using the ·'stacked time" algorithm in TROLL. Sec Armstrong, Black, Laxton, and Rose ( 1995) for a description of this algorithm and its properties.



Figure 3. Linear Model Responses to a Tempormy I Percent Positive Demand Shock

Real GOP (dotted line) and Potential GOP (solid line) (in logs)

Quarters after the shock

Output Gap and Year-on-Year In nation

(Deviation from control in percentage points ) 1 .2 ,_ ______ __;,. _ __..;;..._;__--,

1.0

0.8 0.6 0.4 0.2

Ourpw gap

o��----------� -0.2

-Q. 4 L.i.-'-L4.L..l....L"-;8,-'-'L.L...LI-:;'2 -'--.L..l:-:1 6L..L-'-2!:-;:J0 Quarters after the shock

Cumulative Effect on Real GOP.

(Deviation from control in percent) 3.0 .----------'------,

0.5


Federal Funds Rate and In nation

(Deviation from control in percentage points) r--______ ..;___...;;_.;__---, 3.0 Federal fimds rare 2.5

2.0

1.5

CPI inflation at annual mte.l' 1.0

/ 0.5

�UL��---------� 0


Price Level (Deviation from control in percent) .---------.:...._--..., 0.9

4

,.----------l 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0. 1

1 2 1 6 20 ° Quarters after the shock



Figure 4. Linear Model Responses to a Temporary I Percent Positive Demand Shock: Delayed Monetwy Policy Response

Real GOP (dolled line) and Potential GOP (solid line)

0.12 (in logs)

0.10

0.08

0.06

0.04

0.02

0 4 8 12 16 20 Quarters after the shock

Output Gap and Year-on-Year lnllmion Federal Funds Rate and lnlla!ion

(Deviation from control in percentage points) 1 .2 ,.---------=------"-=---, (Deviation from con!rol in percentage points)

3.5

1.0

0.8

0.6

0.4

Owp111 gap

Year-on-year CPI inflation

0.2

o��nM��----------� -0.2

-0.4 '-L-'-'-4_._._....._8....L...J'--'-..1.1-'2'--'-........ -1 6L..J..-'-2L...JO Quarters after the shock

Cumulative Effect on Real GOP

(Deviation from control in percent) 4.0 .-------------,

0.5

O �....L...J�4L..J......L...J�8L..J......L...J�I 2L..J......L...J�I6L..J......L...J2�0 Quarters after the shock

II

Federalfimds rare

'\ CPI inflation at annual rates

3.0

2.5

2.0

1 .5 1.0

0.5 0 I{

20 -0.5 ·.I.J.L.I� 4 8 1 2 1 6 Quarters after !he shock

Price Level

(Deviation from control in percent) �----=============1 1.4

4 8 1 2 Quarters after the shock

16

1.2

1.0

0.8

0.6

0.4

0.2

20 °



Figure 5. Asymme1ric Model Responses 10 a I Perce111 Posilive Demand Shock

Real GOP (doned line) :md Potential GOP l,oJiu line) (in logs)

0.12

0.10

0.08

0.06

0.04

0.02

0 4 8 1 2 1 6 20 Quarters after the shock

Output Gap and Year-on-Ye:�r lnllation ( Ocvi: uion from contwl in percentage puints)

1.2 .-:--------..:._-�;___---=-, 1.0 0.8 0.6 0.4 0.2

Owpw !((tp

Year-on-year CPI inj1mimt

0 ��--� -0.2 -0.4 -0.6 -0 ·8 LL..J....L4.L.J.--'-

.L8..J....JL....L..LI....I2--L.J....i_I 6L..L..J....2LJO


Cumulative Effect on Real GOP (Deviation from control in percent) 3.0 ,....----------'------,

-0.5 L..L...L..L4---'---"L..L-'-8 '-'--'-.LI..J.2 -'-.L...l-1 6'-'--'-.LJ20 Quarters after the shock

Federal Funds R:ue and lnllation ( Deviation from control in percentage points) r--------..:._-�;_____:__, 4.5

Federaljimds rate 4.0 3.5 3.0 2.5

Kmioo"' ""'"'"' '"'" ll

��u_��-��-------� 0 l....I.-'-.L4-'-L..L-'-8 '-'--'-.LI..J.2 -'-.L...l-16LL-'-'---'20 -0.5


Price Level (Deviation from contml in percent)

.------------'----, 2.5

�------1 2.0

1.5

1.0

0.5

4 8 12 1 6 Quarters after the shock



Figure 6. Asymmetric Model Responses to a I Percent Positive Demand Shock: Delayed Monercuy Policy Response

Real GOP (doucd line) and Pmcntial GOP (�olid line)

O.IZ r---------------------------�(i�n�lo�g�s�)------------------------------, 0.10

0.08

0.06

0.04

0.02

4 8 1 2 16 20 Quarters after the shock

1 .5

1 . 0

-1.0

Output Gap and Year-on· Year lnllation (Deviation from control in percentage points)

Outpw gap

-1.5 L..L...L...l....L...L...J....J....J.....L...L...J....J....J.....L...L...J......L...l....L.J 4 g 12 16 20

-I


Cumulative Effect on Real GOP (Deviation from control in percent)

Quaners after the shock

Federal Funds Rate and lnlla1ion (Deviation from control in percentage points)

Federal funds rare 7

6

5

4

3

Ruion n1 amuwl mres 2

0

[/

Quarters artcr the shock

Price Level CDcvhuion from control in percent)

4.0

3.5

3.0

2.5 2 0

1 . 5

1 . 0

0.5

4 s 12 16 20 ° Quarters after the shock



monetary authority to forestall any tendency for the economy to move into excess demand. To fail to do so necessitates even tougher action later on to keep inflation in check, with unfortunate but unavoidable macroeconomic consequences. Monetary authorities' apparent preoccupation with inflation reflects a concern about the consequences for the real economy; to temporize on inflation is to force the economy to suffer both a cumulative loss of output and more extreme variation in economic conditions.

