Monday, July 6, 2020

A little financial-econometric history

The issues that have cropped up in applying present value ideas to government finance, in my last post, caused me to write up a little financial-econometric history, which seems worth passing on to blog readers. The lessons of the 1980s and 1990s are fading with time, and we should avoid having to re-learn such hard-won lessons. (Warning: this post uses mathjax to display equations.)

Faced with a present value relation, say $p_{t}=E_{t}\sum_{j=1}^{\infty}\beta^{j}d_{t+j},$ what could be more natural than to model dividends, say as an AR(1), $d_{t+1}=\rho_{d}d_{t}+\varepsilon_{t+1},$ to calculate the model-implied price, $E_{t}\sum_{j=1}^{\infty}\beta^{j}d_{t+j}=\frac{\beta\rho_{d}}{1-\beta\rho_{d} }d_{t},$ and to compare the result to $$p_{t}$$? The result is a disaster -- prices do not move one for one with dividends, and they move all over the place with no discernible movement in expected dividends.

The Surplus Process

How should we model surpluses and deficits? In finishing up a recent article and chapter 5 and 6 of a Fiscal Theory of the Price Level update, a bunch of observations coalesced that are worth passing on in blog post form.

Background: The real value of nominal government debt equals the present value of real primary surpluses, $\frac{B_{t-1}}{P_{t}}=b_{t}=E_{t}\sum_{j=0}^{\infty}\beta^{j}s_{t+j}.$ I 'm going to use one-period nominal debt and a constant discount rate for simplicity. In the fiscal theory of the price level, the $$B$$ and $$s$$ decisions cause inflation $$P$$. In other theories, the Fed is in charge of $$P$$, and $$s$$ adjusts passively. This distinction does not matter for this discussion. This equation and all the issues in this blog post hold in both fiscal and standard theories.

The question is, what is a reasonable time-series process for $$\left\{s_{t}\right\}$$ consistent with the debt valuation formula? Here are surpluses

The blue line is the NIPA surplus/GDP ratio. The red line is my preferred measure of primary surplus/GDP, and the green line is the NIPA primary surplus/GDP.

The surplus process is persistent and strongly procyclical, strongly correlated with the unemployment rate.  (The picture is debt to GDP and surplus to GDP ratios, but the same present value identity holds with small modifications so for a blog post I won't add extra notation.)

Something like an AR(1) quickly springs to mind, $s_{t+1}=\rho_{s}s_{t}+\varepsilon_{t+1}.$ The main point of this blog post is that this is a terrible, though common, specification.

Write a general MA process, $s_{t}=a(L)\varepsilon_{t}.$ The question is, what's a reasonable $$a(L)?$$ To that end, look at the innovation version of the present value equation, $\frac{B_{t-1}}{P_{t-1}}\Delta E_{t}\left( \frac{P_{t-1}}{P_{t}}\right) =\Delta E_{t}\sum_{j=0}^{\infty}\beta^{j}s_{t+j}=\sum_{j=0}^{\infty}\beta ^{j}a_{j}\varepsilon_{t}=a(\beta)\varepsilon_{t}%$ where $\Delta E_{t}=E_{t}-E_{t-1}.$ The weighted some of moving average coefficients $$a(\beta)$$ controls the relationship between unexpected inflation and surplus shocks. If $$a(\beta)$$ is large, then small surplus shocks correspond to a lot of inflation and vice versa. For the AR(1), $$a(\beta)=1/(1-\rho_{s}\beta)\approx 2.$$ Unexpected inflation is twice as volatile as unexpected surplus/deficits.

$$a(\beta)$$ captures how much of a deficit is repaid. Consider $$a(\beta)=0$$. Since $$a_{0}=1$$, this means that the moving average is s-shaped. For any $$a(\beta)\lt 1$$, the moving average coefficients must eventually change sign. $$a(\beta)=0$$ is the case that all debts are repaid. If $$\varepsilon_{t}=-1$$, then eventually surpluses rise to pay off the initial debt, and there is no change to the discounted sum of surpluses. Your debt obeys $$a(\beta)=0$$ if you do not default. If you borrow money to buy a house, you have deficits today, but then a string of positive surpluses which pay off the debt with interest.

The MA(1) is a good simple example, $s_{t}=\varepsilon_{t}+\theta\varepsilon_{t-1}%$ Here $$a(\beta)=1+\theta\beta$$. For $$a(\beta)=0$$, you need $$\theta=-\beta ^{-1}=-R$$. The debt -$$\varepsilon_{t}$$ is repaid with interest $$R$$.

Let's look at an estimate. I ran a VAR of surplus and value of debt $$v$$, and I also ran an AR(1).

Here are the response functions to a deficit shock:

The blue solid line with $$s=-0.31$$ comes from a larger VAR, not shown here. The dashed line comes from the two variable VAR, and the line with triangles comes from the AR(1).

The VAR (dashed line) shows a slight s shape. The moving average coefficients gently turn positive. But when you add it up, those overshootings bring us back to $$a(\beta)=0.26$$ despite 5 years of negative responses. (I use $$\beta=1$$). The AR(1) version without debt has $$a(\beta)=2.21$$, a factor of 10 larger!

Clearly, whether you include debt in a VAR and find a slightly overshooting moving average, or leave debt out of the VAR and find something like an AR(1) makes a major difference. Which is right? Just as obviously, looking at $$R^2$$   and t-statistics of the one-step ahead regressions is not going to sort this out.

I now get to the point.

Here are 7 related observations that I think collectively push us to the view that $$a(\beta)$$ should be a quite small number. The observations use this very simple model with one period debt and a constant discount rate, but the size and magnitude of the puzzles are so strong that even I don't think time-varying discount rates can overturn them. If so, well, all the more power to the time-varying discount rate! Again, these observations hold equally for active or passive fiscal policy. This is not about FTPL, at least directly.

1) The correlation of deficits and inflation. Reminder, $\frac{B_{t-1}}{P_{t-1}}\Delta E_{t}\left( \frac{P_{t-1}}{P_{t}}\right) =a(\beta)\varepsilon_{t}.$ If we have an AR(1), $$a(\beta)=1/(1-\rho_{s}\beta)\approx2$$, and with $$\sigma(\varepsilon)\approx5\%$$ in my little VAR, the AR(1) produces 10% inflation in response to a 1 standard deviation deficit shock. We should see 10% unanticipated inflation in recessions! We see if anything slightly less inflation in recessions, and little correlation of inflation with deficits overall. $$a(\beta)$$ near zero solves that puzzle.

2) Inflation volatility. The AR(1) likewise predicts that unexpected inflation has about 10% volatility. Unexpected inflation has about 1% volatility. This observation on its own suggests $$a(\beta)$$ no larger than 0.2.

3) Bond return volatility and cyclical correlation. The one-year treasury bill is (so far) completely safe in nominal terms. Thus the volatility and cyclical correlation of unexpected inflation is also the volatility and cyclical correlation of real treasury bill returns. The AR(1) predicts that one-year bonds have a standard deviation of returns around 10%, and they lose in recessions, when the AR(1) predicts a big inflation. In fact one-year treasury bills have no more than 1% standard deviation, and do better in recessions.

4) Mean bond returns. In the AR(1) model, bonds have a stock-like volatility and move procyclically. They should have a stock-like mean return and risk premium. In fact, bonds have low volatility and have if anything a negative cyclical beta so yield if anything less than the risk free rate. A small  (a(\beta)\) generates low bond mean returns as well.

Jiang, Lustig, Van Nieuwerburgh and Xiaolan recently raised this puzzle, using a VAR estimate of the surplus process that generates a high $$a(\beta)$$. Looking at the valuation formula $\frac{B_{t-1}}{P_{t}}=E_{t}\sum_{j=0}^{\infty}\beta^{j}s_{t+j},$ since surpluses are procyclical, volatile, and serially correlated like dividends, shouldn't surpluses generate a stock-like mean return? But surpluses are crucially different from dividends because debt is not equity. A low surplus $$s_{t}$$ raises  our estimate of subsequent surpluses $$s_{t+j}$$. If we separate out
$b_{t}=s_{t}+E_{t}\sum_{j=1}^{\infty}\beta^{j}s_{t+j}=s_{t}+\beta E_{t}b_{t+1}$ a decline in the "cashflow" $$s_{t}$$ raises the "price" term $$b_{t+1}$$, so the overall return is risk free. Bad cashflow news lowers stock pries, so both cashflow and price terms move in the same direction. In sum a small $$a(\beta)\lt 1$$ resolves the Jiang et. al. puzzle. (Disclosure, I wrote them about this months ago, so this view is not a surprise. They disagree.)

