Abstract
This article examines the nature of the restrictions on the underlying social welfare function that would appear to be required in order to justify the application of a “common” Value of Statistical Life (VSL) for any particular hazard within a given society and considers the way in which the magnitude of this common VSL might relate to the values actually employed in practice. The article also considers the question of whether, by contrast, discounts or premia might legitimately be applied to the VSL in order to take account of factors such as age or current exposure to risk and explores the form that such discounts or premia might reasonably take.
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Notes
One notable exception is apparently Health Canada which, according to Alberini et al. (2002), applies a VSL equal to only 75% of its “standard” value to those aged 65 and over. In addition, in the UK at least some healthcare allocative decisions are based upon the so-called “Quality-Adjusted Life Year” (or “QALY”) methodology, together with a constant WTP-based value of a life-year. Strictly applied, this procedure will clearly also differentiate between patients on the basis of remaining life expectancy and hence age. It is also worth noting that while the US Environmental Protection Agency gave serious consideration to the possibility of requiring age-adjustments to the VSL, this requirement was eventually dropped as a result of the controversy generated by the proposal.
This having been said, it should be stressed that in those countries that use WTP-based values of safety, some attempt is typically made to take account of the different degrees of fear or “dread” with which members of the public tend to view the prospect of death by different causes. However the argument that follows focuses upon a single “homogeneous” cause of death.
Thus, for example, with the UK average annual risk of a fatal road accident for an automobile driver or passenger lying in the region of 5 × 10−5 per annum and a roads VSL of about £1.5 × 106, then even a 20% reduction in this road risk would involve an increase in survival probability of only about 1 × 10−5 per annum (i.e. about 1% of the overall annual risk of death faced by the average 30-year-old) and an average annual willingness to pay of no more than £15 (i.e. a minute fraction of average annual income).
Of course, an alternative possibility would be that \( \frac{{\partial u_{i} }} {{\partial p_{i} }} \) was in fact independent of both w i and p i , in which case Eq. 5 would entail that the a i were constant for all variations in w i and p i , rather than just for marginal variations. But this would require that u i (w i , p i ) was both additive-separable and linear in p i . In the case of an individual who was an expected utility maximizer this in turn would require that the utility of wealth conditional on survival exceeded the utility of wealth conditional on death by a constant amount that remained independent of wealth. While this might not be an entirely implausible assumption for an individual with dependents to support, it would seem to be rather less defensible for, say, a single individual with no dependents.
It has been suggested to us that as insofar as this definition differs from that which results from the conventional cost-benefit analysis methodology, we should not refer to it as the “VSL” but should accord it some other name. We disagree. The value specified in Eq. 14 is the appropriate value to place on a safety improvement that will prevent one statistical fatality, given the ethical prescription embodied in Eq. 5, and is therefore every bit as much a “VSL” as that which emerges from the ethical framework underpinning conventional social cost-benefit analysis.
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Acknowledgements
We are grateful to John Broome for drawing our attention to the assumption concerning the structure of the social welfare function that underpins our argument. We also acknowledge the very perceptive and constructive comments of two referees and the Editor.
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Baker, R., Chilton, S., Jones-Lee, M. et al. Valuing lives equally: Defensible premise or unwarranted compromise?. J Risk Uncertainty 36, 125–138 (2008). https://doi.org/10.1007/s11166-008-9034-0
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DOI: https://doi.org/10.1007/s11166-008-9034-0