Tuesday, 26 March 2013

Why we should stop teaching Mundell Fleming


For economists

I have complained before about IS-LM being the first macromodel most students encounter, when no major current central bank fixes the money supply. The textbook version of Mundell Fleming (TMF) [1] is the first, and often the last, short run open economy model students are taught, and it shares the same deficiency. However the problem with TMF is even greater. It is inconsistent with Uncovered Interest Parity (UIP), and if we use modern macro as our yardstick, this makes it simply wrong.

Lets take a topical issue: the impact of a temporary increase in government spending. We should be immediately worried that TMF makes no distinction between temporary and permanent increases. It says both have no impact on output. So every student learns that fiscal policy is ineffective under flexible exchange rates. For a temporary increase in spending this is incorrect.

The logic of the TMF proposition is usually demonstrated by shifting various curves, but it is in fact trivial. In TMF money demand must equal a fixed money supply. If money demand depends on prices, output and interest rates, and the first is fixed in the short run and the last is tied to world rates, then output cannot change either. This complete crowding is achieved through an appreciation in the real exchange rate.

But why should domestic interest rates equal world interest rates? UIP tells us they need not. A temporary increase in government spending will raise output, which given a fixed money supply will raise interest rates. This will lead to an appreciation, but the temporary nature of the shock means that the long run exchange rate is unchanged. So the current appreciation implies an expected depreciation, which offsets the additional return offered by higher interest rates. The result is a short run equilibrium where output and domestic interest rates are higher. There is partial crowding out through an appreciation but not full crowding out.

Now you might say what is so great about UIP. But at least UIP is based on something: a simple arbitrage theory. As far as I can see the TMF assumption that domestic and world interest rates are equal has no equivalent foundation.

We only get some crowding out in the experiment above because the money supply is fixed. If interest rates are fixed instead then we get none. With fixed interest rates, UIP implies the current exchange rate is unchanged when government spending increases, so there is no crowding out. We get exactly the same result as with fixed exchange rates - the complete opposite of what TMF suggests.

Now you might plead in mitigation for TMF that at least it gets the impact of a permanent increase in government spending right. I think this is a very weak defence. A permanent increase in government spending, assuming it increases aggregate demand, is crowded out because in a small open economy the real exchange rate equates the demand and supply of domestic output in the long run, which is a more basic result than anything in TMF. [2]

Another weak defence of teaching incorrect theories is that they are simpler than better theories. However it we combine this basic idea about the determination of the medium/long run real exchange rate with UIP, we have a complete theory of the small open economy which is no more complicated than TMF. So why does TMF survive?

Perhaps one reason is an addiction to two dimensional, and preferably static, diagrams. Yet the system I’m describing can be represented by just two equations and two periods. The first equation is the familiar aggregate demand curve. It is static, so we have

y = f ( g, r, e )

where g is a shift variable like government spending, r is the real interest rate and e is the log of the real exchange rate. Use stars to denote second period (medium/long run) values:

y* = f( g*, r*, e* )

Now here I can say that r* is equal to the world real interest rate rw (because of UIP and a constant real exchange rate), and y* is determined by some classical supply side, so this equation determines the second period real exchange rate - the basic result I mentioned above.  The only other equation I need is UIP:

e = e* + rw - r

where e is defined so that an increase is a depreciation. Policy determines the short term domestic real interest rate, and therefore the short term real exchange rate.

The aggregate demand curve is already familiar to students, and the adaptation to an open economy is intuitive. UIP is easy to teach: any interest rate differential is offset by expected capital gains or losses. So it seems to me something like this should become our standard introductory short run open economy macromodel. And TMF should disappear.

[1] It is well known that in open economy macro everything important must have a three letter abbreviation.
[2] It is a basic result that may be inconsistent with PPP, but that is another story.

22 comments:

  1. The textbook by D. Romer deals with that problem.
    http://emlab.berkeley.edu/users/webfac/cromer/e134_sp13/Romer%20Short-Run%20Fluctuations%20January%202013.pdf
    Jeremie Cohen-Setton

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    1. Jeremie: the link you sent me does not (unless I'm being really stupid). It looks at imperfect capital mobility, but not UIP.

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  2. Perhaps encouraging: first year economics students in Rotterdam study a IS-Taylor Rule model instead of a IS-LM model (following the 6th edition of Macroeconomics by Burda & Wyplosz)

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  3. But UIP is totally false. Why is consistency with a proposition that has zero empirical support a desirable property of a textbook model?

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  4. SW-L:
    " It is inconsistent with Uncovered Interest Parity (UIP), and if we use modern macro as our yardstick, this makes it simply wrong."

    Surely, a somewhat unorthodox definition of 'wrong'.

    UIP does not hold in the real world -- as Mason notes above. That it does not hold is widely considered a major 'puzzle' or 'anomaly'. So this particular criticism of M-F amounts to saying:
    'The (ratex equilibrium) model is definitive, reality is frequently inaccurate'.

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    1. Your criticism would have some force if the TMF assumption that risk adjusted interest rates across the world were always equal was closer to reality than UIP. Is it?

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    2. Valid point, but but you miss my point. Perhaps I was too brief. I am not defending the simplest TMF [digression: but why must we use the simplest TMF (or ISLM)? Isn't it possible to modify it to allow for UIP or expectations. Yes it will have an 'ad-hoc' flavour, but that is a separate issue. end digression]

      What upset me was *one* particular criticism -- that the model is 'wrong' because its implications differ from the implications of a simple intertemporally optimizing ratex model, when that implication of the eq model is itself false (and quite unambiguously so).

      This sort of claim is par for the course from someone at Minnesota. That a reality-based economist who wrote approvingly of chapter 10 of Blanchard and Fischer, believes it came as a shock.

