Optimal Bandwidth Choice for Interval Estimation in GMM Regression
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.
Sun, Yixiao and Phillips, Peter C.B., "Optimal Bandwidth Choice for Interval Estimation in GMM Regression" (2008). Cowles Foundation Discussion Papers. 1965.