Logarithms and Cost-Benefit Analysis Applied to the Coronavirus Pandemic

Two key tools for economics are coming up in the context of the coronavirus pandemic: logarithms and cost-benefit analysis. As for logarithms, the Financial Times has been producing graphs such as the one above. The vertical axis is logarithmic: that is, every time the number of new cases in a week goes up by a factor of ten, the increase in height shown is the same. The horizontal axis is in days since the first time a country had 200 cases in one week. Given the logarithmic vertical scale and the horizontal scale in days, the slope of each country’s curve shows the growth rate of the number of new cases.

In addition to the graph above of the number of new cases in a week, the Financial Times also creates graphs showing on a logarithmic scale the cumulative total number of cases for each country. The graph below helpfully shows the slope corresponding to the cumulative number of cases cases doubling every day, every two days, every three days and every week:

For more on logarithms, see my 2012 post “The Logarithmic Harmony of Percent Changes and Growth Rates.”

As for cost-benefit analysis, a key idea is to put a dollar value on a human life. We don’t know who, but we know some additional people will die if we don’t shut down big sectors of our economy that involve a dangerously high level of physical human proximity, such as schools and restaurants for dine-in. Someone dying or someone living is called a “statistical life.” Suppose for example that almost everyone ultimately gets the coronavirus and that allowing the number of cases to grow too fast would lead to a shortage of hospital beds that would make .6% of everyone in the US die instead of .3% of everyone in the US dying if we can slow things down enough to give high-quality treatment to everyone who has a serious case of COVID-19. Given the 327.2 million population of the US, that means shutting down big sectors of economy for a while would save almost a million lives. It is a million statistical lives, since we don’t know exactly who it will be, but that would be a lot of real people.

I used $9 million as the value of a statistical life in “Cost Benefit Analysis Applied to Neti Pot Use,” But Cass Sunstein, in the article shown below, says the current value is $10 million per statistical life.

Under both Republican and Democratic administrations, regulatory agencies have relied on a monetary figure to capture “the value of a statistical life.” It is now around $10 million. Monetizing human life seems cold-hearted; our intuition rebels against it. But it’s essential.

Why can’t we say a human life is more valuable than that? Here is one simple calculation that illustrates why not. At $10 million per statistical life, the lives of everyone in the 327 million US population are worth $3.272 quadrillion = 3,272,000,000,000,000. It would take more than 152 years of 2019’s US GDP to add up to that much. (2019 US GDP was $21.427 trillion.) So we don’t really have even $10 million to spend saving each person’s life. To pay $10 million to save a statistical life, we have to pool money from quite a few people to pay for each life saved.

Here is how Cass Sunstein makes the case:

You can ask a lot of questions about that research. But it’s clear that in choosing whether to proceed with lifesaving regulations, or how aggressively to proceed, agencies will be required, if only implicitly, to assign some monetary figure to risks of death. In deciding how to handle risks in the workplace, or risks from air pollution, regulators cannot avoid the existence of trade-offs. They aren’t going to spend billions of dollars to prevent one or two deaths, or even 10 or 20.

…

If you take too many precautions against risks — for example, by banning automobiles — you are going to create different risks. Expensive precautions, by virtue of their expense, can endanger human beings — among other things, by increasing poverty and unemployment, which would mean more death. If we care about human welfare, we will insist on exploring the costs and benefits of various approaches, because the resulting numbers give us indispensable information.

But now turn back to the case of the coronavirus pandemic with a simple back-of-the-envelope calculation. A million statistical lives saved (from reducing the death probability per person by .3%) at $10 million each, multiplies out to $10 trillion. That is a bit less than half a year’s worth of GDP. And no one is talking about totally shutting down the economy. If the economy were shut down about halfway, which is a lot more restrictive than what we are doing now, it takes a whole year of being halfway shut down to equal $10 trillion. So if we can do the trick with less cost than that, it is worth it.

There are some subtleties I should address. First, what if low-income folks are paying most of the economic cost of the induced economic coma? Then, if they are not compensated, the dollars they are losing aren’t just any dollars, they are the precious dollars of those who are struggling financially. (See “Inequality Aversion Utility Functions: Would $1000 Mean More to a Poorer Family than $4000 to One Twice as Rich?”) But we can compensate those who are losing their jobs and as a consequence being thrown into a financial crisis. And we have so far gone some fraction of the way in that direction.

Second, what if most of the lives saved would be older folks who didn’t have many years left anyway? Under one calculation, that cut the benefit in half; Cass Sunstein writes:

… Michael Greenstone and Vishan Nigam of the University of Chicago analyzed the likely benefits of “a moderate form of social distancing,” including a seven-day isolation for anyone showing coronavirus symptoms, a 14-day voluntary quarantine for their entire household and dramatically reduced social contact for all those over 70 years of age. They found that over a period of seven months, the result would be to prevent 1.7 million deaths. Under standard assumptions, that’s $17 trillion in benefits. Because a significant percentage of the avoided mortalities involve older people, Greenstone and Nigam adjusted the number down — but still, it’s over $8 trillion, which is the equivalent of $60,000 per U.S. household.

Some people object to the idea that the life of someone older might be worth less, but when it is family, I think almost all of us would be more comfortable with a grandfather or grandmother volunteering to give his life to save the life of a grandchild than a grandchild volunteering to give their life to save the life of a grandfather or grandmother. But let me continue to keep my arithmetic simple by treating any statistical life as worth $10 million.

The bottom line is that it is worth a lot to save a million lives. So it is worth doing a lot to save a million lives. Almost any anti-COVID-19 measure being contemplated is worth it according to standard cost-benefit calculations if it can save a million lives.

It is possible that after learning more about the coronavirus, we would determine that strict social distancing would only save 200,000 lives (or perhaps the equivalent of 200,000 young lives after adjusting for the actual mix of ages of the lives saved). Then the cost benefit calculation would still say it was worth shutting down half the economy for 9 weeks or so, but perhaps not for more than that. But we haven’t overdone social-distancing and educational and business closures yet, even if the trouble we are taking in that regard can only save 200,000 lives.

