Tobit models: A survey

Abstract

Tobit models refer to regression models in which the range of the dependent variable is constrained in some way. In economics, such a model was first suggested in a pioneering work by Tobin (1958). He analyzed household expenditure on durable goods using a regression model which specifically took account of the fact that the expenditure (the dependent variable of his regression model) cannot be negative. Tobin called his model the model of limited dependent variables. It and its various generalizations are known popularly among economists as Tobit models, a phrase coined by Goldberger (1964) because of similarities to probit models. These models are also known as censored or truncated regression models. The model is called truncated if the observations outside a specified range are totally lost and censored if one can at least observe the exogenous variables. A more precise definition will be given later. Censored and truncated regression models have been developed in other disciplines (notably biometrics and engineering) more or less independently of their development in econometrics. Biometricians use the model to analyze the survival time of a patient. Censoring or truncation occurs either if a patient is still alive at the last observation date or if he or she cannot be located. Similarly, engineers use the model to analyze the time to failure of material or of a machine or a system. These models are called survival models.’ Sociologists and economists have also used survival models to analyse the duration of such phenomena as unemployment, welfare receipt, employment in a particular job, residing in a particular region, marriage, and the period of time between