Category: Medicine

Estimating the COVID-19 Infection Rate: Anatomy of an Inference Problem

That is a recent paper by Manski and Molinari, top people with econometrics.  Here is the abstract:

As a consequence of missing data on tests for infection and imperfect accuracy of tests, reported rates of population infection by the SARS CoV-2 virus are lower than actual rates of infection. Hence, reported rates of severe illness conditional on infection are higher than actual rates. Understanding the time path of the COVID-19 pandemic has been hampered by the absence of bounds on infection rates that are credible and informative. This paper explains the logical problem of bounding these rates and reports illustrative findings, using data from Illinois, New York, and Italy. We combine the data with assumptions on the infection rate in the untested population and on the accuracy of the tests that appear credible in the current context. We find that the infection rate might be substantially higher than reported. We also find that the infection fatality rate in Italy is substantially lower than reported.

Here is a very good tweet storm on their methods, excerpt: “What I love about this paper is its humility in the face of uncertainty.”  And: “…rather than trying to get exact answers using strong assumptions about who opts-in for testing, the characteristics of the tests themselves, etc, they start with what we can credibly know about each to build bounds on each of these quantities of interest.”

I genuinely cannot give a coherent account of “what is going on” with Covid-19 data issues and prevalence.  But at this point I think it is safe to say that the mainstream story we have been living with for some number of weeks now just isn’t holding up.

For the pointer I thank David Joslin.

Pollution is an Attack on Human Capital

Here’s the latest video from MRU where I cover some interesting papers on the effect of pollution on health, cognition and productivity. The video is pre-Covid but one could also note that pollution makes Covid more dangerous. For principles of economics classes the video is a good introduction to externalities and also to causal inference, most notably the difference in difference method.

Might I also remind any instructor that Modern Principles of Economics has more high-quality resources to teach online than any other textbook.

Is there a Hawaii heterogeneity?

Via Michael A. Alcorn, the vertical axis refers to new cases, here is the underlying code.  Or if you care about text:

Hawaii Department of Health officials said today that the state’s tally of coronavirus cases has risen to 553, up 12 from Thursday.

Of all the confirmed cases in Hawaii since the start of the outbreak, 48 have required hospitalizations, with three new cases reported today, health officials said.

The state’s coronavirus death toll stands at nine, unchanged from Thursday. Six of the deaths were on Oahu, while three were in Maui.

The population of Hawaii is about 1.4 million.  Three days ago, Hawaii was the lowest infection rate in the United States, but of course more and better data are needed.  We’ll see, with the passage of time, if this remains a true heterogeneity.  But do note this:

It is also noteworthy that Hawaii tests for coronavirus at a considerably higher rate than most states. According to data compiled by Vox, Hawaii continues to rank among the top 10 states for testing per capita, which suggests Hawaii’s infection rate may be more accurate than rates reported by some other states.



A widely followed model for projecting Covid-19 deaths in the U.S. is producing results that have been bouncing up and down like an unpredictable fever, and now epidemiologists are criticizing it as flawed and misleading for both the public and policy makers. In particular, they warn against relying on it as the basis for government decision-making, including on “re-opening America.”

“It’s not a model that most of us in the infectious disease epidemiology field think is well suited” to projecting Covid-19 deaths, epidemiologist Marc Lipsitch of the Harvard T.H. Chan School of Public Health told reporters this week, referring to projections by the Institute for Health Metrics and Evaluation at the University of Washington.

Others experts, including some colleagues of the model-makers, are even harsher. “That the IHME model keeps changing is evidence of its lack of reliability as a predictive tool,” said epidemiologist Ruth Etzioni of the Fred Hutchinson Cancer Center, home to several of the researchers who created the model, and who has served on a search committee for IHME. “That it is being used for policy decisions and its results interpreted wrongly is a travesty unfolding before our eyes.”

…The chief reason the IHME projections worry some experts, Etzioni said, is that “the fact that they overshot” — initially projecting up to 240,000 U.S. deaths, compared with fewer than 70,000 now — “will be used to suggest that the government response prevented an even greater catastrophe, when in fact the predictions were shaky in the first place.”

