Discussion Paper No. 573

WHY ARE THE WAGES OFJOB STAYERS PROCYCLICAL?

Donggyun Shinand
Kwanho ShinMarch 2003

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

Why Are The Wages of Job Stayers Procyclical?

Donggyun Shin* and Kwanho Shin**January 2003

This paper has greatly benefited from thorough readings and comments made by John
DiNardo and Gary Solon. The authors also thank seminar participants at the Korean
Labor Economic Workshop and the Korean Macroeconomic Workshop for helpful
discussions. Part of this paper was written while Kwanho Shin was affiliated as avisiting foreign scholar with Institute of Social and Economic Research, Osaka
University. All errors and omissions are ours.

* Department of Economics, Hanyang University, 17 Hangdang-Dong, Sungdong-Gu, Seoul,
Korea, dgshin@hangyang.ac.kr** Department of Economics, Korea University, 1-5 Anam-Dong, Sungbuk-Gu, Seoul, Korea
khshin@korea.ac.kr

Abstract
This paper explains how real wages are procyclical for those who stay with the same
employer.

On the basis of the Panel Study of Income Dynamics data for the period of

1974-75 to 1990-91, we find that the substantial wage procyclicality among job stayers
is mostly accounted for by great wage adjustments during the period when theunemployment rate reaches a historical minimum level from the start of the employee’s
current job. This finding explains how the real wages of job stayers behave
asymmetrically over the cycle and more importantly how the evidence of stayers’ great
wage procyclicality accords with the theoretical prediction of implicit contracts thatstresses costless mobility.

JEL Classification: E24, E32

1

I. Introduction

Recent analyses of longitudinal micro data have found that real wages are much moreprocyclical than they appear in aggregate time series data.1 Studies by Vroman (1977),
Bils (1985), and Barlevy (2001) found that this is especially so for those who change
employers.

Numerous studies present reasonable explanations of why the wages ofjob changers are so procyclical.

For example, Beaudry and DiNardo (1991) (hereafterBD) explain this based on implicit insurance between workers and firms.2

Workers

who are forced to change jobs have no access to insurance, and their new wage rates areheavily dependent on the spot market condition, leading to higher fluctuations in thewage rate. In contrast, job stayers are protected against aggregate fluctuations byimplicit insurance offered by employers, implying much smoother wage adjustments.
Recently, Barlevy (2001), based on differences of unemployment risks, provides
another alternative hypothesis that the strong wage procyclicality of job changers is due
to compensating wages; that is, job changers receive higher wages in new jobs that pay
compensating wages for subsequent losses of those jobs.3
However, recent empirical findings suggest that even the wages of job stayers
are procyclical, although they are less so than those of movers.

For example, on thebasis of the Panel Study of Income Dynamics (PSID) for men in the period of 1968-69
to 86-87, Solon, Barsky, and Parker (henceforth SBP, 1994) found that a one percentage
point reduction of the unemployment rate leads to a rise in the real wage rate of stayers
by 1.2 percent.

Similar estimates are found in Bowlus (1993), Shin (1994), andDevereux (2001).
The primary goal of this paper is to explain why real wages are procyclical1

Early studies by Raisian (1979) and Stockman (1983) point out that aggregated time series on real

wages are counter-cyclically biased by their tendency to weigh low skilled workers more heavily in
expansions than in recessions.

Solon, Barsky, and Parker (1994) demonstrate rigorously how important

this composition bias is. The latter study also presents a detailed summary of the time series evidence
and a nice discussion of how this time series evidence has influenced macroeconomic theory.
2

See Azariadis (1975) and Baily (1974) among others for the theoretical underpinnings of the implicit

contract theory.
3

An early work by Okun (1973) explains the large wage procyclicality among job changers based on2among job stayers.

In fact, despite the repeated findings, little study has been

conducted to account for the fact.4

Since job stayers constitute a major fraction of thelabor force, this is an important step in understanding the strong procyclicality of real
wages.

For example, estimates in Table IV of Solon et al. imply that 73% of the entire

year-person observations and 95% of the total number of workers are classified as job
stayers, which results in job stayers contributing from 66% to 85% of the estimatedoverall wage procyclicality (-.0138), respectively.
At first, the finding of substantial wage procyclicality among stayers seems at
odds with the theoretical prediction of implicit contracts, as risk averse workers prefercomplete wage smoothing to be shielded from productivity shocks.

In terms of

empirical conclusions, while SBP, among others, conclude that stayers’ real wages arehighly correlated with the contemporaneous unemployment rate, BD report that stayers’
wages depend not on the contemporaneous unemployment rate but on the minimum
unemployment rate observed since the beginning of the current job.

This paper

confronts the puzzle of the cyclicality of stayers’ wages with new empirical evidence.
In theory, the prediction of wage smoothing in the conventional implicit
contract theory hinges on a presumption that labor mobility is costly.

Without

mobility costs, however, wages need to be renegotiated upward when economic
conditions improve sufficiently enough to prevent the worker from being bid away byother firms. Therefore, a (plausible) variation in the assumption would eliminate theprediction. As will be demonstrated in subsequent sections, once the conventional
implicit contract theory is enriched to encompass free labor mobility across jobs, nofurther departures from the conventional model are needed to accord with theprocyclicality of stayers’ wages.

In fact, BD also distinguish between implicit contract

inter-industry wage differentials and cyclical upgrading of labor.
4

Two papers are related with the current issue. First, using personnel records from the Ford and Byers

companies, Solon, Whatley, and Stevens (1997) found some supporting evidence for the old hypothesisthat a portion of firms’ cyclical adjustment of labor costs is achieved not by changing the wages paid inparticular jobs, but by changing the quality of labor assigned to those jobs. Second, Devereux (2001)
found that the wage procyclicality within employer-employee matches is driven mostly by those who
receive incentive-based pay, such as piece rate, overtime or commissions and that the hourly wage ratefrom hourly and salary workers is not responsive to the business cycle.

