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