Refutable Exclusion Restrictions in Competing Risks with Categorical Covariates

Abstract: Competing-risks data do not identify latent marginal duration distributions or their dependence without additional restrictions. This paper asks whether restrictions introduced to restore identification themselves restrict the observable law. For a two-risk Archimedean model with categorical exclusion restrictions, we derive a necessary-and-sufficient observable characterization. A discrete single-crossing argument identifies the scalar copula parameter from cell-specific overall survival probabilities, while cause indicators recover the remaining allocation and generate additional specification restrictions. We construct an identification-robust, self-normalized quadratic statistic, invert it to obtain confidence sets, and use empty inverted sets as a conservative specification test. Simulations show that the cause indicator can be decisive: under the weakest contrast considered it converts a frequently uninformative survival-based confidence set into an informative joint set without loss of coverage, whereas excessive categorical contrast can eliminate causes from individual cells and make cause-specific recovery inadmissible. The results turn latent exclusion restrictions into refutable restrictions without estimating covariate derivatives.