Simplify massively. Ignore investment, government spending and taxes, and exports and imports. All output is consumed.
Assume a Keynesian consumption function: Cd = a + bY. Draw Samuelson's "Keynesian Cross" diagram. Real consumption demand Cd on the vertical axis, and real output (real income) Y on the horizontal axis. Demand for consumption this current period depends on realised sales of output this current period. "Equilibrium" is where the consumption function crosses the 45 degree line. Because that tells us the level of output at which demand for output equals that same level of output. But that "equilibrium" is not necessarily a full demand = supply equilibrium. Output may be less than "full employment" equilibrium. Firms and households may want to produce and sell more output and labour than they are able to sell, if demand is too low. The multiplier (the change in "equilibrium" output divided by the upward shift in the consumption function that caused it) is 1/(1-b). There is positive feedback in this model, because demand depends on itself.
What does that Keynesian Cross diagram look like in a New Keynesian model, with infinitely-lived consumption-smoothing agents who never face binding borrowing constraints? That depends on how long the "current period" is, and on whether income in the current period affects expected future income.
Assume that the representative agent is perfectly confident that his income will be equal to "full employment" income in all future periods, regardless of what happens to current income. (Yes, this assumption is very questionable.)
If the current period is very short, the consumption function will be almost horizontal (the marginal propensity to consume "b" will be almost zero). Because changes in current income have a negligible effect on permanent income. And if the central bank reduces the current period real interest rate, the consumption function will shift up, causing an increase in "equilibrium" output. If the central bank sets the right interest rate, so the real interest rate equals the "natural rate", the intercept of the consumption function (autonomous consumption "a") will be almost equal to full employment income.
Now let's make the current period longer and longer. So that current income has a bigger and bigger effect on permanent income. Autonomous consumption (the intercept) gets smaller and smaller, and the marginal propensity to consume (the slope) gets bigger and bigger. Less obviously, a given-sized cut in the real interest rate will cause a smaller and smaller upward shift in the consumption function.
Now let's take this lengthening of the current period to the limit. Suppose the current period lasts forever. So my bolded questionable assumption above becomes redundant, because there is no future period. Let us put permanent income on the horizontal axis, and permanent consumption on the vertical axis. Autonomous consumption drops to zero, the marginal propensity to consume rises to one, and the effect of a cut in the real interest rate drops to zero. The budget constraint (plus non-satiation) ensures that permanent consumption must equal permanent income, for any level of permanent income, and for any real interest rate. This means that the consumption function necessarily coincides with the 45 degree line.
And this means that any level of permanent income, between zero and full employment income, is an "equilibrium". Animal spirits are the only thing that determine which of those equilibria will be chosen. Since b=1, the multiplier would be infinite, if it were possible to shift the consumption function up. But the budget constraint says it is not possible to shift the consumption function up, so that infinite multiplier is purely hypothetical.
Now let us introduce a stock of money into the model. The representative agent holds a stock of money. He has a desired stock of money, and an actual stock of money, and the two stocks may not be the same. Introducing money into the model breaks the identity between permanent consumption and permanent income. If an agent holds more money than he wishes to hold, he will plan to run down his stock of money over time, by spending more than his income, so that his permanent consumption will be greater than his permanent income. And if an agent holds less money than he wishes to hold, he will plan to increase his stock of money over time, by spending less than his income, so that his permanent consumption will be less than his permanent income. But even though each individual agent can add to or subtract from his stock of money, by spending less or more than his income, this is not possible in aggregate.
If the desired stock of money is independent of permanent income, an increase in the actual stock of money, so that it is greater than the desired stock, will cause an upward shift in the consumption function. It does not matter if that upward shift is very small, because b=1 and so the multiplier is infinitely big. An extra $1 hot potato in circulation will be enough to expand the economy from 50% unemployment to hit the full employment constraint. And withdrawing a single $1 from circulation would cause the economy to collapse to 100% unemployment.
But a more plausible assumption would be that the desired stock of money is an increasing function of permanent income. This ensures that the consumption function has a slope of slightly less than one, so we get a determinate "equilibrium" level of permanent income where the desired stock of money equals the actual stock.
The model would be more plausible still if we assumed that the desired stock of money depends on permanent nominal income. There is a real stock of money at which equilibrium permanent income is equal to full employment permanent income. Maybe (or maybe not, if it causes destabilising expectations) a slow adjustment of prices, in response to output being greater or less than full employment, would eventually bring the economy to full employment equilibrium.
