Saving and retirement behavior under quasi-hyperbolic discounting

This paper investigates saving and retirement behavior using a quasi-hyperbolic discounting model with endogenous labor supply. The behavior of quasi-hyperbolic-discounting consumers is compared with optimal behavior, which is obtained under exponential discounting. The quasi-hyperbolic discounters, whether naïve or sophisticated, under-save and retire early compared with an exponential discounter, if and only if the present-biased marginal utility of future consumption decreases with stronger present bias. Logarithmic utility functions and constant-absolute-risk-aversion utility functions can both exhibit this property. In other words, quasi-hyperbolic discounting explains why, consistent with previous empirical studies, under-savers might also be early retirers. Under logarithmic utility, a wage tax and an interest subsidy can counteract the under-saving and early retirement and improve consumer welfare.