Wage Discrimination Over the Business Cycle

Using CPS data from 1979-2009 we examine how cyclical downturns and industry-specific demand shocks affect wage differentials between white non-Hispanic men and women, Hispanics and non-Hispanic whites, and African-Americans and non-Hispanic whites. Women's relative earnings are harmed by negative shocks; the wage disadvantage of African-Americans drops with negative shocks, which have slight negative effects on Hispanics' relative wages. Negative shocks also increase the earnings disadvantage of bad-looking workers. A theory of job search suggests two opposite-signed mechanisms that affect these wage differentials. It suggests greater absolute effects among job-movers, which is verified using the longitudinal component of the CPS.


I. Introduction and History
For nearly 50 years the measurement of wage differentials between racial and ethnic groups, and between genders, has been a mainstay of empirical labor economics. Nearly all of the empirical work has implicitly been grounded in Becker's (1957) taste-based approach; and almost the entire oeuvre has either measured cross-section differentials or considered trends in these "discriminatory" differences. Relative to the attention paid to cross-section differences and trends in wage effects, remarkably little attention has been paid to how these differentials vary with the extent of labor-market tightness. The issue was mentioned only in passing in the first Handbook survey (Cain, 1986) and was not even alluded to in subsequent Handbook surveys (Altonji and Blank, 1999;Fryer 2011).
A few studies from the 1970s and 1980s did attempt to measure the cyclicality of discriminatory wage differentials (Ashenfelter, 1970;Freeman, 1973;O'Neill, 1985), analyzing aggregate time series of the ratio of annual earnings of disadvantaged compared to other workers.
Measured cyclical movements in ratios of earnings per hour could arise from two distinct mechanisms: changes over the cycle in the characteristics of the workers in each group (composition effects) and changes over the cycle in pure wage discrimination. The authors recognized this and pointed to both mechanisms as reasons for expecting cyclicality in measured discriminatory wage gaps. Discussions of composition effects pointed to the greater "vulnerability" of women and minorities to cycle-related job loss, but also noted the tendency for women and minorities to be employed in more stable, albeit lower-wage, industries. Both O'Neill and Freeman concluded that composition effects led to a counter-cyclical movement in measured discriminatory wage differentials. Freeman and Ashenfelter offered reasons for suspecting that true wage discrimination would also be counter-cyclical, with the latter referring to an apparently common argument of the time that the perceived cost to employers of discriminating was higher in tight labor markets. But neither found empirical evidence of cyclical movements in pure wage discrimination in the aggregate data.
Since the mid-1990s, despite the continuing volatility of aggregate and local labor markets, including the turmoil caused by the Great Recession, almost no attention has been given to the relationship between labor market tightness and discriminatory wage differentials.
Numerous studies have used the CPS and other individual level data sets to study longer-term movements in discriminatory wage differentials, but with almost no mention made of the possible cyclicality of such differentials. 1 In this study we remedy this neglect. In the next section we document the paths of wage differentials by gender (female/male), ethnicity (Hispanic/non-Hispanic) and race (black/white), using the Current Population Survey Merged Outgoing Rotation Groups (CPS-MORG) from 1979 through 2009. This is a sufficiently long period to cover four (or five, if one considers the early 1980s recessions as distinct) aggregate cycles. Since the CPS-MORG files provide individual level data with industry and geographic identifiers, we can measure more accurately the labor market environment facing each worker; and the longitudinal component of the CPS-MORG data allows us to distinguish changes in measured wage differentials due to changes in pure wage discrimination from those due to composition effects, both observable and unobservable.
