[Update 4 December: after long arguments with Adam P., which finally started to bear fruit in the comments of December 4th, I'm now clearer on what's essential in this model about the difference between "monetary exchange" and "barter exchange". It's this: In monetary exchange, there is no restriction on what the seller can do with the proceeds of a sale. He can spend the proceeds on anything, or save them. In barter exchange, there is a restriction on what the seller can do with the proceeds of a sale; he must spend all the proceeds on the buyer's goods. That is what is driving the results in this model. I think that is one important distinction between monetary and barter exchange. I have left the rest of the post as is.]
Keynesian macroeconomics in general, including New Keynesian macroeconomics in particular, makes absolutely no sense whatsoever in a barter economy. If people could trade goods and labour directly at zero transactions costs, without having to use monetary exchange, all Keynesian macroeconomics would be total rubbish. All Keynesian macroeconomics, either explicitly or implicitly, assumes monetary exchange. It's not just sticky prices that generate Keynesian results. It's sticky prices plus monetary exchange.
I used to think that the above paragraph was totally uncontroversial. I thought everybody understood this. I have learned they don't. So I'm going to do my best to explain why it's true.
I show that if we introduce barter into an otherwise nearly standard New Keynesian model, the solution immediately reverts to the perfectly competitive equilibrium, regardless of the degree of imperfect competition in the original model, regardless of any mistake made by the central bank in setting the nominal rate of interest, and regardless of sticky prices.
Just to be clear, this is in not a criticism of Keynesian macroeconomics. Barter is costly, and people do use monetary exchange. It's entirely reasonable that a model should assume people always use monetary exchange and cannot barter. And Monetarism would also be total rubbish if people could easily use barter instead of monetary exchange.
And just to be clear again, I am not saying that the particular way in which Keynesian models incorporate monetary exchange is unproblematic. I think it is problematic. But that's not the (main) point of this post. It's just an aside.
What I am going to build is a model of a model. Just as a model is an interpretation of the world, my model is an interpretation of a model. It's a model of the canonical New Keynesian model.
Here's my model.
There are n people, where n is a large enough number that each individual ignores the effect of his choices on the aggregate. Each person is a worker/firm, who produces one type of fruit. Each person produces a different fruit. The apple producer gets disutility from working L hours to produce A apples, with a production function A=F(L), and utility from consuming a Dixit-Stiglitz basket of fruit C with elasticity of substitution e (different fruits are imperfect substitutes). Each person maximises an infinite horizon subjectively discounted sum of present and expected future utilities U(C,L) etc.
In other words, exactly the same set-up as in the standard New Keynesian model, except I have suppressed the labour market for simplicity. Each firm is a worker. (If the labour market were perfectly competitive, and money wages were perfectly flexible, it would be exactly like my model.)
I will make one other small simplifying change to the standard New Keynesian model. I will assume that all firms must set prices before the central bank announces the nominal rate of interest. The firms that can change prices in a given period can only do so before observing the nominal rate of interest. This allows me to consider a symmetric equilibrium, where all firms have set the same price, and this makes everything much simpler when the central bank sets the "wrong" rate of interest. (Under the standard Calvo assumption, some firms would change their prices immediately when the central bank sets the wrong interest rate.)
I want to take this same underlying model, and impose two different trading structures. First I will impose "monetary exchange"; then I will add "barter". I want to show that adding barter makes a difference.
In what follows, remember that the Walrasian auctioneer is a great fiction. The auctioneer imposes a trading structure, and also solves the equations. I will introduce auctioneers. Like the Walrasian/Edgeworthian auctioneer, they will use "tatonnement with recontracting" to solve the equations. (Groping towards the solution, and all deals are re-negotiable until the auctioneer finds the solution). Unlike the Walrasian auctioneer, first there will be a tatonnement over prices, prices are then fixed, and only then will there be a tatonnement over quantities.
"Monetary exchange".
There is a central bank that also acts as auctioneer.
First, the central bank holds a tatonnement with recontracting on prices. Each firm announces a price, to maximise expected profits/utility. The auctioneer then announces all those prices, and asks if any firm wishes to change its price (recontract), now that it has seen all the prices set by the other firms. When no firm wishes to recontract, the auctioneer then closes the auction, and those prices are then fixed for the period.
