Tag Archives: Cost-Benefit

The High Cost of Masks

In my debate last night with Tomas Pueyo, after I emphasized the high costs of lockdowns he said lockdowns are over. From now on we’ll let people go out, as long as they (M) wear masks and keep 6 feet apart when not at home. Which let me to wonder: just how much cheaper is M than lockdowns?

So I tried some Twitter polls. I asked:

  1. [1.14%] If you by law had to M unless you paid, what % of income would you pay?
  2. [4.6%] If you didn’t have to, but were offered % of income to M, what would it take?
  3. [19.6%] Like (2), except it is 2019 and there is no pandemic.
  4. [8.0%] Like (3), except half of the folks in your area are already M-ing
  5. [5.2%] Like (4), except only masks, no 6ft distancing.
  6. [15.8%] Like (4), except both at home and away.

In brackets before each question is the median answer (using lognormal fits to % responses re theses 4 options: <3%, 3-6%, 6-12%, >12%). Note how widely these estimates vary!

The following factors plausibly influence these responses: (A) personal pain and trouble of wearing masks and keeping apart, (B) endowment effect of preferring to stick with what current law seems to endorse, (C) not wanting to look or act too differently from others nearby, (D) wanting to be and seem pro-social and helpful in slowing the pandemic, and (E) wanting to support your side of current culture wars.

The big variation in median answers suggests that non-A effects are big! And the big variation within each poll also suggests that these costs vary greatly across individuals. We might gain lots from policies that let some pay to avoid M-like policies.

Question (4) seems to me to offer the best estimate of the real social cost of doing M. It has the best chance of avoiding effects C & D, and I don’t see a way to avoid E. Regarding B, I think we do want the endowment effect to go this direction, because in fact M was not the legal default a year ago. Yes we enjoy helping our community in a crisis, but we wouldn’t endorse creating crises just to enjoy such effects. So we shouldn’t include then when calculating how much to avoid or reduce crises.

Now this 8.0% median (27% mean) of income cost of masks and public distancing doesn’t include all costs; businesses and other places must also pay to accommodate your distancing. But it is probably a big fraction of costs. And it is quite a bit lower than the 32% of GDP estimate for recent strong lockdowns.

However, my estimate of the total cost of having 50% of the population infected at 0.5% IFR was 3 weeks of income, or 6% of one year’s income. So if we wear masks for 9 months, that single cost equals the entire cost of failing to contain. So as with lockdowns, we should be wary of spending more to prevent infections than the infections would cause. Yes, we should be willing to overspend for very effective preventions, with high elasticity. But masks aren’t plausibly such a very effective method.

Added 30May: I added new polls, included on the above list as #5,6. Seems more than half the cost is from the masks alone. It also seems that masks at home would give similar benefits, and the above suggests that it costs about the same too. So why isn’t there more of push to require that?

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Time to Mitigate, Not Contain

In a few hours, I debate “Covid-19: Contain or Mitigate?” with Tomas “Hammer & Dance” Pueyo, author of many popular pandemic posts (e.g. 1 2 3 4 5 6 7). Let me try to summarize my position.

We have long needed a Plan B for the scenario where a big fraction of everyone gets exposed to Covid19, and for this plan I’ve explored variolation and other forms of deliberate exposure. To be ready, variolation just needs a small (~100) short (1-2mo.) trial to verify the quite likely (>75%) case that it works (cuts harm by 3-30x), but alas, while funding and volunteers can be found, med ethics panels have consistently disapproved. (Months later, they haven’t even allowed the widely praised human challenge trials for vaccines, some of which would include variolation trials.)

One big reason we aren’t preparing enough for Plan B is that many of us are mentally stuck in a Plan A “monkey trap.” Like a monkey who gets caught because it won’t let go of a tasty nut held in its fist within a gourd, we are so focused on containing this pandemic that we won’t explore options premised on failing to contain.

