AbstractIn this paper we specify and estimate a flexible parametric proportional hazards model. The model specification is flexibly parametric in the sense that the baseline hazard is non parametric while the effect of the covariates takes a particular functional form. We also add parametric heterogeneity to the underlying hazard model specification. We specify a flexible parametric proportional competing risks model which permits unrestricted correlation among the risks. Unemployment duration data are then analysed using the flexible parametric duration and competing risks specifications. We find an important effect arising from the exhaustion of unemployment insurance and significantly different hazards for the two types of risks, new jobs and recalls.