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by Steve Lowe

Blog by Steve Lowe

In which I present some ideas from a quantitative point of view.


2020-Jul-23    McKinsey Research Report on Covid-19, Student Learning, Summer Vacations

In my earlier posts 2020-Jul-19 and 2020-Jul-20 I posed the question of how much children's live will really be adversely affected by school closures lasting less than a year. I expressed some skepticism regarding the prevailing panic that seems to presume their educational lives will be ruined. I acknowledged that there were ancillary problems, such as the parents' jobs, and how to tend and occupy the kids, problems that are indeed important. I asked, however, whether anyone knew, quantitatively how educational progress would be impaired.

I came across the following article by the research firm McKinsey & Company that looks into just that!

In their section "Learning loss and school closures" the article states that they "created statistical models to estimate the potential impact of school closures on learning" and "evaluated this information in the context of three different epidemiological scenarios", which appear to be "average remote learning", "low-quality remote learning" and "no instruction," which represent different Covid-19-closure-degraded teaching scenarios. The reader may see the details in the article itself, but in all cases they assume everything is as usual up until March 2020, at which point non-standard, non-classroom instruction begins. There is a "baseline" case in which instruction occurs in-classroom as usual.

All sounds good, a very promising introduction to their quantitative simulation. I'm psyched! But then about four paragraphs in they say this:

"In our second scenario (in-class instruction does not resume until January 2021), we estimate that students who remain enrolled could lose three to four months of learning if they receive average remote instruction, seven to 11 months with lower-quality remote instruction, and 12 to 14 months if they do not receive any instruction at all (Exhibit 2)."

Wait a minute. In that last scenario, classroom teaching ends March 2020, then no instruction at all, then resumes January 2021. That's a 10-month gap. And they lose 12 to 14 months of learning, which is more than the gap? How can students lose more months than they were actually out? Even if they received some remote instruction of low-quality, they might still lose more than 10 months of eduction (7&ndash11 months; 11 is more than 10!) These "months" must have some odd definition for these assertions to be true.

They refer to "Exhibit 2" at the end of the quote, which turns out to be a very interesting graph. You may look at it yourself in the article: it shose that scores on a particular reference test rise during the academic year from September 2019 until March 2020, then split into four curves representing different Covid-19 teaching scenarios. In the top (black) curve, there is no closure, teaching continues in-classroom until summer break, after which teaching resumes in-classroom in September 2020; the ensuing school year is also "normal."

Let me draw a schematic of that graph, showing one symbol horizontally for each month. The vertical scale is the educational assesment measurement, the NWEA RIT score, used in the paper as their metric of educational progress: 

                            /\
                           /  \
                          /    \
                         /
                        /
                       /
                /\    /
               /  \  /
              /    \/
             /
            /
           /
          /
         /
        /

This is a faithful, if crude, reproduction of the top (black) line of Exhibit 2. It shows a linearly rising score month by month during the September (2019) through May academic year (9 months), then falling during summer break (3 months), then another rise from September (2020) through May (9 months again), and a fall during summer 2021 (3 months). It is remarkable that the slope of the upward and downward segments appears to be almost exactly the same, as you can see in the article! Students scores rise when they are in school, and drop when they are out, and at the same rate! That seems really weird! I would have assumed that some knowledge is lost over the summer—wouldn't you?—but why would the forgetting rate and the learning rate be the so nearly the same?

Nevertheless, this makes sense of their claim in the previous quotation, because being out of the classroom performs a double whammy: the student's ability doesn't just stop rising during a gap, it actively falls!

However, if this scenario is true, it is also an arguement against summer vacations! According to the graph top line, student achievement rises or falls by about the same amount each month, depending on whether classes are in or out of session. Therefore achievement rises by 9 "steps" during the 9-month academic year, then falls 3 steps during the 3-month summer break, netting a 6 step increase over the whole year. If there were no summer break, achievement per year would rise 12 steps instead of 6, doubling students' educational progress every year of their schooling. That's fantasitic! Why don't we do that all the time? (Note that in my 2020-Jul-19 entry "Out of School: Will Children's Futures be Ruined", before seeing the McKinsey article, I had pointed out that summer vacations consume 3 years time during a K-12 career.)

