Macro Roundup

“…Remember George Box’swise wordsabout models: “All models are wrong but some models are useful”. Or as he put it elsewhere, less dramatically but morespecifically:“Models, of course, are never true, but fortunately it is only necessary that they be useful. For this it is usually needful only that they not be grossly wrong”….”

Jeffrey K Aronson, Jon Brassey, Kamal R Mahtani, "“When will it be over?”: An introduction to viral reproduction numbers, R0 and Re," Centre for Evidence-Based Medicine, Nuffield Department of Primary Care Health Sciences, University of Oxford, April 14, 2020, https://www.cebm.net/covid-19/when-will-it-be-over-an-introduction-to-viral-reproduction-numbers-r0-and-re/

When will it be over?”: An introduction to viral reproduction numbers, R0 and R

The UK Government is regularly reviewing the current lockdown measures, as it is required to do every 3 weeks, by law. With the peak of the pandemic yet to arrive in the UK, it seems certain that the current measures will continue. So when will the UK lockdown end?

On 30 March 2020, Sir Patrick Vallance, the Government’s Chief Scientific Officer, gave an indication of how this decision may be guided, saying that Britain’s lockdown was having a “very big effect” on the R0, bringing it down “below one”.

The figure to which he was referring is the basic reproduction number (or reproductive ratio) of a virus, called R0 (R nought or R zero). And it is important to know how to interpret it.

We include some definitions in the box at the end.

The basic reproduction number

The basic reproduction number is defined as the number of cases that are expected to occur on average in a homogeneous population as a result of infection by a single individual, when the population is susceptible at the start of an epidemic, before widespread immunity starts to develop and before any attempt has been made at immunization. So if one person develops the infection and passes it on to two others, the R0 is 2.

If the average R0 in the population is greater than 1, the infection will spread exponentially. If R0 is less than 1, the infection will spread only slowly, and it will eventually die out. The higher the value of R0, the faster an epidemic will progress.

R0 is estimated from data collected in the field and entered into mathematical models. The estimated value depends on the model used and the data that inform it.

R0 is affected by:

the proportion of susceptible people at the start and the density of the population;
the infectiousness of the organism;
the rate of disappearance of cases by recovery or death, the first of which depends on the time for which an individual is infective;

The denser the population, the more people are susceptible, and the more infective the virus, the larger R0 will be for a given virus; the faster the rate of removal of infected individuals, by recovery or death, the smaller R0 will be.

The zero in “R zero” means that it is estimated when there is zero immunity in the population, even though not everyone will necessarily be susceptible to infection, although that is the usual assumption. In an epidemic with a completely new virus, the earlier the measurements are made the nearer the calculated value is likely to be to the true value of R0, assuming high-quality data. For this reason, it is better to talk about the transmissibility of the virus at the time that it is measured, using a different symbol, Re, the effective reproduction number.

The effective reproduction number, Re

The effective reproduction number, Re, sometimes also called Rt, is the number of people in a population who can be infected by an individual at any specific time. It changes as the population becomes increasingly immunized, either by individual immunity following infection or by vaccination, and also as people die.

Re is affected by the number of people with the infection and the number of susceptibles with whom infected people are in contact. People’s behaviour (e.g. social distancing) can also affect Re.

The number of susceptibles falls as people die or become immunized by exposure. The sooner people recover or die, the smaller the value of Re will be at any given time.

Unfortunately, the symbol R0 is often used in publications when Re is meant. This can be confusing.

Herd immunity

Initial reports suggested that one of the UK Government’s strategies in tackling the pandemic was to allow the virus to spread within the community, in a controlled way, so that immunity, so-called herd immunity, could develop across the population. However, the health secretary, Matt Hancock, later said that this was not part of the UK response to the virus. In contrast, other countries, such as Sweden, have responded to the pandemic in ways that avoid full lockdown. The problem with leaving people to catch the infection spontaneously, leading to herd immunity, is that the death rate would increase as a result. For example, on 10 April, the number of confirmed cases in Sweden was 9685 with 870 deaths (9.0%), compared with Norway with 6219 confirmed cases and 108 deaths (1.7%) and Denmark with 5830 confirmed cases and 237 deaths (4.4%).