Keynes understood that demand depended on itself. General Theory chapter 3. Keynes understood that the only thing that might (or might not) bring the economy to full employment income was some sort of real balance effect on aggregate demand (and that the central bank could do the same thing quicker and better than waiting for prices to adjust to get the right level of real money balances). General Theory chapter 17. New Keynesians have forgotten Keynes' two insights about aggregate demand. They have forgotten that demand depends on itself. They have forgotten that some sort of real balance effect is the only thing that might (or might not) bring the economy to full employment automatically. New Keynesians are guilty of an intertemporal fallacy of composition: even if the right rate of interest will ensure full employment in any single period, it does not follow that the right rate of interest will ensure full employment in all periods. New Keynesians just assume, without any explanation, without anything in their models that would make this the only rational expectation, that agents expect that future income will equal full employment income. New Keynesians are the "classical" economists who just assume (the agents in their models expect) an automatic tendency towards full employment. New Keynesians have models of monetary exchange without money. New Keynesians are not Keynesians.
Just continuing my lovely argument with Roger Farmer about Keynes and modern macro.
Worthwhile Canadian Initiative 
A recession is not a fall in GDP. It is not a fall in economic activity. A recession is a fall in monetary exchange. Non-monetary activity rises in a recession. Home production, barter, etc, increases in a recession. A recession is a change in the mix of monetary vs non-monetary activity. We are just better at measuring the monetary activity. Plus, monetary exchange really is more efficient for a lot of stuff, so when we try to do it without money, we don’t do it as well, and people are worse off. Unemployed growing their own veggies.
“when we talk about AD, we are really talking about the excess demand and excess supply of the medium of exchange. There is no such thing as “AD” in a non-monetary economy.”
I agree with the second statement, but I don’t think it necessarily leads to the first. But I would agree that it may just come down to perspective.
I suppose the real test is not what you call it, but what might work. I can imagine a position where the private sector wants more B+M. You can call that an excess demand for M, but the question is can you fix it buying reducing B and increasing M. If you can’t, I see that as an excess demand for (B+M), not an excess demand for M. I don’t think it would ever be an excess demand for just B, even if it was caused by a change in the demand function for B.
Nick E: why stop at M+B? Why not add land in too? M+B+L. Why not add old houses, old cars, paintings, you name it? Where do you draw the line?
You (I’m guessing, like most “keynesian” economists) divide the world into two groups of things: newly-produced goods; everything else. (And what you have in mind as the archetype for “everything else” is “bonds”.) Why divide the world up this way?
I divide the world into two groups of things: money; everything else. Money is different because everything else is bought and sold for money and priced in money.
This is about ontology. Borges celestial emporium of benevolent knowledge.
Nick-
Oh right, yes I saw the babysitting thing. That was GREAT. Perfect example. The only problem is the Mises guy didn’t understand it, he said it was an example of how monetary stimulus leads to inflation. In fact, inflation is precisely what the babysitting economy needed and didn’t get. Inflation would have brought home back to “full employment” in the same way that deflation is supposed to in the demand-constrained world, via the Keynes/Pigou/real balance effect.
Nick,
You’re obviously entitled to assume an exogenous stock of money and a stable demand for real balances if you want to. That has its attractions. We end up with something much more like IS-LM. But I can understand why New Keynesians don’t want to do that. For one thing, it’s not a satisfactory way of modelling the actual behaviour of central banks. For another, demand-for-money functions don’t fit very neatly into the Lucasian approach which NKs have opted for.
What I don’t think you’re entitled to say is that “New Keynesians are not Keynesians” when, in effect, all they are doing is making money endogenous. If the central bank is following a Taylor rule, M adjusts passively. Since it doesn’t really add anything to the model we may as well leave it out. That’s effectively what Keynes was doing in the passages which John Hicks found so unsettling.
@Nick Rowe: “I’m still thinking about this. I’m thinking about red money.”
Likewise. In particular I’m thinking about a question that’s been vexing me for some time: is your untapped Visa credit limit “money”? Any help appreciated.
I don’t have time to engage in the debate here properly right now. I might write a post on my own blog later. But two points I want to make now.
