1. Assume a representative agent model in which everyone has exactly the same supply and demand for apples. No apples get traded in equilibrium. A law which lowers the price of apples will create an excess demand for apples, but will have no effect on anything else. People will now want to buy apples, but won't be able to, because nobody wants to sell apples. And so they will go on doing whatever they were doing before the price of apples was lowered. OK?
1 is obviously correct. Everybody has an apple tree, and in equilibrium is self-sufficient in apples. Everybody wants to buy extra apples from someone else when the price of apples is lowered by law, but nobody wants to sell, so they go on eating only their own. Life continues just as before across the whole economy.
2. Assume a representative agent model in which everyone has exactly the same supply and demand for bonds. No bonds get traded in equilibrium. A law which lowers the price of bonds will create an excess demand for bonds, but will have no effect on anything else. People will now want to buy bonds, but won't be able to, because nobody wants to sell bonds. And so they will go on doing whatever they were doing before the price of bonds was lowered. OK?
2 is equally correct. It might make some Neo-Wicksellians uncomfortable, because it says raising the rate of interest on bonds won't have any effect. But they can't escape the parallel to 1. Nobody is borrowing or lending in equilibrium. They all want to lend to someone else when the rate of interest is raised by law, but can't find anyone to lend to, so they go on spending their own income. Life continues just as before across the whole economy.
1 and 2 were word-for-word identical, except that "bonds" replaced "apples". Now let's try the same thing with "money".
3. Assume a representative agent model in which everyone has exactly the same supply and demand for money. No money gets traded in equilibrium. A law which lowers the price of money will create an excess demand for money, but will have no effect on anything else. People will now want to buy money, but won't be able to, because nobody wants to sell money. And so they will go on doing whatever they were doing before the price of money was lowered. Not OK.
3 is obviously rubbish.
People trade money, even in a representative agent model. It wouldn't be money otherwise. They might have the same supply and demand for money, but they have different supplies and demands for other goods, and will use monetary exchange to buy and sell those other goods.
If the price of money is lowered by law (i.e. if the price of all other goods is raised, because money is typically the medium of account) there will be an excess demand for money. People will want to hold a bigger stock of money.
They all want to buy more money, by selling more other goods. But they won't be able to sell more other goods, because everybody is trying to do the same thing, so there's an excess supply of all other goods.
They all want to sell less money, by buying less other goods. And each individual will be able to buy less other goods. Because nobody can stop you buying less other goods, even if there's an excess supply of all other goods because everybody else is doing the same thing.
So there's a recession, because everybody buys less goods.
Now let's complicate the story a little.
4. Assume a representative agent model just like 1 and 3, so everybody has the same supply and demand for apples and money. No apples get traded in equilibrium. But now suppose that when the government passes a law to lower the price of money by raising the price of all other goods it forgets to include apples in the law. The price of apples is free to adjust.
There's an excess supply of all other goods, except apples. The price of apples will adjust to ensure equilibrium in the apple market. But the recession is exactly as bad as when the price of apples couldn't adjust, because no apples get traded anyway. A casual observer might think the recession is caused by the price of apples being too low. But we know it isn't.
5. Assume a representative agent model just like 2 and 3, so everybody has the same supply and demand for bonds and money. No bonds get traded in equilibrium. But now suppose that when the government passes a law to lower the price of money by raising the price of all other goods it forgets to include bonds in the law. The price of bonds is free to adjust.
There's an excess supply of all other goods, except bonds. The price of bonds will adjust to ensure equilibrium in the bond market. But the recession is exactly as bad as when the price of bonds couldn't adjust, because no bonds get traded anyway. A casual observer might think the recession is caused by the price of bonds being too low. But we know it isn't.
5 is exactly like 4, except I have substituted "bonds" for "apples". It makes exactly as much sense to blame recessions on bond prices being out of line as it does to blame recessions on apple prices being out of line. Those prices being away from full equilibrium is a consequence of the recession, not the cause.
If apple prices were flexible, they would always adjust to clear the apple market. But that does not mean there is no excess demand for money. An excess demand for money is not the counterpart of an excess supply of apples.
If bond prices were flexible, they would always adjust to clear the bond market. But that does not mean there is no excess demand for money. An excess demand for money is not the counterpart of an excess supply of bonds.
Bond prices are flexible, so they always do adjust to clear the bond market. But that does not mean there is no excess demand for money. An excess demand for money is not the counterpart of an excess supply of bonds. The textbooks which say this (and most do) are wrong.
We see an excess demand for apples in the apple market. We see an excess demand for bonds in the bond market. We do not see an excess demand for money in the money market. There is no money market. Every market is a money market. We see an excess demand for money in every market. The relative price in that market will adjust, if it can. And there will be excess supply in that market, if it can't.
