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Valuing gains in life expectancy: Clarifying some ambiguities

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Abstract

It is well-understood that a given gain in life expectancy can, in principle, be generated by any one of an infinite number of different types of perturbation in an individual’s survival function. Since it seems unlikely that the typical individual will be indifferent between these various types of perturbation, the idea that there exists a unique willingness to pay-based Value of a Statistical Life Year (VSLY), even for individuals within a given age-group, appears to be ill-founded. This paper examines the issue from a theoretical perspective. Within the context of a simple multi-period model it transpires that if gains in life expectancy are computed on an undiscounted basis then it will indeed be necessary to adjust the magnitude of the VSLY to accommodate the nature of the perturbation in the survival function, as well as the age of those affected. If, by contrast, gains in life expectancy are computed on an appropriately discounted basis then a unique VSLY will be applicable in all cases.

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Notes

  1. Or as it is now more commonly referred to in the UK, the Value of Preventing a Statistical Fatality (VPF).

  2. For alternative (but basically similar) definitions of the willingness to pay-based VSL, see Johansson (2001) and Blomqvist (2002).

  3. Or as it is sometimes referred to, the VOLY.

  4. For the sake of analytical simplicity, in the argument that follows it is assumed that if death is to occur in any given year then it does so at the end of the year. Based on this assumption, the gain in life expectancy resulting from a 1/n reduction in the risk of death during the coming year will, strictly speaking, be equal to the product of remaining life expectancy conditional on survival of the coming year and 1/n.

  5. See, for example, Wetterstrand (1981) or Jenkins (2005) Ch.3.

  6. For a more detailed discussion of life insurance and annuity contracts, see Jones-Lee (1989), Ch.3.

  7. So that, for example, an individual of age 40 in year 1 (i.e., the current year) will be of age 40 + t in year t +1.

  8. The summation in equation (12) runs from t = 2 since, by definition, S(2) denotes the probability of survival to the beginning of period 2 and is hence, from equations (1) and (3), the first term in the expression for El that is affected by a variation in p 1 .

  9. With the parameters of the Gompertz Function set at the estimated levels, then it follows from equation (14) that the maximum age at which the hazard rate remains less than unity is 117. In fact, with the hazard rate defined as a probability density—as in equation (17)—it is entirely possible for the rate to exceed unity. However, given that the main body of the argument developed in this paper has been based on a discrete time model with hazard rates treated as probabilities (rather than probability densities), then it is necessary to ensure that they do not exceed unity. Given that the oldest recorded age at death in the UK is 115 years and 228 days, then it seems reasonable to set the maximum possible remaining survival time, T, so that an individual cannot survive beyond his/her 116th year.

  10. In particular, the VSLY computed on the basis of average discounted life expectancy with the discount rate set in the region of 6% would be more than double that which results from applying the rate currently used in UK public sector health and safety decisions (i.e., 1.5%).

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Authors and Affiliations

  1. Newcastle University Business School, 5 Barrack Road, Newcastle upon Tyne, NE1 4SE, UK

    Michael Jones-Lee, Susan Chilton, Hugh Metcalf & Jytte Seested Nielsen

Authors
  1. Michael Jones-Lee
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  2. Susan Chilton
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  3. Hugh Metcalf
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  4. Jytte Seested Nielsen
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Correspondence to Michael Jones-Lee.

Additional information

The authors are grateful to Kip Viscusi, Jim Hammitt and two anonymous referees for very helpful comments and suggestions.

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Jones-Lee, M., Chilton, S., Metcalf, H. et al. Valuing gains in life expectancy: Clarifying some ambiguities. J Risk Uncertain 51, 1–21 (2015). https://doi.org/10.1007/s11166-015-9221-8

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