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This is to certify that the

dissertation entitled

THE DISPERSION OF WAGES OVER THE BUSINESS
CYCLE

presented by

David Patrick Redmon

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THE DISPERSION OF WAGES OVER THE BUSINESS CYCLE

BY

David Patrick Redmon

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Economics
1993

Daniel S. Hamermesh, Adviser

ABSTRACT
THE DISPERSION 0F WAGES OVER THE BUSINESS CYCLE
BY
David Patrick Redmon

A number of studies have examined the effect of the
business cycle on the dispersion of interindustry wages.
However, the time-series models used in these analyses often
lack appropriate labor quality measures to control for
changes in the composition of the labor force. Other
studies have used micro data to examine changes in wage
dispersion over the cycle, but most have not accounted for
the fact that industry wage premia and returns to human
capital characteristics may vary over time.

This research uses both aggregate and micro-level data
to examine the cyclicality of wage dispersion. Time-series
models are used to examine interindustry dispersion for both
one-digit SIC industries and two-digit SIC manufacturing
industries. These models incorporate time-series properties
that have not been taken into account in previous work. The
results show little responsiveness to changes in cyclical
activity. At the one-digit level, increases in the prime

age male unemployment rate are associated with a higher

variance of interindustry wages. Unlike previous authors I
find no relationship between the variance and the
unemployment rate at the two-digit level.

The analysis then turns to a cross-section examination
of the dispersion of individual wages, based on data from a
series of May Current Population Surveys (CPS) chosen at
cyclical peaks and troughs. Unlike time-series models, the
cross-section analysis allows for detailed labor quality
controls. Changes in the variance of the natural logarithm
of wages are decomposed into the proportion attributable to
changes in worker characteristics and the preportion
attributable to changes in the return to worker
characteristics.

The cross-section results show that a significant
portion of the change in dispersion is indeed accounted for
by the omitted labor quality variables. The estimates of
the relationship between wage dispersion and the
unemployment rate are generally positive and larger for
manufacturing than in the total sample. The cyclical

sensitivity of nonwhites and females is relatively large.

ACKNOWLEDGEMENTS

During the course of this work, I have incurred many
debts to advisers, friends, and family. Acknowledgement of
their assistance and support is the minimum payment I owe
them. The first goes to Daniel Hamermesh, who served as
chairman of my dissertation committee. His advice, support,
and patience were critical to completing this work. Perhaps
more important, however, was the chance to see his approach
to research. From him I first learned that there is an
element of art in empirical work. I would also like to
thank Harry Holzer for serving on this dissertation
committee and for his excellence in the classroom. His
introductory class in the graduate labor sequence cemented
my interest in labor economics. Additionally, my thanks go
to both Ed Montgomery and Steve Woodbury for their comments
and advice in the final stages of this work.

I would also like to thank Rob Wassmer and Judy Temple,
both of whom endured lengthy discussions about this work.
Additionally, I thank Jon Ratner and Henry Felder at the
U.S. General Accounting Office for their encouragement and
assistance.

The greatest debt of all I owe to my parents. As

always, their support was total and unconditional, and I

11

iii
will never be able to sufficiently express my gratitude for
all they have done. This acknowledgement is simply the

first installment.

TABLE OF CONTENTS

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . vi

INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . 1

CHAPTER 1

Wage Flexibility over the Business Cycle . . . . . . . 5
Introduction . . . . . . . . . . . . . . . . . 5
The Interindustry Wage Structure . . . . . . . . . . . . 15
Conclusion . . . . . . . . . . . . . . . . 19
CHAPTER 2

A Model of the Cyclicality of Dispersion . . . . . . . . 21
Introduction . . . . . . . . . . . . . . . . . . . . . 21
An Equilibrium Model of the Labor Market . . . . . . . 22
The Heterogeneity of Labor . . . . . . . . . . . . . 27
Disequilibrium in the Labor Market . . . . . . . . . . . 33
Implications . . . . . . . . . . . . . . . . . . . . . . 37
Conclusion . . . . . . . . . . . . . . . . . . . . . . . 39

CHAPTER 3

41
41
42
47

Time-Series Evidence on Interindustry Wage Dispersion
Introduction . . . . . . . . . . . . . . . . . . . .

Estimation . . . . . . . . . . . . . . . . . . . .
Data . . . . . . . . . . . . . . . . . . . . . .
Results. . . . . . . . . . . . . . . . . . . . .
Sensitivity to Omitted Variables . . . . . .
The Adjustment of the Labor Market . . . . . . .
Wage Rigidity and Symmetry over the Cycle. .
Conclusion . . . . . . . . . . . . . . . . . . .

61
65
74

.5
D

. 76
CHAPTER 4
A Cross-Sectional Analysis of Wage Dispersion. . . . . . 79
Introduction . . . . . . . . . . . . . . . . . . 79
Research Strategy. . . . . . . . . . . . . . . . . . 81
The Data . . . . . . . . . . . . . . . . . . . 85
Results 0 O O O O O O 0 O O 0 0 O O O O 0 O O O O O 87
Results by Subgroups . . . . . . . . . . . . . 101
Conclusion . . . . . . . . . . . . . . . . . . 103

iv

CHAPTER 5
Conclusion . . . . .
APPENDIX
Results by Subgroup.

BIBLIOGRAPHY . . . .

LIST OF TABLES

Table 3.1 One- Digit Industries . . . . . . . 53
Table 3.2 Two- digit Manufacturing Industries . . . . . . 54
Table 3.3 One- Digit Industries . . . . . . . . . . 58
Table 3.4 Two- digit Manufacturing Industries . . . . . . 60
Table 3.5 Cyclical Responsiveness of Wage Dispersion . . 61
Table 3.6 Two-digit Manufacturing Industries . . . . . . 63
Table 3.7 Real Wage Estimates, One- Digit . . . . . . . 67
Table 3.8 Real Wage Estimates, Two- Digit . . . . . . . 68
Table 3. 9 Wage and Employment Flexibility, One- Digit . . 72
Table 3.10 Wage and Employment Flexibility, Two- digit. . 73
Table 4.1 Decomposition, Full Sample . . . . . . . . . 89
Table 4.2 Decomposition, Manufacturing . . . . . . . . . 90
Table 4.3 Variance of Wages. . . . . . . . . . . . . . . 97
Table 4.4 Arc Elasticities . . . . . . . . . . . . . . 98
Table A.1 Decomposition, Male--Full Sample . . . . . 109
Table A.2 Decomposition Female--Full Sample. . . . . . . 110
Table A.3 Decomposition, White--Full Sample . . . . . . 111
Table A.4 Decomposition, Nonwhite--Full Sample . . . . . 112
Table A.5 Decomposition, Male-~Manufacturing . . . . 113
Table A.6 Decomposition, Female--Manufacturing . . . . . 114
Table A.7 Decomposition, White--Manufacturing. . . 115
Table A.8 Decomposition, Nonwhite--Manufacturing . . . 116
Table A.9 Arc Elasticities . . . . . . . . . . . . . . 117

vi

INTRODUCTION

In recent years, a number of studies have examined the
flexibility of the interindustry wage structure, noting
trends in--as well as the cyclical performance of--the
dispersion of wages across industries. This topic is
important to economists because, in the competitive model of
the labor market, wages play the central role in resource
allocation across industries, determining the flow of labor
resources to their most efficient use. Contrary to the
competitive model, however, there appear to be persistent
wage differentials across industries that are unaffected by
labor market conditions.1

In the presence of these persistent differentials,
labor market adjustment as predicted by the competitive
model is unlikely to occur. Macroeconomists in the

Keynesian tradition have argued that nominal wages are not

 

1Competitive models of the labor market allow for wage
differentials at times. When the assumption of labor
homogeneity is relaxed, wage differentials may exist because
of the varying productivity of workers. Differentials may
also arise due to differences in working conditions across
firms. If conditions are unpleasant or unsafe, the firm may
have to pay a compensating differential to attract enough
workers to produce. A number of writers have documented
persistent interindustry differentials; however, most
conclude that these competitive sources of differentials are
not enough to explain the interindustry wage structure.

1

2
flexible, as the competitive model assumes. They have
argued that nominal wages are downwardly rigid, inhibiting
the free adjustment of wage rates in the labor market. In a
similar vein, other writers have speculated that under
certain institutional settings real wages may be downwardly
rigid if workers form rational expectations of inflation
rates. Wage flexibility is reduced in both cases, and the
consequence is unemployment. To examine wage flexibility,
several authors have looked at the relationship between the
dispersion of wages and the business cycle.

Economists are also interested in wage dispersion as a
measure of economic Opportunity. If the business cycle
affects the dispersion of wages, income inequality may also
vary over the cycle. And the cyclical effect may not be the
same for all groups in the population.

A number of studies have examined the effect of the
business cycle on the dispersion of interindustry wages.
However, the time-series models used in these analyses often
lack appropriate labor quality measures to control for
changes in the composition of the labor force over the
business cycle. Other studies have used micro data to
examine changes in wages and wage dispersion over the cycle,
but most have not accounted for the fact that industry wage
premia and returns to human capital characteristics may vary
over time.

This research uses both aggregate and micro-level data

to examine the cyclicality of wage dispersion. Time-series

3

models are used to examine interindustry dispersion for both
one-digit SIC industries and two-digit SIC manufacturing
industries. The time-series models are first differenced
because augmented Dickey-Fuller tests cannot reject the
presence of a unit root in the variance of the natural
logarithm of wages at both the one-digit and the two-digit
manufacturing level. As noted earlier, these time-series
properties have not been taken into account in previous
work.

The analysis then turns to a cross-section examination
of the dispersion of individual wages, based on data from a
series of May Current Population Surveys (CPS) chosen at
cyclical peaks and troughs. Unlike time-series models, the
cross-section analysis allows for detailed labor quality
controls. Furthermore, the time-series models (like
previous studies of this subject) presume that the return to
human capital characteristics is constant over time. This
cross-section analysis does not include that assumption.
Changes in the variance of the natural logarithm of wages
are decomposed into the change attributable to worker
characteristics and the change in the return to worker
characteristics. The latter is based on estimated wage
equations corresponding to peaks and troughs of recent
business cycles. Because the coefficients of the models are
not constrained to be the same over time, the estimated
parameters are used to calculate the changes in dispersion

due to these structural changes in the wage equation.

4

Chapter 1 provides a review of the literature on
interindustry wage dispersion. Chapter 2 develops a basic
model of the labor market and explores the implications of
the model for the cyclicality of dispersion. Chapter 3
presents time-series evidence on interindustry dispersion by
one-digit and two-digit SIC industries. Unfortunately,
time-series evidence is limited by the fact that it is very
aggregated and lacks appropriate labor quality controls.
Although considerable attention is devoted to that
shortcoming, explicit quality controls are necessary for a
more conclusive analysis. Therefore, Chapter 4 presents
results based on an analysis cross-sectional data from May
Current Population Surveys to extend the analysis. Chapter
5 concludes the study with a summary and an examination of

the implications of the results.

CHAPTER 1

Wage Flexibility over the Business Cycle

Introduction

Wage flexibility may be measured in a number of ways.
Typically, economists have used some measure of wage
dispersion as an indication of wage responsiveness. Wachter
(1970) uses the coefficient of variation of interindustry
wages; Bell and Freeman (1985) use the standard deviation of
the natural logarithm of interindustry wages; Montgomery and
Stockton (1987) choose the variance. All of these metrics
are natural measures of wage dispersion, but they have
shortcomings as indicators of labor market flexibility. As
an OECD (1985) report points out, the responsiveness of the
interindustry wage structure must be measured along several
dimensions. The authors suggest that the appropriate
dimensions include a changing dispersion of wages, changes
in the relative wage rankings and/or relative wages among
industries, and a higher (lower) growth rate of relative
wages among expanding (contracting) industries, (OECD
(1985), p. 84).

To judge the flexibility of the wage structure on only

one of these criteria might yield misleading results. For

5

6

example, it is possible for the dispersion of wages to
remain relatively stable in the presence of volatile
industry rankings. Or, as in the case of the United States
since 1970, the dispersion of wages has risen according to
almost all available measures.21However, Montgomery and
Stockton (1987) and Krueger and Summers (1987) document the
stability of the U.S. interindustry wage structure in terms
of industry rankings. Hence, the assessment by Bell and
Freeman (1985) that the U.S. wage structure is flexible
might be called into question when one considers the high
correlation between industry wage rankings year after year.

Bell and Freeman note a 35 percent increase in the
standard deviation of wages in the industries they examine,
leading to their assessment. However, the industry rankings
have remained stable over time. A juxtaposition of the Bell
and Freeman results with those from the OECD (1985) provides
a more complete picture. The OECD authors test the
stability of the wage structure in a number of countries by
regressing the wage structure in a series of years on a base
year. For the U.S. 1975 was the base year, and regressions
were performed in this manner from 1976 through 1982. Using
the coefficient of determination as a measure of stability,

they found that the U.S. wage structure is highly stable.

 

2OECD (1985), Montgomery and Stockton (1987), Bell and
Freeman (1985), and Lawrence and Lawrence (1985) each
provide estimates of approximately a 35% increase in
dispersion between 1970 and the early 1980's, even though

they each compute dispersion over somewhat different
industries.

7
The coefficient monotonically declined over time but was
always greater than 0.97, a high correlation between wage
structures separated by as much as seven years.

As for the third criterion, Lawrence and Lawrence
(1985) examine the relationship between employment growth in
high-wage industries and wage changes. They note that the
correlation between 1970 wage levels and wage changes
between 1970 and 1984 was a statistically significant 0.37.
Further, they note that the decade of the 1970's brought a
30 and 15 percent increase in wages to steel workers and
automobile employees, respectively--both are above average
increases for this time period.

While some of these studies address the issue of
cyclical variation of the wage structure, their primary
emphasis is to explain the secular increase in dispersion
since 1970. An early study of cyclical variation in
interindustry wages is the well-known paper by Wachter
(1970). He addressed two issues in this paper: he
acknowledged the persistence of interindustry wage
differentials, and he used a supply-side analysis of the
labor market to address the cyclicality of wage dispersion.

Wachter does not actually explore causes of persistent
wage differentials across industries. The extent of his
analysis on this issue is to briefly survey the literature
that cites heterogeneous skills and market structure as
possible sources of these differentials. In exploring his

first claim that differences in product and labor markets

8
among industries cause inequalities for given skill levels,
he says that differentials have been present for too long to
be considered a random disturbance from the competitive
ideal. He notes that these inequalities, in part, reflect
differences in productivity among workers, but that the
differentials cannot be explained solely by these factors
(Wachter (1970), p. 75).

Two of the noncompetitive elements he stresses are the
industry unionization rate and the industry's ability to
pay. His analysis, however, does not attempt to sort out or
confirm these theories. They are simply captured as the
constant term in a dispersion equation where he uses the
coefficient of variation of interindustry wages as the
dependent variable.

Wachter examines the issue of labor heterogeneity in
more detail, however. Using a constructed skill mix
variable, Wachter finds a positive, statistically
significant relationship between labor quality and the wage
rate. He argues, however, that one industry is primarily the
source of this relationship; to examine the sensitivity of
his results, he performs his statistical analysis with and
without the confounding industry. He finds similar
qualitative results. Consequently, he argues that labor
heterogeneity is not the source of interindustry dispersion
or its cyclical behavior.

To provide a basis for his statistical analysis of

cyclical variation, Wachter discusses the effects of the

9
business cycle on the supply of labor to each industry,
differentiating between high and low-wage industries. He
assumes that high-wage industries hire from a queue created
by this positive wage differential. Low-wage industries
must attract the necessary number of workers by responding
to cyclical conditions. Since, according to Wachter's
model, labor supply to the industry is a function of the
industry's relative wage as well as aggregate demand,
low-wage industries will raise their wages during periods of
high aggregate demand to attract a sufficient number of
workers. In slack periods, they lower wages, and the
differential increases. From this framework, Wachter
predicts that wage dispersion increases during a recession
and declines during a recovery.

To test this hypothesis, Wachter regresses the
coefficient of variation of two-digit SIC manufacturing
industries on a constant term and Almon lags of the
inflation rate and the inverse of the aggregate unemployment
rate.3 He determines that inflation increases dispersion,
but the effect is small with a long-run elasticity of 0.09.
The unemployment rate increases dispersion also, with a
long-run elasticity of 0.25. The positive and significant
elasticity provides statistical support for his view of wage

determination.

 

3The dispersion measure is not weighted by employment in

each industry, giving small industries a disproportionate
influence.