This calculus can provide a path out of the Covid-19 reopening dilemma, in that educational deficits incurred during closures might be overcome quickly by doubling the effectiveness of each school year via summer school in succeeding years. Some students and their families may depend on summer earnings, however, and so this avenue may require the government to provide stipends or grants directed to those most affected by coronavirus school closures.

Now, personally, I am not sure that the "double whammy" interpretation is correct, that summer vacations reduce annual eductional effectiveness to one-half. I would imagine that he number is closer to the three-quarters (i.e., a one-quarter reduction) value one might naively expect—sometimes naive is correct. I imagine that the resolution to this conundrum is that the NWEA RIT metric is somehow adjusted for academic age, and that this produces the result that if one is not learning one is automatically falling behind. I'm sure there is some net forgetting during non-teaching periods, but I would not expect the ascending and descending slopes to be identical as seems to be the case in the Exhibit 2 data. I need to look into this more.

However, this McKinsey article, since it is from McKinsey may be quoted as authoritative by some parties, probably even in the government. So I thought I should point out that taken on its face, this report of severe educational consequences contains its own solution within it: that the rapidly increasing deficits described in the various scenarios might be countered by equally rapid recoveries through increased instruction time (summer school) after Covid-19 is under control.


2020-Jul-21    Hawking Radiation, Ethan Siegel article in Forbes

Here is something a little more mathematical/scientific. My wife ran across this article by in Forbes Magazine about black holes and how they can evaporate through Hawking radiation, which is the great theoretical discovery of Stephen Hawking's career.

Well, that's an eye-grabbing title.

Before I go on, I should mention that I'm not sure of the editorial status of this article vis-a-vis Forbes Magazine. That article is definitely hosted on https://www.forbes.com, as you can see if you mouse-over my link above. But it is under .../sites/startswithabang/.... I originally thought "Starts with a bang" must be a section within the online Forbes Magazine (www.forbes.com/forbes); there is a link to the Magazine from the homepage (well, under the "More" drop down list). But I couldn't find a link to "Starts with a bang" from either the home page or the magazine. A search on that name does turn it up. This Siegel article also appeared under their "Forbes Editors' Picks" link from that same "More" list, so there is some endorsement. But I can't say that I know to what editorial scrutiny the Siegel article has been subjected.

Now to the meat—red meat, as it turns out. Siegel outlines the usual Hawking radiation description that you've probabaly read before: A virtual particle-antiparticle pair forms near but outside the event horizon, one member falls back in, the other flies away carrying its mass, so the black hole total mass is reduced by that little bit. Multiply by many such events and the black hole can evaporate, though only small ones will have time to expire before the end of the universe. All familiar, right?

But then Siegel goes on to say that this description is "egregiously" and "grossly incorrect". He writes

"...it's not the [explanation Hawking] used in the scientific papers he wrote concerning this topic. He knew that this analogy was flawed and would lead to physicists thinking incorrectly about it, but he chose to present it to the general public as though people weren't capable of understanding the real mechanism..."

He goes on to suggest that Hawking did not use the pair-production analogy until his 1988 popularization A Brief History of Time, over a dozen years after the seminal papers. In particular, he writes:

"...in his landmark 1988 book...Hawking paints a picture of this radiation—of spontaneously created particle-antiparticle pairs where one member falls in and the other escapes... For 32 years, it's misinformed physics students, laypersons, and even professionals..."

[Full disclosure: my wife, Marcia Bartusiak, wrote the 1988 review of A Brief History of Time for the New York Times Book Review.]

It is 2020 now, minus 32 years is 1988. So he seems to be saying that the pair model didn't exist to "misinform" people before that. Siegel makes other claims, such as that this model implies the radiation emanates "from the event horizon itself"; I had thought the usual explanation posited pair-formation to be in a region outside that horizon.

I'm not enough of a quantum or gravitational physicist to refute these and other claims out of my head. It seems quite reasonable to me that the mathematical description of Hawking radiation would be much more complicated and based on some nasty field theory, and I imagined that the pair-production model was a simplified though reasonably faithful interpretation. I thought that over the years I had heard enough references to that model that it must have some utility to researchers trying to reason about and extend their understanding of Hawking radiation, even if final calculations required dealing with those nasty field equations. Could the pair-production view be so "grossly incorrect," just a flawed popular analogy and without scientific merit?

And Ethan Siegel is a Ph.D. astrophysicist and science writer, per Wikipedia. So maybe I am wrong.

