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

Federico A. Bugni and Ivan A. Canay
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Federico A. Bugni: Institute for Fiscal Studies and Duke University
Ivan A. Canay: Institute for Fiscal Studies and Northwestern University

No CWP20/18, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

Abstract: 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 a new test for continuity of a density at a point based on the so-called g-order statistics, and study its properties under a novel asymptotic framework. The asymptotic framework is intended to approximate a small sample phenomenon: even though the total number n of observations may be large, the number of effective observations local to the cut-off is often small. Thus, while traditional asymptotics in RDD require a growing number of observations local to the cut-off as n ? 8, our framework allows for the number q of observations local to the cut-off to be fixed as n ? 8. The new test is easy to implement, asymptotically valid under weaker conditions than those used by competing methods, exhibits finite sample validity under stronger conditions than those needed for its asymptotic validity, and has favorable power properties against certain alternatives. In a simulation study, we find that the new test controls size remarkably well across designs. We finally apply our test to the design in Lee (2008), a well-known application of the RDD to study incumbency advantage.

Keywords: Regression discontinuity design; g-ordered statistics; sign tests; continuity; density (search for similar items in EconPapers)
JEL-codes: C12 C14 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm
Date: 2018-03-21
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