A Covariate Selection Criterion for Estimation of Treatment Effects
研究在有多组协变量时如何选择或组合平均处理效应（ATE）和受处理者平均处理效应（ATT）的估计量，提出数据驱动的协变量选择准则（CSC）以最小化渐近均方误差，并构造新平均估计量，模拟显示其效率优于单组协变量估计量。
We study how to select or combine estimators of the average treatment effect (ATE) and the average treatment effect on the treated (ATT) in the presence of multiple sets of covariates. We consider two cases: (1) all sets of covariates satisfy the unconfoundedness assumption and (2) some sets of covariates violate the unconfoundedness assumption locally. For both cases, we propose a data-driven covariate selection criterion (CSC) to minimize the asymptotic mean squared errors (AMSEs). Based on our CSC, we propose new average estimators of ATE and ATT, which include the selected estimators based on a single set of covariates as a special case. We derive the asymptotic distributions of our new estimators and propose how to construct valid confidence intervals. Our Monte Carlo simulations show that in finite samples, our new average estimators achieve substantial efficiency gains over the estimators based on a single set of covariates. We apply our new estimators to study the impact of inherited control on firm performance.