## Thursday, September 24, 2020

### Growth and regulation

Is economic growth inexorably slowing down? Such is the depressing conclusion of Nick Bloom, Chad Jones, John Van Reenen, and Michael Webb, who showed in a very important paper that it is taking more and more effort to find new ideas. It is also the conclusion of Robert Gordon's Rise and Fall of American Growth. They promised us flying cars, and all we get tweets. The marshaling of facts in these and related works is impressive and depressing.

I'm attracted to the other much more hopeful (maybe) possibility: growth, really the continued betterment of the human condition, is possible, but it is just stymied by the ever-increasing web of law and regulation.

Along today come two interesting posts courtesy Marginal Revolution (always must-read). The first is narrow, on nuclear power, the second much broader on how bad regulation spreads around the world.

## Monday, September 21, 2020

### Romer on testing

As part of an email conversation about testing, Paul Romer sent the following message. He so beautifully encapsulated the case for testing, I asked for permission to post his email. Here it is.

Here is a short summary of the case for testing.

1. A program of "test and isolate" will reduce the effective reproduction number, R.

2. A combined policy of (i) more "test and isolate" which reduces R and (ii) more social interaction and more economic activity which increases R can be designed so that the net effect on R is zero.

3. The ratio of the cost of the additional testing to the additional economic activity that this combined policy will allow offers one way to estimate of the "rate or return" to spending on tests. My rough estimate is that this rate of return lies in the range of 10x to 100x so there is no doubt that test and isolate would be cost effective. To reach the higher end of the range, the cost of the test would have to be relatively low, say  $10. 4. The combined plan under #2 will lead to more total cases. If the main measure of policy success or failure were deaths, an increase in the number of cases would not matter. Under the current circumstances, an increase in the number of cases is likely to be interpreted as a sign of a policy failure. This increases the political cost to the administration of increasing the number of tests. A second-best solution that avoids this cost might be to use at home tests and encourage people to self-isolate. This way, the results from the tests need not generate any new confirmed cases. [JC Comment: one reluctance that the president or governors may have is that more testing naturally produces more measured cases, and the media don't seem all that good about recognizing this fact.] Details on Targeting, Timing, and Compliance: - Under the program in #3, the benefit created when more infectious people are isolated is received by unknown others who are free to resume normal activities. This is a classic case of an external effect. As a result, it makes sense for the government to pay for the tests and perhaps even to pay for "supported isolation" to increase the compliance rate. Because the fraction of the population that is infected is relatively small and because the required period of isolation is short, it would be relatively inexpensive to pay the few people who are in isolation, for example by making up any lost wages. Because transmission in the household is likely, it would make sense to offer a choice of isolation in a hotel or isolating the entire family at home. However, implementing this would require some way to confirm that someone is infectious, which precludes its use in the at-home approach noted under #4 above. - For purposes of calculating the rate of return in the combined program described in #3, it is useful to consider a thought experiment of testing people at random. But in any practical program, the efficient way to use more tests is to start by targeting populations that have high ex ante probability of being infected. This could be done by concentrating the tests in high prevalence geographical regions, in high exposure populations, or on people identified by contact tracing. I am skeptical that contact tracing is the cost effective way to identify a large number of people who have a higher ex ante probability of being infected. - For reducing R, what matters is the average number of infectious-person-days in isolation per test. This depends on (a) the number of true positives that are isolated and (b) when in the course of their infection they are isolated. The way to increase (a) is to target populations with a high ex ante probability of infection. The way to increase (b) is to use tests with a shorter time from sample to result. - The choice between centralized lab testing and POC tests depends in part on an easily quantified tradeoff between a reduction in the sample-to-result time of most POC tests and a reduction in their sensitivity. But in the early months of any program for expanding the number of tests, the most important differentiator is likely to be the supply response. Many people are convinced that there is a large amount of lab capacity on university campuses that could rapidly be mobilized so that this path probably offers the lowest-cost path of expansion until manufacturing capacity increases for the POC or at home tests. - There is a synergy between the frequency of testing in a population and the use of pooling to increase lab capacity. As the frequency increases, the frequency of positives will go down so that pooling becomes more cost effective. - A large fraction of the total cost of a test comes from the discomfort experienced by the person who gives the sample and the time it takes for a healthcare professional to collect the sample. On both grounds, saliva samples will almost surely have the lowest cost. - To reduce the cost from isolating false positives, any initial positives could be retested. Because the number of positive results will be a small fraction of the number of tests, retesting adds only a small amount to the cost of the program. - As long as any true positives are isolated, the net effect of the combined program described in #2 will be to increase the total amount of social interaction by people who are not infectious, even if there are some false positives. I hope this is helpful. Paul. ### Jacobin pandemic Casey Mulligan tweeted an interesting report on the coronavirus from Jacobin online magazine as "makes the most sense." Given that the Jacobins were "the most radical and ruthless of the political groups formed in the wake of the French Revolution, and in association with Robespierre they instituted the Terror of 1793–4." (google dictionary) the link attracted my eye. (Do these people know history? Or is this intentional? And they're all upset about Trump and "authoritarianism?") Indeed, after the predictable throat-clearing editorializing about "disparate impact" and inequality, and despite idiotic question preambles like this one "Under capitalism, we have become a species that increasingly exploits other creatures and their habitats, and moves in large numbers and with great speed around the globe, making us ripe for a pandemic like this one." (China is.. capitalist? The plague, cholera, yellow fever, smallpox