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Measurement Error, Skewness, and Risk Analysis: Coping with the Long Tail of the Distribution

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  • Jeryl L. Mumpower
  • Gary McClelland

Abstract

Probabilistic risk analyses often construct multistage chance trees to estimate the joint probability of compound events. If random measurement error is associated with some or all of the estimates, we show that resulting estimates of joint probability may be highly skewed. Joint probability estimates based on the analysis of multistage chance trees are more likely than not to be below the true probability of adverse events, but will sometimes substantially overestimate them. In contexts such as insurance markets for environmental risks, skewed distributions of risk estimates amplify the ``winner's curse'' so that the estimated risk premium for low‐probability events is likely to be lower than the normative value. Skewness may result even in unbiased estimators of expected value from simple lotteries, if measurement error is associated with both the probability and pay‐off terms. Further, skewness may occur even if the error associated with these two estimates is symmetrically distributed. Under certain circumstances, skewed estimates of expected value may result in risk‐neutral decisionmakers exhibiting a tendency to choose a certainty equivalent over a lottery of equal expected value, or vice versa. We show that when distributions of estimates of expected value are positively skewed, under certain circumstances it will be optimal to choose lotteries with nominal values lower than the value of apparently superior certainty equivalents. Extending the previous work of Goodman (1960), we provide an exact formula for the skewness of products.

Suggested Citation

  • Jeryl L. Mumpower & Gary McClelland, 2002. "Measurement Error, Skewness, and Risk Analysis: Coping with the Long Tail of the Distribution," Risk Analysis, John Wiley & Sons, vol. 22(2), pages 277-290, April.
    • Handle: RePEc:wly:riskan:v:22:y:2002:i:2:p:277-290
    DOI: 10.1111/0272-4332.00027
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    References listed on IDEAS

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    1. H. V. Ravinder & Don N. Kleinmuntz & James S. Dyer, 1988. "The Reliability of Subjective Probabilities Obtained Through Decomposition," Management Science, INFORMS, vol. 34(2), pages 186-199, February.
    2. Jeryl L. Mumpower, 1991. "Risk, Ambiguity, Insurance, and the Winner's Curse," Risk Analysis, John Wiley & Sons, vol. 11(3), pages 519-522, September.
    3. Thomas S. Wallsten & David V. Budescu, 1983. "State of the Art---Encoding Subjective Probabilities: A Psychological and Psychometric Review," Management Science, INFORMS, vol. 29(2), pages 151-173, February.
    4. Howard Kunreuther, 1989. "The Role of Actuaries and Underwriters in Insuring Ambiguous Risks," Risk Analysis, John Wiley & Sons, vol. 9(3), pages 319-328, September.
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    Cited by:

    1. Eldad Yechiam & David V. Budescu, 2006. "The Sensitivity of Probability Assessments to Time Units and Performer Characteristics," Decision Analysis, INFORMS, vol. 3(3), pages 177-193, September.

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