## April 02, 2013

### Teaching Mundell-Fleming, Interest Rate Parity, and the LM Curve

Simon Wren-Lewis’s post has sparked vigorous discussion [1] [2] (and rejoinder) of whether the teaching of Mundell-Fleming, omitting uncovered interest parity, to our undergraduate students is defensible. In addition, he wonders whether it makes sense to use an LM curve, given the absence of a stable money demand curve, and the fact that most advanced country central banks target a policy rate. I think these are good questions for teachers, as well as those who provide advice regarding policy measures.

When I teach Mundell-Fleming, I try to convey the intuition in a model without expected depreciation (and without an exchange risk premium), either under fixed or flexible exchange rate regimes. Then, I add expected depreciation, which is consistent with uncovered interest parity. Once one adds expected depreciation, it’s interesting to note that the results of fiscal and monetary expansions do not change qualitatively.

In other cases, I’ll try to incorporate expectations directly. This can be done using the IS-LM framework, or as Paul Krugman has. I use the Blanchard exposition, notes here. What I like in particular is the incorporation of IS-LM as well as the interest rate parity condtion.

Figure 1: Fiscal expansion. Note: Rise in E denotes home currency appreciation. Source: Blanchard.

Figure 2: Monetary expansion contraction. Note: Rise in E denotes home currency appreciation. Source: Blanchard.

Fiscal expansions lead to a rise in GDP, a rise in interest rates, and a currency appreciation, in the absence of an exchange risk premium and default risk premium. A monetary expansion contraction leads to a rise decline in GDP and a currency appreciation, when not at the zero interest rate bound. The same results would obtain assuming capital flows respond to the interest differential.

How’s the model work? Here are the graphs I usually provide to explain "the dazzling dollar" of the mid-1980's:

Figure 3:Federal structural budget balance to potential GDP (solid line), and Fed funds interest rate minus lagged one year CPI inflation. Source: CBO, St. Louis Fed FRED, NBER, and author's calculations.

Figure 4: Fed funds rate minus lagged one year inflation, and log real value of the US dollar against a broad basket of currencies. Source: St. Louis Fed FRED, Federal Reserve Board, and NBER.

Real World Issues

Uncovered interest parity (UIP) is one of the most important concepts in international finance. It is also one of the most difficult ones to verify. Uncovered interest parity is the no-arbitrage condition that one cannot obtain in expectation a higher rate of return in one currency than another. Since expectations are unobservable, tests of UIP are necessarily a joint hypothesis, usually incorporating the rational expectations hypothesis, in which case it is almost universally rejected at short horizons (Thanks to Simon for the cite of my recent work). I guess it’s a question with no particularly good answer whether to incorporate an assumption that is seemingly at variance with so much data (although I certainly object to short run/instantaneous purchasing power parity, the other central tenet of international finance.)

Reflecting my focus on emerging markets, I am somewhat less enthusiastic about assuming UIP in cases where capital mobility is less than infinite. Then “textbook Mundell-Fleming” might not be too bad at conveying the basic intuition.

Simon Wren-Lewis’s larger concern regards the inclusion of the LM curve. Here, I can see the merits of the argument –- in advanced economies, and many emerging market economies, the policy instrument is a policy rate, rather than some sort of aggregate money stock. Moreover, the stable money demand function which underpins the conception of the LM curve is an elusive creature.

That being said, the linkage of the money base to the external accounts is important for less developed countries, under fixed or managed exchange rates – assuming less than perfect capital mobility. When there is a balance of payments surplus, then money base increases, thereby increasing the money supply in the absence of sterilization procedures.

Now, it might be true that the monetary authority still targets a policy rate; but the resulting flat LM curve or MP curve would obscure the fact that sterilization procedures would have to be in place to keep the respective curves in place.

To be honest, I’m not sure what framework works best for conveying intuition when the economy being examined is at the zero lower bound (not relevant for most of the emerging market economies and the LDCs).

Bottom Line

Teaching approaches differ; otherwise, we’d all use the same the textbook. What gets stressed will, I think, necessarily differ depending upon the economies analyzed, and phenomena being explained (US 1985 calls for a slightly different framework than China 2007).

In any case, I think that the conversation represents the best of what the blogosphere can provide –- an informed exchange of views of what works best in conveying economic intuition. (Note: So far, no name-calling, and no admonitions for a rewrite of theory in favor of an Austrian weltanschauung, or a Kondratieff wave approach to the universe.)

