Regression Discontinuity Design: Identication and Estimation of Treatment E¤ects with Multiple Selection Biases1

Previous work on the regression discontinuity (RD) design has emphasized identi…cation and estimation of an e¤ect at the selection threshold (discontinuity). Focusing on the so-called “fuzzy”RD design, this paper examines identi…cation and estimation of the average treatment e¤ect (ATE) under various forms of selection bias— selection on the observables, selection on the unobservables, and selection based on heterogeneity in the e¤ects of the treatment. Easy to implement estimators that are root-N consistent and asymptotically normal are derived. They allow for general functional forms for the selection biases and imply speci…cation tests for the plausibility of the statistical assumptions. This paper also investigates the trade-o¤ between e¢ ciency and bias in estimating the average treatment e¤ect (and average e¤ects local to the discontinuity) when the e¤ects covary with the observables and the unobservables. The theoretical results leverage the dual nature of the RD design— both the “borderline experiment” provided near the threshold and the strong and valid exclusion restriction provided in the selection equation for the choice of treatment. This point is demonstrated through MonteCarlo experiments and empirical applications.