Introduction

Models in which the dependent variable is qualitative or has its range limited in some way are being increasingly used in applied work. Amemiya (1981, 1984) and Maddala (1983) have given detailed accounts of estimation techniques for such models, but unfortunately few results on misspecification tests were available when these authors published their works. This chapter presents checks of model adequacy for some well-known and widely used specifications: the logit and probit models of binary choice and the Tobit (censored regression) model.

Classical likelihood-based procedures and Hausman-type tests are considered in the following sections. Section 6.2 deals with tests for binary choice models. Checks for limited dependent variable (LDV) models are discussed in Section 6.3. In both of these sections, the effects of certain misspecifications are summarized and the corresponding test statistics are described. The test procedures considered are all based upon asymptotic theory and, where possible, reference is made to Monte Carlo evidence on small sample behaviour. Section 6.4 contains some concluding remarks.