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XII. LABLOR ECONOMICS/LABOR MARKETS AND HUMAN RSOURCES REFEREED PAPERS
The Instability of Unskilled Earnings
Michael Mamo
Westminster College
Wei-Chiao Huang
Western Michigan University
Abstract The year-to-year variability of unskilled workers' earnings
increased over the period from the 1970s to the early 1990s. Moreover,
much of the increase in earnings instability occurred in the 1980s, despite
the long economic expansion that took place during the same period. The
decline in average job tenure among less skilled workers and wage instability
(rather than hours instability) seem to have contributed to these results.
The implication is that recent economic growth has failed to reduce earnings
instability and, consequently, the design of income maintenance policies
are better served by explicitly addressing access to capital markets and
tenure instability (or job retention capacity) among the poor.
Introduction This paper is concerned with earnings instability among less-skilled
workers.1 The study is based on data from the Panel Study of Income Dynamics
(PSID), and examines the dynamics of unskilled workers' earnings over
the 1970s, the 1980s, and the early 1990s by focusing on changes in the
covariance structure of earnings. Annual earnings are decomposed into
permanent and transitory components, and the implied covariances are evaluated
over the period to see if the year-to-year variability of earnings has
changed over time.
A study of earnings instability is important for several reasons. First,
most explanations for the changing distribution of income associate the
changes with increases in permanent differentials among individuals such
as the increase in the returns to education. However, changes in the annual
variance also come from increases in the instability of earnings, and
the cause of this increase must be sought in other factors as well. Suggested
explanations point to the importance of institutional factors such as
de-unionization. Second, transitory shocks can be welfare reducing, particularly
for individuals with limited access to capital markets. Zeldes (1989)
examined consumption and liquidity constraints facing a sample of families
selected from the PSID and found evidence that is generally supportive
of the notion that individuals are unable to smooth consumption over the
life cycle. Finally, a study of instability informs the design of income
maintenance policies that could be strengthened by programs to ease access
to capital markets as well.
The rest of the paper is divided in the following order. The next section
describes the data. The third section outlines the methods used to construct
the covariance matrix and to estimate the parameters of the model. Results
from the descriptive and parametric analyses of the earnings data are
presented in the fourth section. The roles of job, hours, and wage instability
are also examined in this section, and the conclusions are given in the
last section.
Longitudinal Data In this paper, twenty-four years of survey data from PSID
that span the period from 1970 to 1993 are used to examine the changes
in the covariance structure of unskilled earnings. The study is restricted
to a sample of annual earnings for male household heads, who have reported
non-zero earnings, are between the ages of eighteen and sixty, and whose
level of education is not more than twelve years. The focus on positive
and male earnings minimizes the confounding effects of entry and exit
in the labor market on the transitory variance of earnings. Although the
PSID provides complete longitudinal history of earnings, it contains relatively
little information on individuals who are not heads of households, limiting
the scope of the sample to only heads of households. The choice of the
entry age to the sample seems to be appropriate for this group of workers
because, presumably for individuals who are no longer going to school,
entry to the labor market takes place at an earlier age than for others.
These restrictions produced a balanced panel of 479 individuals and a
total of 11,496 person-year observations that are used in the construction
of the empirical covariance matrix.2 In line with previous work, all of
the analysis is conducted using residuals from a first stage regression
of the log of annual earnings on a quartic in age. All usable data are
appropriately deflated to 1992 dollars.3
Econometric Specifications
Baker and Solon (1998), among others, have stressed that the simple error
components model above has to be general enough to allow for some patterns
in the earnings data. These patterns include, for example, serially correlated
transitory components that fade within one or two years, a non-mean-reverting
permanent component, a heterogeneous growth factor, and time-varying loading
factors that capture the secular trend in the earnings components.
These extensions are well justified in the context of investigating trends
in overall inequality and particularly in analyzing the role of individual
heterogeneity in shaping lifetime inequality among individuals in all
skill and gender groups. The present study, however, focuses on a less
heterogeneous and smaller group of the population than used in previous
analyses and it emphasizes the evolution of the transitory variance component
of the earnings of unskilled workers. Furthermore, the restrictions on
the sample and the balanced nature of the panel resulted in a limited
number of usable data points for the construction of the empirical covariance
matrix. Instead, a stripped down version of the models of covariance structures
that is capable of accounting for the time variation and serial correlation
in the variance components is developed below and used in the rest of
the analysis.