R0 predicts the extent of immunization that a population requires if herd immunity is to be achieved, the spread of the infection limited, and the population protected against future infection. To prevent sustained spread of the infection the proportion of the population that has to be immunized (Pi) has to be greater than 1 − 1/R0. The relation between Pi and 1 - 1/R0 is shown in Figure 1.

For example, if R0 = 2, immunization needs to be achieved in 50% of the population. However, if R0 = 5 the proportion rises steeply, to 80%. Beyond that the rise is less steep; an increase in R0 to 10 increases the need for immunization to 90%. Measles has an R0 greater than 10, which is why immunization of a large proportion of the population is so important in preventing the disease.

Thus, if R0 is 10, a child with measles will infect 10 others if they are susceptible. When other children become immune the infected child who encounters 10 children will not be able to infect them all; the number infected will depend on Re. When immunity is 90% or more the chances that the child will meet enough unimmunized children to pass on the disease falls to near zero, and the population is protected.

At any time, Re = R0 × (1 - Pi), where Pi is the proportion of the population who are immune at that time. This is illustrated in Figure 2.

For example, immunization of 50% of the population (blue line) will bring Re down below one only if R0 was no greater than 2; in contrast immunization of 90% of the population (brown line) will bring Re down to 1 or less for all values of R0 up to 10.

How R0 is estimated

A typical epidemiological model by which R0 is estimated is based on three factors: individual Susceptibility to the infection, the rate at which infections actually occur (Infectivity), and the rate of Removal of infection from the population, by either recovery or death. This is the so-called S-I-R model.The model involves the solution of simultaneous linear differential equations and was described as long ago as 1927 by W. O. Kermack and A. G. McKendrick. A version of their model is shown in Figure 3.

However, many other methods have been used, including both statistical models and simple calculations. The former range from methods such as the Reed-Frost stochastic model, developed by Lowell J. Reed and Wade Hampton Frost in 1928, similar to a method that was already being developed by H E Soper and which he described in 1929, to the IDEA method, first described by Fisman and colleagues in 2013. Of the methods involving simple mathematical calculation of R0, one that is commonly used involves the following equation: R0 = βS/γ, where β is the transmission rate, S is the number of susceptibles at the start of the epidemic, and γ is the removal rate. There are many other variants of a similar nature.

Figure 4. Estimated values of R0 in different viral infections, culled from a variety of published sources

What is the R0 of SARS-CoV-2?

Estimates of the R0 of SARS-CoV-2 vary widely. Figure 5 shows nine estimates, all from studies in China or South Korea. The mean estimate of R0 is 2.63 (95% CI = 1.85,3.41). From a wider survey of 16 published estimates, the mean estimate is 2.65 (1.97, 3.09). In both cases, the range is 0.4-4.6.

This means that in order to protect us against future epidemics, herd immunity of around 62% will be needed, taking the mean estimate across all these studies. Taking the highest value (4.6), 78% immunization will be needed, and it would be wise to aim for at least that. When a test for neutralizing antibodies to SARS-CoV-2 and a vaccine are available, we shall be able to tell to what extent the population has been immunized by exposure and vaccination.

In the UK, one of the key findings that influenced the Government’s decision to start the lockdown was the model presented by the Imperial College COVID-19 response team. The model explores the effect of two strategies (a) suppression, by which interventions are instituted to bring Re to below 1, and (b) mitigation, by which strategies are instituted to reduce the impact of the epidemic, but not interrupt viral transmission completely, thus reducing Re, but not necessarily below 1. The model assumed an R0 of about 2.4 and predicted that, in the absence of any control measures, 81% of the UK population would become infected, with over half a million deaths. However, this number could be reduced to under 50,000 (and possibly under 6000 deaths) with a suite of suppression strategies in place. Little wonder, given these figures, that the UK government swiftly began the lockdown.

It is important to note that the value of R0 varies considerably in the models used in the COVID-19 pandemic. One systematic review reported that the mean of 29 reported values of R0 from 21 studies was estimated at 3.32 (2.81-3.82), with a range of 1.9 to 6.49; all the included studies were from China. In a statement on 23 January, 2020 about the outbreak of COVID-19 the World Health Organization (WHO) gave a preliminary R0 estimate of 1.4-2.5.