3models with and without mobility costs. With costly mobility, contract wages arenegotiated once at the beginning of contract, and never change thereafter. Without
mobility costs, however, wages are adjusted upward whenever the unemployment rate isat the historically minimum level since the start of the current job. In the empiricalanalyses, they regressed the wage rate on the unemployment rate at the starting point of
the current tenure, the minimum unemployment rate since the start, and the current
unemployment rate and found that only the minimum rate is significant. This provides
a supporting evidence for the implicit contract model without mobility costs.
Nevertheless, we recognize that the BD’s finding that wages do not depend on
the current unemployment rate looks inconsistent with the evidence of procyclicalstayers’ wages, namely that real wages are strongly correlated with the current
unemployment rate.

This happened because of different methodologies adopted by thetwo sets of empirical studies.

While empirical evidence of stayers’ wage

procyclicality focuses on the partial correlation of wages and the current labor market
conditions, BD’s test procedure is based on the link between wages and past as well as
current labor market conditions.

Our strategy is, therefore, to develop a test procedure,

which is equivalent to the BD’s test procedure but uses only the current unemployment
rate, which will be explained in Section II.
By extending the sample period to 1974-1991, which includes one morebusiness cycle than the sample period considered by SBP or BD, we replicate theirresults almost identically.

For example, wages of stayers are found to be quite

procyclical. BD’s estimation results are also confirmed.

Further we find that thewage adjustments of stayers are not uniform over the course of the entire job tenure.
The wage adjustments are much higher when the unemployment rate is decreasing (theexpansion period) than when the unemployment rate is increasing (the recession period).
While most studies find asymmetric adjustments of nominal wages over the businesscycle, our results indicate that this is also true for real wages.

Most importantly, we

find that wage adjustments are not uniform even in the expansion period but are actuallyconcentrated on a special phase of the expansion period, called the period of renegotiation.

This corresponds to the period when the unemployment rate dips below

the historical minimum level observed since the start of the current job.

On thecontrary, wages are not adjusted much even when the unemployment rate decreases as
4

long as it does not dip below the historical minimum.

In short, stayers’ substantial

wage procyclicality as well as asymmetric adjustments of real wages is mostly
accounted for by great wage adjustments during the re-negotiation period, as implied by
the costless mobility version of implicit contracts suggested by BD.

Our evidence

clearly disputes an implicit contract model with costly mobility, because according to it,
wages since the start of the current job should be acyclical, implying no correlation ofwages and the current unemployment rates for the entire job tenure.

Further ourevidence also rejects the spot market model because it predicts that the correlation
should be as great for the period when wages are not re-negotiated as for the renegotiation period.
This paper is organized as follows.

Section II develops an alternative test

procedure that is identical to the BD’s test procedure but uses only the contemporaneous
unemployment rate.

Section III explains data used in our analyses.

reports our main empirical results.

Section IV

We state our major conclusions in Section IV.

II. Test Procedure

Beaudry and DiNardo modified Harris and Holmstrom’s (1982) theory todevelop testable hypotheses of implicit contract models based on the link between
wages and past labor market conditions.

According to BD, if mobility is costless,contractual wage payments depend on the most favorable labor market condition
observed since one has begun his/her job. This implies that the wage rate of anindividual should depend on the minimum unemployment rate in his entire job tenure.
On the contrary, if mobility is costly, contractual wage payments should be fixed for his
entire job tenure.

In this case the wage rate of an individual should depend upon theunemployment rate at the start of his/her current job.

Finally, if wages are determinedat the spot market, wages should depend on the current labor market conditions. In
testing these hypotheses, BD augmented the standard Mincerian wage function by
including the starting unemployment rate at the start of a job, the minimum
unemployment rate observed since the start, and the current unemployment rate andexamined the significance of these variables.
5

More specifically the equation they

estimated is:ln Wit = α ′X it + β ′Z i + γ 1StartingU it+γ 2 MinimumU it + γ 3CurrentU it + vit(1)

where Wit is the ratio of the nominal wage of individual i in year t to the Consumer
Price Index (CPI) in that year5, X it , a vector of time-varying individual characteristics
such as experience, experience squared, tenure, dummies for industry, region, union
status, marital status, and standard metropolitan statistical area (SMSA), and Z i , avector of individual-specific but time-invarient variables, which includes schooling,race, ability, and motivation.

In addition, StartingU it means the unemployment rate

at the starting point of a job held at time t, MinimumU it , the minimum level of theunemployment rate observed between the starting point and time t, and CurrentU it ,the current unemployment rate at time t.

On the basis of the CPS and the PSID for the

1976-84 period, they estimate the Ordinary Least Squares (OLS)6 and the fixed-effects
versions of equation (1) and conclude that the contract model with costless mobility
describes the data best in the sense that the coefficient on MinimumU it is the greatest
and statistically significant.
It is worth noting that their measures of the starting and the minimum
unemployment rate are critically dependent on the duration of the current tenure. As
emphasized by McDonald and Worswick (1999), an incorrect measurement of tenure isdirectly translated into an incorrect measurement of the minimum unemployment rate aswell as the starting unemployment rate.

As already pointed out by many researchers,

tenure responses for the PSID and the National Longitudinal Survey (NLS) data areoften inconsistent with calendar time. 7

For example, Topel reports that, in therecorded tenure data for the 1968-83 period of PSID white males, the year-to-yearchanges in job tenure range from –31 years to 7.5 years, and measured tenure declines
5

We have also tested the GDP deflator and found little difference in the conclusion.

6

Of course, when OLS is applied to equation (1), unobservable time-invarient variables are notcontrolled for.
7

See Altonji and Shakotko (1987), Topel (1991), and Brown and Light (1992) among others.

6between years of a job in 3.8% of all cases.