A great exposition of Mundell-Fleming with rational expectations and UIP by Maurice Obstfeld here. And a simple model to explain apparent deviations from UIP using an McCallum-like "exchange market shock" and central bank reaction function a.k.a. Taylor rule, here.

Posted by Menzie Chinn at April 2, 2013 01:00 PM

digg this | reddit

I think Figure 2 should be titled "Monetary Contraction..."?

Posted by: John Hall at April 2, 2013 02:42 PM

I enjoyed this post and the entire discussion. It is exactly the kind of rational thought one hopes to see about the nature of what one does. Thanks.

Too bad this kind of scrupulousness is relatively rare.

Posted by: jonathan at April 2, 2013 02:47 PM

It's been a pretty listless week at Econbrowser. We've had all of four posts, this last a "vigorous discussion" on teaching M-F to undergraduates. This is pretty thin soup.

If you have nothing to post (or the time to do so), I might note that the internet does allow one to link to interesting stories from elsewhere. Tyler Cowen makes a good living doing just this.

In that spirit, here's is an interesting piece from the Daily Princetonian, the University's paper.

http://www.dailyprincetonian.com/

Search on "Advice for the young women of Princeton", about the importance of securing a Princetonian man for the Princetonian woman.

An excerpt:

Men regularly marry women who are younger, less intelligent, less educated. It’s amazing how forgiving men can be about a woman’s lack of erudition, if she is exceptionally pretty. Smart women can’t (shouldn’t) marry men who aren’t at least their intellectual equal. As Princeton women, we have almost priced ourselves out of the market. Simply put, there is a very limited population of men who are as smart or smarter than we are. And I say again — you will never again be surrounded by this concentration of men who are worthy of you.

Posted by: Steven Kopits at April 2, 2013 02:53 PM

I assume by fiscal expansion you mean real spending on goods and services, not transfers like unemployment and so forth. I guess we are now at about 17% of GDP, and this has been stable for a while. The increase in transfers due to the housing bubble/financial crisis was not a fiscal expansion, correct? I also get confused if we pay soldiers to live overseas, how this is expansionary?

Posted by: pete at April 2, 2013 02:58 PM

John Hall: Yes, you are correct. Thanks for catching the error.

I'll note that for those of us who have to teach, I think the debate is useful. If you had clicked on the links to the Frankel and Obstfeld pieces, you might have learned a little open economy macro. And what's wrong with talking about whether UIP holds? It's the international analog to whether commodity futures have informational content, and you found that an interesting topic.

But just for you, I am going to make sure the next post is on the topic of properly identifing cointegrating relationships with varying assumptions regarding deterministic trends, with some discussion of using finite sample critical versus asymptotic critical values.

Posted by: Menzie Chinn at April 2, 2013 03:22 PM

In normal times it's pretty easy to see why it makes more sense to teach an IS-MP model rather than the old IS-LM model. But what about when the economy is at the zero lower bound? Does the MP curve give you the same intuition as the LM curve? The question isn't whether or not the MP curve can be explained in such a way that it can accommodate a liquidity trap, but whether or not the intuition would be as natural and obvious as it is when you use the LM curve.

Way back in the stone age when I studied Mundell-Fleming we weren't encouraged to take it too seriously or too literally. The takeaway was supposed to be a fairly easy way to understand how changes in the IS curve (fiscal policy) or LM curve (monetary policy) had different effects depending upon the degree of flexibility in the exchange rates. Not every country is on a pure fixed exchange rate or a pure flexible exchange rate. I don't know that you get that with the UIP approach. You certainly don't get it from Romer's textbook.

Posted by: 2slugbaits at April 2, 2013 03:37 PM

Steven, as to the dearth of worthy male coupling partners for female Princeton (Ivy) grads, this is the result of the culmination of a 40-year trend of deindustrialization, financialization, mass immigration, and, dare I say, "feminization" of the US economy and society.

Therefore, it should be no surprise that well-"educated" females are finding it difficult, if not impossible, to find a male partner of similar socioeconomic standing. By definition, when the Ivy male grad with a job has the choice among Ivy females and their lesser peers, probabilistically he will choose the female of lower achievement and credentialing.

http://www.forbes.com/2006/08/23/Marriage-Careers-Divorce_cx_mn_land.html

As for marrying that well-educated career woman if you're a male, Ivy credentialled or otherwise, your risk of a divorce is higher. Sorry, you can't satisfy her by trying to give her "it all", so why try?

