Magnitude Effect in Intertemporal Allocation Tasks

We investigate how the intertemporal allocation of monetary rewards is influenced by the size of the total budget, with a particular interest in the channels of influence. We find a significant magnitude effect: the budget share allocated to the later date increases with the size of the budget. This effect does not depend on whether the sooner reward is paid in the present or in the future, implying that the factors which drive the present bias cannot account for the magnitude effect. At the aggregate level as well as at the individual level, we find magnitude effects both on the discount rate and on intertemporal substitutability (i.e. utility curvature). The latter effect is consistent with theories in which the degree of asset integration is increasing in the stake.