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Although formal conditions for identification in the multinomial probit (MNP) model are now clearly established, little is known about how various estimable MNP specifications perform in practice. This article shows that parameter identification in the MNP model is extremely tenuous in the absence of exclusion restrictions. This previously unnoticed fact is important because formal identification of MNP models does not require exclusion restrictions, and many potential economic applications of MNP are to situations in which exclusion restrictions are not readily available. Thus, failure to be aware of the difficulties present in such situations may lead to reporting of unreliable results.
Michael P. Keane (Wed,) studied this question.