Optimal Bandwidth Choice for Interval Estimation in GMM Regression

Yixiao Sun and Peter Phillips

No 1661, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: In time series regression with nonparametrically autocorrelated errors, it is now standard empirical practice to construct confidence intervals for regression coefficients on the basis of nonparametrically studentized t-statistics. The standard error used in the studentization is typically estimated by a kernel method that involves some smoothing process over the sample autocovariances. The underlying parameter (M) that controls this tuning process is a bandwidth or truncation lag and it plays a key role in the finite sample properties of tests and the actual coverage properties of the associated confidence intervals. The present paper develops a bandwidth choice rule for M that optimizes the coverage accuracy of interval estimators in the context of linear GMM regression. The optimal bandwidth balances the asymptotic variance with the asymptotic bias of the robust standard error estimator. This approach contrasts with the conventional bandwidth choice rule for nonparametric estimation where the focus is the nonparametric quantity itself and the choice rule balances asymptotic variance with squared asymptotic bias. It turns out that the optimal bandwidth for interval estimation has a different expansion rate and is typically substantially larger than the optimal bandwidth for point estimation of the standard errors. The new approach to bandwidth choice calls for refined asymptotic measurement of the coverage probabilities, which are provided by means of an Edgeworth expansion of the finite sample distribution of the nonparametrically studentized t-statistic. This asymptotic expansion extends earlier work and is of independent interest. A simple plug-in procedure for implementing this optimal bandwidth is suggested and simulations confirm that the new plug-in procedure works well in finite samples. Issues of interval length and false coverage probability are also considered, leading to a secondary approach to bandwidth selection with similar properties.

Keywords: Asymptotic expansion; Bias; Confidence interval; Coverage probability; Edgeworth expansion; Lag kernel; Long run variance; Optimal bandwidth; Spectrum (search for similar items in EconPapers)
JEL-codes: C13 C14 C22 C51 (search for similar items in EconPapers)
Pages: 93 pages
Date: 2008-05
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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