Second, the central bank announces a nominal rate of interest.
Third, the auctioneer asks each firm how much fruit it would like to produce and sell.
Fourth, the auctioneer conducts a tatonnement on quantities. The auctioneer announces a tentative initial vector of quantities of fruit sold. That initial vector can be arbitrary (quantities, not prices, criee au hazard). Each firm is assigned monetary credits equal to the quantity of fruit sold times the price it set. The firm then decides how to spend those credits. It can spend them on fruit, or save them. Any unspent credits earn interest and can be spent next period, or saved again. (And any negative credit balance must pay interest, then be deducted from next period's balance.) The auctioneer checks to see if the amount of apples demanded equals the initial guess at the amount of apples sold, then checks bananas, and each fruit in turn. If the initial guess is wrong, all the initial demands are nullified, and the auctioneer guesses again, and repeats the auction. Only when the auctioneer guesses right are the contracts to buy fruit binding.
Fifth, all people then buy what they have contracted to buy, and work to produce and sell the quantity that others demand.
(In principle, the quantity of apples demanded might be larger than the quantity of apples supplied, and the auctioneer might have to ration buyers of apples. But this could only happen in equilibrium if the central bank set a rate of interest that was much too low. In general, because of imperfect competition, so that firms set prices above the competitive equilibrium, the quantity of apples sold will equal the quantity demanded, and will be less than quantity supplied. I will return to this point later.)
The solution to the above model will be identical to the solution to the standard New Keynesian model. Each firm will set price as a markup over marginal cost, where the markup depends on the elasticitity of its demand curve.
For simplicity, I want to consider only the solution where all firms set the same price. This would happen in a world where there were no real shocks, where the central bank had always targeted zero inflation, and where it had always set the nominal interest rate at exactly the right level in the past, and was confidently expected to set exactly the right interest rate in future.
In that long-run symmetric zero inflation equilibrium, the solution for the representative firm would be where the marginal rate of substitution between labour and the consumption basket (the shadow real wage) would equal (1-(1/e)) times the marginal product of labour (where e is the elasticity). Call the solution to that equation C*, or the natural rate of output.
MRS(C*,L*)=(1-(1/e)).MPL(L*) and C*=F(L*) if you want it in math.
(In the third stage of the auction, the firm asks each firm how much it would like to produce and sell. Since prices have already been set, the firm will answer this question exactly like a perfectly competitive firm, which takes the price at which it can sell its output as given. Because that price is now a pre-determined given. The answer to that question will be where the marginal rate of substitution between labour and the consumption basket (the shadow real wage) equals the marginal product of labour. Call the solution to that equation C^, or output supplied. C^ will be greater than C*, unless the labour supply curve is perfectly inelastic, or the firm's demand curve is perfectly elastic (e is infinite). Actual output and sales will be whichever is less, equilibrium quantity demanded, or quantity supplied. Since the natural rate C* is less than C^, the supply constraint will only be binding if a very big positive shock to demand causes demand to rise a long way above C*.)
MRS(C^,L^)=MPL(L^) and C^=F(L^) if you want it in math.
The above defines the solution if the central bank sets exactly the right rate of interest.
Now suppose that, after all firms have set prices, the central bank announces a nominal interest rate that is too high. And, to keep it simple, let's suppose that everyone is confident that this is a one-time mistake by the bank, so that output will return to the natural rate C* in the following period, and firms will choose to keep their prices constant next period. What happens?
Each firm will regret not having set a lower price. But by the time they get the news, it's too late to change price. The higher nominal and real interest rate gives every person an incentive to postpone consumption. In the fourth stage of the auction, if the auctioneer initially guesses that sales will equal the natural rate C*, and tentatively announces credits accordingly, he finds that demand is less than C*, because verybody wants to save some credits. So he learns his initial guess is wrong, and guesses again.