      If all our models are deeply flawed (out-of-sample performance, external consistency) -- and I agree with almost all your criticisms of TMF -- we have no choice but be eclectic. Teach multiple models while also highlighting their domains of applicability and their limitations.

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    3. I understand the point you are making, and have no real quarrel with what you say. However UIP is ubiquitous in modern macro, because there is no obvious alternative, and nothing that I'm aware of that does better empirically. I don't think teaching models that make no sense is being eclectic.

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    4. "I don't think teaching models that make no sense is being eclectic."

      In that case, I look forward to the abolition of models using the aggregate production function and that goal-directed collective: the utility maximizing representative agent.

      (tongue firmly in cheek)

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  5. What is your opinion of the treatment of MF given in Carlin and Soskice (which you use for the 3-equation model)? As I recall, it uses UIP.

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  6. Simon: my response: http://worthwhile.typepad.com/worthwhile_canadian_initi/2013/03/teaching-mundell-fleming.html

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    1. 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?

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  7. Simon,

    Your critique of TMF is valid. The only problem is that while UIP is appealing theoretically, it is a well-established empirical fact that it does not hold in the data and never has. Indeed, in terms of exhange rate determination, the old Meese-Rogoff finding that a random walk beats pretty much all of the competing models (stock-based, flow-based, and especially those in which both stock and flow equilibria hold), even though as they noted in their original article, even random walk does a lousy job of forecasting exchange rate movements.

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    1. I think there is a big danger here of confusing short term and long term predictive power. The FOREX market, like the stock market, is impossible to predict in the short term, but that does not mean there are not medium term/long term fundamentals. There are plenty of people who suggest PPP works in the longer term, and the little bit of empirical work I have done on this suggests we can improve on PPP. So using a random walk assumption is not really an option.

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  8. While agreeing with you on the general point, the U in UIP is specifically meant to indicate that it's not based on an arbitrage relation

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  9. On the more general issue of imposing no-arbitrage in models. While it seems to be almost unquestioned orthodoxy in academic macro, outsiders find the insistence absurd. It would make perfect sense if the models were literally true, or at least correct in the sense engineering models are. But macro models are not valid models in the way physics or engineering models are. They are just metaphors.

    Some insiders do see the absurdity in taking metaphors literally.

    Peter Diamond (Nobel lecture):
    "I disagree with these views[*] because they ignore the incompleteness of models and the role of simplification for tractability. For simplicity, many search models have one-employee firms to simplify the analysis. Yet employment is overwhelmingly in firms with two or more employees. Are we going to learn more from one-employee modeling by invoking considerations that seem plausible in a literal one-employee environment or from involving considerations that seem plausible in many-employee firms and applying them to the one-employee environment? It seems to me that the latter is more likely to yield useful insights. And the alternative of requiring analysis with many-employee firms will yield some new insights, but may not yield additional insights for some questions in return for the extra complexity (e.g., tracking the distribution of firm sizes), indeed may make it harder to find some types of insights."

    [*] The view that a model should not have 'an inefficiency that intelligent actors could easily avoid' (Barro)

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  10. If it makes you feel any better, I learnt the Mundell-Fleming model some three years ago and they integrated uncovered interest parity in the model. Then again, I am a student in a portuguese university.

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  11. I wouldn't worry too much about Mundell-Flemming, it's typically taught at the end of the curriculum and often left out. And students can always get by without answering questions about it. Bottom-line: no-one knows the stuff anyway.

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  12. As JR says, I thought it was normal to discuss UIP in the context of the TMF. It seems sensible to start with the simplest model (with the domestic interest rate equal to the world rate) then extend that model in ways that make it more realistic. In addition to UIP, one could think about imperfect capital mobility, which causes the BP line to slope upwards. Also, there's the possibility of sterilization in a fixed exchange rate system.

    In other words, yes TMF is wrong (as are most, if not all, economic models) but perhaps we learn something by studying it. Same applies to IS-LM in general. I don't think treating the money supply as fixed is a mistake or an anachronism (it predates the monetarist experiments of the 1980s, which in any case involved setting interest rates in the hope of controlling the money supply) but rather a useful abstraction. One problem with assuming interest rates are fixed is that there are obvious implications for inflation, whereas keeping the money supply fixed keeps inflation under control (at least in principle).

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    1. If, as I do, you want to use models where central banks determine interest rates and not the money supply, then starting with TMF is hopeless - it tells you there is no monetary policy is open economies!
      In what sense is the LM curve a useful abstraction? It adds an unnecessary equation. There is no problem about inflation in a model which uses interest rates as the monetary policy instrument - policy just uses interest rates to control inflation! (Like in the real world.)

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    2. It's useful because it tells us something about economics: what would happen if the money supply were fixed (just as IS-LM tells us what would happen if the price level were fixed, which obviously it is not). You can also show how interest rates might change in IS-LM, via open-market operations to change the money supply. This is arguably more realistic than just assuming the CB sets the interest rate, with no regard to the effect on the money supply.

      The problem with assuming that the CB sets interest rates to control inflation is that the behaviour of the CB and the relationship between interest rates and inflation are quite complex in practice. It is not the case that interest rates are adjusted in a mechanical manner to achieve a given level of inflation (or even to achieve a given mix of inflation and unemployment). It's a bit like saying there are no recessions because fluctuations in demand are always offset by monetary policy. Just because they could be doesn't mean it will happen. In other words, macro models should be able to explain inflation and unemployment, not just assume they are under the control of policy makers.

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    3. If you want a realistic rule that explains how central banks use interest rates to control inflation, then use a Taylor rule. Assuming the monetary authorities fix the money supply is a fiction, and it does not tell you how they control interest rates. I just do not understand why we teach students a fantasy, when teaching them about reality is easier!

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