Reduced-Form Trinomial Probit: A Quantal Response Model Without A Priori Restrictions

Abstract

This article develops the direct trivariate extension of the binary probit model. Similar to the binary probit specification, the trivariate model involves an admissible reduction of the nonidentified structural parameters. The reduced-form model is distinguished from other trinomial specifications in that it allows for nonzero covariances among the utility variates that characterize individuals' valuations of the choice alternatives. The independence of irrelevant alternatives is thus avoided. The flexible covariance structure of the reduced-form model, along with its freedom from a priori restrictions, makes it widely applicable. The method is applied to the analysis of individual schooling choice.