No-harm calibration for generalized Oaxaca-Blinder estimators

Abstract

In randomized experiments, linear regression with baseline features can be used to form an estimate of the sample average treatment effect that is asymptotically no less efficient than the treated-minuscontrol difference in means. Randomization alone provides this "do-no-harm" property, with neither truth of a linear model nor a generative model for the outcomes being required. We present a general calibration step which confers the same no-harm property onto estimators leveraging a broad class of nonlinear models. The process recovers the usual regression-adjusted estimator when ordinary least squares is used, and further provides non-inferior treatment effect estimators using methods such as logistic and Poisson regression. The resulting estimators are non-inferior with respect to both the difference in means estimator and with respect to treatment effect estimators that have not undergone calibration.

Model-assisted complier average treatment effect estimates in randomized experiments with non-compliance and a binary outcome

“…However, τOB,Y and τOB,D cannot always improve the asymptotic efficiency compared with the difference-in-means estimators τY and τD . We refer to Cohen and Fogarty (2021) for a counterexample. Thus, τOB may degrade the efficiency in some extreme cases compared with τwald .…”

“…Although the logistic regression model might be more appropriate to predict binary potential outcomes than the linear regression model, τOB cannot ensure efficiency gains. To solve this non-inferiority problem, we propose a calibrated Oaxaca-Blinder estimator, borrowing techniques from Cohen and Fogarty (2021).…”

“…We find that, although the generalized Oaxaca-Blinder estimator is consistent and asymptotically normal, it may reduce the precision compared with the Wald estimator. To address this issue, we propose a calibrated Oaxaca-Blinder estimator, borrowing an idea from Cohen and Fogarty (2021). We show that it is consistent, asymptotically normal, and more efficient than or at least as efficient as the Wald estimator.…”

“…Applying an intermediate result in the proof of Theorem 1 of Cohen and Fogarty (2021) to the calibrated Oaxaca-Blinder estimators τCOB,Y and τCOB,Y separately, we have the following lemma:…”

Covariate Adjustment in Experiments with Matched Pairs

“…The second estimator we consider first obtains an intermediate estimator by using the LASSO to estimate the "working model" for the relevant conditional expectations. In a finite population setting in which treatment is determined according to complete randomization, Cohen and Fogarty (2020) show that such an estimator is necessarily more precise than the unadjusted difference-in-means estimator. When treatment is determined according to "matched pairs," however, this intermediate estimator need not be the case.…”