Bootstrapping Misspecified Over-Identified Models

• Activity Number: 576
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Mihai Giurcanu*+ and Brett Douglas Presnell
• Companies: University of Florida and University of Florida
• Keywords: Over-identified models ; GMM inference ; Misspecification ; Empirical likelihood ; Bootstrap ; Panel data

Abstract

In this paper, we study the properties of standard bootstrap (SB), centered-bootstrap (CB), and empirical likelihood bootstrap (ELB) tests of hypotheses used in conjunction with the generalized method of moments. The SB, the CB, and the ELB estimators of the null distributions of the Wald and quadratic difference (QD) test statistics are shown to be consistent when the model is correctly specified, but higher order expansions show that the CB and the ELB tests have smaller size distortions than the usual analytic chi-square approximations and the SB tests. The SB estimator of the null distribution of the J-test statistic converges in distribution to a random non-central chi-square distribution, verifying its inconsistency, while the CB estimator is shown to be consistent even when the null hypothesis is false. Under misspecification, the SB estimators of the critical values of the Wald and QD tests are consistent while the CB estimators are inconsistent. Finally, a simulation study explores the finite sample behavior of the bootstrap tests for correctly specified and for misspecified versions of an over-identified dynamic panel data model.