The solution will be where the Consumption-Euler equation is satisfied. The marginal rate of intertemporal substitution between current and future consumption, evaluated where future consumption equals C*, must equal (one plus) the (real and nominal) rate of interest set by the central bank. Call that solution Ci. Ci will be less than the natural rate C*.
(And if the central bank had set too low an interest rate, Ci would instead be above C*. And if the central bank had set a very low rate of interest, Ci would be so far above C* that C^ would be a binding constraint on supply.)
If you want math, the solution Ci is defined by MU(Ci)/MU(C*) = (1+r)B
where MU is marginal utility of consumption, B is the subjective discount factor, and r is the real rate of interest. Or something like that.
So far, my model is exactly like the standard New Keynesian model (except for a couple of trivial simplifying assumptions.) Now I'm going to introduce "barter".
"Barter".
Let's introduce a second auctioneer, who only opens for business after the first auctioneer has closed his books. (We can assume, if you like, that there is some trivial cost of using the second auctioneer, so everybody will try to do as much business as possible with the first auctioneer before resorting to the second auctioneer.) The second auctioneer is exactly like the first, except that he enforces Say's Law, at the individual level. No individual can carry a positive or negative balance of credits. Each individual can only swap fruit for fruit. He cannot sell fruit without buying fruit of equal value. He cannot buy fruit without selling fruit of equal value. (And by "value" I mean at the same prices that each firm had previously set, so I am not introducing price flexibility in this second auction.)
Again, let's assume for simplicity we start in a symmetric equilibrium, where all firms have set the same price. When the first auction closes, all firms have contracted to sell Ci, which may be above or below the natural rate C*, but is below the competitive equilibrium C^.
The apple producer maximises U(C,L) subject to the production function A=F(L) and the budget constraint P(C-Ci)=Pa(A-Ai), where Pa, the nominal price of apples, is pre-determined, and is equal to P, the price of a basket of fruit, in symmetric equilibrium.
Each firm will sell (and buy) an additional (C^-Ci) units in the second auction. The equilibrium after the second auction closes will be the competitive equilibrium C^, regardless of the rate of interest seat by the central bank. The proof is obvious. If the marginal rate of substitution of labour for fruit is less than the marginal product of labour, and it is less for any Ci less than C^, the firm/worker would prefer to eat more fruit even if it means working longer to produce it. Now the apple producer doesn't want to consume just apples, but he can swap his apples for bananas and all the other fruits in the second auction. If C is less than C^, there are unexploited gains from trade.
So, at the end of the second auction, C=C^. The economy gets to the competitive equilibrium, regardless of imperfect competition, and regardless of any mistake made by the central bank in setting the rate of interest too high.
Let me try to give the intuition.
First, Say's Law applies in barter. Both the apple producer and the banana producer want to sell more fruit. Each wants to sell more and save part of the proceeds. But neither is willing to borrow from the other. Barter allows both to undertake the mutually advantageous trades that can be made. "I will buy your bananas, but only if you buy my apples in return".
Second, under imperfect competition, each firm sets price above marginal cost. But if there's perfect symmetry (as there is here), that means the relative price of apples and bananas is equal to their relative marginal costs. So we still get the competitive equilibrium volume of trade in direct barter of apples and bananas. The (relative) price is right.
Just to avoid potential misunderstanding, I am not saying that money is the root of all problems. What I'm saying is that barter is very costly, and using monetary exchange is much less costly, so people use monetary exchange. The root of all problems is not money; the root of all problems is the cost of using barter, which means we have to use money.
Worthwhile Canadian Initiative 
Nick, I’m sorry I offended you. I wasn’t trying to make this personal.
Nonetheless, you said: “But the whole point of the barter market is precisely because it doesn’t allow a savings medium.”
I respond: “NK models have bonds, no money, none of the goods cost nothing to produce.”
Your barter market admits no savings medium, NK barter markets do. So how does a result from you barter market that depends entirely on there being no saving medium say anything about the NK barter market where there are bonds?
Your other example had the two monopolisticaly produced goods having zero production costs, of course people will always want more of them. In NK models everything has a cost of production so again, how is this relevant?
You may be taking the argument seriously but the counter examples are irrelevant to the central assertion.
