Dynamic Choices of Hyperbolic Consumers

Abstract

Laboratory and field studies of time preference find that discount rates are much greater in the short-run than in the long-run. Hyperbolic discount functions capture this property. This paper solves the decision problem of a hyperbolic consumer who faces stochastic income and a borrowing constraint. The paper uses the bounded variation calculus to derive the Hyperbolic Euler Relation, a natural generalization of the standard Exponential Euler Relation. The Hyperbolic Euler Relation implies that consumers act as if they have endogenous rates of time preference that rise and fall with the future Ž marginal propensity to consume e.g., discount rates that endogenously range from 5% to . 41% for the example discussed in the paper .

Optimal harvesting of fish stocks under a time-varying discount rate

“…] It is usual to assume that the discount factor is described by an exponentially decaying function with a constant discount rate. However, evidence from behavioral economics discussed in Section 2 suggests that time-declining discount rates are commonly observed in human behaviour (Thaler, 1981;Kirby, 1997;Harris & Laibson, 2001;Ainslie, 1992;Laibson, 1997;Harris & Laibson, 2001) and animal behaviour (Mazur, 1987;Green & Myerson, 1996). Such behaviour can have some surprising and unappealing results, discussed in Section 2 and exemplified by the analysis in this paper.…”

“…In particular, although hyperbolic discounting may place greater weight on the interests of future generations, there are problems with incorporating hyperbolic discounting of utility into social cost-benefit analysis (Pearce et al, 2003;Groom et al, 2005). Because hyperbolic discounting can explain a range of perplexing human behaviours, including drug addiction (Gruber & Koszegi, 2001), sub-optimally low savings rates (Laibson, 1997;Laibson et al, 1998;Harris & Laibson, 2001), procrastination (ODonoghue & Rabin, 1999a,b;Benabou & Tirole, 2004) and various others (Akerlof, 1991), this paper does not make the normative recommendation that hyperbolic preferences be incorporated into optimal policy making. 4 On the other hand, it is important to understand the descriptive implications of what might happen if a planner does use hyperbolic discounting in making policy, if only so that we can be aware of potential problems before they arise.…”

How Soon Is Now? Evidence of Present Bias from Convex Time Budget Experiments

“…More recently, Dean and Sautmann (2016) provide evidence that the intertemporal tradeoffs made by subjects in their (lab-in-the-field) experiment are related to liquidity constraints and accumulated savings outside of the lab -suggesting that the narrow bracketing assumption fails in their data. Building on Harris and Laibson (2001), Dean and Sautmann (2016) propose a model in which sophisticated, potentially credit-constrained consumers make optimal forward-looking plans that integrate their experimental payments into their consumption streams. If the assumptions of their model hold, then lab experiments cannot be used to measure individual time preferences; instead, they measure marginal rates of substitution across periods, which depend on market interest rates and subjects' anticipated income and expenditures in all future periods.…”

Rationality and Dynamic Consistency Under Risk and Uncertainty

“…More recent works on applications of time preferences include Barro (1999), O'Donoghue and Rabin (1999a, 1999b, 2001), Harris and Laibson (2001), as well as Krusell and Smith (2003). Bernheim and Rangel (2007) further explore the policy relevance of "non-constant" discounting models; Hayashi (2003) along with Bleichrodt et al (2009) provide extensions to nonhyperbolic discounting.…”