TY - JOUR
T1 - Testing continuity of a density via g-order statistics in the regression discontinuity design
AU - Bugni, Federico A.
AU - Canay, Ivan A.
N1 - Funding Information:
The research of the first author was supported by NSF, United States of America Grant SES-1729280 and the research of the second author was supported by NSF, United States of America Grant SES-1530534. Special thanks go out to Tim Armstrong for pointing out a problem in Section 4.2 of an earlier manuscript. We also thank Xiaohong Chen, the Associate Editor, and three referees for helpful comments. We finally thank Jackson Bunting, Joe Long, and Deborah Kim for excellent research assistance.
Funding Information:
The research of the first author was supported by NSF, United States of America Grant SES-1729280 and the research of the second author was supported by NSF, United States of America Grant SES-1530534 . Special thanks go out to Tim Armstrong for pointing out a problem in Section 4.2 of an earlier manuscript. We also thank Xiaohong Chen, the Associate Editor, and three referees for helpful comments. We finally thank Jackson Bunting, Joe Long, and Deborah Kim for excellent research assistance.
Publisher Copyright:
© 2020 Elsevier B.V.
PY - 2021/3
Y1 - 2021/3
N2 - 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.
AB - 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.
KW - Continuity
KW - Density
KW - Regression discontinuity design
KW - Sign tests
KW - g-ordered statistics
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U2 - 10.1016/j.jeconom.2020.02.004
DO - 10.1016/j.jeconom.2020.02.004
M3 - Article
AN - SCOPUS:85082517413
VL - 221
SP - 138
EP - 159
JO - Journal of Econometrics
JF - Journal of Econometrics
SN - 0304-4076
IS - 1
ER -