A Unified Theory of Regression Adjustment for Design-based Inference
Seminar | March 21 | 4-5 p.m. | 1011 Evans Hall
Joel Middleton, UC Berkeley
Under the Neyman causal model, a well-known result is that OLS with treatment-by-covariate interactions cannot harm asymptotic precision of estimated treatment effects in completely randomized experiments. But do such guarantees extend to experiments with more complex designs? This paper proposes a general framework for addressing this question and defines a class of generalized regression estimators that are applicable to experiments of any design. The class subsumes common estimators (e.g., OLS). Within that class, two novel estimators are proposed that are applicable to arbitrary designs and asymptotically optimal. The first is composed of three Horvitz-Thompson estimators. The second recursively applies the principle of generalized regression estimation to obtain regression-adjusted regression adjustment. A simulation study illustrates that the latter can be superior to alternatives in finite samples.