Time-inconsistent preferences, borrowing costs, and social security

Can time-inconsistent preferences justify a mandatory saving program like social security? Previous studies have considered this research question speci?fically for the extreme assumptions of missing credit markets and perfect credit markets, but not for the intermediate case in which borrowing is costly. We consider a more general setting
with a credit spread between the interest rates on borrowing and saving. Our setting nests the extremes of missing credit markets (in?nite spread) and perfect credit markets (zero spread), and it also includes the full spectrum of credit spreads in between. We
prove that a fully-funded social security arrangement is irrelevant only at the knife edge of perfect credit markets. In other words, if there are borrowing costs of any size then social security can improve the welfare of individuals with time-inconsistent preferences. We conclude that non-standard preferences provide a more compelling justifi?cation for the mandatory saving role of social security than previously supposed.