APPROXIMATE GENERALIZED EXTREME-VALUE MODELS OF DISCRETE-CHOICE

Estimation of generalized extreme value (GEV) models of discrete choic e is hampered by computational complexity and convergence problems. Ho wever, if the model deviates only modestly from standard multinomial l ogit, a first-order approximation may be useful. This paper presents t hree tests, each based on such an approximation, for the null hypothes is of multinomial logit against any particular GEV model as an alterna tive hypothesis. One test applies the 'universal logit' concept of McF adden, Train, and Tye; the second is the usual Lagrange multiplier tes t; and the third generalizes a regression-based test developed by McFa dden (1987). All three begin with a logit estimation, followed by one further computational step which also produces an approximate estimate of the GEV model. These estimates, as well as the test statistics, ar e asymptotically equivalent under the null hypothesis. Monte Carlo dat a, generated alternatively by logit and by three different GEV models, provide evidence on the small-sample properties of both the test stat istics and the approximate estimators. These properties are found to b e superior in important respects to maximum-likelihood estimation of t he GEV model.