Estimation of Bivariate Copula-Based Seemingly Unrelated Tobit Models

Abstract

This paper extends the analysis of bivariate seemingly unrelated (SUR) Tobit model by modeling its nonlinear dependence structure through copulas. The capability in coupling together the different marginal distributions allows the flexible modeling for the SUR Tobit. The ability in capturing tail dependence is an additionally useful feature of the copulas, especially in modeling the lower tail dependence of the SUR Tobit where some data are censored. We employ the data augmentation technique to generate the censored observations and proceed the model implementation through the Bayesian Markov Chain Monte Carlo approach. The satisfactory results from the simulation and empirical studies indicate the good performance of our proposed model and method where they are applied to model the U.S. out-of-pocket and non-out-of-pocket medical expenses data and the Thai wage earnings income data.