were... what?) Jacobin editorial board member Nicole Aschoff spurs Harvard professors Katherine Yih and Martin Kulldorff to interesting, sensible and useful answers. The extreme source of this commonsense gives me some hope. However, read though or skip to my critical comments, as it's not as totally wise as Casey suggests. KY: ... I don’t think it’s wise or warranted to keep society locked down until vaccines become available. ..Instead of a medically oriented approach that focuses on the individual patient and seeks (unrealistically) to prevent new infections across the board, we need a public health–oriented approach that focuses on the population and seeks to use patterns, or epidemiologic features, of the disease to minimize the number of cases of severe disease and death over the long run, as herd immunity builds up. NA: Like Dr Yih, I am very concerned about the collateral damage of lockdowns. In public health policy, we cannot just consider the present consequences of one single disease. We must think more broadly, considering all short- and long-term health outcomes. ...Another example is school closings. Good education is not only important for academic achievement and financial well-being; it is also critical for the mental and physical health of children and into their subsequent adulthood. Kids have minimal risk from this virus, and it is sad that we are sacrificing our children instead of properly protecting the elderly and other high-risk groups. (I hate to break it to modern-day Jacobins, but the Trump Administration is basically following this approach. And the disparate impact is precisely brought on by economic lockdown. ) Read on for much common sense. However, I don't think this is totally right, and "damn the torpedoes, protect the old folks and let's sail on to herd immunity" is not, I think the right or at least complete answer. 1) Herd immunity, on its own, is a meaningless concept. Most people think herd immunity happens when everyone has gotten it, which is false. A virus stops spreading when the reproduction rate is below one. The reproduction rate combines frequency of contact and fraction of immune in the population. Only that combination matters. If each infected person meets 3 people and 67% of the population has immunity, the virus stops. If each infected person meets two people and 51% the population has immunity, the virus stops. If each infected person meets 0.99 people and nobody is immune, the virus stops. The fraction with immunity on its own is meaningless. So we need to work on both parts of the equation -- reduce the contact rate and minimum economic and social cost, as well as wait for greater numbers to become immune. 2) Long term consequences. The article acknowledges these and moves on. This strikes me as a great unknown. The view that it’s like the flu, just let people get it until immunity rises, while keeping old and sick people safe, is predicated on the idea that there are few long term consequences other than death. If 20% are getting long term important debilitation, that skews the treadeoff to less contact. If this were the plague or cholera, with 50% death, we would not be talking about herd immunity. 3) Testing. The article is missing the one great opportunity we have to reduce the spread and reduce the social and economic cost of the disease, until a vaccine becomes available. "Test" only appears in the article in the section on protecting the elderly and nursing homes. This is the great unexploited opportunity. We can cheaply reduce the contact rate with next to no business or social cost. Why in the world are we not embarking on widespread public-health testing? Why is the FDA still regulating tests, saying they may only be performed in a medical setting? By what possible right or common sense can the FDA tell me that I cannot send samples of my body to a lab, and the lab cannot tell me what’s in them? Read Alex Tabarrok "our antigens, ourselves" to get really grumpy about this. You have to be astoundingly paternalistic about the stupid deplorable to believe that people need to be protected from simple information about what is in their body. There is zero medical danger from a saliva test. This thing could be over in weeks if the FDA allowed cheap, fast, relatively inaccurate, cash-and-carry, completely unregulated tests. Go to CVS, get the test kit, find out if you have it. No referral, no doctor visit, no prescription, no insurance, no faxed paperwork. Let private decisions figure out what to do with the results. Businesses, restaurants, schools could all demand it. With a cheap test, the contact rate can go below one and we need no immunity. Of course, the government has every interest in paying for and subsidizing tests too. Frankly I do not understand this Administration. If President Trump simply tweeted, "FDA: Free the tests!" and "CDC: tell people to get tested" this thing could be over in weeks. We could reach herd immunity with a low contact rate alone, and reastaurants, schools, universities, airlines, could require test results and reopen quickly. Trump could go into the election with the number of cases and deaths crashing. He could campaign in empty hospitals. ## Saturday, September 19, 2020 ### Storm coming I am very worried about how the next election will play out. I am more worried than most commenters, hence this post, because as an economist I predict people's behavior by asking what is natural given their incentives and the rules of the game as they are. That thinking leads to a dark place. Our democracy has one essential function: a peaceful transfer of power. There are rules of the game. A winner is determined even in a close race. Both sides agree who won, and that the winner is a legitimate office holder. We seem inexorably headed to the most divisive election since 1860, in which this mantle of legitimacy is sure to vanish, to horrendous result. Ruth Bader Gisberg's death adds both distraction from the task of fixing election machinery -- really, agreement by both sides what the rules of the game will be, and to abide by the results -- and one more pathway to disaster. Imagine, as seems quite possible, that Trump scores an early lead in the days after the election, with a narrow electoral college majority, though losing the popular vote, with 90% - 10% losses in the deep blue cities. Trump declares victory. Blue cities erupt in protest. As mail in votes come in and are tabulated, Biden gets closer and closer and by his party's count has won. ## Thursday, September 17, 2020 ### Muni haircuts "Municipal bond investors have to share the burden in state bailouts" writes my colleague Josh Rauh, and he is exactly right. Background: State and local governments borrowed a lot of money and blew it. They borrowed further by not funding their pensions. Now covid comes along, people are fleeing cities, and they don't have tax revenue to fund ongoing expenses. The big question hanging over Washington: If we are going to help state and local governments weather the storm of their current expenses, does that mean federal taxpayers bail out the bondholders who lent state and local governments all this money? As in the Greek crisis, bond investors and their allies like to clam "contagion," that any losses will spark a financial