We find that the male-female wage gap is counter-cyclical, that is, the wage disadvantage faced by women grows when and where unemployment is temporarily higher. This does not appear to be due to a composition effect, but rather to changes in pure wage discrimination. The measured discriminatory gap for African-Americans, on the other hand, is pro-cyclical, but this is partly the result of composition effects. The wage disadvantage faced by Hispanics is slightly counter-cyclical. In Section III we offer suggestive evidence of the counter-cyclicality of still another possibly discriminatory wage differential, one based on looks. 1 See, e.g., Blau and Kahn (2006), or Mulligan and Rubinstein (2008). Blanchflower and Oswald (1994) did relate wages to unemployment rates for separate demographic groups without comparing cyclical responses. Kuhn and Shen (2010) is a rare exception to this generalization, although in a very specific context; and Dustmann et al (2010) did examine the cyclicality of immigrant-native wage differentials.
3 Section IV sets out a search-theoretic model of discrimination to aid in interpreting the evidence. We show that a standard random search model with employer discrimination implies a cost to employers of indulging discriminatory tastes that varies pro-cyclically, thus providing a formal version of the argument cited in early work; but the model also points to other ways that discriminatory wage differentials will be affected by a changing unemployment-vacancy ratio that work in the opposite direction. One implication of this model, that economic fluctuations will change discriminatory wage differentials chiefly through their impact on the wage changes experienced by job-changers, is supported in the data.

A. Basic Estimates
Throughout this section we use the Current Population Survey Merged Outgoing Rotation Groups beginning 1979, the first year for which they are available. We proxy wages by reported usual weekly earnings but adjust weekly earnings by including a quadratic in usual weekly hours among the independent variables. We divide the working population into four mutually exclusive groups, non-Hispanic white males, non-Hispanic white females, non-black Hispanics, and African-Americans, and create indicator variables M for the last three groups. 2 In addition, except in the initial estimates we adjust wages by holding constant for a wide range of CPS covariates, X, including a vector of indicators of educational attainment, a quadratic in potential experience, and indicators of marital status, metropolitan location, veteran status and private/public sector employment. The samples are restricted to wage and salary workers-the self-employed are excluded, as are members of the armed forces.
For each year we calculate the unemployment rate U in each state and use that as the cyclical indicator. We thus estimate: where i denotes an individual, s a state and t a year, and W is the logarithm of weekly earnings.
The ν s and τ t are state and year fixed effects respectively. While we initially estimate (1) without either of these vectors, and then include only the year fixed effects, to save space most of the tables shown below report results from regressions that include both vectors (although Table 1 also reports results excluding the vector of state fixed effects). Separate equations are estimated for non-Hispanic whites only, then excluding African-Americans, and then excluding non-Hispanic African-Americans. The estimates of α 1 + α 3 U thus denote the wage differential relative to non-Hispanic white men, and, in the latter two cases, to non-Hispanic whites. The coefficients on U listed in the Table treat unemployment as a fraction of the labor force.
When we estimate (1) with the vector of state fixed effects we are implicitly focusing on temporary variations in the tightness of state labor markets. This specification accounts for the possibility that in certain states unemployment may be above or below the national average in most or all years (although Marston, 1985, suggests not). Such long-term differences are arguably related to wage differences (e.g., Hall, 1970, but going back to Smith, 1776) and may also be correlated, coincidentally or not, with interstate differences in general attitudes towards various minorities. When we estimate (1) including the vector of year fixed effects, we are implicitly abstracting from aggregate cycles. Adding both state and year fixed effects to the regression reduces the precision in our estimates of the impact of changes in unemployment on discriminatory wage differentials, but alleviates any bias caused by a correlation between secular changes in the natural rate of unemployment and secular changes in attitudes towards women and minorities.
Before turning to the estimates of (1), we focus on the effect of the cycle on these wage differentials absent any demographic controls, year or state fixed effects, controlling only for hours worked and a time trend. Without any controls we estimate that white women's wages relative to white men's fall by 1.2 percent with each one percentage-point increase in the 5 unemployment rate. Non-black Hispanics' wages rise relative to non-Hispanic whites' wages by 0.9 percent in response to the same rise in unemployment, and African-Americans' wages similarly rise by 0.3 percentage points. Even without any adjustments it is clear that no single pattern characterizes cyclical changes in "discriminatory" wage differentials. 3 The impacts of a typical recession vary sharply across gender/race/ethnic groups, with the biggest effect among women. For them an increase of 4.7 percentage-points in average unemployment (which occurred in the Great Recession) increases their wage disadvantage by over 4 percentage points; among Hispanics the effect is tiny-an increase in their wage disadvantage of slightly more than 0.1 percentage points, while among African-Americans this severe a recession reduces their wage disadvantage by about 1.7 percentage points.

