Tracking COVID-19

FIGURES UPDATED 3-15-20

You’ve probably seen various graphs online showing the increase in coronavirus cases in various countries.

I don’t know that I am adding any value here, but I decided to reproduce those graphs using the convenient data from Johns Hopkins Coronavirus Research Center. (I can’t vouch for  the reliability of the Johns Hopkins data, but it seems to be what most news organizations are relying on.) Here’s one showing cases for all countries other than China that have reported at least 100 cases. The x axis is days after the 100-case mark was reached.

 

What we see here is that most countries show a consistent 35-45 percent daily growth in reported cases. Only Japan, at 20 percent, and Singapore and more recently Korea, at around 10 percent, depart significantly from this. It’s also interesting how stable the growth of cases in Japan has been over the past three weeks.

Now here is the same figure, but for US counties that have reported at least 10 cases. The x axis here is days since the first day with a least 10 cases. [UPDATE: I have stopped updating this graph since the Johns Hopkins site now reports cases only for US states.]

What surprises me here is that we basically see the same ~40 percent daily growth rate in cases. I would have thought that given all the insitutional differences and issues around testing, the US picture would have looked somehow different. But it seems like we might reasonably extrapolate from the international experience, that New York or Seattle could reach 10,000 cases in the next two weeks.

I have no expertise whatsoever on infectious diseases, so I am not going to say anything else about this.

Anyway, here is the R code if you want to produce figures like these from the most current data on the Johns Hopkins site. They also give latitude and longitude for every place included, so it wouldn’t be much more work to make an interactive map. Could be an interesting excercise for anyone teaching a statistics or data science course.

UPDATE: I had to change the code because Johns Hopkins is no longer reporting data for US places other than states. Here is the equivalent state-level figure. As you can see, the states with significant numbers of cases all show the same 40 percent daily growth rate.

 

#install.packages('reshape2')
#install.packages('ggplot2')
library(reshape2)
library(ggplot2)

corona <- read.csv('https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series/time_series_19-covid-Confirmed.csv',
                   stringsAsFactors = F)
state.abbrevs <- read.csv('https://raw.githubusercontent.com/jasonong/List-of-US-States/master/states.csv', stringsAsFactors = F)
corona[,-1:-4] <- apply(corona[,-1:-4], 1:2, FUN=as.numeric)
US <- corona[corona$Country.Region=='US', ]
USplaces <-  US[grep(',',US[,1]),][,-2:-4]
USstates <- US[grep(',',US[,1], invert=T),][,-2:-4]
USstates <- USstates[grep('Princess',USstates[,1], invert=T),]
states.temp <- USstates
for (i in 1:nrow(USstates)){
  abbrev <- state.abbrevs[state.abbrevs[,1]==USstates[i,1],2]
  rows <- grep(abbrev, USplaces[,1])
  states.temp[i, -1] <- colSums(USplaces[rows, -1])
}
states.temp<- states.temp[!is.na(states.temp[,1]),]
USstates[,-1] <- USstates[,-1] + states.temp[,-1]
corona <- rbind(corona, c('', 'United States', NA, NA, colSums(USplaces[,-1])))
corona[,-1:-4] <- apply(corona[,-1:-4], 1:2, FUN=as.numeric)
china <-  corona[corona$Country.Region=='China',-2:-4]
corona <- rbind(corona, c('', 'China', NA, NA, colSums(china[,-1])))
corona[,-1:-4] <- apply(corona[,-1:-4], 1:2, FUN=as.numeric)
countries <- corona[corona$Province.State =='', c(-1, -3:-4)]

makePlot <- function (x, threshold){
  cases <- redate(x, threshold)
  data <- melt(cases, id.vars=1)
  names(data) <- c('place', 'day', 'cases')
  
  p <- ggplot(data, aes(x=day, y=cases, group=place)) +
    geom_line(aes(color=place))+
    geom_point(aes(color=place, shape=place))
  p <- p + scale_shape_manual(values=1:length(levels(as.factor(data$place))))
  p <- p + theme(axis.text.x = element_text(angle=45))
  p <- p + scale_y_continuous(trans='log10')
  p
}

