Testing continuity of a density via g-order statistics in the regression discontinuity design

By Federico A. Bugni, Ivan A. Canay. Journal of Econometrics, 2018

51 citations recorded by the source corpus.

In the regression discontinuity design (RDD), it is common practice to assess the credibility of the design by testing the continuity of the density of the running variable at the cut-off, e.g., McCrary (2008). In this paper we propose an approximate sign test for continuity of a density at a point based on the so-called g-order statistics, and study its properties under two complementary asymptotic frameworks. In the first asymptotic framework, the number q of observations local to the cut-off is fixed as the sample size n diverges to infinity, while in the second framework q diverges to infinity slowly as n diverges to infinity. Under both of these frameworks, we show that the test we propose is asymptotically valid in the sense that it has limiting rejection probability under the null hypothesis not exceeding the nominal level. More importantly, the test is easy to implement, asymptotically valid under weaker conditions than those used by competing methods, and exhibits finite sample validity under stronger conditions than those needed for its asymptotic validity. In a simulation study, we find that the approximate sign test provides good control of the rejection probability under the null hypothesis while remaining competitive under the alternative hypothesis. We finally apply our test to the design in Lee (2008), a well-known application of the RDD to study incumbency advantage.

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Citations in the corpus

Regression Discontinuity Designs (2021, unknown): “Frandsen (2017) proposes a manipulation test for discrete scores and Bugni and Canay (2021) propose a binomial-like test using an asymptotic argument to justify local randomization near the cutoff, both employing a uniform-in-bias approach that requires the manual choice of a theoretical smoothness ”
Breaking Ties: Regression Discontinuity Design Meets Market Design (2019, background): “This work is likely to build on the asymptotic framework in Bugni and Canay (2018) and the study of RD designs with multiple tie-breakers in Papay et al. (2011), Zajonc (2012), Wong et al. (2013b) and Cattaneo et al. (2020). It may be possible to extend the reasoning behind doubly robust nonparametr”