Estimation and inference of discontinuity in density

Taisuke Otsu, Ke Li Xu, Yukitoshi Matsushita

研究成果: Article査読

20 被引用数 (Scopus)


Continuity or discontinuity of probability density functions of data often plays a fundamental role in empirical economic analysis. For example, for identification and inference of causal effects in regression discontinuity designs it is typically assumed that the density function of a conditioning variable is continuous at a cutoff point that determines assignment of a treatment. Also, discontinuity in density functions can be a parameter of economic interest, such as in analysis of bunching behaviors of taxpayers. To facilitate researchers to conduct valid inference for these problems, this article extends the binning and local likelihood approaches to estimate discontinuity of density functions and proposes empirical likelihood-based tests and confidence sets for the discontinuity. In contrast to the conventional Wald-type test and confidence set using the binning estimator, our empirical likelihood-based methods (i) circumvent asymptotic variance estimation to construct the test statistics and confidence sets; (ii) are invariant to nonlinear transformations of the parameters of interest; (iii) offer confidence sets whose shapes are automatically determined by data; and (iv) admit higher-order refinements, so-called Bartlett corrections. Firstand second-order asymptotic theories are developed. Simulations demonstrate the superior finite sample behaviors of the proposed methods. In an empirical application, we assess the identifying assumption of no manipulation of class sizes in the regression discontinuity design studied by Angrist and Lavy (1999).

ジャーナルJournal of Business and Economic Statistics
出版ステータスPublished - 2013

ASJC Scopus subject areas

  • 統計学および確率
  • 社会科学(その他)
  • 経済学、計量経済学
  • 統計学、確率および不確実性


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