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Joint measurement of risk aversion, prudence, and temperance

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Abstract

Risk aversion—but also the higher-order risk preferences of prudence and temperance—are fundamental concepts in the study of economic decision making. We propose a method to jointly measure the intensity of risk aversion, prudence, and temperance. Our theoretical approach is to define risk compensations of different orders, and in an experiment we elicit these compensations with a price list technique. We find evidence for risk aversion, prudence, and temperance. These traits correlate within subjects. The compensations elicited for prudence are significantly larger than those for risk aversion and temperance. In contrast to commonly used utility functions, prospect theory can predict this behavioral pattern. In our experiment, risk-averse, risk-loving, and risk-neutral subjects are prudent. This supports a recent theoretical observation that prudence may be a more universal trait than previously realized.

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Notes

  1. Dittmar (2002) presents weak evidence for kurtosis aversion in asset returns. Also, results in Guiso et al. (1996) from an Italian household survey on pension-investment decisions are consistent with temperate behavior; see Deck and Schlesinger (2010) for a brief discussion.

  2. Deck and Schlesinger (2010) are the first to provide an intuitive, qualitative discussion on the issue. They analyze in what direction probability weighting, reference dependence, and loss aversion influence preference among the risk apportionment lottery pairs in their experiment. They also compute the prospect theory values of their lotteries for the estimates of Tversky and Kahneman (1992).

  3. Eeckhoudt and Schlesinger (2006) originally considered the lotteries \(\tilde {B}_2=0\) and \(\tilde {A}_2=[0,\tilde {\epsilon }],\) where \(\tilde {\epsilon }\) is a zero-mean risk, and show that preferring \(\tilde {B}_2\) over \(\tilde {A}_2\) for all \(\tilde {\epsilon }\) is equivalent to u ′′ < 0. We use the lotteries B 2 and A 2 to avoid experimental certainty effects.

  4. Many different compensations or premia are possible. For example, the (second-order) risk premium defined in Ross (1981) corresponds to an amount subtracted from B 2 for sure in our setting. Crainich and Eeckhoudt (2008) define a prudence compensation similar to ours that is subtracted in the good state of A 3 only. We have chosen the compensation that, we think, is most convenient for experimentation; see Section 2.3 for a discussion. It has been termed “compensating risk compensation” in Pope and Chavas (1985), and Kimball (1990) considers a “compensating precautionary compensation” in the context of prudence. The earliest analysis of this compensation we are aware of is LaValle (1968). Pratt (1964) briefly mentioned that this compensation relates to the “bid price,” while his “equivalent premium” relates to the “ask price” of a risk.

  5. The corresponding intervals in stage PR is also (−5,5) for all three tasks, while in stage TE they are (−3.5,3.5) and (−2.8,2.8) for tasks TE1 and TE2, respectively. Therefore, in stage TE this caveat is less pronounced.

  6. Aggregated over six tasks, 85% of individuals switched once and 8% did not switch. That is, 93% of subjects never violated transitivity. For 3% we observe two switches, and in about 4% of responses subjects switch back and forth more than two times. This latter fraction is slightly lower than reported in other price list experiments to elicit risk preferences. Holt and Laury (2002), for example, report between 5 to 6% of multiple switches.

  7. We do so simply because the observations for the six task compensations are similar and because comparisons of six compensations throughout would be cumbersome. Nevertheless, for the interested reader we collect further results on the task compensations in Section C of the web appendix. One result on task level we would like to highlight concerns the impact of differently skewed zero-mean risks \(\tilde {\epsilon }_1\) employed in tasks PR1, PR2, and PR3. Similar to Ebert and Wiesen (2011), we find some support for “stronger prudence” when \(\tilde {\epsilon }_1\) is more left-skewed. Ebert (2012) provides a theoretical analysis of this result.

  8. Ebert and Wiesen (2011), Noussair et al. (2014), and Deck and Schlesinger (forthcoming) do not observe gender differences when testing for prudence, and only Noussair et al. find that women are more temperate. Deck and Schlesinger (2010) and Maier and Rüger (2011) do not report any gender-related results.

  9. For the functional forms of these utility classes see Section E of the web appendix. Analogously to the empirical stage compensations \(\overline {\hat {m}}^{\overline {\text {\tiny PR}}}\) and \(\overline {\hat {m}}^{\overline {\text {\tiny TE}}},\) the predicted stage compensations mPR and mTE are the means of the predicted task compensations in stage PR and TE, respectively.

  10. For a risk averter who prefers more to less, sure reductions in wealth are “bad” and zero-mean risks are also “bad.” For a risk lover who prefers more to less, sure reductions in wealth are “bad” but zero-mean risks are “good.”

  11. Risk lovers are those subjects that demanded a negative compensation in stage RA whereas risk-averse (risk-neutral) subjects demanded a positive (zero) compensation in stage RA.

  12. Mixed risk aversion is a preference for combining “good with bad” at any order higher than one (see Caballé and Pomansky 1996; Eeckhoudt et al. 2009), and mixed risk loving is a preference for combining “good with good” at any order higher than one (see Crainich et al. 2013 ; Ebert 2013 .)

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Acknowledgments

We are grateful for valuable comments and suggestions by Han Bleichrodt, Louis Eeckhoudt, Armin Falk, Thomas Gehrig, Holger Gerhardt, Glenn Harrison, Lorens Imhof, Harris Schlesinger, Reinhard Selten, anonymous referees, and the editor. We also thank conference participants of the 2012 ESEM (Malaga), 2011 ESA European Meeting (Luxembourg), the 2011 EEA (Oslo), the 2010 GfeW Meeting (Luxembourg), and the 2010 LMU Excellence Symposium in Munich. We further thank seminar participants in Bonn, Essen, Freiburg, Rotterdam, Tilburg, and participants of the Sino-German Summer School workshop in Bonn in January 2010. We thank Emanuel Castillo for his z-Tree programming assistance as well as Martin Acht and Javier Sanchez for their help with conducting the experiment. Christian Hilpert and Johannes Pfeifer provided very valuable consultation on Matlab programming. Furthermore, we thank Michael Borss, Mara Ewers, Stefanie Lehmann, Jan Meise, and Gert Pönitzsch for their participation in a pilot experiment and their helpful comments on the experiment at that stage. The experiment was financed through the Geneva Association Research Grant 2009. During their doctoral studies, Ebert received financial support from the Bonn Graduate School of Economics, and Wiesen from the Konrad-Adenauer-Stiftung e.V.

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  1. Department of Finance, Tilburg University, PO Box 90153, 5000, LE, Tilburg, The Netherlands

    Sebastian Ebert

  2. Seminar of Personnel Economics and HRM, Faculty of Management, Economics, and Social Sciences, University of Cologne, Universitätsstr. 22, 50937, Cologne, Germany

    Daniel Wiesen

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Ebert, S., Wiesen, D. Joint measurement of risk aversion, prudence, and temperance. J Risk Uncertain 48, 231–252 (2014). https://doi.org/10.1007/s11166-014-9193-0

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