As it happens, a friend and I had been bullshitting about Hawking radiation just a couple of days before the article came out—he had a conjecture about the way they might lose charge in addition to mass. That's probably what prompted Marcia to point the Forbes/Siegel article out to us. Consequently, I had collected a few journal articles on the subject, particularly some older ones.

Turns out that at least some of Siegel's statements are themselves wrong, and that calls his entire thesis into question. He points out that Hawking radiation is exclusively photon radiation, which I think is true, but does not ask whether researchers have looked at the question of non-photon particle radiation; and they have from the beginning! Hawking himself referred to particle radiation as well as electromagnetic (EM) radiation in the original Nature paper in 1974, which mentions neutrino and photon (EM) emission (Granted, he would have thought both were massless at the time; neutrino mass wasn't discovered until 1998). His contemporaneous paper in Communications in Mathematical Physics (Springer, 1975, pp. 199–220) does, however, discuss emission of particles with non-zero rest mass:

“As the [black hole] temperature rose, it would exceed the rest mass of particles such as the electron and the muon and the black hole would begin to emit them also.”

That would include positrons (anti-electrons) and anti-muons, which have the same mass as the particles mentioned. I do not know, but might conjecture, that particle-antiparticle annihilation could reduce the particle field to the expected EM radiation field. The conjecture would be testable, in that one could consider the density in the particle radiation field and the annihilation cross-sections to determine whether this would be consistent with the black-body EM field predicted by a more rigorous theory (those nasty field equations). In any event, people were looking at particle emission as far back as 1975.

Moreover, the same paper describes the pair-production model supposedly not enunciated until 1988:

“One might picture this negative energy flux in the following way. Just outside the event horizon there will be virtual pairs of particles, one with negative energy and one with positive energy. The negative particle is in a region which is classically forbidden but it can tunnel through the event horizon..."

Lastly I will cite another author, G. W. Gibbons, in the same issue of Communications in Mathematical Physics (Springer, 1975, pp. 245–264), "Vacuum Polarization and the Spontaneous Loss of Charge by Black Holes" which states at one point:

"...where we have used the mass and charge of the electron since it is the lightest and hence most easily emitted particle..."

I presume by "particle" he means "charged particle", because the article is about disposing of charge. If I am not mistaken, the electron is the lightest charged particle.

So I think these citations show that it is nonsense to contend that the pair-production model was manufactured by Hawking for the 1988 popularization. It is also not true that Hawking and other researchers thought black holes produced only electromagnetic and not particle radiation, though it may be true that in the far field limit the field becomes black-body EM via some process.

Now, as I said, I'm not versed enough in this field to fully resolve this matter. I can only say that Siegel's contentions did not seem right, and what little literature investigation I have put together seems to support that impression. I imagine that the mathematical analysis that Hawking used was more refined than the pair-production imagery, but that the latter more descriptive model has been used productively by working physicists for 45 years. It was not created simply as a popular allegory for Hawking's 1988 book.

Perhaps other, more informed physicists would care to comment.


2020-Jul-20    CDC Article, South Korean Covid-19 Contact Tracing

Centers for Disease Control and Prevention just released a preprint (not final) of an article on Covid-19 transmission within households and outside households, broken out by the age of the infected individual (or "index" individual, as they call it), and also by whether contacts are living in the same household or not. Here is the citation:

I think their Table 2 says it all. Looks like, ballpark, a 7 to 15% in-household transmission rate. The data for the 0-19 year olds is a little slight, that should be pointed out before someone else tries to question the reliability of the study. But the 7–15% range is still within the error bars even for that younger group. For out-of-household, the transmission rate seems to be 1–2% across the board, until one reaches much older index individuals (more than 60 years old).

As I read it, the data do not provide evidence for a substantially different transmission rate for the young versus adults. Within the error bars it's about 7–15% in-household, 1–2% out-of-household. But more data is needed to refine the accuracy of youth transmission rates.

More specifically, the 0–9 set has only 57 contacts in-household, 3 positive, which is 5.3%; but it is also a very small sample to rely on. The 10–19 set has an 18.6% in-household positive rate, the highest of any group. But then it is also the only group in which the number in- and out-of-household total contacts are about the same (231 and 226, respectively); for all other groups the number of out-of-household contacts is about 4 times or more greater than the in-household count. So there might be something peculiar happening with the data for the teens, maybe some reporting inconsistency.