1. Nick R.’s argument is logically coherent and can be four in lots of postwar Keynesian as well as monetarist stuff. But it cannot be found in Keynes. The margin between current consumption and money holdings plays zero role in Keynes’ account of how aggregate demand varies.
Keynes’ story goes like this: current consumption, and therefore current saving, is strictly a function of income. (There is some discussion of changes in the propensity to consume in the GT, but in terms of secular trends, not business-cycle scale fluctuations.) With the level of saving fixed by income, savers (i.e. asset owners) have a choice between more and less liquid stores of wealth, conceived as money and bonds. Bond prices adjust to get equilibrium in this market, which determines the interest rate. The interest rate then determines the discount rate applied to future earnings from produced capital goods. This discount rate, combined with variation in expectations about future income streams, determines the demand price for capital goods; combined with the supply price, this determines the volume of new capital goods produced. Production of capital goods then determines income and closes the system.
In this story, nobody is reducing expenditure on non-money goods in order to acquire more money. All the action is in what Nick calls the “Junker fallacy.”
2. Nick R. writes:
when we talk about AD, we are really talking about the excess demand and excess supply of the medium of exchange.
You say this a lot. So do other people. But I don’t understand how you can be so insistent on this, when right here in this post you have described variation in AD that has nothing to do with excess supply or demand for the medium of exchange. Consider your NK model where the current period is very long — that is, where people base their expectations about future income entirely on current income. In this economy, any level of activity is possible, depending on people’s initial beliefs. If they believe there will be a high level of activity, they will be right, and if they believe there will be a low level of activity, they will also be right. In neither case need there be any excess supply or demand of the medium of exchange. This is also a form of AD, and as I emphasized above, it is the source of variation in AD that Keynes thought was most important in explaining fluctuations in real economies. Now, you are right that a fixed stock of money could help coordinate expectations on a particular level of income. But so could lots of other things.
On reflection, I’m wrong to say that Keynes’ story is a form of the Junker fallacy. That would be true if we had wealth owners directly making the choice between capital goods and money, but that’s not how Keynes tells the story. The distinction between rentiers and entrepreneurs is important to him — nobody is making a choice to hold wealth in the form of fixed capital. Presumably the entrepreneurs operate with borrowed funds, and the banking system passively accommodates their desired borrowing. This is a bit of gap in Keynes story. But that doesn’t change the fact that it’s the story he tells.
“A recession is a fall in monetary exchange. Non-monetary activity rises in a recession. Home production, barter, etc, increases in a recession…Unemployed growing their own veggies.”
I see where you are coming from but doubt it is really that clear cut. People will certainly try to substitute indispensable goods/services with their own labor but discretionary activity will also take a (big) hit. Not going on vacation, not attending college, not buying the new household appliance/furniture etc. Real losses of output that will not be substituted. Just look at the consumption of natural resources (oil, metals, lumber etc.); all indicators of real losses in economic activity not just substitution between monetary and non-monetary exchanges.
“Where do you draw the line?”
I don’t think there’s an easy answer to that.
There is an important line between produced goods and the rest. But there’s also an important line between fixed income monetary assets and the rest. And how important these lines are depend on elasticities, both for demand and supply. As I said, if the demand and supply of money are highly inelastic, then that might indeed be the only line that matters.
@Nick Rowe: “I divide the world into two groups of things: money; everything else. Money is different because everything else is bought and sold for money and priced in money.”
My highchair again: I divide the world into two groups of things: real assets (long-term “capital” and and short-term consumption goods), and financial assets. Financial assets are claims on real assets. They are not money (no, even currency isn’t), they are embodiments of money — exchange value. They cannot be consumed; they have no use value (but can be exchanged for things that do). They require no inputs to production (just lay down your credit card instead of your debit card and you’ve created money), and they are not inputs to production (they can only be exchanged for inputs to production). “Financial capital” is an oxymoron.
Money is different because it (and the financial assets that embody it) is produced for free, and can only be exchanged, not consumed.
What are the demand dynamics for a “commodity” that is produced with no inputs or cost, and that cannot be, is never, consumed? Are they identical to the dynamics for things that do require inputs, and are consumed? That’s the (a) crux I’ve been wrestling with.
oh RIGHT, now I remember. This was another problem Keynes acknowledged after the publication of the GT. (I can’t find the exact cite right now.) In the GT, he implicitly was considering a period of time long enough for capital projects to be carried to completion. Then the income resulting from investment would have generated savings equal to the value of the investment, presumably held in the form of equities, so that we don’t need to consider any change in asset-market equilibrium. But in a later article, he acknowledged that the financing needs of investment while it was being carried out would create additional demand for liquidity, and that this factor probably explained a large part of interest rate movements over the business cycle.
