Teaching Mundell Fleming

The Mundell Fleming model is usually taught in second year macroeconomics. It's the open economy version of the ISLM model.

This post is me disagreeing with Simon Wren-Lewis about teaching open economy macro (in textbooks and in the classroom). It is not a disagreement about open economy macroeconomics.

Simon says that the textbook Mundell Fleming model, in some circumstances (like a temporary increase in government spending), violates Uncovered Interest Parity.

I say that the textbook Mundell Fleming model always preserves Uncovered Interest Parity, but in some circumstances (like a temporary increase in government spending), violates model-consistent ("rational") expectations.

Big disagreement? Not really. But I think my way of looking at it is more intuitive.

Here's how I teach it:

The students already know the closed economy ISLM model.

I explain how the IS curve is different in an open economy. Changes in the real exchange rate will cause changes in demand for net exports, which cause the IS curve to shift.

I explain how the LM curve may be different in an open economy, depending on whether the central bank responds to changes in the exchange rate (for example, fixing the exchange rate).

I then explain the BP curve, and write down the equation: Canadian nominal (or real) interest rate = US nominal (or real) interest rate minus expected rate of nominal (or real) appreciation of the Loonie exchange rate. I then show how changes in expected rate of appreciation will shift the BP curve.

I then ask what determines the expected rate of appreciation? And reply "Hmmm, I don't know. Let's assume it's constant for now. But we might need to check back on that assumption if the model tells us the actual rate of appreciation will change."

A constant expected rate of appreciation of the exchange rate is only a rational expectation if the exchange rate follows a random walk (with drift). That's not a bad assumption, but it won't always work. But then no simple assumption always works.

In the case of a temporary increase in government purchases (and in other cases too), the model tells us that the actual exchange rate will first appreciate, then depreciate again when government purchases return to normal. If people know that the increase in government purchases is only temporary, and if they are smart enough to use the model to figure out how that will affect the future exchange rate, they will expect the exchange rate to depreciate in future. That causes the BP curve to shift up. (Whether that upward shift in the BP curve increases Aggregate Demand depends on how the central bank responds.)

Lots of other things can cause the expected rate of appreciation to change. So we need to teach this anyway.

The difference between Simon and me is this: in Simon's benchmark model the exchange rate is expected to revert to the mean (or trend) in the "next period"; in my benchmark model the exchange rate follows a random walk (plus drift), so is expected to be the same next period as this period (plus drift).

Just a quickie between admin and teaching.

Comments

[pcle]

or you just scrap the whole thing as not fit for purpose and teach the ex rate is indeterminate like in Champ & Freeman

[JW Mason]

I score this one for Nick. Rational-expectations UIP is not a description of the real world. It gets zero support in the data, and isn't part of any practical policy debate. Making "consistency with UIP" the standard for textbook treatments of open-economy macro is perverse, it's a kind of anti-education. Tho sadly it's quite common -- David Romer's intermediate macro textbook takes exactly Wren-Lewis' approach, for example.

You are right that it's natural and plausible to motivate Mundell-Fleming with exchange rate expectations based on a random walk. But it could also be because capital is never perfectly mobile, or because bearing exchange rate risk is costly so market participants will pay a premium to hold assets denominated in the same currency as their liabilities.

[JW Mason]

pcle -

Even if the exchange rate is in some sense indeterminant, people must act **as if** they held some expectations about future exchange rates. I think the default expectations Nick starts with -- that future exchange rates will be the same as current ones -- is the most natural one.

[Nick Rowe]

pcle: saying "the exchange rate is indeterminate" isn't a very good answer to give to a student who asks "what makes the exchange rate go up or down?" Especially since I have already proved to the students, with the help of one international student volunteer, that even Purchasing Power Parity, while not a perfect theory, is a lot better theory than "it's indeterminate".

JW: Thanks! But I confess I'm having some second thoughts. Simon's way of teaching it *is* very simple, even though it does make RE implicit.

One nice thing about ISLMBP (whether or not we call it "Mundell-Fleming") is that it's very easy to make the BP curve upward-sloping, if we want to relax the small open economy + perfect capital mobility assumption. (Or relax Simon's assumption that the central bank sets the real interest rate).

[Giovanni]

Back in the Jurassic age, when I taught intermediate macro, I would always treat uncovered interest parity as a “special topic” apart from the flexible-rate MF model. If pressed, my justification for this approach would have been: (1) MF is primarily a model of aggregate demand determination in a small open economy; (2) yes, in principle, UIP-type interest rate effects can influence AD in an MF world; (3) but one has to recognize these effects operate on AD through the interest elasticity of money demand; (4) considering historical variations of (say) Canada-US interest rates differentials in conjunction with standard estimates of the interest elasticity, there’s good reason to believe a typical UIP-type AD effect amounts at most to only a few tenths of one percent of aggregate expenditure; (5) therefore, ignoring these effects is no big deal - and, for the purpose of intermediate-level instruction, probably advisable.

[genauer]

has there ever been one empirical, quantitative example for any version of Fleming Mundell ?

