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The Amateur Epidemiologist II

Summary:
I am interested in critiquing my understanding of the simplest SIR epidemiological model and also praising a critique of an effort to extend the model and guide policy developed by some very smart economic theorists. First the useful point is that this post by Noah Smith is brilliant. As is typical, Smith argues that the useful implications economic models depend on strong assumptions so economic theory isn’t very useful. He praises simple empirical work instead. I will discuss Smith contra Acemoglu, Chernozhukov, Werning and Whinston and Smith pro Sergio Correia, Stephan Luck and Emil Verner after the jump, but really Smith is better at presenting Smith than I am. It made me wonder. In the simplest model herd immunity stops an epidemic when 1-1/R0 of

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I am interested in critiquing my understanding of the simplest SIR epidemiological model and also praising a critique of an effort to extend the model and guide policy developed by some very smart economic theorists.

First the useful point is that this post by Noah Smith is brilliant. As is typical, Smith argues that the useful implications economic models depend on strong assumptions so economic theory isn’t very useful. He praises simple empirical work instead.

I will discuss Smith contra Acemoglu, Chernozhukov, Werning and Whinston and Smith pro Sergio Correia, Stephan Luck and Emil Verner after the jump, but really Smith is better at presenting Smith than I am.

It made me wonder. In the simplest model herd immunity stops an epidemic when 1-1/R0 of people have been infected. R0 as I recently learned and everyone now knows is the number of people who would catch a pathogen from one infected person if no one had any resistence. Over time people develop resistence so Rt

OK now I consider Smith’s criticisms of Acemoglu et al. He is right, their conclusions depend entirely on arbutrary assumptions made for convenience. The 4 include at least two of the very smartest economic theorists in the world (no I won’t name them). The problem is the poverty of theory.

I don’t agree with all of Smith’s criticisms. He notes that A et al assume one can only get infected once “before a voccine is developed”. Infection and recovery confers stronger immunity than any vaccine (basically without acquired immunity one doesn’t recover). The data now show almost all convalescent patients have neutralizing antibodies. I think the discussion was based on small c conservatism of science in which one must stress that something isn’t proven even when it is very likely.

In particular the alleged examples of losing immunity are no such thing. We get many colds because there are hundreds of different viruses which cause colds (very different with RNA and with DNA genomes with and without envelopes pretty much the whole array of viruses which have the same evolutionary trick of being heat sensitive so they stay in our noses and don’t kill us before we spread them)

Seasonal flu occurs because the flu mutates a lot and has a sloppy hemaglutanin protein whose sequence doesn’t matter for the virus but does matter for our antibodies. Coronaviruses have spike proteins whose sequnces are critical (determining for example whether they infect bats, humans, or both)

Over decades immunity can fade. Over decades SARS CoV2 may mutate to evade the immunity of those who have recovered. Neither is likely to happen before a vaccine is developed (I can cheat and say the vaccine which will be massively used exists already – we just don’t know which of the dozens of canidate vaccines will be elected).

Smith also says that A et al ignore the structure of the population. Heh indeed, that’s what I discussed above. A et al propose isolating the old and letting the young get infected. They assume it is possible to isolate the old from the young — not just the few percent infected with lockdown followed by containment but of enough for young people herd immunity.

He correctly notes that when discussing policy they ask what society should do not what policymakers should do given the fact that people break the rules and sue and stuff.

I agree that the main A et al weakness is the economics not the epidemiology. They assume that lockdown causes productivity to go to 0 (so how did they manage to be so productive during a lockdown ?). More importantly, they assume reopening implies no effect of Covid 19 on the economy. This is a very strong assumption. Smith presents data which pretty much prove it false. Fear of Covid 19 *before* governor’s spoke already had an impact roughly on the order of the lockdown.

Importantly thos does *not* mean that lockdowns have a small effect on the number infected before a vaccine is deployed. A small effect on behavior implies a small effect on R0. If a lockdown gets it down from 1.1 to 0.9 then it has a huge effect on the caseload a few months from now (also weeks from now).

Since US R0 appears to be very close to 1, the gain from making lockdowns soewhat stricter is likely to be huge and the cost of partially opening up is also likely to be huge (except it won’t last –we will lock down again with more cases and probably more days of lockdown and higher economic costs from the lockdown).

Anyway, the patient reader will notice that I don’t mind typing a lot on topics about which I know little

Robert Waldmann
Robert J. Waldmann is a Professor of Economics at Univeristy of Rome “Tor Vergata” and received his PhD in Economics from Harvard University. Robert runs his personal blog and is an active contributor to Angrybear.

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