globalization and the convergence in the marginal product

Globalization and the Convergence in the Marginal Product ofCapital

Elena Bondarenko∗

and

Shuichiro Nishioka†

June 7, 2012

Abstract

This paper examines whether globalization of finance and trade can help explain the convergencein the marginal product of capital. From Solow’s growth model, we develop an empirical modelshowing that the marginal product of capital is a function of domestic factors: investment rateand effective depreciation rate. We then augment it to include global factors of net financialinflow and capital embodied in trade. Using data from developed and developing countries from1970 to 2000 and dynamic panel estimation techniques, we provide evidence that the marginalproduct of capital converges across countries over the period. Investment rate, effective depre-ciation rate, net financial inflow, and capital embodied in trade are all statistically significantdeterminants for the convergence. Although previous literature focuses on the role of the globalfinancial market for the convergence, our findings reveal that the convergence rate dependslargely on country-specific factors.

Keywords: Marginal product of capital; Conditional convergence; Factor price equalization; Finan-cial capital inflow; Capital content of tradeJEL Classification: F15, F21, F40, O47.

∗Cassidy Turley, 2101 L Street NW Suite 700 Washington DC 20037 USA, Tel: +1-202-266-1314, E-mail:[email protected]†Corresponding author. Department of Economics, West Virginia University, 1601 University Avenue Morgantown

WV 26506-6025 USA, Tel: +1-304-293-7875, E-mail: [email protected]

1 Introduction

Whether or not world capital stock is allocated proportionally to developing countries is funda-

mental to understanding global differences in economic development. One of the basic economic

measures used to explore this question is the marginal product of capital (MPK), which is equal

to capital return when production technology exhibits constant return to scale and commodity

and factor markets are perfectly competitive. Conventional wisdom suggests that the marginal

product of capital converges across countries if the financial market effectively allocates worldwide

production capital. Although recent literature focuses on the role of the financial market for the

convergence of MPK (i.e., Caselli and Feyrer, 2007), there is no systematic study that includes

all potential domestic and global factors and examines the magnitude of their contribution on the

convergence rate of MPK.

The Solow growth model (Solow, 1956; 1957), for example, predicts that poor countries will

catch up with rich countries in terms of capital returns and per capita gross domestic product

(GDP). In fact, the long-run convergence process of MPK can be identical to that of economic

growth (e.g., Mankiw et al., 1992; Caselli et al., 1996) if countries have no access to the global

financial market. A country that opens its financial market will receive foreign capital if its capital

return is higher than foreign countries’ returns. The global flows of financial capital from low-

to high-return countries would promote MPK convergence. Although financial flows are likely to

be a primary global factor, international trade would also contribute to the convergence. As in

Stopler and Samuelson (1941) and Samuelson (1949), convergence in product prices due to freer

trade causes convergence in factor prices. International trade leads countries to specialize in the

production of comparative advantage goods, creating upward pressure on prices of factors used

intensively in the production process. While capital returns in capital-scarce developing countries

would decline because of trade liberalization, those in capital-abundant developed countries would

increase.

This paper examines both domestic and global factors as potential determinants of MPK con-

vergence. We first develop an empirical model from Solow’s growth model (Mankiw et al., 1992)

and augment it to include international factors of finance and trade. We are particularly interested

in comparing the contributions of domestic and international factors for MPK convergence. We

use several measures of MPK and develop a data set of developed and developing countries from

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1970 to 2000. The data confirm evidence for MPK convergence over the period we consider (e.g.,

Caselli and Feyrer, 2007; Mello, 2009; Chatterjee and Naknoi, 2010). We then use dynamic panel

estimation techniques (i.e., two-step difference generalized method of moments (GMM) in Arellano

and Bond (1991)) and estimate the determinants for MPK convergence. All domestic and global

factors we consider—investment rate, effective depreciation rate (i.e., the sum of the labor growth

rate, the labor productivity growth rate, and the depreciation rate), aggregate financial net-inflow,

and capital embodied to international trade—are found to be statistically significant determinants

of the convergence. Moreover, the domestic factors contribute more to the convergence rate than

the global factors do. We believe that these results are consistent with the conflicting evidence

shown in previous literature. While the global financial market plays a relatively minor role in the

convergence rate (e.g., Feldstein and Horioka, 1980; Lucas, 1990), the country-specific economic

factors contribute significantly (e.g., Mankiw et al., 1992; Caselli et al., 1996; Caselli and Feyrer,

2007).

The remainder of this paper is organized into four sections. In Section 2, we present an empirical

measure of MPK and its convergence trend. In Section 3, we develop an empirical strategy by

deriving the marginal product of capital from Solow’s model and augmenting it with international

finance and trade factors. Section 4 presents the baseline empirical results and the results for

various robustness checks. We discuss our conclusions in the last section.

2 Marginal Product of Capital

We consider the following Cobb-Douglas production function, in which output is linked to the two

factor inputs, capital and effective labor:

Yit = Kαiit (AitLit)

1−αi

where Yit is the real output (GDP) of country i at time t, Kit is capital stock, Lit is labor, and Ait

is labor-augmenting productivity. The cost-based share of capital in national income is represented

by αi.

To employ constant return to scale (CRS) production technology, we make two assumptions.

The first one states that the economy is large enough to increase the output once factor inputs are

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increased. The second one specifies the relative unimportance of land and other natural resources

in production. 1 Under these assumptions and perfectly competitive markets of goods and factors,

the compensation for one unit of physical capital (rit) is equal to the marginal product of capital

(MPKit):

MPKit = αiYitKit

. (1)

We develop our baseline empirical measure of MPKit by using a constant capital share (αi =

1/3),2 the real GDP (Yit) in constant 2005 international dollars, and the capital stock (Kit), which

is developed from the perpetual inventory method.3

To understand the convergence process of the marginal product of capital, we employ the

measure of beta (β) in the following equation:4

ln(MPKit)− ln(MPKi,t−τ ) = φ+ β ln(MPKi,t−τ ) + εi. (2)

Beta-convergence examines the relationship between the growth rates over the period τ against

the initial levels across countries. If MPK converges over time across countries, we expect that β

would be a negative value between -1 and 0. A value of β closer to -1 indicates a greater tendency

towards convergence because the average growth rate, ln(MPKit) − ln(MPKi,t−τ ), is inversely

related to the initial value, ln(MPKi,t−τ ). Here, we have β = − [1− exp(−λτ)] where λ is the

estimate of the speed at which a country’s MPK converges toward its steady state value. In this

paper, we refer to λ as a "convergence rate." Figure 1 reports β-convergence across 92 countries

when αi=1/3, t=2000, and τ=30. We find β = −0.61, suggesting the presence of a long run

equalization mechanism with the annual convergence rate (λ) of 3.1%. A country relatively close

to its steady-state MPK value experiences a slowdown in the evolution of MPK.

