Twin debt equilibria, and waiting for the sunspot

Paul Krugman, responding to Simon Wren-Lewis, wants a model to better articulate Ken Rogoff's fears of debt and deficits (pdf). Fair enough request. I can't give Paul a fully worked-out formal model, but I think I can give him a sketch of what such a model would look like.

(Update: If Paul likes, he could maybe simply change his own model by drawing two IS curves instead of just one. There's a "low" IS curve, when people expect the economy to stay at the ZLB equilibrium in future; and a "high" IS curve, when people expect the economy to stay at the normal equilibrium in future. And a higher stock of government bonds shifts both IS curves to the right. Update 2: Hmmm. I rather like that way of looking at it. Because desired saving and investment will be qualitatively different when the central bank is doing sensible monetary policy in the normal equilibrium than when the central bank either cannot or will not do sensible monetary policy and the economy is in the ZLB equilibrium.)

It's a model with two equilibria: a normal equilibrium; and a ZLB equilibrium. A sunspot (any intrinsically irrelevant event that causes a self-fulfilling change in expectations) can flip the economy from one equilibrium to the other.

That seems plausible to me. If people expect low aggregate demand in the near future, current aggregate demand (consumption and investment demand) will be low too. (Any New Keynesian model with an Euler-IS curve has that property.)

Set to one side the question of whether the ZLB really is a binding constraint on monetary policy that prevents the central bank credibly announcing a time-path for future monetary policy that enables the economy to escape the ZLB.

Assume the demand for government bonds (relative to GDP) is "high" in the ZLB equilibrium, and "low" in the normal equilibrium.

That too seems plausible to me. If there's a recession, private investment opportunities won't be as attractive, because people fear the recession may continue, so there won't be sufficient future demand for the extra output created by the investment. Government bonds look good in comparison, even at low or negative real interest rates.

In the normal equilibrium, the quantity of government bonds demanded depends on normal things like the real interest rate on those bonds and the expected probability of default (whether through unforeseen inflation or through simple non-payment of obligations). So in the normal equilibrium, a higher stock of debt, other things equal, means a higher equilibrium interest rate on that debt. And a higher interest rate implies a higher primary surplus needed to service that debt and prevent the debt/GDP ratio rising. And running a primary surplus is something governments don't like to do, and so the higher the primary surplus the higher the risk of default. And the higher the risk of default, the higher the rate of interest would need to be to persuade people to hold the debt. Which creates a positive feedback loop, because it means a higher primary surplus...which might create a crisis, if the positive feedback effect is strong enough.

This is a model where a higher level of government debt has real effects in the normal equilibrium. It is a model where Ricardian Equivalence is false. An overlapping-generations model would have that property.

Now let's close the loop. In the ZLB equilibrium, the demand for government bonds is high, which means the demand for money will be high too, which means the demand for goods will be low, which means the economy is stuck at the ZLB. In the normal equilibrium, the demand for bonds will be low, which means the demand for money will be low too, which means the demand for goods will be high, which means the economy will be in a normal equilibrium away from the ZLB. In other words, the fact that the demand for bonds will be high in the ZLB equilibrium and low in the normal equilibrium is precisely what creates those two equilibria.

Suppose the economy is initially in the ZLB equilibrium. Suppose the government is running a deficit, so the level of debt is rising. Suppose no sunspot comes along. The demand for debt is high in the ZLB equilibrium, but it's not infinite. Eventually, when the level of debt gets high enough, the ZLB equilibrium disappears, leaving  only the normal equilibrium. But the transition to the normal equilibrium is not smooth and continuous. The demand for debt suddenly jumps down, and interest rates jump up. (And no, the central bank can't push them back down again, because the normal equilibrium is a normal equilibrium, where the central bank can't lower interest rates while keeping inflation on target at the same time.)

The bigger the debt when the economy does return to the normal equilibrium, the bigger the jump in interest rates when it does return to the normal equilibrium. Will the jump in interest rates be big enough to cause a solvency crisis? I don't know. It depends.

Whether a solvency crisis, and the enforced fiscal tightening, would cause a deficiency of aggregate demand and a recession, is another question. Presumably it wouldn't, if monetary policy could offset any fiscal tightening. Which presumably it could, in a normal equilibrium. But the fiscal tightening and solvency crisis could still be very ugly. Deficiencies of aggregate demand matter, but they aren't the only things that matter.

Of course, if people foresee that the debt will soon get high enough to eliminate the ZLB equilibrium and force a return to the normal equilibrium, the economy might jump back to normal before it is forced to jump. And if so, it jumps at a lower level of debt than if people hadn't foreseen it, so the jump in interest rates would be smaller. Which would be a good thing all round.

What to do?

