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The Amateur Epidemiologist II

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 < R0. If 1-1/R0 of people are resistent, then Rt =1. A bit later Rt<1 so each infected person will lead to a geometrical decreasing series of expected infections so total infections would be 1-1/R0 plus a (small) constant over the number infected at that critical time t. The SIR has susceptible, infected and resistent. The idea is that if one has not been exposed one is vulnerable. If one becomes infected, one carries and sheds the pathogen for a while and then one recovers. After one recovers one is immune and won't get it again. The key assumption in the model is that for every infected people R0 people are exposed (and infected if not immune) and that those people are chosen at random out of the entire population. It is necessary to assume that spread is equally likely from Mr A to Ms B if they share a house or live on opposite sides of the country. This is a silly assumption and the model is the old model used to teach kids and not, I'm sure, current research. It is also the model always used to guide public policy decisions (see me contra benchmark models ) In population biology and evolutionary biology the silly assumption is called "pan mictic" in economics it is called "random matching". The assumption is made very often because doing without it can get one stuck in really hard math. I would like to put a few minutes of effort into trying to figure out if the random matching assumption affects the level of infection needed for herd immunity (of course everyone knows it matters a lot). Below I will always assume R0 =3. Model 2 the population is actually divided into N equal subpopulations and there is no spread from one to the other. The disease starts with one case in one sub population. It will spread until a few more than two thirds of that population has been infected. Spread will stop when 1/(3N) of the whole population is infected. the relaxation of random matching assumption reduceces the incidence needed for herd ommunity by the factor N. This works for any N. Model 3 very like model 2. Half of people have innate immunity to the virus. People transmit the virus to on average 6 other people (on average 3 have innate immunity). the virus will spread until 5 of 6 are immune. that means (5/6)-(1/2) = 1/3 must acquire immunity (by getting infected). So 1/3 not 2/3. OK can we be sure that the number who will get onfected is less than 2/3 ? Consider Model 4. people live one to a square of an invisible chess board (which is a really big square) they transmit the pathogen to those with whoù they share an edge. R0 = 3 (I get it from 1 neighbor and early in the epidemic give it to my other 3 not yet infected neighbors). How many people get infected ? All of them Katy. The currently infected are always in the border zone between the resistent and the vulnerable. So R0 = 3 implies herd immunity will stop the spread at some level which ranges from 1/(3N) for N as big as I like, to 100%. R0=3 and a priori reasoning without arbitrary assumptions which we know are false and make for convenience tells us nothing at all. Without some assumption about mixing, matching, and population structure, the core SIR assumptions have no implications. Maybe economists and epidemiologists have more in common than we thought.

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Asking the Wrong Questions: Reflections on Amazon, the Post Office, and the Greater Good

The Greater Good

“If they can get you asking the wrong questions, they don’t have to worry about answers.” — Thomas Pynchon, Gravity’s Rainbow


Originally written in 2018 on the Save The Post Office blog and featured at Angry Bear in 2019, retired North Carolina Post Master Mark Jamison wrote on the issues facing USPS while in competition with Amazon, UPS, and FedX. The same issue has been brought to the forefront again with President Trump refusing to give a subsidy to the USPS, unless the USPS raises prices to deliver packages for Amazon, and also punishes Amazon’s Owner Bezos. The answer remains the same, “no” and Mark explains why.

I have not written or said much about postal issues for the last couple of years. After seven years of writing articles for Save the Post Office and other websites, as well as contributing numerous comments to the Postal Regulatory Commission, what more was there to say?

I spent thirty years of my working life at the Postal Service. I’ve put in countless hours reading USPS reports, OIG reports, GAO reports, and who knows how many pleadings before the PRC. I have written numerous articles about the general idea of the postal network as an essential public infrastructure, the arcane minutiae of postal costing and the actions of the PRC, and the machinations of a Congress that seemed more inclined to bloviate and posture than attempt to solve a serious problem affecting millions of Americans and thousands of communities, large and small, rural and urban.

I never stopped thinking about these issues, but what more was there to say? And why bother, really, when the politicians and managers that could actually make changes seemed inclined to let inertia and the status quo slowly erode the capabilities of the postal network while degrading hundreds of thousands of good middle-class jobs?

