Social security in an analytically tractable overlapping generations model with aggregate and idiosyncratic risk

When markets are incomplete, social security can partially insure against idiosyncratic and aggregate risks. We incorporate both risks into an analytically tractable model with two overlapping generations and demonstrate that they interact over the life-cycle. The interactions appear even though the two risks are orthogonal and they amplify the welfare consequences of introducing social security. On the one hand, the interactions increase the welfare benefits from insurance. On the other hand, they can in- or decrease the welfare costs from crowding out of capital formation. This ambiguous effect on crowding out means that the net effect of these two channels is positive, hence the interactions of risks increase the total welfare benefits of social security.