  Diagnostic tests for regression discontinuity design face a size-control
problem. We document a massive over-rejection of the identifying restriction
among empirical studies in the top five economics journals. At least one
diagnostic test was rejected for 21 out of 60 studies, whereas less than 5% of
the collected 799 tests rejected the null hypotheses. In other words, more than
one-third of the studies rejected at least one of their diagnostic tests,
whereas their underlying identifying restrictions appear valid. Multiple
testing causes this problem because the median number of tests per study was as
high as 12. Therefore, we offer unified tests to overcome the size-control
problem. Our procedure is based on the new joint asymptotic normality of local
polynomial mean and density estimates. In simulation studies, our unified tests
outperformed the Bonferroni correction. We implement the procedure as an R
package rdtest with two empirical examples in its vignettes.