If wanting to get money out of the model makes one a non-Keynesian, then Joan Robinson was as non-Keynesian as any New Keynesian:
https://www.jacobinmag.com/2011/07/joan-robinsons-open-letter-from-a-keynesian-to-a-marxist-2/
I think my previous might have been spammified.
@Nick Rowe: “I’m still thinking about this. I’m thinking about red money.”
Likewise. In particular I’m thinking about a question that’s been vexing me for some time: is your untapped Visa credit-line “money”? Or does it only become money when you lay down your credit card (instead of your debit card)? Any help appreciated.
“If the current period is very short, the consumption function will be almost horizontal (the marginal propensity to consume “b” will be almost zero).”
I would suggest that b is fluctuating between 0 and 1 in very short time periods. Think of a car that travels 50 km from A to B in 1 hour. The average speed is 50 km/h. Now, when you look at very short time periods the speed of the car can be anything between 0 or 100 km/h. You are looking at a distribution around the mean speed that gets more defined the longer time periods you look at. Same with b and the marginal propensity to consume.
“Now let us introduce a stock of money into the model.”
Did you not just introduce “a” again? What is money other than future consumption? (And should it not be 0 when looking at the end of human economic activity and assuming rational agents?)
Odie: when there is a shortage of metal, people switch from metal tools to stone tools, even when metal would be better, and total production drops as a consequence. When there is a shortage of money, people switch from money to non-money, even when money would be better, and total production drops as a consequence.
JW: “But I don’t understand how you can be so insistent on this, when right here in this post you have described variation in AD that has nothing to do with excess supply or demand for the medium of exchange.”
The model I have sketched here makes no sense except as a model of monetary exchange. If we allowed (costless) barter, unemployed hairdressers would always barter haircuts to get to full employment. The model with a continuum of equilibria was implicitly a red-green money world with a perfectly nominal income-elastic supply (or demand) of money. AD(Y)=Y for all levels of Y, because Md=MS for all levels of Y.
Looking forward to your post. Thanks for all the really great comments here (and on other posts).
Kevin: JR has forgotten about money as medium of exchange. Yes, I think she is non-Keynesian. I was going to say, in my OP, that NK macro was the bastard offspring of a threesome between Joan Robinson, Knut Wicksell, and Milton Friedman, but then this is a family blog. I was thinking of JR in terms of imperfect competition, but your quote from her there adds more.
“Introduce a fixed stock of land into the model.”
Is there a fixed stock of bonds?
“Either the price of land is perfectly flexible or it is not perfectly flexible. If the price of land is perfectly flexible, the price of land jumps up instantly, to eliminate the excess demand for land.”
Don’t bond prices have a cap so the price is not perfectly flexible?
“If the price of land is not perfectly flexible, there is an excess demand for land, but people will not be able to buy land, because there aren’t enough willing sellers. Unable to buy land, people buy consumption instead.”
Why can they not just hold money instead and wait for future buying opportunities?
“There are two ways an individual can satisfy his excess demand for money: sell more goods; buy fewer goods. Nobody can stop him buying fewer goods.”
Does that not assume the person with the demand for money already has it?
Odie:
“Is there a fixed stock of bonds?”
No. But it doesn’t affect my argument.
“Don’t bond prices have a cap so the price is not perfectly flexible?”
No. But it wouldn’t affect my argument if they did.
“Why can they not just hold money instead and wait for future buying opportunities?”
If they do, that will cause a recession. Anything that causes an excess demand for money causes a recession.
“Does that not assume the person with the demand for money already has it?”
Yes. But if he didn’t have any money he would not be buying anything anyhow, so it doesn’t matter.
@Nick Rowe: “Nick E: why stop at M+B? Why not add land in too? M+B+L. Why not add old houses, old cars, paintings, you name it? Where do you draw the line?”
Interesting (to me) that this suggests exactly what I’m suggesting: all financial assets (in which I include currency and deeds*) are embodiments of money. The money stock is the aggregate market value of all financial assets.