Speaking of divorce, it should therefore be no surprise that the US divorce rate for 1st marriages is ~50% by year 20 of marriage, and over 70% for all marriages (1st, 2nd, 3rd, and more). Men could never afford to "have it all" themselves, but women are still being socialized that they can "have it all"; but someone forgot to tell them that "having it all" comes with the increasing costs associated with not getting "it" and not getting "it" alone.

Solutions? There is a surplus of Chinese males needing/wanting spouses, so why not study Mandarin and head for the Middle Kingdom to find that male Chinese equal? The female Ivy grad might have to give up those high heels so she is not 4-5 inches taller than her Chinese male partner, and she might outweight him by 10-20 lbs., but why would these factors matter when it's true love and lots of money?

Then there's the option of becoming a lesbian (if she is not one already) and hooking up with another lesbian Ivy grad til death do them part (or probabilistics).

Adopting a Shih Tzu, French bulldog, or chihuahua is also an option (with or without a lesbian partner), but most canines don't earn six to seven figures and buy his spouse a McMansion and a new Mercedes, BMW, or Range Rover every couple of years; however, if the little critter is cute enough, it might make her girlfriends and female relatives jealous for a few days.

Then again, the enviable female Ivy grad could always consider a sex (or is that gender?) change to increase her/his probability of finding a female partner to please and live happily ever after.

There are other options, of course, but I assume this is a PG-rate blog.

Posted by: Bruce Carman at April 2, 2013 03:51 PM

I'd didn't meant to criticize your post specifically. There's obviously nothing wrong talking about MF--but, yes, it's been a pretty weak stretch for the blog in aggregate, in my opinion.

For example, we're now two weeks into Cyprus, and nary a word from you folks. I obviously do frequent other blogs. Zero Hedge has just killed you for share of read in the last two weeks, because Tyler Durden could be bothered to talk about what seems to me a critical macro topic unfolding before our eyes.

I might add that I would assume that you'd be looking for feedback. If you want an audience, you got to feed it. If you're not going to post, at least put up a few timely links, and let the piranhas feed.

And you know, it doesn't have to be all macro or dissing Scott Walker. I think the whole Princetonian match thing is pretty interesting. I'd certainly be curious to hear your views. You went to Harvard. What's your take on on the matter?

Posted by: Steven Kopits at April 2, 2013 04:26 PM

I think you're being a bit harsh, Bruce.

I can see the difficulties that worthy women--not just Ivy grads--have finding suitable partners. And I think the whole matter of marriage is treated far too casually. It matters much more than where you went to college. I thought Patton's article made some valid points. It begs some questions of biology versus individualism, the importance of bonding versus self-actualization, career versus family. It raises a number of interesting themes regarding liberalism, conservatism and egalitarianism--many of the topics we debate here at Econbrowser.

Posted by: Steven Kopits at April 2, 2013 04:48 PM

Menzie,

I may be misinterpreting your graph in (b) but if the domestic interest rate rises, holding the foreign interest rate constant, then the domestic currency is expected to depreciate under uncovered interest parity. However, the graph appears to say that the domestic currency is appreciating. What am I missing?

Posted by: Rick Stryker at April 2, 2013 05:07 PM

Steven Kopits Zero Hedge??? Seriously? Why not Larry Kudlow or Jim Cramer at CNBC? At least Cramer can entertain you with loud sounds as you wait breathlessly to see if he's going to stroke out on camera.

I'm glad to see that academia is questioning the pedagogic value of what it teaches. If for no other reason because doing so reminds professors that they have an obligation to teach undergraduates as well as write obscure papers that will be published five years after the working paper made a splash, read by 20 people and understood by 5 former grad students.

Posted by: 2slugbaits at April 2, 2013 05:34 PM

Rick Stryker: Implicitly, the Dornbusch overshooting model is incorporated. In this treatment, the expected exchange rate is fixed. A higher interest rate now, combined with sticky prices, leads to an immediate appreciation so that over time a depreciation consistent with UIP occurs. A similar formulation holds in other textbooks, e.g., Hall and Papell (which I used to use for intermediate macro). In both cases, the exchange rate or UIP relationship is collapsed into the IS curve.

