Beyond the Sheer Numbers

April 5, 2020

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This has been a week in which hospitals in New York and many other states began to be overwhelmed by the exponential growth of coronavirus cases. When every patient counts and every death is a tragedy, the sheer number of cases is daunting.

Having said that, epidemiologists have to look at rates and growth trends as well as sheer numbers to understand an epidemic, and so do the rest of us. In last week’s post, I used the concept of doubling time to compare mortality trends in different countries, based on data from Our World in Data. The good news this week is that the doubling times in days are increasing a little in most countries, meaning that the rate at which deaths are multiplying is slowing. The bad news is that exponential growth curves are still very steep in many places. Deaths are doubling every four days in the United States and United Kingdom, apparently the fastest growth in the world. The doubling times are five days for Germany, six days for France and Netherlands, seven days for Spain, and ten days for Italy.

To appreciate the implications, if Italy’s deaths would keep doubling every 10 days for the next 30 days, its 15,362 deaths would double three times, increasing by a factor of 8 to 122,896. But if US mortality would keep doubling every 4 days in the same period, its 8,501 deaths would double at least 7 times, increasing by a factor of 128 to 1,088,128. To put that in perspective, 405,000 Americans died fighting World War II. No one knows what the real numbers will be, since no one knows how much and how fast we can bend the growth curve. What is clear is that the United States is poised to become the world leader in coronavirus deaths very soon. How the country that prides itself on the world’s most advanced health care system could accomplish that feat is a topic for another time.

State mortality rates

Within the United States, death rates also provide additional perspective to raw numbers. As of this morning, the ten states with the highest number of deaths are New York, New Jersey, Michigan, Louisiana, Washington, California, Illinois, Massachusetts, Georgia, and Florida, based on data from the Washington Post. Taking into account state size by using deaths per 100,000 population changes the picture somewhat. California’s 289 deaths no longer look so large, and Vermont’s 20 deaths become more significant. California’s rate of less than 1 death per 100,000 drops it down to 30th in death rate, while Vermont’s 3 per 100,000 brings it up to 7th. Illinois, Georgia and Florida also drop out of the top ten, to be replaced by Connecticut, Colorado and the District of Columbia. The number of deaths in a small state may get less attention, but it can have a large proportional impact on the smaller number of medical personnel and hospital beds.

Not only do states differ greatly in total deaths and death rates per 100,000 to date, they are also adding deaths at very different rates. Most of the states with the most deaths—either raw numbers or deaths per 100,000—have also had relatively large percentage increases over the past week. Increases of 300% or more are common—New York’s is 331%—but Michigan and New Jersey have seen increases over 500%. One notable exception is Washington, which has the sixth highest death rate so far, but one of the slower rates of weekly growth, 67%. The virus hit Washington first, but stay-at-home measures seem to be working. California has both a low rate of death and a below-average rate of weekly increase, having been the first state to issue a stay-at-home order.

Meanwhile, other states have had relatively low numbers and rates of death so far, but now have above-average rates of growth. Tennessee’s mortality rate is less than 1 per 100,000, but its deaths increased from 7 to 50 in a week, an increase of 614%. Other states that experienced significant jumps from low beginnings were Alabama, Kentucky and Maryland.

Given the potential for exponential growth to change the situation with dizzying speed, current low numbers are no excuse for complacency, anywhere in the country.

No Time to Lose

March 28, 2020

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In my state of North Carolina, Governor Roy Cooper has now issued a statewide stay-at-home order to slow the spread of the coronavirus. Effective March 30 to April 29, the order prohibits gatherings of over ten people, requires people to remain six feet apart, and limits activities outside the home to visits to essential businesses, outside exercise, and assistance to relatives.

One might ask why a state with only four deaths, in contrast to over 600 in the state of New York, is taking such drastic action, with obvious economic implications. Why not wait until the situation is more clearly a crisis? Why not do as President Trump recommends—try to identify “low-risk” counties where life can be allowed to go on as usual?