1 If natural resources were important, production function would not be CRS since the increase in capital andlabor would deliver less than proportional increase in output.

2We will relax this assumption in the robustness check section. In particular, we use the country-specific repro-ducible capital share from Caselli and Feyrer (2007).

3See Table 1 for the summary statistics and data sources. To develop capital stock, we employ the followingequation: Kit = (1− δ)Ki,t−1 + Iit where δ is the depreciation rate of physical capital and Iit is real investment (inconstant 2005 international dollars). Following Caselli and Feyrer (2007), we use the depreciation rate of 6%. Toobtain the initial value of the real capital stock, we compute: Ki,t1 = (Ii,t1)/(δ + gi) where gi is the average growthrate of real investment in country i from t1 to t1+15. Although we use the real investment data from 1961 for mostcountries, the capital stock measures used in the empirical analysis are from 1970 to 2000.

4This type of convergence is referred to as catching-up convergence. See Barro and Sala-i-Martin (1992) andSala-i-Martin (1996) for the discussion on convergence measures in neoclassical growth model.

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3 Theory for MPK Convergence

3.1 Domestic Factors

We wish to examine the economic factors causing the convergence in the marginal product of

capital. We start by considering domestic factors likely to play essential roles in MPK convergence.

Our theoretical basis is built upon the Solow growth model in Mankiw et al. (1992). Here, we

use Solow’s model as a theoretical baseline to associate our discussion with empirical literature on

conditional convergence in economic growth. The Solow model assumes that a constant fraction

of output, ii,t−τ , is saved and invested in the production process. The investment rate is defined

as the share of real domestic investment to real GDP. We define kit as the stock of capital per

effective unit of labor, kit = Kit/(AitLit), and yit as the level of output per effective unit of labor,

yit = Yit/(AitLit). Since kit converges to a steady-state capital to effective labor ratio, we can

derive the marginal product of capital as the following:5

MPKit = αi

[nit + git + δ

ii,t−τ

](3)

where nit is the average annual growth rate of labor between t− τ to t, and git is the growth rate

of labor productivity from t− τ to t.6

Equation (3) corresponds to equation (17) in Mankiw et al. (1992). The equation predicts

that while the marginal product of capital would be negatively correlated with initial investment

rate (ii,t−τ ), it would be positively correlated with the capital share (αi), labor growth (nit), labor

productivity growth (git), and depreciation rate (δ). Here, we call the sum of nit, git and δ,

nit + git + δ, an effective depreciation rate. Because depreciation rate (δ = 0.06) is constant across

5The evolution of kit is characterized by the following equation:

∆kit = ii,t−τyit − (nit + git + δ)kit.

Equation above implies that kit converges to a steady-state capital to effective labor ratio:

Kit

AitLit=

[ii,t−τ

nit + git + δ

] 11−αi

.

We derive equation (3) from these two equations and equation (1).

6To obtain the growth rate of labor-augmenting productivity, we employ the following equation from Trefler (1993):Ait = wit. The average wage of country i at time t (wit) can be derived from labor compensation: (1-αi)Yit, dividedby the number of workers: Lit. Since the measure of labor share (1-αi) is constant over the period, the growth rateof labor-augmenting productivity is that of real GDP per worker.

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countries and years, the effective depreciation rate depends only on the labor-side variables (nit

and git). Equation (3) indicates that these domestic factors would be predictors of the marginal

product of capital if countries have no access to international financial and trade markets. Taking

the log to both sides of equation (3) and rewriting it as a dynamic model in the level of the marginal

product of capital similar to Caselli et al. (1996), we can derive the following equation:

ln(MPKit) = β1 ln(MPKi,t−τ ) + β2 ln(αi) + β3 ln(ii,t−τ ) + β4 ln(nit + git + δ) + εit. (4)

In equation (4), β1−1 corresponds to β in equation (2). Thus, we expect that β1 is in the range

between 0 and 1. A value of β1 closer to zero indicates a greater tendency towards convergence

because the growth rate, ln(MPKit) − ln(MPKi,t−τ ), is inversely related to the initial value,

(β1 − 1) ln(MPKi,t−τ ).

3.2 International Flows of Financial Assets

We now turn to the global factors that may cause convergence in MPK. In particular, international

financial flow is believed to be the primary factor that equalizes capital returns across countries.

In the absence of barriers to capital mobility, capital owners seek more productive opportunities in

countries with higher returns of capital until capital returns are equalized worldwide. Although the

financial market has become increasingly globalized, there could be several reasons that prevent

financial flows from flowing into the countries with high returns of capital. For example, Lucas

(1990) discusses the presence of credit frictions, and Caselli and Feyrer (2007) propose that the

high costs of installing capital in poor countries could prevent financial capital from flowing to

them.

We add a measure of international financial flows to the main equation (4) to examine whether

financial flows, potentially transformed into reproducible capital, influence the convergence. We

develop a ratio of net cross-border financial flows (i.e., assets minus liabilities) to nominal GDP.

Financial flows are the aggregate of portfolio equity, foreign direct investment (FDI), debt, and

other financial flows from Lane and Milesi-Ferretti (2007).7 Here, the values of the net aggregate

7Lane and Milesi-Ferretti (2007) provide details on data definitions as well as data development strategy. Inter-national portfolio flows refer to investors’ purchase of issued equity containing country-funds, depository receipts,and direct purchases of shares. Portfolio equity holdings include direct purchases of shares in local companies and

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financial flows would be negative for countries that experience more inflows (liabilities) than outflows

(assets).

