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 
They all want to buy more money, by selling more other goods. But they won’t be able to buy sell more other goods, because everybody is trying to do the same thing, so there’s an excess supply of all other goods.
I think “buy sell” more other goods is a typo, right?
Changing just the price of apples is clearly not consistent with an equilibrium. But, I take issue with your statement that this change “will have no effect on anything else.”
The value of the excess demand in the market for apples is equal to the value of excess supply in one or more other markets. An obvious candidate is the market for apple trees (since apples are so cheap, it is no longer as important or profitable to produce apples).
Bill: yes. Thanks. Fixed.
Aaron: apples are cheap, but you can’t buy any. So you need to keep your tree. If you sell your tree, you won’t get any apples to eat.
“The value of the excess demand in the market for apples is equal to the value of excess supply in one or more other markets.”
Walras’ Law. It’s wrong. Or incredibly misleading. It has mislead you. In the market for apples, there’s an excess demand for apples and an excess supply of money. It’s a monetary exchange economy, so you buy apples with money. Or, you try to. But you can’t, so exactly nothing happens in any of the other markets.
“Assume a representative agent model in which everyone has exactly the same supply and demand for bonds. No bonds get traded in equilibrium. ”
I always have a problem with this. “Bonds” — when you say bonds, you really mean all financial assets, including common equity, preferred shares, convertibles, etc. — are the liability side of capital, so saying bonds = 0 means capital = 0. What you really must mean is that bonds are not zero, but no bonds are traded, so that no investment occurs (and no consumption occurs, no labor is supplied, no production occurs, etc.)
But this isn’t a good model of the economy, because your definition of equilibrium should have ongoing investment, consumption, and production. The equilibrium should be a steady flow of production, investment, bond sales, labor supply.
This means your representative agents must be in different states. Some are producers that are selling bonds, or they are just buying the house, while others have already bought the house and are repaying the debt, etc. You have young and old, savers and dissavers, all distinguished (at a minimum) by their state.
But if you have representative agents that all have the same state, then your model applies to a null economy in which nothing happens.
RSJ: macroeconomists will recognise that assumption as a standard part of the (simple) canonical New Keynesian model. Since this post is a critique of that model, they can’t fault me for that.
We could argue about whether that assumption is a good one or not (it does not imply no investment, production, or consumption, only that it is self-financed in equilibrium), but that’s not what this post is about.
I understand the assumptions are standard, but still they do assume a null economy.
In terms of self-financing, I would say that in all cases, real capital is deployed with an expectation of earning a return, so that there is a corresponding liability and a corresponding cost of capital. The small businessman is not running a charity, and will liquidate his own capital just as the bondholder will force the firm into bankruptcy when the liability is not met.
You might as well call this obligation a bond (since you are calling everything else a bond) so that all (real) capital is backed by bonds on the liability side. And that means investment requires an increase in the quantity of bonds outstanding.
And that means that there are savings demands which, when not met, will trigger liquidation. If you have invested in the past, then in the present you have an obligation for savings (to repay your bond), which requires the present investment of others.
If that investment does not occur, then there will be liquidation.
Things wont continue as before with no change if the quantity of bonds outstanding stops increasing. That will only occur if the capital stock is at zero, or if the interest rate is zero (so that businessmen are running charities).
RSJ: you are: wrong; off-topic. Please stop.
“A casual observer might think the recession is caused by the price of apples being too low. But we know it isn’t.”
I think the casual observer is right, or at least no more wrong than “we” are. The recession is caused by the price of a certain basket of goods — a basket which in this case consists of apples and money — being too low. If the Central Orchard were to grow enough apples, it would end the recession. A quasi-monetarist will focus on money, and quasi-Applist will focus on apples, both equally valid — and equally incomplete — theories.
Andy: but only one good in the basket is doing all the work. In this model, if you fix the price of apples too low (and leave the price of money unchanged) there’s no recession. If you fix the price of money too low (and leave the price of apples unchanged) there’s a recession.
“Doing all the work” is, at the very least, an insufficient metaphor. Suppose a professor and a graduate student write a paper together. Perhaps the paper couldn’t have gotten published if the graduate student did it alone (whereas it could, if the professor did it alone), but we still don’t say that the professor did all the work. We can’t even necessarily conclude that the professor did more than a small fraction of the work.