Exponential growth

I think that such objections reflect a misunderstanding of the problem. They underestimate the power of exponential growth to turn a numerically small problem into a major disaster very quickly. We should have learned that lesson by now from observing what happened in Italy (which leads the world in coronavirus deaths) or New York (which leads the states).

The numbers of cases and deaths are changing as I write this. Within a few days, the numbers I cite in this post may well have doubled. Infections and deaths from infectious diseases increase exponentially rather than linearly. They increase not by the same increment every day, but by an increasing increment every day. The greater the number of people already infected, the greater the number of others who can contract it from them, until the virus runs out of people to infect.

At first, the rate of exponential growth can be extremely high, with infections doubling every day or two. This is especially true for a new virus, for several reasons. No one has immunity yet; there isn’t widespread testing to identify and quarantine the infected; and countermeasures like physical distancing have not yet been adopted. Eventually, the rate of spread will slow because all these things change. Many people have recovered from the disease and are now immune; testing becomes more routine; and people take more precautions.

The best way to grasp the implications of exponential growth is to consider the time it takes infections to double. If they double every six days, they will double five times in a month, which is an increase by a factor of 32. A hundred cases would grow to 3,200 cases in a month. But if infections double every two days, which is quite common in the initial stage of the process, that is fifteen doublings in a months, or an increase by a factor of 32,768. At that rate the initial hundred cases grows into 3,276,800!

Slowing the growth rate by increasing the doubling time by even a day or two can make the difference between a serious problem and a catastrophe. Graphically, it is known as bending or flattening the curve. That spreads the cases out over a longer time, so that health care facilities are not overwhelmed. After all, most hospitalizations are resolved either by recovery (hopefully) or death (sadly) within a few days or weeks. In addition, the longer people can put off getting sick, the greater the possibility of a better treatment or even a vaccine.

Mortality trends

Now for some real numbers. I’ve taken these mortality numbers from Our World in Data for countries, and The Washington Post for states. Again I caution that they are changing rapidly.

Coronavirus deaths for the world as a whole are currently doubling every six days. Doubling times are shorter for the most affected countries—three days for the United States and Germany, four days for Spain, France, United Kingdom and Netherlands. A glimmer of hope is that Italy, the country with the most deaths so far, has now increased its doubling time to seven days. China, where the virus apparently originated, has flattened its curve even more, although the official numbers may not be entirely reliable.

The United States is now the leading country in known infections. Its rapid growth in deaths will probably make it the mortality leader as well in the near future. The US response has been scandalously slow, especially in the area of testing. Our failure to test and quarantine suspected cases has made a general lockdown more essential.

In the states with the most rapid growth in infections, such as New York, New Jersey, Michigan and Louisiana, deaths are doubling every two days. On the other hand, the state with the first big surge in mortality—Washington—has flattened its curve somewhat and is now doubling only every six days. More states need to move in that direction.

Safe places?

The most important point is that a relatively low caseload at the moment is no reason to carry on business as usual. What matters is the rate of growth, and states like North Carolina need to take preventive measures now to keep it as low as possible.

Nor can we assume that the rural counties or states with fewer cases so far are not at risk. If the distribution of mortality turns out to resemble that of flu, then states like Nebraska and the Dakotas will eventually exceed more urbanized states in death rates, perhaps because of more limited access to hospital care.

Governors like Roy Cooper are doing the right thing by telling people to stay home throughout the state, not just in areas initially affected, like Charlotte and Raleigh-Durham. More complacent governors ought to pay attention.

Trump Beyond Reach of Law

February 3, 2020

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Let me get this straight. The House of Representatives has impeached President Trump for abuse of power and obstruction of Congress. The abuse of power is that he allegedly made assistance to Ukraine–a contrary invaded by Russia–conditional upon its government’s initiation of investigations that would help Trump’s reelection campaign. That scheme included illegally holding up military aid already authorized by Congress. The obstruction of Congress involved refusing to comply with lawful subpoenas for witnesses and documents related to the investigation of the abuse of power.

