the elusive phillips curve

JACK JOHNSTON University of California, Irvine

The Elusive Phillips Curve *

The empirical evidence that has accumulated over the past twenty years for major countries, and especially the United States, Canada, and the U.K., suggests three distinct “phases” for the Phillips curve. In the “early” phase the coefficient on the unemployment variable was correctly signed and statistically significant; in the “middle” phase, as further studies were made and the data period extended, the unemployment coefficient tended to become numerically smaller and often to be statistically insignificant; in the “late” phase, as yet more studies accumulated and the data period was extended into the seventies, the unemployment coefficient was sometimes perversely signed and also statistically significant. This paper offers a possible theoretical interpretation of this phenomenon. The theoretical analysis is supplemented with some empirical simulations.

1. Introduction The theoretical analysis in this paper is divided into three

sections. Section 2 provides a very brief summary of the empirical evidence of the last twenty years on the effect of the unemployment, or excess demand, variable in standard Phillips curve equations. Section 3 develops a simple dynamic macro model, which is then used to explore the conditions under which patterns similar to the empirical observations might have been produced. Finally, Section 4 presents a few preliminary simulations based on the theoretical model, which illustrate how conventional econometric procedures might yield misleading inferences about the nature of the Phillips curve.

2. The Pattern in the Empirical Evidence’ A study of the empirical evidence on the Phillips curve for

the United States, Canada, and the U.K. indicates a similar pattern for all three countries. As in the study of the works of a great

*I am indebted to Christopher Curran, Emory University, who carried out the empirical simulations reported in Section 4 and to Peter Stalder, Center for Economic Research, Zurich, for valuable comments.

‘A detailed study of the empirical evidence is available on request from the author.

Journal of Macroeconomics, Fall 1980, Vol. 2, No. 4, pp. 265-286 0 Wayne State University Press, 1980.

26.5

Jack Johnston

TABLE 1. ‘t’ Statistics on Unemployment Variables

Country Study Sample Period

U.K.

USA

Early Phase Studies Dicks-Mireaux and Dow (1959) Klein and Ball (1959) Lipsey (1960) Lipsey (1960)

1950-1956 1948-1958 1862-1913 1923-1939, 1948-1957

Bhatia (1961) France (1962) Bowen and Berry (1963) Bowen and Berry (1963) Perry (1964) Simler and Tella (1968) Ashenfelter, Johnson, and Pencavel

(1972)

1900-1932 1890-1932 1900-1932 1900-1958 1947-1960 1948-1964 1914-1963

Kaliski (1964) 1946-1958 Canada Kaliski (1964) 1946- 1958

Reuber (1964) 1949-1961

U.K.

Middle and Late Phase Studies

i

Johnston and Timbre11 (1973) 1959-1971 Johnston and Timbre11 (1973) 1952-1971 Henry, Sawyer, and Smith (1976) 1948-1966 Henry, Sawyer, and Smith (1976) 1948-1971 Henry, Sawyer, and Smith (1976) 1948-1974

USA 1

Gordon (1972) 1954- 1966 Gordon (1972) 1954-1968 Gordon (1972) 1954-1970

Freedman (1976) 1961-1967 Freedman (1976) 1961-1974

Canada Freedman (1976) 1961-1975 Riddell (1979) 1953- 1965 Riddell (1979) 1965-1973

l A indicates annual data, Q quarterly and M monthly.

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Elusive Phillips Curve

TABLE 1. Continued

‘t’ Statistics on

Time Unit’

