COWLES FOUNDATION FOR RESEARCH IN
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COWLES FOUNDATION DISCUSSION PAPER NO. 1724 Optimal Comparison of Misspecified Moment Restriction Models Vadim Marmer and Taisuke Otsu August 2009 Suppose that the econometrician is interested in comparing two
misspecified moment restriction models, where the comparison is performed in terms of some
chosen measure of fit. This paper is concerned with describing an optimal test of the
Vuong (1989) and Rivers and Vuong (2002) type null hypothesis that the two models are
equivalent under the given measure of fit (the ranking may vary for different measures).
We adopt the generalized Neyman-Pearson optimality criterion, which focuses on the decay
rates of the type I and II error probabilities under fixed non-local alternatives, and
derive an optimal but practically infeasible test. Then, as an illustration, by
considering the model comparison hypothesis defined by the weighted Euclidean norm of
moment restrictions, we propose a feasible approximate test statistic to the optimal one
and study its asymptotic properties. Local power properties, one-sided test, and
comparison under the generalized empirical likelihood-based measure of fit are also
investigated. A simulation study illustrates that our approximate test is more powerful
than the Rivers-Vuong test. |