And if you want to make the analogy between apples and bonds, you have to suppose that apples and money become ever closer substitutes as the price of apples rises. In that case growing apples will be a more effective stimulus than printing money, and applism will be a more useful theory than monetarism.
Andy: OK. I understand you now. Yes, even if the cause was one thing, it is possible that some other thing could also be a cure.
I’m not conceding the money is “the” cause, only that it’s a necessary (and potentially sufficient) element in the cause. Money can be critical (in the sense of being a necessary element) and still not be important (in the sense of being something one ought to spend much time thinking about).
What is really necessary, though, is not money as such but the ability to sell something without simultaneously buying something. You’re going to say that, whenever such a transaction occurs, the seller is ipso facto obtaining a medium of exchange, but there’s no a priori reason that such a medium must have the properties we normally associate with a good (e.g., being of finite quantity). There’s quite a bit of epistemological ambiguity here. Perhaps money in this sense is more properly considered a verb (“to have sold”) than a noun.
Andy: I think we can imagine some sort of multilateral exchange system like that. Imagine a centralised exchange, where you could not put in an offer to sell without at the same time putting in an offer to buy from some other member. And the person running the exchange (or the computer) would hunt for “circles”(?) of exchanges that could all be executed out simultaneously.
I would call that a barter system. Because any good could be traded for any other good. The only difference would be that we normally think of barter as 2-person. But the circles here could have any number of people in a given trade.
The Walrasian auctioneer is conducting one big n-person barter deal for everybody in the whole economy.
My mind is not 100% clear on this.
You are saying: “what matters is that there be a simultaneous offer to buy and sell, so you can’t sell without buying”.
I am saying: “what matters is that anything can be traded for anything else with as many people involved in the trade as necessary.”
I see what you are saying, and recognise the truth in it. But at the same time I’m thinking “Andy can’t be right, because when we sell something we do buy something — we buy money”
Nick, explain to me why why the demand for some goods won’t go up and others down relative to one another.
If my demands change, my relative demands will change.
Why am I wrong here. Why am I worong in seeing this obvious implication — there will NOT be an excess supply of all goods, with relative price changes and relative demand changes, some thing will not have an excess supply.
Nick writes,
“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.”
Greg: In the canonical New Keynesian model, everybody has identical Dixit-Stiglitz preferences, and preferences are also perfectly symmetric over the n varieties of ice cream, where each agent specialises in producing one variety. That’s the sort of model I have at the back of my mind.
We could relax that though. If all goods are normal, then when an excess demand for money causes a drop in demand for all goods, and a recession, and so income drops, the demand for all goods drops, though some demands may drop more than others. So all goods will be in excess supply, even if some are in greater excess supply than others.
Remember Greg: this is a monetary exchange economy. Goods are bought with money. Goods are not bought with goods.
Damn. Wish I had given this post a more provocative title. “A proof that all modern textbook macro is totally wrong”, or “Why Paul Krugman, Brad DeLong, and Steve Williamson are all totally wrong”, or something like that. Where are the New Keynesians and Neo-Wicksellians?
With Bill Woolsey I’m preaching to the converted. RSJ and Greg are coming from totally different perspectives, so get hung up on my New Keynesian assumptions, and so don’t go to the main point. Aaron gets the point that this contradicts what he has learned from the textbooks, but won’t go further. Only Andy gets the real point and gives me a run for my money.
RA from the Economist has picked it up.
Ah well.
Lesson: always put the punchline above the fold, or in the title. Don’t start a post with some obviously true statement about apples.
all seems reasonable and well developed
but for the uninitiated, could you restate succinctly what the thesis is that you are disproving here?
i.e. its a little hard to focus in on “all textbook macro is totally wrong”
Nick,
Again, you are NOT making NK assumptions here, this is NOT an NK model. As such this post is not a critique of such models, it says nothing at all about them.
The canonical NK model can be written equivalently with or without money. In Woodford’s book he actually does work everything out twice, once with money and once without to show the equivalence.
NK models only claim to be equivalent to a very specific kind of monetary exchange economy and it is an economy entirely different from the one you’ve assumed in this post.
