Limited dependent panel data models: a comparative analysis of classical and Bayesian inference among econometric packages

Advances in computing power allow the empirical researcher to use intensive computional techniques to solve and estimate nonlinear panel-data models, specifically those arising from nonlinear panel data such as Probit and Tobit models. In these cases, maximum-likelihood estimation can be cumbersome if not analytically intractable, requiring a T-variate multiple integration whose numerical approximation can sometimes be very poor. Different solutions are offered based variously on integral approximation through simulation, some form of Generalized Method of Moments (GMM), or Markov Chain Monte Carlo (MCMC) methods. This paper compares the outcomes of those methods available in standard econometric packages, providing illustrations among prepackaged algorithms and a MCMC Gibbs sampler for nonlinear panel data. Using Chib (1992) and Chib and Carlin (1999), I derive a sampler for Probit/Tobit panel data and provide easy-to-use software for implementing the Gibbs sampler in panel data with discrete/limited dependent variable. I show that, when dealing with a large dataset, MCMC methods may replace the procedures provided in standard econometric packages