Which, by the way, is leading me to a rather straightforward monetarist way of thinking about the economy, in terms of the money stock and velocity — but with a coherent definition of “money.”
Changes in desired portfolio allocations result in the total stock increasing/decreasing, but that has nothing to do with “demand for money.” All those assets embody money.
* Tricky area, art and other such collectibles as financial assets: can we call your ownership of a Vermeer — which will never be consumed — a financial asset? I think it’s useful to do so.
The model I have sketched here makes no sense except as a model of monetary exchange.
It’s one thing to say that there is no such thing as AD in a world without money. It’s a different thing to say that AD constitutes excess supply or demand for money.
Steve Roth: is human capital (labour) also money? Are all newly-produced goods and services, and the ability to produce them, money? What is not money, in your view?
Odie: “Have you ever looked how bonds are priced?”
Yes, I have looked at how bonds are priced. Have you ever looked at a first year economics textbook to see the difference between a demand curve that is perfectly elastic at some price, and something that prevents the price rising so that there is excess demand at some price?
“He could take out a loan in expectation of future income.”
Taking out a loan means selling an IOU for money.
Just stop.
@Nick Rowe: “Steve Roth: is human capital (labour) also money? Are all newly-produced goods and services, and the ability to produce them, money? What is not money, in your view?”
Great question.
First, tangential: human capital is the ability to work/produce. (Stock.) Not synonymous with work/labor. (Flow.)
In my term-of-art definition (in my Celestial Emporium of Benevolent Knowledge), none of those things is money or could even be conceived as money, for multiple reasons. They’re all real assets.
Key conceptual distinction in this Emporium, between money and its embodiments:
Money is exchange value embodied in financial assets — claims on real assets. The assets aren’t money (even currency isn’t); they’re embodiments of money. Money doesn’t exist absent its embodiment in financial assets (claims, credits).
Financial assets are distinguished from real assets by the fact that they require no inputs to production and cannot be consumed.
So while the apple on my counter does embody value, it does not embody money, because that value can be consumed, converted into human utility. Money can’t. It can only be exchanged.
I find this whole conceptual construct useful because it lets us think coherently like monetarists, with the money stock consisting of the total market value of financial assets (designated in the unit of account). Portfolio readjustments change that market value, hence the money stock. And yes, that portfolio readjustment is often driven by change in demand for currency-like financial assets — embodiments of money that are historically, nominally stable, relative to the unit of account. But that’s not demand for “money.” It’s demand for certainty, or stability, or similar.
I’m basically trying to distinguish, conceptually, between money and and currency (and other currency-like financial assets), suggesting they’re most usefully understood as not being conceptually comparable. That confution is at the root of much of our confusion, IMNSHO. (You’ll remember I wanted Mankiw to start his textbook discussing money and value…)
This thinking is not hermetic; I’m still poking holes in it. But I think it’s letting me think more clearly about how economies work.
@Nick: “Taking out a loan means selling an IOU for money.”
In my emporium:
There’s no “selling” involved. Taking out a loan is creating two financial assets — an IOU and a bank deposit. Each is an embodiment of money. Both balance sheets grow. “Selling” in this context seems like a serious conceptual stretch, perhaps to the point of breaking. Likewise the obverse: buying money for an IOU?
Steve: if I lend you money, that does not create money. If you repay your loan to me that does not destroy money.
If a (central or commercial) bank creates money, it creates money. It can buy something with that money it has created (including buying an IOU), or it can simply give that money away. A bank buying a computer creates money. A bank giving money to charity creates money.
“Loans create deposits!!!” is a very misleading MMT slogan. Best avoided. Not all loans create money. Not all creations of money create loans.
But this is now totally off-topic.
Nick, an easy one for you. You write:
“when we talk about AD, we are really talking about the excess demand and excess supply of the medium of exchange.”
Would Sumner agree? (I’m trying to get straight in my head your differences on MOA vs MOE)
Also, is MOA the “money” in the concept of “long term neutrality of money?”
Nick, I’m trying to give you a Get Out of Jail Free card. I read the GT a bit everyday, more or less continuously now, but it’s all there in the Introduction. Step back and read it rhetorically and philosophically. Is there a stranger Intro that comes to mind? Godel didn’t even feel the need to say that.
Donald Pretari: “it’s all there in the Introduction.” I wonder what you’re getting at. Book I of the GT (Chs 1-3) is the Introduction. There’s an awful lot there, so what, in particular, do you have in mind?
