Eliciting utility curvature in time preference

Abstract

This paper examines the effects of alternative assumptions regarding the curvature of utility upon estimated discount rates in experimental data. To do so, it introduces a novel design to elicit time preference building upon a translation of the Holt and Laury method for risk. The results demonstrate that utility elicited directly from choice over time is significantly concave, but far closer to linear than utility elicited under risk. As a result, the effect of adjusting discount rates for this curvature is modest compared to assuming linear utility, and considerably less than when utility from a risk preference task is imposed.

Present Bias for Monetary and Dietary Rewards: Evidence from Chinese Teenagers

“…Our findings regarding the curvature of utility are notable in light of recent controversy over the nature of utility in choice over time (Abdellaoui et al, 2013;Andreoni & Sprenger, 2012a;Cheung, 2020). Consistent with these recent studies, we find near-linear utility for money in choice over time.…”

“…Next, in contrast to previous results in the domain of risk, we find differences in the curvature of utility between monetary and primary rewards. For money, we confirm recent findings in the time preference literature that instantaneous utility is close to linear (Abdellaoui et al, 2013;Andreoni & Sprenger, 2012a;Cheung, 2020). However, for both healthy and unhealthy foods we find strong evidence of concave utility (implying a preference to spread rewards evenly over time), more in line with conventional findings in the domain of risk.…”

Looking ahead: Subjective time perception and individual discounting

“…It is thus possible that some, or most, of the hyperbolic curvature of the discounting function that we find using objective time would disappear if risk and time preferences would be structurally estimated jointly. 8 Third, and again relatedly, our design does not allow us to directly measure and control for the curvature of utility for risk and time as done in Abdellaoui et al (2013), Cheung (2015b), and Epper and Fehr-Duda (2015). Addressing each of these questions would require a different design and/or a more structural econometric approach, and we leave to further research the intriguing questions of whether the Weber-Fechner-shaped curvature of the individual perception of time may be related to the curvature of utility for risk and time, to non-linear probability weighting, and to decreasing impatience and other forms of non-stationary time preferences in the sense of Prelec (2004) and Bleichrodt et al (2009).…”

Prediction and Model Selection in Experiments

“…The convex budget set and varying interest rates used by Andreoni and Sprenger (2012) allow for a simultaneous estimation of both curvature and discounting parameters. A variety of methods have been implemented to measure curvature and overcome this potential bias (Abdellaoui, Kemel, Panin, & Vieider, 2019;Andersen, Harrison, Lau, & Rutstr€ om, 2008;Cheung, 2019;Luckman, Donkin, & Newell, 2018). 7 The analysis here follows Andreoni and Sprenger (2012) and most of the subsequent literature in allowing for curvature parameters to vary between subjects (Abdellaoui et al, 2019;Andersen, Harrison, Lau, & Rutstr€ om, 2014;Augenblick & Rabin, 2019).…”

“…Generally, estimated discount rates are much higher than market interest rates, implying that subjects either have credit constraints or do not consider credit markets when making their decisions (Frederick et al, 2002). Furthermore, utility for time-dated monetary transfers has been estimated to be near linear (Andreoni & Sprenger, 2012;Cheung, 2019), which leads to choices on the corners of the budget constraint. An estimated model predicting the 'wrong' corner is particularly harshly punished by a convex loss function like the one used in nonlinear least squares.…”