The Covariance Structure of the Earnings Panel
Descriptive Analysis of Earnings Data The model in (2) implies that the variances and covariances
in the data can be used to approximate the permanent and transitory variances
of earnings. For example, the difference between the variance and the
covariance estimators for each time period, i.e., the difference between
the estimates for (3) and (4), can be used to estimate the transitory
variance. In this case, changes in the stability of earnings can be approximated
by changes in the difference between the estimated variances and covariances.
These covariances are summarized for different lag orders in Figure 1.
Generally, the variances and covariances tend to rise over time. There
is a clear indication of a growing gap between the variances and the corresponding
covariances especially during the later years of the sample. Because this
gap can be viewed as an approximate measure of the transitory variance
there is graphical evidence that earnings instability has increased during
the more recent years of the sample. Moreover, earnings became more unstable
throughout the 1980s despite the long economic expansion during the decade,
exhibiting a marked departure from the general cyclical trend in those
variances.
The covariances from the error components
model in (2) can also be cast in a simple regression framework. The distinct
second moment estimates in C^ are stacked in a vector m and
can be viewed as related to a lower dimensional vector of population moments
in f(b) through the model m = f(b) +
 , where
is a vector of sampling errors and we wish to estimate the parameter vector
b. Assuming for the moment that f(b) is linear in b,
the model becomes m = Xb + ,
where the "explanatory" variables in X consist of an intercept term and
a diagonal dummy variable, D. The diagonal dummy equals 1 if the corresponding
element in m is a variance (i.e., if it falls on the main diagonal
of C) and 0 if not, thus capturing the difference between the variances
and covariances. The intercept term is therefore an estimate of the permanent
variance and the coefficient on D is an estimate of the transitory variance.
The results of this approximation are in the four columns of Table 1.
The second column shows how the intercept term and the slope coefficients
have trended over time by including a time trend and an interaction between
the time trend and the diagonal dummy. The numbers indicate that the transitory
variance trended at 0.0047 per year throughout the sample period.
The last two columns of Table 1 show that the transitory variance declined
over the first sample period and exhibits a large growth in the second
period, indicating once again a marked increase in earnings instability
during the expansionary years of the 1980s.
The 'Embellished' Error Components Model As alluded to above, the simple decompositions above have
many limitations. The sample variances and covariances in Table 2, for
instance, indicate the presence of a long declining tail that tends to
asymptote, mimicking an autoregressive process. In this section, time-specific
factor loadings are also included on the permanent and the transitory
components of earnings.
The estimation results from equations (5) and (6) are shown in Table 3.
For comparison purposes, Column 2 presents estimates from fitting the
earnings dynamics model with no calendar time effects but one with an
individual effect and an AR(1) transitory term. All estimates are significant
and there is evidence of a strong permanent individual component of earnings
as well as a serially correlated transitory component that exhibits a
degree of persistence.
Column 3 indicates that the transitory component still exhibits similar
variance but one with a stronger indication of serial correlation. The year-specific
factor loadings are reported in the second and fifth blocks of twenty-three
rows, where, for identification purposes the estimate on p69 and f69 are
set to equal one.
During the pre-1980 period, the factor loadings on the transitory component
appear to be countercyclical, which is not the case for the post-1980
period. During the pre-1980 expansionary years of 1970 to 1973 and 1975
to 1980, for example, the estimates on the transitory factor loadings
appear to have consistently declined and become statistically insignificant
during most of the 1975 to 1980 period. The parameter estimates exceed
the zero statistical thresholds only in four out of the eleven years considered.
By contrast, the 1982 to 1990 expansion produced a series of statistically
significant and rising estimates on the factor loadings. In other words,
estimates of the factor loadings trended upward despite the long expansion
that took place during the post-1980 period, suggesting once again a rising
instability of low skilled workers' earnings during the period that spans
the decade of high economic growth.
Although the focus here is on the transitory variance, it is instructive
to note the parameter estimates for the permanent factor. The estimates
show that permanent differentials started to increase in the early 1970s.
The increase in the permanent variance is an indication of increases in
within-group inequality that precedes overall inequality by several years.
From a separate data set, Katz and Murphy (1992) find that the rise in
U.S. within-group inequality began in 1973, several years before most
measures of between-group inequality began to rise. The results from PSID
in this paper are therefore consistent with Katz and Murphy's observations
from other samples.
