Papers › Contamination Bias in Linear Regressions

Contamination Bias in Linear Regressions

9 Jun 2021arXiv:2106.05024archive 2025-07-28

Paul Goldsmith-Pinkham, Peter Hull, Michal Kolesár

We study regressions with multiple treatments and a set of controls that is flexible enough to purge omitted variable bias. We show that these regressions generally fail to estimate convex averages of heterogeneous treatment effects -- instead, estimates of each treatment's effect are contaminated by non-convex 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 re-analysis 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.

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