Update, April 1, 2020: Don’t miss Aatish Bhatia’s graphs with log cumulative cases on one axis and log new cases on the other and time shown dynamically.

Don’t miss these related posts:

Vicky Biggs Pradhan: How Crises Make Us Rethink Our Lives

CPCC certificate.png

I am now a Certified Professional Co-Active Coach. I posted “Co-Active Coaching as a Tool for Maximizing Utility—Getting Where You Want in Life” at the beginning of that journey. Because of my day job as an economics professor and side job as a blogger, I can’t take on any more coaching clients at this point, but I have met other coaches that I can recommend.

The Co-Active Training Institute does a ten-month long Leadership Program as well as training in being a co-active coach. Among other things, the Leadership Program is a very intense interpersonal experience; after the first six-day retreat I already know the other sixteen members of my “tribe” very well. Vicky Pradhan, like me, is a Certified Professional Co-Active Coach, and someone I think would be an especially good fit as a coach for readers of my blog. I had Vicky coach me for a session in order to get a good sense of her style. She is both extremely logical and very emotionally perceptive, and works hard to get to the bottom of things.

I asked Vicky to write a guest post so you could get a sense of her yourself. Also, it is traditional for coaches to offer a free sample session, so it is easy for you to see from your own experience what a powerful coach Vicky is if you have a free half hour. E-mail Vicky (victoriapradhan@gmail.com) if you are interested in trying out the idea of having a coach. I am also happy to answer questions about co-active coaching in the comments section.

I should say that in “diet and health” I include mental health and soul health. The coronavirus crisis is trying to our souls—but maybe in ways that can lead us to dig deep and get new insights on our lives. Here is Vicky:

The coronavirus has required the human race to slow down in ways I never thought imaginable.

In early March our nation was focused on presidential candidates, environmental policy, and the growing tech-lash. Within two weeks we were sheltering-in-place, fearing for our health and regularly checking in on loved ones. Many have lost their jobs. For some, the isolation, deep fear and abundance of free time has created the perfect storm of uncertainty.  For others, who are fortunate enough to have kept their job, it’s been a time to slow down, reflect, reevaluate and contemplate what is really important. 

I recently had a chance to reevaluate my own life while being in isolation for seven months. What I learned was unexpected and it’s helping me to cope during this unprecedented time.

While on vacation in the countryside of France, I was leaving a charming cottage we had stayed at when I accidentally hit my head against the low door threshold that was made out of stone. This misstep changed my life forever. In a blink of an eye, or in this case, a bonk of the head, a severe concussion ensued, and my vision blurred, my ability to concentrate vanished and even the most transactional conversations with my husband and kids became impossible. I spent the remaining week of our trip in a dark room, resting alone before returning home to San Francisco.

With concussion recovery, most neurologists insist on strict cognitive and physical rest until all post-concussion symptoms have subsided. However, in recent years, new research has emerged which challenges this approach and instead suggests returning to daily activities within a few days of the incident allows for a more expedient recovery. Regardless of what I believed in theory, I quickly learned there was no negotiating with my body. By default, my brain chose cognitive rest which meant isolation in a dim, quiet room with no visuals, audio or mental stimulation. It came down to turning off all screens, closing books and turning off podcasts; anything that required my brain to focus. It was a matter of days before I sunk into a deep depression. Anxiety took over, as I lost my executive functioning skills, ability to find words, drive a car or even care for my children.    

Prior to this incident, I was labeled an overachiever. I worked myself too hard and held myself to unrealistic standards; this is what made me successful, or so I thought. Having spent twenty years in the music streaming and tech industries building teams during start-up phase and beyond, I took great pleasure in tackling big challenges so I could prove myself to others. With a husband, two kids in two different schools, a seat on a board and roles as an active volunteer, my world felt like one big box that needed to be checked. That is, until, I experienced being coached by a professional Executive Coach. I was captivated and I knew within a couple sessions that this is the path I would pursue as the next phase of my career. I decided to complete a year-long coach training program. Just as I was about to complete my professional coach certification and launch my own coaching practice, it all came to a screeching halt with the concussion. My vision of being a coach, which was two years in the making seemed to melt away.

By week four of my recovery, I was angrier than ever.  I refused to accept that my life was on hold. I would lay in bed hour after hour doing math equations in my head to see how far I could get. I would rehearse the various principles and contexts of the coaching model. I’d make plans, with my eyes closed, about the places I would visit after climbing out of this dark hole I was stuck in. I fought my reality every step of the way. This newly found depression was uncharted territory for me. I felt new levels of loneliness and desperation for normalcy as I watched my family drive away for short road trips, witnessed my team at Reddit carry on to new heights without me, and saw my coaching clients move along to find other coaches as they needed support in their own lives.

At my lowest point, I turned to my coach. During this time of stress and despair I was truly seen by her. No judgement, no formality, just unconditional support; the kind of support I hadn’t felt before. She encouraged me to surrender to my recovery, and I’m proud to say, I did. Once I surrendered, I had the space and capacity to explore where I’d been and where I wanted to go.

My coach helped me find the courage to investigate the areas of my life that I had boarded up and didn’t permit anyone to access including myself. She held up a mirror so I could see how I was abandoning myself in order to achieve goals and tasks intended to please others. We also covered value clarification which taught me that making resonant choices both professionally and personally can only be done if they are made in accordance with my values. Conversely, conflict, unrest and dissonance almost always arise when I’ve ignored a value, which would ultimately take me off course.