Our calculations show that, in therecorded tenure data for the 1975-91 period of PSID men, a little over 20% of all job
spells have an initial reported tenure of ‘more than 14 months.’

All these figuressuggest that (1) extreme care should be taken when using these error-ridden tenurevariables and (2) other test procedures that are not critically dependent upon the
duration of tenure are desirable.
To overcome these difficulties and, more importantly, to make our estimatescomparable to estimates of the stayers’ wage procycliclaity, we use the following
alternative test procedure, which depends only on the contemporaneous unemployment
rate. If, as concluded by BD, an implicit contract with costless mobility governs therelationship between wages and past labor market conditions, wages should be adjusted
to the contemporaneous unemployment rate whenever it goes below the historicalminimum unemployment rate since the start of the current tenure.

This is the period

when re-negotiation takes place under the BD’s theory. Therefore, once we selectthese years, the unemployment rate is monotonically decreasing over time within thecurrent tenure. If the BD’s conclusion is valid, the partial correlation of wages andcontemporaneous unemployment rates would be high for this re-negotiation period, notfor the rest of the period.

On the other hand, if an implicit contract model with costly

mobility is dominant, wages since the start of the current job are to be acyclical,
implying no correlation of wages and contemporaneous unemployment rates.

To put it

conversely, the stayers’ wage procyclicality itself rejects the hypothesis of an implicit
contract with costly mobility.

Finally, if wages are primarily determined at thestandard spot market, then the correlation is expected to be as great for the period whenwages are not re-negotiated as for the re-negotiation period.
Figure 1 illustrates these points. Suppose a person has a job as of 1991,
which began in 1975.

The BD model implies that, in each year for the 1976-79 period,

wages are renegotiated as the unemployment rate is historically lowered.

This happens

because employers want to retain quality workers in cyclical upturns. Renegotiations
do not take place as the unemployment rate goes up for the 1980-82 period.

The BD-

specific feature of implicit contracts is that re-negotiation does not take place even when
the unemployment rate goes down as long as it is not lowered below the historicalminimum level.

This corresponds to the 1983-1987 period.
7

In 1988, as theunemployment rate goes below the 1979 level, they revise the old ‘contract’ and do it
again in 1989.

As the labor market starts to deteriorate in 1990, wages are set at the

1989 level. Therefore, we consider three sample sub-periods: the entire sample period
since the start of the current job, the sub-period when renegotiations take place (marked
by large squares), and the sub-period when renegotiations do not take place.

Then, foreach sub-sample period, we estimate the correlation of real wages and contemporaneous
unemployment rates. What we want to measure for each sub-sample period is the
direction and the magnitude of composition-corrected and detrended mean wagechanges associated with one unit change in the unemployment rate.
If wages are determined at the spot market, they are procyclical for the entire
sample period since the start of a job, and wage adjustments are as great for the nonnegotiation period as for the re-negotiation period.

If an implicit contract with costly

mobility explains the data, wages will be noncyclical for the entire period since the startof a job.

Finally, if an implicit contract with costless mobility describes the data, great

upward wage adjustments will be made for the re-negotiation period, not for the other.
Note that, if the last hypothesis is true, little wage adjustment takes place even for theperiod of falling unemployment as long as the rate does not reach the historicalminimum.
Compared with the BD’s, our test results are expected to be less sensitive toincorrect measurement of tenure. In our test procedure, incorrect measurement oftenure changes sub-sample periods slightly, with relatively little change in the mean
wage adjustment within each sub-sample period.

On the contrary, as previously

mentioned, miss-measurement of tenure directly affects the starting and the minimum
unemployment rates and, therefore, the corresponding coefficient estimates in the BD’s
specification.
To estimate wage cyclicality for stayers, we estimate the following augmented
Mincerian wage function:log Wit = γ 1 + γ 2 t + γ 3 t 2 + γ 4 EX it + γ 5 EX it2 + γ 6' Z i + γ 7URt + ε it(2)

where Wit is again the ratio of the nominal wage of individual i in year t to the8Consumer Price Index (CPI) in that year.

Work experience EX it is measured simply

as the number of years since individual i completed schooling.

Z i is a vector ofindividual-specific, but time-independent, characteristics such as years of schooling,race, gender, ability, and motivation. URt is the civilian unemployment rate in year t
and is used as a cycle indicator. Both individuals’ wages and the unemployment rateare expressed as deviations from quadratic time trends to focus on cyclical componentsof the two variables. Equation (2) is precisely the same specification used by SBP(1994) and many other longitudinal studies that investigate the cyclicality of real wages.
First-differencing equation (2) eliminates observable and unobservablecharacteristics, Z i :∆ log Wit = β 1 + β 2 t + β 3 EX it + β 4 ∆URt + ∆ε it
where β1 = γ 2 − γ 3 + γ 4 − γ 5 , β 2 = 2γ 3 , and β 3 = 2γ 5 .

(3)

β 4 = γ 7 is greater than,equal to, or less than zero as real wages are countercyclical, noncyclical, or procyclical.
Applying OLS to equation (3) produces inefficient estimates ofcoefficients.

β

The differenced error term is cross-sectionally correlated because

different workers share common time effects. Usual standard error estimators arebiased downwardly by neglecting this effect. Moreover, the differenced error term
may be serially correlated.

To correct this, we apply a two-step estimation procedurethat has been adopted by SBP (1994) and Shin (1994) among others. In the first step,
we apply OLS to the regression of the logarithm of real wage growth on experience anda vector of year dummies.

In the second step, we apply Generalized Least Squares(GLS) to the regression of the estimated year effects on a time trend and changes in theunemployment rate.

As proved by Amemiya (1978), the two-step estimator that

corrects for the non-sphericality of the second-stage error term is identical to the GLS
estimator applied to the first-differenced equation in a single stage.

