Wednesday, November 30, 2011

Shifts of curves vs. shifts along curves

Lots of people are rightly excited about concerted central bank action this morning. Scott Sumner notes that it lead to an immediate increase in interest rates. He then opines:

"With easier money we had a small rise in real interest rates, which mostly reflect expected real economic growth. Inflation expectations also rose. Of course this is all completely inconsistent with the Fed’s operating model; they think we need to lower long term rates. And it’s also completely inconsistent with the standard IS-LM model, as interpreted by Keynesians. But it’s completely consistent with the market monetarist version of IS-LM, as developed by Nick Rowe...

...Authors need to re-write the IS-LM model to show upward-sloping IS curves.

Market monetarism: Describing the world as it is, not as textbooks say it is."

Now I don't have a real problem with market monetarism, but this whole business of an upward sloping IS curve seems to make a mistake that you see intro students make a lot: confusing shifting curves with shifts along curves. Part of me is hesitant to make so simple a critique of guys like Scott Sumner and I suppose Nick Rowe (it's been a while since I've read the post on why he thinks the IS curve should be upward sloping), but since other intellectually formidable guys think it's nonsense, it's worth throwing this out there.

The IS curve is downward sloping because holding all else constant, a reduction in interest rates increases investment. Changing only interest rates, demand increases. But this is very different from interest rates changing as a result of a shift of the IS curve itself due to changes in demand that are unrelated to changes in interest rates. This bugs my students a lot - it takes a couple weeks to get used to the idea that "increasing demand" is an ambiguous statement. I press them - do you mean increasing quantity demanded or increasing the demand schedule? It all depends on what's causing the change - is it due to a change in price or a change in something else? One is a shift of the curve, one is a shift along the curve.

So what are we dealing with here? We have increasing interest rates. Why? Sumner himself says we have increasing interest rates because of growth expectations. Anticipated increases in future income shift the IS curve to the right. And if we can sum up the impact of this morning's policy announcement in one phrase it would be "anticipated increase in future income". We try to segment monetary policy into movements of the LM curve and fiscal policy into movements of the IS curve for obvious reasons, but when we're talking about changes in expected future income we have to be careful. There are two questions to ask:

1. Is demand changing because interest rates are lower? If the answer is "yes", then you are moving along the IS curve.

2. Is demand changing because something other than interest rates is making investors willing to invest more than before, given the same interest rate as before? If the answer is "yes", then you are shifting the IS curve itself.

It is quite plausible to have both. But saying "we observe demand increasing with interest rates" is not the same as saying "holding all else constant, an increase in interest rates increases demand".

We often see prices and demand both go up simultaneously in other markets - one need not throw out downward sloping demand curves over that.

Right? Tell me if I'm thinking about this the wrong way, please.


  1. Yeah i feel like from that quote "expected real economic growth" is literally a textbook cause of a shift of the IS curve to the left. For there to be an increase if the LM curve also shifts though the IS curve has to shift by more than the LM curve.

    But this is an expectation effect, right, because it doesnt go into effect until dec 6th, so the LM curve hasnt actually shifted?

    I dunno.

  2. Indeed - I pulled it word for word from Williamson, in case he jumps into the fray.

  3. 'Market monetarism: Describing the world as it is, not as textbooks say it is.'

    I have to admit I am in continual amazement at Sumner. This is coming from the guy who defends the EMH and RET post-2008?

  4. Nick Rowe in the post Summer links to:

    "Now, if you insist you could say that the IS curve slopes down, as normal, but the expected future monetary tightening, and consequent drop in expected future income, causes the IS curve to shift down/left. Each IS curve is drawn holding expected future income constant.

    You could say that, but is it useful to say that? The whole point of drawing two curves -- a supply and demand curve, an indifference curve and budget constraint, an IS curve and LM curve -- is that most of the time the things that shift one curve are different from the things that shift the other curve. If an expected future shift of the LM curve automatically shifts the current IS curve, the two curves are not independent."

  5. Anon I think a substantial criticism, originally made my Piero Sraffa (?) of every equilibrium model - including both IS/LM and supply/demand - is that the curves *cannot* move independently because a change in one creates ripple effects throughout the rest of the economy, as well as changes in expectations.

  6. Daniel:

    First: an IS curve isn't strictly a *demand* curve. It's a *semi-equilibrium condition*. It's combinations {r,Y} such that Y demanded given r and Y equals Y. (The AD curve isn't strictly a demand curve either, for the same reason.). In micro, the quantity of apples demanded doesn't depend on the quantity of apples sold. But strictly, it should, because the more apples that are sold the higher will be the incomes of apple producers, and the higher are incomes the greater is demand for goods, including apples. We ignore that effect in micro, because income from selling apples is too small a part of total income to matter much, and apple producers probably eat their own apples anyway, rather than buying them for money in the apple market. But we can't ignore that effect in macro. It's the Old Keynesian multiplier. (Yey for Old Keynesians!)

    Second: if you take the textbook derivation of an IS curve, but add the assumption that MPC+MPI>1, you will find that it slopes up. (MPI is marginal propensity to invest). Because the slope of the IS curve has (1-MPC-MPI) in the denominator, and the "elasticity" of investment plus consumption wrt the rate of interest in the numerator.

    Third: what Anonymous above said that I said. If you like to think of this as a shift in the IS curve, that's OK. But the whole point of drawing an IS curve is that it is the curve that is supposed to stay fixed when the LM curve shifts. I'm almost tempted to *define* the IS curve as "the other curve, whatever the hell it is, that stays fixed when monetary policy changes"!

    Fourth: whether you want to think of it as a shift, or movement along, depends in part on how closely related you think Y and E(Y) are. Do C and I depend on Y, or E(Y), or both? How long is the "present period"? How does expected future income change if current income changes?

    Unlearningecon: This has nothing really to do with *equilibrium* per se. It's whether we can depict equilibrium with 2 curves in a 2 dimensional diagram, where the two curves move independently. Life is really simple when we can, but sometimes we can't, and we have to resort to n-dimensional math.

    General thought: the ISLM model, which we teach in second year, is really much more complicated than anyone thinks it is.

  7. Oh, Daniel: I just noticed a minor glitch in your terminology. We normally contrast a shift in a curve vs a *movement* along a given curve. I think this normal terminology is easier to remember than when you talk about "shifts along" a curve. Not that it really matters, but students need all the help they can get remembering this difference, and using totally different words helps a bit.

  8. Nick I think you might have missed my point. It was basically that a movement of any curve on one of those models creates effects that move the other curve, which in turn creates more effects etc.


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