Here is the full story, from StatNews, by Sharon Begley with assistance from Helen Branswell, two very good and knowledgeable sources.  Via Matt Yglesias.

To be clear, I am (and always have been) fully aware that there are more nuanced epidemiological models “sitting on on the shelf,” just as is true for macroeconomics and many other areas.  But I ask you, where are the numerous cases of leading epidemiologists screaming bloody murder to the press, or on their blogs, or in any other manner, that the most commonly used model for this all-important policy analysis is deeply wrong and in some regards close to a fraud?  Yes I know you can point to a few tweets from the more serious people, but where has the profession as a whole been?  Who organized the protest letter and petition to The Wall Street Journal?

And to be clear, I have heard this model cited and discussed in many (off the record) policy discussions, this is not just something you can pin on the Trump administration narrowly construed (though they are at fault as well).

“Social Distancing is Working so Well!”

How do you feel about that statement?  I take this as one psychometric test.

If your reaction is: “My goodness, these are tragic times but it is splendid and noble how we all can come together and sacrifice for a common endeavor!”…well…

…you have failed my test and I will suspect a wee bit of mood affiliation.  Most likely it is bad news if the relative safety (for some) of the current moment comes from social distancing.  Because at some point social distancing must end, or at least be significantly curtailed, and then a higher danger level may well reemerge.

Possibly you have inside information that a cure will be ready next week, but somehow I doubt it.  You are happy because you like something about the process.

Alternatively, if you hear “social distancing is working so well!” and immediately feel a deep sense of foreboding, and begin to calculate whether good short-term results are correlated with better or worse long-term results.  And then you calculate how how long the distancing can last for, due to governmental budget constraints, and then try to figure out what kinds of progress we might make in the meantime while the distancing lasts, and then start worrying about how reliant on social distancing we are becoming…

…But then you undertake a second-order calculation about how the greater danger spurred by the forthcoming decline in social distancing also might spur innovation…

And then you think “would it not be better if the current progress came from a more sustainable source, what might that be, how about faster than expected herd immunity amongst a relatively small group of heterogeneous super-spreaders, now what is the chance of that?”…

…and finish your analysis confused…

Then you are my kind of weirdo.

We are living in a time of psychometric tests.

Will the coronavirus make the digital divide worse?

That is the topic of my latest Bloomberg column, here is one excerpt:

Now consider issues beyond specific user groups. The U.S. will almost certainly need to introduce a “track and trace” system, using information technology, preferably with privacy safeguards. One version of this idea uses geolocation methods, which tracks where people are in physical space and sends individuals a text message if they come into close contact with others diagnosed with Covid-19.

That technology requires participants to have a smartphone. The federal government probably will not mandate smartphone usage, which would both be politically unpopular and difficult to enforce. Nonetheless, businesses are likely to turn to such schemes to increase workplace safety. But again, exactly who already owns or afford a smartphone? Some of the jobs with the closest physical contact, such as service jobs, employ relatively low paid workers.

Companies may well decide to help workers buy smartphones, perhaps with government subsidies too. But that would then make having a smartphone a job requirement, including in the retail and public sectors.

This would create a new and in some ways more serious digital divide. Imagine you want to visit your local shopping mall. Its owners might require that you subscribe to one of the Covid-19 tracing apps. Or imagine not being able to get your license renewed without a smartphone certifying your health status.

All of a sudden the U.S. will have a new segregation — between those who have smartphones and those who don’t. If you’re on the wrong side of that divide, many places and services will be hard if not impossible to reach.

And to close:

It is plausible that the U.S. could end up with 10% or more of the population exiled from many key institutions of American life — simply because they lack the right kind of technology.

Don’t get me wrong; the digital divide deserves the additional attention soon to come its way. The trick will be ensuring that any proposed solutions don’t just trade one kind of divide for another.

I can’t even figure out how to work those parking spots that are “app only” for the parking meter.  Pity me!

Fast Grants, a project of Emergent Ventures against Covid-19, status update

As you may recall, the goal of Fast Grants is to support biomedical research to fight back Covid-19, thus restoring prosperity and liberty.