5) Surpluses and debt. Looking at that last equation, with a positively correlated surplus process $$a(\beta)>1$$, as in the AR(1), a surplus today leads to  larger value of the debt tomorrow. A deficit today leads to lower value of the debt tomorrow. The data scream the opposite pattern. Higher deficits raise the value of debt, higher surpluses pay down that debt. Cumby_Canzoneri_Diba (AER 2001) pointed this out 20 years ago and how it indicates an s-shaped surplus process.  An $$a(\beta)\lt 1$$ solves their puzzle as well. (They viewed $$a(\beta)\lt 1$$ as inconsistent with fiscal theory which is not the case.)

6) Financing deficits. With $$a(\beta)\geq1$$, the government finances all of each deficit by inflating away outstanding debt, and more. With $$a(\beta)=0$$, the government finances deficits by selling debt. This statement just adds up what's missing from the last one. If a deficit leads to lower value of the subsequent debt, how did the government finance the deficit? It has to be by inflating away outstanding debt. To see this, look again at inflation, which I write $\frac{B_{t-1}}{P_{t-1}}\Delta E_{t}\left( \frac{P_{t-1}}{P_{t}}\right) =\Delta E_{t}s_{t}+\Delta E_{t}\sum_{j=1}^{\infty}\beta^{j}s_{t+j}=\Delta E_{t}s_{t}+\Delta E_{t}\beta b_{t+1}=1+\left[ a(\beta)-1\right] \varepsilon_{t}.$ If $$\Delta E_{t}s_{t}=\varepsilon_{t}$$ is negative -- a deficit -- where does that come from? With $$a(\beta)>1$$, the second term is also negative. So the deficit, and more, comes from a big inflation on the left hand side, inflating away outstanding debt. If $$a(\beta)=0$$, there is no inflation, and the second term on the right side is positive -- the deficit is financed by selling additional debt. The data scream this pattern as well.

7) And, perhaps most of all, when the government sells debt, it raises revenue by so doing. How is that possible? Only if investors think that higher surpluses will eventually pay off that debt. Investors think the surplus process is s-shaped.

All of these phenomena are tied together.  You can't fix one without the others. If you want to fix the mean government bond return by, say, alluding to a liquidity premium for government bonds, you still have a model that predicts tremendously volatile and procyclical bond returns, volatile and countercyclical inflation, deficits financed by inflating away debt, and deficits that lead to lower values of subsequent debt.

So, I think the VAR gives the right sort of estimate. You can quibble with any estimate, but the overall view of the world required for any estimate that produces a large $$a(\beta)$$ seems so thoroughly counterfactual it's beyond rescue. The US has persuaded investors, so far, that when it issues debt it will mostly repay that debt and not inflate it all away.

Yes, a moving average that overshoots is a little unusual. But that's what we should expect from debt. Borrow today, pay back tomorrow. Finding the opposite, something like the AR(1), would be truly amazing. And in retrospect, amazing that so many papers (including my own) write this down. Well, clarity only comes in hindsight after a lot of hard work and puzzles.

In more general settings $$a(\beta)$$ above zero gives a little bit of inflation from fiscal shocks, but there are also time-varying discount rates and long term debt in the present value formula. I leave all that to the book and papers.

(Jiang et al say they tried it with debt in the VAR and claim it doesn't make much difference.  But their response functions with debt in the VAR, at left,  show even more overshooting than in my example, so I don't see how they avoid all the predictions of a small $$a(\beta)$$, including a low bond premium.)

A lot of literature on fiscal theory and fiscal sustainability, including my own past papers, used AR(1) or similar surplus processes that don't allow $$a(\beta)$$ near zero. I think a lot of the puzzles that literature encountered comes out of this auxiliary specification. Nothing in fiscal theory prohibits a surplus process with $$a(\beta)=0$$ and certainly not $$0 \lt a(\beta)\lt 1$$.

Update

Jiang et al. also claim that it is impossible for any government with a unit root in GDP to issue risk free debt. The hidden assumption is easy to root out. Consider the permanent income model, $c_t = rk_t + r \beta \sum \beta^j y_{t+j}$ Consumption is cointegrated with income and the value of debt. Similarly, we would normally write the surplus process $s_t = \alpha b_t + \gamma y_t.$ responding to both debt and GDP. If surplus is only cointegrated with GDP, one imposes $$\alpha = 0$$, which amounts to assuming that governments do not repay debts. The surplus should be cointegrated with GDP and with the value of debt.  Governments with unit roots in GDP can indeed promise to repay their debts.

The filibuster and partisanship

The Wall Street Journal reports that the movement among Senate Democrats to get rid of the filibuster entirely is gaining steam. I think this is a bad idea and will lead to more polarized politics.

Why are our politics so polarized? One answer is that elections are more and more winner take all. The more it is winner take all, the more incentive there is for scorched-earth tactics to win, or to keep from losing.

Imagine a not so distant future in which winning an administration and both houses of Congress by 50.5% means a party can pass any legislation it likes, pack the Supreme Court or better yet impeach the lot and replace them, take control of the Department of Justice and FBI, swiftly jail anyone involved with the previous administration, take control of voting law and regulation, further hand out money to political organizations on its side, and by regulation and high taxes force businesses and wealthy individuals to its side. One person, one vote, one time.

That's extreme, but our political system has headed a lot in this direction already. As the stakes in each election get higher, do not be surprised that the scorched-earth partisanship and polarization of politics gets stronger.

The first function of a democracy is a peaceful transition of power. That requires losers to accept their fate, acknowledge the legitimacy of the outcome, regroup and try again. And they have to be able to do that.  We are not a pure democracy. We are set up as a republic, with elaborate protections for electoral minorities. The point is to keep those electoral minorities from rebelling. Union first, "progress" second.

The filibuster is a small and imperfect part of this protection. It evolved by tradition, not design. It has a sordid racial history, being used for decades by southern democrats to block civil rights legislation. To work, both sides had to accept certain rules of the game. You use it only to block core issues of great importance. You do not use it as willy-nilly obstructionism. It has to be costly to those who use it.  It, and other protections could be improved for sure. But we need somehow the space that a narrow election loss does not mean utter defeat and devastation.

Like the other protections for electoral minorities, it has already been mostly torn down, as the WSJ reports. But if, say, Republicans can shove guns, immigrant deportation, and abortion prohibition down Democratic throats with a tiny majority, or Democrats can shove unions, wealth taxes, and national health insurance down Republican throats with a tiny majority; if, more importantly, either party can take a tiny majority to entrench their hold on power and disenfranchise the other, we have not seen anything yet in the partisanship and polarization department.

Sunday, July 5, 2020

Magical monetary theory full review

I read Stephanie Kelton's book, The Deficit Myth: Modern Monetary Theory and the Birth of the People’s Economy,” and wrote this review for the Wall Street Journal. Now that 30 days have passed I can post the whole thing.

I approached this task with an open mind. What I had heard of MMT has some overlap with fiscal theory of the price level, on which I work, and I hoped to see some commonality.

I was disappointed.

The review:

Modern monetary theory, known as MMT, erupted suddenly into the public consciousness when it won the attention of high-profile politicians including Bernie Sanders and Alexandria Ocasio-Cortez and their media admirers. Its central proposition states that the U.S. federal government can and should freely print money to finance a massive spending agenda, with no concern about debt and deficits.

What is MMT? Its advocates have told us in essays, blog posts, videos and tweets what MMT says about this and that, but what is its logic and evidence? As a monetary theorist who is also skeptical of conventional wisdom, I looked forward to a definitive exposition from Stephanie Kelton’s “The Deficit Myth: Modern Monetary Theory and the Birth of the People’s Economy.”

Ms. Kelton, a professor of economics at Stony Brook University and senior economic adviser to Bernie Sanders’s presidential campaign, starts with a few correct observations. But when the implications don’t lead to her desired conclusions, her logic, facts and language turn into pretzels.

