Heterogeneous impatience and dynamic inconsistency

It has been shown in the literature that if the individual consumers have constant but unequal time discount rates, then the representative consumer has discount rates that is a strictly decreasing function of time, just as is the case of hyperbolic discounting. No contribution, however, has so far established a general relationship between the degree of heterogeneity of individual consumers' subjective discount rates on the one hand and the degree of dynamic inconsistency of the representative consumer's discount rate function on the other. In this paper, we show that the more convex the cumulant generating function of the approximately wealth-weighted distribution of individual consumers' subjective discount rates is, the more dynamically inconsistent the representative consumer is in the sense of Prelec (2004), and vice versa. Applications to the term structure of interest rates are explored and the special case where the distributions of subjective discount rates are taken from an exponential family is investigated.