The IS curve

You might think you understand the IS curve. You probably don't. And your failure to understand it properly means you don't understand how an excess demand for money is an integral part of the theory of the IS curve, underlying any state of deficient-demand unemployment. And you don't understand the monetary transmission mechanism properly. I don't understand it as well as I would like to either. Nobody does.

This is my attempt to understand the IS curve better. It will probably help you understand it better too.

It's a downward-sloping curve in {r,Y} space, the r is the real interest rate, and Y is real income. If r is at the right level (call it the "natural rate"), Y will be at the right level (call it "full employment" income). If r is above the natural rate, there will be insufficient demand for newly-produced goods, so Y will be below full employment, so there will be unemployment caused by a deficient demand for goods.

What is the theory behind the IS curve?

Let's simplify massively. Forget net exports, forget government spending and taxes, forget investment, forget consumer durables. The only source of demand is consumption demand for newly-produced goods (or services). Forget firms and the labour market. All consumers are producers who are self-employed workers, who convert their labour into output. One unit of labour produces one unit of output, so Y=L is the production function, and employment and output and income are all the same thing. Labour has no opportunity cost, and no disutility, and each worker-producer is endowed with E units of labour each period. So the labour supply curve is vertical at E. "Full employment" is when Y=L=E.

Should be simple, right?

Let's start with the simplest traditional textbook model. Consumption demanded is a function of income and the real rate of interest: C= c(Y,r). In "equilibrium", consumption demanded equals output: C=Y. Putting the two together defines the IS curve as combinations of r and Y that satisfy: Y=c(Y,r). If the marginal propensity to consume out of income is between 0 and 1, and an increase in r reduces consumption demand, the IS will slope down.

If r is above the natural rate, output and employment will be less than full employment. There will be excess supply of labour and output.

That's what you learn in first or second year macro. What more do you need to learn? What will you learn if you continue to study macro?

You need to learn two more things. But you will probably only learn one of them if you continue in macro.

The first thing you need to learn, and what you will learn if you continue in macro, is where that consumption function C=C(Y,r) comes from. You will learn about the permanent income hypothesis, how borrowing-constrained agents' consumption is determined by current income, how the real interest rate is the relative price of present vs future consumption. You may eventually learn to interpret the IS curve as a consumption-Euler equation, and write it as C=c(C(1),r), where C(1) is next period's consumption, and the IS curve represents the equilibrium condition that the marginal rate of substitution between present and future consumption equals the real interest rate (for a household that is not borrowing constrained).

All that is very interesting, and useful. But it's not the most important thing you need to learn. The most important thing you need to learn is something you will probably not learn if you continue to study macro. So listen up.

The second thing you need to learn is that the IS curve implicitly assumes a monetary exchange economy. And an immediate implication of that fact is that all those theories of the IS curve cannot be exactly right. They leave something out, and that something cannot be left out, without the IS curve making no logical sense at all. (It's M/P).

Let's take this slowly.

The key message of the IS curve is that if the real rate of interest is too high (above the natural rate), there will be deficient aggregate demand and unemployment.

Suppose all the goods produced by all the workers were identical. If we mean that literally, there could never be unemployment, no matter how high the rate of interest were stuck. The unemployed workers would want to work and sell their output so they could save it, at that high rate of interest. But if nobody wants to buy their output, so they can't sell it, each worker would just consume his own output instead. From each individual worker's perspective, working and saving is first-best, but if he can't find anyone to buy his output so he can save the proceeds at that high rate of interest, the second-best option is to work full time and consume it all himself. Sitting idle and wasting his labour is definitely third-best.

OK, so we have to change the assumption so that workers cannot consume their own output. Let's do that. Output is back-scratching services, and you can't scratch your own back.

That still doesn't work. There still can't be unemployment, even if the real interest rate were stuck too high. Unemployed workers would just do barter exchanges. I scratch your back and you scratch mine. Full employment is each worker's second-best option.

The only way we can make sense of the IS curve, of its claim that too high an interest rate will cause deficient-demand for goods and unemployment, is if we prevent barter exchange and enforce monetary exchange. So make what ever assumptions you like to make this happen. Each worker produces a different variety of the good, and all have a taste for variety, so want to buy from every worker, and you have to buy sequentially, from different locations, and you can't carry your goods around with you, and when you buy you are anonymous, so the seller will only accept cash. Whatever. Just make barter so difficult that people will only use monetary exchange.

Now, finally, we can get deficient-demand unemployment if the interest rate is stuck too high.

At an interest rate above the natural rate, each worker's first-best choice would be to be fully employed, sell all his output for money, use some of that money to buy goods for consumption, save the rest of the money, and lend it to another worker at the high rate of interest. But that's impossible in aggregate of course. The quantity of output actually sold is always the lesser of quantity demanded and quantity supplied, and quantity demanded will be less than quantity supplied in this case, with the interest rate stuck too high. Collectively, their second best choice would be to produce and consume at full employment, and save nothing. But each individual's attempt to get to his first-best leads to the third-best option - unemployment.

In a full equilibrium, output demanded = output = output supplied. In the semi-equilibrium of a point on the IS curve, output demanded = output =/= output supplied. There is an excess supply of output.

