Estimating Contaminated Limited Dependent Variable Models

Smith for helpful comments and to Richard Blundell for kindly making his data available. In 1imi ted dependent variable models the estimators obtained by maximising the normal likelihood function are generally inconsistent when the assumption of normality ls falseo Arabmazar and Schmidt (1982) have shown that the bias trom non-normality can be substantial when the degree of censoring (or truncation) in the populatlon is relative1y large. The issue is relevant because usua1ly we do not have any a priori reason to believe that our disturbances are normal1y distributed. While extensive research has recent1y been carried out on non-normality tests, 1ittle has been done on ways of relaxing the normality assumption itself. The view is usually taken that evidence of non-normallty is a signal of structural misspecification. Although this will often be the case, i t may also be indicating genuine non-normal features in the distribution of the errors. In the latter situation more general distributional assumptions are called foro In cross section or panel data a common source of non-normality ls due to the existence of extreme values in the samples which determine thick tails. We propose to use mixtures of normal distributions when the objective is to allow for leptokurtosis. Essential1y, the advantages of this approach are that the normal model ls nested as a special case and also the computational simplicity of the normal model ls maintained. This track also allows us to construct simple tests for non-normality. Both estimation and testing issues are discussed in the paper and illustrations are provided. 2