“he will plan to run down his stock of money over time”
Wait, just to clarify. Is this still in the b=1, one period, case? If so, is there some distinction between “model time” and “historical time” (=one) here? (I might be just getting hung up on the “over time” part and getting rid of that in the sentence might not matter for the point being made)
A probably naïve question from someone who took second-year macro many years ago.
I’m thinking about the standard Keynesian-cross analysis where an exogenous increase in spending produces an increase in equilibrium national income through the multiplier. What’s happening on the monetary side here? I remember the identity PY = VM. We’re assuming P is fixed, and Y is increasing in this case. Did Keynes think V would automatically adjust for some reason? Or did he assume the private sector held a pool of idle money that would be re-injected into the circular flow of money to make all the additional buying-and-selling at the new equilibrium possible?
And if it’s V that’s supposed to be adjusting, my question is “How could he assume this?” In setting up the IS-LM model there’s this whole thing about V being either determined by the interest rate or determined exogenously by economic institutions. If V is determined exogenously then (if I recall correctly) national income gets determined by the LM curve only and all the Keynesian multiplier stuff becomes irrelevant. Why wouldn’t this thinking also apply in the Keynesian-cross case?
(I think this might be related to some of the discussion above, although I’m not sure.)
Nick,
I’ve greatly enjoyed this exchange. I don’t think you’ve convinced me of your position, but you have certainly made me think more deeply about my own and probably caused me to revise my perspective somewhat.
notsneaky: “(I might be just getting hung up on the “over time” part and getting rid of that in the sentence might not matter for the point being made)”
Hmmm. I think that’s right. I think I should have just deleted the “over time” part. It doesn’t quite make sense in the context, as you say, but I don’t think it’s needed to make my point. If you have $100 you plan to get rid of, your permanent consumption will rise by $100.r above your permanent income for the individual experiment. And when you recognise that everyone else is planning to do the same, your permanent income rises by that times the (infinite) multiplier for the aggregate experiment.
Maurice: think of the ISLM model. If V really is fixed (and if M is fixed) the LM curve is vertical, so shifting the IS curve right won’t increase AD. Keynes assumed that V was an increasing function of the rate of interest, so the LM curve slopes up, so shifts in the IS curve increase both r and AD.
Nick E: thanks for saying that. I would say exactly the same thing! The discussion here has been very good.
Don: OK, I have re-read the first 3 chapters to the GT, and I still don’t see what you are getting at. My only thought was: “God, this would have been so much clearer if he had simply drawn a labour market diagram, W/P on the vertical axis, L on the horizontal, downward-sloping W/P=MPL curve for the classical labour demand curve, upward-sloping W/P=MRS curve for the classical labour supply curve, where they cross at L*, which can produce a level of output Y=F(L), and then said: “OK guys, now what happens if Yd < Y*, so firms can’t actually sell Y?” (It’s a shame he never read Patinkin!) And then said that Yd depends on Y, and asked what else Yd might depend on, and whether there would be any process that would bring Yd automatically to Y?
Kevin: “What I don’t think you’re entitled to say is that “New Keynesians are not Keynesians” when, in effect, all they are doing is making money endogenous. If the central bank is following a Taylor rule, M adjusts passively. Since it doesn’t really add anything to the model we may as well leave it out.”
Hmm. OK. I think I see your point. JMK did in fact say that Yd was a negative function of r, so that the central bank setting the right level of r would get you to full employment. But if the NKs then change Keynes’ model, so that it is not the level but the growth rate of Yd that depends on r, and if that growth rate depends positively on r, for a given time path of Y, and if the mpc out of permanent Y equals 1, you would think they might go back and re-ask Keynes’ Big Question: “what, if anything, ensures that permanent Yd equals permanent full-employment Y?”. And not make that appallingly un-Keynesian intertemporal fallacy of composition.
“Keynes assumed that V was an increasing function of the rate of interest, so the LM curve slopes up, so shifts in the IS curve increase both r and AD.”
That make sense. So Keynes’ baseline model was really the standard IS-LM model. And the Keynesian-cross multiplier analysis is really a kind of warm-up for the real thing, which takes the LM curve into account. But then why bother with the Keynesian-cross multiplier stuff at all? I seem to recall the evidence says the connection between r and V is very weak, which means the fixed-V/vertical-LM story is close to being true. Why not just start there? Wouldn’t that make macro a lot less complicated and possibly a lot less controversial?
