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Sieve Wald and QLR Inferences on Semi/nonparametric Conditional Moment Models

Author

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  • Xiaohong Chen
  • Demian Pouzo
Abstract
This paper considers inference on functionals of semi/nonparametric conditional moment restrictions with possibly nonsmooth generalized residuals, which include all of the (nonlinear) nonparametric instrumental variables (IV) as special cases. There models are often illposed and hence it is difficult to verify whether a (possibly nonlinear) functional is root-n estimable or not. We provide computationally simple, unied inference procedures that are asymptotically valid regardless of whether a functional is root-n estimable or not. We establish the following new useful results: (1) the asymptotic normality of a plug-in penalized sieve minimum distance (PSMD) estimator of a (possibly nonlinear) functional; (2) the consistency of simple sieve variance estimators for the plug-in PSMD estimator, and hence the asymptotic chi-square distribution of the sieve Wald statistic; (3) the asymptotic chi-square distribution of an optimally weighted sieve quasi likelihood ratio (QLR) test under the null hypothesis; (4) the asymptotic tight distribution of a non-optimally weighted sieve QLR statistic under the null; (5) the consistency of generalized residual bootstrap sieve Wald and QLR tests; (6) local power properties of sieve Wald and QLR tests and of their bootstrap versions; (7) asymptotic properties of sieve Wald and SQLR for functionals of increasing dimension. Simulation studies and an empirical illustration of a nonparametric quantile IV regression are presented.

Suggested Citation

  • Xiaohong Chen & Demian Pouzo, 2014. "Sieve Wald and QLR Inferences on Semi/nonparametric Conditional Moment Models," CeMMAP working papers 38/14, Institute for Fiscal Studies.
    • Handle: RePEc:azt:cemmap:38/14
    DOI: 10.1920/wp.cem.2014.3814
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    Cited by:

    1. Spokoiny, Vladimir & Zhilova, Mayya, 2014. "Bootstrap confidence sets under model misspecification," SFB 649 Discussion Papers 2014-067, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    2. Xiaohong Chen & Timothy M. Christensen, 2015. "Optimal sup-norm rates, adaptivity and inference in nonparametric instrumental variables estimation," CeMMAP working papers 32/15, Institute for Fiscal Studies.

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