In any case, this is very relevant to the school reopening issue, and it does not support the argument that children are non-transmissive, as some who advocate immediate school reopening would claim. It does provide support to the statement that in-household transmission rates are greater than out-of-household rates, which suggests that disease could be brought home to spread.


2020-Jul-19    Out of School: Will Children's Futures be Ruined?

There are a lot of people advocating immediate reopening of schools despite the continuing Covid-19 epidemic, as though children will be educationally ruined if they cannot return to classrooms by September 1.

I find it difficult to accept that students and their educations are so fragile that they will be hampered for life by a classroom gap of six months or a year. I have not seen anyone pose the issue publicly in quite this way, i.e., to ask what would happen if we just accept an interruption in classroom instruction as the price of public safety.

After all, we already have three years worth of gaps built into each student's K-12 progress---they are called summer vacations. Granted, an unplanned additional break is not desirable; but even an additional year is likely surmountable. (Unrelated to the pandemic, some have called for making classes year-round to salvage this precious time, but communities have generally not done so. It would appear few agree that those three years are crucial.)

I imagine that the public's first thought about closings is that their kids will be educationally short-changed. Oh, no, they will fall behind their peers! Gotta stay on that fast track to Princeton! If education is such a foot race, then something is wrong with our methods of educational evaluation. We should re-think that. Also, I acknowledge that studies show in-class education to be better than alternatives such as on-line learning, but the point here is not to compare those alternatives. It is to contrast the damage of an educational gap with, well, dying or having a relative die.

Closely following education are home life problems. Parents are in a pickle because they need to work, either at home where the kids are present and perhaps rowdy; or at a place of business, but then who tends the children left at home? And how will those children productively occupy their time? Not all families have equal resources to address these matters.

Schools provide more than just education, including daily child care, nutrition, physical and mental health services, somewhat more equitable access to learning resources, and an opportunity for socialization. Continuing provision of these services is an important question, but perhaps can be decomposed into multiple questions, which under current circumstances need to have separate solutions. Ones that do not require dragging everyone back into a potential Petri dish

(And regarding mental health, how do you think little Timmy will be affected when he overhears whispers around the family that he brought home the infection that killed Aunt Ellie?)

The National Academies for Science, Engineering and Medicine has just released a lengthy committee report Reopening K-12 Schools During the COVID-19 Pandemic Prioritizing Health, Equity, and Communities.

The New York Times immediately printed an article headlined Scientific Panel Urges Opening Schools to Younger Pupils.

This NASEM report and headlines like this will inevitably be wielded as cudgels to force unsafe school reopenings that will risk the lives of children, parents, educators, non-teaching school staff and all their relatives. Parties with vested interests in reopening will read just the top line and ignore all the carefully written caveats—such as the warning on the report's page 2 about "insufficient evidence" regarding contracting and transmitting Covid-19 by youth. That's really the key, isn't it? We don't yet understand transmissibilty via classrooms, but we should rush to reopen them anyway?

The report spends most of its time marshalling reasons in favor of reopening, largely regarding those extended functions of schools, and outlining methods for mitigating transmission—the same methods we've all heard for months, and that have been ignored or even condemned by officials at several levels of government. They also describe studies that show classroom instruction is particularly valuable for K-5 and special needs students (that accounts for the phrase "to Younger Pupils" in the NYT headline).

But I don't see where they answer the question of how much damage is done by a gap in classroom study.

To be fair, the NASEM report seems very carefully written and factual. Its first "Recommendation 1" is rather mild, as I read it, stating that school districts should "weigh...health risks...against the educational risks" and to "prioritize reopening with emphasisis on...K-5 and students with special needs", hardly justifying the word "Urges" in the Times headline. But the report does seem to have an overall tone that presumes immediate reopening, despite its own many caveats.

As to that New York Times article, it also was reasonable, much of it following the NASEM report's Summary and Recommendations. It's just that headline "Scientific Panel Urges Opening...": you just know how that will be used.

We should work towards reopening schools when feasible, but I do not think we need to panic that children's lives will be ruined if they cannot return to class by Sept. 1. A study gap is surmountable; death is not. Life is long, and diversions can be an opportunity.


2020-Jun-03    What Buckets Are In Your Brain?