Variations in Annual Hours of Work To examine relative changes in hours and hourly earnings,
annual earnings are decomposed into annual hours and average hourly earnings
and the covariance structures from the previous sections are imposed separately
on hours and earnings. The dependent variables in these models are now
average annual hours of work and hourly earnings.
The results from fitting the simple descriptive regressions on annual
hours and wages are given in Table 4. All estimates are statistically
significant and the estimate on the diagonal dummy indicates that hourly
earnings appear to be more unstable than annual hours. The estimates from
fitting the covariance structures implied by equations (5) and (6) are
reported in the last two columns of Table 3. The estimates on the transitory
variance components in Table 3 are displayed graphically in Figures 2
and 3 for hourly earnings and annual hours, respectively. The figures
indicate that the transitory variance component of annual hours tends
to remain high throughout the sample period. This is especially true when
one considers the recessionary years of the early and mid-1970s and the
early 1980s. A different picture emerges when we consider the time profile
of transitory variances of hourly earnings. Higher variances become more
frequent, particularly after the late 1970s, suggesting that wage variability,
as opposed to hours variability, may have been the primary force behind
the post-1980 earnings instability reported in the previous section.
Job Turnover Another potential explanation for secular changes in transitory
variances is the trend in job turnover rates. Documenting changes in job
turnover rates, however, has become a controversial exercise. Studies
based on the PSID and the Current Population Survey generally yield conflicting
evidence on the trends in job stability. However, there is at least consistent
evidence in most data of increased job turnover among the unskilled during
the post-1980 period (Jaeger and Steven 1998).
To assess the role of job instability, this section compares variance
parameter estimates for "job stayers," defined as individuals who stayed
with the present employer for more than the average tenure in the sample,
and "job changers," those who stayed with their present employer for less
than the same average. The estimates in Table 5 are obtained from running
a regression of the type in Table 1 separately for the two groups.
The numbers indicate that while the estimates for the permanent variance
components are virtually identical, the estimate for the transitory variance
for job changers is substantially larger than the same for job stayers.
In other words, while tenure differences, as to be expected, are not important
in explaining permanent differences among workers, the increased tenure
instability of the 1980s and the early 1990s has accounted for part of
the corresponding earnings instability of less skilled workers.
Conclusions The findings above suggest that earnings became increasingly
unstable in the second half of the sample period. Indeed, instability
appears to have diminished during the early 1970s, suggesting that declining
stability of earnings is presumably caused by changes that may have occurred
during the 1980s. Moreover, periods of economic expansion that occurred
during the 1970s tend to reduce the instability of earnings, consistent
with what is expected. By contrast, earnings instability trended upward
during the 1980s despite one of the longest peacetime expansions on record.
Studies have suggested that the high growth years of the 1980s failed
to offset the incidence of high poverty unlike similar expansions during
the previous decades. The present study is yet another indication of fundamental
changes of the low-wage labor market of the 1980s and 1990s that may have
transformed the dynamics of poverty as well as pay instability.
The results in this paper also suggest that tenure instability and limited
access to credit and capital markets are issues that need to be taken
into account in the design of effective income maintenance policies. While
the above findings point to the need for further research to assess the
determinants of instability, they are also suggestive of an important
area that seems to have been overlooked in the design of policies as well
as academic research.
Notes 1. Throughout the paper the less-skilled are defined as individuals
with no more than a high school education.
2. An obvious shortcoming of using a fully balanced panel as in the present
paper is the inability to separate age effects from time effects. The
results in this paper should be interpreted with this caution in mind.
However, if age effects are primarily reflected in annual hours of work
rather than hourly earnings, then separating the variance of annual earnings
into the variances of annual hours and hourly earnings could provide an
indirect but imprecise means to evaluate age and time effects. As the
analysis in the next sections shows, the instability of hourly earnings
mimics that of annual earnings, suggesting that perhaps age effects were
not crucial in explaining the observed patterns in annual earnings instability.
3. Attrition in the PSID has been significant--reaching about 50 percent
by 1988. Gottschalk and Moffitt (1995), among others, noted that the attrition
has been mainly related to observables and the sample weights have been
adjusted to reflect this, considerably minimizing the bias in the selection.
References
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Baker, Michael. 1997. "Growth Rate Heterogeneity and the Covariance Structure
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Baker, Michael, and Gary Solon. 1998. "Earnings Dynamics and Inequality
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