Containment seeks to keep infections permanently low, via keeping most from being exposed, for at least several years until a strong lasting vaccine is widely applied. Mitigation, in contrast, accepts that most will be exposed, and seeks only to limit the rate or exposure to keep medical systems from being overwhelmed, and to maintain enough critical workers in key roles.

Succeeding at containment is of course a much bigger win, which is why containment is the usual focus early in a pandemic. Catch it fast enough, and hit it hard enough with testing, tracing, and isolation, and the world is saved. But eventually, if you fail at that Plan A, and it grows big enough across across a wide enough area, you may need to admit failure and switch to a Plan B.

And, alas, that’s where we seem to be now with Covid-19. Over the last 7 weeks since the cases peak the official worldwide case count has been rising slowly, while official deaths are down ~25%. In the US, deaths are down ~1/2 since he peak 6 weeks ago. You might think, “yay, declines, we are winning!” But no, these declines are just too slow, as well as too uncertain.

Most of the US decline has been in New York, which has just now reached bottom, with no more room to decline. And even if US could maintain the rate of declining by 1/3 every 6 weeks, and repeat that 5 times over 30 weeks (= 7 months), not at all a sure thing, that would only bring daily US cases from 31K at the peak down to 4.2K. Which isn’t clearly low enough for test and trace to keep it under control without lockdown. And, more important, we just can’t afford to lockdown for that long.

You see, lockdown is very expensive. On average, around the world, lockdowns seems to cost about one third of local average income. Yet I estimate the cost of failing to contain, and letting half the population get infected with Covid-19 (at IFR ~0.5%), to be about 3 weeks of income. (Each death loses ~8 QALY.) So 9 weeks of strong lockdown produces about the same total harm as failing to contain! And where I live, we have almost had 10 weeks of lockdown.

If without lockdown the death rate would double due to an overloaded medical system, then paying for less than 9 weeks of added lockdown to prevent that is a good deal. But at that point, paying more than an additional 9 weeks of strong lockdown to prevent all deaths would not be a good deal. So our willingness to pay for lockdowns to cut deaths should really be quite limited. Sure, if we were at a tipping point where spending just a bit more would make all the difference between success and failure, then sure we should spend that bit more. But that’s just not plausibly where we are now.

Yes, sometimes we pay more to prevent harm than we suffer on average from such harms. For example, we pay more for door locks, and security guards, than we lose on average from theft. But those are very effective ways to prevent harm; paying 10% more there cuts harms by much more than 10%. Yet according to my Twitters polls, most see 10% more spent on lockdown as producing much less than 10% fewer deaths. If so, we should spend much less on lockdowns than we suffer from pandemic deaths.

Now if Pueyo is reading this, I suspect he’s screaming “But we’ve been doing it all wrong! Other possible policies exist that are far more effective, and if we use them containment becomes cost-effective. See Taiwan or South Korea.” And yes, other places have achieved better outcomes via better policies. We might not be able to do as well as them now that we’ve lost so much time, but we might well do much better than currently. Pueyo has sketched out plans, and they even seem to be good sketches.

So if we suddenly made Tomas Pueyo into a policy czar tomorrow, with an unlimited budget and able to run roughshod across most related laws or policies, we’d probably get much better Covid-19 outcomes, perhaps even cost-effective containment. But once such a precedent was set, I’d fear for the effectiveness of future czars. Ambitious politicians and rent-seekers would seek to manufacture crises and pseudo-Pueyo-czar candidates, all to get access to those unlimited budgets and legal powers.

Which is a big part of why we have the political systems we do. All around the world, we have created public health agencies tasked with pandemic policy, and political systems that oversee them. These agencies are staffed with experts trained in various schools of thought, who consult with academic experts of varying degrees of prestige. And all are constrained by local legal precedent, and by public perceptions, distrust, and axes of political conflict. These are the people and systems that have produced the varying policies we have now, all around the world.

