Pictures of Ireland?

In countries like Ireland, there is currently an abnormally large Gap between nominal interest rates and the expected growth rate of nominal GDP. That Gap creates a nasty positive feedback loop, through two channels:

The Risk Channel. It's hard to pay down debt when the debt is compounding a lot faster than the growth in your income. The bigger the Gap, the bigger the risk of default, and the higher the interest rate new lenders will require.

The Aggregate Demand channel. The Gap between nominal interest rates and expected nominal GDP growth is a rough proxy for the tightness of monetary policy. The bigger the Gap, and so the tighter is monetary policy, the slower will be the growth in nominal GDP.

Adding both channels together, we see that any exogenous increase in the Gap will cause higher nominal interest rates and lower expected growth in nominal GDP, and so a further endogenous increase in the Gap. There's positive feedback. If positive feedback is strong enough, you can get an unstable equilibrium, and perhaps multiple equilibria. Or perhaps no equilibrium.

Ever since writing my post on Ireland's sovereign debt problem, an inchoate picture has been slowly forming in my mind. It's a bit clearer now.

But my mind is still not as clear on this as I want it to be. This is a work in progress. Continue at your own risk.

Here's the first picture:

The horizontal axis shows the Gap -- i.e. the nominal rate of interest minus the expected growth rate of nominal GDP. The vertical axis is used for both the nominal interest rate, i, and the expected growth rate of nominal GDP, g. (Both variables have the same units, so it's OK to have both on the same axis.)

The blue curve shows the effect of the Gap on risk, and on the nominal interest rate i. When the Gap is zero, risk of default is very low, so market interest rates will also be low. As the Gap increases, the risk premium rises, and so market interest rates rise too. My guess is that the risk curve will be concave. When the Gap is low, a small increase in the Gap will have little effect on risk. But the bigger the Gap, the bigger that effect will be. There is some maximimum Gap, beyond which it will be impossible to pay the debt.

The red curve shows the effect of the Gap on Aggregate Demand, and on the expected growth rate of nominal GDP g. As the Gap increases, Aggregate Demand falls, and so actual and expected growth of nominal GDP will fall too. I don't know if this curve should be concave or convex, so I have drawn it as a straight line.

An exogenously given Gap, a point on the horizontal axis, implies a nominal interest rate from the blue risk curve, and an expected growth rate from the red AD curve. And the green vertical gap between the blue and red curves is itself the same Gap, only this time it's endogenous.

From the first picture we can derive the second picture. I think Ireland looks something like this:

The second picture has the same horizontal axis as the first. It's the exogenous Gap. The vertical axis is the endogenous Gap. The green curve shows the vertical distance between the blue and red curves in the first picture. The black line is the 45 degree line. It's the equilibrium condition. Where the green curve cuts the 45 degree line is an equilibrium. At an equilibrium, the Gap is consistent with the risk and AD it creates. At an equilibrium, the Gap re-creates itself.

I have shown two equilibria. At the good equilibrium, the Gap is low, so risk is low and interest rates are low; and AD is high, so growth is high. So the Gap is low. At the bad equilibrium, the Gap is high, so risk is high and interest rates are high; and AD is low, so growth is low. So the Gap is high. It's a liquidity problem. A looser monetary policy could be self-sustaining.

The good equilibrium is locally stable. An exogenous 1% rise in the Gap above equilibrium will cause the endogenous Gap to rise by less than 1%, so it reverts towards the equilibrium. But the bad equilibrium is unstable. If the economy ever finds itself to the right of the bad equilibrium, the Gap will rise without limit.

But maybe there is no equilibrium. If the green curve never crosses the 45 degree line, there is no equilibrium Gap. The country is not illiquid; it's insolvent. Perhaps Greece looks like the third picture?

Yes. This is still a work in progress. It's not as clear as I want it to be. That's because my mind is not as clear as I want it to be. I did warn you.

And, I've got 300 exams to mark.