Nick: “But the whole point of the barter market is precisely because it doesn’t allow a savings medium.”
Ha! Now I get what you’re saying. But, I don’t think ‘barter’ means what think it means. Barter does not imply no wealth. For your model to hold there would have to be no stores of value what so ever, and capital goods. Is that what economist’s mean typically when they talk about ‘barter economies?’ Is doesn’t seems so.
Here’s Robert Waldman from a year ago or so talking about John Cochrane, but that also seems to anticipate your model:
Cochrane has to assume that people have no wealth of any kind. Anything durable, not just money invalidates his argument.
Let’s say we all plan to sell our shares (commmon stock) to buy goods and services. That way planned consumption plus taxes plus investment plus net exports can be greater than GNP. The distinction between money and other financial assets is very important in many ways, but it is not relevant to Say’s law which would be invalid even if we bought and sold stock with non-durable consumption goods (apples) and not with money.
Cochrane is right in a Walrasian model with one period or in a Walrasian model in which nothing nothing at all lasts from period to period. So a model where we trade apples for oranges is a model in which my yearly planned consumption must be roughtly equal to my yearly income. However, if the model also includes apple trees and orange trees, then this is no longer true….
If I own apple trees then my demand can be greater than my income. I have wealth (the trees). I can buy apples and oranges by selling my trees. If everyone wan’t to sell trees (not made this period) to buy fruit (made this period) then planned consumption of goods produced this period will be greater than production of goods produced this period.
The value of trees does not appear in GNP unless they just matured (the value of pruning trees does). The budget constraint includes, at least, current income plus wealth (with perfect financial markets it also includes the expected present value of future labor income).
Cochrane is assuming that income = wealth. This is a much stronger assumption than that there is no money or no financial instruments.
http://rjwaldmann.blogspot.com/search?q=SAY%27S+LAW+APPLES+ORANGES+TREES
Oh, I should have proof read that, multiple typo’s. Sorry. Anyway, the Waldman quote is clear enough.
I have been trying to make the same point as Adam. NK models are 100% barter, have savings, have monetary policy, and have misallocations. Your baseline model is NOT NK.
While I may not be quite as aggressive as Adam :P, I do wish you would stop saying that this post and the comments have said anything at all about NK models. Instead, it’s been about two alternative models, which may be informative in general, but is not proving or disproving anything about NK.
And, to repeat myself, the best way to discuss NK models is to actually use NK models, by which I mean, USE MATH! All this confusion would be immediately resolved if you wrote up your original model in conventional macro math where it would be clear how different your set-up is from a Woodford-style set-up (it’s a lot).
Adam: OK.
This is what I think is going on:
Suppose I start with the same underlying structure, preferences etc. as in the standard NK model, but said that the only trades allowed were barter trades, with no savings medium. Then it is definitely unsurprising that I don’t get NK results. Then you would be right to say it’s not really a NK model, and that I haven’t proved my point.
Is that maybe what you think I’m doing? If so, I understand your critique.
But I think I’m doing something different. This is what I think I’m doing:
I start out with the same underlying structure, preferences etc. as in the standard NK model. I then add in a trading mechanism, with a savings medium, that I think is the same trading mechanism as in the standard NK model. And I get what (I think) is the standard NK equilibrium.
Starting in that standard NK equilibrium, I add in an additional trading mechanism (I call it “barter”), on top of the existing trading mechanism, which does have a savings medium. And I get different results.
I am not taking away a savings medium. It’s still there.
I want to compare two equilibria:
The first with only the “Monetary” auctioneer.
The second with two auctioneers: the “Monetary” auctioneer (with savings), plus the “Barter” (without savings) auctioneer.
I have no idea if that will clarify anything.
@Nick Rowe,
Yes, that is all true provided the average price level remains the same but there is no guarantee that this will be the case; in fact it would be extraordinarily unlikely. Think about what that means, in the context of your relative-price economy; a shock alteration in the quantity of any product has only small impacts on relative prices but a direct impact on (real) GDP. National income has changed but real wages (or the price of a representative consumption basket) are denominated in those old units.
