Ricardian Equivalence confirmed

According to the so-called Ricardian Equivalence theorem, cutting taxes or increasing transfers does not stimulate aggregate demand, because private households offset tax cuts or transfer increases by saving more.

The proof of the theorem is as follows: If the government cuts taxes (or raises transfers) by 1 euro today without cutting government spending, the public debt increases by 1 euro. To service the additional debt, the government must raise taxes by r euros, r being the interest rate, in every future period from tomorrow to infinity. The present value of those future tax payments is 1 euro (=r/r). This is the amount households need to save today to pay those future taxes.

David Ricardo was the first to lay out this simple point of arithmetic in a debate over how the British government should pay for the Napoleonic Wars. But he went on to reject the conclusion that government deficits are offset by private saving arguing that households are too short-sighted to take into account those future tax payments in their saving decisions. So David Ricardo did not believe in Ricardian Equivalence.

Whatever.

In preparation for my Principles of Macroeconomics class, I wanted to check if there is any correlation between government deficits and private saving. I didn’t expect to find much. So I was surprised when after a few minutes of fiddling with FRED, the awesome data base of the St. Louis Fed, I got this:

The red line is the primary government budget balance in percent of GDP, (T-G)/Y in conventional macroeconomic notation. The blue line is personal saving in percent of disposable income (Y-T-C)/(Y-T).

Look how the blue line tends to move up whenever the red line moves down, and vice versa. Your eyes do not lie. The correlation coefficient between government saving and private saving is -0.12, statistically different from zero at usual confidence levels (the t-statistic is -1.85).

Is this the most solid econometric evidence ever? No, but it is a sign that Ricardian Equivalence is not so out of touch with the data as you might think.

Coronavirus und Lebenserwartung: Statistik Austria verwirrt

Der Standard berichtet:

Die Corona-Pandemie hat den stärksten Rückgang der Lebenserwartung seit Beginn der Aufzeichnungen 1951 ausgelöst. Während wir es in den letzten Jahren gewohnt waren, immer älter und älter zu werden, gibt es nun erstmals einen massiven Knick in der Lebenserwartungsstatistik.

Grund dafür ist eine sehr hohe Übersterblichkeit in den letzten Wochen des Jahres 2020. Neue Daten der Statistik Austria zeigen, dass im gesamten Vorjahr etwa zehn Prozent mehr Menschen starben als im Durchschnitt der vergangenen fünf Jahre. Insgesamt waren es rund 90.000. […]

Konkret heißt das, dass ein Mann, der heute in Österreich geboren wird, im Durchschnitt 78,9 Jahre lang leben wird. Bei einer Frau sind es durchschnittlich 83,7 Jahre. 

https://www.derstandard.at/story/2000123287763/statistik-austria-ueber-90-000-todesfaelle-2020-lebenserwartung-sinkt

Damit sank die Lebenserwartung im Vergleich zum Vorjahr bei Frauen um ein halbes Jahr, bei Männern um etwas mehr. Die Statistischen Ämter anderer Länder lieferten ähnlich verheerende Zahlen: die amerikanische Gesundheitsbehörde CDC meldete sogar einen Rückgang der Lebenserwartung von einem ganzen Jahr.

Diese Zahlen können nicht stimmen.

Experten schätzen, dass ein an COVID-19 Verstorbener im Schnitt 12 Jahre seiner Lebens verlor. Multipliziert man das mit den 8.500 Corona-Toten in Österreich kommt man auf 102.000 verlorene Lebensjahre. Bezogen auf die Gesamtbevölkerung von 8,86 Millionen ergibt das eine durchschnittliche Reduktion der Lebenserwartung von 0,01 Jahren. Das ist ein Rückgang von etwa vier Tagen, nicht sechs Monaten wie der “Standard” berichtet. Der von der Statistik Austria gemeldete Wert ist um das 40-fache zu hoch. Wie kann das sein?

Wie in diesem kurzen Artikel erklärt wird, gehen die Statistikämter bei der Schätzung der Lebenserwartung von einer wesentlichen Annahme aus: nämlich, dass das Sterberisiko in jeder Alterskohorte in Zukunft genauso bleibt wie im Jahr 2020. D.h. die Wahrscheinlichkeit, dass ein im Jahr 2020 geborener Mensch im Alter von X Jahren sterben wird, ist gleich der Sterbewahrscheinlichkeit eines X Jahre alten Menschen im Jahr 2020. Das ist eine sinnvolle Annahme in einem gewöhnlichen Jahr. Aber 2020 war kein gewöhnliches Jahr.