B. Extensions
The results thus far have been based on samples covering thirty-one years. Given the documented changes in the labor markets for members of all three "minorities," perhaps the extent of cyclical variation in their wages over this period changed too. To examine this possibility we first divide the entire sample period into two parts, 1979-92 and 1993-2009 (each thus comprising two aggregate business cycles) and re-estimate the equations.

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The estimates over these two sub-periods are shown in Table 2. Among women the results in the earlier sub-period are the same as before-apparently increasing discrimination as unemployment increases; but in the later sub-period the results reverse, with apparent discrimination falling as unemployment increases. Among Hispanics the estimates are consistent with those in Table 1, and perhaps even stronger, showing that the wage disadvantage increases as unemployment increases. Among African-Americans the estimates suggest a roughly similar conclusion as those for the entire time period-that the wage disadvantage declines when the unemployment rate rises-although the relationship in the latter sub-period is weak.
The cyclicality of wage differentials measured in the regressions reported thus far could arise from both cyclicality in pure wage discrimination and from unemployment-related changes in the unobservable characteristics of the sample of employed workers-a composition effect in the unobservables. Using the short longitudinal structure of the CPS-MORG we can examine the co-movement of unemployment rates and discriminatory wage differentials in a group of workers of constant unobservable composition. This analysis thus controls for possible interactions between a wide range of unobservable individual characteristics with the unemployment rate. Table 3 presents the results of regressions in which the sample is restricted to observations that had positive earnings in both months 4 and 8 (one year apart) of their participation in the CPS and which include person fixed effects, so that state fixed effects are implicit in the estimation. 7 We present estimates for the entire sample period and then separately for the two sub-periods. 8 Essentially we difference (1) so that the dependent variable is the change in log-earnings, and the only independent variables are M, the change in the state 8 unemployment rate, their interaction, and linear terms in experience and current and year-lagged weekly hours.
The results for women are unambiguous-for the whole sample and the two sub-periods the wage disadvantage of women grows when and where unemployment is temporarily higher, just as it did in the cross sections. Thus, the positive relationship between the unemployment rate and the wage disadvantage faced by women is the result of cyclical movements in pure wage discrimination. Table 3 even shows that the apparent reversal of sign of the relationship between unemployment and the male-female wage gap during the latter half of the sample period was due to a change in the impact of unobservable, unemployment-related composition effects on the measured gap rather than a change in the cyclicality of wage discrimination. This observation is consistent with Mulligan and Rubinstein's (2008) finding that the nature of selection into the female labor force changed between the 1970s and the 1990s.
The estimates also show that the relatively weak positive relationship between unemployment and the wage disadvantage facing Hispanics in the cross-section becomes considerably stronger when composition effects arising from unobservables are removed.
Hispanic workers who keep their jobs as unemployment rises implicitly have increasingly more desirable unobservable characteristics than do non-Hispanic white workers who keep their jobs.
The positive co-movement of the relative wages of African-Americans and unemployment that we saw in Table 1 diminishes in magnitude and becomes insignificant when measured in this sample with unchanging unobservable composition.
While we have carefully accounted for labor-market-wide effects, treating states as labor markets, we have ignored the job-specific impacts of changes in demand. The question is whether, given the state's labor market, the impact of job-specific shocks mirrors that of a labormarket-wide shock. To examine this we re-specify (1) as: where ∆H it is the percentage change in total person-hours worked in the CPS industry between years t-1 and t.