You can’t just say “oh that’s okay, I am paid in apples so I only need to consider the second-order change in relative prices of apples to the shocked good” – there will be more or less total stuff for you to buy, aggregated together.
Yes, David. Nick let the barter market transact at different prices. He dropped the sticky price assumption.
Barter had nothing to do with anything. Flex prices neant no recession.
Andy: Yep. Maths might help some readers, but:
1. I am cr@p at math, and even worse when trying to write it in TypePad.
2. Sometimes, and I think this might be one of those times, the math may actually hide things. It’s the implicit assumptions about the trading structure that need to be clarified, and you can’t always see that in the math. And my auctioneers are my attempt to make explicit exactly what I am assuming about the trading structure. For example, the standard Walrasian auctioneer story clarifies for me the implicit assumption about the trading structure of Walrasian/Arrow-Debreu GE theory, in a way that the mathematical existence proofs and equilibrium conditions can never do. That’s why the Walrasian auctioneer was invented in the first place.
OGT: “Here’s Robert Waldman from a year ago or so talking about John Cochrane, but that also seems to anticipate your model:
‘Cochrane has to assume that people have no wealth of any kind. Anything durable, not just money invalidates his argument.’ ”
I actually disagree with Robert Waldman here. I think it is money (the medium of exchange), and only money, that invalidates Say’s Law. An excess demand for other non-produced storeable goods, like land, or antique furniture, cannot cause a general glut. An excess demand for money will cause a general glut.
This is a moderately radical position. Many think I am wrong. I am denying Walras’ Law. I did some old posts on this. Here’s one of them:
http://worthwhile.typepad.com/worthwhile_canadian_initi/2010/10/the-paradox-of-thrift-vs-the-paradox-of-hoarding.html
Andy P is starting to make a little bit of sense to me now. I can sorta see where he’s coming from.
That said, I have a general question: does the term ‘sticky prices’ make sense in a barter economy with N(N-1)/2 markets and prices? The concept of sticky prices in a monetary economy is clear to me, but the concept of sticky prices in a barter economy is not. Can someone elaborate?
@Nick: Now would be a good time to get better at math! I always think of math as a language we use so that everyone agrees on what each sentence means. A lot of confusion arose here because of semantical distractions, IMO.
@jsalvatier: Prices are just exchange rates and don’t have meaningful units in a barter economy or a monetary economy. Economists will often just choose one good and call it the numeraire and denote everything in units of that good. For instance, if we choose oranges as the numeraire, then the price of an orange is 1, the price of apples is apples per orange, and so forth. It is a straightforward result that this denomination is contentless; any good could have been chosen as a price unit. Money is totally irrelevant for the concept.
What are sticky prices? Just fixed exchange rates – say 2 apples for one orange – regardless of demand or supply conditions.
Nick at 1:09pm.
I understood perfectly that you were doing the second thing you describe. However, I assume that you wanted the second, barter, market to have all the same structure as the first one with the one exception of no money used in trade. Only then do you make your point, yet you didn’t do that.
Question from someone a lap behind. What is it about having a non monetary savings medium that creates the sticky price induced output gap in the nk model? I am used to thinking about price distortions as frustrated deflation caused by an excess demand for the medium of exchange. I don’t understand how the price stickiness (calvo or whatever) comes to matter in a woodford cashless economy.
Can there be recessions in barter economies? Sure. A bad crop due to weather can do that. Can there be a general glut? No, there would always have to be something in excess demand. That excess demand, or more appropriately short supply, which historically has been for food, can lead to excess supply in all other goods. Says law, production equal consumption, holds even if production and consumption includes investment goods, it just doesn’t mean production must equal consumption excluding investment. One can’t really save in a barter economy; the closest one can ‘save’ is invest in inventory, a speculation at best. While one can try to construct a numeraire of a consumption basket, it’s value in terms of other goods or of other goods in terms of it would be subject to fluctuation. While a consumption basket may include storables, it cannot be totally storable or it wouldn’t be a consumption basket. While a bank might set a consumption basket interest rate, this would mean foregoing setting a money interest rate. While a barter economy could have bonds, there is no assurance those bonds could be met; they would at best remain hopes.
jsalvatier: There’s the “numeraire”, which is the good the economic modeler measures prices in. And there’s the “medium of account”, which is the good agents in the model (or real world) measure prices in.
