Sieve semiparametric two-step GMM under weak dependence

This paper considers semiparametric two-step GMM estimation and inference with weakly dependent data, where unknown nuisance functions are estimated via sieve extremum estimation in the first step. We show that although the asymptotic variance of the second-step GMM estimator may not have a closed f...

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Bibliographic Details
Published in:Journal of econometrics 2015-11, Vol.189 (1), p.163-186
Main Authors: Chen, Xiaohong, Liao, Zhipeng
Format: Article
Language:English
Subjects:
Asymptotic methods
Auto-correlation robust inference
Generalized method of moments
Numerical equivalence
Parameter estimation
Random perturbation derivative estimator
Semiparametric over-identification test
Sieve two-step GMM
Statistical inference
Studies
Weakly dependent data
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Summary:This paper considers semiparametric two-step GMM estimation and inference with weakly dependent data, where unknown nuisance functions are estimated via sieve extremum estimation in the first step. We show that although the asymptotic variance of the second-step GMM estimator may not have a closed form expression, it can be well approximated by sieve variances that have simple closed form expressions. We present consistent or robust variance estimation, Wald tests and Hansen’s (1982) over-identification tests for the second step GMM that properly reflect the first-step estimated functions and the weak dependence of the data. Our sieve semiparametric two-step GMM inference procedures are shown to be numerically equivalent to the ones computed as if the first step were parametric. A new consistent random-perturbation estimator of the derivative of the expectation of the non-smooth moment function is also provided.
ISSN:0304-4076
1872-6895
DOI:10.1016/j.jeconom.2015.07.001