A unified test for regression discontinuity designs

TL;DR

This paper identifies a size-control problem in diagnostic tests for regression discontinuity designs, documents its prevalence in top economics journals, and proposes unified tests based on joint asymptotic normality to improve validity.

Contribution

It introduces a new unified testing procedure for regression discontinuity diagnostics that addresses multiple testing issues and outperforms traditional corrections.

Findings

High over-rejection rate in empirical studies.

Unified tests outperform Bonferroni correction in simulations.

Implementation available as R package rdtest.

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.