Misspecification-robust bootstrap for moment condition models.

摘要

This dissertation consists of three independent essays in econometric theory.;In the first chapter, I propose a nonparametric iid bootstrap that achieves asymptotic refinements for t tests and confidence intervals (CI's) 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 in the absence of misspecification using recentering. 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.;In the second chapter, I propose a nonparametric iid bootstrap for the empirical likelihood (EL) estimators, including the exponentially tilted empirical likelihood estimator. My bootstrap achieves sharp asymptotic refinements for t tests and CI's regardless of whether the assumed moment condition model is correctly specified or not. This result is new, because asymptotic refinements of bootstrapping for the EL estimators have not been established in the literature even under correct model specifications. Monte Carlo simulation results are provided.;In the third chapter, I examine first-order validity and asymptotic refinements of the bootstrap methods for GMM estimators, when the moment condition model is locally misspecified. Local misspecification implies that the moment condition is misspecified for any finite sample size, but the misspecification vanishes as the sample size grows. I find that the conventional bootstrap methods are still first-order valid, but they do not achieve asymptotic refinements anymore.