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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.”

http://www.econ.brown.edu/fac/Peter_Howitt/publication/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.

Nick: "it's saying that a bond-financed increase in government purchases of goods will cause a recession? "

No, not at all. Where do you get that idea?

First of all, the government can't raise more than the market will bear at the prevailing rate. Second the government spends the money so it goes right back in to aggregate demand.

As I said above, if the CB ends up holding goods then it returns it's profit to the Treasury and the Treasury returns it to the private secotor as a tax-rebate so no recession. If the real rate is too high and fiscal policy unchanged then we get a recession.

The recession in this case comes from excess demand for bonds (real rate too high) causing people to *attempt* to buy bonds with their output. If, in aggregate this is attempted they don't succeed. Instead their incomes fall.

It is exactly the same mechanism as an excess demand for money and it's resolved the same way.

In the excess demand for money, if no more money is supplied, then incomes fall and the demand for real balances falls with income. When income has fallen enough we're back to equilibrium but at a lower level of employment and output.

In the excess demand for bonds, if the real rate isn't changed, then incomes fall and the demand for bonds falls with income (basically the demand for savings). When income has fallen enough we're back to equilibrium but at a lower level of employment and output.

Nick & Adam: thanks very much for your patient explanations. Your courtesy is appreciated.

"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."

Adam, apart from the RA's preferences not being the "average" of the preferences of each agent, you may also want to take a look at this essay

In particular, this passage, in Section 2.4

"A state of the world in this model is a complete specification of the physical environment and of spot market equilibrium prices as well, for all dates from the present to the end of the history of the economic system....[I]ndividuals will not know what state of the world has actually occurred until the history of the economic system is completed, hence there is no way that securities paying off on the basis of states of the world can be cashed in prior to that time, and hence no way that consumption plans can be implemented in the spot markets. It appears that incorporating spot market prices into the specification of states of the world leads to a restriction of the model to a two-period framework, today's security markets and tomorrow's spot markets and consumption. "

I think it's impossible, even in theory, to have an economy in which agents are consuming and producing in real time and to say that these agents have access to complete markets, in which prices are incorporated into the the state of the world. In that case, you can't (always) reduce to a representative agent that is also consuming and producing in real time.


"apart from the RA's preferences not being the "average" of the preferences of each agent"

At which point did I say they were?

As for the rest of your comment I take it your again responding to something other than what was said.

Though actually, I suppose it's worth pointing out that the quotation you cite is all wrong. Not really relevant to the discussion either way but interesting to notice.

"It is a theorem that under complete contingent claims markets the economy can be represented by a representative agent."

To whom do we owe this theorem? Is there a published reference? Are "contingent claims" here the state prices of the next period? Is there some sort of no-arbitrage/one-price condition (e.g. does "equilibrium" imply no arbitrage?)

Just curious, and trying to guess how the complete market comes into it.

Darrel Duffie, Dyanamic Asset Pricing Theory section 1.E and exercise 1.15. (second edition)

Also see chapter 10 for implementation of dynamic completeness, particularly 10D, 10J and the notes and excercises for extensions and a guide to the original papers. (again, referring to the second edition)

"It is a theorem that under complete contingent claims markets the economy can be represented by a representative agent."

Very interesting and elegant.

Can you summarize the intuition for this?

thx

In a complete market you can (and will if you are risk averse) eliminate all sources of uncertainty. Therefore your wealth grows at the risk free rate. You no longer have to make choices or optimize utility since all events are hedged. So your preferences don't matter. No?

But completeness really is ridiculous. Even an equity option isn't completed in the market of its stock. In a macroeconomy it's just plain absurd. To first order *nothing* rather than everything can be hedged. And there are profound reasons why that's the case. First, as everyone knows, there are idiosyncratic risks that can't be eliminated due to moral hazard. But as I see it, for a macroeconomy, there is a deeper issue: *Who* is going to insure the systemic risk factors? If the insurer is inside the economy, then the risk is still there, just transferred from one agent to another. So completeness can't create a single agent. If the insurer is outside the economy then it's, well, not a macroeconomy. Admittedly, my background is in micro complete markets. So maybe there is something about the definition of the standard macroeconomy or about the meaning of completeness in macro that I'm missing. But it strikes me as an important issue for the *real* macro economy, or any model pretending to capture it's salient properties, even in principle.

