Just when social distancing gained broad adoption to stem the spread of the coronavirus, some are now urging that the American economy be restarted even before the virus has yet to be fully mitigated. This stands in contrast with stronger measures taken in Europe and England, which on Tuesday announced that its entire population should shelter in place during the next three weeks.
In our estimation, sending the public back to work at this time would be premature, put far more individuals at risk and run the risk of another series of economic shutdowns should there be a second or third wave this fall and next winter. Based on our economic analysis, the U.S. is better off taking a one-time hit to economic growth, as efforts to terminate the virus continue, rather than run the risk of multiple economic shutdowns.
Sending the public back to work at this time would put far more individuals at risk and run the risk of another series of economic shutdowns.
We are sensitive to the fact that mayors and governors face the dilemma of how to mitigate the spread of the coronavirus while supporting the economic and financial well-being of residents. But our estimation of the probability of contact, spreading of the virus and the panoply of risks around the economy does not support taking the equally risky step of reopening the economy before the virus can be mitigated.
Since the federal government has not yet chosen to implement a comprehensive policy to address the health, financial and economic consequences of the crisis, it is understandable that individuals are looking for a way to feed themselves, pay the rent and keep the lights on.
It is perfectly rational that individuals are itching to get back to work with many surviving from paycheck to paycheck. But based on the best scientific information, that is not in the interests of the private sector firms, the economy or the country.
Public policy dilemma
The public policy dilemma of this most unique of crises has left political actors to make extraordinarily difficult decisions. For example, Mayor Bill de Blasio of New York City chose to keep schools open to feed the many students who rely on school meals each day. Only after it became apparent that the outbreak had created extraordinary circumstances were schools, restaurants and bars closed for the duration, leaving the city scrambling on how to feed those individuals.
Decisions by governors to order individuals to shelter in place have created impossible decisions for owners of small and medium-size firms that now face similar issues. How exactly does one keep a business running and guarantee income for the employees amid the risk of spreading the disease among workers and clients?
Using concepts familiar to most business school grads and other graduate students, we can see that – despite the best intentions — a moderate response to the virus might not be the optimal way to protect lives and eventually get the economy back on its footings.
And in the absence of government direction, it might be in the best interests of each business to use social distancing and work-at-home practices and for all non-essential businesses to take a holiday until the spread of the virus is contained.
Drawing on financial principles
Here, it may make the most sense to use the framework of portfolio management, where the most common concept is diversifying investments among various assets with different maturity profiles and rates of return. We can apply those financial principles to containing the virus and perhaps maintaining the viability of the economy.
Consider a classic financial and economic problem. Would you rather have:
- An investment that grows by 100% for one year and by 0% for the next nine years
- An investment that grows by 10% every year for the whole 10 years?
The second choice is clearly preferable because your money grows by a factor of 1.1010 = 2.6, whereas the first choice only doubles your money.
It’s better to have more money than less. But the logic of policy in the time of the coronavirus is counterintuitive and may be more efficient to think like a bad investor and to flip the portfolio analysis on its head. Instead of maximizing return, we need to minimize return, which in our case is the spread of the coronavirus.
So rather than wait until the weather warms up in April to see if the virus plays itself out, we should pull out all the stops at the earliest moment and shut down public interaction to the extent that it is socially acceptable and possible.
The shutdown should last until the number of cases diminishes to the point where it seems reasonable to permit limited interaction. If the number of cases were to increase again, we should revert to a complete shutdown, and so on, until a vaccine is discovered or the number of cases ceases to grow.
This is essentially what the U.S. private sector and families did in the 1950s, when polio was killing a half a million people each year. Children were told not to play in the water (polio was thought to be transmitted through the water), limit interaction with other children with the exception of public education and follow the advice of the scientific community.
Over time, vaccines were found and administered to everyone free of charge. The vaccines were thanks to the work of Dr. Jonas Salk and Dr. Albert Sabin and to a government that had the sense to know that eradication of disease was in everyone’s long-term best interest despite near-term economic and political risks.