Yes, those of us in places which have seen worse outcomes should ask ourselves how strong a critique that fact offers of our existing institutions and political cultures, and what we might do to reform them. But there is no easy and fast answer there; good reforms will have to be carefully considered, tested, and debated. We can hope to eventually improve via reforms, but, and this is the key point, we have no good reason to expect much better pandemic policy in the near future than we have seen in the near past. Even when policy makers have access to well-considered policy analyses by folks like Pueyo.

Now it might be possible to get faster political action if Pueyo and many other elites would coordinate and publicly back one specific standard plan, say the “John Hopkins Plan”, that specifies many details on how to do testing, tracing, isolation, etc. Especially if this plan pretty directly copied a particular successful policy package from, say, Taiwan. If enough people yelled in unison “We must do this or millions will die!”, why then politicians might well cave and make it happen.

But that is just not what is happening. Instead, we have dozens of essays and white papers pushing for dozens of related but different proposals. So there’s no clear political threat for politicians to fear defying. Whatever they do, come re-election time politicians can point to some who pushed for some of what they did. So all these divergent essays have mainly limited short term political effects, though they may do much more to raise the status of their authors.

So if political complexity argues against containment now in many places, why doesn’t that same argument apply equally well to mitigation? After all, mitigation can also be done well or badly, and it must be overseen by the same agencies and politicians that would oversee containment. As there is no escaping the fact that many detailed policy choices must be made, why not push for the best detailed packages of choices that we know?

Imagine that you were driving from A to B, and your first instinct was to take a simple route via two interstate freeways, both in big valleys. Your friend instead suggests that you take a backroad mountain short cut, using eight different road segments, many of them with only one lane, and some very wiggly. (Assume no phone or GPS.) That plan might look like it would take less total time, but you should worry about your competence to follow it. If you are very tired, bad at following road directions, or bad at sticking to wiggly roads, you might prefer to instead take the interstates. Especially if it was your tired 16 year old teen son who will do the driving.

Like the wiggly backroad short cut, containment is a more fragile plan, more sensitive to details; it has to be done more exactly right to work. To contain well, we need the right combination of the right rules about who can work and shop, and with what masks, gloves, and distance, tests going to the right people run by the right testing orgs, the right tracing done the right way by the right orgs with the right supporting apps, and the right rules requiring who gets isolated where upon what indications of possible infection. All run by the right sort of people using the right sort of local orgs and legal authority. And coordinated to right degree with neighboring jurisdictions, to avoid “peeing section of the pool” problems.

Yes, we might relax lockdown badly, but we are relaxing toward a known standard policy: no lockdown. So there are fewer ways to go wrong there. In contrast, there are just more ways to go wrong in trying to lockdown even more strictly. And that’s why it can make sense for the public to say to the government, “you guys haven’t been doing so well at containment, so let’s quit that and relax lockdown faster, shooting only for mitigation.” Yes, that might go badly, but it can’t go quite as badly as the worse possible scenario, where we trash the economy with long painful lockdowns, and yet still fail and most everyone gets exposed.

And that’s my argument for mitigation, relative to containment.

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Constant Elasticity Prevention

While many engaged Analysis #1 in my last post, only one engaged Analysis #2. So let me try again, this time with a graph.

This is about a simple model of prevention, one that assumes a constant elasticity (= power law) between harm and prevention effort. An elasticity of 1 means that 1% more effort cuts harm by 1%. For an elasticity of 2, then 1% more effort cuts harm by 2%, while for an elasticity of 0.5, 1% more effort cuts harm by 0.5%.

Such simple “reduced form” models are common in many fields, including economics. Yes of course the real situation is far more complex than this. Even so, reduced forms are typically decent approximations for at least small variations around a reference policy. As with all models, they are wrong, but can be useful.

Each line in the following graph shows how total loss, i.e., the sum of harm and prevention effort, varies with the fraction of that loss coming from prevention. The different lines are for different elasticities, and the big dots which match the color of their lines show the optimum choice on each line to min total loss. (The lines all intersect at prevention = 1/20, harm = 20.)