I would be interested to take a look at

[Nick Rowe]

genauer: Google is your friend.

Giovanni: you lost me a little there. What would your "benchmark" open economy macro model look like, if you were ignoring UIP for simplicity? Vertical BP curve?

[Giovanni]

Nick,

Standard textbook MF: horizontal BP at the "world" interest rate, standard trade-augmented IS, standard LM.

My understanding of what Simon Wren-Lewis is saying: the MF model is wrong because it doesn't account for movements in the "home" interest rate caused by expected changes in the exchange rate, as per uncovered interest parity. I claim that because changes in interest rate differentials (1) only affect AD through the interest-elasticity of money demand and (2) and are themselves historically small (certainly for Canada)then their effects are likely to be small. In other words, we're close enough to a vertical LM world so that UIP effects can be ignored.

If someone wanted to rubbish the textbook MF model I think a better place to start would be its failure to account for the effect of exchange rate movements on the "home" price level. With imported goods having, say, a 20% weight in the real balance deflator, a 10% depreciation of the currency (following a cut in government spending, for example) translates into a 2% decline in real balances: that's something that needs to be taken account of.

[Giovanni]

Nick,

Another way of looking at this.

In your teaching you assume the exchange rate follows a random walk with drift and people have rational expectations. This means people always expect the same rate of currency depreciation and (under UIP) the "home" interest rate doesn't change as long the "world" interest rate doesn't. Which means no macro impacts arising from endogenous interest rate adjustments to deal with.

I say your assumption isn't quite right. Expected rates of currency depreciation do change from time to time, and these are reflected in interest rate differentials. But given the actual size of these changes and the fact they operate through the interest elasticity of money demand to influence other variables in the model, their effects are likely to be very small. So, for all practical purposes, your constant expected depreciation assumption might as well be true.

Simon Wren-Lewis, on the other hand, appears to believe the UIP effects you've (justifiably, I think) assumed away and I've dismissed as empirically negligible are in fact large enough to make standard MF analysis unreliable and unteachworthy. On that basis, I think your disagreement with him goes beyond a mere matter of teaching method.

And now, having put the cat among the pigeons, I will quietly leave...

[Frank Restly]

Giovanni and Nick,

"Canadian nominal (or real) interest rate = US nominal (or real) interest rate minus expected rate of nominal (or real) appreciation of the Loonie exchange rate."

But don't different levels of debt also play a part? If one country had a debt to GDP level of 400% and one country had a debt to GDP level of 25%, where would you invest your money? That is the one part that does not make sense with regard to Mundell-Fleming.

[Nick Rowe]

Giovanni: OK I understand you now. That makes sense to me. My version would be a little bit different from yours. I would say the LM is vertical because the Bank of Canada makes it vertical. The BoC adjusts the money supply (in the medium run) to keep AD at the level it thinks will be consistent with 2% inflation.

Frank: fair point. That is normally handled by sticking a risk premium into the BP curve. (The only problem with doing that is that the risk premium is assumed exogenous, whereas you might argue that it depends on expected future debt/GDP ratio, which in turn depends on current fiscal policy.)

[Frank Restly]

Nick,

But how would you quantify that risk premium? Obviously if you are an investor from Canada buying US debt your real return on investment would be:

( Nominal US Investment Interest Rate * Nominal Exchange Rate ( $C / $US ) - Nominal Canadian Borrowing Rate ) / Canadian Inflation Rate

This assumes you are buying government debt. With other forms you would need to add a default risk premium. No where in your return on investment is the US inflation rate.

Consider what the US did to reduce its budget deficit during the 1990's. It shortened the average maturity of its debt (and courtesy of the federal reserve is still doing it today ). Now suppose you bought a 30 year bond back in the mid 1980's and the U.S. federal government decided to pay you accrued interest and principal during the 1990's. The risk on government debt is not default and as a foreign buyer it is not even local inflation, it is pre-payment risk. That is not a big risk for short term debt but is huge on longer dated securities.

[Nick Rowe]

Frank: let i = nominal, r = real interest rate, and p = inflation rate. Let * mean US. Let e = rate of appreciation of the nominal exchange rate.

In nominal terms, we can write the BP curve as:

i = i* - e

Subtract p and p* from both sides to get:

i-p = i*-p* -(e+p-p*) which simplifies to (since r=i-p):

r = r* -(rate of appreciation of the real exchange rate)

[Frank Restly]

Nick,

First let me try to correct some things in my statement above:

Real Rate of Return on Investment = Nominal US Investment Interest Rate - % Change in Nominal Exchange Rate ( $US / $C ) - Nominal Canadian Borrowing Rate - Canadian Inflation Rate

R = i* - e - i - p

Assuming that real returns are arbitraged away (R = 0):

i = i* - e - p

I don't see how you can eliminate local inflation in what amounts to an investing choice. If Canadian inflation rate > nominal US interest rate > nominal Canadian interest rate would you be buying US debt? Getting back to the risk premium you would need to add a pre-payment risk factor (pp) that is a function of how much debt a government owes (D).

i - pp(D) = i* - pp*(D*) - e - p

[Giovanni]

Frank,

Let E0 = the Canada/US exchange rate today ($CDN per $US)
E1 = the expected Canada/US exchange rate tomorrow
e = E1/E0 - 1 = the expected rate of depreciation of the Canadian dollar.
i = Canadian nominal interest rate
i* = US nominal interest rate

Suppose that today I lend one Canadian dollar in Canada. Then I get (1 + i) Canadian dollars tomorrow.