Walras Law says that an excess supply of one good must be matched by an equal excess demand for some other good. In one sense, there is an excess demand for money, matching that excess supply of goods. But if an unemployed worker did succeed in selling more goods for an equal value of money, he would not want to hold that money (or not all of it). He would want to lend some of it (buy bonds) and spend some on buying consumption.

So, the IS curve, with its prediction that a too high real rate of interest will cause deficient-demand unemployment, only makes logical sense in a monetary exchange economy, where people can only buy goods in exchange for money. So what's missing from the IS equation? Money, of course.

Let's take this slowly.

We could model the IS curve in continuous time or discrete time. If we choose continuous time and also suppose that there are perfectly smooth flows of output and consumption, at both the aggregate and individual level, we hit a problem. Each individual would have a smooth flow of money income, a smooth flow of money expenditure on consumption, and a smooth flow of lending any excess money (or borrowing any deficiency), and nobody would ever hold any stock of money. (So where does the LM curve come from?). So we either model lumpy flows (which is hard), or we switch to discrete time.

But if we model the IS curve in discrete time, who is holding the money between periods? And if our worker/producer/consumers are holding money between periods (since someone must be), it must be because they will need to spend money in the next period before they earn money from some other worker spending it.

Here is a simple way to introduce the demand for a stock of money into the model. At the beginning of the period, workers are divided at random into two equal groups. The first group shop first and work later. The second group work first and shop later. The "early shoppers" can only spend the money they saved from the previous period. The "late shoppers" can also spend the money they earned from the early shoppers. At the end of the period, when all shopping and working is done, workers can borrow or lend money in the bond market.

In the bond market, each worker knows he faces a 50% risk of being an early shopper. If loans pay interest, and money doesn't, he trades off the loss of interest from holding more money against the loss of utility from having to restrict his consumption if he is an early shopper and therefore cash-constrained. Unless next period's real interest rate is significantly higher than he forecast, an early shopper will always be cash-constrained; he regrets not having held more money, so he could consume more.

Early shoppers' demand for consumption will be C(early)=M/P. Late shoppers will have the normal consumption demand like C(late)=c(Y,r). Take the average of the two groups, and the consumption demand function will be C=(1/2)M/P + (1/2)c(Y,r). Or C=(1/2)M/P + (1/2)c(C(1),r) if you prefer the Euler equation interpretation. That means that M/P will appear as an argument in the IS curve. An increase in the real quantity of the stock of medium of exchange will shift the IS curve to the right. There is a real balance effect in the IS curve.

Derivation of the LM curve is left as an exercise for the reader (it looks simple, but my math is no good).

Now you can play around with my little toy model of the IS curve all you like. (One interesting modification would be to randomly call out the order of shopping from first to last). But the IS curve only makes sense with monetary exchange, using a medium of exchange. And if people hold stocks of that medium of exchange, and it pays a lower rate of interest than all other assets (because by definition it is the most liquid of all assets, and so has the biggest negative liquidity premium) then they must sometimes be cash-constrained when they want to buy things. So there must be a real balance effect in the IS curve. So it cannot be true that the monetary transmission mechanism works only through interest rates, even in the ISLM model.

The monetarists were right. Even that least monetarist model, the ISLM, must recognise they were right.

(It won't work with a zero nominal interest rate though, in the simple model I have sketched above. I need to complicate it a bit more for that.)

There are a couple more loose ends to clear up.

What is the IS curve? Is it a demand curve, or an equilibrium condition? And where did the Keynesian multiplier go, especially in the Euler equation interpretation? These two questions are related.

In micro, there's no distinction between a demand curve and an equilibrium condition. The demand curve for apples is one of the two equilibrium conditions for the market in apples (the supply curve is the other one). In macro, there is a distinction between the IS as a demand curve and the IS as an equilibrium condition. The difference is because in micro the actual quantity of apples bought and sold has no effect on the quantity of apples demanded. In macro, the actual quantity of total goods bought and sold does affect the quantity of total goods demanded. Because if producers cannot sell their goods, their income is lower, and so their demand for goods may be lower too. That's why 'Y' appears as an argument in the consumption function, affecting the demand for goods. It's what creates the multiplier effect. If we are being very picky, the quantity of apples traded ought also appear in the demand function for apples, because if apple producers can't sell their apples, their income is lower, and they won't demand as many apples. But for apples, this multiplier effect is so small that we ignore it. Apple producers are too small a part of the total market demand for apples to matter. But in macro, where we are talking about the demand for all newly-produced goods, we can't ignore this effect.

That's why we need to interpret the IS curve as an equilibrium condition, not as a demand curve. Only if we are at a point on the IS curve will it tell us what demand is (it tells us that demand equals the level of output at the point where we're at). If we are at a point to the right of the IS curve, so output is greater than the point on the IS at the same interest rate, output demanded will also be greater than the IS tells us it would be. Because income is higher. All the IS curve can tell us is that output demanded will be less than output; not how much less it is. The demand curve for apples, by contrast, still tells us what the demand for apples is, even when we are at a point off that demand curve.

