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Is imprecise knowledge better than conflicting expertise? Evidence from insurers’ decisions in the United States

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Abstract

This paper reports the results of the first experiment in the United States designed to distinguish between two sources of ambiguity: imprecise ambiguity (expert groups agree on a range of probability, but not on any point estimate) versus conflict ambiguity (each expert group provides a precise probability estimate which differs from one group to another). The specific context is whether risk professionals (here, insurers) behave differently under risk (when probability is well-specified) and different types of ambiguity in pricing catastrophic risks (floods and hurricanes) and non-catastrophic risks (house fires). The data show that insurers charge higher premiums when faced with ambiguity than when the probability of a loss is well specified (risk). Furthermore, they tend to charge more for conflict ambiguity than imprecise ambiguity for flood and hurricane hazards, but less in the case of fire. The source of ambiguity also impacts causal inferences insurers make to reduce their uncertainty.

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Notes

  1. Formal models of aggregation of beliefs with conflicting probability estimates are proposed in Cres et al. (2010); Gajdos and Vergnaud (2009); Gollier (2007).

  2. See Cabantous (2007), Gajdos and Vergnaud (2009), Smithson (1999) for further discussion on these three contexts (“risk,” “imprecise ambiguity,” “conflict ambiguity”). Our example is such that the risk situation (probability 1/2) is the mean of the interval boundaries (1/4 and 3/4).

  3. See Michel-Kerjan (2010) for an economic analysis of the operation of this program.

  4. We could have used two qualitatively different advisors, like a risk modeling firm and the internal technical team of the insurance company. However, because the study focuses on situations where no a priori information about the reliability of the advisors is available, we used two similar advisors. If we had introduced a risk modeling firm and an internal team of experts, the participants would have been less likely to consider that the two sources of information were a priori equally reliable.

  5. The geometric mean in this case is (0.5 × 2)1/2 = 1%. In Section 3 we compare the premiums that insurers would charge with actuarially-priced insurance under the arithmetic mean of the probability interval (1.25%); where equal weight is given to the two estimates (conflict) and the interval frontiers (imprecise).

  6. For more details on the structure of a multi-year policy see Kunreuther and Michel-Kerjan (2009); Jaffee, Kunreuther and Michel-Kerjan (2010).

  7. Two insurance trade associations announced the existence of this survey to their members. Because of the way it was made available to all their members without being sent individually to each one of them, it is difficult to determine the response rate.

  8. For example, Ho et al. (2005) report the results of a series of experiments conducted with a total of 92 participants (30 managers in Experiment 1, and 62 participants in Experiment 2). In Ho et al. (2002), the same authors ran an experiment with a total of 79 MBA students (39 MBA students in Experiment 1, and 40 MBA students in Experiment 2).

  9. Descriptive statistics revealed that the premium distributions violated the normality assumption (skewness coefficient = 2.98 and 6.82 for the 1-year contract and the 20-year contract respectively). We therefore performed a log transformation (skewness coefficient = 0.53 and 0.76 for the log(1-year premium) and log(20-year premium) respectively). Such a procedure allows counteracting the effect of outliers and is useful when the distribution of the dependent variable is highly skewed (see Kunreuther et al. 1995 for a similar analysis).

  10. Specifically, 41 (51.25%) participants charged simultaneously a smaller premium under risk than under imprecise ambiguity, and a smaller premium under risk than under conflict ambiguity. Sixteen (20%) participants charged a higher premium under one source of ambiguity than under risk.

  11. In the text, we report the main effect of the Natural Hazard factor only when it was significant.

  12. It is worth noting that the same pattern was obtained when the responders were asked about the level of confidence they had in their estimates of the premium (see question 8 in appendix 1). A MANOVA on confidence scores across all respondents revealed that insurers were much more confident in their decisions under risk (3.55 and 3.15) than under imprecise ambiguity (3.11 and 2.89) (F = 11.22, p = 0.001 and F = 16.34, p = 0.000 for 1-year and 20-year contracts, respectively); and under risk than under conflict ambiguity (3.16 and 2.79) (F = 6.55, p = 0.012; and F = 9.37, p = 0.003 for 1-year and 20-year contracts, respectively). In addition, we did not find any statistically significant difference between the confidence scores under imprecise ambiguity and conflict ambiguity (F = 0.24, p = 0.63 and F = 0.07, p = 0.79 for the 1-year and 20-year premiums, respectively).

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Acknowledgements

We would like to thank the editor, Kip Viscusi, an anonymous referee, Diemo Urbig and seminar participants at the Wharton School, the University of Toulouse-Le Mirail and the Centre for Risk and Insurance Studies at Nottingham University Business School for insightful comments on a previous version of this article. Carol Heller provided excellent research assistance. We also would like to thank the American Insurance Association, the Property Casualty Insurance Association of America, and the National Association of Mutual Insurance Companies for helping us distribute the survey among their members. Partial financial support by the Wharton Risk Management and Decision Processes Center, the Center for Climate and Energy Decision Making (SES-0949710; cooperative agreement between the National Science Foundation and Carnegie Mellon University), NSF Cooperative Agreement SES-0345840 to Columbia University’s Center for Research on Environmental Decisions (CRED), the Travelers Companies, Inc. and the Fulbright program is acknowledged.