True, the federal government can spend any amount by simply printing up the needed money (in reality, creating bank reserves). True, our government need never default since it can always print dollars to repay Treasury bonds. But if the government prints up and spends, say, $10 trillion, will that not lead to inflation? Ms. Kelton acknowledges the possibility: “If the government tries to spend too much in an economy that’s already running at full speed, inflation will accelerate.” So how do we determine if the economy is running at full speed, or full of “slack,” with unemployed people and idle businesses that extra money might put to work without inflation? Ms. Kelton disdains the Federal Reserve’s noninflationary or “natural” unemployment rate measure of slack as a “doctrine that relies on human suffering to fight inflation.” Even the recent 3.5% unemployment is heartlessly too high for her. “MMT urges us to think of slack more broadly.” OK, but how? She offers only one vaguely concrete suggestion: When evaluating spending bills, “careful analysis of the economy’s . . . slack would guide lawmakers. . . . If the CBO [Congressional Budget Office] and other independent analysts concluded it would risk pushing inflation above some desired inflation rate, then lawmakers could begin to assemble a venue of options to identify the most effective ways to mitigate that risk.” She doesn’t otherwise define slack or even offer a conceptual basis for its measurement. She just supposes that the CBO will somehow figure it out. She doesn't mention that the CBO now calculates a measure, potential GDP, which does not reveal perpetual slack. And she later excoriates the CBO for its deficit hawkishness. Really her answer is: Don’t worry about it. She simply asserts that “there is always slack in the form of unemployed resources, including labor.” We’re not talking about a little slack either. Ms. Kelton’s “people’s economy” starts with the full Green New Deal and moves on to a federal job for anyone, free health care, free child care, the immediate cancelation of student debt, free college, “affordable housing for all our people,” national high-speed rail, “expanded Social Security,” “a more robust public retirement system,” “middle-class tax cuts,” and more. How much does this add up to?$20 trillion? $50 trillion? She offers no numbers. How is it vaguely plausible that the U.S. has this much productive capacity lying around going to waste? In a book about money, the inflation of the 1970s and its defeat are astonishingly absent. History starts with Franklin Roosevelt—a hero for enacting the New Deal but a villain for paying for it with payroll taxes rather than fresh dollars. Ms. Kelton praises John F. Kennedy, too. He “pressured unions and private industry, urging them to keep wage and price increases to a minimum to avoid driving inflation higher. It worked. The economy grew, unemployment fell sharply and inflation remained below 1.5 percent for the first half of the decade.” The second half of that decade—Lyndon Johnson’s Great Society and Vietnam War spending, inflation’s breakout, Richard Nixon’s [1971] disastrous price controls—is AWOL. Did we not try MMT once and see the inflation? Did not every committee of worthies always see slack in the economy? Did not the 1970s see stagflation, refuting Ms. Kelton’s assertion that inflation comes only when there is no “slack”? Don’t look for answers in “The Deficit Myth.” Victory over inflation under Ronald Reagan and Margaret Thatcher goes likewise unmentioned. History starts up again when Ms. Kelton excoriates Thatcher for saying that government spending has to be paid for with taxes. She insinuates, outrageously, that Thatcher deliberately lied on this point in order to “discourage the British people from demanding more from their government.” If spending can be financed by printing money, “why not eliminate taxes altogether?” Ms. Kelton begins consistently. She criticizes Sens. Bernie Sanders and Elizabeth Warren for claiming that they need to raise taxes to pay for spending programs. But then why raise taxes? Taxes exist to decapitate the wealthy, not to fund spending or transfers: “We should tax billionaires to rebalance the distribution of wealth and income and to protect the health of our democracy.” She offers a second answer, more subtle, and revealingly wrong. She starts well: “Taxes are there to create a demand for government currency.” This is a deep truth, which goes back to Adam Smith. Soaking up extra money with fiscal surpluses [higher taxes or less spending] is, in fact, the ultimate control over inflation. But then arithmetic fails her. To avoid inflation, all the new money must eventually be soaked up in taxes. The new spending, then, is ultimately paid for with those taxes. What about the debt? Ms. Kelton asserts the government can wipe it out. Again, she starts correctly: The Fed could purchase all of the debt in return for newly created reserves. She continues correctly: The Fed could stop paying interest on reserves. But in conventional thinking, these steps would result in a swift inflation that is equivalent to default. Ms. Kelton asserts instead that these steps “would tend to push prices lower, not higher.” She reasons that not paying interest would reduce bondholders’ income and hence their spending. The mistake is easy to spot: People value government debt and reserves as an asset, in a portfolio. If the government stops paying interest, people try to dump the debt in favor of assets that pay a return and to buy goods and services, driving up prices. What about all the countries that have suffered inflation, devaluation and debt crises even though they print their own currencies? To Ms. Kelton, developing nations suffer a “deficit” of “monetary sovereignty” because they “rely on imports to meet vital social needs,” which requires foreign currency. Why not earn that currency by exporting other goods and services? “Export-led growth . . . rarely succeeds.” China? Japan? Taiwan? South Korea? Her goal posts for “success” must lie far down field. The problem is that “the rest of the world refuses to accept the currencies of developing countries in payment for crucial imports.” Darn right we do. Her solution: more printed money from Uncle Sam—a “global job guarantee.” She also advises small and poor countries to cut themselves off from international commerce. They should develop “efficient hydroponic and aquaponics food production” and install “solar and wind farms” rather than import cheap food and oil. They should refuse international investment, with the “classical form of capital controls” under Bretton Woods as an ideal. “We share only one planet,” she writes, yet apparently that planet must have hard national borders. By weight, however, most of the book is not about monetary theory. It’s rather a recitation of every perceived problem in America: the “good jobs deficit,” the “savings deficit,” the “health-care deficit,” the “infrastructure deficit,” the “democracy deficit” and—of course —the “climate deficit.” None of this is original or relevant. The desire to spend is not evidence of its feasibility. Much of “The Deficit Myth” is a memoir of Ms. Kelton’s conversion to MMT beliefs and of her time in the hallways of power. She criticizes Democrats, including President Obama and his all-star economic team, for their thick skulls or their timidity to state her truth in public. Republicans, such as former House Speaker Paul Ryan, are just motivated by dark desires to keep the people down and enrich big corporations and wealthy fat cats. President Trump’s tax cuts are a “crime.” How insightful. In a revealing moment, Ms. Kelton admits that “MMT can be used to defend policies that are traditionally more liberal . . . or more conservative (e.g., military spending or corporate tax cuts).” Well, if so, why fill a book on monetary theory with far-left wish lists? Why insult and annoy any reader to the right of Bernie Sanders’s left pinkie? Writing the book to “defend” an immense left-wing spending agenda destroys her argument. If you could only feel her singular empathy for the downtrodden, if you could, as she does, view the federal budget as a “moral document,” if you could just close your eyes and need it to be true as much as she does, your “Copernican moment” will arrive, and logic and evidence will no longer trouble you. That effect is compounded by her refusal to abide by the conventional norms of economic and public-policy discourse. She cites no articles in major peer-reviewed journals, monographs with explicit models and evidence, or any of the other trappings of economic discourse. The rest of us read and compare ideas. Ms. Kelton does not grapple with the vast and deep economic thinking since the 1940s on money, inflation, debts, stimulus and slack measurement. Each item on Ms. Kelton’s well-worn spending wish list has raised many obvious objections. She mentions none. Skeptics have called it “magical monetary theory.” They’re right. **** Update. To "jabmorris" and "rob." How could you possibly know if I have or have not read the book? As a matter of fact, I read every word of it. You offer a false accusation of impropriety, that you could not possibly know anything about, instead of a shred of fact or logic. This seems about par for the course in MMT land. Wednesday, July 1, 2020 New "Fiscal theory of the price level" draft. I posted a new draft of The fiscal theory of the price level, a slowly emerging book manuscript. It's heavily revised through Chapter 6. Chapter 5 has a much better treatment of sticky price models. The mechanics of writing new-Keynesian + fiscal theory models are really easy. Invitation: there is a great paper-writing recipe in here! Chapter 6 includes empirical work, also ripe for extension. Both chapters summarize recent papers A fiscal theory of monetary policy with partially repaid long term debt and The fiscal roots of inflation. I've clarified and emphasized a point that's been floating around but not clearly enough: governments who borrow (deficits) do convince markets that they will subsequently repay debts (surpluses) at least in part. The surplus process has an s-shape, not an AR(1) shape. If governments do not do so, then they cannot raise revenue from bond sales, and they cannot finance deficits by selling debt. The evident fact that they do both is some of the strongest evidence for an s-shaped surplus process. Much fiscal theory analysis, apparent rejections, and puzzles come down to ruling out this (with hindsight) simple fact, and also forgetting some lessons of 1980s time-series econometrics. The book draft is up to solicit comments, which I welcome, best by private email. The links take you to a new website. I discourage browsing around for the moment as it is heavily under construction. I can't access my Booth website anymore, so a new one is coming but slowly. Update: LAL, yes, thanks. (I can't seem to post comments on my own blog, so I have to answer here.) Tuesday, June 30, 2020 Rethinking production under uncertainty Even at my age, I get a little tingle when a paper is finally published. "Rethinking production under uncertainty" is now out at RAPS (free access for a while) and on my website. The basic idea is simple. Our standard way of writing production technologies under uncertainty tacks a shock on to an intertemporal technology. We might write $y(s) = \varepsilon (s) f(k)$ where $$k$$ is capital invested at time 0, $$s$$ indexes the state of nature (rain or shine) $$y(s)$$ is output in state $$s$$. That production technology does not allow producers to transform output across states at time 1. No matter high the contingent claim pricer for rain vs. shine, the producer can't make more in the rain state at the expense of making less in the shine state. This is the production set of a farmer, say, with initial wheat that can be eaten providing $$y(0)$$ or planted to give $$\{y(h), y(l)\}$$ in states $$h, l$$. As a result, marginal rates of transformation are not defined, and you can't write a true production-based asset pricing model, based on marginal rate of transformation = contingent claim price ratio. So, why don't we write down technologies that do allow producers to transform output across states as well as dates? Our farmer could plant wheat in a field that does better in rainy weather than shiny weather, for example. (You can feel an aggregation theory coming.) The result is a smooth production technology, Monday, June 29, 2020 Interview and Goodfellows I did an interview on Covid-19 and economics last week with Carlos Carvalho who runs the Salem Center for Policy at the McCombs School of Business, UT Austin. Carlos is doing a series of these interviews. I objected that anything on this subject will be out of date in 5 minutes, but Carlos wants to look at broader issues, and also see how well the interviewee's prognostication bears out. We'll see about that. So far, I would score that I underestimated just how much Americans were itching to go to bars and party. (Really, fellow citizens, pub crawling? Are you out of your minds?) Niall, H.R. and I also did a Goodfellows interview with Hoover's own Condoleezza Rice. This was a really interesting conversation on Russia, China, the place of the US in the world, and inevitably Condi's thoughtful views on race in the US. All Goodfellows here Podcast version: Monday, June 15, 2020 The cancel culture twitter mob comes to economics Last week we learned the twitter mob has taken over economics too. In case you aren't following, here is the short version of the story. Harald Uhlig, a distingushed macroeconomist at the University of Chicago, sent out a few tweets questioning the wisdom of quickly "defunding the police." The twitter mob, led by Paul Krugman and Justin Wolfers, swiftly attacked. A petition circulated, reportedly gaining 500 signatories, demanding his removal as editor of the Journal of Political Economy. I saw an astonishing number of tweets from economists that I formerly respected and considered to be level headed, fact-and-logic, cause-and-effect analysts of public policies pile on. The media piled on, with coverage at New York TimesWall Street Journal Chicago Tribune and a bit of a counterpoint at Fox NewsBreitbart National Review and others. By Friday, the University of Chicago caved in and threw Harald under the bus. Start by actually reading Harald's tweets. Friday, June 12, 2020 Grumpy podcast: MMT, debt, and perpetuities A podcast on this week's topics, MMT and debt. Monday, June 8, 2020 Perpetuities, debt crises, and inflation My brief exchange with Markus Brunnermeier at the end of a Covid-19 talk attracted some attention, and merits a more detailed intervention. Gavin Davies at FT made some comments (more later) as did the Economist. My proposal to fund the US with perpetuities comes from a paper, here. (Sorry regular readers for the repeated plug.) The rest is standard fiscal theory of the price level, spread over too many papers to give one more plug. There are three main points. First, inflation is not about money anymore -- the choice of money vs. bonds. Money -- reserves -- pay interest, so reserves are just very short-term government bonds. Inflation is about the the overall demand for government debt. That demand comes from the likelihood of the debt being repaid, and the rate of return people require to hold debt. Second, if we have inflation, the mechanism will be very much like a run or debt crisis. Our government rolls over very short term debt. Roughly every two years on average, the government must find new lenders to pay off the old lenders. If new lenders sniff trouble they refuse to roll over the debt and we're suddenly in big trouble. This is what happened to Greece. It's what happened to Lehman Bros. In our case, our government can redeem debt with non-interest-paying reserves, resulting in a large inflation rather than an explicit default. 2a, a run is always unpredictable. If you knew there would be a roll-over crisis next year, you would dump your government bonds this year, and the run would be on. There is a whiff of multiple equilibrium too. Our debt is nicely sustainable at 1% interest. If interest rates go up to 5%, we suddenly have north of$1 trillion additional deficits, which are not sustainable. The government  is like a family who, buying a home, got the 0.1% adjustable rate mortgage rather than the 1% (government debt prices) fixed rate mortgage because it seemed cheaper. Then rates go up. A lot.