Interpreting the news

The Chinese data suggest little change in the reproduction numbers measured at various times over the last 3 months. So when you read a report that the reproduction number (Re) has fallen below 1, which should be cause for rejoicing, be cautious. The calculated value depends on the quality of the data, which may be poor, and the epidemiological model used, which may distort the outcome. Remember George Box’s wise words about models:

“All models are wrong but some models are useful”.

Or as he put it elsewhere, less dramatically but more specifically:

“Models, of course, are never true, but fortunately it is only necessary that they be useful. For this it is usually needful only that they not be grossly wrong”.

Definitions
Some definitions of terms used in this article are given below.
Immunity to a viral infection is the state of being non-susceptible to it, by virtue of being able to produce neutralizing antibodies when challenged by it; such antibodies may be produced by prior exposure or by immunization following vaccination.
Herd immunity is a form of protection from an infectious disease that results when a large enough proportion of the population has become immune, conferring indirect protection from infection on individuals who are not themselves immune.
Vaccination against a viral infection is the administration of a vaccine to an individual with the intention of immunizing that individual or boosting pre-existing immunity.
Immunization against a viral infection is the production of immunity to the infection by virtue of successful vaccination or exposure to the virus.

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Disclaimer: the article has not been peer-reviewed; it should not replace individual clinical judgement and the sources cited should be checked. The views expressed in this commentary represent the views of the authors and not necessarily those of the host institution, the NHS, the NIHR, or the Department of Health and Social Care. The views are not a substitute for professional medical advice.

Brad Setser, "Five Points about U.S. Trade Over the Last Thirty Years," Council On Foreign Relations, May 8, 2020, https://www.cfr.org/blog/five-points-about-us-trade-over-last-thirty-years

Five Points about U.S. Trade Over the Last Thirty Years

1. Globalization hasn’t meant increased demand for U.S. exports of manufactures over time…

Exports of manufactures (using the SITC data from chemicals through miscellaneous manufactures) are no higher, as a share of U.S. GDP, than they were in the 1990s…

In fact, exports of manufactures are now, after the dollar's 2014 appreciation, about a percentage point of GDP below their average level in the 1990s.

If trade with NAFTA is set aside, the broadest possible definition of U.S. manufacturing exports—using the NAICS data here, which includes a lot of food processing*—puts exports beyond North America at less than 4 percent of U.S. GDP. Around a sixth of those exports are civil aircraft, aircraft engines, and aircraft parts—and thus are in a sector that is particularly exposed to the corona virus shock.

The United States’ limited extra-regional exports are also not just a function of the United States’ large size—European (EA) exports to the United States and China are now almost three times bigger than U.S. exports to Europe (EU) and China (as a share of each region's GDP). Back in 2009 and 2010, the Obama Administration liked to talk about how the U.S. recovery from the global financial crisis would be led by exports and investment.

But it turned out that Europe’s recovery was the one that was led by exports…

2. U.S. exports of IP related services haven’t grown all that fast since the 1990s

This one surprises people. The U.S. is a service driven economy after all. And San Francisco and Seattle are home to a lot of very profitable technology companies (I used a broad definition of IP related services as well, one that includes business services to capture R&D exports).

I wish a tax knock-down of Apple (showing the huge share of the profit that ends up in Ireland) was as widely known as the supply chain knock down that purports to show that only a small fraction of the manufactured value-add in an iPhone comes from China (that study is out of date by the way even if the fact checkers at large newspaper haven't noticed—China now accounts for about a quarter of the manufacturing value add).

3. The dollar’s strength from 2000 to 2003 really hurt the U.S. economy—having a currency that rallies in a recession isn’t necessarily a good thing.

Strong demand growth often pulls in imports and leads to an increase in the trade deficit.

But rising imports aren’t always a sign of strong demand and a booming economy.

For example, the dollar’s strength from 2000 to 2003 weighed on exports and pulled in imports. In the period immediately after the dot-com crash imports of goods (the redline below) were almost as strong as they were during the dot-com boom even though U.S. goods demand was much weaker. That meant that U.S. production bore the brunt of the fall in demand for goods.

