Joint Inference for the Regression Discontinuity Effect and Its External Validity

Abstract: The external validity of regression discontinuity (RD) designs is essential for informing policy and remains an active research area in econometrics and statistics. However, we document that only a limited number of empirical studies explicitly address the external validity of standard RD effects. To advance empirical practice, we propose a simple joint inference procedure for the RD effect and its local external validity, building on Calonico, Cattaneo, and Titiunik (2014, Econometrica) and Dong and Lewbel (2015, Review of Economics and Statistics). We further introduce a locally linear treatment effects assumption, which enhances the interpretability of the treatment effect derivative proposed by Dong and Lewbel. Under this assumption, we establish identification and derive a uniform confidence band for the extrapolated treatment effects. Our approaches require no additional covariates or design features, making them applicable to virtually all RD settings and thereby enhancing the policy relevance of many empirical RD studies. The usefulness of the method is demonstrated through an empirical application, highlighting its complementarity to existing approaches.