Nick Rendell: Comments on a Covid cost-benefit analysis

An article by Nick Rendell.

The paper ‘Living with Covid-19: Balancing costs against benefits in the face of the virus’ has been published by the National Institute Economic Review (No. 253, August 2020). It was produced by Professor David Miles, Professor of Economics at Imperial College London, Mike Stedman and Adrian Heald.

The Daily Mail produced a very distorted view of the report by Lucy White on July 24 which reports only one of forty possible outcomes detailed by the Imperial team, that one possible outcome chosen being the one least critical of the policy of Lockdown.

The full Imperial report is available here. It looks at how a cost/benefit analysis may be produced for the Covid-19 emergency. It is interesting to compare and contrast the findings with the report produced by the NHS and Government Actuaries published April 8, 2020.

The Imperial report attempts to quantify the ‘cost’ of deaths by using the figure used by NICE, £30,000 per year of life (this figure is used by NICE to determine the upper limit of health resources that should be expended to save a year of life). The paper discusses various alternative measures but as this figure is in widespread use it seems as a good a figure to use as any. Thus, for someone dying of Covid-19 who, had they not died, would have gone on to enjoy ten years of life, the lost ten years is valued at 10 x £30,000 = £300,000. The key drivers on the ‘benefits’ or savings side of the equation are: how many lives did lockdown save and how many years of life on average would those victims have enjoyed if not cut down by Covid-19?

On the other side of the equation, the ‘cost’ side of Lockdown, the Imperial team take the figures from the Bank of England and the Office for Budget Responsibility to estimate the cost at various levels between 9% and 25% of GDP which equate to a range from £200bn to £550bn.

The lives saved by Lockdown are placed at anywhere between 440,000 and 20,000 lives. That’s a x22 variance and goes to illustrate the dire situation we are in when our top economists and statisticians can’t narrow the range of possible lived saved any more accurately than that. Of course the higher number is derived from Imperial’s very own Professor Neil Ferguson, who projected 500,000 lives lost. This figure was dependent upon the IFR (infection/fatality rate) being 1% and the susceptibility rate of the UK population to be about 80%. In reality the IFR looks like being about 0.25% and the susceptibility of the population to be far lower than initially thought.

The NHS/Actuaries paper of April 8 is valuable in that it quantifies the lives lost to conditions other than Covid-19 due to the Lockdown. It puts this figure at 200,000, these are mainly due to cancer deaths and heart-related problems but also suicide and a range of other conditions exacerbated by the cessation or postponement of treatments by the NHS during the Lockdown. The paper estimates that these victims will lose on average 4.2 years of life, in other words if the NHS had been working normally they would have lived a further 4.2 years on average. These figures carry a far higher confidence level than those associated with Covid 19 fatalities. NHS statisticians know pretty well the consequential health outcomes of postponed treatments. Costing each life year at £30,000 we can then, with quite a high level of confidence, calculate that the non-Covid 19 lost life years equate to 4.2 x £30,000 x 200,000 = £25.2bn. Somewhat surprisingly the Imperial team do not include this figure in their calculations.

But, let’s go back to the Imperial paper and look again at what drives the ‘benefit’ side of the equation. We’ve already established that Imperial calculate the lives saved by Lockdown are somewhere between 440,000 and 20,000. But what about the lost years of life for each victim? We know that the average age of a Covid-19 fatality is about 80. We also know that the average age of death of women in the UK is just over 81 and for men just under 80. We know that more men die from Covid-19 than women so intuitively it looks like the life years lost for the average fatality would be about one year. So how come Imperial are claiming that the average lost years is ten years? The answer is that having reached 80 you’ve already outlived all the people who brought the average down by dying relatively early, anyone at 80 is still likely to go on living for a while yet, Imperial acknowledge this and produce figures for people living five more years and ten more years. The argument that Imperial give for cutting the residual life expectancy from a possible ten years to five years is that the Covid-19 fatalities over 80 are likely to have other health problems, indeed something like 97% of the over-80 years fatalities had a co-morbidity sufficiently serious to be mentioned on the death certificate. In truth, the residual years of the cohort that have fallen victim to Covid-19 look, in general, to have been the illest of the ill, it may be that their expected residual life expectancy may have been significantly less than five years. If the lost years of life are lower than five years this would depress the ‘savings’ from the Lockdown.

