Regression discontinuity designs with unknown state-dependent discontinuity points: estimation and testing

Abstract

Abstract This paper extends Regression discontinuity designs with unknown discontinuity points developed by (Porter, J., and P. Yu. 2015. “Regression Discontinuity Designs with Unknown Discontinuity Points: Testing and Estimation.” Journal of Econometrics 189: 132–147.) to allow for state-dependent discontinuity points. We discuss the estimation of the model, and propose test statistics for treatment effect and state dependency in the discontinuity points. We conduct Monte Carlo simulations to compare the proposed estimator with these based on the constant discontinuity RDD and the classic fuzzy RDD, and find that overlooking the state dependency can lead to biased estimates of treatment effects, while the proposed estimator works well and is robust when applied to constant discontinuity RDDs. Monte Carlo experiments also point out that the sizes and powers of the proposed test statistics are generally satisfactory. The model is illustrated with an empirical application.