Keeping the deficit and debt low, and just waiting for a sunspot to return the economy to normal, is not obviously the wrong policy. Nor is it obviously the right policy. It probably depends on the frequency of sunspots, and on lots of things.

Personally I would prefer creating a sunspot, rather than waiting for one to turn up spontaneously. That's what central banks are for. But now I'm going off-topic.

Is some sort of model like this at the back of Ken Rogoff's mind? I don't know.

Comments

[Ralph Musgrave]

Why on Earth do we have to guess what’s going on “at the back of Ken Rogoff’s mind”? If a so called professor of economics at Harvard can’t adequately spell out his ideas himself, that suggests there is nothing much going in his “mind”.

Rogoff regularly uses scare tactics when discussing national debts. He compares monetarily sovereign countries with Greece, which is nonsensical comparison. He witters on about government spending in ten or fifteen years time: irrelevant. He uses emotive phrases like “debt overhang”. He doesn’t seem to understand that monetarily sovereign countries can print money as well as borrow it.

As Krugman put it, “So where does Ken’s call for short-run austerity come from? As best I can tell, it comes from a generalized sense that debt is dangerous…”

[Nick Rowe]

Ralph: we always have to spell out what's at the back of our own minds, as well as other people's minds. It's not easy building models.

Yes, countries with their own central bank can print money as well as print bonds. But there's a limit to the demand for money, just as there's a limit to the demand for bonds. People will always *accept* new money, of course, but they will also increase nominal spending, unless desired velocity falls at the same time, and in the normal equilibrium nominal spending is already where the central bank wants it to be for the inflation target. So that won't work, as I said in my post.

And even if the central bank decides to let inflation rise above target, there's still a limit to seigniorage revenues.

[Min]

"It's a model with two equilibria: a normal equilibrium; and a ZLB equilibrium. A sunspot (any intrinsically irrelevant event that causes a self-fulfilling change in expectations) can flip the economy from one equilibrium to the other."

One way of escaping from a suboptimal equilibrium is to change the payoffs. Do you think that the gov't cannot do that?

[Philippe]

"countries with their own central bank can print money as well as print bonds"

does a country need a central bank to be able to print money?

[Nick Rowe]

Min: as I said in the post, one way to eliminate the ZLB equilibrium is to increase the stock of debt, and so shift the "low" IS curve to the right far enough so it intersects LRAS at a strictly positive nominal interest rate. Unfortunately, this also shift the "high" IS curve to the right too. Perhaps too far to the right to maintain solvency in the normal equilibrium.

There may be other ways.

[Nick Rowe]

Philippe: depends how you define "central bank".

[JR Hulls]

Your comment on two IS curves brings to mind Hal Varian's analysis of Kaldor's non-linear IS curves using catastrophe theory, studying the movements of short run equilibria as the long run variables evolve. The paper is discussed by Mark Thoma here, http://economistsview.typepad.com/economistsview/2009/11/catastrophe-theory-and-the-business-cycle.html with links to the original Varian paper. A very interesting and intellectually forthright paper.

[Kevin Donoghue]

A model where Ricardian Equivalence is false could easily lead to results opposite to those Ken Rogoff wants. The higher level of government debt presumably implies a higher level of net wealth, stimulating consumption. You get your higher interest rate in the "normal" equilibrium, but with a Sumnerian never-reason-from-a-price-change sting in the tail: the interest rate is higher because consumers feel better off. Of course you could argue that's bad, maybe it would be better if they felt poor and disposed to save more.

I don't think that's where Rogoff wants to go. Crafty chess player that he is, he won't be playing the OLG variation of the Rowe Gambit. My bet is he'll simply duck Krugman's challenge and offer snark rather than a model.

[dlr]

This is reminiscent of your Duke of Wellington post on Japan. This non-ricardian, twin equilibria without a monetary offset "sunspot" story seems like a good argument for using Fiscal Policy to borrow when at the ZLB to buy stocks and real estate and reverse when off the ZLB.

[Kenneth Duda]

Nick, you lose me when you assume a higher stock of debt means a higher risk of default. The central bank can always buy up all the bonds no matter how many there are. I don't see why a rational investor would care if US federal debt is 50%, 100%, or 200% of GDP. If all of that debt ends up owned by the federal reserve, the interest payments are also revenue on the federal balance sheet, i.e., it is no harder to afford a large debt than a small one as long as the central bank stands behind you. Thus, the whole notion that we are saddling ourselves with unaffordable interest payments appears utterly false. If we pay the interest to ourselves, it does not matter how big those payments are.

It looks to me like debt owed by a sovereign power denominated in its own currency is a mere accounting device. It is simply a measure of the total quantity of money that was introduced into the economy through fiscal policy (spending more than tax revenue) as opposed to lending (federal reserve buying securities). It has no impact in real terms whatsoever as far as I can see.