And then President Trump had one of those brain farts he periodically shovels out over Twitter.

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bu Dale Coberly



[a few years ago the word “du jour” among journalists about SS was “it’s the math.” Of ourse none of them actually did the math.]

[note: i use the tax rate for each the worker and the employer because this is what the worker “sees” and it is what the employer sees. It is also the legally correct division. The Trustees Report usually combines the separate tax rates into one “combined” tax rate. So, where they say a 3% immediate and permanent increase, or an eventual increase of 4%, I say a 1.5% or 2% increase “each.” Debating which is “correct” is a waste of time: it is what it is.]

I wrote a recent post I called “What the Trustees Report Really says.” This post takes a little further look at the possible futures that can be mathematically deduced from the 2020 Report.

The 2020 Report says that Social Security is now not in “short range financial adequacy”. This means that ten years from now the Trust Fund will be less than the prudent reserve of one year’s full benefit payments. This is not an emergency, but it does mean the one tenth of one percent per year increase in the payroll tax, for each the worker and the employer, that would have avoided this projection will no longer work.

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by Dale Coberly


WORST CASE:  we wait until 2035 and then have to raise the payroll tax 4.13% (2% for workers, 2% for employers) in order to pay for promised benefits. OR have to cut benefits by 25%.

The trade-off is about 20 dollars per week extra “tax” (really “savings”) for an average worker making 50k per year, versus a 500 dollar per month cut in benefits, from about 2000 dollars per month to about 1500 dollars per month, when he retires.

People won’t be able to live on 75% of promised benefits unless they have other sources of income.  About 50% of retired workers will not have enough other sources.  Please remember that those future retirees would be paying for ALL of the required tax raise.

NOT SO BAD CASE: an “immediate and permanent” increase in the payroll tax of 3.14% (1.6% for workers, 1.6% for employers), or about 16 dollars per week. OR a 20% cut in benefits.. from about $2000 per month to $1600.

This is really the whole story.  Everything else you hear is misdirection: arm waving and shouting “Fire! Fire! We Are All going To Die!”

There is an even BETTER OPTION:  raise the payroll tax a little more than one tenth of one percent per year (about a dollar per week per year). This must be done very soon;  delaying will require a larger gradual increase.  The ultimate increase needed will be about the same 4% that will be otherwise needed in 2035 if we wait.  But that 4% (2% for the worker) will be delayed about 30 years. And the per year increases will be reduced to much less than one tenth percent per year,  because the gradual increase will reduce the “actuarial deficit” each year while providing an Increase in income to the Trust Fund.  
The interest earned by the gradual increase will actually reduce the ultimate tax needed by about 1% of income.  AND it will eliminate the need for  Congress to repay the money it borrowed FROM Social Security over the past thirty eight years.

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First Pass of Small Business Loans to States

This was the first pass (Ernie Tedeschi of Evercore prepared the data) and it is arranged by the percentage of loans completed in each state. As you can see Nebraska received ~81% of the loans applied for by the small businesses in Nebraska. One million, 35 thousand and 86 SBA PPP Loans (1,035, 086) were approved by April 13 totally $247, 543, 397, 521 by 4,664 lenders. Seventy percent of the funds were already allocated by April 13.

Some Applicant Complaints:

  • Applied at Bank 0f America on April 3. Got 3 calls on Friday Saturday and Tuesday asking if I uploaded my documents. They were already there!! Instead of approving my loan BOA is delaying and stalling to run out the clock.
  • In Michigan, one small company dealing with Comerica was told repeatedly Comerica had not received the code to apply for the loans yet. The small ten person  applied when the program first started.

Some detail from Bob Clough at “CloughNotes” which looks at the numbers in a different manner after the leap.

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The actual US coronavirus trajectory: “flattening the curve” at least until 2021

The actual US coronavirus trajectory: “flattening the curve” at least until 2021

“Flattening the curve” was not such an appetizing option either, because it meant that *everybody* got infected with the disease during the period of flattening, and so the death toll would still be horrifying, perhaps 1% to 3%. It also meant that the period that the infection would curtail society was extended to several years.