That said, like Adam says, you can learn useful things from almost any self-consistent model. But completeness is a *really* strong assumption.

I'm going to clarify my 8:30 PM comment above:

In a complete market you will sell all future labour and satisfy all future consumption for all future states of the world, *right now*. That portfolio of future labour/consumption depends on your innate skills and consumption preferences. But once you have established that hedging portfolio (and future trading strategy), you no longer have a risky portfolio. So, by no arbitrage, it will grow at the risk free rate (minus your planned consumption rate) until the day you die (with exactly zero dollars left if you so choose). After you are hedged, the only thing that matters is your labour/consumption plan. Your original preferences are irrelevant. I would then imagine that the aggregate equilibrium labour/consumption plan of all agents imply a set of preferences/skills of a representative agent (but again, macro not my forte).

you forgot to say that you've merely shown this for a model which excludes aspects of the real world which would produce a different result.

"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."

Just stepping back a bit, saying that in any given equilibrium you can approximate the resulting vector of prices and quantities as if there was a single utilioty function that was maximized does not mean that you can model the time evolution of the economy as a single agent that is optimizing an objective function of the form sum{B^i w(.)}, where B and w are independent of the period.

The sequence of competitive representative agent's utility functions arising from a sequence of auctions will not, in general, be constant across time, even if there are complete markets.

If the households have differing utilities or time preferences and they save when young and dissave when old (driving their wealth from 0 to a maximum and then back to zero), then your RA's utility function and time preference will change in each period of the economy as the relative endowment of each type of agent changes. As the wealth of the more patient agents increases, the representative agent will appear to be more patient in each period, etc.

The aggregation issues remain, you've just transformed them into a different form, from heterogenous time-invariant preferences to a single set of time varying preferences. In terms of solving the intertemporal optimization problem, this approach isn't any simpler unless you go ahead and assume some homogeneity of preferences; there wouldn't be much point in writing out euler equations if you needed to solve the heterogenous competitive equilibrium problem for every period, in order to determine what your representative marginal utility function and time discount factor was for that period.

So it's a bit misleading to argue that "well, in the general case it still reduces to a representative agent", when what you mean is "we will go ahead and assume a large amount of homogeneity as it makes the math simpler".

Not that I have a problem with making that assumption, as long as we are clear that it is being made, and that there is a possibility that having an economy with agents in different states can make a material difference.

Adam: representative agent model, in 3 versions: autarky; barter; and monetary exchange. Each agent owns one apple tree. Each tree produces 100 apples per year. The only goods are apples, and bonds, (and money in the third version). A bond is a real bond that pays 1 apple next year.

Start in full equilibrium. Each agent consumes 100 apples. Then the CB increases the real interest rate, for 1 period only.

Version 1: "Autarky". No tabus. Each agent is indifferent between eating his own apples and eating anyone else's apples.

Version 2: "Barter". There is a tabu against eating your own apples. Pairs of agents can get together and swap apples.

Version 3: "Monetary". There is a tabu against eating your own apples, and also a tabu against eating the apples grown by someone who is eating the apples you have grown. So you need monetary exchange because it's impossible for 3 agents to meet in the forest.

When the CB sets r too high, each agent wants to consume (say) 60 apples, and buy bonds with the other 40. But can't, of course.

The Woodfordian model says that C will drop to 60.

I say that C will drop to 60 in version 3, but will stay at 100 in versions 1 and 2.

Version 1 is quite clear. How could we have an equilibrium where one agent has 40 uneaten apples left on his tree? He will eat them.

To my mind, version 2 is equally clear. How could we have an equilibrium where 2 agents have 40 uneaten apples each left on their trees? They will simply swap apples, and then eat them.

It's only in version 3 where there will be 40 apples left uneaten on the tree. You can't get 3 agents together at the same time to do a mutually improving exchange.

Greg: "you forgot to say that you've merely shown this for a model which excludes aspects of the real world which would produce a different result."

That goes without saying. In general, if the law sets a price above or below equilibrium, bad things will happen. But will those bad things look like a recession?

