# Eliciting ambiguity aversion in unknown and in compound lotteries: a smooth ambiguity model experimental study

- 415 Downloads
- 5 Citations

## Abstract

Coherent-ambiguity aversion is defined within the (Klibanoff et al., Econometrica 73:1849–1892, 2005) smooth-ambiguity model (henceforth *KMM*) as the combination of choice-ambiguity and value-ambiguity aversion. Five ambiguous decision tasks are analyzed theoretically, where an individual faces two-stage lotteries with binomial, uniform, or unknown second-order probabilities. Theoretical predictions are then tested through a 10-task experiment. In (unambiguous) tasks 1–5, risk aversion is elicited through both a portfolio choice method and a *BDM* mechanism. In (ambiguous) tasks 6–10, choice-ambiguity aversion is elicited through the portfolio choice method, while value-ambiguity aversion comes about through the *BDM* mechanism. The behavior of over 75 % of classified subjects is in line with the *KMM* model in all tasks 6–10, independent of their degree of risk aversion. Furthermore, the percentage of coherent-ambiguity-averse subjects is lower in the binomial than in the uniform and in the unknown treatments, with only the latter difference being significant. The most part of coherent-ambiguity-loving subjects show a high risk aversion.

## Keywords

Coherent-ambiguity aversion Value-ambiguity aversion Choice-ambiguity aversion Smooth ambiguity model Binomial distribution Uniform distribution Unknown urn## JEL Classification

D81 D83 C91## Notes

### Acknowledgments

The research leading to these results has received funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007–2013) Grant Agreement No. 230589. G. Attanasi gratefully acknowledges financial support by the Chair Georges Meyer in Mathematical Economics at Jean-Jacques Laffont Foundation (TSE). N. Pace gratefully acknowledges financial support by the Swiss&Global and Fondazione Ca’ Foscari. The authors gratefully thank Michèle Cohen, Sandrine Spaeter, Lorenzo Vantaggiato, participants at the 15th Conference on the Foundations and Applications of Utility, Risk and Decision Theory at Georgia State University in Atlanta, at the Workshop on New Developments in Decision Making under Uncertainty at Université de Cergy-Pontoise, and at a Cournot seminar at University of Strasbourg for their useful comments and suggestions.