Comments

[RSJ]

What is the definition of the endogenous Gap?

[reason]

Ah, so all feedbacks are not negative after all!

[Nick Rowe]

reason: you meant "Not all feedbacks are negative after all!" ;-) Yep. Some feedbacks are negative; some are positive.

RSJ:

1. i = R(i-g)
2. g = A(i-g)
subtract 2 from 1 to get:
3. i-g = R(i-g)-A(i-g)
or:
4. i-g = F(i-g)

"endogenous gap" is just my way of describing the LHS of equation 4.

[Sergei]

Does it argue for a "risk-less" closure of the gap? i.e. central government just spends without issuing any bonds (whatever you call it)?

[OGT]

I noticed you don't mention roll-over risk, debt structure matters. I'd encourage you to check out this very interesting post by Micheal Pettis on sovereign default:

http://mpettis.com/2010/07/do-sovereign-debt-ratios-matter/

Last time you wrote about Ireland I noticed a good number of commenters believed that the state's contigent liabilities in regards to the banks were heavily correlated with Ireland's AD. That's partially true, many of those loans, however are bad at nearly any likely NGDP (though recovery would effected). But more importantly a significant number of bad assets owned by Irish banks aren't even in Ireland, at least two very large recent commercial foreclosures in the Boston area had Anglo-Irish Bank as the lender.

[Nick Rowe]

Sergei: if Ireland had control over its own monetary policy, they wouldn't tolerate a Gap of about 9% between bond rates and expected nominal GDP growth. They would loosen monetary policy immediately.

This isn't formally incorporated into my "model", but I would see that as shifting the economy from the bad equilibrium to the good equilibrium.

In one sense, a country that can print money, and borrows only in its own currency, cannot "default" on its pre-existing debt. "We owe $10 trillion? OK, so print $10 trillion". But in another sense, you could argue that the resulting inflation might amount to a default, by other means. And that only works for pre-existing debt, because its ability to borrow would be seriously harmed by doing this.

OGT: Yep. Debt structure matters. If you never needed to roll over debt, an increase in current interest rates would have no direct effect on your ability to re-pay existing debt, with previously-fixed interest rates. The blue Risk curve would be flatter. Though the higher interest rates would still reduce NGDP growth and increase default risk through that channel.

The existing debt/GDP ratio matters too. And increase in the debt/GDP ratio would shift the blue curve up.

[Nick Rowe]

Yep. Interesting article by Michael Pettis. What I'm trying to model here is related to what he says about virtuous and vicious cycles. I'm just trying to bring in the Aggregate Demand effects too.

[Determinant]

Nick:

I agree that "printing money" or inflation amounts to a back-door default. Or at least that's how the bondholders see it. In fact this is the main problem whenever you bring up a situation that generates a "excess demand for funds" as you say. The obvious answer is to print more money but the "Inflationistas" hate that.

Would you please clarify your thinking (perhaps through another thread) on whether printing money to cure an excess demand for funds would actually trigger price level inflation or another form of inflation and what, if anything, bondholders have to fear from such a printing operation.

[Nick Rowe]

Determinant: Let me try to clarify it here.

There are two questions:

1. If money is non-neutral in the short run (which it is), then printing money may increase *real* GDP (or prevent it falling), and that would increase the government's (and others') real income from which to make real payments on the debt. So creditors would actually gain.

2. Ignore the above, and assume money is neutral. You could say that printing money then causes inflation, so rips off creditors by the back door. Or, you could say that printing money prevents the deflation that would otherwise occur, and so prevents creditors getting too much, in real terms. (or, prevents inflation falling below what the creditors expected when they made the loans).

[Determinant]

Which I agree with, but would observe that since creditors want the highest return they prefer inflation to be as low as possible and therefore reap the windfall for themselves. Rational greed and all that.

It seems to me that public discourse on the subject passes over the fact that lower than expected inflation gives windfall profits to creditors.