This distinction between an equilibrium condition and a demand curve matters in two cases. First, if adjustment costs cause output to adjust slowly to the demand for output, we will be off the IS curve in real time, and see the multiplier process working slowly in real time. Second, if the actual rate of interest is below the natural rate, output will be supply-constrained rather than demand-constrained. (Remember, actual output bought and sold will always be the lesser of demand and supply). So if output is stuck at full employment, with excess demand, the IS curve will exaggerate the amount of excess demand. If we wanted to model excess demand correctly, we would need a kink in the IS curve at full employment, so it gets suddenly steeper to the right of full employment, because output cannot respond to demand for output, so the multiplier is short-circuited. (This kink in the IS is to the right of the LRAS "full employment" output if firms are monopolistically competitive, because at fixed prices monopolistically competitive firms will continue to expand output up to the point where MC=P if demand is sufficient.)

But what is the multiplier, and why doesn't the Euler equation interpretation of the IS seem to have a multiplier?

In Walrasian general equilibrium theory, you solve for a demand (or supply) function by maximising utility subject to the price vector and the endowment vector. A Walrasian version of an IS curve in a 2-period model would be Y=C=c(E,E(1),r). Y would not appear as an argument in the consumption function. But in non-Walrasian Keynesian disequilibrium macro you solve for a demand (or supply) function by maximising utility subject to the price vector and the endowment vector, and subject to any additional binding constraints on the quantities of other goods an agent is actually able to buy and sell. If we have deficient demand unemployment in period 0, so workers cannot sell their endowment of labour, but we have full employment in period 1, the consumption function would be C=c(Y,E(1),r). And when we model those constraints on the quantities agents are able to buy and sell, it is crucially important that we remember whether we are in a monetary exchange economy or a barter economy. A barter economy has additional markets, where you can swap goods directly for goods, so even if you cannot sell your goods for money, you may be able to sell them for someone else's goods.

The Keynesian consumption function, and multiplier, is a quantity-constrained non-Walrasian demand function. And it only makes sense in a monetary exchange economy. We would get a very different consumption function in a barter economy, because the quantity constraints would be different, with additional markets of goods for goods.

If agents are not borrowing-constrained, or cash-constrained, and if they have long lives, and if the recession is expected to be short, the constraint on sales during the recession will have little impact on their current consumption demand. And the multiplier effects will be very small. Consumption demand depends on permanent income, and a short recession's effect on current income will have little effect on permanent income.

The Euler equation interpretation of the IS curve assumes that agents are not borrowing constrained (or cash constrained). That's why Y (and M/P) do not appear in the consumption function. But next period's consumption does appear.

But this Euler equation version of the IS creates a problem, even if you accept those assumptions (and it's not logically coherent to accept the assumption that M/P does not appear in the IS, but let that pass). Take a 2-period-lived agent, for simplicity. Suppose his current income falls, because of demand-deficient unemployment. His permanent income will also fall. For a given real interest rate, he will plan to spread that loss in income across both periods' consumption. So anything that affects his current income will also affect his future consumption. That means we cannot treat his future consumption as fixed exogenously when we move along the IS curve in the current period. But that is exactly what is assumed when we draw an Euler equation IS curve holding future consumption fixed. A movement along the IS curve will necessarily cause a shift in the IS curve. That means the Euler equation IS curve, drawn to show how current consumption demand varies with the real interest rate, holding future consumption fixed, is logically incoherent.

It is no defence of the Euler equation IS curve to assume that the economy returns to full employment in the future period, so future consumption is pinned down exogenously. The future real interest rate may adjust to pin down aggregate consumption to full-employment, but the future consumption of the current cohort is not pinned down; it will vary.

The only way to salvage the Euler equation IS curve is to assume that agents are very long-lived, and the recession will be very short. In which case movements along the current IS curve will have negligible effects on permanent income, and so negligible effects on next period's consumption. The marginal propensity to consume out of current income is almost zero, so the multiplier effect is negligible.

But if the recession is expected to last for some time, so we cannot ignore its effect on permanent income, this won't work. In that case, we need to ditch the Euler equation IS curve, write consumption as a function of permanent income, and make an explicit assumption about how long the recession will last, and how big an effect a fall in current income will have on permanent income.

I thank Adam P for helping and forcing me to think this through. But he is not to blame, and may not share my views.

Comments

[Leigh Caldwell]

Wow. Four things:

1. Your blog is like the edited highlights of a great macro class. I must start reading Adam P's too. Can you recommend a good macro text for when I am finished with Mas-Collel's micro?

2. Readers interested in this post might find it helpful also to read Paul Krugman's "World's smallest macro model" at http://www.pkarchive.org/theory/MINIMAC.html which I was coincidentally reading this morning (h/t Brad DeLong's assorted links, which incidentally I only bothered looking at because of the "theory of assorted links" discussion on Marginal Revolution this week). Do work through the algebra in Krugman's posting as it is not too hard and will sharpen your understanding. There are overlaps between Krugman's explanation and Nick's discussion, but Nick's goes much further. Reading both will round out your understanding.

3. "Imagine there's no money", this posting and a few other recent ones from Nick and Scott Sumner are helping me towards a vastly better understanding of monetary economics and a far better appreciation of how monetary policy can help get out of recessions. You are both getting me to question my belief in fiscal stimulus, though I do still retain some faith in it when invested in public goods.

4. I am still not convinced that barter exchange makes any difference!

[Scott Sumner]

Leigh, I'm sure I could make an even smaller one, but I doubt anyone would like it. Maybe I'll email it to you privately, so I don't make a complete fool of myself.