The baseline model is augmented to include an additional measure of net financial flows:

ln(MPKit) = β1 ln(MPKi,t−5) + β2 ln(αi) + β3 ln(ii,t−5)

+β4 ln(nit + git + δ) + β5(NetF lowi,t−5/GDPi,t−5) + εit. (5)

We expect a negative relationship between the net financial flow and MPK, as the higher

return to capital would induce financial inflow. Figures 2.1 and 2.2 exhibit the scatter plots of

NetF lowit/GDPit against ln(MPKit) for years 1970 and 2000, respectively. In 1970, there is no

clear correlation between these two measures. For example, the second highest value of MPK

in 1970 is Oman (OMN). If capital owners seek productive opportunities worldwide, Oman would

experience inflow of foreign capital (or would have a negative value of NetF lowit/GDPit). However,

this net-flow measure for Oman is positive, indicating outflow of financial assets. In 2000, we find

a rough but negative association between these two measures. These two figures suggest that the

financial market plays an increasingly influential role in the convergence of MPK.

3.3 International Trade

While financial globalization is likely to be a primary cause of the convergence, international trade

and production specialization would also reduce the international difference in MPK. As in Stopler

and Samuelson (1941) and Samuelson (1949), convergence in product prices due to freer trade

causes convergence in factor prices. This concept, factor price equalization (FPE), is a well-known

theory of international trade.8 International trade causes countries to specialize in producing their

comparative advantage goods, creating upward (downward) pressure on the prices of factors that

are used heavily (lightly) in production process. For example, freer trade causes a capital-abundant

country to specialize in producing capital-intensive goods and a capital-scarce country to specialize

mutual funds that are below 10% of ownership level. Foreign direct investment (FDI) includes direct investment in alocal company to control stakes (above 10% of ownership level) as well as green field investment. The debt categoryincludes debt securities, bank loans, deposits, and other debt instruments. Other flows include financial derivativesand total reserves minus gold.

8The empirical study of international trade, however, has not provided significant evidence for the FPE theory.See Davis and Weinstein (2001) who argue that the breakdown of the FPE theory is essential to support the globalproduction and trade data.

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in labor-intensive goods. Because specialization in capital-intensive (labor-intensive) goods requires

more (less) capital and less (more) labor, capital return in the capital-abundant (capital-scarce)

country increases (decreases), creating the equalization force in capital returns.

To examine how international trade influences return to capital across countries, we introduce

a measure of capital content of trade:

KCTit = EXitKit

GDPit−

∑j∈C78,j 6=i

IMijtKjt

GDPjt(6)

where C78 is the set of 78 countries that provide bilateral trade data during the period we consider,

EXit is export (nominal $US) of country i to the aggregate of the 78 countries, GDPit is nominal

GDP (nominal $US), and IMijt is bilateral import of country i from j.9

This measure is motivated by the Heckscher-Ohlin-Vanek (HOV) model (e.g., Vanek, 1968;

Leamer, 1980).10 The HOV model predicts that a capital-abundant country is an exporter of

embodied capital, and a capital-scarce country is an importer of embodied capital. In other words,

a capital-abundant country that exports capital content more than its imports is a net exporter of

capital with a positive measure of KCTit. To adjust for the size of capital stock, we divide KCTit

by Kit. Then, we augment equation (4) by including an additional measure of KCTi,t−5/Ki,t−5:

ln(MPKit) = β1 ln(MPKi,t−5) + β2 ln(αi) + β3 ln(ii,t−5)

+β4 ln(nit + git + δ) + β6(KCTi,t−5/Ki,t−5) + εit. (7)

We expect a negative relationship betweenKCTi,t−5/Ki,t−5 and ln(MPKit). A capital-abundant

9 In our study, the data on bilateral exports and imports are obtained from the United Nations Commodity TradeStatistics Database for years 1970, 1975, 1980, 1985, 1990, 1995, and 2000. We exclude 14 countries (Benin, Botswana,Burundi, Chad, Congo, Guinea, Lebanon, Nepal, Papua New Guinea, Rwanda, Swaziland, Taiwan, Tanzania, andUganda) from the original set of 92 countries due to the data availability. Because the bilateral exports and importsare not available for some of 78 countries for certain years, we use the data from the closest available year to interpolatethe missing values. For example, while we do not have data of Zambia (ZMB) for 1980, we have the correspondingdata for 1979. We calculate capital content of trade for 1980 by using GDP and capital values from 1980 and bilateraltrade values from 1979.10Typically, the empirical literature on the HOV model employs production and trade data from input-output

tables because the primary objective of the HOV model is to examine factor trade arising from industry composition.However, we develop the measure of capital content of trade from equation (6), which is similarly to the measureof R&D content of trade proposed by Lichtenberg and van Pottelsberghe de la Potterie (1998). Thus, we cannotclearly account for capital content of trade arising from industry composition. Because the subject of this paper isthe long-run effect of capital content of trade for MPK convergence, and because input-output tables are not availableacross countries and years, we employ the measure used by Lichtenberg and van Pottelsberghe de la Potterie (1998).

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country is a net-exporter of KCTit, and its return to capital is lower than a capital-scarce country.

Figures 3.1 and 3.2 present the scatter plots of KCTit/Kit against ln(MPKit) for years 1970 and

2000, respectively. In 1970, there is a clear negative association between these two measures. The

MPK for net importers of embodied capital are higher than those for net exporters of embodied

capital. However, this correlation becomes weak in 2000. More importantly, both ln(MPKit)

and KCTit/Kit are clustered together within narrow ranges, indicating that both measures have

equalized over the period.

4 Empirical Evidence

4.1 Baseline Results

To study the convergence mechanism of the marginal product of capital, we use equation (4) as a

baseline and augment it to include international factors. We are particularly interested in financial

capital flows as in equation (5) and embodied capital flows as in equation (7). The baseline results

are based on the balanced panel consisting of 468 observations from 78 countries at 5-year intervals

(τ=5) during the period from 1970 to 2000.