Bond prices are flexible, so we never see an excess demand for money showing up as an excess supply of bonds in the market for bonds. Instead, we see an excess demand for money as an excess supply only in those markets where prices are not flexible. But that doesn't mean there isn't an excess demand for money in all markets. It's just that the symptoms are masked by price adjustment in some markets.
Just one more attack on the non-quasi-monetarist orthodoxy.
Worthwhile Canadian Initiative 
RSJ: the Fisher separation theorem only holds if you can freely borrow and lend at rate r. Which will only be true if r is the equilibrium rate. If the government sets r above (or below) the equilibrium, there will be excess demand (supply) of bonds, so people will be unable to lend (borrow) as much as they would like.
Nick writes,
“Darwinian biologists build simple stylised models that exclude massive amounts of the real world too.”
Biologists can track actual causal pathways in the actual world — these explanations aren’t “stylized models”, these are real causal explanations involving real stuff.
And the only viable alternative to this causal mechanism is “And then a miracle occurred”.
Economists don’t map out actual causal pathways in the actual world — and they have dozens of rival “stylized models” that can’t be adjudicated between — in part because these models don’t make contact with the structure of the actual causal world in any genuine or deep or persuasive way.
The differences — e.g. in the providing of genuine causal pathways — between how Darwinian biologists explain phenomena and how economists in far more immense than are the similarities.
But what is more, Darwinian biologists run into the same pathological problems economists do when they mistake their math constructs for the real causal world. As one example, see the work of Alex Rosenberg on tautological / non-explanatory uses of the concept of “fitness” in formal math work in Darwinian biology. Much of the conceptual debate between paleontologists and math jock Darwinians comes does conflicts over the failure of the concepts in the math models to make contact with real biological pathways. See the work of David Hull and Alex Rosenberg, for example, on the conceptual issues involved the ties between Darwinian math models and real biological pathways.
“Fisher separation theorem only holds if you can freely borrow and lend at rate r.”
Yes, and that’s a good point. But you need that in your assumption that “nothing changes” as well.
“Which will only be true if r is the equilibrium rate.”
Hmm, I think there is a school that argues that incomes will adjust so that supply (as a function of income) equals demand (as a function of income) at the higher rate, in which case there would be free lending and borrowing at that (higher) rate, but a lower level of output.
Now in your example, the full output rate is 5%, and government makes it illegal to sell a bond with a YTM < 10%. Then everyone sells stocks and nothing changes. So the government makes it illegal to sell stocks that yield a dividend of < 10%. Then all the firms re-invest their earnings and stop paying dividends, but still the return is 5%. Then the government puts caps on the ratio of price to earnings. Now you see how this would directly reduce investment. This goes back to Bills argument the last time you raised this issue, namely that you need to either put a floor under MPK or everyone will just ignore your law and work around it, and they will continue to buy “bonds” that pay 5%.
In your specific example — if two households want to pool their money and invest in a project that pays 5%, they wont be able to (as that is equivalent to selling 5% bonds) but if just one household wants to invest in a project that pays 5%, then it will. It gets an exemption. So in your model everyone switches to home production and then continues to get 5%, so even though the law requires 10%, no one borrows or lends at 10%, everyone borrows and lends at 5%, but they only do it from each other.
Therefore the economy either goes into a recession (if everyone’s wealth is not identical and production is not CRS) or things continue as they were. But the only way they continue as they were is if the actual rate of interest remains 5%, irrespective of the law, because everyone has found a way of avoiding the law by purchasing equity in single-owner firms rather than in joint-ownership firms, all while maintaining the same interest rate (5%) that will produce the necessary investment for the economy to operate at full output.
Ooops, in the above I should have said “then the firms pay a dividend of 10%, of which 5% is earnings and 5% is return of capital. Now you see how this would directly reduce investment. Then the government puts in a law, requiring the firms to pay 10% in dividends, not return of capital.”
Anyways, the point is that the bond market always clears, but incomes adjust to make it clear, at least in some models.
RSJ: “Anyways, the point is that the bond market always clears, but incomes adjust to make it clear, at least in some models.”
Yes. That is precisely the point. And not just in “some” models (i.e. not just in a few obscure models).
And that is precisely the point I am disputing in this post.
And in other models (i.e. in a really obscure model I am making up on the spot right now), the market for blueberries always clears, and income adjusts to make it clear. So if the government sets the price of blueberries too low, income will fall until people’s demand for blueberries equals the supply of blueberries.
