A Unified Robust Bootstrap Method for Sharp/Fuzzy Mean/Quantile Regression Discontinuity/Kink Designs

Computation of asymptotic distributions is known to be a nontrivial and delicate task for the regression discontinuity designs (RDD) and the regression kink designs (RKD). It is even more complicated when a researcher is... [ view full abstract ]

Computation of asymptotic distributions is known to be a nontrivial and delicate task for the regression discontinuity designs (RDD) and the regression kink designs (RKD). It is even more complicated when a researcher is interested in joint or uniform inference across heterogeneous subpopulations indexed by covariates or quantiles. Hence, bootstrap procedures are often preferred in practice. This paper develops a robust multiplier bootstrap method for a general class of local Wald estimators. It applies to the sharp mean RDD, the fuzzy mean RDD, the sharp mean RKD, the fuzzy mean RKD, the sharp quantile RDD, the fuzzy quantile RDD, the sharp quantile RKD, and the fuzzy quantile RKD, to list a few examples, as well as covariate-indexed versions of them. In addition to its generic applicability to a wide variety of local Wald estimators, our method also enjoys robustness against large bandwidths commonly used in practice. This robustness is achieved through a bias correction approach incorporated into our multiplier bootstrap framework. We demonstrate the generic applicability of our theory through ten examples of local Wald estimators including those listed above, and show by simulation studies that it indeed performs well, robustly, and uniformly across different examples.