Mit anderen Worten: Die Statistik Austria geht implizit davon aus, dass sich die Corona-Pandemie von 2020 jedes Jahr genauso wiederholen wird. Die Mitarbeiter der Statistik Austria sind sich dieser Annahme natürlich bewusst, weshalb auch auf ihrer Website folgender der Hinweis steht:

Die für ein Kalenderjahr berechnete Lebenserwartung bei der Geburt gibt an, wie viele Jahre ein neugeborenes Kind im Durchschnitt leben würde, wenn sich die im Kalenderjahr beobachteten altersspezifischen Sterberaten in Zukunft nicht mehr ändern würden.

https://www.statistik.at/web_de/presse/125167.html

Nur das Problem ist: Die so geschätzte Lebenserwartung macht für das Jahr 2020 eben leider keinen Sinn. Und der Warnhinweis geht erwartungsgemäß in der medialen Berichterstattung völlig unter. Sogar der “Standard”, der für sich in Anspruch nimmt ein Qualitätsmedium zu sein, (des-)informiert seine Leser, dass ihre Lebenserwartung um 6 Monate gesunken sei, ohne auf die falsche Annahme, die diesem Wert zugrunde liegt, hinzuweisen.

Einigermaßen bizarr ist auch der Titel, den die österreichische Akademie der Wissenschaften für ihren Beitrag zu diesem Thema gewählt hat:

COVID VERRINGERT LEBENSERWARTUNG, STIEHLT ABER KEINE LEBENSJAHRE

Die durchschnittliche Lebenserwartung in Österreich ist laut vorläufigen Zahlen der Statistik Austria im Corona-Jahr 2020 um sechs Monate gesunken. Das heißt aber nicht, dass die Österreicher/innen jetzt weniger alt werden, erklärt Demograph Marc Luy von der ÖAW.

https://www.oeaw.ac.at/detail/news/covid-verringert-lebenserwartung-stiehlt-aber-keine-lebensjahre

Hä? Wenn COVID keine Lebensjahre stiehlt, wie kann sie dann die Lebenserwartung um ein halbes Jahr verringern? Wenn die Lebenserwartung nicht die zu erwartenden Lebensjahre misst, was misst sie dann? Und wozu braucht man dann diese “Lebenserwartung” überhaupt?

In einem normalen Jahr misst die Lebenserwartung das, was jeder glaubt, dass sie misst. Aber eben nicht in einer Pandemie. Die Statistik Austria täte gut daran, die Berechnung der Lebenserwartung für 2020 anzupassen.

(Hat tip to David Friedman, durch den ich auf das Problem aufmerksam wurde.)

Two riddles

Riddle #1: Are you better off if your wealth increases?

Julia owns shares in a company which pays her a dividend of 100,000 a year. She spends all of her dividend income. At an interest rate of 10 percent, the market value of her wealth is 1 million. When the interest rate falls to 1 percent, her wealth goes up to 10 million.

How much better off is Julia?

adapted from Ben Moll: https://benjaminmoll.com/wp-content/uploads/2020/06/HKS_comment.pdf

Riddle #2: Are you better off if the price of your house increases?

Joe lives in a house worth 1 million. He has borrowed 1 million at 10% interest to finance the house purchase. Due to a sudden increase in demand for local houses, Joe’s house rises in value to 1.2 million.

How much better off is Joe?

The obvious answer is wrong. Ben Moll has the correct answers in this short paper.

The point: Wealth isn’t welfare. Wealth statistics (and a fortiori wealth distribution statistics) are often misleading.

(Here’s a graphical clue:)

Isn’t it amazing how well the Consumption Euler Equation works?

While preparing graphs for my Principles of Macroeconomics class, I made this one:

fredgraph

The blue line is the growth rate of nominal consumption spending in the US, the red line is the nominal interest rate on a risk-free asset (a 10-year US government bond). See the way the red line tracks the blue line? That’s a beautiful confirmation of the Consumption Euler Equation which is the cornerstone of all modern macro models. (And no, I didn’t tweak this graph by restricting the time period or choosing different axes for the two lines or transforming the data somehow. This is a plot of the raw data without any editing. No funny stuff.)

PS: I’m actually not going to teach the Euler Equation in my Principles Class. Nobody seems to. Mankiw’s textbook doesn’t. But I’m increasingly asking myself why not?

