Monday, January 11, 2021

Low Interest Rates and Government Debt

This is a talk I gave for IGIER at Bocconi (zoom, sadly) Jan 11 2021. Olivier Blanchard also gave a talk and a good discussion followed. Yes, some content is recycled, but on an important topic one must go back to refine and rethink ideas. This post has mathjax equations and graphs. If you don't see them, come back to the blog or read the pdf version. Update: Video of the presentations. 

Low Interest Rates and Government Debt
John H. Cochrane
Hoover Institution
Prepared for the IGIER policy seminar, January 11 2021

1. Why are real interest rates so low? (And thus, when and how will that change?)

Figure 1. 10 year US treasury rate and core CPI.

As Figure 1 shows, real and nominal interest rates have been on a steady downward trend since 1980. The size, steadiness and durability of that trend mean that we must look for large basic economic forces. “Savings gluts,” foreign exchange reserves, quantitative easing, lower bounds, forward guidance bond market frictions and so forth may be important icing on the cake, but they are not the cake. They cannot account for such a long-lasting steady trend.

The most basic economics states that the real interest rate equals people’s rate of impatience, plus growth times a coefficient usually thought to be between one and two. The interest rate is also equal to the marginal product of capital. In equations*, \[r = \delta + \gamma g \].  

Figure 2. Real potential GDP growth. 

Figure 2 presents the growth of potential GDP, as one easy way to look at long run growth trends. Potential GDP grew 4.5% in the 1960s, 3% in the 1970s, had a spurt in the late 1990s, and then settled down to less than 2% now. This slowdown in long-term growth is the great and unheralded economic disaster of our time. But that’s for another day.

The most natural explanation for the decline in real interest rates, then, is that growth has declined. A coefficient greater than one brings interest rates down faster than growth rates, opening the question that the interest rate r might even be below the growth rate g.

Basic supply and demand suggests that lower growth, driven by a lower marginal product of capital, or “supply” is the cause. People often allude to extra savings, or demographics, changing “demand.” That force would be captured by a decline in \(\delta\), an increase in patience. That would lower interest rates without changing growth, or would raise growth without changing interest rates. Changing growth g and constant \(\delta\) produces what we see.

Why did the marginal product of capital decline, and what would change this event? There are three common stories: First, as we move to services and away from capital-intensive goods, we just need less capital. I’m not persuaded. We need different capital, and a lot of the world looks like it could use capital. Second, we are simply running out of ideas, growth is over, is lower. I’m still a techno-optimist. Third, ever-growing marginal tax rates, protections, and regulations are hamstringing the innovation and ruthless competition that it takes to get new ideas into practice. That’s my favorite explanation.

But this is beside the point today. The point: declining growth is a plausible cake, a usually overlooked basic economic force that accounts for the four-decade steady decline in interest rates. More generally, to describe a steady 40 year trend, we should start with basics, the neoclassical growth model. 

Looking again at Figure 1, we cannot have a successful understanding of lower interest rates without saying something about what changed in 1980. Well, obviously, inflation changed. Here is a second basic economic force: average return is proportional to risk, measured by beta, \[ E(R_i) = R^f + \beta_i \lambda.\] In the recessions of the 1970s, inflation went up (stagflation) and bond prices went down (yields went up). Government bonds lost real and nominal value. Government bonds were a risky, positive-beta security. In the recessions since 1980, and especially 2008, inflation went down, bond prices went up, and the dollar went up, while private securities collapsed in value. There was a “flight to quality,” and government bonds were quality. Government bonds became a negative beta security, a hedge against recessions and financial crises. That insurance value drives average bond returns even below the “risk free rate.” With an equity premium of 5% or more, it doesn’t take much negative beta to seriously drive down a return.

Underlying this transformation, inflation expectations have become “anchored.” But by what? Better speeches by central bankers promising what they might do in the future? Everyone admits this “anchoring” is poorly understood. We must then admit it is tenuous, and the pattern of the 1970s could return. (One story with some ring to it is that it is the high ex-post real rates of the 1980s that are unusual and we are only going back to normal, like the late 19th century. It is still puzzling that one year rates were higher than inflation for so long -- markets were apparently betting on inflation and wrong for 20 years in a row.) 

Most discussions are much more fun, involving more interesting economics and lots of frictions. I think these are at best icing on the cake. 

 Figure 3. 30 year treasury (black), Moody’s AAA (blue), and 30 year mortgage rates (red).

Perhaps US Treasury debt is special, due to its liquidity and use in financial transactions. Figure 3 presents the 30-year Treasury against the Moody’s AAA and 30-year mortgage rates, which are quite illiquid. There might be a percent of spread here, some of which is credit spread. It isn’t obviously getting bigger over time. Spreads in shorter-term maturities are similar. Widening liquidity spreads do not account for the huge trend seen in Figure 1. 

 Figure 4. US and Euro 10 year government bonds.

