Cold hard maths
April 15, 2020
Paul Christensen posted a comment and directed my attention to something he had written in the SCMP
The cold, hard maths of whether a coronavirus shutdown is worth everyone’s loss of quality of life
Do the benefits of the Covid-19 economic shutdown justify the costs? This is a fundamental question that governments need to address, and they should address it explicitly, regardless of how uncomfortable it may make people feel.
In his comment he said that “Much more rational analysis is needed on whether the years of poverty that will result for many people from this lockdown are worth the lives saved.”
Rational analysis like this?
An argument for lockdowns is that the alternative would be an overloaded hospital system. But this shouldn’t be a factor that overrides all others.
There is no doubt that a rigorous triage system could be put in place to keep the hospital system functioning for cases where larger numbers of QALYs are at stake. If society keeps running, then the government could spend the tax revenue it receives on expanding hospital capacity so that fewer hard decisions have to be made when, say, Covid-25 comes along.
Yes, sure, a rigorous triage system would solve the problem.
And after a few thousand (mainly old) people had died we'd definitely spend more money on hospitals and facilities and nurses so we’d be ready next time.
No, of course we wouldn’t. Both in the US and the UK (and elsewhere, no doubt) there have been exercises done to test readiness for a pandemic. And governments have decided not to spend the money needed to be fully prepared. Hospitals in the UK were running at close to full capacity when it is recommended that they should be operating at around 85% in order to be able to handle any emergencies. That, of course, is because of lack of money.
Currently hospitals in most developed countries are just about coping, but many staff are exhausted from over-work, and tough decisions have to be made about who can be transferred to Intensive Care.
This is with lockdowns in place. What would it be like without them?
Lockdowns aren’t just needed to ensure that hospitals will be able to handle the outbreak. There’s also the hope that better treatments can be identified and a vaccine can be found (and progress seems fairly encouraging on both fronts).
Paul Christensen seems to be getting carried away:
The current restrictions on economic activity are condemning many thousands of people who had basically comfortable lives to years or decades of poverty. There may be significant increases in suicide, divorce and domestic violence rates as people are cooped up to an unprecedented degree in small living spaces
Decades of poverty? Restrictions apply to a relatively small part of the economy. We are talking about Hong Kong here, aren’t we?
[To summarize what I wrote in my response by Paul's comment, I accept that some people will suffer significant hardship from the lockdown (UK) / restrictions (HK). But the solution to that is not to accept more deaths it's for the government to make payments to people who lose their jobs.]
And Hong Kong apartments are definitely small, but we don’t have a lockdown and the only people who can’t go out are those who are in quarantine. Those social problems are real, but they existed before COVID-19 and they will be there afterwards. The impact of a few thousand people being in quarantine for 14 days is not really significant.
Certainly the restrictions everywhere will be eased in the coming weeks and months and maybe Hong Kong (and Singapore) offer a template for how it can be done:
‘Suppress and lift’: Hong Kong and Singapore say they have a coronavirus strategy that works
Despite setbacks, Hong Kong’s and Singapore’s targeted strategies for fighting COVID-19 may yet succeed—and provide a model for other countries emerging from their first wave of cases.
Thanks for reading the piece and engaging in discussion.
The title I proposed to the SCMP for the piece was "Why don't we do this every year?", the point being that it is now clear that having this lockdown has saved hundreds of lives from influenza. Are lives lost to influenza somehow less valuable than those lost to Covid-19? If not, then surely we should all accept the hardships necessary every year to save those lives?
In terms of analysis, what I am asking for is data and calculations. These are extremely lacking in Hong Kong at the moment. I don't claim to have the answers to any of these questions, not least because I don't have the data to do the analysis.
And to your point about decades of poverty, let me posit an example:
Take a single person who is on median income (that's about HK$18,000/month). They pay about HK$1150/month in tax and MPF. They just get by renting a small apartment/room for about $9,000 per month. They pay an average (over the year) of about $1000/month for electricity, mobile phone, internet, water, maybe gas. They pay about HK$500/month for travel, mainly to and from work. They are left with about HK$200/day for food, clothes, toiletries, and (very rare) entertainment. They are unable to build up any significant amount of savings.
And then they are made redundant. Their costs continue; they don't travel, they don't buy clothes or any entertainment, but that's still ~$14,000 per month at least. They have to borrow money almost immediately. After 6 months they are $84,000 in debt. Let's assume, charitably, that they can borrow money at 20% interest per year. So that's $1400/month in interest charges alone. Maybe they managed to get CSSA for those 6 months, so that's about $15,000 less. So maybe $69,000 in debt and $1100/month in interest.
