Parallel Temporal & Probabilistic Discounting of Costs Stephen Jones & Mike Oaksford July 2009

Background to Discounting Choice in one dimension is straightforward Prefer $10 today to next year, and a sure thing to a risk Two dimensions - subjective evaluation of alternatives $10 today or $25 next year A certain $100 or a $250 bet on a coin-toss Most work has considered discounting of rewards Delay and risk interact – is one more fundamental? Little work on costs – more frequent & valid context

When was the last time someone came up to you in the street and offered you $100 now…. …or $150 in a year’s time? Evaluation of Rewards Lacks Validity

Sales - Credit

Purchase pull-forward

Insurance

Magnitude Effect for Rewards Size of reward affects discounting rate 2 Not predicted by economic theory Opposite effect for delay and risk 2 Expect a parallel preference for immediate & certain Our research question – is there a similar magnitude effect for costs? Previous cost discounting study inconclusive 1 Small sample Homogeneous – psychology undergraduate students, 18 – 21 Sequential presentation of delays & risks – anchoring?

Magnitude Effect for Rewards Source: Green & Myerson (2004)

Method Experimental, within-subject design Independent variables Delay/Risk – 5 levels Amount – 3 levels Random presentation Forced choice with 5 iterations Measured point of subjective indifference Web-based experiment Allows for much larger sample – 153 participants Heterogeneous sample population Safeguards against identified web problems 3

Analysis – Area Under Curve Normalised point of subjective indifference Delay Proposed by Myerson et al (2001) 4 Avoids curve fitting debate Approx normally distributed Can use parametric analysis

Analysis – Area Under Curve Normalised point of subjective indifference Delay Proposed by Myerson et al (2001) 4 Avoids curve fitting debate Approx normally distributed Can use parametric analysis

Analysis – Area Under Curve Normalised point of subjective indifference Delay Proposed by Myerson et al (2001) 4 Avoids curve fitting debate Approx normally distributed Can use parametric analysis

Analysis – Area Under Curve Normalised point of subjective indifference Delay Proposed by Myerson et al (2001) 4 Avoids curve fitting debate Approx normally distributed Can use parametric analysis

Results

Corresponding Effect of Amount of Reward on AUC Source Myerson et al (2003) 5

Results Significant effect of amount on temporal & probabilistic discounting rate as measured by AUC F (1.88, ) = 8.93, p < Parallel effect of amount for delay & risk Larger cost amount increases preference for delay & risk Also found significant correlation between individual temporal & probabilistic discounting rates £200 cost, r(143) = 0.22, p < £2,500 cost, r(143) = 0.27, p < £15,000 cost, r(143) = 0.27, p <.005

Conclusions Costs appear to handled differently from rewards Delay and risk may be parallel effects for costs This seems intuitively reasonable – delay = risk Established platform to investigate interaction Hard to explain opposite effect with rewards Immediate = risky Lack of practice at this type of evaluation? No observed methodological anchoring effect

References 1. Estle,et al (2006) Differential effects of amount on temporal & probability discounting of gains & losses, Memory & Cognition, Vol 34 (4), Green, L & Myerson, J (2004) A discounting framework for choice with delayed & probabilistic reward, Psychological Bulletin, Vol 130 (5), Birnbaum, M H (ed) (2000) Psychological experiments on the internet, London: Academic Press 4. Myerson, J., Green, L., & Warusawitharana, M. (2001). Area under the curve as a measure of discounting. Journal of the Experimental Analysis of Behavior, 76, 235– Myerson, J., Green, L., Hanson, J. S., Holt, D. D., & Estle, S. J. (2003) Discounting delayed and probabilistic rewards: Processes and traits. Journal of Economic Psychology, 24, 619–635.