The other point is that if a Government/Central Bank accelerates inflation, there is the danger that they will overshoot their target and rip off creditors unintentionally.

Further, could you please explain why nobody seems to recognize [1] very much, far less argue for it? It seems to me that Printing Money = Inflation = Evil is the dominant opinion.

[Nick Rowe]

Determinant; I don't really know. My guess would be recent history, i.e. the inflation of the 60's, 70's and 80's is salient in the minds of creditors, who are mostly older?

[RSJ]

I don't think that the advantages of the currency issuer are that they can print money to pay off debt. As has been pointed out, investors are forward looking and you are not going to fool them too much, on average, by inflating away debt.

Rather, by having the ability to print money, investors don't need to add an additional default risk premium to their bids. It's this lack of a default risk premium that is the advantage of the currency issuer, not that that investors misprice the bond due to unexpected inflation.

The question that remains is -- is the currency issuing government more likely to cause inflation, so that whatever lower yields it enjoys due to a lack of default risk are negated by increased inflation risks? And here, it may be a wash in normal times, but during a deflationary crisis it's clearly not a wash, and this is where the difference between currency issuing governments and currency using governments becomes apparent.

Unfortunately the euro was born during a period of credit expansion, so it could be that the member nations set the system up assuming that they were merely exchanging one risk premium for another, and only discovered later that they were wrong.

[White Rabbit]

RSJ wrote: "As has been pointed out, investors are forward looking and you are not going to fool them too much, on average, by inflating away debt."

That's only partially true. The average investment time horizon for foreign bonds is somewhere around 3 years. (sorry, no link) Beyond that it gets fuzzy. Active investors use long-term bonds are typically used speculatively for interest rate leverage over 1-2 macro events, not in a long-term investment manner. (And the passive investors, sovereign and pension funds, are losing money.)

If a country gets into a "ouch, banks crashed and we just got a debt burden of +60% of GDP, what do we do?" unexpected situation, then partially inflating away that debt is a totally rational solution that worked numerous times in recent history.

Creditors would still prefer that over an explicit default that results in a 100% loss of their capital ...

And as we are seeing it very clearly, holders of Irish and Greek bonds have not considered that situation at all, so they are not rational 'forward lookers'. It was an unexpected tail event that was clearly not priced in and the result is a panic and a disorderly, illiquid bond market out of equilibrium. It happens all the time.

[Nick Rowe]

Compare countries that can print their own money, and so can inflate away their debt, and that currently do have (in some cases, like the UK, though maybe not in others, like Japan) higher inflation rates than Ireland. Yet they still have lower, much lower, nominal interest rates.

[Sergei]

Lets play a mainstream game and assume that "printing" leads to inflation. A statement is made that creditors are not happy with inflation because it erodes their real claims. However, not printing leads to defaults which also lead to diminishing real claims of creditors. So some printing is perfectly rational from their point of view. Where was this "insight" lost in the current mainstream debates? I have never seen a cost/benefit analysis. It is always either all or nothing which sounds like we are loosing hopelessly in terms of bargaining power.

And yes, this implicitly validates the mainstream assumption that we need to bargain with creditors because otherwise ... there will be inflation and ... creditors will loose.

Not my claims though. Just trying to figure out who is who and what is what.

[Nick Rowe]

Sergei: let me re-state your point another way:

If deflation leads to a reduction in real income, or if there are costs of lawyers etc. in a default, then the optimal rate of printing, from the point of view of creditors, may sometimes be positive.

Where was this insight lost? I don't know. Maybe it was never found? (Though I think Scott Sumner said something similar, IIRC.)

[Determinant]

It may have been lost sometime around the 1980's when Central Banks committed to wrestling inflation to the ground. When you cast inflation as a Bad Thing, it's hard to turn around and start to see it as a Good Thing.

It seems that we will not or can not see inflation/monetary expansion as a spectrum with both good and bad outcomes, depending on the ends we desire and the choices we make.