IV. Some Issues in the Specification and Estimation of Phillips Curves

On Methods of Measuring Potential Output and Their Implications

This study might be criticized on the grounds that it has relied on an ad hoc, two-sided, moving average filter to measure potential output. In principle, it would be preferable to specify a dynamic structural model that nested both the linear and asymmetric views of the world, and to derive model-consistent measures of the output gap under both hypotheses. This would place the models on an equal statistical footing and, i n principle, permit a clearer test of the restriction to linearity. Although such an endeavor might well be worthwhile, it is not clear that it would be possible to identify many more parameters and to discriminate between more complex models, given the limited number of observations of business cycles available in the data. We leave this as an interesting topic for future research.20

We would be remiss, however, if we did not check whether our results stand up if we use other univariate techniques to measure potential output. This could be important; Harvey and Jaeger ( 1993), for example, have shown that reliance on simple filters may induce spurious relationships in regressions.2 1 A related example is provided in Laxton, Shoom, and Tetlow ( 1 992). They show that the use of simple univariate filters to measure gaps can cause spurious change-in-the-gap terms to have significant coefficients in estimated Phillips curves in cases where the true data generating process has only pure level gap effects.22 Thus, there is a risk that our use of the two-

2° Kuttner (1991) implements a Kalman filter procedure to provide modelconsistent estimates of the gap when the Phillips curve is linear. An obvious extension of our work would be to develop a similar procedure that could be used for nonlinear models.

2 1 See also Nelson and Kang ( 1 98 1 ) and Cogley and Nason ( 1995). 22 It is not uncommon for researchers to use such techniques and then discard level gap variables because their estimated coefficients are not significantly different from zero, despite the implications this has for monetary policy. The lack of any level gap effects in the Phillips curve is sometimes interpreted as evidence of hysteresis.



sided moving average filter to measure potential output has somehow biased our results in favor of the asymmetric model.

Harvey and Jaeger ( 1993) present a trend-plus-cycle or unobserved components (UC) model that is quite flexible and encompasses many other popular detrending procedures. For our purposes, their model can be thought of as a simple reduced form of a more general dynamjc stochastic sttuctural model of the U.S. economy. They show that the Hodrick and Prescott ( 1981 ) filter and the two-sided moving average filter used in this paper are generally suboptimal for estimating trends of economic variables.23 Indeed, they show that estimates from the Hodrick-Prescott (HP) filter are optimal-in the class of univariate filters-only under very specific parameterizations, which vary from case to case. Using several economic series as examples, they show how the arbitrary use of the HP filter can result in biased estimates of the cyclical component and can even induce spurious correlations and regression results when the variables are detrended this way. These potential problems also apply to our filter.

Harvey and Jaeger also argue that their model has several advantages over simple time trends or segmented time trends. Despite the fact that it is impossible to discriminate between deterministic segmented time trends and stochastic representations of output in small samples, they argue that the latter is preferable because segmented time trends are based on arbitrary assumptions on when the trends break.24

The validity of their general argument notwithstanding, Harvey and Jaeger show that in the particular case of the U.S. GNP their model produces estimates that are very similar to the HP (A. = 1,600) estimates. They conclude (p. 236) that this "suggests that the HP filter is tailormade for extracting the business cycle component from U.S. GNP." The bottom panel of Figure 7 shows the estimates obtained from the Harvey and Jaeger unobserved components (UC) model along with the estimates obtained from the HP filter with A. set equal to 1 ,600.25 It is evident that the

23 HP filter estimates Ur) are derived by minimizing the sum of squares of T �2

the gap L (y, - Yr)**2 and a ''smoother" A L L(Y,+� - Yr+ l ) - cYr+l - Yr)P. I I

Many users set the smoothness parameter, A, at 1 ,600 despite the fact that, in principle, the "optimal" value will depend on the properties of the particular series. HP (A = 1 ,600) filtered values of U.S. GOP resemble closely those from a two-sided moving average filter with geometrically declining weights. Our simple filter is similar but has equal weights.

24 For an example of the segmented-trend approach, see Braun ( 1990), with details in Table A.2, p. 302.

25 We thank Paula De Masi and Michael Funke for supplying us with these estimates. The estimates in both cases are based on the level U.S. real GOP.



Harvey-Jaeger conclusion is not altered by the change in the output measure; the two methods produce very similar estimates of the U.S. GDP output gap.

Another common procedure for providing trend estimates and gap measures is to fit polynomial, often quadratic, trend lines to the data. For example, Roberts ( 1 994c) reports estimates of inflation models that use quadratic time trend approximations to measure potential output.

Table 4 reports estimates of our inflation model based on these alternative estimates of the output gap. Again, to give some indication of the bias associated with using pure measures of central tendency in deriving gap measures for estimating the Phillips curve, we report results with and without the a shift effect. Equation (2a) in Table 4 reports the estimates for our model with the Harvey-Jaeger output gaps. Note that the fit of the model is slightly better with the Harvey-Jaeger gaps than in our best result. In our estimation, both -y and � are slightly larger than in Table I . Moreover, all the parameters are statistically significantly different from zero, and a Wald test indicates that we can reject the joint restriction that a, � = 0 with considerable confidence. Equation (2b) reports the results when a is imposed to be equal to zero. In this case, the estimate of the coefficient on the positive output gaps (-y) falls from 1 .092 in the unrestricted model to 0.331 in the restricted model. In addition, the coefficient on the output gap (�) rises from 0.281 in the unrestricted model to 0.403 in the restricted model. This confirms the direction of bias from the Monte Carlo evidence reviewed above. Moreover, as in our exercise using the simple filter, an econometrician would not be able to reject the hypothesis -y = 0 at the traditional high levels of confidence, although with these results an objective researcher might think long and hard about the risks of assuming that this gave license to throw the gappos* variable out of the model.