“I would change what you said to “That’s because bonds are not a medium of exchange and therefore having nothing to do with money payments to factors of production – so there can’t be a holdback of money as there is with money paid to those who produce goods.”
+
“Anyways, the point is that the bond market always clears, but incomes adjust to make it clear, at least in some models.” Yes. That is precisely the point. And not just in “some” models (i.e. not just in a few obscure models). And that is precisely the point I am disputing in this post.
yes:
i.e. factor payments NOT = f(bond price clearing)?
anon: “i.e. factor payments NOT = f(bond price clearing)?”
Correct. An excess demand for bonds does not mean that factor markets won’t clear. Factors are paid in money, not bonds. But an excess demand for money will mean that factor markets won’t clear.
Most models say that, if prices are sticky, real income must adjust until the demand for bonds equals the supply of bonds.
I say: if prices are sticky, real income must adjust until the demand for the medium of exchange equals the supply of the medium of exchange.
So, at least someone is still reading, and seems to be getting it. What’s your economics background, anon, out of interest?
mostly finance Nick
I find the easiest way to demonstrate your point is simply to hold new bond issuance to zero in a growth economy scenario – that’s easy enough to do and shouldn’t wreck any generality. To prevent bonds from “getting in the way”, you simply assume that any required financing is either zero (its still possible to grow from the existing money stock) or comes from bank lending (which adds to money stock). Then you start looking at the effect of the demand for money once it is in the hands of the factors of production. Whether or not money supply has increased is all relative and immaterial to your main point then. Demand for money can theoretically increase more than enough to offset any new money creation.
I think you may have effectively held new bond issuance to zero somewhere along the line when you assume the supply of bonds was fixed? I can’t remember now.
on the other hand, maybe that bank lending part I mentioned above isn’t something you really want to convey either, because economists look at the bond part of the model more generally? I don’t know. But that’s how I would think about the difference in the effects as between bonds and money.
Nick: “Most models say that, if prices are sticky, real income must adjust until the demand for bonds equals the supply of bonds.
I say: if prices are sticky, real income must adjust until the demand for the medium of exchange equals the supply of the medium of exchange.”
Nick, virtually every model I ever learned that had money in it said both of those things. Moreover, they’re hardly independent of each other. If there’s an excess demand for money don’t you think that shows up in a higher interest rate? If not then why not? So is an excess demand for money really different from an excess demand for bonds?
Now, perhaps I’m wrong but I think I get what you’re saying. I also think you’re correct that an excess demand for money causes a recession.
I think you’re wrong that that’s the only thing that can cause a recession. And I don’t see that you’ve demonstrated that Woodford is wrong, you’ve just asserted it repeatedly. Woodford’s cashless model is completely equivalent in every way to a monetary exchange economy where the CB supplies just enough money to maintain an interest rate target.
So how can it be that you can have a recession in one but not the other?
But if you can have a recession in both then it follows that you can have a recession in the cashless model. So where is Woodford wrong?
Adam: this is the question that has always puzzled me: do we interpret Woodford’s “cashless” model as barter? I few month’s back, I got into an argument with Steve Williamson, in comments on his blog. Steve said that Woodford’s model is a model of a barter economy. I said it couldn’t possibly be, because the results would make no sense if it were interpreted as a barter economy. I thought Steve was out to lunch in his interpretation of the model. Now I see others interpret it the same way.
So now I’m going to say, that if we interpret his model as a model of a barter economy, where output can be exchanged directly for output, then his model is wrong. No matter how badly the central bank screws up, the under-employed firms/workers could just barter. Any recession would mean there are unexploited gains from trade just waiting to be exploited by mutually advantageous barter exchanges. The two underemployed backscratchers do a deal: “I will scratch your back if you scratch mine”.
Now let’s instead interpret Woodford’s model as a model of a monetary exchange economy. You can’t do direct barter. So my above argument that the economy will always stay at full employment, even if the CB screws up, now doesn’t work. I agree with Woodford that in this case, if the central bank screws up there will be a recession. (The underemployed worker/firms can’t barter their way to “full-employment”). Now, the question becomes: how do we interpret the rate of interest in Woodford’s model? Is it the rate of interest on bonds, or is it the rate of interest on the medium of exchange? I say it has to be interpreted as the rate of interest on the medium of exchange. My thought-experiment, where I have the government pass a law to raise the rate of interest on bonds, but leave the rate of interest on the MOE unchanged, is a way to distinguish the two.
Well, we’re getting somewhere, finally. Strictly speaking what Woodford models is the “cashless limit” and not the limit point. So Williamson as a purely technical matter is wrong and you’re right. Woodford, in the book, is quite clear that he is modeling monetary exchange with an interest rate peg. He then takes the limit as money balances tend to zero and obtains all the same results, this is not the same as pure frictionless barter.
