A Bivariate Fractional Probit Model

This paper develops a bivariate fractional probit model for fractional response variables, i.e., variables bounded between zero and one. The model can be applied when there are two seemingly unrelated fractional response variables. Since the model relies on a quite strong bivariate normality assumption, specification tests are discussed and the consequences of misspecification are investigated. It is shown that the model performs well when normal marginal distributions can be established (this can be tested), and does not perform worse when the joint distribution is not characterized by bivariate normality. Simulation evidence shows that the bivariate model generates more efficient estimates than two univariate models applied to each fractional response variable separately. An empirical application illustrates the usefulness of the proposed model in empirical practice.