Estimability in the Multinomial Probit Model

Random utility models often involve terms which represent alternative-specific errors, and the main attractive feature of the multinomial probit (MNP) model is that it allows a rather general covariance structure for these errors. However, since observed choices only reveal information regarding utility differences, and since scale cannot be determined, not all parameters in an arbitrary MNP specification may be identified. This paper examines identification restrictions that arise in the linear-in-parameters multinomial probit framework, and provides discussion and recommendations for estimation and analysis of probit normalizations.