Continuous Outcome Tests for Discrimination

Nicolas Grau

Working Papers from University of Chile, Department of Economics

Abstract: The outcome test (Becker, 1957) is a robust way to detect discrimination when selection is based on a predicted outcome. It compares the realized outcomes of the marginal admits of two groups. This paper develops two notions of discrimination for continuous outcomes, which I call risk-adjusted and risk-neutral. They differ in whether the decision maker sets the admission bar on a floor for realized performance or on a threshold for projected performance. I show that, under the risk-adjusted notion, the outcome test reduces to comparing the realized outcomes of the worst-performing admitted individuals of each group. Under the risk-neutral notion, the test reduces to the same comparison plus a correction term that is proportional to the difference between the standard deviations of the realization noise of the two groups, and it is identified under normality. The continuity of the outcome is what makes the inframarginality problem tractable. Neither test requires an instrument, the random assignment of decision makers, or data on rejected applicants. I apply both tests to two settings in Chile. The first one is first-grade admissions to primary schools for the 2014 cohort, where I test for discrimination against applicants who live in a municipality other than the school's. The second one is hiring, where I test for discrimination against individuals with a pretrial detention history. In the school application, I find strong evidence of discrimination under both notions. In the hiring application, the evidence of risk-adjusted discrimination is weak. Once I correct for the different predictability of the outcomes of the two groups, the result reverses.

Pages: 64 pages
Date: 2026-10
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