Estimation and Inference in Regression Discontinuity Designs with Clustered Sampling

Regression Discontinuity (RD) designs have become popular in empirical studies due to their attractive properties for estimating causal effects under transparent assumptions. Nonetheless, most popular procedures assume i.i.d. data, which is not reasonable in many common applications. To relax this assumption, we derive the properties of traditional non-parametric estimators in a setting that incorporates potential clustering at the level of the running variable, and propose an accompanying optimal-MSE bandwidth selection rule. Simulation results demonstrate that falsely assuming data are i.i.d. when selecting the bandwidth may lead to the choice of bandwidths that are too small relative to the optimal-MSE bandwidth. Last, we apply our procedure using person-level microdata that exhibits clustering at the census tract level to analyze the impact of the Low-Income Housing Tax Credit program on neighborhood characteristics and low-income housing supply.