New misspecification tests for multinomial logit models

Abstract

Multinomial Logit [MNL] models are misspecified when the Independence of Irrelevant Assumption [IIA] does not hold. In this paper we compare existing tests for IIA with two newly proposed tests. Both new tests use that, when MNL is the true model, preferences across pairs of alternatives can be described by independent binary logit models. The first test compares Composite Likelihood parameter estimates based on pairs of alternatives with standard Maximum Likelihood estimates using a Hausman (1978) test. The second is a test for overidentification in a GMM framework using more pairs than necessary. A detailed Monte Carlo study shows that the GMM test is in general superior with respect to the performance under the null and under the alternative hypothesis. An empirical illustration demonstrates the practical usefulness of the tests.