As you can see, for min total loss you want to be on a line with higher elasticity, where prevention effort is more effective at cutting harm. And the more effective is prevention effort, then the more effort you want to put in, which will result in a larger fraction of the total harm coming from prevention effort.

So if locks are very effective at preventing theft, you may well pay a lot more for locks on than you ever suffer on average in theft. And in the US today, the elasticity of crime with respect to spending on police is ~0.3, explaining why we suffer ~3x more losses from crime than we spend on police to prevent crime.

Recently, I asked a few polls on using lockdown duration as a way to prevent pandemic deaths. In these polls, I asked directly for estimates of elasticity, and in this poll, I asked for estimates of the ratio of prevention to health harm loss. And here I asked if if the ratio is above one.

In the above graph there is a red dot on the 0.5 elasticity line. In the polls, 56% estimate that our position will be somewhere to the right of the red dot on the graph, while 58% estimate that we will be somewhere above that grey 0.5% elasticity line (with less elasticity). Which means they expect us to do too much lockdown.

Fortunately, the loss at that red dot is “only” 26% higher than at the min of the grey line. So if this pandemic hurts the US by ~$4T, the median poll respondent expects “only” an extra $1T lost due to extra lockdown. Whew.

Added 26May: Follow-up surveys on US find (via lognormal fit) median effort to harm ratio of 3.6, median elasticity of 0.23. For optimum these should be equal – so far more than optimal lockdown!

Added 1Aug: Repeating same questions now gives median effort to harm ratio of 4.0, median elasticity of 0.18. That is, they see the situation as even worse than they saw it before.

Added 22Oct: Repeating the questions now gives median effort to harm ratio of 5.2, median elasticity of 0.10. The estimated deviation between these two key numbers has continued to increase over time.

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2 Lockdown Cost-Benefit Analyses

Back on Mar. 21 I complained that I hadn’t seen any cost-benefit analyses of the lockdown policies that had just been applied where I live. Some have been posted since, but I’ve finally bothered to make my own. Here are two.

ANALYSIS #1: One the one side are costs of economic disruption. Let us estimate that a typical strong lockdown cuts ~1/3 of income of econ/social value gained per unit time. (It would be more due to harm from time needed to recover afterward, and to due to for stress and mental health harms.) If one adds 9 weeks of lockdown, perhaps on and off spread out over a longer period, that’s a total of 3 week’s income lost.

On the other side are losses due to infection. I estimate an average infection fatality rate (IFR) of 0.5%, and half as much additional harm to those who don’t die, due to other infection harms. (E.g., 3% have severe symptoms, and 40% of those get 20% disabled.) I estimate that eventually half would get infected, and assume the recovered are immune. Because most victims are old, the average number of life years lost seems to be about 12. But time discounting, quality-of-life adjustment, and the fact that they are poorer, sicker, and wouldn’t live as long as others their age, together arguably cuts that figure by 1/3. And a standard health-econ estimate is that a life-year is worth about twice annual income. Multiply these together and you get an expected loss of 3 week’s income..

As these equal the same amount, it seems a convenient reference point for analysis. Thus, if we believed these estimates, we should be indifferent between doing nothing and a policy of spending 9 added weeks of lockdown (beyond the perhaps 4-8 weeks that might happen without government rules) to prevent all deaths, perhaps because a vaccine would come by then. Or, if death rates would actually be double this estimate due to an overloaded medical system, we should be indifferent between doing nothing and spending 9 added weeks of lockdown to avoid that overloading. Or we should be indifferent between doing nothing and 4 added weeks of lockdown which somehow cuts the above estimated death rate in half.

Unfortunately, the usual “aspirational” estimate for a time till vaccine is far longer, or over 18 months. And a doubling of death rates seems a high estimate for medical system overload effects, perhaps valid sometimes but not usually. It seems hard to use that to argue for longer lockdown periods when medical systems are not nearly overwhelmed. Especially in places like the US with far more medical capacity.