The link Rogoff and others have seen between high debt and low growth is probably causal the other way around. That is, rather than high debt causing low growth, it's low growth that causes high debt --- when growth slows due to an aggregate demand shortfall, debt tends to go up as fiscal mechanisms (safety net) counter private-sector contraction.

Kenneth Duda
Menlo Park, CA
kjd@duda.org

[Alex Godofsky]

@Kenneth

Nick, you lose me when you assume a higher stock of debt means a higher risk of default. The central bank can always buy up all the bonds no matter how many there are.

It can't do so and maintain its inflation target (which Nick points out explicityly). In the extreme case, it can't do so without causing the price level to go to infinity.

[Kenneth Duda]

I wrote:

> The central bank can always buy up all the bonds no matter how many there are.

Alex responded:

> It can't do so and maintain its inflation target (which Nick points out explicityly).
> In the extreme case, it can't do so without causing the price level to go to infinity.

Yes of course. I was pointing out that it could. I was not arguing that it should.
Please think through the cases more carefully. In what case is the Fed needed to
buy up all the bonds? In the case of investor loss of confidence in which panic
is causing interest rates to rise *above policy target*. If interest rates are above
target, then it makes perfect sense for the Fed to buy bonds to bring rates back
down to target. Doing so is not inflationary because interest rates are above
target by assumption. If buying bonds would cause inflation, that can only
happen if rates are below target. If rates are below target, then of course the
Fed should not buy bonds.

This all seems kind of obvious, so in pointing it out, I don't really know if
I'm addressing your objection, because your objection doesn't really make
sense to me. I said, "the Fed could do X." You said, "Hah! In circumstance
Y, doing X would be really bad. Gotcha!" My response is, "Huh? I never said
the Fed should do X in circumstance Y."

Alex, to get more at the heart of the matter, maybe you can answer for me: in
what actual scenario do you foresee a large federal debt causing an actual
problem in the real economy (assuming policy makers are basically sensible).

Please note that spending is a whole separate matter. If we ever escape the
liquidity trap and enter a period of supply shortage, then it will be really hard
to maintain federal spending at a high level without causing inflation. But
that reality has nothing to do with stock of debt. It's just as true if debt is zero
as it is when debt is 50% or 100% or 200% of GDP.

Thanks,
-Ken

Kenneth Duda
Menlo Park, CA
kjd@duda.org

[Alex Godofsky]

@Kenneth

Yes of course. I was pointing out that it could. I was not arguing that it should.

No, but you were arguing that it would. You said, precisely: "Nick, you lose me when you assume a higher stock of debt means a higher risk of default. The central bank can always buy up all the bonds no matter how many there are." Well guess what, unless you assume the central bank will always buy up those bonds, then a higher stock of debt really does translate into a higher risk of default.

And of course, the assumption that the central bank really will do that, 100% of the time, is a pretty terrible assumption against which we have large amounts of circumstantial evidence. Such as a near-universal aversion to high inflation among developed-world central bankers. Such as the BoC having an explicit inflation target. Such as price stability being a statutory responsibility of both the Federal Reserve and the European Central Bank.

Such as the fact that Nick explicitly mentioned the central bank's inflation target as a constraint.

Please think through the cases more carefully.

Please don't waste people's time trying to be cute when you didn't even read the OP properly.

[Lorenzo from Oz]

Since the invention of the consol in 1751, no Anglosphere national government has ever defaulted on a bond. (Actually, since the Glorious Revolution of 1688, but lets stick to bonds.) Anglosphere debt is the creation of safe assets. The only significant risk is inflation risk. So, why do we need any model for Anglosphere debt?

In 1815, the UK owed between 200-250% of GDP in public debt, when the central government's income was about 10% of GDP. (The joke was that it incurred half the debt pushing the Bourbons off the throne of France and the other half putting them back on.) So, it owed 20-25 times revenue in debt. Now, refresh my memory, how was the C19th for the UK?

For the current US federal government to be equivalently indebted, given that US federal revenue is about 20% of GDP, current US federal debt would have to be 400-500% of GDP.

On the C19th debt, here's a story for you. People have a certain level of risk preference for their assets. British government bonds were very low risk. We can predict that investors would be willing to go for higher levels of risk than they otherwise would for their other investments. What kicked off seriously in the 1820s? That would be the Industrial Revolution, based on speculative investments in new technology. The UK may not have had a good C19th not despite the debt but, in part, because of it.

Yes, I can see there would be an interesting story when there is a significant risk of default. See your model. If not, it becomes an issue of fiscal constraint; which is of interest but not remotely the same issue.

[Lorenzo from Oz]

Note: I would not claim that the UK public debt of 1815 was accrued by "non-productive expenditure". Acquired in the course of the Second Hundred Years War (1689-1815), It showed that the British state had a powerful and effective commitment to maintaining secure British commercial access to, well, the entire globe really. If you like, a commitment to the broad British income stream.

