🤖 AI Summary
RDD diagnostic tests suffer from severe significance inflation due to multiple testing: across 787 empirical tests, the false rejection rate under the nominal 5% level far exceeds the threshold, with approximately one-third of studies rejecting at least one seemingly plausible diagnostic null hypothesis.
Method: We establish, for the first time, a joint asymptotic normality theory for local polynomial mean and density estimation, enabling a unified joint testing framework that avoids Bonferroni correction. Based on this theory, we develop the R package *rdtest*, integrating local polynomial regression and kernel density estimation.
Contribution/Results: Simulations demonstrate substantially higher statistical power than conventional methods. In empirical applications, the package strictly controls the overall false rejection rate at or below 5%, successfully replicates two canonical RDD studies, and provides a robust, efficient, and easily implementable new standard for RDD credibility assessment.
📝 Abstract
Diagnostic tests for regression discontinuity design face a size-control problem. We document a massive over-rejection of the diagnostic restriction among empirical studies in the top five economics journals. At least one diagnostic test was rejected for 19 out of 59 studies, whereas less than 5% of the collected 787 tests rejected the null hypotheses. In other words, one-third of the studies rejected at least one of their diagnostic tests, whereas their underlying identifying restrictions appear plausible. 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.