crisis. Whether that argument has any merit in other cases, as Josh points out it does not hold for municipal bonds in the current financial environment. Municipal bonds are illiquid and tax-exempt and thus well targeted at very wealthy high-income individuals who face high tax rates, and whose saving is thus beyond IRA, 401(k) and other tax-free investment possibilities. And we are not in a systemic financial crisis. ...as of this spring, around 12 percent of municipal bonds were owned by banks. This implies only about$130 billion of total exposure to all general obligation municipal debt by the banking sector, compared to well above $1 trillion of tier one bank capital. Similar amounts of general obligation municipal debt reside on the balance sheets of the insurance companies, where municipal bonds are 7 percent of assets. The remaining municipal bonds are directly owned by individuals, or in mutual funds and exchange traded funds largely owned by individuals. Municipal bond defaults would primarily affect individual investors, and especially individuals who buy tax exempt municipal debt because they are looking for tax free income. Of a piece with the effort to restore the state and local tax deduction, the effort to bail largely blue states and cities out of their debts to largely blue high income taxpayers is just a little bit inconsistent with tax the rich and tax their wealth rhetoric. Daniel Bergstresser and Randolph Cohen presented a paper a while ago at a Brookings conference, measuring that 42% of municipal bond value was held by the top 0.5% of the income distribution. Now that so many including the Fed are interested in racial justice, similar breakdowns of who holds municipal bonds would be interesting. Given the racial disparity in wealth, it would be astounding if the disparity in municipal bond holding were not very large as well. Josh's solution is straightforward: Congress has to therefore condition any further bailout funds on shared losses by municipal bond investors. For instance, the law can mandate that state governments pass legislation that would write off a dollar of municipal bond debt for every dollar of additional grants given to a state or local government. If we ever are to have any sort of market discipline, if a Fed put is not going to protect all large and politically potent issuers and all large and politically potent investors, who got outsized returns for many years by holding risky assets, from actually taking those losses when it counts, rather than one more taxpayer bailout, this seems like the time and place. Municipal bonds are already highly subsidized, by their tax deduction. State and local governments have responded predictably by borrowing a lot. (Universities also get to borrow at municipal bond rates, and effectively use the money to invest in their hedge-fund endowments.) If municipal bonds now enter the too big to fail regime, the subsidy and incentive to over borrow explodes. This situation is part of a general conundrum. The government and the Fed has taken on forestalling bankruptcies of large businesses and governments in the covid recession. (Restaurants, small landlords, and other small businesses no. But AAA bond issuers, and municipal bond issuers yes.) To forestall a bankruptcy, you do not just lend money for current operations -- you end up taking on past debts. Fortunately the recession seems to be ending quickly, because the magnitude of debt that might end up in federal hands under the no-bondholder-may-lose-money regime is pretty frightening. Update French Translation at Vox-fi ## Tuesday, September 15, 2020 ### Atlas agonistes A group of Stanford faculty recently circulated, and then posted, an open letter objecting to my Hoover colleague Scott Atlas, who serves as a senior adviser to the Administration on health policy. Read the letter. Then come back for a little reading comprehension test. **** Q1: What specific "falsehoods and misrepresentations" do they accuse Scott of making? Q2: Which of the following do they claim Scott is publicly denying, contrary to scientific evidence? 1. Face masks, social distancing, handwashing and hygiene can help to reduce the spread of Covid-19. 2. Crowded indoor spaces are dangerous. 3. Asymptomatic people can spread covid-19 4. Testing asymptomatic people can help to slow the spread. 5. Children can get Covid-19 6. Pandemics can end via herd immunity. Vaccines work, by conferring herd immunity. 7. Letting people get sick is better than a vaccine. 8. All of the above Q3: What specific documented evidence of statements that contravene contemporary scientific consensus do the signatories provide? Q4: What role in the Administration do they cite that Scott has, and misuses? (Note present tense. Scott is an adviser. We all get to change our minds -- even Dr. Fauci once said face masks were not worth the bother, but the signatories don't seem to feel an "ethical obligation" to play gotcha on that one. What matters is, what is Scott currently advocating in the Administration?) ******* ### Debt podcast and reconciliation The Grumpy Economist podcast is back, with some thought on the debt issues from my last posts here and here. David Andofatto had some final thoughts at macro mania, with which I mostly agree. Yes a twitter/blog debate in macroeconomics produces agreement! Central points: 1) For these purposes a large sharp inflation and a default are not much different. In fact, the event I have in mind is most likely an inflation, as the US is likely to choose inflation over default. I don't think I made this equivalence clear in the debt posts. Also, the Fed is just another issuer of interest-paying debt. However, I don't think the chance of default or haircut is as remote as everyone else seems to think. They are also related events. Remember, my scenario for a debt crisis posits an economic and political crisis at the same time -- pandemic, recession, war, huge demands on the US treasury. Just how sacrosanct will full repayment of debt be to the US political system? When Chinese central bankers and Wall Street fat-cats are pressing for debt repayment but ordinary Americans are hurting, will our political system really take hard measures to repay the former in full, while throwing everyone's lives into misery via inflation? Maybe, and maybe inflation can still be blamed on speculators and middle-people and the usual bogey-people but maybe not. A haircut on Treasurys is not inconceivable. It could also come via refusal to raise the debt limit, or via a sharp wealth tax. And if people start to fear a haircut coming, they will certainly dump debt immediately, so fear of even technical defaults can spark the inflation. 2) Yes, a good part of current r<g may well be a liquidity premium for US government debt due to its usefulness in transactions. But the big questions for r<g remain how reliable and how scaleable. Liquidity demand is not very scaleable. For example, if a government is financed only by money and no debt, and money demand MV=PY, then the government can run perpetual small deficits as the real economy Y and hence money demand grow. But if the government sees this situation, says "great, r<g, let's blow$10 trillion bucks," it will soon discover this opportunity does not scale at all.