In a more general model, where bonds are traded in equilibrium, setting the real rate too high by law will cause bad things to happen. There won't be enough borrowing or lending. Borrowers will have to reduce their level of investment, and lenders will have to do their own investments. Backyard steel furnaces instead of big efficient ones. Malinvestment. A drop in aggregate supply. But no excess supply of goods.

anon: on the intuition. This may or may not help. If you have complete competitive markets, then the allocation of resources is Pareto Optimal. It duplicates the allocation that would be chosen by a central planner who was trying to maximise some weighted sum of the utilities of individual agents. Think of that central planner as the representative agent?

Complete competitive markets is a *sufficient* condition. It's not necessary. But if you move outside that world, you will need stronger conditions, such as all agents having the same preferences. Those stronger conditions will be needed in the sorts of models we are talking about here, with sticky prices and incomplete markets.

Nick: are you saying that having a Pareto optimal competitive equilibrium implies the existence of an equivalent representative agent?

Also, Im not sure that everyone having the same preferences is a worse assumption than complete markets. At least it's possible. Hedging of systemic risk factors by all agents in a macroeconomy is not. Unless they are buying insurance from the Martians - which is no longer macro.

K: It's not something I've thought about a lot. But it seems to me that it does.

But complete markets does not mean you have to buy insurance from the Martians. If there's a 10% probability of an aggregate shock, for example, complete markets does not mean that the insurance premium must be 10% of the payout. If agents are risk averse, and some risks are undiversifiable, the insurance in complete markets will not be actuarily fair. The hypothetical central planner can't fix aggregate risk either.

Nick -- the key thing is that your model excludes by assumption all of the mechanisms that allow money & credit & leverage to produce Hayekian malinvestment / discoordination effects.

I.e. when Hayek establishes the monetary basis of economic discoordination across time in a book like _Monetary Theory and the Trade Cycle_, he's showing this result for elements that necessarily exist in any actual world -- and the math models which are fashionable today necessarily exclude these non-optional real world elements by formal necessity.

For those of us attempting to understand the real world, the game is rigged by assumptions which necessarily block access to an understanding of the real world.

Greg: all models exclude a lot of the real world. That's what they are supposed to do. My model sketched above includes only the absolute bare minimum necessary for a monetary disequilibrium theory of the business cycle. And I am trying to see if it can also capture the bare minimum needed for a New Keynesian theory of the business cycle. It wasn't designed to represent the Austrian theory. Sure it leaves out everything the Austrians consider important.

Nick: I wasn't suggesting that it would be priced under the actuarial measure. Here's what I'm saying: I suspect the representative agent result depends on the ability of *all* agents in the economy to hedge their exposures (which they can under completeness). If some agents can't hedge then they are still exposed to some risks and then their individual risk tolerances matter, and it may not be possible to aggregate them as one agent. And my point is: *they can't all hedge their systemic risk exposures*. If one agent buys protection (e.g.) against a general market collapse, then another agent must be selling it to him. The protection seller then has more systemic risk exposure. You simply can't take the systemic risk exposures out of the system via *internal* trades between the agents. So the idea of completeness is inconsistent with the basic idea of a macroeconomy. The only way that an economy can be complete is if an insurer outside the economy is taking on the risks.

"Borrowers will have to reduce their level of investment, and lenders will have to do their own investments. "

The back-yard steel furnace is just a small business that will be funded by equity. Fischer's separation theorem tells you that you should treat it as a distinct entity that is maximizing its own present value rather than as a "good" that is owned by the household, as the household is not going to gain any utility from the steel furnace other than the stream of income it delivers, or the ability to sell this income stream to someone else.

So as far as modeling the household is concerned, it does not "have" a steel furnace in its back-yard, it owns stock in a steel making firm and supplies labor to this firm. And as far as that firm is concerned, it is agnostic as to how it structures it's liabilities, so you might as well assume that all the liabilities are "bonds" that are always rolled over.

Moreover, households will not build individual steel furnaces, they will pool their resources and purchase shares of one big steel furnace, if one big steel furnace is more efficient than many small ones, for a given amount of investment.