Nick, Two questions:

1. Does your discussion have any bearing on the question of the proper role of money? It seems like you didn't talk much about wage and price stickiness. If you had sticky wages and prices, but money was simply in the background as a unit of account (not medium of exchange) would that be enough? Or do you need money as a medium of exchange?

2. I seem to vaguely recall Keynesians arguing that "yes, deflation will increase real balances, and thus boost AD, but the effect is small." Does that have any bearing on your discussion of the need to have real balances in any IS curve.

Sorry that these questions are so ignorant, but IS-LM is not my area. The essay looked very impressive, as Leigh said, and I plan to reread it after hearing responses to the two questions.

[Nick Rowe]

Leigh: Thanks!

I really ought to be finding good macro texts myself, but I'm afraid I'm really out of it. For the last several years, all I have done is teach ECON1000 and do university administration. Anyone else have any good recommendations?

I just read PK's world's smallest macromodel this morning (Saw Brad DeLong's link). I like it. I think I saw it before, years ago. It's really a simplified version of Barro and Grossman 1971. The main difference between his model and my post here, is that PK's model only has one asset: money, which is both the medium of exchange and the only store of value. I have loans (bonds) as well as money. If you have no bonds, the IS and LM really collapse into one equation.

There are some public goods the government ought to be spending money on, for perfectly good micro reasons, and regardless of any macro stimulus effects. But I think fiscal policy can stimulate AD too. Just that monetary policy is normally better.

You are STILL not convinced that barter could make a difference?!! What does it take to convince you guys? If barter were costless (it isn't, which is why it doesn't happen, but suppose it were) the IS would be useless. There could never be deficient demand unemployment in my model. The unemployed would just swap services.

Scott: glad to see you one here. Again, I had you partly in mind when writing this post (except that you, unlike most economists, have the guts/integrity/ornirariness to say you don't understand the ISLM). Everyone else pretends they understand it. They don't.

1. I have ignored the LM, taking the interest rate as exogenous. If the price level were perfectly flexible, and M were fixed, the LM would shift until the real interest rate became equal to the natural rate, so we would get full employment.

Yes, money's role as a medium of exchange is absolutely crucial in this model. If you allow barter, even if prices are fixed, you get to full employment. You need 2 things for unemployment: sticky prices (so the real interest rate is above the natural rate); and barter is not allowed. Put it another way: both roles are essential; medium of account (to get price stickiness); medium of exchange (so barter doesn't happen).

2. I forgot to include the wealth effect from real balances in the model. Agreed, normally it's trivial. The real balance effect in my IS curve is not a wealth effect. It's a cash constraint on expenditure, due to the fact that you can't use barter.

The ISLM, properly understood, is a beautiful model Scott. But there's a hell of a lot more going on in that model than anyone ever gives credit.

[Scott Sumner]

Nick, I just added a long answer/question to your "John Lennon" post, so I'll see what you say there before forming an opinion of the whole barter/medium of exchange/medium of account issue. Your second answer seems fine.

Is ISLM a beautiful model? Maybe, but I am a pragmatist, who messes around with ugly realities. As I said, I never studied ISLM in school, although of course have a vague idea of what it's all about. But as I got out and started researching issues like the Great Contraction, I kept coming across really wrongheaded observations, and almost invariably they were justified on ISLM grounds. Now I certainly don't hold you accountable for the misuse of this model, but these were often pretty well-known economists from salt water universities. This is what I'd read:

1. Money couldn't have been tight in 1929-30, because interest rates fell sharply.

2. Money couldn't have been tight in 1929-30, because real money balances rose.

Of course tight money would be expected to produce deflation (and did) and that would be expected to increase the demand for real cash balances (and it did) and to reduce interest rates through the Fisher effect (and it did) and also reduce the real interest rate by depressing investment (which it did.) So this made me prejudiced against ISLM. When I'd read that tight money was defined as a reduction of real cash balances, I couldn't help thinking of the German hyperinflation, when real cash balances plummeted. It was like my daughter's "opposite day" at school, where everything one says is supposed to be the opposite of what you really mean.
Before I'd be willing to use ISLM, I'd want to see people use it to examine issues like the Great Depression in a way that was consistent with what we know happened. Of course you also know my view of the last 8 months, another situation that I don't think is well-explained by ISLM. (I say it was really tight money.)
Can it be explained with ISLM? Yes. But that's also true of MV=PY, and not many people consider that a beautiful model.
I'm glad you are trying to take it apart and rethink it in a way that is more justifiable. And I certainly agree that you can't rely on interest rates only, that money must be in the model somewhere. The weakness of my approach is I have gone to the other extreme, essentially ejecting interest rates from my macro analysis. The only role they play is in affecting the demand for money. That's how I ended up in "opposite world" where the low rates of 1930 and 1938 and 2009 are tight money and the high (German) rates of 1923 are easy money.

[Adam P]

Nick, this is a nice post. In particular I like the random early shopper idea to make the CIA constraint behave like a liquidity preference.

However, I disagree with some of your general conclusions on the IS curve. Basically my problem is that throughout this post you're leaving productivity exongenous. That's just not right, THERE ARE GAINS FROM TRADE, PRODUCTIVITY IS ENDOGENOUSLY DETERMINED. All of your examples where the interest rate is too high but there is still no unemployment (bilaterl barter or consuming your own output) do reduce productivity and thus output. Nothing here is inconsistent with the standard IS curve, it relates r to Y, not r to employment.