We use this two-

step method in estimating the cyclicality of stayers’ wages.
For the purpose of estimating the correlation of real wages andcontemporaneous unemployment rates for various sub-sample periods previously

9defined, we modify the above two step procedures. In the first step, we apply OLS tothe regression of the logarithm of real wage growth on experience and vectors of year
dummies for those sub-sample periods.

In the second step, we apply a system of

seemingly unrelated regressions with the coefficients on the intercept and the time trend
restricted to be equal across equations.

We correct for serial correlation within eachequation. The unemployment coefficient of each equation represents the compositioncorrected and detrended mean wage change for each subsample period that the equation
stands for associated with one unit change in the unemployment rate. For the sake ofsimplicity, estimated coefficients only on the unemployment rate are reported anddiscussed.

III. Data

We choose to use the PSID data for the following reasons. First, as noted bymany researchers, tenure responses from survey-based data are often inconsistent withcalendar time.

Therefore, it is essential to make tenure series internally consistent atleast within job duration using longitudinal surveys such as the PSID.

Second, among

existing longitudinal surveys, the PSID is preferable to the NLS mainly because theformer represents the entire working age population better than the latter. Third, since
BD and many existing empirical studies on stayers’ wage procyclicality used the PSID,
we use the same data set to avoid any possible outcome that may result from using
different samples.
We do not use data prior to 1975 because tenure is recorded as a continuous
measure only since 1975.

The tenure variable needs to be continuous because we needto know the starting point of a current job in order to divide the entire period of staywith the same employer into various sub-periods.

Like most studies in this literature,

we focus on men and exclude the self-employed because they are less likely to beaffected by implicit contracts.

To check the robustness of the results, we also test an

extended data set with female heads included. However, we do not use data for wives
because the self-employed can not be excluded until 1979.
Like BD, we work with the average hourly earnings variable, which is10computed as the ratio of total earnings from all labor income sources for the preceding
calendar year to annual hours worked in that year.

Therefore, the data from the 1976-

92 interviews include labor income and hour measures for 1975-91.8

This measureincludes, in addition to basic wages and salaries, other sources of labor income such as
overtime, bonus, and commission.

We believe this average hourly earnings variable ispreferable to basic wages and salaries because wages in implicit contracts, as suggested
by ‘implicit’, are supposed to include every form of payments to workers.

Following

BD, we include in the sample respondents aged 21-64 who had positive earnings andwho started their job after 1947.

We exclude, however, the Survey of Economic

Opportunity (SEO) sample from the analyses because, as indicated by BD, inclusion of
the SEO sample makes little difference in the estimates and because existing estimatesof real wage cyclicality are based only on the Survey Research Center (SRC) sample.
Numerous algorithms are developed by Altonji and Shakotko (1987), Topel(1991), Altonji and Williams (1992), Brown and Light (1992), and Altonji and
Devereux (2000) to generate internally consistent tenure variables.

Our method is very

close to Altonji and Williams (1992) and Altonji and Devereux (2000).9First, indefining job changers and/or stayers, employer tenure is compared with time elapsed
since the previous interview. Accordingly, a job change is defined as having occurred
if time with employer was less than elapsed time since the previous interview.

The

second step is to assign different weights on different observations within a job
depending on how consistent the reported tenure values are with all of the otherreported tenure values on the job.10

In the third step, we calculate a weighted averageof reported tenure minus the time elapsed since the start of the job. This weighted
average represents initial job tenure at the start of the current job.

The fourth step is todetermine the initial tenure level of a job. Like Altonji and Williams, we set the initial
tenure level to one month whenever the estimated initial tenure is negative and discard
8

We use 1974 data only for the purpose of obtaining data on 1974-75 wage changes.

9

We also tried the method adopted by Beaudry and DiNardo (1991) and the ‘Partion P’ method

developed by Brown and Light (1992).

Although different tenure-generating algorithms produce

somewhat different tenure levels, the current conclusions are robust to these exercises. Our conclusions
still preserve even when reported tenure variables are used.
10

See Altonji and Williams (1992) for generating weights.

11the entire observations in a job spell when the estimated initial tenure is more than two
years.
The fourth step is not applicable for jobs that were in progress as of 1975, thefirst year of our sample period, because we cannot determine the starting point of a job
spell following the first step.

For these ‘left-censored’ jobs, we apply the sameprocedure up to the third step.11

In the fourth step, however, we determine the starting

point of a job by simply using the estimated tenure as of 1975 and set to one month.
Finally, starting from the first year of a job, we force tenure to increase exactly by thetime elapsed between interviews.12

IV. Empirical findings

Table 1 reports sample means of selected variables.

In general, our sample means are

somewhat different from those of BD (Table 1, p. 673, 1991) and very similar withthose of Devereux (Table A1, p. 849, 2001). The latter two tables are based on PSID
male heads for 1976-84 and 1971-91, respectively, in comparison with our sample of
PSID male heads for the 1975-91 period.

The differences between our sample means(or Devereux’s) and BD’s are largely attributed to the fact that, while BD included the
SEO sample in their analyses, the current study and the Devereux’s use only the SRC
random sample.
Female heads constitute approximately 19.8% of the entire sample of heads,
have lower wages, tenure, union membership rate, and proportion of marriage
experience. There is no gender difference in the educational level. Therefore, thegreater level of potential experience for women indicates that women are on averageolder than men in our sample, which in turn implies that the tenure gap between genders
would be greater when the age difference between genders is controlled for.

As willbe demonstrated in subsequent subsections, however, our conclusions hold whether or
not female heads are included in the sample.
11

At least three yearly observations are required to calculate the weighted average.

12

If the predicted starting point of a job is before 1968, the first year of PSID surveys, we assume an

12

The average tenure on the current job, which is the most important variablebecause the starting and the minimum unemployment rates are critically dependent on
the variable, is 8.79 years in our sample of male heads. This figure is somewhat
greater than the BD’s estimate (6.92 years with the SEO included), but smaller thanTopel (9.98 years) and Devereux (2001: 10.11 years).