The differenc of course is the endogeneity of the money supply. If you actually were operating under NK assumptions, in the variant with money, your case 3 would have read as:
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, [and this will put upward pressure on the interest rate in money markets as everyone wants to borrow money (sell bonds) but nobody wants to lend (buy bonds). The central bank, which is committed to fixing this interest rate will respond by increasing the money supply (buying bods) enough to keep this rate on target, this amount will be exactly the right amount that] people will go on doing whatever they were doing before the price of money was lowered.
That would in fact be an NK economy, what you talk about in the post is not.
In an actual NK economy then it’s only if the CB gets the price of bonds wrong, the interest rate that is, then we have problems. Money is never the problem and thus if we remove it, and remove the trading frictions in goods markets that made it necessary, but keep the bonds we get an entirely equivalent economy.
Furthermore, casting your example into the NK variant without money allows us to learn something your post appears to miss (I know that you do know this but were making a different point). Let’s see what case 3 looks like in the NK model without money. In this case lowering the price of money has to mean raising the price of everything else since we don’t actually have money.
3. Assume a representative agent model in which everyone has exactly the same supply and demand for money. No money gets traded or held in equilibrium. A law which raises the price of all goods by the same proportion will FOR JUST THIS PERIOD will create an excess demand for bonds (since the real rate has been raised due to the expected deflation) as people try to save purchasing power earned today for tomorrow when things get cheaper, but will have no effect on anything else. On the other hand, if the law raises the price of all goods by the same proportion for today and all future periods then nothing changes and people will go on doing whatever they were doing before the price of goods was raised.
So, translating your example into an actual NK economy shows that money is not as important as you think and we learn that intertemporal stuff can matter. It’s not just monetary policy today but the path that matters. Simply taliing about the supply and demand for real balances obscures this point.
Adam P.
that is a very good critique. By the way neither the way Nick thinks about things or the way you think about them are the way I think about them (because to me the only way we can reach a situation of imbalance is because some propensity somewhere has shifted and this shift and how it works through the economy is what we should think about, not the imbalance itself). Sorry I’m just not into equilibrium.
Nick,
I don’t see how your model helps here – it is just confusing things – because NOTHING is happening. This is a model of autarky, and nobody suffers from the recession. There is no spending to stop, because there is no spending. Obviously in the background you are thinking there are other goods and wages and stuff, but because they are not explicitly modelled, it is not obvious that you have captured everything important.
(Besides which – isn’t this EXACTLY the problem with representative agent models – if everybody is alike – why would they trade at all.)
My initial reaction was similar to RSJ and Greg, in that it is the broader critique of the over reliance on the Representative Agent model that pops out to me. The use of the Rep Agent model is saying, in effect, assume perfectly normal distributions in everything, nothing is multi-modal, no negative skew, no positive skew, and so on. This just isn’t a terribly convincing model for anything, especially to anyone familiar with financial markets. At least this assumption is not one that deserves special deference or to be checked against more relaxed and varied assumptions.
I know, of course, that you are making an inside argument so playing on their terms makes sense. But they can be wrong for multiple reasons!
Within the terms of the model you’ve layed out, I am also struck by the lack of endogenous money and a time element. Wouldn’t people’s reaction to a change in the price of money be markedly different if this was a one time event rather than an on-going trend? If my current stock of money is worth 5% more in real terms, but I expect previous price trends to reassert themselves, how is my demand for money changed? Is money adjusted against all goods including labor wages?
OGT: “The use of the Rep Agent model is saying, in effect, assume perfectly normal distributions in everything, nothing is multi-modal, no negative skew, no positive skew, and so on”
None of that is accurate. Assuming a rep agent does not assume any of that.
It doesn’t imply a “null economy” either.
Not sure why that’s not clear.
Thanks Nick.
By assumption, what makes money significant for boom / bust theory has been eliminated …
OGT,lamppost economics is all about confusing mathematical tractability for a certified understanding of an economic world which does not to conform to the formal requirements of tractable mathematics. In physics, when this happens, they acknowledge that some aspects of reality are mathematically untractable. In economics, when this happens, they insist that the phenomena itself does not exist. E.g. the elimination of heterogeneous production goods from academic economics.
OGT wrote,
“My initial reaction was similar to RSJ and Greg, in that it is the broader critique of the over reliance on the Representative Agent model that pops out to me. The use of the Rep Agent model is saying, in effect, assume perfectly normal distributions in everything, nothing is multi-modal, no negative skew, no positive skew, and so on. This just isn’t a terribly convincing model for anything, especially to anyone familiar with financial markets. At least this assumption is not one that deserves special deference or to be checked against more relaxed and varied assumptions.”
