Diminishing Impatience: Disentangling Time Preference from Uncertain Lifetime

A decision maker with time consistent preferences may exhibit diminishing impatience, when uncertain lifetime is accounted for. Uncertain lifetime captures not only the risk of mortality, but also the possibility that a promise for a delayed reward might be breached, or a postponed consumption might not be realized. The restrictions that time consistency imposes on additive intertemporal preferences are characterized. It is shown that if the hazard rate of mortality is diminishing, then a time consistent agent will exhibit diminishing impatience. A demographic model that allows for unobservable heterogeneity in frailty (risk of mortality) accommodates diminishing impatience, even in the presence of stationarity and time consistency.