A Simple Parametric Model Selection Test

Abstract

We propose a simple model selection test for choosing among two parametric likelihoods, which can be applied in the most general setting without any assumptions on the relation between the candidate models and the true distribution. That is, both, one or neither is allowed to be correctly specified or misspecified, they may be nested, nonnested, strictly nonnested, or overlapping. Unlike in previous testing approaches, no pretesting is needed, since in each case, the same test statistic together with a standard normal critical value can be used. The new procedure controls asymptotic size uniformly over a large class of data-generating processes. We demonstrate its finite sample properties in a Monte Carlo experiment and its practical relevance in an empirical application comparing Keynesian versus new classical macroeconomic models. Supplementary materials for this article are available online.