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Sieve Quasi Likelihood Ratio Inference on Semi/nonparametric Conditional Moment Models

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Abstract

This paper considers inference on functionals of semi/nonparametric conditional moment restrictions with possibly nonsmooth generalized residuals. These models belong to the difficult (nonlinear) ill-posed inverse problems with unknown operators, and include all of the (nonlinear) nonparametric instrumental variables (IV) as special cases. For these models it is generally difficult to verify whether a functional is regular (i.e., root-n estimable) or irregular (i.e., slower than root-n estimable). In this paper we provide computationally simple, unified inference procedures that are asymptotically valid regardless of whether a functional is regular or irregular. We establish the following new results: (1) the asymptotic normality of the plug-in penalized sieve minimum distance (PSMD) estimators of the (possibly irregular) functionals; (2) the consistency of sieve variance estimators of the plug-in PSMD estimators; (3) the asymptotic chi-square distribution of an optimally weighted sieve quasi likelihood ratio (SQLR) statistic; (4) the asymptotic tight distribution of a possibly non-optimally weighted SQLR statistic; (5) the consistency of the nonparametric bootstrap and the weighted bootstrap (possibly non-optimally weighted) SQLR and sieve Wald statistics, which are proved under virtually the same conditions as those for the original-sample statistics. Small simulation studies and an empirical illustration of a nonparametric quantile IV regression are presented.

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  • Xiaohong Chen & Demian Pouzo, 2013. "Sieve Quasi Likelihood Ratio Inference on Semi/nonparametric Conditional Moment Models," Cowles Foundation Discussion Papers 1897, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1897
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    File URL: http://cowles.yale.edu/sites/default/files/files/pub/d18/d1897.pdf
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    5. Otsu, Taisuke, 2011. "Empirical Likelihood Estimation Of Conditional Moment Restriction Models With Unknown Functions," Econometric Theory, Cambridge University Press, vol. 27(01), pages 8-46, February.
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    Cited by:

    1. Christoph Breunig & Enno Mammen & Anna Simoni, "undated". "Nonparametric Estimation in case of Endogenous Selection," SFB 649 Discussion Papers SFB649DP2015-050, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    2. Chernozhukov, Victor & Fernández-Val, Iván & Hoderlein, Stefan & Holzmann, Hajo & Newey, Whitney, 2015. "Nonparametric identification in panels using quantiles," Journal of Econometrics, Elsevier, vol. 188(2), pages 378-392.
    3. Christoph Breunig & Stefan Hoderlein, "undated". "Specification Testing in Random Coefficient Models," SFB 649 Discussion Papers SFB649DP2015-053, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

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