Author Archives: Arnold Kling

Working backwards, again

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Two reasons to do this.
1. I messed up the arithmetic the first time. Now corrected.

2. Let’s check this approach against New York information. New York is at 4159 deaths. Lower bound estimate for cases would be 4159 times 50 times 8 = 1.64 million cases. Upper bound estimate would be 4159 times 500 times 32 = 64 million cases, which is more than the population of the state. So I think we can rule that out. Probably because the true case fatality rate is significantly higher than 0.2 percent. If you believe that the case fatality rate is that low, then I think you have to believe that the number of cases stopped doubling every three days in NY at least a week ago, which is another plausible scenario.

Please check my arithmetic!

Working backwards from deaths to cases

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[corrected at 12:40 PM–bad arithmetic error before. Thanks to David Henderson for spotting it]
Because we have not done random-sample testing, we have no idea of the true number of cases in the United States. Reported numbers are worthless. Below, when I refer to cases I mean the (unknown) true total number of people who have ever been infected, not the reported case numbers.

Suppose that we try to work backward. Suppose that we assume a lag of n days from the time of infection to the time of death. Then the number of cases as of n days ago is equal to the number of deaths as of today, divided by the true (unknown) case fatality rate.

The more cases (meaning actual cases, not reported cases) that it took to generate all of the deaths as of today, the happier we should be. A higher number means that there are more people who have already been infected, so we are closer to the peak of the curve.

For example, as of yesterday, there were 8314 deaths. If we assume a true case fatality rate per 1000 of 20, that means that as of n days ago there were 50 times 8314, or 41,570 415,700 cases. If both cases and deaths has doubled every three days (3DDRR = 2.0), then the number of cases today is 2^(n/3) times 415,700. If n is 9, then that means we had about 3.3 million cases as of yesterday. Is that a lower bound? Or is the cfr higher than 20 per 1000 (higher than 2 percent)?

If we raise n to 15 and keep the cfr at 20 in 1000, then the true number of cases as of yesterday was about 13 million. If we raise n to 15 but assume a cfr of only 2 in 1000, then the true number of cases as of yesterday was about 130 million. Is that the upper bound? If we are anywhere near that, we are close to a peak.

FEE tests the three-axes model

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[Note: askblog had an existence prior to the virus crisis. I still schedule occasional posts like this one.]
The Foundation for Economic Education has published a report on its “youth education and audience research” project. Part of that project tested the three-axes model. FEE developed didactic stories, such as a city taking property from a small-business owner to give it to a hotel chain. They then tuned the narrative of the stories to either emphasize oppressor/oppressed, civilization/barbarism, or liberty/coercion. Tuning helped to increase engagement in the targeted audience.

The 3-Axes Model is a genuinely useful way to understand major differences in the way that Progressives, Conservatives, and Libertarians fundamentally understand and process the world. When presenting messaging to these groups, using the language and themes that each group prefers is a good way to present your message without activating their ideological defenses.

General update

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1. John Cochrane writes,

Ask yourself, if you are lucky enough as I am to work from home and still have a paycheck, just when and under what conditions are you ready to go back to the office, to have people breathing the air in the seat next to you in the seminar room, to go touch the salad bar tongs, to go give a talk, shake a lot of hands and meet a lot of people, to get on a plane, to stand in a line? The virus may be contained, with aggressive testing and public health playing whack-a-mole, but authorities relenting and allowing business to open, in a highly regulated way. But will you just go back to normal? Likely not.

That assumes that the Expert Yet Idiots will continue to flail in the dark. Suppose that we ran experiments that let us know how spreading actually works. If doorknobs cause the virus to spread, what would we have to spray on doorknobs to make them safe? If breathing is the main source of spread, what sort of masks are needed?

Should people who have the antibodies for the disease be given “immunity badges” that allow them special privileges? I would not go to a dance session now, but if I can see someone’s immunity badge before I ask her to be my partner. . .

2. Mencius Moldbug, using a pseudonym, writes,

The strongest possible response will come from a new agency, built as a startup. This Coronavirus Authority will scale up faster than any existing organization can execute. It will use the old agencies only where it finds them useful. And it will dissolve itself once the virus is beaten.

Sounds like a typical Internet Engineering Task Force. Pointer from Tyler Cowen, who says he thinks some of the essay is off base.

I wish that this sentence were sourced:

On March 9, dear old Dr. Fauci said: “If you are a healthy young person, if you want to go on a cruise ship, go on a cruise ship.”

Can anyone find a link for this quote?

[UPDATE: Several commenters came through with links. Here is the transcript of the March 9 briefing.

Q Would you recommend that anybody, even a healthy person, get onboard a cruise ship?