Yesterday 40 awards were made, totaling about $7 million, and money is already going out the door with ongoing transfers today.  Winners are from MIT, Harvard, Stanford, Rockefeller University, UCSF, UC Berkeley, Yale, Oxford, and other locales of note.  The applications are of remarkably high quality.

Nearly 4000 applications have been turned down, and many others are being put in touch with other institutions for possible funding support, with that ancillary number set to top $5 million.

The project was announced April 8, 2020, only eight days ago.  And Fast Grants was conceived of only about a week before that, and with zero dedicated funding at the time.

I wish to thank everyone who has worked so hard to make this a reality, including the very generous donors to the program, those at Stripe who contributed by writing new software, the quality-conscious and conscientious referees and academic panel members (about twenty of them), and my co-workers at Mercatus at George Mason University, which is home to Emergent Ventures.

I hope soon to give you an update on some of the supported projects.

Supply curves slope upward, Switzerland fact of the day, and how to get more tests done

Under Swiss law, every resident is required to purchase health insurance from one of several non-profit providers. Those on low incomes receive a subsidy for the cost of cover. As early as March 4, the federal health office announced that the cost of the test — CHF 180 ($189) — would be reimbursed for all policyholders.

Here is the article, that reimbursement is about 4x where U.S. levels had been.  The semi-good news is that the payments to Abbott are going up:

The U.S. government will nearly double the amount it pays hospitals and medical centers to run Abbott Laboratories’ large-scale coronavirus tests, an incentive to get the facilities to hire more technicians and expand testing that has fallen significantly short of the machines’ potential.

Abbott’s m2000 machines, which can process up to 1 million tests per week, haven’t been fully used because not enough technicians have been hired to run them, according to a person familiar with the matter.

In other words, we have policymakers who do not know that supply curves slope upwards (who ever might have taught them that?).

The same person who sent me that Swiss link also sends along this advice, which I will not further indent:

“As you know, there are 3 main venues for diagnostic tests in the U.S., which are:

1.       Centralized labs, dominated by Quest and LabCorp

2.       Labs at hospitals and large clinics

3.       Point-of-care tests

There is also the CDC, although my understanding is that its testing capacity is very limited.  There may be reliability issues with POC tests, because apparently the most accurate test is derived from sticking a cotton swab far down in a patient’s nasal cavity.  So I think this leaves centralized labs and hospital labs.  Centralized labs perform lots of diagnostic tests in the U.S. and my understanding is this occurs because of their inherent lower costs structures compared to hospital labs.  Hospital labs could conduct many diagnostic tests, but they choose not to because of their higher costs.

In this context, my assumption is that the relatively poor CMS reimbursement of COVID-19 tests of around $40 per test, means that only the centralized labs are able to test at volume and not lose money in the process.  Even in the case of centralized labs, they may have issues, because I don’t think they are set up to test deadly infection diseases at volume.  I’m guessing you read the NY Times article on New Jersey testing yesterday, and that made me aware that patients often sneeze when the cotton swab is inserted in their noses.  Thus, it may be difficult to extract samples from suspected COVID-19 patients in a typical lab setting.  This can be diligence easily by visiting a Quest or LabCorp facility.  Thus, additional cost may be required to set up the infrastructure (e.g., testing tents in the parking lot?) to perform the sample extraction.

Thus, if I were testing czar, which I obviously am not, I would recommend the following steps to substantially ramp up U.S. testing:

1.       Perform a rough and rapid diligence process lasting 2 or 3 days to validate the assumptions above and the approach described below, and specifically the $200 reimbursement number (see below).  Importantly, estimate the amount of unused COVID-19 testing capacity that currently exists in U.S. hospitals, but is not being used because of a shortage of kits/reagents and because of low reimbursement.  This number could be very low, very high or anywhere in between.  I suspect it is high to very high, but I’m not sure.

