Econometric Seminar - "Improved Inference for Nonparametric Regression and Regression - Discontinuity Designs"

ABSTRACT: The presence of asymptotic bias complicates inference in nonparametric regression and hence in regression-discontinuity designs (RDD). Nonetheless, RDD remains an extremely relevant andimportant tool in empirical analysis in many fields. Extant solutions to the problem include undersmoothing, which is inefficient, and debiasing methods. The latter includes the current state-of-the-art, which is the well-known and widely applied robust bias corrected (RBC) confidence interval ofCalonico et al. (2014). We show that the RBC interval is equivalent to a prepivoted bootstrap intervalbased on an invalid residual-based bootstrap method. Specifically, prepivoting performs an implicit bias correction while adjusting the nonparametric regression estimator’s standard error to account for the additional uncertainty introduced by debiasing. We also show how these (prepivoted bootstrap-based) intervals can be implemented in a manner similar to RBC without the need for resampling. This idea can be applied also to other bootstrap schemes which leads to other implicit bias corrections and corresponding standard error adjustments. In particular, we consider prepivoting a bootstrap method that generates observations using a fixed-regressor approach derived from nonparametric regression estimates at each regressor value, and we show that for MSE-optimal bandwidths, it has 17% shorter interval length compared to the RBC interval while maintaining accurate coverage probability. These results extend to inference based on local polynomial estimators evaluated at both interior or boundary points, thus encompassing empirically relevant RDD.