Equation (3a) reports the results when we use the HP (X. = I ,600) filter to measure the output gaps. The results confirm the earlier indication that these gaps are not significantly different from the Harvey-Jaeger gaps from the unobserved components model. Indeed, the parameter estimates are almost identical to those in equation (2a). And, again, the case for asymmetry weakens when we impose a = 0.

In general, univariate techniques can be expected to produce very uncertain estimates of the true relative variance of the gap term. Consequently, it may be reasonable to presume that potential output is smoother than is implied by the HP (X. = I ,600) filter or the unobserved components model. To test the sensitivity of our results to this assumption we re-estimated our model with larger weights on the smoothness parameter of the HP filter. In



Figure 7. Harvey and Jaeger ·s Measure of POTelllial Our put

Real GDP (bar) and Harvey/Jaeger Potclllial GDP in logs (solid line) 8.75

8.50

8.25

8.00

7.75

7.50 1964 66 68 70 72 74 76 78 80 82 H4 86 8& 90 92 94

20 CPI lnO:Ilion (b:lr) and Harvey/Jaeger Output Gaps (solid line)

1 5

1 0

5

0

-5 1964 66 68 70 72 74 76 78 80 S2 84 86 88 90 92 94

Harvey/Jaeger Output Gaps (bar) and HP 1.600 Output Gap (solid line) 6

4

2

0

-2

-4 -6 1964 66 68 70 72 74 76 78 80 82 &4 86 88 90 92 94



Table 4. Tests with Alternative Measures of the Output Gap

(r-statistics in parentheses)

Estimated equation: TI, = OTI�+4 + ( 1 - 1>)TI,_1 + � gapf + -y gappost + E;',

where: gap* = y - y* = y - y +a, gappos* = positive values of gap* 7f�+4 = .2(,TI�N + r- ITI�+3 + 1-1TI�+1 + r-JTI;·+ I + r-41Tr)

TI == percent change in the CPI at annual rates Tif+4 == Michigan Survey measure of inflation expectations

SL == significance level.

Model #I : Case of k = 1 2 from Table I Model #2: Harvey and Jaeger's ( 1993) Trend Plus Cycle Model Model #3: Hodrick-Prescott filter with A. = I ,600 Model #4: Hodrick-Prescott filter with A. = I 0,000 Model #5: Hodrick-Prescott filter with A. = 100,000 Model #6: Hodrick-Prescott filter with A. = 500 Model #7: Quadratic time trend (sample period = 1961 : 1-1994:4) Inflation equation estimation period: sample 1964: 1-1990:4

Wa!d test: Model Cl 'Y � 0 R2 (T SL(a, -y = 0) Ia - 1 .256 0.925 0.202 0.593 .7892 1.6010 0.001

(3.66) (3.16) (2.43) (6.13) l b 0.000 0.134 0.326 0.557 .7761 1 .6421

(0.79) (3.14) (5.33) 2a -0.791 1 .092 0.281 0.6 1 1 .7927 1 .5877 0.018

(2.48) (2.80) (2.40) (6. 1 8) 2b 0.000 0.331 0.403 0.583 .7849 1 .6094

( 1.52) (2.75) (5.58) 3a -0.848 0.943 0.248 0.6 1 1 .7927 1 .5874 0.008

(2.34) (3.05) (2.46) (5.88) 3b 0.000 0.283 0.344 0.581 .7827 1 .6175

( 1 .52) (2.94) (5.40) 4a - 1 .498 1.081 0.175 0.589 .7833 1.6231 0.000

(4.28) (3.03) (2.67) (5.25) 4b 0.000 0.148 0.298 0.558 .7745 1 .6477

(0.88) (3.63) (5.00) Sa -0.506 0.176 0.226 0.530 .7652 1 .6895 0.782

(0.53) (0.70) (2.71) (4.69) Sb 0.000 0.046 0.266 0.528 .7649 1 .6826

6a -0.713 1 .066 0.303 0.6 1 1 .7920 1 .5902 0.013 (2.48) (2.92) (2.53) (5.80)

6b 0.000 0.328 0.424 0.583 .7842 1 . 6 1 1 9 ( 1 .49) (2.80) (5.47)

7a 1 .458 -0.205 0.335 0.5 1 5 .7581 1 .7 148 0.160 ( 1 .74) ( 1 .57) (3.28) (4.15)

7b 0.000 -0.013 0.222 0.5 1 2 .7567 1 .7 1 1 7 (0.10) (3.86) (4.29)



the limit, an extremely high weight on smoothness implies that potential output is treated as a linear time trend. Equations ( 4a) and (Sa) provide additional estimates when A, the HP smoothing parameter, is set equal to I 0,000 and I 00,000, respectively. Note that the fit of the inflation equation deteriorates as larger values of A are imposed. Thus, a view that supply shocks are irrelevant for changing the growth rate of potential output is inconsistent with explaining the time series properties of both U.S. output and inflation.

For completeness, we also offer a result with a smaller value, A = 500, which gives the supply component of shocks more weight so that the trend estimate follows the data somewhat more closely. The fit is not quite as good as with A = I ,600, or the Harvey-Jaeger gaps, but the results look very much like those from these two estimations.