## References

- Abdellaoui, M., Klibanoff, P., & Placido, L. (2011).
*Ambiguity and compound risk attitudes: An experiment*. Working paper. Northwestern University.Google Scholar - Ahn, D., Choi, S., Gale, D., & Kariv, S. (2011).
*Estimating ambiguity aversion in a portfolio choice experiment*. Working paper. University of California, Berkeley.Google Scholar - Andersen, S., Fountain, J., Harrison, G., & Rutström, E. (2009).
*Estimating aversion to uncertainty*. Working paper. University of Central Florida.Google Scholar - Arrow, K. (1964). The role of securities in the optimal allocation of risk bearing.
*Review of Economic Studies*,*31*, 91–96.CrossRefGoogle Scholar - Attanasi, G., & Montesano, A. (2012). The price for information about probabilities and its relation with risk and ambiguity.
*Theory and Decision*,*73*, 125–160.CrossRefGoogle Scholar - Becker, G., DeGroot, M. H., & Marschak, J. (1964). Measuring utility by a single response sequential method.
*Behavioral Science*,*9*, 226–232.CrossRefGoogle Scholar - Becker, S. W., & Brownson, F. O. (1964). What price ambiguity? Or the role of ambiguity in decision making.
*Journal of Political Economy*,*72*, 62–73.CrossRefGoogle Scholar - Bossaerts, P., Ghirardato, P., Guarnaschelli, S., & Zame, W. (2010). Prices and allocations in asset markets with heterogeneous attitudes towards ambiguity.
*Review of Financial Studies*,*23*, 1325–1359.CrossRefGoogle Scholar - Camerer, C. (1995). Individual decision making. In J. Kagel & A. Roth (Eds.),
*Handbook of experimental economics*(pp. 587–703). Princeton University Press.Google Scholar - Camerer, C., & Weber, M. (1992). Recent development in modeling preferences: Uncertainty and ambiguity.
*Journal of Risk and Uncertainty*,*5*, 325–370.CrossRefGoogle Scholar - Chakravarty, S., & Roy, J. (2009). Recursive expected utility and the separation of attitudes towards risk and ambiguity: An experimental study.
*Theory and Decision*,*66*, 199–228.CrossRefGoogle Scholar - Cohen, M., Jaffray, J.-Y., & Said, T. (1987). Experimental comparison of individual behavior under risk and under uncertainty for gains and for losses.
*Organizational Behavior and Human Decision Processes*,*39*, 1–22.CrossRefGoogle Scholar - Cohen, M., Tallon, J. M., & Vergnaud, J. C. (2011). An experimental investigation of imprecision attitude and its relation with risk attitude and impatience.
*Theory and Decision*,*71*, 81–109.CrossRefGoogle Scholar - Conte, A., Hey, J. D. (2013). Assessing multiple prior models of behavior under ambiguity.
*Journal of Risk and Uncertainty*,*46*, 113–132.Google Scholar - Conte, A., Hey, J. D., & Moffatt, P. G. (2011). Mixture models of choice under risk.
*Journal of Econometrics*,*162*, 79–82.CrossRefGoogle Scholar - Cox J. C., Sadiraj V., & Schmidt U. (2012).
*Paradoxes and mechanisms for choice under risk*. Experimental Economics Center Working Paper Series 2012-08, Experimental Economics Center, Andrew Young School of Policy Studies, Georgia State University.Google Scholar - Di Mauro, C., & Maffioletti, A. (2004). Attitudes to risk and attitudes to uncertainty: Experimental evidence.
*Applied Economics*,*36*, 357–372.CrossRefGoogle Scholar - Ellsberg, D. (1961). Risk, ambiguity and the Savage axioms.
*Quarterly Journal of Economics*,*75*, 643–669.CrossRefGoogle Scholar - Epstein, L. G. (2010). A paradox for the “smooth ambiguity” model of preference.
*Econometrica*,*78*, 2085–2099.CrossRefGoogle Scholar - Fischbacher, U. (2007). z-Tree: Zurich toolbox for ready-made economic experiments.
*Experimental Economics*,*10*, 171–178.CrossRefGoogle Scholar - Ghirardato, P. (2004). Defining ambiguity and ambiguity attitude. In I. Gilboa (Ed.),
*Uncertainty in economic theory: A collection of essays in honor of David Schmeidler’s 65th birthday*(pp. 36–45). London: Routledge.CrossRefGoogle Scholar - Ghirardato, P., Maccheroni, F., & Marinacci, M. (2004). Differentiating ambiguity and ambiguity attitude.
*Journal of Economic Theory*,*118*, 133–173.CrossRefGoogle Scholar - Gollier, C. (2001). Should we beware of the precautionary principle?
*Economic Policy*,*16*, 301–328.CrossRefGoogle Scholar - Gollier C. (2012).
*Optimal insurance design of ambiguous risks*. IDEI Working Paper no. 718.Google Scholar - Halevy, Y. (2007). Ellsberg revisited: An experimental study.
*Econometrica*,*75*, 503–536.CrossRefGoogle Scholar - Harrison, G. W. (2011). Experimental methods and the welfare evaluation of policy lotteries.
*European Review of Agricultural Economics*,*38*, 335–360.CrossRefGoogle Scholar - Harrison, G. W., Johnson, E., McInnes, M. M., & Rutström, E. E. (2005). Risk aversion and incentive effects: Comment.