[Uploaded June 8.]

Rereading my previous post, 2020-May-30 Liberal Bias in the Media, I thought perhaps I took too long to get to the point. So here is a more direct formulation.

Asked the question "What do we use logic and reason for?" many of us would respond "to find truth," taking this viewpoint to be obvious. But perhaps this belief is neither universal nor obvious.

What is the alternative use for logic and reason? To win arguments. There is a concept called the "argumentative theory of reason" which asserts that our reasoning faculties evolved for the purpose of winning arguments against other humans, not to find objective truth, and that modern rhetoric reflects this winning and persuasion aspect.

Whether or not this is completely correct, it suggests a point on which people may disagree at a very fundamental level. One person may in their mind group statements into buckets labeled "true" and "false"; another person might use "for me" and "against me". We may be wired into one of these configurations based on our inheritance and upbringing, and it may difficult for us to even conceive of thinking in the other way.

One might ask if I am just rephrasing the idea "they lie; we don't". I hope I am expressing an idea that is more useful than just a whine. What I want to say is that people may differ from each other about how strongly they feel that truth always has priority over other considerations. Put that way, the alternative looks possibly supportable—maybe sometimes there are consequences so great that they outweigh the quest for ideal truth. I doubt this idea is novel, but perhaps it should enter our dialog more frequently.

Now, I stridently do not support giving up on the primacy knowledge and truth. I think that direction is ultimately self-defeating, as knowledge has proven so useful in the advancement of humans. To say it another way, I do not want to give the impression that I believe denial of facts is OK, that it is just an alternative, equally valid, useful and effective manner of thought. But seeing that other point of view and what its internal logic is might aid in grasping more accurately the motivation of its adherents. To paraphrase Star Trek's Spock, my objective is not to approve, but to understand.

And before anyone says it, yes, I'm sure that we all make use of both types of reasoning at one time or another. Nobody is completely pure nor perfect. But we can ask which type of reasoner we aspire to be, even if we fail to fully achieve those aspirations in practice. I aspire to be "true/false," what about you?

As I suggested above, these configurations might be deep within our brains. If so, we could perhaps accept that some, perhaps most, of the people who have the other, "for me/against me" reasoning pattern are not duplicitous, evil, self-serving and conniving; they may simply be wired to assess priorities in a differently. (Sorry, there are a number high-profile individuals who I am not willing to let "off the hook" quite so easily: I think they are duplicitous, etc! But that's just my personal perception of a few examples.) Now, merely understanding will not be enough to resolve all conflicts; actions do have consequences, parties will still disagree on which actions will best manage the future, some choices will be proven to be wrong based on the facts. But perhaps understanding will help "true/false" types to frame arguments to better—uh, ahem—persuade the others.

2020-May-30    Liberal Bias in the Media

This topic is not really quantitative, but it involves logic and reasoning. A few days ago the Wall Street Journal (5/25/2020) published an article by Van Gordon Sauter, a former television news executive at CBS and Fox News. In "The 'Liberal Leaning' Media Has Passed Its Tipping Point," the author proposed that the mainstream media clearly has a liberal bias, and that it has become more extreme, more "left" in recent years. He claims that journalists have given up on "objectivity, balance and fairness", and cites their increasingly negative statements about President Trump to support his assertion—indeed, really the only evidence he provides. Sauter calls on those journalists to admit and embrace their "left of center" tendencies in order to preserve press credibility.

Now, this is a nice trap, of course. Mr. Sauter may applaud their forthcomingness, but you know that the moment journalists start to step up for their "I am Spartacus!" moment, right-wing pundits will pounce with denouncements of "See, they ADMIT IT!" So I hope no one falls for this.

How do logic and reasoning relate to this matter? I submit that the huge division between the press and this president has almost nothing to do with traditional left/right, liberal/conservative policy positions, although specific events are described in terms of these familiar matters. Instead, the division has everything to do with what you think logic and reasoning are for. If you think the purpose logic and reasoning (and their friends, study, research and investigation) is to figure out what is true and what is not, then you will have a certain view of this contretemps. If you think their purpose is to win an argument, and that truth is only a secondary concern, then you will have another, opposite, view. I believe that that is the dichotomy: truth vs. winning.

As a mathematical scientist, I throw in my lot with the "truth" camp. I presume that's how most journalists would self-identify as well. And who do we know who seems to be really obsessed with "winning"?

