Opportunities Denied, Wages Diminished: Using Search Theory to Translate Audit-Pair Study Findings into Wage Differentials

Heckman and Siegelman (1993) and Heckman (1998) note a number of additional factors that may also limit the accuracy and precision of the audit studies, including how the job openings were identified, the types of jobs audited, the non-double-blind protocol used, and paying less attention to the vast majority of the cases where auditors received equal treatment.

These potential reactions to adverse stereotyping are actually quite similar to the ones that can result from Affirmative Action policies. See Coate and Loury (1993) for a complete development of these and other equilibria.

In this well-known song, a father gives his son the traditional female name Sue. He does this because he believes that his child will face a rough world and that giving him this name will force him to develop the toughness necessary to overcome adversity (Cash and Silverstein 1969).

By this, I mean studies that collect and analyze data on job identification, when an applicant’s race is revealed, the nature of the jobs and wages exhibiting differential treatment, etc., could address some critiques. However, the question about whether any audit study of the labor market can pair applicants effectively enough to yield precise results is decidedly open and depends largely on the ability for the experimenter to match unobserved qualities and signals between applicants.

As in Black (1995), the job creation and firm entry dynamics often associated with “general equilibria” are not developed by the model. This maintains the proportion of prejudiced firms in the market, a situation that might be unstable in a model with endogenous firm entry. Alternatively, the issue of firm entry and job creation can be addressed by assuming that any new firms or jobs are created according to the existing proportion of firm types.

This effectively assumes that the cost of search is simply an opportunity cost. Including a “standard” per period search cost would have minimal impact on the results. Alternatively, more complex cost functions (e.g. those that depend on the number of postings, the time spent unemployed, etc.) may have greater impact on the results, but this is beyond the scope necessary to address this article’s primary concerns. This is especially true when simulating the impact of audit study differentials, as these studies focused on publicly advertised, entry-level jobs with low-skill requirements (i.e. jobs that would be expected to have a fairly elastic supply and be easily and consistently searched).

This effectively assumes that the prospects facing a worker are identical from period to period. This is a somewhat strong assumption and allows for a simplified reduced form for reservation wages. But, provided a worker has no knowledge of upcoming changes to labor market conditions in the short run and discounts future earnings, it should not significantly impact the resulting reservation wage’s magnitude. For low-skill and entry-level jobs (like those tested by audit studies), this assumption seems especially appropriate.

This assumption removes any wage differentials offered by firms driven by different costs or patience levels. The assumption of perfect patience also avoids the problem of firms altering their wages when in competition for a worker who has received multiple offers in a given period. Since, patient firms are more willing to wait for a future match than to adjust their wage offer in the current period to ensure a match. This assumption seems especially appropriate for entry-level jobs, which are particularly relevant to this analysis.

Black himself notes this, stating that policies of offering different wages based on an applicant’s race is illegal, and firms would likely only adopt this regime in those cases where they can segregate by job or occupation (Black 1995, 317). While the implication is clear in his article that some employers could choose not to exploit the discriminatory preferences of other market agents, the profit motives of employers are assumed to trump any equity or Equal Employment Opportunity compliance considerations.

The specific form of utility assumed both in this article and in Black (1995) is linear in w and , i.e. .

These conditions follow from setting the first derivatives of eqs [6] and [7] equal to 0 and rearranging. These derivatives are and (MP-wu)-(1-G_u(W^h - W_u))]+ (l/h+1) [gu](W^l - W_u) (MP-W_u)-(1-G_u(W^l - W_u))], respectively.

Note that the UI and FEC studies have record data for both Pr(offer | interview) and Pr(interview | application), but that the Bertrand and Mullainathan study only collect data for Pr(interview | application) (as no face-to-face interviews are conducted). Therefore, the data from the Bertrand and Mullainathan study will only impact the values of Pr(interview | application) used in the Cross-Study simulations.

Adjusting the level of the top code and/or trimming extreme values in place of recoding them have little impact on this analysis. Additionally, there are so few of these observations that it is unlikely they represent an important subset of exceptionally high or low earners. Recoding was chosen for its generally desirable properties relative to trimming. For a complete discussion of the appropriateness, limits, and desirability of recoding extreme wages compared to trimming them or leaving them unaltered, see Bollinger and Chandra (2005).

While the importance of selection is mitigated here, it is not eliminated. Specifically, while the classical concern regarding the (intensive) selection of wage offers is less important with this specification, the selection into the labor force is still relevant. This is especially true, since the NLSY79 data on reservation wages is only collected for respondents who are unemployed at the time of their interview. As many more would-be black workers find themselves out of the labor force, this extensive margin for selection into the labor force still provides a relevant concern (for example, see Brown 1984).

Estimates were also calculated using values of 0, 0.05, and 0.10 for the proportion of rejected offers, with F(w_h) > Fw_l, and the results proved highly robust.

A range of values from β = 0:90 to β = 0:999 were also tested, and no substantive differences from the reported results were realized.

Unfortunately, these responses were only collected from respondents who were unemployed at the time of their interview. It is clear that these reservation wages may systematically differ from the reservation wages of individuals that are currently employed; unfortunately it is unclear that how they would differ. It could be that the reservation wages of unemployed workers are higher than those of the employed population, which would help account for their unemployment status. It is equally plausible that these unemployed individuals are not employed due to lower skill, motivation, and/or other qualities desirable to employers, which would lead to lower reservation wages compared to the general population.

Alternative assumptions about the underlying wage distribution that preserve the common nature of the wages facing black and white workers (e.g. using the observed distribution of wages realized by white workers, changing the relative proportions of offers rejected, etc.) results in minimal differences to the estimated gaps in reservation wages.

An alternative set of simulations using a random draw from the actual wages in the NLSY79 in place of the chi-square distribution yielded very similar results. However, there is a fair amount of “lumpiness” in reported wages that may imply rounding by NLSY79 respondents. This “smoothed” chi-square representation of the distribution mimics the reported distribution well and may be a better representation for the population of possible wage offers facing searchers.

Similar sensitivity/robustness checks were run for each audit study’s data, for each group of NLSY respondents and with additional changes to the distributions. Most showed similar patterns in results. For the sake of brevity, I only provide the output for this representative set of simulations.

For all density estimates, I use the Epanechnikov kernel and allow STATA to select the optimal bandwidth. For the NLSY79 density estimates, I restrict the data to include only those wages that fall within the range of simulated wages and again use the Epanechnikov kernel (but select a bandwidth of 1 to achieve comparable smoothing to that of the simulated values). The choice of kernel and bandwidth does not appear to be important for this article’s use of the graphs, as each plot looks very similar when Gaussian kernels and/or alternative bandwidths are used.

It should be noted that I perform no formal tests of fit here. These distributions are meant only to offer evidence that the baseline assumptions are preferred to the alternatives, at least for the purposes of this article (i.e. to show that the hiring differences reported by audit studies can yield non-trivial wage gaps).