Our final alternative is a gap measure based on a simple quadratic time trend to measure potential output, as in Roberts ( 1994c), for example. These estimates are reported in Equations (7a) and (7b) of Table 4. Note that when we estimate our model with these gaps we obtain a positive estimate of a and a negative estimate of -y, although neither is significantly different from zero. This result is very similar to the finding of Eisner ( 1994) and has the exact opposite policy implications of short-run capacity constraints. Note, however, that this particular model has the worst fit of the models considered here.

The conclusion that emerges from these supplementary regressions is that, while the particular choice of a gap measure does matter to the details of the estimates, the overall case that there is an important asymmetry in the U.S. Phillips curve is quite robust. In particular, our conclusions are robust to testing with the Harvey and Jaeger ( I 993) measure of output gaps, which those authors have subjected to careful scrutiny and for which they claim some important optimality properties. What emerges very clearly from the results is that it is not so much the gap measure that matters, but how it is used i n estimating the Phillips curve. Consistently, tests for asymmetry are shown to be seriously biased if the logical implications of the asymmetric model are not taken into account in the estimation.

Some Additional Robustness Tests

Two common criticisms of the work presented in Laxton, Meredith, and Rose ( 1995) and in earlier drafts of this paper were that our a was merely capturing omitted influences that would normally be picked up in a free constant and that our asymmetry was likely a reflection largely of special effects associated with the major oil-price shocks. We now show that nei-



ther of these arguments stands up to scrutiny. The results we cite are reported in Table 5.

Is a Simply Capturing Omitted Variables?

No. When we add a free constant to the preferred model, using our filter, or to the Harvey-Jaeger estimation from Table 4, it is small and insignificantly different from zero. For example, the significance level of the restriction of this constant to zero is about 86 percent in the extension based on our simple filter. Moreover, none of our other conclusions are affected.

What this tells us, quite clearly, is that the estimation strongly prefers our interpretation and use of a to alter the form of the curvature in the Phillips curve over the competing hypothesis that it is capturing the influence of omitted variables. Moreover, as a bonus, the theoretically preferred specification with no exogenous component to inflation is entirely consistent with the data.

Table 5. Tests with Constant Term and Oil Prices

(/-statistics in parentheses)

Estimated equation: 'IT, = 8'1T�+• + ( I - 8)'1Tt-� + 13 gapf + -y gapposr + f.;',

where gap* = y - y + a:. gappos* = positive values of gap* Tir+ .. = .2<,1rr+ .. + ,_(rrf+3 + ,_trrr+2 + ,_J1Tf+l + ,_"'7Tr)

'IT = percent change in the CPI at annual rates 'TTr+J = Michigan Survey measure of inflation expectations

SL = significance level.

Model # 1 : Add a constant (A.) term to the model a: Case of k = 1 2 from Table I with a constant (a: estimated) b: Harvey and Jaeger's ( 1993) Trend Plus Cycle Model

Model #2: Add relative oil prices to the model (see A.) a: Case of k = 12 from Table I with a constant (a: estimated) b: Harvey and Jaeger's ( 1993) Trend Plus Cycle Model

Inflation equation estimation period: sample 1964: 1-1990:4

Wald test: Model a 'Y 13 8 A. R1 (J SL(a, -y = 0)

Ia - 1 .281 0.876 0.222 0.592 0.070 .7893 1 .6083 0.003 ( -2.52) (3.04) ( 1.641) (6.20) (0.17)

lb -0.798 0.972 0.318 0.610 0.099 .7929 1 .5944 0.014 (-2.13) (2.73) ( 1.97) (6.08) (0.30)

2a - 1 .391 1 .019 0. 196 0.620 0.000 .7990 L5708 0.000 (-4.47) (3.99) (2 .47) (7.77) (6.25)

2b -0.798 1 .068 0.284 0.632 0.000 .8006 1 .5644 0.002 ( - 2.95) (3.37) (2.30) (7.46) (6.98)



Is the Asymmetry Capturing the Particular lnjiuence of Oil-Price Shocks?

No. When we add the rate of change of the relative price of crude oil to our preferred model or to the model with Harvey-Jaeger gaps, there are no changes in any of the conclusions. In fact, the case for asymmetry is strengthened. The new variable enters significantly and improves the fit of the equations. All the other coefficients become slightly better determined, and there are no important changes i n any of the point estimates.26

V. Conclusions

In this paper, we present estimates of a simple asymmetric Phillips curve for the United States. We find that a restriction to a linear version of the model is strongly rejected. This confirms recent evidence presented by Laxton, Meredith, and Rose ( 1 995) using the pooled G-7 data and by Turner ( 1995) using the U.S. data.

We also show why other researchers may have been misled in reaching the opposite conclusion. Following arguments advanced in Laxton, Meredith, and Rose ( 1995), we demonstrate that in a stochastic economy the presence of an asymmetry in the Phillips curve has an important implication as to how output gaps should appear in the function to be estimated. In particular, we show that it is inconsistent to use mean-zero gaps in the estimation, as this vitiates the implementation of the asymmetric alternative hypothesis. We cite Monte Carlo evidence that the use of such gaps will bias standard statistical tests of the restriction to linearity, and we show that this is confirmed by the results with U.S. data.

We also provide a number of tests of the robustness of our conclusions. Our conclusions come initially from results based on output gaps obtained using a simple, two-sided moving average filter to measure potential output. However, we show that if the above implication of asymmetry is taken into account in the estimation and testing, then the precise method used to provide the measure of potential output and the mean-zero output gap does not matter as much. In particular, we show that if we use the Harvey-Jaeger ( 1 993) approach to derive gap measures or a variety of measures based on the Hodrick-Prescott filter, our conclusions are not affected.