Jonathan Swift on the Laffer Curve

But I will tell you a secret, which I learned many years ago from the commissioners of the customs in London; they said, when any commodity appeared to be taxed above a moderate rate, the consequence was, to lessen that branch of the revenue by one half; and one of those gentlemen pleasantly told me, that the mistake of parliaments, on such occasions, was owing to an errour of computing two and two to make four; whereas in the business of laying impositions, two and two never made more than one; which happens by lessening the import, and the strong temptation of running such goods as paid high duties, at least in this kingdom.

From An Answer to a Paper called a Memorial of the Poor Inhabitants, Tradesmen, and Labourers of Ireland, The Works of the Rev. Jonathan Swift, Volume 9

I found this reference in David Hume’s classic essay Of the Balance of Trade which is on the reading list of my International Economics class next Fall.

The radical transformation of the ECB

Students of my generation will remember what we learned about how the European Central Bank conducts monetary policy: The ECB makes one-week loans to commercial banks against top-rated collateral. This was called “Main Refinancing Operations”. The interest rate charged on these loans was known as the Main Refinancing Rate and was considered the key policy rate of the ECB, like the Fed Funds Rate in the United States. Then we learned something about Marginal Lending Facilities and Long-Term Refinancing Operations, but were told they were relatively unimportant.

This was indeed how the ECB operated – before 2009. Since then the ECB has changed its operations. It seems to me that the radical nature of this change has not been recognized enough by economists – let alone the general public.

Look at the chart below. It shows the assets held by the ECB system for purposes of monetary policy operations. The Main Refinancing Operations (the yellow area) have disappeared. In 2019 they constituted a mere 0.25% of the total monetary-policy related assets! The Long-Term Refinancing Operations (blue area) have replaced them and make up about 20% of the total now.

But the elephant in the room is the grey area that first appears in 2009 and then explodes after 2014. The ECB labels it “Securities held for monetary policy purposes”. What are those securities? Government bonds and a couple of corporate bonds as well. The ECB started to buy them with the “Securities Market Program” in 2009 and hugely expanded the purchases with the “Public Sector Purchase Program” in 2015. Last year, the ECB system held 2.6 trillion of assets in relationship with those programs. That is more than 80% of their total policy-related assets.

This means that the ECB of our old textbooks, the ECB that was envisioned by the founders of the euro, has ceased to exist. It has been replaced by an altogether different beast. The primary way in which the ECB conducts monetary policy these days consists in buying Eurozone government bonds in the open market.

This has made the ECB the single biggest lender to Eurozone governments. As I showed in my last post, 91% of all new government debt issued after 2010 is now being held by the ECB. It resembles a 3.2 trillion euro hedge fund, financed by short-term commercial bank deposits (aka “reserves”), holding a diversified portfolio of Eurozone government bonds. The equity owners of this fund are the Eurozone government themselves: they “own” the ECB, they are responsible for replenishing its equity if and when it is deemed necessary.

One implication of this radical transformation should be immediately obvious: Eurozone governments have in effect mutualized 91% of their post-2009 debt. Whenever a Eurozone government defaults on the bonds held by the ECB, the losses would be absorbed, eventually, by the other Eurozone governments.

I’m not saying that’s a bad thing or a good thing. I’m not saying it is illegal or legal. But nobody should delude themselves or others that this is not what has been happing.

How much monetary financing did the ECB provide to Eurozone governments?

Last week, the German constitutional court ruled that the large-scale purchases of government bonds by the ECB since 2015 fell outside the ECB’s legal competences. But the Court also held that this purchasing program did non violate the “prohibition of monetary financing of Member State budgets” in Art. 123 of the TFEU.

It’s unclear whether the ruling will have any effect in practice, because the Court allowed the ECB to continue its program provided they come up with some kind of explanation of what they are doing in the next few months (I’m simplifying).

I admit that I have no idea if the ECB transgressed its legal authorities. But I’m a little bit shocked by the second aspect of the ruling, the finding that the ECB did not provide monetary financing of Member States budgets.

Because the ECB clearly did.

The figure below shows the change in the aggregate outstanding debt of all Eurozone governments (blue line) as well as the change in the ECB’s holdings of such debt (red line) since 2010.

All Eurozone governments combined have issued 1.845 trillion euros* in new debt since 2010. During the same time, the ECB has increased its holdings of Eurozone government debt by 1.683 trillion euros. Ergo, the ECB has bought 91 cents of every euro of new debt issued by Eurozone governments. Notice also the clear break in the red curve in the year 2015. That’s exactly when the PSPP started.

How can this not be “monetary financing” of Eurozone governments?

*) All debt numbers here refer to face values, not market values, and are not adjusted for inflation.