The response of Senate Republicans to the obstruction charge is to assist Trump in the obstruction by blocking any attempt to obtain the very witnesses or documents that Trump is withholding. That makes Senators accomplices to the obstruction. Majority Leader Mitch McConnell admitted as much when he promised to coordinate the Senate trial with the White House to get Trump acquitted, just before he raised his right hand and swore an oath to consider the evidence impartially.

The response of Senate Republicans to the abuse of power charge was first to deny that it happened. Now it has evolved into an admission that it happened, but Trump should be acquitted anyway. Why? Because his intent was only to get reelected, which he thought was in the “public interest.” And because the people should decide his fate in this year’s election. You know, the same election that Trump has been trying to corrupt. And what’s to stop him now? We have a justice department that says that a sitting president cannot be indicted. We have a Senate majority that says that he shouldn’t be impeached. We have a Congress that can’t even exercise oversight because Trump acknowledges no obligation to provide witnesses or turn over documents.

The Senate has failed to fulfill its constitutional obligation for a fair trial. That’s not too surprising, considering that it has not been functioning as a democratic institution for some time. The Majority Leader refused to provide even a hearing for a highly respected, moderate Supreme Court nominee who had previously been praised by both parties, despite the constitutional obligation to “advise and consent.” Meanwhile, he fills the courts with judges whose views are far to the right of most Americans. Few bills passed by the House or sponsored by Senate Democrats are even debated in the Senate. That includes bills to protect the integrity of our elections against foreign interference. This Senate will go down in history as an enabler of the most serious assault on our democracy in our lifetimes.

One can only hope that our faith in democracy–although shaken by this administration and its congressional enablers–will not be destroyed. Very often in public affairs, the tide does turn. Truth comes out; corruption is revealed; the rule of law is strengthened; would-be dictators fall; and commitments to democratic principles are renewed.

Don’t forget to vote, or at least try to!

Prosperity (part 3)

October 4, 2019

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Here I will summarize Colin Mayer’s ideas about the relationship between the corporation and the government.


The idea that a corporation is more than a profit-making machine requires a new way of thinking about corporate law.

It should not simply be considered as a set of rules that define rights and responsibilities and what firms can and should do, but instead as a way of allowing different parties to commit to the common purposes that the corporation promotes. The remarkable contribution of corporate law has been to provide commitment devices that bind people and organizations together in such a way that they fulfill purposes that would otherwise be infeasible.

The commitments Mayer is talking about are more than contractual obligations. They are “self-imposed restraints” that build trust in such relationships as employer-employee or supplier-customer.

Corporate law affects commitments by “establishing the range of relations a corporation can sustain.” It:

  • Enables corporations to adopt a range of forms for different purposes
  • Empowers various parties, no longer just corporate directors and shareholders
  • Enforces the rights of different parties through such means as “voting within their particular class, voting corporately in conjunction with other classes, initiating class actions, or publicizing the opinions of members of the class in social media.”

If this seems rather abstract, that is typical of the book, which is stronger on general principles than on practical examples. An example of at least the first point is the innovation of the “benefit corporation,” which is allowed by the laws of thirty-five states and the District of Columbia. This B-corporation is similar to a C-corporation, except that it requires its directors to consider the impact of its activities on employees, customers, the community and/or the environment.


Mayer sees an inverse relationship between the level of commitment and trust in the economy, and the need for government regulation. The UK, described previously as an economy dominated by widely dispersed corporate owners, is a low-commitment economy. Many other countries, on the other hand, have various ways of building commitment:

Nordic countries confer control on long-term owners, in particular families, who are actively engaged in the oversight of corporations. These long-term owners are able to uphold self-regarding commitments. Central European countries, such as Austria and Germany, confer control rights on stakeholders, in particular employees, as well as shareholders through workers councils and co-determination on supervisory boards. These allow Austrian and German corporations to offer credible communal commitments beyond those that are self-regarding. In the industrial foundations of, in particular, Denmark, founders of corporations relinquish control rights to a board that is responsible for ensuring that the corporations act in trust for the philanthropic benefit of other members of society. The foundations are therefore able to offer social as well as communal and self-regarding commitments.

