A Meta-Analysis of Quasi-Hyperbolic Discounting

This paper reports a meta-analysis of 86 studies of the two parameters of quasi-hyperbolic ($\beta -\delta$) discounting, the dominant model of self-control failures in behavioral economics. The central tenet of the model is that decision makers have a “present bias,” $\beta$, for immediate rewards, on top of standard exponential discounting of the future, $\delta$. After correcting for selective reporting, we obtain a meta-analytic estimate of $\beta$ for money of 0.938, with 95% confidence interval [0.905, 0.972]. For nonmonetary rewards, our estimate of $\beta$ is 0.750, with 95% confidence interval [0.643, 0.857], and there is no evidence of selective reporting. We find that present bias for real effort, although stronger than for money, is weaker than for other rewards such as real consumption.

This paper was accepted by Manel Baucells, behavioral economics and decision analysis.

Funding: This research was partly supported by the Australian Government through the Australian Research Council’s Centre of Excellence for Children and Families over the Life Course [Project IDs CE140100027 and CE200100025]. S. L. Cheung received financial support from the Australian Research Council [Grant DP160101794]. A. Tymula received financial support from the University of Sydney [Bridging Grant G199763].

Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2023.04003.