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

By Xiaohong Chen, Demian Pouzo. 2014

126 citations recorded by the source corpus.

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. These models are often ill-posed and hence it is difficult to verify whether a (possibly nonlinear) functional is root-n estimable or not. We provide computationally simple, unified 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.

Subfields: Economics and Econometrics, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/7eeb29ac9965d0cbe05b0651fd23fc454fcd352c

How researchers see this paper

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In Economics and Econometrics

1. Peng Ding
2. Linbo Wang
3. L. Davezies
4. Shu Yang
5. T. L. Barbanchon

In Finance

1. Peng Ding
2. Linbo Wang
3. L. Davezies
4. Shu Yang
5. T. L. Barbanchon

In Statistics and Probability

1. Shu Yang
2. Peng Ding
3. Linbo Wang
4. L. Davezies
5. T. L. Barbanchon
6. Xinran Li
7. Kevin Guo
8. Guillaume W. Basse

Citations in the corpus

• Regression Discontinuity Design with Continuous Measurement Error in the Running Variable (2017, background): “Chen & Pouzo (2015) prove that bootstrapping is valid in sieve semi-parametric IV estimation in a framework that slightly differs from ours.”
• Causal inference with confounders missing not at random (2017, methodology): “Alternatively, Chen and Pouzo (2015) provided Wald and quasi-likelihood ratio inference results for the general models in Chen and Pouzo (2012), including series two stage least squares as an example.”