Thus, the IS curve does not NEED a monetary exchange economy. When you say " the second-best option is to work full time and consume it all himself" what do you mean by second best? It can only mean less output, less productivity. Thus, when the real rate is too high you may not get unemployment but you DO GET LOWER OUTPUT and that's all the IS curve says. The IS curve relates the real rate to output, it says nothing at all about employment. For that you need to model the labour market explicitly.

Now, this does take us into RBC type modeling but what's wrong with that? RBC theorists are people too and Prescott's Nobel paid the same as Krugman's. And yes, in an RBC model the only unemployment is voluntary so it doesn't seem like a good description of reality, certainly not the current state of things. BUT, the difference is in the labour market not the IS curve.

You are not correct to claim that IS curve is in any sense wrong without money in it, money is the LM part. The IS curve looks the same either way.

[Adam P]

Leigh,

I seem to recall you saying on one of the blogs (here or at Scott's place) that you're a mathematician by training. Based on that I have a couple of recommendations for reading:

1) Acemoglu, 'An Introduction to Modern Economic Growth', elegant and rigorous but not discussion of the business cycle.

2) Sargent, 'Dynamic Macroeconomic Theory', rigorous intro to monetary theory plus nice treatment of basics in first 3 chapters. However, doesn't really treat the business cycle either. The monetary theory part is all about neutrality or not neutrality, that is the question. Sargent also has a book 'Macroeconomic Theory' that is more general and covers stuff like the Philips curve but this one I find a bit dated and tougher reading than it needs to be, still nice, thorough intro to classical issues though. Be warned though, Sargent likes lots of symbolic computations...

3) Romer's 'Advanced Macroeconomics' is readable, not very difficult analytically and fairly comprehensive. If you can only read one, that might be the best bet. But for depth you might need to go further in some other books.

[Nick Rowe]

I strongly second Romer's Advanced Macro (though it's many years since I read it, though^2 it might be revised since then).

Thanks Adam!

I like the random shopping time too. But it makes me feel very guilty. I dumped on PK's model because he introduced money via a CIA, now I've done the same thing! I'm a hypocrite.

But it's much nicer having a CIA constraint which only binds on some people, or some of the time. And mine does that. I would like it better still if I could work out the model where you randomly line up all the shoppers from first to last. It would get rid of that clunky "1/2...1/2" functional form, and replace it with something smoother. Some people would be very cash constrained, some a little, and many not at all. Instead of having 1/2 the people a little bit cash constrained. Wish I could do the math.

Gotta go to Tim Horton's, then buy tomato plants. Will respond later to the RBC thoughts.

[RebelEconomist]

I shall not pretend to fully understand this Nick, but your way of adding the demand for a stock of money for transactions into the model seems to me to build LM into IS. But anyway, when a model needs so much qualification and interpretation, it is probably wrong, like the complexities that were added to the geocentric model of the solar system in an attempt to sustain it. ISLM certainly seems too tentative and controversial to be taught to undergraduate students.

Perhaps I can ask a related question which really belongs on the QE and M1 post, but that discussion is probably too old to reopen. My question is how there can be a real balance effect. In the case of currency (which I assume is what Nick had in mind above), currency is ultimately a public liability, in which case people overall should be indifferent to changes in the relative value of currency. In the case of deposit / inside money, to the extent that bank deposits are matched by bank loans, it would make no difference whether QE boosted M1 or not. Thanks for any enlightenment!

[RebelEconomist]

By the way, for any macro teachers reading this, one point about the IS curve that confused me was that the Keynesian cross is described as an iterative convergence process when the IS curve is really a one period model.

[Adam P]

Rebel, you're exactly right. Nick has mixed LM into his IS.

[Adam P]

And btw Nick, each point on the IS curve is such that investment demand equals saving demand and as such, NO POINT ON THE CURVE HAS AN EXCESS DEMAND FOR MONEY.

Any excess demand for money can only be if savings demand is higher than investment demand.

[Adam P]

I should explain what I'm saying in the last comment. It is true that in general recessions are caused by an excess demand for money. The causal change goes like this though:

1) start at full employment equilibrium. Now, at the full employment income, increase demand for savings, reduce the demand for investment or increase the demand for liquidity (money). Thus, before the interest rate or income has changed, we have an excess of savings demand over investemnt demand = excess demand for money or an excess demand for money directly.

2) The excess demand for money, with a constant money supply, causes the nominal interest rate to rise. THE HIGHER r HAS ELIMINATED THE EXCESS DEMAND FOR MONEY. Since prices are sticky (in IS-LM they're fixed) the rise in nominal rate is exactly a rise in the real rate. THIS PART IS A SHIFT IN THE LM CURVE.

3) The higher rate drives saving and investment demand even farther apart. The lack of aggregate demand causes income to fall.

4) Falling income reduces savings. Income falls until savings demand and investment demand are equalized. At the new equilibrium we have lower Y and higher r.

Thus, an excess demand for money changes the interest rate. The higher rate eliminates the excess demand for money. With the original value for r we had an excess demand for money. The original value of Y with the new value of r is not on IS curve. Income falls to get us back on the IS curve.

[anon]

It would be helpful if you could summarize the distinction between the money effect via IS (non-conventional) versus via the money effect via LM (conventional).

[Nick Rowe]

Scott: Glad you spotted the John Lennon reference, in my "Imagine.." post!

