The Regression Discontinuity (RD) design is one of the most popular and credible research designs for program evaluation and causal inference. This volume 38 of Advances in Econometrics collects twelve innovative and thought-provoking contributions to the RD literature, covering a wide range of methodological and practical topics. Some chapters touch on foundational methodological issues such as identification, interpretation, implementation, falsification testing, estimation and inference, while others focus on more recent and related topics such as identification and interpretation in a discontinuity-in-density framework, empirical structural estimation, comparative RD methods, and extrapolation. These chapters not only give new insights for current methodological and empirical research, but also provide new bases and frameworks for future work in this area. This volume contributes to the rapidly expanding RD literature by bringing together theoretical and applied econometricians, statisticians, and social, behavioural and biomedical scientists, in the hope that these interactions will further spark innovative practical developments in this important and active research area.

In this Element and its accompanying second Element, A Practical Introduction to Regression Discontinuity Designs: Extensions, Matias Cattaneo, Nicolas Idrobo, and Rociio Titiunik provide an accessible and practical guide for the analysis and interpretation of regression discontinuity (RD) designs that encourages the use of a common set of practices and facilitates the accumulation of RD-based empirical evidence. In this Element, the authors discuss the foundations of the canonical Sharp RD design, which has the following features: (i) the score is continuously distributed and has only one dimension, (ii) there is only one cutoff, and (iii) compliance with the treatment assignment is perfect. In the second Element, the authors discuss practical and conceptual extensions to this basic RD setup.