The difference in the average

tenure between our sample and the BD’s makes us to check first if the BD’s results holdeven in our extended sample period which includes one more business cycle than thesample period considered by BD.
Table 2 reports estimated coefficients of various unemployment variables inequation (1), and compares them with the BD’s.

For the sake of simplicity, we present

only the estimated coefficients of three unemployment measures, the starting, theminimum, and the contemporaneous unemployment rate.

Comparing the numbers in

the first two columns reveals that the BD’s estimates are successfully replicated. Most
importantly, for both the OLS and fixed-effects estimates, the minimum unemployment
rate variable clearly dominates the other two variables in both studies.13

As minordifferences, the estimated coefficient on the current unemployment rate is somewhat
greater and statistically more significant in our study than in the BD’s, and the fixedeffects estimates of the coefficient on the starting unemployment rate is positive andsignificant in our study, but insignificant in the BD’s.14

As demonstrated in the fourthequal interval of 12 months between interviews.
13

A trend variable is not included in the BD’s specification. At first, we suspected that the effects ofthe minimum unemployment rate on wages might be overstated due to this omission.
follows.

The reason is as

For the 1947-84 period, the local minimum unemployment rate as well as the overall

unemployment rate has been increasing.

Therefore, the elapsed time since the minimum rate is

negatively correlated with the minimum rate.

Since wages grow over time, omitting the variable, theelapsed time since the minimum, would exaggerate the effect of the minimum rate.

However, omitting

the trend variable purposefully in our specification makes little difference due to the weak correlation of
the minimum rate and the elapsed time since the minimum rate.
14

When we restrict our sample to the 1976-84 period as in BD, the replication is almost exact in terms ofmagnitudes of estimated coefficients and their statistical significance. To summarize, as in the extended
period, the minimum unemployment rate clearly dominates the other two variables in explaining thecurrent wage rate.

Moreover, as in BD, although the estimated coefficient on the contemporaneous

unemployment rate is virtually zero and imprecise from OLS, the estimate from the fixed-effects model is

13column, similar patterns are observed even when female heads are included in thesample.

It is generally concluded that the contract model with costless mobility

describes best the pattern of real wage movements over the cycle.
One can suspect that the large negative coefficient of the minimum
unemployment rate may be due to nonlinearities in the effect of tenure. Especially if
the effect of tenure on the wage rate is intensified when the unemployment rate is very
low, the BD’s results can be obtained.

As an easy way to check this possibility, we

include squared tenure as an additional regressor and re-estimate equation (1). The
results are reported in the third and fifth columns of Table 2.

The addition of thesquared tenure variable has different effects depending on the econometrics model
adopted.

In OLS, the role of the minimum unemployment rate is dramatically reduced

when squared tenure is included. For example, for the male heads, the estimatedcoefficient on the minimum rate is reduced from .0379 to .0129 in an absolute value.
OLS estimates seem to suggest that the large coefficient on the minimum
unemployment rate in the Beaudry and DiNardo’s results was at least partly picking up
nonlinearities in the effect of tenure. However, when we use the fixed-effects model,
the effect becomes more or less negligible.

For male heads, estimated coefficient isreduced in an absolute value from .0288 to .0269.

Therefore, once unobservable

individual fixed effects are controlled for, the nonlinearities in the effect of tenure
observed in the OLS estimates are no longer important in explaining the large negative
effect of the minimum unemployment rate on wages.

Overall, the BD’s conclusionthat the minimum unemployment rate is dominant in explaining current wages stillpreserves even in our extended sample with more recent years and female heads.

A. Are real wages procyclical among job stayers?

On the basis of equation (3), this subsection investigates if our extended
sample produces substantial wage procyclicality among job stayers as well.
results are reported in Table 3.

The

For the 1974-75 to 1990-91 period, the estimate turns

a small negative number and statistically significant.

Finally, the coefficient on the starting

unemployment rate is positive and significant from OLS, but insignificant from the fixed-effects model.

14

out to be -.0093 for male heads, which is statistically significant at the 5 percent level.
This implies that a one percentage point increase in the unemployment rate reduces
stayers’ real wages by .93 percent. When female heads are included in the sample, theestimate falls slightly to -.0088.

This reflects the fact that real wages are less15

procyclical for women than men.

Comparison of our estimates with those of existing studies is in order.

At first,

our estimate of -.0093 seems to be smaller than the SBP’s estimate in an absolute value.
Using the PSID male heads for the 1968-69 to 1986-87 period, SBP estimated thestayers’ wage procyclicality as -.0124.

The gap between our estimate and SBP’s isexplained by, among others, the following two factors.

First of all, our sample period

covers only part of 1970s, while the SBP’s sample period is dominated by the 1970s.
This tendency is mentioned by Kniesner and Goldsmith (1987, p. 1257) among others.
Extending the sample to the 1970-71 to 1990-91 period increases the estimate up to-.0107 with an estimated standard error of .0024.

Second, SBP included self-

employed stayers in their sample, while our sample does not.

As observed by

Carrington, McCue, and Pierce (1996) among others, hourly wages are much moreprocyclical for the self-employed than for “wage and salary” workers.

In fact,

including self-employed stayers in the above extended sample period increases theestimated procycliclaity further to -.0121 with estimated standard error .0029, which isvirtually identical to the SBP’s estimate.

Our estimate of -.0107 for the 1970-71 to

1990-91 period is slightly greater than Devereux’s estimate of -.0081, which is also
based on the PSID male heads who are not self-employed for the same sample period
and Shin’s estimate of -.0095, which is obtained from the NLS young men data for the
1966-67 to 1980-81 period. 16

For the purpose of explaining stayers’ wage

procyclicality based on the subperiods defined in Section II, we stick to our estimate of-.0093 for the 1974-75 to 1990-91 period.