We present estimates of the α j in (2) in Table 4  The estimates of ∂ 2 W/∂M∂U at the average ∆H differ only very slightly from the estimates in Table 1 (not surprisingly, given the lack of correlation between state unemployment rates and annual changes in economy-wide industry hours worked). Thus accounting for industry-specific changes in employment does not alter the conclusion that the female wage disadvantage increases as unemployment rises, the African-American wage disadvantage falls, and the Hispanic disadvantage may increase slightly.
To answer whether industry-specific shocks affect gender/racial/ethnic wage differentials in the same way as market-wide shocks, we focus on the estimates of ∂ 2 W/∂M∂∆H at the averages of U, shown at the bottom of Table 4. Among women we observe the same negative effect on wage differentials of declines in industry demand that we observed for cyclical labormarket rises in unemployment in Table 1-as ∆H is more negative, women's wages fall relative to men's. Among Hispanics too the generally negative impacts of rising unemployment shown above are mirrored by the negative effects on their relative wages of negative industry demand shocks. Only among African-Americans is there no impact of industry demand shocks.
A fair conclusion is that the effects of industry-specific shocks are in the same directions as those of cyclical, market-wide shocks. Their impacts are not so large, however: For example, 10 among women even a decline in average industry employment equaling the difference between the smallest (most negative) and the largest in the sample period would increase white women's wage disadvantage by 1.8 percent points-less than half of the increase occurring in a deep recession.

III. Another "Discriminatory" Dimension-Looks
There is by now a wide array of studies demonstrating that, other things equal, worselooking workers of both sexes earn less than their better-looking peers, both generally and within a wide array of occupations (summarized in Hamermesh, 2011, Chapters 3 and 4). As another illustration of the cyclical variation in "discriminatory" wage differences, we can combine evidence from two studies of the earnings of attorneys to examine cyclicality in the pay penalty for bad looks. In Biddle and Hamermesh (1998) we examined twelve cohorts of graduates from a prestigious law school whose earnings were observed one, five and fifteen years post-graduation.
The estimated effects of a one-standard deviation improvement in attorneys' looks are reproduced in Table 5. The cohorts of attorneys who entered the labor market for lawyers between 1972 and 1977 faced a growing and significant beauty premium (and ugliness penalty) as their careers progressed. The earnings of attorneys in the cohorts that graduated between 1982 and 1987 were unaffected by differences in their looks, at least early in their careers. Figure 1 reproduces Rosen's (1992) graphical description of lifetime earnings forecasts facing entrants into this labor market at each year of graduation, 1967-1987. We can compare the earnings that could have been expected by those attorneys who graduated in the early to mid-1970s to those who graduated in the early to mid-1980s. Clearly, real and relative earnings were higher in the latter period; and Rosen (1992) demonstrates that this difference arose from the tighter labor market for attorneys. Comparing these findings to the results in Table 5 suggests that the impact of looks on earnings-and the "discriminatory" disadvantage in pay of badlooking workers-was smaller in the tighter legal labor market of the 1980s than in the looser 11 legal market of the 1970s. The findings for this occupational labor market are similar to those for female workers, but opposite that for African-American workers.

IV. Modeling Discrimination over the Cycle
The previous sections have presented compelling evidence that discriminatory wage gaps are related to labor market tightness, a relationship that shows up even in analyses of comovements of wage and unemployment over a year in samples of unchanging composition. The intellectual problem, however, is that the direction of the effects differs among "minority" groups.
In this section we outline an equilibrium search model that provides insights into why pure wage discrimination might be related to labor market tightness, a model that builds on the work of Black (1995) and Rosén (2003), and why this relationship might differ among groups. It contains two types of workers, one of which is subject to employer discrimination in the labor market. The model explores the intuition that the rising ratio of job seekers to vacancies during a recession might give employers more scope to indulge discriminatory tastes, while bringing to light other ways that cyclical fluctuations might reduce discriminatory wage differentials. We present enough of the model to make clear the key mechanisms; an appendix available from the authors contains a complete characterization of the equilibrium.
