A meta-analysis of quasi-hyperbolic discounting

Abstract

This paper reports a meta-analysis of 86 studies of the two parameters of quasi-hyperbolic (β-δ) discounting, the dominant model of self-control failures in behavioural economics. The central tenet of the model is that decision-makers have a "present-bias", β , for immediate rewards, on top of standard exponential discounting of the future, δ. After correcting for selective reporting, we obtain a meta-analytic estimate of β for money of 0.938, with 95% confidence interval [0.905, 0.972]. For non-monetary rewards, our estimate of β 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, while stronger than for money, is weaker than for other rewards such as real consumption.

Keywords: quasi-hyperbolic discounting, present bias, discount factor, beta-delta model

JEL Classification: C91, D12, D80, D91