Australia’s decision to restrict physical movement during the COVID-19 crisis has been overwhelmingly vindicated by the evidence. On a per-capita basis, the United States still experiences roughly the same number of deaths per day as Australia has overall.
In Sweden — which pursued a private lockdown rather than a government-coordinated one — the death rate is 418.9 per million, more than 100 times that of Australia, yet its central bank forecasts worse economic outcomes than Australia both this year and next.
This decision was also justified by any reasonable cost-benefit analysis (CBA) of lives lost under an unmitigated “herd immunity” strategy compared to a partial lockdown, and the additional economic costs of a lockdown as distinct from the general economic costs of COVID-19.
Yet this kind of CBA requires putting a dollar figure on the value of human life — a number the Australia government puts at $4.9 million.
But there is good reason to believe that the “value of a statistical life” (VSL) number the Australian government uses is far too low.
The $4.9 million figure is not based on any stated criterion or even Australian data. The basis was simply that it is “plausible”.
This is despite international numbers for countries such as the United States being substantial higher, and the author of the Australian government document himself saying that international numbers supported by Harvard economists Joe Aldy and Kip Viscusi, who consider the true number to be between US$5 million and US$12 million, should be granted more weight as they are genuine experts.
Given the exchange rate between the US and Australia dollar, that implies that the Australian VSL should actually be between A$7.7 million and A$18.5 million, or 1.6 to 3.8 times the figure the government uses.
Were the Australian government to use the more internationally credible figures, it would have significant policy implications for health, occupational health and safety, transport, and environmental regulation.
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Suppose, for example, that VSL numbers were used to determine what medicines are covered by the Pharmaceutical Benefits Scheme. That calculation involves a tradeoff between the cost of the medication involved and the probability of it saving a life, along with the VSL.
A higher VSL means more medications would be covered — leading to health improvements but a hit to the government’s bottom line.
Now, when calculating the benefits of lives saved one might argue that the value of lives saved should depend on the age of the person in question. Whether all lives should be valued equally by society is a philosophical and value-laden question — one that should, and does, make us uncomfortable.
But if one does want to calculate the Value of a Statistical Life Year (VSLY), the arithmetic is more subtle than some people — including some with advanced economics degrees — seem to appreciate.
To begin, there is a large amount of literature that looks to measure VSL conditional on a range of characteristics, including age. This literature finds that VSLs have an inverted “U” shape, with VSLs often peaking in the 40-50 age bracket then declining over the subsequent years of working life.
The fall tapers off slowly relative to the pace of increase early in life. Older workers have a higher VSL than younger.
To understand this, it is important to remember that VSL measures what individuals are willing to pay to reduce mortality risk. Many studies infer this willingness to pay by using market data, specifically labour-market data.
There are other approaches based on stated preferences from surveys, but hypothetical surveys often suffer from issues related to framing as well as the difficulty that respondents have understanding the consequences of small changes in risks.
Moreover, economists are generally sceptical of simply asking someone an important question rather than seeing what their behaviour — so-called “revealed preference” — tells us about their underlying preferences.
So why does VSL have a peak in middle age? This is because there are two competing effects of age.
The first is the obvious one that, all else equal, people value a longer life more. But all else is not equal. A life with higher human capital, a better job, and more money is preferable.
This latter effect generally increases with age, while the former “term of life” effect decreases mechanically with age. These two forces shake out to produce an inverted U-shaped VSL.
To account for the age distribution, we would actually need to calculate a VSL for all ages. But the Australian government recommends using a single number, $4.9 million, to approximate the age distribution. This number is the value of a “typical 40-year-old” who has life expectancy of 80 years — that is, expects to live another 40 years.
The government estimates this value assuming a 40-year-old values each future life year equally (contrary to the findings just discussed) and that they discount those future years at 3% per annum. The number that makes the present discount value of those future life years equal to the VSL of $4.9 million is $213,000.
Both the government’s method and basic economics make it clear that to simply divide the VSL by 80 to estimate the VSLY, as some have proposed during the current pandemic, is flat out incorrect.
But matters are more complicated still. Arguing that saving someone aged 78 if life expectancy is 80 saves two statistical life years is also incorrect.
One needs to look at life expectancy conditional on getting to that age. So, going back to our original calculation, even if we took the VSLY to be $213,000 and note the life expectancy of someone aged 80 in Australia was 89.58 in 2015, then saving that 80-year old would be worth roughly $2 million.
Of course, when thinking about COVID-19 policy it is important to get the counterfactual right. Under herd immunity, younger people would comprise a greater fraction of total deaths than under the lockdown we pursued.
The young have substantially longer life expectancy. For this reason, they will matter disproportionately and dramatically increase the calculated benefits.
And that doesn’t measure what family and relatives would be prepared to pay to save the life of their loved ones, which various studies suggest give corrections of 1.1 to 1.4, or what an individual would pay to reduce the risk of infecting many others with a deadly virus.
If this all sounds very complicated, well, it is.
The Australian government figure on the VSL is between 1.6 and 3.8 times too low. It doesn’t account for the impact of deaths on people other than the deceased. And, even if one wants to adjust the value of life for years left to live then an 80-year old is, by the strictures of arithmetic, still worth about 40% of a 40-year-old.
Factoring all that in suggests that the Australian government should value the life of an 80-year old at between 70% and 215% of what it does. And for a 40-year-old the government undershoots by between 1.7- and 5.3-fold in its valuation.
Using the correct number would have huge implications for the drugs the government pays for, and many other public policy decisions from mandatory vehicle cameras to speed limits.
Putting a dollar value on life is both uncomfortable and difficult. But when cost-benefit analysis is required, it is also deeply consequential.
Richard Holden and Bruce Preston are professors of economics at UNSW Business School and the University of Melbourne, respectively.