Author information

Authors and Affiliations

  1. Nottingham University Business School, The University of Nottingham, Jubilee Campus, Wollaton Road, Nottingham, NG8 1BB, UK

    Laure Cabantous

  2. Laboratoire Cognition, Langues, Langage, et Ergonomie (CLLE) Maison de la Recherche, Université de Toulouse II - le Mirail, 5, allées Antonio Machado, 31058, Toulouse Cedex 9, France

    Denis Hilton

  3. Center for Risk Management and Decision Processes, The Wharton School, University of Pennsylvania, Jon Huntsman Hall, Suite 500, 3730 Walnut Street, Philadelphia, PA, 19104, USA

    Howard Kunreuther & Erwann Michel-Kerjan

Authors
  1. Laure Cabantous
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  2. Denis Hilton
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  3. Howard Kunreuther
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  4. Erwann Michel-Kerjan
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Corresponding author

Correspondence to Erwann Michel-Kerjan.

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The authors have contributed equally to this paper.

Appendices

Appendix 1: Experiment questions

For each scenario, the participants were asked to answer 10 questions, presented in the following order:

  1. 1.

    Perception of disagreement. We asked participants to answer the question “To what extent do you have the impression that the two modeling firms are in agreement on the estimate of the probability of the damage?” Participants could answer this question on a on a 7-point scale, ranging from −3 = “Not in agreement at all” to +3 = “In complete agreement.”

  2. 2.

    Degree of “unusualness.” We asked participants to rate on a 7-point scale, ranging from −3 = “Nothing unusual at all” to +3 = “Extremely unusual” the degree of “unusualness” of the scenario. The question was: “To what extent do you have the impression that there is something unusual about the estimates of the probability of the damage you have been given?”

  3. 3.

    Positive person attribution. We asked participants: How strongly do you agree with the following statement? “Both modeling firms did their work, i.e., estimating the probability of the [flood/fire/hurricane] damage in this case, very well.” Participants could answer this question on a 7-point scale ranging from −3 = “Strongly disagree” to +3 = “Strongly agree.”

  4. 4.

    Negative person attribution. We asked participants: “How strongly do you agree with the following statement? “At least one of the two modeling firms did not do its work, i.e., estimating the probability of the [flood/fire/hurricane] damage in this case, very well.” We used the same scale as for question 3.

  5. 5.

    External (Task) attribution. We asked participants: “How strongly do you agree with the following statement?: “Estimating the probability of the [flood/fire/hurricane] damage in this case is a highly difficult task.” We used the same scale as for question 3.

  6. 6.

    Perception of the competence of the advisors. The participants were asked to answer the question “To what extent do you have the impression that the two modeling firms are both competent in estimating the probability of the [flood/fire/hurricane] damage in this case?” on a 7-point scale, ranging from −3 = “Both firms are not competent at all”; 0 = “At least one firm is not competent”; +3 = “Both firms are extremely competent.”

  7. 7.

    Pricing (1-year contract). Participants were told that they had the possibility of offering a typical 1-year contract. We asked them to report the “minimum annual premium (excluding administrative costs)” that they would charge against the risk.

  8. 8.

    Confidence (1-year contract). Participants were asked to rate on a 7-point scale ranging from 1 = “Not at all confident” to 7 = “Extremely confident,” the degree of confidence in their estimate of the premium.

  9. 9.

    Pricing (20-year contract). Participants were asked to give “the minimum annual premium (excluding administrative costs)” that they would like to charge against the risk in a case where they could offer a “20-year insurance contract against the damage to the property that would be tied to the homeowner mortgage.”

  10. 10.

    Confidence (20-year contract). Participants were asked to give “the minimum annual premium (excluding administrative costs)” that they would like to charge against the risk in the 20-year contract case.

Appendix 2: Information about the participants and their company

This appendix provides descriptive statistics on our random sample of 80 U.S. insurers. Sixty-five percent of the participants were actuaries, 8.8 percent were risk managers, 3.8 percent were underwriters, 6.3 percent were in a general management function, and 16.3 percent were in the “other” category.

With regard to past experience, 12 percent of our sample had less than 1 year of experience in their job, 65 percent had between 1 and 5 years of experience in their job, 14 percent had between 6 and 11 years of experience in their job, and 9 percent had more than 12 years of experience in their job.

With regard to age, 27 percent of the participants were between 20 and 29 years old, 35 percent were between 30 and 39 years old, 24 percent were between 40 and 49 years old, and 14 percent were 50 years old or more. Eighty percent of the participants had a bachelor’s degree as their highest degree, 14 percent had a master’s degree, 4 percent had a PhD, and 2 percent had a high school degree as their highest degree.

On average, a majority of participants (56 percent) were working for a publicly-traded company, 34 percent were working for a mutual, and 5 percent were working in a private company (5 percent were in the “Do not know” category).

With regard to the policyholders’ surplus of the company, 25 percent of the participants worked for a company having a surplus larger than $10 billion; 51 percent worked for a company with a surplus between $5 and $10 billion; 5 percent of the participants worked for a company having a surplus between $1 and $5 billion; 14 percent worked for a company having a surplus smaller than $1 billion; and 5 percent of the participants did not answer the question.

In terms of number of employees, 5 percent of the participants were in companies with more than 20,000 employees, 69 percent of the participants reported working for a company having between 5,000 and 20,000 employees, and 13 percent were in companies having between 1,000 and 5,000 employees; 11 percent said they did not know.

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Cabantous, L., Hilton, D., Kunreuther, H. et al. Is imprecise knowledge better than conflicting expertise? Evidence from insurers’ decisions in the United States. J Risk Uncertain 42, 211–232 (2011). https://doi.org/10.1007/s11166-011-9117-1

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