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Dynamics in risk taking with a low-probability hazard

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Abstract

The experiment reported in this paper identifies the effects of experience on revealed attitudes toward risk. Subjects in the experiment encountered an uncertain risk of experiencing a negative income shock over multiple periods and were able to purchase insurance at the start of each period. Subjects engaged in greater risk taking, insuring less frequently, when faced with the same risk over multiple periods. Subjects weighted experienced outcomes proportionately, in a manner consistent with rational Bayesian inference and contrary to the theory that individuals exhibit recency bias. On the other hand, subjects assigned a greater weight to outcomes that directly impacted their earnings compared to observed outcomes that had no effect on income. Unexplained autocorrelation across subjects’ choices suggests that inertia also plays an important role in repeated risk settings. I explore the relevance of these findings to public policy aimed at influencing market outcomes in the presence of infrequent environmental hazards.

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Notes

  1. The term “Matched Property” was used to emphasize the fact that subjects would be matched with the same property for 50 decision periods, in contrast with the One-shot round, where the property, and associated risk, changed for each decision period.

  2. Which sequence the subject encountered in the Repeat round was varied between subjects, so that no subject encountered the same sequence in both One-shot and Repeat rounds.

  3. There is, however, substantial evidence that people weight probabilities idiosyncratically (Tversky & Kahneman 1992) and behave differently when risk is ambiguously described (Ellsberg 1961). Nevertheless, these tendencies are better understood as manifestations of preference or perception rather than a reflection of incomplete information.

  4. Shafran estimates a similar model using subjects’ decisions in a repeated risk task. A key difference in his model is that the memory parameter weights the effects of both prior outcomes and prior choices, whereas the memory parameter expressed in Eqs. 4 and 5 weights only prior outcomes. The weighting of prior choices represents the persistence of choice inertia effects, which I model in Section 3.2.6.

  5. One can also reframe the example so that choosing to insure at t = 1 imparts a positive inertia effect on the probability of insuring at t = 2. The probability of insuring at t = 2 would then be p q(1 + δ). The same comparison with respect to p still obtains because lower probability risks now imply diminished chances of receiving positive inertia from insuring at time 1.

  6. Subjects in the low premium treatment completed only 45 periods in the dynamic round and did not complete a post-experiment survey.

  7. Note that the regression including the survey variables has fewer observations and does not control for the insurance premium. The reason for this is that surveys were not added to the experiment until after low premium treatment was completed, so no survey data are available for the 23 subjects who encountered the low premium.

  8. The details of this method are discussed in Section 8.7 of Train (2009).

  9. Shafran does report structural estimates for an adaptive learning model, but not for a strictly Bayesian one.

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Acknowledgements

I would like to thank Josh Tasoff, Monica Capra, Paul Zak, Thomas Kniesner, Margaret Walls, and Peiran Jiao for discussion and valuable input. Insightful comments from Kip Viscusi, Justin Gallagher and an anonymous referee helped shape the final version of the paper. I would also like to thank Michael McBride and the ESSL staff for assisting with sessions run at UC Irvine. Institutional Review Board approval was obtained from Claremont Graduate University (CGU) [IRB #2251].

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    Andrew Royal

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Correspondence to Andrew Royal.

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Appendices

Appendix A: Additional Tables & Figures

Table 5 Predetermined disaster sequences
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Appendix B: Selected screenshots

(See Online Appendix for full instrument.)

Fig. 3
figure 3

Example of One-shot round decision screen

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Fig. 4
figure 4

Example of repeated choice round decision screen

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Royal, A. Dynamics in risk taking with a low-probability hazard. J Risk Uncertain 55, 41–69 (2017). https://doi.org/10.1007/s11166-017-9263-1

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