Agnostic Notes on Regression Adjustments to Experimental Data:
Reexamining Freedman's Critique
Freedman [Adv. in Appl. Math. 40 (2008a) 180–193; Ann. Appl. Stat. (2008b) 2 176–196] critiqued OLS regression adjustment of estimated treatment effects in randomized experiments, using Neyman’s model for randomization inference. This paper argues that in sufficiently large samples, the statistical problems he raised are either minor or easily fixed. OLS adjustment improves or does not hurt asymptotic precision when the regression includes a full set of treatment-covariate interactions. Asymptotically valid confidence intervals can be constructed with the Huber-White sandwich standard error estimator. Even the traditional OLS adjustment has benign large-sample properties when subjects are randomly assigned to two groups of equal size. The strongest reasons to support Freedman’s preference for unadjusted estimates are transparency and the dangers of specification search.
Neyman's repeated sampling approach
Document ID Number