For me, being present and living in the moment has always been a value. I discovered that I was not honoring this value by holding onto a belief that I once I “arrive” at my destination, I would be more fulfilled and ultimately a happier person. “Arriving” in this case meant becoming a certified coach and forming my own coaching practice. I learned that arriving doesn’t exist, as everything is impermanent. I only have today. And, today I can choose how I want to show up in my life. While in silence I continued to be open to recognizing other patterns and used various tools that I had previously ignored to help me stay present and being to change some patterns. Mindfulness, meditating (even for 10 minutes a day), journaling, and turning down the volume of my inner critic are just a few things that helped me to ground myself and take steps towards transformation. Having made a full recovery, I continue to be committed to these daily practices.

Concussion recovery was the sole topic I wanted to cover with my coach, however, like many skilled professional coaches she was able to look at me as a complete, whole person.  She wasn’t there to examine one compartmentalized issue, she could zoom out to see the whole picture. With each new day, I slowly regained my cognitive functionality and by month seven I was back on my feet; however, I had an entirely new way of looking at my life and the way in which I approach it. My outlook included gratitude, humility, and the desire to be in service of others finding their path or returning to it.

Today, we find ourselves in uncharted territory. We are having to make sense of the unimaginable while doing it in isolation. There is an overwhelming feeling of fear, desperation, and sadness. From where I stand, it’s almost as if our nation is recovering from a massive concussion. We are having to surrender. Surrender to the end for quite some time of normalcy in our lives. My hope is that we find the silver lining in this unusual time by looking inward and to find our strength by digging deep within ourselves. Each of us must decide if we are on the track we intended to put ourselves on. Whether on your own or with the support of others now is the time to refocus our lens and get clear on what is important in our lives.

Here is some contact information:

Vicky Pradhan, vicky@v2executivecoaching.com

V2 Executive Coaching, www.v2executivecoaching.com

Vicky is the founder of V2 Executive Coaching. She is a certified Co-Active® Coach, CPCC, who coaches entrepreneurs, executives, founders, creators and musicians on their mission towards something bigger than themselves. Her clients are passionate and aspiring towards more fulfillment, stronger leadership, better communication and in some cases more self-acceptance. The one element they have in common is they’ve identified there is a gap between where they are right now and where they want to be. 

Vicky brings nearly twenty years of experience in the tech and music streaming industry to her coaching practice. Her journey began at CBS Radio where she held positions in Los Angeles, New York and San Francisco. She then entered the tech industry and spent several years at Google then went on to lead brand partnerships teams at both Pandora and Reddit, as start-ups. She earned her Bachelor’s Degree in Business Administration from Loyola Marymount University, where she specialized in Business Management. Other certifications include Creative Resources® Facilitator, Decker Communications® Communicate to Influence Program, Co-Active® Coach Training and is currently participating in the Co-Active® Leadership Program.

How Does This Pandemic End?

Note: Don’t miss the related post “Avoiding Economic Carnage from the Coronavirus: There are Better Policies than Sending Everyone $1000.”

The novel coronavirus behind COVID-19 is extremely good at spreading. It is likely to take a long time to get an effective vaccine. Restrictions on interaction that apply to the vast bulk of the population quickly come to seem quite onerous. As a result, the most serious part of the pandemic is likely to end only when a substantial fraction of the population has had COVID-19 and is immune. (As of today, it is still not known for sure how strong the immunity is from having had COVID-19. I’ll assume the best on that score—that having had COVID-19, even asymptomatically, confers immunity.)

The idea that a large fraction of the population will end up getting infected may seem grim. Is it possible, though, that

  • those who have only a small risk of dying if they get the disease—the young and otherwise healthy—will get exposed and become immune, ultimately bringing the pandemic under control because of their immunity, but

  • those who have a higher risk of dying if they get the disease—the old or already compromised—could largely escape?

To answer this question, I need to modify the SIR model that divides people into the Susceptible, the Infectious and the Recovered. Above and at this link is a wonderful video that provides a primer on the SIR model. I need to modify the SIR model into a model that tracks the fraction of the population in each of these categories within group A and within group B. I will think of group A as the young and otherwise healthy, who are less careful about social distancing but also at lower risk of death should they get infected by the coronavirus. Group B is then the old or compromised, who I assume understand the risk they face and so are more careful at social distancing. (The old or compromised may also suffer a lower economic and lifestyle cost of social distancing.)

With six subgroups (SIR within group A and SIR within group B) the dynamic solution to the differential equation for the modified SIR model is quite complex, but the conditions for the number of infected in group A and the number of infected in group B to be shrinking can be readily analyzed. Define this notation. First, notation for population shares:

SA = share of the overall population that is both in group A and is susceptible

IA = share of the overall population that is both in group A and is infectious

RA = share of the overall population that is both in group A and is recovered (or dead)

SB = share of the overall population that is both in group B and is susceptible

IB = share of the overall population that is both in group B and is infectious

RB = share of the overall population that is both in group B and is recovered (or dead)

Note that SA + IA + RA + SB + IB + RB = 1. Second, notation for constants of transmission:

KAA = constant indicating the risk of transmission between two people in group A

KAB = constant indicating the risk of transmission from someone in group A to someone in group B

KBA = constant indicating the risk of transmission from someone in group B to someone in group A

KBB = constant indicating the risk of transmission between two people in group B

Third, the rate of resolution of an infection:

C = rate at which those who are infectious make the transition to “recovered” which includes being dead, since the dead, like the recovered, will not contribute to further transmission.

All of these are nonnegative quantities.

The two crucial inequalities in this modified SIR model are the conditions for the number of infected within a group to be shrinking. Those two inequalities are:

d IA/dt = KAA * IA * SA + KBA * IB * SA - C * IA < 0

d IB/dt = KBB * IB * SB + KAB * IA * SB - C * IB < 0

Let’s divide each inequality by the share of infected in the corresponding group to get the logarithmic growth rates:

d log(IA)/dt = (1/IA) d IA/dt = [KAA + KBA * (IB/IA)] * SA - C < 0

d log(IB)/dt = (1/IB) d IB/dt = [KBB + KAB * (IA/IB)] * SB - C < 0

Now, let’s define x as the key ratio IB/IA:

x = IB/IA

Substituting into the logarithmic form of the crucial inequalities yields:

d log(IA)/dt = [KAA + x KBA] * SA - C < 0

d log(IB)/dt = [KBB + (1/x) KAB] * SB - C < 0

Note that

d log(x)/dt = d log(IB)/dt - d log(IA)/dt = [KBB + (1/x) KAB] * SB - [KAA + x KBA] * SA.