Where the Friedman doctrine is most influential, in the UK and US, it has tended to erode social commitments and encourage calls for government regulation.

We need to break out of this destructive spiral of declining commitment and intensifying regulation by conceiving what corporate commitment is capable of achieving and creating the context within which it can realize its full potential to perform communal and social as well as self-regarding purposes.

Government regulation is no substitute for corporate cultures with pro-social purposes, self-imposed constraint and trust. External regulation without internal commitment leads corporations to find ways of evading the laws. For example, banking regulations have fostered the rise of financial institutions that perform banking functions without being classified as banks because they don’t take a traditional form (with depositors).

Mayer suggests that regulations be based more on function than on form. Institutions performing similar functions should be regulated in similar ways, or else activities will move from a regulated sector to an informal unregulated sector, like “shadow banking.” “This will potentially be a cause of a systems-wide financial failure that will be more serious than the financial crisis of 2008.”

A second principle is that regulations be based on a clearly defined public purpose. An emerging purpose today is verifying the security of data storage systems.

A third principle is that regulations must address past failures, such as the failure to recognize and manage the risks of highly leveraged hedge funds, or derivative securities like collateralized debt obligations.


Conflicts between the private and public sector have gotten in the way of providing many public goods, such as adequate infrastructure. “There is a chronic under-provision of it around the world,” including in some of the wealthiest countries.

Part of the problem, noted in the last post, is an accounting system that excludes many social costs from private accounting, while excluding many social benefits from public accounting, thus exaggerating both private profits and public deficits.

When the public sector relies on private companies to help provide public goods, the two sectors have a conflict of interest: “Governments and regulators want maximum quality at lowest prices for the largest number of, in particular disadvantaged, consumers. Companies want the highest revenues from the provision of the lowest-cost projects and services.”

Mayer recommends that public obligations be specified in company articles of association, somewhat as they were when monarchs and parliaments granted charters to build canals or railroads. Complete freedom to incorporate and operate “may or may not have been appropriate for private companies that were not supplying public goods, [but] it is most certainly not right for the provision of infrastructure.”

For its part, government needs to engage the private sector in the design and regulation of infrastructure services. Corporate responsibility cuts both ways, conferring some legitimacy as well as obligation.

As I noted in the first post, the Friedman doctrine seems to be based on the assumption that the pursuit of private interest ultimately serves the public interest through the miracle of free-market competition. Mayer views this as naive, overlooking the enormous power of the corporation to enrich its shareholders at the expense of the public good. The profit-making machine rolls on, increasingly out of control, while the democratic state struggles to remain viable. The times require a thorough rethinking of the corporation, so that private gain may be reconciled with the well-being of society and nature.

The corporation is a conscious entity that has values. But when its sphere of operation is public not private, when it interacts with others in fulfilling its function, and when it is collectively part of a bigger whole, its consciousness has to embrace its environment, not just itself. That is the challenge of the twenty-first-century corporation, government, and world, and it is what will make the subject of the corporation one of the most fascinating for many years to come. We await the coming of the [next] age of the corporation as the trusted corporation.


Prosperity (part 2)

October 3, 2019

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What would it take to implement Mayer’s vision of a corporation that is more than just a slave to its shareholders’ demand for profit? Here I will describe some of what he has to say about corporate ownership, governance, and the measurement of performance.


Henry Ford’s first two corporations, the Detroit Automobile Company and the Henry Ford Company, did not work out very well. In both cases, investors wanted him to bring an automobile to market before he thought it was good enough. He learned his lesson and retained more family control in his third effort, the Ford Motor Company. “This time, with no outside investor interference, Ford transformed his ideas for car design and production into one of the great corporate success stories of all time.”

