Hyperbolic Discount Functions, Undersaving, and Savings Policy

Studies of animal and human behavior suggest that discount functions are approximately hyperbolic (Ainslie, 1992). I analyze an economy with complete markets which is populated by hyperbolic consumers. I identify two ways in which this economy can be distinguished from an exponential economy. First, hyperbolic discounting predicts the empirical regularity that the elasticity of intertemporal substitution is less than the inverse of the coefficient of relative risk aversion. Second, hyperbolic discounting explains many features of the policy debate about undersaving. The calibrated hyperbolic economy matches Bernheim's (1994) survey data on self-reported undersaving, and predicts pro-savings government interventions like capital-income subsidies and penalties for early withdrawal from retirement accounts. Hyperbolic consumers are willing to sacrifice 9/10 of a year's worth of income to induce the government to implement optimal revenue-neutral saving incentives.