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Insurance decisions for low-probability losses

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Abstract

It is widely accepted that individuals tend to underinsure against low-probability, high-loss events relative to high-probability, low-loss events. This conventional wisdom is based largely on field studies, as there is very little experimental evidence. We reexamine this issue with an experiment that accounts for possible confounds in prior insurance experiments. Our results are counter to the prior experimental evidence, as we observe subjects buying more insurance for lower-probability events than for higher-probability events, given a constant expected loss and load factor. Insofar as underinsurance for catastrophic risk is observed in the field, our results suggest that this can be attributed to factors other than only the relative probability of the loss events.

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Notes

  1. The level of insurance purchase reported by Slovic et al. varied depending on the treatment, but the overall pattern of behavior (higher rates of insurance purchase as the probability of a loss increased) was consistent across treatments.

  2. The p-value for McNemar’s one-tailed test conditional on the sum of discordant pairs is p=.0096 comparing the purchase rates for loss probabilities of .001 and .01, and p=.0461 comparing purchase rates for loss probabilities of .01 and .5. We provide a more detailed description of McNemar’s test below.

  3. All but one subject earned $60. The remaining subject was omitted from this analysis.

  4. These revision procedures follow Harbaugh et al. (2005).

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Acknowledgements

We thank seminar participants at Fordham University, Medical University of South Carolina, University of Michigan, and University of North Carolina at Charlotte. Funding was provided by the National Science Foundation (SBR-9753125 and SBR-0094800).

Author information

Authors and Affiliations

  1. Georgia State University, Atlanta, GA, USA

    Susan K. Laury & J. Todd Swarthout

  2. University of South Carolina, Columbia, SC, USA

    Melayne Morgan McInnes

Authors
  1. Susan K. Laury
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  2. Melayne Morgan McInnes
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  3. J. Todd Swarthout
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Corresponding author

Correspondence to Melayne Morgan McInnes.

Appendices

Appendix A Instructions for Slovic et al. replication

In this survey, I am going to describe a series of gambling games. Each game has the possibility of negative outcomes. Each allows you to buy insurance against the negative outcomes, although it is not required. I am not going to ask you to play any of the games. Instead, I am going to ask you to consider each and then tell me how you would play were they for real. Try to take each as seriously as possible, even though nothing is at stake.

Each game consists of drawing one ball from each set of baskets. Each contains a different mixture of orange and white balls. If I were to draw a white ball, no loss would occur. If I were to draw an orange ball, this would result a loss, unless you had purchased insurance. (Remember, we will not actually play any of these gambles, but I want you to think about each as if you were really going to play each one.)

As you can see, you can only lose in this sort of game (either by drawing an orange ball or by buying insurance). Your object is to lose as little as possible. For each game figure out what insurance you would buy to end up with the fewest negative points.

Appendix B General knowledge quiz

The following questions test your knowledge of current events, American history, and geography. Please indicate the correct answer in the blank beside each question. You will be paid based on the number of questions you answer correctly.

If you answer 8 or more questions correctly, you will be paid $60.

If you answer 7 or fewer questions correctly, you will be paid $30

______1. The current Secretary of State is

  1. a.

    Dick Cheney

  2. b.

    John Snow

  3. c.

    Donald Rumsfeld

  4. d.

    Condoleezza Rice

______2. The winner of the 2006 Superbowl was

  1. a.

    Pittsburg Steelers

  2. b.

    Indianapolis Colts

  3. c.

    Carolina Panthers

  4. d.

    Seattle Seahawks

______3. Which of the following states borders the Gulf of Mexico?

  1. a.

    California

  2. b.

    Texas

  3. c.

    Maine

  4. d.

    North Carolina

______4. Who was the last President to die in office?

  1. a.

    John Kennedy

  2. b.

    Bill Clinton

  3. c.

    Gerald Ford

  4. d.

    Ronald Reagan

______5. What is the capital of Arkansas?

  1. a.

    Pierre

  2. b.

    Sacramento

  3. c.

    Albany

  4. d.

    Little Rock

______6. Which of the following was one of the first 13 colonies?

  1. a.

    a. Montana

  2. b.

    Virginia

  3. c.

    Louisiana

  4. d.

    Texas

______7. Who is the host of American Idol?

  1. a.

    Howie Mandel

  2. b.

    Regis Philbin

  3. c.

    Jeff Probst

  4. d.

    Ryan Seacrest

______8. Which of the following toys was named for a U.S. President?

  1. a.

    Jacks

  2. b.

    Raggedy Andy

  3. c.

    Marco Polo

  4. d.

    Teddy bear

______9. “Only you can prevent forest fires.” was the slogan of

  1. a.

    Toucan Sam

  2. b.

    Polly the Parrot

  3. c.

    Woodsy the Owl

  4. d.

    Smokey the Bear

______10. Which of the following was an ally of the United States in World War II?

  1. a.

    Germany

  2. b.

    Switzerland

  3. c.

    Italy

  4. d.

    Great Britain

______11. Which of the following is a movie about twin girls raised separately who meet at camp and eventually persuade their parents to reunite?

  1. a.

    Freaky Friday

  2. b.

    The Pajama Game

  3. c.

    The Parent Trap

  4. d.