Perhaps the dollar is special, the “reserve currency” that gets “exorbitant privilege.” That may be true in quantities but it does not show up in prices. As shown in Figure 4, Euro bond yields are now 1% lower than US Treasury yields, and have drifted down more. Inflation is a bit lower but not that much lower, so European real rates are lower. Japanese rates show the same patter. Sadly, but consistent with my story, European and Japanese growth rates are even lower than the US. This also suggests that government debt, not the dollar per se, is the negative-beta security. 

I don't want to pretend this is a solved question. If you want an indication of just how right Haeyek was, the fact that economists don't have a solid answer to why this most important of all prices has moved slowly down for 40 years it is. On the other hand, solid quantitative exploration of the options still has plenty of room to go, if you're writing a PhD thesis. 

2. Low rates, r<g, and government finances

What do these low rates mean for government finances? The debt/GDP ratio B/Y grows at the difference between interest rate and growth rate, less any real primary surpluses.\[ \frac{d}{dt} \left(\frac{B}{Y} \right) = (r-g) \left(\frac{B}{Y} \right) - \frac{s}{Y}.\]

This equation, and the possibility that r<g, leads to some tantalizing possibilities.

First, if r<g, then the government can run a steady primary deficit, s less than zero, forever, and the debt/GDP ratio will not change.

Second, if r<g, the government can run a big one-time fiscal expansion, borrowing a lot of money, and then simply grow out of it without running any surpluses. With s=0, the debt/GDP ratio will revert all on its own at rate r-g. In that sense the fiscal expansion does not have to be repaid with later surpluses!

The latter is not a money machine, meaning nobody ever has to work or pay taxes again. It only works as far as the opportunity scales, if borrowing a ton of money and spending it does not drive up r or drive down g. The marginal r is higher than the average r. At some point we all recognize that more borrowing must drive up r, by a variety of mechanisms. But that point may be far above today’s debt.

And we still have to pay taxes! Zero surplus means zero surplus, not deficits forever. After the one-time expansion, future spending is fully paid with future taxes.

These are tantalizing possibilities and technically very interesting. If you have not done so, you should immediately read Olivier Blanchard’s brilliant AEA presidential address which analyzes these issues. Written just before the US embarked on a $5 Trillion borrowing binge, with larger fiscal plans on the table, I believe Blanchard’s fiscal policy address will be as influential in our age as Milton Friedman’s 1968 monetary policy address was in his. Almost all our current and projected borrowing is going to transfers -- writing checks to people and businesses -- and I am curious to hear is view of that fact. And if you read his last section, you will see a suggestion of how it could all go wrong, which I repeat much more loudly later today. 

We do not diagree on analysis. However, I put different weight on different possibilities.  My bottom line:  though the r<g possibility is tantalizing and technically fun, I argue that it is quantitatively irrelevant to the fiscal issues facing the US and the eurozone today.

Figure 5. Deficits. Source: CBO 2020 Long-Run Budget Outlook

Figure 5 presents projected deficits from the latest CBO long-term budget outlook.

An r-g equal to 1% means that, at 100% debt/GDP, the US can run 1% deficit to GDP forever. That’s nice. But the US has been running 5% deficit to GDP in good times, 10% in bad times, and 20% in this crisis. (Figure 6 is clearer about the total increase in debt to the 2008 and 2020 recessions.)  The CBO forecast starts close to 5% after recovery, but then grows unboundedly  as unfunded entitlements kick in. And this forecast is before one adds big new spending programs — green energy subsidies, medicare for all,  universal basic income, infrastructure, and so on. And this forecast does not count the 20% that each decades’ once-in-a-century crisis seems to engender. And this forecast presumes GDP continues to grow at an anemic but positive pace of 1.6% per year. Lower makes it all worse.  

The chance to have 1% debt to GDP deficit forever is simply couch change compared to these numbers. R greater or less than g by one percentage point is truly irrelevant to the fiscal challenge at hand.

Figure 6. Debt to GDP ratio

Figure 6 presents the CBO debt forecast. Again, this forecast is before the contemplated “one time” expansion to spend on worthy causes (mostly transfers), and does not include 25% in the next crises. There will be more crises, you know. I indicated a line that suggests a path extrapolating from the last two crises.

This is not the backdrop — steady debt/GDP, zero primary surplus or deficit — on which one contemplates a one-time expansion which we grow out of with continued zero primary surpluses.

r<g of 1% or so does not justify exponentially growing debt/GDP! That is the fiscal challenge today.

Growing out of debt also takes an awfully long time. Table 1 calculates the path of debt if the US borrows up to 150% debt/GDP and 200% debt/GDP, and then “grows out” of the debt with zero surpluses. As you can see it takes over 100 years to get back to normal values, 50% debt/GDP ratio.

