Comparison of MCMC algorithms for the estimation of Tobit model with non-normal error: The case of asymmetric Laplace distribution

The analysis of Tobit model with non-normal error distribution is extended to the case of asymmetric Laplace distribution (ALD). Since the ALD probability density function is known to be continuous but not differentiable, the usual mode-finding algorithms such as maximum likelihood can be difficult and result in the inconsistent parameter estimates. Various Markov chain Monte Carlo algorithms including probability integral transformation, griddy Gibbs, random walk Metropolis–Hastings, and tailored randomized block Metropolis–Hastings (TaRB-MH) are applied and compared. Results from a simulation study suggest that TaRB-MH is the best performing algorithm. Using a survey dataset on the wage earnings of Thai male workers to compare the Tobit model with normal and ALD errors through the model marginal likelihood and deviance information criterion, the results reveal that the model with the ALD error is preferred.