2.       Increase CMS reimbursement per COVID-19 tests from about $40 to about $200.  Explain to whomever is necessary to convince (CMS?…Congress?…) why this dramatic increase is necessary, i.e., to offset higher costs for reagents, etc. and to fund necessary improvements in testing infrastructure, facilities and personnel.  Explain that this increase is necessary so hospital labs to ramp up testing, and not lose money in the process.  Explain how $200 is similar to what some other countries are paying (e.g., Switzerland at $189)

3.       Make this higher reimbursement temporary, but through June 30, 2020. Hopefully testing expands by then, and whatever parties bring on additional testing by then have recouped their fixed costs.

4.       If necessary, justify the math, i.e., $200 per test, multiplied by roughly 1 or 2 million tests per day (roughly the target) x 75 days equals $15 to $30 billion, which is probably a bargain in the circumstances.

5.       Work with the centralized labs (e.g., Quest, LabCorp., etc.), hospitals and healthcare clinics and manufactures of testing equipment and reagents (e.g., ThermoFisher, Roche, Abbott, etc.) to hopefully accelerate the testing process.

6.       Try to get other payors (e.g., HMOs, PPOs, etc.) to follow CMS lead on reimbursement.  This should not be difficult as other payors often follow CMS lead.

Just my $0.02.”

TC again: Here is a Politico article on why testing growth has been slow.

Re-starting the economy

Will the U.S. economy re-open prematurely?:

New NBER survey of U.S. small companies Here is the percent, by industry, saying their business will still exist if the crisis lasts 6 months: All retail (except grocers): 33% Hotels: 27% Personal services: 22% Restaurants and bars: 15%

That is from Derek Thompson.  Or when will the non-payment of mortgages render the banking system insolvent and beyond saving by the Fed?

At some point, irreversible, non-linear economic damage sets in, and we won’t let that happen, no matter how many times someone tells you “there is no trade-off between money and lives.”

For some time now I have thought that America will reopen prematurely, with a very partial and indeed hypocritical reopening, but a reopening nonetheless.  In May, in most states but at varying speeds, including across cities.

You can see from this Chicago poll of top economists that virtually all of them oppose an early reopening.  I don’t disagree with their analysis, but they are too far removed from the actual debate.

America is a democracy, and the median voter will not die of coronavirus (this sentence is not repeated enough times in most analyses).  And so we will reopen pretty soon, no matter what the full calculus of lives and longer-run gdp might suggest.

Lyman Stone favors ending the lockdown.  It does not matter whether you agree with him or not.  Matt Parlmer predicts revolution if we don’t reopen in time.  I don’t agree with that assessment, but he is thinking along the right lines by not regarding the reopening date as entirely a choice variable.

The key is to come up with a better reopening rather than a worse reopening.

Any model of optimal policy should be “what should we do now, knowing the lockdown can’t last very long?” rather than “what is the optimal length of lockdown?”

And our best hope is that the risk of an early reopening spurs America to become more innovative more quickly with masks, testing, and other methods of reducing viral and economic risk.

Some realistic thinking, including about 2024

It is urgent to understand the future of severe acute respiratory syndrome–coronavirus 2 (SARS-CoV-2) transmission. We used estimates of seasonality, immunity, and cross-immunity for betacoronaviruses OC43 and HKU1 from time series data from the USA to inform a model of SARS-CoV-2 transmission. We projected that recurrent wintertime outbreaks of SARS-CoV-2 will probably occur after the initial, most severe pandemic wave. Absent other interventions, a key metric for the success of social distancing is whether critical care capacities are exceeded. To avoid this, prolonged or intermittent social distancing may be necessary into 2022. Additional interventions, including expanded critical care capacity and an effective therapeutic, would improve the success of intermittent distancing and hasten the acquisition of herd immunity. Longitudinal serological studies are urgently needed to determine the extent and duration of immunity to SARS-CoV-2. Even in the event of apparent elimination, SARS-CoV-2 surveillance should be maintained since a resurgence in contagion could be possible as late as 2024.

That is the abstract of a new piece by Stephen M. Kissler, Christine Tedijanto, Edward Goldstein, Yonatan H. Grad, and Marc Lipsitch.

