P. M. Aronow — Page 2

arXiv2021

Exact Bias Correction for Linear Adjustment of Randomized Controlled Trials

In an influential critique of empirical practice, Freedman (2008) showed that the linear regression estimator was biased for the analysis of randomized controlled trials under the randomization model. Under Freedman's assumptions, we derive exact closed-form bias corrections for the linear regression estimator with and without treatment-by-covariate interactions. We show that the limiting distribution of the bias corrected estimator is identical to the uncorrected estimator, implying that the asymptotic gains from adjustment can be attained without introducing any risk of bias. Taken together with results from Lin (2013), our results show that Freedman's theoretical arguments against the use of regression adjustment can be completely resolved with minor modifications to practice.

stat.ME↗

arXiv2021

Nonparametric identification is not enough, but randomized controlled trials are

We argue that randomized controlled trials (RCTs) are special even among settings where average treatment effects are identified by a nonparametric unconfoundedness assumption. This claim follows from two results of Robins and Ritov (1997): (1) with at least one continuous covariate control, no estimator of the average treatment effect exists which is uniformly consistent without further assumptions, (2) knowledge of the propensity score yields a uniformly consistent estimator and honest confidence intervals that shrink at parametric rates with increasing sample size, regardless of how complicated the propensity score function is. We emphasize the latter point, and note that successfully-conducted RCTs provide knowledge of the propensity score to the researcher. We discuss modern developments in covariate adjustment for RCTs, noting that statistical models and machine learning methods can be used to improve efficiency while preserving finite sample unbiasedness. We conclude that statistical inference has the potential to be fundamentally more difficult in observational settings than it is in RCTs, even when all confounders are measured.

stat.ME↗