Net goods trade subtracted an average of a half a percentage point from U.S. growth between 2001 and 2004—with most of the cumulative two percentage point drag coming in 2002 (the strong dollar effect) and in 2004 (likely the China shock).

In fact, goods trade was a drag on the U.S. economy in two of the last four slowdowns in domestic manufacturing demand. Goods imports didn’t fall that much when demand fell during the dot-com recession and the rise in imports then weighed on the subsequent recovery. Falling exports added to the impact of the oil investment crash in 2014 and 2015 and thus contributed to the mini recession in manufacturing.

4. Those who argue that imports from China simply displaced imports from the rest of Asia haven’t spent enough time playing with the detailed U.S. trade data.

Between the end of 2002 and the end of 2006 (the “China shock” period) imports of all manufactured goods rose by about a percentage point of U.S. GDP.

The China shock documented by David Autor and his co-authors was real. It also was about a percentage point of GDP, not more.

5. The big U.S. gains from globalization—setting aside the gains to consumers from lower goods prices, —have gone to those who own intellectual property that can be off-shored to a tax haven.

As I noted at the start, the past twenty-five years haven’t seen any growth in manufactured exports as a share of GDP. The same is broadly true for agricultural exports. The U.S. exports commodity crops like soybeans, wheat and corn. But the U.S. imports a lot of wine and spirits—and a lot of seafood—so overall trade in foods and feeds is pretty balanced. Nor has there been especially strong growth in exports of IP related services.

But there has been rapid growth in the offshore profits of U.S. firms—and the net income (offshore profits from U.S. firms vs. the U.S. profits of foreign firms)—over this period. And a large share of that income is now booked in global centers of corporate tax avoidance. Those who own the income streams from those offshore profits generally have done well (see Herman Mark Schwartz).

Yet the sum of offshore profits and the surplus in IP related services trade still falls short of covering the deficit in manufactures. That is especially the case after the dollar’s 2014-15 rise increased the size of the manufacturing deficit while reducing the dollar value of the profits U.S. firms earn abroad.

That is again clear in the data after the one-off impact of the Tax Cuts and Jobs Act has faded (the repatriation of profits held offshore reduced U.S. foreign direct investment abroad and reduced foreign holdings of U.S. debt—this shows up clearly for example if you look at the U.S. balance of payments with Ireland).

Assessments of the winners from globalization therefore need to include the owners of offshored intellectual property and the associated profits (easy enough) and those who benefit from large exports of bonds (a harder question).

All of the points above are somewhat controversial, though I believe all are also well grounded in the actual trade and balance of payments data. Persistent trade deficits do have distributional consequences (see Yakov Feygin and Dominik Leusder).

And the persistent deficit in manufacturing trade is to a degree a function of political choices both here and abroad—President Trump isn’t wrong about this, though his efforts to pin the entire deficit on bad trade deals have fallen short of the mark. His trade policy has at best offset the trade impact of his stimulus, and done so—to date—largely by driving down overall U.S. demand for manufactures rather than by raising U.S. production.

What U.S. policy choices then that have had the biggest impact on the trade balance over time? Two stand out in my view.

A de-industrial policy carried out through the tax code, which has long favored offshore manufacturing of high value-added components (especially in the pharmaceutical sector/hence the large goods trade deficit with Ireland). The “Ireland first” provisions of the tax code for example have contributed to the recent large rise in the trade deficit with Europe.

Obviously relative fiscal policy stances also matter—the United States has tended to make up for weakness in private demand with fiscal policy, while Europe, Korea, Taiwan and others have not. But with overall global demand weak, I find it hard to fault the United States for excessive deficits more than the balance of payments surplus countries for running persistent twin surpluses and relying on (weak) global demand to offset their fiscal tightness.

In any case, one central feature of America' experience with globalization over the last twenty five years is that it hasn't delivered, in aggregate, a positive shock to manufactured exports. The big gains haven't gone to workers in those sectors, but rather to the owners of profits that have been shifted to low tax jurisdictions. It is time, in my view, for a debate over the policies that contributed to these outcomes—policies that go well beyond standard trade policy.

