A Time-Series Analysis of the Real Wages-Employment Relationship

8/13/2019 A Time-Series Analysis of the Real Wages-Employment Relationship

http://slidepdf.com/reader/full/a-time-series-analysis-of-the-real-wages-employment-relationship 1/12

A Time-Series Analysis of the Real Wages-Employment RelationshipAuthor(s): Salih N. NeftçiSource: Journal of Political Economy, Vol. 86, No. 2, Part 1 (Apr., 1978), pp. 281-291Published by: The University of Chicago Press

Stable URL: http://www.jstor.org/stable/1830065 .

Accessed: 27/11/2013 04:13

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .

http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of

content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms

of scholarship. For more information about JSTOR, please contact [email protected].

.

The University of Chicago Press is collaborating with JSTOR to digitize, preserve and extend access to Journal

of Political Economy.

http://www.jstor.org

This content downloaded from 128.243.253.108 on Wed, 27 Nov 2013 04:13:24 AMAll use subject to JSTOR Terms and Conditions

http://www.jstor.org/action/showPublisher?publisherCode=ucpress

http://www.jstor.org/stable/1830065?origin=JSTOR-pdf






http://www.jstor.org/stable/1830065?origin=JSTOR-pdf

http://www.jstor.org/action/showPublisher?publisherCode=ucpress



A Time-Series Analysis of theReal Wages-Employment Relationship

Salih N. NeftyGeorgeWashingtonUniversity

In this paper, the theory of covariance-stationary stochastic processes isused in order to investigate the sign and thesignificanceofthe relationshipbetween employment and real wages. It is shown that when appropriatedistributed lags are estimated the data suggest that employment andreal wages are negatively correlated. The response appears to be non-contemporaneous and statistically significant.

The observed correlation between real wages and employment has

puzzled macroeconomists ever since Keynes (1936). Several economists,

including Kuh (1966), Bodkin (1969), and Modigliani (1977), have noted

that the contemporaneous correlation between real wages and employ-

ment is usually not statistically significant, and even when it is, is often

positive. For example, in a typical regression of real wages on a trend,

constant, and unemployment, Bodkin (1969) finds the coefficient of the

unemployment variable insignificant most of the time and negative when

it is significant.' Such findings seem to hold for most real wage, unemploy-

ment, and employment series in the U.S. and Canadian economies. Thus,

Bodkin (1969) concludes that . . . the majority of the analyses performed

with the U.S. data support the view that real wages are positively related

I have benefited from discussions with Thomas Sargent and Christopher Sims. Mycolleagues, James Barth and Robin Sickles, made several improvements in the presenta-tion. All remaining errors are my own.

' In the GeneralTheory,Keynes asserts: .. . in general an increase in employment canonly occur through the accompaniment of a decline in real wages. Thus, I am not dis-puting this vital fact which the classical economists have (rightly) asserted as indefeasible(1936, p. 17). More recently, Modigliani (1977) makes the same point in his AmericanEconomic Association presidential address: Similar tests of my own, using quarterlydata, provide striking confirmation that for the last two decades . . . the association oftrend adjusted real compensations of the private non-farm sector with ... employment ...is prevailingly positive and very significant (p. 7).

[Journal of Poli/ical lconoooy, 1978, vol. 86, no. 2, pt. 1]? 1978 by The University of Chicago. All rights reserved. 0022-3808/78/8602-0006$01.02

28I







282 JOURNAL OF POLITICAL ECONOMY

to the cyclical utilisation of the labor force. 2 This paper shows by using

the time series methodology that the relationship between real wages and

employment is significantly different from the one reported in Bodkin

(1969).It is not clear at the outset why such an observed correlation should be

puzzling in any way. In a market such as the one for labor, the supply

and demand curves will shift over the business cycle and generate a se-

quence of observations on real wages and employment which, depending

on the magnitude of the corresponding shifts, may be positively or nega-

tively contemporaneously correlated. However, in this particular case,

one does have some additional information on the magnitude of these

shifts. Observations on major macrovariables indicate that in Westerneconomies employment is positively correlated with interest rates on the