Correctly Perversely Signed Signed

Coefficients Coefficients

Q 4.2 Q 7.0 A 3.04, 1.06, 4.75 A 0.20, 1.86, 3.17

A 6.2 A 3.2, 2.9 A 5.3, 3.1 A 1.9, 5.0 Q 6.7 Q 7.5 A 3.5

A 1.4, 2.8 A 4.6, 1.7 Q 4.5

A A

: Q

Q” Q Q

Q” M M

2.4 1.1

1.58 2.12 0.53

3.25 1.62 2.30 2.15

1.96 1.82

0.13

8.26

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Jack lohnston

painter, one might label the pattern as consisting of the “early,” “middle,” and “late” periods. The evidence for the patterns comes from numerous studies by various authors. There is not complete uniformity among authors in their econometric procedures. In some studies the wage change variable (w) is in terms of wage rates, in others it relates to earnings. The unemployment rate (u) is sometimes entered in linear or reciprocal or logarithmic form, while in other equations a group of unemployment variables is used such as u-r, up2, up4, as well as a proportionate or absolute change in u. These studies all stemmed from the original Phillips (1958) article, which employed only makeshift statistical methods without benefit of standard errors or any formal inference procedures. However, the scatter in w, u space was clearly nonlinear, the magical curve was drawn and a new growth industry initiated.

Table 1 presents a summary of the reported ‘t’ statistics on the unemployment variables in various equations for the USA, Canada and the U.K. The early phase studies in the first section of the table show a fairly strong and significant effect, which is robust across sample periods, time units, varying measures of wage change, and varying subsets of other explanatory variables. The end of this phase may be dated around 1965. In the second section of the table, two types of evidence are particularly important. The first comes from studies in which the authors employed successively longer sample periods. Examples are Henry, Sawyer, and Smith (1976), Gordon (1972), and Freedman (1976), which show a downward trend in the ‘t’ statistics as the end of the sample period is extended into the seventies. The second type of evidence comes from Riddell (1979), where the data have been split into two distinct sub-periods and the ‘t’ statistic changes from being moderately well determined with conventional sign in the early period to being strongly determined but perversely signed in the later period.

Figure 1 is a fairly dramatic picture of the data contained in Table 1. The ‘t’ statistics are plotted against the end date of the sample period. Where a study employed several unemployment variables, we have simply plotted the average ‘t’ statistic. Solid lines join values from a single study employing extended sample periods, and a dotted line joins values from distinct sub-periods. Perversely signed coefficients are shown below the horizontal axis. The figure suggests 1965 as the date of the watershed.

The data relate to the partial association between w and u, conditional on the other explanatory variables used in the various equations. As we have seen, these data raise the question of whether

268


Figure 1. ‘t’ Statistics on Unemployment Variables

‘1’ ~talirticr

7-

6-

5-

4-

3-

2-

l-

UKe

us0 UKe

us0 US.

use C0

UKc us.

US.

UK&@

O-

-1 -

-2- \ UK%K -3- !

-4-

-5- \ -6- \

-7-

-8- Ci

the partial association has become weak if not indeed perverse. Study of data on the simple association between inflation and unemployment has led Friedman in his Nobel lecture to speculate on the existence of a positively sloped Phillips curve. He concentrat- ed on the rate of price inflation (p) rather than the rate of wage inflation (w), but p, a and w, u scatters will be very similar.

In recent years higher inflation has often been accompanied by higher, not lower, unemployment, especially for periods of several years in length. A simple statistical Phillips curve for such periods seems to be positively sloped, not vertical [Friedman (1977), p. 4591.

Friedman assembled data for France, Germany, Italy, Japan, Swe- den, the U.K., and the USA for 1956-1975 and computed simple averages of the inflation and unemployment rates across all seven countries in five year periods. The results are reproduced in Table 2. Lines 1 and 2 of the table show the conventional scissors effect to be expected from a negatively sloped Phillips curve, that is, a rise in inflation and a fall in unemployment. The movements

Jack ]ohnston

TABLE 2. Average Znflation and Unemployment in Seven Coun- tries: 1956- 75”

Period Average p

19561960 2.8 1961-1965 3.7 1966-1970 4.1 1971-1975 9.3

Average u

3.0 2.0 2.2 2.9

“Friedman (1977). p. 461.

from lines 2 through 4 show a positive association between inflation and unemployment. Scatter diagrams in p (or w), u space for most of the major industrialized countries in recent years show a positive relationship instead of the more prevalent negative relationship of earlier years.

The interesting and crucial question, however, is whether the partial association between w and u is now positive, or, in other words, whether the coefficient on the unemployment variable in a properly specified wage equation containing other relevant explanatory variables has a perverse sign. We will approach this question in two stages and ask:

1) What forces might account for positively sloped scatters in w, u space as compared with negatively sloped scatters?