If you want to bring debt down faster, what do you do? Run surpluses! In that sense, though the technical issues right around r just above and r just below g — transversality conditions, limits, and so forth — are fascinating, that question does not make any difference to our fiscal issues. At r-g of negative one basis point the opportunity to grow out of debt in 1000 years is simply of no practical importance.

And r-g of negative one percent is of almost no practical importance to  current fiscal questions. Deficits of 5, 10 and occasionally 20% of GDP will have to be repaid by subsequent surpluses, sooner or later, more or less painfully. An extra 1% of fiscal space is nice, but does not fundamentally change our fiscal challenges.

3. The iceberg ahead.

So how will r rise, and what does that mean for government finances?

My first mechanism, that interest rates are low because growth is low, turns around if we return to robust, innovation-driven supply side growth. That’s the only kind that lasts 20 or 50 years. Forget stimulus. That growth needs the techno-optimists to be right, and the growth-is-over crows to be wrong. That growth needs the regulation-and-protection-is-strangling-growth crowd to be right, and our governments to finally get around to structural reform. If as g grows r grows more, reversing the path we came down, that fact will put some strain on government finances. But that strain will be easy to accommodate in an economy growing 4% or more. We should have such problems. And higher growth need not mean higher government bond returns, through a variety of mechanisms.

My second mechanism, negative beta, disappears when inflation expectations become a bit unglued, or nominal bonds to stop being safe havens in recessions. That is a more tenuous phenomenon. It could change quickly, as it did in 1972 an again in 1980. I think of this possibility as an element of the larger danger.

The larger danger is a doom loop, or sovereign debt crisis, a lot more r with a lot less g, all of a sudden.

Suppose we have run our “one time” final expansion and are at 200% debt to GDP ratio. The next big crisis hits — a war, pandemic, financial mess, or all three. The US wants to borrow another 20% of GDP, and roll over the outstanding debt. Markets get worried and demand, say, 5% rates. That means 10% of GDP more primary deficit, or 10% of GDP more borrowing, 30% of GDP, plus the roll-over. Moreover, the consequent write-down of asset values leads inevitably to another big Wall Street bailout and asset purchases, all with more borrowed money.  Markets get more worried, and demand 10% rates. And so on.  When this spirals out of control, you have a debt crisis. It must lead to sharp inflation, or default. And there is no Germany to bail us out, no Mario Draghi to “do what it takes.”

Default is not impossible, just because the US and eurozone print our own currencies. Imagine my scenario and add policy chaos. The US is just getting going on political chaos. Bond markets are demanding 5% or 10%. Are the US Congress and Administration, really going to put interest payments to the Chinese central bank, “the rich,” and “Wall Street” ahead of writing checks to needy Americans? Don’t bet on it. It won’t be a simple default. It will be a complex restructuring, as it always is. T bills may get forcibly rolled over to low-coupon long term debt for example.

But this would be a financial and economic catastrophe. “Riskless” US debt and the US ability to bail out any financial institution in trouble are at the heart of our current financial system. And discussions of such a haircut would lead to an immense run and inflation, provoking the event.

(This is not a novel, or crazy scenario. Read "Greater risk of a financial crisis" in the CBO long-term budget outlook.) 

No, financial markets do not see this coming. But financial markets never see it coming. Look at Figure 1 again. Interest rates did not force the swings in 1970s inflation, nor the end of inflation in the 1980s. 

As Olivier pointed out, there is no magic debt/GDP ratio dividing safe from dangerous. Debt crises have happened with 50% debt/GDP. Japan is trundling along at 250% of GDP. A crisis blends current debt with a look at the future. At the end of WWII, the US had more than 100% debt/GDP ratio. But the war was over, we headed into an era of unparalleled supply-side growth, fiscal policy ran steady primary surpluses, politics was much more united,  there was considerable financial repression, much of the debt was long-term, and we still had two bouts of inflation. None of that applies now. Markets now must look not just at today's debt/GDP ratio but the looming entitlements crisis, out of control spending, sclerotic growth at best and political chaos.  

How should we avoid this? Well, again, there is nothing like unleashing faster productivity-led growth to solve all wounds. But growth is blocked as it has always been by politically important constituencies who make money from the old way of doing things. And no political movement in the US or Europe has any interest in growth-oriented structural reform at the moment.

At a minimum, our politicians should could again start spending as if they have to pay back borrowed money. They do. We do.

It would help enormously if our Treasuries funded their governments with long-term debt, ideally perpetuities. Long-term financing makes my doom loop debt crisis much less likely, and will give our political systems some space for well-structured fiscal reforms when the end comes. (The long-term debt should not be held, leveraged, by too big to fail banks however!) 

And finally, don’t count on r one percent less than g to bail us out. It needs zero surpluses, which represent an immense fiscal contraction already, and it needs markets to be patient for centuries, through all the upheavals to come.

