S-shaped probability weighting and hyperbolic discounting - an intimate relationship

Intertemporal decision-making has to account for the inevitable uncertainty surrounding the realization of delayed gains and losses. As this paper demonstrates, time-dependent uncertainty implies that S-shaped probability weighting and hyperbolic discounting will be positively correlated traits. Both phenomena are explained within state-dependent expected utility theory by considering elation and disappointment in addition to the wealth effects associated with the realization of (delayed) gains and losses. Various other `anomalies` are analyzed within the same framework. It is shown that constant relative risk aversion is sufficient to generate (1) a `sign effect' (losses are discounted less than gains), (2) a `delay/speed-up' asymmetry (delays are discounted at higher rates) and (3) a `magnitude effect' for losses (larger outcomes are discounted less). However, a `reverse' magnitude effect develops for gains (larger outcomes are discounted more). The `magnitude effect' for gains observed in experimental settings is rationalized by incorporating transaction costs within the domain of `small' gains. (4) As a corollary, a wealth effect is identified, implying that the poor subject will be less patient with regard to gains and losses.
Keywords: Hyperbolic time preferences, Decision-Making under Uncertainty, Probability Weighting

JEL classification: D11, D81, D91