Why do I like the ISLM?

1.Because it has 3 goods (output, money, bonds), that seem to me to be about the minimum possible (though I have an admiration for the even simpler models, like the simple Krugman model Leigh linked to, with only output and money). (It's based on the Barro-Grossman 1971 model, BTW.)

2. Because it recognises the importance, even if implicitly, of monetary exchange.

Most of the problems with people using it come from their failure to recognise that expected future monetary policy (plus other expected future stuff) affect the current equilibrium: by introducing a wedge of expected inflation between nominal and real interest rates (and hence between the IS and LM curves; by affecting expected real income and shifting the IS (and maybe LM) curves.

Its main drawback, if used properly, is that it only has one interest rate (or two, if you count the real vs nominal distinction). It only has one type of financial asset (apart from money). So lumping everything from Tbills to commercial paper to shares into one "bond" is a disasterous assumption in a time like the last few months when the spreads between interest rates have changed by much more than the average interest rate changed (and did the latter go up or down?).

Wasn't there a similar increase in yield spreads during the Depression? If so, I don't think the ISLM, with its single interest rate, would do very well there either.

Rebel, Adam: On mixing the IS and LM: I have one equation that desribes what happens in the output market, taking as given the stock of money with which they enter the output market. I call that an IS curve. I have another equation that describes what happens in the bond market (or, I would if I could do the simple math!). I call that an LM equation. You say I'm mixing the two equations. Why? Because I find that M/P appears in the IS? Maybe it belongs there? Sure, I could substitute it out, and get rid of it, by using my LM equation. But then nominal interest rate would appear in the IS, as well as the real rate. And if anything happened to the price level or M, between periods, it would have to be taken into account in the IS.

Adam @12.54 and 1.39: There are two markets: the bond market (LM) and the output market (IS). Start in full employment equilibrium. Now introduce a shock.

Suppose the shock is to M, just before the bond market opens, say, the govt. vacuums up half the stock of M. Excess demand for money in the bond market. Suppose the interest rate is perfectly flexible, but the price level is fixed. Interest rate rises. That eliminates the excess demand for money in the bond market. The output market opens, Y falls, to a point on the IS curve. In the output market, there is an excess supply of output and an excess demand for money. In other words, people want to sell goods for money, but can't. I call that an excess demand of money.

If there are n goods, including money, there are n-1 markets. Each of the other goods has just one market in which it is traded. Money is traded in all n-1 markets. We can talk about the excess demand for apples in the apple market, the excess demand for bananas in the banana market, etc. Where do we see any excess demand for money? We see it (potentially) in all n-1 markets. In some markets there will be an excess demand for money and an excess supply of the good. In others, and excess supply of money and an excess demand for the good. in others, an equilibrium. Which of the different n-1 different definitions of the excess demand for money is the true one? Why is the bond market the only market that tells us the truth?

Adam @8.45: On productivity. You really lost me here. I am assuming the average and marginal product of labour is always 1, for simplicity, so I can talk about output and employment interchangeably. Nothing more.

If the real interest rate is forced above the natural rate, for some reason, what happens?

In a monetary exchange economy, output and employment fall (by the same amount, in my model).

In a barter economy, output and employment stay at full employment. People work full time and either consume their own output or swap it for another worker's output, and consume that. They would like to lend output to another person, but can't find anyone to lend to. There is an excess supply of loans. No worker is going to throw away his output, or waste his labour by not working, just because he can't find anyone to borrow the output he produces. If he can't get anyone to borrow it, he eats it himself.

Rebel @10.27 (iterative multiplier). You normally don't see the iterative multiplier in the IS, and only see it in the Keynesian Cross. But that's only because it's a little bit harder to show it in the IS. I could show you an iterative multiplier in an IS, if you gave me a nice blackboard and a bit of chalk. I would draw a steep short-run IS, which holds actual output constant, and shows how the demand for output varies with r. Then I would slowly iterate that IS, doing a leftward creep following a rise in r, as output falls to match the fall in demand, then demand falls further to respond to that fall in output, etc., eventually getting to a "long-run" IS (the normal Keynesian IS), which is flatter than the short-run IS.

If consumption depends on current income, and output adjusts slowly to demand, we get a slow iterative multiplier in the IS, as it creeps leftwards. But if consumption depends on expected income, and output on expected demand, and expectations are rational, we jump immediately to the new "long-run" IS, and skip the iterative multiplier.

Rebel on the real balance effect: There's the real balance effect as a wealth effect.

There used to be a view (Gurley and Shaw) that "outside money" (central bank money) was net wealth, and "inside money" (commercial bank money" was not net wealth, because there is an offsetting liability.

That inside/outside view is wrong. The key distinction is between monopoly and competitive money (Pecek and Saving). If the issuer has a monopoly, so zero interest is paid on money, it's net wealth. If it's competitive, so pays a competitive interest rate, and the issuer earns zero profit, it's not net wealth.

[Nick Rowe]

anon:

Conventional view: Increase in M, people try to lend it to each other, interest rate falls, which causes people to want to consume more now and consume less later.

My view: the conventional view is correct, but leaves something out, namely:

Unconventional view: Increase in M, fewer people run out of money when they want to buy something, so some people buy more stuff.

