Identifiability and estimation of the competing risks model under exclusion restrictions

The nonidentifiability of the competing risks model precludes the empirical researcher from obtaining informative estimation results unless she is willing to impose restrictions on the model. Inspired by the heavy use of exclusion restrictions in other areas of statistics, we impose an exclusion restriction to derive a new identifiability result for the competing risks model. This exclusion restriction could be more easy to justify than the restrictions of existing approaches which are on the dependence structure or marginal distributions. It is shown that the degree of risk dependence of an Archimedean copula is identifiable without parametric restrictions on the marginal distributions of the competing risks. We introduce a semiparametric estimation approach for the nonparametric marginals and the parametric copula. Our simulation results demonstrate that the degree of risk dependence can be estimated without parametric restrictions on the marginal distributions. It therefore overcomes the main disadvantage of the copula graphic estimator.