10

While Wachter's statistical results match his
expectations, his statistical analysis does not reveal much
about the dynamics of wage adjustment in the labor market.
While his discussion provides a rationale for the cyclical
effect he finds statistically, it is hardly a confirmation
of the dynamic adjustment he suggests.

In an attempt to examine labor market adjustment when
moving from a slack to a tight economy, Okun (1973) suggests
that a process he terms "cyclical upgrading" occurs. His
view is based on a dual labor market approach, and the
premise underlying his analysis is that prime-age males have
a stronger attachment to the labor force than other
demographic groups such as females or young workers. He
notes that the simplest view of labor market adjustment
suggests that industries experiencing the largest employment
growth would be expected to experience the largest wage
increases during an upturn in economic activity;
consequently, one would expect wage differentials across
industries to widen. Yet, citing the Wachter paper along
with others, Okun notes that both skill differentials and
wage differentials tend to narrow in a high-pressure
economy. Okun, unlike Wachter, argues that a major part of
wage adjustment occurs due to the change in the skill
composition of the labor force.

Okun suggests a process of adjustment during an
economic recovery where prime-age males leave low-paying

sectors to enter high-wage industries. They are replaced in

11
the low-wage sector by young workers or women. This gain in
male employment is most substantial in high-wage
manufacturing, transportation, construction, and mining
jobs. The evidence that Okun presents suggests that perhaps
Wachter underestimates the consequences of ignoring the
changing skill composition of the labor force in analyzing
dispersion (Okun (1973), p. 216).

At least two subsequent studies, as a by-product of
their examination of the secular increase in dispersion,
have examined the cyclicality of wage dispersion. Bell and
Freeman note that the cyclicality of dispersion accounts for
very little of the wage variability observed since 1970.‘

In a simple regression of the standard deviation of the
logarithm of industry wages on real GNP and a time trend,
they do not find a statistically significant cyclical
effect. Hence, they look to productivity shocks at the
industry level to explain the evolution of the interindustry
wage structure as an alternative to the competitive model of
the labor market.

Montgomery and Stockton (1987) construct a neoclassical
model of the labor market in an attempt to explain the
increase in the dispersion of wages. Using a model that
incorporates technological progress, labor heterogeneity,

and exogenously supplied capital, they find that most of the

 

‘Note that the combination of industries examined by Bell
and Freeman is somewhat different than those examined by the
previous authors.

12

change in dispersion may be accounted for by microeconomic
factors.5 To account for labor heterogeneity, they use the
Gollop-Jorgenson labor quality indexes to develop a measure
of the dispersion of labor skills; the inclusion of this
measure highlights the role of skill differentials in wage
determination across industries. Along with the labor
quality controls, Montgomery and Stockton include capital
(or capital-labor ratios), expected income, and a nonlinear
time trend. The time trend is an attempt to incorporate
technological progress. While they note the statistical
significance of the trend and the theoretical interpretation
associated with it, they caution against a literal
interpretation of technological progress. Omitted factors
correlated with the trend could easily be picked up in the
estimation of such trends or factors other than
technological progress could account for any observed trend.

While these factors seem to primarily explain wage
dispersion in the Montgomery and Stockton analysis, the
authors also explore the impact of macroeconomic variables.
They repeat several of their regressions including
macroeconomic measures such as the prime-age male

unemployment rate and the inflation rate.6 'They

 

5They examine the dispersion of wages across two-digit
manufacturing industries from 1948 to 1981.

6The prime-age male unemployment rate refers to males from
25 to 54 years old. It is a better cyclical measure than

the aggregate unemployment rate, which lags current cyclical
activity.

13
consistently found no role for inflation (expected or
unexpected) as a source of wage variability, but they find a
positive, statistically significant impact for the
unemployment rate: during recessions (booms) dispersion
increases (decreases). However, the explanatory power of
the unemployment rate is small relative to the microeconomic
factors according to Montgomery and Stockton.

Their findings stand in contrast to the results of a
new literature that finds significant inflationary effects
on wage adjustment across industries. Hamermesh (1986),
Drazen and Hamermesh (1986), Fackler and Holland (1989), and
Allen (1986) all focus on the effects of inflation on labor
market adjustment. Hamermesh (1986) develops a model of the
dispersion of wage changes across industries based on the
Keynesian concept of downwardly rigid nominal wages. The
model demonstrates that, with downward nominal wage
rigidity, wage change dispersion should increase with
increases in inflation. If real rather than nominal wages
are downwardly rigid, only unexpected inflation should have
the effect of increasing dispersion.

To test this model, Hamermesh obtains maximum
likelihood estimates of the effects of expected and

unanticipated inflation on wage change dispersion.7 He

 

7The dependent variables in this analysis is the variance of
wage changes across one-digit industries (1965-1981) and
two-digit manufacturing (1955-1981). He uses a number of
measures of anticipated inflation: The Livingston Survey,
the Survey Research Center survey of households, and an ARMA
forecast.

14
finds no consistent effect for expected inflation, and
contrary to the Keynesian analysis he finds that the
dispersion of wage changes across industries is reduced by
unexpected inflation. Drazen and Hamermesh (1986) find
similar results using Israeli data. Hamermesh suggests that
implicit indexation may be the source of this unexpected
finding, but Fackler and Holland (1989) present evidence
disputing that suggestion. At any rate, these results
suggest a responsiveness of interindustry wage changes to
the rate of change in prices, unlike the Montgomery and
Stockton results.

Montgomery and Stockton note that their results account
for microeconomic factors, while the inflation studies
ignore those characteristics for the most part. Their
suggestion implies that the impact of inflation is a
statistical relic rather than a real phenomenon, resulting
from the omission of labor quality variables from the
analysis.

Several recent papers have dealt with the issue of wage
cyclicality, and their findings bear upon this research.
Several authors (8118 (1985), Keane et. a1. (1989), and
Blank (1989, 1990), for example) have revisited the question
of how wages vary over they cycle. 8113 notes that the
variety of results presented in the debate over the
cyclicality of wages is clouded by aggregation bias in many
of the previous studies. He attempts to remedy this

shortcoming by using micro panel data. Keane et. al. note

15
that Bils estimates may be biased, however, since he
eliminates those that fall from the sample over the cycle.
They find that selectivity is important to in the
cyclicality of real manufacturing wages, but like 8118, they
found that wages are slightly procyclical. In a related
vein, Shaw finds that real wages are much more sensitive to
persistent sectorial shocks than to temporary cyclical
shocks.

Blank (1989) disaggregates the effect of the business
cycle on the distribution of income. Here she finds that
both wages and hours show evidence of cyclicality, although
hours seem more cyclically sensitive. Blank (1990)
investigates wage cyclicality in the 1970's. She focuses
further attention on the issue of worker selection over the
cycle as well as the cyclicality of returns to worker
skills. She finds that wages are affected by movement
between broad sectors but that selectivity is not an
important statistical issue since their is no statistical
correlation between wage determination and sectorial choice.
She also finds cyclicality in the returns to worker

characteristics.

The Interindustry Wage Structure

A rather large literature has recently re-emerged
examining the interindustry wage structure. The studies

attempt to explain certain stylized facts of the labor

16
market: of particular interest to these writers is the
persistence of wage differentials and the stability of the
interindustry wage structure over time and across countries.
The persistence of these differentials has been noted by
writers such as Katz and Summers (1989), Krueger and Summers
(1987), Dickens and Katz (1987), and Murphy and Topel
(1987).

As noted earlier, the stability of industry wage
rankings is well known. Krueger and Summers (1987) document
other regularities as well. They estimate industry wage
differentials from Current Population Survey data (1984) and
find that the differentials are basically unaffected by the
inclusion of explicit labor quality controls, although they
concede that unobserved labor quality might account for the
differentials. Katz and Summers (1989), however, examine
this issue further, concluding that unobserved labor quality
is not the source of interindustry differentials. They
argue that, contrary to the findings of Murphy and Topel
(1987), the evidence is not consistent with this
explanation. If education and experience are correlated
with unobserved ability, high-wage industries would hire a
disproportionately large number of these workers. That is
not the case. They also show that gains (losses) to workers
entering (leaving) an industry are equal to the industry
differential, which is unlikely if unobserved labor quality

accounts for industry wage differentials.

l7

Krueger and Summers (1987) and Katz and Summers (1989)
also show that the interindustry wage structure across
industrialized countries is similar. They present evidence
of a large positive correlation between industry wages
across countries, and they speculate that certain
regularities may lead to this occurrence.

Furthermore, certain characteristics seem to be
correlated with the industry rankings. One interesting and
somewhat mystifying phenomenon is that high-wage industries
pay high wages to all occupations within the industry.
Krueger and Summers argue that profitable industries share
some of these rents with workers. Katz and Summers, upon
further examination, argue that workers reap most of the
rents.

Dickens and Katz (1987) examine other correlates of
interindustry wage differences such as industry product
market concentration, plant size, and unionization. They
note that such determinants are important, but they argue
the structural relationship between the differentials and
these factors is not well established. These papers, as a
group, suggest that efficiency wage models of labor market
adjustment may be appropriate, though there is no structural
evidence to support any particular version of these models.

An implication of the work on interindustry wage
differentials is that the interindustry wage structure is
relatively rigid and unresponsive to changes in aggregate

demand. Some of the papers conjecture that the labor market

18

may be more appropriately viewed as a dual labor market with
a rigid high-wage sector and a relatively flexible low-wage
sector. There is no real evidence to exclusively support
that view, nor is it crucial to the analysis of
interindustry wage differentials presented in these papers.

The fixed wage structure implies a different sort of
labor market adjustment than the competitive model--or the
dual approach described by Wachter. In this framework, the
industry simply adjusts the quantity of employment to labor
market conditions.8 With a fixed interindustry wage
structure, involuntary unemployment exists. Katz and
Summers (1989) argue that in the case of a rigid wage
structure, economic welfare may be increased by encouraging
employment in high-wage industries. They suggest the
possibility of subsidies to high-wage industries as a
welfare-augmenting policy.9 This also suggests that some
benefits of countercyclical policy may be ignored in
fighting recessions. If high-wage industries lose
proportionally more employment in a downturn, then the cost
of a recession is greater than in the competitive view of

the labor market. The rents accruing to high-wage workers

 

BHamermesh (1989) examines employment adjustment by seven
plants of an unnamed firm and finds that the plants alter
their workforces in response to rather large shocks but
maintain steady employment for smaller shocks. Employment
at the industry level appears to adjust to at the margin,
however, due to the aggregation of responses from
heterogeneous firms.

9The authors note that distributional and collateral costs
may offset the desirability of this policy.

19
are best viewed as real losses to the economy during a

downturn.10

Conclusion

The dispersion of wages over the business cycle may be
measured in a number of ways. Most studies reviewed here
use some measure of variability, such as the variance or
standard deviation of wages across industries, but the
rankings of industries are also a component of flexibility.
The U.S. wage structure has demonstrated significant
flexibility in terms of wage dispersion, with variability
increasing by 35 percent from 1970 to 1982. However, the
ranking of industries by wages is stable, changing little
over the period of the 1970's. In fact, there is a
significant, positive correlation between the level of wages
and wage changes. So the picture of U.S. wage flexibility
is not so clear as the dispersion literature might suggest.

In fact, the labor literature has long provided
evidence for persistent wage differentials. Some authors
suggest that the differentials do not support the
competitive view of labor market adjustment, and they
advocate policies based on this view of market adjustment.

To examine the flexibility of wages over the business

cycle, the next chapter presents a simple model of wage

 

10Katz and Summers (1989) address this argument in detail in
the context of international trade and industrial policy.

20
dispersion and several resulting hypotheses to be tested

empirically.

CHAPTER 2

A Model of the Cyclicality of Dispersion

Introduction

In order to analyze the flexibility of interindustry
wages, a simple model of the labor market provides a useful
point of departure. The following model examines the effect
of the business cycle on the short run determination of
wages by industry. Labor market flexibility across
industries in response to cyclical fluctuations may then be
measured by computing the variance of the natural logarithm
of the wage rate across industries.

The simplest form of the model analyzes labor market
flexibility by assuming that workers have homogeneous skills
with constant labor demand and supply elasticities across
industries. A second assumption of the model is that the
labor market in each industry clears in each time period.
Aggregate demand affects the labor market through the
product market since labor is a derived demand. This model
counterfactually predicts that dispersion increases with
cyclical upswings.

To provide a more complete picture, the assumptions of

homogenous labor skills and market clearing are relaxed to

21

22
extend the implications of the analysis. The relaxation of
these assumptions allows alternatives to price flexibility
for labor market adjustment. A variety of scenarios are
developed under these assumptions to examine interindustry
behavior. These models show that the cyclically changing
skill composition offsets the direct effects of the cycle on
interindustry dispersion. Further, the assumption of
downward wage rigidity implies asymmetry in the dispersion

of wages over the cycle.

An Equilibrium Model of the Labor Market

Since the focus of this work is on labor market
flexibility and the existence of persistent interindustry
wage differentials, I begin my analysis with an examination
of wage determination in each industry. To simplify the
analysis, I assume that labor is homogeneous in ability, so
that one worker may fill a position as productively as

another in a firm. Let the demand for labor be given by

(2.1) Lidc=di +a(wit-p1,.)

where Lflt is the quantity of labor demanded, a is the labor
demand elasticity, wit is the nominal wage rate, and pit is
the product price.1 .According to this equation, the sole

determinant of labor demand in the industry is the value of

 

HRH: Wu: and pit are the natural logarithms of the actual
values. All the variables in this chapter are stated in
natural logarithms unless otherwise noted.

23
the worker's marginal contribution to the firm, the real
wage from the industry's perspective.2

Labor supply in the industry is given by

”-2) Li. = 81-43 (Wu-P.)
where Lit is the quantity of labor supplied, B is the labor
supply elasticity, and P; is the expected price level.
Equilibrium in the labor market of each industry is given
where labor demand and supply are equated in each industry
in each time period. Then,

s;-d
2.3 ' = 1 1+ a _ P .
( ) wit a_p a_ppit a_p t

In this model, the nominal industry wage rate is an
increasing function of the product price and of the expected
price level. I assume that individuals form rational

expectations of the aggregate price level so that expected

 

2In this and subsequent equations, the price elasticity is
constrained to be equal across industries. While this
assumption is restrictive, I have no information about
differences in responsiveness by industry. While a richer
specification is desirable, it is not necessary to model the
impact of cyclical activity on wage dispersion.

24
real wages are the determinant of labor supply.3 The
expected aggregate price level does not vary by industry.
The price, p”, for an industry is formed in the
product market. To close the model, it is necessary to
describe equilibrium price determination in the industry.

Let demand in the product market be given by

(2-4) Qidc = a11+a2pit+a3iDt
0%, is the quantity of the product demanded, a2 is the
product price elasticity that is assumed to be constant
across industries, pit is the price of the product, a3i is
the elasticity of demand with respect to aggregate shocks,
and Dt is a measure of real aggregate demand.

Supply is given by

(2-5) 01:9: : b1i+bzpit
where the quantity supplied of the industry's product is a
function of the price. t» is the supply price elasticity,

common to all industries in this analysis. In equilibrium,

the product price is

 

3Notice that the equation can be written as

 

(2.3-) wit = 8:31” “ET,- («pit-spa

where the nominal industry wage is determined by a weighted
average of the industry price and the expected price level.
The constant term captures the industry-specific productive
characteristics and noncompetitive elements that are time
invariant.

25

bii‘au _ 531'
‘32 'b2 32 'b2

 

pit = Dr: '

Substituting the product price into the reduced form wage

equation (2.3) yields,

 

 

where
= Si—di+ a 1311-311
Co “'B “'B( az’bz ) I
a an
= > O,

and

cz==-—E— > 0.
a-B

Equation (2.6) gives the equilibrium industry wage rate
in terms of the expected price level and aggregate demand.
To examine labor market wage flexibility over the business
cycle, it is natural to compute the variance of the natural
logarithm of the wage rate, which states the variance as a
function of the exogenous variables. This relationship is

given by

(2.7) of.“ = to+t1D§ .

26

 

 

where
= l 2 2 a2 2 2
t0 __(¢-B)2 (051+Odi) + [(a_p) (a2_b2)]2 (abli+aa11)
and
11 = “20:31 > 0
[(a-B) (az-sz2

From this formulation, 11 is clearly positive, and the
derivative of the variance with respect to the aggregate
demand measure is greater than zero. These parameters are
functions of labor and product market elasticities, the
dispersion of sector-specific nonvarying parameters, and the
variance of industry responses to cyclical shocks.

