Optimal comparison of misspecified moment restriction models under a chosen measure of fit

Abstract

JEL classification: C12 C14 C52 Keywords:Moment restriction Model comparison Misspecification Generalized Neyman-Pearson optimality Generalized method of moments a b s t r a c t 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.

Solution and Estimation Methods for DSGE Models

“…Frequentist versions of this approach have been developed inHnatkosvaka, Marmer, and Tang (2012) andMarmer and Otsu (2012).…”

Asymptotic refinements of a misspecification-robust bootstrap for generalized method of moments estimators

“…Vuong (1989), Rivers andVuong (2002), andKitamura (2003) suggest various tests of the null hypothesis that test whether two possibly misspecified models provide equivalent approximation to the true model in terms of the Kullback-Leibler information criteria (KLIC). Recent studies such as Chen, Hong, and Shum (2007), Marmer andOtsu (2012), andShi (2013) generalize and modify the test in broader settings. Hall and Pelletier (2011) show that the limiting distribution of the Rivers-Vuong test statistic may not be consistently estimable unless both models are misspecified.…”

Testing Firm Conduct

“…This paper is also related to econometric work on the testing of non-nested hypotheses (e.g., Pesaran and Weeks, 2001). We build on the insights of the econometrics literature that performs inference under misspecification and highlights the importance of model selection procedures (e.g., White, 1982;Vuong, 1989;Hall and Inoue, 2003;Kitamura, 2003;Marmer and Otsu, 2012;Liao and Shi, 2020). Two recent contributions, Shi (2015) and Schennach and Wilhelm (2017), modify the likelihood based test in Vuong (1989) to correct size distortions under degeneracy.…”