There will be a (temporary) steady-state level of x when

d log(x)/dt = [KBB + (1/x) KAB] * SB - [KAA + x KBA] * SA = 0.

We can solve this for a temporary-steady-state level of x that might be a good approximation. Let’s plug in some plausible numbers to get some sense of what will happen.

First, let’s start with almost everyone susceptible. In particular, assume that, approximately,

SA = 2/3

SB = 1/3

Let’s use a week as the time unit. A two-week course of the disease can be represented by C = .5/week. And the idea that someone infected infects roughly 3 other people when not putting much effort into social distancing can be represented by KAA = 1.5/week. Let’s imagine that KBB = KAB = KBA = .3/week because those in group B are putting great effort into social distancing. (This is optimistic.)

This yields a quadratic equation in x. It is the positive root that is relevant: .108 with these parameters.

By contrast, suppose that no one was doing social distancing so that KAA = KBB = KAB = KBA = 1.5. Then the temporary-steady-state level of x is .616.

At the temporary-steady-state level of x, looking at either of the crucial inequalities will give us an equivalent answer for when the number of infectious people will begin declining. Let’s look at the first of the crucial inequalities, plugging in the numbers when almost everyone is still susceptible and when group B is making strenuous efforts to do social distancing but group A isn’t:

d log(IA)/dt = [(1.5/week) + .108 (.3/week)] * 2/3 - (.5/week) = .522

This clearly fails to satisfy the inequality for a shrinking number of infectious people of group A, and the number of infectious people of group is an approximately a constant ratio to this.

If half of group A had the disease (many perhaps asymptomatically) and became immune, that would reduce SA to 1/3, and the inequality would be close to being satisfied. Not quite, because x would go up from .108 because of the influence of SA getting lower faster than SB gets lower on the quadratic equation. But when a bit more than half of group A becomes immune, then the number of those who are infectious will begin to drop.

The bottom line is that if these parameters are in the right ballpark, things will only end when a large fraction of group A has had the disease and becomes immune or dies, which will also involve a substantial but considerably smaller fraction of group B has had the disease and becomes immune or dies.

Note that this ending of the pandemic doesn’t require continuing restrictions on group A. Indeed, the assumption was that group A never really took the restrictions seriously in the first place. Restrictions on group B may be necessary for quite a while.

The Key Question

The biggest unknown about COVID-19 right now is what fraction of people have already had the disease and become immune. We may know within a couple of weeks: scientists are eager to deploy tests for antibodies to the virus (which would be a good indication of immunity) on random samples of the population.

Because we know quite well how many people have died from COVID-19, it would be good news in several ways if we find that a large fraction of the population has already had the disease and has become immune. First, and most important, it would mean that the fatality rate when infected is lower than people have been thinking. Second, it would mean the symptoms are often too mild for people to have gotten diagnosed already during a period when, for the most part, only those who seemed quite sick were tested. Third, if a large fraction of people have already had the disease and have become immune, it means we are closer to the moment when it is safe to lift restrictions on the bulk of the population, which would lessen the economic impact of measures to control the pandemic.

Note that a large fraction of the population already having had the disease and having become immune would go along with the coronavirus having been fiendishly good at spreading, which is quite possibly true.

One thing that doesn’t depend on knowing how many people have already been infected is the disaster of overloaded hospitals in the next few weeks. For the next few weeks, the number of people who are in critical condition and the growth rate are enough to enable prediction. (However, one does need to guess how effective any change in social distancing measures will be.)

Discussion of Similar Perspectives in the News and the News as It Relates to Likely Values of the Relevant Parameters and Values of State Variables for the Coronavirus

Clive Cookson in the Financial Times: “Coronavirus may have infected half of UK population — Oxford study: New epidemiological model suggests the vast majority of people suffer little or no illness”

The new coronavirus may already have infected far more people in the UK than scientists had previously estimated — perhaps as much as half the population — according to modelling by researchers at the University of Oxford.

If the results are confirmed, they imply that fewer than one in a thousand of those infected with Covid-19 become ill enough to need hospital treatment, said Sunetra Gupta, professor of theoretical epidemiology, who led the study. The vast majority develop very mild symptoms or none at all.

Max Colchester and Denise Roland in the Wall Street Journal: “U.K. Trials Coronavirus-Immunity Tests for Home Use: The tests, if successful, would ease disruptions and lockdowns, but some experts have doubts”

In Britain, the government said Wednesday it is trialing personal blood-testing kits that it hopes to distribute as soon as next week. The test—if it functions—could clear the way for people who have caught and recovered from Covid-19 to return to work or volunteer to help others, potentially easing the disruption caused by the pandemic.

Across the world, laboratories and diagnostics companies are racing to fine-tune a cheap, portable, mass-testing device that can quickly show if a person has acquired immunity to the virus. The U.S. Centers for Disease Control and Prevention has said it is also working on its own antibody test for the virus.

…

If the test does work, it could not only help a portion of the population go back to work but also help answer questions about the virus itself including how widespread it is.

“In China, why is it going down? Is it because the virus is dying out or is it because many more people are getting infected than we think and are developing antibodies?” said Mr. Wraith.

Rebecca Ballhaus and Stephanie Armour in the Wall Street Journal: “Trump Says Parts of U.S. Could Go Back to Work in a Few Weeks: White House weighs proposing workplace coronavirus testing, but capacity remains limited; governors suggest they will go their own way”

Tedros Adhanom Ghebreyesus, director-general of the World Health Organization, warned in a briefing Wednesday that in the absence of necessary preparations, the virus could resurge once restrictions are eased. “The last thing any country needs is to open schools and businesses, only to be forced to close them again because of a resurgence,” he said.