4. Last words

Why are long term rates low? It’s a good question. My simple graphs and equations are just a suggestion, not an answer by themselves. Real understanding needs real models and quantitative evaluation. There is a lot of work on this topic, which I do not survey here. But too much of this pursuit, in my opinion, searches for novel models with sexy frictions, ignoring the sort of basic neoclassical growth theory and simple finance that should be the starting point for understanding a 40 year trend.

We need a real, solid, simple, and communicable understanding. Only real understanding will let us know how long it will last.

The low interest rate trend has been going on for a long time. But we should not count on trends without solid economic foundations. Remember Irving Fisher, who said in 1929, “Stocks are at a permanently higher plateau.” Unless we really understand why, “r is on a permanently low trend” has a similar ring to it.

Updates: Olivier Blanchard's slides here. 

A longer term trend, from Radek Stefanski and Alex Trew


*Yes, a better equation is \[r = \delta + \gamma(g-n) - \gamma(\gamma-1)\sigma^2/2\] where n is population growth and \(\sigma\) is consumption volatility. The difference is not important for issues in this post. You need n to get r<g, but changes in n are not driving the decline in r. Also, in many models the slope of individual consumption is not the same as aggregate consumption. For example, in an OLG model without population growth, individual consumption slopes up but aggregate consumption may not grow at all. But we're talking about 10-20 year horizons, not 80 year horizons, and this does not seem to me a force that changed dramatically in the last decades, accounting for the steady downward trend. As above, however, this is the beginning of an exploration, not the end. Even these alternatives are basic econ 101 sorts of stories we should investigate first. Thanks to Olivier for a nice discussion on the latter points. 


  1. John,

    Where is risk tolerance or equity / stocks in your equations?

    "My first mechanism, that interest rates are low because growth is low, turns around if we return to robust, innovation-driven supply side growth."

    Or interest rates are low because risk tolerance is low. Improve opportunities for investors to take risk and interest rates will rise AND total debt will fall.

    Or growth is low because interest rates are low. Does the dog wag the tail or does the tail wag the dog?

  2. "In the recessions since 1980, and especially recently, inflation went down, bond prices went up, and the dollar went up, while private securities collapsed in value"---JC

    In recession-year 2020, equities indices in Germany, India and the US hit all-time zeniths, and 30-year highs in Japan. (I don't know why.)

    As an amateur, I wonder what it means when a national government issues sovereign debt that the national central bank buys back. The mobius strip of debt seems to defy conventional analysis.

    Under QE, the private-sector bondholders have been paid off. Should US national debt outstanding calculations subtract that portion held by the central bank?

    Sure, there is IOER, but that is volitional and probably just a sop to the commercial-banking industry. Would banks go bananas and lend more if there were no interest on excess reserves? Banks have fiduciary obligations to shareholders to lend prudently.

    I would not so easily dismiss the "savings glut" or "capital gluts" idea. Large portions of the global economy are run by regimes which engage in policies to repress labor share of income, including mainland China, much of the Far East and Germany.

    As a practical matter, it seems that every venture capitalist, hedge fund manager, real estate investment fund or trust and so on has capital to burn.

    If there are artificial gluts of capital, should perhaps return on capital be negative?

    1. Ben,

      "In recession-year 2020, equities indices in Germany, India and the US hit all-time zeniths, and 30-year highs in Japan. (I don't know why.)"

      A lot of equity indices are price weighted, and so that doesn't tell you the whole story. Better to look at market capitalization (total shares x price per share) to give an indication of how much capital is being directed towards stock investment.

    2. Ben,

      The St. Louis Fred website has started to include a total debt / total equity measure for the U. S. The data don't go all the way back to the 1960's, but you should still see the trend:

      John advocates mandating that banks (more regulation) must fund investments through either the sale of shares (publicly traded equity) or through retained earnings (aka The Chicago Plan).

      I advocate that the U. S. Treasury department should sell equity claims against the federal government's tax revenue (no additional regulation or mandate required).

      Both plans seek to do the same thing - inject more equity into the economic system, and by extension lift the natural rate of interest and economic growth rate.

      The difference is government equity sold by the U. S. Treasury is risk by choice (Liberatarian). John's Chicago Plan is risk by government mandate (Socialist).

    3. As much as I enjoy being called a socialist, I must point out that my proposals go pretty short of "mandate." For example, a pigouvian tax on short-term debt (rather than subsidy via deductibility and favorable treatment as an asset), or a slow ramp up of existing regulation based on market value of equity/face value of debt are, I hope, a little closer to rule-of-law, acknowledges-exeternality practical libertarianism than government-owns-means-of-production socialism!

    4. I forgot to add, or simply getting out of the way (my favorite always) and allowing narrow banks to operate. (That means you, Fed).

    5. John,

      If I understand your (the Chicago Plan) proposal, banks MUST fund investment through either the sale of equity shares or through retained earnings. That sure sounds like a mandate to me.