* The SITC data is a bit too narrow, but it goes back a long ways. The NAICs data is better and more detailed, but my data series only starts in 2002. The NAICs data matches the definition of manufacturing used in the monthly trade release. I did not attempt to adjust for reexports though. And the NAICS definition of manufacturing actually captures a decent amount of agricultural exports, as, for example, most pork will be exported after slaughter and show up as a pork product (processing into chops and bacon is a substantial transformation) and exports of spirits are considered a manufactured good. I did adjust for refined petrol. These differences account for the differences in levels in the charts.

** I used the NIPA contributions series for real goods trade and real demand for goods. Drawing on the insight in Bussière, Callegari, Ghironi, Sestieri, and Yamano, I added business fixed investment to goods consumption to roughly approximate domestic demand for goods

"Globalization hasn’t meant increased demand for U.S. exports of manufactures over time…U.S. exports of IP related services haven’t grown all that fast since the 1990s... (I used a broad definition of IP related services as well, one that includes business services to capture R&D exports)….This stylized fact also surprised me to be honest. Following the money led me into the world of corporate tax avoidance. $30 billion a year in software exports does seem to be too low, but that is what is in the reported trade data. And yes, a quarter of those exports do go to Ireland. Go figure. I wish a tax knock-down of Apple (showing the huge share of the profit that ends up in Ireland) was as widely known as the supply chain knock down that purports to show that only a small fraction of the manufactured value-add in an iPhone comes from China (that study is out of date by the way even if the fact checkers at large newspaper haven't noticed—China now accounts for about a quarter of the manufacturing value add)….The dollar’s strength from 2000 to 2003 really hurt the U.S. economy—having a currency that rallies in a recession isn’t necessarily a good thing....Those who argue that imports from China simply displaced imports from the rest of Asia haven’t spent enough time playing with the detailed U.S. trade data....The big U.S. gains from globalization—setting aside the gains to consumers from lower goods prices, —have gone to those who own intellectual property that can be off-shored to a tax haven…”

+ what I found to be surprising fact that exports of IP related services haven’t really grown since the 1990s:

Great charts from Brad as he argues that too many of the gains to the US from globalization have turned up as offshore profits from us firms, and not from rising exports of technologically sophisticated goods.

New Haltiwanger finds structural changes at industry level help explain rising earnings inequality:

“….We provide evidence thatmost (about 75%) of the rising between firm inequality is from rising inequality across detailed 4-digit NAICS industries. Most of this rise in inequality across industries is due to rising inter-industry earnings differentials and not due to changing distribution of employment across industries. We also find that the rising inter-industry earnings differentials are almost completely accounted for by occupation effects. For the raw rise in rising inter-industry earnings differentials, we find that about 92% of the increase is accounted for by occupation effects. About 66% of this is due to changing occupation mix across industries and 27% due to changing occupation mix differentials given the existing differences in the occupation mix across industries…. Consistent with their findings, we find that the occupations with the sharpest rise in earnings differentials that differ by industry are managerial, professional and technical with occupations like production and sales being left far behind.Our contribution is to integrate the changing role of occupations with the rise in between firm and in turn between industry inequality. Our findings show that the changing demand for tasks as evidenced in the changing occupational mix and occupational differentials is closely linked to between firm and between industry inequality....Specifically, we find that the rise in between firm inequality is dominated by a rise in between industry inequality. We find the latter is dominated by rising inter-industry earnings differentials with a more modest role for the changing distribution of employment across industries. In turn, we find that virtually all of the rising inter-industry earnings differentials is accounted for by occupation effects. This includes both changing mix of occupations within and across industries and rising occupation differentials. We find, after controlling for the mix of workers in terms of age, gender, and education (as well as other controls), that the occupations with especially sharp increases in earnings differentials that differ across industries are managerial, business and financial, sciences, legal, and healthcare, with occupations like protective services, sales, and construction being left behind. The increase in the management occupation differential across industries is especially striking…. Put differently, this task based framework helps motivate why changes in inequality associated with the changing role of occupations is linked to the changing role of firms in inequality. Driving forces such as technology and globalization that induce changing demand for occupations impact firms differentially. In principle, this differential impact could be between firms or between industries. Our findings suggest there is a dominant role for the between industry impact. An important direction for future research is to explore the changing role of occupations across industries...."