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OPTIMAL BANDWIDTH SELECTION FOR ROBUST GENERALIZED METHOD OF MOMENTS ESTIMATION

Published online by Cambridge University Press:  02 October 2014

Daniel Wilhelm
Daniel Wilhelm*
Affiliation:
UCL and CeMMAP
*
*Address correspondence to Daniel Wilhelm, Department of Economics, University College London, 30 Gordon St, London WC1H 0AX, United Kingdom; e-mail: d.wilhelm@ucl.ac.uk.
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Abstract

A two-step generalized method of moments estimation procedure can be made robust to heteroskedasticity and autocorrelation in the data by using a nonparametric estimator of the optimal weighting matrix. This paper addresses the issue of choosing the corresponding smoothing parameter (or bandwidth) so that the resulting point estimate is optimal in a certain sense. We derive an asymptotically optimal bandwidth that minimizes a higher-order approximation to the asymptotic mean-squared error of the estimator of interest. We show that the optimal bandwidth is of the same order as the one minimizing the mean-squared error of the nonparametric plugin estimator, but the constants of proportionality are significantly different. Finally, we develop a data-driven bandwidth selection rule and show, in a simulation experiment, that it may substantially reduce the estimator’s mean-squared error relative to existing bandwidth choices, especially when the number of moment conditions is large.

Type
ARTICLES
Information
Econometric Theory , Volume 31 , Issue 5 , October 2015 , pp. 1054 - 1077
Copyright
Copyright © Cambridge University Press 2014 

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