Feliz Solomon, Betsy McKay and Jon Emont in the Wall Street Journal: “When Will It Be Safe to Loosen Coronavirus Lockdowns? Governments prepare for the long haul as authorities grapple with how much economic pain countries can endure”

Months of isolation, social distancing and economic distress could lead to more health problems than Covid-19 itself, said David Katz, founding director of Yale University’s Prevention Research Center. Job losses lead to lack of health insurance, food insecurity, stress, and sometimes drug and alcohol abuse and suicides, he said.

He has proposed a stratified approach in which those most vulnerable to Covid-19—people ages 75 and older, and those of any age with heart disease or another serious underlying condition—would remain isolated or maintain social distancing. Meanwhile, people under age 60 would largely go back to their daily lives after a few weeks, while following hand-washing and other precautions.

“What I’ve been concerned about is we can hurt people if we let them get this infection, and we can hurt people with an all-out war that destroys their lives in other ways,” said Dr. Katz, who said he has spoken with two U.S. governors about his proposal. “I’m saying how about we do this in phases.”

The first phase is the current one: strict social distancing for a few weeks to avoid sharp peaks of infection and prevent the health-care system from being overwhelmed, he said. Testing should be expanded in the U.S. to figure out how many people are sick, he said.

Then experts in epidemiology, virology, mathematical modeling and other fields should analyze the data and figure out a way to protect the vulnerable while allowing others to get on with their lives, he said.

Holman Jenkins in the Wall Street Journal: “The Happy Few Are the Cured: Now let’s get on with saving the economy while protecting the vulnerable.”

The giddiest among us soon will be those who tested positive and now have it behind them. The world will be their oyster. A Craigslist page will soon appear for coronavirus antibody-positive personal services. People will get paid hundreds of dollars an hour if they can document their immunity. Starbucks is opening up again in Wuhan. In the U.S., Seattle or New York will get the first antibody-positive Starbucks: Every barista will be able to prove they’ve had the coronavirus.

Eran Bendavid and Jay Bhattacharya in the Wall Street Journal: “Is the Coronavirus as Deadly as They Say? Current estimates about the Covid-19 fatality rate may be too high by orders of magnitude.”

Eran Bendavid and Jay Bhattacharya do a good job of assembling the shreds of evidence relevant to how many people are infected but don’t have serious symptoms. But they dramatically overinterpret this evidence. When comprehensive samples certain classes of people are tested for the coronavirus, the infection will be detected, on average, several days before it would have been detected if they were only tested after showing symptoms. With prevalence growing so fast, that makes the numbers from comprehensive samples comparable only after adjusting for how early in an infection something is detected.

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Plots like the one just above suggest the incidence of the virus was doubling every two or three days when the data was collected, so a difference of a little over a week in how early an infection is detected could reduce the adjustment factors Eran and Jay adduce by a factor of ten. That is, the mortality rates and serious symptom rates might need to be adjusted upward by a factor of ten to account for growth over a little more than a week to make the numbers comparable. Still, these numbers give some hope that COVID-19 is better at spreading and less deadly given infection than most people have been thinking. Here are the shreds of evidence Eran and Jay assemble:

Population samples from China, Italy, Iceland and the U.S. provide relevant evidence. On or around Jan. 31, countries sent planes to evacuate citizens from Wuhan, China. When those planes landed, the passengers were tested for Covid-19 and quarantined. After 14 days, the percentage who tested positive was 0.9%. If this was the prevalence in the greater Wuhan area on Jan. 31, then, with a population of about 20 million, greater Wuhan had 178,000 infections, about 30-fold more than the number of reported cases. The fatality rate, then, would be at least 10-fold lower than estimates based on reported cases.

Next, the northeastern Italian town of Vò, near the provincial capital of Padua. On March 6, all 3,300 people of Vò were tested, and 90 were positive, a prevalence of 2.7%. Applying that prevalence to the whole province (population 955,000), which had 198 reported cases, suggests there were actually 26,000 infections at that time. That’s more than 130-fold the number of actual reported cases. Since Italy’s case fatality rate of 8% is estimated using the confirmed cases, the real fatality rate could in fact be closer to 0.06%.

In Iceland, deCode Genetics is working with the government to perform widespread testing. In a sample of nearly 2,000 entirely asymptomatic people, researchers estimated disease prevalence of just over 1%. Iceland’s first case was reported on Feb. 28, weeks behind the U.S. It’s plausible that the proportion of the U.S. population that has been infected is double, triple or even 10 times as high as the estimates from Iceland. That also implies a dramatically lower fatality rate.

The best (albeit very weak) evidence in the U.S. comes from the National Basketball Association. Between March 11 and 19, a substantial number of NBA players and teams received testing. By March 19, 10 out of 450 rostered players were positive. Since not everyone was tested, that represents a lower bound on the prevalence of 2.2%. The NBA isn’t a representative population, and contact among players might have facilitated transmission. But if we extend that lower-bound assumption to cities with NBA teams (population 45 million), we get at least 990,000 infections in the U.S. The number of cases reported on March 19 in the U.S. was 13,677, more than 72-fold lower. These numbers imply a fatality rate from Covid-19 orders of magnitude smaller than it appears.

John Cochrane in the Wall Street Journal: “Flatten the Coronavirus Curve at a Lower Cost: A total shutdown could cost the economy $1 trillion a month. We need more tailored measures.”

A blanket lockdown can’t go on. Keeping every business closed and every worker at home until a vaccine is available won’t work. Replacing the private economy with borrowed federal money for months on end won’t work. If this were the plague, with 50% of the infected dying, it might be a different story. But people won’t put up with losing many trillions of dollars to flatten the curve of this virus.

