Testing the Presence of Implicit Hiring Quotas with Application to German Universities

Abstract: It is widely accepted that women are underrepresented in academia in general and economics in particular. This paper introduces a test to detect an under-researched form of hiring bias: implicit quotas. I derive a test under the Null of random hiring that requires no information about individual hires under some assumptions. I derive the asymptotic distribution of this test statistic and, as an alternative, propose a parametric bootstrap procedure that samples from the exact distribution. This test can be used to analyze a variety of other hiring settings. I analyze the distribution of female professors at German universities across 50 different disciplines. I show that the distribution of women, given the average number of women in the respective field, is highly unlikely to result from a random allocation of women across departments and more likely to stem from an implicit quota of one or two women on the department level. I also show that a large part of the variation in the share of women across STEM and non-STEM disciplines could be explained by a two-women quota on the department level. These findings have important implications for the potential effectiveness of policies aimed at reducing underrepresentation and providing evidence of how stakeholders perceive and evaluate diversity.