redate <- function (x, threshold) {
  out <- data.frame(place='', stringsAsFactors = F)
  values <- matrix(nrow=99, ncol=99)
  n <- 0
  for (i in 1:nrow(x)) {
    v <- x[i,-1][x[i,-1] > threshold]
    l <- length(v)
    if (l > 1) {
      n <- n + 1
      out[n,1] <- x[i,1]
      values[n,1:l] <- v
    }
  }
  values <- values[!is.na(values[,1]),]
  cols <- length(colSums(values, na.rm=T)[colSums(values, na.rm=T) > 0])
  values <- values[,1:cols]
  out <- cbind(out, values)
}

makePlot(USplaces, 9)
makePlot(USstates, 10)
makePlot(countries[countries$Country.Region != 'China',], 99)

Unemployment and Productivity Growth

I write here frequently about “the money view” — the idea that we need to see economic relationships as a system of money flows and money commitments, that is not reducible to the “real” production and exchange of goods and services. Seeing the money-game as a self-contained system is the first step; the next step is to ask how this system interacts with the concrete activities of production.

One way to look at this interface is through the concept of potential output, and its relationship to current expenditure, or demand. In the textbook view, there is no connection between the long-run evolution of potential output with demand. This is a natural view if you think that economic quantities have an independent material existence. First we have scarce resources, then the choice about which end to devote them to. Knut Wicksell suggests somewhere an evocative metaphor for this view of economic growth: It’s as if we had a cellar full off wine in barrels, which will improve with age. The problem of economic growth is then equivalent to choosing the optimal tradeoff between having better wine, and drinking it sooner than later. But whatever choice we make, all the wine is already there. Ramsey and Solow growth models, with their “golden rule” growth rate, are descriptions of this kind of problem. Aggregate demand doesn’t come into it.

From our point of view, on the other hand, production is a creative, social activity. Economic growth is not a matter of allowing an exiting material process to continue operating through time, but of learning how to work together in new ways. The fundamental problem is coordination, not allocation.  From this point of view, the technical conditions of production are endogenous to the organization of production, and the money payments that structure it. So it’s natural to think that aggregate expenditure could be an important factor determining the pace at which productive activity can be reorganized.

Now, whether demand actually does matter in the longer run is hotly debated point in heterodox economics. You can find very smart Post Keynesians like Steve Fazzari arguing that it does, and equally smart Marxists like Dumenil and Levy arguing that it does not. (Amitava Dutt has a good summary; Mark Setterfield has a good recent discussion of the formal issues of incorporating demand into Kaldorian growth models.) But within our framework, at least it is possible to ask the question.

Which brings me to this recent article in the Real World Economic Review. I don’t recommend the piece — it is not written in a way to inspire confidence. But it does make an interesting claim, that over the long run there is an inverse relationship between unemployment and labor productivity growth in the US, with average labor productivity growth equal to 8 minus the unemployment rate. This is consistent with the idea that demand conditions influence productivity growth, most obviously because pressures to economize on labor will be greater when labor is scarce.

A strong empirical regularity like this would be interesting, if it was real. But is it?

Here is one obvious test (a bit more sensible to me than the approach in the RWER article). The figure below shows the average US unemployment rate and real growth rate of hourly labor productivity for rolling ten-year windows.

It’s not exactly “the rule of 8” — the slope of the regression line is just a big greater than -0.5, rather than -1. But it is still a striking relationship. Ten-year periods with high growth of productivity invariably also have low unemployment rates; periods of high average unemployment are invariably also periods of slow productivity growth.

Of course these are overlapping periods, so this tells us much less than it would if they were independent observations. But the association of above-average productivity growth with below-average unemployment is indeed a historical fact, at least for the postwar US. (As it turns out, this relationship is not present in most other advanced countries — see below.) So what could it mean?

1. It might mean nothing. We really only have four periods here — two high-productivity-growth, low-unemployment periods, one in the 1950s-1960s and one in the 1990s; and two low-productivity-growth, high-unemployment periods, one in the 1970s-1980s and one in the past decade or so. It’s quite possible these two phenomena have separate causes that just happened to shake out this way. It’s also possible that a common factor is responsible for both — a new technology-induced investment boom is the obvious candidate.

2. It might be that high productivity growth leads to lower unemployment. The story here I guess would be the Fed responding to a positive supply shock. I don’t find this very plausible.

