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Optimal bandwidth selection for robust generalized method of moments estimation

Authors: Daniel Wilhelm
Date: 31 October 2015
Type: Journal Article, Econometric Theory, Vol. 31, No. 5, pp. 1054--1077
DOI: 10.1017/S026646661400067X

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.

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Previous version:
Daniel Wilhelm March 2014, Optimal bandwidth selection for robust generalized method of moments estimation, cemmap Working Paper, CWP15/14, Cemmap

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