    Yours, Mine and Ours

______12. Which television network carries the OC?

  1. a.

    Fox

  2. b.

    PBS

  3. c.

    HBO

  4. d.

    MTV

______13. “Scrubs” is a television series centered around

  1. a.

    a carwash

  2. b.

    a hospital

  3. c.

    a baseball team

  4. d.

    hotel maid service

______14. Who is credited with inventing the light bulb?

  1. a.

    Eli Whitney

  2. b.

    Oprah Winfrey

  3. c.

    Thomas Edison

  4. d.

    Enrico Marconi

______15. “First in Flight” is the slogan of which of the following states?

  1. a.

    Texas

  2. b.

    Montana

  3. c.

    Maine

  4. d.

    North Carolina

Appendix C Experiment instructions

Today you will make choices about a series of gambles. Each gamble has the possibility of a negative outcome. In each gamble, you will be allowed to buy insurance against the negative outcome, although you are not required to buy the insurance.

Each gamble consists of drawing one ball from a basket. Each basket contains a different mixture of orange and white balls. If I draw a white ball, no loss occurs. If I draw an orange ball, this will result in a loss. Any loss you incur will be paid out of the money you earned by taking the Current Events Quiz, unless you choose to purchase insurance.

Here is how this will work: if you choose to purchase insurance, you will pay for this out of the money that you earned by taking the Current Events Quiz. If you do not purchase insurance and I draw a white ball, you will keep all of the money that you earned. If you do not purchase insurance and I draw an orange ball, you will lose some or all of the money that you earned by taking the Current Events Quiz. Each gamble will specify how much you may lose and how much the insurance will cost.

Each gamble that you face will be similar to the following (though the numbers used in the experiment will be different than this example):

If you faced the gamble in this example and you chose to purchase insurance you would pay me $1.20 from the money you earned by taking the Current Events Quiz. You would pay this $1.20 before I drew a ball from the basket, so you would pay it regardless of whether I drew a white ball or an orange ball. However, if you purchased this insurance and I drew an orange ball, you would not lose $12 in this example.

You will make decisions for 18 gambles during this part of the experiment. You should read the information provided to you in each one carefully: the number of orange and white balls, the loss you incur if an orange ball is drawn, and the insurance premium may change from one gamble to another.

Even though you will face 18 gambles in this experiment, only ONE of them will be used to determine your earnings. After you have made all 18 choices, we will put 18 numbered ping-pong balls into a cage. We will mix up these balls and then draw one ball from the cage. The number that appears on the ball that we draw will determine which choice will count.

For example, if we drew a ball with a 12 written on it, only your choice in Gamble 12 would count. None of your other choices would have any effect on your earnings. If you chose to purchase insurance in Gamble 12, you would pay the stated price of insurance in this decision. If you did not choose to purchase insurance in Gamble 12, the color of the ball drawn in this gamble would determine whether you lost any money in this experiment.

Even though only one of your 18 choices will count, you will not know in advance which gamble will be used to determine your earnings. Therefore, you should think about each of them carefully before submitting your choice.

Although each of you will make 18 choices, you may not face the same 18 gambles. Also, we have already shuffled your decision-sheets so each of you will receive your gambles in a different order. For example, one person may see Gamble 5 and then Gamble 3, while another person may see Gamble 7 first, and then Gamble 10. However, each of you will make decisions in 18 different gambles.

To summarize, this is what will happen during the rest of today’s experiment:

  1. 1.

    We will show you 18 gambles; in each you must choose whether or not you wish to purchase insurance at the stated price. We will show you these gambles one at a time. After everyone has made their first choice, we will show you a second gamble, and so on for all 18 gambles.

  2. 2.

    After everyone has made all 18 choices, we will draw a numbered ping-pong ball to determine which ONE of these gambles will count. We will not look at your choices for any other gamble when determining your earnings.

  3. 3.

    We will come to each of you and see if you chose to purchase insurance in this gamble. If you purchased insurance, we will collect the stated price of insurance from you.

  4. 4.

    We will place into this bucket the number of orange and white ping-pong balls specified in the gamble.

  5. 5.

    We will mix up these ping-pong balls and then draw ONE ball from the bucket.

  6. 6.

    If we draw a white ball, no one will incur a loss. If we draw an orange ball, you will lose the amount specified in this gamble, unless you chose to purchase insurance.

  7. 7.

    You will sign a receipt form and then may leave the experiment.

We ask that you not talk to one another during this experiment. If you have any questions at any time, please raise your hand and one of us will come to you to answer the question. Before we begin do you have any questions about these procedures or how your earnings will be determined?

Appendix D Descriptive statistics for demographic and insurance purchase questionnaire

Table 8 Experiment 2 demographics and insurance purchase experience
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Table 9 Experiment 3 demographics and insurance purchase experience
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Table 10 Experiment 2 random effects probit models of experiment insurance purchase with demographic and real insurance experience data
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Table 11 Experiment 3 random effects probit models of experiment insurance purchase with demographic and real insurance experience data
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Laury, S.K., McInnes, M.M. & Swarthout, J.T. Insurance decisions for low-probability losses. J Risk Uncertain 39, 17–44 (2009). https://doi.org/10.1007/s11166-009-9072-2

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