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Past experience of uncertainty affects risk aversion

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Abstract

In an experiment with more than 500 participants we study how past experience of uncertainty (imperfect knowledge of the state space) affects risk preferences. Participants in our experiment choose between a sure outcome and a lottery in 32 periods. All treatments are exactly identical in periods 17–32 but differ in periods 1–16. In the early periods of the risk treatment there is perfect information about the lottery; in the ambiguity Treatment participants perfectly know the outcome space but not the associated probabilities; in the unawareness treatment participants have imperfect knowledge about both outcomes and probabilities. We observe strong treatment effects on behavior in periods 17–32. In particular, participants who have been exposed to an environment with very imperfect knowledge of the state space subsequently choose lotteries with high (low) variance less (more) often compared to other participants. Estimating individual risk attitudes from choices in periods 17–32 we find that the distribution of risk attitude parameters across our treatments can be ranked in terms of first order stochastic dominance. Our results show how exposure to environments with different degrees of uncertainty can affect individuals’ subsequent risk-taking behavior.

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Notes

  1. See the literature surveyed below.

  2. Distinguishing zero probability events from unawareness is a topic which has attracted attention in theoretical research. See, for example, Feinberg (2009) for discussion.

  3. See for example Ellsberg (1961), Halevy (2007), Gollier (2011) among many others.

  4. Similarly, Malmendier and Nagel (2011) show that subjective expectations about future inflation are shaped by people’s lifetime experience of inflation.

  5. In a different strand of literature it has been demonstrated that individual decisions are affected by whether a choice situation displays only risk or whether it is ambiguous (Ellsberg 1961; Halevy 2007; Gollier 2011, among many others). Other authors have tried to establish correlations between risk aversion and ambiguity aversion. These results are quite different from our experiment in that we do not compare behavior in risky/ambigous environments but rather investigate how having been exposed to such an environment affects risk attitudes in subsequent unrelated choices.

  6. See for instance Feinberg (2009), Halpern and Rêgo (2008), Gossner and Tsakas (2010, 2012).

  7. The sequence of sure outcomes was the same for all participants: 7, 7.4, 8.2, 5.4, 6, 8, 5.8, 6.6, 7.2, 7.6, 8.4, 7.8, 6.4, 6.8, 6.2, 5.6. The lottery realizations (when lottery was chosen) were generated randomly for each participant.

  8. If the reader wants to think in terms of a state space and subjective probabilities, here is one example of such a state space. Think of an urn with 1000 balls. Some of these balls have written −20 on them, some Twix, some 10 etc. The decision maker does not know the number of balls of each kind. However, s/he knows all the possible numbers (labels of balls) that are allowed.

  9. We ran the treatments in the order unawareness, ambiguity, risk to avoid communication among participants regarding the information provided in different treatments.

  10. See Section A in the Supplementary Material (http://www.vostroknutov.com/pdfs/awarexp04supp.pdf) for more details.

  11. We disregard the data from one session of the unawareness treatment where there was a substantial programming error.

  12. Starmer and Sugden (1991) study the validity of the random lottery incentive system and find that participants treat every choice situation as isolated.

  13. See Markowitz (1952), Levy and Markowitz (1979) or the textbook by Sharpe (2008) among many others.

  14. We use standard deviation instead of variance, because standard deviation is measured in the same units as expected value, which makes it easier to compare coefficients. Non-surprisingly our results are robust to using either standard deviation or variance.

  15. See Table 2 for definitions of the independent variables and the Supplementary Material (http://www.vostroknutov.com/pdfs/awarexp04supp.pdf) for a description of all lotteries.

  16. Note that only very few values of dexp are negative since the sure outcome typically is lower than the expected value of the lottery.

  17. In fact the correlation between period and dexp (stdv) is \(0.1733^{***}\) (\(0.0044\)) respectively (Spearman correlation test).

  18. In Appendix B of the Supplementary Material the same figure with error bars (plus minus one standard error) is shown.

  19. We dropped participants who always chose either lottery or sure outcome. This left us with 96 participants in the unawareness treatment, 87 in ambiguity and 97 in the risk treatment.

  20. The graph plots the distribution of the negative of the risk aversion parameter. Hence indeed the distribution of β’s in the unawareness treatment first-order stochastically dominates that of the risk treatment.

  21. The CRRA estimations reported in Section D of the Supplemental Material show the same patterns: (1) the cdfs for the three treatments are still ranked according to stochastic dominance in the same way; (2) the individual CRRA coefficients and β coefficients have significantly positive correlation.

  22. One may wonder why we didn’t control for the number of “bad” or “good” outcomes a participant experienced in our main regressions. The reason is that this is endogenous to the degree of risk aversion of participants.

  23. Supplementary Material can be found at http://www.vostroknutov.com/pdfs/awarexp04supp.pdf.

  24. The tests reported here were extremely sensitive to outliers in \(\beta _i\)’s. Hence, observations with \(|\beta _i| > 6\) were omitted.

  25. Alesina and Fuchs-Schuendeln (2007) have shown how experiencing different political systems can affect preferences for redistribution.

  26. Supplementary Material can be found at http://www.vostroknutov.com/pdfs/awarexp04supp.pdf.

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Acknowledgments

We would like to thank Douglas Bernheim, Elena Cettolin, David Cooper, Vincent Crawford, Matt Embrey, Jayant Ganguli, David Huffman, David Laibson, Dan Levin, Ulrike Malmendier, Ronald Peeters, Arno Riedl, David Schmeidler, Kaj Thomsson, Huanxin Yang, two anonymous reviewers as well as seminar participants at Göteborg University , Maastricht University, Ohio State University, RUD 2011, SAET 2011, EEA-ESEM 2011 and SITE Psychology and Economics Workshop 2011 for invaluable comments and help. All mistakes are ours. Friederike Mengel thanks the European Union (grant PERG08-GA-2010-277026) for financial support. A previous version was circulated under the title “Decision-making with imperfect knowledge of the state space”.

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Authors and Affiliations

  1. Department of Economics, University of Essex, Wivenhoe Park, Colchester, CO4 3SQ, UK

    Friederike Mengel

  2. Department of Economics (AE1), Maastricht University, PO Box 616, 6200 MD, Maastricht, The Netherlands

    Friederike Mengel, Elias Tsakas & Alexander Vostroknutov

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  1. Friederike Mengel
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Correspondence to Alexander Vostroknutov.

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Mengel, F., Tsakas, E. & Vostroknutov, A. Past experience of uncertainty affects risk aversion. Exp Econ 19, 151–176 (2016). https://doi.org/10.1007/s10683-015-9431-6

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