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“Is the IS a demand curve for output? Well, not really, if you want to be picky. And I do want to be picky.”

I think you’re quite right to be picky. Hopefully students who are meeting the IS curve for the first time will have encountered (in micro classes) the idea that demand for a good is a function of its own price (obviously) and also the price of a complement or substitute. So they should have seen a diagram with prices on both axes, and a curve showing the locus of points (Px, Py) such that both markets are in equilibrium. Like, say, Figure 1.

Isn’t the IS curve analogous to a curve like that? The essential difference is that the goods market is cleared by quantity adjustment because the price level is fixed, whereas the bond market price (actually 1/r if we’re talking about perpetuities, a.k.a. consols) is flexible.

"If monetary policy depends on what the central bank governor had for breakfast, maybe you had better add the relative price of eggs into the model."

I wish I'd written that.

I'm confused. You wrote:

"Over longer periods still, the Bank of Canada does whatever is necessary to try to keep its expectation of two-year-ahead inflation at the 2% target. So if you put inflation on the horizontal axis, the "long run" LM curve is horizontal at 2% in {inflation,anything} space."

If inflation is on the horizontal axis, and the goal is to hold inflation constant at 2% (over longer periods), isn't the long run LM curve VERTICAL in {inflation, anything} space, at inflation = 2%?

Also: "The IS is not strictly a demand curve, and nor is the AD curve."

The IS curve is in no way a demand curve. It is a schedule of {r,Y} values where the goods market is in equilibrium.

For any value of r (r here, referring of course to the real interest rate), it indicates the value of Y where AS=AD.

The best way to think about IS-LM, imho, is in a differential equations framework (if only because I recently completed a video refresher course on the topic.)

dY/dt = f(Y,r)

dr/dt = g(Y,r)

IS is the nullcline for income, the line that shows values of {Y, r} where Y does not change: IS tells us where dY/dt = 0.

LM is the nullcline for interest rates, the line that shows values of {Y, r} where r does not change, and dr/dt = 0.

The intersection indicates the unique value of {Y, r} where dY/dt = dr/dt = 0.

Of course, as Tobin used to say, this is a snapshot of the economy, true for a moment in time. Over time, both lines are shifting around as the economy is beset by various shocks outside of the model.

I should have previewed!

"The biggest problem with ISLM is that cheapskate university administrators only supply us with two-dimensional chalkboards. And cheapskate textbook publishers only supply us with two-dimensional paper. And many of us, and even more of our students, find it hard to see things in more than two dimensions. (Actually, I'm teaching demand and supply right now, and two dimensions is hard for those who think that either P causes Q or Q causes P.)"

Ergo, differential equations. No? :)

marcel: well-spotted! I have changed "horizontal axis" to "vertical axis".

I'd be curious to know your thoughts on Sumner's recent post, particularly this section:

"I favor an ad hoc approach to models–use the simplest model that gets at the issues you are interested in. Start with a simple economy with money and goods, no bonds. The supply and demand for money determines the price level and/or NGDP. That’s most of human history. Add wage price stickiness and you get demand-side business cycles. Add interest rates and you get . . . well it’s not clear what you get."

That makes sense to me. ISLM focuses most of the attention on the short-term risk-free interest rates (i.e. "the interest rate"), but, meanwhile, no one can even agree as to the shape of the IS curve. What good is a model in which one of the central dynamics can either be upward-sloping or downward-sloping depending on exogenous, generally-unspecified circumstances?

marcel: "The IS curve is in no way a demand curve. It is a schedule of {r,Y} values where the goods market is in equilibrium."

*If* the IS is about the goods market, and that's a big "if", it is not a full equilibrium condition. It is a semi-equilibrium condition. Yd(Y,r)=Y. It says nothing about Ys. For full equilibrium Yd=Y=Ys, where Ys is what firms/households *want* to sell.

Tobin was right to be thinking about these questions. But I'm not sure he was right about the answers. I think Tobin was wrong about hot potato money in "banks as creators of money". And that monetary hot potato is an inherent part of the stability analysis. I'm still getting my head around this. Don't expect a coherent answer from me! My previous post as as far as I have got, so far.

I want to know whose behaviour is behind those differential equations of yours, and behaviour in which market. Who is learning what, and what expectations and plans are they revising? I think it's as or more coherent to think of the output market as adjusting to LM equilibrium, and the bond market adjusting to IS equilibrium.

Yep, the money and fiscal multipliers have the "wrong" sign if IS is steeper than LM. But if it's not stable, that's to be expected.

Kevin: I think that's part of it. But those diagrams seem to just show Walrasian equilibrium for 3 goods. If one of those goods is the medium of exchange, we cannot be talking about some sort of Walrasian equilibrium.

Ritvik: yes, in equations we can do multiple axes at once. When I look at the equations in Steve Williamson's textbook, his New Keynesian model looks exactly like ISLM (with one minor exception, because he has labour supply depend on the real interest rate as well as real wage). But the pictures look very different.

IS-LM is not keynes. I mean it is not the keynes valid still today, and i´m not sure if it is still good for something. Perhaps for "normal times"...
I think the problem is one interest rate for three markets: money, bonds and capital. And to reach equilibrium in the three with only one interest rate is really a rare circunstance.
Interest rates trend to converge when cycle is booming (because risk premia fall), but to diverge when cycle is in recession, as today, because risk premia rise a lot.
All that don´t fit well with IS-LM. I think Keynes´analysis, for current circunstances, is valid. but I don´t mean that expansionary fiscal policy is useful.