As Andy says, the numeraire doesn’t matter at all. (Except, maybe, what’s most convenient for the modeller).
And in a world of perfectly flexible prices, it doesn’t matter what the medium of account is either, except for people’s convenience. In a monetary exchange economy, people nearly always use the medium of exchange as the medium of account, simply because it’s more convenient. (If we paid in dollars, but talked about prices measured in peanuts, we would have to divide by the price of dollars in terms of peanuts to figure out how many dollars to hand over, which is a hassle.)
In a barter economy, since we can pay in anything, it’s not obvious which good would be most convenient to use as medium of account.
But, convenience aside, all the exchange ratios (relative prices) can still adjust whichever good is used as medium of account.
But if some prices are sticky, it matters which good is the medium of account. If there are 3 goods, A,B, and C, and if the price of A is sticky, then the relative price of A to B is sticky if B is the medium of account. If C is the medium of account, then it’s the relative price of A to C that is sticky.
For example, if the relative price that is sticky is a relative price whose equilibrium never changes anyway, then sticky prices are not a problem for the economy. All prices stay in equilibrium, because the one that cannot change never needs to change anyway. But if the relative price that is sticky is an important relative price, whose equilibrium value does change, then it matters. It means a relative price that needs to change cannot change. So the economy is forced away from equilibrium.
Lord: Yes, a bad harvest will cause a drop in GDP, even if all prices are flexible, or even if the economy is responding to that real shock in a perfectly efficient manner. Some economists (Real Business Cycle theorists) would call that a recessions. I wouldn’t. It doesn’t have the (to me) key feature of a recession — that it gets harder to sell stuff (goods and labour) in a recession — which is what we call a general glut.
When we say “harder to sell stuff”, we mean “harder to sell stuff for money“. (It’s easy to sell money and get stuff in return in a recession). Barter is like selling stuff and buying stuff in the very same act. So, to me, recessions look like essentially monetary phenomenon, because it’s the exchange of stuff for money that gets harder for the person on one side of the transaction (the one who has the stuff and wants money), and easier for the person on the other side of the transaction (the one who has money and wants stuff).
But Nick,
A bad harvest in barter economy does make it harder to sell stuff, all stuff! Thus, even in your terminology Lord’s example is a recession.
Well, I should say it gets harder to sell all stuff that isn’t agricultural.
Dlr; “I don’t understand how the price stickiness (calvo or whatever) comes to matter in a woodford cashless economy.”
good question! Normally, in an economy with cash, sticky prices cause a recession because they prevent the real stock of cash adjusting to the equilibrium value. If prices fell, the real stock of cash would increase, and increase aggregate demand, and get the economy out of the recession. And that can’t be what’s going on in a cashless economy.
Instead, a recession happens because the central bank sets the interest rate too high. The only role of the degree of price stickiness is to help determine how quickly prices will adjust in future, and how quickly they will be expected to adjust in future, and that determines the real interest rate for any given nominal interest rate set by the central bank.
But, as Andy said (somewhere above in the comments, IIRC) it is less than clear how exactly the central bank can set the rate of interest in a Woodfordian cashless economy. Normally, a central bank can set the rate of interest by changing the nominal supply of cash which, if prices are sticky, also changes the real supply of cash. But it can’t do that if there is no cash.
One way to resolve this puzzle is to think of the cashless economy as just the limiting case of an economy with cash. That’s how Woodford does it, IIRC.
In my model above, I made the central bank the monopoly supplier (and monopsonist demander) of all inter-period loans in the form of trading credits. I assumed that agents cannot borrow or lend trading credits between themselves, but can only borrow from or lend to the central bank. So the central bank can set whatever (nominal) rate of interest it wants.
Nick,
Take a barter economy and divide output into A for agricultural and C for all other consumption. Now, hit the economy with a poor harvest so A has fallen.
Now it has gotten harder to sell C! A unit of C used to trarde for x units of A, now it trades for less than x units of A. Doesn’t that mean it’s gotten harder to sell C?