Sure demand is high for US government debt, rates are low, and there is no inflation. But don't count on trends to continue just because they are trends. How long does high demand last? Ask Greece. Ask an airline.

Third, for this reason, I argue the US should quickly move its debt to extremely long maturities. The best are perpetuities -- bonds that pay a fixed coupon forever, and have no principal payment. When the day of surpluses arrives, the government repurchases them at market prices. By replacing 300 ore more separate government bonds with three (fixed rate, floating rate, and indexed perpetuities), treasury markets would be much more liquid. Perpetuities never need to be rolled over. As you can imagine the big dealer banks hate the idea, and then wander off to reasons that make MMT sound like bells of clarity. That they would lose the opportunity to earn the bid/ask spread off the entire stock of US treasury debt as it is rolled over might just contribute.

But we don't have to wait for perpetuities. 30 year bonds would be a good start. 50 year bonds better. The treasury could tomorrow swap floating for fixed payments.

Then we would be like the family that got the 30 year fixed mortgage. Rates go up? We don't care. By funding long, the US could eliminate the possibility of a debt crisis, a rollover crisis, a sharp inflation for a generation.

Friday, June 5, 2020

Magical Monetary Theory

I read Stephanie Kelton's book, The Deficit Myth: Modern Monetary Theory and the Birth of the People’s Economy,” and wrote this review for the Wall Street Journal. As usual I have to wait 30 days to post the whole thing here.

I approached this task with an open mind. What I had heard of MMT has some overlap with fiscal theory of the price level, on which I work, and I hoped to see some commonality.

I was disappointed. Short version:
"Ms. Kelton...starts with a few correct observations. But when the implications don’t lead to her desired conclusions, her logic, facts and language turn into pretzels."
Full version in 30 days, if you can't find a way around WSJ paywall.

Friday, May 29, 2020

Podcast and Goodfellows

Here are links to this week's grumpy economist podcast, and Goodfellows discussion with Niall Ferguson and H.R.  McMaster. Grumpy on the careful reopening and debt. Goodfellows on Europe.

Carnivorous Moose (?)

Thursday, May 28, 2020

Unemployment insurance weaning

As the economy recovers, public policy faces an inevitable dilemma. How do we wean the economy from support?

