  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.
