Buiter, Krugman, Steinbrueck, free-riding, and the exchange rate

Warning: this post is difficult, and I'm not at all sure I've got it right. But I'm going to post it anyway.

What determines the exchange rate in a liquidity trap? [Prerequisite: second year Open Economy Macro]

In case you hadn't noticed, there's a small war going on, with Willem Buiter (UK) and Paul Krugman (USA) on one side, and the German Finance Minister Peer Steinbrueck on the other. In a nutshell, Buiter and Krugman are saying that Germany (and other countries) should run deficits to stimulate their and the world's economies, and Germany is saying "No, and it's your big spending on borrowed money which got us into this mess in the first place".

You can see why countries restricted trade during the Great Depression (even though it made things worse for the world as a whole). Look at it this way: there's the Germans, with their big net export surplus, taking scarce demand away from other countries, refusing to pull their fair share of the fiscal weight, free-riding off other countries' deficit spending, even adding insult to injury by calling their benefactors "crass Keynesians". The temptation to view the world this way, and stick it to Germany, will grow over time. But is this view right?

Paul Krugman has presented his simple model of free-riding and the need for policy coordination (my own previous thoughts are here). Krugman's model is taken from the first-year Macro textbook, and it works just fine. Or rather, it works fine for a world of fixed exchange rates or a common currency, like within the Eurozone (which is what Krugman was writing about anyway). But it doesn't work with flexible exchange rates.

In a liquidity trap, what happens to the exchange rate when one country runs a deficit and the others don't? Do we still get a free-rider problem?

It's a dirty job, but someone has to do it: what happens to the simple, second-year textbook Mundell-Fleming model in a liquidity trap? (By the way, a quick question: Robert Mundell is Canadian; was Marcus Fleming British?)

I will assume imperfect capital mobility. (Under perfect capital mobility, the interest rate is over-determined and the exchange rate under-determined, so let's not go there.)

LM:  Nominal interest rate = 0

BP:  Net Capital Outflow = Net Exports

IS:  Real Income = Domestic Absorption + Net Exports

To solve the model, first substitute the BP curve into the IS curve, to eliminate Net Exports, which gives us:

Real Income = Domestic Absorption + Net Capital Outflows

Now, this is just an accounting identity. We could do the same thing with the normal Mundell-Fleming model (when we are not in a liquidity trap), but it wouldn't get us very far, because Domestic Absorption and Net Capital Outflows depend on the interest rate, which depends on everything else. But in a liquidity trap, this accounting identity gets us a long way, because the interest rate is fixed at zero.

Domestic Absorption (C+I+G) depends on fiscal policy, and on the real interest rate. The real interest rate is equal to expected deflation, so Domestic Absorption depends (positively) on fiscal policy deficits and (negatively) on expected deflation. Net Exports depends (negatively) on real income and (negatively) on the real exchange rate (i.e. a real exchange rate appreciation reduces net exports). Net Capital Outflows depend on the interest rate differential (but we can ignore this, since zero minus zero equals zero) and (positively) on expected exchange rate depreciation.

We can write the solution for real income (Y) to incorporate {the things which affect Domestic Absorption and Net Capital Outflows}:

Y = DA{+deficit, -expected deflation} + NCO{+expected forex depreciation}

We can do the same for net exports:

NX{-Y,-real exchange rate} = NCO{+expected forex depreciation}

Let's make the standard short-run assumptions: the exchange rate is expected to stay constant (expected forex depreciation is zero), and expected deflation is exogenous.

Note that with expected forex depreciation taken as fixed, NCO is fixed, and so is NX. A fixed NX means that increases in Y (which cause imports to rise and so net exports to fall) must cause the real exchange rate to depreciate (which causes net exports to rise) to offset the rise in Y. That is weird: a strong economy causes the exchange rate to depreciate. It's the exact opposite result to the normal Mundell-Fleming model with high capital mobility.

What happens if the UK runs a bigger deficit? The result is an increase in UK domestic absorption, and no change in net exports. The UK gets the whole benefit of its deficit spending. None of it spills over into increased demand for German (or US) goods. The rise in UK income causes imports to increase, but the pound will depreciate enough to hold UK net exports constant. There is no free-rider problem. There is no need for international coordination; the exchange rate internalises the externalities.

