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