rbicopula: Recursive bivariate copula estimation and decomposition of marginal effects

This presentation describes a new Stata command, rbicopula, for fitting copula-based maximum-likelihood estimation of recursive bivariate models that enable a flexible residual distribution and differ from bivariate copula or probit models in allowing the first dependent variable to appear on the right-hand side of the second dependent variable. The new command provides various copulas, allowing the user to choose a copula that best captures the dependence features of the data caused by the presence of common unobserved heterogeneity. Although the estimation of model parameters does not differ from the bivariate case, the existing community-contributed command bicop does not consider the structural model's recursive nature for predictions and doesn't enable margins as a postestimation command. rbicopula 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 two goodness-of-fit tests. Dependent variables of the recursive bivariate model may be binary, ordinal, or a mixture of both. I present and explain the rbicopula command and the available postestimation commands using data from the Stata website.