one hand and with prices on the other. The first of these correlations can be

explained by positing that, in terms of the traditional textbook model, it is

the I-S schedule that usually shifts. If, in addition, the aggregate supply

relation remains relatively more stable, then this would also explain the

positive correlation between employment and prices. But, under these

conditions, sticky nominal wages would imply a counter-cyclical movement

in real wages, which in turn implies a negative correlation between real

wages and employment. Since Keynesian economics is based on such wage

inflexibilities, a student of Keynesian macroeconomics might, on a priori

grounds, expect a negative correlation between real wages and employ-

ment. However, as Lucas (1977) notes, real wages do (not) exhibit con-

sistent pro- and counter-cyclical tendencies. If anything, they seem to be

positively related to movements in employment.

A series of recent important papers have been motivated, at least

partially, by these observations. The studies by Lucas (1970), Azariadis

(1975), Baily (1976), and in a different context by Barro and Grossman

(1971, 1976) are all notable examples. Of these authors, Barro and Gross-

man (1971) explain these phenomena by using a macro disequilibrium

model where economic agents are allowed to move away from their res-

pective supply and demand curves in response to exogenous shocks to the

system. Although it is not explicit, their discussion gives the impression

that what is really involved is a system where the underlying variables are

related to each other through distributed lags: A decline in commodity

demand and output produces a decline in employment . . . to the extentthat real wages decline . . . , a fall in real wages will accompany the decline

in employment . . . If. . . some action is taken to restore effective com-

modity demand, excess demand for labor will result. In that case a rising

real wage may accompany the recovery of output and employment. The

immediate significance of this theory is that it is able to generate un-

2 Bodkin (1969) estimates the same relation in first difference form. He also usesstatistical tools other than regression analysis.







REAL WAGES-EMPLOYMENT RELATIONSHIP 283

employment without placing any restrictions on the level or movement

of real wages (p. 87).

The presence of lags seems to be the main characteristic of this causal

chain of events. If so, such lagged responses can be generated by adjust-ment costs to labor input and by price inflexibilities. But the important

point is that the presence of distributed lags implies that one cannot com-

pletely characterize the relationship between two variables by using simple

regression. In the presence of distributed lags, simple regression will not,

in general, detect lagged responses and thus could give the erroneous

impression that real wages and employment are positively correlated.

In this paper it will be shown that this is indeed the case. An application

of the appropriate time-series methodology reveals that real wages andemployment are negatively related and that the puzzling positive corre-

lation reported by Bodkin (1969) is a result of ignoring the dynamics of

the underlying problem.

In the next section we describe the statistical model used in this paper

to analyze the relationship between real wages and employment. We

then report the empirical results. The estimation methodology and the

data are described in the Appendix.

Model

In order to examine the relationship between real wages and employment

we will use an explicit stochastic representation known to exist for every

multivariate linearly regular and jointly covariance-stationary time

series. Thus, let W(t) and L(t) denote the real wage and employment,

respectively. Also, assume that these series are linearly regular and jointly

covariance-stationary.3 Then W(t) and L(t) admit the following represen-tation (Sims 1972):

14(t) = E b1(s)L(t -s) + E b2(s) S(t-s) (1)S - 0S

00 00

L(t) = E a1(s)W(t -s) + E a2(s)W2(t - s) (2)S= -X S= 0

The first term on the right-hand side of equation (1) represents theprojection of W(t) on the L2 space4 generated by [L(t): -o < t < oo].

Similarly, the first term on the right-hand side of equation (2) represents

the projection of L(t) on the L2 space generated by [W(t): - o < t < coCI.The random variables el (t) and p2 (t) are jointly covariance-stationary and

3 A time series is linearly regular (nondeterministic) if the best linear forecast of itsinfinitely removed future consists only of knowledge of its mean (Rozanov 1967).

4 For a definition of L 2 spaces used in the present context, see Ash and Gardner (1975).








linearly regular. They also have the following properties:

E[=l(t)] 0, E[E2(t)] = 0

E[el(s).s,(t - S)] = 1o h E192(S)82(t -5S)] = (o2 t) 0 otherwise' [2s~( otherwises'

More importantly, ?1(t) and ?2(t) are orthogonal to the corresponding

independent variables. That is to say, E[e8(s)L(t - s)] = 0 and

E[82(s) W(t - s)] = 0 for all s.