Maurice: “So Keynes’ baseline model was really the standard IS-LM model.”
Well, that is a rather controversial statement, that some “fundamentalist” Keynesians would strongly dispute, but I’m staying out of that one.
You can view the Keynesian Cross model as just a warm-up exercise, as one way to derive the IS curve, when you add an effect of r shifting the AE curve up or down. (The other way is to derive it from the I(r)=S(r,Y) condition.)
I read the evidence differently from you. For example, hyperinflations (when the opportunity cost of holding money is very high) are associated with very high V. Plus, the slope of the LM curve depends not only on the interest-elasticity of the demand for money, but also on the interest-elasticity of the supply of money. And central banks can make that elasticity very high (or very low, or negative), if they want to.
The best case for a vertical LM curve is to assume it is vertical because the central bank makes it vertical, by adjusting the supply of money to keep Y at “potential”, to keep inflation on target.
Keynes’ baseline model has a clear, one-way causal structure:
1. Nominal wages set the price level.
2. Given the price level, the money supply and the (exogenously fixed) stock of “bonds” determine the interest rate. Demand for money varies only due to liquidity preference.
3. The interest rate plus the (exogenously fixed) expectations of entrepreneurs about the income streams expected from newly produced capital assets, determine the level of investment.
4. The level of investment determines the level of output.
There is some contemplation of feedback from 4 to 3, as expectations adjust in light of current output. But variation in output and investment have no effect on asset prices/the interest rate, or on the price level. You could say it’s ISLM but with the LM curve horizontal everywhere.
There is a good discussion in chapter 4 of Lance Taylor’s Reconstructing Macroeconomics, but in general, this is not controversial. Needless to say, the fact that Keynes said this does not necessarily mean that is logically consistent, or that it is a useful way of describing the economy either in his time or in ours.
In other words: If you think money holdings — and by extension balance sheet positions in general — are basically about transactions requirements, you draw a vertical LM curve and you’re a monetarist. If you think money holdings — and balance sheet positions in general — are basically about liquidity, you draw a horizontal LM curve and you’re a Keynesian.
JW: I think I would roughly agree. Keynes seems to “forget” the feedback effect from Y to changes in the demand for money, to interest rates. Even though Y affects the transactions motive for holding money. ISLM closes that feedback loop.
Nick-
Yes, that’s part of it.
In fact, Keynes leaves out two feedbacks. The one you mention, from Y to asset markets via transactions demand for money. And also, from investment to asset markets, as the creation and financing of new capital assets changes the stock of assets available to wealth holders. Personally, I’m not worried about the first one — I’m happy to assume that velocity adjusts freely as needed. But the second omission is a problem. There are more or less convincing stories you could tell for why investment decisions don’t affect equilibrium in the bond market. But the GT does not provide one.
“Plus, the slope of the LM curve depends not only on the interest-elasticity of the demand for money, but also on the interest-elasticity of the supply of money.And central banks can make that elasticity very high (or very low, or negative), if they want to.”
OK. But then let me go back to my original question, somewhat revised. If Keynes thought more government spending would help countries get out of the Great Depression was it because:
(1) he thought resulting increases in r would cause V to rise by a lot (in which case, he evidence suggests he was probably wrong),
(2) he thought governments would increase M to prevent the increases in r that would otherwise occur (if so why didn’t he just argue for more M?), or
(3) he thought an increase in G would necessarily involve the government drawing from pools of idle money (which the private sector held because rates-of-return were very low and good investments very scarce) and putting this money back into circulation?
JW: OK. But ISLM also omits that second feedback (in the simple textbook version). It assumes the length of the period is short, relative to the time it takes for the capital stock to adjust (and it does ignore feedback from expectations of future capital stock adjustment).
Maurice: there isn’t a lot of talk about fiscal policy in the General Theory. Keynes’ case for fiscal policy is more based on your 1, the liquidity trap (which is the same as your 3).
JW could probably give a better answer than me.
Re IS-LM, velocity and all that, I suggest a look at Keynes’s GT Ch 15, Section II:
http://www.marxists.org/reference/subject/economics/keynes/general-theory/ch15.htm
Nick: “But if the NKs then change Keynes’ model, so that it is not the level but the growth rate of Yd that depends on r….”
