Asymptotic Refinements of a Misspecification-Robust i.i.d. Bootstrap for Generalized Method of Moments Estimators

This paper proposes a misspecification-robust iid bootstrap for the generalized method of moment estimators and establishes asymptotic refinements of the symmetric percentile-t bootstrap confidence interval. The paper extends results of Hall and Horowitz (1996) and Andrews (2002). In particular, the proposed method does not involve recentering the moment function in implementing the bootstrap, which has been considered critical in geting asymptotic refinements. By using Hall and Inoue (2003)’s misspecification-robust covariance matrix of the GMM estimator in constructing the t statistic, we solve the problem that the moment condition is not satisfied in the sample, i.e., in the bootstrap population. Therefore, under correct specification, the proposed bootstrap is equivalent to the existing bootstrap method in terms of magnitudes of errors, O(n−2), which is sharp. If the model happens to be misspecified, however, the existing bootstrap method with recentering fails to be consistent for a two-step GMM estimator, while the proposed bootstrap method using the misspecification-robust covariance matrix still achieve asymptotic refinements. An example that describes a misspecified model and compares the asymptotic confidence intervals and the bootstrap symmetric percentile-t intervals is presented. Monte Carlo simulation results are also provided.