Exclusion of the SEO sample does not change any of the results, which is also noted by BD.
15

For a similar finding, see Blank (1989), Tremblay (1990), and Solon , Barsky, and Parker (1994).

16

On the basis of the NLSY data for the 1978-79 to 1996-97 period, we redo the above analyses and findthat estimated wage procyclicality for stayers is -.0114 (s.e.=.0051) for males and -.0037 (s.e.=.0043) for
females.

15

B. Asymmetric effects of unemployment on wages

While Subsection A confirms the previously established finding that stayers’
real wages are procyclical, we believe that the conventional approach has a major
drawback. The conventional approach implicitly assumes that composition-corrected
mean wage changes following a one point change in the unemployment rate are uniform
during the entire period of a job tenure.

However, as suggested in Section II, the two

versions of the implicit contract models and the spot market model can be distinguishedfrom each other by different degrees of wage adjustment for different subsample
periods.

However, before we further investigate this important implication of themodels, we first examine if the wage adjustment is asymmetric in expansions andrecessions. This is needed because there is a long tradition of Keynesian economics
that asserts that the nominal wage is downwardly rigid, and there is a possibility that
this is also true for the real wages of stayers.17

If this is so, stayers’ real wages are

upwardly adjusted in expansions and while stay put in recessions, leading to an estimateof overall procyclicality of stayers’ wages.

Upon accepting the asymmetry hypothesis,

we further explore, in Subsection C, if the greater wage adjustment is uniform during
the entire boom period or solely accounted for by wage re-negotiation during the renegotiation period, as implied by the BD version of implicit contracts.
Before running regressions based on equation (3), we can do the simple
following exercise to get a flavor of asymmetry.

A real wage change for an individual(in logarithm) is divided by corresponding change in the unemployment rate.

Then,

the cycle-adjusted wage changes are averaged over individuals and years for each of the
expansion and the recession period.

These figures present roughly how wage

adjustments to a unit change in the unemployment rate differ between expansions andrecessions, although they are contaminated by differences in worker composition
between the two sample periods and by secular components of wage growth.
reported in the first two columns of Table 4.

17

They are

Two interesting patterns emerge.

First,For recent empirical studies on nominal wage rigidity, see Mclaughlin (1994) and Cardand Hyslop (1997).

16

among male heads, wage growth in expansions (.0615) is much greater than wage
reduction in recessions (-.0044).

Second, standard deviation of wage changes is muchgreater in expansions (1.1706) than in recessions (.4686). These seem to suggest that
there may be a downward wage rigidity even in the real term.

The gap in mean wagechanges between expansions and recessions becomes greater when female heads areincluded in the sample.
To see these points more clearly, Figure 2-1 through 2-4 display percent
distributions of real wage changes in expansions and recessions, respectively.

The

first two figures correspond to male heads, while the latter two include female heads.
Each cell width is .09 and tales of the distribution are massed at the extremes.

The

latter is to allow a better view of the intermediate categories. First, comparison of thefirst two figures reveals that the sample proportion of wage increases in expansions isgreater than the proportion of wage decreases in recessions. In fact, the distribution isquite skewed to the right in expansions, but is more or less symmetric in recessions,
implying that adjustments in wages are on average made in expansions only.

Second,the sample proportion of ‘relatively negligible wage changes,’ that is, wage changes
between -.045 and .045, is 15.6% in expansions but 27.9% in recessions. These findings
imply that, for a given change in unemployment, wage changes are more sizable inexpansions than recessions.

To put it another way, there seems to be downward wage

rigidity even in the real term.

The same patterns are observed even when female heads

are included, as demonstrated in Figure 2-3 and Figure 2-4.
Now we investigate more formally the possibility of asymmetry based onequation (3) by including expansion and recession dummies and their interaction termswith the unemployment rate.
of Table 4.

The results are reported in the third and fourth columns

Unlike the figures in the first and the second columns, these numbers

represent mean wage changes for a unit change in the unemployment rate obtained bycontrolling for cyclical changes in worker composition and secular components ofwages.

For the sample of male heads, the estimated wage change in expansions is –.0158 and that in recessions is .0029, which clearly shows that there is strong evidenceof asymmetrical wage adjustment.

Corresponding numbers for the sample of heads are–.0165 and -.0024 in expansions and in recessions, respectively. In short, asymmetryof wage adjustment still preserves even when we focus on the cyclical components of17

wages and control for unobservable as well as observable individual characteristics.
This finding is consistent with Hines et al. (2001)’s finding that the impact of a given
unemployment change on real hourly wages is larger in expansions than in recessions.18
This asymmetric adjustment of real wages has an important implication that the spot
market model does not explain the procyclicality of real wages for stayers because if the
spot market model holds, real wage adjustment must be as great in recession as inexpansions.
The finding of little real wages adjustment in recessions may surprise somebecause there is a common notion that wages are adjusted downward when therecession is severe, as in 1982.

It should be noted, however, that the current

conclusion is based only on job stayers.

In fact, as noted by Barlevy (2001), a

significant portion of the decrease in aggregate wages in recessions comes from wage
losses among workers changing into lower-wage jobs.19

C. Why are wages so greatly adjusted during expansions?

In Section B, we have found that stayers’ real wages are procyclical mainly due
to significant wage adjustment in expansions.

As noted in Section II, however, theimplicit contract model with costless mobility can be entirely consistent with thefindings in Subsection B as well as an overall procyclicality estimate of stayers’ real
wages.

In addition, the implicit contract model with costless mobility holds anotherimportant implication that distinguishes it from the implicit contract model with costly
mobility, the spot market model as well as the downward rigidity model.