I don’t think this is an accurate characterisation of what the NKs do. I’ve never tried pasting an image in comments here before, but if this works I might try it again. What you will hopefully see is a “simple” version of a NK consumption function, which is not to be confused with the Euler equation. It’s the steady-state case with log utility.
Hopefully that monstrosity hasn’t done anything harmful to the blog. Obviously Y(t) is disposable income. What I’m getting at is that this consumption function wouldn’t have looked so very strange to an Old Keynesian like Modigliani, except for the fact that the sum is infinite. He wasn’t too struck on the idea that we should think of households as being immortal and neither am I. In other respects though, it’s not much different from his own theory.
Sorry to be late to the party. As endogenous money was mentioned above I’d like to point that the normal MMT explanations are deficient but it can be done better. Double entry accounting properties causes that some temporary amount will be created when extending loans. That practice then opens the road for substantial amounts. For funding investments we have retained earnings + exogenous money from CB + endogenous from banks. For details see http://olliranta.wordpress.com/endogenousmoney/
@Nick Rowe:
Yes far off topic my apologies. I go here because I’m having trouble buying into the basic terms of the conversation. Or think other terms are more illuminative.
Yes lending by commercial and central banks. (I find it useful to conceive of comms as licensees, subsidiaries of the fed, given how reserve resolution works.)
Those loans — mortgages, consumer credit, student loans — dominate the lending in the real economy. $12tn HH debt outstanding compared to $8tn corp bonds. (Not sure about net/gross flows.)
If you buy a $10 watermelon with your credit card instead of your debit card, two financial assets are created — $10 in bank deposits and a $10 IOU — that would not have been created if you’d used your debit card.*
You’ve created and given away a new claim against your real asset, your ability to work, and held on to $10. Those financial assets embody money. You’ve caused the money stock to increase.
When you pay down that debt, you cause the money stock (total value of financial assets) to decrease.
I think equating the money stock with currency-like financial assets is a core conceptual problem, rooted in the conventional-wisdom fairy tale about how “money” was created (coins rather than credit tallies).
Still thinking very hard, can’t quite figure, to what extent your unused credit limit can be conceived of as part of the money stock Seems right in the thick of your red-money thinking. If all credit limits were cut in half tomorrow, there would be less spending on real goods…
* The retailer gets the $10 deposit (and gives you the watermelon), but they would have gotten it if you’d used your debit card. So that asset appears on your books (your bank balance doesn’t decline), not the retailer’s, relative to the counterfactual. Your balance sheet expands, not the retailer’s.
“Keynes’ case for fiscal policy is more based on your 1, the liquidity trap (which is the same as your 3).”
To tell the truth, (3) is only way the Keynesian-cross analysis ever made sense to me. My background is math and stats, so let me use a bit of algebra to do a riff on the haircut-economy model you had in a previous post. Two identical cohorts. Each period one cohort sells haircuts to the other for cash. Only form of saving: hoarding cash. In any period spending by the cohort buying haircuts [Yd(t)] depends on the amount of cash it earned in the previous period [Y(t)]:
(1) Yd(t) = A + bY(t) 0 < b < 1.
But Y(t) is just the amount of cash spent on haircuts in the previous period:
(2) Y(t) = Yd(t-1).
From (1) and (2):
(3) Yd(t) – Yd(t-1) = A – (1-b)Yd(t-1).
The system is governed by (3) in or out of equilibrium. The l.h.s. of (3) represents the change in the amount spent on haircuts from one period to the next. Alternatively, this is the amount by which people draw down their reserves of cash to pay for the additional haircuts they want to buy beyond what their current earnings allow. We have equilibrium when the amount of cash exchanged remains the same from one period to the next. This occurs at some Y^ where:
(4) 0 = A – (1-b)Y^
That is:
(5) Y^ = A/(1-b).
The famous 45-degree line in [Yd, Y] space is the set of all points where Yd(t) = Y(t) = Yd(t-1). At the particular point (Y^ ,Y^) that also satisfies (3) the system reaches equilibrium. My set-up implicitly sets V = 1, because cash-in-circulation changes hands only once a period. The multiplier that comes from (5)
(6) dY^/dA = 1/(1-b)
thus represents both the change in equilibrium income associated with a unit change in A and the corresponding change in the equilibrium amount of cash-in-circulation.