Regression Discontinuity Designs

Abstract

The regression discontinuity (RD) design is one of the most widely used nonexperimental methods for causal inference and program evaluation. Over the last two decades, statistical and econometric methods for RD analysis have expanded and matured, and there is now a large number of methodological results for RD identification, estimation, inference, and validation. We offer a curated review of this methodological literature organized around the two most popular frameworks for the analysis and interpretation of RD designs: the continuity framework and the local randomization framework. For each framework, we discuss three main topics: ( a) designs and parameters, focusing on different types of RD settings and treatment effects of interest; ( b) estimation and inference, presenting the most popular methods based on local polynomial regression and methods for the analysis of experiments, as well as refinements, extensions, and alternatives; and ( c) validation and falsification, summarizing an array of mostly empirical approaches to support the validity of RD designs in practice.

A Practical Introduction to Regression Discontinuity Designs: Extensions

“…The goal of our two-part monograph is purposely practical and hence we focus on the empirical analysis of RD designs. We do not seek to provide a comprehensive review of the methodological literature on RD designs, which we do in Cattaneo and Titiunik (2022), nor discuss theoretical aspects in detail. As we did in our the first volume, we mostly refrain from citing prior literature on the main sections; instead, we provide a short list of references at the end of each section to guide readers who are interested in further methodological details and formal theoretical results.…”

“…The interpretation of the RD design as a local experiment and its connection to the continuity-based framework is also discussed by Sekhon and. Other refinements are surveyed in Cattaneo and Titiunik (2022). For an RD application where the treatment is truly randomized in a window around the cutoff, see Hyytinen, Meriläinen, Saarimaa, Toivanen, and Tukiainen (2018).…”

“…We warn the reader, however, that these references are not meant to be exhaustive. A comprehensive review of the RD literature can be found in Cattaneo and Titiunik (2022).…”

Regression discontinuity design to evaluate the effect of statins on myocardial infarction in electronic health records

“…RDD, an increasingly popular quasiexperimental method, [5][6][7][8][9] is aimed at deriving causal estimates from observational data. [10][11][12][13] RDD leverages clinical or policy decision rules in which people fall on either side of a threshold or cutoff for recommending treatment. The assumption is that persons falling just above or below the threshold, as in the 20% CVD risk score cutoff of the UK guideline, are exchangeable, and thus causal estimates can be made near this threshold.…”

Regression discontinuity design with right-censored survival data

“…The regression discontinuity design is a widely used technique for causal inference in economics, political science, and sociology (see Van der Klaauw (2008), Imbens and Lemieux (2008), Lee and Lemieux (2010), and Cattaneo and Titiunik (2022) for recent reviews). In the regression discontinuity design, possible confounders are 'controlled for' by exploiting that units are assigned to treatment based on whether their value of an observed covariate is above or below some known cutoff, the idea being that units with values of this observed covariate just above the known cut-off are similar to the subjects with values just below the cut-off.…”