2) Can the forces causing positively sloped w, u scatters also produce misleading estimates of the partial assocation between w and u?

3. A Simple Dynamic Model Traditionally, people who have done intensive empirical re-

search on the Phillips curve have worked either with a single-equation, wage-change model or, at best, with a two-equation, wage-price model. The crucial weakness of the wage-price models is that unemployment is exogenous to the model, and thus, there is no feedback from wage-price movements to the unemployment rate. Our purpose in this section is to construct the simplest model possible to allow such a feedback.’

*The large econometric models usually incorporate such feedbacks, but it is difficult to trace analytically hypothetical causal sequences owing to the size and complexity of the models.

270


Using upper case letters to denote levels, let us write two equilibrium macro equations

P.F’(N) = W; (1)

P.F(N) = G, (2)

where

P = price level; N = employment; W = wage rate; G = exogenous expenditure; J3 = a scalar parameter which is a function of underlying

expenditure and taxation parameters; F(N) = short-run production function for given capital stock and

technology.

Equations (1) and (2) are taken directly from Johnston (1975). That paper focused on the dichotomy between the market and non-market sector of the economy, so that P, W, and N referred to the price, wage, and employment levels in the market sector and G represented “pure” expenditure by the government on non-marketed services. The first equation is the conventional statement of equilibrium in the labor market, on the assumption of a perfectly elastic labor supply at the current wage rate, and the second that of equilibrium in the goods market, where G is measured in current dollars. Here we will take the equations to apply to the whole macro economy, even though there are difficulties about the application of the marginal productivity condition to an aggregate of market and non-market sectors. To these equations add a conventional, short- run, macro-production function

F(N) =K.N’,O<r<l, (3)

where K serves as a proxy for capital stock and technology. Substitute (3) in (1) and (2), take logarithms and then first differences of the results to give the two-equation system:

p+k+(y-1)n = w; (4)

p+k+yn=g. (5)

271

Jack Johnston

The lower case letters denote proportionate rates of change in the corresponding upper case variables. In principle we are allowing K to vary over time, but S has been treated as a strict constant in deriving (5). Next we need to switch from the rate of change in employment (n) to an expression in terms of the unemployment rate (u).” Let

then,

thus

giving

1nN

L = labor force,

NIL = I- u,

ZnL = Zn(1 - U) = -U ,

n - I= -Au.

For simplicity we will treat the rate of growth of the labor force (I) as fixed, and we do not affect the properties of the model by setting it at zero. Thus we have, finally,

n--Au. (6)

Substituting (6) in (4) and (5) and adding the simplest form of Phillips curve gives the three equation, dynamic model:

p, + k + (1 - y)Au, = w, ; (7)

P, + k - Y Au, = g, ; (8)

Wt = c4,+a,u,+~p,;a,>0,

O<cX,<l. (9)

For the moment we treat k, as constant at k. The Phillips curve

3The use of a lower case u to denote the unemployment rate is the one exception to the use of lower-case letters to indicate rates of change.

272


specified in (9) is somewhat unrealistic in being linear and also in incorporating the current rate of inflation rather than some measure of inflationary expectations. This specification has been used in many of the early empirical studies, but we adopt it solely in the interest of keeping the model as simple as possible. We have also, for the moment, specified less than full adjustment to the inflation rate.

Equilibrium Growth The model essentially assumes continuous equilibrium in the

labor and goods markets. The current endogenous variables in the model are the inflation rate (p,), the rate of wage change (w,), and the unemployment rate (u,), while the predetermined variables are the rate of change of the capital/technology proxy (k), the current rate of change in nominal exogenous expenditure (g,), and the lagged unemployment rate (u,-, ). The model is stable so that if g, is held constant at some level g the system will tend to steady equilibrium growth at

$ = g; (10)

jj= g--k=w-k; (11)

f7 = (l/q) [%I - cu,k - (1 - o&l . (12)

The condition 0 < o2 < 1 ensures a negatively sloped, long-run Phillips curve. If, however, a2 = 1, the long-run curve is vertical at a “natural” unemployment rate given by (o, - k)/cx,.