Equation (4) represents a dynamic model with a lagged-dependent variable on the right-hand

side, which gives rise to autocorrelation and other econometric problems typical of dynamic time-

series panel data. In particular, it is critical to account for endogeneity problems to obtain consistent

estimators. To avoid this problem, Caselli et al. (1996) introduce difference GMM (Arellano and

Bond, 1991) and estimate a cross-country convergence rate of economic growth. We follow Caselli

et al. (1996) and employ difference GMM as our preferred estimator. It is a good fit for our study

because we have a short time-span (T=6) and a large cross-section (N=78). We use the two-step

estimator instead of the one-step because it is asymptotically effi cient and robust to panel-specific

autocorrelation, different patterns of heteroskedasticity, and cross-country correlation (Bond et al.,

2001).

Nevertheless, it is worthwhile to start estimation of the dynamic equation with ordinary least

squares (OLS). Although the estimators from OLS are biased, the results provide us with the

rough ranges of the true parameters. The problem with applying OLS is that the lagged dependent

variable is positively correlated with the fixed effects in the error term, which gives rise to dynamic

8

panel bias. The coeffi cient for the lagged dependent variable (β1) is upward biased because it

captures the power that is supposed to belong to country fixed effects (Hsiao, 1986). This bias

results in a downward bias in the estimate of the speed of convergence (λ).

We start our estimation with a simple convergence model that includes only a lagged dependent

variable as Model 1. Then, Model 2 adds domestic factors as shown in equation (4).11 Next, we

estimate equation (5) as Model 3 and equation (7) as Model 4. Finally, Model 5 augments equation

(4) by including both financial and embodied capital flows. We include time dummy variables that

have the same effect as transforming the variables into deviations from time means. They remove

universal time-related shocks from errors, preventing any sort of cross-country and contemporaneous

correlations.

Estimation results from OLS are reported in Table 2.1. The coeffi cient on the initial level of the

marginal product of capital (β1) in Model 1 is close to one (0.866), implying that the convergence

rate (λ) is slow (2.9%). In Model 2, β1 declines from 0.866 to 0.679 and the convergence rate

increases from 2.9% to 7.7%, indicating the importance of domestic factors for MPK convergence.

Investment rate (ii,t−5) and effective depreciation rate (nit + git + δ) have opposite effects in signs

as the theory suggests. While a 1% increase in the initial investment rate leads to a 0.26% de-

crease in MPK, a 1% increase in the effective depreciation rate leads to a 0.14% increase. These

coeffi cients are statistically significant at the 1% confidence level, confirming that the convergence

is "conditional" upon country-specific domestic growth factors (e.g., Mankiw et al., 1992). The

values of β1 remain stable in the subsequent models. Models 3, 4, and 5 introduce financial and

trade flows. Although we obtain the expected signs for financial and trade flows, the trade variable

is statistically insignificant. Overall, the OLS results indicate that the inclusion of domestic factors

improves the fit of the regressions,12 although the results are subject to econometric problems such

as endogeneity.

Next, we estimate the five models explained above with the least squares dummy variables

(LSDV). Here, we include not only time- but also country-specific dummy variables. The LSDV

estimators do not eliminate dynamic panel bias because the estimators are only consistent when all

right-hand-side variables are strictly exogenous. The results from LSDV estimations are reported in

11Because we use a constant capital share (αi = 1/3) for the daseline specification, β2 ln(1/3) belongs to a constantterm in OLS.12Adjusted R2 increases from 0.881 (Model 1) to 0.956 (Model 2). However, they do not improve when we introduce

global factors (Models 3, 4, and 5).

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Table 2.2. As shown in the table, β1 is 0.596 for Model 1. In comparison to the corresponding OLS

result, the convergence rate increases significantly from 2.9% to 10.4% when we include country-

specific fixed effects. MPK convergence is crucially conditional on country-specific factors, which

may include country-specific reproducible capital share (Caselli and Feyrer, 2007). Across all

models, the coeffi cients on investment rates (β3) and effective depreciation rates (β4) are statistically

significant at the 1% confidence level. While the coeffi cient of capital content of trade in Model

4 is statistically insignificant, the financial variables in both Models 3 and 5 are negative and

statistically significant at the 1% confidence level. The results from LSDV imply the important

role of finance in the convergence of MPK.

Although the results from OLS and LSDV provide insight regarding the magnitudes and signs of

domestic and global factors affecting MPK convergence, these results are subject to the econometric

problems discussed above. Now, we employ the difference GMM estimator that suits our econo-

metric needs.13 The difference GMM uses equation (4) by transforming it into a first-difference

equation and including a time-specific constant, which captures factors common to all countries.

Note that the first-difference transformation removes country-specific fixed effects.

We treat all right-hand-side variables in the equation above as endogenous variables. Although

the Solow model assumes that the domestic variables are exogenous (e.g., Mankiw et al., 1992),14

we follow Caselli et al. (1996) and consider that the domestic variables are endogenous. Moreover,

international variables could be endogenous because financial and embodied capital flows arise

simultaneously from the global difference in returns to capital. See, for example, Mundell (1957)

and Antràs and Caballero (2009) for theoretical consideration of this concept.

The results of difference GMM and its specification tests are reported in Table 2.3. The coeffi -

cients on the initial level of log of MPK (β1) in all models are positive and statistically significant

at the 1% confidence level. The convergence rate ranges from 7.7% in Model 1 to 10.8% in Model 4.

13Bond et al. (2001) argue that the first-differenced GMM estimator can be a poor estimator of cross-country growthregressions due to a possible weak correlation of the lagged levels of series with the subsequent first-differences. Toexamine the validity of specifications, we use several specification tests: the Hansen J test (1982) for overidentifyingrestrictions, and the Arellano-Bond (AR) test for first- and second-order serial correlations in differences. We find astrong relationship between the first-differences and the second lags of the level variables. Therefore, at a minimum,the second lags of endogenous variables can serve as valid instruments for our purpose. We use the second andthird lags of endogenous variables as instruments for the baseline models in Table 2.3. Although we reject the nullhypothesis of the joint validity of instruments for Model 1 according to the Hansen J test, we keep the consistentinstruments (i.e., the second and third lags of the dependent variable) even for Model 1. Thus, our results do notdepend on the selection of instruments. See also Roodman (2009) for these test specifications of difference GMM.14See robustness checks below for the results when we treat these variables other than the lagged dependent variable

as exogenous.

