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Estimating ambiguity preferences and perceptions in multiple prior models: Evidence from the field

Journal of Risk and Uncertainty volume 51, pages 219–244 (2015)Cite this article

Abstract

We develop a tractable method to estimate multiple prior models of decision-making under ambiguity. In a representative sample of the U.S. population, we measure ambiguity attitudes in the gain and loss domains. We find that ambiguity aversion is common for uncertain events of moderate to high likelihood involving gains, but ambiguity seeking prevails for low likelihoods and for losses. We show that choices made under ambiguity in the gain domain are best explained by the α-MaxMin model, with one parameter measuring ambiguity aversion (ambiguity preferences) and a second parameter quantifying the perceived degree of ambiguity (perceptions about ambiguity). The ambiguity aversion parameter α is constant and prior probability sets are asymmetric for low and high likelihood events. The data reject several other models, such as MaxMin and MaxMax, as well as symmetric probability intervals. Ambiguity aversion and the perceived degree of ambiguity are both higher for men and for the college-educated. Ambiguity aversion (but not perceived ambiguity) is also positively related to risk aversion. In the loss domain, we find evidence of reflection, implying that ambiguity aversion for gains tends to reverse into ambiguity seeking for losses. Our model’s estimates for preferences and perceptions about ambiguity can be used to analyze the economic and financial implications of such preferences.

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Notes

  1. See Ghirardato et al. (2004) for a behavioral foundation of the α-MaxMin model. In this paper we use the specification of the α-MaxMin model by Chateauneuf et al. (2007).

  2. For instance, regarding consumption and investment see Dow and Werlang (1992) and Epstein and Wang (1994). On healthcare investment see Asano and Shibata (2011).

  3. We chose to implement our ambiguity question involving losses without real incentives to avoid house money effects (Thaler and Johnson 1990). The house money effect refers to empirical evidence that people’s risk taking can depend on prior gains and losses. In our setting, if we had given the respondent an initial endowment to implement real losses, the presence of an endowment could influence people’s subsequent decisions (e.g., more risk taking after a windfall). Exposing respondents to real losses without giving an initial endowment raises ethical issues.

  4. A related paper by Attanasi et al. (2014) tests the behavioral predictions of the smooth model using several decision tasks with varying levels of ambiguity (perceived ambiguity).

  5. The sophisticated approach of Hey et al. (2010) involves joint estimation of risk and ambiguity preferences, as well as beliefs; implementation used 135 choice problems per subject (students). As our objective is to measure ambiguity preferences and perceptions in a survey of the general population, we use a relatively simple elicitation method involving only 17 choices per subject that does not require joint estimation of risk preferences.

  6. Similarly, Conte and Hey (2013) evaluate the predictive ability of several multiple prior models based on subjects’ choices between two compound lotteries with known probabilities (i.e., two-stage lotteries).

  7. For more information about how the ALP recruits respondents see the American Life Panel website at https://mmicdata.rand.org/alp/. One advantage of the ALP is that respondents who lack Internet access are provided with either a laptop and Internet access, or a so-called WebTV that allows them to use their television to participate in the panel.

  8. Dimmock et al. (2015a) describe the fielding of the ALP module in more detail.

  9. The survey module uses “box” instead of “urn,” as the word “urn” might be unfamiliar to some.

  10. This approach is similar to that of Kahn and Sarin (1988), Baillon et al. (2012), Baillon and Bleichrodt (2015), and Dimmock et al. (2015b).

  11. See, for example, Abdellaoui et al. (2011) and Dimmock et al. (2015b). The latter study finds that fewer than two percent of respondents changed the winning color.

  12. In August 2013, we fielded an additional survey (N = 500) identical to the original except one: it offered some respondents a choice for the winning ball color. Specifically, a randomly selected half of the sample was allowed to select the winning color (purple or orange), while the other half could not. Fewer than one percent of the respondents in the group allowed to change the color did so, and the mean matching probabilities of the ‘color choice’ and ‘no color choice’ subgroups were not significantly different. Results are available upon request.

  13. Similarly, Baillon and Bleichrodt (2015) find no significant differences between ambiguity attitudes in the loss domain measured with real incentives and with hypothetical losses.

  14. Butler et al. (2014) report that 52% of 1686 Italian bank customers are ambiguity averse (without real incentives), while in Akay et al. (2012) 57% of 92 Ethiopian farmers are ambiguity averse. In a sample of 666 subjects from the Dutch population, Dimmock et al. (2015b) find that 68% were ambiguity averse, 10% neutral, and 22% seeking, suggesting that ambiguity aversion is more common among the Dutch.

  15. A signed rank test for the median gives similar results: p-value < 0.01 for no reference dependence (median AA 50 = median AA −50); p-value = 0.13 for reflection (median AA 50 = − median AA −50).