DR. FAUCI: Yeah. Yeah. Yeah. I think if you’re a healthy, young person, that there is no reason, if you want to go on a cruise ship, to go on a cruise ship. Personally, I would never go on a cruise ship because I don’t like cruises — (laughter) — but that’s another story.

But the fact — the fact is that if you have — if you have the conditions that I’ve been speaking about over and over again to this group, namely an individual who has an underlying condition, particularly an elderly person that has an underlying condition, I would recommend strongly that they do not go on a cruise ship.

As Tyler would say, that was then, this is now.]

Moldbug’s idea amounts to putting a Silicon Valley CEO in charge of the hypothetical CVA. The authority of this person would supersede that of the President.

It turns out that everyone’s reaction to this crisis is to say that it proves the correctness of their political ideology. Economists did pretty much the same thing with the 2008 Financial Crisis. Moldbug has always disdained democracy in preference for a more corporation-like form of government. I find it easy to nod my head in agreement as he describes the current failure. But any untried alternative form of government looks better only because we have not had a chance to observe its unintended consequences.

The economic section of the essay struck me as sketchy and unconvincing. But I am not going to spend time writing a point-by-point critique.

3. A reader forwards an article from the South China Morning Post.

On Friday, both the US and Singapore switched to advising citizens to wear masks when they leave their homes. The WHO also made a U-turn itself, with Ryan saying: “We can certainly see circumstances on which the use of masks, both home-made and cloth masks, at the community level may help with an overall comprehensive response to this disease.”

Leading from behind. Another quote:

“Universal masking, as a package of anti-epidemic measures, including greater social distancing and hand hygiene, has been instrumental in keeping Covid-19 in check,” said infectious diseases expert Professor David Hui Shu-cheong of the Chinese University of Hong Kong.

4. Another reader forwarded this from the Israel Ministry of Health.

Masks covering the mouth and nose greatly reduce the chance of getting infected and infecting others. These masks prevent the emission of droplets that carry the disease from reaching the nose and mouth. The masks protect those who wear it, as well as others around them, therefore, when a carrier of the virus meets a non-carrier, if both are wearing a mask, the protection against infection is doubled.

Therefore, we are instructing everyone to wear a mask at all times in public to prevent exposing acquaintances, bystanders, and coworkers.

Experiments and lockdown exit

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How will we know when and how to exit from the lockdown strategy? I think we need to conduct experiments.

I know this is a pipe dream. The only experiment we will ever see will be “Lift the lockdown and see what happens.”

But I would suggest that we recruit young, healthy people who are uninfected and have never had the virus as experimental subjects for the following experiments. Note that I would be willing to see the one child of mine who qualifies as healthy to participate as an experimental subject, because I think that these experiments would be safe. Note that for these experiments the “infected person” is either asymptomatic or has only very mild symptoms.

1. The doorknob effect. Have the infected person open a door, and have the experimental subjects follow at one-minute intervals and open that same door. Quarantine the experimental subjects for two weeks and meanwhile test them for the virus.

2. The classroom with masks and scarves. Have the infected person sit in a classroom with one hundred experimental subjects. Everyone, including the infected person (whose identity is known only to the investigator, not to the experimental subjects), wears a face covering of some sort. Try this experiment with the infected person having different types of face coverings. Quarantine and test.

3. The virus-in-the-air experiment. Have a person known to have the disease in mild form walk through a hallway. Have experimental subjects follow at one-minute intervals. Repeat this experiment with a different combinations of face covering. One version would have nobody wear face covering. Another version would have both the infected person and the experimental subjects wear face covering. etc. Quarantine and test.

These sorts of experiments would provide a better scientific basis for making decisions regarding modifying or lifting the lockdowns.

The 3DDRR

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The number that I use to track the virus crisis is the Three Day Death Reproduction Rate. It sounds ghoulish, and it is. It also is a lagging indicator. I wish I had some other indicator. But I do not trust case numbers, because testing criteria are undergoing constant revision.

The 3DDRR is calculated using the data from this site, which is updated every day late in the afternoon, eastern time. It gives the total number of deaths as of each date. The 3DDRR for, say, March 29, is the total number of deaths on March 29 (2428) divided by the number on March 26 (1163), which gives 2.09.

We can say that if the 3DDRR stays close to 2, then that is awful. If it stays over 1.1, then that is still pretty bad. If it is just barely over 1, say 1.002, then that is better. Getting below 1 would require resurrections.