According to this model, an increase in aggregate
demand increases interindustry dispersion. Industries that
are very responsive to aggregate demand experience positive
shifts in their labor demand curves when aggregate demand
rises due to the rise in product price. Wages in these
sectors rise to attract labor from other industries. Changes
in the expected price level should have no effect across
sectors since expectations are formed in the same manner for
all workers. Hence, the variance across industries is zero.

In the frictionless world of the perfectly competitive
model, these differentials would exist only for a short

period of time because labor would be immediately

27
reallocated to the high-wage sectors. Labor supply in the
low wage sectors of the economy would shift upward, forcing
wage rates to rise in order to attract enough labor to
produce at the profit-maximizing level. Wages would continue
to rise in the low wage sectors (and of course, wages would
decline in the high wage sector as labor entered) until no
interindustry differential existed. All wage differentials
would be eliminated in a short period of time, except for

those that were compensating differentials.

The Heterogeneity of Labor

In a somewhat more complex world where actors face
dynamic instead of purely static choices, economic actors
may not respond as quickly as the competitive model assumes.
Firms and workers may invest in human capital specific to
the firm or industry. Since this training is most
effectively gained on the job, productivity increases by
undertaking this investment. Both the worker and the
employer have an incentive to make the investment, but
specific human capital is immobile. As a consequence,
neither actor is willing to undertake the investment alone;
therefore, both share the cost of investing in specific

human capital so that neither side bears the complete loss

28
in the event of a job separation.4 .As Oi (1962) points out,
this type of investment introduces a degree of fixity into
the analysis.

Due to this fixity, firms may be less likely to release
labor during a downturn. Workers also take into account the
joint investment in analyzing the net benefits of moving
from current employment to a new job. Instead of simply
responding to a wage differential, the worker must evaluate
the expected net benefit of a job change. For the worker
who has invested to a significant degree in specific human
capital, larger differentials are required for this calculus
to move the worker to scrap the previous investment. During
an upswing, the firm is slower to take on additional workers
since training is required for the worker to be as
productive as desired. In short, the demand is less
sensitive to changes in aggregate demand as a result of
their use of specific human capital in the production
process.

The result of this joint investment in specific human
capital is reduced mobility across sectors due to wage
differentials. Consequently, differentials are likely to
persist for a longer period of time than the simplest
competitive framework would imply. Even if the investment

by the firm and the worker do not add to the productive

 

‘Becker (1975) details the choices of the actors and
analyzes the decision to invest in human capital, general or
specific.

29
ability of the employee, the search and recruitment costs
for each party reduce the mobility of labor across sectors
to some degree.

Specific human capital has another effect besides the
reduced mobility of labor across sectors. It also implies
that workers have different productivities due to
differences in skills. These differences undoubtedly
account for some of the dispersion across industries.
Workers may be more productive as a result of superior
innate ability, specific training, or general training such
as formal education. Differences in labor quality should
naturally result in a dispersion of wages both within and
between sectors. As industries form to use generally
skilled or unskilled workers to produce output, the wage
rate paid should reflect the skill differences. Skilled
workers are able to attract a higher wage rate than those
who have not undertaken investment in human capital.
Workers would never undertake such an investment if the
expected net benefit was not at least as great as their next
best alternative. If some industries consistently use
higher quality labor, permanent differentials across
industries exist.

The business cycle may then affect wage dispersion
across industries by altering the skill mix of the economy.

When rigidities are introduced into the framework discussed

30
above, unemployment occurs.5 .As fewer workers are needed
during a recession, those who have invested little are the
first to be dismissed since both they and the firm have
incurred a relatively small loss should they decide to leave
the industry. Since jobs in other sectors either pay less or
require some investment in specific human capital (assuming
jobs are available in such a sector), the worker must decide
to either wait until the current industry rehires or to
search for employment in another sector. The worker may
remain unemployed for some time if many other sectors are
rather rigid as well. The alternative may be to take
employment in a low-wage industry.

The effect of this behavior is not clear a priori. If
workers leave the sectors that are relatively unresponsive
to wage changes during downturns to become unemployed, the
dispersion of wages may decrease. The remaining workers
would be more homogeneous, reducing the differential
associated with human capital differences. A stylized fact
of business cycle analysis is that relatively unskilled
workers are the first to lose their jobs during a downturn.

This is particularly evident in the manufacturing sector.6

 

5In the discussion thus far, unemployment may be viewed as
voluntary since workers decide not to change sectors in
anticipation of being rehired in the sector with which they
are currently affiliated. Labor markets still clear in this

analysis, but the responsiveness of the sector to aggregate
demand is reduced.

6See Bils (1985) for a summary of the basic stylized facts
of aggregate wage performance over the business cycle.

31

Of course, all these workers will not remain
unemployed. Some move to industries that rely less on
skilled labor--especially those with specific skills. The
laid-off workers may enter these industries, increasing the
supply of labor to these sectors. Wages are depressed as a
result, increasing the dispersion of wages. Unlike the
simple competitive model, the heterogeneity of labor skills
allows wage dispersion to increase during a recession as
aggregate demand declines. The stylized facts of the labor
market over the business cycle are consistent with such a
decline.

To incorporate this analysis into the simple model
developed above, assume that skill (SM) increases both the
demand for and supply of labor. Interindustry dispersion

can then be described as

2 __ 2 2
(2-3) a'ic"t0+trDt+t2°51c'

32

where interindustry dispersion is also determined by the
skill distribution of the labor force.7 If the skill
distribution is unaffected by the business cycle,
interindustry dispersion is altered only by the cyclical
measure and the marginal impact of a shock is the same as in
equation 2.7. If, however, the dispersion of skills is a
function of cyclical activity as described above, then
C = 2r D +t 51‘

‘325- 1 c 2‘32;—
where OOZSit/th < 0. If labor quality varies inversely with

the cycle, then the overall impact of the cycle on

dispersion is ambiguous, a priori.

 

7It is plausible to think of the demand for workers to
increase as skill rises since worker productivity increases.
One might also think of increasing skills as increasing
labor supply since the worker has an investment in these
skills that he must recoup. However, these assumptions are
not necessary for the following to hold:

t2 = M ) 0
(at-l3)2

where 9 is the supply-side coefficient of skill and u is the
coefficient of skill in the labor demand equation. to and
11 are the same as above.

33
Diseguilibrium in the Labor Market

The human capital story provides a rationale for the
reduced responsiveness of an industry's labor market to
aggregate demand. Both the workers and the firms have an
incentive to protect investments in human capital. Any
worker who does not leave the sector to look for work
elsewhere is voluntarily out of the market, waiting for an
increase in aggregate demand to draw him back. However,
macroeconomists in the Keynesian tradition have argued that
wages do not adjust to changes in aggregate demand. In such
a case, the adjustment described above would understate the
quantity adjustment in the labor market that occurs from
changes in aggregate demand.

The Keynesian assumption of downward nominal wage
rigidity leads to an asymmetry in the cyclical movements of
the variance of interindustry wages over the cycle. When
the economy is expanding, the equilibrium model derived
describes the determination of the industry wage rate by
Equation 2.6. But downward nominal rigidity means that the
current wage remains unchanged if aggregate demand declines.

So the model becomes

wit = co+c1Dt+c2Pt if (1-L)Dt 2 0

= Wi't_1 if (l-L)Dt < 0 I

where (l-L)Dt = Dt - DH.

34
Under such a regime (and allowing for labor

heterogeneity), the variance of interindustry wages is

2 2 2 .
(2.10) a,“ = to+t1Dt+tzoSit 1f (1—L)Dt 2 O

_ 2 2 - _
- 0'1,t-1”2°Su 1f (1 L) Dc < O .

Under these assumptions, the behavior of interindustry
dispersion depends on the cycle itself. The response is
asymmetric, producing a testable hypothesis about the
behavior of dispersion over the cycle.8 'The effect of
growth in aggregate demand is ambiguous, but a recession
will reduce dispersion by decreasing the dispersion of
skills across industries: that is,
not... = 60:. (0

when the economy is in recession.°

Another possible model of disequilibrium is based on
empirical evidence about the labor market without a strong
foundation in theory. As noted in chapter 1, persistent
differentials have been noted across industries, and those

differentials appear to change with relative productivity

 

8This assumes the same behavior for all industries. The

empirical viability of the assumption is explored in Chapter
3.

9The derivative is not defined at (l-L)Dt== 0 since the
function is discontinuous at that point. The derivative is
only valid when (1-L)Dt'< 0. When (1-L)Dt:> 0, the effect
is the same as the symmetric case.

35
changes across industries rather than cyclical factors.
Such a view of the labor market suggests that wages do not
adjust to market conditions. Instead, labor would be
reallocated across sectors during a recession, or workers
become involuntarily unemployed.

To motivate this analysis, assume that all wages are
downwardly rigid. When aggregate demand declines, the
industry is unable to lower wages. Instead, the firms in
the industry use fewer workers. If all industries
experience such rigidity and are affected by a downturn to
the same degree, then the distribution of wages is
unaffected; the unemployment rate merely increases and there
is no visible relationship between wage dispersion and the
business cycle.

If all industries are not equally responsive to a
downturn (perhaps because of the varying use of specific
human capital in production), than wage dispersion can
change with the cycle, not because of wage flexibility, but
because of a change in the industrial composition of the
workforce.10 Those industries that retain relatively more
labor receive a larger weight during a recession; hence,
even if wages are completely rigid for all industries,

dispersion could change simply because relatively high wage

 

10Bils (1985) addresses the importance of aggregation bias

in examining the cyclicality of mean wages over the business
cycle.

36
and low wage industries react differently to the change in
aggregate demand.

Several writers have recently suggested that wage
rigidity may be a profit maximizing choice on the firm's
part. The analysis may be appropriate to the industry if
firms choose similar technology in production. The implicit
contract literature has attempted to explain wage rigidity
as a risksharing proposition between the firm and workers.
More recently, the efficiency wage literature has attempted
to provide possible reasons that firms would pay above the
competitive market wage and why wages would not clear the
market in such an industry.

If some industries choose to forgo flexibility and
others do not, then a recession means that the effects on
dispersion are more severe than implied by the specific
human capital story. In this case, workers become
involuntarily unemployed, willing to work at the industry
wage but unable to do so. The worker becomes unemployed or
moves to a flexible-wage sector. Wages in this industry are
depressed by a decrease in aggregate demand since the
marginal revenue product of labor decline and the supply of
labor to the industry decrease. The dispersion of wages
increases due to the downturn, unlike the decrease
experienced in the flexible market case. Wage rigidity
results in quantity adjustment as the primary method of

reallocation in the labor market.

37
The human capital analysis is congruent with the wage
rigidity explanation. Since unskilled workers are primarily
the workers affected in a cyclical downturn, firms
implicitly alter the skill composition of the workforce over

the cycle.

Implications

The method of labor market adjustment is more than a
question of passing interest to economists. The properties
of the competitive model are well known to economists, and
the welfare characteristics are well established. If wages
are not free to adjust to shocks, however, the efficiency of
the market may be improved through governmental policy.

Katz and Summers (1989) discuss welfare-augmenting policies
in the presence of wage differentials in the context of
trade policy. They suggest that under conditions of
persistent wage differentials, the government may increase
economic welfare by encouraging the expansion of high-wage
industries --perhaps by subsidizing industries.

While the wisdom of such policy is still suspect when
one considers the collateral costs and distributional
effects of the policy, their analysis also has implications
for government countercyclical policy. If wages are
flexible to adjust to aggregate market conditions, workers
who choose not to work are making a free, utility-maximizing

choice. Unemployment may be considered voluntary; the

38
worker has simply chosen not to take employment at the
current market wage rate. When wages rise, the worker
returns to a job. Even if the worker reports his labor
market status as unemployed, he may simply be looking for
work at or above his reservation wage rate.

If the wage rate in high-wage industries is rigid,
giving rise to a persistent, positive differential, then
unemployment from these industries may be viewed as
involuntary to some degree. If the entire wage structure is
rigid in the short run, it may be literally true that a
worker willing to supply labor may be unable to find work.
If as segmented labor market advocates claim, there is a
secondary flexible-wage sector, the issue is fuzzier. Under
either of these structures, however, the welfare analysis
reviewed by Katz and Summers is applicable because the
differentials present in either case provide a window of
opportunity for government to expand welfare by encouraging
employment in the high-wage industries.

While Katz and Summers focus on trade policy, the
analysis has implications for countercyclical policy. When
high-wage employment is decreased, economic welfare declines
under such a regime. And if high-wage employment (such as
durable goods in manufacturing) is particularly hurt by a
recession, the social cost of a negative shock to aggregate
demand is greater under the limited-flexibility model than

is recognized by the flexible wage model.

39

For policymakers, such a consideration is important.
In inflationary periods, activist policymakers would
generally call for a decrease in aggregate demand. In
analyzing the consequences to economic welfare, however, the
associated costs of such a policy may differ considerably
under these different views of labor market adjustment. The
costs of a recession would be larger in the limited
flexibility case, reducing the attractiveness of restricting
aggregate demand as a means of slowing inflation.11 The
remainder of this research attempts to decipher which view
of labor market adjustment is more appropriate by describing

the links between cyclical activity and wage dispersion.

Conclusion

The competitive, flexible model of the labor market
presented argues that wage dispersion in the short run would
be unrelated to the business cycle if there were no
frictions in the market. Given that some exist, however,
the model demonstrates that under the assumptions of

homogenous labor and flexible wages, short-lived wage

 

11The macroeconomic literature in recent years has noted
that countercyclical policy may be ineffective in
manipulating economic activity. This is particularly true
in models with flexible markets and economic actors who are
endowed with Muthian rational expectations. Other models
have noted that policy may be effective in the absence of
the immediate adjustment of markets. This class of neo-
Keynesian models would be congruent with the analysis of
persistent wage differentials.

40
differentials would exist, and wage dispersion would
increase during an increase in aggregate demand, stimulating
labor mobility to high wage sectors. Conversely, a downturn
would reduce dispersion since wage differentials would be
smaller in high wage industries with the withering of
aggregate stimulus.

The assumptions of wage flexibility and labor
homogeneity are not innocuous, however. Skill differences
are a source of wage differentials; if labor skills vary
over the cycle, then a portion of the variance of wage over
the cycle must result from labor heterogeneity, having an
ambiguous affect on dispersion. When the model is extended
to account for disequilibrium, wage dispersion does not
behave symmetrically over the cycle.

Given well-documented interindustry wage differentials
that persist over long periods of time, several authors have
suggested that wages are not flexible in some industries
while they are more flexible in others. Wage rigidity in
some sectors could account for the stylized fact that wage
dispersion increases during a cyclical downturn; these
methods of labor market adjustment imply different social
costs of economic downturns. In a cost-benefit analysis of
countercyclical policy, these two models imply different
returns to activist policy. The flexible wage structure
leaves less room for governmental interference in the labor

market.

CHAPTER 3

Time-Series Evidence on Interindustry Wage Dispersion

Introductign

Many of the studies that have examined labor market
flexibility have used time-series data from one-digit
industries or two-digit manufacturing industries as defined
by the Standard Industrial Classification. In order to
provide a basis for comparison to these studies, this
chapter presents time-series evidence on the responsiveness
of interindustry wage dispersion to the business cycle. The
model described in chapter 2 provides the basis for the
estimation.

The results of the estimation below show that the
dispersion of wages across one-digit industries is sensitive
to the business cycle, increasing as unemployment rises.

The responsiveness, though statistically significant, is
rather small. For two-digit manufacturing industries, there
is no distinguishable impact of unemployment on the
dispersion of wages. Furthermore, wage dispersion across
both one-digit and two-digit SIC industries does not exhibit

the asymmetric behavior predicted under the assumption of

41

42
nominal wage rigidity--though some manufacturing industries
exhibit such behavior.

To distinguish between the possible sources of labor
market adjustment, I then present evidence on the
responsiveness of industry employment and real wage rates to
the business cycle. Real industry wage rates are not very
sensitive to cyclical activity; industry employment responds
considerably more than wages to cyclical shocks. However,
the Wachter view that high-wage industries respond through
employment changes and low-wage industries adapt by altering
wages is not supported.

This chapter presents evidence not only on two-digit
manufacturing industries but also on one-digit industries.
The dispersion estimates are also dissected in order to
obtain a picture of what happens across industries rather
than rely solely on summary measures between dispersion
measures and the unemployment rate. Furthermore, the
estimates are generated from a model that utilizes the time-
series properties of the data to correct for labor

heterogeneity over the cycle.