The implication of course is that changes to the structure of production will be far-reaching unlike say in 2008.  Ongoing social distancing will limit productivity and very drastically shape demand.  This to some extent militates against response measures that assume “the economy as we knew it” will be bouncing back in a few months’ time.

The new (old) federalism under coronavirus

That is the topic of my Bloomberg column, here is one bit:

As May begins, it seems highly likely that the states will be reopening at their own paces and with their own sets of accompanying restrictions, with some places not reopening at all. There is likely to be further divergence at the city and county level, with say New York City having very different policies and practices than Utica or Rochester upstate.

Such divergence in state policy is hardly new. But until now states have typically had many policies in common, on such broad issues as education and law enforcement and on narrower ones such as support for Medicaid. Now and suddenly, on the No. 1 issue by far, the states will radically diverge.

Hence the idea that America is inching closer to what it was under the Articles of Confederation, which governed the U.S. from 1781 to 1789. The U.S. constitutional order has not changed in any explicit manner, but the issues on which the states are allowed to diverge have gone from being modest and relatively inconsequential to significant and meaningful if not dominant.


This divergence may create further pressures on federalism. In Rhode Island, for example, state police have sought to stop cars with New York state license plates at the border, hindering or delaying their entrance. Whether such activities are constitutional, most governors do have broad authority to invoke far-reaching emergency powers.

As some states maintain strict lockdowns while others reopen and allow Covid-19 to spread, such border-crossing restrictions could become more common — and more important. Maryland has been stricter with pandemic control than has Virginia, so perhaps Maryland will deny or discourage entry from Virginia — in metropolitan Washington, there are only a few bridges crossing the river that divides the two states. Or maybe Delaware won’t be so keen to take in so many visitors from New Jersey, while Texas will want to discourage or block migration from Louisiana.

To be clear, I think this unusual situation will recede once Covid-19 is no longer such a serious risk.

Why isn’t Sweden exploding?

…Swedish state epidemiologist Anders Tegnell remains calm: he is not seeing the kind of rapid increase that might threaten to overwhelm the Swedish health service, and unlike policymakers in the UK, he has been entirely consistent that that is his main objective.

That is from a new piece by Freddie Sayers, asserting that “the jury is still out” when it comes to Sweden.  I cannot reproduce all of the graphs in that piece, but scroll through and please note that in terms of per capita deaths Sweden seems to be doing better than Belgium, France, or the United Kingdom, all of which have serious lockdowns (Sweden does not).  If you measure extant trends, Sweden is in the middle of the pack for Europe.  And here is data on new hospital admissions:

Now I understand that ideally one should compare similar “time cohorts” across countries, not absolute numbers or percentages.  That point is logically impeccable, but still as the clock ticks it seems less likely to account for the Swedish anomaly.

Of course we still need more days and weeks of data.

To be clear, I am not saying the United States can or should copy Sweden.  Sweden has an especially large percentage of people living alone, the Swedes are probably much better at complying with informal norms for social distancing, and obesity is much less of a problem in Sweden than America, probably hypertension too.

But I’d like to ask a simple question: who predicted this and who did not?  And which of our priors should this cause us to update?

I fully recognize it is possible and maybe even likely that Sweden ends up being like Japan, in the sense of having a period when things seem (relatively) fine and then discovering they are not.  (Even in Singapore the second wave has arrived, from in-migration, and may well be worse than the first.)  But surely the chance of that scenario has gone down just a little?

And here is a new study on Lombardy by Daniil Gorbatenko:

The data clearly suggest that the spread had been trending down significantly even before the initial lockdown. They invalidate the fundamental assumption of the Covid-19 epidemiological models and with it, probably also the rationale for the harshest measures of suppression.

One possibility (and I stress that word possibility) is that these Lombardy data, shown at the link, are reflecting the importance of potent “early spreaders,” often family members, who give Covid-19 to their families fairly quickly, but after which the average rate of spread falls rapidly.

I’ll stand by my claim that the pieces on this one show an increasing probability of not really adding up.  In the meantime, I am very happy to pull out and signal boost the best criticisms of these results.