So for all the dates from March 20 through today, we have

Date 3DDRR
3-20 2.43
3-21 2.43
3-22 2.49
3-23 2.15
3-24 2.48
3-25 2.26
3-26 2.47
3-27 2.27
3-28 2.18
3-29 2.09
3-30 1.92
3-31 1.91
4-1 1.94
4-2 1.97
4-3 1.86
4-4 1.77

The trend is in the right direction, but the 3DDRR is still disturbingly high. It would be nice to see, say, 1.5 by April 7, 1.3 by April 10, 1.1 by April 13, and 1.002 from April 16 on. That would raise April 4ths total deaths of 8314 to 17,834 (exactly, right?) on April 13, with slow increases beyond that.

That is a numerical scenario, but it is hard to know what has to happen in the real world to achieve that. Presumably it would require a continued reduction in the spread rate of the disease, along with improvements in triage and treatment.

The problem is that even in such an optimistic scenario, we won’t know how much of the lockdown policy was needed to achieve it. I keep saying that we need experiments in order to better understand the spreading process, but no one listens.

Thoughts on testing for the virus

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There are two purposes of tests.

Individual: To tell whether a particular patient has the virus.
Social: To enable public health officials and policy makers to know the prevalence of the virus in the population.

For the individual purpose, the quantity of tests and the speed with which results can be read matters more than quality. There is hardly any point in testing someone who is unlikely to be infected. And if a hospital uses one type of test on one patient and a different type of test on a different patient, that is hardly a problem.

For the social purpose, the quantity of tests does not matter, as long as enough people are tested to produce a reliable sample. If you have to wait a week for a test result, that is ok. You want to include a representative sample of the entire population, including people without any reason to believe that they have been infected. It is important that every person tested using the same method.

What level of accuracy do you need? Suppose that 95 percent of the people who test positive are in fact positive, and 95 percent of the people who test negative are in fact negative. Is that good enough? Imagine that out of 1000 people, 40 test positive and 960 test negative. You would have:

test positive test negative
have virus 38 48
virus-free 2 912

Do you see the problem? More people who have the virus test negative for it than test positive for it. That is certainly not good for the individual purpose.

For the social purpose, you can back out the true prevalence of the virus provided you know precisely the rate of false positives and false negatives. But if you don’t know those, and if you just go by the test results, in this example you would say that only 4 percent of people have the virus, even though 8.6 percent of people actually have the virus. But at least you would be in the right ballpark. In the absence of rigorous testing, right now the estimates from different “experts” are orders of magnitude apart.

For the individual purpose, I would prefer the testing method with the lowest rate of false negatives. For the social purpose, I would prefer the test where we have the most precise estimate of the false positive and false negative rates, even if the false negative rate is a bit higher than that of some other test.

Public Service Announcement

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For people who are new to this blog:

1. The tradition here is for respectful, constructive discussion. For five years up until the past week, I probably deleted fewer than 10 comments for violating that tradition.

2. My wife and I began a self-quarantine on March 12, which was before most people were doing so, and before almost any public official recommended it. I became a doubter of the quarantine approach when it occurred to me that a public hygiene approach could be a more cost-effective alternative. By public hygiene, I mean masks and scarves, handwashing, and efforts to frequently sanitize surfaces that are touched by many people. I will not stand for accusations that my motives are selfish.

Trying to raise the status of Edward Leamer

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[Note: askblog had an existence prior to the virus crisis. I still schedule occasional posts like this one.]

In this article, I say that Edward Leamer deserves a Nobel Prize.

Edward Leamer deserves the Nobel Prize in Economic Sciences for launching the movement to examine critically the uses of statistical methods in empirical research. The movement has had repercussions that go beyond econometrics. It has affected medicine and epidemiology, where John P. A. Ioannidis has been a leading figure in pointing out methodological failures (Ioannidis 2005; 2016; Begley and Ioannidis 2015). It has impelled psychology and behavioral economics to confront what has become known as the ‘replication crisis’ (Camerer et al. 2018).

. . .After Leamer pointed out problems inherent in the multiple-regression
approach and the inevitable specification searching that it involves, economists
have turned to quasi-experimental methods

The policy of Econ Journal Watch is not to allow the author to give acknowledgments to editorial staff, but Brendan Beare and Jason Briggeman did a great deal to improve the essay.

Underlying conditions, age, and deaths in NYC

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To summarize this table (pointer from Russ Roberts):

Of 1584 Covid deaths, 25 were people with no underlying conditions, 380 were people with “underlying conditions pending,” which I guess means that they are not sure whether or not the person had an underlying condition, and the other 1179 all had underlying conditions.

Of those with “pending underlying conditions,” 234 were aged 75 and over. So another way to look at the data is that of the 1584 deaths, 1413 either were aged 75 and over or had definite underlying conditions. That is 89 percent.

Perhaps those of us under age 75 and healthy ought to be given more freedom to go out in public, provided that we wear face covering. Also, it would help to sort out which “underlying conditions” really matter, to know who should be considered healthy.