Short-Run Dynamics Our main concern is the short-run behavior of the system

and, in particular, the types of scatter diagrams that might be generated in (w, u) space. To explore this, eliminate p, from equations (7), (8), and (9) to obtain

D:w, = (%I - G4 + 41 - Y k, % -

1 - a27 1 - “2Y u, ; (13)

s: w, = (g, - u,-1) + u,. (14)

This system consists of two equations, describing the joint deter-

273

Jack Johnston

mination of w, and u,, period by period. To facilitate future reference to these equations we have labelled the first one D, not because it is a demand curve, but simply because it is downward sloping. Notice that it is neither the short-run nor the long-run Phillips curve. The second equation is then labelled S. Notice that:

D shifts upward with: A rise in oO, which may be interpreted as an increase in the natural rate of unemployment and/or an increase in labor “militancy” or employer “apathy;” A fall in k (capital growth/technical change / productivitity growth); A rise in g,

while S shifts upward with: A rise in g;

A fall in the previous unemployment rate.

Also a given increase in g, say Ag, produces a greater upward shift in S than in D, so long as 0 < a2 < 1.

We now wish to examine the effect of some postulated {g,} sequences. We will take some initial equilibrium as the starting point which can be shown using the D,S curves. If d has prevailed sufficiently long to give dynamic equilibrium in period zero, we may write

bo - 44 + 41 - D

rE (~1 0: w _ o- - 2(, ;

1 - “21/ 1 - a,?

so: w, = (g - ii) + 24,.

The intersection of these two curves gives the initial equilibrium position (u, = ii, w. = iz) shown in Figure 2. We have shown So with a negative intercept which merely assumes that 2 was less than ii, but the (g - 6) value may be zero or positive, depending on the nature of the initial equilibrium. Suppose now that in Period 1 there is a one-step increase from 2 to g. and the new g level is sustained indefinitely after period one. Thus, in Period 1, D and S both shift upward, but the former by less than the latter, to give the (u,, w,) values at the intersection of D, and S,. Therefore, the impact effect of the rise in 2 is a reduction in unemployment and a rise in wage inflation. In subsequent periods the D curve

274


Figure 2. A One-Step Sustained Increase in g to g’

D,-D2-Da-...=Dm

shifts no further, so D, = D, = D,, etc. The S, curve, however, will be above the S, curve because of the fall in unemployment from u. to u,. The unit slope of the S curve provides a very simple graphical means of determining the position of subsequent S curves. Extend a perpendicular from u, to meet S, and there draw a horizontal line to the left. Where this meets a perpendicular from U, draw the S, curve with unit slope. The conjunction of D, andS, generates a new pair of (u,, w2) values, showing a further rise in wage inflation and a further reduction in unemployment. This sequence continues with ever smaller steps until a new long-run equilibrium is reached at the intersection of D, and S,. Notice that the intersection of So, Do indicates the value of g on the vertical axis. Since S, is displaced upwards from So by the exact amount of the increase in g, it follows that the new equilibrium value Z = g is indicated by the dotted horizontal line from the intersection of S, with the perpendicular erected at uo.

275

jack Johnston

Thus a one-step increase in g generates a path in (w, U) space climbing in a north-westerly direction, Similarly a one-step decrease in g will generate a descending path in the south-easterly direction. Cyclical behavior in g, that is, a sequence of low values for g followed by a sequence of high values, will generate a counter-clockwise loop with a negative slope in (w, u) space.

Since G represents all exogenous expenditure, alternations of high and low values in its rate of change would be characteristics of many economies in the nineteenth and first several decades of the twentieth century, when investment was the major component of G. The simple macro model presented would then lead one to expect a series of counter-clockwise, negatively sloped loops in (w, U) space. Phillips, of course, first drew his famous curve through a series of counter-clockwise, negatively sloped loops for the British economy from 1861 to 1913.