This comes to the head with federal support for unemployment insurance -- $600 per week, set to expire at the end of July. The unemployment rate will still be high in July. Congress seems to have largely given up, in public, of thinking clearly about the economic purpose of policies, and now the discussion is entirely in terms of who deserves additional "help," often in moral terms -- "people" vs "corporations," various regions, sizes of business, "communities," and so on. How can we reduce "help" while unemployment surely ravages the land? On the other hand, for many workers right now, unemployment benefits pay more than working. Unemployment pays more than going back to their old job as it opens, and it pays more than taking one of the many new jobs that are available now -- Amazon, Wal-Mart are hiring, and there is surely going to be demand for contact tracers, temperature takers, building disinfecters, social distance monitors, and so on. So, the age old question of economic policy emerges. How do we balance help -- insurance -- with incentives -- the need to get people back to work ASAP when jobs are available? Lost in the policy discussion, let us not forget the hard fact of life. Work is not fun. People in the real world (not economics bloggers!) don't work because it's fulfilling or enjoyable. They work because they need the money and the health insurance. Work is a necessary evil for our economy to produce the things we all need and want to consume. People don't take lower paying jobs willingly, no matter how much society needs you, right now, to stop binging Netflix and go spend 8 hours wiping down carts at the local Safeway. With that, here are some clever ideas. 1) Pay anyway. If you take a job, you can keep the unemployment benefit, at least for a period of time. Or, better, you can get a nice cash check,$1200 (two weeks of federal, another stimulus check) or even $2400 (a month). In return, you can't get unemployment again for, say, 4 or 6 months. 2) Community service. If you stay on unemployment past July 31, you have to do (say) 20 hours a week of community service. What will they do? Well, I've been reading Stephanie Kelton's book (review coming), and she has a proposal for a federal jobs program. Apparently, she thinks there was an immense amount of good work that governments and communities needed done before the pandemic, WPA style. There is much more now -- trace contacts, disinfect playgrounds, take temperatures in public buildings, you name it. Workers could be rented out to monitor temperatures in front of struggling businesses. So, put Kelton and company -- Bernie Sanders, AOC -- in charge of the community service part. I offer this latter suggestion only half-jokingly. Obviously there is a political divide on what to do about unemployment. If the government is already paying people, there isn't much damage to letting the left try out its jobs program. If like me you're a little cynical about government jobs programs, well, we'll find out, and we'll save money to boot as the prospect of working for local government might just scare a lot of people back to work. And I love an offer they can't refuse. Imagine the Trump Administration calling the left's bluff on this one -- how can they say no? (A response to a commenter: It doesn't matter for this purpose if there is any value to the work. I'm looking for a disincentive to stay on unemployment when there are jobs available, that will be politically palatable.) 3) Jobs board. Sweden has (had?) an interesting system that combined a carrot with a stick. Generous unemployment, but a national job registry and you had to take a job offer. I doubt the bureaucratic competence of the US, especially in the month or so we have to get it going, but something similar could happen. To get Federal unemployment top-up after July 31, you have to fill out a one page form with work experience that reads like a job application. Employers can search and offer you a job. If you get the job offer, you take it or lose unemployment. 4) Just who? Obviously it's time to restrict just a little bit who gets generous unemployment. If your old company is still in business and wants to hire you back, the gig is up. If it's hiring at all, even lesser job categories, you have to apply. If there are more than X job vacancies in your county, the extra unemployment insurance dries up. A currently popular idea is temporarily cutting or eliminating payroll taxes. This is a nice inducement to work, but even I am a little behavioralist and I wonder just how many people who earn$20 an hour are really clear on how much extra they will get by returning to their old jobs if there is a payroll tax reduction. My 2400 check seems like a more salient incentive. Airlines and information Airlines are in big trouble. Even after reopening, nobody wants to fly, perceiving them as dangerous. But are airline flights dangerous? As I read the super-spreading literature, I have not seen a single case of an airline flight charged with spreading the virus. (Please chime in if you have seen any documented cases of virus spread on airline flights.) That's remarkable. From January to March, people were flying all over the world. People were flying from Wuhan to all over the world. But while we have seen super spreading events in restaurants, bars, cruise ships, aircraft carriers, nursing homes, jails, beach parties, Mardi Gras, choir practice, and more, I have not seen one from an airline flight. Even though people are cooped up for hours in close quarters. One can speculate why. Airliners actually have very good ventilation systems and hospital grade HEPA filters. Except for the occasional chatty seat mate with cat videos to show, people are usually completely silent. Talking loudly seems to be a big part of spreading the virus. An airline with reasonable extra precautions, such as taking temperatures, certifying no symptoms (and you get your money back if you say you have symptoms, please), masks, wipe downs, is likely safer still. The worry may be for nothing. But how will we know? Now I get to the point. In the tens, and probably eventually hundred or more billion dollars our government is spending to prop up airlines, how about 1 billion for research on the question, is an airline flight safe? For a billion dollars we ought to be able to answer this question definitively in about a week. Actually 10 million -- 1/1,000 of the money our government will shovel out to boost airlines -- ought to do the trick. If I'm right, that would do more good than an MMTers dream of stimulus. Tuesday, May 26, 2020 Jones and Fernández-Villaverde update Chad Jones and Jesús Fernández-Villaverde have updated their SIR model with social distancing. A part I find very intriguing is that they impute the infection rate and the reproduction rate from death rate data. The infection rate $$I_t$$ is given by $I_t = \frac{1}{\delta \gamma} \left( \frac{d_{t+2}-d_{t+1}}{\theta} - d_{t+1} \right)$ where the greek letters are parameters they estimate by fitting the path of deaths over time, and $$d_t$$ is the daily death rate. Though deaths only happen a few weeks after infection, you can reverse the model dynamics to figure out how many are infected today from how many are dying today. (Well, tomorrow and the day after). They similarly infer today's reproduction rate $$R_0$$ from the next three days death rates. Now, there is clearly some inaccuracy here, and I've been pestering them to provide standard errors. There is some noise in daily deaths and once you start double and triple differencing them, the noise is larger. But as I think about behavioral and policy responses, these are the numbers we need. How many people in this state, city, zip code, grocery store, bar, are infectious right now? 1 in 10? 1 in 100? 1 in 1000? 1 in 10,000? Is the virus spreading or slowly decaying, with reproduction rate below one? Just how careful do we need to be? Is wiping down, surfaces or spraying luggage with disinfectant remotely cost-effective? Where are hot spots? Good Fellows -- International Man of History A new lively Good Fellows discussion video and podcast Direct links here if the above embed codes don't work. Get Ready for the Careful Economy  Source: Wall Street Journal Ready or not—mostly not—the reopening is at hand. The economic carnage of a continued lockdown is simply too great to sustain. But the virus is still with us, so the carefully reopened economy will be less efficient than the pre-pandemic economy..... A Wall Street Journal Oped on where we are and peering in to the muck. Much is inspired by my "dumb reopening" blog post of a week or so ago. I must say my faith in human wisdom is a bit shaken by the videos of massive crowds on Memorial Day. Spring break and Mardi Gras were super-spreader events, and being outdoors is good but not perfect. On the other hand, in many parts of the country maybe 1/1000 people are infected at most. And the media has been known on occasion to pick one or two sensational stories and let them stand in. The oped is cut to the bone, as there things are. I did not emphasize enough that isolating the vulnerable and making sure they don't get it -- testing anyone who wants to walk in to a nursing home -- is a much more effective tool than a blanket business lockdown. This disease is very concentrated Also I wanted to hammer home that parties are dangerous, business per se is not. Locking down all business will likely be seen as a huge waste. We will see if Americans are able to refrain from partying. Indeed I worry that by focusing attention on business closings as the main policy tool, people get the idea that business is dangerous, staying at home is not. Let's party. One worry on regulation is that it will provide a recipe for a wave of lawsuits. That may have been a reason the Administration tried to hold back CDC guidance. A long, expensive, and impractical list of things you must do to reopen is catnip when someone gets sick and wants to blame a business. Show us the records that you wiped down the bathrooms every half hour. A legal system that can sue over talcum powder is not above this. Saturday, May 23, 2020 School of sustainability In a few recent posts, I was critical of university endowment practices. Why build up a stock of investment, rather than invest in faculty, research, or other core activities? Why wall that pile of assets from being spent, especially when budgets are cratering in a pandemic? When we see businesses with piles of cash, we infer they don't have any good investment projects, and the piles are ripe for diversion to bad ideas. But universities are non-profits, and one major piece of being a non-profit is that the business is protected from the market for corporate control. If you see a business wasting money on bad investments, buy up the stock, fire management, and run it right. Repurchases were part of an earlier reform effort, to stop management from wasting money on aggrandizing projects. Perhaps restrictions on endowment spending serve a somewhat parallel function for universities. Perhaps I was wrong to criticize so harshly. These thoughts are brought to mind by Stanford's announcement of a new school "focused on climate and sustainability." A "school" is bigger than a center, an institute, a department, a division. Stanford has seven "schools," Business, Education, Engineering, Humanities & Sciences, Law, Medicine, and, yes, Earth, Energy & Environmental Sciences. Why a new school? It will "amplify our contributions in education, research and impact further by aligning people and resources more effectively. Says university President Tessier-Lavigne. Vice Provost Kathryn Moller will "lead an inclusive process designing the school’s structure....consult with key internal and external stakeholders to develop a school organization that amplifies faculty and student contributions to address the most urgent climate and sustainability challenges." creating an "impact-focused community, with new opportunities to enhance the impact of their work on the issues they deeply care about,” "Impact" and "amplify" repeat quite a few times. Tuesday, May 19, 2020 Reopening the economy, and aftermath, now on Youtube My Bendheim Center talk and discussion with Markus Brunnermeier on all things Covid-19 and economics is now on YouTube, direct link here. I start at 14:08. If you like the paintings behind me and you're getting bored, more info here. (Shameless nepotism disclaimer.) Monday, May 18, 2020 Endowment humor Steven Wood writes a wonderful letter from a university president, responding to suggestions that a university dip in to its endowment, As president of this University, there is nothing more important to me than the health and safety of our community. Though I’m currently away from campus, summering on my private island off of Maine, my thoughts are almost always with you, and my secretary is literally always available to field your questions and hear your concerns. ...a number of you have reached out to provide us with valuable feedback regarding our recently announced budget adjustments. Specifically, many of you have asked why an institution with a46 billion endowment is freezing salaries, rescinding job offers, refusing to adjust tenure tracks, and laying off staff instead of using an endowment the size of Iceland’s GDP to keep our community afloat.
Let me say this: We hear you. You are valid. You. Matter. Secondly, and no less importantly, let me make something clear: The. Endowment. Is. Not. For. You.
...the first rule of the endowment was “Never talk about the endowment.” At the end of every quarter, they blindfold me, take me to an undisclosed location which I suspect is the Chairman of the Board’s rumpus room, show me the quarterly returns, rough me up a little, then blindfold me again, and dump me on the lawn of my University-owned home. This is as close as I’ve ever gotten to the endowment, so good luck getting anywhere near that money.
Oh, I give up, just go read the whole (short) thing and have a nice chuckle.