Nick, yes, I noticed the deafening silence coming from other macroeconomists before you posted on the matter. It’s doubtful, though, whether the remedy is to be too provocative: that risks being dismissed as a crank. Is that not exactly how you have responded to some of the provocative posts here?
Anyway, given the lack of professional excitement, you might as well clarify your post so that it is intelligible to the rest of us. Remember, all of your NK posts are attacks; this does not motivate anybody to run out and read up on NK models.
When you write “assume a representative agent model in which everyone has exactly the same supply and demand for X. No X get traded in equilibrium”, do you mean that only X is not traded? That all other goods in the economy are actively being exchanged for money? How does this work, for bonds, which are just time-shifted money? (A bond being money today in exchange for money tomorrow.) Bonds therefore have the special property that too high a price rise extinguishes trading because it would imply negative rates. The argument would be a lot easier to follow if you enriched the basket of goods in the economy to 1. include some other spot commodity (oranges) 2. some other time-shifted commodity (apples today in exchange for apples tomorrow) and 3. specify what happens over two periods.
Adam P- Perhaps you are right. It doesn’t change the fact that there are significant theoretical and, more importantly, empirical problems with the aggregation assumptions underlying represenative agent based macro models.
“Maybe there is in human nature a deep-seated perverse pleasure in adopting and defending a wholly counterintuitive doctrine that leaves the uninitiated peasant wondering what planet he or she is on.”— Robert Solow
Robert Solow (2006) made this statement when he was reflecting on how the macro model had gone so far astray. He further states that “(flaws in the previous model) would not explain why the macro community bought so incontinently into an alternative model that seems to lack all credibility.”
Click to access complex%20macro6.pdf
Nick- BTW, I more interested in your response to the second half of my comment.
Adam, I did not say that representative agent models only applied to null economies, but that RA models in which you assume that — in every period — zero bonds are sold — amount to a null economy. If, in a given period, no bonds are sold, then this is a stationary economy with no savings or investment occurring in that period.
If the above isn’t obvious, then what goes on the liability side of firms’ books when they increase their (real) capital stock, and what goes on the asset side of household balance sheets when they save?
OGT, I am right. I know I’m right because I know how to construct representative agent models.
So how do statements like the one you made advance the debate? Especially since your most recent reply implies you didn’t actually know if the statement was true or not.
It seems that a great deal of the debate in the blogoshpere takes the form of someone, like the MMTers or RSJ, making a statement of the form “mainstream macro is wrong because it says _________” where the blank is filled in by something mainstream macro does not in fact say. Very often the blank has a statement that mainstream macro says exactly the opposite of.
Does this sort of thing advance or hold back the debate?
Now, if we’re trading quotes here’s a favourite of mine from Angus Deaton:
“The main puzzle is not why these representative agent models do not account for the evidence, but why anyone ever thought that they might…” (Understanding Consumption, pg. 70)
So, even if we accept that the models don’t account well for the data does that make them useless?
I think no, there value is primarily as counter-examples. Another feature of the debates on blogs is people making very general A implies B type statements. Quite often A is true in the simplified world of an economy that can be described by a representative agent but B is not in that simple world, we then conclude that as a general matter A implies B is false.
The implication may well be true in the real world but now we’ve advanced the discussion, now the claimant needs to explain the why the implication is true in our world but not in the more simple ones.
Finally, it is important to point out that the assumption of a representative agent is NOT the same as the assumption of a single agent. NK models are an example, there are a continum of different agents but their preferences and firms producition functions are specified to have an exact aggregation so that the economy can be described by a representative agent, that does not mean the economy has only one agent.
“now the claimant needs to explain the why the implication is true in our world but not in the more simple ones.”
No, that would be a Type II error.
The original model builder need to explain why his implausible assumption does not materially change the outcome of the model, as the burden of proof rests on him, not on the one pointing out the implausibility of the assumption.
RSJ, did you read what I wrote? you seem to be responding to a different statement.
Try to follow the logic. For expositional purposes I’llassign us roles in the story.
Suppose that you, RSJ, make a claim that A implies B. This is a general statement that should apply to economies that are complex like our real one and economies that are simple with all sorts of implausible assumptions. You didn’t say A and (other stuff) implies B, where perhaps (other stuff) rules out the simple economies. You just said “A implies B”.
