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Nothing matters but reproduction rate R

The new strain and the need for speed by Alex Tabarrok on Marginal Revolution makes an excellent point. The new strain is more transmissible. That means the reproduction rate R is higher. For given behavior, the exponential growth is faster. If or where R was a bit below one and the virus contracting, now the virus ...

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The new strain and the need for speed by Alex Tabarrok on Marginal Revolution makes an excellent point. The new strain is more transmissible. That means the reproduction rate R is higher. For given behavior, the exponential growth is faster. If or where R was a bit below one and the virus contracting, now the virus is spreading exponentially again. 

 "a more transmissible variant is in some ways much more dangerous than a more severe variant. That’s because higher transmissibility subjects us to a more contagious virus spreading with exponential growth, whereas the risk from increased severity would have increased in a linear manner, affecting only those infected."

The recurring failure of our government response to this pandemic has been to get behind exponential growth. Here we go again. Wasted months when the vaccines were known to be safe. Wasted weeks to have thanksgiving dinner rather than  approve vaccine. Snafu after snafu in vaccine distribution. And CDC rationing that is designed to just about nothing to stop the spread. 

When I suggested free market vaccine allocation on top of government distribution, critics lambasted me. Only the government can artfully offset externalities and information problems, they say. Implicitly every single dose must be requisitioned to the government's majestic planning effort, not one may be sold letting willingness to pay guide the usefulness of the vaccine. Not even a hospital emergency room treating covid patients may spring money and butt the line.  

There is one big externality: infectious diseases are, well, infectious.  If you want to stop a pandemic that is growing exponentially there is one rule. Give it fast to the people most likely to get it and to spread it to others. Over and over Nothing Matters but the Reproduction rate.

This has been about the last criterion on the CDC's allocation scheme. First it goes to protect old folks in nursing homes. The UK gave its first dose to a 91 year old. Germany to a 101 year old. That's nice. Then to old people in general, even though most non-nursing home old people are retired and doing fine staying home. 

Well, it appears kind-hearted to protect those who are most likely to die if they get it. It is a purely private benefit, so one might ask why they aren't asked to pay anything for it. So it's really an income transfer to old people in the form of a vaccine. 

Then as widely reported, "equity" has become their mantra, explicitly racial but also geographical. 

OK, I like old people and social justice too. But if that same vaccine were given to a front line health care worker, or to a young partier who just can't seem to help themselves from giving it to 25 other people, including 3 grandparents, we solve the disease, we address the externality, and we protect old people, much more effectively.

This is a hard choice, but it is one that competent public health (and military) bureaucracies are supposed to know how to handle. It's a classic trolley problem with one person on the left and thousands on the right. Do you first give a vaccine to old people who are likely to die if they get it, freeing them to go out a bit and freeing nursing homes from having to implement stringent protection requirements? But in doing so you let the disease run rampant and the economy tank for another six months. Or do you give it in a way that stops the pandemic, to people who individually won't die but will thereby not spread the disease? The overall death rate is lower in the latter case, but only in secondary infections, which you, the CDC cannot claim to have saved. 

Public health knows how to do this. Or used to know how to do this. When eradicating smallpox, and when an outbreak was noticed, they ring-fenced the outbreak and vaccinated in order to contain the spread of the disease. They did not give it randomly to the whole population in a country, taking six moths to a year to get everyone, protecting people by age and demographic class, and meanwhile letting the disease spread exponentially. 

When combating exponential growth and heterogeneous spreaders, targeting matters and speed matters even more. Alex

"the FDA should have approved the Pfizer vaccine, on a revocable basis, as soon as the data on the safety and efficacy of its vaccine were made available around Nov. 20. But the FDA scheduled it’s meeting of experts for weeks later and didn’t approve until Dec. 11, even as thousands of people were dying daily. We could have been weeks ahead of where we are today. Now the epidemiologists are telling us that weeks are critical.

It's not really that "thousands were dying daily." It's that the disease was growing exponentially in this crucial 20 days, and thousands upon thousands will die in a few months as a result of delay. A lesson which should have been painfully obvious from the January-March delays in addressing travel, not allowing tests to be used, not ramping up tracing while it could do any good, and so on. 

In a year, our bureaucracies just have not wrapped their heads around a simple fact. The point is to stop the exponential spread of a disease, not (just) to protect individuals. Tests should be evaluated by their usefulness in stopping spread -- and there imperfect is far better than nothing -- not only by their usefulness in diagnosing a given patient for treatment. Vaccines, used right, can stop exponential spread of a disease, not just protect individuals -- or, more accurately, enable them greater social interactions. 

So what good has been achieved by banning a private market on top of government allocation? The government is basically not even thinking about the prime market failure -- the externality that if I get it I might give it to you.  In doing that it is mostly just achieving an income transfer to favored groups. 

Suppose there were a free market in vaccines. The only difference is, the government would have to buy at market prices. How would this look different? First, I think we would see much quicker allocation to health workers. Even if the government were not willing to buy and give it to them, hospitals would figure out they need to give it to their covid staffs immediately, and pay whatever it takes. They are forbidden from doing that now. Second, people and businesses that know they are host to spreading events could buy the vaccine. There is a lot of private incentive to combat an externality! Third,  the government could do exactly what it is doing now. It just might have to pay a bit more. If you are a huge fan of the CDCs allocation scheme, and its brilliant targeting of externalities, public goods, information problems and every other fable from econ 101, good for you. It can keep doing that. The treasury just might have to pay a bit more. 

So the ban on private sales comes down to one thing only. Money. The government is keeping down the price it has to pay by forbidding you and me and businesses that could hire back lots of employees from bidding for the vaccine. 

This is the same government that has borrowed $5 trillion dollars already, and is currently discussing $2,000 checks, far more than the free-market cost of a vaccine. Penny wise and pound foolish.  

I think we can summarize epidemiology by the one maxim: nothing matters but the reproduction rate. R<1 and it goes away. R>1 and it explodes. And given a reproduction rate, nothing matters but how quickly you get on top of exponential growth. Time is exponentially valuable. 


John H. Cochrane
In real life I'm a Senior Fellow of the Hoover Institution at Stanford. I was formerly a professor at the University of Chicago Booth School of Business. I'm also an adjunct scholar of the Cato Institute. I'm not really grumpy by the way!

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