rbprobit: Recursive bivariate probit estimation and decomposition of marginal effects

This article describes a new Stata command, rbprobit, for fitting recursive bivariate probit models, which differ from bivariate probit models in allowing the first dependent variable to appear on the right-hand side of the second dependent variable. Although the estimation of model parameters does not differ from the bivariate case, the existing commands biprobit and cmp do not consider the structural model’s recursive nature for postestimation commands. rbprobit estimates the model parameters, computes treatment effects of the first dependent variable, and gives the marginal effects of independent variables. In addition, marginal effects can be decomposed into direct and indirect effects if covariates appear in both equations. Moreover, the postestimation commands incorporate the two community-contributed goodness-of-fit tests scoregof and bphltest. Dependent variables of the recursive probit model may be binary, ordinal, or a mixture of both. I present and explain the rbprobit command and the available postestimation commands using data from the European Social Survey. Finally, I show an application of the difference-in-differences methodology if there is an interaction term between the first dependent variable and a group variable.