From ISLM to NK Macro

Let me try it this way. This is written for macro students, and their teachers. But it's aimed at researchers too. It's about the role of money in macro models.

Ignore what New Keynesian macroeconomists say about their own models. Listen to me instead.

Start with the second-year textbook ISLM model. The price level P is fixed, so real and nominal interest rates R are the same thing. The nominal money supply M is also fixed. Which means the real money supply M/P is fixed too, and the LM curve slopes up. And the IS curve slopes down.

How could we convert that standard ISLM model into a New Keynesian model?

Assume that nobody uses paper currency, and everybody has a chequing account at the central bank instead. That makes it administratively very easy for the central bank to set the interest Rm it pays on those chequing account balances. (Assume the central bank has nationalised the commercial banks, and has abolished currency.) This means the opportunity cost of holding money is now (R-Rm) instead of R like in the textbook model (which implicitly assumes money pays 0% interest). This gives the central bank a second instrument of monetary policy. It can shift the LM curve right/down by increasing M (using Open Market Operations), just like in the standard model. But it can also shift the LM curve right/down by cutting Rm (which makes people less willing to hold money, for any given R and Y, so is like a fall in money demand).

Now bear with me for a minute (I will come back to this assumption below) and assume that the marginal propensity to spend out of income is one, not less than one like your textbook assumes. That makes the IS curve horizontal. Don't believe me? Do the math. Because the slope of the IS curve equals [(1 - marginal propensity to spend)/interest elasticity of spending].

So we now have a horizontal IS curve and upward-sloping LM curve. And you know what that means: the IS curve determines the rate of interest (call it the "natural rate" R*); fiscal policy doesn't work; and monetary policy determines Y at that rate of interest.

"But", I hear you ask, "why should we assume that the marginal propensity to spend is one?". Well, it depends on whether we have got permanent income or current income on the horizontal axis, doesn't it? If it's permanent income, it's quite plausible to assume that everything just scales up in proportion, so if permanent income doubles then consumption and investment spending should both double too, just like if our country annexed a second identical country. But if it's current income on the horizontal axis, and we hold expected future income constant, then sure, the IS curve will slope down just like in the regular model, because the marginal propensity to spend out of current income is less than one. And an increase in expected future income shifts the IS curve to the right, by exactly the same amount.

Now let's drop the assumption that the price level is fixed, and replace it with an expectations-augmented Phillips Curve. And we must now remember to distinguish between real and nominal interest rates. Investment and saving depend on the real interest rate, but the central bank sets a nominal interest rate that it pays on chequing accounts. So we need a vertical wedge, whose height equals expected inflation, stuck between the LM and IS curves, to the right of where those two curves cross, to determine Y. If expected inflation increases, the size of that wedge increases, and Y increases too (holding constant M/P, Rm, and expected future income).

Got it? All you need now is some math. But math is not my comparative advantage, so I will leave that to you.

There is just one difference between my modified ISLM model above and the textbook NK model. My model has got M in it, and Open Market Operations in it. The textbook NK model doesn't. That's a problem for the textbook NK model.

1. The first problem is that the textbook NK model is less realistic than my model. I can talk about Open Market Operations (aka "Quantitative Easing") and the textbook NK model can't.

2. The second problem is deeper. If we don't have M in the model, then how is permanent income determined? It's no good saying that permanent income is determined by the supply side, and must equal the natural level of output Y* in the expectations-augmented Phillips Curve; that's just begging the question of whether there will be enough permanent demand for that level of output. There won't be enough permanent demand for permanent output, if M/P isn't big enough. With a horizontal IS curve for permanent Y, we need an upward-sloping LM curve to pin down a long run equilibrium. My model has an upward-sloping LM curve. The textbook NK model does not. It just assumes, with no justification for that assumption, that permanent income equals Y*, and so current income only diverges temporarily from Y* if the central bank makes random mistakes in setting Rm. Keynes wouldn't like that assumption, because it means just assuming long run full employment, with no explanation of why the economy might get there.

Comments

[Tel]

I thought it was "sticky prices" that were supposed to cause unemployment (and sticky wages of course, that being a price of labour).

