Model Selection in Panel Data Models: A Generalization of the Vuong Test

This paper generalizes the classical Vuong (1989) test to panel data models by employing modified profile likelihoods and the Kullback-Leibler information criterion. Unlike the standard likelihood function, the profile likelihood lacks certain regular properties, making modification necessary. We adopt a generalized panel data framework that incorporates group fixed effects for time and individual pairs, rather than traditional individual fixed effects. Applications of our approach include linear models with non-nested specifications of individual-time effects.