Table 1, below, is taken directly from the Imperial report. At various levels of GDP loss and lives lost it compares cost and benefit. The Daily Mail story reported the loss of £134bn; the excess cost of saving 440,000 lives with the (relatively) small loss of 9% of GDP as the key finding. However, if we look at the other end of the table if lives saved by Lockdown were 20,000 and we end up with an economic cost of 25% of GDP, which they put at £550bn, then the cost over the benefit is £547bn. It is worth noting that these figures ignore the projected £25.2bn cost of lost non-Covid-19 lives which would make the cost greater still over the benefit.

Table 1

Benefits (+), costs (–) and net benefits(a) of March-June UK lockdown; converted to an index of £bn, 5 QALY are assumed lost for each COVID-19 death
Lives lost 9% GDP Loss   15% GDP Loss   20% GDP Loss   25% GDP Loss
  £bn £bn   £bn £bn   £bn £bn   £bn £bn
440,000 66 200 66 330 66 440 66 550
-134 -264 -374 -484
200000 30 200 30 330 30 440 30 550
-170 -300 -410 -520
100000 15 200 15 330 15 440 15 550
-185 -315 -425 -535
50000 8 200 8 330 8 440 8 550
-192 -322 -432 -542
20000 3 200 3 330 3 440 3 550
-197 -327 -437 -547


We can look at these figures in a different way by asking, given these outcomes what is the cost/year of a life saved or how many times greater is the cost of Lockdown than the notional value of the life/years saved? The answer is given in table 2 (below). With a 9% GDP loss and the saving of 440,000 lives the cost of each saved life/year would be £90,909 which means the cost of saving the life was only three times the value of the life saved. Conversely, if we end up with a cost to the economy of 25% of GDP and Lockdown only saving 20,000 lives then the cost per life/year saved is £5.5m and the cost of saving each life equates to 183 x the value of the life years saved.

Table 2

  Cost/life year saved Cost v benefit multiple   Cost/life year saved Cost v benefit multiple   Cost/life year saved Cost v benefit multiple   Cost/life year saved Cost v benefit multiple
  9% GDP Loss   15% GDP Loss   20% GDP Loss   25% GDP Loss
  £     £     £     £  
440,000          90,909             3.0       150,000             5.0       200,000             6.7       250,000             8.3
200000       200,000             6.7       330,000           11.0       440,000           14.7       550,000           18.3
100000       400,000           13.3       660,000           22.0       880,000           29.3    1,100,000           36.7
50000       800,000           25.0    1,320,000           41.3    1,760,000           55.0    2,200,000           68.8
20000    2,000,000           66.7    3,300,000         110.0    4,400,000         146.7    5,500,000         183.3


One conclusion that cannot be ignored is that in all these findings that while we are happy to value a lost non-Covid-19 death at £30,000 per year/life lost we are putting a value on the life/years lost to Covid-19 at between 3 and 183 times greater than this.

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6 thoughts on “Nick Rendell: Comments on a Covid cost-benefit analysis

  1. I think there is a big problem with the Imperial assumption that the people over 80, who died from Covid, would have lived another 5 to 10 years. A large percentage of the old people who died had at least one metabolic co-morbidity. Because of their cancer, diabetes or heart disease they were not likely to live a lot longer. Plenty of older people contracted Covid but did not die. It is reasonable to assume that they survived because they were metabolically more healthy than their peers who did die. While a cost/benefit analysis is a good idea, I think it would be far useful to research the immunity factors of the elderly people who survived, so we can prepare the vulnerable for a better outcome when the next virus comes along.

  2. “What Difference, At This Point, Does It Make?” was famously asked by a political scoundrel whose wicked actions had deliberately killed lots of people. At least our shower are incompetent rather than murderous.

    Personally I’m inclined to put much of the blame on the people they consulted: the charlatans of mathematical modelling, and the dud scientists.

    They seem not to have consulted anyone capable of back-of-the-envelope economic calculations. But then imagine the howls of fake outrage from the media if they had consulted such a person.

  3. Nearly half UK deaths from Covid were in care homes. The reason anyone is in a care home is because they are in poor health. One figure I’ve seen is 2 years left expectancy in a care home.

    Given that the Covid casualties in care homes may have been sicker than average or in fact killed by something else along with Covid I think a 1 year life loss is plausible for care home deaths. Certainly nowhere near 10.

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