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2016 | OriginalPaper | Buchkapitel

20. Subjective Random Discounting and Intertemporal Choice

verfasst von : Youichiro Higashi, Kazuya Hyogo, Norio Takeoka

Erschienen in: Behavioral Economics of Preferences, Choices, and Happiness

Verlag: Springer Japan

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Abstract

This chapter provides an axiomatic foundation for a particular type of preference shock model called the random discounting representation where a decision maker believes that her discount factors change randomly over time. For this purpose, we formulate an infinite horizon extension of Dekel, Lipman, and Rustichini (Econometrica 69:891–934, 2001), and identify the behavior that reduces all subjective uncertainties to those about future discount factors. We also show uniqueness of subjective belief about discount factors. Moreover, a behavioral comparison about preference for flexibility characterizes the condition that one’s subjective belief second-order stochastically dominates the other. Finally, the resulting model is applied to a consumption-savings problem.

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See Mehra and Sah (2002, Section 1.1, pp. 871–873) for more examples about fluctuations in subjective parameters.

The set \(\mathcal{K}(\varDelta (C \times \mathcal{Z}))\) is endowed with the Hausdorff metric. Details are relegated to Appendix section “Hausdorff Metric”.

DLR consider preference over \(\mathcal{K}(\varDelta (C))\) with finite set C.

A sophisticated DM, who is fully aware of time-inconsistency caused by hyperbolic discounting, may be viewed as a limiting case of their model, where the DM never exercises self-control at the moment of choice.

The DM may care about timing of resolution of risk and prefer earlier or later resolution of multistage lotteries. Such distinction is examined in Kreps and Porteus (1978). Epstein et al. (2007) argue against Timing Indifference and provide a model with nonlinear future preferences.

Their Nondegeneracy axiom requires the existence of menus x, y with \(x \succ y\) and \(x \subset y\). That is, this axiom captures preference for commitment—a DM may prefer a smaller menu.

A sophisticated DM with hyperbolic discounting exhibits preference for commitment rather than for flexibility. Thus, such a DM is excluded by this axiom.

Dekel et al. (2007) fill a gap in DLR surrounding this representation result.

See Gul and Pesendorfer (2004, p. 125, footnote 7) for more details.

To prevent arbitrary manipulations, DLR (p. 912) suggest that probability measures can be identified if some aspect of the ex post utility functions is state-independent. Such a condition is satisfied in our model.

Strategic Rationality implies Monotonicity. Indeed, assume \(y \subset x\). Arguing by contradiction, suppose \(y \succ x\). Strategic Rationality implies \(x = x \cup y \sim y \succ x\), which is a contradiction.

In literature on ambiguity in the Savage-type model, Epstein (1999) and Ghirardato and Marinacci (2002) adopt closely related conditions to capture comparative attitudes toward ambiguity aversion. They compare an arbitrary act with an unambiguous act instead of comparing an arbitrary menu with a commitment menu.

Notice that continuity is not redundant because a concave function is continuous in the interior of the domain. In the original definition by Rothschild and Stiglitz (1970), continuity is not imposed.

Their argument for this equivalence works even when continuity is imposed on v.

Since u is CRRA, ϕ ⁱ is independent of s.

They fix the argument (Lemma 12, p. 929) of DLR.

This addendum has been newly written for this book chapter.

In their model, C is assumed to be finite.

In the supplement to Krishna and Sadowski (2014), Krishna and Sadowski (2013) show a similar result for a preference \(\succapprox\) on \(\mathcal{Z}\simeq \mathcal{K}(\varDelta (C \times \mathcal{Z}))\).

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Titel: Subjective Random Discounting and Intertemporal Choice
verfasst von: Youichiro Higashi
Kazuya Hyogo
Norio Takeoka
Verlag: Springer Japan
Buch: Behavioral Economics of Preferences, Choices, and Happiness
Print ISBN: 978-4-431-55401-1

Electronic ISBN: 978-4-431-55402-8

Copyright-Jahr: 2016
DOI: https://doi.org/10.1007/978-4-431-55402-8_20