Intertemporal choice: The reasons why a tradeoff model works and discounting models don't - PTDC/PSI-PCO/101447/2008 (2010 - 2013)

Reaserch Team:

Marc Scholten (Project Leader)
Daniel Read

 

Project's Summary:

Economic analyses of intertemporal choice have been dominated by Samuelson’s (1937) discounted-utility model (DUM). In this model, utilities are assigned to all outcomes of a decision, these utilities are discounted in function of the delay to the outcomes, and the option with the highest overall discounted utility is chosen. Utilities are assigned to final states of wealth and utilities are discounted at a constant rate, which ensures consistent intertemporal choice. The normative status of this model is beyond doubt: It convincingly prescribes what economic agents should do. However, its descriptive merits are severely limited: It fails to accurately describe how people actually make their intertemporal decisions.

There are many anomalies to DUM. Three classics, due to Thaler (1981), are the following ones: More remote outcomes are discounted at a lower rate than more proximate ones (delay effect), larger outcomes are discounted at a lower rate than smaller ones (magnitude effect), and losses are discounted at a lower rate than gains (sign effect). These and other anomalies were accommodated by Loewenstein and Prelec’s (1992) hyperbolic-discounting model (HDM). This model retains the basic format of DUM, in that an overall discounted value is assigned to each option and the option with the highest value is chosen, but the model components are different: Values are assigned to changes in wealth and, to explain the delay effect, values are discounted at a decreasing rate. To explain the magnitude effect, the sign effect, and other anomalies, the model invokes several assumptions about the way in which values are assigned to outcomes.

Recent data, most of which collected by ourselves, reveal descriptive failures of HDM as well: Discounting seems to be a function not only of the delay to the outcomes but also of the interval between the outcomes. A first demonstration was subadditive discounting (Read, 2001; Read & Roelofsma, 2003): Outcomes are discounted more when the interval between the outcomes is divided into shorter subintervals. For instance, an entire year might weigh less than a sequence of 12 months. But we also discovered that subadditive discounting reverses into superadditive discounting when intervals are further divided into very short subintervals (Scholten & Read, 2006). For instance, an entire week might weigh more than a sequence of 7 days. These patterns of discounting, called interval effects, can be held responsible for occurrences of intransitive intertemporal choice (Roelofsma & Read, 2000; Scholten & Read, 2006). To accommodate all these anomalies, we developed the interval-discounting model (IDM), in which discounting is a function of the perceived interval between the outcomes (Scholten & Read, 2006).

Basically, discounting models are alternative-based choice models, as most other choice models. IDM, however, smuggles attribute-based comparisons into the discounting process, in that the perceived delays to the outcomes are directly compared with one another. This was necessary to salvage the discounting paradigm in the presence of interval effects, but leaves us with a very simple question: If the options are directly compared in terms of delays, why wouldn’t they be directly compared in terms of outcomes as well?

Intuition seems to favor attribute-based choice models. When asked about decision making, people often say that decisions involve comparisons between the options. And they don’t mean comparisons between overall values: They mean that, for instance, outcomes are directly compared with one another (“how much more will I receive by waiting longer?”) and delays as well (“how much longer will I have to wait?”). Although attribute-based choice models are not unknown to the psychology of decision making (e.g., González-Vallejo, 2002; Restle, 1961; Tversky, 1969), an attribute-based intertemporal choice model has never been developed. The objective of this project is to show the theoretical and empirical advantages of such a model over discounting models.

Our research will go through several stages. First, we will conduct choice experiments to obtain qualitative evidence against discounting models. Second, we will develop an attribute-based model of intertemporal choice, the tradeoff model (TM), to account for all anomalies, those from the literature and the new ones. Third, we will develop parametric specifications of both TM and IDM, which is the most general discounting model available. Fourth, we will conduct choice-based matching experiments to make quantitative comparisons between TM and IDM. It is expected that our research will provide a viable solution to the failures of discounting theory, and, thus, a valuable contribution to analyses of intertemporal choice in psychology and economics.

 

Project’s aims:

Firstly, full operationalization of a descriptive discounting model for application in concrete data analyses, however limited its empirical applicability may be. Secondly, development of a tradeoff model (TM) that accounts for anomalies to both normative and descriptive discounting models. It should also be a model that is more plausible psychologically, a model that is more parsimonious, a model that is easier to apply, and a model that can be applied more broadly than discounting models. A descriptive model of intertemporal choice that excels in empirical accuracy and empirical applicability should be a valuable contribution to analyses of intertemporal choice in psychology and economics.

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