Your IndustryOct 9 2014

Counting the cost of preserving a life

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What is the value of life? Whose, yours or mine? Why do you want to know? In fact, you might want to know if you were designing an industrial plant such as a boiler that could conceivably explode and kill nearby workers.

Or perhaps rail operators might want to know that a train they are running is not about to come off the tracks, with some passengers dying in the resulting crash. Others may be operating a sea-going freighter that might sink with the loss of all hands. And so on. It will normally be possible to reduce the risk to life by spending more, but how much expenditure is rational? Does a time come when it is unreasonable to pay more out to preserve life?

This point is reached, according to the government, when the cost of taking one off the expected toll of preventable deaths rises above the value of a prevented fatality (VPF). In fact the department for transport publishes the UK’s official VPF each year, normally increased to account for rising GDP a head, although the absence of such growth recently means that it is currently pegged at its 2010 value of £1.65m.

This VPF has been adopted by the Health and Safety Executive and other UK regulatory bodies, resulting in its widespread use by the process and nuclear industries, as well as transport, as the yardstick for judging how much to spend on protection systems. But where did the original figure come from? And can we be confident that decisions founded on it give us all a fair degree of protection?

The figure’s origin is revealed in a 2009 report by Jonathan Wolff and Shepley Orr to the inter-departmental group for the valuation of life and health, a committee involving 12 government departments, including the department for transport, the health and safety executive, the department of health and the home office. The source of the DfT’s VPF figure is identified there as a paper by Carthy, Chilton, Covey, Hopkins, Jones-Lee, Loomes, Pidgeon and Spencer published in the Journal of Risk and Uncertainty in 1999. That paper reported on an opinion survey carried out on 167 people in the UK in 1997, but just three years ago Michael Spackman of National Economic Research Associates (who included two authors from the Carthy paper in his team) advised the DfT that the Carthy methodology was superior to its competitors and recommended against any major new investigation to update the VPF figure.

So what was the “superior” method used in the Carthy study? Rather than adopting John Locke’s precept: “I have always thought the actions of men the best interpreters of their thoughts”, the authors chose to appeal to “stated preferences” instead. Here people are asked to state the maximum price they will notionally pay for a good in the absence of a free market. But the Carthy authors believed people could not be expected to say with any accuracy how much they would spend to reduce further a risk of fatality that was already low and therefore decided to pursue their estimate of the VPF indirectly.

They devised the two-injury chained method, which, although it is based on complex economic utility theory, boils down to the following. The respondent is asked to imagine he has been injured in a road accident and is offered two hospital operations, A or B, each of which will leave him with a serious type-two injury should it fail. Operation A is potentially less effective than operation B, however, because whereas a successful operation B will return the patient to full health almost immediately, operation A will still leave him with a type-one injury even if it succeeds, albeit type-one is less severe than type-two.

The Carthy authors thought that Operation B’s potentially better outcome should cause the patient to accept a higher failure rate for that operation. They then theorised that information on the acceptable failure rate should determine the ratio of the individual’s value of a prevented injury (VPI) of type-two to his type-one VPI.

Meanwhile his VPI of type one would be calculated after eliciting the maximum price the individual would pay to cut his chance of incurring a type-one injury. Multiplying this sum and the VPI ratio together gives his type-two VPI in pounds sterling. This equals his personal VPF if the type-two injury is taken as fatal, when averaging over all the people in the sample yields the VPF for the group as a whole.

All very fine, but does it work? The answer is unfortunately ‘no’, which means that the VPF figure used so widely in judging protection systems in the UK for the past 15 years can be regarded as no more than an arbitrary statistic. The method may be shown to be invalid using data provided by the Carthy authors. Two VPI figures per individual can be calculated for one specified serious but non-fatal injury cited in the 1999 paper, with one VPI being calculated directly and the other through two-injury chaining. The two figures should be the same or at least very similar, but they turn out to be completely different. Moreover, there is barely any correlation between the two values in the 167-strong sample. Thus the supposedly superior method advanced in the 1999 paper fails a fundamental test of its validity.

It has to be said that the 1999 paper also has other flaws, including inconsistencies in the predicted wealth of the respondents, indications that the range of wealth in the sample did not represent the true spread in the UK population by a very wide margin and difficulties with the way the data were manipulated, including misattribution, unjustified “trimming” out of high personal VPF figures (but not low ones) and the rejection of some data because they did not fit with the researchers’ model. But even if these additional flaws had been absent, the method’s failure in the key validity test just described means that the evidential base for the VPF figure recommended by the DfT and the Health and Safety Executive has already long disappeared.

This puts the spotlight on the very large number of safety spending decisions taken in the UK’s road, rail, chemical, nuclear and other industries over the past 15 years. Was enough spent to safeguard workers and the general public? The severe methodological shortcomings that have been identified may well have led to the true value of the UK’s VPF being underestimated – it is less than half the US figure and only two-thirds of the Canadian figure, after all – and this would imply poor protection for UK citizens. Getting the value of life wrong can cost lives.

Fortunately, it is perfectly possible to value human life using the “revealed preferences” likely to have been favoured by John Locke (1632-1704). The government should surely now discard its invalid, stated preference approach and consider using a revealed preference technique to help it discharge its literally vital duty to place the correct value on life and provide its citizens with the protection that is their due.

Philip Thomas is a professor with the School of Mathematics, Computer Science and Engineering, City University London

Key points:

The department for transport publishes the UK’s official VPF each year, normally increased to account for rising GDP per head

In the Carthy study, people are asked to state the maximum price they will notionally pay for a good in the absence of a free market

Questions have been raised on whether enough has been spent to safeguard workers and the general public