Optimal Social Security with Moral Hazard
AbstractSocial security is a form of insurance that protects individuals against interruption or loss of earning power. However, in virtually every developed country, employees are leaving the labor force at younger and younger ages and such early retirement trend compounds the financial pressure on social security system. Some analyses suggest that the current structures of social security benefits biased to the early retiree lead people to seek early retirement. To consider this incentive problem and to design the optimal benefit structures, a model of dynamic insurance against the risk of permanent shocks is developed by modifying Atkeson and Lucas' (1995) model of repeated principal agent problem. The existence and the characteristics of the optimal contract are established. The characteristics of the optimal contract established in this paper exactly confirm Diamond and Mirrlees (1978); this contract involves a decreasing social security tax and an increasing annuity with tenure. And it is optimal for people to retire after a finite period of work even if they are still able to work. In addition to the characterization, we establish that there also exists an optimal contract that balances the budget in every period. Usually, the possibility of hidden saving is assumed away in repeated principal agent models. We consider the effect of hidden saving on the model and show that the presence of hidden saving does not completely upset the efficiency of the optimal contract over autarky with saving. An example of simulation is presented that suggests that the benefit structure of the current system might be biased to the early retirees and thus the gains could be made by changing the current systems to the optimal program.
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