Design-Based RCT Estimators and Central Limit Theorems for Baseline Subgroup and Related Analyses

There is a growing literature on design-based methods to estimate average treatment effects (ATEs) for randomized controlled trials (RCTs) for full sample analyses. This article extends these methods to estimate ATEs for discrete subgroups defined by pre-treatment variables, with an application to an RCT testing subgroup effects for a school voucher experiment in New York City. We consider ratio estimators for subgroup effects using regression methods, allowing for model covariates to improve precision, and prove a finite population central limit theorem. We discuss extensions to blocked and clustered RCT designs, and to other common estimators with random treatment-control sample sizes (or weights): post-stratification estimators, weighted estimators that adjust for data nonresponse, and estimators for Bernoulli trials. We also develop simple variance estimators that share features with robust estimators. Simulations show that the design-based subgroup estimators yield confidence interval coverage near nominal levels, even for small subgroups

Design-Based Estimation and Central Limit Theorems for Local Average Treatment Effects for RCTs

There is a growing literature on design-based methods to estimate average treatment effects for randomized controlled trials (RCTs) using the underpinnings of experiments. In this article, we build on these methods to consider design-based regression estimators for the local average treatment effect (LATE) estimand for RCTs with treatment noncompliance. We prove new finite-population central limit theorems for a range of designs, including blocked and clustered RCTs, allowing for baseline covariates to improve precision. We discuss consistent variance estimators based on model residuals and conduct simulations that show the estimators yield confidence interval coverage near nominal levels. We demonstrate the methods using data from a private school voucher RCT in New York City USA.Comment: arXiv admin note: substantial text overlap with arXiv:2310.0872