We also show that our results stand up to a number of other tests for robustness. These include adding a free constant to the estimation and testing for the influence of changes in the relative price of crude oil.

The paper also discusses some issues i n policy modeling. We are concerned that with the small samples of business cycle variation available to researchers, there will be significant limitations on one's ability to measure

26 This conclusion also holds if we add funher lags of the relative price of oil.



important variables, such as potential output and expectations, and to discriminate among competing hypotheses. We would argue that policy analysis should not be conducted by the rules of classical econometrics and Occam's razor. Most researchers who have opted for a linear null hypothesis because it could not be clearly rejected in their results could just as easily have argued that the same results were consistent at the same confidence levels with the presence of an important asymmetry. But our main point is that policy modeling should be concerned with the costs of policy errors, regardless of the specific strengths of one empirical case or another. We show here in a simple form, citing the more complete discussion in Laxton, Rose, and Tetlow ( 1993c), that policy errors arising from an incorrect assumption that the world is linear will be much more costly than the errors arising from making an error the other way around.

Another important point concerns the manner in which policy simulations are conducted. Some researchers, such as Robert Gordon ( 1994), appear to be willing to ignore completely the possibility that expectations ihave a forward-looking component. In our view, this is dangerous and can produce misleading policy advice. It is one thing to deal with the problem of representing expectations for historical estimation by using long distributed lags; it is quite another to assume that this procedure captures stable parameters that wilJ be invariant to a policy shock. While we do not think that using distributed lags is an efficient estimation strategy, we might grudgingly accept it as part of an empirical strategy if survey measures were not available. However, we would reject completely the notion that simulations of the resulting models have anything useful to say about the implications of alternative policies. Indeed, such simulations are likely to be quite misleading.

The limited policy experiments we present in this paper are designed to ilJustrate the power of the asymmetry hypothesis to provide a logic for monetary policyY We show that if the world is linear, then delaying the response to a positive demand shock may be beneficial if the metric is simply cumulative output. In such a world, a fast response is essential only for negative shocks. Thus the linear world produces asymmetric policy advice, i.e., take risks with inflation but not with disinflation. If this view of the world is wrong, however, as our evidence suggests, the consequences of such a policy will be higher volatility in the real economy and a lower average level of output. In the presence of asymmetry, it is critical to respond as quickly as possible to signs of excess demand because failure to do so results in much greater volatility in output and a lower average level of output over time. In this case, moreover, the policy advice is roughly symmetrical with respect to negative shocks. While delay is not as costly when there is excess supply, it is still preferable to act sooner rather than Dater.

27 The policy implications of asymmeLry are discussed in greater detail in Clark, Laxton, and Rose ( l995a).



REFERENCES

Andrews, Donald W.K., and Werner Ploberger, "Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative," Econometrica, Vol. 62 (November 1994), pp. 138-414.

Armstrong, John, Richard Black, Douglas Laxton, and David Rose, "A Robust Method for Simulating Forward-Looking Models," Bank of Canada Technical Report No. 73 (Ottawa: Bank of Canada, February 1995).

Ball, Laurence, and N . Gregory Mankiw, "Asymmetric Price Adjustment and Economic Fluctuations," Economic Journal, Vol. 104 (March 1994), pp. 247-61 .

Braun, Steven N . , "Productivity and the N IIRU (And Other Phillips Curve Issues),'' Working Paper No. 34 (Washington: Economic Activity Section, Division of Research and Statistics. Board of Governors of the Federal Reserve System, June 1984).

---. "Estimation of Current-Quarter Gross National Product by Pooling Preliminary Labor-Market Data," in Journal of Business and Economic Statistics, Vol. 8 (July I990), pp. 293-304.

Bryant, Ralph C., Peter Hooper, and Catherine L. Mann, Evaluating Policy Regimes: New Research in Empirical Macroeconomics (Washington: Brookings Institution, 1993).

Suiter, Willem, and Marcus Miller, "Costs and Benefits of an Anti-Inflationary Policy: Questions and Issues," in Inflation and Unemployment: Theory. Experience, and Policy-Making, ed. by Victor Argy and John Neville (London: Allen and Unwin, 1985). pp. 1 1-38.

Calvo, Guillermo A., "Staggered Prices in a Utility-Maximizing Framework,'' Journal of Monetary Economics, Vol. 1 2 (September 1983), pp. 383-98.

Clark, Peter, Douglas Laxton, and David Rose ( 1995a). "Capacity Constraints, Inflation, and the Transmission Mechanism: Forward-Looking Versus Myopic Policy Rules," IMF Working Paper 95175 (Washington: International Monetary Fund, July 1995).

--- ( 1995b), "Asymmetry in the U.S. Output-Inflation Nexus: Issues and Evidence," IMF Working Paper 95176 (Washington: International Monetary Fund, July 1995).

Cogley, Timothy, and James M. Nason, "Effects of the Hodrick-Prescott Filter on Trend and Difference Stationary Time Series: Implications for Business Cycle Research," Journal of Economic Dynamics and Control, Vol. 1 9 (January/ February 1995), pp. 253-78.

Cozier, Barry V., "On the Aggregate Implications of Optimal Price Adjustment,'' Bank of Canada Working Paper 89-4 (Ottawa: Bank of Canada, November 1989).

Eichenbaum, Martin, "Real Business Cycle Theory: Wisdom or Whimsy?" Journal of Economic Dynamics and Comrol, Vol. 15 (October 1991), pp. 607-26.