…

State and local governments need to work with businesses to figure out a satisfactory combination of personal distance, self-isolation, frequent testing, stricter rules for those who must interact with customers, cleaning protocols and so on. Each industry will likely be different. Even onerous rules, which can be eased as officials and businesses gain information and experience, are better than a blanket ban.

…

Government officials need to work with a scalpel, not a sledgehammer. Isolate old people and those with pre-existing health conditions, who are much more likely to end up needing emergency care, while letting the young and healthy get back to work, carefully. Retired people have income streams that aren’t as disrupted by the virus. They can stay home. Lock down hotspots, but not entire states. Follow the Taiwan, South Korea and Singapore models: extensive testing, contact tracing, detailed people tracking. But keep the economy open, subject to stringent safety rules.

Wall Street Journal Editorial Board: “Parks and Virus Recreation: Cutting off access to outdoor space strains the cooped-up public.”

Officials seeking to slow the spread of coronavirus have imposed sweeping restrictions on roughly one in four Americans. Several states have closed churches, restaurants and bars, gyms and other businesses. Some governors and mayors are now moving to limit access to parks and other outdoor spaces. The goal as always is to slow the virus’s spread, but with cabin fever raging for shut-ins, we have to wonder whether closing down large open spaces does more harm than good.

…

Mr. Cuomo also suggested opening some streets to pedestrians only. Increasing the amount of outdoor space would be helpful in highly populated cities like New York, and it’s feasible now that vehicle traffic has fallen amid the shutdowns. But other officials have threatened or acted to decrease the amount of outdoor space.

…

Surely some middle ground can be found between asking for public compliance with personal distancing and then making large public spaces inaccessible. Compared to grocery stores or pharmacies, outdoor spaces are lower-risk for contagion. Especially in big cities, people can’t be expected to stay cooped up in their tiny apartments indefinitely. The phrase “stir crazy” comes to mind. If officials push too far, many people will ignore both reasonable and unreasonable restrictions.






Fasting Helps Avoid Collateral Damage in Fighting Bacterial Infections; Glucose Helps Avoid Collateral Damage in Fighting Viral Infections

The experiment flagged above about the effect of diet on fighting infection was only “performed on a single mouse strain (C57BL/6J) in one mouse facility,” but its results are striking. The three-minute video abstract is well done. (You can see it at the bottom of the image above.) The brief summary from that video is:

  • When the mice are not fed, or glucose is blocked, the mice with the bacterial infection live, while those with the viral infection live.

  • When the mice are fed glucose, the mice with the bacterial infection die, while those with the viral infection live.

If I understand the discussion section at the end of the paper, the issue is not effectiveness at killing the bacteria or viruses, but rather the damage to one’s own cells of the immune response. Ketones seemed to help protect cells from collateral damage when fighting bacteria, while glucose seemed to help protect cells from collateral damage when fighting viruses.

Note that collateral damage of this sort is only likely to be occurring in a big way if one is feeling symptoms. But if one is feeling symptoms of a viral infection, it might be OK to have some carbs, while if one is feeling symptoms of a bacterial infection, fasting might be helpful.

Again, this is one study in one laboratory using one strain of mice, but this shred of evidence might be useful given our current state of ignorance.

For annotated links to other posts on diet and health, see:

The Federalist Papers #7 B: Without Union, Economic Disagreements Would Drive the States toward Conflict with One Another—Alexander Hamilton

In the second half of The Federalist Papers #7, Alexander Hamilton shows a keen understanding of psychology when discussing the animosity between the states that could be engendered by economic disagreements if the states are not united.

Alexander Hamilton points to three areas of potential economic disagreement. Quoting him in each case,

  1. Each State, or separate confederacy, would pursue a system of commercial policy [that is, tariff policy] peculiar to itself.

  2. The public debt of the Union would be a further cause of collision between the separate States or confederacies. The apportionment, in the first instance, and the progressive extinguishment afterward, would be alike productive of ill-humor and animosity.

    • How would it be possible to agree upon a rule of apportionment satisfactory to all?

    • There are even dissimilar views among the States as to the general principle of discharging the public debt.

  3. Laws in violation of private contracts, as they amount to aggressions on the rights of those States whose citizens are injured by them, may be considered as another probable source of hostility.

The psychological reaction to these disagreements is similar whatever the particular cause among these three. Here are some of the key passages Alexander Hamilton pens on that score:

  • … distinctions, preferences, and exclusions … would beget discontent.

  • The habits of intercourse, on the basis of equal privileges, to which we have been accustomed since the earliest settlement of the country, would give a keener edge to those causes of discontent than they would naturally have independent of this circumstance.

  • WE SHOULD BE READY TO DENOMINATE INJURIES THOSE THINGS WHICH WERE IN REALITY THE JUSTIFIABLE ACTS OF INDEPENDENT SOVEREIGNTIES CONSULTING A DISTINCT INTEREST. [All caps is in the original]

  • It is not at all probable that this unbridled spirit would pay much respect to those regulations of trade by which particular States might endeavor to secure exclusive benefits to their own citizens. The infractions of these regulations, on one side, the efforts to prevent and repel them, on the other, would naturally lead to outrages, and these to reprisals and wars.

  • There is scarcely any that can be proposed which is entirely free from real objections. These, as usual, would be exaggerated by the adverse interest of the parties.

  • The procrastinations of the former would excite the resentments of the latter.

  • The citizens of the States interested would clamour; foreign powers would urge for the satisfaction of their just demands, and the peace of the States would be hazarded to the double contingency of external invasion and internal contention.

  • Their refusal would be too plausible a pretext to the complaining States to withhold their contributions, not to be embraced with avidity; and the non-compliance of these States with their engagements would be a ground of bitter discussion and altercation.

  • … delinquencies in payments on the part of some of the States would result from a diversity of other causes--the real deficiency of resources; the mismanagement of their finances; accidental disorders in the management of the government; and, in addition to the rest, the reluctance with which men commonly part with money for purposes that have outlived the exigencies which produced them, and interfere with the supply of immediate wants. Delinquencies, from whatever causes, would be productive of complaints, recriminations, and quarrels.