Here’s the lesson Mayer draws from this: “Where ownership coincides with vision…, vision is supported not extinguished by ownership.” The danger of public stock ownership is “the mundane views of investors stifling and snubbing the spark of creative inspiration.”

Widely dispersed ownership is especially common in Mayer’s United Kingdom. It has the advantage of expanding the available supply of capital, making capital cheaper. It allows small investors to get an average market return on investment without incurring excessive risk, assuming they have a diversified portfolio. But it has the disadvantage of undermining “the ability of entrepreneurs and innovators to pursue idiosyncratic value that the market does not immediately recognize.”

In many parts of the world, such as Asia, South America and continental Europe (especially Germany), family control remains common. In the United States, family businesses have declined but other forms of block ownership are more common than in the UK. Mayer hopes that large institutional investors like pension funds will invest less for short-term financial returns and more for long-term social benefits. Unlike the UK, the US also allows dual-class share structures, where the shares of company founders and top executives carry more voting rights than shares offered publicly. In theory, this also gives visionary leaders some protection from short-term financial demands.


Mayer sees three main aspects of good governance–“purpose, practice, and performance. You have to want to do it, you have to bring others along in doing it, and you have to demonstrate you have done it.”

Mayer links purpose both with corporate cultural values and with the various types of capital and their constituencies:

One way of determining a company’s purpose is to answer the question what is its value proposition? What value is it seeking to create for whom over what period of time? Is it predominantly looking to enhance or maximize shareholder value, or consumer value, or the human capital of its employees, the social capital of its communities and societies, or the natural capital it owns and in its supply chain?

Mayer’s first principle of management is, “Corporate control should be exercised and value maximized by scarce capitals.” That is, control should be shared with those who represent the kind of capital the corporation is most trying to grow. If a company is dedicated to growing its human capital, then it should share control with its workers.

Natural capital poses a special problem for governance, since its human representatives are not obvious, but some people may represent it better than others:

There are therefore two possible solutions to the protection of natural capital. The first is to allocate control rights predominantly to younger generations of owners and require them to relinquish control to their successors as they age. The second is to put natural capital ownership in trust of older generations whose concern about their reputation will make them take their role as custodians seriously….

Measuring performance

“The long-run growth of the firm requires the balanced growth of all its capitals not just material and financial capital.” If a company cares about its impact on other forms of capital, it must find ways to measure that impact in its profit-loss accounting.

To take an obvious example, corporations should not just cut down a forest or pay wages too low to live on, and then count their financial gains as profits while leaving the societal costs to be borne by someone else. Technically, sustainable corporate activity must address the problem of “externalities,” which are “benefits [or costs] that accrue to one party from activities undertaken by another without the latter being rewarded [or penalized] for the former.”

The theoretical solution is to internalize the externalities. The corporation should shoulder the costs of depleting natural capital or human capital, and receive some benefit from growing them. It should count all forms of capital investment as costs, and subtract all those costs when calculating profits. Failure to do so makes corporations seem more profitable than they are. Oil companies aren’t actually worth as much as they would be if their activities were sustainable. It also leads corporations to misallocate resources, devoting too many to the kinds of capital growth–material and financial–that are customarily accounted for.

National accounting is similarly distorted. National accounts overstate national income and growth by ignoring the deterioration of natural capital. The nation also misallocates resources by counting money spent on education, infrastructure and the environment as a cost, but having no comprehensive system for measuring the benefits. Thus public spending appears more wasteful than it is, while a corporate tax cut appears more profitable than it is.

Mayer acknowledges that “it is much harder to measure such nebulous concepts as human well-being, social capital, and natural capital, or at least to attach monetary values to them with the same precision as profit.” Nevertheless, some progress is being made. Several international agencies have cooperated to produce the System of Environmental-Economic Accounting (SEEA), which has provided measures of natural capital for twenty countries.

Individual corporations do not have to put a monetary value on their environments, but just reckon the costs of both acquiring and replenishing natural resources before claiming a profit. They need a similar approach for growing and sustaining other forms of wealth.