Eisner, Robert, "A New View of the NAIRU," Northwestern University Working Paper (Evanston, Illinois: Northwestern University, November 29, 1994).

Evans, Martin, and Paul Wachtel, "Inflation Regimes and the Sources of Inflation Uncertainty," Journal of Money. Credit and Banking, Vol. 25 (August 1993). pp. 475-51 I .



Fuhrer, Jeffrey C., and George R. Moore, "Monetary Policy Trade-offs and the Correlation Between Nominal Interest Rates and Real Output,'' American Economic Review, Vol. 85 (March 1995). pp. 2 19-39.

Gordon, Robert, "Inflation and Unemployment: Where Is the NAIRU?'' Paper presented lO Board of Governors of the Federal Reserve System, Meeting of Academic Consultants, December l , 1994 (Washington: Federal Reserve System, 1994).

Greenspan, Allan, "Statement to the U.S. Senate Committee on Banking, Housing, and Urban Affairs,'' February 22, I 995, printed in Federal Reserve Bulletin, Vol. 8 1 (April l995), pp. 342-48.

Harvey, Andrew C., and Alben Jaeger, "Detrending, Stylized Facts and the Business Cycle," Journal of Applied Econometrics. Vol. 8 (July/September 1993), pp. 231-47.

Hodrick, Robert J., and Edward C. Prescott, "Post-War U.S. Business Cycles: An Empirical Investigation," Carnegie-Mellon Discussion Paper No. 451 (Pittsburgh: Carnegie-Mellon University, May 1981 ).

Kuttner, Kenneth N., "Using Noisy Indicators to Measure Potential Output," Federal Reserve Bank of Chicago Working Paper No. 1991-14 (Chicago: Federal Reserve Bank of Chicago, June 1991 ).

Laxton, Douglas, Guy Meredith, and David Rose, "Asymmetric Effects of Economic Activity on Inflation: Evidence and Policy Implications," Staff Papers, International Monetary Fund (Washington: JMF, June 1995), pp. 344-74.

Laxton, Douglas, Nicholas Ricketts, and David Rose, "Uncertainty, Learning and Policy Credibility," in Economic Behaviour and Policy Choice Under Price Stability (Ottawa: Bank of Canada, June 1994).

Laxton. Douglas, David Rose, and Robert Tetlow ( 1993a), "Problems in Identifying Non-linear Phillips Curves: Some Further Consequences of Mismeasuring Potential Output," Bank of Canada Working Paper 93-6 (Ottawa: Bank of Canada, June 1993).

--- ( 1 993b), "Is the Canadian Phillips Curve Non-linear?" Bank of Canada Working Paper 93-7 (Ottawa: Bank of Canada, July 1993).

---( 1 993c), "Monetary Policy, Uncertainty and the Presumption of Linearity," Bank of Canada Technical Report No. 63 (Ottawa: Bank of Canada, August 1993).

Laxton, Douglas, Kevin Shoom, and Robert Tetlow, "Should the Change in the Gap Appear in the Phillips Curve? Some Consequences of Mismeasuring Potential Output," Bank of Canada Working Paper 92-1 (Ottawa: Bank of Canada, January 1992).

Mauskopf, Eileen, 'The Transmission Channels of Monetary Policy: How Have They Changed?" Federal Reserve Bulletin, Vol. 76 (Washington: Board of Governors of the Federal Reserve System, December 1990), pp. 985-1008.

Nelson. Charles R., and Heejoon Kang, "Spurious Periodicity in Inappropriately Detrended Time Series," Econometrica, Vol. 49 (May 1981), pp. 741-5 1 .

Perron, Pierre, "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Vol. 57 (November 1989), pp. 1361-1401.



Ricketts, Nicholas, and David Rose, "Inflation, Learning and Monetary Policy Regimes in the G-7 Economies," Bank of Canada Working Paper 95-6 (Ottawa: Bank of Canada. June I 995).

Roberts, John M. ( I 994a), "Evidence on the Monetary Transmission Mechanism: An Instrumental Variables Approach," Board of Governo rs of the Federal Reserve System Working Paper (Washington: Federal Reserve System, 1994 ).

--- ( 1 994b), "New Keynesian Economics and the Phillips Curve," Journal of Money, Credit and Banking, Vol. 27 (November I 995), pp. 975-85.

--- ( 1994c), "Is Inflation Sticky?" Board of Governors of the Federal Reserve System Working Paper No. I 52 (Washington: Economic Activity Section, Division of Research and Statistics, Board of Governors of the Federal Reserve System, July 1994).

Rotemberg, Julio J., "The New Keynesian Microfoundations," in NBER Macroeconomics Annual 1987, ed. by Stanley Fischer (Cambridge: MIT Press, 1987), pp. 69-I I 6.

Taylor, John, "Aggregate Dynamics and Staggered Contracts," Journal of Political Economy, Vol. 88 (February 1980), pp. 1-23.

Tsiddon, Daniel, "On the Stubbornness of Sticky Prices," International Economic Review. Vol. 32 (February 1991 ), pp. 69-75.

---, 'The (Mis)Behavior of the Aggregate Price Level," Review of Economic Studies, Vol. 60 (October 1993), pp. 889-902.

Turner, David, "Speed Limit and Asymmetric Inflation Effects from the Output Gap in the Major Seven Economies," OECD Economic Studies, Vol. 24 ( 199511), pp. 57-88.



Corrigendum

The following material was inadvertently omitted from Annex II of "Conditionality: Past, Present, and Future," by Manuel Guitian, which appeared in the December 1995 issue of Staff Papers.