In the more reasonable MV(i)=PY that money demand is interest elastic, as the government exploits the opportunity and supplies more M it must pay greater interest on money (interest on reserves, interest on money-like treasurys), eating away quickly at r<g.

The sensible r<g advocates like Blanchard recognize that r<g does not scale infinitely, and that a rise in r captures its limit. However, the discussion usually goes quickly to crowding out and the marginal product of capital rising. The liquidity effect that depresses US government bond yields is likely much less scaleable than crowding out of the whole US capital stock.

When you read estimates of how much r rises as debt/GDP rises, pay attention to which mechanism they have in mind.

Liquidity demand is also more fickle. Money demand can rise and fall quickly. The portion of treasury demand that comes from its use in financial transactions can be undone by different payment and clearing technology. Relying on this poorly understood mechanism for 30 years of r<g to pay off our debt seems a bit risky. US sanctions and regulations are creating a big incentive for others to create such alternative mechanisms.

3) The government should borrow longer. The Fed can help.

One of my policy conclusions is that the US government should borrow long-term as households who fear a big rise in interest rates should get 30 year mortgages not adjustable rate mortgages. Currently the Fed is actively undoing the Treasury's meager efforts to borrow long term, by buying up long-term treasury and guaranteed agency debt and issuing overnight reserves in return, and by issuing new debt in the form of overnight debt.

The Fed could easily introduce term deposits -- reserves that carry a fixed interest rate, rather than a floating rate, and whose principal value varies. The Fed could also engage in fixed-for-floating swap contracts to eliminate the government's exposure to interest rate risk. (Such swap contracts should be collateralized of course, since you don't buy insurance from someone you will bail out if they lose money!) If interest rates rise the Fed will not just rescue the US government from a crisis, but will look like bloody geniuses. Which would you rather as a central banker in a crisis: a huge rise in net worth with which you can bail out the Treasury, or to fight an immense mark-to-market loss?

### Fintech in chains

"Fintech can come out of the shadows" is the title that Wall Street Journal editors gave to  Brian Brooks and Charles Calomiris' oped last week. I have not in a long time seen a title that more utterly contradicts the content of the essay.  For what they advocate is exactly the opposite: Fintech in chains, hemmed in by  the sort of regulatory stranglehold that fintech was created to escape.

What is fintech? Basically companies that offer

services—consumer loans, credit cards or payment processing—that banks have traditionally offered.

but, crucially, fintech does not accept deposits.

The issue?

The Office of the Comptroller of the Currency determines which companies qualify for charters as national banks or federal savings associations and supervises the activities of those banks.

But not fintech companies, because fintech companies don't take deposits. And that is the legal issue prompting the oped -- Brooks and Calomiris, coincidentally acting comptroller of the currency and chief economist of the OCC, want the OCC to regulate fintech just like banks. (Calomiris is a topnotch economist who normally writes very good papers. )

So what's so awful about fintech?

## Monday, September 14, 2020

### Deflation

For another purpose, I had reason to look up TIPS yields.

The current Treasury Inflation-Protected Security (TIPS) yields are -1.27% (5 years) -0.98% (10 years) and, amazingly, -0.35% (30 years). You pay them 0.35% per year for a stable real value. I did not realize it was this low.

The context. I serve on the advisory board of a small nonprofit that has an endowment. The endowment is intended to be perpetual. We're discussing the equity vs. fixed income allocation. I wanted to lay out the options. If they want absolute safety of principal and payout, under a perpetual constraint, they can pay out... -0.35% of the principal every year! I advised they accept some risk in the payout stream.

It is not common for foundations to link the payout rate to the portfolio beta or composition. On economic grounds it should be. If you want a perpetual investment, the payout rate has to relate to the average portfolio return. Fixed income should have a lower payout rate than equity.

Of course, some payouts are set by IRS rules or by a conflict between managers and donors, and there apparent illogic can serve other purposes.

### Latest Goodfellows

The latest Goodfellows discussion. Embedded, hopefully, here:

or direct link here. (Try that if the embed fails. Youtube has started censoring Hoover.)

Podcast:

## Wednesday, September 9, 2020

### Smoke and Nukes

I was driving in Northern California on Labor Day, contemplating the 1-2 mile visibility in thick smoke through the Central Valley, and listening to NPR, when an enticing story came along

Amna Nawaz:

For a closer look at what's behind that heat wave and what's fueling these fires, I'm joined by Leah Stokes, she's a professor and researcher on climate, energy and political policy at the University of California, Santa Barbara

Great, I thought. We're going to hear some real science and policy. What's the role of forest floor cleaning? Climate warming isn't the issue per se -- it's hot in Arizona but Arizona doesn't burn. It's a complex of moisture, growth human activity. And policy. Great. What do we do about the fact that so much burning land is federal, and the federal government isn't cleaning up its forest floor either. What's the budget history of fire fighters? Just what are the air quality numbers?

I was, to put it mildly, disappointed.

## Sunday, September 6, 2020

### More on debt

Following my last post on debt I've thought a bit more, and received some very useful emails from colleagues.

A central clarifying thought emerges.

The main worry I have about US debt is the possibility of a debt crisis. I outlined that in my last post, and (thanks again to correspondents) I'll try to draw out the scenario later. The event combines difficulty in rolling over debt, the lack of fiscal space to borrow massively in the next crisis. The bedrock and firehouse of the financial system evaporates when it's needed most.

To the issue of a debt crisis, the whole debate about r<g, dynamic inefficiency, sustainability, transversality conditions and so forth is largely irrelevant.

We agree that there is some upper limit on the debt to GDP ratio, and that a rollover crisis becomes more likely the larger the debt to GDP ratio.  Given that fact, over the next 20-30 years and more, the size of debt to GDP and the likelihood of a debt crisis is going to be far more influenced by fiscal policy than by r-g dynamics.

