St John’s Economics tutor Dr Kate Doornik set our Year 11 course one of the more challenging competitions this year. Through Dr Doornik’s article What’s the price on your head?, pupils explored the difficulty of putting a monetary value on saving lives, and in their competition responses, pupils grappled with this challenge themselves. This series of questions asked pupils to calculate the value of a statistical life, as well as to examine the principles and values at play behind such a calculation.
Read on to check your work on calculating the value of a statistical life (the correct answers are given below), and to read the winning entries! While nobody got the VSL calculations exactly right, all these entries raise some excellent points from many different perspectives.
Competition 2.2: What’s the price on your head?
1. Returning to Mount St John, how much would the value of a (statistical) life have to be in this case to justify spending £10 million pounds or £100 million pounds?
Justified spending = VSL × population × risk of eruption × decrease in probability of death in case of eruption.
Substituting in figures for £10 million case:
£10,000,000 = VSL × 100,000 × 0.01 × 0.01
Rearranging gives VSL = 10,000,000/(100,000 × 0.01× 0.01) = £1 million
Similarly to justify spending £100 million the VSL must be £10 million.
(Note that the assumption is that the effects of the spending last for the 20 years mentioned)
2. How much would you be willing to pay to reduce the risk of a fatal road accident from 5 in 100,000 to 4 in 100,000? What does this imply for your estimated VSL? Try asking other people and compare answers.
The VSL will be calculated in a similar way as above:
WTP = VSL × decrease in probability of fatal accident.
WTP = VSL × 1/100,000.
VSL = WTP × 100,000
3. How easy do people find it to answer questions like Q2? Are there different ways of asking the question that make it easier? For example, does it help if you use population figures to work out the absolute number of road deaths that the probabilities imply?
4. How do the answers you get from Q2 compare to the answers you would get if you took a human capital approach?
1st place: Himank K.
2nd place: Eloise P.
Can we put a price on life?
1) £10 million spend VSL = £100
£100 million spend VSL = £1000
2,3,4) As there is no provable right or wrong method for prediction, it is ultimately impossible to find a ‘correct’ value for VSL. How much people are prepared to pay to spare their lives is obviously a very different question to how much a life itself is worth – yet the answers to both give us a so called comparable value for life; controversy between figures is inevitable.
On a personal level, I would not be willing to pay to reduce my chance of death in a car accident from 5/100,000 to 4/100,000. If you take into account the average number of car journeys per year taken by older children living in London (357.7)(1), multiplied by UK life expectancy for a 15 year old girl (89 years)(2), I will most likely take only 31,840 car journeys in my lifetime, thus my personal risk would only decrease from 1.591 to 1.273. Less than one death is reduced, therefore there is little point investment.
But it turns out some people will invest in reducing their chances of death, however small. 12 participants were asked the same question worded slightly differently;
- With equivalent values of the same risk reduction:
- 5/100,000 to 4/100,000
- 4.4 to 3.5 times in a lifetime for females and 4.3 – 3.4 times in a lifetime for males
Calculated using average car journeys per person per year in the UK (975) (3) multiplied by life expectancy at birth (90 for females, 88 for males)(2) for a total of 87750 journeys for females and 85800 for males.
- With different amounts money as starting points for VSL:
- Given amounts of money (£100 and £1000) and if they would pay more/less than that figure:
- How much they would pay without a starting figure.
Most respondents would pay to have their chances of a fatal car accident reduced, although the values varied from £100 to over £1 million. However, values showed a strong correlation to the way the question was asked. Most respondents didn’t stray far from the value suggested, whereas when no value was attached respondents gave much greater answers. Moreover, respondents were more likely to pay when life expectancy and average car usage was not taken into account, as the ‘20% reduction’ as identified by one participant was much more attractive than the alternative figures. The power of question manipulation is showcased quite shockingly here.
Taking a human capital approach, perhaps governments should consider contributions per person when estimating VSL, thus determining whether saving a life is economically viable. Everyone employed in the UK earning above £12,500 pays at least £2,500 in tax per year, so perhaps this should be a starting point for VSL. But if we spent all taxes on saving lives, how would we live worthwhile ones due to lack of government spending on education and culture?
- London Travel Demand Survey, 2011/12
- Office for National Statistics, 2019
- Department for Transport, Survey 2017
Look out for the winning entries to the last Class 2 competition, coming next week! And don’t forget–the next competition deadline is 5pm on Monday 23 March.