For how long is lockdown politically sustainable?

Introduction

Lockdown has economic costs. It also has the benefit of saving many lives. As lockdown goes on, it is likely that people will start to think about whether the economic losses they are suffering are justified by the lives saved. In the UK, this cost-benefit analysis is not yet part of the public debate; in the US, Donald Trump and others have already begun to talk about the trade-off.

The Deputy Chief Medical Officer has said that lockdown could continue for six months. But politicians, not scientists, will decide its duration. For the sake of this paper I think of politicians as a pass-through mechanism that connects public opinion to policy, and I think of public opinion as a single aggregate (as if it was the opinion of one person). In this framework, the question of how long lockdown will be politically sustainable is the same as the question of when public opinion will decide that the costs of lockdown outweigh the benefits.

To be clear, I am not recommending any particular course of policy. Rather, I am trying to understand what is likely to happen politically as lockdown continues. Although applying the concept of cost-benefit analysis to the question of saving lives seems heartless, it is done all the time in any decision about expending resources to improve health, both by governments and by individuals (for example, in deciding how much to spend on health insurance). The fact that we do not write down the calculations does not mean that they are not implicitly being made. Politicians are presently making the judgement that the costs of lockdown are worth suffering to control the epidemic (I tend to agree).

This paper sets out a very rough model of the costs and benefits of lockdown. It concludes that public opinion may accept a three-month lockdown, but not a six-month lockdown. The conclusion depends on the amount of economic damage that is done. If GDP falls 20% in three months, lockdown is still accepted; if it falls 40%, lockdown is seen as too costly. It also depends crucially on how much people are prepared to pay to save life, for which I have used the best estimate I can find.

Quality-adjusted life years

In the UK, the National Institute for Health and Care Excellence uses a concept called the quality-adjusted life year (QALY) to decide whether to recommend that treatments be made available on the NHS. The QALY is a way of thinking about the benefit of a medical intervention. It combines the number of additional years of life provided by the treatment with the quality of life experienced. The most expensive treatments recommended cost ￡20,000 to ￡30,000 per QALY.

In order to model the cost-benefit analysis that the average person will do for the COVID-19 lockdown, we need to know: (i) how many QALY are saved by lockdown, (ii) what is the economic cost of lockdown and (iii) how much economic cost are people prepared to bear in order to save one QALY. All three of these quantities are highly uncertain, making this very much a back-of-the-envelope analysis.

How many QALY are saved by lockdown?

To calculate the number of QALY saved by lockdown I use the following information.

1. Expected COVID-19 case-fatality rates by age from the 16 March Imperial paper.
2. UK population broken down by age.
3. Estimated quality-adjusted life expectancy by age group from this paper.

All three data sets are broken down by age in a different way. The UK population statistics have the most granular breakdown. I map case-fatality rates to the broader population by (i) simply applying reported rates from the wider age buckets in source (1) above to the narrower age buckets in source (2) for younger people (this makes little difference because fatality rates are low) and (ii) by regressing the natural logarithm of case fatality rates on age bucket mid-points for older people. Data can then be aggregated to fit the four age buckets used in source (3), which are under 45, 45-64, 65-74, and 75 and over. I assume that with no controls at all 81% of the population would become infected and that the number of deaths would be halved by the milder measures of quarantining cases, household quarantine and social distancing of the over-70s (both taken from the Imperial paper). I compare the case of full lockdown to a case where milder control measures are used. My back-of-the-envelope model gives roughly the same expected number of deaths as the Imperial paper: 539,000 with no controls and 269,000 with mild controls. Deaths are assumed to stop completely in lockdown.

Putting all of this together, the model suggests that 3,069,000 QALY are saved by lockdown in the UK relative to milder control measures.

What is the economic cost of lockdown?

Capital Economics has estimated that UK GDP could fall by 15% because of the lockdown, but has also said that the fall could be 20-40%. I assume that these falls would take place in one calendar quarter, and after that the GDP lost remains a fixed percentage below where it would have been otherwise. When lockdown is relaxed, GDP immediately snaps back to where it would have been without lockdown, such that the output lost from lockdown is just the output lost while lockdown is in force.

I take UK GDP in Q4 2019 as the starting point. I guess that the virus, together with milder control measures, would have caused a decline of 5% in GDP in the absence of lockdown measures, which means that the GDP cost of lockdown is 10% in the base case and 15% to 35% in the downside case given by Capital Economics.

On this basis the cost of lockdown is between ￡52bn and ￡183bn per quarter.

How much economic cost are people willing to bear to save one QALY?

The economic value of life is something that economists approach in two ways. The first way is to look at “revealed preferences”, for example by finding out how much extra people are paid for working in dangerous jobs. The second way is to look at “stated preferences”, asking people how much they think should be paid to save life in hypothetical cases. The first method tends to find much higher numbers for the economic value of life than the second. For this analysis, I favour the “stated preferences” method, which tends to give a lower value, because I am creating a model of political action and that will depend on the explicit judgements people make when thinking about COVID-19 rather than their behaviour in terms of taking risky jobs and so on.

I use this relatively recent literature review to find the economic value of one QALY. Omitting one paper that is an extreme outlier, the trimmed mean value of one QALY derived from “stated preference” studies is ￡25,381. Note that estimates of this value vary widely across different studies.

Putting it all together

We now have estimates for how many QALY are saved by lockdown and what lockdown will cost, which allows us to calculate the economic cost per QALY saved. We can compare this to the amount people normally say they are willing to pay per QALY.

In the following chart, I assume that the economic cost is the same each quarter, that the lives saved by lockdown are all saved at the point when lockdown ends and that the discount rate is zero (again, simple model!).

Observations

In the model:

1. If GDP is reduced an extra 35% by lockdown then, based on research into people’s stated views of the value of life, the cost exceeds the benefit in terms of lives saved.
2. If GDP is reduced by an extra 10-15% by lockdown, a three-month lockdown is consistent with people’s stated views: the cost is worth paying.
3. The costs of a two-quarter (i.e., six-month) lockdown are above the estimate of the average person’s view on the value of life.

Conclusion

This is a very rough model indeed. However, it shows that reasonable estimates of how much lockdown could cost and how much people are normally prepared to pay to save life are consistent with the idea that people will see a three-month lockdown as being justified and a six-month lockdown as being too economically costly.

UPDATE 29 March 2020

I have found some more estimates of quality-adjusted life expectancy by age that are UK-specific and broken down into more age buckets. These do not make a difference to the broad conclusions above. Updated chart below.