3. It might be that low unemployment, or strong demand in general, fosters faster productivity growth. This is the most interesting for our purposes. I can think of several versions of this story. First is the increasing-returns story that originally motivated Verdoorn’s law. High demand allows firms to produce further out on declining cost curves. Second, low unemployment could encourage firms to adopt more labor-saving production techniques. Third, low unemployment might associated with more rapid movement of labor from lower-productivity to higher-productivity activities. (In other words, the relationship might be due to lower visible unemployment being associated with lower disguised unemployment.) Or fourth, low unemployment might be associated with a relaxing of the constraints that normally limit productivity-boosting investment — demand itself, and also financing. In any of these stories, the figure above shows a causal relationship running from the x-axis to the y-axis.

One scatterplot of course hardly proves anything. I’m really just posing the question. Still, this one figure is enough to establish one thing: A positive relationship between unemployment and labor productivity has not been the dominant influence on either variable in the postwar US. In particular, this is strong evidence against the idea the idea of technological unemployment, beloved by everyone from Jeremy Rifkin to Lawrence Summers. (At least as far as this period is concerned — the future could be different.) To tell a story in which paid labor is progressively displaced by machines, you must have a positive relationship between labor productivity and unemployment. But historically, high unemployment has been associated with slower growth in labor productivity, not faster. So we can say with confidence that whatever has driven changes in unemployment over the past 75 years, it has not been changes in the pace at which human labor is replaced by technology.

The negative relationship between unemployment and productivity growth, whatever it means, turns out to be almost unique to the US. Of the dozen or so other countries I looked at, the only one with a similar pattern is Japan, and even there the relationship is weaker. I honestly don’t know what to make of this. But if you’re interested, the other scatterplots are below the fold.

Note: Labor productivity is based on real GDP per hour, from the BLS International Labor Comparisons project; unemployment is the harmonized unemployment rate for all persons from the OECD Main Economic Indicators database. I used these because they are (supposed to be) defined consistently across countries and were available on FRED. Because the international data covers shorter periods than the US data does, I used 8-year windows instead of 10-year windows.

Are Wages Too High?

Here’s a good one for the right-for-the-wrong-reasons file.

David Glasner is one of an increasing number of Fed critics who would like to see a higher inflation target. Today, he takes aim at a Wall Street Journal editorial that claims that the real victims of cheaper money wouldn’t be, you know, people who own money — creditors — as one might think, but working people. Higher inflation just means lower real wages, says the Journal. Crocodile tears, says Glasner — since when does the Journal care about wage workers? So far, so good, says me.

“What makes this argument so disreputable,”he goes on,

is not just the obviously insincere pretense of concern for the welfare of the working class, but the dishonest implication that employment in a recession or depression can be increased without an, at least temporary, reduction in real wages. Rising unemployment during a contraction implies that real wages are, in some sense, too high, so that a falling real wage tends to be a characteristic of any recovery, at least in its early stages. The only question is whether the falling real wage is brought about through prices rising faster than wages or by wages falling faster than prices. If the Wall Street Journal and other opponents of rising prices don’t want prices to erode real wages, they are ipso facto in favor of falling money wages.

And here we have taken a serious wrong turn.

Glasner is certainly not alone in thinking that rising prices are associated with falling real wages, and vice versa. And he’s also got plenty of company in his belief that since the wage is equal to the marginal product of labor, and marginal products should decline, in the short run higher employment implies a lower real wage. But is he right? Is it true that if employment is to rise, “the only question” is whether wages fall directly or via inflation? Is it true that unemployment necessarily means that wages are too high?

Empirically, it seems questionable. Let’s look at unemployment and wages in the past few decades in the United States. The graph below shows the real hourly wage on the x-axis and the unemployment rate on the y-axis. The red dots show the two years after the peak of unemployment in each of the past five recessions. If reducing unemployment always required lower real wages, the red dots should consistently make upward sloping lines. The real picture, though, is more complicated.

