Abstract

It is a routine procedure to perform two diagnostic tests for validating regression discontinuity (RD) designs. However, their joint test has not been proposed. Therefore, the practices of these tests suffer from the multiple-testing problem. We show the joint asymptotic normality of multiple local-polynomial RD estimators and the local-polynomial density estimator. The joint distribution allows us to construct a joint testing procedure. The proposed test has better size control and power properties than the naive procedure or the Bonferroni correction. We apply our test to a controversy over the validity of the RD application to the U.S. House of Representatives elections.