Futhermore, if this is RBC world thereal wage accruing to the producers of C is lower (they can’t buy as much A as they could before so the real value of their output is less). Thus the producers of C supply less labour and output of C falls!
The fall in C means it’s now harder to sell A! So, there is no money, it is pure barter and yet the recession looks exactly like a situation where it’s gotten harder to sell stuff. Just as you asked. Someone living in this world would say it’s gotten harder to sell stuff just as he does in the monetary exchange world, he would not be able to tell the differenc.
Monetary exchange is not needed.
Adam: honestly, I am doing my best to understand your criticisms, but I still don’t get it.
“Yes, David. Nick let the barter market transact at different prices. He dropped the sticky price assumption.”
I don’t think I did. I started in equilibrium with all prices the same, and so all relative prices were 1. I held all prices fixed, so all relative prices stayed at 1. In my barter auction, all relative prices stay at 1. Why do you think they are not 1?
“However, I assume that you wanted the second, barter, market to have all the same structure as the first one with the one exception of no money used in trade. Only then do you make your point, yet you didn’t do that.”
I thought I did. What do you see as the difference?
Adam:
1. Suppose I noticed that when GDP dropped it was easier to sell food, and harder to sell non-food. I would suspect that the drop in GDP had something to do with an excess demand for food.
2. Suppose I noticed that when GDP dropped it was easier to sell money, and harder to sell non-money. I would suspect that the drop in GDP had something to do with an excess demand for money.
2 seems to fit the facts much better than 1.
“2 seems to fit the facts much better than 1.”
Not in a barter economy.
Nick,
Lord’s first sentance was: “Can there be recessions in barter economies? Sure.”
We’re talking about barter economies here. You respond by claiming that a recession, IN A BARTER ECONOMY, that was caused by a bad harvest would not look or feel like it got “harder to sell stuff”.
I then respond that, IN A BARTER ECONOMY, a recession caused by a bad harvest would look and feel like it got “harder to sell stuff”.
You then respond by going back to a money economy. Are you even reading the comments?
Since this is mostly about NK models I’m going to sit on the sidelines, but I do see a problem with this from Nick: “Suppose I noticed that when GDP dropped it was easier to sell money, and harder to sell non-money. I would suspect that the drop in GDP had something to do with an excess demand for money.”
What if it’s easier to sell bearer bonds, foreign currency, gold, forged passports and tickets on the next plane out of the country? You would surely then suspect that the drop in demand for locally-produced goods had something to do with fears for the future of that particular locality. It seems to be that this argument revolves around the question of whether an increased demand for money necessarily has to do with money’s role as a medium of exchange, rather than its role as a store of value when other assets look too risky. At the moment it’s quite easy to sell US and German government debt. That suggests to me that the demand is not for the medium of exchange as such, but for safe assets of any kind.
I don’t think Nick should look for a home among the Post-Keynesians. Paul Davidson is awfully insistent on the significance of the fact that “money is a one-way time vehicle or time machine for store of value purposes” (his emphasis). I don’t think money’s role as a medium of exchange is especially important to him. Joan Robinson was also very insistent that the crucial differences between her views and those of “the bastard Keynesians” related to uncertainty and time. I seem to remember that she and John Eatwell actually used a Keynesian barter model in their ill-fated textbook, but it’s a long time since I read it.
Kevin: suppose we used cows as money. Suppose there were an increased demand for milk. That would increase the demand for cows, not because people want more money, but because people want more milk. But it would still cause a recession.
Cows, the medium of exchange in that example, also give milk. Money, the medium of exchange, is also a store of value. If there’s an increased demand for a store of value that happens to be a medium of exchange, that could cause a recession.
But yes. Perhaps I shouldn’t join the post-keynesians quite yet. They are a disparate lot, though.
I don’t think the fall in C means it’s now harder to sell A; the fall in A has made it harder to sell A, not due to diminished demand but diminished supply. Someone with stores of A or unaffected by a fall in A would do well. It is just A would be in short supply so most would be worse off, even producers of A. I don’t think it would be more difficult for the barleyman to barter with the cornman, assuming they were similarly affected, or the tailor with the weaver other than weakness due to starvation, but more difficult for the other trades due to the change in relative price between A and C, and would make selling A easier if it existed and selling C harder. Real output would be lower due to nature.