According to

the implicit contract model with costless mobility, large upward wage adjustments areto be concentrated on the re-negotiation period, which is a sub-sample period of
18

Their CPS-based analyses for the 1976-99 period report comparable estimates as -.0057 and -.0020 for

expansions and recessions respectively with their respective standard errors .0022 and .0028. For hours
and total earnings, however, the impact of a change in unemployment rates is larger in recessions.
19

Bleakley, Ferris, and Fuhrer (1999), among others, report that worker flows into unemployment andinto employment are simultaneously high (particularly in manufacturing) in severe recessions as in 1982.
Moreover, as concluded by Ruhm (1991) and Jacobson, LaLonde, and Sullivan (1993), displaced workers
suffer from long-term earnings losses.

18expansions.

In other words, wages are adjusted when and only when theunemployment rate records the historical minimum level. This peculiar pattern of real
wage adjustments can create a fair degree of wage procyclicality for the entire period ofstaying with the same employer and, at the same time, some degree of asymmetry ofwage adjustments.

The purpose of this subsection is to examine if the implicit contract

model with costless mobility explains all these empirical regularities in a unified way.
As emphasized, our test is implemented by dividing the entire period of job
stay into various sub-sample periods. Before running regressions based on equation(3), we draw figures similar to Figure 2’s. While Figure 2-1 through Figure 2-4
illustrate asymmetric wage adjustment in expansions and recessions, Figure 3-1 through3-4 focus only on expansions and display percent distributions of real wage changes forthe re-negotiation period and for the period of falling unemployment without renegotiation.

The first two figures correspond to male heads, while the latter two

include female heads in the sample.

A glance at the figures is enough to see thatcycle-adjusted wage adjustments are not uniform between the two sub-sample periods,
as the two distributions look different.

More specifically, the proportion of wage

increase is much greater for the re-negotiation period than for the other period. In fact
the distribution is quite skewed to the right for the renegotiation period, suggesting thatthe skewness in expansions in Figure 2.1 and 2.3 is due mostly to the skewness in therenegotiation period.

Calculations show that, for male heads, the average wage

increase in the renegotiation period (.073) is greater than that in the non-negotiation
period during expansions (.056).

Again, same patterns are preserved even in thesample of heads.
Now, we test more formally the three competing hypotheses proposed by BD
in the alternative way described in Section II, which focuses on the relationship between
wages and contemporaneous unemployment rates.

We compute composition-corrected and detrended mean wage changes for the three sub-sample periods: the renegotiation period, the period of falling unemployment without re-negotiation, and therecession period.

The two-step estimation results are reported in Table 5.

The most

important finding is that wages are much more greatly adjusted during the renegotiation period than the other expansion period.

For the sample of male heads, theestimated coefficient on the unemployment rate is -0.0264, implying that a one
19percentage point reduction in the unemployment rate is associated with a 2.64 percent
rise in real wages for the re-negotiation period. The estimate for the period of falling
unemployment without re-negotiation is -.0076 percent, which is much smaller inabsolute value and statistically insignificant. Finally in recessions, the estimate is .0031, which implies that little wage adjustment is made.

Hence, the substantial wage

procyclicality of stayers’ wages is mostly accounted for by the great upward wage
adjustment during the re-negotiation period only.

When female heads are included in

the sample, the estimate for the period of falling unemployment without re-negotiation
is -.0121. While this estimate is somewhat large, it is significantly smaller than thatfor the re-negotiation period (-.0361).
While the findings in Sub-section B suggest that there is strong evidence ofasymmetry, this asymmetric adjustment in real wages is due to significant upward
movement of real wages in the re-negotiation period.

In fact, the estimates for the

non-negotiation period during expansions are insignificant among male heads andmarginally significant at the 10 percent level when female heads are included.

Thesefindings reject the possibility that the downward rigidity in real wages drives theasymmetric effects because, if the downward rigidity holds, then upward wage
adjustment for the period of falling unemployment without re-negotiation should be as
great as for the re-negotiation period.

This peculiar pattern of real wages adjustment is

consistent with the prediction of the implicit contract model with costless mobility
suggested by BD.
Figures in the second and the fourth columns of Table 5 represent estimatesobtained by including squared tenure as an additional regressor in equation (2).

Thatcorresponds to including the tenure variable itself as an additional regressor in equation(3).

Inclusion of the variable also reduces the magnitude of upward wage adjustment

slightly for the re-negotiation period, but the magnitude is minor. That is exactly thesame conclusion with the fixed-effects estimates of the coefficient of the minimum
unemployment rate in Table 2.

To repeat, once individual-specific fixed-effects are

fully controlled for, estimated upward wage adjustment for the re-negotiation period is
not biased by not controlling for nonlinearity in the effect of tenure.

20

IV. Conclusion

Our major conclusions are as follows. First, as with previous studies, we find that real
wages are substantially procyclical.

This large magnitude of wage procyclicality

among stayers itself rejects the hypothesis that wages are primarily determined by thelabor market condition at the start of the current tenure.

Evidence in the many current

existing studies shows that wages are substantially adjusted from the start of a current
job.

Second, the effects of unemployment on wages are asymmetric in expansions andin recessions: most of the substantial procyclicality of stayers’ wages is attributed to the
expansionary period and little real wage adjustment is made during recessions. Thisfinding rejects the spot market hypothesis because, under the spot market model, wage
adjustments are to be symmetric across expansions and recessions in terms of direction
and magnitude.

Third, asymmetric adjustments of real wages mostly occur during there-negotiation period, and therefore, this adjustment solely explains procyclicality ofreal wages for stayers. Therefore, the substantial wage procyclicality and the peculiar
pattern of asymmetric wage adjustments for job stayers are consistent with an implicit
contract theory with costless mobility, as developed and concluded by Beaudry and
DiNardo (1991).
Our findings imply that, for an ‘average’ stayer, real wages are a convex function of
the unemployment rate, that is, wages tend to be adjusted greatly when the unemployment rate
is relatively low, and little wage adjustment occurs during the period of high unemployment.
This happens because the falling unemployment rate increases the probability of recording thebest labor market condition since the start of the current job, which in turn makes the chance of
re-negotiation greater.