Later on, you can make things more complicated by adding separate markets for common equity and bonds, or adding an external finance premiums, or different tax treatments of interest and dividends, or introducing principle-agent problems in which a household that owns and operates the steel-making furnace will behave differently than a publicly held firm.

But in a simple model, why wouldn't you just assume that all investment is funded by firms selling bonds, and household savings is realized as purchases of bonds (or money).

Is this view really so bizarre? I *thought* this was the orthodox view. If this isn't the orthodox view, then what is?

K: all agents can buy apples. But if some agents buy apples, some other agents must be selling apples. That doesn't mean markets aren't complete. It might be better to describe complete markets as *any* agent, rather than *all* agents, can buy insurance.

RSJ: a minimum wage law will reduce the amount of labour traded. But it doesn't prevent you "buying" labour from yourself at below minimum wage. A minimum real interest rate law will reduce the amount of bonds traded, but it won't stop you "borrowing" from yourself, at below the legal rate of interest. If prices are at equilibrium, it makes no difference. If prices are away from equilbrium, it will make a difference.

Nick -- Ahh, OK.

You are pointing out a loophole. When I think the government sets a floor under the price of labor to be X, then I assume it is X, and this would include, say, those working for themselves. Say the tax rate on profits is much lower than on wages, and the small businessman reports very low wage income "to himself" and much higher capital income to himself. In my model, he would get in trouble for violating the minimum wage, whereas in your model he would not. Moreover in my model, he would just pay himself the MPL (or whatever the model predicts the wage rate should be).

Similarly, in my model, when the government says, "all 'bonds' need be sold so that their YTM is greater than 10%", then if this only applies to bonds, households can get together and jointly invest in new firms, creating equity liabilities that pay less than 10%. So either the bond market is destroyed and replaced with stocks, or the law applies equally to both, in which case a similar argument would prevent anyone from investing if they demand a return less than 10%.

I see what you are saying, but it seems to me that your model becomes much more complicated, as you now need to talk about the boundaries of enforcement, and the actors in your economy will behave differently if they are able to work for themselves or if they aren't. And a simple model shouldn't care about who you are working for, or whether your business is funded by equity or bonds, or even who funds the business.

But a priori, there is nothing wrong with doing a thought experiment along the lines of "say only 50% of the labor force can be self-employed, and the government raises the minimum wage on non self-employed households to be X", etc. But I'm not sure what the significance of such a thought experiment would be for general questions about labor supply and wages.

OK. But in that case, is the existence of a representative agent guaranteed? If some agents can't eliminate their market exposure then their risk tolerance will matter. And then, how can aggregation be guaranteed? It is the ability to hedge all risk that guarantees the existence of a unique martingale measure. I suspect it is a very similar argument that guarantees the existence of a representative agent (i.e. a risk neutral agent who optimizes returns under that unique martingale measure).

Also, if some risks can't be hedged out in aggregate, then, from the perspective of the representative agent, how can you say the market is complete? The RA is left with an unhedged whole market portfolio with all it's systemic risk factors.

Nick,

Nick, my interest is in what models can and can't do, and what any explanatory strategy _must_ do to explain the actual world (not a fake "economy" existing only in an economists head).

It interest me as a purely intellectual matter if you can actually get a monetary equilibrium without the structure Hayek argues is in fact required.

But I'm not sure it should interest anyone if we are attempting to explain that actual world.

The case, I hardly need to say, has not been made.

In fact, there's far stronger reason to think it cannot be made than there is to think that it can.

Saying that all models leave things out begs the question about what _must_ be in an economic explanation that actually causlly explains anything.

Ecomomists are notorious among all of those who have thought about for there signal failure to successfullynadressmthis problem.

Building "models" is fun, but answering that question is hard. Maybe that is why economists skipt it and wave their hands at unserious second hand accounts of "science" instead.

Again, the point isn't to square these models with some school or other in economics, the point is to square these account with non-optional features of the actual world -- and with the demands any successful causal explanation must meet. Hayek is important because he's again and again forced the profession to address realities they'd rather pretend don't exist -- via the hand wave of excuding them from their "models". But these facts about the world don't disappeat because the don't fit in the imagined "economy" of a math weilding macroeconomist.


