On Social Preferences and the Intensity of Risk Aversion

Date01 September 2019
Published date01 September 2019
DOIhttp://doi.org/10.1111/jori.12239
ONSOCIAL PREFERENCES AND THE INTENSITY OF RISK
AVERSION
Oded Stark
ABSTRACT
We study the relative risk aversion of an individual with particular social
preferences: his wellbeing is influenced by his relative wealth, and by how
concerned he is about having low relative wealth. Holding constant the
individual’s absolute wealth, we obtain two results. First, if the individual’s
level of concern about low relative wealth does not change, the individual
becomes more risk averse when he rises in the wealth hierarchy. Second, if the
individual’s level of concern about low relative wealth intensifies when he
rises in the wealth hierarchy and if, in precise sense, this intensification is
strong enough, then the individual becomes less risk averse: the individual’s
desire to advance further in the wealth hierarchy is more important to him
than possibly missing out on a better rank.
INTRODUCTION
Pratt (1964) and Arrow (1965, 1970) introduced measures of risk aversion, drawing
the profession’s attention to the need to study the relationship between wealth and
attitudes towards risk: “the behavior of these measures as wealth varies is of the
greatest importance for prediction of economic reactions in the presence of
uncertainty” (Arrow, 1970, p. 35). Arrow and Pratt hypothesized that relative risk
aversion increases with wealth.
Although many subsequent studies, based both on laboratory data (e.g., Holt and
Laury, 2002) and on field data (e.g., Szpiro, 1983, and Eisenhauer and Halek,
1999), lend support to the hypothesis of increasing relative risk aversion, a
considerable amount of empirical work fails to align with Arrow and Pratt’s
hypothesis. Several researchers find that relative risk aversion decreases with
wealth (e.g., Cohn et al., 1975, and Bellante and Saba, 1986, using field data; Levy,
1994, using laboratory data); that relative risk aversion is constant regardless of
Oded Stark is at the Universities of Bonn and Warsaw, and at Georgetown University. Oded
Stark, ZEF, University of Bonn, Walter-Flex-Strasse 3, D-53113 Bonn, Germany. Oded Stark can
be contacted via e-mail: ostark@uni-bonn.de.
I am indebted to two referees for kind words and thoughtful comments, and to an Associate
Editor for advice and guidance. I benefited greatly from the suggestions and remarks of Wiktor
Budzinski, Marcin Jakubek, Krzysztof Szczygielski, and Ewa Zawojska.
2018 The Journal of Risk and Insurance. Vol. 9999, No. 9999, 1–20 (2018).
DOI: 10.1111/jori.12239
1
807
Vol. 86, No. 3, 807–826 (2019).
wealth (e.g., Szpiro, 1986, and Chiappori and Paiella, 2011, based on field data); or
that the relationship between wealth and relative risk aversion is nonlinear (e.g.,
Morin and Suarez, 1983, and Halek and Eisenhauer, 2001, who use field data, find
that relative risk aversion increases with wealth for low levels of wealth and
decreases with wealth for high levels of wealth; the first of these studies concludes
that for the richest, the pattern of decreasing relative risk aversion is so weak that
relative risk aversion can be considered constant). One reason for the apparent
divergence could be that in the received studies, the “behavior” of the measure of
relative risk aversion is related to changes in absolute wealth, neglecting to account
for changes in relative wealth; implicitly, relative wealth is kept constant. In
seeking to deepen our understanding of the impact of wealth on attitudes towards
risk, in this article we relate the varying “behavior” of the measure of relative risk
aversion not to variation in absolute wealth, which we keep constant, but to
variationinrelativewealthand,inparticular,tovariationinthelevelofconcern
about having low relative wealth.
The perception that differences in risk preferences are attributable to relative wealth is
supported by research in development economics (Thai villages) which finds that
these differences “turn out not to be related to wealth,” and that “there is no
correlation of risk aversion with wealth, and so the more risk-tolerant are not
necessarily more wealthy” (Townsend, 2016, p. 207).
While there is some acknowledgement in the received literature of a link between
relative wealth/status and risk-taking/gambling behavior, the received writings
do not follow the track that we pursue in this article. Most notably, Gregory
(1980) and Robson (1992) allude to a link between relative wealth and gambling
behavior, remarking that the incorporation of relative wealth/status in an
individual’s utility function can explain the Friedman and Savage (1948) paradox
of seemingly inconsistent risk-taking behavior of an individual following a
change in his wealth. However, Gregory does not specify a link between relative
wealth and any concrete measure of risk aversion. Robson investigates
connections between wealth distributions and fair gambles, yet he too does
not link status with any measure of risk aversion. Robson expands the
individual’s utility function to include a status term based on the individual’s
rank in the wealth distribution. There are, though, two notable differences
between Robson’s approach and ours: one difference relates to the rank character
of Robson’s measure, the other - to the direction of wealth-related comparisons.
First, in Robson’s model, an increase in the wealth of individuals to the right of
individual iin the ascendingly-ordered wealth distribution which occurs while
i’s rank remains unchanged does not change i’s status and, consequently, i’s
utility is not affected. However, the relative wealth deprivation of individual i
does change (it increases) when the wealth of individuals to his right increases
(even when i’s rank does not change) which, in turn, impinges on i’s utility. (As
explained and defined in the next section, we use the received cardinal index of
relative deprivation of individual ias a measure of the individual’s relative
wealth deprivation.) Second, incorporating rank in the preferences can be
interpreted as looking towards both the poorer and richer individuals when
evaluating utility, whereas the measure of relative wealth deprivation that we use
2THE JOURNAL OF RISK AND INSURANCE
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