      Whereas if the U. S. Treasury sells equity, then there is no mandate - if you want to buy what the Treasury is selling, fine, if not, that's fine too.

    6. Also, long term debt eventually becomes short term debt. The plan is to tax long term debt once it becomes short term (via a Pigouvian tax)? And what determines how long short term debt is and long term debt is - another regulation?

    7. If I was calling anyone a socialist, I was calling the authors of the Chicago Plan a bunch of socialists. You are simply regurgitating their plan (that was ultimately rejected). So if you took offense, then my apologies. My objection to equity financed banking (by mandate) is directed toward the original authors.

    8. The political limitations are this:

      1. For a pigouvian tax on short term debt (presuming that you can even define what is short term and what is long term debt), you need a voting majority in both the U. S. House and Senate to approve such a tax.

      2. For a government regulation that says that a bank(presuming that you can even define what is and is not a bank) MUST (yes you are asking for a mandate) fund investments with either retained earnings or the sale of equity shares, you need a voting majority in both the U. S. House and Senate for approval of such a regulation.

      Meanwhile, for the U. S. Treasury to sell equity there are no political hurdles to overcome, other than perhaps convincing the sitting President that it is a worthwhile endeavor - Janet Yellen are you listening?

    9. Ben,

      "Large portions of the global economy are run by regimes which engage in policies to repress labor share of income, including mainland China, much of the Far East and Germany."

      Those same regimes restrict capital investment by individuals in the global economy.

    10. FRestly:

      I see from the FRED chart you provided that debt to equity is rising.

      Perhaps the US should fund deficits through money-financed fiscal programs, rather than debt issuance.

      Also, if a government buys back debt through quantitative easing, is that truly debt anymore?

      I do not advocate moderate inflation as a solution to the national debt problem. However, 10 years of 7% inflation would cut the national debt in half, roughly speaking. Many economies have flourished while undergoing moderate inflation.

      Some people call themselves supply-side liberals. Perhaps I should be called a demand-side conservative.

      I think the federal government should keep demand high nd rising while reducing the size of the federal governmen dramatically. Think tax cuts.

      For the US free market system to work, we must always keep property markets loose and labor markets tight. Make those your iron principles, and reason forward from there.

    11. Ben,

      "Perhaps the US should fund deficits through money-financed fiscal programs, rather than debt issuance."

      That's the MMT position - why borrow money when government is capable and legally permitted to print the stuff.

      It comes down to whether you think money should be a risk asset (via inflation) and that risk should be forced down the throat of everyone.

      My position (Liberatarian) is why not have Treasury sell equity that is separate and distinct from money and let people who want to take risk, do so.

      We don't force people to invest in the publicly traded equity markets, why should we force people to accept equity risk in the money that they use.

    12. Ben,

      "Some people call themselves supply-side liberals. Perhaps I should be called a demand-side conservative."

      Above all I am an individualist, not a collectivist meaning that I believe that each person is ultimately responsible for their own outcome. I am a progressive, not a liberal meaning I believe that government should try to equalize opportunities, not equalize outcomes.

      I originally started writing on this website because I thought that these were shared principles among Libertarians.

      Government bonds are a collective form of finance, taxpayers as a whole make the payments on that debt. Government equity would be an individualistic form of finance, each taxpayer would ultimately have a say in their own returns on investment.

      And so, I would think that other Libertarians would jump at the idea of individualistic government finance. Instead, all I get is the Republican line - Medicare, Medicaid, Social Security and all of the other "entitlement programs" are driving the run up in debt (not their unpaid for wars, bank bailouts, and tax breaks).

      What Republicans (and apparently Libertarians) seem to forget is that interest paying government bonds ARE A FREAKING ENTITLEMENT PROGRAM.

  3. "And this forecast does not count the 20% that each decades’ once-in-a-century crisis seems to engender."

    This great line is now a common refrain in budget analyses. When will budget outlooks catch up to the fact that these jokes convey reality? Government interventions are increasing, at an increasing pace.

  4. Really great post! I want to focus on your basic point that rather than running around dreaming up all sorts of frictions and other overcomplicated models to explain what we see in the data, we should go back to basics and look for more fundamental (and simple) answers. Long live Ockham's Razor!

    One other point is that your assessment of the quantitative significance of r<g is also dead on and an excellent example of how we need to move beyond qualitative talking points and confront the data quantitatively.

    I wish more economists would heed your first suggestion and I wish more reporters and economic prognosticators would heed your second suggestion!

  5. We agree on the value of starting with a simple picture. If you are doing empirical work, a linear model estimated by OLS is often a good start. Sometimes, you learn that qualitatively plausible stories have little quantitative impact on your estimates when you take them on board by doing something fancy.

    The same is true in theory: starting out with a "theory of everything" is the surest way to loose the forest in the trees.