Estimation

To statistically determine the effect of the business
cycle on wage dispersion, it is necessary to estimate

Equation 2.7 from Chapter 2,

43

2 _ 2

This equation was derived under the assumption of homogenous
labor, but as discussed, the business cycle is likely to
alter the mix of labor skills used by each industry. Hence,'
it becomes necessary to include human capital variables to
control for skill differences.1 Unfortunately, labor
quality controls do not exist at the industry level.2 Some
other method of estimation will be necessary to estimate the
effect of the cycle on wage dispersion, controlling for
labor quality.

Ideally, one should include observed worker
characteristics in the regressions to account for the
variance across industries. Equation 2.8 provides the

relation between interindustry dispersion and these

variables:

 

1The typical controls would include years of schooling,
experience, and the square of experience. When these
variables are included in the wage equation, they control
for human capital differences in the industry wage equation.
When the variance of the wage rate is computed to get
equation (2.8), the human capital controls become variances
and covariances of schooling, experience and its square.

2Gollop and Jorgenson (1983) have developed a labor quality
index for manufacturing industries. The indexes are
computed annually from 1948 to 1978. Since the data in this
analysis is monthly, the annual indexes are of little use.

Below, I test the injury caused by not using the indexes on
annual data.

44

2 _ 2 2

The greater the dispersion of education and experience
across industries, the more dispersed wages should be.3
Hence, an accurate statistical analysis must account for
variation in these characteristics. Unfortunately, time-
series data do not exist (generally) at the industry level
to allow such controls to be included.4 So it becomes
necessary to ask under what circumstances estimation is
valid without the inclusion of human capital variances and
covariances.

They may be omitted if they are uncorrelated with the
other regressors. No bias would be imparted in the results,
though efficiency would be reduced. The variances and
covariances of human capital characteristics may also be
omitted under another circumstance. Assume that experience

and its square, along with schooling (and any other human

 

3Unobserved characteristics may also account for dispersion.
Murphy and Topel (1986) note that this is a serious
potential problem in analyzing the structure of
interindustry wages, but Katz and Summers (1989) present
evidence to the contrary and demonstrate shortcomings in the
Murphy and Topel work.

‘As noted in chapter 1, Montgomery and Stockton (1987)
control for labor quality by using the Gollop and Jorgenson
(1983) labor quality indexes. These are constructed under
the assumption of homogeneity within broad demographic
categories and are available only on an annual basis. They
incorporate the assumption of intra-group homogeneity within
broad demographic categories and are available only on an
annual basis. The assumption of intra-group homogeneity,
while necessary, is restrictive (Sedalek and Heckman,
(1985)).

45
capital characteristic), may be viewed as stationary time-
series processes. Then these variables display no trend and
a constant variance. More generally, these variables may be
trend stationary, displaying a trend with a constant
variance around that trend. The relationship between the
variance of wages and the business cycle may be estimated
without bias from these omitted variables, then, by
differencing the variables in equation 2.8.5 With constant
variances and covariances, the omitted human capital

variables will impart no bias to the estimation of

 

5Given the work of other researchers that shows that the
variance of w” has increased in recent years, one might
expect that neither it, nor the human capital variables are
stationary. The differenced model of Equation 2.8 is
further justified, however, in order to avoid spurious
regressions in tests of the cyclical hypothesis.
Differencing removes the unconditional mean of the
variables, and the spurious results that occur from
regressing trending variables on one another are avoided. A
final justification lies in the method of modeling
technological change, which accounts for much of the secular
increase in interindustry wage dispersion. Montgomery and
Stockton (1987) use linear and quadratic time trends to
model the evolution of technology. Although they do not
claim that such a specification excludes other
interpretations, they explicitly include time in the model
to account for technological change. Their model may be
viewed as a trend-stationary model. The differenced model
in Equation 2.8 eliminates these trends also, but the
implication is that the variance is subject to permanent
shocks rather than smooth growth that occurs over time. If
technological progress may be viewed as a permanent shock to
the variance of w“, then the differenced specification may
be more appropriate than the trend-stationary model. See
Plosser and Schwert (1977) for a discussion of the
differenced model.

46

(3.1) (1—L)af,it t1(1—L)Df+(1—L)<-:t ,

where L is the lag Operator indicating for a variable xt
that L(xt)== x...1 and (1-L)et is an MA(1) process with a unit
root.6 Assuming that fl is constant over time, t5 may be
interpreted as the marginal change in interindustry
dispersion resulting from a small increase in the aggregate
measure of economic activity. Note that the error term of
this relationship will be first differenced also when one
accounts for measurement error in the statistical estimation
of this relationship. This creates a first-order moving
average process with a unit root if the error term follows
the typical assumptions of the classical regression model.
Plosser and Schwert (1977) discuss the estimation of such a

model.7

 

6If the constant term in Equation 2.8 does not change over
time, it will be differenced away. If there is drift in
ct” over time, (l-L)1:0t will not equal 0. This is a
testable hypothesis. The constant term is never
significantly different from zero in any of the estimated
monthly equations reported below.

7According to the structure of the model in Equation 2.8,
the error process in this equation is a MA(1) process with a
unit root. In the estimates below, I present OLS estimates
without the MA(1) because tests easily rejected the null
hypothesis of a unit root. In no circumstance could I
reject the hypothesis that the MA(1) parameter equals zero.

 

47

 

To estimate this equation, I used average industry
wages for one-digit SIC industries and two-digit SIC
manufacturing industries, available on a monthly basis from
Citibase.8 ‘Wage data are available for one-digit industries
from 1964 while two-digit data are available from 1956.9
Using this information, I compute the variance of the

natural logarithm of industry wages by the following

formula:

02 _ 21": (wit—Wt)2Eit]

w:
it
Nt

 

where Wk is the weighted average of the natural logarithm of
wage rates across industries, Eit is industry employment at
time t, and Nt is total employment in the sector at time t.
The cyclical measure is also taken from Citibase. It is the
prime-age male unemployment rate, which is a better measure

of cyclical activity than the aggregate unemployment rate,

 

8The one-digit industries include mining, construction,
manufacturing, transportation, wholesale trade, retail
trade, finance, and services. The two-digit industries are
food, tobacco, textiles, apparel, lumber, furniture, paper,
printing, chemicals, petroleum, rubber, leather, stone,
primary metals, fabricated metals, machinery, electrical

equipment, transportation, instruments, and miscellaneous
manufacturing.

9Since the control variables begin in 1956, this is all that

I can use. However, two-digit wage information is available
from 1948.

48
although it moves opposite to aggregate demand, changing the
expected sign of the estimated coefficients.”

While the method of estimation is chosen to eliminate
the bias associated with omitting the variances and
covariances of human capital variables, the hypothesis is
not directly testable with this data. In a rather ad hoc
attempt to capture this possible omission, I have included
demographic variables to gauge possible change in labor
quality. If labor quality differs systematically with
demographic characteristics, they control for differences in
labor quality over the business cycle. These variables,
also taken from Citibase, are the percentage of those
working who are (1) 16 to 19 years old, (2) female, (3)
nonwhite, and (4) part-time for noneconomic reasons. Like
the unemployment rate, the variables are squared and then
first differenced as the derivation of the model requires.

As discussed in chapter 1, a significant literature has
recently addressed the impact of inflation on the adjustment
of the labor market. I use the annualized inflation rate
computed from the consumer price index to measure inflation.
To examine the effects of expected and unexpected inflation

separately, I use an ARIMA (1,1,1) process to predict the

 

”The prime-age male unemployment is computed for males 25
to 54 years old.

49
inflation rate and residuals from the process become

unanticipated inflation.11

Results

Tables 3.1 and 3.2 report OLS results for one-digit and
two-digit SIC industries, respectively. Although the error-
term implied by the differenced equation is a MA(1) process
with a unit root, tests for such a process reject that
conclusion.12 Hence, only OLS results are reported here.

All the regressions in Table 3.1 show a positive,
statistically significant relationship between the
unemployment rate and the dispersion of wages across one-
digit industries. This result concurs with the findings in
the literature discussed in chapter 1. The dispersion of
wages increases as the unemployment rate rises; this means

that a decrease in aggregate demand increases dispersion.

 

11An ARIMA (1,1,1) model was the simplest of several models
that were used to predict the inflation, the results of less
parsimonious models yielded substantially the same results.

12The test is described by Plosser and Schwert (1977). This
result described here is not surprising. Many economic
variables exhibit the time-series property of a unit root.
The regressions would only have an non-invertible MA(1)
process under classical assumptions about the error term.
The fact that the MA(1) parameter is not different than zero
after differencing suggests that the dependent variable is
difference stationary-~that is, the variance in the natural
logarithm of interindustry wages contains a unit root.
Augmented Dickey-Fuller tests for stationarity support that
conclusion. The implication of nonstationarity is that
interindustry dispersion is subject to shocks that persist
over time--technological innovation, perhaps.

50
The standard neoclassical view of the labor market would
either predict no relationship or an increase in dispersion
over the cycle. So as most writers have noted, the results
do not appear to concur with the standard view of labor
market adjustment. Even after controlling for other factors
that potentially affect dispersion, the relationship is
still positive and significant.

It is worth noting the effects of inflation in these
results. Unlike the literature that finds significant
effects of inflation, Table 3.1 does not show any
statistically significant relationship between inflation and
wage dispersion. When inflation is decomposed into expected
and unexpected components, there is still no significant
relationship between dispersion and either component, as
Montgomery and Stockton (1987) find in their analysis.

Other controls included in columns 2-4 of Table 3.1 are
the demographic controls. These variables do appear to
exert a significant influence on dispersion. In columns 2
and 4, the youth measure (the percent of those working who
are 16-19 years old) and the nonwhite variable (the percent
of those working who are nonwhite) reduce the dispersion of
wages. The results support Okun (1973) who argues that
"secondary" workers move into the low-wage industries to

replace adult males who are upgraded to high-wage

51
industries.” He argues that low-wage industries are more
flexible with respect to wages, so the increase in wages in
these industries is necessary to attract these marginal
workers. Unfortunately, the method of labor market
adjustment is not clear from these results, even though
Okun's and Wachter's analyses both predict the cyclical
observed in these regressions. There are differences in
their views that cannot be sorted out for the results
presented in Tables 3.1 and 3.2. That issue will be
addressed later in this chapter.”

Table 3.2 provides results for two-digit manufacturing
industries. In these results, I cannot find any statistical
relationship between the unemployment rate and wage
dispersion. The result is robust to all specifications
attempted. This outcome stands in contrast to the
literature reviewed in Chapter 1. While Wachter (1970) and
Montgomery and Stockton (1987) show a positive,
statistically significant relationship between the
unemployment rate and wage dispersion in two-digit
manufacturing, I am unable to find such a result. The

finding is closer in spirit to Montgomery and Stockton's

 

13Okun refers to women, youth, and minority workers as
secondary workers since they are the major participants in
the "secondary labor market."

1“Note that the demographic variables are transformed with
the rest of the model. Therefore, they are also squared and
differenced. I am assuming that the coefficient is constant
over time, so the discussion proceeds in terms of levels of
the variables instead of changes in the variables.

52
since the effect they find is very small, though

significant.

53
Table 3.1 One-Digit Industries

Dependent Variable:

Changes in the variance of

log wages1

 

 

l 2 3 4

Time 1964.02 1964.02 1977.02 1964.02
Period 1987.06 1987.06 1987.06 1987.06
Changes in the square of
Unemployment 2.11 1.88 1.50 1.88
rate (3.60) (3.19) (2.20) (3.15)
inflation rate - -0.00 -0.06 -

(-0.03) (-1.62)
expected - - - 0.03
inflation rate (0.26)
unexpected - - - 0.01
inflation rate (0.36)
net exports - - -0.00 -

(-0.85)

% 16-19 - -2.16 -1.07 -2.18
years old (-2.94) (-0.80) (-2.95)
8 female - 0.12 —0.13 0.13

(0.82) (-0.53) (0.82)
% nonwhite - -2.14 -0.87 -2.15

(-2.76) (-0.82) (-2.77)
8 voluntarily - -0.34 0.03 -0.35
part time (-1.50) (0.83) {-1.51)
adj R2 0.04 0.08 0.03 0.08
D.W. 2.06 2.00 1.82 2.00
F-statistic - 6.09 1.67 5.24

 

(t-statistics in parentheses.)
1Multiplied by 108.

54

Table 3.2 Two-digit Manufacturing Industries

Dependent Variable:

Changes in the variance

of log wages1

 

 

1 2 3 4

Time 1956.02 1956.02 1956.02 1977.02
Period 1987.08 1987.08 1987.08 1987.08
Changes in the square of
Unemployment -2.31 -10.18 -0.00 16.56
rate (-0.12) (-0.51) (-0.00) (0.60)
inflation rate - -1.09 -1.08 -0.12

(—1.51) (-1.51) (-0.90)
overtime hours - - 129.04 119.14
in mfg (2.71) (1.45)
net exports - - - -0.00
% 16 - 19 - -14.47 -14.95 2.02
years old (-0.55) (-0.57) (0.04)
% female - 7.57 6.68 1.59

(1.44) (1.28) (0.17)
% nonwhite - 22.07 23.50 4.70

(0.87) (0.93) (0.11)
% voluntarily - -8.44 -11.31 17.14
part time (-1.05) (-1.41) (0.43)
adj R2 -0.003 -0.001 0.016 -0.01
D.W. 2.16 2.15 2.18 2.31

 

(t-statistics in parentheses.)
‘Multiplied by 10“.

55
Table 3.2 (continued)

Dependent Variable: Changes in the variance of log wages1

 

5 6
Time 1956.02 1977.02
Period 1987.08 1987.08

 

Changes in the square of

Unemployment 1.38 15.80
rate (0.07) (0.56)
expected -0.17 8.15
inflation rate (-0.24) (1.37)
unexpected -1.28 2.63
inflation rate (-1.20) (-0.39)
overtime hours 129.05 125.81
in mfg (2.69) (1.55)
net exports - -0.00
(-1.53)

% 16-19 -16.46 -11.45
years old (-0.63) (0.06)
8 female 6.79 2.55
(1.29) (0.27)

% nonwhite 20.09 -4.10
(0.79) (-0.10)

% voluntarily -11.36 3.44
part time (-1.41) (0.21)
adj R2 0.01 -0.01
D.W. 2.17 2.31
F-statistic 1.65 0.96

 

(t-statistics in parentheses.)
1Multiplied by 106.

56

This finding is not a complete surprise. If the
interindustry wage structure is somewhat rigid (as suggested
by the literature reviewed in Chapter 1), it is not
surprising to find that manufacturing dispersion is not much
affected by changes in aggregate demand. A rigid wage
structure implies quantity rather than price adjustment. If
quantity adjustment is the correct description of labor
market adjustment, the reallocation of labor will not be
limited to movements within manufacturing. Since the range
of industries is more narrow, significant quantity
adjustment may occur without reallocating within the
manufacturing sector itself. Workers who lose their job
during a recession either leave the work force, go to
another manufacturing job, or move to a nonmanufacturing
job. Since the scope for choice is greater when the focus
on industries is more limited, it is not surprising to find
little evidence of cyclicality in the two-digit
manufacturing sector.

Conversely, the positive relationship between the
unemployment rate and one-digit dispersion may be accounted
for by the fact that all industries are accounted for (save
agriculture). Whether quantity allocation, price
allocation, or a combination is correct in describing market
adjustment, the relationship is more likely to be observed
in the broader context. While aggregate data are not

sufficient to examine this behavior, below I present

57

comparisons of industry wage and employment responses to the
cycle in order to examine the validity of this argument.

Several writers have speculated that the OPEC oil
embargo of the mid-1970's induced a structural change in the
economy. This explanation is a possible source of the
increased dispersion of the 1970's and 1980's, although
dispersion began increasing as early as 1970. In order to
examine the potential impact of the shift on the
unemployment/dispersion relationship, I split the sample at
the peak of the business cycle nearest the embargo, November
1973. Table 3.3 presents the results of this analysis
before and after 1973.11 for one-digit industries. Before
November, 1973, the effect of the business cycle was
somewhat larger than after, though both are statistically
significant at the conventional level.15 The controls for
labor quality also have more impact before 1973, with the
youth and nonwhite variables showing statistical
significance. However, a test for structural change at
1973.11 rejects the hypothesis at the 5 percent level. So
for one-digit industries, the relationship does not appear

to have been significantly affected by the embargo.

