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Inference of local regression in the presence of nuisance parameters

Ke-Li Xu

Journal of Econometrics, 2020, vol. 218, issue 2, 532-560

Abstract: We consider inference based on local estimating equations in the presence of nuisance parameters. The framework is useful for a number of applications including those in economic policy evaluation based on discontinuities or kinks and in real-time financial risk management. We focus on the criterion-function-based (in particular, empirical likelihood-based) inference, and establish conditions under which the test statistic has a pivotal asymptotic distribution. In the key step of eliminating nuisance parameters in the (possibly non-smooth) criterion function, we consider two different approaches based on either concentration or Laplace-type plug-in estimation. The former is natural, and the latter does not require optimization and can be computationally attractive in applications. Our framework can easily incorporate bias correction induced by localization, and the inference is robust to the identification strength of the parameter of interest. The high-level assumptions are illustrated with several examples. We also conduct Monte Carlo simulations and provide an empirical application which assesses heterogeneous effects of academic probation in college and gender differences under the quantile regression discontinuity design.

Keywords: Bias correction; Empirical likelihood; Laplace-type estimator; Local estimating equations; Non-smooth criterion function; Nonparametric and semiparametric inference; Nuisance parameter; Quantile regression discontinuity; Weak identification (search for similar items in EconPapers)
JEL-codes: C12 C14 C21 C22 (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:218:y:2020:i:2:p:532-560

DOI: 10.1016/j.jeconom.2020.04.028

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Journal of Econometrics is currently edited by T. Amemiya, A. R. Gallant, J. F. Geweke, C. Hsiao and P. M. Robinson

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