Heterogeneous Time Preferences within the Household
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Substantial evidence suggests that discount factors vary significantly between individuals and that this variation exists between members of the same household. This paper introduces a model of consumption and savings in which household members discount the utility from their future consumption at different rates. Each period household members bargain efficiently over their consumption and saving choices. The ex-ante optimal consumption plan will prescribe a declining share of household consumption to the impatient household member and a savings rate later in life that is determined primarily by the time preferences of the patient member. However, as evidence suggests, the household lacks dynamic commitment and can renegotiate any consumption plan that was made in an earlier period. I show that if both members have constant bargaining power the ex-ante optimal consumption plan is time inconsistent despite both members being rational forward looking agents with time consistent preferences. Later in life the impatient member will bargain for both a higher share of consumption and a higher propensity to consume out of wealth than under the agreed ex-ante optimum. The household can achieve an optimal path of consumption and savings by increasing the bargaining power of the patient member over time. The household's ability to achieve the full commitment optimum is constrained by the altruism between household members.
Hertzberg, Andrew. "Heterogeneous Time Preferences within the Household." Columbia Business School, 2013.