*American Economic Review*,*95*, 897–901.CrossRefGoogle Scholar - Harrison, G. W., Martinez-Correa, J., & Swarthout J. T. (2012).
*Reduction of compound lotteries with objective probabilities: Theory and evidence*. Working Paper 2012–05, Center for the Economic Analysis of Risk, Robinson College of Business, Georgia State University.Google Scholar - Harrison, G. W., & Rutström, E. E. (2008). Risk aversion in the laboratory. In G. W. Harrison & J. Cox (Eds.),
*Risk aversion in experiments*(pp. 41–196). Bradford, UK: JAI Press.CrossRefGoogle Scholar - Harrison, G. W., & Rutström, E. (2009). Expected utility theory and prospect theory: One wedding and a decent funeral.
*Experimental Economics*,*12*, 133–158.CrossRefGoogle Scholar - Harrison G. W., & Swarthout T. (2012).
*The independence axiom and the bipolar behaviorist*. Experimental Economics Center Working Paper Series 2012–01, Experimental Economics Center, Andrew Young School of Policy Studies, Georgia State University.Google Scholar - Hey, J. D., & Lee, J. (2005). Do subjects separate (or are they sophisticated)?
*Experimental Economics*,*8*, 233–265.CrossRefGoogle Scholar - Hey, J. D., Lotito, G., & Maffioletti, A. (2010). The descriptive and predictive adequacy of theories of decision making under uncertainty/ambiguity.
*Journal of Risk and Uncertainty*,*41*, 81–111.CrossRefGoogle Scholar - Hey, J. D., & Pace, N. (2014). The explanatory and predictive power of non two-stage-probability theories of decision making under ambiguity.
*Journal of Risk and Uncertainty*(forthcoming).Google Scholar - Holt, C. A. (1986). Preference reversal and the independence axiom.
*American Economic Review*,*76*, 508–515.Google Scholar - Holt, C. A., & Laury, S. K. (2002). Risk aversion and incentive effects.
*American Economic Review*,*92*, 1644–1655.CrossRefGoogle Scholar - Holt, C. A., & Laury, S. K. (2005). Risk aversion and incentive effects: New data without order effects.
*American Economic Review*,*95*, 902–912.CrossRefGoogle Scholar - Kadane J. B. (1992). Healthy skepticism as an expected-utility explanation of the phenomena of Allais and Ellsberg. In: Geweke J. (Ed.),
*Decision making under risk and uncertainty: New models and empirical findings*. Boston: Kluwer. (And in*Theory and Decision*,*32*, 57–64).Google Scholar - Karni, E., & Safra, Z. (1987). ‘Preference reversal’ and the observability of preferences by experimental methods.
*Econometrica*,*55*, 675–685.CrossRefGoogle Scholar - Klibanoff, P., Marinacci, M., & Mukerji, S. (2005). A smooth model of decision making under ambiguity.
*Econometrica*,*73*, 1849–1892.CrossRefGoogle Scholar - Klibanoff, P., Marinacci, M., & Mukerji, S. (2012). On the smooth ambiguity model: A reply.
*Econometrica*,*80*, 1303–1321.CrossRefGoogle Scholar - Knight, F. (1921).
*Risk, uncertainty, and profit*. Boston: Houghton Mifflin.Google Scholar - Lauriola, M., & Levin, I. P. (2001). Relating individual differences in attitude toward ambiguity and risky choices.
*Journal of Behavioral Decision Making*,*14*, 107–122.CrossRefGoogle Scholar - Lee, J. (2008). The effect of the background risk in a simple chance improving decision model.
*The Journal of Risk and Uncertainty*,*36*, 19–41.CrossRefGoogle Scholar - Plott, C. R., & Zeiler, K. (2005). The willingness to pay-willingness to accept gap, the “endowment effect”, subject misconceptions, and experimental procedures for eliciting valuations.
*American Economic Review*,*95*, 530–545.CrossRefGoogle Scholar - Pratt, J. W. (1964). Risk aversion in the small in the large.
*Econometrica*,*32*, 122–136.CrossRefGoogle Scholar - Quiggin, J. (2007). Ambiguity and the value of information: An almost-objective events analysis.
*Economic Theory*,*30*, 409–414.CrossRefGoogle Scholar - Savage, L. J. (1954).
*The foundations of statistics*. New York: Wiley.Google Scholar - Schneeweiss, H. (1973). The Ellsberg Paradox from the point of view of game theory.
*Inference and Decision*,*1*, 65–78.Google Scholar - Snow, A. (2010). Ambiguity and the value of information.
*Journal of Risk and Uncertainty*,*40*, 133–145.CrossRefGoogle Scholar - Starmer, C., & Sugden, R. (1991). Does the random-lottery incentive system elicit true preferences? An experimental investigation.
*American Economic Review*,*81*, 971–978.Google Scholar - Tversky, A., & Kahneman, D. (1992). Advances in prospect theory: Cumulative pepresentation of uncertainty.
*Journal of Risk and Uncertainty*,*5*, 297–323.CrossRefGoogle Scholar