Estimation of Multivariate Probit Models via Bivariate Probit

In this article, I suggest the utility of fitting multivariate probit models using a chain of bivariate probit estimators. This approach is based on Stata's biprobit and suest commands and is driven by a Mata function, bvpmvp(). I discuss two potential advantages of the approach over the mvprobit command (Cappellari and Jenkins, 2003, Stata Journal 3: 278–294): significant reductions in computation time and essentially unlimited dimensionality of the outcome set. Computation time is reduced because the approach does not rely on simulation methods; unlimited dimensionality arises because only pairs of outcomes are considered at each estimation stage. This approach provides a consistent estimator of all the multivariate probit model's parameters under the same assumptions required for consistent estimation via mvprobit, and simulation exercises I provide suggest no loss of estimator precision relative to mvprobit.