Revisiting regression adjustment in experiments with heterogeneous treatment effects

In the context of random sampling, we show that linear full (separate) regression adjustment (FRA) on the control and treatment groups is, asymptotically, no less efficient than both the simple difference-in-means estimator and the pooled regression adjustment estimator; with heterogeneous treatment effects, FRA is usually strictly more efficient. We also propose a class of nonlinear regression adjustment estimators where consistency is ensured despite arbitrary misspecification of the conditional mean function. A simulation study confirms that nontrivial efficiency gains are possible with linear FRA, and that further gains are possible, even under severe mean misspecification, using nonlinear FRA.