  16. Ghirardato et al. (2004) and Eichberger et al. (2011) provide a behavioral (i.e., axiomatic) foundation for the α-MaxMin model.

  17. E c contains all states s except those contained in event E: E∪ E c  = S and E ∩ E c = ∅.

  18. Note that P(E) = 0 for E ∈ N, where N denotes a set of all null events E ∈ N with π(E) = 0.

  19. Given sufficient experimental time one could elicit a subjective measure π for uncertain events from revealed preferences at the individual level as in Abdellaoui et al. (2011).

  20. The measures of ambiguity aversion and a-insensitivity introduced by Abdellaoui et al. (2011), named Index b and Index a, also derive from a neo-additive capacity and can therefore be linked to α and δ. That is, for their a-insensitivity measure: Index \( a \)=\( \delta \). For their ambiguity aversion measure: Index b = (2α − 1)δ. Hence, Index b is positive if and only if α > 0.5 and δ > 0.

  21. For now, we defer discussion of the ambiguity loss question (k = 4) to Section 4.4.

  22. Out of the 3258 original respondents, 3 did not answer any questions, 85 did not complete all of our ambiguity questions, and 179 spent less than two minutes on answering the ambiguity questions. After excluding these 267 respondents, we have a final sample of 2991 respondents.

  23. Pooled OLS estimates are consistent in the presence of random effects, but the standard errors may be inefficient. As we use clustered (robust) standard errors, the results of pooled OLS are similar to a random effects model.

  24. Our estimate of α is similar to values of α = 0.515 reported in Ahn et al. (2014) for a small sample of students and α = 0.556 in Potamites and Zhang (2012) for Chinese investors. Baillon et al. (2015) estimate α = 0.61 and δ = 0.51 in a sample of 64 students, with the source of ambiguity being the returns of an unknown stock.

  25. We test the single restriction δ = 1, implied by all three models with [0,1] as the prior set. Joint tests of δ = 1, α = 1 for MaxMin-[0,1], or δ = 1, α = 0 for MaxMax-[0,1] give the same result.

  26. The equations for m ik and m L ik have different constant terms, (1–α)δ and α L δ, so the model in Equation (11) is no longer applicable (it would imply the restriction 1–α = α L). Introducing a dummy variable for the loss question permits us to separately estimate and identify α and α L.

  27. A drawback of the model in Equation (12) is that the random effect u i has opposite effects on ambiguity aversion for gains and losses, an assumption inconsistent with the positive correlation between AA 50 and AA −50. As a result the estimated correlation of the random effect (ρ) is relatively low in Table 3. We have also estimated a model with two separate random effects for the constant c and loss dummy d L, but we find no difference in the main results concerning α, α L and δ. Results are available on request.

  28. If we could measure more matching probabilities for ambiguous events involving loss outcomes with other likelihoods (e.g., similar to the 10 % and 90 % gains questions), we could also estimate δ separately in the loss domain. We leave to future research additional refinements of ambiguity surveys and tests for reference dependence.

  29. Borghans et al. (2009) find that men are more ambiguity averse than women in a sample of 347 high school students. In a study of the Dutch population, Dimmock et al. (2015b) estimate the relation between ambiguity attitudes and control variables; there, however, few effects are statistically significant (sample size: N = 666). Using our ALP Module, Dimmock et al. (2015a) show in a web appendix that the non-parametric ambiguity aversion measure AA 50 is higher for men than for women, and positively related to risk aversion.

  30. This is measured on a reversed scale from 0 to 5, with higher values indicating lower trust.

  31. As in Tanaka et al. (2010), utility is defined over the payoffs of the gambles (not integrated with total wealth), and the power coefficient is limited to the range from 0 to 1.5. Risk aversion, defined as ‘1 – power function coefficient’, varies from −0.5 (risk seeking) to +1 (strongest level of risk aversion), and a value of zero implies risk neutrality.

  32. The derivative of α i with of respect to x ih is : − c h /δ i  − s h (c 0 + ∑ H h = 1 c h x ih )/δ 2 i , which we evaluate at the mean values of x ih and δ i .

References

  • Abdellaoui, M., Baillon, A., Placido, L., & Wakker, P. P. (2011). The rich domain of uncertainty: source functions and their experimental implementation. American Economic Review, 101, 695–723.

  • Abdellaoui, M., Vossmann, F., & Weber, M. (2005). Choice-based elicitation and decomposition of decision weights for gains and losses under uncertainty. Management Science, 51, 1384–1399.

  • Ahn, D., Choi, S., Gale, D., & Kariv, S. (2014). Estimating ambiguity aversion in a portfolio choice experiment. Quantitative Economics, 5, 192–223.