Nick writes,

"Greg: all models exclude a lot of the real world. That's what they are supposed to do. My model sketched above includes only the absolute bare minimum necessary for a monetary disequilibrium theory of the business cycle. And I am trying to see if it can also capture the bare minimum needed for a New Keynesian theory of the business cycle. It wasn't designed to represent the Austrian theory. Sure it leaves out everything the Austrians consider important."

Sorry, make that,

"It interest me as a purely intellectual matter if you can actually get a monetary _disequilibrium_ / economic discoordination without the structure Hayek argues is in fact required.

Nick, I'm misled by the impression I often get that you are concluding consequences for the actuaul world based on these models which leave out non-optional features of the actual world which would produce results contrary to the logic of your model (e.g. that monetary disequilibrium would reduce the demand for each and all outputs, etc.)

Economists pretend they "excuded a lot of the real world" because they are doing science and creating scientic models on analogy with natural scientists -- but the motivation proves nonanalogous. Darwinian bioligist include whatever is needed to provide a sound and legitimate, non-magical causal mechanism Economists "exclude" from their "models" whatever is requred to achieve clever, tractable mathematical constructs, and to produce a mechanism for producing policy recommendations. And if this means excluding elements required to provide a sound, legitimate, non-magine, of-this-world causal mechansim, well, no sacrifice is to great to achieve tractability, cleverness and policy relevance, for those in the market for credited "scientific" justification for their policy decisions.

Nick writes,

"Greg: all models exclude a lot of the real world. That's what they are supposed to do."

LOL, everyone is ganging up on Nick! But this is meant well, or in the spirit of friendly debate.

I want to also continue to pile on about the representative agent.

The representative agent is not the same as an "average" person. The average person can do things that the representative agent cannot: I.e. in an economy with many different people, you can say that some are self-employed, but the representative agent cannot be self-employed. Even though it may seem as if he is working for himself, he is still a price taker, and must still sell his labor to the market, even though he is also the only buyer in the market. The average person can earn more than he spends, but the representative agent cannot.

Similarly, there are some things that the representative agent can do, but the average person cannot.

For example, consider an economy in which every household owns a house worth $100, and every household has a loan for $100, so that they have zero equity -- zero net-worth. In that case, the representative agent also has zero equity.

But now suppose everyone buys the house of their next door neighbor, taking out a loan for $200. They borrow $200 to buy their neighbor's house, but also receive $200 from their neighbor, leaving them with $100 of debt, but now they have $100 of equity, as they are living in a $200 house but only owe $100 on it.

If modeled as a representative agent, it was as if this agent gave themselves $100 of equity just by increasing their debt. Of course, the average person cannot create equity for themselves by borrowing, but the representative agent can. Similarly, the average person will not decrease their net-worth by repaying debt, but the representative agent will. And this goes to the heart of why the economy will not be the same if fewer bonds are sold.

So the behavior of the representative agent is qualitatively different. You cannot impose the same constraints on him that you impose on the average person The accounting is different, and the behavior is different. At least, that is why I am coming to a different conclusion about the effects of an increase in interest rates on the economy, even in a simple banana-selling economy.

RSJ: All agents have an endowment. Differences between agents cause agents to trade. If the government taxes trade, or sets prices at disequilibrium levels, there is less trade, and agents will consume more of their own endowment, which makes them worse off. That's no clever "loophole"; that's just econ1000.

K: we can't eliminate aggregate risk. Risk aversion does matter. Asset prices (generally) won't follow martingales. I don't see what that has to do with complete markets or the existence or non-existence of a representative agent. (We can have a model with identical risk-averse agents, for example, in an economy with aggregate shocks). If there is aggregate risk, then the price of apples-delivered-in-the-bad-state will be higher than the price of apples-delivered-in-the-good-state. Those are two different goods, and one is more valuable than the other. Apples and bananas are two different goods, and apples may have a higher price than bananas. That doesn't mean markets are incomplete or that there is no representative agent.

Greg: "It interest me as a purely intellectual matter if you can actually get a monetary _disequilibrium_ / economic discoordination without the structure Hayek argues is in fact required."

