New Results On Censored Regression with Applications to Transactions Costs, Household Decisions and Food Purchases

We generalize the Tobit censored regression to permit unique unobserved censoring thresholds conditioned by covariates and a set of common response coefficients. This situation , we argue, is one arising frequently in applications of censored regression and we provide three diverse examples to motivate the theory. We derive a robust estimation algorithm with three noteworthy features. First, by augmenting the observed-data likelihood with the censored observations, the estimation strategy is the same as Chib (1992) who derives Bayes estimates of the conventional censored regression. Second, by virtue of its generality, the model is applicable to a much broader set of circumstances than the conventional Tobit regression, which is nested as a special case of the more general framework. Third, despite its generality and wide applicability, the estimation algorithm is very simple, evidencing routine application of Markov chain Monte Carlo methods (MCMC)-Gibbs sampling in particular- and requiring only modest extensions of the basic algorithm in Chib (1992). The model and procedures are illustrated empirically in three applications that we use to motivate the theory, namely problems in transactions-costs economics, household decision-making and food-consumption.