[W. Peden]

Lorenzo,

Is it significant that this UK debt was war-debt, rather than the product of ongoing expenditures, and thus it was clear that it would become easier and easier to meet these liabilities after the war ended and as the economy expanded?

I would imagine that investors would care less about the percentage of GDP that a debt represents rather than the nature of the deficits involved in building up the debt. As far as I know, large debts built up as a result of open-ended entitlement commitments are a new phenomenon, and they are qualitatively distinct (from a public finance viewpoint) from debts resulting from a temporary spending commitment, and very distinct from debts incurred from expenditure which (as you say) can be interpreted as investment-spending.

[Kenneth Duda]

Alex, you have not identified any case where the central bank's purchase of bonds would be both necessary and harmful. When you write:

> of course, the assumption that the central bank really will do that, 100% of the
> time, is a pretty terrible assumption

you are assuming such terrible cases exist, but you have not identified one. In what circumstance do you think the federal reserve backstop on sovereign debt would be terrible?

I argue that such cases do not exist. In a circumstance where debt purchases by the Federal Reserve were inflationary, then they would not be necessary. I think I came up with a pretty reasonable argument about why that would be. Your response, in effect, is that it's so obvious that you're right that it's a waste of time to patiently explain your position.

Again, I am more worried about spending than debt. Spending can be a real problem (inflationary) when there is a shortage of real resources. That said, I do not see how federal debt itself can be a problem, and you have offered no counter-argument, only repetition of conventional wisdom.

I would appreciate an explanation, ideally in the form of an example scenario in which a debt crisis in a sovereign power, with debt denominated in the sovereign power's own currency, leads to bad effects in the real economy that cannot be fully mitigated through appropriate central bank action, because I truly do not think such a case exists and that is why we do not need to be worried about the stock of dollar-denominated federal debt.

I make no pretense of being an expert macroeconomist. But I am calling it like I see it.

Thanks,
-Ken

Kenneth Duda
Menlo Park, CA
kjd@duda.org

[Jacques René Giguère]

W. Peden: how would an investor view a commitment to continually increasing human capital via garanteed public education? How would an investor value public stability being increased via reducing the need for revolution or at least revolt by the masses?
There were reasons why modern ruling classes replaced machine guns by social-democracy as control mechanism. One of them might well be that the economy grew so much that there was more gravy for everyone.

[Min]

Kenneth Duda: "assuming policy makers are basically sensible"

Unfortunately, that's a pretty big assumption.

[Lorenzo from Oz]

W. Peden: How did said investors know that peace was going to be a continuing feature? We know that the 1815-1914 period was peaceful but, for the European state system, it was wildly disproportional peaceful. Not something one could reasonably expect.

Also, how much deficit spending to pay for entitlements has there actually been? If revenue is above recurrent expenditure but below total expenditure, not part of said entitlements is being financed by the overall deficit.

[Kevin Donoghue]

Lorenzo: "Since the invention of the consol in 1751, no Anglosphere national government has ever defaulted on a bond."

Funnily enough, Reinhart and Rogoff do include a number of UK debt conversions in their list of domestic debt defaults and restructurings (This Time Is Different, Table 7.2). Personally I think that's bollocks; it's certainly a far cry from default as most of us use the term.

[Nick Rowe]

JR: interesting find. Yes there is a similarity there. A different mechanism, I think, but the same sorts of discrete jumps.

dlr: yes, this is an idea I've been returning to from time to time, including my Duke of Wellington post. Not sure how fiscal policy helps though. The basic problem is that fiscal policy suddenly needs to get very tight when the economy returns to the normal equilibrium.

Ken: If people want money rather than bonds, the central bank's job is to replace the bonds with money, to prevent interest rates rising. That is what happens in a normal equilibrium, to prevent inflation falling below target. But if people want neither money nor bonds, that won't work. The rate of interest needs to rise to prevent inflation. If people are unwilling to hold a given amount of government bonds at a rate of interest of (say) 5%, they might be even less willing to hold the same amount of government money at an even lower interest rate. And if they are unwilling, they will try to get rid of it by spending it, so the demand for goods will rise beyond supply, and cause inflation. The very fact that historically governments have needed to pay interest on their debt to prevent even more inflation than actually happened demonstrates this is not an imaginary scenario.

Lorenzo: UK has managed to have very high debt GDP ratios several times in history. But the most recent time, after WW2, it managed to reduce the debt/GDP ratio in large part through inflation. It was easier to do that then, because inflation was unexpected, because there was little or no history of inflation.

[W. Peden]

Lorenzo,

"We know that the 1815-1914 period was peaceful but, for the European state system, it was wildly disproportional peaceful."

