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 
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.