Estimation of Multivariate Probit Models via Bivariate Probit

Models having multivariate probit and related structures arise often in applied health economics. When the outcome dimensions of such models are large, however, estimation can be challenging owing to numerical computation constraints and/or speed. This paper suggests the utility of estimating multivariate probit (MVP) models using a chain of bivariate probit estimators. The proposed approach offers two potential advantages over standard multivariate probit estimation procedures: significant reductions in computation time; and essentially unlimited dimensionality of the outcome set. The time savings arise because the proposed approach does not rely simulation methods; the dimension advantage arises because only pairs of outcomes are considered at each estimation stage. Importantly, the proposed approach provides a consistent estimator of all the MVP model's parameters under the same assumptions required for consistent estimation based on standard methods, and simulation exercises suggest no loss of estimator precision.