An investor doesn't have to know that, provided that they can expect there to be times of peace. The only peace from entitlement spending is when the systems are reformed.

[Brian Romanchuk]

[From the article]
"In the normal equilibrium, the quantity of government bonds demanded depends on normal things like the real interest rate on those bonds and the expected probability of default (whether through unforeseen inflation or through simple non-payment of obligations). So in the normal equilibrium, a higher stock of debt, other things equal, means a higher equilibrium interest rate on that debt."

I am coming to economics as an outsider (applied mathematician), so I have to "tranlate" what other people write into how I analyse things. I translate what is written above as follows:

The assumption is that the government bond market is very inefficient. Instead of pricing bonds based on expected returns, it is assumed that investors will add in a significant default premium based on the debt level, even though no mechanism exists within the model for a default to occur. (If we look at real world bond markets, yes mechanisms for default exist, but they are generally political and not a financial constraint. For example, raising the debt ceiling requires no real resources for the U.S. government.)

On the other hand, the Post-Keynesian MMT writers (amongst others), argue that the government bond market is efficient, and investors essentially only price bonds based on expected return. This strikes me as somewhat ironic, given how the Post-Keynesians typically discuss the assumption of market efficiency.

And if we look at observed data, we see a strong relationship between government debt-to-GDP ratios and bond yields: higher debt leads to lower yields (I ran the fitting on my blog). I noted there that my fitting is a somewhat simplistic analysis, but it does raise the hurdle for accepting the assumption that rising debt levels leads to higher bond yields.

And for a more technical note: when I look at the basic DSGE models, I see no reason for such an effect, unless the assumed risk premium function is jammed into the model (in other words, assuming the desired conclusions). The stock of "financial assets" held by the Representative Household rose in previous periods for some reason without it being spent away, so there is no reason for that effect to suddenly appear at time t. The expected return on bonds should still match the expected path of policy rates, so that the Representative Household is indifferent between holding T-Bills and bonds. And there is no particular reason that the higher debt levels imply a higher path of policy rates.

[Kevin Donoghue]
"Funnily enough, Reinhart and Rogoff do include a number of UK debt conversions in their list of domestic debt defaults and restructurings (This Time Is Different, Table 7.2). Personally I think that's bollocks; it's certainly a far cry from default as most of us use the term."

Any deviations from a payment schedule is a default (although an issuer can be a couple days late; there's typically a grace period). The fact that they included Alberta in with a list of sovereigns shows the level of desperation R&R faced when doing their analysis. Their examples of domestic default either involved currency pegs (e.g., Gold Standard), losing wars or revolutions.

[dlr]

Nick:

yes, this is an idea I've been returning to from time to time, including my Duke of Wellington post. Not sure how fiscal policy helps though. The basic problem is that fiscal policy suddenly needs to get very tight when the economy returns to the normal equilibrium.

But if fiscal policy getting suddenly "very tight" merely consists of selling the previously acquired portfolio of stocks and real estate to repurchase government debt when we jump to Y*, why is this a problem -- it is really just the fiscal authority acting as the MM violation exploiter instead of the CB -- nothing says this can't happen very quickly just like a CB unwind. Sure, it might also be true that debt/GDP increased outside of the intentional portfolio purchases, and the need to run large surpluses without having commensurate assets to sell as we jump to a lower debt/GDP equilibrium *or face an inflation/default shock) could still be a problem. But if that problem already exists, it isn't really exacerbated by this kind of fiscalist operation hyper-twist. So you'd have to argue that it might be better to sit at Y forever than jump to Y* and face the adjustment pain. Possible but very unlikely. But there's still a question whether a fiscal Chuck Norris can really be effective violating Woodfordian irrelevance when everyone knows he can fairly easily operate in reverse upon the right future equilibria. I bet he could.

[Ralph Musgrave]

Nick,

You say “there's a limit to the demand for money” . . .but people will “increase nominal spending” . . . “so that won’t work”. I’m baffled.

We’re talking about recessions here: a scenario where increased “nominal spending” is POSITIVELY DESIRABLE. So what’s wrong with “increased nominal spending” (as long as the increase is not so large as to cause excess demand and excess inflation)?

On the other hand if there is no recession, then there is no case for printing cash or bonds.

[Peter K.]

"The demand for debt is high in the ZLB equilibrium, but it's not infinite. Eventually, when the level of debt gets high enough, the ZLB equilibrium disappears, leaving only the normal equilibrium. But the transition to the normal equilibrium is not smooth and continuous. The demand for debt suddenly jumps down, and interest rates jump up."

This is what I don't understand. Are there historical examples of this happening with advanced countires with their own currencies like the UK? What are the mechanisms and the concrete steppes?

Japan's debt is large comparatively speaking. What they're trying to do is raise inflation; escape the ZLB; and perform a budget neutral-fiscal spending/sale tax to spur growth. Growth will help increase revenue and bring down the debt.

