Limited Dependet Panel Data: a Bayesian Approach

Computing power now allows empirical researchers to use intensive computing estimation techniques with nonlinear panel-data models. Maximum Likelihood estimation is often cumbersome, if not analytically intractable, when dealing with such models. Even the simple calculation of the likelihood function can require a joint T-variate multiple integration whose numerical approximation can be poor. Different solutions have been proposed: integral approximation by simulation, the Generalized Method of Moments (GMM), and Markov Chain Monte Carlo (MCMC) algorithms. I examine these techniques using a software application employing Gibbs sampling and Metropolis-Hastings Markov chains. My aims are twofold: first, I assess the numerical reliability of standard econometric packages with nonlinear panel-data models, and second, I develop a posterior simulation for Tobit panel-data models in the presence of serial correlation, where high-dimensional integrals are induced by the serial correlation among censored variables. In this circumstance, although the standard Tobit estimator is consistent it will be inefficient. Building on Wei's work, I implement and test a sampling scheme for the unobserved (censored) data that allows effective Gibbs sampling to be used with the data augmentation algorithm. The Gibbs sampler includes a Metropolis-Hastings step to generate the posterior distribution of the serial correlation coefficient of the model