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Survey of time preference, delay discounting models

Doyle, John R. 2012. Survey of time preference, delay discounting models. [Working Paper]. Social Science Research Network. Available at: http://dx.doi.org/10.2139/ssrn.1685861

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Abstract

The paper surveys over twenty models of delay discounting (also known as temporal discounting, time preference, time discounting), that psychologists and economists have put forward to explain the way people actually trade off time and money. Using little more than the basic algebra of powers and logarithms, we show how the models are derived, what assumptions they are based upon, and how different models relate to each other. Rather than concentrate only on discount functions themselves, we show how discount functions may be manipulated to isolate rate parameters for each model. This approach, consistently applied, helps focus attention on the three main components in any discounting model: subjectively perceived money; subjectively perceived time; and how these elements are combined. We group models by the number of parameters that have to be estimated, which means our exposition follows a trajectory of increasing complexity to the models. However, as the story unfolds it becomes clear that most models fall into a smaller number of families. We also show how new models may be constructed by combining elements of different models. The surveyed models are: Exponential; Hyperbolic; Arithmetic; Hyperboloid (Green & Myerson, Rachlin); Loewenstein and Prelec Generalized Hyperboloid; quasi-Hyperbolic (β-δ); Benhabib et al’s fixed cost; Benhabib et al’s Exponential/Hyperbolic/quasi-Hyperbolic; Read’s discounting fractions; Roelofsma’s exponential time; Scholten and Read’s discounting-by-intervals (DBI); Ebert and Prelec’s constant sensitivity (CS); Bleichrodt et al.’s constant absolute decreasing impatience (CADI); Bleichrodt et al.’s constant relative decreasing impatience (CRDI); Green, Myerson, and Macaux’s hyperboloid over intervals models; Killeen’s additive utility; size-sensitive additive utility; Yi, Reid, and Bickel’s memory trace models; McClure et al.’s two exponentials; Scholten and Read’s trade-off model; and Decision-by-Sampling (DbS). For a convenient overview, a single “cheat sheet” table captures the notation and essential mathematics behind all but one of the models.

Item Type: Monograph (Working Paper)
Date Type: Publication
Status: Published
Schools: Business (Including Economics)
Subjects: H Social Sciences > H Social Sciences (General)
H Social Sciences > HB Economic Theory
H Social Sciences > HG Finance
Q Science > QA Mathematics
Uncontrolled Keywords: Time Preference ; Delay Discounting ; Intertemporal Choice ; Survey ; JDM ; Behavioral Economics
Publisher: Social Science Research Network
ISSN: 15565068
Last Modified: 05 Nov 2019 03:29
URI: https://orca.cardiff.ac.uk/id/eprint/27496

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