Some descriptive COVID-19 regressions

Having raised the bar so incredibly high with my last post, I now want to bring it down again and show you some unsophisticated data analysis.

Every day now you can see people comparing countries on performance in this pandemic all over the place. How well ist Germany doing? How does the UK compare to France? And what about Sweden: should we have followed their hands-off approach?

All of these comparisons lack one fundamental ingredient: meaningful data. The data everybody is using (and which I will be using in a minute) is riddled with measurement issues. Most important among them is the issue of testing: who gets tested, how fast, how many gest tested – all of that varies from country to country and across time within a given country. Not even the death statistics are reliable as we learned only this week when the UK drastically corrected their number upwards.

But I thought to myself, what the heck. If everyone’s doing it, I might be forgiven for having some fun as well. And so, in between grading final exams, I pulled together some country-level data and ran some regressions.

It goes without saying that this analysis has some, shall we say, shortcomings. All I’m doing is using regressions to describe some patterns in the data. Although I did have some mental model when deciding which variables to include in my regressions, they were of the sort “I imagine X could have effect on COVID deaths” rather than any deep causal understanding of how the epidemic works (but, frankly, does anyone have that?)

So without further ado, here’s what I did. I took the data from the European Center for Disease Prevention and Control (ECDC), giving me daily new cases and new deaths for each country reporting those things, which I summed up until April 30th to get the cumulative cases and deaths. I then divided by population to get cases and deaths per capita. These are my dependent variables.

For my regressors I went on a wild hunt on the World Bank and OECD databases and downloaded everything that I thought would be interesting to regress on COVID-19. After some fooling around, I settled on the following two models:

Model 1: cumulative COVID-19 cases per capita (in logs)

The first variable (lrgdp_pc) here is PPP-adjusted GDP per capita (in logs). This is the single most important variable in “explaining” the number of cases: richer countries have more official cases. The relationship is 1:1, i.e. one percent more income is associated with one percent more cases. It is almost useless to speculate about the “causal channels” for this effect. If I were to guess, I’d say that rich countries got the virus earlier and perform more tests per capita and therefore detect more cases.

The second variable (pop65) is the share of population above the age of 65. We know that seniors are more susceptible to this disease, so any sensible model must take the age structure into account. It’s reassuring that the coefficient is positive and significant. I take this as a sanity check for my model.

The next two variables is population density (pop_dens) and share of urban population (urban). My “theory” here is that denser, more urban countries provide a more fertile environment for the virus to spread. Somewhat disappointingly population density seems to have no effect and urbanization only has a small one (a 1 percentage point higher urban share gives you 1.4% more cases per capita). And no, density and urbanization are not highly correlated (corr=0.17), glad that you’ve asked.

Lastly, I wanted to check if more open countries are more exposed. I tried to capture that with the trade share (exports plus imports divided by GDP). The answer seems to be a clear no. Being more open to international trade is not associated with more infections. In an alternative specification I checked if imports from China had a positive effect and was disappointed.

I direct your attention to the fact that the R-squared of this regression is 68.5%. I have seen papers published in decent journals with much worse goodness of fit given the sample size and number of regressors. Just saying.

Model 2: cumulative COVID-19 deaths per capita

Turning to coronavirus deaths, the first important “explanatory” variable is the number of cases (lcases_pc). Again, this is nothing more than a sanity check.

I then add all the variables from the previous model to see if they have an effect on deaths over and above the effect they have through the number of cases. Unsurprisingly, an older population has the expected positive effect on deaths: raising the share of old people by 1 percentage point raises deaths per capita by 11% (in addition to the effect through cases).

More surprising are the effects of population density and urbanization. It looks like, after controlling for the number of cases, being a denser, more urban country reduces the number of deaths. I suppose this can make sense: given the number of infections, living closer together and in cities means living closer to hospitals, which might improve the chances of getting timely and effective treatment. But this is getting dangerously close to over-interpretation of weak effect estimates (small, barely significant coefficients).

The last variable is the number of hospital beds per 1000 people. The estimated coefficient suggests that each additional bed per 1000 inhabitants lowers the number of deaths by about 15%. Austria has 7.37 beds per 1000 people, the European average is 5. So bringing all the countries of Europe to the level of Austria would cut the death rate by about 36%. That’s a big effect.

I also toyed around with various measures of health care spending (per capita or as a share of GDP). In all the regressions I checked, health spending had a positive effect, which I couldn’t make sense of. My best guess is that, conditional on hospital beds per capita, spending more on health is a sign that your health system is too expensive and inefficient which is associated both with more cases and more deaths. But it’s still kind of a head scratcher.

