We ask whether a pay‐as‐you‐go financed social security system is welfare improving in an economy with idiosyncratic and aggregate risk. We show that the whole welfare benefit from insurance against both risks is greater than the sum of benefits from insurance against the isolated risks. One reason is the convexity of the welfare gain. The other reason is a direct risk interaction amplifying the utility losses from risk. Our quantitative evaluation shows that introducing a minimum pension leads to sizeable welfare gains, despite substantial crowding out. About 60% of these gains would be missing from summing up the isolated benefits.
International Economic Review, Vol. 60, Issue 2, pp.661-692, 2019