Alternatively, suppose that today I convert one Canadian dollar to get (1/E0) US dollars. Suppose I then lend those US dollars in the US. Then I get (1/E0)(1 + i*) US dollars tomorrow, from which I can expect to get E1(1/E0)(1 + i*) Canadian dollars after conversion.

In arbitrage equilibrium these two investment strategies must be equally attractive to investors - so:

(1 + i) = (E1/E0)(1 + i*)

which implies

(1 + i) = (1 + e)(1 + i*)

which implies

i = i* + e + ei*

which implies that to a close approximation

(#) i = i* + e

provided both e and i* are both small (which is almost always the case).

This is where the uncovered interest parity condition comes from. Minor modification: if for some reason investors require a premium v to invest in Canada rather than the US all of the foregoing still goes through with the UIP condition becoming:

(##) i = i* + v + e.

The bottom line is that under UIP the Canadian nominal interest rate should move point-for-point with the expected depreciation of the Canadian dollar. You can certainly include a relationship such as (##) in a Mundell-Fleming model and ask “What happens if the risk premium v changes?” But unless you’re actually interested in analyzing that sort of question you can use (#) instead of (##) and still get valid results.

[Frank Restly]

Giovanni,

But if the rate of return you are receiving on the money is less than the inflation rate you are experiencing, why would you lend at all instead of say - buying goods or paying down previously incurred debt? That was the point I was making.

[Simon Wren-Lewis]

Nick: When we teach the LM curve to first year students, we complicate things by pretending the central bank does something it does not. But at least it is something they might do, so we are not being inconsistent. Its fiction, not fantasy.

To assume that agents treat the exchange rate as a random walk when using models where there is a well defined long run exchange rate, and where these agents spend huge amounts of money trying to predict things, seems more like fantasy to me. Why not make the much more reasonable assumption that agents expect the exchange rate to go back to its fundamental level next period.

Of course if you teach reality rather than fantasy from the off, and have central banks determining the interest rate, then your assumption would mean there can be no independent monetary policy in an open economy. Would you really want to teach that?

[genauer]

Simon (WL),

how about to just tell the people the simple truth that "there can be no independent monetary policy in an open economy", in your words?

http://worthwhile.typepad.com/worthwhile_canadian_initi/2013/01/what-is-going-on-with-the-bank-of-canadas-balance-sheet.html?cid=6a00d83451688169e2017c366896e0970b#comment-6a00d83451688169e2017c366896e0970b

Good people, with good character, want the truth.

[Nick Rowe]

genauer: mind your manners please. And you are wrong, regardless of whether Simon or I is the one who is right on this.

Hi Simon!

1. I think the horizontal LM curve is a fantasy (for any period longer than 6 weeks in Canada). Because the BoC adjusts the overnight rate target every 6 weeks to try to keep the output gap closed and try to keep inflation at the 2% target. A much better approximation to reality would be to draw the LM curve vertical, at that level of Y which the BoC thinks is potential output. Because the Mundell Fleming model (and ISLM too) was designed for short run analysis, and anything less than 6 weeks is very very short run indeed, where the economy can't hope to get anywhere near the IS curve (or even the LM curve, for that matter).

2. Even if you reject my vertical LM model, I think it would be closer to reality to say that central banks in a SOE with PCM choose the real exchange rate, rather than the real interest rate. (Of course, the BoC would never describe itself as doing that, because it would upset the Americans! But we don't have to buy into the same social construction of reality that central banks use to describe what they are doing.)

3. I wouldn't go to the wall on the question of whether the real exchange rate is a random walk or reverts to mean. I can see the merits of your way of doing it. I know it can't be a true random walk, because if it did then its long run variance would be infinite, and PPP wouldn't work any better than a random guess, and PPP does work better than a random guess. But *some* shocks will be permanent. And even if they aren't strictly permanent, it is possible for the shocks to increase over time, at least initially. And even if the shocks do decay over time, the rate of decay might be very slow, relative to the time period over which the MF model is useful, so a random walk might be a good approximation to reality. If I remember the empirical literature (Stephen did a post on this some time back) it is very hard to reject the random walk assumption over any moderate length of data.

[JW Mason]

Why not make the much more reasonable assumption that agents expect the exchange rate to go back to its fundamental level next period.

Sweet mother of god, do you ever, ever look at data?

Make a graph of exchange rate changes based on the "back to fundamentals [whatever they are] next period" and actual changes. See how well they match up. And ask again, why don't private actors adopt this wildly counterfactual assumption? Why don't profit-maximizing agents behave in a way that would lose them lots of money? Why don't risk-averse agents bear lots of extra risk, with no compensation? Gee, why not?