Why is LM still there?

With all the recent discussion of IS-LM, I can’t help but repeat a longstanding question of mine: what on earth is “LM” still doing in the diagram?

The “IS” curve is logical enough: by encouraging investment (not to mention spending more generally), lower interest rates lead to higher output. Sure, there are some flaws. We should really be looking at the full future path of interest rates (which is what matters for spending and investment decisions), not today’s interest rate in isolation. We should also emphasize the difference between nominal and real interest rates—so that if the vertical axis denotes nominal interest rates, inflation will shift the IS curve (which depends on real rates) upward. But as a starting point, this isn’t really so bad: the fact that higher real interest rates, all else equal, push down output is probably the most fundamental observation in macroeconomics.

But the “LM” curve? It’s implicitly describing a monetary policy rule that disappeared decades ago. Here’s the story: the central bank has a target for the nominal money supply. Due to sticky prices, in the short run this corresponds to a target for real money balances as well. Generally, higher real output (“Y”) will increase the demand for real money balances, while higher nominal interest rates (“i”) decrease it. The set of possible equilibrium pairs (Y,i), therefore, has positive slope: when high Y is elevating demand for real money, i has to rise as well to bring demand back into line with the fixed supply.

Fair enough. But central banks today don’t target the nominal money supply: in the short run, they target nominal interest rates directly. In this light, a more sensible “LM” curve would be horizontal. Now, admittedly central banks try to operate according to policy rules, under which the response of interest rates to output (or, more accurately, deviations of output from its potential level) is generally positive. If we reinterpret LM as a monetary policy rule, the upward slope makes a little more sense. In the past few decades, however, the most important feature in central banks’ policy rules has been the response to inflation, not output; the runaway inflation of the 1970s was blamed on an overeager response to the (misperceived) output gap, and for better or worse no one wanted to repeat the same mistake twice. Meanwhile, although the US has never officially joined the bandwagon, many countries now operate under an inflation targeting framework, in which responding to inflation is the key feature of the policy rule. In this environment, depicting policy as a relationship between “Y” and “i” misses what’s really going on—better to abandon the upward-sloping LM curve altogether and use a simple horizontal line to depict the current policy rate.

I’m not alone in this sentiment. David Romer wrote an entire piece for the JEP in 2000 called Keynesian Macroeconomics without the LM Curve. (As the title suggests, he shares my feelings on the matter.) Tyler Cowen puts this at #6 on his list of grievances. It’s a pretty obvious point—yet, for reasons I don’t entirely understand, we still print thousands of undergraduate textbooks a year with LM front and center.

This is nothing, of course, compared to the abomination that is the AD/AS model, also included in undergraduate textbooks. AD slopes down for the same outdated reason that LM slopes up: given a constant money supply rule, lower prices imply higher real money balances and therefore lower real interest rates, which lead to higher demand. (It can also be justified using real balance effects, which are quantitatively irrelevant, or fixed exchange rates, which only exist in a few cases.) This has absolutely nothing to do with monetary policy as it’s currently implemented. Yet the simple AS and AD curves, made appealing by the apparent (but false) analogy to ordinary supply and demand, lurk somewhere in the minds of countless former economics students. This leads to all kinds of bad intuition—like the notion that sticky prices are problematic because they prevent the adjustment to equilibrium on the AD/AS diagram. (Wrong. Under current Fed policy, the price decrease -> lower interest rate -> improvement in demand mechanism is no longer operative, unless deflation combines with the Taylor rule to force a policy that the Fed should have chosen anyway. Certainly this is no use at the zero lower bound, where price flexibility is actually harmful, because it leads to more deflation and higher real interest rates.)

Somehow, the economics profession hasn’t quite completed the transition to a world where money supply is no longer the target of choice. In research papers, of course, the change happened years ago—but intuition and the hallowed undergraduate canon are much slower to change. Meanwhile, we’re left with LM, the strange vestige of an earlier era.

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25 Comments

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25 responses to “Why is LM still there?

  1. jcs

    mitt,
    here is an undergraduate book without LM built on the DR’s 2000 JEP paper http://elsa.berkeley.edu/~dromer/papers/text2006.pdf
    j.

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  3. Matt, saying we can drop the LM curve because the bank doesn’t target the money supply I think is correct.