 

15The difference between the means is statistically
significant at the 5 percent level.

58

Table 3.3 One-Digit Industries

Dependent Variable:

Changes in the variance of

log wages1

 

 

1 2 3 4

Time 1964.02 1973.12 1964.02 1973.12
Period 1973.11 1987.06 1973.11 1987.06
Changes in the square of
Unemployment 5.42 1.78 5.32 1.85
rate (2.23) (2.88) (2.19) (2.99)
inflation rate 0.01 -0.03 - -

(OeSO) (‘0e93)
expected - - -0.00 0.01
inflation rate (-0.13) (0.37)
unexpected - - 0.04 -0.07
inflation rate (1.16) (-0.89)
% 16 - 19 —3.10 -0.53 -3.08 -0.48
years old (-3.31) (-0.44) (-3.30) (-0.40)
% female 0.33 0.06 0.33 0.05

(1.42) (0.28) (1.41) (0.24)
% HODWhite -3e95 _0e71 -3e87 -0e79

(-3.26) (-0.71) (-3.19) (-0.79)
% voluntarily -0.41 -0.28 -0.43 -0.31
adj R2 0.18 0.04 0.18 0.04
D.W. 2.08 1.87 2.10 1.87
F-statistic 6.08 2.49 5.26 2.06

 

(t-statistics in parentheses.)

1Multiplied by 108.

59

Table 3.4 similar estimates for two-digit manufacturing
industries, with similar conclusions. There is no evidence
of structural change from the OPEC embargo at the two-digit
manufacturing level. There is still no evidence of a
cyclical relationship between aggregate demand and wage
dispersion at this level, in either period.

These results strongly reject cyclicality at the two-
digit level, but it is worth asking how sensitive dispersion
is at the one-digit level to changes in the unemployment
rate. To gain some insight into the economic significance
of the relationship, I have calculated the elasticities of
the dispersion measure with respect to the unemployment rate
for one-digit industries.

Although these results cannot be directly compared to
the results surveyed in Chapter 1, one may gain some insight
as to the sensitivity implied by these results versus the
results of previous writers. Table 3.5 presents the
elasticities for each regression estimated in Tables 3.1 and
3.3, evaluated at the means of the variables. These
elasticities range from 0.07 to 0.11, numbers that are far
smaller than Wachter found for two-digit manufacturing --
0.25. I have not computed the elasticities at the two-digit
level because the coefficients are not statistically

significant.

60

Table 3.4 Two-digit Manufacturing Industries

Dependent Variable:

Changes in the variance of log wages1

 

 

1 2 3 4

Time 1956.02 1973.11 1956.02 1973.12
Period 1973.11 1987.08 1973.11 1987.08
Changes in the square of
Unemployment -41.60 21.73 -40.63 23.20
rate (-1.23) (0.84) (-1.l9) (0.90)
inflation rate -1.17 -0.96 - -

(-1.30) (-0.78)
expected - - 0.19 -0.61
inflation rate (0.21) (-0.49)
unexpected - - -1.13 -2.19
inflation rate (-0.98) (-0.73)
overtime hours 153.70 105.40 156.37 107.27
in mfg (2.04) (1.62) (2.06) (1.64)
% 16 - 19 —23.53 -12.24 -25.33 -10.09
years old (-0.73) (-0.25) (-0.78) (-0.21)
8 female 12.15 0.25 11.83 0.69

(1.71) (0.03) (1.67) (0.08)
% nonwhite 29.82 9.96 27.59 5.51

(0.90) (0.25) (0.83) (0.14)
% voluntarily -23.15 0.68 -22.69 0.03
adj R2 0.03 -0.02 0.03 -0.02
D.W. 2.12 2.21 2.12 2.21
F-statistic 2.26 0.53 1.82 0.50

 

(t-statistics in parentheses.)
1Multiplied by 106.

61

Table 3.5 Cyclical Responsiveness of Wage Dispersion

 

 

Column1
1 2 3 4
Table 3.1 0.08 0.07 0.08 0.07
Table 3.3 0.07 0.10 0.07 0.11

 

1This table presents elasticities of the variance of
interindustry wages with respect to the unemployment rate
for columns 1-4 of tables 3.1 and 3.3. The elasticities are
evaluated at the mean of the variables in each equation. No
calculations are done for two-digit industries because the
coefficient is not statistically different from zero in any
specification.

 

Sensitivity to Omitted Variables

Even though I have attempted to control for changes in
the skill composition of the workforce over time, there are
no guarantees that the differenced specification or the
employment composition variables will be adequate to do so.
In order to get some idea of the sensitivity of the results
reported in Tables 3.1-3.5, I rely on the model estimated by
Montgomery and Stockton (1987).

These authors estimate a neoclassical model of wage
dispersion where the variance in wit depends on the
dispersion of skill and capital across industries as well as
the covariance of the two. They also include expected
income and its square, dummies for the Korean Conflict and
the Nixon price controls, and a quadratic in time where the

linear term is also interacted with expected income. The

62

dependent variable is the variance of the logarithm of wages
across two-digit manufacturing industries from 1948-1981.16

I estimate a rough replication of their model with
annual data that ranges from 1948 to 1978. Since their
model contains explicit controls for labor quality, by re-
estimating their model in differenced form, I can gain some
insight into the sensitivity of my previous estimates to
omitted labor quality.17 These estimates are contained in

Table 3.6.

 

16Since I use monthly data to estimate my model, the
Montgomery and Stockton estimates might be more appropriate
since capital in the short run is generally considered
fixed. Monthly data for capital in these industries is not
available, however. The following empirical exercise is an
attempt to determine the implications of omitting these
variables.

17The estimates do not duplicate their results completely.
The estimates in table 6 do not include the dummy variables
they use for the Korean Conflict and for the Nixon price
controls. And while I use the same technique to construct
the skill index described in appendix A to their paper, my
data are taken from the 1976 May CPS tape. Instead of
tenure, I must use potential experience in my construction
of the variable. And while Montgomery and Stockton report
their results in capital intensive form, I use the variance
of the capital stock and its covariance with the skill
index. I was generally successful in replicating the sign
and order of magnitude of their estimates when I estimated
their model in levels, although I was not successful in
every specification they report.

63
Table 3.6 Two-digit Manufacturing Industries

Dependent Variable: Changes in the variance of log wages

 

Annual data

 

1949 - 1978 1 2 3 4
Constant - 0.00 - 0.01
(1.74) (2.49)
variance in 0.17 -0.12 0.11 -0.19
skill (0.55) (-0.34) (0.35) (-0.64)
variance in 0.00 -0.00 -0.00 -0.00
capital (0.55) (-0.05) (-l.23) (-0.66)
covariance of 0.00 0.00 -0.00 -0.00
skill & capital (0.29) (0.09) (-0.17) (-0.51)
unemployment 0.00 0.00 0.00 0.00
rate (0.51) (0.55) (0.52) (1.36)
inflation -0.00 -0.00 -0.00 -0.00
rate (-2.28) (-1.91) (-1.59) (-2.80)
expected income - - -0.00 -0.00
(-0.82) (-2.64)
square of - - 8.6E-08 2.5E-07
expected income (2.05) (3.27)
adj R2 -0.04 0.04 0.21 0.35
D.W. 1.24 1.08 1.46 2.01
F-statistic 0.73 1.24 2.25 3.25

 

(t-statistics in parentheses.)

64

In differenced form the estimates are sensitive to
specification, but in no case is the variance of skill or
its covariance with capital statistically significant. For
all the regressions in the table, F-tests cannot reject the
null hypothesis that differences in the variance of skill,
capital, and the covariance of skill have no effect. From
this evidence, it seems reasonable to conclude that there is
no serious damage done in Tables 3.1-5 by omitting the skill
indexes. The differenced form seems to adequately handle
the problem. Like the monthly two-digit results presented
in Tables 3.2 and 3.4, the unemployment rate does not have a
significant impact. In contrast to those results, however,
the constant term is significant.” And other variables
that Montgomery and Stockton include seem to account for
much of the variation. In particular, expected income and
its square are important determinants in these results.
Note that unlike the Montgomery and Stockton results or the
results presented in Tables 3.1-3.4, the inflation rate
causes a statistically significant reduction in dispersion;
this result is similar to those of Hamermesh (1986) and

other writers discussed in Chapter 1.

 

18The MA(1) process with a unit root is still rejected in
this specification.

65
The Adjustment of the Labor Market

The results presented above provide evidence consistent
with a few possible explanations of labor market adjustment
to the cycle. Is the positive correlation between
unemployment and one-digit dispersion solid evidence of the
Wachter version of dual labor markets, one high-wage and
inflexible and another low-wage and flexible? Or is the
result more consistent with a rigid interindustry wage
structure which relies almost exclusively on quantity
adjustment? And would the two-digit result imply a rigid
manufacturing wage structure, or is it in line with rapid
market adjustment in the neoclassical framework? The only
way to gain more conclusive evidence is to examine the
impact of the cycle on an industry-by-industry basis.

In order to estimate the impact of aggregate demand on
the industry wage rate, I estimate the reduced form industry

wage equation, Equation 2.6, from chapter 2:
wit: = Co+Cipc+C2Pt

where c0 and c1 are parameters to be estimated, and c2 is
restricted to 1. The cyclical measure is again the prime-
age male unemployment rate, and wit is the natural logarithm
of the nominal wage for the industry. This equation is
first differenced to induce stationary and reduce spurious
correlation by regressing trending variables on one another.

Also, omitted variable bias is reduced since the correlation

66

of first differences is usually less than of levels of the
variables. I have, however, included the first differences
of the demographic variables to control for changing labor
force composition since it is not likely that labor is
homogeneous and unchanging over the cycle. I have also
included the inflation rate to see if the rate of price
increase has an effect at the level of the individual
industry. The results are presented in Tables 3.7 and 3.8.

While the magnitudes are small, several industries at
both the one- and two-digit level exhibit some cyclical
sensitivity.” A comparison of these industry results with
the dispersion estimates suggests that industry responses at
the one-digit level vary enough to account for some of the
observed relationship between dispersion and the
unemployment rate. At the two-digit level, however,
sensitivity is small and relatively homogeneous across
industries, accounting for no observed relationship between

wage dispersion and the unemployment rate.

 

19See Tables 3.7 and 3.8.

67
Table 3.7 Real Wage Estimates, One-Digit
1964.02--1987.06

natural logarithm of the industry
wage rate1

Sample:
Dependent Variable:

 

 

Industry Unemployment? Inf lation2 Adj . R2

Mining 0.0029 -0.0002 0.021
(0.77) (0.93)

Construction 0.0002 -0.0004 0.026
(0.07) (2.26)

Manufacturing -0.0027 -0.0004 0.087
(1.61) (5.02)

Transportation -0.0039 -0.0004 0.037
(2.02) (3.74)

Wholesale Trade -0.0045 -0.0004 0.097
(2.83) (5.23)

Retail Trade -0.0039 -0.0003 0.021
(1.75) (2 - 53)

Finance -0.0049 -0.0003 0.028
(2.17) (3.12)

Service -0.0033 -0.0004 0.050
(1.61) (4.16)

1Control variables are not shown. They are

(1) percent of the workforce 16 to 19 years old,

(2) percent of the workforce that is nonwhite,

(3) percent of the workforce that is female, and

(4) percent of the workforce employed part-time. The
absolute value of t-statistics are show in parentheses.

ZAll variables are first differenced.

68
Table 3.8 Real Wage Estimates, Two-Digit
Sample: l956.02--1987.08

Dependent Variable: natural logarithm of the industry
wage rate1

 

Industry Unemployment2 I nf lation" Adj . R2
Food -0.0006 -0.0004 0.040
(0.38) (3.97)
Tobacco 0.0028 -0.0010 0.004
(0.35) (2.28)
Textiles -0.0029 -0.0004 0.036
(1 . 65) (3 . 90)
Apparel -0.0046 0.0000 0.004
(2.43) (0.03)
Lumber and -0.0033 -0.0001 -0.001
Wood (1.43) (1.04)
Furniture and -0.0043 -0.0001 0.018
Fixtures (2.98) (1.52)
Paper and -0.0014 -0.0004 0.073
Allied Products (1.03) (5.61)
Print and -0.0028 -0.0004 0.077
Publishing (2.30) (5.80)
Chemical and -0.0001 -0.0003 0.059
Allied (0.08) (4.33)
Petroleum and -0.0024 -0.0004 0.022
Coal (0.90) (2.72)
Rubber and -0.0014 -0.0004 0.011
Misc. Plastics (0.63) (3.07)
Leather -0.0035 -0.0001 0.003
(2.22) (0.96)
Stone, Clay, -0.0032 -0.0003 0.050
and Glass (2.53) (4.02)

Table 3.8 (continued)

 

 

Industry Unemployment2 Inflation? .Adj. R2
Primary Metal -0.0078 -0.0005 0.081
(3.61) (4.20)
Fabricated -0.0041 -0.0003 0.040
Metal (2.66) (3.85)
Machinery (except -0.0037 -0.0004 0.068
electric) (2.84) (5.09)
Electric Equip. -0.0014 -0.0003 0.043
(1.06) (4.49)
Transportation -0.0053 -0.0003 0.012
Equip. (2.14) (2.54)
Instruments -0.0026 -0.0004 0.090
(2.09) (6.09)
Misc. Mfg. -0.0037 -0.0003 0.042
(2.38) (4.02)
1Control variables are not shown. They are

(1) percent of the workforce 16 to 19 years old,

(2) percent of the workforce that is nonwhite,

(3) percent of the workforce that is female, and

(4) percent of the workforce employed part-time. The
absolute value of t-statistics are show in parentheses.

2All variables are first differenced.

70

While the real wage estimates provide some support for
wage flexibility in response to cyclical activity, the
responses are quite small. They do not rule out the rigid
wage structure hypothesis since many of the industries show
no responsiveness to the cycle.

To examine this further, I estimated the reduced form
Equation 2.6, solved for employment instead of wages.
Tables 3.9 and 3.10 contain these results for one-digit and
two-digit manufacturing industries respectively, where the
natural logarithm of industry employment is the dependent
variable in each equation. The results are quite
interesting. All the industry employment regressions show a
negative elasticity with respect to the unemployment rate.20
The elasticities vary widely, ranging between 0 and -0.15
for two-digit manufacturing industries. For one-digit
industries, the range is narrower, 0 to -0.06. This result
also argues against the Wachter hypothesis in favor of the
fixed industry wage structure. A cyclical shock seems to

cause quantity adjustments with little movement in prices.

 

20There may be endogeneity in using the prime-age male
unemployment rate as the measure of the cycle since the
measure should be correlated to some degree with the error
term of each equation. However, the problem is less serious
than it first appears since each industry alone does not
have an overwhelming impact on the on the unemployment rate.
Two stage least squares and OLS estimates generally yielded
similar results although_the TSLS elasticities were not
different from zero in some cases. Generally, signs and
magnitudes did not change; hence, only OLS results are
reported.

71

In fact these results show that one-digit high-wage
industries have no less wage flexibility than low-wage
industries, contrary to the dual labor market view. Table
3.9 shows the nominal one-digit wage rate as of June 1987,
the estimated employment elasticity with respect to the
unemployment rate, and the estimated wage elasticity with
respect to the unemployment rate. The correlation between
the nominal wage and the real wage elasticity is 0.61.21
The positive correlation indicates that high-wage industries
exhibit more wage responsiveness over the cycle. Since the
estimates of the wage elasticity are not precise (e.g., many
of the estimated coefficients were not statistically
different than zero), the correlation of the two may not be
such a good measure. The rank correlation might be more
useful since the numbers themselves are subject to question.
The rank correlation does not alter the picture--it is 0.57,
but the relationship is not statistically significant.
Hence, there seems to be no discernable relationship between
high-wage industries and wage flexibility.

For two-digit manufacturing industries the numbers
(shown in Table 3.10) are lower but still positive. The

correlation coefficient is 0.29 and the rank correlation is

 

21When the correlation is weighted by industry employment,
the correlation is 0.5.

72

0.26, and neither of these numbers are statistically
different than zero.22

For one-digit industries, the correlation between wages
and employment elasticities is negative and not
statistically significant. The same is true for the two-
digit results until the sample is weighted by employment.
The weighted correlation between industry wages and the
employment elasticity is -0.51 and is statistically

different than zero.

