Federico A. Bugni, Ivan A. Canay
arXiv 21 Mar 2018 · Econometrics · publishedJournal of Econometrics (2020) · 36 citations (OpenAlex)
arXiv:1803.07951 · PDF · DOI · OpenAlex · Extracted main text
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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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | McCrary, J (2008) Manipulation of the running variable in the regression discontinuity design: A density test | 1.000 | 12 | 6 | 100% |
| 2 | Cattaneo, M. D., Jansson, M. and Ma, X (2019) Simple local polynomial density estimators | 1.000 | 8 | 4 | 100% |
| 3 | Otsu, T., Xu, K.-L. and Matsushita, Y (2013) Estimation and inference of discontinuity in density | 1.000 | 5 | 3 | 100% |
| 4 | Lee, D. S (2008) Randomized experiments from non-random selection in U.S. house elections | 0.961 | 9 | 6 | 89% |
| 5 | Canay, I. A. and Kamat, V (2018) Approximate permutation tests and induced order statistics in the regression discontinuity design self | 0.941 | 6 | 4 | 83% |
| 6 | Kaufmann, E. and Reiss, R.-D (1992) On conditional distributions of nearest neighbors | 0.894 | 7 | 5 | 71% |
| 7 | Canay, I. A., Romano, J. P. and Shaikh, A. M (2017) Randomization tests under an approximate symmetry assumption self | 0.874 | 5 | 2 | 100% |
| 8 | Armstrong, T. B. and Kolesár, M (2018) Optimal inference in a class of regression models | 0.843 | 3 | 3 | 100% |
| 9 | Low, M. G (1997) On nonparametric confidence intervals | 0.843 | 3 | 3 | 100% |
| 10 | Armstrong, T. B. and Kolesár, M (2019) Simple and Honest Confidence Intervals in Nonparametric Regression | 0.811 | 4 | 2 | 100% |
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