I then respond by building a simple model economy, so simple that it couldn’t possible represent the real world but is nonetheless an internally consistent model economy. In my model economy A is true yet B is false. I’ve shown your claim to be false.
As I said above, representative agent models can often make good counter examples exactly because of their simplicity. I’m not the “original model builder” here, I’m just giving a counter example. The plausablity of the assumptions are irrelevant.
If you think that the counter example I provided doesn’t invalidate your claim because you really meant A and (other stuff) implies B then you have to explain what (other stuff) is. Then we’ve advanced the discussion.
Ugh. Adam you are right. I was stuck between Nick’s Model and your argument about RA models. Yes, Nick is the model builder here.
FYI, I like RA models, and I’ve also built some (easy, not NK) RA models. It’s fun, and optimization is fun. I’m not criticizing the approach at all, and I don’t think MMT is doing this either.
A flow of funds model or any structural model contains sectors which are treated on a consolidated balance sheet basis, and this is equivalent to having a representative agent, one for each sector. You have to use some kind of representative agent. What the heterodox people complain about is how the aggregation is done, and how financial assets are treated in the model.
At least, I hope you see the point I was making about bonds. Saying that prices reach a level of indifference is not the same as saying that no bonds are sold, just as saying that wages reach the level of indifference is not the same as saying that no labor is supplied. The equilibrium needs to have some flow of labor supply, bond, sales, and investment, and if the CB shocks the system by raising the interest rate, then it can disturb the equilibrium so that less than the optimal amount of bonds will be sold and less than the optimal amount of labor will be supplied. People will not continue to transact as if nothing had happened.
Hmmm. This post is warming up nicely. A busy day for me yesterday. let’s see if I can handle these comments. They are helping me be more clear in my own mind.
anon: yes, I should have made this more explicit. There are two “textbook” statements I want to dispute:
1. Recessions are caused by the real interest rate being too high.
2. An excess demand for money means an excess supply of bonds.
I want to argue instead that recessions (an excess supply of newly-produced goods, and a decline in output) are caused by an excess demand for money.
The textbook models assume the bond market always clears, and that the central bank tightens monetary policy by raising the rate of interest. So it’s not possible to distinguish in that model between what’s happening to the supply and demand for money and what’s happening to the rate of interest. My “trick” was to allow the government to control the rate of interest directly by law, independently of what is happening to the supply of money. That trick gives me a thought-experiment where I can set the rate of interest too high without changing the supply or demand for money, and vice versa.
I show that setting the rate of interest too high (by law) does not cause a recession. But that creating an excess demand for money (by reducing the real supply of money by raising all goods prices) does create a recession.
Adam: I was hoping you would show up!
You are correct in saying my (implicit) model is not an NK model. (Or, at least, it’s very different in at least one important way).
My (implicit) model has one thing in common with (simple) NK models: it’s a representative agent model. I needed to use an representative agent model, (for exactly the same reason NK models typically use a representative agent) because it helps me make my point much more simply. (I like representative agent models for some purposes, though they obviously won’t work well for others, and I have no quarrel with NK models for using a representative agent for most purposes, and I think we agree here). I knew I would get flak for using a representative agent model, so I said “Hey, NK models use them too, so you can’t knock me for that if I’m criticising NK models”.
As you note, there is one big difference between my (implicit) model and NK models: how the interest rate is set. In NK models the nominal rate of interest is set by the central bank’s monetary policy (and the real rate gets determined by that plus expectations of future monetary policy and Calvo pricing). In my model the real rate of interest is set by law.
In an NK model (like nearly all “textbook” models), you cannot distinguish between the rate of interest being set too high and the supply of money being set too low. The bond market always clears. The central bank sets the interest rate, so monetary policy and interest rate policy are the same thing. So you can’t ask the question “are recessions caused by too high an interest rate or too low a supply of money?” So I needed a different thought-experiment. So I changed the NK assumption, and allowed the government to set the rate of interest by law.