    However, I'd say that going for complicated models here would be more than an aesthetic concern. The entire problem requires us to tie asset prices to macroeconomic factors and this is one place where our standard models do not perform particularly well, even in a partial equilibrium setting, let alone in the middle of a general equilibrium model.

    Of course, someone could always try to fit a basic model and see where it fails to get a better sense of what sort of complications might be relevant. We like fancy, just not when it is "gratuitous."

  6. Our "debt" crisis is really an unfunded liability crisis. Almost all future growth in debt to gdp is due to deficits in the Social Security and Medicare trust funds.
    To fix Social Security, I'd suggest the following:
    -Eliminate the tax cap, provide a credit for benefits
    -Index the retirement age to life expectancy
    -Switch COLAs to Chained CPI
    -Allow the trust fund to be invested in the stock market

    For Medicare, I hope Eli Lilly's Alzheimer's Drug passes its Phase 3 trials

  7. Also, treasury bonds linked to growth in nominal GDP would be helpful. It would reduce r:g fluctuation

    1. Kernals,

      Robert Shiller already suggested this - they are called Trills.


      Shiller proposes that Trills pay a dividend commensurate with the GDP growth rate. What Bob doesn't address is contractions in GDP. For r:g fluctuations you would need clawbacks (negative dividends) during periods of negative GDP growth.

      At this point you should realize that GDP linked securities are a pretty bad idea because of the perverse incentives they create.

      Why shouldn't every worker and every company take market short positions in GDP securities and then close their doors / quit their jobs?

    2. I think the principal rather than the coupon should be indexed to GDP. And your idea could be done today if all businesses took short positions in the stock market and then closed their doors, but word about this sort of conspiracy would leak out and market prices would adjust accordingly

    3. Kernals,

      "And your idea could be done today if all businesses took short positions in the stock market and then closed their doors..."

      Except each business has an obligation to its shareholders / stakeholders and there is competition between businesses. Each business would need to weigh the risk of losing market share to another competing company in closing it's doors.

      No business has an obligation toward holders of GDP linked securities and there is no competitor to GDP.

    4. Kernals,

      Think of government as one giant insurance company. Government should either pay larger claims on it's insurance policies when times are bad or offer a larger discount on it's premiums when times are bad.

      And so, any government equity should be linked to the output gap (difference between actual and possible GDP).

      We can argue whether measures of possible / potential GDP are accurate, but government equity (as an insurance policy) only makes sense when either it's premiums or it's payments operate in a countercyclical fashion.

  8. Thank you for a very interesting post! Perhaps you could make another post about your thoughts on the marginal product of capital decline and talk about your second and third possible explanations: "Second, we are simply running out of ideas, growth is over, is lower. I’m still a techno-optimist. Third, ever-growing marginal tax rates, protections, and regulations are hamstringing the innovation and ruthless competition that it takes to get new ideas into practice." Back in 2000 I read Robert Gordon’s skepticism about innovation and growth, and in 2012 he still seems skeptical! I’m skeptical increasing information efficiency fuels continued large increases in growth. I’d like to be an optimist like you (maybe we say, figure out nuclear fusion), but I’d appreciate your thoughts on the “low growth” or “over-regulation and taxes” explanations.

    1. I don't want to get too off topic or condense too much to a short reply. Take a look at the "growth" tag for lots of blog posts on this.

  9. John, illuminating post! Question: Re your CAPM β. Beta = Covariance(stock return, market return)/Variance of market return. What are you covarying bond returns with? It seems that while betas can be negative, they can also be significantly less than 1 and remain positive, indicating the public's aversion to market risk by lending (buying bonds). As flawed as CAPM is, it demonstrates, reasonably well, the level of time varying risk investors take.

    1. David, thanks as this is an important qualification. I was trying to be short. I don't think CAPM beta is the important one here, as the relevant investors don't hold the market portfolio, have a lot of outside income, and are worried about crash risk. I have a nebulous sort of recession-disaster-financial crisis risk beta in mind. Yet another paper that needs to be written...

  10. Sebastian HillenbrandJanuary 13, 2021 at 4:24 AM

    Thanks a lot for this very inspiring blog post!

    Your preferred explanation for lower growth is increased protection, regulation and taxes. While I have nothing to disagree on the former two, I was wondering about the latter:

    The average tax rate paid by corporations declined over the same during which GDP growth declined, and is at historically low levels according to:
    Moreover, I guess there is an increased trend that multinationals avoid paying taxes by shifting their profits to tax haven countries. Now, the average tax rate is not equal to marginal tax rate, but this might nevertheless suggest that we could raise taxes (potentially by just avoiding tax “evasion”) without suffering too much of a loss in productivity?

    On the same token, didn’t the large budget deficits also come from lowering the corporate tax rate in the US? Raising the tax revenues collected from large corporations might be one simple way to reverse the trend in primary deficits.