    Saying that, if we insist on drawing it with an interest rate rule then it should be horizental I think is incorrect. The LM curve is supposed to represent (Y,i) pairs that clear a certain market. As such, it represents primitives in the economy that determine what is or isn’t a possible equilibrium outcome. It doesn’t represent the policy rule, it represents a constraint on what the policy rule can imply.

    Just because the bank chooses i in whatever manner does not at all mean that the bond market will clear at that i for any value of Y, it means that in this model, by setting i the bank is also setting Y. (In this model I would stress).

    • my point is just that saying that the LM curve describes policy rule is, I think, incorrect.

      It describes equilibrium in the choice of savings media – liquidity vs yield, money vs bonds.

    • Since we’re talking about the money vs. bonds margin, the specification of the monetary rule is pretty crucial here. There is a different LM curve corresponding to every M (in particular, higher M pushes the LM curve downward); economic primitives alone aren’t restrictive enough to guarantee a particular correspondence between Y and i.

      In practice, in the short term the Fed says “we will provide whatever M is necessary so that i is an equilibrium nominal interest rate, conditional on the current Y and other features of the market”. I think this is best depicted by a horizontal LM curve. In the longer term, the Fed obeys a monetary rule in which “Y” plays some part but is not the dominant feature. Either way, LM seems more confusing than edifying.

      • Adam P

        Matt, that is not how this model works. Yes the fed chooses M to imply i they want but different choices of M don’t yield the same i or Y.

        In a fully fexible price model money is neutral, the fed can’t change the real interest rate and thus can’t change Y. Does that mean the IS curve is vertical? No, It means the choice of nominal rate determines P instead of Y. ISLM fixes P completely, thus choosing the nominal rate amounts to choosing the real rate and this amounts to choosing Y.

        Still the fed behaviour of choosing M to imply the i they want is not at all the same as saying the money/bond market clears at that i for all values of Y.

        After all, the LM curve just traces out points at which money demand = money supply where money demand depends on Y and i, these are economic primitives.

  4. Bill Woolsey

    I like using IS and potential output to show the natural interest rate.

    I do think you should think again about to what degree you are developing a macroeconomic framework soley based upon central bank preferences for policy operations.

    How do you evaluate alternative monetary institutions? For example, an aggregate demand curve is great for looking at a target for the growth path of nominal GDP.

    You say it is worthless because central banks in fact target short term interest rates? Or they must target short term interest rates? Or they should target short term interest rates?

    Of course, I think a major problem we have today is that central banks, and some economists, are too wed to targeting short term interest rates and there was an inability to smoothly switch over to an alternative approach at the zero bound.

    • I do think you should think again about to what degree you are developing a macroeconomic framework soley based upon central bank preferences for policy operations.

      To a large extent I agree—that’s why I’m not a huge fan of IS-LM, and in my own work I use a much richer specification that allows for a wide variety of policy rules. But as long as we’re going to draw this kind of diagram, I think that drawing a horizontal LM that corresponds to a target interest rate is the most “neutral” choice: it illustrates the direct mechanism via which the Fed exercises control, no matter what its medium and long-term policy rule is. A richer LM that embeds a particular policy rule would be too model-specific.

      Of course, I think a major problem we have today is that central banks, and some economists, are too wed to targeting short term interest rates and there was an inability to smoothly switch over to an alternative approach at the zero bound.

      I think it’s fair to blame this partly on IS-LM and the accompanying intuition: by failing to emphasize that spending and investment depend on the entire path of interest rates, not just the current interest rate depicted in the “IS” curve, the model obscures the fact that even if you’re constrained by the zero lower bound today, credibly pledging to cut rates tomorrow (assuming expectations are not already at zero) is just as effective.

  5. JKH

    As a non-academic, but closer to the practitioner side, I remember noticing that Romer paper a few years back and it made immediate intuitive sense on the surface.

    As a hybrid interpretation of the traditional diagram, does anyone ever look at the upper half of IS-LM as an interest rate cycle?

    I.e. the economy expands as a function of central bank easing (upper IS), followed by the central bank tightening as a result of economic expansion (upper LM).

    (Maybe that’s similar to interpreting LM as a monetary policy rule – or expectation.)

  6. Kevin Donoghue

    I don’t see that an introductory model, which is what IS/LM is meant to be, is much improved by trying to reflect present-day central banking practice. Thinking about how an economy behaves if the money supply is exogenous is a good enough place to start learning macro. But I heartily agree about the AD/AS picture. That creates awful confusion.