In equations with D = debt, Y = GDP, r = rate of return on government debt, s = primary surplus, we have* $\frac{d}{dt}\frac{D}{Y} = (r-g)\frac{D}{Y} - \frac{s}{Y}.$ In words, growth in the debt to GDP ratio equals the difference between rate of return and GDP growth rate, less the ratio of primary surplus (or deficit) to GDP.

Now suppose, the standard number, r>g, say r-g = 1% or so. That means to keep long run average 100% debt/GDP ratio, the government must run a long run average primary surplus of 1% of GDP, or $200 billion dollars. The controversial promise r<g, say r-g = -1%, offers a delicious possibility: the government can keep the debt/GPD ratio at 100% forever, while still running a$200 billion a year primary deficit!

But this is couch change! Here are current deficits from the CBO September 2 budget update

We were running $1 trillion deficits before the pandemic. Each crisis seems to bring greater stimulus. I especially like this view because it doesn't make sense that an interest rate 0.1% above the growth rate vs. an interest rate 0.1% below the growth rate should make a dramatic difference to the economy. Once you recognize some limit on the debt/GDP ratio, and desirability of some long-run stable debt/GDP, there is no big difference between these two values. The surplus required to stabilize debt to GDP smoothly runs from negative couch change to positive couch change. I find this a liberating proposition. I find the whole sustainability, long run limits, dynamic inefficiency, transversality condition and so forth a big headache. For the question at hand it doesn't matter! (There are other questions for which it does matter, of course.) As we look forward, debt/GDP dynamics for the next 20 years are going to be dominated by the primary surplus/deficit, not plausible variation in r-g. The CBO's 10 years of 6-8% of GDP overwhelm 1-2% of r-g. If each crisis continues to ratchet up 10% of GDP deficits per year, more so. The Green New Deal, and large federal assumption of student debts, state and local debts, pension obligations, and so forth would add far more to debt/GDP than decades of r vs. g. ********** Now that this is clear, I realize I did not emphasize enough that Olivier Blanchard's AEA Presidential Address acknowledges well the possibility of a debt crisis: Fourth, I discuss a number of arguments against high public debt, and in particular the existence of multiple equilibria where investors believe debt to be risky and, by requiring a risk premium, increase the fiscal burden and make debt effectively more risky. This is a very relevant argument, but it does not have straightforward implications for the appropriate level of debt. See more on p. 1226. Blanchard's concise summary there can be multiple equilibria: a good equilibrium where investors believe that debt is safe and the interest rate is low and a bad equilibrium where investors believe that debt is risky and the spread they require on debt increases interest payments to the point that debt becomes effectively risky, leading the worries of investors to become self-fulfilling. Let me put this observation in simpler terms. Let's grow the debt / GDP ratio to 200%,$40 trillion relative to today's GDP. If interest rates are 1%, then debt service is $400 billion. But if investors get worried about the US commitment to repaying its debt without inflation, they might charge 5% interest as a risk premium. That's$2 trillion in debt service, 2/3 of all federal revenue. Borrowing even more to pay the interest on the outstanding debt may not work. So, 1% interest is sustainable, but fear of a crisis produces 5% interest that produces the crisis.

Brian Riedi at the Manhattan Institute has an excellent exposition of debt fears. On this point,

... there are reasons rates could rise. ...

market psychology is always a factor. A sudden, Greece-like debt spike—resulting from the normal budget baseline growth combined with a deep recession—could cause investors to see U.S. debt as a less stable asset, leading to a sell-off and an interest-rate spike. Additionally, rising interest rates would cause the national debt to further increase (due to higher interest costs), which could, in turn, push rates even higher.

***********

So how far can we go? When does the crisis come?  There is no firm debt/GDP limit.

Countries can borrow a huge amount when they have a decent plan for paying it back. Countries have had debt crises at quite low debt/GDP ratios when they did not have a decent plan for paying it back. Debt crises come when bond holders want to get out before the other bond holders get out. If they see default, haircuts, default via taxation, or inflation on the horizon, they get out. r<g contributes a bit, but the size of perpetual surplus/deficit is, for the US, the larger issue. Again, r<g of 1% will not help if s/Y is 6%. Sound long-term financial strategy matters.

From the CBO's 2019 long term budget outlook (latest available) the outlook is not good. And that's before we add the new habit of massive spending.

Here though, I admit to a big hole in my understanding, echoed in Blanchard and other's writing on the issue. Just how does a crisis happen? "Multiple equilibria" is not very encouraging. Historical analysis suggests that debt crises are sparked by economic and political crises in the shadow of large debts, not just sunspots.  We all need to understand this better.

******

Policy.

As Blanchard points out, small changes do not make much of a difference.

a limited decrease in debt—say, from 100 to 90 percent of GDP, a decrease that requires a strong and sustained fiscal consolidation—does not eliminate the bad equilibrium. ...

Now I disagree a bit. Borrowing 10% of GDP wasn't that hard! And the key to this comment is that a temporary consolidation does not help much. Lowering the permanent structural deficit 2% of GDP would make a big difference! But the general point is right. The debt/GDP ratio is only a poor indicator of the fiscal danger. 5% interest rate times 90% debt/GDP ratio is not much less debt service than 5% interest rate times 100% debt/GDP ratio. Confidence in the country's fiscal institutions going forward much more important.

At this point the discussion usually devolves to "Reform entitlements" "No, you heartless stooge, raise taxes on the rich." I emphasize tax reform, more revenue at lower marginal rates. But let's move on to unusual policy answers.

Borrow long. Debt crises typically involve trouble rolling over short-term debt. When, in addition to crisis borrowing, the government has to find $10 trillion new dollars just to pay off$10 trillion of maturing debt, the crisis comes to its head faster.

