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There is a growing literature on design-based methods to estimate averagetreatment effects for randomized controlled trials (RCTs) using theunderpinnings of experiments. In this article, we build on these methods toconsider design-based regression estimators for the local average treatmenteffect (LATE) estimand for RCTs with treatment noncompliance. We prove newfinite-population central limit theorems for a range of designs, includingblocked and clustered RCTs, allowing for baseline covariates to improveprecision. We discuss consistent variance estimators based on model residualsand conduct simulations that show the estimators yield confidence intervalcoverage near nominal levels. We demonstrate the methods using data from aprivate school voucher RCT in New York City USA.

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