Let’s look at the numbers • The Berkeley Blog

by nyljaouadi1
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There have been plenty of COVID editorials about how it would be wrong to trade lives to save businesses, and also (less stridently) that the cost of shutting down the country is “unacceptable.” The problem is, practically all commentators treat lives and GDP as a binary choice, when what we really want is to know what the reasonable tradeoffs look like. Because whatever we do, there are going to be tradeoffs, and we can’t call our choices intelligent, much less moral, until we have looked them in the face.

Justifying the Lockdown. 

We begin with a baseline case. Suppose government just stood back and let the epidemic run wild. How do the lives lost compare to the cost of a lockdown ?

Start with the lockdown. The U.S. is currently running at about 3/4 its normal GDP, so if the lockdown goes on for four months (which seems reasonable, see below) it will cost about $2 trillion.

As for the value of lost lives, suppose that the lockdown had never happened. Then simple models where infectivity (the famous R0) = 3 predict that the U.S. gets herd immunity when 66% of the population has had the disease and become immune. With 2% mortality that’s 4 million dead. Economists and regulators normally say lives are worth about $10m each, so that’s $4 trillion and well-worth a lockdown if the country can substantially reduce casualties.

There are many caveats, but two big ones come to mind here. The first is about putting a dollar value on human life. The short answer is that you have to start someplace if you want to end up making a dollars-to-dollars judgment. But the long answer is worth mentioning. Because attaching a dollar value to life is actually pretty reasonable.

All of us have a limited lifespan and the opportunity to spend it different ways. This means that we can make trades, and this includes trading a greater risk of dying early for the chance to live more fully. Workers in hazardous professions like lumberjacking do this trade so routinely that it has a market price. (This is not very different from what the philosophers say: Camus’ Myth of Sisyphus is emphatic that the best lives always make trades.) So like it or don’t, but that’s where the $9m figure comes from.

The other point is specific to epidemics. We talk about trading economics for public health, but this is at least partly an illusion. Once the epidemic takes off, people will start quarantining no matter what government says. So the economic cost might not really be avoidable. The best the government can do is cajole citizens in the direction of being more reasonable. (We should remember this when, inevitably, the politicians start second-guessing the pandemic’s early stages. Suppose California had ordered social-distancing on February 1. Would anyone have listened?)

Can We Do Better? 

The argument so far is that the cost of a shutdown is less than the value in lives we expect to lose. But the real question is whether a shutdown will do any good, i.e. how many lives it can save. The basic point is that our 2% mortality figure is not really a constant. Once the hospitals are overwhelmed, people who should have gotten hospital care, but don’t, will die about 10 times more frequently.

This is why governments want to “flatten the curve.” Granted that people will still get sick, it’s still better to keep the rate down to levels that give everyone a fighting chance. Press accounts of COVID suggest a back-of-the-envelope estimate on how fast the country can follow such a trajectory and get back to normal. Consider:

  • There is 1 hospital bed in America for every 1,000 people. Say we can surge that to two beds and one is dedicated to COVID patients.
  • Only 1 in 20 COVID patients will ever need a bed. That means the US can safely have 20/1000 x 300m = 15 million people sick at the same time.That’s well above the 0.5 m who are sick today. Then again, the disease hasn’t really taken off yet. Most cases are in the Tri-State area which hosts less than 10% of the country’s population.
  • Suppose the average person is sick for a week. Then R0 falls below 1 after 33 weeks, after which cases fall even without social distancing so that the epidemic dies out on its own. The numbers are even more favorable if the current inadequate testing means that COVID is asymptomatic and undetected 50% of the time. Then it only takes 16 weeks = 4 months to get there.

In practice, of course, charting an optimal path through the pandemic will be tough. This is because none of numbers in our calculation is particularly well known. Probably the biggest uncertainty has to do with infectivity (R0) which depends among other things on social distancing. The trick will be to relax distancing slowly enough that the number of new cases stays flat. But if our leaders relax too fast it will take weeks before the mistake becomes visible as an increase in new cases. That ought to make government cautious until testing improves.

Vaccines

So far we have assumed that there is only herd immunity, but scientists tell us that the country should (with luck) have vaccines in 18 months. This makes the situation markedly more hopeful. For now, the most extreme outbreak is New York City. As of mid-April, social distancing had driven the City’s new case rate down to 6,000 per day. The number is still falling, but suppose for the sake of argument that it plateaued there. Then it would take New York 26 months to reach herd immunity (60% x 8m New Yorkers).

In this scenario, roughly one-third of the cases arrive after there’s a vaccine (or cure) so that they never become casualties at all. All of these people would owe their lives to New York’s current-and-very-stringent social distancing rules.

The big question concerns the economy: How much can New York relax distancing without forcing new cases back up again? At the moment, government knows little beyond the enormously encouraging fact that strong distancing is an effective way to reduce R0. When leaders do relax distancing, they will be learning as they go.

How Fast Will The Economy Come Back?

The final big uncertainty involves just how fast the economy will recover. Whether it will be short and sharp or more U-shaped is unknowable. But we should be at least somewhat optimistic. France’s GDP ran at 70% in WWI (all those guys in the trenches followed by 1918 flu) and 50% in WWII (all those slave laborers deported to work for the Nazis). Yet it came back quickly after both wars. So while our estimate of one month’s GDP loss is plainly a guess, it is at least consistent with precedent.

In the meantime Americans ought to give themselves credit. The lockdown was a good decision, and since then we have shown that we can “bend the curve” even in ultra-dense New York City. The task now is to steer ourselves back out of the crisis. But we have made a good beginning.



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