During the 1918 flu epidemic, duration variations around the typical one month lockdown had no noticeable effect on overall deaths. In the US lately we’ve also so far seen no correlation between earlier lockdowns and deaths. And people consistently overestimate the value of medical treatment. Also, as death rates for patients on the oft-celebrated ventilators is 85%, they can’t cut deaths by more than 15%.

We’ve had about 6 weeks of lockdown so far where I live. A short added lockdown seems likely to just delay deaths by a few months, not to cut them much, while a long one seems likely to do more damage than could possibly be saved by cutting deaths.

Of course you don’t have to agree with my reference estimates above. But ask yourself how you’d change them, and what indifferences your new estimates imply. Yes, there are places in the world that seem to have done the right sort of lockdown early enough in the process to get big gains, at least so far. But if your place didn’t start that early nor is doing that right sort of lockdown, can you really expect similar benefits now?

ANALYSIS #2: Consider the related question: how much should we pay to prevent crime?

Assume a simple power-law (= constant elasticity) relation between the cost H of the harm resulting directly from the crimes committed, and the cost P of efforts to prevent crime:

H = k*Pa,  or  dln/ dlnP = –a ,

where a is the (positive) elasticity of harm H with respect to prevention P. To minimize total loss L = H + P, you set P = (k*a)1/(1+a), at which point we have a nice simple expression for the cost ratio, namely P/H = a.

So, when you do it right, the more effective is prevention at stopping harm, then the larger is the fraction of total loss due to prevention. If 1% more prevention effort cuts 1% of crime, you should lose about the same amounts from harm and prevention. If 1% more prevention cuts 2% of crime, then you should lose twice as much in prevention as you do in harm. And if it takes 2% more prevention effort to cut 1% of crime, you should lose about twice as much in harm as you do in prevention.

This model roughly fits two facts about US crime spending: the elasticity is less than one, and most loss comes from the crimes themselves, rather than prevention efforts. Typical estimates of elasticity are around 0.3 (ranging 0.1-0.7). US governments spend $280B a year on police, courts, and jails, and private security spends <$34B. Estimates of the total costs of crime range $690-3410B.

Now consider Covid19 prevention efforts. In this poll respondents said 3.44 to 1 that more harm will come from econ disruption than from direct health harms. And in this poll, 56% say that more than twice the loss will come from econ disruption. For that to be optimal in this constant elasticity model, a 10% increase in lockdown, say adding 12 days to a 4 month lockdown, must cut total eventual deaths (and other illness harm) by over 20%. That seems very hard to achieve, and in this poll 42% said they expect us to see too much econ disruption, while only 29% thought we’d see too little.

(More on Analysis #2 in the next post.)

In this post I’ve outlined two simple analyses of lockdown tradeoffs. Both suggest that we are at serious risk of doing too much lockdown.

10am: On reflection, I changed my estimate of the lockdown from 25% to 27% of income, and my estimate of non-death harm from as-much-as to half-as-much-as the death harm. So my reference added shutdown duration is now 4 months instead of 6.

12pm: Even if recovery gave immunity for only a limited period, then as long as you were considering lockdown durations less than that period, the above calculation still applies, but now it applies to each such period. For example, if immunity only lasts a year, then these are annual costs, not eventual costs. And that’s only if infection chances are independent each period. If, more likely, it is the same people who at more at risk each year, then in later years gains from lockdowns decline.

29Apr, 3am: We are now at 73 comments, and so far all of them are about analysis #1, and none about analysis #2. Also, tweet on #1 got 18 retweets, tweet on #2 got none.

29Apr, 1pm: In two more polls. over half estimate a 10% increase in lockdown duration gives <5% decrease in deaths, for both world and US. Instead of the >20% that would be required to justify allowing twice the damage of lockdowns as health harms. See also results on the cost of masks.

28May:  I’ve updated the numbers a bit.

22Oct: This analysis from March 22, based on happiness, also suggests far more harm from the economy dip than from deaths. And I confirm my analysis with more recent estimates here.

23Oct: I’ve just shown that the above condition that =dln/ dlnP = P/H holds for any function H(P).

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