A two-sector model with sector-dependent disability risks is presented. Working in the low-risk sector requires skills that can be obtained by investments in education. Moral hazard precludes full insurance. The labour force allocation is responsive to the incentives created by a social insurance system. The rationale for intervention lies in the government's power to cross-subsidize between the sectors, and it is demonstrated how the responsiveness of the labour force allocation limits cross-subsidization. The second-best policy is time-inconsistent. The consistent equilibrium is explored and is argued to provide weak incentives to reduce risks.