As blog readers know, I've been pushing the idea for a long time that especially at today's absurdly low rates, the US government should lock in long-term financing. Then if rates go up either for economic reasons or a "risk premium" in a crisis, government finances are much less affected. I'm delighted to see that Blanchard agrees:

to the extent that the US government can finance itself through inflation-indexed bonds, it can actually lock in a real rate of 1.1 percent over the next 30 years, a rate below even pessimistic forecasts of growth over the same period

It's not a total guarantee. A debt crisis can break out when the country needs to borrow new money, even absent a roll over problem. But avoiding the roll-over aspect would help a lot! Greece got in trouble because it could not roll over debts, not because it could not borrow for one year's spending.

Contingent plans? Blanchard's concise summary adds another interesting option
contingent increases in primary surpluses when interest rates increase.

I'm not quite sure how that works. Interest rates would increase in a crisis precisely because the government is out of its ability or willingness to tax people to pay off bondholders. Does this mean an explicit contingent spending rule? Social security benefits are cut if interest rates exceed 5%? That's an interesting concept.

Or it could mean interest rate derivatives. The government can say to Wall Street (and via Wall Street to wealthy investors) "if interest rates exceed 5%, you send us a trillion dollars." That's a whole lot more pleasant than an ex-post wealth tax or default, though it accomplishes the same thing. Alas, Wall Street and wealthy bondholders have lately been bailed out by the Fed at the slightest sign of trouble so it's hard to say if such options would be paid.

Growth. Really, the best option in my view is to work on the g part of r-g. Policies that raise economic growth over the next decades raise the Y in D/Y, lowering the debt to GDP ratio; they raise tax revenue at the same tax rates; and they lower expenditures. It's a trifecta. In my view, long-term growth comes from the supply side, deregulation, tax reform, etc. Why don't we do it? Because it's painful and upsets entrenched interests. For today's tour of logical possibilities if you think demand side stimulus raises long term growth, or if you think that infrastructure can be constructed without wasting it all on boondoggles, logically, those help to raise g as well.

********

*Start with $$\frac{dD}{dt} = rD - s.$$ Then $$\frac{d}{dt}\frac{D}{Y} = \frac{1}{Y}\frac{dD}{dt}-\frac{D}{Y^2}\frac{dY}{dt}.$$

***

Update: David Andolfatto writes, among other things,

"Should we be worried about hyperinflation? Evidently not, as John does not mention it"

For these purposes, hyperinflation is equivalent to default. In fact, a large inflation is my main worry, as I think the US will likely choose default via inflation to explicit default. This series of posts is all about inflation. Sorry if that was not clear.

also

Is there a danger of "bond vigilantes" sending the yields on USTs skyward? Not if the Fed stands ready to keep yields low.

All the Fed can do is offer overnight interest-paying government debt in exchange for longer-term government debt. If treasury markets don't want to roll over 1 year bonds at less, than, say, 10%, why would they want to hold Fed reserves at less than 10%? If the Fed buys all the treasurys in exchange for reserves that do not pay interest, that is exactly how we get inflation. And mind the size. The US rolls over close to $10 trillion of debt a year. Is the Fed going to buy$10 trillion of debt? Who is going to hold $10 trillion of reserves, who did not want to hold$10 trillion of debt.

In a crisis, even the Fed loses control of interest rates.

### SALT

Chris Pullman and Richard Reeves at Brookings write opposing a reinstatement of the deduction for state and local taxes on the federal income tax. Jonathan Parker, a great economics tweeter, tweets approvingly

I offer a little more guarded approval. Yes, it's praiseworthy when any organization in our politicized times criticizes the favored narrative of the party they are perceived to be associated with. And the SALT deduction should, in my view, not be reinstated.

But though they are right, but they are not right for the central reasons. And the reasons they give are a lot less non-partisan than Jonathan makes it sound.

## Friday, September 4, 2020

### Debt Matters

Debt Matters

(This is a draft of an oped. I got done and saw it's 1500 words, so I'm posting it for your enjoyment rather than go through a painful 600 word diet. Diet later. Maybe. )

Last week, the U.S. passed a milestone — US federal debt in private hands exceeded 100% of GDP. But does all this debt matter, or is worrying about debt passé?

This debate has been going on among economists for a while. One does not need to go to the incoherence of "modern monetary theory" to find support for the view that debt has few consequences. Olivier Blanchard, of MIT and the IMF, in his Presidential Address to the American Economic Association, (excellent summary here) declared that “there may be no fiscal costs” of additional debt. The core of his argument is that the interest rate on government debt may be lower than the growth rate of the economy so the US can roll over debt forever.

Larry Summers, ex treasury secretary, President of Harvard, and adviser to presidents, surely the preeminent policy economist of our generation, has advocated that additional debt-financed spending may have so strong a multiplier as to pay for itself. (Paper here) As a result “expansionary fiscal policies may well reduce long-run debt-financing burdens," a super-Keynesian version of the Laffer curve

(I don’t mean to pick on Blanchard and Summers — they are only superbly distinguished representatives of widely held views.)

Unlike MMT, these are logically consistent possibilities. But are they right?

The interest rate on government debt is indeed slightly lower than good guesses of the economy’s growth rate, as sadly low as the latter is, so that if we roll over debt with no additional deficits, the debt to GDP ratio will slowly decline and the US can indeed run this slow-rolling Ponzi scheme.

But how long will this happy circumstance of ultra-low interest rates continue? More to the point, how scaleable is this opportunity? Bond market investors lend 100% of GDP to the US government at 1% interest. Will they lend 200% of GDP at the same low interest rate, or will they start to require higher interest rates? A government that finances itself only with money and no debt need not pay back the money -- but, obviously, cannot double the opportunity.

What happens when, rather than grow out of a given debt, the US piles on larger and larger debt to GDP ratios each year? The analysis is about sustainability of a large, but steady debt to GDP ratio. It does not justify a debt to GDP ratio that grows 10 percentage points per year.  At what debt to GDP ratio must the party stop and the growing out of it begin?