Annex II

Access to Resources Based on Need, Strength of Adjustment Effort1

The rules governing access to the IMF's general resources-that is, its holdings of the currencies of member countries and SDRs, as well as borrowed resources-apply uniformly to all members. Access is determined primarily by the member's balance of payments need and the strength of its adjustment policies, and may be permitted up to limits that are defined in relation to the member's quota. The access limits may be exceeded in exceptional circumstances.

The Executive Board reviewed policies on access to IMF resources on several occasions in 1 994, weighing the organization's experience since 1990 and the prospective financing needs of member countries and its own liquidity position. Guided by the principle that strong programs deserve strong support and by the need to safeguard the monetary character and catalytic role of the IMF, the Board decided that, for a three-year period beginning on October 24, 1994, the annual limit for access to the IMF's general resources under the credit tranches and extended arrangements would be increased to I 00 percent of quota from 68 percent of quota. This higher annual access limit under stand-by and extended arrangements would permit increased actual access to the JMF's resources commensurate with the strength of programs. The cumulative access limit was left unchanged at 300 percent of quota, net of scheduled repayments. These limits exclude drawings under the compensatory and contingency financing facility (CCFF), the buffer stock financing facility, the enhanced structural adjustment facility (ESAF), and the systemic transformation facility (STF).

The current overall access limit under the CCFF is set at 95 percent of a member's quota. Sublimits provide maximum access equivalent to 30 percent of quota under the external contingency element; 30 percent of quota for the export-shortfall element; 1 5 percent of quota for the excess cereal import element; plus an "optional" 20 percent of quota, which may be used to supplement any of the three elements of the CCFF. When a member has a satisfactory balance of payments position-except for the effect of an ex-

1Excerpted from IMF Survey (September 1995).

252


CONDITIONALITY: PAST, PRESENT, FUTURE 253

port earnings shortfall or an excess in cereal import costs-a maximum access of 65 percent of quota applies to either the export or cereal element of the CCFF. Under the buffer stock financing facility, the access limit is 35 percent of quota. The maximum access under the STF is equal to 50 percent of a member's quota.

Access under ESAF anangements differs according to members' balance of payments needs and the strength of their adjustment efforts. An eligible member country may borrow a maximum of 190 percent of its quota under a three-year arrangement, although this limit may be increased, under exceptional circumstances, up to a maximum of255 percent of quota. ESAF access is expected to average about I I 0 percent of quota for first-time users. The maximum access under the STF is equal to 50 percent of a member's quota.

The IMF' s access limits are reviewed annually in light of many elements, including the magnitude of members' payments problems and developments in the IMF's liquidity.

Access Limits (percent of member's quota)

Under stand-by and extended arrangements' Annual 100 Cumulative 300 Under special facilities Compensat01y and contingency financing facility (CCFF)

Export earnings shortfaiJl 30 Excess cereal import costs2 1 5 Contingency financing3 30 Optional tranche4 20 Combined4 95

Buffer stock financing facility 35 Systemic 1 ransformation faci I i ty

Cumulative 50 Under SAF and ESAF arrangements Structural adjustment facility

First year 1 5 Second year 20 Third year 1 5 Cumulative 50

Enhanced structural adjustment facility' Three-year accesss 190

1 Under exceptional circumstances, these limits may be exceeded. 2When a member has a satisfactory balance of payments position-except fo

the effect of an export earnings shortfall or an excess in cereal import costs-a limi of 65 percent of quota applies to either the export earnings shortfall or the excess cereal import costs, with a joint limit of 80 percent.

3A sublimit of 25 percent of quota applies on accoum of deviations in imeres ates.

4 May be applied to supplement the amounts for export earnings shortfalls, ex-esses in cereal imports costs, or contingency financing. 5 Average access expected at I I 0 percent of quota for first-time ESAF users.


IMF Staff Papers Vol. 43. No. I (M�rch. 1996)

© 1996 International Monetary Fund

IMP Working Papers

Staff Papers draws on IMF Working Papers, which are research studies by members of the Fund's staff A list of Working Papers issued in 1995:4 follows.

"Imports Under a Foreign Exchange Constraint: The Case of the Islamic Republic of Iran:· by Adnan Mazarei [95/97)

"Growth in East Asia: What We Can and What We Cannot Infer From II.'' by Michael Sarel [95/98]

"Disinflation and the Recession-Now-Versus-Recession-Later Hypothesis: Evidence from Uruguay," by Alexander W. Hoffmaister and Carlos A. Vegh [95/99]

"Government Role and the Efficiency of Policy Instruments," by Vito Tanzi [95/ 1 00]

'The Underground Economy: Estimation, and Economic and Policy ImplicationsThe Case of Pakistan, .. by Ghiath Shabsigh L 95/1 0 I I

"Stock Market Volatility and Corporate Investment." by Zuliu Hu ]95/102] ·'Linkages Between Financial Variables, Financial Sector Reform and Economic

Growth and Efficiency," by Barry Johnston and Ceyla Pazarbasioglu [951103] ''Discretionary Trading and Asset Price Volatility," by Jahangir Aziz [95/104] "The Fiscal Stance in Sweden: A Generational Accounting Perspective," by Robert

Hagemann and Christoph John [95/105] ''Methodologies of Price Indices in Transition Countries," by Kimberly Zieschang

[951106) ''Spain: Unemployment, Debt Management and Interest Rate Differentials," by

Gustavo Caiionero [95/1 07] "Consumption Smoothing and Exchange Rate Volatility," by Bart Turtelboom

195/108] "Is Regionalism Simply a Diversion? Evidence from the Evolution of the EC and

EFTA," by Tamim Bayoumi and Barry Eichengreen [95/1091 "International Integration of Equity Markets and Contagion Effects;· by Paul

