Beta-Delta or Delta-Tau? A Reformulation of Quasi-Hyperbolic Discounting
提出一个衡量时间不一致性和自我控制问题脆弱性的指标，该指标独立于效用函数，可比较不同贴现函数形式下的时间不一致程度，对行为经济学和决策分析研究者有用。
This paper introduces the index [Formula: see text] as a measure of time inconsistency and vulnerability to self-control problems in the quasi-hyperbolic, beta-delta ([Formula: see text] discounting model. We provide a preference foundation for [Formula: see text] and, consequently, a revealed preference definition of failed self-control. The [Formula: see text] index is independent of utility and has an intuitive interpretation as the maximum number of future selves who can disagree with the current self with respect to uniform deviations from an intertemporal plan. The index is also computable for continuous discount functions after an appropriate mapping of functions onto the ([Formula: see text] family. The [Formula: see text] index thus provides a common yardstick for comparing temporal inconsistency across different functional forms. This paper was accepted by Manel Baucells, behavioral economics and decision analysis.