Limited dependent variable models and estimation methods

In the regression model, the dependent variable which takes only two values or do not take a negative value or takes values at certain intervals are defined as the limited dependent variable. If the continuous dependent variable takes values at a certain range, this situation is expressed as the censored variable. In this case, ordinary least squares estimates give biased and inconsistent results. To solve a part of this problem, the censored normal regression model or tobit model, was proposed by Tobin (1958). However, the maximum likelihood estimation of the tobit model depends on the assumption of normality and if the errors are non-normally distributed, the tobit model yields inefficient results. Various estimators have been proposed to relax the normality assumption. To cope with non-normality, one of the proposed estimator is partially adaptive estimators. In this thesis, well-known limited dependent variable models and estimation methods for these models are examined. The considered estimators are maximum likelihood, two-stage heckit, two-stage least squares, probit and logit. Besides that, a partially adaptive estimator based on the generalized normal distribution is considered in the case of non-normallity problem. Furthermore, a simulation study is used to analyze the estimators' relative performance in the case of different error distributions. Different estimators are compared in this way. The results obtained show that the performance of the partially adaptive estimator is better than the maximum likelihood estimator when the errors are non-normally distributed. All other results obtained are presented and discussed regarding the relevant literature.