As we can see, the early 2000s recovery and, arguably, the early 1980s recovery were associated with falling real wages. but in the early 1990s, employment recovered with constant real wages — that’s what the vertical line over on the left means. And in the two recessions of the 1970s, the recoveries combined falling unemployment with strongly rising real wages. If we look at other advanced countries, it’s this last pattern we see most often. (I show some examples after the fold.) So while rising employment is sometimes accompanied by a falling real wage, it is clearly not true that, as Glasner claims, it necessarily must be.

This is an important question to get straight. There seems to be a certain convergence happening between progressive-liberal economists and neo-monetarists like Glasner on the desirability of higher inflation in general and nominal GDP targeting in particular. There’s something to be said for this; inflation is the course of least resistance to cancel the debts. But we in the party of movement can’t support this idea or make it part of a broader popular economic program if it’s really a stalking horse for lower wages.

Fortunately, the macroeconomic benefits of a rising price level don’t depend on a falling real wage.
More broadly, the idea that reducing unemployment necessarily means reducing wages doesn’t hold up. It’s wrong empirically, and it involves a basic misunderstanding of what’s going on in recessions.

Yes, labor is idle in a recession, but does that mean its price, the wage, is too high? There is also more excess capacity in the capital stock in a recession; by the same logic, that would mean profits are too high. Real estate vacancy rates are high in a recession, so rents must also be too high. In fact, every factor of production is underutilized in recessions, but it’s logically impossible for the relative price of all factors to be too high. A shortfall in demand for output as a whole (or excess demand for the means of payment, if you’re a monetarist) doesn’t tell us anything about whether relative prices are out of line, or in which direction. If we were seeing technological unemployment — people thrown out of work by the adoption of more capital-intensive forms of production — then there might be something to the statement that “unemployment … implies that real wages are, in some sense, too high.” But that’s not what we see in recessions at all.

Glasner is hardly the only one who thinks that unemployment must somehow involve excessive wages. If he were, he’d hardly be worth arguing with. It’s a common view today, and it was even more common before World War II. Glasner quotes Mises (yikes!), but Schumpeter said the same thing. More interestingly, so did Keynes. In Chapter Two of the General Theory, he announces that he is not challenging what he calls the first postulate of the classical theory of employment, that the wage is equal to the marginal product of labor. And he draws the same conclusion from this that Glasner does:

with a given organisation, equipment and technique, real wages and the volume of output (and hence of employment) are uniquely correlated, so that, in general, an increase in employment can only occur to the accompaniment of a decline in the rate of real wages. Thus I am not disputing this vital fact which the classical economists have (rightly) asserted… [that] the real wage earned by a unit of labour has a unique (inverse) correlation with the volume of employment. Thus if employment increases, then, in the short period, the reward per unit of labour in terms of wage-goods must, in general, decline… This is simply the obverse of the familiar proposition that industry is normally working subject to decreasing returns… So long, indeed, as this proposition holds, any means of increasing employment must lead at the same time to a diminution of the marginal product and hence of the rate of wages measured in terms of this product.

So, wait, if Keynes says it then it can’t be a basic misunderstanding of the principle of aggregate demand, can it? Well, here’s where things get interesting.

Keynes didn’t participate much in the academic discussions following the The General Theory; the last decade of his life was taken up with practical policy work. (As Hyman Minsky observed, this may be one reason why many of his more profound ideas never made into postwar Keynesianism.) But he take part in a discussion in the pages of the Quarterly Journal of Economics, in which the “most important” contribution, per Keynes, was from Jacob Viner, who zeroed in on exactly this question. Viner:

Keynes’ reasoning points obviously to the superiority of inflationary remedies for unemployment over money-wage reductions. … there would be a constant race between the printing press and the business agents of the trade unions, with the problem of unemployment largely solved if the printing press could maintain a constant lead…  [But] Keynes follows the classical doctrine too closely when he concedes that “an increase in employment can only occur to the accompaniment of a decline in the rate of real wages.” This conclusion results from too unqualified an application of law-of-diminishing-returns analysis, and needs to be modified for cyclical unemployment… If a plant geared to work at say 80 per cent of rated capacity is being operated at say only 30 per cent, both the per capita and the marginal output of labor may well be lower at the low rate of operations than at the higher rate, the law of diminishing returns notwithstanding. There is the further empirical consideration that if employers operate in their wage policy in accordance with marginal cost analysis, it is done only imperfectly and unconsciously…

