Tobit Models in Social Science Research

The use of tobit models to study censored and limited dependent variables has become increasingly common in applied social science research over the past two decades. Importantly, the likelihood function for a tobit model involves two distinct components: (1) the process that determines whether the outcome variable is fully observed or not and (2) the process that determines the score on the dependent variable for individuals whose outcome is fully observed. One limitation of the tobit model is its assumption that the processes in both regimes of the outcome are equal up to a constant of proportionality. In this article, the authors use Monte Carlo simulation evidence and an empirical example to illustrate the restrictive nature of this assumption and the consequences of disproportionality for the tobit model. They conclude that an alternative model proposed by Cragg should replace the tobit model as the estimator of first resort in situations such as those considered here.