NBER WORKING PAPER SERIES
THIRTY YEARS OF PROSPECT THEORY IN ECONOMICS:
A REVIEW AND ASSESSMENT
Nicholas C. Barberis
Working Paper 18621
http://www.nber.org/papers/w18621
NATIONAL BUREAU OF ECONOMIC RESEARCH
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December 2012
I am grateful to David Autor, Botond Koszegi, John List, Ted O'Donoghue, Matthew Rabin, Andrei
Shleifer, and Timothy Taylor for extensive comments on an early draft. The views expressed herein
are those of the author and do not necessarily reflect the views of the National Bureau of Economic
Research.
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© 2012 by Nicholas C. Barberis. All rights reserved. Short sections of text, not to exceed two paragraphs,
may be quoted without explicit permission provided that full credit, including © notice, is given to
the source.
Thirty Years of Prospect Theory in Economics: A Review and Assessment
Nicholas C. Barberis
NBER Working Paper No. 18621
December 2012
JEL No. D03,D81,G02
ABSTRACT
Prospect theory, first described in a 1979 paper by Daniel Kahneman and Amos Tversky, is widely
viewed as the best available description of how people evaluate risk in experimental settings. While
the theory contains many remarkable insights, economists have found it challenging to apply these
insights, and it is only recently that there has been real progress in doing so. In this paper, after first
reviewing prospect theory and the difficulties inherent in applying it, I discuss some of this recent
work. While it is too early to declare this research effort an unqualified success, the rapid progress
of the last decade makes me optimistic that at least some of the insights of prospect theory will eventually
find a permanent and significant place in mainstream economic analysis.
Nicholas C. Barberis
Yale School of Management
135 Prospect Street
P O Box 208200
New Haven, CT 06520-8200
and NBER
nick.barberis@yale.edu
2
In 1979, two Israeli psychologists, Daniel Kahneman and Amos Tversky, already
famous for their work on judgment heuristics, published a paper in the journal
Econometrica titled “Prospect Theory: An Analysis of Decision under Risk.” The paper
accomplished two things. It collected in one place a series of simple but compelling
demonstrations that, in laboratory settings, people systematically violate the predictions
of expected utility theory, economists’ workhorse model of decision-making under risk.
It also presented a new model of risk attitudes called “prospect theory,” which elegantly
captured the experimental evidence on risk-taking, including the documented violations
of expected utility.
More than 30 years later, prospect theory is still widely viewed as the best
available description of how people evaluate risk in experimental settings. Kahneman and
Tversky’s papers on prospect theory have been cited tens of thousands of times and were
decisive in the awarding to Kahneman, in 2002, of the Nobel Prize in economic sciences.
(Tversky would surely have shared the prize had he not passed away in 1996 at the age of
59).
It is curious, then, that so many years after the publication of the 1979 paper, there
are relatively few well-known and broadly accepted applications of prospect theory in
economics. One might be tempted to conclude that, even if prospect theory is an excellent
description of behavior in experimental settings, it is less relevant outside the laboratory.
In my view, this lesson would be incorrect. Rather, the main reason that applying
prospect theory in economics has taken so long is that, in a sense that I make precise in
the next section, it is hard to know exactly how to apply it. While prospect theory
contains many remarkable insights, it is not ready-made for economic applications.
Over the past decade, researchers in the field of behavioral economics have put a
lot of thought into how prospect theory should be applied in economic settings. This
effort is bearing fruit. A significant body of theoretical work now incorporates the ideas
in prospect theory into more traditional models of economic behavior; and a growing
body of empirical work tests the predictions of these new theories. In this essay, after first
reviewing prospect theory and the difficulties inherent in applying it, I discuss some of
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this recent work. It is too early to declare this research effort an unqualified success, but
the rapid progress of the last decade makes me optimistic that at least some of the insights
of prospect theory will eventually find a permanent and significant place in mainstream
economic analysis.
Prospect Theory
The Model
The original version of prospect theory is described in Kahneman and Tversky
(1979). While this paper contains all of the theory’s essential insights, the specific model
it proposes has some limitations: it can be applied to gambles with at most two non-zero
outcomes, and it predicts that people will sometimes choose dominated gambles. In 1992,
Kahneman and Tversky published a modified version of their theory known as
“cumulative prospect theory” which resolves these problems. This version is the one
typically used in economic analysis and it is the version I briefly review here.
Consider a gamble
,
;
,
;…;
,
;…;
,
;
,
,
where the notation should be read as “gain
with probability
,
with
probability
, and so on,” where the outcomes are arranged in increasing order, so
that
for , and where
0. For example, a 50:50 bet to lose $100 or gain
$200 would be expressed as $100,
;$200,
. Under expected utility theory, an
individual evaluates the above gamble as
,
where is current wealth and · is an increasing and concave utility function. Under
cumulative prospect theory, by contrast, the gamble is evaluated as
4
,
where ·, the “value function,” is an increasing function with
0
0, and where
are “decision weights.”
2
This formulation illustrates the four elements of prospect theory: 1) reference-
dependence, 2) loss aversion, 3) diminishing sensitivity, and 4) probability weighting.
First, in prospect theory, people derive utility from gains and losses, measured relative to
some reference point, rather than from absolute levels of wealth: the argument of · is
, not
. Kahneman and Tversky motivate this assumption, known as “reference
dependence,” with explicit experimental evidence (see, for example, Problems 11 and 12
in their 1979 paper), but also by noting that our perceptual system works in a similar
way: we are more attuned to changes in attributes such as brightness, loudness, and
temperature than we are to their absolute magnitudes.
Second, the value function · captures “loss aversion,” the idea that people are
much more sensitive to losses – even small losses -- than to gains of the same magnitude.
Informally, loss aversion is generated by making the value function steeper in the region
of losses than in the region of gains. This can be seen in Figure 1, which plots a typical
value function; the horizontal axis represents the dollar gain or loss , and the vertical
axis, the value assigned to that gain or loss. Notice that the value placed on a $100
gain, 100, is smaller in absolute magnitude than 100, the value placed on a $100
loss. Kahneman and Tversky infer loss aversion from the fact that most people turn down
the gamble $100,
;$110,
). As Rabin (2000) shows, it is very hard to understand this
fact in the expected utility framework: the dollar amounts are so small relative to typical
wealth levels that, under expected utility, the gamble is evaluated in a risk-neutral way;
given its positive expected value, it is therefore attractive. For a loss averse individual,
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In taking · to be increasing and concave and its argument to be the level of wealth, I am following the
standard convention in applications of expected utility. The assumptions about the form of · capture a
simple intuition: that people prefer more wealth to less, and that an additional dollar has a smaller utility
impact at higher wealth levels. The concavity assumption generates risk aversion: it predicts that people
will prefer a gamble’s expected value to the gamble itself.