Once we do this, so we can vary the interest rate and the supply/demand for money independently, we see (in this representative agent model) that varying the rate of interest has no effect on the rest of the economy.
reason: “Nick,I don’t see how your model helps here – it is just confusing things – because NOTHING is happening. This is a model of autarky, and nobody suffers from the recession. There is no spending to stop, because there is no spending. Obviously in the background you are thinking there are other goods and wages and stuff, but because they are not explicitly modelled, it is not obvious that you have captured everything important.
(Besides which – isn’t this EXACTLY the problem with representative agent models – if everybody is alike – why would they trade at all.)”
OK. I should have been more explicit here. There is no trade in apples, and no trade in bonds. But yes, there must be trade in some other goods, or there wouldn’t be any need for using money, and there couldn’t be a recession.
There can actually be trade in a representative agent model. You just have to make sure the differences are all symmetric. Since that’s hard to explain, let me sketch an example.
200 identical agents. 100 are given a peach tree, and 100 are given a plum tree. Trees yield identical quantities of fruit. Peach growers hate the thought of eating peaches, and plum-growers hate the thought of eating plums. (You’ve spent all day working on them, and can’t stand the sight of them). So they trade peaches for plums, at a price of 1 for 1 in equilibrium. If you know what one agent is doing, you know what all agents are doing (just change “peaches” to “plums” or vice versa. That’s a barter model.
For a monetary exchange economy: 300 identical agents, peaches, plums, and pears. Peach growers only eat plums, plum growers only eat pears, and pear growers only eat peaches. They meet at random in the forest, and when 2 agents meet they never have a double-coincidence of wants, so need money. (Fruit rots quickly, must be eaten on the spot, so they can’t use fruit as money).
Give every agent one apple tree, and they never trade apples in equilibrium. And they never trade bonds either (bonds promise to pay one bit of fruit next year). They are all identical in apples and bonds. But they do trade plums, peaches, and pears for money. When there’s a shortage of money, trade in peaches, plums, and pears breaks down, and they all eat less.
OGT: I agree with Adam in defence of representative agent models. It doesn’t mean an economy with no trade. See my example for reason above. Of course, there are some questions where a representative agent model will not work (like if some people are in debt to other people).
“Wouldn’t people’s reaction to a change in the price of money be markedly different if this was a one time event rather than an on-going trend?”
Yes, it would be. Adam makes a similar point above. A temporary and a permanent reduction in the price of money would both increase the demand for money, but by different amounts. I should have been explicit. I was thinking of a permanent change. Don’t think it affects my argument though.
Phil: yep. I wish I had been a bit more explicit about what was going on in the rest of the economy. There’s no trade in apples or bonds, but there must be trade in some other goods if there’s going to be a recession. My example for reason above, with peaches plums and pears, is the sort of thing I have in mind. That’s similar to an NK model in some respects, in that it’s a representative agent model with specialised production and trade. But different and simpler in other respects. (With 100 agents producing each fruit, it will be a competitive economy, not monopolistic competition, plus every agent has an apple tree.)
Adam (or anyone): BTW, I have never been able to figure out how Woodford can have the central bank set the interest rate in a barter economy. I have the government set the rate of interest by law, like a minimum wage law, or rent controls. But I can’t see how Woodford does it.
I can see a central bank running a clearing house for goods, and setting the rate of interest it pays on positive or negative balances. But that is the rate of interest paid for holding positive quantities of money (or charged on negative quantities like an overdraft rate). That’s different from the rate of interest on bonds. Unless bonds are used as a medium of exchange. And in that case an increase in the rate of interest paid on holding the medium of exchange will cause an increase in the demand for money, and cause a recession by creating an excess demand for money.
They buy and sell bonds.
To get comfortable with this you need to notice several things:
1) Goods trade is frictionless, so if the central bank needs to sell bonds in return for units of the consumption basket, in the model it is not as combursome as you might think.
2) Number 1 implies that CB does need to be fiscally backed by a government that can tax units of the consumption basket and use the them to capitilize the CB. Again, feasible because goods trade is fricitonless. Shows why this led Woodford naturally to fiscl theories of the price level!
Now, (1) and (2) sound horribly unrealistic but the model is actually much better than it appears looking at that. The reason is that:
(3) In equilibrium the CB never needs to trade the consumption basket. This is implied by the CB following the Taylor rule! Thus, if we lived in such an economy we’d never see the CB trading the consumption basket.