Then maybe after 6 months they get a job back at the old salary. If they try really hard, with no entertainment, no eating out, and so on, they can probably just about eke out the $1100 interest every month and not go further into debt. But they are still $69,000 in debt with no apparent escape route.
And remember that 50% of people earn less than this, and many of them have family to support, and that in practice unsecured debt from credit cards or finance agencies tends to be around 30%/year interest not 20%.
The result is clear: putting tens of thousands of people out of work for, say, 6 months condemns them to unrepayable debt for the foreseeable future. Let's say that they are 35 years old and that this debt reduces their quality of life (because they have to forego any entertainment or discretionary income just to pay the interest) for the next 30 years by 20%. For each person thus affected the impact is -6 QALYs.
Now look at the people whose life might be shortened by a Covid-19 infection. The vast majority of them have chronic underlying illnesses and are old. I don't have any data here (I wish I did), but let's guess that the average life expectancy in the absence of Covid-19 of those dying with it is 10 years of quality life (which, frankly, I feel is very generous). So each life lost is worth 10 QALYs.
In this simplified analysis the maths then says: for every 600 people who we could save from Covid-19 by locking down, it is "worth" condemning 1000 people to that life of indebtedness. Or, in other words, if the lockdown puts 100,000 people into that life, then it is worth doing if it saves 60,000 deaths from Covid-19.
Now obviously the government should have much better numbers than me to perform this analysis more accurately. I'm just trying to illustrate the point I was making. But my assumptions would need to be very wrong, or the death rate from Covid-19 would need to be far far higher than it appears to be for the current policies to be justified.
That's the point I was trying to make. I would love to see your (or anyone else's) quantified analysis of these issues.
Posted by: Paul | April 15, 2020 at 07:05 PM
As you say, the problem is that we don't have that data. Plus the QALY calculation is always going to be somewhat subjective.
My answer to all this is simple (though you might disagree). Governments need to ensure that people who lose their jobs get money so that they can live reasonably normally until this is over.
If we are talking about the UK, then the issue is the people who don't qualify for any of the schemes that are available (such as 80% of salary when placed on "furlough").
For Hong Kong, there is very little being done to help individuals. The HK$10,000 per person payment is not going to be paid until July, which is ridiculous, and it's being paid to non-residents who happen to have a Permanent ID card (which might make sense if this allowed them to make payment immediately, but they aren't doing that).
The Hong Kong government has plenty of money and could easily afford to do more.
Posted by: Chris | April 16, 2020 at 12:59 PM
I don't disagree at all. But governments can't, in general, just print extra money - it's our money (from taxes of various sorts) that they are simply redistributing. So then the question becomes, what is the best way of redistributing it? I'm absolutely all for a universal unemployment benefit at a decent level - even if this was at the official poverty line of $9,000/month (half of median wage) then it would still be four times more than they utterly ridiculous CSSA. If that meant that the government didn't have the cash to line the construction cartel's pockets through absurd projects like the East Lantau Metropolis then so much the better.
But again, we need to see the calculations, and, again, I'm sorry if this makes you uncomfortable, but at some point in those calculations you would need to put a value on a life (or a QALY) "saved" through the measures.
The point of my article was not to propose answers (although you and several other commenters have tried to infer that I did). I simply want to have a public discussion which is backed by some rational, quantified analysis, and not just by emotional appeals to "save lives".
Posted by: Paul | April 19, 2020 at 07:14 PM
Actually, I don't disagree with you at all on the principle of doing proper analysis of cost vs. QALY. Tim Harford (author of many excellent books and presenter of the BBC's "More or Less" radio show and podcast) wrote about this recently in The Financial Times, and it's now available on his own website: How do we value a statistical life?
"At the EPA’s $10 per micromort, it would be worth spending $100,000 to prevent a single infection with Covid-19......If an economic lockdown in the US saves [2 million] lives, and costs less than $20tn, then it would seem to be value for money."
He freely admits that those calculations might be wrong, but concludes that it's better to err by doing too much than too little. I agree with him!
However, I am very interested to see the results of countries arriving at a different strategy. The most obvious example is Sweden not imposing a "lockdown", but sadly they seem to have failed in the execution, notably in care homes for the elderly. Singapore seemed to have got it just about right, but forgot about their foreign workers living in dormitories.
You claim that you didn't propose answers, but you did say that money saved by not treating some people could then then be invested in improving health services for a future outbreak of something similar. I still think that is a fanciful notion, and it was that to which I took exception and certainly not the idea of doing proper analysis.
Posted by: Chris | April 19, 2020 at 09:49 PM