Thanks to a colleague for the pointer.

Schmitz on monopoly

Jim Schmitz has released the first salvo in what promises to be a monumental work on monopoly, titled Monopolies Inflict Great Harm on Low- and Middle-Income Americans. (I love titles with answers and no colons.)
Today, monopolies inflict great harm on low- and middle-income Americans. One particularly pernicious way they harm them is by sabotaging low-cost products that are substitutes for the monopoly products. I'll argue that the U.S. housing crisis, legal crisis, and oral health crisis facing the low- and middle-income Americans are, in large part, the result of monopolies destroying low-cost alternatives in these industries that the poor would purchase.
He promises more to come
Legal Services, Residential Construction, Hearing Aids, Eyecare and ...Repair, Pharmaceutals, Credit Cards, Public Education...
There is a huge one right there.

To Jim the main characteristics of monopoly are
A. Monopolies sabotage and destroy markets. They typically destroy substitutes for their products, those that would be purchased by low-income Americans.
B. Monopolies also use their weapons to manipulate and sabotage public institutions for their own gains...

Reopening the economy -- and the aftermath

I'm doing a Zoom talk at the Bendheim Center, Princeton, with Markus Brunnermeier, 12:30 Eastern today (Monday May 18) on this, tune in if you're interested. It's mostly based on recent blogs and opeds. Sign up here. I'll post a link to the video when it's over.

Thursday, May 14, 2020

Strategies for Monetary Policy

Strategies for Monetary Policy is a new book from the Hoover Press based on the conference by that name John Taylor and I ran last May. (John Taylor gets most of the credit.) This year's conference is sadly postponed due to Covid-19. We'll have lots to talk about May 2021.

At that link, you can see the table of contents and read Chapter pdfs for free. You can buy the book for \$14.95 or get a free ebook.

The conference program and videos are still up.

Much of the conference was about the question, what will the Fed do during the next downturn? Here we are, and I think it is a valuable snapshot. Of course I have some self interest in that view.

As long as I'm shamelessly promoting, I'll put in another plug for my related Homer Jones Lecture at the St. Louis Fed, video here and the article Strategic Review and Beyond: Rethinking Monetary Policy and Independence here. That was written and delivered in early March, about 5 minutes before the lookouts said "Iceberg ahead." John and I don't put a lot of our own work into the conference books, but it sparked a lot of thoughts.  I am grateful to Jim Bullard and the St. Louis Fed for the chance to put those together.

Monetary policy is back to "forget about moral hazard, rules, strategies and the rest, the world is ending." This is a philosophy that happens quite regularly and now has become the rule and strategy. So strategic thinking about monetary policy is more important than ever.  This is a philosophy very much due to John Taylor.

The last part of my Homer Jones paper delves into just what risks the big thinkers of central banking were worried about on the eve of the pandemic. Pandemic was not in any stress test.  BIS, BoE, FSB and IMF  wanted everyone to start stress testing ... climate change and inequality. This is a story that needs more telling.

Monday, May 11, 2020

Comment apology

To my commenters: I hit the wrong button this morning while cleaning up the huge amount of spam that comes in the comments, and many good comments got deleted. I appreciate your thoughts and I apologize for inadvertently deleting them.

Thursday, May 7, 2020

Markets work even in crisis

A lovely result of the corona virus outbreak has been how we see stifling aspects of regulations. Right left and center are figuring out that the regulations need reform. Now, the forces for regulatory stagnation are always strong, so the insight may fade with the virus. Still, let us enjoy it while it lasts.

The trouble with regulations is that, unlike "stimulus," the action is all in minute detail not grand sweeping plan.

John Goodman writes in Forbes
The Americans for Tax Reform calculates that 397 regulations have been waived in order to fight COVID-19. That count is probably way too low. The federal Food and Drug Administration (FDA) has eliminated so many restrictions it would be hard to count them all. ...
Consider that, up until a few months ago:
·     The only tests for the coronavirus that were approved for use in the United States were produced by the Centers for Disease Control (CDC) and half of those tests turned out to be defective.
·     It was illegal to produce, sell and distribute ventilators, respirators, and other  medical equipment without complicated and burdensome government regulatory permission.

Covid and economics publishing

The pandemic is dramatically illustrating one area in which the epidemiologists are beating the economists about 100-1: publishing. Scientific publications are reviewed and posted in days, contributing in real time to the policy debate.

Economists are writing papers in a similar flurry. They are writing really good, thoughtful, well done papers that are useful to the policy debate. See the NBER website for example, or SSRN. See my last post and previous one for several great examples.

But when will these papers be peer reviewed? Where will they be published?

Monday, May 4, 2020

An SIR model with behavior

Following my last post, the SIR model has been completely and totally wrong. Answers follow from assumptions. It assumes a constant reproduction rate, and the virus peters out when sick people run in to recovered and immune people. That's not what's happening -- people responded by lowering the contact rate, long before we ran in to herd immunity.

I speculated last time about a model in which people respond to the severity of the disease by reducing contacts. Let's do it. (Warning: this post uses MathJax to show equations. It may not work on all devices.)

I modify the SIR model as presented by Chad Jones and JesúsFernández-Villaverde: \begin{align*} \Delta S_{t+1} & =-\beta S_{t}I_{t}/N\\ \Delta I_{t+1} & =\beta S_{t}I_{t}/N-\gamma I_{t}\\ \Delta R_{t+1} & =\gamma I_{t}-\theta R_{t}\\ \Delta D_{t+1} & =\delta\theta R_{t}\\ \Delta C_{t+1} & =(1-\delta)\theta R_{t}% \end{align*} S = susceptible, I = infected (and infectious), R resolving, i.e. sick but not infectious, D = dead, C = recovered and immune, N = population. The lags give the model momentum. Lowering the reproduction rate does not immediately stop the disease. The model uses exponential decays rather than fixed lags to capture timing. $$\beta$$ is the number of contacts per day. A susceptible person meets $$\beta$$ people per day. $$I/N$$ of them are infected, so $$\beta S_{t}I_{t}/N$$ become infected each day. We parameterize $$\beta$$ in terms of the reproduction rate $$R_{0}$$, $R_{0}=\beta/\gamma$ The number of infections from one sick person = number of contacts per day times the number of days contacts are infectious (on average).

The standard SIR model uses a constant $$\beta$$ and hence a constant $$R_{0}$$. The disease grows exponentially, then becomes limited by the declining number of susceptible people in the population. Each infected person runs in to recovered people, not susceptible people. The whole point is, that did not happen. We lowered $$\beta$$ instead.

I model the evolution of $$\beta$$ behaviorally. First, suppose people reduce their contacts in proportion to the chance of getting the disease. As people see more infectious people around, the danger of getting infected rises. They reduce their contacts proportionally to the number of infectious people. $\log(\beta_{t})=\log\beta_{0}-\alpha_I I_{t}/N_{t}.$ This function could also model a policy response.

However, due to the lack of testing we don't really know how many people are infectious at any time. So as a second model, suppose instead people or policy reduce contacts according to the current death rate, $\log(\beta_{t})=\log\beta_{0}-\alpha_D \Delta D_{t}/N.$ $$\beta$$ is a rate, how many people do you bump in to per day. I use the log because it can't be negative. The log also captures the idea that early declines in $$\beta$$ are easy, by eliminating superspreading activities. Later declines in $$\beta$$ are more costly.

I use Chad and Jesús  numbers, $$\gamma=0.2$$ or 5 days of infectiousness on average, $$\theta=0.1$$ implying 10 more days on average with the disease before it resolves, $$\delta=0.08$$ $$(0.8\%)$$ death rate. They parameterize and estimate $$\beta$$ $$\$$via $$R_{0}=\beta/\gamma$$. I take the original $$R_{0}% =5$$, which is typical of their estimates, and implies $$\beta_{0}=\gamma R_{0}=1$$. They estimate $$R_{0}^{\ast}=0.5$$ so $$\beta^{\ast}=0.1$$, which I will use to calibrate $$\alpha$$. New York peaked at 90 deaths per million, but we will see the dynamics overshoot. So I'll pick $$\alpha$$ in that case so that $$\beta=\beta^{\ast}$$ at 50 daily deaths per milllion triggers $$R_{0}% =0.5$$, i.e. $$\alpha_D$$ solves $\log\left( 0.1\right) =\log\left( 1\right) -\alpha_D\times50/10^{6}.$ The death rate is about 1%, so I calibrate the infection model so that $$R_{0}=R_{0}^{\ast}=0.5$$ at an infection rate of 5000 per million or 0.5%. $$\alpha_I$$ solves $\log(0.1)=\log\left( 1\right) -\alpha_I \times 5000 / 10^{6}.$

Here is my assumed reproduction rate as a function of deaths per million. The red dot is the calibration point: at 50 deaths per day, people and policy will drive the reproduction rate to 0.5. The red dashed line is a much more aggressive response, which I'll investigate later.