Posted by: Menzie Chinn at April 2, 2013 05:52 PM

"But just for you, I am going to make sure the next post is on the topic of properly identifing cointegrating relationships with varying assumptions regarding deterministic trends, with some discussion of using finite sample critical versus asymptotic critical values."

Menzie, flirting with participants with the intention to seduce them with your analytical prowess in this manner is leaving me a bit breathless, blushing, and not a little bit flustered. Please refrain in future from such overwhelming displays. Obliged.

Posted by: Bruce Carman at April 2, 2013 07:30 PM

Steven thoughtfully writes: "I can see the difficulties that worthy women--not just Ivy grads--have finding suitable partners. And I think the whole matter of marriage is treated far too casually. It matters much more than where you went to college. I thought Patton's article made some valid points. It begs some questions of biology versus individualism, the importance of bonding versus self-actualization, career versus family. It raises a number of interesting themes regarding liberalism, conservatism and egalitarianism--many of the topics we debate here at Econbrowser."

http://papers.nber.org/papers/w18901

Consider, however, that 50% or more of new college grads (with average student loan debt equivalent to a new car loan or average after-tax salary of a college grad) are unemployed, return to school (because they can't find a job in their field), or are underemployed (business, liberal arts, or social science grad working at Wal-Mart and/or Starbucks) with few prospects for full-time, living-wage employment with benefits.

Adjust the average salary of a college grad who obtains employment at \$44,000/year for higher payroll taxes, higher cost of housing as a share of income, and higher cost of energy per after-tax income, and that typical grad earns an equivalent in purchasing power of the minimum wage in 1970 (!!!).

Now, that's what young American women, Ivy credentialled or not, face in terms of prospects for themselves, let alone hoping to find a male partner who can earn a durable, secure income of \$125,000-\$150,000/year in order to afford to support a mortgage, spouse, children, out-of-pocket medical costs, and save for college costs AND retirement; but only about 8-10% of males 35 and older earn that kind of money, whereas only about 1% of those below age 35 do.

The 1920s-30s had the "Lost Generation" of Hemingway and Fitzgerald, but we have today what I regrettably refer to as the "Last Generation" in the North America, UK, and Europe.

Posted by: Bruce Carman at April 2, 2013 07:58 PM

To the regret of few, there is nothing of a « cause célèbre » in debating the worthiness of synthesised diagrams or models as taught in the field of economics. Yet there is plenty in the form and substance, it deals with artificial intelligence when implanting the output as opposed to the critical path to the output and the ability to understand fully its merits if any and limits. It involves the responsibility of a teaching content, the right of students to think and to agree. The basic principles of intelligence is to question and opine or to question and improve or reject. Should these rights be denied, the planet ape will not be long lasting.
On the models and diagrams, they reflect an egocentric world where the model by pass the mechanism of transmission of monetary policies predominantly the exchange rate, assume rational expectations that is described by the psychologist « as better five cents today than ten cents tomorrow », neglect as referred in the comments the ZLB and ignore the balance of payment.
It does not cure and even worse does not prevent or warn.

Posted by: ppcm at April 2, 2013 09:17 PM

"When there is a balance of payments surplus, then money base increases, thereby increasing the money supply in the absence of sterilization procedures."

Could you define money supply?

Posted by: Get Rid of the Fed at April 3, 2013 12:17 AM

Good post.

Regarding the LM curve: Now it's true that central banks (nowadays) don't hold the money supply constant in the face of IS shocks. But it's even more true to say they don't hold the interest rate constant in the face of IS shocks. An inflation-targeting central bank will hold expected inflation constant in the face of (perceived) IS shocks. And that means the LM curve will be vertical! Because if it weren't vertical, AD would increase, and so would future inflation.

Posted by: Nick Rowe at April 3, 2013 08:25 AM

Thanks for the clarification Menzie.

My problem with Mundell-Fleming is not that it's not consistent with uncovered interest rate parity, which is a problem. But I have a more fundamental problem with the IS LM model itself.

That's not to say I wouldn't teach it, since it's very important for students to understand the logic of such a model. But I think students are ill-served if they leave the class not understanding the limitations and different policy conclusions that arise from modern extensions of the model.