Viner makes two key points here: First, it is not necessarily the case that the marginal product of labor declines with output, especially in a recession or depression when businesses are producing well below capacity. And second, the assumption that wages are equal to marginal product is not a safe one. A third criticism came from Kalecki, that under imperfect competition firms would not set price equal to marginal cost but at some markup above it, a markup that will vary over the course of the business cycle. Keynes fully agreed that all three criticisms — along with some others, which seem less central to me — were correct, and that the first classical postulate was no better grounded than the second. In what I believe was his last substantive economic publication, a 1939 article in the Economic Journal, he returned to the question, showing that it was not true empirically that real wage fall when employment rises and exploring why he and other economists had gotten this wrong. The claim that higher employment must be accommpanied by a lower real wage, he wrote, “is the portion of my book which most needs to be revised.” Indeed, it was the only substantive modification of the argument of the General Theory that he made in his lifetime.

I bring all this up because — well, partly just because I think it’s interesting. But it’s worth being reminded, how much of our current economic debate is  recapitulating what people were figuring out in the 1930s. And it’s interesting to see how just how seductive is the idea that high unemployment means that “real wages are, in some sense, too high.” Even Keynes had to be talked out of it, even though it runs counter to the logic of his whole system, and even though there’s no good theoretical or empirical reason to believe it’s true.

Right, back to empirics. Here are a few more graphs, showing, like the US one above, unemployment on the vertical axis and real hourly wages on the horizontal. Data is from the OECD.

The first picture shows five Western European countries in the decade before the crisis. The important part is the left side; what you see there is that in all five countries unemployment fell sharply in the late 90s/early 2000s, even while real wages increased. In Belgium, for example, unemployment fell from 10 percent to a bit over six percent between 1996 and 2002, at the same time as real wages rose by close to 10 percent. The other four (and almost every country in the EU) show similar patterns.

The second one shows Korea. The 1997 Asian crisis is clearly visible here as the huge spike in unemployment in the middle of the graph. But what’s relevant here is the way it seems to slope backward. That’s because real wages fell along with employment in the crisis, and rose with employment in the recovery. Over the same period that unemployment comes back down from 8 to 4 percent, the real wage index rises from 70 to 80. This is the opposite of what we would expect in the Glasner story.

The third one shows Australia and New Zealand. Australia shows two periods of sharply falling unemployment — one in the 1980s accompanied by flat wages (a vertical line) and one in the 1990s accompanied by rising wages. Of all these countries, only New Zealand’s recoveries show a pattern of falling unemployment accompanied by falling real wages — clearly after 1992, and for a quarter or two in 2000.

You may object that these are mostly small open economies. So while the real wage is deflated by the domestic price level, the real question is whether labor costs are rising or falling relative to trade partners. If employment and wages are rising together, that probably just means the currency is depreciating. I don’t think this is true either. Countries often improve their trade balance even when real wages as measured in a common currency are rising, and conversely. That’s “Kaldor’s paradox” — countries with persistently strengthening trade balances tend to be precisely those with rising relative labor costs. But that will have to wait for a future post.

UPDATE: In comments, Will Boisvert calls the graphs above the worst he’s ever seen. OK!

So, here is the same data presented in a hopefully more legible way. The red line is unemployment, the blue line is the real hourly wage. The key question is, when the red line is falling from a peak, is the blue line falling too, or at least decelerating? And the answer, as above, is: Sometimes, but not usually. There is nothing dishonest in the claim that, in a recession, unemployment can be reduced without a decline in the real wage.



What Does a Credit Crunch Look Like?


What doesn’t it look like? Krugman has a picture:

His point here is right, for sure: Business investment is being held back by weak demand, not lack of credit. Would Tufte approve of that graph, tho? (It looks like one of those images of disk usage you get when you defragment your hard drive.) And more importantly: Why does it start in 1986?

It’s an arbitrary date, and an especially weird one to pick in this context, because of what happens if you go back just a couple years. You call that a credit crunch, mate? Now this is a credit crunch:


See that spike over on the left? That’s a country full of businessmen screaming as Papa Volcker stomps on their necks. (To be fair, it’s their workers he was mainly interested in strangling, but the credit squeeze for business was no less real for that.) And that’s what a credit crunch looks like.