Estimation of a type 2 Tobit model with generalized Box-Cox transformation

This article considers estimation of a Type 2 Tobit model with Bickel-Doksum transformation of the dependent variable of the regression equation. The basic idea is that while the transformed dependent variable is assumed to be normally distributed prior to any censoring, the inverse Bickel-Doksum transformation allows the underlying dependent variable to follow a wide variety of distributions having differing degrees of skewness and kurtosis. This adds flexibility to the shape of the distribution used to model quantitative variation in the dependent variable for the observed subsample. The log-likelihood function of this Generalized Type 2 Tobit model is globally concave conditional on the parameter of the Bickel-Doksum transformation and the correlation coefficient of the errors. A bivariate grid search over the space of these parameters may be used to find the neighbourhood of the global maximum to the log-likelihood function, provided one exists. The grid search process is important because: 1) the log-likelihood function of the Type 2 Tobit model, even with fixed functional form, often exhibits distinct local and global maxima and 2) use of consistent estimates as starting values is not sufficient to insure convergence to the global Maximum Likelihood Estimator.