American Economic Review
ISSN 0002-8282 (Print) | ISSN 1944-7981 (Online)
Contamination Bias in Linear Regressions
American Economic Review
vol. 114,
no. 12, December 2024
(pp. 4015–51)
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.Citation
Goldsmith-Pinkham, Paul, Peter Hull, and Michal Kolesár. 2024. "Contamination Bias in Linear Regressions." American Economic Review, 114 (12): 4015–51. DOI: 10.1257/aer.20221116Additional Materials
JEL Classification
- C21 Single Equation Models; Single Variables: Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions
- C31 Multiple or Simultaneous Equation Models: Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
- C51 Model Construction and Estimation
- H75 State and Local Government: Health; Education; Welfare; Public Pensions
- I21 Analysis of Education
- I28 Education: Government Policy