As a second experiment, let us again start from a position of initial equilibrium, but now keep g, constant at g, and consider instead a two-step increase in the parameter (CX, - a,k). Many influences might separately, or in combination, produce such a change. As we have seen earlier, o0 is a parameter linked to the determinants of the natural rate of unemployment and/or labor militancy. The term (a, - ol,k) could also increase because of a fall in capital (technological, productivity) growth. The k term might also be interpreted in terms of external inflationary shocks. For example, the real income reduction consequent upon a substantial rise in the price of imported oil might be seen in terms of the members of OPEC waiting at factory gates to claim a larger share of output so that less is available for the growth of domestic consumption, just as happens when k falls due to a reduction in productivity growth.

The initial steps in the sequence of (w, U) positions are:

Period 1: D shifts upwards to D,, as a consequence of the assumed increase in (a, - cxZk). There is no shift in the S curve, so s, = S,. The (w,, u,) position shown in Figure 3 results; that is, wage inflation and unemployment both rise.

Period 2: There is a further upward shift from D, to D,. The S curve now shifts downward because of the Period 1 rise in unemployment. The geometrical construction in the diagram, once again exploiting the unit slope of the S curve, shows the position of S,. The resultant

276


Figure 3. A Two-Step Upward Shift in D, followed by an increase in g

W3

' Y

Wl

- - g-w-w0 _-- - - - - - -

0 "

(w,, u,) position shows still higher wage inflation and still greater unemployment.

What happens in subsequent periods essentially depends on whether the government “gets into the act.” If it keeps g resolutely fixed at g, then there is no further movement in the D curves beyond D,. Successive S curves, however, will shift to the right and downwards by ever decreasing steps until the rate of wage inflation reaches its old equilibrium value, but now in conjunction with a much higher level of equilibrium unemployment. This movement would trace out part of a clockwise loop. There are, however, two strong pressures for a rise in g. Insofar as government expenditures are a major part of G, keeping g constant while price inflation accelerates will produce a declining share of real resources for the government and its employees. More importantly organized labor may be expected by the end of Period 2 to be clamoring

277

lack lohnston

for expansion measures. The recent acceleration of inflation, of course, will also be causing other groups to call for retrenchment, and governments are traditionally caught on the horns of this particular dilemma. Suppose, however, that on balance the two arguments for expansion outweigh that for retrenchment. The subsequent scenario might then unfold:

Period 3: The D curve shifts further outward to D,, caused this time by the government setting g, in excess of the old 2. The relation of S, to S, is now ambiguous, as it depends on the net balance between two opposing forces. The increase in g will push it upwards and the rise in the unemployment rate between Periods 1 and 2 will push it downward. In Figure 3 we have assumed the second force to be greater than its first and have thus drawn S, slightly below S,. Notice that if we postulate some larger increase in g, it will, of course, push the S curve upwards in Figure 3, but it will also shift the D, curve upwards at the same time. However, as noted earlier, any given increase in g displaces the S curve by more than the D curve, so that, in principle, the government could halt the rise in unemployment in Period 3 if it acted on a sufficiently massive scale. Let us assume the odds to be against it so that the sequence shown in Figure 3 is produced, namely, yet another concurrent rise in wage inflation and in unemployment.

Period 4: All now depends on how the “evidence” from Period 3 is interpreted. The government intervened because of rising unemployment, and yet unemployment has risen still higher. It would not be surprising for many to argue that the expansionary impulse had been inade- quate and that g should be raised well beyond g,. Cabinet members, seeing the purchasing power of their departments further eroded, are likely to give the same advice. If the government accedes D, will be above D,. S, will be subject to two opposing forces, as was S,, and the northeast path in (w, U) space may well continue through Period 4 and beyond.

The two main conclusions from these hypothetical sequences are :

278


1) If the g series cycles independently of the w and u sequences, this model would generate negatively sloped, counter-clockwise loops in (w, u) space;

2) If the g series reacts to the evolution of the w and u series the model would generate positively sloped scatters in (w, u) space. Clockwise or counter-clockwise loops or quite hap- hazard paths with positive slopes might be generated depending on how the government reacts each period to recent developments.