Sure you can. All you need is: monetary exchange; sticky prices. That's enough to get a monetary disequilibrium business cycle. If you want to explain what happens to (say) investment over the business cycle you (obviously) need to add investment to the model. If you want to explain malinvestment over the business cycle, you need to add different types of investment to the model. If you want to explain tax revenues over the cycle you need to add taxes to the model. If you want to explain what happens to jewelry prices over the cycle you need to add jewelry to the model. If you want to explain what happens to clothes fashions over the cycle you need to add clothes fashions to the model.

All those things are real features of the actual world. All of us exclude 99.9% of the real world. There is not a single mention of skirt lengths in Prices and Production, IIRC.

Darwinian biologists build simple stylised models that exclude massive amounts of the real world too.

The output and consumption of inferior goods may rise in a recession. Skirt lengths may rise too. So what? Why is it essential to build this into our model?

RSJ @1.21: Ah well. Everybody (including me) was arguing against Adam yesterday (but he held his end up well, as usual).

I prefer to distinguish between the individual agent experiment and the market experiment. For example, the individual agent can always get more money by buying less goods, but if the total stock of money is fixed they can't all get more money, whatever they do. That very distinction was at the heart of my model of why an excess demand for money causes a recession.

But there is no way an individual agent can buy more bonds if every agent is also trying to buy more bonds. Nobody wants to sell more bonds.

Money, being a medium of exchange, is different.

"All agents have an endowment. Differences between agents cause agents to trade"

Sure -- playground econ, where we are swapping marbles.

But the big stuff, the important stuff (for me, at least) is not *trading*, but *producing* new things that didn't exist at the beginning of the period.

And doing that requires that workers get hired by firms. They don't make stuff on their own.

The baseline model should not be barter, but the creation of new value as a result of production, not the exchange of exogenously determined pre-existing value.

Once you consolidate all consumption goods into a "c", then there isn't a lot of trade going on.

But there is production, investment, and consumption, none of which is naturally modeled as trading, but rather as the creation of a new endowment.

The endowment of an unemployed worker is zero, and the endowment of a firm without workers is also zero, but when you combine the two, then the endowment becomes positive as the result of production. To me, that's not trade. But maybe that's just me.


RSJ: "The endowment of an unemployed worker is zero,...."

No it's not. The endowment of any worker, employed or unemployed, is 24 hours of labour per day. If employed, he exchanges 8 hours of that labour with other agents, and consumes 16 hours himself. If unemployed, he consumes all 24 hours himself. Unemployment is bad because (if) the worker's utility from consuming the goods he could get in return for selling 8 hours of his endowment exceed the utility he could get from consuming that endowment himself.

"But the big stuff, the important stuff (for me, at least) is not *trading*, but *producing* new things that didn't exist at the beginning of the period."

No it's not. Or rather, that's a false dichotomy. If workers could produce equally well without trading, we wouldn't have to worry about unemployment, prices, or money. Everything I wanted to consume I would produce myself. It is *because* efficient production requires trade that a disruption in trade causes a loss in production. Trade is the important stuff.

Consider my simple model where an apple tree produces 100 apples per year, but only 60 get consumed, because you can't eat your own apples and an excess demand for money means that only 60 get traded and the other 40 rot on the tree. That's a metaphor for a worker who wants to work 10 hours a day but only works 6. It's a metaphor for a 40% unemployment rate.

The only thing any economy produces is backscratching services. In autarky, we scratch or own backs. In simple barter, I scratch your back and you scratch mine. In monetary exchange, A scratches B's back, B scratches C's back, and C scratches A's back.

A recession is a reduction in trade. It doesn't stop us scratching our own backs. It does stop us scratching each other's backs. It is more efficient to scratch each other's backs than to scratch our own. That's why recessions are bad.

Central banks can screw up as badly as they like, setting money supplies or interest rates at stupid levels. It can't stop me scratching my own back. It can't stop 2 people scratching each other's backs. But it can stop 3 people scratching each other's backs, if the lack of double coincidence of wants means that 3-person exchange requires money.

"that's just econ1000"

what's econ1000?

is it what we used to call econ100 back in the day?

what level is it?

