Introduction

The proliferation of random effects is one of the most troublesome characteristics of the multinomial probit (MNP) model. Given recent developments in simulation based inference (see McFadden (1989), Hajivassiliou and Ruud (1994), and Weeks (1994)), the original “curse of dimensionality,” a characteristic of many limited dependent variable models, has been partially lifted. Monte Carlo simulation is now commonly used to estimate analytically intractable integrals. Further, in much of the emerging literature considerable space has been devoted to a discussion of simulation-based estimation, to the relative neglect of specification testing. Although it must be said that studies in this area will logically follow the development of reliable and consistent estimation techniques, it would appear that at this juncture there is a relative neglect of model evaluation.

The focus of this chapter is twofold. First, we extend the recent work of Pesaran and Pesaran (1993) by implementing and attempting to evaluate the Cox non-nested test for binomial and multinomial choice models. To our knowledge this represents the first study of this type. Second, focusing upon a number of asymptotically equivalent procedures for estimating the Kullback–Leibler (KL) measure of closeness and the variance of the test statistic, we compare a number of variants of the computationally intensive Cox test statistic. The variants considered are based upon asymptotically equivalent procedures for estimating the numerator and denominator of the Cox test statistic.

The outline of the chapter is as follows. In section 2 we present a brief overview of some key issues in the testing of multinomial choice models.