    Incidentally, Greg Mankiw did a post about IS-LM versus IS-MP years ago:

    http://gregmankiw.blogspot.com/2006/05/is-lm-model.html

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  8. For Canada:
    In the very short run, which means the 6 weeks between Fixed Announcements Dates, the LM is horizontal in {i,Y} space. In the medium run, which means between 6 weeks and about 18 months, the LM is vertical in {i,Y} space, because the Bank of Canada adjusts the overnight rate target to try to keep output at what it thinks is potential output. In the longer run, which means longer than 18 months, the LM curve is horizontal at 2% in {inflation,anything} space.

    For a price-level targeting central bank, the long run AD curve is horizontal in {P,Y} space. For an inflation targeting central bank, the long run AD curve is horizontal in {inflation,Y} space.

  9. anon

    “Yet the simple AS and AD curves, made appealing by the apparent (but false) analogy to ordinary supply and demand, lurk somewhere in the minds of countless former economics students.”

    In my view, the AS-AD diagram is a bona-fide supply-and-demand story. AS is the supply of “everything but money”, i.e. goods and services, and AD is the demand for “everything but money balances”. It’s true that the “prices” on the _y_ axis and the equilibrium processes are generally more complex than a simple S-D diagram, but this is justified since macro is ultimately about market imperfections.

  10. anon

    “like the notion that sticky prices are problematic because they prevent the adjustment to equilibrium on the AD/AS diagram.”

    Not sure what you mean here. Sticky prices are “problematic”, in that an economy with no price stickiness at all would behave classically and be consistently at full-employment. Admittedly, we now suspect that complete price flexibility is unfeasible, because very small rigidities seem to have sizable effects when combined with other market imperfections such as monop-comp. Thus, we may have cases where a little rigidity is worse than a lot of it. But this has nothing to do with IS/LM or AS/AD. Whether nominal frictions “prevent the adjustment to equilibrium” will presumably depend on your preferred version of AS/AD.

  11. Frank

    I posted some 40 year old “history of economic thought” on Marginal Revolution: My exposure to IS-LM was from Thomas Sargent, ca. 1971. It was far richer than what’s in undergraduate textbooks today, and not all that hard to manipulate. All was consistent with an AS-AD framework. We had sticky wages in short run, flexible wages in long-run; real-nominal interest rate distinction clear, as a simple form of expectations was considered; and on and on]. And one can obviously represent various policies, as Nick says, but not just for Canada.

    Whatever, the merits or demirits of IS-LM as part of modern macro, and I don’t want to stand in anybody’s way, the problem of its presentation to undergraduates is not a macro problem, but an education problem.

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  13. JKH

    “In practice, in the short term the Fed says “we will provide whatever M is necessary so that i is an equilibrium nominal interest rate, conditional on the current Y and other features of the market”. I think this is best depicted by a horizontal LM curve.”

    The best you can say in this context is that in the short term, the Fed provides whatever delta M is necessary to set the target rate, where equilibrium is defined as the actual rate equal to the target rate.

    The Fed adds and withdraws delta M continuously toward this objective.

    There is no correlation between the actual level of M and the equilibrium nominal rate defined in this way – see the historic time series on excess reserves.

    “The best you can say” also reflects the power of the announcement effect, in which the required initial add or withdraw on an announced change is muted by the efficiency and anticipation of arbitrage.

    This all assumes M is reserves balances at the Fed. Nothing else matters in the short run.

    Horizontal LM works in this sense in the short run.

    • JKH

      meant “the Fed provides whatever delta M is necessary to move the actual rate toward the target rate”

    • JKH

      The more appropriate and relevant measure of M in the short run is excess reserves, as suggested. That captures the necessary delta M impact without the need to reference the (integral) level of required reserves, the latter being on its own irrelevant to the LM dynamic.

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  16. Pedagogically speaking, I like the vertical money supply curve because it allows you to show students what the fed is doing when it responds to demand shocks. It is also a little easier (and a little more dramatic) to illustrate what liquidity traps mean.

    Also, it underscores the idea that the Fed does not “control” interest rates, but rather targets interest rates imperfectly which I’ve always thought was a more important subtlety than whether the money supply curve is horizontal or vertical.

  17. Actually, I should say that i think it’s even becomes more important to stress the “target” idea when you are talking about the more general LM curve where you are simply talking about the “money supply”. That way you get a better sense that the Fed is reacting to changes in the market for money.

    Anyway, i definitely agree that the AS/AD model is an abomination.

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