[RebelEconomist]

Nick,

Thanks. If monopoly is the key to the wealth effect of money, then the Gurley&Shaw and Pesek&Saving distinctions are practically the same anyway aren't they, because bank deposits are supplied competitively and currency is (legally) supplied by the central bank only?

If that is the case, it suggests that our discussion of whether QE boosts M1 was moot, because the Q effect of M1 is offset by that of M1 lending.

[Nick Rowe]

Rebel:
" If monopoly is the key to the wealth effect of money, then the Gurley&Shaw and Pesek&Saving distinctions are practically the same anyway aren't they, because bank deposits are supplied competitively and currency is (legally) supplied by the central bank only?"

If you believe the commercial banks are competitive (I do, roughly), then yes, they get the same result, only for different reasons.

"If that is the case, it suggests that our discussion of whether QE boosts M1 was moot, because the Q effect of M1 is offset by that of M1 lending."

Hang on. You are assuming that an increase in M affects AD only via a wealth effect.

[RebelEconomist]

A wealth-in-the-form-of-money effect, I suppose. How would you say that the Q effect works, Nick?

[Nick Rowe]

Dunno Rebel; but I sure hope it's not wealth effects, because they're way too small!

[himaginary]

I may not have fully understood this, but I think Nick's early/late-shopper model becomes similar to conventional one, if you introduce permanent income hypothesis. That is, if you assume that everyone consumes according to permanent income (or what he thinks so). Let's denote this permanent income as Yp.

In this setup, C(early) = C(late) = c(Yp,r).

In the bond market, each worker borrows or lends money according to his bet on whether he will be an early shopper or a late shopper the next day. Let's denote total borrowing amount as B(r). If the bet is correct on the aggregate basis (or, if you assume that each worker in fact knows at the beginning of bond market which shopper he becomes the next day), and would-be early shoppers could just fund the shortage,
B(r) = (1/2)(Yp - M/P)

If you redefine B(r)=2B(r), it can be written as
Yp = M/P + B(r)

Here we've got something looks like conventional LM curve.

[Nick Rowe]

I'm not sure I follow you, himaginary. Though that might be just because it's late ;)

I couldn't quite solve out for the LM curve (which shows agents' optimal choice in the bond market between money and bonds), but as far as I can see, the LM curve should indeed look quite conventional. The more money you hold, coming out of the bond market, the less you will lose utility by being forced to temporarily reduce consumption if you are an unlucky early shopper next period, but the more money (and less bonds) you hold, the less interest you earn. So the expected utility-maximising quantity of real money to hold will depend on the nominal rate of interest, on your expected level of consumption, and on the curvature of your utility function. Same arguments as a normal LM curve.

But the IS curve has to look different. The early shoppers will never be satiated in cash, they lose the nominal interest rate on bonds. So M/P, as well as r, (and Yp if permanent income hypothesis is true) has to appear in the IS.

[Adam P]

Nick,

the gains-from-trade/productivity point was a counter example to this claim of yours: "They leave something out, and that something cannot be left out, without the IS curve making no logical sense at all. (It's M/P)."

We can produce an IS curve identical to the usual case in an economy where people trade by barter and can consume their own production. You just need to assume that their are gains from trade, something you yourself imply when you say "the second-best option is to work full time and consume it all himself". That's second best because it's less effecient.

Presumably their are productivity gains from specialization. Thus, when r is above its natural rate and trade breaks down, yes their is no unemployment because those that can't sell their output consume it themselves. However, losing the productivity gains from specialization reduces aggregate output. Thus, higher r does correspond to lower Y without the need for monetary exchange and ruling the possibility to consume your own output.

[Adam P]

I just re-read my last comment. Please change "their" to "there" in the last paragraph twice. The last sentance should read "ruling out...".

[himaginary]

Nick, thank you for responding to my crude idea.

"which shows agents' optimal choice in the bond market between money and bonds"

I forgot to articulate another implicit assumption in my idea. As there is no investment nor government nor firm in your original assumption, I assumed bond issuers as well as buyers are all workers. No other bonds. That is, all bond issuers are next early shoppers (or who thinks he will be), and all bond buyers are next late shoppers (or who thinks he will be).

"The early shoppers will never be satiated in cash, they lose the nominal interest rate on bonds."

From the above assumption, late shoppers will earn that interest rate. What I thought was that if chance to be either type of shopper is even, gain/loss from interest rate cancel out on aggregate- or expectation-value basis.

[Nick Rowe]

Adam: Got it! I understand you now. (I think)

That's a very different way of looking at the IS curve, but it does make good sense. It's asking what exactly we have on the horizontal axis. Is it employment? Output? Or useful output? I would push your interpretation to the extreme, and say that perhaps what we ought to have on the horizontal axis is utility. So that even in a recession, the "unemployed" are still spending their time as usefully as they can, given the breakdown in monetary exchange when r is above rN, digging their gardens perhaps, but it's just that they don't get much utility from doing that.

So, if I understand your point correctly, the slope of the IS curve depends very much on what we have on the horizontal axis.

With "employment" on the axis, understood in the widest sense, the IS is vertical. With utility from employment and trade on the axis, it is flatly-sloped.

Did I understand you right? I hope I did. Because it's an interesting way of interpreting what's going on. I like the idea of an IS curve with utility on the axis. That's the one that matters.