  • … there is nothing men differ so readily about as the payment of money.

  • We are not authorized to expect that a more liberal or more equitable spirit would preside over the legislations of the individual States hereafter, if unrestrained by any additional checks, than we have heretofore seen in too many instances disgracing their several codes.

  • We have observed the disposition to retaliation excited in Connecticut in consequence of the enormities perpetrated by the Legislature of Rhode Island …

Below is the relevant section of The Federalist Papers #7 in full, showing the context for these points:

The competitions of commerce would be another fruitful source of contention. The States less favorably circumstanced would be desirous of escaping from the disadvantages of local situation, and of sharing in the advantages of their more fortunate neighbors. Each State, or separate confederacy, would pursue a system of commercial policy peculiar to itself. This would occasion distinctions, preferences, and exclusions, which would beget discontent. The habits of intercourse, on the basis of equal privileges, to which we have been accustomed since the earliest settlement of the country, would give a keener edge to those causes of discontent than they would naturally have independent of this circumstance. WE SHOULD BE READY TO DENOMINATE INJURIES THOSE THINGS WHICH WERE IN REALITY THE JUSTIFIABLE ACTS OF INDEPENDENT SOVEREIGNTIES CONSULTING A DISTINCT INTEREST. The spirit of enterprise, which characterizes the commercial part of America, has left no occasion of displaying itself unimproved. It is not at all probable that this unbridled spirit would pay much respect to those regulations of trade by which particular States might endeavor to secure exclusive benefits to their own citizens. The infractions of these regulations, on one side, the efforts to prevent and repel them, on the other, would naturally lead to outrages, and these to reprisals and wars.

The opportunities which some States would have of rendering others tributary to them by commercial regulations would be impatiently submitted to by the tributary States. The relative situation of New York, Connecticut, and New Jersey would afford an example of this kind. New York, from the necessities of revenue, must lay duties on her importations. A great part of these duties must be paid by the inhabitants of the two other States in the capacity of consumers of what we import. New York would neither be willing nor able to forego this advantage. Her citizens would not consent that a duty paid by them should be remitted in favor of the citizens of her neighbors; nor would it be practicable, if there were not this impediment in the way, to distinguish the customers in our own markets. Would Connecticut and New Jersey long submit to be taxed by New York for her exclusive benefit? Should we be long permitted to remain in the quiet and undisturbed enjoyment of a metropolis, from the possession of which we derived an advantage so odious to our neighbors, and, in their opinion, so oppressive? Should we be able to preserve it against the incumbent weight of Connecticut on the one side, and the co-operating pressure of New Jersey on the other? These are questions that temerity alone will answer in the affirmative.

The public debt of the Union would be a further cause of collision between the separate States or confederacies. The apportionment, in the first instance, and the progressive extinguishment afterward, would be alike productive of ill-humor and animosity. How would it be possible to agree upon a rule of apportionment satisfactory to all? There is scarcely any that can be proposed which is entirely free from real objections. These, as usual, would be exaggerated by the adverse interest of the parties. There are even dissimilar views among the States as to the general principle of discharging the public debt. Some of them, either less impressed with the importance of national credit, or because their citizens have little, if any, immediate interest in the question, feel an indifference, if not a repugnance, to the payment of the domestic debt at any rate. These would be inclined to magnify the difficulties of a distribution. Others of them, a numerous body of whose citizens are creditors to the public beyond proportion of the State in the total amount of the national debt, would be strenuous for some equitable and effective provision. The procrastinations of the former would excite the resentments of the latter. The settlement of a rule would, in the meantime, be postponed by real differences of opinion and affected delays. The citizens of the States interested would clamour; foreign powers would urge for the satisfaction of their just demands, and the peace of the States would be hazarded to the double contingency of external invasion and internal contention.

Suppose the difficulties of agreeing upon a rule surmounted, and the apportionment made. Still there is great room to suppose that the rule agreed upon would, upon experiment, be found to bear harder upon some States than upon others. Those which were sufferers by it would naturally seek for a mitigation of the burden. The others would as naturally be disinclined to a revision, which was likely to end in an increase of their own incumbrances. Their refusal would be too plausible a pretext to the complaining States to withhold their contributions, not to be embraced with avidity; and the non-compliance of these States with their engagements would be a ground of bitter discussion and altercation. If even the rule adopted should in practice justify the equality of its principle, still delinquencies in payments on the part of some of the States would result from a diversity of other causes--the real deficiency of resources; the mismanagement of their finances; accidental disorders in the management of the government; and, in addition to the rest, the reluctance with which men commonly part with money for purposes that have outlived the exigencies which produced them, and interfere with the supply of immediate wants. Delinquencies, from whatever causes, would be productive of complaints, recriminations, and quarrels. There is, perhaps, nothing more likely to disturb the tranquillity of nations than their being bound to mutual contributions for any common object that does not yield an equal and coincident benefit. For it is an observation, as true as it is trite, that there is nothing men differ so readily about as the payment of money.

Laws in violation of private contracts, as they amount to aggressions on the rights of those States whose citizens are injured by them, may be considered as another probable source of hostility. We are not authorized to expect that a more liberal or more equitable spirit would preside over the legislations of the individual States hereafter, if unrestrained by any additional checks, than we have heretofore seen in too many instances disgracing their several codes. We have observed the disposition to retaliation excited in Connecticut in consequence of the enormities perpetrated by the Legislature of Rhode Island; and we reasonably infer that, in similar cases, under other circumstances, a war, not of PARCHMENT, but of the sword, would chastise such atrocious breaches of moral obligation and social justice.