There are two types of worker, type A and type B. Type A workers are favored and account for a fraction λ of job seekers. Workers search randomly across vacancies offered by employers. Each potential vacancy is associated with a value of the discrimination coefficient c, which is distributed across vacancies over a range from zero to c max . A vacancy's discrimination coefficient manifests itself as a tax on the employer who hires a type B worker into the vacancy, but it may influence the wage paid to a type A worker hired into that vacancy.
Equations (2) and (3) express the value to a worker of type i of being unemployed (U i ) versus being employed in a position with discrimination coefficient c (W i (c)).
In (3) r is the discount rate, θ is the rate at which workers receive job offers, z i is the probability that the employer will be willing to hire the worker of type i, and E(W i (c) ) is the expected value, for worker type i, of being employed, where the expectation is taken over the distribution of c. In (4) s is an exogenous separation rate, and w i (c) the wage earned by a type i worker at a job with a discrimination coefficient of c.
Equations (5) and (6) give the value to the employer of a vacancy and a filled job as functions of the job's discrimination coefficient, c.
In (5) k is the cost of keeping a vacancy open for a period, φ is the rate at which workers arrive at employers, and y(c) is the probability that the randomly arriving worker will be acceptable to the employer, which depends on the vacancy's c value. The expectation in (5) is taken over the distribution of worker types. In (6) x is the value of a worker's product, assumed the same for all workers in all jobs, and c i is equal to zero if a type A worker is hired, and equal to the vacancy's discrimination coefficient if a type B worker is hired.
Because it costs to keep a vacancy open, and there is a foregone surplus from a filled job, the employer offering a vacancy with a non-zero c faces a tradeoff. Hiring a type B worker has a psychic cost, c, which for some vacancies will be greater than the equilibrium wage discount for type B workers; but turning the worker away and waiting for a type A worker to apply generates a cost in terms of k and forgone x that is proportional to the waiting time.
Following common practice, we assume that, when a worker meets an employer in the search process, the wage is determined by a Nash bargaining process, which gives the worker a share β of the surplus. The potential surplus for an i worker and a c vacancy is (W i (c) -U i ) + (J i (c) -V(c)). Replacing W i (c) and J i (c) in this expression with (4) and (6) yields a wage equation for a type-i worker in a c vacancy: 13 Equations (5)- (7) can be used to derive two possible values for a c-vacancy. Let V AB represent the value of the vacancy if the employer is willing to fill it with either type of worker, and V A stand for the value of the vacancy if the employer hires only A type workers. Then: Whether a vacancy is segregated or integrated depends on which of these values is higher, and that depends on the value of c. Setting (8a) equal to (8b) gives a cutoff value c*, such that vacancies for which c>c* will be filled only with A workers: A higher c* means less discrimination. A higher cost of waiting (k) or a higher value of production (x) leads to less discrimination, since the cost of discriminating is waiting for the next worker to come along if a B worker is denied the job.
Let H(c*) be the probability that c<c*, so that z B , the probability that a vacancy found by a type B worker will be filled by him, is H(c*), while z A = 1. Then (3) and (4) where the expectations are over the distribution of c. These equations can be used to show that U A > U B , which, given the wage equation (7), implies that in equilibrium the B worker receives a lower wage than the A worker at any employer willing to hire both types. 10 Also, as V AB is declining in c, wages for both A and B workers fall as c increases up to c*, at which point there is no wage for B workers and the A wage remains constant.
14 The arrival rate of workers φ, which is one factor determining the cost to employers of discrimination, depends on the processes governing the number of searching workers and the number of vacancies offered. Letting the total number of workers equal 1, a fraction α of whom are type A, and letting the number unemployed for type A and type B workers be u A and u B , the change over time in the number unemployed can be written as du A = s(α -u A ) -θu A and du B = s((1 -α) -u B ) -θH(c*)u B . In a steady state unemployment is constant, so that the steady-state rates of unemployment are given by: Group-specific unemployment rates can be found by dividing (11a) and (11b) by α and (1 -α), respectively, leading to the unsurprising result that the unemployment rate for B type workers will always be higher than the unemployment rate for A type workers. Also, λ, the share of unemployed workers who are Type A, will always be lower than α, the share of type A workers in the economy.