And yes, my crude Y=L production function totally ducks these issues. It's the vice of one good macro.

himaginary: Yes, the only bond issuers and buyers are the worker/producers themselves. They are just lending each other money. Though if we introduce a central bank, doing open market operations, the central bank could be buying those private bonds too (i.e. lending workers money).

All agents are identical ex ante, looking forward, since early/late shoppers will be chosen at random. But agents have different histories, depending on whether they were picked as early or late shoppers in the past. Those who were early shoppers will have more money (and wealth) than those who were late shoppers (since the late shoppers will have spent some of the money they earned in the current period, while early shoppers were cash-constrained, and were forced to save part of their current income).

Interest payments between agents may change the distribution of wealth, but not aggregate wealth. It's not the wealth effect from interest that matters. It's the incentive effect. The fact that bonds pay interest, and money doesn't, means that each agent has an incentive to hold less money and more bonds. He balances this incentive with the risks of being cash-constrained as an early shopper, and therefore having a non-smooth consumption profile over time, looking forward.

Looking forward, an agent who holds a lot of bonds and little money will have higher average consumption (because of the interest earned), but a more volatile consumption (because he will be more cash-constrained when he is unlucky and picked to be an early shopper).

The LM curve picks the individual agent's utility-maximising point on that trade-off between high average consumption vs less volatile consumption over time.

Can anyone solve that LM problem for me? (Pick your own utility function, to make it easier.) I would be grateful and admire your technical skill.

[Adam P]

Nick, yes I think we basically understand each other now. However, to me it was you who was asking what really goes on the horizental axis. My point, in part was to remind you that it's real output and not unemployment. In your model you didn't need to make that distinction because with productivity exogenous the only way for Y to fall is for employment to fall.

Thus, my point was twofold. One is to provide an example where output falls even at full employment and this is associated with a higher real rate.

The second point is to show that you can get a normal looking IS curve without money. You do need an exchange economy I think, on that we agree, but it doesn't need to be a monetary exchange economy. This is also a property of RBC type models, lots of them don't have money.

That's what I had in mind in mentioning RBC models since that's how they work. Although in those models causality usually goes from productivity shock to output to the real rate. That is, productivity is assumed to mean revert so low productivity is associated with high productivity growth, thus high consumption growth, thus a high real rate.

[Nick Rowe]

Adam: I now understand your second point too. I now realise that's one of the things you were asking way back in the beginning. RBC models need their own version of the IS curve. (I would perhaps quibble about calling it an "IS curve", because it's so different in a non-monetary economy, but that's beside the point. RBC models need something, call it what I will.)

Hmm. That takes some re-thinking on my part. Gonna mull it over.

[Nick Rowe]

Adam: OK. If there is a negative shock to the current level of output supplied, due to a drop in the endowment or productivity, holding future output constant, then the standard Euler-equation approach you originally put forward seems to work just fine, as far as I can see (assuming of course that agents are not credit constrained). Full employment output is lower, and you move up along the "IS curve".

In that example, you "read" the "IS curve" starting at Y, go up to the curve, then across to r, to find out what r is compatible with that Y. In any case I can think of where r changes, but it's not due to a change in full-employment Y, it's because the "IS curve" has shifted.

And to supplement that IS curve, you need an AS curve drawn in the same space. If there is intertemporal substitution of leisure, for example, the AS curve would slope up. Equilibrium output and real rate of interest (the "natural rates" of each) would be where AS intersects IS.

But crumbs, that is a very different sort of "IS curve" from the keynesian case, where we ask what happens when the real rate gets forced away from the natural rate of interest, and so output and employment get forced away from their natural rates too.

But that clears an awful lot of things up. I now see where you are coming from. Yep, RBC theorists are people too, and they need their own "IS curve"!

[Nick Rowe]

Yep. The "monetary disequilibrium IS curve is defined as the set of points in {r,Y} space traced out by the LM curve as it shifts. r is changing relative to rN, so Y changes relative to YN.

The RBC IS curve is defined as the set of points in {r,Y} space traced out by the LRAS curve as it shifts. r=rN and Y=YN change together.

[Jon]

Nick:

This got me thinking about one advantage of a simple commodity standard (such as gold). The social problem is one of a mismatch between the goods supplied and the goods demanded. Either the kind is wrong or some people are left with goods for which there is no market by which they can trade and acquire the goods they want.

In this later case then, the benefit of the commodity standard is that there is a universal good which any man can produce. In a fiat money system, the government monopoly excludes this behavior. So long as 'money' is a good reasonably produced by individuals, surely then we must approximate a barter economy.

[Nick Rowe]

Yes, with a commodity money that anyone can produce, we get an automatic DIY monetary stabiliser. Gold is not great though, since the supply curve is too inelastic. You need workers plus a gold mine. The downside though, is that it takes real resources, that could be producing useful goods, while the central bank just printed the money for almost free.

If the central bank financed EI, it would have a similar effect.

[Jon]

Surely though that's a feature. Again the problem is a dislocation. Although the government can print the money for free, the government is not the right owner. So what to do? Does the government give the money away? This isn't costless; it creates disincentives.

Taking real resources is a feature: the distortion in labor allocation matches the distortion in wants (under a commodity standard).

[Leigh Caldwell]

Thanks for the recommendations Adam. I have the Acemoglu book so I'll start with that, and will take a look at the other two to see which one looks like it will work best for me.