So can you have long run sticky prices? Not an entirely outrageous assumption that they would eventually come unstuck, and at least approach full employment.

[Henry]

"And you know what that means: the IS curve determines the rate of interest (call it the "natural rate" R*); fiscal policy doesn't work; and monetary policy determines Y at that rate of interest."

Nick,

I was wondering whether liquity trap conditions can be fitted into this model?

Do you believe in the liquidity trap?

[Nick Rowe]

Henry: Yes. No. And that quote about horizontal IS curve is irrelevant to your question, because liquidity trap is horizontal LM curve.

[Henry]

"because liquidity trap is horizontal LM curve."

Yes I know. I was pointing to the "monetary policy determines the interest rate" part. If there was a liquidity trap then that point would not apply.

Given that monetary policy seems to have been ineffective in the last 8 years (you might disagree?), I am wondering whether this points to liquidity trap effect?

I was just wondering if you believed in the liquidity trap and if you did, how you would rationalize it within your model.

[Nick Rowe]

Henry: In that quote, I did not say "monetary policy determines the interest rate" . I said the exact opposite. I said monetary policy determines Y (income), at the rate of interest determined by the IS curve.

[Henry]

Sorry. Misquoted you. Same questions apply. If these questions aren't where you want to go with the blog, that's OK.

[Antti Jokinen]

Nick:

I'm not a fan of ISLM, because I don't believe in M :-) And I cannot discuss neither of these models at the same level as you can, because even though I've used some time in trying to understand them, how they relate to the real world, I can't say I've really succeeded.

But what you said here got me thinking: "There won't be enough permanent demand for permanent output, if M/P isn't big enough."

Are these some kind of permanent M's and P's you are talking about? Or what? Going back to your talk about non-synchronisation, don't you have to assume the degree of non-sync if you are saying something about M in this context? Perhaps I just miss the point. As I said, I don't get these models.

[Nick Rowe]

Antti: I'm using "permanent" in the special sense of the Permanent Income Hypothesis (a hypothetical constant stream of income that has the same present value as the expected stream).

Non-synchronisation of payments and receipts (and increasing costs of increasing synchronisation) is implicitly assumed in the money demand function that underlies the LM curve.

But this post won't make much sense to anyone who is not already very comfortable with ISLM. Even then, it won't be easy.

[JKH]

"the IS curve determines the rate of interest (call it the "natural rate" R*)"

graphically de defacto yes

but causally the rate determines the IS curve ?

[JKH]

can you go backwards and explain again intuitively why the NK model implies the equivalent of a horizontal IS curve - i.e. explain that without any further reference to ISLM ?

[Antti Jokinen]

Nick: Thanks! I think I'll focus my comments on your posts which deal with real-life fundamentals. Like your posts on red money ;-)

One casual comment on this one: "Non-synchronisation of payments and receipts (and increasing costs of increasing synchronisation) is implicitly assumed in the money demand function that underlies the LM curve."

Yes, but how badly are those non-synchronised? For instance, in Patinkin's world you do not need M at all to have enough permament demand for permanent output, because there can be -- if I dare to try to use economists' language -- a barter equilibrium. Starting from that, I would think that M can be whatever, if we assume (shouldn't we?) that (some) goods can also be bartered without the use of 'money' even in a "monetary economy".

[Antti Jokinen]

Please don't mention Clower... ;-) If you feel that I just don't get it, that I don't speak the same language with you, the feel free to let this be. I cannot discuss ISLM, or any other model, without at the same time keeping one eye on the real world.

[Matías Vernengo]

Not sure why you call the horizontal IS with conventional, positively sloped LM, a New Keynesian (NK) model. If anything the ISMP model (regular IS and horizontal LM) is often presented as the NK model. What textbook you have in mind. I prefer the simple Wicksellian model (monetary rate determined by central bank, and natural rate by IS) with price rigidity, since the NK model is really neo-Wickesellian (something like thishttp://nakedkeynesianism.blogspot.com/2011/11/neo-wicksellian-macroeconomics.html).