To endogenize the number of vacancies, assume that there are M potential vacancies that will become actual vacancies if their value is greater than zero. In order to have an equilibrium in which discriminators can survive long-run entry, we follow Black (1995) by assuming differences in entrepreneurial ability that are attached to potential employers. Entrepreneurial ability is represented by a fixed cost that is incurred if a vacancy is opened (and persists whether it is filled or not). We represent this cost by the parameter ε, assumed to be distributed uniformly across vacancies on the interval 0 to R ε , independent of the discrimination coefficient c, which is also assumed to be distributed uniformly across potential vacancies. The fixed cost parameter appears as a term subtracted from the value equations (7a) and (7b).
Potential vacancies will become actual vacancies if: can characterize the arrival rates θ and φ. As is common in the literature, we assume a matching function m(u A +u B , v) that describes the number of meetings between searching workers and vacancies that will occur in a period. Adding the conventional assumption that the matching function exhibits constant returns to scale allows the rate at which a searching worker meets a vacancy to be written as: while the rate at which employers see workers showing up at vacancies is: In the context of this model, we represent macroeconomic fluctuations as changes in x, the value to the firm of a workers' output. It is possible to differentiate the equilibrium value of the wage gap with respect to changes in x, but this leads to a complex and non-transparent expression with an ambiguous sign. The model can, however, be used to think through the stepby-step impact of a recession on employers, workers, and market-level variables, thus providing some insight into the sources of this ambiguity and their possible correspondence to real world phenomena.
As discussed above, one cost to discriminating is the opportunity cost of the longer expected wait until an acceptable worker arrives, and this cost falls with a fall in the value of output. Employers who might not discriminate when the value of output is high will do so when 16 it is low. Thus the model captures the idea that discrimination will be more costly in a tighter labor market. A greater proportion of discriminating employers in the labor market lowers the bargaining power of type B workers relative to type A workers, increasing the wage gap.
Another immediate impact of a drop in x, however, serves to increase the bargaining power of type B workers. Other things equal, the fall in the value of workers' product lowers the perceived value of both filled jobs and vacancies, causing some vacancies and jobs to be  As positions disappear, the rate at which workers arrive at employers rises, but the rate at which workers find new vacancies drops. As noted above, the higher arrival rate of workers at vacancies lowers the cost of discriminating, because a faster arrival of the next worker means less foregone output when a type B worker is turned away. 11 This lowers the cutoff value of c*, which in turn lowers the value of search for type B workers relative to type A workers. A similar effect results from disproportionately more type A than type B workers losing jobs, raising the share of type A workers among the searchers and lowering the expected waiting time for the next type A applicant for firms who turn away type B workers. The lower arrival rate of job offers to workers lowers the value of search for both type A and type B workers, which lowers the wage of both types; but it lowers the value of search more for type A workers. This decreases the wage gap, but is a rather subtle, non-intuitive effect, as are the impacts of the many of the subsequent equilibrating reactions of the model's variables to the initial events set in motion by a fall in x.
Although our model leaves open the question of whether discriminatory wage differentials are pro-cyclical or counter-cyclical, it does identify several distinct mechanisms through which business-cycle fluctuations could plausibly alter discriminatory wage differentials.
These include cycle-induced changes in the costs and benefits of discrimination in hiring and changes in the mix of discriminators vs. non-discriminators in the labor market caused by entry or exit. In addition, our argument suggests that changes in discriminatory wage differentials accompanying aggregate fluctuations will arise from the impact of these fluctuations on changes in the relative wages of advantaged vs. disadvantaged workers who leave one job and search for another, not on their impact on wages of workers continuing in the same job. Indeed, there is no mechanism in the model through which wages change for workers who do not change employers.