    1. What counts for economics is the marginal tax rate, the disincentives, not the overall tax rate, how much you pay. (Incentive economics, not Keynesian economics which is all bout money not incentives.) We have a system that doesn't collect much money but has a lot of disincentives. Also don't look at federal income or corporate in isolation. You have to add up federal state local estate excise corporate etc. Yes, not so much illegal evasion but perfectly legal evasion, "loopholes" is a big reason we have high marginal rates and not much collection. The stimulus has a special provision for race horse deductions. Many local governments charge high taxes then give special carve outs for friends. Low marginal rate, large base, simple, is the key to raising revenue without distortions. The recent tax changes mostly lowered revenue from the individual side not the corporate side. See mulligan for extensive analysis

    2. And Pigouvian taxes?

      Out of one side of the mouth comes what counts for economics is the marginal tax rate....low marginal rate, large base, simple, is the key to raising revenue without distortions.

      Out of the other side comes we should assess Pigouvian taxes on short term debt, greenhouse gas emissions, or whatever other flavor of economic activity you might despise this week.

      You mention the carve outs for friends (which you seem to despise). You fail to mention the hammer to the toes Pigouvian penalties (which you seem to endorse).

  11. JC: "First, if r (s/Y)ₒ leads to a decreasing debt:GDP ratio.

    The political processes that generate (s/Y) cannot be relied upon to achieve a constant (s/Y)ₒ, let alone consider attainment of that goal to be the optimal policy. The quoted sentence can only be true for a very restrictive case.

    1. Old Eagle Eye,

      TR = Tax Revenue
      EX = Government Expenditures
      s = TR - EX
      EQ = Government Equity

      Change the equation to:

      d/dt(B/Y) = (r - g) * (B - Y) - (TR - EX)/Y - EQ/Y

      Now imagine that equity sales (by the U. S. Treasury) are determined through an apolitical process. Finally imagine that equity sold by Treasury is:

      1. Non-transferrable - when the owner of the equity dies, the government's liability with that equity dies (see Social Security as example of non-transferrable government liability)

      2. Fixed term - it goes without saying that to achieve broad appeal (and make any significant dent in debt / GDP), Treasury would need to sell fixed term securities rather than perpetual (very few of us are going to live forever)

      3. Zero coupon - This has the political advantage of not requiring Congressional authorization for cash payment of dividends / interest payments.

      4. Only redeemable against a future tax liability.

      Equity in this fashion has the advantage that returns are commensurate with future economic activity (similar to GDP linked bonds, except there is no government spending in the form of returns on investment). During a recession, returns on equity fall (irrespective of monetary policy stance).

    2. FRestly, your equation is incorrect in the first term on the RHS of the equation. Your term EQ/Y has the characteristics of debt (B) and would be incorporated in the term d(B/Y)/dt, i.e., EQ/Y would not appear on the RHS of the equals sign.

      For r < g, (r, and g, constants) and s < 0, there is only one value of s for which d(B/Y)/dt = 0 identically, and that is s = (r - g)B. Let s* = (r - g)B. Then d(B/Y)/dt = s*/Y - s/Y. If s > s*, then d(B/Y)/dt is less than zero. If s < s*, then d(B/Y)/dt is greater than zero. The condition, s = s*, is restrictive because it is a single value which the federal political processes would be unlikely to attain consistently over any realistic length of time.

    3. Old Eagle Eye,

      See U. S. Constitution Article 1, Section 8, Clause 2:
      The Congress shall have Power To ... borrow Money on the credit of the United States...

      In lay terms, to borrow means to transfer an asset with the expectation of that asset being returned. If I borrow a car from someone, that person expects me to return the car (not a pony) that I borrowed. When a Congress borrows money, the expectation is that the lender will receive money back.

      The equity that I have described does not constitute government borrowing since money is used to purchase the equity, but no monetary compensation is given once the equity reaches maturity. Instead the equity is used to fulfill a tax liability at maturity.

    4. If I give you $25,000 today and two weeks, three months, five years from now, you give me a car, you have not borrowed money from me. Instead, we have engaged in a trade (money now for a car in the future).

      If I give the federal government $25,000 today and two weeks, three months, five years from now, the federal government allows the $25,000 to offset $30,000 of tax liability, the federal government has not borrowed money from me. Instead, the federal government and I have engaged in a trade (money now for a reduced tax liability in the future).

  12. This comment has been removed by the author.

    1. Old Eagle Eye,

      "Lambda is the market price of risk. Difficulties because the market rate of return is for all assets, not just those assets traded on the stock markets, and Lambda is not directly observable."

      Also, not all risk assets even have a rate of return determined by markets. See Social Security or any other type of insurance.