On the international side, there are a number of ways to introduce uncovered interest rate parity, which I think are fine for clarifying the economic logic. But students in my view should leave the class understanding that uncovered interest rate parity fails empirically. The 1980s is a very good time to raise for that discussion. In spite of the fact the US rates were above foreign rates in the early to mid-80s, the dollar appreciated. Explanations such as peso problems or failure of rational expectations can't really explain that sustained appreciation. You can posit a risk premium in which investors are paid the interest rate differential plus the appreciation to hold the dollar, but you have to wonder why the dollar would have been riskier, especially since the US economy was being called a safe haven at the time. In the second half of that decade, the dollar started to depreciate, implying it was less risky. Why was that? You could also relate it to the carry trade, talk about the risk, etc.

That's my view anyway.

Posted by: Rick Stryker at April 3, 2013 09:54 AM

Rick Stryker: I don't think we "know" UIP fails. We know the unbiasedness hypothesis (UIP plus unbiased expectations) fails at short horizons. If one uses survey data to infer expectations, the evidence is more mixed with respect to rejection -- see here. That being said, there is evidence of a time-varying exchange risk premium, when using survey data. In those cases, UIP would be violated (of course, subject to the joint null hypothesis).

Posted by: Menzie Chinn at April 3, 2013 10:11 AM

I think, the exchange rate of the Dollar until Plaza / Louvre 1987 can be very easily explained by the geopolitical risk of those times.

Our infantry and tankers were all winter in the field close to the border in 1984. Many lost body parts to the cold. A friend of mine was close to mutiny charges.

Posted by: genauer at April 3, 2013 12:01 PM

"Now it's true that central banks (nowadays) don't hold the money supply constant in the face of IS shocks."

Sounds like the money supply is being defined as monetary base. What if that is not the money supply that matters?

Posted by: Get Rid of the Fed at April 3, 2013 12:23 PM

Menzie,

Yes, I agree. I was referring to unbiasedness failing--it's a joint hypothesis of course.

By the way, in international macro at least I think it's important that students understand the Meese and Rogoff and subsequent results that suggest the exchange rates do not seem to be related to any macroeconomic fundamentals. That's important context when discussing Mundell Fleming or some other macro model that purports to relate the exchange rate to GDP, the money supply, or other variables.

Posted by: Rick Stryker at April 3, 2013 02:00 PM

Steven,

I hope Menzie or JDH don't start linking to stories just to get content. What makes this blog unique is the depth of analysis coupled with the quantity, which I don't think is matched anywhere. Given the time that it must take to write these posts, I'm amazed that we get as much as we do, given that both of these guys have full time jobs. And the price is certainly right.

I also think this is a useful post. How and what undergraduates are taught is important and I'm glad to see that some professors are worried about it.

Posted by: Rick Stryker at April 3, 2013 02:26 PM

Patton's letter is absurd and harmful. I can't see any merit in it all. Here's how I'd summarize her advice:

"Princeton students are uniquely brilliant and so shouldn't squander the opportunity to marry each other. However, all men are pigs and will prefer to marry younger, more beautiful, and less intelligent women. But Princeton women will realize that intelligence in a mate is more important than any other quality, such as kindness, good character, or responsibility. Therefore Princeton women should get started early, probably in their freshman year, since by the time they are seniors, only the senior men-pigs will be interested while the other men-pigs will think they are too old. Hitching your star to a Princeton man is the most important step a Princeton woman can take. When you graduate, you might encounter some men as brilliant as the Princeton men, but don't count on it. Outside of Princeton, the brilliant men are few and far between. Better act now.

My older son's wife did the smart thing and married a Princeton man. Lucky for her--he could have married anyone. My younger son could marry anyone--women of Princeton, better get in line."

I wonder if this advice had anything do with this quote from NY magazine, in which the author of the letter discusses her recent divorce:

http://nymag.com/thecut/2013/03/qa-princeton-mom-wishes-she-married-classmate.html

"He went to a school of almost no name recognition," she said, declining to name the institution. "Almost no name recognition. A school that nobody has respect for, including him, really."

Posted by: Rick Stryker at April 3, 2013 04:47 PM

Menzie,

Thanks, this is helpful. I've been trying to decide how to teach MF, and this post convinces me that Wren-Lewis is wrong. But your Blanchard figures raise the question: what happens to expectations of the exchange rate? Carlin/Soskice deal with this using adaptive expectations, so eventually the interest rate gets pushed down to the world rate. I raised this in comments on Wren-Lewis but he doesn't seem to get it that one can teach textbook MF with UIP.

Posted by: tom m at April 4, 2013 06:07 AM