Table 3.9 Wage and Employment Flexibility, One-Digit

 

Employment Wage
Industry Wage Elasticity Elasticity
Mining 12.44 -0.005 0.011
Construction 12.61 -0.058 0.001
Manufacturing 9.45 -0.058 -0.001
Transportation 11.91 -0.028 -0.016
Wholesale 9.57 -0.012 -0.019
Retail 6.08 -0.021 -0.016
Finance 8.68 -0.006 -0.020
Service 8.35 -0.008 -0.014

 

The wage rate is the nominal average wage for each
industry as of June, 1987. The employment
elasticity is the elasticity of industry employment
with respect to the unemployment rate. The wage
elasticity is the elasticity of the real industry
wage with respect to the unemployment rate.

 

 

"When weighted by employment, the sign reverses, and the
correlation is -0.09. It is still not statistically
different that zero, however.

Table 3.10 Wage

73

and Employment Flexibility, Two-Digit

 

Employment Wage
Wage Elasticity Elasticity

Food 8.91 -0.013 -0.002
Tobacco 15.57 -0.001 0.011
Textiles 7.15 -0.042 -0.011
Apparel 5.91 -0.038 -0.019
Lumber 8.44 -0.070 -0.014
Furniture 7.66 -0.034 -0.018
Paper 11.41 -0.027 -0.006
Printing 10.19 -0.014 -0.011
Chemicals 12.27 -0.027 -0.001
Petroleum 14.43 -0.055 -0.010
Rubber 8.87 -0.065 -0.006
Leather 6.04 -0.044 -0.014
Stone 10.29 -0.063 —0.013
Primary Metal 11.97 -0.113 -0.032
Fabricated 10.00 -0.091 -0.017
Machinery 10.76 -0.058 -0.015
Electric Equip. 9.84 -0.082 0.006
Transportation 12.88 ~0.159 -0.022
Instruments 9.70 -0.048 -0.011
Miscellaneous 7.74 -0.040 -0.015

 

The wage rate is the nominal average wage for each

industry as of June 1987.

The employment

elasticity is the elasticity of employment with

respect to the unemployment rate.

The wage

elasticity is the elasticity of the real industry
wage with respect to the unemployment rate.

 

74

Wage Rigiditv and Symmetry over the Cvcle

In Chapter 2, I discussed the implications of assuming
that the labor market clears in every period. If
unemployment is not correctly viewed as voluntary, the
assumption clearly leads to a misspecified model. If the
Keynesian description of wage adjustment is correct, the

dispersion of wage would be described by Equation 2.10:

of,” = to+tlDt2+1$20§~it if (l—L)Dt 2 0

_ 2 2 - _
- °"1,c-1+t2°-91c If (1 L)Dt < 0.

Dispersion would behave asymmetrically over the cycle if
industry wage rates were downwardly rigid.

To test the proposition, I estimated this model. This
equation is simply a switching regression with a known
switching point. To test for asymmetry, I included a dummy
variable equal to one when the unemployment rate rises
(corresponding to (1-L)Dt'< 0 ) and interacted the dummy
with the unemployment measure. The test for asymmetry was

an F-test of the joint significance of the two variables--or

75
a t-test of the statistical significance of the interaction
term.23

F-tests (or the t-tests) could not reject the null
hypothesis of symmetry over the cycle. Neither model
demonstrated different behavior during booms and recessions.
It is possible, however, that this test is too crude to pick
up asymmetry even if it exists. If industry cyclical
responses differ, it is possible that each industry
demonstrates asymmetric behavior that is masked by looking
at dispersion alone. Hence, I performed the same test for
each industry individually.

One-digit industries do not behave asymmetrically, with
the exception of manufacturing. Nominal manufacturing wage
estimates reject the null hypothesis of symmetry, but real
wages do not--even for manufacturing. The Keynesian model
is rejected at this level.

Two-digit manufacturing industries demonstrate more
variety that the one-digit industries. The null hypothesis
of symmetry over the cycle (that is, that the dummy and
interaction are not significantly different from zero) is

rejected in four of the twenty manufacturing industries for

 

“Joint significance of the dummy and the interaction term
would imply that the mean dispersion changes during a
downturn and the impact of the cycle is different when
unemployment is rising and falling. The t-test for the
significance of the interaction term examines the
differential response to the unemployment rate alone.

76
both nominal and real wages.“ In this instance, some
disequilibrium behavior is masked by considering the

interindustry variance without examining the components.

Conclusion

This chapter provides time-series estimates of the
effect of the business cycle on wage dispersion across one-
digit SIC and two-digit SIC manufacturing industries, where
the cyclical measure is the prime-age male unemployment
rate. At the two-digit level I could find no evidence of a
cyclical relationship, unlike previous research. Since
differencing removes much of the variation, this approach is
rather conservative but avoids spurious results from
regressing unrelated trending variables on one another.
One-digit industries show a significant increase in
dispersion when aggregate demand declines, though the
elasticity with respect to the unemployment rate (evaluated
at the mean) is rather small. The source of the cyclical
effect appears to be changes in the relative employment
weights rather than wage flexibility.

Other controls exert some influence. The demographic
variables are at times significant, supporting Okun's

cyclical upgrading hypothesis. The monthly time-series did

 

“Those four industries are food and kindred products,
electrical equipment, instruments and related products, and
miscellaneous manufacturing.

77
not show an inflationary effect, but the replication of
Montgomery and Stockton's work does show a decrease in
dispersion due to inflation. These replicated results from
annual data are much more sensitive to specification than
the monthly data.

The use of the differenced model in this work is a
specific attempt to eliminate the effects of omitted
variables: there are no good labor quality controls, and
labor quality is almost certain to vary over the cycle.
These results are conditional on the assumption of the
stationarity of the human capital variables. This
hypothesis is not testable, and to a degree, limits the
confidence one can place in these results. Chapter 4 will
attempt to address this shortcoming.

In examining the dynamics of labor market adjustment,
these results seem to suggest a rather fixed wage structure
that, at least in the short run, relies on quantity
reallocation across industries over the cycle rather than
wage adjustment to allocate labor flows. One cannot tell
from these results if one-digit dispersion shows some
cyclical sensitivity due to a reweighting of the industries
over the cycle as industries change relative sizes or a
change in the quality of the labor force due to the cycle.
Even though the differenced estimation was chosen to
alleviate that difficulty, the assumptions required are

stringent and nontestable. In order to explore this issue

78
further, Chapter 4 presents results from cross-section data

from various years of the May Current Population Survey.

CHAPTER 4

A Cross—Sectional Analysis of Wage Dispersion

Introduction

Unfortunately, time-series data on the dispersion of
interindustry wages can provide only limited information
about wage dispersion over the business cycle. Even if the
problems noted earlier did not exist, these data could only
provide information about dispersion across industries.

That information is important, but economists also have
broader interests that should be addressed: For example,
how does economic opportunity vary over the cycle for males
versus females or whites versus nonwhites? Time-series data
to perform such analyses are not available, but cross-
sectional data may be used for such purposes. Large data
sets provide a large number of observations on earnings,
hours, and wages for individuals along with more appropriate
controls for human capital characteristics. While problems
are present in these data also, such information makes
possible a different research strategy to analyze some of
the relevant issues.

The chief advantage granted by these large data sets is

the availability of detailed human capital controls. The

79

80
time-series work in chapter 3 relies on stationarity to
difference away human capital variables. Unfortunately,
economic data are rarely stationary without detrending or
differencing, so the assumption is difficult to accept. And
since the information is not available at the industry
level, the hypothesis is not directly testable. Other work,
such as Montgomery and Stockton (1987), has used labor
quality controls developed by Gollop and Jorgenson (1983) to
control for differences in human capital. As Heckman and
Sedlacek (1985) point out, however, Gollop and Jorgenson
develop their measure with the assumption that labor within
a particular demographic group or industry is relatively
homogeneous. That assumption is probably not a good one, as
the Heckman-Sedlacek results indicate. Consequently, little
work has been done that adequately controls for human
capital differences.

To provide such an analysis requires a disaggregated
look at dispersion. This chapter presents estimates from
cross-section data to conduct such an analysis. The May
Current Population Surveys (CPS) for selected years provide
information on race, sex, industry, wages, earnings, and
hours worked along with other information to control for
differences in individual earnings. The chosen years
roughly correspond to peaks and troughs in the business
cycle. By examining dispersion at peaks versus troughs over

relatively short periods of time, this cross-sectional

81
analysis will provide further insight into the changes in

dispersion caused by the business cycle.1

Research Strategy

To examine the dispersion of wages while accounting for
human capital characteristics, I will attempt to decompose
the source of the variance. A standard technique for such a
decomposition can be found in Freeman (1980). Freeman uses
the technique to decompose the variance in the natural
logarithm of wages into explained and unexplained variation
to examine the effects of unions on the dispersion of wages.
This analysis will use that variance decomposition in order
to examine the cyclical dispersion of wages.

Suppose that wages are represented by the following

equation:

(4'1) ln(w)5 : pas+zipisxis+es

Let s = 1,2 represent two possible states of the world, the

trough of a recession or the peak of a business cycle. 80

 

1Blank (1989, 1990) uses micro data from the Panel Survey of
Income Dynamics (PSID) to decompose the distribution of
income and examine the cyclical responsiveness of each. She
also uses these data to examine the effect of changes in GNP
on the wage rate. She regresses the measures of interest,
constructed from the micro data, on the percentage change in
GNP to compute an elasticity. The focus in this research is
to decompose the variance of log wages into the variances
and covariances of worker characteristics, the estimated
coefficients corresponding to those characteristics, and the
residual variance in order to determine the routes by which
the business cycle affects dispersion.

82
is a constant term and x., i= 1,...,n are human capital
variables included in the earnings function to control for
individual differences in earning potential. 6 is the error
term, which is lognormally distributed. As shown earlier,

the variance of the natural log of the wage rate is
(4-2) OInUv) = 02+21910§i+21ojpipj°x1xj I

where 02 is the variance of the error term, 0%“ is the
variance of the human capital characteristic 1, and oXixj is
the covariance of any two human capital characteristics 1
and j, given a state of the world.

Freeman provides a decomposition for this framework
which he uses in his analysis of the effect of unions on
dispersion. This decomposition allows changes in the
dependent variable to be broken into differences in
characteristics, differences in returns to characteristics,
and differences in the unexplained variation in the
equation. For the present analysis, differences in
variation resulting from differences in the covariances of

human capital characteristics may be represented as follows:
2 2 2
(4 ° 3) 2191 ”Kama-1,1) +212jpipj (°x..x.,’°X.-.,.X.-.,,) 3

t represents the current turning point of the business cycle
and t-l represents the previous turning point. This

expression is the sum of the differences in the variances of
the human capital characteristics at the peak and the trough

of the cycle (or vice versa), weighted by the estimated

83
coefficients of the earnings equation. There is no a priori
reason to choose either the peak or the trough estimates to
use as weights for the variances and covariances. Since the
estimates are not sensitive to the choice of the base year,
I have performed the calculations using the earliest year in
the comparison of each turning point.

Cyclical differences in the variance may also arise
because the return to human capital characteristics differs
from peak to trough. If returns differ, the portion of the
variance attributable to alternative earnings functions is

given by the following expression:
(4.4) Edna-02.4,.)0143212.-(B..B.,--fl.-1,.-B._1,j)0m,:

where the differences in estimated coefficients are weighted
by the appropriate variances and covariances of the
explanatory variables. Again I used the earliest year of
each pairwise comparison since the results are not sensitive
to the base year chosen.

Finally, the residual variance represents the variance
in the natural log of the wage rate controlling for the
human capital characteristics included in the earnings
regression. If the variables determine the wage rate, one
could then attribute these differences in the residual
variance to the business cycle. This residual dispersion is
given by the square of the estimated standard error of the

regression.

84

These quantities, taken together, may provide useful
information about the cyclicality of wage dispersion in
addition to the time-series estimates obtained in Chapter 3.
Expression 4.3 gives the portion of dispersion accounted for
by changes in the variance and covariances of human capital
characteristics. Expression 4.4 gives the portion accounted
for by changes in the regression coefficients—-these may be
interpreted as differences in the returns to individual
characteristics between peaks and troughs of the cycle.
Differences in the residual variance reflect the impact of
the cycle after controlling for individual characteristics
and changes in their returns over the cycle.

Dooley and Gottschalk (1984) used March CPS data to
form a time series which they used to examine the
cyclicality of the variance of the natural logarithm of wage
rates, controlling for education, potential experience,
part-time status, and a time trend. The approach described
above differs from theirs in a number of ways. First, the
derivation above suggests that dispersion is a function of
the variances and covariances of the exogenous variables.
Secondly, the composition of the labor force changes over
the business cycle through layoffs and changes in labor
force participation. In the Dooley and Gottschalk paper,
this is picked up by the coefficient measuring the impact of
the unemployment rate on dispersion, controlling for the
human capital variables. The decomposition above, however,

allows one to see the effects of the cycle on dispersion by

85
breaking the effects into their component parts. Not only
can the variances and covariances changes over the peak and

trough of the cycle, so can the regression coefficients.2

The Data

As noted earlier, the May CPS tapes contain information
that is useful in analyzing the dispersion of wages over the
business cycle. My strategy here is to choose the surveys
conducted near the peaks and troughs of the most recent
complete business cycles in order to form the decomposition
described above.

My goal is to choose CPS cross sections to match
economic peaks and troughs. I selected 1974, 1975, 1980,
and 1983. The 1974 survey reflects the peak of 1973.1V, and
the 1975 tape corresponds to the 1975.1 trough. The 1980
tape corresponds to the 1979.1V peak, and 1983 reflects the
1982.IV trough.3 ‘Unfortunately, the May surveys cannot
correspond to the cyclical turning points precisely, so I
have attempted to select the surveys as judiciously as
possible to reflect the cycle and improve the accuracy of
the analysis. The most difficult choice is for the short

recession of 1980. After the credit controls imposed by the

 

2Note that Dooley and Gottschalk allow the coefficient of
experience to vary over time, but the other coefficients are
restricted to remain constant.

3The business cycles are defined by the National Bureau for
Economic Research.

86
Federal Reserve in 1979, the economy experienced a short,
dramatic slowdown. From the peak in 1979.IV, the slide
lasted only until 1980.11 with the next peak happening in
1981.II. Since some of the survey questions for wages,
hours, and earnings are retrospective, I have chosen the
tapes for the year following the turning point; and I have
ignored the minirecession of 1980, focusing on the turning
points in 1979 and 1982. I also included data from the 1985
May CPS, which is two years into the expansion following the
1982 trough.

The sample I use for this analysis includes all private
and government workers in the sample, excluding all self-
employed, private household, and agriculturally employed
workers. I also eliminated those workers who did not report
weekly hours and earnings. The data set includes
individuals who report both usual weekly earnings and hours
in order to compute of a wage rate for that person. The
wage attributed to each individual in this set is simply
their usual weekly earnings divided by usual weekly hours.4

In order to estimate the wage equations for the

decomposition described above, I need information on the

 

‘The May CPS includes reported wage rates for individuals
paid on an hourly basis. To restrict estimation to this
group limits the sample size available, and the sample
cannot be considered random since these workers are likely
to differ considerably from the sample at large. I did
estimate the wage equations using the reported wage for
hourly workers and the calculated wage for the rest of the
sample. The results differed little; the results reported
here are those using only the calculated wage for the entire
sample.

87
schooling and work experience of each person in the sample.
The CPS contains each individual's age and schooling, but
actual work experience is not contained in the survey.
Hence, I compute potential experience for each person by
subtracting 6 and the number of years in school from the
individual's age. I also calculate the square of experience
in order to estimate the quadratic form of the earnings

function.

Results

The results of the decomposition are given in Tables
4.1 and 4.2. Table 4.1 gives the decomposition for
estimates based on the full sample in each of the years
corresponding to peaks and troughs of the business cycle.
In this analysis, the decomposition is based on a wage
equation that regresses the natural logarithm of the real
wage rate (deflated by the CPI) on years of schooling,
experience, experience squared, dummies for race and sex,
and a group of industry dummy variables for major industry

affiliation as defined in the 1970 Census classification.5

 

5The dummies are included for construction, durable
manufacturing, nondurable manufacturing, railroads, retail
trade, finance, business and repair, personal services
(except household), entertainment and recreation, medical
(except hospitals), hospitals, welfare and religious,
education, other professional services, forestry and
fisheries, and public administration. As stated before,
agriculture, private household workers, and those who have
never worked are eliminated form the sample. The remaining
industries are included in the intercept term. These are

88
Table 4.1 gives the results of the decomposition described
above based on the estimated wage equations in each of the
sample years. These results may be viewed, rather crudely
however, as counterparts to the one-digit time series

results presented in Chapter 3.