10

From the GMM estimates, we confirm that the convergence in MPK is strongly conditional to the

domestic factors. We also find that the global factors are statistically significant with the expected

signs. However, these global factors do not improve the annual convergence rates significantly (i.e.,

λ is 9.9% for Model 3, 10.8% for Model 4, and 10.6% for Model 5) when we use data from the 78

countries.

4.2 Robustness Check

4.2.1 Model Specifications

In this section, we report the robustness checks for Models 1, 2, and 5. First, we introduce an alter-

native measure for MPK (MPKLit), which is developed with the reproducible capital share (αi)

from Caselli and Feyrer (2007).15 Caselli and Feyrer (2007) argue that capital in agricultural and

natural-resource sectors is non-reproducible. Thus, it should not be a part of a country’s physical

capital stock. To have a greater number of countries, we use αi = 1/3 for our baseline analysis.

Although country-fixed effects can take account of the time-invariant component of ln(MPKit)

and ln(MPKLit) in the dynamic OLS and LSDV estimations, country-specific capital share would

affect the results for difference GMM because the lagged levels of dependent variables are included

in the set of instruments. Panel 1 in Table 3 reports the results when we use the non-reproducible

capital shares.16 This alternative measure of MPK provides us with the results similar to the base-

line ones, although the global factors have a somewhat stronger contribution for the convergence

rate.17 While the annual convergence rate is 8.5% for Model 2, it is 11.3% for Model 5. This result

suggests that finance and trade contribute to the convergence rate by the annual rate of 2.8%.

Second, we replace investment rate (iit) with domestic saving rate (sit). Under Solow’s model,

15Caselli and Feyrer (2007) build an estimate of αi from Bernanke and Gurkaynak (2001) and the World Bank"Where is The Wealth of Nations." Since the data is available only for 1996, we assume that αi is constant over time.16Due to the availability of the reproducible capital shares, our sample declines to 49 countries. Most of the dropped

countries are developing countries. The 49 countries are Algeria (DZA), Australia (AUS), Austria (AUT), Belgium(BEL), Bolivia (BOL), Canada (CAN), Chile (CHL), Colombia (COL), Costa Rica (CRI), Cote d‘Ivoire (CIV),Denmark (DNK), Ecuador (ECU), Egypt (EGY), El Salvador (SLV), Finland (FIN), France (FRA), Greece (GRC),Ireland (IRL), Israel (ISR), Italy (ITA), Jamaica (JAM), Japan (JPN), Jordan (JOR), Korea (KOR), Malaysia (MYS),Mauritius (MUS), Mexico (MEX), Morocco (MAR), the Netherlands (NLD), New Zealand (NZL), Norway (NOR),Panama (PAN), Paraguay (PRY), Peru (PER), Philippines (PHL), Portugal (PRT), Singapore (SGP), South Africa(ZAF), Spain (ESP), Sri Lanka (LKA), Sweden (SWE), Switzerland (CHE), Trinidad &Tobago (TTO), Tunisia(TUN), the United Kingdom (GBR), the United States (USA), Uruguay (URY), Venezuela (VEN), and Zambia(ZMB).17The stronger contribution of globalization stems not from the measure ofMPKLit but from the country selection.

The results with MPKit with 49 countries are available upon request.

11

without the access to the international financial market, the saving rate should be identical to the

investment rate. Feldstein and Horioka (1980), in particular, hypothesize that there should not be a

correlation between the investment and saving rates if the global financial market allocates capital

effectively across countries. However, they find a high correlation between these two variables,

concluding that the pace of globalization for the financial market is limited. We obtain the domestic

saving rate from the World Development Indicators (the World Bank) and estimate the baseline

models by replacing ii,t−5 with si,t−5.18 We report the results with the domestic saving rate in

Panel 2 in Table 3. Interestingly, the saving rate has a smaller or insignificant effect on the marginal

product of capital although it does not greatly affect the other variables.

Finally, we treat all variables other than the lagged dependent variable as exogenous variables.

Here, we include all lagged levels (second and higher) of MPK as instruments. We report the

results in Panel 3 of Table 3. Regardless of the treatment in endogenous variables, we find that

both domestic and global factors are critical determinants of the convergence in MPK.

4.2.2 Alternative Measures for Trade and Financial Variables

Next, we introduce alternative measures for financial and trade variables. The first column in Table

4 reports the model with financial and trade openness variables with their interaction term. Here,

we develop a measure of financial openness as the sum of assets and liabilities divided by GDP.

Trade openness is the sum of exports and imports divided by GDP. We introduce the interaction

term of these two openness measures following the spirit in Baltagi et al. (2009). For example,

the contribution of trade openness for MPK convergence would be conditional to financial open-

ness. Thus, we expect that the coeffi cients of financial and trade openness would be negative and

their interaction term would be positive. Indeed, we obtain the statistically significant fit for this

specification with the expected signs for all variables. In addition, we confirm that the estimated

speed of convergence is similar to the baseline results. The second column in Table 4 reports the

result from alternative measure of trade variable. In stead of using capital content of trade, we use

the revealed comparative advantage index of capital-intensive goods (i.e., machinery) from Balassa

(1965):

RCAit =EXm

it /EXit∑i∈C78 EX

mit /∑

i∈C78 EXit

18 If the saving rate is negative, we use the positive value of the closest year.

12

where EXmit is country i’s machinery export to the subset of the 78 countries at time t.

19 If RCAit

is greater than unity, country i is revealed to have a comparative advantage in machinery. We find

that the measure of revealed comparative advantage correlates negatively with MPK, indicating

that countries with comparative advantage in machinery have lower values of MPK.

