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We study regressions with multiple treatments and a set of controls that is flexible enough to purge omitted variable bias. We show these regressions generally fail to estimate convex averages of heterogeneous treatment effects—instead, estimates of each treatment’s effect are contaminated by nonconvex averages of the effects of other treatments. We discuss three estimation approaches that avoid such contamination bias, including the targeting of easiest-to-estimate weighted average effects. A reanalysis of nine empirical applications finds economically and statistically meaningful contamination bias in observational studies; contamination bias in experimental studies is more limited due to smaller variability in propensity scores.more » « lessFree, publicly-accessible full text available December 1, 2025
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Arnold, David; Dobbie, Will; Hull, Peter (, AEA Papers and Proceedings)Algorithmic decision-making can lead to discrimination against legally protected groups, but measuring such discrimination is often hampered by a fundamental selection challenge. We develop new quasi-experimental tools to overcome this challenge and measure algorithmic discrimination in pretrial bail decisions. We show that the selection challenge reduces to the challenge of measuring four moments, which can be estimated by extrapolating quasi-experimental variation across as-good-as-randomly assigned decision-makers. Estimates from New York City show that both a sophisticated machine learning algorithm and a simpler regression model discriminate against Black defendants even though defendant race and ethnicity are not included in the training data.more » « less
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Angrist, Joshua D.; Hull, Peter D.; Pathak, Parag A.; Walters, Christopher R. (, The Quarterly Journal of Economics)
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Abdulkadiroğlu, Atila; Angrist, Joshua D.; Hull, Peter D.; Pathak, Parag A. (, American Economic Review)
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