Equations (1) and (2) constitute a nonstructural but still a well-

defined system which can be used to estimate the relationship between real

wages and employment. This last point is important, since the previous

empirical work in this area has been in terms of nonstructural regressionmodels (e.g., Bodkin 1969).5 To me such uses of nonstructural models

seem to be fruitful, because the purpose of these studies is to determine the

empirical evidence which structural models of the labor market should be

able to explain. However, these nonstructural models should at least be

justifiable on statistical grounds so that the properties of the estimated

parameters and of the test statistics can be objectively evaluated. The

representation given by equations (1) and (2) is one such model, since one

can always obtain consistent and asymptotically efficient estimates of theparameters [ai(s), bi(s): - o < s < so, i = 1, 2] by using generalized

least squares, or as in this paper, a version of the Hannan efficient pro-

cedure (see Hannan 1965, 1970).

Empirical Results

In this section we first estimate the two-sided distributed lags represented

by equations (1) and (2) and then test the significance of the future lags

in order to see which one (if any) of these expressions can be collapsed to

a one-sided distributed lag. These one-sided distributed lags are then

estimated for several employment and unemployment series in the U.S.

economy.

In order to estimate the parameters in equations (1) and (2), one natu-

rally has to truncate the length of the lag distributions. Accordingly, these

expressions were estimated with 12 future and 24 past lags. This particular

truncation was expected not to affect the results in any significant way, for

in a two-sided relation such as equation (1) or (2) there exists a finitetruncation point so that the omitted tails of the lag distributions contribute

negligible explanatory power (Sims 1974).

The distributed lags in equations (1) and (2) were estimated using the

time series on the manufacturing employment, the number of employees

5 Bodkin (1969) never states explicitly whether the reported regressions are estimates

of structural relationships. Yet, one gets the impression that he is estimating demand

schedules.








