Regression discontinuity designs: A guide to practice

Abstract

In regression discontinuity (RD) designs for evaluating causal effects of interventions, assignment to a treatment is determined at least partly by the value of an observed covariate lying on either side of a fixed threshold. These designs were first introduced in the evaluation literature by Thistlewaite and Campbell [1960. Regression-discontinuity analysis: an alternative to the ex-post Facto experiment. Journal of Educational Psychology 51, 309–317] With the exception of a few unpublished theoretical papers, these methods did not attract much attention in the economics literature until recently. Starting in the late 1990s, there has been a large number of studies in economics applying and extending RD methods. In this paper we review some of the practical and theoretical issues in implementation of RD methods.

Introduction

Since the late 1990s there has been a large number of studies in economics applying and extending regression discontinuity (RD) methods, including Van Der Klaauw (2002), Black (1999), Angrist and Lavy (1999), Lee (2007), Chay and Greenstone (2005), DiNardo and Lee (2004), Chay et al. (2005), and Card et al. (2006). Key theoretical and conceptual contributions include the interpretation of estimates for fuzzy regression discontinuity (FRD) designs allowing for general heterogeneity of treatment effects (Hahn et al., 2001, HTV from hereon), adaptive estimation methods (Sun, 2005), specific methods for choosing bandwidths (Ludwig and Miller, 2005), and various tests for discontinuities in means and distributions of non-affected variables (Lee, 2007, McCrary, 2007).

In this paper, we review some of the practical issues in implementation of RD methods. There is relatively little novel in this discussion. Our general goal is instead to address practical issues in implementing RD designs and review some of the new theoretical developments.

After reviewing some basic concepts in Section 2, the paper focuses on five specific issues in the implementation of RD designs. In Section 3 we stress graphical analyses as powerful methods for illustrating the design. In Section 4 we discuss estimation and suggest using local linear regression methods using only the observations close to the discontinuity point. In Section 5 we propose choosing the bandwidth using cross-validation. In Section 6 we provide a simple plug-in estimator for the asymptotic variance and a second estimator that exploits the link with instrumental variable methods derived by HTV. In Section 7 we discuss a number of specification tests and sensitivity analyses based on tests for (a) discontinuities in the average values for covariates, (b) discontinuities in the conditional density of the forcing variable, as suggested by McCrary, and (c) discontinuities in the average outcome at other values of the forcing variable.