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Testing Continuity of a Density via g-order statistics in the Regression Discontinuity Design

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

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 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.

Citation extraction

25
references
90
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Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1McCrary, J (2008) Manipulation of the running variable in the regression discontinuity design: A density test1.000126100%
2Cattaneo, M. D., Jansson, M. and Ma, X (2019) Simple local polynomial density estimators1.00084100%
3Otsu, T., Xu, K.-L. and Matsushita, Y (2013) Estimation and inference of discontinuity in density1.00053100%
4Lee, D. S (2008) Randomized experiments from non-random selection in U.S. house elections0.9619689%
5Canay, I. A. and Kamat, V (2018) Approximate permutation tests and induced order statistics in the regression discontinuity design self0.9416483%
6Kaufmann, E. and Reiss, R.-D (1992) On conditional distributions of nearest neighbors0.8947571%
7Canay, I. A., Romano, J. P. and Shaikh, A. M (2017) Randomization tests under an approximate symmetry assumption self0.87452100%
8Armstrong, T. B. and Kolesár, M (2018) Optimal inference in a class of regression models0.84333100%
9Low, M. G (1997) On nonparametric confidence intervals0.84333100%
10Armstrong, T. B. and Kolesár, M (2019) Simple and Honest Confidence Intervals in Nonparametric Regression0.81142100%

Showing the top 10 of 25 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1On the Rates of Convergence of Induced Ordered Statistics and their Applications0.84333
2Manipulation Test for Multidimensional RDD0.73732
31 Some Finite Sample Properties of the Sign Test0.51121
4Permutation-based tests for discontinuities in event studies0.40511
52009.075510.40511
6Permutation Tests at Nonparametric Rates0.40511
7Regression Discontinuity Designs0.40511
8A unified test for regression discontinuity designs0.40511
9Sensitivity Analysis for Linear Estimators0.40511
10On the Asymptotic Properties of Debiased Machine Learning Estimators0.40511