To see why (3) is true lets say that potential output is 100 and the conumption good is non-storable. Now suppose the CB sets the interest rate such that there is an excess demand for bonds, to meet this demand the CB must sell bonds for consumption goods. However, since this output is being pledged to the CB it isn’t being traded in the goods market. AD is to low, prices want to fall and the CB sees this and lowers the rate.
If there is excess supply of bonds then in principle the CB needs to buy them, using units of consumption obtained from the Treasury as taxes. However, as the treasury competes with private traders for the same 100 units of consumption the CB sees prices want to rise and responds by lowering the interest rate.
The CB reaction function that the model assumes guarantees that the CB holds none of the consumption basket in equilibrium, nor is it short the basket at close of trading.
Now, as for trades by individual agents. We assume that at period zero the CB was capitalized by the treasury and created a stock of outstanding bonds (say all 1 period maturities). Then, individuals can use maturing bonds to buy goods from the CB which the CB in turn purchases with the issue of new bonds to someone else. From (3) we know the interest rate is set just right so that the CB can do this in aggregate and end up with no consumption goods at the close of the day’s trading.
Alternatively, one can use the maturing bond to buy goods from someone who wants to turn the bond in to the CB for a new bond. Or the maturiing bond is traded several times as a medium of exchange, accepted at each point by the possibility of redemption at the CB, until it finds itself in the hands of someone who anyway just wants a new bond. This person then just redeems it for the new bond.
All three trades may be taking place at the same time, thus maturiing bonds are a medium of exchange but they aren’t the only medium, barter works, and they aren’t money because they aren’t long lived. They’re not a store of value, they may well be the medium of account but maybe not.
Real balances, both demanded and supplied are zero. Obviously since holding the maturing bond overnight makes it worthless. So the economy is cashless.
Now, in the real world goods trade is not fricitonless and so we do use a medium of exchange that people want to hold. However, since aggregate quantities in the cashless model are exactly the same as they are as the variant with cash (Woodford shows this!) then we know that the existence of money is not driving things.
I stress, this is not to say excess money demand is never the problem. The NK model is a counter example to the claim that an excess demand for the medium of exchange is the only way to cause a problem! It is a counter example to Nick Rowe.
Sorry, (3) should read that the CB never holds the consumption basket. It may trade it, though actually the subsequent arguments show this is not actually necessary.
Adam: that makes sense.
1. But it also means that if the CB ever did hold a positive position in goods, having bought them with bonds, what it is really doing is fiscal policy.
2. My guess is that it is never optimal for the CB to do fiscal policy in this model (the economy gets to the second-best, given monopolistic competition, by itself). And the Taylor Rule duplicates that same equilibrium. And doing fiscal policy, if it’s not needed, would cause a problem in almost any model. OK, in a monopolistic competition model with perfectly flexible prices, if the government does a temporary bond-financed purchase of goods, and redistributes those goods as a lump-sum transfer to the population. And then does a lump sum tax of goods the following period, to repay the bonds. This will cause welfare to increase in the first period and decline in the second period (due to monopolistic competition having output too low. But lifetime welfare would be lower. Fiscal policy has real effects, and bad ones, in this model.
Well, actually what would happen if the CB ended up holding a position in goods is that it would return its “trading profit” to the treasury which would return them to the private sector as a transfer and/or reduction in taxes.
Just as our Fed returns it’s reveue to the Treasury.
But reasoning it through does show how:
1) an excess demand for bonds can cause a recession as the goods are taken out of the market and pledged to the CB causing a shortfall in AD in the economy.
2) How fiscal policy is the other side of the same coin to monetary policy. If the CB does as I said and returns the “profit” to the Treasury which then gives it back to the private sector then full demand is restored by the “fiscal stimulus” of a tax cut/rebate.
Nonetheless, I stress again that in this barter economy you can have a recession without money. An excess demand for bonds, meaning the real rate too high, will cause a recession which policy has to correct.
Agreed though that any outcome which had the CB doing this “fiscal” policy is sub-optimal from a welfare standpoint.
Adam P: “So how do statements like the one you made advance the debate? Especially since your most recent reply implies you didn’t actually know if the statement was true or not.”
I’ll give you my take. I am fairly well aware of the debate between heterogenuous agent and representative agent models. My understanding has been that there are some inherent differences in the assumptions about the ability to aggregate data in the two approaches and that the recent Krugman/Eggertsson paper seemed to bear that out. Relaxing that assumption gave them results quite different from ones they would have gotten in a single rep agent model.