The standard SIR model

As background, here is a simulation of the standard SIR model with these numbers, and a constant $$\beta=1$$ meaning $$R_0=5$$.

I start at day 1 with a single infected person. The virus grows exponentially. The number infected peaks at about half the population. Around day 25 however, herd immunity starts to kick in. The number infected peaks. Sick people (resolving) peaks a bit later. The pandemic goes away almost as quickly as it came and it's over after two months. With $$R_0=5$$ everyone gets it and 0.8% or 8000 people die.

This is  the nightmare scenario presented to policy makers in February and caused the economic shutdowns. It is completely wrong -- it's not what happened anywhere.

The behavioral SIR model

Here is the simulation of the behavioral SIR model, in which people (or policy) reacts by lowering the contact rate in response to the number infected.

The vertical scale is different. Only about 4000 people get infected here, not 1 million! The pandemic gets going with the same exponential speed (blue line), but now once infections get up to  1000 per million we see the sharp reduction in the reproduction rate (dashed black line).

This is a lot more like what we saw! A rapid rise, to a plateau, with a much more sensible set of numbers. That's the good news. The bad news is that it goes on and on and on. The minute infections decline people slack off just enough to get it going again. Responding to infections, even though there is a lag, produces very stable dynamics.

The reproduction rate asymptotes to $$R_0=1$$.  This is both the good news and the bad news outlined in my last post. It doesn't get worse with second waves. But it doesn't get better either.

That result not at all related to the calibration. The reproduction rate always asymptotes to one in this model, with a steady number of infections and a steady number of deaths per day, until finally after years and years we get herd immunity and all efforts to reduce contacts are turned off.

Here is the same simulation with the much stronger response, $$alpha$$ is raised by a factor of 5 to the red dashed line in my first graph. No, it's not the same graph. Notice the vertical scale. This response is much less tolerant of infections, so the overall rate of infection is much lower. But the path is exactly the same.

Being more forceful does not change the reproduction rate, which still asymptotes to one. We just trundle along with much lower infections and daily death rates.

This comparison makes nice sense of what we see, per the last post. Far different regimes give rise to essentially the same dynamics, but some at much higher and some at much lower levels.

Technology offers some hope. What happens if the costs of reducing $$\beta$$ become lower over time, so people can slowly become more careful while also letting the economy grow? Widespread individual testing and tracing, for example, are ways of distancing that are less costly. In this case, we steadily move from the second to last graph to the last graph. To model that, I let $$\alpha$$ vary over time, growing by a factor of 2 from time 0 to time 100,

This accounts for a plateau with a slow tail. The actual reproduction rate still is close to one, but it's just enough below one to gently let the virus decay.

Deaths and information

A big objection: here I keyed behavior to the infection rate -- people are more careful the more infected people are around. But we don't see how many people are infected. We do see deaths.
Here is the simulation when people respond to the death rate rather than the infection rate

Since deaths lag infections by a few weeks, responding to the death rate leads to over controlling. The pandemic quickly gets out of control before deaths crank up, causing the crash in the reproduction rate. Then people really are careful, and the infection declines quickly. As deaths lower though, people ease up, and a second wave happens and so forth.

The positive feedback does eventually control the pandemic. Each wave is smaller. And this model also trends to $$R_0 = 1$$ by the same mechanism. It just takes a lot of wiggles to get there.

Information, rational exceptions, and externalitities

The contrast between the first and second graphs gives a quick policy suggestion: good information on how many people are infected in one's local area would be really helpful to avoid waves of infections.  If we had just enough random testing to know how many people are infected in our local area, people and  officials could follow the top graphs not the bottom graph. It is not expensive. In the model, one can back out the number of people infected from the increase in the number "resolving." The rate of hospital admissions might be a widely publicized number now available that could be a very good guess.

Widespread, available (no protocol, no prescription, just go get it, free market) testing would radically reduce the economic costs of social distancing, and end this fast. (The optimal $$\alpha$$ would rise by orders of magnitude. Yes, you point to externality, why should I test myself. But you ignore economic and social demands. If such testing is available, it's really easy for customers to demand you show your test. Paul Romer is right.

Of course now we get to the delicate question of public vs. private incentives. My first model seems like a reasonable guess of how people will behave -- take actions to be careful the greater my chance of getting sick is by going out.

We want, naturally, a dynamic model in which people's actions incorporate an understanding of the dynamics. In that vein, the latter graph seems unduly pessimistic. People are pretty smart and they know that the death rate is high when the danger of going out has passed. Thus, one may well expect them to foresee the dynamics, be careful when the death rate is increasing, and slack off when it is decreasing. More generally, in this deterministic model, you can back out what the state of all the variables is if you observe one of them. Thus, the rational expectations equilibrium of this model if people want to react to the number of infections is the first one, even if they can't  see infections. They can back infections out of the death data. That may be too much to hope for, but reality is likely in between.

Being careful has an externality, of course, so people following a private optimum of costly but careful behavior vs. getting sick is not necessarily the social optimum. Most economists jump quickly from this observation to calibrated time-varying lockdown policies to try to control $$\beta$$. But let us not forget the other side of that coin: The public policy tools are sledgehammers, which do a poor job of controlling interactions $$\beta$$ at reasonable economic cost. Really, what we have are at best exhortations to be careful in the details of daily life, plus extremely expensive business shutdowns. As a concrete example, in the model one may be tempted to advocate that officials lie about the number of infected to get people to be more careful than they would be privately. But once a lie is found out, nobody believes anything anymore, and the next step is China. I still think timely and accurate information is better.

To do list

Some more thought on functional form would be useful. Do we have any data or other ways of measuring how people behave?

Obviously a real economic model would derive these behavioral responses from a maximization problem, and consider the tradeoff between more distancing $$\beta$$ and economic costs.

Optimal policy may differ most from individual behavior in the dynamics. It is not worth it to an individual to be careful early when there are few sick people around, but policy considers the effect of you getting sick on everyone who gets it from you.  Optimal control of $$\beta$$ beckons. But to be realistic we must include the fact that public control of $$\beta$$ against private wishes will be much less efficient.

On the other papers: Chad and Jesús model social distancing, whether voluntary or by policy, via a deterministic and permanent exponential decay from a state of nature $$\beta_{0}$$ to a new lower value $$\beta^{\ast}$$ over a period $\beta_{t}=\beta_{0}e^{-\lambda t}+\beta^{\ast}(1-e^{-\lambda t}).$ The point here is to realize there is feedback, and both people and policy behavior respond to facts. Their paper fits the data so far beautifully. My goal is to think about what happens next. That $$\beta$$ just sits at $$beta^\ast$$ as it does in their model, seems unrealistic because people aren't going to keep distancing voluntarily or involuntarily.

Eichenbaum, Rebelo and Trabandt,  have an economic model of $$\beta$$. People work and shop less when they are more afraid of getting sick.  But  the tradeoff is not very attractive. Here is their model (solid) vs. the basic SIR model (dash)

In their model all people can do to avoid getting sick is to avoid work or consumption, both of which offer very little protection for great economic cost. So you still see the basic -- and false -- prediction of the SIR model. I think a good direction is to modify their model, calibrating it to data as Chad and Jesús do, which would imply an economically easier reduction in reproduction rate.

Update:

1) Equilibrium social distancing by Flavio Toxvaerd is a simple economic model with endogenous social distancing. It also produces plateaus when people choose to be safer

(Thanks to a tweet from Chryssi Giannitsarou @giannitsarou)

2) Economists vs. epidemiologists has a long history. Economists point out that disease transmission is not a biological constant, but varies with human behavior. And human behavior varies predictably in response to incentives (and information).  Many beautiful facts and stories on this point are collected in Tomas Phillipson and Richard Posner's book, Private Choices and Public Health: The AIDS Epidemic in an Economic Perspective. For example, AIDS patients in clinical trials would mix their medicines together. Half of the drug for sure is better than a 50 50 chance of nothing. Thanks to a correspondent for the reminder.

3) A Multi-Risk SIR Model with Optimally Targeted Lockdown by  Daron Acemoglu, Victor Chernozhukov Michael Whinston and Ivan Werning just came out. I haven't read it yet, but it is an obvious addition to the stack for people working on epidemiology models with economic incentives. It has diverse populations and transmission mechanisms, which have long struck me as a key insight. We are not all average, and that really matters here.