Previous research analyzing the wage-unemployment relationshipeither presumes linearity or, as in the Blanchflower-Oswald-type wage curve, explores how
wages are nonlinearly dependent upon the current unemployment rate assuming that wages are
determined at the spot market.

The current study departs from those studies by examining how

wages of a given worker respond nonlinearly at different phases of the business cycle and why
wages of different individuals respond differently to the same unemployment change.

In thissense, our paper goes beyond simply exploring functional forms of the wage-unemployment
relationship and uncovers sources of the nonlinearity.

21

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24

Figure 1
Timing of Re-negotiation
Re-negotiations take place whenever the unemployment rate reaches a historicalminimum level from the start of a job.

12

Unemployment Rate

10
8
6
4
2
0
75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91
Y ear

25

Figure 2-1
Distribution of Real Wage Changes in Expansions: Male Heads, 1974-75 to 1990-91
%
25
20
15
10
5
0
0

Figure 2-2
Distribution of Real Wage Changes in Recessions: Male Heads, 1974-75 to 1990-91
%
25
20
15
10
5
0
0

Figure 2-3
Distribution of Real Wage Changes in Expansions: Heads, 1974-75 to 1990-91
%
25
20
15
10
5
0
0

Figure 2-4
Distribution of Real Wage Changes in Recessions: Heads, 1974-75 to 1990-91
%
25
20
15
10
5
0
0

26

Figure 3-1

Distribution of Real Wage Changes for the re-negotiation period: Male Heads
%
25
20
15
10
5
0

Figure 3-2
Distribution of Real Wage Changes for the period of expansion without re-negotiation: Male
Heads
%
25
20
15
10
5
0

0

Figure 3-3
Distribution of Real Wage Changes for the re-negotiation period: Heads
%
25
20
15
10
5
0
0

Figure 3-4
Distribution of Real Wage Changes for the period of expansion without re-negotiation: Heads
%
25
20
15
10
5
0

0

27

Table 1
Summary Statistics
Panel Study of Income Dynamics: 1975 to 1991
Male Heads
Average log hourly earnings (19962.36
dollars)(units: dollar, year, percent)Female Heads
2.30

Education

13.13

13.12

Tenure8.79

8.40

Age-education –6

18.09

18.22

Union
Nonwhite
SMSA
Ever married
No. of observations

23.99
8.65
57.06
92.24
28,707

22.72
10.19
58.80
87.22
5,691

Table 2
Effects of Past and Current Unemployment Rates on Wages
Panel Study of Income Dynamics: 1975 to 1991

Model

Beaudry &DiNardo
UnemploymMaleent
Heads, SEO
Measuresincluded
1976-84
Current U

OLSa

Start UMin U
Current U

Fixedeffects

Start UMin U

No. of Observations-.000(.002).013***(.006)-.059***(.006)-.007***(.0025)-.006(.007)-.029***(.008)

Current Study
SEO excluded
1975-91
Male Heads

Heads

withoutwithtenure2tenure2-.0093*** -.0138***(.0028)(.0028).0193***.0130***(.0031)(.0031)-.0379***-.0129**(.0052)(.0056)-.0123***-.0127***(.0016)(.0017).0122***.0117***(.0029)(.0030)-.0288***-.0269***(.0039)(.0042)
28,707

withoutwithtenure2tenure2-.0078***-.0117***(.0026)(.0027).0195***.0141***(.0029)(.0029)-.0366***-.0154***(.0049)(.0052)-.0111***-.0118***(.0015)(.0016).0129***.0113***(.0027)(.0028)-.0285***-.0245***(.0036)(.0039)34,398aIn addition to the above three unemployment measures, the following explanatory variables areincluded: a quadratic time trend, experience, experience squared, schooling, tenure, anddummies for industry, region, race, union status, marital status, standard metropolitan statisticalarea. Estimated standard errors are in parentheses.
**, *** = significant at the 5% and 1% level, respectively.

28

Table 3
Estimates of Real Wage Cyclicality for Employer Stayersa
Panel Study of Income Dynamics: 1974-75 to 1990-91
Male Heads

Heads-.0093**(.0040)-.0088**(.0041)

Estimates

No. of differenced year-person observations
22,019in the first stepa
Estimates are based on the two-step method described in Section II.
errors are in parentheses.
** Significant at the 5 percent level.

25,891
Estimated standard

Table 4
Asymmetric Effects of Unemployment on Wages in Expansions and Recessionsa
Panel Study of Income Dynamics: 1974-75 to 1990-91
Mean Wage Change

Expansion
RecessionComposition Corrected and
Detrended Mean Wage Change

Male Heads

Heads

Male Heads

Heads

.0615
[1.1706]-.0044[.4686].0765[1.1956].0033[.4992]-.0158(.0071).0029(.0049)-.0165(.0094)-.0024(.0060)a

Estimates are based on the two-step method described in Section II. Numbers in brackets andparentheses are sample standard deviations of individuals’ wage changes and estimated standard
errors, respectively.

Table 5
Explaining Stayers’ Wage Procyclicalitya
Panel Study of Income Dynamics: 1974-75 to 1990-91
Male Heads
Sub-sample Periods
withwithout
tenure2tenure2-.0264**-.0243**
Expansion: Re-negotiation(.0076)(.0075)-.0076-.0073
Expansion: Non-negotiation(.0034)(.0033)-.0031-.0033
Recession(.0034)(.0035)aHeads
without
tenure2-.0361**(.0103)-.0121*(.0040).0087(.0051)

Estimates are based on the two-step method described in Section II.
errors are in parentheses.
*, ** = significant at the 10% and 5% level, respectively.

29

with
tenure2-.0343**(.0103)-.0122*(.0041).0079(.0052)Estimated standard