Now, about barter. Suppose we’re living in the cashless limit but the real rate is too high. What you haven’t explained is how the idea of “people buy fewer goods and service in order to acquire money” is different from “people buy fewer goods and service in order to acquire bonds”.
Imagine it’s frictionless barter. I am offered an exchange “I’ll scratch your back if you’ll scratch mine” and I refuse because the deal I want is “I’ll scratch your back and you give me a bond”. I can only give one backscratch per period.
I think you’re answer will be that they can’t acquire the bonds and so the do the second best deal. But, as I explained above, that’s not what happens in the NK model! In the model the CB accepts backscratches as payment for bonds and stands ready to supply bonds in return for backscratches in whatever amount of bonds are demanded! If the CB didn’t do this the price of bonds would rise which would mean the interest rate fell, but the rate is pegged! NK models have sticky goods prices, not stick bond prices.
So I don’t do the second best deal, I trade my backscratch to the CB in exchange for a bond. But now the other guy has nobody to trade with, so he loses his opportunity for exchange, meaning his income falls.
You’ve never given the counter argument to this because you’ve always assumed people do the second best deal, but in the model they don’t. They do first best deals that result in a loss of aggregate income.
Adam: Are bonds the medium of exchange? Are bonds money?
If this is a monetary exchange economy (people only trade backscratches for money), and if people trade backscratches for bonds, then — bonds are money.
Assume full employment Consumption is 100, with r=6%, but if the CB sets r too high, at 10%, for one period only, Consumption falls to 60 (according to the Euler equation). But that means the CB would have to buy 40 backscratches, in exchange for bonds, in order to get r up to 10%.
I can understand that. But that’s fiscal policy, and that is not what’s going on in Woodford’s model.
Assume instead that bonds are not money. There is no market in which backscratches trade for bonds. There is only a market in which backscratches trade for money, and bonds trade for money.
Start in full employment. Then the CB raises r to 10%, and announces it will buy and sell bonds for money at 10%. The CB buys money and sells bonds. (In the limit, as we approach the cashless economy, the amount of bonds the CB sells (and the amount of money it buys) approach zero.) The fall in the supply of money causes a recession, as people refuse to buy backscratches for money, and C falls to 60.
I can agree with that. But:
Suppose the CB refused to buy or sell bonds.
1. You could get exactly the same recession by vacuuming the supply of money by the same small amount.
2. Passing a law to raise r to 10%, and leaving M unchanged, would not cause a recession. It would just cause an excess demand for bonds.
Nick, is it fair to say that you largely agree with Rogers’ critique of Woodford (assuming Woodford and Adam P. would not agree that bonds become a MOE in the cashless limit):
“Formal credit is extinguished in the cashless limit leaving only informal credit. Informal credit turns out to be code for an accounting system of exchange…Models based on accounting systems of exchange could be characterized as models of ideal or perfect barter because money is not required to resolve problems arising from the double coincidence of wants….and having nothing to say about how the equilibrium trades are actually executed.”
Click to access 0411001.pdf
dlr: very good find! I didn’t know Colin had written that. I have skimmed through the paper. Colin is more concerned with the question of whether the price level is determinate under flexible prices in Woodford’s model. I am concerned with the question of whether there can be recessions under sticky prices in Woodford’s model. But we are very much on the same page.
My interpretation of Woodford’s model differs a little from Colin’s. (But that’s probably because Colin is more concerned with what Woodford actually says and I am more concerned with what Woodford would need to say in order for his model to make sense.) I would interpret Woodford’s “informal credit system” (the only payments system that remains in the cashless limit) as a monetary exchange system in which bonds are the medium of exchange.
If we accept Colin’s interpretation, that “informal credit” is equivalent to barter, then Woodford’s model cannot get recessions. If we accept my interpretation, that “informal credit” is equivalent to monetary exchange, in which bonds are money, then we can get recessions.
Yes, I think I disagree with Colin’s interpretation of what is implicitly going on in Woodford’s model. But it all hinges on what happens to unspent credits in the “informal credit” system in Woodford’s model. If they are converted into bonds, then bonds are money (my interpretation). If they cannot be converted into bonds, but must be spent, then it’s equivalent to barter (Colin’s interpretation).
Actually, scratch that. If bonds are the MOE, then the CB can only raise the rate of interest by buying apples (fiscal policy). The rate of interest rises. Consumption falls, but C+G does not fall, so it’s not a recession. And if unspent credits do not get converted into bonds, then Colin is right. The informal trading system is equivalent to barter. But then there can’t be a recession.