Before you say I've cast the dichotomy unfairly, let me point out that there is some academic support for the "logic is for winning" position! In 2011, Hugo Mercier and Dan Sperber introduced the "argumentative theory of reason" in the journal Behavioral and Brain Science (Vol. 34(2), 2011). Their paper argued that our logical and reasoning faculties evolved exactly for the purpose of winning arguments, not for finding truth.

(Sigh. See? I just could not leave that last paragraph out, even though it might, to some minds, undermine my argument. Truth vs. winning.)

Journalists are not perfect, and their personal opinions may leak into their coverage, and some of those opinions might be socially or politically left of center. I think most of them are aware of these risks and that they take steps to mitigate them. I do not see Sauter's claim of increased expression of "liberal bias" in the media's treatment of social and political policy. Rather, it is a specific, novel epistemological threat that they are defying—these matters should not be conflated.


2020-May-29    Paying for Health Care: Medicaid and Medicare

Finally, following the 2020-May-28 post, let's look at the two traditional big government health care programs in the U.S., Medicaid and Medicare. I knew these were big in terms of cost, but until I investigated the numbers I did not realize that they cover so many Americans. Remember, we discussed earlier (2020-Jan-17) that employer-sponsored insurance covers only about 190 million of the 325 million people in the country; what's up with the rest?

According to the Merck/Schreck reference, in 2017 there were 73 million recipients of Medicaid support, totaling $586 billion, which is around 1/6 of total health care spending. It is also around $8,000 per individual. For Medicare, there were 57 million participants with about a $700 billion total outlay, about $12,000 per person. So that's about $1.3 trillion dollars total. I believe there is some overlap between the Medicaid and Medicare recipients, for example a low-income senior staying in a long-term care facility under Medicaid support, but with Medicare health coverage. So the total number of people covered is probably lower than the 120 million you'd get from just adding the figures.

Now, per person these costs are higher than the private insurance numbers we discussed earlier (more like $6,000), but remember that Medicare and Medicaid recipients tend to be older, and consequently to have more health problems, so we should expect higher costs.

Medicaid is provided based on need, and so generally the recipient pays nothing or very little for services.

Consumers pay for Medicare through lifetime payroll taxes, but also through copays and decuctibles when they consume services. This last is actually an important one to consider as some politicians today are promoting "Medicare for All": as currently implemented, coverage under Medicare does not totally cover expenses, and 20% copays for expensive medical procedures are common. Consequently, many Medicare enrollees also purchase private supplementary insurance to cover the gaps. This is another expense that accrues directly to the consumer. So "Medicare for All" which allows everyong to enroll in the Medicare program regardless of age, would not in and of itself, fully alleviate the medical expense problems of many consumers. To be fair, some of the "Medicare for All" proposals are actually for an enhanced plan that would eliminate copays, deductibles and other gaps, but that's a story for another day.

But now we're coming near the end of the story, and the financial picture is clearer than it was, at least it seems so to me. Here it is. In the United States, and using figures from 2017:

So to close out, it seems that in the U.S., about 2/3 of people are covered by private health insurance (much of it employer-subsidized), costing about 1/3 of the total health care expenses; and 1/3 of people are covered by Medicare and Medicaid, and they consume another 1/3. The remaining 1/3 of the costs are born by individuals as out-of-pocket expenses when they get sick, or by a variety government and private providers.

What does this all mean? Well, I'm not entirely sure, but with 1/3 of the population being on government-run programs, it seems that we may be closer to a "national" system than most people realize. Many of us may receive a lot of out lifetime health services when we are old and on Medicare (full disclosure: I'm not there yet, but getting close!), even after decades of having available, but perhaps infrequently using, private health insurance. (Though again, full disclosure, I did break something expensive once. Ouch.) But, the numbers are above, and in the references, and others can make of them what they will.

If you would to follow my commentary on this subject from the beginning, please jump to my first entry on health care, which is at the beginning (bottom) of this blog and follow the posts upward from there.


2020-May-28    Paying for Health Care: Out-of-pocket

It's been a while since I posted to this blog, and much has changed regarding public views on health care as a result of the Covid-19 pandemic. So I think in this and the next couple of posts I'll just wind up the thoughts that motivated me in January when I started in on this topic, and make my final points. Then I'll move on to some new subjects.