In the first half or The Federalist Papers #7, Alexander Hamilton talks about the likelihood of territorial disputes if the states are not part of a union. (See “The Federalist Papers #7 A: Divided, the States Would Fall into Territorial Disputes Likely to Lead to War Between the States—Alexander Hamilton.”) In the final paragraph of The Federalist Papers #7 Alexander Hamilton goes in a bit different direction, repeating an argument given by John Jay in The Federalist Papers #5. (See “The Federalist Papers #5: Unless United, the States Will Be at Each Others' Throats.”) Here is how he seconds that argument:

The probability of incompatible alliances between the different States or confederacies and different foreign nations, and the effects of this situation upon the peace of the whole, have been sufficiently unfolded in some preceding papers. From the view they have exhibited of this part of the subject, this conclusion is to be drawn, that America, if not connected at all, or only by the feeble tie of a simple league, offensive and defensive, would, by the operation of such jarring alliances, be gradually entangled in all the pernicious labyrinths of European politics and wars; and by the destructive contentions of the parts into which she was divided, would be likely to become a prey to the artifices and machinations of powers equally the enemies of them all. Divide et impera [divide and command] must be the motto of every nation that either hates or fears us. [In order that the whole subject of these papers may as soon as possible be laid before the public, it is proposed to publish them four times a week--on Tuesday in the New York Packet and on Thursday in the Daily Advertiser.]

PUBLIUS.

Here are links to my other posts on The Federalist Papers so far:

Avoiding Economic Carnage from the Coronavirus: There are Better Policies than Sending Everyone $1000

I had a chance to talk through economic policy responses to Covid-19 in my graduate business cycle class yesterday. I very much like Donald Marron’s take on it, which you can see in this Twitter thread, whose first tweet is shown above. I think what I have to say is very much consistent with what he says. He writes that while the epidemic is raging, we want to reduce economic activity in sectors such as restaurants, travel and in-person entertainment in order to reduce transmission of the coronavirus. I am on the side favoring very strong social-distancing measures. I am glad our republic is taking things more seriously than it did 10 days ago. Strong social-distancing measures should result in an intentional sharp recession of an unusual type: things that can be done remotely or at low enough human densities to be reasonably safe, or are essential, such as groceries, will continue, and health-care-related activities will increase, but other virus-unsafe and not-absolutely-essential sectors will basically shut down or contract markedly.

After we have brought the epidemic under enough control to allow economic activity to resume in almost all sectors, a big issue we face is that many people will have lost their jobs or self-employment income but still face bills such as the rent, mortgage payments, groceries, etc. There are many people of low and moderate incomes who would face serious economic hardship without aid. We should help them. Legally requiring forbearance by landlords and creditors is probably appropriate, but then puts a financial strain on those landlords and creditors which might need to be addressed in some cases.

More generally, small businesses and nonprofits that were totally sound in the absence of the epidemic may be facing bankruptcy. Personally, I don’t want my favorite restaurants to go under financially simply because they have to keep paying rent during the epidemic but have almost no revenue. Since the financial hit from the epidemic is not their fault, I am very sympathetic to the idea of bailing out small businesses that would fail without help only because of the coronavirus.

Note that I am not so worried about big businesses. For them, bankruptcy simply means that they end up owned by the bondholders instead of the stockholders, who are wiped out, but they can continue in operation. The government should only bail them out if their operations would be affected by the financial hit. Note that banks should be OK if appropriate aid is given to the people who owe money to banks and would be drive to bankruptcy in the absence of aid.

But how can we get aid to people quickly and still have time to carefully think through how to target it? Here is my proposal:

  1. Instead of mailing $1000 check to each person as is being discussed, mail each adult a government credit card with a $5000 line of credit. Mail similar government credit cards with lines of credit that are a certain percentage of previous revenue to small businesses that would be most strongly affected by the coronavirus. (Businesses that have filed a tax return at least once would be eligible according to a formula. Businesses newer than that would have to apply.) This allows households and business to meet their immediate bills to a much greater extent than a mere $1000.

  2. Couple the issuance of these government credit cards with their associated lines of credit with an announcement that the government would do means-tested loan forgiveness according to criteria that the government will take the needed time to work out.

This proposal is a version of my “Federal Lines of Credit” proposal. I have links to my posts on this proposal collected at the bottom of my post “Helicopter Drops of Money Are Not the Answer.” There is, however carefully targeted transfers in the form of loan forgiveness added to the Federal Lines of Credit.

The Federal Lines of Credit combined with the promise of means-tested loan forgiveness should go a long way toward supporting aggregate demand after the worst of the epidemic is over. But it may be necessary for the Fed to support aggregate demand by cutting interest rates further—into negative territory. My judgment of Fed performance so far in this epidemic is that they are doing a good job except for too much reluctance to consider negative interesting rates. (For example, they are doing a good job of keeping the functioning of the financial markets reasonably normal, and cut interest rates quickly to near zero.) I have links to my posts on negative interest rate policy here:

Also, I wrote a major post about negative interest rate policy just last Thursday:

Right now, the focus for fighting the coronavirus is appropriately on public health and medical interventions. But economists are tasked with thinking ahead to how we can avoid long-lasting economic carnage from the Covid-19 epidemic.

Update March 26, 2020: Ed Glaeser says in a Wall Street Journal op-ed that you can do the equivalent of loans through the tax system. Here is the relevant passage:

One way to do this would be to offer the payments to every American regardless of income, but then assess each recipient’s need after the fact and recoup the expense in a progressive manner. Everyone could get $2,000 right away, but if their household income exceeded $200,000 the following year they would be charged for 100% of the payment in taxes. Households below $100,000 might pay no tax, and intermediate earners could pay something in between. That way the money would be conditional, but people wouldn’t have to worry about it until the next tax season.

For the US, most of the details of a $2 trillion package are already baked in, but the policy for economic policy response to the novel coronavirus is likely still in flux in some other countries, and there is a chance additional economic policy response packages will be necessary in both the US and elsewhere. Economically, a lot depends on how long the unsafe, non-essential sector is shut down (as well as how broadly “essential” is interpreted). I discuss some relevant issues in today’s post “How Does this Pandemic End?”