  We develop tools for utilizing correspondence experiments to detect illegal
discrimination by individual employers. Employers violate US employment law if
their propensity to contact applicants depends on protected characteristics
such as race or sex. We establish identification of higher moments of the
causal effects of protected characteristics on callback rates as a function of
the number of fictitious applications sent to each job ad. These moments are
used to bound the fraction of jobs that illegally discriminate. Applying our
results to three experimental datasets, we find evidence of significant
employer heterogeneity in discriminatory behavior, with the standard deviation
of gaps in job-specific callback probabilities across protected groups
averaging roughly twice the mean gap. In a recent experiment manipulating
racially distinctive names, we estimate that at least 85% of jobs that contact
both of two white applications and neither of two black applications are
engaged in illegal discrimination. To assess the tradeoff between type I and II
errors presented by these patterns, we consider the performance of a series of
decision rules for investigating suspicious callback behavior under a simple
two-type model that rationalizes the experimental data. Though, in our
preferred specification, only 17% of employers are estimated to discriminate on
the basis of race, we find that an experiment sending 10 applications to each
job would enable accurate detection of 7-10% of discriminators while falsely
accusing fewer than 0.2% of non-discriminators. A minimax decision rule
acknowledging partial identification of the joint distribution of callback
rates yields higher error rates but more investigations than our baseline
two-type model. Our results suggest illegal labor market discrimination can be
reliably monitored with relatively small modifications to existing audit
designs.