[Nick Rowe]

Matias: Welcome!

On the LM curve: you are right. The "cashless" (whatever that means) NK model has a horizontal LM curve. My model deliberately stops short of going fully NK, so I keep the LM curve upward-sloping. Because if we have a horizontal IS curve, you can see why a horizontal LM creates a big problem.

On the IS curve: most economists think the NK model has a downward-sloping IS curve. But that is only true in the short run, if we assume expected future income constant. And that is exactly what NK macroeconomists do, but it's an assumption that is totally unjustifiable. They assume that the economy approaches full employment output in the limit as time goes to infinity. With no justification for that assumption coming from the model. Keynes would scream blue murder, and rightly so. If we take the consumption-only NK model, for simplicity, you can see that if we cut present and future C by the same percentage, the MRS between present and future consumption is unaffected, so the rate of interest compatible with that being an IS equilibrium is also unaffected. The "long run" IS curve is horizontal. So with horizontal IS and LM, equilibrium output is indeterminate, even if the central bank sets exactly the right interest rate. They slipped in the "long run full employment" assumption by the back door.

[Market Fiscalist]

For the NK model to fail to work people need to be pessimistic about the future and expect output never to get back to full-employment levels, right ?

If you introduce money into the model then the CB has the option of varying the money supply instead of just setting interest rates. If the CB gives everyone more money and this doesn't make people more optimistic why won't prices just adjust to the new money supply and everything else stay the same? If prices are sticky then increasing M may work in the short term, but won't people get used to it, and things will revert to the pessimistic underemployment equilibrium unless the CB constantly increases the rate of increase of M?

Is there an assumption that introducing M into the models also allows people's expectations to be better controlled ?

[Market Fiscalist]

For the NK model to fail to work people need to be pessimistic about the future and expect output never to get back to full-employment levels, right ?

If you introduce money into the model then the CB has the option of varying the money supply instead of just setting interest rates. If the CB gives everyone more money and this doesn't make people more optimistic why won't prices just adjust to the new money supply and everything else stay the same? If prices are sticky then increasing M may work in the short term, but won't people get used to it, and things will revert to the pessimistic underemployment equilibrium unless the CB constantly increases the rate of increase of M?

Is there an assumption that introducing M into the models also allows people's expectations to be better controlled ?

[Nick Rowe]

JKH: I've been trying to think of a simple thought-experiment to explain why the long run IS curve is (at least roughly) horizontal. A closed economy merging with the identical closed economy next door is the best I can think of; I and S and Y all double, but the rate of interest compatible with I=S stays exactly the same when the two countries join up. (I'm assuming constant returns to scale in everything.)

Antti: the ISLM model (implicitly) assumes that barter is impossible. It's either a model of a monetary exchange economy, or it makes no sense at all (because unemployed workers and firms would barter their way back to full employment, even if the rate of interest was too high). It only makes sense from a Clowerian perspective, not just on monetary exchange, but on the Dual Decision Hypothesis (where a constraint on sales of labour or goods spills over to reduce your effective demand for goods or labour).

[dan thorn]

Nick,
isn't the more rudimentary issue that IS-LM doesn't model the entire economy. It only models the part of the economy sensitive to interest rates.
It surely has to be clear at this point that there is a portion of the economy not directly sensitive to interest rates.

You had a terrific post a few years ago I wish I could find that explained why fiscal stimulus is never good policy. It was one of the best posts you had and clarified a really important issue. I wish you would have extended the idea to include what regulates fiscal spending, which is essentially a plug, or assumed level in your analysis. and equally of interest, what is the right level of fiscal spending, and why.

If anyone remembers that post and can send refer me to it. I'd be very grateful.

It makes no sense to increase fiscal spending if interest rate sensitive economic activity is below potential.
It does leave the interesting question, however, what regulates fiscal spending, and what measure is there to know whether or not it is above or below potential.

thank you,
Dan

BTW, for what its worth, I think your use of math is one of your strongest attributes. It seems to be the case that math creates a distraction for whatever reason, and rather than being merely a useful language to model assumptions with precision it becomes an end in itself and ends up not illuminating much.