Plot of { a(s) }:**

~~~~~~~~~~~~~~~~~~~s

Test statistic for the hypothesis that{a1 Is) = 0, 0< s< - 12} is F* = 1.25

R2 = .48

D.W. = 1.96

Plot of{ b1 (s) }:**

5

Test statistic for the hypothesis that { b1 (s) = 0, 0 < < - 12} is F* = 3.26

R2 = .45

D.W. = 1.93

*Degrees of freedom: Numerator 12. denominator 128 [F12, 128(.05) 1.8].**Dotted horizontal lines represent typical standard errors.

FIG. 1.-Estimates of the lag distributions in eqq. (1) and (2)

at the payroll of manufacturing establishments, the nonagricultural em-ployment, and the layoff rate. The estimates for these variables are basi-

cally similar. Here we report the case of manufacturing employment, which

we consider to be the most representative result.

The results reported in figure 1 show that the future coefficients of the

real wages in equation (2) are insignificant. The F-statistic for the hypo-

thesis that equation (2) is one sided is equal to 1.2, which is insignificant

at the 25 percent level. This indicates that a one-sided distributed lag

relation of employment on real wages can be estimated consistently andwithout loss of any significant explanatory power. The appropriate F-

statistic for equation (1) is 3.2, which suggests that relation (1) is indeed

two sided.6

6 Some caution is warranted in interpreting this test. Although the corresponding t-and F-statistics are insignificant, the future coefficients of aI(s) seem to have some pattern;they are not randomly distributed around the horizontal axis. For the skeptic who has

reservations about the so-called exogeneity test, equation (3) was also estimated withW(t) on the right-hand side. None of the conclusions changed.








These results suggest that the following equation can be used to

determine the relationship between employment and real wages:

k r

L(t) = c(s)W(t -s) + A, d(u)c(t- u), (3)s=O u0=

where the variables W(t) and e(t) have the same propertiesas in equations

(1) and (2).Since the disturbances in this expressionare orthogonal to the indepen-

dent variables, equation (3) can be consistently estimated by ordinaryleast squares (OLS), even in the presence of serial correlation. Statedanother way, expression (3) is a projection and under our assumptions,

projections can be consistently estimated by OLS (Ljung 1976). However,our purpose is not only to determine the sign of

k

E C(S)s=O

but also to see whether the relationship is significant. As is well known(Theil 1971), the appropriate test for significance requires correction forserial correlation. Accordingly, an adjustment for serial correlation was

made, as explained in the Appendix.The estimates of equation (3) using several employment and unemploy-

ment series are very similar. Here we report the results for manufacturingemployment and the unemployment rate.

To explore the adequacy of the contemporaneous relations used byBodkin (1969), equation (3) was estimated for different values of k:k = 24, 18, 12, 6, and finally for k = 0. This latter case is equivalent toBodkin's equation. By varying the length of the distributed lags, we

demonstrate how the use of the simple regression misrepresents the cor-relation between real wages and employment and therefore gives theincorrect impression that real wages and employment are positivelyrelated.

The estimates of c(s) for different values of k are shown in tables 1 and

2.7 These results are strikingly different from the ones reported in Bodkin

(1969). An analysis of tables 1 and 2 shows that the long-run relation-

ship between real wages and employment is not only significant but nega-

tive. The sumof the coefficients in the distributed lag is negative foremployment and positive for unemployment. The only significant coeffi-

cient which has the wrong sign is the contemporaneous one. This

coefficient is positive in the case of employment and negative in the case

of unemployment. As may be seen from these tables, it is this coefficient

that eventually dominates the correlation between the two variables when

7 The results with k = 24 are very similar to the ones with k = 18. Thus, they areomitted.








TABLE 1k

in [Manufacturing Employment (t)]=

Co + E C1(s) In [Real Wage (t - s)] + E(t)

Coefficient Run 1: k = 18 Run 2: k = 12 Run 3: k = 6 Run4: k= 0

t .................. .863 .856 .750 .864t- I.............. -.090 -.080 -.248 ...t-2 2.............. .018 -.057 -.207 ...t-3 3.............. -.143 -.169 -.260 ...t-4 4.............. -.253 -.282 -.345 ...t-5 5.............. -.083 -.151 -.202 ...t-6 6.............. .151 -.023 ... ...t-7 7.............. -.143 -.209 ... ...t-8 8.............. -.248 -.250