V. Job-Movers vs. Job Stayers
There is substantial evidence (e.g., Devereux and Hart, 2006) that wages generally are more procyclical among job-movers than job-stayers. The question suggested by Section IV is whether gender/ethnic/racial wage differentials are more cyclical (either pro-or countercyclical) among job-movers than among job-stayers. The short longitudinal structure of the CPS allows us to answer this question, thus providing a test of the model's implication that changes in unemployment affect wage gaps through their impact on the wage changes experienced by jobchangers.
The CPS does not identify employers, so we assume that workers who list the same small industry of employment in interviews in years t-1 and t are job-stayers, while those who list different industries are job-movers. Given evidence of substantial reporting error in the selfclassification of industry affiliation (Freeman, 1984), our test will thus underestimate the differences in effects between job-stayers and job-movers, since some job-stayers will mistakenly be classified as job-movers. Finally, with losses of perhaps 1/3 of the CPS observations due to an inability to match across the pair of years, and other observations dropped because individuals enter or leave employment, the sample sizes here are smaller than those used in the cross-section analyses in Section III (but, of course, the same as in the analyses reflected in Table 3).
To save space, in Table 6 we present only estimates of the interaction terms ∂ 2 ∆W/∂M∂U Only for women compared to men are the differences between job-movers and jobstayers statistically significant. The difference for blacks is large but only statistically significant at a very low level, while the results for Hispanics at least do not contradict our interpretation of our theory. Remembering that our method of distinguishing job-movers and stayers necessarily blurs the distinction between them, however, these results do seem somewhat convincing. They suggest that it is through wage-setting as new implicit contracts are entered into that the changing market effects of discrimination become felt. Short-run increases in unemployment have less effect on wage differentials within jobs.

VI. Conclusion and Implications
We have documented a relationship between measured discriminatory wage differentials and labor market tightness, as indicated by either state unemployment rates or industry-based measures of shifts in labor demand. We use the longitudinal component of the CPS to explore the extent to which this relationship is due to the changing composition of the labor force as the unemployment rate fluctuates vs. changes in pure wage discrimination. The evidence that a tighter labor market leads to a smaller discriminatory wage gap is strongest and most robust when comparing male and female wages, and is observed in samples of workers of unchanging composition. We also find that the measured African-American-white wage gap increases when the labor market tightens, but this appears to be due mainly to composition effects. There is evidence that pure wage discrimination against Hispanics decreases with lower unemployment, but the effect is only marginally significant. 12 12 The filing of discrimination complaints with the Equal Employment Opportunity Commission is countercyclical for all groups. In a regression describing total annual filings from 1997 through 2011 and including a trend term, the total rose by about 4 percent for each 1 percentage-point increase in the aggregate unemployment rate. Similar responses exist for regressions estimated separately for claims based on sex, national origin or race, despite our evidence that wage effects by race decrease as unemployment increases. (Based on data available at http://eeoc.gov/eeoc/statistics/enforcement/charges.cfm .)

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We develop a search-theoretic model of wage discrimination driven by employer preferences to explore possible causes for these findings. In the model, the cost to the employer of discriminating rises with the tightness of the labor market, which lowers the proportion of discriminators in the market; but recession leads to disproportionately greater exit by discriminating firms, so that the net effect on the amount of discrimination in the labor market and the tightness of the labor market is ambiguous.
In the search model, changes in discriminatory wage differences must come through the wage changes experienced by workers who change jobs, as it includes no mechanism through which employers change the wages paid to continuing employees. We do find that the relationship between changes in the unemployment rate and changes in discriminatory wage differentials is stronger in samples of workers who did change jobs than in samples of job-stayers.
"Discriminatory" wage disadvantages, rising with unemployment among women and falling among African-Americans, are observed disproportionally in the wage changes experienced by job-movers. The next step in re-opening this long-neglected area of study, one that seems especially relevant in the aftermath of the Great Recession, might be to use more detailed sets of data to infer the differential roles of the mechanisms indicated in our model that generate cyclical changes in pure wage discrimination and infer why the net effects differ among the groups we have studied.     Biddle and Hamermesh (1998, Table 3). The estimates are adjusted for a wide variety of control variables.  Table 3.