Specification Tests for Multinomial Choice Models

This paper proposes consistent specification tests for multinomial choice model, namely, the tests for the functional forms and the cdf of error terms in latent variable models. Multinomial choice models are applied in various fields, since data used in empirical works often contain discrete variables. While the specification of the latent variable models must be one of the essential issues for employing multinomial choice models, no specification tests have been developed so far. We thus construct tests that reject null hypothesis, if at least one of our specifications on latent variable models are not correct. We show that the test statistics converges weakly to chi-squared distribution under some assumptions. Note that the computation of variance-covariance matrix which is necessary for constructing the quadratic form is exceedingly simple owing to the binary dependent variables. We also compare the performance of the specification tests in terms of the size and the power by conducting Monte Carlo experiments. The typical departures from the null are non-linearity and heterogeneity of coefficients. We take them into account in designing our experiments.