By introducing net debt and FDI flows separately, we can study which components of aggregate

financial flow are effectively transformed into physical capital. We intend to compare our results

with those in Chatterjee and Naknoi (2010), who study the frictions in the transformation of

financial capital into physical capital. The coeffi cients for debt and FDI net inflows are negative

and statistically significant at the 1% confidence level. Moreover, FDI has a greater coeffi cient,

implying that FDI inflows are likely to be transformed into physical capital. Finally, columns 5 and

6 report the estimations of Model 5 in Table 2.3 at the different time periods. While the coeffi cient

on total net financial flows in the period from 1970 to 1990 is statistically significant only at the

10% confidence level, it is statistically significant at the 1% confidence level in the period from 1980

to 2000. These results suggest that the influence of financial flow in the early period is weaker than

that in later period, which corresponds to the findings previously shown in Figures 2.1 and 2.2.

4.2.3 A Multisector Model

Caselli and Feyrer (2007) develop a multisector model to consider the role of the global difference

in the relative price of capital to consumption goods for the convergence in MPK. We assume that

a country has m sectors that produce final goods. We keep the assumptions of constant returns to

scale production technology and perfect competition in good and factor markets. Now, consider the

investment opportunity for a capital owner who purchases a piece of capital and invests it in the

production of one of the final goods (i.e., good 1). Then, the expected return from this transaction

(reit) would be

reit = (1− σit)[P 1itMPK1

it + Pkit(1 + π

eit − δ)

P kit

](8)

where P 1it is domestic price of the final good (good 1) in country i at time t, Pkit is domestic price of

capital goods, πeit is the expected inflation rate of capital goods, andMPK1it is the marginal product

19We obtain EXmit from the UN comtrade database. We derive the export values of machinery from the 1-digit

group 7 "Machinery and Transport Equipment" (SITC Rev.1).

13

of capital in the production of good 1. Caselli and Feyrer (2007) assume that the expected return

(reit) would be equalized completely across countries when the global capital market is frictionless.

We, however, would like to avoid this strong assumption. In particular, we introduce a measure

of friction (σit where 0 < σit ≤ 1) so that the expected return would be lower for countries with

financial market friction.

Assuming that capital is effi ciently allocated domestically, we can find the following equation:20

αi =P 1itMPK1

itKit

PitYit(9)

where Pit is price of GDP. Using equations (8) and (9) and assuming that the expected return

would be equalized across countries: reit = r∗t , we can derive the price-adjusted measure of MPK as

follows:

PMPKLit =r∗t

1− σit− (1 + πeit − δ) (10)

where PMPKLit = (αiPitYit)/(PkitKit), in which αi is the reproducible capital share.21 This equa-

tion implies that the price-adjusted measure of MPK (i.e., equation (8) in Caselli and Feyrer, 2007)

would be a positive function of financial friction (or a negative function of "financial openness") and

a negative function of the expected inflation rate of capital goods (πeit) although we cannot have the

log-linear relationship. The inflation rates of capital goods could depend on the international trade

in capital goods because their production is highly concentrated in a handful of advanced countries

(Eaton and Kortum, 2001). Thus, PMPKLit would be equalized perfectly if the financial market

is frictionless (σit = 0), and the price for investment goods is equalized across countries due to free

trade (πeit = πet ).

We start the estimation for the unadjusted-measure, ln(MPKit), and the price-adjusted mea-

sure, ln(PMPKLit), with a simple convergence model that includes only a lagged dependent vari-

able as Models 1 and 2, respectively. Then, Model 3 adds the expected inflation rate: ln(1+πeit−δ)22,20We can find the following equation due to the assumption that returns of capital are equalized domestically within

country i: PitmMPKitm = P 1itMPK1

it where the subscript m indicates sectors. Total compensation for capital inthis country is

∑m PitmMPKitmKitm =

∑m P

1itMPK1

itKitm

= P 1itMPK1

it

∑mKitm = P 1

itMPK1itKit. Thus, we can find αit = (P 1

itMPK1itKit)/PitYit.

21We obtain the price of investment goods (P kit) and that of GDP (Pit) from the Penn World Table 7.0 (Heston etal., 2011).22We employ the inflation rate of P kit from t-5 to t, assuming the capital owners’expected inflation would be the

one observed at time t.

14

Models 4 adds the de-facto financial openness from Lane and Milesi-Ferretti (2007), and Model 5

adds the de-jure financial openness from Chinn and Ito (2008), who develop the country-level index

of restrictions on capital mobility.23

Due to the limitation in data on the reproducible capital shares, we have at most 52 countries

in these estimations. Estimation results from difference GMM are reported in Table 5.24 The

coeffi cient of the initial level of the marginal product of capital in Model 1 is 0.674, implying that

the convergence rate (λ) is 7.9%. In Model 2, this coeffi cient declines slightly from 0.674 to 0.633

and the convergence rate increases from 7.9% to 9.1%. We confirm that the convergence rate based

on Caselli and Feyrer’s preferred specification is in the range of our baseline results. Although we

obtain the expected signs and statistically significant magnitudes for financial openness and the

expected inflation in capital goods, they do not improve the convergence rates. Finally, similar to

Baltagi et al. (2009), we find insignificant effect from the de-jure financial openness index.

5 Conclusion

This paper examined the economic factors that drive convergence in the marginal product of capital.

We developed the empirical model from Solow’s growth model (Mankiw et al., 1992) and augmented

it to include international factors of finance and trade. We also used a measure and a model of

MPK from Caselli and Feyrer (2007) and examined a data set of developed and developing countries

from 1970 to 2000. Using the two-step difference GMM estimators (Arellano and Bond, 1991), we

found that investment rate, effective depreciation rate, financial inflow, and trade flow are all

important determinants for the convergence of MPK. Similar to the literature on the conditional

convergence in economic growth (e.g., Mankiw et al., 1992; Caselli et al., 1996), we found that

MPK convergence is conditional to country-specific growth factors. Not only investment rate but

also labor-side growth rates (i.e., labor growth and labor productivity growth) play significant roles

in the convergence. While we found the significant effects of global factors of finance and trade

23This index is developed from IMF’s "Annual Report on Exchange Arrangements and Exchange Restrictions(AREAER)" and captures the intensity of regulatory restrictions on cross-border capital flows. Specifically, it is basedon the principal components of four IMF binary variables: (1) existence of multiple exchange rates, (2) restrictionson current account transactions, (3) restrictions on capital account transactions, and (4) required surrender of exportproceeds. This index represents the existence of different types of financial restrictions and ranges from -2.5 to 2.5 torepresent a spectrum from full control to complete liberalization. We scaled the index by adding 3.5 to avoid negativevalues. Note that developed countries have higher index values than developing and emerging countries.24We treat the lagged dependent variable alone as an endogeneous variable. We use all the lagged levels (second

and higher) of the dependent variable as instruments.