It's either changed, or I've forgotten, or I never new

And that, in a nutshell, is why Michael Woodford's "Interest and Prices", the most important and influential work in Macroeconomics and Monetary Policy over the last 3? decades, that is taught to all graduate students, is wrong.

Central banks can do whatever they like, but they cannot prevent 2 unemployed workers from scratching each other's backs. They can only prevent the production of backscratching services for money.

anon: yep. At Carleton we changed all the numbers a few years back. 43.100 became ECON1000. First year Intro to Econ.

inflation

Nope. An increase in real output. We ran out of numbers for courses!

"But there is no way an individual agent can buy more bonds if every agent is also trying to buy more bonds. Nobody wants to sell more bonds."

That's because bonds are not goods 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.

i.e. bonds have nothing directly to do with recessions

the excess money demand dynamic is reasonable, but I'm not sure why it's even necessary to refer to bonds

anon: you lost me on your 8.13 comment. 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."

But I agree with your 8.27 comment. But it is highly controversial. Most economists argue that recessions are caused by "the" rate of interest being too high. And by "the" rate of interest, they are referring to the rate(s) of interest paid on bonds, not the rate(s) of interest paid on holding money.

"A recession is a reduction in trade."

Yes, very good. And this causes a reduction in output! Unless Nick Rowe's theory of the business cycle assumes zero gains from trade, no productivity enhancement due to specialization!

And if Nick's business cycle theory does say that I really think he should explain why we see so much trade.

So, even though scratching your own back goes on their is a reduction in consumption and output.

We conclude that Woodford is right, Nick is wrong and all is well in the econ world!

Need I remind Nick that the technical definition of recession refers to a decline in output without even looking at what happens to employment.

"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."

Agreed. That's my idea, but much clearer.

"Most economists argue that recessions are caused by "the" rate of interest being too high. And by "the" rate of interest, they are referring to the rate(s) of interest paid on bonds, not the rate(s) of interest paid on holding money."

BTW, at least as far is Woodford is concerned that's not true. I doubt it's true in general. Woodford considers interst bearing money, a form of perpetual bond, and gets all the same conclusions.

Nick, just posted a response to your question.

OK, Nick, there are just some differences in definitions standing between us, but I think these differences in definitions lead to differences in substantive conclusions, which they shouldn't.

In my model, "labor supply" is all labor supply, whether for one's self or not. Labor demand is all labor demand. And there is a single wage. The alternative of the worker to selling is labor is to consume leisure, not to work for himself.

To say that the government sets the wage means that it sets the wage for everyone. Obviously, this requires magical powers for government, but "government" is just a rhetorical device for an exogenous factor.

Similarly, the demand for bonds is anyone who wants to buy a bond, and the supply of bonds is anyone who wants to sell (or issue) a bond, and there is a single rate for everyone. In this economy, someone who invests $100 will get that rate, and that investment is realized as purchasing a bond.

It doesn't matter if he is selling the bond to himself -- what the fischer separation theorem tells you is that the (legal) ownership boundary is not the same as the decision-making boundary, so that for purposes of modeling the behavior of decision makers, just assume that no one is working for himself or self-financing.

Later on, if you want to make your model more complicated, you would include things like an external finance premium that would allow you to demand a lower rate of return for lending money to a firm that you own as opposed to lending money to a firm that someone else owns.

But if your result critically depends on this external finance premium, then I don't think you have a robust result, or are making general statements, and in that case you need to specify why and how the ownership structure of the firms is responsible for your effects.

The bond rate is the rate of return that any investment must earn, just as the wage rate is the payment that anyone supplying labor must obtain.

I *think* my definitions are standard.

Similarly, I view "production" as being separate from trading, irrespective of whether production occurs by one person or by a group of people.

Production increases the (real) endowment, and trade allocates the endowments. Production requires trade in both factor markets as well as output markets, so restrictions on trade can cause production to decline, but in any definition of competitive equilibrium, the total (real) endowments must be fixed as a result of making a trade, and only the utility of having those endowments is maximized, whereas total endowments increase as a result of production, and in an idealized complete market, the total endowment would increase by the (positive) risk-free rate, which is the growth rate of the capital stock, and which is also the growth rate of the number of bonds in the economy.


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