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

I propose a nonparametric iid bootstrap that achieves asymptotic refinements for t tests and confidence intervals based on the generalized method of moments (GMM) estimators even when the model is misspecified. In addition, my bootstrap does not require recentering the bootstrap moment function, which has been considered as a critical procedure for bootstrapping GMM. The elimination of the recentering combined with a robust covariance matrix renders the bootstrap robust to misspecification. Regardless of whether the assumed model is correctly specified or not, the misspecification-robust bootstrap achieves the same sharp magnitude of refinements as the conventional bootstrap methods which establish asymptotic refinements by recentering in the absence of misspecification. The key procedure is to use a misspecification-robust variance estimator for GMM in constructing the sample and the bootstrap versions of the t statistic. Two examples of overidentified and possibly misspecified moment condition models are provided: (i) Combining data sets, and (ii) invalid instrumental variables. Monte Carlo simulation results are provided as well.