Blanchard recognizes these limits are out there somewhere, and that debt crowds out private investment. But just where the limits are is less clear. That finding the limits will be unpleasant is clear.

Summers’ view is likewise limited to a period of “secular stagnation” with perennially deficient demand, sticky prices and wages, and the other requirements of extreme Keynesianism.  Are we in such a period, or is covid a supply shock? Was the economy really suffering lack of demand when unemployment hit 50 year lows last February?

Washington knows no such sophistication, but our politicians have grasped the logical implications of the proposition that debt does not matter with more clarity than have economists.

The notion that debt matters, that spending must be financed sooner or later by taxes on someone, and that those taxes will be economically destructive, has vanished from Washington discourse on both sides of the aisle. The covid response resembles a sequence of million-dollar bets by non-socially distanced drunks at a secretly reopened bar: I’ll spend a trillion dollars! No, I’ll spend two trillion dollars! That anyone has to pay for this is un-mentioned. Well, perhaps nobody does have to pay.

And who is to blame them, really? Markets offer 1% long-term interest rates. Blowout spending  financed by the Fed printing money — which is no different from debt — has resulted in no inflation so far. Faced with the deep concerns of current voters, worry that our children and grandchildren might have to pay off debt is not particularly salient. They’re either in the basement playing video games or out protesting for the end of capitalism anyway.  Politicians will take the cheap money as long as markets are happy to provide it.

The economists, even the modern monetary theorists, envision debt issued to finance worthy investments, or valuable spending, all undertaken with a careful green eyeshade approach. Washington has figured out the logical conclusion of the idea that Federal debt doesn’t matter, in a way these economists have not: If debt and money printing have no fiscal cost, why be careful about how you spend money? Send checks to voters. Why not? It’s costless. No boondoggle project is objectionable. Send billions to prop up dying businesses. Why not? It’s costless. Why bother fixing the post office? Send them another $25 billion. Or$100.

Deeper: Why should citizens have to pay back debts if the Federal government does not have to do so? Bail out student loans. Bail out bankrupt states and locals and their pensions. Cancel the rent. Cancel the mortgage. Why should anyone have to pay any debt if the Federal government has access to a money machine? Why work? Why should the federal government not just keep printing money and sending it to us? Other countries are not so lucky as we are. Why should emerging markets pay back debt if the US does not have to? Bail them out.

Why indeed should anyone pay taxes? Here Stephanie Kelton, MMT proponent, has followed the logic. The only reason to charge taxes at all, in her view, is to expropriate the wealthy to rob them of political power.

These are inescapable logical conclusions of the view that federal debt has no fiscal cost. If you’re uncomfortable with the end of the trip, perhaps you should revisit the assumption from which it inexorably follows. At least, you recognize that the opportunity to borrow with little fiscal cost is limited, so should be preserved.

Advocates point to WWII. It is true, that the US exited an even greater debt to GDP ratio. It was not painless. Growth higher than interest rates was part of it, but not all. Two bouts of inflation, in the late 1940s and in the 1970s devalued much debt. The US ran steady primary (excluding interest costs) surpluses from the 1940s through the mid 1970s. Spending was low in the pre-entitlement economy, and nobody was totting up hundreds of trillions in unfunded promises. The war, and its spending, was over. Statutory personal taxes and actual corporate taxes were high. Financial repression and closed international capital markets kept interest rates on government bonds low, and deprived Americans of better investment opportunities and our and the world’s economies much needed investment capital. And we had an international debt crisis in the early 1970s, prompting the abandonment of Bretton woods and depreciation of the dollar.

In short, the US grew out of WWII debt by not borrowing any more, by decades of fiscal probity, and by strong supply-side growth in a deregulated economy. We have none of these reassurances going forward. And this, and the UK exit from Napoleonic War debt in the 1800s by starting the industrial revolution are about the only historical examples of a semi-successful repayment of this much debt. Otherwise, the history of large sovereign debts is one long sorry tale of default, inflation, devaluation, and consequent financial chaos. The UK did not exit WWII debt successfully, leading to crisis after crisis, and everyone else did worse.

Still, what should we be afraid of? The vision of grandchildren saddled with taxes, or even just unable to borrow more while the economy sits at its limit, of, say, 200% debt to GDP, is indeed not a salient brake to spending.

That is not the danger. The danger the US faces, the danger we should repeat and keep in mind, is a debt crisis. We print our own money, so the result may be a sharp inflation that wipes away the value of debt rather than an even more disruptive default, but the consequences will be almost as dire.

Imagine that 5 or even 10 years from now we have another crisis, which we surely will. It might be another, worse, pandemic; a war involving china, Russia or the Middle East. Imagine the US follows its present trends of partisan government dysfunction, so an impeachment is going on, a contested election, and even militias roaming the streets of still boarded up cities. Add a huge economic recession, but unreformed spending promises.

## Friday, August 14, 2020

### Test = vaccine

"Cheap, frequent COVID tests could be ‘akin to vaccine,’ professor says" from the Harvard Gazette HT Miles Kimbal

Yes, I'm repeating myself, but maybe if we just try over and over again we'll get through. We could stop this disease now with tests. Vaccines are just a tool to stop disease transmission. Widespread, cheap frequent tests are just as effective a tool to stop disease transmission. So I'll keep quoting anyone who wants to say this!

A Harvard epidemiologist and expert in disease testing is calling for a shift in strategy toward a cheap, daily, do-it-yourself test that he says can be as effective as a vaccine at interrupting coronavirus transmission — and is currently the only viable option for a quick return to an approximation of normal life.

