Time-inconsistent preferences and social security: Revisited in continuous time

?mrohoro?lu et al. (2003) prove that it is impossible in a three period partial equilibrium model for social security to improve the welfare of a naive quasi-hyperbolic agent if the program has a negative net present value. This paper first generalizes their impossibility theorem to a continuous time setting and then proves analytically that no discount function exists that can rationalize a social security program with a negative net present value.