Does the design of correspondence studies influence the measurement of discrimination?

Correspondence studies can identify the extent of discrimination in hiring as typically defined by the law, which includes discrimination against ethnic minorities and females. However, as Heckman and Siegelman (1993) show, if employers act upon a group difference in the variance of unobserved variables, this measure of discrimination may not be very informative. This issue has essentially been ignored in the empirical literature until the recent methodological development by Neumark (2012). We apply Neumark's method to a number of already published correspondence studies. We find the Heckman and Siegelman critique relevant for empirical work and give suggestions on how future correspondence studies may address this critique.