Marginal Effects in Multivariate Probit and Kindred Discrete and Count Outcome Models

Estimation of marginal or partial effects of covariates x on various conditional parameters or functionals is often the main target of applied microeconometric analysis. In the specific context of probit models, estimation of partial effects involving outcome probabilities will often be of interest. Such estimation is straightforward in univariate models, and Greene, 1996, 1998, has extended these results to cover the case of quadrant probability marginal effects in bivariate probit models. The first purpose of this paper is to extend these results to encompass the general !"!# multivariate probit (MVP) context for arbitrary orthant probabilities. It is suggested that such partial effects are broadly useful in situations wherein multivariate outcomes are of concern. The paper derives the general result on orthant probability partial effects, which contains Greene's bivariate result as a special case. These results are then extended to models that condition on subvectors of y, to count data structures that derive from the probability structure of y, to multivariate ordered probit data structures, and to the multinomial probit model whose marginal effects turn out to be a special case of those of the multivariate probit model. Numerical simulations suggest that use of the analytical formulae versus fully numerical