Seminario IECON: Continuous Outcome Tests for Discrimination

Becker's (1957) outcome test detects discrimination by comparing the outcomes of each group's marginal admitted individual. In practice, marginal individuals are rarely observed (the inframarginality problem). I show that the problem becomes tractable when the outcome is continuous. I propose two notions of discrimination, depending on whether the decision maker sets a minimum realized performance (risk-adjusted) or a minimum expected performance (risk-neutral). Under the risk-adjusted notion, the test compares the realized outcomes of the lowest-performing admitted individual in each group. Under the risk-neutral notion, this comparison is corrected by a term proportional to the difference between the groups' standard deviations of outcome noise. Neither test requires an instrument, random assignment of decision makers, or data on rejected applicants. I apply both tests to two Chilean settings. In first-grade school admissions (2014 cohort), I find strong evidence of discrimination against applicants who live outside the school's municipality under both notions. The effect is concentrated in schools that select students and persists when outcomes are measured with tests the schools do not grade. In hiring, evidence of discrimination against individuals with a pretrial detention history is weak under the risk-adjusted notion but is reversed under the risk-neutral one. Because the two notions disagree, realized outcomes alone cannot determine whether this employer discriminates

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