Regression adjustment in completely randomized experiments with many covariates

Harold D Chiang, Yukitoshi Matsushita and Taisuke Otsu

Papers from arXiv.org

Abstract: This paper investigates estimation and inference for average treatment effects in completely randomized experiments when researchers observe potentially many covariates. Within Neyman's (1923) design-based framework, allowing the number of covariates to grow more slowly than the sample size, we demonstrate that a cross-fitted regression adjustment estimator--adapted from Aronow and Middleton (2013)--exhibits more favorable asymptotic properties than existing alternatives, such as Lin's (2013) regression adjustment estimator and the bias-corrected estimator of Lei and Ding (2021). For inference, we derive the first- and second-order terms in the stochastic expansions of regression-adjusted estimators, analyze the higher-order behavior of existing inference procedures, and introduce a modified version of the HC3 standard error. The proposed methods extend naturally to stratified experiments with large strata. Simulation studies show that the cross-fitted estimator, in combination with the modified HC3, provides accurate point estimates and reliable size control across a wide range of data-generating processes.

Date: 2023-02, Revised 2025-11
New Economics Papers: this item is included in nep-exp
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