4) From the comments, a many-authored paper arguing that herd immunity may be much lower. Essentially the super spreaders are more likely to get the disease, so they are more likely to be immune first. "Super spreader" includes people in nursing homes, emergency room technicians, bus drivers, etc., not just jet setting partiers.

5) I missed Macroeconomic Dynamics and Reallocation in an Epidemic by  Dirk Krueger Harald Uhlig and  Taojun Xie
...we distinguish goods by their degree to which they can be consumed at home rather than in a social (and thus possibly contagious) context. We demonstrate that, within the model the “Swedish solution” of letting the epidemic play out without government intervention and allowing agents to shift their sectoral behavior on their own can lead to a substantial mitigation of the economic and human costs of the COVID-19 crisis, avoiding more than 80 of the decline in output and of number of deaths within one year, compared to a model in which sectors are assumed to be homogeneous. For different parameter configurations that capture the additional social distancing and hygiene activities individuals might engage in voluntarily, we show that infections may decline entirely on their own, simply due to the individually rational re-allocation of economic activity: the curve not only just flattens, it gets reversed.
6) A behavioral SIR model YouTube talk from Lones Smith

7) Systematic biases in disease forecasting – The role of behavior change  by Ceyhun Eksina Keith Paarpornb Joshua S. Weitzcde
...during real-world outbreaks, individuals may modify their behavior and take preventative steps to reduce infection risk. ... we evaluate this hypothesis by comparing the dynamics arising from a simple SIR epidemic model with those from a modified SIR model in which individuals reduce contacts as a function of the current or cumulative number of cases.
Thanks to Andy Atkeson for the tip. See his A note on the economic impact of coronavirus and Talk at NBER

8)...I'm sure more updates will follow.

Code

Here is the Matlab code for my plots

close all
clear all

gam = 0.2;
thet = 0.1;
delt = 0.008;
R0 = 5;
alphaD = (0 - log(0.1))*1E6/50;
alphaI = (0 - log(0.1))*1E4/50;

beta0 = R0*gam;
N = 1E6;

T = 100;

% plot beta

figure
drate = (0:100)'/1E6;
betat = exp(log(beta0) - alphaD*drate);
betat1 = exp(log(beta0) - 5*alphaD*drate);
plot(drate*1E6, betat/gam,'linewidth',2);
hold on
plot(drate*1E6, betat1/gam,'--','linewidth',2);
hold on
plot(50, 0.5, 'o','markerfacecolor','r')
legend('Original','\alpha multiplied by 5','location','best')
xlabel('Daily deaths/million');
ylabel('Reproduction rate R0 = \beta / \gamma')
axis([0 80 0 5]);
print -dpng betafig.png

% standard SIR model

S = zeros(T,1);
I = S;
R = S;
D = S;
C = S;

S(1) = N-1;
I(1) = 1;

for t = 1:T-1;

S(t+1) = S(t) -beta0*S(t)*I(t)/N;
I(t+1) = I(t) + beta0*S(t)*I(t)/N - gam*I(t);
R(t+1) = R(t) + gam*I(t)-thet*R(t);
D(t+1) = D(t) + delt*thet*R(t);
C(t+1) = C(t) + (1-delt)*thet*R(t);

end;

figure;
plot((1:T)',[S I R 100*D C]/1E6, 'linewidth',2);
xlabel('Days')
ylabel('Millions');
axis([10 70 0 1]);
title('SIR model, constant R0 = 5');
print -dpng std_sir.png

figure;
plot((2:T)',[ I(2:T) -(S(2:T)-S(1:T-1)) 100*(D(2:T)-D(1:T-1))]/1E6, 'linewidth',2);
legend('Infected','New Infections','100 x New Dead','location','best')
xlabel('Days')
ylabel('Millions');
axis([10 70 0 0.6]);
title('SIR model, constant R0 = 5');
print -dpng std_sir_diffs.png

disp('last s i r d');
disp([S(T) I(T) R(T) D(T)]);

% my model,  response to infections

S = zeros(T,1);
I = S;
R = S;
D = S;
C = S;
betat = S;

S(1) = N-1;
I(1) = 1;
I(1) = 1;

S1 = S;
I1 = I;
R1 = R;
D1 = D;
C1 = C;
betat1 = betat;

S2 = S;
I2 = I;
R2 = R;
D2 = D;
C2 = C;
betat2 = betat;

for t = 1:T-1;

betat(t) = exp(log(beta0) - alphaI*((I(t))/N));
S(t+1) = S(t) -betat(t)*S(t)*I(t)/N;
I(t+1) = I(t) + betat(t)*S(t)*I(t)/N - gam*I(t);
R(t+1) = R(t) + gam*I(t)-thet*R(t);
D(t+1) = D(t) + delt*thet*R(t);
C(t+1) = C(t) + (1-delt)*thet*R(t);

betat1(t) = exp(log(beta0) - 5*alphaI*((I1(t))/N));
S1(t+1) = S1(t) -betat1(t)*S1(t)*I1(t)/N;
I1(t+1) = I1(t) + betat1(t)*S1(t)*I1(t)/N - gam*I1(t);
R1(t+1) = R1(t) + gam*I1(t)-thet*R1(t);
D1(t+1) = D1(t) + delt*thet*R1(t);
C1(t+1) = C1(t) + (1-delt)*thet*R1(t);

betat2(t) = exp(log(beta0) - (1+1*t/T)*alphaI*((I2(t))/N));
S2(t+1) = S2(t) -betat2(t)*S2(t)*I2(t)/N;
I2(t+1) = I2(t) + betat2(t)*S2(t)*I2(t)/N - gam*I2(t);
R2(t+1) = R2(t) + gam*I2(t)-thet*R2(t);
D2(t+1) = D2(t) + delt*thet*R2(t);
C2(t+1) = C2(t) + (1-delt)*thet*R2(t);

end;

figure;
%yyaxis left
plot((2:T)',[ I(2:T) 100*(D(2:T)-D(1:T-1)) ],'linewidth',2)
xlabel('Days')
ylabel('People');
axis([0 70 0 inf]);

yyaxis right
plot((1:T)',betat/gam,'--k','linewidth',2);
ylabel('Reproduction rate R0','color','k')
axis([0 70 0 inf]);

legend('Infected','100 x Deaths/day','R0 (right scale)','location','best')

title('BSIR model, R0 varies with infection rate');
print -dpng std_sir_aI.png

figure;
%yyaxis left
plot((2:T)',[ I1(2:T) 100*(D1(2:T)-D1(1:T-1)) ],'linewidth',2)
xlabel('Days')
ylabel('People');
axis([0 70 0 inf]);

yyaxis right
plot((1:T)',betat1/gam,'--k','linewidth',2);
ylabel('Reproduction rate R0','color','k')
axis([0 70 0 inf]);

legend('Infected','100 x Deaths/day','R0 (right scale)','location','best')

title('BSIR model, R0 varies with infection rate, higher \alpha');
print -dpng std_sir_aI1.png

figure;
%yyaxis left
plot((2:T)',[ I2(2:T) 100*(D2(2:T)-D2(1:T-1)) ],'linewidth',2)
xlabel('Days')
ylabel('People');
axis([0 70 0 inf]);

yyaxis right
plot((1:T)',betat2/gam,'--k','linewidth',2);
ylabel('Reproduction rate R0','color','k')
axis([0 70 0 inf]);

legend('Infected','100 x Deaths/day','R0 (right scale)','location','best')

title('BSIR model, R0 varies with infection rate, \alpha increases over time');
print -dpng std_sir_aI2.png

% my model,  response to deaths

S = zeros(T,1);
I = S;
R = S;
D = S;
C = S;
betat = S;

S(1) = N-1;
I(1) = 1;
I(1) = 1;
betat(1) = beta0;

for t = 1:T-1;

S(t+1) = S(t) -betat(t)*S(t)*I(t)/N;
I(t+1) = I(t) + betat(t)*S(t)*I(t)/N - gam*I(t);
R(t+1) = R(t) + gam*I(t)-thet*R(t);
D(t+1) = D(t) + delt*thet*R(t);
C(t+1) = C(t) + (1-delt)*thet*R(t);
betat(t+1) = exp(log(beta0) - alphaD*((D(t+1)-D(t))/N));

end;

figure;
%yyaxis left
plot((2:T)',[ I(2:T) 100*(D(2:T)-D(1:T-1)) ],'linewidth',2)
xlabel('Days')
ylabel('People');
axis([0 100 0 inf]);

yyaxis right
plot((1:T)',betat/gam,'--k','linewidth',2);
ylabel('Reproduction rate R0','color','k')
axis([0 100 0 inf]);

legend('Infected','100 x Deaths/day','R0 (right scale)','location','best')

title('BSIR model, R0 varies with death rate');