Three Essays on Regression Discontinuity Design

Abstract

My dissertation comprises three chapters, each offering a new methodological approach related to the regression discontinuity design, or RDD. In Chapter 1 I discuss a novel method to estimate the causal effect of an intervention on so-called always-takers. This is relevant for causal inference because standard RDD only identifies the local average treatment effect (LATE) for compliers, often a subset of the actually treated members in the sample. I offer several approaches that require assumptions of different strength, such that the practitioner can draw the most informative inference given the limits of the assumptions they are willing to make.Chapter 2 discusses how to improve the bias correction procedures that are used in RDD inference. My method draws on Bayesian inference and the Gaussian processes literature to incorporate data away from the threshold to inform the typically noisy estimate of the second derivative that plays a key role in bias correction. I demonstrate under broad circumstances that the econometrician can observe my method can significantly improve on the current standard methods in terms of mean-square error. Chapter 3 extends the logic of RDD from inferring the mean of the treatment effect distribution with the relevant discontinuity to inferring the variance of the discontinuity, and even its distribution. This is a useful methodology because there are few credible ways to estimate the variability or distribution of treatment effects in the causal inference literature. The method presented in chapter 3 requires barely any assumptions beyond what is required to identify the LATE, and uses the same intuition that makes RDD one of the more credible types of instrumental variable designs in the first place.