Picking up from my 2020-Jan-19 post, I want to talk about Out-of-Pocket expenses. Insurance often does not pay a person's entire medical bill; the patient is expected to pay some part in the form of deductibles or copays. These amounts are in addition to the regular premium payments, and are charged for medical services obtained, sometimes as a fixed amount and sometimes as a percentage; for example, $20 for a doctor's office visit, or 20% for a surgical procedure. That is, these are payments based on how sick you are, and while some charges are mere tokens, others can run to thousands of dollars. From the Merck/Shreck reference as before, Table 5-2, in 2017 the total out-of-pocket expenditures for all households in the U.S. was $365 billion. That is over $1000 per person, or about $3000 per household on average. (there are about 126 million households in the U.S.)

The out-of-pocket category includes expenditures by people who have no insurance, and so pay everything, but also applies to people who have insurance policies that require deductibles and copays. I have not dug into the numbers to separate out the no-insurance versus some-insurance cases, but the total shown above ($365 billion) is about 10% of total spending. In other words, even after insurance premiums and institutional spending on health care, there is still a remaining cost of $1000 per person per year that people have to pay on their own!

Next: Medicaid and Medicare.


2020-Jan-19    Paying for Health Care: Insurance (2)

In my post 2020-Jan-17, I concluded based on the Merck/Schreck reference that in 2017 private insurance paid out about $1.1 trillion for 190 million covered individuals, or about $6000 per person. But people with employer-sponsored insurance don't pay that much for their premiums, why?

I turns out that employers pay an average of about 3/4 of the premiums for sponsored plans; the employee pays the remaining 1/4. (This is the average. The percentage differs between employers.) Those premiums total $1.2 trillion per year. If we also include the premiums from people who buy private insurance but are not in an employer-sponsored plan, plus the ACA/Obamacare subsidies, the total premium payment is a little under $1.3 trillion.

So the books balance: more money in than out, with the difference being the cost of operations, plus profit. People may differ in their opinions about how much the cost + profit should be, but at least we can see now how the system is able to work out financially.

There is one more important thing we need to look at before we leave the subject of Private Insurance. That's out-of-pocket expenses. Next time.


2020-Jan-17    Paying for Health Care: Insurance

Following my post 2020-Jan-02, I thought we could first take a look at private health insurance, the most common form of coverage in the U.S.

In 2017, about 190 million Americans had medical bills that were covered by private insurance, both individually purchased and employer sponsored plans; this head count includes the subscribers/employees and their covered family members. The total outlay for the covered services was a bit over $1.1 trillion.

These numbers come from a great reference with lots of numbers that I came across at the Merck pharmaceutical company website. I'll refer to it as the Merck/Schreck document:

I will round and otherwise adjust figures to keep the story clean. For example, I excluded Medigap subscribers from the private insurance figures because I presume all or almost of them are on Medicare, which I'll take up at a later date. Of course, any errors I make in interpretation or inferences are mine alone.

Back to the show! So we have 190 million people whose private insurance paid out $1.1 trillion. That's almost 60% of the population, and around $6,000 per person. For a family of three or four, that comes to $18k to $24k per year! And if the insurance providers are to survive financially, at least this much money must also be coming into the providers (on average).

If you have employer-sponsored insurance, you probably pay less than this amount in premiums, because the employer covers part of the cost. But counting both the employer and employee contributions, the annual premium is in the ballpark of $6000 per person. Your employer might provide this information when you sign up for health coverage each year, or you might be able to ask your HR department for it.

(Note that private insurance, including employer-sponsored, usually makes available a "family plan" that covers the parent(s) and any number of dependent children for the same premium, i.e., they stop counting heads within the same family. I am not sure how that works financially for the insurer, I'll have to look into it. But a cost of $18k for such a family policy, split between employer and employee, is again in the right ballpark.)

Finally, even if you have coverage, there can be deductibles and copays that you must pay for certain treatments, that is, you pay when you get sick. I will have more to say on that subject, and on what the other 40% of the population is doing, in future posts.


2020-Jan-02    Paying for Health Care

Some thoughts on health care insurance.

There is a lot of discussion going on now regarding health care insurance coverage. Several candidates have put forward plans that include the details for where the money will come from to pay for coverage, but some of those details invollve policy changes that are themselves controversial, like wealth taxes or changing the way capital gains are taxed. I certainly cannot match the effort that the large campaign staffs have put into developing those plans, but I thought I might be able to construct a simplified, high level view.

