Agnostic notes on regression adjustments to experimental data: Reexamining Freedman's critique

TL;DR

This paper reexamines Freedman's critique of regression adjustment in randomized experiments, showing that with proper modeling and large samples, adjustment improves precision and valid inference, while also discussing transparency concerns.

Contribution

It demonstrates that regression adjustment, when correctly specified and in large samples, does not harm asymptotic precision and provides valid confidence intervals, addressing Freedman's concerns.

Findings

OLS adjustment with treatment-covariate interactions improves precision

Asymptotically valid confidence intervals can be constructed using sandwich estimators

Large samples mitigate Freedman's identified issues

Abstract

Freedman [Adv. in Appl. Math. 40 (2008) 180-193; Ann. Appl. Stat. 2 (2008) 176-196] critiqued ordinary least squares regression adjustment of estimated treatment effects in randomized experiments, using Neyman's model for randomization inference. Contrary to conventional wisdom, he argued that adjustment can lead to worsened asymptotic precision, invalid measures of precision, and small-sample bias. This paper shows that in sufficiently large samples, those problems are either minor or easily fixed. OLS adjustment cannot hurt asymptotic precision when a full set of treatment-covariate interactions is included. Asymptotically valid confidence intervals can be constructed with the Huber-White sandwich standard error estimator. Checks on the asymptotic approximations are illustrated with data from Angrist, Lang, and Oreopoulos's [Am. Econ. J.: Appl. Econ. 1:1 (2009) 136--163] evaluation of strategies to improve college students' achievement. The strongest reasons to support Freedman's preference for unadjusted estimates are transparency and the dangers of specification search.