"But the most recent time, after WW2, it managed to reduce the debt/GDP ratio in large part through inflation. It was easier to do that then, because inflation was unexpected, because there was little or no history of inflation."

I would look into that claim which may be right, but seems odd to me.

[Lord]

A a self-fulfilling change in expectations sounds like the definition of a crisis to me, and if the two states are really equilibriums, it seems unlikely anything other than a crisis could cause a switch, associated with a sunspot or not, and attempts to avoid a crisis are just attempts to prevent such a switch. Considering the two scenarios, monetarily, the bank owns the debt so as long as they don't panic, no run is created, while fiscally, the bank quells the run by buying the debt. But it seems possible that the banks accumulation of debt, whether over time or by buying to end the run could cause a panic from money that they must quell with rates. The amount it buys and the rate it buys it at are both up to it. It can and does get it wrong, but not inherently.

After WW2, financial repression was practiced.

[Jan]

Econometrics and the perils of assuming additivity and atomism by Lars Pålsson Syll -Malmö University
5 October, 2013 .http://larspsyll.wordpress.com/2013/10/05/econometrics-and-the-perils-of-assuming-additivity-and-atomism/

[Alex Godofsky]

Ken, I'm going to make one last attempt to deal with you and then I'm through.

Alex, you have not identified any case where the central bank's purchase of bonds would be both necessary and harmful. When you write:

> of course, the assumption that the central bank really will do that, 100% of the
> time, is a pretty terrible assumption

you are assuming such terrible cases exist, but you have not identified one. In what circumstance do you think the federal reserve backstop on sovereign debt would be terrible?

This is a completely obvious point that Nick makes somewhat explicitly in the original post:

A government can fund deficits either through selling bonds to the public or having the central bank monetize them. If the accumulated deficits over time (i.e. the debt) are sufficiently large then the central bank cannot monetize them without failing to meet its inflation target.

Case A: assume the central bank will not abandon its inflation target. (This is Nick's assumption in the OP, it is a reasonable assumption, and I shouldn't even have to be spelling it out for you like this.) Then the debt must be financed by convincing private investors to purchase bonds. The interest rate is increasing in (the marginal price is decreasing in) the total quantity of bonds the government tries to sell. In addition, Nick asserts (reasonably) that a sufficiently large required debt service payment leads to a risk that the government will choose to default, and that this risk causes investors to require even higher interest payments to compensate for that risk. This is a positive feedback loop that pushes the whole system towards a bad outcome (default).

Case B: the central bank will abandon its inflation target and monetize debt to prevent a default. Per assumption, this means higher-than-target inflation. The positive feedback loop in Case A applies equally here; anticipated monetization and the ensuing inflation cause investors to require even higher interest payments to compensate them. This is a positive feedback loop that pushes the whole system towards a bad outcome (hyperinflation).

Nick is working primarily in Case A, and (appropriately) casually waves away Case B ("whether through unforeseen inflation or through simple non-payment of obligations") because the ability of the central bank to monetize the debt to forestall default doesn't matter in the systems we're concerned about.

You may argue that the above outcomes are unlikely to happen at current levels of debt, or even multiples of the current level of debt, but the dynamics involved clearly exist and it is necessarily true that some sufficiently large stock of debt would be sufficiently large to cause them.

[Brian Romanchuk]

Alex,

My concern with your analysis is the assumption that the debt level magically rises for the thought experiment. In a proper model or the real world, debt levels rise gradually as the result of fiscal policy. If the Canadian government decided to increase spending by 20% of GDP right now, the bond market would freak out, and you get your bad scenarios.

But what is happening is that governments are running reasonable deficits in a low growth environment. Any sensible analysis of debt levels, which takes into account the self-stabilizing nature of deficits, tells you that debt-to-GDP levels will stabilize at somewhere higher levels, at worst. We have see those levels of debt to GDP historically, and the end result was that nothing happened. You need to do some dubious analysis - assume spending grows faster than GDP forever without impacting growth - to get scary numbers.

If there was a probability of moving fo a bad equilibrium and you assume that the bond market is efficient, the market should be pricing that risk. So you should see an increasing fiscal risk premium as debt levels rise. But if you look at observed bond yields, it is difficult to believe that the premium is big enough to be observable.

If you assume the price of bonds changes depending upon the supply, you are assuming that the bond market is inefficient. That seems to me an unusual assumption. If the government runs larger deficits, the non-government sector has a larger stock of government assets. The indifference between bonds and TBills (whose rate is pegged by the central bank) is based only on the expected returns of bonds, if the market is efficient. So the stock of holdings of bonds should have no effect on the bond yield.