t-9 9.............. -.296 -.290 ...t-10 ............. -.061 -.106 .. ...t- I I............. -.381 -.296 ...t-12 ............. -.349 -.185 ... ...t-13 ............. -.283 ... ... ...t-14 ............. .007 ... ... ...t-15 ............. -.178 .. ... ...t-16 ............. -.153 ... ...t-17............. -.078 ... ... ...t-18 ............. .173 ...SEa . (.120) (.110) (.101) (.105)

Sum of coefficientsb .. -1.52 (.27) -1.24 (.31) -.51 (.45) .864 (.105)

Relevant Test Statistics

R ................. .38 .35 .30 .24F(k, 142 - k) ....... 6.88 8.88 16.13 72.54D-W .............. 1.98 1.99 1.90 1.78F*C ................ ... 1.49 2.00 2.44

NOTE.-Estimation period, 1948-71; F6, 136 (.05) _ 2.1; F6, 136 (.1) n 2.9. See the Appendix fora description of the estimation methodology.

a Typical standard error of the estimates.b

Standard error of the sum in parentheses.c Statistic for the hypothesis that six additional lagged terms are insignificant.

the length of the lag distribution is decreased from 24 to 0, thereby giving

the erroneous impression that real wages are positively correlated with

employment-and negatively correlated with unemployment. This

suggests that the estimate of the contemporaneous coefficient remains

consistent when the length of the lag distribution is decreased, which will

be the case if real wages are a white noise process.

These facts imply that the puzzling positive correlation noted inKuh (1966), Bodkin (1969), and Modigliani (1977) is partly a result of

ignoring the dynamics of the problem. 8

What is the significance of these results from the point of view of

macroeconomic theory? An empirical finding does not become puzzling

until it is confronted with a theory. Thus, one may be puzzled if one is

8 This may also be a result of their using wage series not corrected for overtime (Lucas

1970).








TABLE 2k

in [Unemployment (t)]=

C0 + E Cl(s) in [Real Wage (t -s)] + e(t)0

Coefficient Run 1: k = 18 Run 2: k = 12 Run 3: k 6 Run 4: k 0

.................. -.115 -.087 -.028 -.027t-I .-.047 -.027 .089 ...t-2 ..115 -.001 .073 ...t - 3 .............. .231 .198 .218 ...t - 4 .............. .017 .066 .132 ...t - 5 .............. -.102 .016 .081

-6 .-.060 .062-7 ..022 .055 ... ...

t-8 ..094 .150 ... ...

t - 9 .............. -.064 -.007 ... ...t- 10 ..156 .142 ... ...t- 11..257 .174t- 12..124 .068 ... ...t-13 ..028 ... ... ...t-14 ..112 ... ...t-15 ..281 ... ... ...t-16 ..115 ... ... ...t-17 .-.001 ... ... ...t-18 .-.119 ...SEa.(.085) (.080) (.073) (.073)

Sum of coefficientsb .. .948 (.14) .804 (.16) .591 (.21) .027 (.073)

Relevant Test Statistics

R ................. .195 .12 .08 .0006F(k, 142 -k) 2.66 2.28 3.05 .137D-W . .1.90 1.81 1.76 1.66F*c ............ ... 1.15 1.34 1.68

NOTE.-Estimation period, 1948-71; F6, 136 (.05) 2.1; F6, 136 (.1) _ 2.9. See the Appendix fora description of the estimation methodology.

a Typical standard error of the estimates.b Standard error of the sum in parentheses.

c Statistic for the hypothesis that six additional lagged terms are insignificant.

using a model characterized by a labor market where producers observe

an exogenously given real wage and purchase labor by moving along a

downward-sloping demand schedule and where the supply-side equilib-

rium is ignored. The positive contemporaneous correlation between real

wages and employment becomes puzzling in this framework.

The empirical results reported in this paper, however, indicate that the

relationship between real wages and employment may have a natural

interpretation in a different setup. In particular, the results suggest a

labor market where both sides optimize by solving a dynamic maximi-

zation problem and where both the producers and the suppliers of labor

will be in equilibrium. Such a model would contrast dramatically with the

approach taken by Barro and Grossman (1971), who, after analyzing the

work reported by Bodkin (1969), suggest abandoning the equilibrium








approach altogether.9 But until more theoretical work is done, we cannot

say whether our results are inconsistent with an equilibrium theory in

which, as a result of the dynamic optimization problems faced by economic

agents, the respective demand and supply equations involve distributedlags.

Conclusions

The major conclusion of this paper concerns the sign and significance of

the relationship between employment and real wages. Specifically, con-

trary to the results reported in Bodkin (1969), it has been shown that when

appropriate distributed lags are estimated the data suggest that employ-

ment and real wages are negatively correlated. Furthermore, this responseappears to be noncontemporaneous and statistically significant.

These empirical results do not confirm one model over another. Yet, as