Ken: I'm sympathetic. The basic macro model must have goods and money. Bonds come in third. Paul Krugman and Brad De Long agree. (Not all Keynesians do; the NK model *seems* to have just goods and bonds.) But at times like these (for the US anyway) I think it's important to bring in bonds, and try to figure out what the IS looks like, and how things adjust if we are "off" the curves.

Scott's a pragmatist. I'm less so. But Scott keeps asking me: "So Nick, what are the policy implications?" And I'm slowly trying to answer him.

Luis: "I think the problem is one interest rate for three markets: money, bonds and capital."

Stop right there! What is the "money market"? All markets are money markets!

"If one of those goods is the medium of exchange, we cannot be talking about some sort of Walrasian equilibrium."

Agreed it's not Walrasian; there is (notional) excess supply in the labour market. To me it's just a Barro-Grossman type equilibrium, i.e. Yd=Ys and the stocks of bonds and money are willingly held given r and P. I'm pretty sure Hicks understood that in 1937. There was a conference in the 1970s where all that stuff was being thrashed out and Hicks's reaction was, isn't this all rather obvious? (However he did acknowledge that there is a lot to be said for having a rigorous proof of things that look obvious.)

To me it seems you have a problem: neither Hicks nor Barro-Grossman made any fuss of the fact that money is the medium of exchange. It's just an asset. You want IS/LM to be a Market Monetarist model, but Hicks did not design it as such. But if it’s any comfort to you, his last book, A Market Theory of Money, suggests to me at any rate that he would sympathise with your aims. Surely there’s some way of getting IS/LM using CIA constraints or whatever?

Incidentally Mankiw has weighed in (see blog) on Krugman’s side in favour of IS/LM. The cynic in me suggests that this is just solidarity between textbook writers, but in fairness I’d say they both believe in what they are saying.

I thought Greg Mankiw's post was very sensible.

I think Hicks did ISLM as a quick and dirty way to stop people arguing at cross purposes, but then, yes, he spent the rest of his life wondering what was really going on underneath all that. I think he would have been sympathetic to this. I like to think so, anyway. Take his temporary equilibrium, replace the single auctioneer with several, including some slow ones, and add money.

GRRRH! My response disappeared into the ether! I'll try again.

Nick responded:

*If* the IS is about the goods market, and that's a big "if", it is not a full equilibrium condition. It is a semi-equilibrium condition. Yd(Y,r)=Y. It says nothing about Ys. For full equilibrium Yd=Y=Ys, where Ys is what firms/households *want* to sell.

...

I want to know whose behaviour is behind those differential equations of yours, and behaviour in which market. Who is learning what, and what expectations and plans are they revising? I think it's as or more coherent to think of the output market as adjusting to LM equilibrium, and the bond market adjusting to IS equilibrium.

My response to para 1: I don't think *want* is the correct way to think about this. On each schedule (IS, LM) participants in the relevant market (both buyers and sellers in that market) find that their short run expectations are fulfilled. Whether or not they would like to buy or sell more in that market they are not receiving any information that tells them how to alter their behavior in such a way as to improve their situation. Each schedule traces out (Y,r) combinations in which that market is in Nash equilibrium. Each represents a partial equilibrium, for that market alone. Put all the partial equilibria together and you find the point that is the GE. IS-LM is a graphical exposition of a very simple GE model.

A caveat about the last 2 sentences.

The GE is the equilibrium for a moment in time. As expectations are revised, the K stock changes in response to investment, and the economy experiences various *shocks*, the GE, the intersection of IS and LM shifts as each curve responds to these phenomena. It is a temporary equilibrium, by no means a steady or stationary state. In this sense, it corresponds to one period in the sequence traced out by a DSGE model over time.

My response to para 2: This is a legitimate question, but I am going to throw up my hands here. IIRC, there is, or was, a very large literature consisting of stories that explained the dynamics when:

(a) away from full employment equilibrium (but at the intersection of IS & LM):

(b) away from the intersection of IS-LM wherever that occurs (above or below full employment), and:

(c) away from either or both of the schedules (i.e., away from equilibrium in either or both of the underlying markets).

I suppose I could come up with a set of stories, but I doubt that I would persuade anyone, likely not even myself. I think Bewley's book on sticky wages was a very useful step in that direction.

Keynes, in section 2 of his chapter 19, "Changes in Money-Wages", explored possibilities for (a) above. The basic story IIRC was

w --> p --> M/p --> r --> AD

in the short run (I'm ignoring here his treatment of issues of open vs. closed economies), but with long run implications through effects on expectations about future wage and price cuts.

good, that´s right

"Cheapskate university administrators only supply us with two-dimensional chalkboards. And cheapskate textbook publishers only supply us with two-dimensional paper."

I know this is a joke, but really it's increasingly untrue.

To what extent should eBooks and (laptop-driven) video projectors, with animated 3-D graphs, change how economics is taught?

Jon: I was wondering if anyone would pick me up on that.

When I was a young prof, I once made a pathetic cardboard cutout of a model in 3D. It didn't really work. Even now, I sometimes stand in the corner of the classroom and wave my arms around to try to mimic a 2D curve in 3D space. I think that some students get it, but I'm not really sure.

I would like to see some profs try this with modern technology. Probably some already are. I'm too old and technophobic to try, but that doesn't really matter, because the next generation will be better, I hope.

re 3d.

Back in the spring, when I was having the brain wave of the multidimensional cube around spherical search space, a visual that kind of worked for me, was the axis of M/P being equivalent to the shaft of one of the old mechanical umbrellas, and raising lowering the umbrella support had an effect along each of the other goods axis, so if it was lowered, it could penetrate a point where commodity swapping or barter, frictions, alternate money showed up between goods. And the level that all of the supports were at was the price level.

Think it was kind of micro, but had a hard time, with the AS/AD, and interest.

new gary gorton is out.

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