What sort of beggar-thy-neighbour policy could a country run? If (say) the UK could get people to believe that the pound would depreciate in future, this would increase Net Capital Outflow from the UK, and increase UK net exports equally (and cause a depreciation of the pound now). Here's how to do it: the UK needs to run a tight fiscal policy now, but then announce it will slowly loosen fiscal policy over time. The pound rises immediately, then is expected to depreciate (I am now assuming rational expectations for the exchange rate).

A tight fiscal policy is not a beggar-thy-neighbour policy. But a fiscal policy which is expected to get slowly looser over time is a beggar-thy-neighbour policy.

Comments

[Stephen Gordon]

Curse you!

I wanted to get a head start on next term's course notes today, but now this will be nagging at me all day.

[Nick Rowe]

I'm so lucky to be on sabbatical this year! (Just wondering how I'm going to explain to the Dean "What I did on my sabbatical").

But I would really value your comments (or the comments of any macroeconomist) on the above. I thought it would be straightforward, but it was just so weird. I started doing the post assuming perfect capital mobility, thinking it would be simpler. But the result was even weirder: the equilibrium exchange rate was whatever number people thought it should be. A range of equilibria, in other words.

But I was tired when I wrote the post, and may have screwed something up.

[Stephen Gordon]

One thing I wonder about is that you'd ordinarily expect that expectations about exchange rate depreciation would be determined by differentials in rates of deflation.

[Nick Rowe]

Good point.

Holding deficits constant over time, so the real exchange rate is constant over time, the rate of change of the exchange rate will equal the deflation differential. Assume rational expectations, so the expected rate of nominal depreciation of the pound will equal expected UK deflation minus expected German deflation.

This means that bigger UK deflation will have an ambiguous effect on Y. It increases NX, but reduces DA, so it depends on the elasticities.

I'm relieved to hear you haven't (yet) found anything obviously wrong with the model!

[Meh]

Uh... but unfortunately, various parts of the Eurozone need stimulus, it's not just the good old profligate UK (outside the euro) who is in trouble.

And that's why it's a real live issue.

[Nick Rowe]

Meh: The way I see it, there are two real live issues:

1. Within the Eurozone itself, should each country decide its own fiscal policy, or will this lead to free riding? Paul Krugman's model is fine for handling this question, even though it ignores exchange rates, because all the Eurozone countries share a common currency, so there is no exchange rate.

2. For the wider world, UK, US, Eurozone, Canada, Sweden, etc. we face the same question of whether each country should decide its own fiscal policy, and whether free-riding will be a problem. But Paul Krugman's model won't work for this question, because it doesn't have exchange rates. So I am trying to build a model to answer this question.

[Phillip Huggan]

(not a HS graduate so I don't meet the thread criteria, feel free to delete)
Nick, haven't you already answered your question? You've mentioned some capital is subject to exchange rates and some is more "sticky" where it already is. Can't you just measure/estimate the fraction that is liquid and plug that into the model, and put a time-delay on more viscuous capital?
If you want to make the stimulus prefer domestic suppliers, that is doable, though you lose some productivity gains by having American factories make lead toys and plastic food instead of China. The USA 2008 isn't a sustainable economic model; been borrowing heavily since GWB and giving all the goodies to very rich since Reagan. The Germans have their own issues (IDK what) and if they think increasing federal debt is worse than giving the USA consumer addict another fix... I guess America can screen out German stimulus contractors, but if there are any two countries who have similiar industrial competancies and who should trade it is USA and Germany. Freer trade is co-ordinated tariffs and subsidies, not debt. In return for matching stimulus, will the USA match Germany's social spending, defense outlays and higher income tax rates? Maybe if Gore were prez the Germans should submit.

[ClaudeB]

I too lack the prerequisite :) Will this class help me understand this post in the next couple of months (Stephen could chime in, since he has some personal knowledge of this boutique of higher learning)?

So, at the risk of showing my utter ignorance of all things macro, but aren't you jumping the gun here? The ECB (2.5%), BoE (2%), BoJ (1.675%) and BoC (1.5%) all have some leeway, so most of the major monetary players (save the Fed) can still tinker with the money supply and there is no widespread ZIRP as we speak.

[Nick Rowe]

Phillip: as long as capital mobility is not perfect (when weird things happen in the model), the degree of capital mobility does not affect the result that there is no free-rider problem. But at this stage, I'm more concerned with whether I've got the model right than with any policy prescriptions.