The main point I want to propose is that, pertaining to how individuals pay for their health care, there is just one major question to decide, which is

Should we expect each person to contribute the
  1. same amount
  2. an amount based on how sick they are
  3. an amount based on income
for their medical costs?

I am looking only at the matter of how individuals pay for their health care, not at the issue of how much medical providers charge. Reducing costs will be a question for another day. Today, I ask you to think about how you would answer this one question.

Employer-sponsored insurance with no deductibles or copays most closely follows pattern 1: everyone pays the same amount on a continuing basis, and gets the same coverage when they are sick. On the other hand, being uninsured is the most pure form of pattern 2: when you get sick, you pay. Government-sponsored plans often embody pattern 3: money is collected from everyone through taxes which are usually based on income. In the U.S., the Medicare tax is a percentage of income, so the amount you pay is proportional to your salary.

Most insurance options are a mixture of some of the 3 patterns. Employer-sponsored plans usually have deductibles and/or copays that mean you pay extra each time you visit the doctor. These plans are a mixture of patterns 1 and 2. Even Medicare has copays that can be substantial (many expenses are covered only 80%, the other 20% is paid by the patient), a mixture of 3 and 2. In the past, private non-group insurance premiums could depend on your personal health, such as pre-existing conditions or family history, so you would pay more just for being predisposed to get sick. Ending this practice seems to be one of the most-liked elements of the Affordable Care Act (ACA, or Obamacare).

Now, how much do we pay? As most people know, we pay a lot. The media have often reported that health spending is around 17 to 18 percent of gross domestic produce (GDP). Since I want to tie the costs to incomes, I dug up some figures on health expenditures and total personal income in the U.S. in 2017:

Total Health Care Spending $   3.5 trillion
Total Personal Income $  16.9 trillion
References:

So by dividing those two numbers, it looks like U.S. health spending is about 21% of total personal income. This value is consistent with the media reports, since according to the same FRED source the GDB runs a few trillion dollars higher than income.

21% is a scary number, as we shall see below.

By the way, the FRED website operated by the Federal Reserve Bank of St. Louis (one of the 12 member banks that comprise the Federal Reserve) is a great source of financial data and tools to organized and interpret them.

Now let's bring in the number of people that have to be covered, and see what implication the above numbers have.

Population 325 million
Number of Households 126 million
References:

If we spread the spending evenly across the whole population, (pattern 1: everyone pays the same) it comes to $10,700 spending per year ($900/month) for each person in the U.S., including non-working people such as children. So for a family of four, that would be about $43,000 a year, or over $3500/month. No wonder health care seems so expensive! But how can that family of 4, if making the median household income of $61,000, pay $43k, nearly 3/4 of their pay, every year for insurance?

What if instead we spread the cost based on income (pattern 3). Suppose eveyone paid a flat rate of 21%, the "scary" number that we found by dividing Total Health Spending by Total Personal Income. (We could also charge on a progressive scale rather than a flat percentage, but let us use this simple formulation as a starting point.) For a family making the median ($61k), that would be an insurance payment of about $12,800/year, or about $1100/month. An individual making the federal minimum wage of $7.25/hour working a full 40 hours/week would pay about $250/month. On the other hand, a household earning $200,000/year would pay $42,000/year or $3500/month. Lower earners will be happier, but high earners will be less happy under this scenario.

You might think that I'm about to propose a new health care plan that requires a 21% increase in new taxes. I am not. I'm not proposing any plan, but instead I want to identify the basic numbers that place limits on what might be accomplished. To a first approximation, we need to get $3.5 trillion from 325 million people who earn an aggregate of $16.9 trillion. What are the possible ways to distribute that load, and what consequences ensue?

And it is important to keep in mind that as a country we are paying that $3.5 trillion now! So we are not necessarily looking for more money, but initially just to understand how the cost burden is distributed over the population now. Even with complaints we hear about insurance costs, it doesn't seem that families with insurance are paying amounts like $40k/year. So where is the money coming from?

To find answers, I looked into a report by the pharmaceutical and health products company Merck. More about that in a future post.


2020-Jan-02    Beginning of Blog

Welcome to my blog. This is the earliest entry.