Contamination Bias in Linear Regressions
Paul Goldsmith-Pinkham, Peter Hull, Michal Kolesár
American Economic Review · 2024 · Volume 114 · Issue 12
Abstract
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.
Keywords
Single Equation Models, Single Variables: Cross-Sectional Models, Spatial Models, Treatment Effect Models, Quantile Regressions, Multiple or Simultaneous Equation Models: Cross-Sectional Models, Social Interaction Models, Model Construction and Estimation, State and Local Government: Health, Education, Welfare, Public Pensions, Analysis of Education, Education: Government Policy
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