RESEARCH REPOSITORY
This is the author’s final version of the work, as accepted for publication
following peer review but without the publisher’s layout or pagination.
The definitive version is available at:
http://dx.doi.org/10.1007/s00199-015-0931-6
Blavatskyy, P.R. (2016) A monotone model of intertemporal choice.
Economic Theory, 62 (4). pp. 785-812.
http://researchrepository.murdoch.edu.au/id/eprint/29017/
Copyright: © 2015 Springer-Verlag Berlin Heidelberg.
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ECONOMIC THEORY
A Monotone Model of Intertemporal Choice
--Manuscript Draft--
Manuscript Number: ECTH-D-14-00353R2
Full Title: A Monotone Model of Intertemporal Choice
Article Type: Research Article
Corresponding Author: Pavlo Blavatskyy, Ph.D.
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Abstract: Existing models of intertemporal choice such as discounted utility (also known as
constant or exponential discounting), quasi-hyperbolic discounting and generalized
hyperbolic discounting are not monotone: a decision maker with a concave utility
function generally prefers receiving $1m today plus $1m tomorrow over receiving $2m
today. This paper proposes a new model of intertemporal choice. In this model, a
decision maker cannot increase his/her satisfaction when a larger payoff is split into
two smaller payoffs, one of which is slightly delayed in time. The model can rationalize
several behavioral regularities such as a greater impatience for immediate outcomes.
An application of the model to intertemporal consumption/saving reveals that
consumers may exhibit dynamic inconsistency. Initially, they commit to saving for
future consumption but, as time passes, they prefer to renegotiate such a contract for
an advance payment. Behavioral characterization (axiomatization) of the model is
presented. The model allows for intertemporal wealth, complementarity and
substitution effects (utility is not separable across time periods).
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Summary of main changes in the revised version
1) I restructured the manuscript to focus on the main issue: existing models of intertemporal
choice violate intertemporal monotonicity and this paper proposes a new model to remedy
this problem. I dropped all discussion of separability as this is a secondary point (even though
interesting in itself) which diverts reader’s attention from the main issue.
2) I dropped my criticism of discontinuity and pointed out that violations of monotonicity may
arise in a discrete time framework (and they are more severe in a continuous time
framework).
3) Since the referee did not criticize the macroeconomic application but found axiomatization
“not more appealing than those used in decision under risk” I moved the section with
macroeconomic application to section 3 and axiomatization—to section 4 (I am also happy to
delegate axiomatization to the appendix, if required).
With best regards, Pavlo
Response to Reviewer Comments
- 1 -
A Monotone Model of Intertemporal Choice
Pavlo R. Blavatskyy
School of Management and Governance
Murdoch University, 90 South Street,
Murdoch, WA 6150 AUSTRALIA
Ph: (08)9360 2838 Fax: (08)9360 6966
Email: P.Blavatskyy@murdoch.edu.au
Abstract Existing models of intertemporal choice such as discounted utility (also known as constant
or exponential discounting), quasi-hyperbolic discounting and generalized hyperbolic discounting are
not monotone: a decision maker with a concave utility function generally prefers receiving $1m
today plus $1m tomorrow over receiving $2m today. This paper proposes a new model of
intertemporal choice. In this model, a decision maker cannot increase his/her satisfaction when a
larger payoff is split into two smaller payoffs, one of which is slightly delayed in time. The model can
rationalize several behavioral regularities such as a greater impatience for immediate outcomes. An
application of the model to intertemporal consumption/saving reveals that consumers may exhibit
dynamic inconsistency. Initially, they commit to saving for future consumption but, as time passes,
they prefer to renegotiate such a contract for an advance payment. Behavioral characterization
(axiomatization) of the model is presented. The model allows for intertemporal wealth,
complementarity and substitution effects (utility is not separable across time periods).
Keywords: Intertemporal Choice; Discounted Utility; Time Preference; Dynamic Inconsistency;
Expected Utility Theory; Rank-Dependent Utility
JEL Classification Codes: D01; D03; D81; D90
Manuscript Click here to download Manuscript IRDU_final.docx
Click here to view linked References
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A Monotone Model of Intertemporal Choice
1. Introduction
Intertemporal choice involves payoffs to be received at different points in time. Samuelson
(1937) proposed a classical model of intertemporal choice that is known as discounted utility or
constant (exponential) discounting. The model is parsimonious and analytically convenient but its
descriptive validity has been questioned. For instance, Thaler (1981, p. 202) argued that some people
may prefer one apple today over two apples tomorrow but, at the same time, they may prefer two
apples in one year plus one day over one apple in one year. Discounted utility cannot account for
such a switching choice pattern. The descriptive limitations of discounted utility motivated the
development of alternative models such as quasi-hyperbolic discounting (Phelps and Pollak, 1968)
and generalized hyperbolic discounting (Loewenstein and Prelec, 1992). These models replaced a
constant (exponential) discount factor in discounted utility with a more general discount function.
Discounted utility and its subsequent generalizations such as quasi-hyperbolic and generalized
hyperbolic discounting may produce rather counterintuitive results which are seldom discussed in
the literature. These models may violate intertemporal monotonicity when utility function is
concave (as usually assumed in economics). For example, consider a decision maker who receives
one million dollars now as well as one million dollars at a later moment of time t (with a convention
that t=0 denotes the present moment).
1
According to the above mentioned models, this decision
maker behaves as if maximizing utility
(1)
where u(.) is utility function and D(.) is a discount function. According to the same models, receiving
two million now yields utility u($2m). For a decision maker with a concave utility function u(.) and
enough patience (i.e. with a discount function D(t) sufficiently close to one) utility (1) is greater than
u($2m) due to Jensen’s inequality. Moreover, in a continuous time framework, for any decision
maker with a concave utility function u(.) it is always possible to find a moment of time t sufficiently
close to the present moment such that utility (1) is greater than u($2m) due to the property
(cf. Figure 1 in Loewenstein and Prelec, 1992, p. 581). In other words, the above
mentioned models predict that a decision maker with a concave utility function prefers receiving
one million now plus one million at a later moment of time t over receiving two million immediately.
More generally, according to the existing models of intertemporal choice, the desirability of
any payoff may increase if this payoff is split into two smaller payoffs one of which is slightly delayed
in time. Such an implication is clearly testable in a controlled laboratory experiment. Yet, readers
would probably agree with my tentative conjecture that very few people are likely to reveal such a
1
This example is also given in Blavatskyy (2015, p. 143).
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