15

with the expected signs, their contributions to the convergence rates are relatively small.

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18

19

Tables and Figures

Table 1 Summary Statistics

Figure 1 Beta convergence of the Marginal Product of Capital (ln(MPKit))

Year 1985 1970-2000

Mean Std. dev Min value Max value β (s.e.) R-sq λ

ln(MPKit) PWT 7.0 92 -1.9 0.4 -2.8 (GHA) -0.8 (TCD) -0.611 (0.057) 0.560 3.1%

ln(MPKLit) PWT 7.0, Caselli and Feyrer (2007) 52 -2.7 0.5 -4.0 (TTO) -1.8 (SLV) -0.514 (0.083) 0.438 2.4%

ln(PMPKLit) PWT 7.0, Caselli and Feyrer (2007) 52 -2.7 0.5 -4.2 (ZMB) -1.7 (BWA) -0.331 (0.108) 0.157 1.3%

Investment rate (iit) PWT 7.0 92 22.0 10.0 2.9 (SDN) 52.7 (LBN) -0.531 (0.060) 0.469 2.5%

Saving rate (s it) WDI (World Bank) 92 17.4 12.2 -15.2 (JOR) 47.6 (BHR) -0.607 (0.115) 0.236 3.1%

ln(Lit) PWT 7.0 92 8.3 1.5 4.8 (ISL) 12.5 (IND) -0.077 (0.020) 0.140 0.3%

ln(Ait) PWT 7.0 92 9.4 1.2 6.7 (BDI) 11.4 (LBN) 0.002 (0.043) 0.000 0.0%

KCTit/Kit PWT 7.0, UN comtrade 78 0.0 0.1 -0.3 (SYR) 0.4 (SGP) -0.986 (0.101) 0.557 14.2%

RCAit PWT 7.0, UN comtrade 78 0.3 0.4 0.0 (NGA) 1.7 (JPN) -0.216 (0.115) 0.045 0.8%

NetFlowit/GDPit Lane and Milesi-Ferretti (2007) 91 -0.5 0.5 -2.1 (ZMB) 1.4 (BHR) -0.054 (0.173) 0.001 0.2%

Sources Obs.

20

Figure 2.1 ln(MPKit) and NetFlowit/GDPit in 1970

Figure 2.2 ln(MPKit) and NetFlowit/GDPit in 2000

21

Figure 2.3 ln(MPKit) and KCTit/Kit in 1970

Figure 2.4 ln(MPKit) and KCTit/Kit in 2000

22

Table 2 Main Results: Conditional Convergence of MPK

2.1 OLS (with time-fixed effects)

Model 1 Model 2 Model 3 Model 4 Model 5

Convergence rate λ 2.9% 7.7% 7.7% 7.9% 7.9%

β1 0.866*** 0.679*** 0.680*** 0.672*** 0.672***

(s.e.) (0.024) (0.019) (0.019) (0.020) (0.020)

β3 -0.259*** -0.249*** -0.260*** -0.249***

(s.e.) (0.016) (0.016) (0.016) (0.016)

β4 0.141*** 0.140*** 0.142*** 0.141***

(s.e.) (0.025) (0.025) (0.025) (0.025)

β5 -0.028*** -0.031***

(s.e.) (0.010) (0.011)

β6 -0.052 -0.068

(s.e.) (0.046) (0.045)

Obs. 468 468 468 468 468

Adjusted R-squares 0.881 0.956 0.957 0.956 0.957

2.2. LSDV (with time- and country-fixed effects)



β1 0.596*** 0.578*** 0.589*** 0.573*** 0.578***

(s.e.) (0.047) (0.030) (0.029) (0.031) (0.029)

β3 -0.181*** -0.166*** -0.183*** -0.170***

(s.e.) (0.021) (0.021) (0.022) (0.021)

β4 0.151*** 0.150*** 0.152*** 0.152***

(s.e.) (0.028) (0.027) (0.029) (0.027)

β5 -0.073*** -0.086***

(s.e.) (0.017) (0.017)

β6 -0.046 -0.121**

(s.e.) (0.062) (0.058)

Obs. 468 468 468 468 468

Adjusted R-squares 0.916 0.964 0.966 0.964 0.967

2.3. Dynamic GMM (with time-fixed effects)



β1 0.681*** 0.615*** 0.611*** 0.584*** 0.588***

(s.e.) (0.055) (0.025) (0.020) (0.021) (0.019)

β3 -0.189*** -0.190*** -0.180*** -0.189***

(s.e.) (0.016) (0.010) (0.014) (0.009)

β4 0.146*** 0.144*** 0.146*** 0.143***

(s.e.) (0.006) (0.006) (0.005) (0.005)

β5 -0.062*** -0.095***

(s.e.) (0.015) (0.012)

β6 -0.073* -0.179***

(s.e.) (0.038) (0.018)

Obs. 390 390 390 390 390

# of N 78 78 78 78 78

# of Instruments 14 33 42 42 51

16.11 33.01 41.37 43.51 50.83

(0.041) (0.131) (0.150) (0.104) (0.140)

-2.834 -3.616 -3.619 -3.483 -3.398

(0.005) (0.000) (0.000) (0.000) (0.001)

-0.486 -1.794 -1.936 -1.790 -1.957

(0.627) (0.073) (0.053) (0.073) (0.050)

ln(nit+git+δ)

ln(MPKi, t-5)

ln(ii,t-5)

ln(MPKi, t-5)

ln(nit+git+δ)

ln(ii,t-5)