indicated above, they do suggest a certain line of research and a more

careful look at the dynamic optimization problems faced by economic

agents in the labor market.

Appendix

Estimation Procedure and the Data

In this Appendix, the estimation procedure is summarized, the statistical proper-ties of this procedure are discussed, and the data are described.

The empirical results reported in this paper are estimates of {a(s)} in equations

of the following form:

k2 r

Xl(t) C-O E a(s)X2(t - s) -4 d(s) n(t - s), (Al)s= -k, s=

where X1(t) and X2(t) are assumed to be jointly covariance-stationary and

linearly regular. Similarly, n(t) is assumed to be a covariance-stationary, linearly

regular, and serially uncorrelated process. It is orthogonal to the X2(t -S),

-k1 < s < k2.

To estimate {a(s)} the data were first prefiltered. To do this logarithms of raw

series were taken. Then each series was filtered through the filter (1 - .9L)

(where L denotes the lag operator).

Next, in order to purge the series of their nonstationary components, each serieswas regressed on a constant, linear trend and a set of seasonal dummy variables.

The residuals from this regression were then seasonally adjusted and used as thenondeterministic part of the series under consideration. In order to remove

seasonality the residuals were Fourier transformed and set to zero for a band of-r-/24 around the seasonal frequencies. 0 The resulting series were then inverseFourier transformed.

9 Modiglieni (1977), on the other hand, suggests that the evidence can be accotinted

for by the oligopolistic pricing model according to which price is determined by long-runminimum average cost up to a mark-up reflecting entry-preventing considerations (p. 7).

'o Following Sargent (1976) the same regressions were run using seasonally unadjusteddata which were then purged of only the deterministic seasonals (i.e., without erasing aband around the exact seasonal frequencies). Doing this, however, yielded essentiallythe same results.









REAL WAGES-EMPLOYMENT RELATIONSHIP 29I

References

Ash, Robert B., and Gardner, Melvin F. Topics in StochasticProcesses.New York:

Academic Press, 1975.

Azariadis, Costas. Implicit Contracts and Underemployment Equilibria.J.P.E. 83, no. 6 (December 1975): 1183-1202.

Baily, M. N. Wages and Employment under Uncertain Demand. Rev. Econ.Studies 41 (January 1976): 37-50.

Barro, Robert J., and Grossman, Herschel I. A General Disequilibrium Modelof Income and Employment. A.E.R. 61 (March 1971): 82-93.

. Money, Employmentand Inflation. Cambridge: Cambridge Univ. Press, 1976.Bodkin, Ronald G. Real Wages and Cyclical Variations in Employment: A

Reexamination of the Evidence. Canadian J. Econ. 2 (August 1969): 353-74.BusinessStatistics. Suppl. to Surveyof CurrentBusiness. 18th biennial ed. Washington:

Dept. Commerce, 1971.Hannan, Edward J. The Estimation of Relationships Involving Distributed

Lags. Econometrica33 (January 1965): 206-24.

. Multiple Time Series. New York: Wiley, 1970.

Keynes, John NI. The General Theory of Employment, Interest and Money. London:

Macmillan, 1936.

Kuh, E. Unemployment, Production Functions and Effective Demand. J.P.E.

74, no. 3 (June 1966): 238-49.

Ljung, L. Consistency of the Least-Squares Identification Method. IEEE Trans-actions on Automatic Control (October 1976): 779-81.

Lucas, Robert E., Jr. Capacity, Overtime and Empirical Production Functions.A.E.R. 60, no. 2 (May 1970): 23-27.

- . Understanding Business Cycles. In Stabilisation of the Domestic and theInternationalEconomy,edited by Karl Brunner and Allan H. Meltzer. Amsterdam:

North-Holland, 1977. Supplement to J. Monetary Econ. 5 (1977): 7-29.Modigliani, Franco. The Monetarist Controversy or, Should We Foresake

Stabilization Policies? A.E.R. 67, no. 2 (March 1977): 1-19.

Rozanov, Yu A. StationaryRandomProcesses.San Francisco: Holden-Day, 1967.Sargent, T. 'Comment' on 'Seasonal Adjustment and Multiple Time Series

Analysis' by K. Wallis. Paper presented at the NBER/Bureau of Census con-

ference on Seasonal Analysis of Economic Time Series. Washington, September9-10, 1976.

Sims, Christopher A. Money, Income and Causality. A.E.R. 62, no. 4 (Sep-tember 1972): 540-52.

. Distributed Lags. In Frontiersof Quantitative Economics.Vol. 2. Edited byMichael D. Intriligator and D. A. Kendrick. Amsterdam: North-Holland,1974.

'Comment' on 'Relationship-and the Lack Thereof...' by D. A.

Pierce. J. AmericanStatis. Assoc. 72 (March 1977): 23-24.Theil, Henri. Principles of Econometrics.New York: Wiley, 1971.

Date post:	04-Jun-2018
Category:	Documents
Upload:	kai-shen-lim
View:	219 times
Download:	0 times

A Time-Series Analysis of the Real Wages-Employment Relationship

Documents