Questions with no answers
The questions that cannot be answered at this time are “When will the pandemic stop?” and “Will it come back at a later date?” As to the first question, and as the figure below suggests, the spread of the virus in the U.S. appears to be following an exponential path. At the start (January 21 was the first reported U.S. case), the virus was growing at a rate of 2n, where n is the number of weeks. In other words, an infected person was likely to infect two others in a week, and those two would infect two others, and so on.
Disturbingly, that rate has been accelerating. By March 8, each infected person led to the infection of 2.2n other people. And then 10 days later, the rate of change was approaching 3n and continues to accelerate.
The rate of infection in the United States has been accelerating.
So when the president of the United States proclaims at a press conference on February 26 that there were 15 reported cases and then adds, “When you have 15 people, and the 15 within a couple of days is going to be down to close to zero, that’s a pretty good job we’ve done,” that sows confusion in the public about the science and math around disease. In reality, by February 26, there were already 59 cases. That would more than double in six days.
Less than a month later, there are more than 32,000 cases in the U.S., and that could more than double in days unless people have accepted the danger and have quarantined themselves. The evolution of the data strongly implies that a change in policy at this time would not be constructive.
The acceleration in coronavirus cases in the U.S. shows a pattern similar to the spread of the virus in Italy. While pockets of the virus are showing up across the U.S., most cases in Italy are concentrated in the northern state of Lombardy, which includes the industrial area around Milan. This concentration might explain the more rapid spread of the virus in Italy early in the outbreak, with the same exponential spreading of the disease, though with a higher incidence of contact.
Until a week ago, that rate of acceleration in Italy was nearly 5n, when n is the number of weeks. That rate appears to be slowing, and there are hints of a point of inflection occurring in recent case reporting. Nevertheless, there have been 5,500 deaths among the 59,000 reported cases, for a disturbing mortality rate of more than 9%.
The incidence of an inflection point is observable in South Korea, which took drastic steps to limit contact. In the first week of March, the exponential spread of disease became a log function, with a decelerating rate of increase.
That is not to say the spread is over. It’s important to note that the spread is still increasing, but at a lower rate of growth. And as with all human endeavors, there are just too many possible outcomes to know if the steps that the South Korean government has taken will have been enough to completely stop the spread.
The case for social distancing
To contain the illness, U.S. local governments are limiting the size of gatherings, and schools and corporations are requiring study and work from home wherever possible. A simple analysis shows these steps should be taken as quickly as possible by individuals to avert catastrophic outcomes and by corporations to avoid potential liability issues.
Let’s start by basing the analysis on data from Wuhan, which has a population of 11 million and 68,000 reported cases of the Covid-19 virus. That implies an infection rate of about 0.6% for the population at large.
Based on the Wuhan infection ratio of 0.6%, a healthy person would have only a 99.4% chance of avoiding contact with the disease if they were to come in contact with only one other person. But as the figure below shows, the risk of coming into contact with an infected person increases exponentially as the number of contacts increases.
If the healthy person were to come in contact with 100 people, the probability of avoiding contact with an infected person decreases to 54%. Being in proximity to 250 people reduces the odds to 21% of avoiding an infected person. At 500 people, the odds of avoiding an infected person drops to 4%.
The extent of Covid-19 infections in Wuhan are thought to be under-reported, with 100,000 cases perhaps a more realistic number. That implies an infection ratio of 0.9%, which, as the figure below shows, results in a much steeper profile, reaching a 40% odds of avoiding contact with an infected person if total contacts include 100 people; a 10% chance with contacts of 250 people, and only a 1% chance of avoidance when contacts are with 500 people.
The risks of contact with an infected person are likely to increase if personal decisions are not restricted by the government. According to an Associated Press report, Italian officials said the number of cases jumped 20% to 21,000 in one day, with 3,500 cases in one 24-hour period, blaming the increase on poor behavior of Italian citizens.
If citizens are unwilling to self-quarantine or to wash their hands or to avoid large crowds, we could expect an exponential increase in the number of Covid-19 cases. If the U.S. government – which was unwilling to accept that the disease is everywhere and has been here for quite a while — is unwilling to take steps to control the spread or to supply the equipment needed by the medical community, the nation faces what could be catastrophic consequences.