In fact your last paragraph is closer to what my conception of the assumptions of a rep agent model would be, namely this part, “continum of different agents but their preferences and firms production functions are specified to have an exact aggregation that the economy can be described by a representative agent.”
There are, to me, underlying assumptions about the coordination and distribution of said preferences and production functions that seem at least questionable. Again, as I read it, the Krugman/Eggertsson essentially changed the distribution of patience preferences to a basically bi-modal distribution of patience and impatience.
As I think Nick notes, whether a representative agent model is effective in demonstrating the effects of debt in the real world (reading my mind since that was the primary distribution I had in mind) is an open question.
Lastly, I didn’t intend to question the legitimacy of rep agent models, only what, to an outsider, seems like their dispropotionate use in current economic work. As you noted Woodford ran his model twice, once with money and once without, that gives him much more interesting and authoritative results! I would think that the rerunning rep agent models with the introduction of some heterogenuous agents with varying production functions or preferences could lead to interesting results that either strengthen or question the original rep agent model results. And, very possibly, advance the debate.
Nick- Thanks for the reply. Again for my edification, does your implicit model have varying lags for price adjustments?
OGT, that’s a more reasonable response than one usually gets on blogs. My apologies for being a bit flippant.
Now, here’s the interesting thing. It is a theorem that under complete contingent claims markets the economy can be represented by a representative agent.
That’s how I know assuming the existence of one doesn’t rule out what you said, the heterogenous agents and stuff. Put all that in there, add enough securities for them to trade relative to the “amount” of uncertainty they face (dynamicaly complete is enough) and you can still describe the outcome as having come from a representative agent economy.
This tells us that in, say, Krugman and Eggertson the heterogeneous agents part is not the whole story. The market incompletenes is the key to just about everything. The marke incompleteness in that paper is introduced through the borrowing constraint that is tighter than the wealth constraint.
In fact, the market incompleteness is really what drives the a lot of their results. I’ve seen papers with the assumed form of market incompleteness but without the bi-modal distribution of the preference parameter that give broadly similar results to what Krugman and Eggertson get. Those other papers have various different shocks to substitute for the heterogenous agents.
In general though I think we’re in agreement. There is a reason I remember the quote from Deaton down to the page number, I first read it years ago when I was in grad school and used to think of it as the most intelligent thing on economics I’d ever read.
Nonetheless, models are for understanding and in that sense unrealistic ones can be valuable.
OGT: “Again for my edification, does your implicit model have varying lags for price adjustments?”
Sort of, but not really. My model is far too crude and simplified. Any price is either perfectly flexible, or just set by law at whatever level the government feels like setting. That’s a crude way of capturing the idea that some prices are more flexible than others.
Still thinking about Adam’s comment.
Adam: “1) an excess demand for bonds can cause a recession as the goods are taken out of the market and pledged to the CB causing a shortfall in AD in the economy.”
In my model:
1. Starting in equilibrium, if the government raises the real interest rate by law, there’s an excess demand for bonds but nothing changes. There’s no recession.
2. Starting in equilibrium, if the government holds the real interest rate fixed by law, and then all agents suddenly become more patient, there’s an excess demand for bonds, but nobody can buy any. So the demand for money increases as agents try to save by holding more money. And if the government fixes the price of money (the prices of all goods) by law, there will be a recession. But if there’s no money (if barter is allowed) there is no recession. Agents just swap plums and peaches as before, exhausting all mutually advantageous trades in a competitive barter market.
Now, if the Woodford model is giving different results, what is the key difference in underlying assumptions that is generating that result?
The difference is that you fix the supply of bonds and change the price with a law.
Woodford’s government can’t do that, in the standard model the only way for the CB to peg the price of bonds is to freely trade them. Thus, in order to maintain the peg the CB stands ready to issue as many bonds as are demanded so an excess demand for bonds translates into a larger supply of bonds instead of a higher price. The consumption goods that are used to buy the newly issued bonds come out of aggregate demand.
Adam: that makes sense, but is also very strange. Because it’s saying that a bond-financed increase in government purchases of goods will cause a recession? Normally, in an RBC model for example, a temporary increase in government spending will cause a boom, (and an increase in the real rate of interest) even given Ricardian Equivalence.