As we have seen earlier in Section 2 and as this model also demonstrates, positively sloped scatters in (w, u) space do not necessarily mean that the Phillips curve has turned around and now has a perversely signed coefficient on the unemployment variable. As Figure 3 shows, a two-period rise in the intercept (oL,,) of the Phillips curve might trigger off a sequence of points forming a positive scatter in (w, u) space. Yet after Period 2 the Phillips curve is stable and its properly signed coefficient on unemployment has never changed at all. The crucial question then is: Might an econometrician be led to draw completely erroneous inferences about the slope of the Phillips curve from this data? We have also seen that patterns such as those in Figure 3 might come about from changes in k without any change at all in the position of the Phillips curve. Could this type of shock cause problems in the estimation of the Phillips curve? The first question is briefly examined in Section 4.

4. An Exploratory Simulation Although the model of Section 3 is very simple, it has not

proved possible to determine unambiguous answers by analytical means to the questions raised at the end of that section. To explore whether it might be worthwhile to carry out extensive simulations, a few exploratory empirical runs were made. These tentative results are reported here and a proper simulation study will be reported in a future paper.

The parameters of the model were set:

k = 0.03, a, = 0.05, aI = 0.2, CQ = 0.6, y = 0.6.

These parameters have the property that if g is set at 0.05 the equilibrium values for the exogenous variables are

Jack Johnston

W = 0.05, pi = 0.02, ii = 0.06.

Next let us consider the possible components of a government reaction function:

1) The government may be concerned with the growth of G in real terms. In the original equilibrium,

so that the equilibrium real growth in G was given by the rate of productivity growth (k). However, if p,-, exceeds fi, the government suffers a decline in its accustomed real growth rate in period t - 1. An attempt to recoup some or all of this loss in period t might be expressed as

g, = g + &(p,-, - P), 6, > 0 .

Even 6, = 1 would not give full replacement unless price inflation stabilized in period t.

2) The government may be concerned about preventing the rate of unemployment deviating too far from the accustomed level, ii, giving

g, = g + 8, (u,-, - ii), sz > 0.

3) The government may be concerned about the rate of price inflation which would give a component

g, = g + &(P,-, - a. 6, < 0 . Merging all three components gives a reaction function of the form

where

P, = 6, + 63,

and


A priori expectations are

and p, may be positive or negative, but probably less than unity. The specification of the reaction function in (15) now makes

a four equation model, and the stability of the model places restrictions on the pi, S, values. We have started the model at the initial equilibrium corresponding to the assumed parameters and then administered a shock in the form of four upward steps in a,, each of size 0.005. After Period 4, a, remains steady at its new value of 0.07. The reaction function (15) comes into play after Period 1. Eight different reaction functions are specified. The sequence of observations is allowed to continue until the new equilibrium position is reached which gives a variable sample size since adjustments take different lengths of time for different pi, S, values. From the numerical data so generated, the short-run Phillips curve,

w, = a, - %% + %P, 9

is estimated by OLS and by two variants of SSLS. In BSLS,, the econometrician is assumed to be unaware of the existence of the government reaction function, and thus he specifies his predetermined variables to be ut-r and g, in accordance with equations (7), (8), and (9). In 2SLS, a “sophisticated” econometrician guesses at the existence of a reaction function and correctly specifies the predetermined variables to be u,-, and p,-,. We present results only for the estimation of the coefficient on u,, whose true value is -0.2. Only one set of estimates is presented for each reaction function since, as yet, no disturbances have been incorporated in the structural or reduced-form equations of the model. The postulated shift in CX,, is thus equivalent to a sequence of four postive disturbances in the Phillips curve with all other disturbances zero. If estimation methods go awry in such a simplified model, one would expect even greater variations when a fully specified set of structural disturbances is added to the model.

The first two columns of Table 3 specify reaction functions where the government only reacts to the unemployment rate, the next three a reaction only to price inflation, and the last three a reaction to both inflation and unemployment. Considering all twenty-four estimates of CQ, thirteen are perversely positive. Consid-

281

TABL

E 3.

Es

timat

es

of

the

Une

mpl

oym

ent

Coe

ffici

ent

(-0.2

) by

Va

rious

M

etho

ds

for

Vario

us

Rea

ctio

n Fu

nctio

ns”

(9

(ii)

(iii)

64

(v)

(vi)

(vii)

(v

iii)

Rea

ctio

n 0.

0 0.

0 1.

2 0.

7 -0

.5

-0.5

0.

5 1.

