Specification Tests for The Multinomial Logit Model Revisited: The Role of Alternative-Specific Constants

This paper shows that Hausman-McFadden and related tests for the multinomial logit model are not informative about failure of IIA, but only about specification error in the deterministic part of the utilities attached to choice alternatives. It is shown that the multinomial logit cannot be distinguished from any more general additive random utility model when a full set of alternative specific constants is present. Estimation of such more general models only addresses specification error in the deterministic parts of the utilities and is not informative about the true specification of the random terms of the utilities.