A comparison study on the estimation in Tobit regression models

Abstract

The goal of this report is to compare various estimation procedures on regression models in which the dependent variable has a restricted range. These models, called Tobit models, are seeing an increase in use among economists and market researchers, specifically. Only the standard Tobit regression model is discussed in the report. First we will examine the five estimation methods discussed in Amemiya (1984) for standard Tobit model. These methods include Probit maximum likelihood, least squares, Heckman’s two-step, Tobit maximum likelihood, and the EM algorithm. We will examine the algorithm utilized in each method’s estimation process. We will then conduct simulation studies using these estimation procedures. Twelve scenarios have been considered consisting of three different truncation threshold on the response variable, two distributions of covariates, and the error variance known and unknown. The results are reported and a discussion of the goodness of each method follows. The study shows that the best method for estimating Tobit regression models is indeed the Tobit maximum likelihood estimation. Heckman’s two-step method and the EM algorithm also estimate these models well when the truncation rate is low and the sample size is large. The simulation results show that the Least squares estimation procedure is far less efficient than other estimation procedures.