Quasi-Hyperbolic Discounting And Retirement

Abstract

There is overwhelming psychological evidence that some people run into self-control problems regularly, yet the effect of these findings on major life-cycle decisions hasn't been studied in detail. This paper extends Laibson's quasi-hyperbolic discounting savings model, in which each intertemporal self realizes that her time discount structure will lead to preference changes, and thus plays a game with her future selves. By making retirement endogenous, savings affect both consumption and work in the future. From earlier selves' points of view, the deciding self tends to retire too early, and, so it is possible that the self before saves less to induce her to work. However, still earlier selves think the pre-retirement self may do this too much, leading to possible higher saving on their part and eventual early retirement. Thus, the consumption path exhibits observational non-equivalence with exponential discounting. Observational non-equivalence also obtains on a number of comparative statics questions. For example, a self could have a negative marginal propensity to consume out of changes in future income. The outcome with naive agents, who fail to realize their self-control problem, is also briefly discussed. In that case, the deciding self's potential decision to retire despite earlier selves' plans results in a downward updating of available lifetime resources, and an empirically observed downward jump in the consumption path.