A two-part model using quantile regression under a Bayesian perspective.

We develop an extension of the two-part model proposed by Cragg (1971) considering the asymmetric Laplace distribution for the continuous density, proposing a quantile regression analysis in the process, within a Bayesian approach. We also consider the case where there could be a zero inflation process while estimating a Bayesian tobit quantile regression, and by the imputation of the latent variable indicating whether a zero observation belongs to a point mass or the continuous distribution, we are able to obtain a generalization of our two-part model. We illustrate our method in a known data set in the field of econometrics.