We show that social disability insurance may better society-wide welfare even when there is a perfect private market for similar insurance. In essence, the public system complements the private. The latter cover risks when personal characteristics are known, whereas the first mitigates effects of unfavorable characteristics. Large social insurance benefits will induce more education among agents with expected good health. These same agents also experience a negative redistributive income effect from social insurance. Incentive effects to redistribution are therefore nonstandard since individuals that are adversely affected by redistribution will respond with more educational vigor.