    Article  Google Scholar 

  • Akay, A., Martinsson, P., Medhin, H., & Trautmann, S. T. (2012). Attitudes towards uncertainty among the poor: an experiment in rural Ethiopia. Theory and Decision, 73, 453–464.

    Article  Google Scholar 

  • Andersen, S., Fountain, J., Harrison, G. W., Hole, A. R., & Rutström, E. E. (2012). Inferring beliefs as subjectively imprecise probabilities. Theory and Decision, 73, 161–184.

  • Andersen, S., Fountain, J., Harrison, G. W., & Rutström, E. E. (2009). Estimating aversion to uncertainty. Working Paper, University of Central Florida.

  • Asano, T., & Shibata, A. (2011). Risk and uncertainty in health investment. European Journal of Health Economics, 12, 79–85.

    Article  Google Scholar 

  • Attanasi, G., Gollier, C., Montesano, A., & Pace, N. (2014). Eliciting ambiguity aversion in unknown and in compound lotteries: a smooth ambiguity model experimental study. Theory and Decision, 77, 485–530.

    Article  Google Scholar 

  • Baillon, A., & Bleichrodt, H. (2015). Testing ambiguity models through the measurement of probabilities for gains and losses. American Economic Journal: Microeconomics, 7, 77–100.

    Google Scholar 

  • Baillon, A., Bleichrodt, H., Keskin, U., L’Haridon, O., & Li, C. (2015). The effect of learning on ambiguity attitudes. Working paper.

  • Baillon, A., Cabantous, L., & Wakker, P. P. (2012). Aggregating imprecise or conflicting beliefs: an experimental investigation using modern ambiguity theories. Journal of Risk and Uncertainty, 44, 115–147.

    Article  Google Scholar 

  • Binmore, K., Stewart, L., & Voorhoeve, A. (2012). How much ambiguity aversion? Journal of Risk and Uncertainty, 45, 215–238.

    Article  Google Scholar 

  • Borghans, L., Heckman, J. J., Golsteyn, B. H. H., & Meijers, L. (2009). Gender differences in risk aversion and ambiguity aversion. Journal of the European Economic Association, 7, 649–658.

    Article  Google Scholar 

  • Bostic, R., Herrnstein, R. J., & Luce, R. D. (1990). The effect on the preference-reversal phenomenon of using choice indifferences. Journal of Economic Behavior and Organization, 13, 193–212.

    Article  Google Scholar 

  • Butler, J. V., Guiso, L., & Jappelli, T. (2014). The role of intuition and reasoning in driving aversion to risk and ambiguity. Theory and Decision, 77, 455–484.

    Article  Google Scholar 

  • Chateauneuf, A., Eichberger, J., & Grant, S. (2007). Choice under uncertainty with the best and worst in mind: neo-additive capacities. Journal of Economic Theory, 137, 538–567.

    Article  Google Scholar 

  • Cohen, M., Jaffray, J.-Y., & Said, T. (1987). Experimental comparisons of individual behavior under risk and under uncertainty for gains and for losses. Organizational Behavior and Human Decision Processes, 39, 1–22.

    Article  Google Scholar 

  • Conte, A., & Hey, J. D. (2013). Assessing multiple prior models of behaviour under ambiguity. Journal of Risk and Uncertainty, 46, 113–132.

    Article  Google Scholar 

  • Dimmock, S. G., Kouwenberg, R., Mitchell, O. S., & Peijnenburg, K. (2015a). Ambiguity aversion and household portfolio choice puzzles: empirical evidence. Journal of Financial Economics, forthcoming.

  • Dimmock, S. G., Kouwenberg, R., & Wakker, P. P. (2015b). Ambiguity attitudes in a large representative sample. Management Science, forthcoming.

  • Dow, J., & Werlang, S. R. C. (1992). Uncertainty aversion, risk aversion and the optimal choice of portfolio. Econometrica, 60, 197–204.

    Article  Google Scholar 

  • Eichberger, J., Grant, S., Kelsey, D., & Koshevoy, G. A. (2011). The α-MEU model: a comment. Journal of Economic Theory, 146, 1684–1698.

    Article  Google Scholar 

  • Ellsberg, D. (1961). Risk, ambiguity, and the Savage axioms. Quarterly Journal of Economics, 75, 643–669.

    Article  Google Scholar 

  • Epstein, L. G., & Wang, T. (1994). Intertemporal asset pricing under Knightian uncertainty. Econometrica, 62, 283–322.

    Article  Google Scholar 

  • Etchart-Vincent, N., & l’Haridon, O. (2011). Monetary incentives in the loss domain and behavior toward risk: an experimental comparison of three reward schemes including real losses. Journal of Risk and Uncertainty, 42, 61–83.

    Article  Google Scholar 

  • Fox, C. R., & Tversky, A. (1995). Ambiguity aversion and comparative ignorance. Quarterly Journal of Economics, 110, 585–603.