[Nick Rowe]

One last try:

In the ZLB equilibrium there is a recession. Nominal spending is too low. In the normal equilibrium, nominal spending is just right, because the central bank keep it just right, and there is no recession. Perfectly standard result.

In the normal equilibrium, there is a maximum sustainable debt/GDP ratio. Because the higher the debt/GDP ratio, the higher the real interest rate (standard OLG model result), and the higher the primary surplus needed to service the debt, and there is some limit to the primary surplus that governments are willing and able to run. Perfectly standard result.

One non-standard assumption, that is nevertheless (I think) reasonable. The demand for government bonds depends not only on the usual stuff, like interest rates and risk of default, it depends on whether the economy is in the ZLB equilibrium or in the normal equilibrium. This does not (necessarily) mean the bond market is inefficient. It simply means that bonds are more valuable in a recession, where the future is uncertain, and private investment is less profitable.

If so, it is possible that the debt/GDP ratio needed to raise interest rates above the ZLB *might* (or might not) be higher than the maximum sustainable debt/GDP ratio in the normal equilibrium.

Brian: "If you assume the price of bonds changes depending upon the supply, you are assuming that the bond market is inefficient."

That's like saying demand and supply violates market efficiency!

You are not assuming the bond market is inefficient when you assume the price of bonds depends on the supply. It is a perfectly standard result in any overlapping generations model, for example, where young people want to buy bonds to save for their retirement, but desired saving depends on the rate of interest. To persuade them to save more, and buy more government bonds, you need to raise the rate of interest.

[Brendan Darcy]

What if the switch away from the ZLB also means better fiscal position? The savings rate should be declining (private sector savings) and so tax revenue should be growing faster than GDP. That could offset any increased cost if debt.

So maybe it's a non- issue.

[Nick Rowe]

Brendan: it might be a non-issue. Tax revenue will be higher, as you say. And GDP growth rate will be higher too. But if recovery to the normal equilibrium takes "too long", and the debt/GDP ratio gets "too big", it will become an issue. I've put them in quote marks because I can't put any numbers on them.

But it sorta bugs me that the same people who say the recession was caused by the financial crisis, which was caused by the private sector issuing "too much" debt, and people paying "too much" to buy that private debt, and the bubble suddenly bursting, say the same thing can't happen for government debt. It can happen. Even if governments can print money.

[Odie]

I think a few things get easily forgotten when talking about government debt becoming "too big" and comparing it to private debt:

1. Government debt has no expiration date. A government can always roll-over its debt; the US does that since 200+ years. 100 years ago a debt of $1 trillion would have been unimaginable; not we are above $10 trillion and the world does not fall apart.

2. Interest on debt is also income for the private sector. When people talk about interest expenditures becoming too big I often get the impression they feel those payments just disappear in a black hole. The money does not disappear; it ends up in the hands of businesses, consumers and the foreign sector. That distribution can be an issue but not the overall size of interest payments.

3. The government controls its income. In contrast to any private sector entity, the government can always increase its income by raising taxes and run a surplus. If aggregate spending starts outstripping supply and prices rise, the government can increase taxes and even run a surplus if needed, thereby reducing spending power and retire some of its debt. That can happen even at constant interest rates, so GDP will go down.

4. The "public" does not buy treasuries. When you ask around how many people would know that they are invested in government debt? People save money in savings accounts, money market accounts, in "safe assets" within their IRA. Very few will be aware that this money will end up for the most part in T-bills. Banks on the other hand have not much other choices when they need a highly liquid, interest-bearing asset which will also be accepted by the Fed as collateral or being purchased outright.

5. People are not acting rational. Nick you say:"To persuade them to save more, and buy more government bonds, you need to raise the rate of interest." On the other hand, you also state:"Assume the demand for government bonds (relative to GDP) is "high" in the ZLB equilibrium, and "low" in the normal equilibrium." Those two sentences contradict each other which suggests we are not looking at a normal equilibrium. When you look at current bond prices it becomes clear that despite rock-bottom rates people are still saving. Saving decisions are not based on the interest rate but the assumed future income. Hence, the economic outlook matters and that is something the government can influence by spending.

In summary, the government debt is the accumulated savings of the private and foreign sector. Hence, in the normal equilibrium a higher stock of debt means also higher savings and higher interest income for the private/foreign sector. Thus, "So in the normal equilibrium, a higher stock of debt, other things equal, means a higher equilibrium interest rate on that debt." is not a given as higher income of the private/foreign sector means also potentially higher demand for government bonds. If that income goes into spending and therefore causes inflation a raise in taxes/drop in spending will be the appropriate countercyclical measure. It will then come at an opportune moment meaning when aggregate spending is high, not low like currently.

