A Regression Model for the Copula Graphic Estimator

We consider a dependent competing risks model with many risks and many covariates. We show identifiability of the marginal distributions of latent variables for a given dependence structure. Instead of directly estimating these distributions, we suggest a plug-in regression framework for the Copula-Graphic estimator which utilises a consistent estimator for the cumulative incidence curves. Our model is an attractive empirical approach as it does not require knowledge of the marginal distributions which are typically unknown in applications. We illustrate the applicability of our approach with the help of a parametric unemployment duration model with an unknown dependence structure. We construct identification bounds for the marginal distributions and partial effects in response to covariate changes. The bounds for the partial effects are surprisingly tight and often reveal the direction of the covariate effect.