COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1661 Optimal Bandwidth Choice for Interval Estimation in GMM Regression Yixiao Sun and Peter C.B. Phillips May 2008 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. |