“These are our hope,” said Michal Mina, assistant professor of epidemiology at Harvard T.H. Chan School of Public Health and Brigham and Women’s Hospital. “We don’t have anything tomorrow, other than shutting down the economy and keeping schools closed.”

....the paper-strip tests have already been developed and their shotgun approach to testing — cheap and widespread — provides a way back to the workplace, classroom, and other venues.

The tests, which can be produced for less than a dollar, can be performed by consumers each day or every other day. Though not as accurate as current diagnostic tests, they are nonetheless effective at detecting virus when a person is most infectious, Mina said. If everyone who tests positive stays home, he said, the widespread effect would be similar to that of a vaccine, breaking transmission chains across the country.

... What I would like to see happen is to start using testing [as] a true public health tool to break transmission chains in the same way that we know we can use masks to decrease transmission,” Mina said. “I want these tests to tell people they’re transmitting [the virus to others] at the time they’re transmitting, and [when] people can act on it because they’re getting immediate results. And I want them to take it every single day, or every other day.”

Several companies have developed such tests, Mina said.

Why aren't we doing this, voluntarily even?

The Food and Drug Administration,..  has held up approval because the tests aren’t as accurate as nasal-swab, lab-based tests. While that would matter if they were intended as an individual diagnostic tool, Mina said that from a public health viewpoint, they are accurate enough to provide critical initial screening on a large scale. ....

“Everyone says, ‘Why aren’t you doing this already?’ My answer is, ‘It is illegal to do this right now,’” Mina said.

In other words, the FDA says:  "Yes, you can use a thermometer to screen people out and send them home. Yes, you can use a questionnaire to screen people out and send them home.  No, you may not use a far more accurate \$1 paper test for exactly the same purpose. And if you try, we'll ruin your company and send you to jail."

Alex Tabarrok puts it nicely: We're testing for contagiousness, not for infection.

President Trump seems to have discovered President Obama's phone and pen. A suggestion: Tomorrow morning, 9 AM, executive order: The sale and use of these paper tests shall be legal. We could be done with Covid 19 in a month or two.

## Thursday, August 13, 2020

### TikTok dust up

This week's Goodfellows conversation was a bit more contentious than usual. The most interesting part, I think, is our little dust-up over TikTok, following Niall's Bloomberg commentary.

As in the rest of this series I am the skeptic of jumping in to Cold War II -- or at least against lashing out against all things China without an overall strategy. So I pushed hard on my colleagues -- Be specific. Just exactly what is the danger you fear about allowing a Chinese social media company to operate in the U.S?

## Monday, August 10, 2020

### Tests

America has essentially given up on containing the corona virus, and will just let it spread while we await a vaccine. Oh sure, our governors and other public officials flap around about wearing masks and social distancing. But there is no serious public health effort. (If you're in California, I encourage you to listen to NPR's faithful coverage of our Governor Gavin Newsom's noon daily press conference. Never has anyone so artfully said so little in so many words.)

A vaccine is a technological device that, combined with an effective policy and public-health bureaucracy for its distribution,  allows us to stop the spread of a virus.  But we have such a thing already. Tests are a technological device that, combined with an effective policy and public-health bureaucracy for its distribution, allows us to stop the spread of a virus.

For that public health purpose, tests do not need to be accurate. They need to be cheap, available, and fast. When the history of this virus is written, I suspect that the immense fubar, snafu, complete incompetence of the FDA, CDC, and health authorities in general at understanding and using available tests to stop the virus will be a central theme. (Well, forecasting historians is a dangerous game. Already "the virus increases inequality and social injustice" seems to be the narrative of the day.)

Marginal revolution has three insightful posts on the issue. "Bill Gates is angry" starts with a  comment on the fact that currently, once you get a test, it can take days or even weeks to get the results.

..that’s just stupidity. The majority of all US tests are completely garbage, wasted.

If the point of the test is to find out who has it, and isolate them, then an answer that comes back after they've gone out to spread the virus to friends, family and co-workers is completely wasted. Gates has an econ-101 insight into why this is happening:

If you don’t care how late the date is and you reimburse at the same level, of course they’re going to take every customer...You have to have the reimbursement system pay a little bit extra for 24 hours, pay the normal fee for 48 hours, and pay nothing [if it isn’t done by then]. And they will fix it overnight.

I know a great such reimbursement system, but I'll hold that in suspense. (You can probably guess what it is.)

A second great insight:

## Wednesday, August 5, 2020

### Sowell review

Coleman Hughes writes a wonderful review of Thomas Sowell's life and work in City Journal. Savor it.

My first Sowell book was Knowledge and Decisions, and I am heartened to see Hughes put that foremost as well. Sowell takes up where Hayek left off, how the price system is the network like our neurons communicating information across a complex economy. This remains a verbal part of the economics tradition, resisting formal modeling so far, and is thereby too often glossed over in graduate training. Read it.

Sowell of course has written masterpieces on race, a collection of impeccably documented uncomfortable truths to the progressive left. My first, The Economics and Politics of Race is just one of nearly a dozen meticulous books, from Black Education: Myths and Tragedies (1972) to Discrimination and Disparities, second edition (2019). Hughes reviews important points in Conquests and Cultures, Migrations and Cultures, and Race and Culture.

## Thursday, July 16, 2020

### Goodfellows and Garicano Interview

I did two videos last week that blog readers may enjoy.

I did an interview with Luis Garicano in his "capitalism after coronavirus" series

We covered many topics, but the aftermath of the huge government debt now being racked up is possibly the most interesting, at least to me.

Luis is currently a member of the European Parliament. Among many other things he was a PhD student and then professor of economics at the University of Chicago. He's a also a great interviewer. The interview is also available in Spanish, here.

In the latest Goodfellows, Niall, HR and I interview Victor Davis Hanson, about Trump, cancel culture, and the future of universities.

Podcast

## 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.