[Miguel Madeira]

«"But", I hear you ask, "why should we assume that the marginal propensity to spend is one?". Well, it depends on whether we have got permanent income or current income on the horizontal axis, doesn't it? If it's permanent income, it's quite plausible to assume that everything just scales up in proportion, so if permanent income doubles then consumption and investment spending should both double too, just like if our country annexed a second identical country.»

Even in that situation, I don't think that this will mean a marginal propensity to spend of one.

Assuming a consumption function "C = a + b*Y", the rule that everything just scales up in proportion will mean a=0, not b=1.

[dan thorn]

Miguel, you need to write a function for MARGINAL consumption.

[Nick Rowe]

Dan: thanks!

I can't remember that particular post. But then I can't remember half the posts I write.

Some sectors are less interest-sensitive than others; but like all simple macro models, ISLM is trying to take an average.

Miguel: In a consumption only economy, with no I or G, we know that C=Y in equilibrium. If we assume a utility function like U=log(C), so marginal utility is 1/C, then C = permanent income, provided r = the rate of time preference. So at that rate of interest, any constant level of C=Y is an IS equilibrium. We can add in investment too, and the long run result stays the same, provided the depreciation rate and K/Y ratio stay the same as Y increases.

By "marginal propensity to spend" I mean "marginal propensity to consume plus marginal propensity to invest".

[Nick Rowe]

Tel: (Just found your comment in the spam filter) "I thought it was "sticky prices" that were supposed to cause unemployment (and sticky wages of course, that being a price of labour)."

Many people say that, but it isn't quite right. If the AD curve doesn't cross the LRAS curve, for example, flexible prices don't help. And if the AD curve slopes the wrong way, it will even make things worse.

[Donald A. Coffin]

Even if it's permanent income, wouldn't the MPC be less than 1 unless the APC = 1? E.g.:

PI = 100
C = 90

Double them
PI = 200
C = 180

MPC = .9

Unless I am misunderstanding something.

[Donald A. Coffin]

I see. You have a consumption only model, in which Y = C. But as soon as you bring I into the model...?

[Nick Rowe]

Donald: wouldn't I scale up too (in the long run), to keep the K/Y ratio the same?

And in the shorter run, since K adjusts slowly, the IS curve would likely slope the wrong way. Lower Y means lower desired K, so I drops, so you could need r to drop to keep I=S.

[JKH]

minor question:

Its been a long time since I took a (introductory) macro course, but doesn't the idea of merging mpc with a marginal propensity to invest muck up the concept of the multiplier and the Keynesian cross?

[Nick Rowe]

JKH: No. The multiplier and Keynesian Cross still work fine.

Assume Y=C+I+G

C=a+bY

I=d+eY

So AE=[a+d+G] + [b+e]Y

Solving for Y=AE gives us:

Y = [1/(1-b-e]x[a+d+G] where [1/(1-b-e] is the multiplier.

But if (b+e) > 1 we get an "unstable" equilibrium, an apparently negative multiplier, and we need [a+d+G] < 0 to have Y > 0. Intuitively, the AE curve is steeper than the AE=Y 45 degree line, which means positive feedback from Y to AE is so strong the economy explodes or implodes if it ever gets away from equilibrium.

[Jamie]

Nick: “The nominal money supply M is also fixed”

That’s my favourite assumption in the whole of economics. Seriously. It’s a great assumption because it forces us to think clearly about our logic of money.

Nick: “That makes it administratively very easy for the central bank to set the interest Rm it pays on those chequing account balances”

If the money supply is fixed, where does the central bank get the money to pay the interest? It seems to me that we must to add a source for that money to the model, or the model doesn’t make sense within an assumption of a fixed money supply.

Assume that the central bank earns interest on its government bond holdings. That solves the central bank interest problem. However, it creates another problem. Where does the government get the money to pay the interest on the bonds? It must have raised the money through tax or further bond issue. Assume tax.

