The Finite Sample Properties of the Estimators of the Tobit Model: A Monte Carlo Study

Abstract

This study examines the small sample properties of some of the estimators of the tobit model. These estimators include, among others, the maximum likelihood estimator (MLE), Heckman's 2-step (H2S) estimator and its weighted version, the weighted Heckman's 2-step (WH2S) estimator, other Heckman-type 2-step estimators based on the unconditional expectation of the model, nonlinear and ordinary least squares estimators. Further, an improved Heckman-type estimator which is referred to as the three-step estimator (3SE) and its weighted version, the weighted three-step estimator (W3SE), are suggested and their properties investigated. The study investigates the effects of sample size, degree (level) of censoring and error distribution on the properties of the estimators. Furthermore, it examines, among other things, the effects of correlation between the explanatory variables and the estimated inverse of Mill's ratio on the performance of the (Heckman-type) estimators.