The problem is this: I have taken an absolutely standard 40 year old textbook model, the one I learned as a second-year undergrad 30 years ago, and have taught at least a dozen times since, then asked what that model would predict in a liquidity trap, and I'm stumbling around in the dark. And I really don't think it's just me. Normally I rely on my economic intuition, and use the math as a back-up. Here my intuition is lost, and I using the math. It's like pilots must feel when they are flying on instruments only: I don't like it.

ClaudeB: my guess is that this course would be better. But I am unfamiliar with Quebec 1st year course; it's all different, because of CEGEP.

Yes, my post might be a little premature, but not I think by much. And we ought to start thinking about this stuff ahead of time, even if we are uncertain about whether the world will be in a liquidity trap.

[ignorantmike]

As Buiter puts it in the context of possible hyperinflationary scenarios, its never too early to anticipate the next crisis. I can't comment extensively on the validity of the model (hence my nom de guerre ici), but it seems to me that within the eurozone at least, Buiter is right to question Steinbrueck. Similarly, I think it correct to question the role and "plans" of the dollar-peggers. There is some articles about global trade balances by Michael Pettis worth perusing.

PS I like this blog in spite of my tyro economist status. Any effort to abstract away the poison of political division is nice (tho' probably somewhat futile!) keep up the good work in spite of a world (and Canada) apparently headed for confrontation.

[Stephen Gordon]

A niggling concern I have here is that deflation is exogenous in the model. A fiscal stimulus would presumably slow the rate of deflation, and that could be a mechanism for an appreciation in the exchange rate.

[Nick Rowe]

Yep, it's a short-run model. Suppose we add a Phillips curve, with slow adjustment of deflation to the output gap. Canada increases the deficit, output rises, the gap falls, and so deflation slows, and slows relative to other countries. The real exchange rate depreciated immediately when the deficit increased, but will now stay constant. With lower deflation, the nominal exchange rate will now be appreciating (or depreciating less than before). Sooner or later, the same will happen to expected appreciation. So the NCO will fall. So NX will fall. So there will be some benefit for the rest of the world if Canada increases its deficit.

So I think you are right. How important is this effect? Dunno. It seems to depend on the slope of the Phillips curve, and on the degree of capital mobility, plus how quickly expectations adjust.

Probably I should have mentioned this in my latest post. But it complicates a simple story.

I had a useful discussion with my Carleton colleague Steve Ferris. He showed me how to think of the liquidity trap as the limiting case of the model where the LM is flatter than the BP, and keeps on getting flatter. It helps the intuition.

[Phillip Huggan]

"So I think you are right. How important is this effect? Dunno. It seems to depend on the slope of the Phillips curve, and on the degree of capital mobility, plus how quickly expectations adjust."

Most of this convestion is above me probably because I don't understand why you can't (I'm not saying you should now) just have negative interest rates as a monetary prescription (I've heard it is inconvenient to have account service fees cost more than interest rates but this is minor). But for the "expectations adjust" portion of your formula, I'd guess not too quickly right now. We are getting decades worth of oscillations in the past year and a half.

[Phillip Huggan]

To elaborate, maybe the reason economics text-books don't work in a liquidity trap is the standard monetary response (not saying it is good or bad) is to cut interest rates lower and this isn't practised below 0-0.25%? So it is a whole bunch of fuss to look for an elaborate way to trigger borrowing that would be equivalent to cutting to -0.5% interest rates? Good to know the 4 years I spent trying to save money manually labouring would've been equally wasted getting an economics degree :)

[Nick Rowe]

Phillip: I don't think there are any administrative difficulties in having negative interest rates on balances in chequeing accounts, but it would be harder to do it on cash. So people would just withdraw cash from chequeing accounts, and hold it in a safety deposit box, or under the mattress.

Yes, I think expectations are all over the place right now, since so much is so new for so many people, so we can't rely on simple rules of thumb that worked in the past.

[Phillip Huggan]

Physcial dollar bills are a small percentage of total currency denominated assets. Are you saying the main problem is no one has devised a good way of getting bills out of circulation, or are you saying the main problem is that the withdrawal of bank savings accounts would wreck the finance industry? Or maybe both?

[Nick Rowe]

Phillip: neither really. I just assumed that notes and coins are here to stay, and as long as they are here, and you can't find a way to tax holding them, we can't get negative interest rates.

Chap called Silvio Gessel (sp?) did propose various methods of taxing notes. It's not impossible.