Copula-Based Random Effects Models for Clustered Data

In a binary choice panel data framework, probabilities of the outcomes of several individuals depend on the correlation of the unobserved heterogeneity. I propose a random effects estimator that models the correlation of the unobserved heterogeneity among individuals in the same cluster using a copula. I discuss the asymptotic efficiency of the estimator relative to standard random effects estimators, and to choose the copula I propose a specification test. The implementation of the estimator requires the numerical approximation of high-dimensional integrals, for which I propose an algorithm that works for Archimedean copulas that does not suffer from the curse of dimensionality. This method is illustrated with an application of labor supply in married couples, finding that about one half of the difference in probability of a woman being employed when her husband is also employed, relative to those whose husband is unemployed, is explained by correlation in the unobservables. Supplementary materials for this article are available online.