KCTi,t-5/Ki,t-5

NetFlowi,t-5/GDPi,t-5

ln(nit+git+δ)

KCTi,t-5/Ki,t-5


ln(MPKi, t-5)

ln(ii,t-5)


Hansen J test

Arellano-Bond AR(1)

Arellano-Bond AR(2)

KCTi,t-5/Ki,t-5

23

Table 3 Robustness Checks

1. Capital Shares (Casseli & Feyrer, 2007) 2. Domestic Saving Rates 3. Exogenous Variables

Model 1 Model 2 Model 5 Model 1 Model 2 Model 5 Model 1 Model 2 Model 5

Convergence rate λ 2.9% 8.5% 11.3% 7.7% 9.7% 9.8% 8.1% 8.9% 9.1%

β1 0.867*** 0.654*** 0.568*** 0.681*** 0.615*** 0.613*** 0.668*** 0.641*** 0.635***

(s.e.) (0.078) (0.017) (0.006) (0.055) (0.020) (0.013) (0.051) (0.037) (0.037)

β3 -0.227*** -0.179*** -0.008 -0.012*** -0.108*** -0.121***

(s.e.) (0.013) (0.006) (0.006) (0.003) (0.013) (0.013)

β4 0.182*** 0.165*** 0.189*** 0.170*** 0.153*** 0.151***

(s.e.) (0.008) (0.004) (0.011) (0.008) (0.011) (0.011)

β5 -0.101*** -0.080*** -0.083***

(s.e.) (0.005) (0.012) (0.015)

β6 -0.225*** -0.060* -0.166***

(s.e.) (0.008) (0.035) (0.053)

Obs. 245 245 245 390 390 390 390 390 390

# of N 49 49 49 78 78 78 78 78 78

# of Instruments 14 33 51 14 33 51 20 22 24

5.93 30.38 44.36 16.11 42.47 59.74 18.21 12.55 17.44

(0.655) (0.211) (0.332) (0.041) (0.016) (0.029) (0.198) (0.562) (0.233)

-3.180 -3.093 -2.436 -2.834 -2.654 -3.384 -2.898 -3.618 -3.578

(0.001) (0.002) (0.015) (0.005) (0.008) (0.001) (0.004) (0.000) (0.000)

-1.156 -0.700 -0.849 -0.486 -2.049 -2.310 -0.489 -2.024 -2.151

(0.248) (0.484) (0.396) (0.627) (0.041) (0.021) (0.625) (0.043) (0.032)

Hansen J test

Arellano-Bond AR(1)

Arellano-Bond AR(2)

ln(MPKi, t-5)

ln(ii,t-5) or ln(s i,t-5)

ln(nit+git+δ)

KCTi,t-5/Ki,t-5


24

Table 4 Alternative Trade and Financial Variables

Table 5 Price-Adjusted MPK (PMPKL) in Caselli and Feyrer (2007)

Openness ln(RCA) Debt FDI 1970-1990 1980-2000

Convergence rate λ 10.0% 10.1% 10.8% 11.3% 11.4% 11.4%

β1 0.606*** 0.603*** 0.584*** 0.567*** 0.566*** 0.565***

(s.e.) (0.027) (0.014) (0.019) (0.015) (0.034) (0.043)

β3 -0.162*** -0.203*** -0.193*** -0.186*** -0.186*** -0.097***

(s.e.) (0.020) (0.010) (0.010) (0.013) (0.024) (0.030)

β4 0.112*** 0.136*** 0.145*** 0.140*** 0.134*** 0.218***

(s.e.) (0.004) (0.004) (0.005) (0.004) (0.007) (0.018)

β5 -0.104*** -0.064*** -0.095*** -0.055* -0.043**

(s.e.) (0.012) (0.008) (0.022) (0.031) (0.022)

β6 -0.153*** -0.084*** -0.185*** -0.231**

(s.e.) (0.020) (0.025) (0.066) (0.098)

β7 -0.100***

(s.e.) (0.030)

β8 -0.131***

(s.e.) (0.049)

β9 0.029***

(s.e.) (0.008)

β10 -0.013***

(s.e.) (0.004)

Obs. 455 390 390 390 234 234

# of N 91 78 78 78 78 78

# of Instruments 36 51 51 51 29 29

36.95 47.51 45.01 50.33 25.59 29.16

(0.058) (0.224) (0.308) (0.151) (0.222) (0.110)

-3.999 -3.920 -3.422 -3.337 -2.842 -1.701

(0.000) (0.000) (0.000) (0.000) (0.000) (0.089)

-1.894 -1.990 -1.928 -1.798 -1.634 0.537

(0.058) (0.047) (0.054) (0.072) (0.102) (0.591)

Hansen J test

Arellano-Bond AR(1)

Arellano-Bond AR(2)

ln(TOi,t-5)

ln(FOi,t-5)

ln(TOi,t-5) × ln(FOi,t-5)

ln(RCAi,t-5)

ln(MPKi, t-5)

ln(ii,t-5)

ln(nit+git+δ)

KCTi,t-5/Ki,t-5



Type of MPK MPK PMPKL PMPKL PMPKL PMPKL


coef 0.674*** 0.633*** 0.602*** 0.643*** 0.660***

(s.e.) (0.039) (0.067) (0.061) (0.073) (0.066)

coef -0.552***

(s.e.) (0.175)

coef -0.132***

(s.e.) (0.037)

coef 0.016

(s.e.) (0.034)

Obs. 260 260 260 255 255

# of N 52 52 52 51 51

# of Instruments 20 20 21 21 21

9.797 10.39 10.96 13.52 10.87

(0.777) (0.733) 0.689 0.486 0.696

-3.776 -3.022 -3.340 -2.67 -3.050

(0.000) (0.003) 0.001 0.007 0.002

-0.382 -1.185 -0.950 -0.92 -1.160

(0.703) (0.236) 0.342 0.357 0.245

Hansen J test

Arellano-Bond AR(1)

Arellano-Bond AR(2)

ln(MPKi, t-5)

ln(1+πit-0.06)

ln(FOit)

ln(Kaopenit)

globalization and the convergence in the marginal product

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