  13. Thanks for a great post that raises the question of why growth is declining. One of the areas that you did not dwell on and deserves attention is the impact of changing demographics on growth. Perhaps the rise of technology including robots will off set a general trend. I hope so, but there is no guarantee. This podcast contains a discussion of the impact of changing population structure on growth.
    The authors use a measure they call "the Dependency Ratio". This ration is simply (people under 20 plus people over 65) / (people between those ages). I have calculated the ratio based on US census data I had available for the periods below.
    1969 0.75
    1979 0.92
    1989 0.72
    1999 0.71
    2009 0.71
    I think if you plotted this data, it would look a lot like your Figure 1.
    The podcast also discusses the difference in the likely change in the dependency ratio itself. Proportionately more old in the dependents group.

  14. In your explanation of negative beta mechanism, you implicitly assume that gov bonds maturities (durations) are longer than investors horizon. But if it were the other way around, wouldn't we have the opposite result? (i.e. recessions with interest rate drops would harm investors due to the reinvestment risk.)

  15. Anyone else having an issue downloading the Blanchard slides linked to above?

  16. Thought-provoking post, but I wonder about "... declining growth is a plausible cake ..."
    I would think it a sad as well as a plausible cake, unless it be a typo.

  17. Prof. John Cochrane, thanks a lot for the very insightful discussion and for the transcript of the main points of the video here in the blog.

    I have tried to download Prof. Blanchard slides from the link you provided but it directs to PIIE sharepoint website - which I do not have access to.

    Would it be possible to share a public link to the slides?

  18. "Real understanding needs real models and quantitative evaluation. "

    Not for something like this. Almost certainly the real answer will not be found this way. Underneath this is something requires a understanding of the long run dynamics of capitalism which probably covers everything from geopolitics to (real) psychology. You need people going down to archives looking at business reports of borrowers, lenders, and much, much, more to get to the what - and then the why. The explanation will not be unquantiifiable in any truly meaningful way but the evidence totally verifiable. A good historian and writer will then be able to put a lot of conflicting and seemingly contradictory information into a compelling narrative - seemlessly like the motives that come together into an overall spine that yo see in a Bach fugue. It's a hell of a lot of work, but you will finally get your answer.

    This is work for an historian.

    Models, rational expectations ones and all the others, will only continue to distract - with, as you can see, very costly political and other consequences.

    There are people who can do this, and it is a real skill that has to be learned; but the people who can do this no longer work in Anglo-Saxon economics departments.

  19. Many thanks for offering your interesting thoughts on this. I am impressed and puzzled when you seem to justify low growth by "growth is blocked as it has always been by politically important constituencies who make money from the old way of doing things. And no political movement in the US or Europe has any interest in growth-oriented structural reform at the moment." I thought politicians like growth and that is why they borrow, it helps to get consensus, normally voters confirm government if they feel they are getting better off. what you write seems to me a bit conpiracist and I wonder if you could provide evidence. thanks and best regards

    1. Politicians like growth, but not what it takes to produce growth. Borrowing money and spreading it around does not produce long term growth. For a microcosm, see uber vs. taxis. Uber gives growth -- better, cheaper taxi services, better employment opportunities for lots of people. But they displace the existing and well connected taxi companies and labor unions who have an interest in restricting supply and keeping prices up. And look which side politicians are on.

    2. Many thanks for your very interesting clarification: I guess uber and the sharing economy are the kind of things L. Zingales had in mind when in the wonderful "A capitalism for the people" he stressed the trade off between growth and equity. Or Mario Draghi had in mind in 2012 when in an interview to the German newspaper "The Bild" he said "The old European welfare state model is in fact dead". On the other hand, I googled "the economic and social consequences of uber" and found file IPOL_BRI(2015)563398_EN.pdf: "To shed some light on these issues, the Committee on Transport and Tourism of the European Parliament (EP) has requested an internal briefing to provide a first analysis at the social, economic and legal aspects of Uber and similar Transportation Network Companies (TNCs)." I mean, those consequences might be a bit multifaced and complex; my immediate reaction would be that uber and similars lead to more efficiency, not necessarily growth lasting 20 or 30 years. But perhaps digitalisation (or internet) is the innovation and uber is one application of it. Anyway, perhaps this takes us too far. I was in your 330 class in the fall of 1987, very nice talking to you again. I got interested not in being in a crowd, rather in trying to see what is good in each crowd, to pursue the fairest word; I like the first chapter of K. Basu "Beyond the invisible hand" or Tirole's "Economics of the common good". So I like people who in good faith and intellectual honesty pursue efficiency and growth, although I believe other things matter too and especially if we can achieve only limited growth, we should care about other things too. I mean that I am not sure we can forecast or determine the curve of growth over time: I have in mind Figure 2 "Economic growth in the long run" in the paper by C. Jones "The facts of economic growth", and when I look at it I wonder how people can claim simply that it must or can continue like that forever (a part from the equivalence with the curve about envirnmental damage). It seems to me there is randomness with technological progress, which seems to lead lasting, large growth. Anyway, great you have this blog. Probably someone has also deepened the analysis of the consequences of uber. thanks and best regards


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