Robust Nonparametric Con\u85dence Intervals for Regression-Discontinuity Designs

In the regression-discontinuity (RD) design, units are assigned to treatment based on whether their value of an observed covariate exceeds a known cuto¤. In this design, local polynomial estimators are now routinely employed to construct con\u85dence intervals for treatment e¤ects. The performance of these con\u85dence intervals in applications, however, may be seriously hampered by their sensitivity to the speci\u85c bandwidth employed. Available bandwidth selectors typically yield a large bandwidth, leading to data-driven con\u85dence intervals that may be biased, with empirical coverage well below their nominal target. We propose new theory-based, more robust con\u85dence interval estimators for average treatment e¤ects at the cuto ¤ in sharp RD, sharp kink RD, fuzzy RD and fuzzy kink RD designs. Our proposed con\u85dence intervals are constructed using a bias-corrected RD estimator together with a novel standard error estimator. For practical implementation, we discuss mean-square error optimal bandwidths, which are by construction not valid for conventional con\u85dence intervals but are valid with our robust approach, and consistent standard error estimators based on our new variance formulas. In a special case of practical interest, our procedure amounts to running a quadratic instead of a linear local regression. More generally, our results give a formal justi\u85cation to simple inference procedures based on increasing the order of the local polynomial estimator employed. We \u85nd in a simulation study that our con\u85dence intervals exhibit close-to-correct empirical coverage and good empirical interval length on average, remarkably improving upon the alternatives available in the literature. All results are readily available in R and STATA using our companion software packages described in Calonico, Cattaneo an