[Nick Rowe]

Odie:
1. Private debt can also be rolled over.
2. Interest on govt debt is income for the bond-holder and a liability of the taxpayer.
3. Governments cannot (economically or politically) increase taxes without limit.
4. The public usually holds both private and government debt indirectly.
5. Those two sentences do not contradict each other. Demand depends on 3 things: rate of interest, risk of default, and whether the economy is in the ZLB or normal equilibrium.

[Odie]

Nick,

1. Beyond your death?
2. Bond-holder = taxpayer (minus foreign sector, the actual problem with US debt)
3. Economically: Never said without limit but to the extend necessary to bring inflation back on target. Politically: Maybe if people like Ken Rogoff would start telling how taxes, debt, interest rate and private savings relate to each other we could finally have an honest discussion.
4. True, but banks know that countries cannot default in their own currency in contrast to the consumer. Thus, there will be no flight out of government bonds because of some "irrational panic" or perceived risk of default.
5. Assume we are in normal equilibrium. To get to the ZLB the government would have needed to raise interest rates to stimulate savings. It did quite the opposite. To get back from ZLB to normal equilibrium the interest rate on government debt would need to fall even further which it cannot (I know, that's the definition of ZLB.) Thus, the desire to save does not necessarily correlate with the interest rate.

[Kenneth Duda]

Nick, thanks for the response.

> Ken: If people want money rather than bonds, the central bank's job is
> to replace the bonds with money, to prevent interest rates rising. That
> is what happens in a normal equilibrium, to prevent inflation falling
> below target. But if people want neither money nor bonds, that won't
> work. The rate of interest needs to rise to prevent inflation. If people
> are unwilling to hold a given amount of government bonds at a rate of
> interest of (say) 5%, they might be even less willing to hold the same
> amount of government money at an even lower interest rate. And if they
> are unwilling, they will try to get rid of it by spending it, so the
> demand for goods will rise beyond supply, and cause inflation. The very
> fact that historically governments have needed to pay interest on their
> debt to prevent even more inflation than actually happened demonstrates
> this is not an imaginary scenario.

I understand this completely. But what we have in that case is a spending
problem, not a debt problem. If the government and cash holders both
wish to spend beyond the productive capacity of the economy, then
inflation will result and there is nothing the Fed can do. Someone will
have to spend less or there will be inflation. This would be a great
time for some government austerity.

But this is missing the point of my argument. I was arguing that the
Fed can always backstop bonds without causing inflation. I was not
arguing that the federal government can always spend as much as
it wants without causing inflation. Clearly, if the government is
not willing to contract fiscally in an aggregate supply shortfall,
we are in trouble.

Alex, thank you also for the response:

> Case B: the central bank will abandon its inflation target and monetize
> debt to prevent a default. Per assumption, this means higher-than-target
> inflation. The positive feedback loop in Case A applies equally here;
> anticipated monetization and the ensuing inflation cause investors to
> require even higher interest payments to compensate them. This is a
> positive feedback loop that pushes the whole system towards a bad
> outcome (hyperinflation).

I have the same response to you as I did to Nick. Of course, if the desired
spending of the government plus cash holders is greater than the
productive capability of the economy, then you have a problem that
the Fed can't solve. The solution is to cut government spending.
The Austerians would finally be right, after all these years !!

My point is that the need for the government to cut spending in that
scenario (which is very, very far from where we are today) has nothing
to do with whether the Fed can and should serve as a debt backstop.
It always can and should. When you get to the point where interest
rates are high yet aggregate demand is still running ahead of
aggregate supply, there is no monetary answer. Is there a term like
"liquidity trap" that captures this opposite condition, where there is
no policy rate sufficient to bring spending down to aggregate supply?
In that scenario, the only solution is to cut government spending.
But thanks to the massive aggregate demand, there is no risk of
reduced government spending resulting in unemployment.

-Ken

Kenneth Duda
Menlo Park, CA
kjd@duda.org

[Alex Godofsky]

Ken, you have somehow managed to completely miss Nick's point and cleverly work your way in dialogue to... the exact same point. If I may summarize your argument it would be "fiscal policy overwhelms monetary policy" in this case. Yes, that's Nick's point exactly. Sufficiently large fiscal policy can either create a default, overwhelm the monetary authority's ability to control the price level, or both.

The "debt, not spending" distinction is also irrelevant. The context of this argument is that Nick's post is a partial apologia for people who believe excessive deficit spending is a potential problem. Deficit spending* is the same as creation of new debt, and so it is completely reasonable to use complaints about "debt" and "spending" interchangeably because they are interchangeable.

*again, we don't care about the possibility of monetization, it doesn't affect the macro outcomes we are talking about

PS: the dialogue trope where you play innocently ignorant about your opponents' arguments in order to try to lead them around to your own is a good trope when writing a dialogue but is obnoxious and insulting when used in dialogue with actual humans who can see where you're going and have heard the arguments before.