Excess Cases and Deaths

OK. Having run these regressions and found some interesting patterns, what else can we learn from then?

One thing is that the regression model provides a benchmark to evaluate how individual countries are doing. Admittedly, this is risky business, given the poor data quality. But I’m putting it out there nevertheless.

Below, I’m plotting the excess cases and excess deaths per capita for a number of countries. Excess cases is the difference between the actual cases and the number of cases predicted by the model. Excess deaths are calculated analogously. (Attentive readers will realize that these are just the regression residuals.) The vertical axis shows cases and deaths per 100,000 people.

Three countries stand out in terms of excess cases: Italy, UK and US. Their case numbers are far higher than what one would expect on the basis of their country characteristics.

The “worst performers” among the selected countries in terms of excess deaths are France, Britain and Italy.

China and Korea have negative excess cases and no excess deaths. That is, these countries have fewer cases (and neither fewer nor more deaths) than the model predicts.

Notice that Sweden has similar excess cases as Germany and Austria, but far higher excess deaths. Make of that what you will.

(Data file and STATA code are available on request.)

The case for rational expectations in COVID-19 modeling

British biologist Carl Bergstrom recently gave an interview to the Guardian on the topic of “bullshit”. In it, the interviewer asked Bergstrom about shortcomings of existing epidemiological models as well as their use (and misuse) by political decision makers.

[Guardian] If you had the ability to arm every person with one tool – a statistical tool or scientific concept – to help them understand and contextualize scientific information as we look to the future of this pandemic, what would it be?

[Bergstrom] I would like people to understand that there are interactions between the models we make, the science we do and the way that we behave. The models that we make influence the decisions that we take individually and as a society, which then feed back into the models and the models often don’t treat that part explicitly. Once you put a model out there that then creates changes in behavior that pull you out of the domain that the model was trying to model in the first place. We have to be very attuned to that as we try to use the models for guiding policy.

In the context of the coronavirus, the problem was this: Early models such as the one by the Imperial College in London predicted between 1.1 and 2.2 millions of Americans could die from COVID-19, depending on the severity of mitigation efforts. This eye-popping number jolted the political decision makers (Trump, Congress, the Governors, etc.) into action, locking down schools and businesses and issuing stay-home orders. The media publicity around the study probably scared many people which made them take the social distancing measures much more seriously. All of this probably helped in slowing the spread of the disease such that the same researchers had to revise their predictions downward only weeks later.

That is, the publication of the initial predictions changed the behavior of people which rendered those predictions obsolete.

Bergstrom seems to say that the problem here is with the general public. They don’t understand that the models rely on behavioral assumptions which no longer hold once people learn about the models’ predictions and adjust their actions accordingly.

But, with apologies to Shakespeare: The fault, dear Bergstrom, is not in the general public, but in your models!

The problem with those epidemiological models (at least with the SIR-types of models) is that some of their key parameters (such as the reproduction rate R0, for instance) depend, in various ways, on people’s expectations about the future path of the disease. If you don’t take that into account, your predictions will be way off.

And way off they were! Here’s the summary of a statistical evaluation of a model similar to the one used in the Imperial study:

In excess of 70% of US states had actual death rates falling outside the 95% prediction interval for that state (Figure 1)

The ability of the model to make accurate predictions decreases with increasing amount of data. (figure 2)

You might say that prediction is not the point with those models. Maybe their only purpose is to produce scary headlines to make people listen to the experts. But that is a weird proposition. If experts want the general public to take them more seriously, making wildly erroneous predictions seems like a bad strategy.

So how are we going to take people’s expectations into account in epidemiological models? Let’s see.

March: Imperial predicts 2 million deaths. Government imposes lockdown. People are scared and stay at home.

April: Imperial revises his model, now predicts 50,000 deaths. Government partially re-opens the economy. People cautiously start going out again.

May: Imperial revises his model, now predicts 200,000 deaths. Government re-imposes some lockdown measures. People are scared again.

June: Imperial revises his model, now predicts 75,000 deaths. Government opens up again. People relax again.

And so on until we have converged to a situation in which the number of deaths Imperial predicts is consistent with the government’s (and the people’s) expectations and actions.

Such a situation is what economists call a rational expectations equilibrium. I think that trying to model people’s expectations in a consistent way would improve the usefulness of epidemiological models. This is, of course, a tall order. But perhaps if economists, statisticians, and epidemiologists would put their heads together, we could move in this direction.