0 Pa

ram

eter

s 0.

3 0.

7 0.

0 0.

0 0.

0 0.

5 0.

5 1.

0

Sam

ple

Size

n

31

25

20

64

40

30

25

36

Estim

atio

n O

LS

-0.4

00

2.80

0 0.

041

-0.0

31

0.00

9 -0

.696

0.

587

(0.0

55)

Met

hod

BSLS

, -0

.400

2.

800

(0.0

24)

-0.0

32

0.01

0 -0

.749

0.

539

(-0.0

01)

BSLS

, -0

.400

2.

800

(0.0

24)

-0.0

32

0.01

0 -0

.749

0.

539

(-0.0

01)

*Coe

fficien

ts in

pare

nthes

es

are

not s

ignific

antly

dif

feren

t fro

m ze

ro at

the

five

per

cent

level.

Th

e re

maini

ng

coeff

icien

ts ar

e al

l sig

nifica

ntly

differ

ent

from

zero

at the

fiv

e pe

r ce

nt lev

el at

least.

Co

lumns

(i)

and

(ii)

with

f3

= 0

resu

lt in

a no

n-ide

ntifie

d Ph

illips

cu

rve,

so

that

if, in

this

mode

l, the

go

vern

ment

reacts

on

ly to

the

unem

ploym

ent

rate,

the

re

is no

wa

y to

estim

ate

the

Philli

ps

curve

. Th

e tw

o ve

rsion

s of

2SLS

giv

e ide

ntica

l es

timate

s be

caus

e fro

m eq

uatio

n (15

), g,

is a

linea

r fun

ction

.


ering only those which are significantly different from zero, ten out of the nineteen are positive. Thus, more than half the specifi- cations give coefficients on unemployment which are signi&zntZy positive even though the true coefficient is negative. There are negligible differences between OLS and 2SLS and zero differences between the two versions of BSLS. The eight cases may be subdivid- ed into the three periods (distinguished earlier), namely,

Period 1: Coefficient correctly signed and statistically significant: Columns (i) and (vi)

Period 2: Coefficient numerically small and sometimes insignificant: Columns (iv) and

(viii) Period 3: Coefficient incorrectly signed

and statistically significant: Columns (ii), (iii), (v), and (vii).

It is not possible on the basis of such a small experiment to infer which reaction functions produce which kinds of distortion in the estimation of the Phillips curve. These apparently bizarre results arise simply from the injection of a four-period shock in one structural equation, with all other disturbances zero. The sample data include observations on the initial and final equilibrium positions and also on the adjustment path from one to the other. However, the four periods subject to shocks account for less than twelve per cent of the average sample size over the eight specifi- cations.

The estimates of the coefficient on the rate of price inflation (a,) also show a wide variation, but only one of the eight specifi- cations gives an incorrectly signed coefficient. The unemployment and price coefficients have a negative covariance due to the positive covariance between u, and p, in the sample, but because of the small disturbances, this collinearity does not increase the sampling variance unduly. As a result, the majority of the coefficients on U, are not only perversely signed but also statistically significant.

The main conclusion from this exploratory simulation is that it appears that completely misleading inferences might be drawn from statistical investigations of the Phillips curve. In the model, the Phillips curve is still “alive and well,” in the sense that the true coefficients on unemployment and price inflation are correctly signed and have never changed, the only change being an earlier

lack Johnston

movement in the intercept which has now ceased. Nonetheless, straightforward econometric application yields erroneous results.

This conclusion is only tentative and raises a number of further questions:

1) Will the conclusion stand up when extensive simulations are run incorporating properly specified structural disturbances and varying sets of parameter values?

2) Will similar results appear for perturbations in parameters other than the Phillips curve intercept ((u,), such as the capital/technology parameter (k)?

3) Will similar results appear in richer and more plausibly specified models with the incorporation of a nonlinear employment effect and a proper treatment of inflationary expectations?

4) If the source of the problem is traced to structural shifts (however brief and temporary) in one or more relations, how do the various tests for structural change compare in detecting it and yielding reliable estimates of unchanged parameters- given that the econometrician can never really know a priori when a structural change takes place or what form the change will take?

Received: October, 1979

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