We now have a model where the government taxes the private sector, uses the tax to pay interest on bonds to the central bank, which, in turn, uses the bond interest to pay interest on money accounts held at the bank … to the private sector. This is redistribution from tax payers to money account holders. In other words, it rewards people who hoard their money at the bank at the expense of people who earn and spend money in the wider economy. Hmmm.

I don’t think that elaborate alternative models are required to question the absence of money in New Keynesian models. I would simply ask where profit fits into New Keynesians economics? If we don’t have money, we don’t have profit, and who on earth is going to believe an account of capitalism without profit? Even Karl Marx recognised the importance of profit – and he wanted to abolish it! It the 20th century taught us anything at all, surely it was the importance of profit as a galvanising force in economics. An account of economics without money or profit is not credible. It does, however, fit well with the rest of our post-factual world, so perhaps we deserve it.

[Matías Vernengo]

Yep, you're right about the long run IS curve, which by the way means that the policy game is to pin the exogenous interest rate correctly at the natural level. Thanks. Very useful post, by the way.

[Nick Rowe]

Matias: thanks!

Jamie: Here is my recent post where I lay out the model that describes what the NK model must implicitly be assuming about money

[Gerard MacDonell]

I was thinking you might write something along these lines. It seems to me that this would be central to the case against neo-Fisherianism. Do you see it that way? If you were to elaborate on that, then I could guarantee at least one reader!

Separately, I don't think QE has anything to do with money. Bringing it into money or money into it does not seem to be clarifying. But I guess that is a whole nother debate.

[Nick Rowe]

Gerard: lovely question! I hadn't thought of that. But now I have.

The question that must be asked of Neo-Fisherians is this: what happens to the money supply when the central bank pegs a higher nominal interest rate?

For simplicity assume we are initially at Y=Y*, with zero inflation, constant money supply, stationary economy, rational expectations and perfectly flexible prices. The central bank then suddenly announces a permanent 1% increase in Rm (the nominal interest rate paid on holding money). What happens?

In order to get the Neo-Fisherian result that inflation immediately rises by 1% (with no jumps in the price level) , we would need to assume that the central bank announces at the same time that the money supply will henceforth also be growing at 1% too. The LM curve shifts vertically upwards on the announced 1% increase in Rm, but at the same time expected inflation jumps by 1%, creating a 1% vertical wedge between the IS and LM curves, keeping the economy at Y* with the same M/P (no jump in either M or P). Thereafter, M and P both rise at 1% per year, so M/P stays constant, and the economy remains at Y*.

What is driving this result is that the central bank announces a growing money supply. That's what causes inflation to rise, not the higher nominal interest rate set by the central bank.

If the central bank announced a growing money supply, without at the same time announcing a higher nominal interest rate Rm paid on holding money, the result would be an initial one-time upward jump in P, to cut M/P. (The standard "inflation overshooting" result when the money growth rate increases). Followed by 1% inflation.

If the central bank announced a higher Rm, while holding the money supply constant, the result would be an initial one time fall in P, to increase M/P. Followed by 0% inflation.

[Boyan Zahariev]

Hi Nick.
Yet more food for thought from you, but I have one clarifying question: A lot seems to hinge on the idea of permanent income. Putting it on the horizontal axis, do you thus assume that consumption (and investment) behaviour is driven by the PI hypothesis? What bugs me is the exact justification for using permanent vs current income on the horizontal axis. If it really is the PI hypothesis, do you not think that credit constraints (thus rationing) deliver a serious blow to the viability of the PI idea, hence making current income consumption a believable alternative?
Thanks

[Nick Rowe]

Boyan: the standard (simplest version) New Keynesian model assumes PIH. And since I wanted to concentrate on the monetary side of the model, I just took the consumption side as it is. As you say, things like credit constraints will make PIH only a half-truth at the individual level. But credit constraints are not exogenous. If (say) half the individuals are credit-constrained and Hand-To-Mouth in an initial equilibrium, if permanent income then halves, across the whole economy, lenders will tighten those credit constraints in proportion, and we should still see half the individuals credit-constrained in that new IS equilibrium. So the Long Run IS curve would still be horizontal.