On Some Implications of Backward Discounting

We study a model in which lifetime individual felicities are derived from both present and past consumption streams. Each of these streams is discounted, the former forward in the usual way, the latter backward. This discounting method is timeinconsistent, and implies constant regrets by the individual. We assume that an individual at date t evaluates consumption programs according to some weighted average of his own felicity (as perceived at date t) and that of a “future self” at some date T > t. This simple model shows that individuals may exhibit impatience across alternatives that are positioned in periods adjacent to the present, but patience across similar choices positioned in the more distant future, that such impatience is attenuated as an individual grows older, and that lifetime choice plans are generally time-inconsistent. The model can also be used to capture the notion of parental influence and investigate its impact on savings. We finally examine other applications of “backward discounting” in the paper. ———————————————— Ray acknowledges financial support under a John Simon Guggenheim Fellowship for 1997-98, when these ideas were first developed. Wang acknowledges financial support from SSHRC of Canada. We thank Gregor Smith, George Loewenstein, and seminar participants at CEA, Queen’s, and SITE Summer Conference for helpful comments. A previous version of the paper was distributed under the title “A Simple Model of Parental Influence.” Parenting: older versus younger parents.