Beta-Delta or Delta-Tau? A Reformulation of Quasi-Hyperbolic Discounting

Han Bleichrodt*, Rogier J.D. Potter van Loon, Drazen Prelec

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)
72 Downloads (Pure)


This paper introduces the index τ = ln β=ln δ as a measure of time inconsistency and vulnerability to self-control problems in the quasi-hyperbolic, beta-delta (β, δ) discounting model. We provide a preference foundation for τ and, consequently, a revealed preference definition of failed self-control. The τ 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 (β, δ) family. The τ index thus provides a common yardstick for comparing temporal inconsistency across different functional forms.

Original languageEnglish
Pages (from-to)6326-6335
Number of pages10
JournalManagement Science
Issue number8
Publication statusPublished - Aug 2022

Bibliographical note

Funding Information:
Helpful comments were received from the department editor Manel Baucells, an associate editor, two anonymous reviewers, and from Jose Apesteguia, Adam Sanjurjo, and Peter P. Wakker.

Publisher Copyright:
© 2022 INFORMS.


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