 

mining, other transportation, other utilities, and wholesale
trade. The constant includes these industries since mining
was chosen arbitrarily as the base industry for comparison;
the other industry definitions were altered in the 1983 and

1985 CPS, disallowing comparison over the entire 1974-1985
period.

89

Table 4.1 Decomposition, Full Sample

 

 

YEARS1 1974-75 1975-80 1980-83 1983-85
Differencesz

in covariances -0.013 0.011 -0.003 -0.002
(human capital only) (-0.005) (0.003) (-0.001) (-0.001)
Differences3

in coefficients -0.014 -0.000 0.009 0.009
(human capital only) (0.000) (-0.008) (-0.003) (0.006)
Differences

in residual

variance -0.017 -0.014 0.018 0.006
Actual

difference in

variance -0.038 -0.009 0.025 0.015

 

1Differences in covariances and coefficients are weighted by
the earliest year in the calculation, 1974 in the first
column, 1975 in the second, and 1980 in the third. The
decomposition may not add up to the actual difference in the
variance since the decomposition is an approximation. The
remainder may be attributed to rounding error and the
interaction of the differences in the covariances and the
differences in the coefficients.

2Estimates were obtained by computing the following
expression:

2 2 2
21'p1(a"'t1-axt-1.i) +21216i61 (oxcxxcj_axc-1.1xc-1.J)

3Estimates were obtained by computing the following
expression:

21' (Bil-Ping) °§i+212J(Pcipcj‘B t-1,iBt-1,j) "mgrj

90

Table 4.2 Decomposition, Manufacturing

 

 

YEARS1 1974-75 1975-80 1980-83 1983-85
Differences2

in covariances 0.001 0.002 0.002 -0.015
(human capital only) (0.001) (0.002) (0.009) (-0.017)
Differences3

in coefficients 0.005 0.001 0.034 -0.015
(human capital only) (0.004) (-0.001) (0.026) (-0.015)
Differences

in residual

variance -0.007 0.011 0.035 -0.032
Actual

difference in

variance -0.002 0.011 0.080 -0.060

 

1Differences in covariances and coefficients are weighted by
the earliest year in the calculation, 1974 in the first
column, 1975 in the second, and 1980 in the third. The
decomposition may not add up to the actual difference in the
variance since the decomposition is an approximation. The
remainder may be attributed to rounding error and the
interaction of the differences in the covariances and the
differences in the coefficients.

2Estimates were obtained by computing the following
expression:

2 2 2
2191 (oxti—oxt-1,i) +212161p1(axc1xcj—oxc-1,1xc-1.1)

3Estimates were obtained by computing the following
expression:

21(pii—pi-1Ii)o§i+212J(ptiBtj-pt—1,iBt—1,j)oxixj

91

Table 4.2 does a similar analysis for manufacturing
workers in each of the sample years in order to compare
cross-section evidence to the two-digit times-series
results. A similar wage equation is estimated for
manufacturing workers to perform this decomposition; while
the controls include schooling, experience, experience
squared, and race and sex dummies, this equation includes
industry dummies for affiliation with two-digit
manufacturing industries that closely correspond to those
used in the time-series data.6 The decomposition presented
in these tables shows the portion of the change in the
variance between peaks and troughs of the business cycle
that may be attributed to changes in the variance and
covariances of worker characteristics, changes due to
differences in the coefficients of these characteristics in
each year, and changes in the residual variance».7 Changes
in the residual variance may be viewed as the effect of the
business cycle on dispersion, although some caution must be

exercised in doing so.

 

6The industry dummies are lumber, furniture, stone (clay and
glass), primary metals, fabricated metals, machinery,
electrical equipment, automobiles, aircraft, other
transportation, miscellaneous, food, tobacco, textiles,
apparel, paper, printing, chemicals, and petroleum. The
constant includes leather (and not specified manufacturing),
rubber and plastics, instruments, and ordnance.

7Note that this decomposition is only an approximation, so
the three elements may not add up to the total change in the
variance in the natural logarithm of wages. Rounding error
and the interaction of differences in the covariances and
coefficients account for the remainder.

92

Recall that the time-series evidence presented in
Chapter 3 relied on the presumed stationarity of the
characteristics of workers to remove the influence of these
variables from the dispersion equations. The decomposition
presented in Table 4.1 demonstrates the importance of
changes in labor quality over the business cycle. When
examining the change in the variation of the natural
logarithm of wages attributable to changes in worker
characteristics (the first line of Table 4.1), it is clear
that the changing variation in worker characteristics causes
a significant portion of the altered dispersion. This
portion of the change in dispersion accounts for as little
as 13 percent of the total change at times and is actually
larger than the total change in dispersion at other times.
Nor is the direction of the change consistent: only in 1974
to 1975 did the change in the covariances move in the same
direction as the total change in the variance. One cannot
interpret this as the countercyclical adjustment of labor
quality, however, since too few data points exist to examine
the correlation between the cycle and the portion of the
change in dispersion attributable to the covariances of
human capital characteristics. The information does show
that the change is substantial and highlights the potential
bias existing in the time-series estimation presented in
Chapter 3.

From the arguments presented in Chapter 2 and the

evidence of Chapter 3, one would expect that much of the

93

change in dispersion that occurs would result from a
reallocation of workers across industries and not from the
changes in the returns to industry affiliation. As a
consequence, the bulk of the change attributable to the
covariances should come from the variances and covariances
of industry dummies. In order to examine that proposition,
I have shown the portion of the change in characteristic
covariances due to non-industry factors, the human capital
characteristics. These numbers are given in parentheses.
Human capital covariances alone account for 27 to 50 percent
of the total change from worker characteristics, leaving the
bulk attributable to changes in industry covariances. This
result seems consistent with the quantity adjustment
hypothesis.8

According to the quantity adjustment idea, little of
the change over the cycle should come from the change in the
industry differentials experienced by workers since the
interindustry wage structure is relatively stable over time.
In the decomposition shown in Table 4.1, the second row
shows the change in dispersion that results from changes in

the estimated coefficients of the wage equation. The

 

8This fact is derived by looking at the portion of the
variance attributed to industry affiliation, controlling for
other characteristics and changes in the estimated
coefficients of the wage equation. In short, by looking at
the change in the variances and covariances of the industry
dummies and weighting by the estimated regression
coefficients, I conclude that one-half to three-quarters of
the change in the variance is accounted for by industry
affiliation.

94
industry dummies measure the industry differential; the
decomposition can then be used to determine the change in
dispersion that results from changes in the relative wage
structure. In the second row of Table 4.1, the change in
dispersion attributable human capital coefficients is
shown.9 The change attributable to changes is industry wage
premia is the difference between the total coefficient
effect and the human capital coefficient effect.

The industry effect is substantial, ranging from 20 to
more than 100 percent of the total change in dispersion.
This fact does not negate the quantity adjustment
hypothesis, however. Except for the 1974-1975 period,
differences in coefficients served to increase wage
dispersion. This result is no surprise given the positive
correlation between wage levels and wage changes noted by
Lawrence and Lawrence (1985) and mentioned in Chapter 2.
This correlation suggests that the wage structure, while
quite stable in terms of industry wage rankings, is changing
with increasing wage premia to high-wage industries. This
evidence is also consistent with the Bell and Freeman
findings that sector-specific productivity shocks, not the
business cycle, are the major source of increased dispersion
since 1970. There is too little information here to sort

out the cyclical impact versus the secular trend, but the

 

9The estimated wage equations do not account for selection
bias, and part of the change in coefficients from peak to
trough may be due to changes in unobserved characteristics
correlated with the variables in the model.

95
body of available research suggests that the relatively
large portion of the change in dispersion is best
interpreted as noncyclical. The time-series results provide
little support for wage sensitivity to the business cycle.
However, no clear judgement may be made from these cross-
section results alone.

The unexplained variation, the square of the standard
error of the equation, is the last component of the total
change in dispersion to analyze. If the residual variance
is viewed as the dispersion of wages controlling for human
capital and industry affiliation, observed changes in the
adjusted dispersion measure between cyclical peaks and
troughs might be attributed to the business cycle. These
differences are given in the third row of Table 4.1. These
differences do not display the clear cyclical pattern found
in the time-series estimates in Chapter 3 as well as the
literature. According to these estimates, dispersion
decreased during the downturn between 1974 and 1975. Time-
series estimates, however, lead one to expect an increase in
dispersion. And during the upswing between 1983 and 1985,
dispersion increased contrary to expectations.”

One must exercise caution in interpreting the change in
the unexplained variation as a pure cyclical effect. Other

factors such as inflation, international trade, and

 

”F-tests for the equality of the explained variation in
each adjacent year reject equality at the 5 percent level as
do tests for the equality of the unexplained variation.

96
industry-specific productivity shocks are ignored in these
estimates since their impact occurs over time.11 Given that
the time-series results show a small cyclical impact on wage
dispersion, the cyclical impact captured here may be
overshadowed by these other factors. And these factors will
also affect the portion of the decomposition that shows the
change in dispersion attributable to changes in the
covariances of human capital characteristics and changes in
the returns to these characteristics. Hence, to interpret
the change in the residual variance as a cyclical effect
involves some peril.

A particular difficulty in interpreting these results
is the secular increase in dispersion noted in several of
the papers discussed in Chapter 1. The cross sections do
not provide enough data points to extract a trend and
accurately estimate a cyclical impact. As a consequence,
the trend is subsumed in these results. Since a secular
increase has been documented by most accounts in Chapter 1
(though not all), increases in dispersion appear too large,
and decreases are understated. As a rough-and-ready method
of calculating the trend, I calculated the increase from
peak to peak (1974 to 1980) and from trough to trough (1975

to 1983).12 I then took the average of these changes as the

 

11A bright spot in the analysis, however, is that inflation
and international trade do not have a statistically
significant impact in the time-series results.

12I do not use 1985 in computing the trend since it is only
two years into the recovery rather than at a cyclical peak.

97
trend in dispersion. Table 4.3 shows the variances, both

adjusted and unadjusted, before and after detrending.13

Table 4.3 Variance of Wages

 

YEAR 1974 1975 1980 1983 1985

 

Full Sample

Total variance 0.337 0.299 0.290 0.315 0.331

(detrended) (0.337) (0.302) (0.307) (0.341) (0.362)

Adjusted variance 0.193 0.176 0.163 0.181 0.187

(detrended) (0.193) (0.179) (0.176) (0.201) (0.211)
Manufacturing

Total variance 0.223 0.222 0.233 0.314 0.254

(detrended) (0.223) (0.215) (0.194) (0.255) (0.182)

Adjusted variance 0.129 0.121 0.132 0.167 0.135
(detrended) (0.129) (0.118) (0.115) (0.141) (0.104)

 

In order to compare the cross section results to the
time series estimates, it is useful to look at the cyclical
responsiveness implied by these results. Since too few
observations are available for time-series analysis, I have

computed the simple arc elasticity for each peak-to-trough

 

13Note that the trend in the total sample is decreasing

0.002 per year; manufacturing shows an increase of 0.007 per
year. The decrease in the total sample, while in conflict
with the industry results of most of the studies surveyed in
Chapter 1, in consistent with the results reported by

Krueger and Summers who also use micro-level data from the
CPS.

98
(or trough-to-peak) comparison by dividing the percentage
change in the dispersion measure by the percentage change in
the prime-age male unemployment rate over the corresponding
time period. The results for the total sample and for
manufacturing are given in Table 4.4. I have shown the
elasticity implied before and after detrending and before
and after adjusting for worker characteristics in order to

highlight the impact of these alterations.

Table 4.4 Arc Elasticities

 

detrended detrended
total total adjusted adjusted
variance variance variance variance

 

Total sample

1974-1975 -0.l42 -0.131 -0.111 -0.096
1975-1980 0.229 0.134 0.581 0.095
1980-1983 0.173 0.218 0.217 0.276
1983-1985 -0.161 -0.204 -0.106 -0.169
Manufacturing
1974-1975 -0.010 -0.047 -0.073 -0.104
1975-1980 -0.387 0.750 -0.673 0.310
1980-1983 0.679 0.618 0.519 0.441
1983-1985 0.627 0.942 0.624 0.899

 

The first column of Table 4.4 shows the elasticity
before controlling for human capital characteristics and
industry affiliation. The elasticities are small, and they

do not provide a clear picture of cyclical sensitivity.

99
These estimates range form -0.16 to 0.23 compared to time-
series estimates of 0.06 to 0.11. As noted in Chapter 3,
however, the omission of human capital characteristics may
bias the results. The third column of Table 4.4 shows the
elasticities after controlling for these factors. The range
widens, -0.111 to 0.581. The upper end of this range is
five to six times as large as the time-series estimates,
which examine industry averages instead of individual data.

The fourth column of Table 4.4 is the most important of
these results. It contains the detrended estimates of
dispersion, controlling for individual characteristics.
After removing the secular trend, the range of the
elasticities is reduced (-0.17 to 0.28), and the mean of the
estimates is 0.03 in the total sample, a number not unlike
the corresponding time-series estimates. It is important
that this comparison not be taken too literally, however,
because the dispersion measured in Chapter 3 is across
industries; the cyclical effect shown here controls for
industry affiliation. Given that the industry definitions
are broad, however, there is much room for quantity and
price reallocation within these broad industries to account
for the cyclical sensitivity.

Table 4.2 provides the results of this decomposition
for the manufacturing sector. Like the total sample, the
proportion of the change in the total variance accounted for
by the covariances and coefficients is substantial. It is

interesting to note, however, that most of the changes are

100
attributable to differences in the covariances and
coefficients of the human capital variables, not from
industry affiliation. Quantity reallocation as measured by
the variance and covariances of the industries within the
manufacturing sector is less important than the changes in
labor quality, measured by potential experience and
education.

The portion of the change in dispersion attributable to
changes in the industry coefficients (which may be
interpreted as wage premia), however, is remarkably small,
which lends additional support to the quantity
adjustment approach. Almost all of the change in
coefficients is accounted for by the human capital
variables. The interindustry wage structure is relatively
fixed over the cycle.

Finally, the fourth column of Table 4.4 shows the
elasticity of dispersion over the business cycle among
manufacturing workers. The range here is significantly
wider than in the total sample, -0.10 to 0.90. The average
of these estimates is 0.39. While the time-series results
for the full sample were comparable to the cross-section
results above, the results are considerably different here.
There was no significant impact of the cycle on the
dispersion of wages in the manufacturing sector, but the
elasticities here are surprisingly large. A direct
comparison is difficult here, however. While F-tests of the

equality of the residual variances reject the hypothesis in

101
each pairwise analysis, the 0.39 elasticity is estimated
imprecisely, and one should not have great confidence in the
number as a point estimate of the cyclical elasticity.“
Given that the range of the estimates is rather broad, the

cyclical sensitivity may be illusory.

Results by Subgroups

That demographic groups have different labor market
outcomes is a well established fact among labor economists.
For example, women earn less than men on average. Blacks
earn less than whites on average. Of relevance here is the
impact of the business cycle on the dispersion of wages
within subgroups of workers.

One might expect differences in the cycle's effect on
dispersion because of differences in group labor market
behavior on average. If skills or industry affiliation
differ by group, the business cycle may affect within-group
dispersion differently than the workforce as a whole.

To begin the analysis of these potential differences, a
logical point of departure is the portion of changes in the
variance of wages attributable to changes in the variance

and coefficients of the race and sex dummies. For each of

 

14Assuming that the assumptions under which the elasticities
in the manufacturing section of column 4 of Table 4.4 are
correct, a t-test for the hypothesis that the elasticity is
0 could not be rejected. This is also true of the full
sample.

102
these dummies, this calculation is computed by using
portions of Expressions 4.3 and 4.4. As above, 4.3 measures
the portion of the change in the variance of log wages
accounted for by the variance of worker characteristics. In
this case, the race and sex dummies (and their covariances
with the other independent variables) in Tables 4.1 and 4.2
are the portions of the formula of concern.” And I
Expression 4.4 summed only over terms involving race and sex
coefficients gives the portion of the change in variance
attributable to the change in the sex and race coefficients.
Both of these quantities are small relative to the total
change in dispersion, each accounting for 2 to 11 percent of
the total change from one turning point to another. These
numbers are consistent for both the total sample and the
sample of manufacturing workers.