    Article  Google Scholar 

  • Ghirardato, P., Maccheroni, F., & Marinacci, M. (2004). Differentiating ambiguity and ambiguity attitude. Journal of Economic Theory, 118, 133–173.

    Article  Google Scholar 

  • Gilboa, I., & Schmeidler, D. (1989). Maxmin expected utility with non-unique priors. Journal of Mathematical Economics, 18, 141–153.

    Article  Google 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.

    Article  Google Scholar 

  • Kahn, B. E., & Sarin, R. K. (1988). Modeling ambiguity in decisions under uncertainty. Journal of Consumer Research, 15, 265–272.

    Article  Google Scholar 

  • Klibanoff, P., Marinacci, M., & Mukerji, S. (2005). A smooth model of decision making under ambiguity. Econometrica, 73, 1849–1892.

    Article  Google Scholar 

  • Kothiyal, A., Spinu, V., & Wakker, P. P. (2014). An experimental test of prospect theory for predicting choice under ambiguity. Journal of Risk and Uncertainty, 48, 1–17.

    Article  Google Scholar 

  • Potamites, E., & Zhang, B. (2012). Measuring ambiguity attitudes: a field experiment among small-scale stock investors in China. Review of Economic Design, 16, 193–213.

    Article  Google Scholar 

  • Stahl, D. O. (2014). Heterogeneity of ambiguity preferences. Review of Economics and Statistics, 96, 609–617.

    Article  Google Scholar 

  • Tanaka, T., Camerer, C. F., & Nguyen, Q. (2010). Risk and time preferences: linking experimental and household survey data from Vietnam. American Economic Review, 100, 557–571.

    Article  Google Scholar 

  • Thaler, R. H., & Johnson, E. J. (1990). Gambling with the house money and trying to break even: the effects of prior outcomes on risky choice. Management Science, 36, 643–660.

    Article  Google Scholar 

  • Trautmann, S. T., & van de Kuilen, G. (2015). Ambiguity attitudes. In G. Wu & G. Keren (Eds.), The Wiley-Blackwell handbook of judgment and decision making. Oxford: Blackwell.

    Google Scholar 

  • Tversky, A., & Kahneman, D. (1992). Advances in prospect theory: cumulative representation of uncertainty. Journal of Risk and Uncertainty, 5, 292–323.

    Article  Google Scholar 

  • Vieider, F. M., Martinsson, P., & Medhin, H. (2012). Stake effects on ambiguity attitudes for gains and losses. Working paper.

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Acknowledgments

The survey module fielded by the authors in the RAND American Life Panel (ALP) was approved by the Institutional Review Board of the University of Pennsylvania. The authors gratefully acknowledge financial support from Netspar, and grants to the University of Pennsylvania from the National Institute on Aging (P30 AG-012836-18), and a grant from the National Institutes of Health–National Institute of Child Health and Development Population Research Infrastructure Program (R24 HD-044964-9). Support was also provided by the Pension Research Council/Boettner Center and the Wharton Behavioral Labs at the University of Pennsylvania. We also thank the ALP teams at RAND and the University of Southern California. We are grateful to Aurelien Baillon, Peter Wakker and participants at FUR 2014 for helpful comments, and to Tania Gutsche, Arie Kapteyn, Bart Orriens, and Bas Weerman for assistance with the survey. Yong Yu provided outstanding programming assistance. The content is solely the responsibility of the authors and does not represent the official views of the National Institute of Aging, the National Institutes of Health, or any of the other institutions providing funding for this study or with which the authors are affiliated.

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Authors and Affiliations

  1. Nanyang Technological University, Nanyang Business School, Singapore, Singapore

    Stephen G. Dimmock

  2. College of Management, Mahidol University, 69 Vipawadee Rangsit Road, Bangkok, 10140, Thailand

    Roy Kouwenberg

  3. Erasmus School of Economics, Erasmus University Rotterdam, Rotterdam, Netherlands

    Roy Kouwenberg

  4. The Wharton School, University of Pennsylvania, NBER, Philadelphia, PA, USA

    Olivia S. Mitchell

  5. Bocconi University, NETSPAR, and IGIER, Milan, Italy

    Kim Peijnenburg

Authors
  1. Stephen G. Dimmock
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  2. Roy Kouwenberg
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Correspondence to Roy Kouwenberg.

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Dimmock, S.G., Kouwenberg, R., Mitchell, O.S. et al. Estimating ambiguity preferences and perceptions in multiple prior models: Evidence from the field. J Risk Uncertain 51, 219–244 (2015). https://doi.org/10.1007/s11166-015-9227-2

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Keywords

  • Ambiguity
  • Decision-making under uncertainty
  • Multiple prior models
  • Alpha-MaxMin model

JEL Classification

  • D81
  • C93
  • C23