Shortly a much better alternative, based on the success of South Korea, was embraced. Described as “crush the curve,” it meant imposing firm lockdowns for a long enough period of time for thoroughgoing testing of the population, tracing contracts of those infected, and isolating the infected to be ramped up and in place.

Here’s what the three alternatives look like in a diagram:

Throughout the latter part of March and into early April, one by one all but a few, mainly rural, States imposed lockdowns, and the rate of new infections quickly plateaued. But, due to the intransigence of Donald Trump personally and key members of his Administration, the ability to test in the number required was never implemented. In particular, Trump resisted for weeks making use of the Defense Procurement Act for obtaining the necessary medical equipment quickly.  He has never given the slightest indication that he views doing widespread testing as either necessary nor (politically) desirable.

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The Social Security Trustees Report

by Dale Coberly

The Social Security Trustees Report

is out.  SS now in “short term actuarial insolvency”  Much (lies) will be made of this.  The Report does not lie,  but it does obscure the fact that a 2% increase in the payroll tax will still solve the problem.  the one tenth percent per year gradual approach will now need to be a little bit higher…  increasing each year we delay, but at the end of the day no higher than the 2%.
The biggest reason for the projected “insolvency” now has nothing to do with SS itself,  but predicted increase in employers shifting pay to non taxable health care benefits.
I may be able to write more about this but not very motivated since no one seems to listen.
Also it is getting harder for me to find the energy and correct the typos.
2% is the cost to workers.  employers pay another 2%.  people who like pointless arguments will argue this is “really” a 4% increase.
doesn’t matter.  the workers will only “see” 2%,  and even a 4% increase is cheap for what it buys.

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Starve the Beast

It should be worth noting that the federal deficit under Trump is already at 5% of GDP even before the Coronavirus stimulus begins.

Figure 1

Interestingly, if you look at the long term record the only policy or strategy that fits the data is the Republican policy of starve the beast. That policy is to enlarge the  federal deficit so much when they control the purse strings that democrats will be unable to enact policies increasing spending that benefits the lower and middle classes.  That is why you repeatedly see a pattern of republicans presidents leaving office with a much larger deficit than they inherited while democratic presidents reduce the deficit..  With US savings rates so low this forces the US to borrow abroad to finance the savings-investment gap. We lucked out that in the 1980s OPEC and Japan had  savings surpluses that they used to finance the US deficits.  Under Bush it was the Chinese that had a savings surplus to invest in the US.  But OPEC and Japan no longer have surpluses to finance the US deficit and the Chinese have started to draw down their savings as they shift to consumption led growth.  Because the Japanese and Chinese had large surpluses to invest the  long feared crowding out worked through the dollar and large trade deficit rather than higher interest rates and weakness in the credit sensitive economic sectors. The hollowing out of US manufacturing was a direct consequence of the republican tax cuts.

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Stairway to Serfdom

Stairway to Serfdom

I posted the above chart four days ago in “From Social Distance to Social Justice” to illustrate Arthur Dahlberg’s argument about the eventual consequences of a declining labor share of income. Dahlberg was inspired by Stephen Leacock’s The Unsolved Riddle of Social Justice and both Leacock and Dahlberg were influenced by Thorsten Veblen.

The chart also illuminates arguments made by Moishe Postone about Marx’s theory of capitalist production. I happen to agree substantially with Postone’s interpretation of Marx even though I find his presentation repetitive and difficult to follow. That is, I think I agree with what I think he was trying to say in Time, Labor and Social Domination.

What the chart shows is that in spite of a more than threefold increase in productivity over roughly the last half-century, the per capita hours of work increased in a series of steps with each successive business cycle culminating in a higher level of hours per capita. “Because total value created is a function only of abstract labor time expenditure.” Postone wrote, “increased productivity yields a greater amount of material wealth but results only in short-term increases in value yielded per unit time.” Postone later remarks that one consequence of this dynamic “is the accelerating destruction of the natural environment.”

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Trends in US States compared by coronavirus response

Trends in US States compared by coronavirus response

I mentioned over the weekend that I wanted to break out and look at some different aspects of the coronavirus pandemic.

Here’s the first: how are States at different ends of the restrictions and testing spectrums faring?

Seven States have never even mandated lockdowns. Let’s look at these, alphabetically:



Figure 1

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