The Multinomial Probit Model Revisited: A Discussion of Parameter Estimability, Identification and Specification Testing

Abstract

In this paper we examine the multinomial probit model in the light of recent developments in the field of simulation‐based inference. We focus upon five broad areas: specification of multinomial choice models; parameter estimability and the use of simulation techniques, parameter identification; specification testing; and practical issues in simulation‐based inference. Although the substitution of simulated probabilities for difficult to compute multidimensional integrals represents a significant step, by examining the more tenuous task of identification and in particular the identification of covariance parameters, we show how the specification and estimation of the multinomial probit still represents a formidable task.