Cashin, Manmohan Kumar, and John McDermott [9511 101 "Exchange Rate Movements. Inflation Expectations. and Currency Substitution in

Turkey," by Fabio Scacciavillani [9511 1 1 ] "Speculative Attacks and Currency Crises: The Mexican Experience," by lnci

Otker and Ceyla Pazarbasioglu [95/1 12)

254


JMF WORKING PAPERS 255

"Relative Prices, Economic Growth, and Tax Policy.'' by Michael Sarel (95/l i 3 J ''Target Zones and Realignment Expectations: The Israeli and Mexican

Experience," by Alejandro M. Werner [95/1 14) "Monetary Policy and Inflation Indicators for Finland'' by Martin Miihleisen

[9511 15] "Flexible Estimation of Demand Schedules and Revenue Under Different Auction

Formats," by Robert Feldman and Vincent Reinhart [95/1 16] "The Microstructure of Government Securities Markets" by Peter Dauels [9511 17 ] "The Fisher Hypothesis and Inflation Persistence-Evidence from Five Major

Industrial Coumries'' by Wensheng Peng [95/ 1 1 8] "Consumption Smoothing and the Current Account: Evidence for France, 1970-

94," by Pierre-Richard Agenor, Claude Bismut, Paul Cashin, and John McDermott [95/ I 19]

"Effective Taxation for Recipients of Social Assistance in Germany and the Consequences of the 1996 Tax Reform" by Christian Thirnann [95/ 120]

"Does the Nominal Exchange Rate Regime Matter?," by Atish Ghosh, Anne-Marie Guide, Jonathan D. Ostry and Holger C. Wolf [95/1 2 1 ]

"Skill Heterogeneity and Aggregation Bias over the Business Cycle." by Eswar Prasad L 95/1221

"Financial Indicators and Financial Change in Africa and Asia," by Huw Pill and Mahmood Pradhan [95/ 123 J

"Welfare Reform in the United States," by Ellen Nedde [95/124] "The Labor Market and Economic Adjustment," by Pierre-Richard Agenor

(95/125] "Health Care Cost Containment,'' by Ellen Nedde [951126] "A Survey of Academic Literature on Controls Over International Capital

Transactions," by Michael P. Dooley [951127) ''Long-Term Tendencies in Budget Deficits and Debt," by Paul Masson and

Michael Mussa [95/128] "Real Interest Rates, Real Exchange Rates, and Net Foreign Assets in the

Adjustment Process," by Thomas Helbling and Bart Turtelboom (95/ 1 29) "The Growth of Government and the Reform of the State in Industrial Countries,''

by Vito Tanzi and Ludger Schuknecht [951130) "Capital Account Liberalization in Finland: Analysis of Structural Changes'' by

Arto Kovanen [951 1 3 1 ] "The Mexican Financial Crisis: A Test of the Resilience of Developing Country

Securities," by David Andrews and Shogo Ishii (95/ 132] "Capital Market Integration in the Pacific Basin Region: An Analysis of Real

Interest Rate Linkages," by Kate Phylaktis [95/133) "Deposit Protection Arrangements: A Survey," by Alexander Kyei [951134] "On the Measurement of Horizontal inequity." by Peter Lambert [95/135] "Growth in Sub-Saharan Africa." by Dhaneshwar Ghura and Michael T.

Hadjimichael [95/ 1361 "Competitiveness and External Trade Performance of the French Manufacturing

Industry," by Pierre-Richard Agenor [951137]


256 IMF WORKING PAPERS

'Trade Policies and Lithuania's Reintegration into the Global Economy,'' by Jonas Cicinskas, Peter Cornelius, and Dalia Treigiene [95/L38]

"A Survey of Economic Policies and Macroeconomic Performance in Chile and Colombia," by Sergio Clavijo [95/139]

"Inflation Dynamics in Kazakstan,'' by Mark De Broeck, Paula De Masi, and Vincent Koen [951140)

"Financial Sector Reforms in Eight Countries: Issues a:nd Results" by Vicente Galbis [951 1 4 1 ]

"Macroeconomic Shocks and Trade Flows Within Sub-Saharan Africa: Implications for Optimum Currency Arrangements," by Tamim Bayoumi and Jonathan D. Ostry [95/142)

'The Uruguay Round and Net Food Importers," by Uwe Eiteljoerge and Clinton Shiells [95/ 143]

"A Model of the Bimetallic System," by Erik Oppers [95/144] "A General Equilibrium Approach to Interenterprise Arrears in Transition

Economies and Applicability to Russia," by Se-Jik Kim and Goohoon Kwon [95/145]

"Transformation of Markets and Policy Instruments for Open Market Operations." by Stephen H. Axilrod [951146]


WORKING PAPERS and PPAAS 257

IMF Papers on Policy Analysis and Assessment

Papers on Policy Analysis and Assessment are intended to make staff work in the area of policy design available to a wide audience. A list ofPPAAs issued in 1995:4 follows. Papers may also be considered for inclusion in the journal.

"Singapore's Central Provident Fund," by Robert Carling and Geoffrey Oestreicher [95/ 1 1 )

A n annual subscription to IMF Working Papers is available for US$21 0, and an annual subscription to Papers on Policy Analysis and Assessment, for US$80. Each subscription includes 1 2 monthly shipments and priority mail delivery. Individual Working Papers and Papers on Policy Analysis and Assessment are available on request for US$7 a copy. Prepayment is required. Please specify the series name. issue date, paper number, and complete title. American Express, MasterCard, and Visa credit cards are accepted, as well as checks in US dollars. Requests should be made to:

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Telephone: (202) 623-7430 Telefax: (202) 623-720 I Internet: publications@ imf.org


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