Optimal Comparison of Misspecified Moment Restriction Models
This paper considers optimal testing of model comparison hypotheses for misspecified unconditional moment restriction models. We adopt the generalized Neyman-Pearson optimality criterion, which focuses on the convergence rates of the type I and II error probabilities under fixed global alternatives, and derive an optimal but practically infeasible test. We then propose feasible approximation test statistics to the optimal one. For linear instrumental variable regression models, the conventional empirical likelihood ratio test statistic emerges. For general nonlinear moment restrictions, we propose a new test statistic based on an iterative algorithm. We derive the asymptotic properties of these test statistics.
Moment restriction; Model comparison; Misspecification; Generalized Neyman-Pearson optimality; Empirical likelihood; GMM
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