Title

Contamination Bias in Linear Regressions

Author(s)

Paul Goldsmith-Pinkham Paul Goldsmith-Pinkham (Yale University)

Peter Hull Peter Hull (Brown University)

Michal Kolesár Michal Kolesár (Princeton University)

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 non-convex averages of the effects of other treatments. We discuss three estimation approaches that avoid such contamination bias, including a new estimator of efficiently weighted average effects. We find minimal bias in a re-analysis of Project STAR, due to idiosyncratic effect heterogeneity. But sizeable contamination bias arises when effect heterogeneity becomes correlated with treatment propensity scores.

Creation Date

2022-08

Section URL ID

Paper Number

2022-15

URL

https://www.princeton.edu/~mkolesar/papers/contamination.pdf

File Function

Jel

C14, C21, C22, C90

Keyword(s)

Bias, Decision making, Contamination, Heterogeneity

Suppress

false

Series

13