The next logical step in the analysis is to decompose
the variance of the natural logarithm of the wage rate for
each subgroup. The results of the decomposition for whites,
nonwhites, females, and males are given in the appendix.

The estimates suggest that the cyclical sensitivity of
dispersion for nonwhites and females in the manufacturing
sector is probably larger than for whites and males,
respectively. The evidence is less clear for the full

sample: nonwhites appear slightly more sensitive to the

 

15These calculations are not shown separately in the tables.
This calculation is a subset of the entire sum show in
Expressions 4.3 and 4.4.

103
cycle than whites; females may actually have a slight
decline in dispersion as unemployment rises, though the
effect appears to be quite small. In both the full and
manufacturing samples, the range of estimates is wide and
imprecise.”

The decomposition for manufacturing and the full sample
yields no consistent cyclical patterns of adjustment over
the cycle due to changes in the variance of worker
characteristics or the coefficients of those
characteristics. While the magnitudes of the changes differ
by subgroup, the direction of the effects are generally the

Conclggion

This chapter estimates wage equations in order to
decompose the variance of into its component parts-~the
variances and covariances of characteristics, the
coefficients of those characteristics, and the residual
variance. The residual provides information on dispersion,
controlling for worker heterogeneity and changing returns to
characteristics over the cycle.”

Using data from several years of the Current Population

Survey, this decomposition shows that changes in worker

 

16See Tables A.9 and A.10 in the appendix.

1’See Blank (1990) for speculation regarding this point.

104

characteristics over the business cycle are an important
part of cyclical adjustment. However, the estimates of the
relationship between the unemployment and dispersion is
still generally small and positive. The pattern among
subgroups of the population was less clear, however. The
race and gender composition of the workforce seemed to have
little to do with changes in dispersion, but the cyclical
sensitivity of nonwhites and females in the manufacturing

sector seemed relatively large.

CHAPTER 5

Conclusion

The time-series and cross-section results presented
here provide an interesting picture of what happens to
dispersion over the business cycle. The time-series results
lead one to believe that changes in dispersion across
industries are small in the economy as a whole and
practically non-existent in the manufacturing sector. The
importance of the omitted labor quality variables makes the
conclusions tenuous, even though the estimation technique
attempts to compensate for the deficiencies.

The cross-section results show that a significant
portion of the change in dispersion is indeed accounted for
by the omitted labor quality variables in both the
manufacturing and total samples.1 The omission may be more
serious in the manufacturing sector. While the time-series
estimates show no cyclical impact, the cross-sections yield
estimates of the elasticity that are generally positive and

larger for manufacturing than in the total sample (though

 

1Note that the importance of the variables does not
necessarily mean that the time-series results will be biased
from their omission. The bias would occur if the human
capital variables are not stationary and if the first
difference of these variables is correlated with the
independent variables.

105

106

the range of estimates is rather broad). The mean of the
estimates is 0.39. The cross-sectional estimates are even
larger than the two—digit interindustry estimates by
Wachter, who found a long-run elasticity of interindustry
wage dispersion of 0.25.2

Chapter 2 noted several possible scenarios that would
explain the positive relationship between the unemployment
rate and the dispersion of wages. Chapter 3 results suggest
that most of the responsiveness of dispersion to the cycle
occurs because of the reallocation of labor to industries
that have relatively fixed wage premia. The cross-section
estimates confirm that this reallocation is a contributor to
the change in dispersion over the cycle, but this
explanation is only a part of what happens. The dispersion
of wages is also altered by the changes in industry wage
premia, though the change in these estimated industry
coefficients is not cyclical in nature. The results
presented in this chapter cannot clearly distinguish the
cause of these changes in the relative return to industry
affiliation. As Bell and Freeman have shown, sector-
specific productivity shocks rather than cyclical activity
may largely account for this phenomenon. There is no
reliable way to separate the two in these cross sections.

The time-series estimates indicate that the short-term wage

 

2This number is not directly comparable since the dispersion
measure is different, and the total unemployment rate was
used in that computation.

107
responsiveness to the cycle is small. Consequently, the
change in the industry differentials may be safely assumed
to be largely acyclical.

The cross-section results control for individual
characteristics, and the decomposition accounts for the
portion of the change in the dispersion attributable to
changes in the returns to these characteristics. In the
cross-sections, the cyclical activity comes from
intraindustry variation. Since broad industry
classifications are used in the analysis, there is
considerable scope for intraindustry variation with both
wage and quantity adjustment within the industry. How much
is due to each is impossible to say, but in comparing the
broad one-digit results to the narrower two-digit results,
the analysis suggests that, in the short run, quantity
adjustment is more important.

This work has shown that wages show little response to
the cyclical variation of the economy. Instead, the labor
market is characterized by persistent differentials across
industries, and labor market adjustment to the cycle occurs
by adjusting the number of workers, not their wages. The
cross-sectional evidence of Chapter 4 shows that observed
labor quality also changes to some degree, more so for the
manufacturing sector than the economy as a whole.

Katz and Summers (1989) have argued that government
policies that subsidize high-wage industries may be welfare

augmenting in the presence of persistent wage differentials,

108
ignoring the collateral cost of the policy. While this
analysis does not address their argument directly, it does
highlight the persistence of the differentials and their
lack of sensitivity to the cycle.

Under the Katz-Summers framework, increases in high-
wage employment would be welfare augmenting. If employment
in high wage industries is relatively less sensitive to
business cycle activity, as suggested by the manufacturing
results in Chapter 3, then macroeconomic policies might be
less effective than specific policies directed toward high-
wage industries. Persistent wage differentials provide some
scope for government action to increase economic welfare.
The appropriateness of such action is determined not by the
ability to increase welfare but by the benefits (and,
perhaps, distributional consequences) of any action relative

to its costs.

APPENDIX

APPENDIX

Results by Subgroup

Table A.1 Decomposition, Male--Full Sample

 

YEARS1 1974-75 1975-80 1980-83 1983-85

 

Differences2
in
covariances -0.019 0.015 -0.003 -0.001

Differences3
in
coefficients -0.017 -0.003 0.025 0.008

Differences
in residual
variance -0.012 -0.012 0.020 0.005

Actual
difference in
variance -0.008 -0.020 0.037 0.012

 

1Differences in covariances and coefficients are weighted by
the earliest year in the calculation, 1974 in the first
column, 1975 in the second, and 1980 in the third. The
decomposition may not add up to the actual difference in the
variance since the decomposition is an approximation.

2Estimates were obtained by computing the following
expression:

2 2 2
szi (axti 0Xt_1’i) +zisziflj (oxuxcj axe-1.1xc-1J)

3Estimates were obtained by computing the following
expression:

21(p2ti_pzt-1Ii)a§i+212J(ptiptj—pt-1,ipt-1,j)axjxj

109

110

Table A.2 Decomposition, Female-~Full Sample

 

YEARSI 1974-75 1975-80 1980-83 1983-85

 

Differencesz
in
covariances -0.027 0.007 0.002 0.001

Differences3
in
coefficients -0.033 -0.005 0.028 0.013

Differences
in residual
variance -0.023 -0.011 0.015 0.008

Actual
difference in
variance -0.005 0.001 0.031 0.026

 

1Differences in covariances and coefficients are weighted by
the earliest year in the calculation, 1974 in the first
column, 1975 in the second, and 1980 in the third. The
decomposition may not add up to the actual difference in the
variance since the decomposition is an approximation. The
remainder may be attributed to rounding error and the
interaction of the differences in the covariances and the
differences in the coefficients.

2Estimates were obtained by computing the following
expression:

2 2 2
2191 (axti'axt_1,1) +ziszipj(oxcxxcj—axc-1,IXt-1,j)

3Estimates were obtained by computing the following
expression:

Ema-pi-..)011mm0.14.1-0.-.,.-o.-.,j) a...

111

Table A.3 Decomposition, White—~Full Sample

 

YEARS1 1974-75 1975-80 1980-83 1983-85

 

Differences2
in
covariances -0.021 -0.015 -0.003 0.000

Differences3
in
coefficients -0.013 -0.032 0.009 0.005

Differences
in residual

Actual
difference in
variance -0.038 -0.009 0.027 0.015

 

1Differences in covariances and coefficients are weighted by
the earliest year in the calculation, 1974 in the first
column, 1975 in the second, and 1980 in the third. The
decomposition may not add up to the actual difference in the
variance since the decomposition is an approximation. The
remainder may be attributed to rounding error and the
interaction of the differences in the covariances and the
differences in the coefficients.

2Estimates were obtained by computing the following
expression:

2 2 2
219.1 (Oxti-oxt_1'1) +212jpipj (OXuch—oxt-L1xt-1,j)

3Estimates were obtained by computing the following
expression:

21 (pati'pzt-lJ) oii+BIBJ(pciptj—pt-1,ipt—1,j) 0x119

112

Table A.4 Decomposition, Nonwhite—-Full Sample

 

YEARS1 1974-75 1975-80 1980-83 1983-85

 

Differences2
in
covariances -0.024 0.014 -0.007 -0.008

Differences‘
in .
coefficients -0.026 0.010 -0.003 0.038

Differences
in residual
variance -0.009 -0.018 0.019 0.005

Actual
difference in
variance -0.032 -0.003 0.013 0.026

 

1Differences in covariances and coefficients are weighted by
the earliest year in the calculation, 1974 in the first
column, 1975 in the second, and 1980 in the third. The
decomposition may not add up to the actual difference in the
variance since the decomposition is an approximation. The
remainder may be attributed to rounding error and the
interaction of the differences in the covariances and the
differences in the coefficients.

2Estimates were obtained by computing the following
expression:

2 2 2
2161(0Xt1-0Xt-1,j) +2iszipj (axcixcj_oXc-1.1xt-1.j)

3Estimates were obtained by computing the following
expression:

21(5221‘578-1J) o§i+212J(ptiptj-pt-1,ipt-1,j) 01mg

113

Table A.5 Decomposition, Male--Manufacturing

 

YEARS1 1974-75 1975-80 1980-83 1983-85

 

Differences2
in
covariances 0.001 0.001 0.009 -0.011

Differences3
in
coefficients 0.004 0.000 0.031 -0.014

Differences
in residual
variance -0.010 0.008 0.028 -0.029

Actual
difference in
variance -0.005 0.007 0.076 -0.051

 

1Differences in covariances and coefficients are weighted by
the earliest year in the calculation, 1974 in the first
column, 1975 in the second, and 1980 in the third. The
decomposition may not add up to the actual difference in the
variance since the decomposition is an approximation. The
remainder may be attributed to rounding error and the
interaction of the differences in the covariances and the
differences in the coefficients.

2Estimates were obtained by computing the following
expression:

2 2 2
2101 (axti'axt_1'1) Tsiszjflj (axuxcj'ox.-1,1xc-1,,)

3Estimates were obtained by computing the following
expression:

21' (Pii’pi-Li) 021+212J(ptifltj-Bt-1,iBt-1,j) 0x123

114

Table A.6 Decomposition, Female--Manufacturing

 

YEARS1 1974-75 1975-80 1980-83 1983-85

 

Differences2
in
covariances 0.001 0.000 0.001 -0.013

Differences3
in
coefficients 0.002 0.019 0.021 -0.008

Differences
in residual
variance -0.000 0.013 0.055 -0.037

Actual
difference in
variance 0.003 0.027 0.089 -0.048

 

1Differences in covariances and coefficients are weighted by
the earliest year in the calculation, 1974 in the first
column, 1975 in the second, and 1980 in the third. The
decomposition may not add up to the actual difference in the
variance since the decomposition is an approximation. The
remainder may be attributed to rounding error and the
interaction of the differences in the covariances and the
differences in the coefficients.

2Estimates were obtained by computing the following
expression:

2 2 2
21p1(0xti-oxt-1.i) +2513119151("24.x”“’41r.....24r....1)

3Estimates were obtained by computing the following
expression:

Edna-pi-..)oipzss0.10..-o.-.,.o.-.,.->0...,

115

Table A.7 Decomposition, White--Manufacturing

 

YEARS1 1974-75 1975-80 1980-83 1983*85

 

Differences2
in
covariances 0.000 0.004 0.004 -0.018

Differences3
in
coefficients 0.004 0.001 0.032 0.005

Differences
in residual
variance -0.006 0.011 0.031 -0.034

Actual
difference in
variance -0.001 0.013 0.081 -0.069

 

1Differences in covariances and coefficients are weighted by
the earliest year in the calculation, 1974 in the first
column, 1975 in the second, and 1980 in the third. The
decomposition may not add up to the actual difference in the
variance since the decomposition is an approximation. The
remainder may be attributed to rounding error and the
interaction of the differences in the covariances and the
differences in the coefficients.

2Estimates were obtained by computing the following
expression:

2 2 2
BIB-i (axtj-oXt—Lj) +Eiszipj (oxcixc1_axc-1,1xt-i,j)

3Estimates were obtained by computing the following
expression:

21 (Bii—flZt-1J) °§1+212J(pciptj_Bt-1,iBt-1J) axixj

116

Table A.8 Decomposition, Nonwhite--Manufacturing

 

YEARS1 1974-75 1975-80 1980-83 1983-85

 

Differences?
in
covariances 0.001 -0.008 0.012 -0.009

Differences‘
in
coefficients 0.017 0.003 0.013 -0.041

Differences
in residual
variance -0.018 0.014 0.061 -0.023

Actual
difference in
variance -0.004 0.006 0.089 0.005

 

‘Differences in covariances and coefficients are weighted by
the earliest year in the calculation, 1974 in the first
column, 1975 in the second, and 1980 in the third. The
decomposition may not add up to the actual difference in the
variance since the decomposition is an approximation. The
remainder may be attributed to rounding error and the
interaction of the differences in the covariances and the
differences in the coefficients.

2Estimates were obtained by computing the following
expression:

)

2 2 _ 2 _
2191(0xt1’ oxt-1,i) +212jpjflj(axuxu Oxc-mxc-ld

3Estimates were obtained by computing the following
expression:

BABE-911,1) °§1+212J(ptiptj—Bt-1,ipt-1.j) oxixj

117

Table A.9 Arc Elasticities

 

 

detrended

adjusted adjusted detrended total
variance variance variance total variance

Nonwhite (Total sample)
1974-1975 -0.134 -0.124 -0.056 -0.042
1975-1980 0.099 -0.230 0.741 0.289
1980-1983 0.097 0.509 0.219 0.275
1983-1985 -0.314 -0.344 -0.088 -0.151
average 0.093
White (Total sample)
1974-1975 -0.141 -0.131 -0.114 -0.099
1975-1980 0.224 -0.119 0.577 0.085
1980-1983 0.183 0.226 0.217 0.277
1983-1985 -0.153 -0.194 -0.111 -0.175
average 0.022
Nonwhite (Manufacturing)
1974-1975 -0.025 -0.066 -0.183 -0.228
1975-1980 -0.264 1.032 -0.997 0.600
1980-1983 0.911 0.894 1.013 1.021
1983-1985 -0.063 0.103 0.412 0.732
average 0.531
White (Manufacturing)

1974-1975 -0.003 -0.042 -0.061 -0.090
1975-1980 -0.434 0.755 -0.648 0.259
1980-1983 0.675 0.609 0.451 0.370
1983-1985 0.714 1.065 0.679 0.949
average 0.372

 

118

Table A.9 (continued)

 

 

detrended
adjusted adjusted detrended total
variance variance variance total variance
Male (Total sample)
1974-1975 _0e033 -0e028 -0e082 -0e071
1975-1980 0.525 0.356 0.524 0.187
1980-1983 0.269 0.289 0.236 0.277
1983-1985 -0.l31 -0.153 -0.092 -0.138
average 0.064
Female (Total sample)
1974-1975 -0.251 -0.362 -0.161 -0.143
1975-1980 -0.035 0.320 0.499 -0.107
1980-1983 0.276 —0.451 0.190 0.265
1983-1985 -0.330 -0.240 -0.154 -0.226
average -0.053
Male (Manufacturing)
1974-1975 -0.029 -0.062 -0.098 -0.l38
1975-1980 -0.267 0.768 -0.500 0.815
1980-1983 0.718 0.669 0.424 0.291
1983-1985 0.595 0.869 0.594 1.004
average 0.493
Female (Manufacturing)
1974-1975 0.027 -0.067 -0.005 -0.067
1975-1980 -l.539 1.307 -0.011 0.991
1980-1983 1.081 1.137 0.893 0.860
1983-1985 0.634 1.574 0.696 1.227
average 0.753

 

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