So what would inflation look like in a barter economy? Hyperinflation?
Greg: in a pure barter economy, with no money, it would depend on what good prices were measured in. For example, we might all quote prices in apples, even if we exchanged bananas and carrots directly.
I’ve got a sort of impure barter economy. People start out using monetary exchange, with prices quoted in money, then a barter market opens up afterward, for any trades that people can’t carry out in the monetary exchange system. The idea is that people sell as much as they can for money, and buy goods with money. Then, if they still want to sell more (they will) they do swaps on the barter exchange. But they still use the same money prices to determine the relative prices in the barter exchange. So if apples and bananas each are priced at (say) $5 in terms of money, one apple will swap for one banana in the barter exchange.
“Yes, David. Nick let the barter market transact at different prices. He dropped the sticky price assumption.”
I don’t think I did. I started in equilibrium with all prices the same, and so all relative prices were 1. I held all prices fixed, so all relative prices stayed at 1. In my barter auction, all relative prices stay at 1. Why do you think they are not 1?
Yes, your barter-economy no-excess-supplies result obtains when there is one firm, one good, or one consumer (or identical duplications thereof). It’s a bit tricky once those assumptions are dropped, though… your barter market in your reply to my question does, indeed, have flexible prices*, since you asserted that you could drop the assumption of identical firms.
* to be precise, depending how you formulate it (since you left this undefined in your model), prices are fixed at full employment or at goods-market-clearing levels, but not both.
You didn’t reply to my latest reply but Adam P covered the point I was trying to make (I think).
Hm, no, wait, I think I see where you’re coming from. You’re taking a monetary economy, then removing money and imposing a barter structure, which shunts any excess demand (for money) that exists into whatever there was excess supply of. Conclusion: no excess demands remain.
But that’s only true if the shock was a monetary shock (and, strictly speaking, if there is only one good – however, the excess demands from wrong relative prices of multiple goods in this case would be second-order small). Unsurprisingly, monetary shocks have no effect on a barter economy (no demand for money), and little-to-no effect on a monetary-then-barter economy, and so I presume that this wasn’t the point you were intending to make! If the shock was a real shock, then any real shock large enough to generate first-order losses in a monetary economy will also generate first-order losses in a barter economy, unless you relax the presumption of stickiness among enough real (relative) prices so much so that excess demands can be shunted into them.
The reason we disagree (I think) is this: if all real relative prices are fixed, then no adjustment can take place and we have unemployment or excess supply at first-order levels; if none are fixed, then total adjustment takes place and no excess supply or unemployment exists. In between (with some prices sticky and others flexible), we add or remove Harberger triangles to fill the Okun gap. Intuitively, you started thinking from the latter and applied Tobin’s dictum; I started from the former and applied the dictum. But formally I think you are wrong, too 😛 – you buried flexible wages in your model, in a non-obvious manner, and since your model only has labor and fruit, all relative real prices are flexible.
You’re not grokking my earlier attempts to convince you of the first-order losses, so let me try to convince you instead that your barter model does have changing prices. Your model only has fruit as a good, so wages are paid in fruit (or, identically, the price of fruit is labor). There is hence only one possible relative set of prices. A real shock must affect prices, and there is only one price to affect here, so how do labor wages, or the price of fruit, remain sticky?
*”A real shock must affect real prices”
David: “Hm, no, wait, I think I see where you’re coming from. You’re taking a monetary economy, then removing money and imposing a barter structure, which shunts any excess demand (for money) that exists into whatever there was excess supply of. Conclusion: no excess demands remain.”
Almost. I’m taking a monetary economy, then I’m not removing money but I am adding the possibility of barter trades. And then yes, that does shunt any excess demand (for money) that exists into whatever there is excess supply of.
“But that’s only true if the shock was a monetary shock (and, strictly speaking, if there is only one good – however, the excess demands from wrong relative prices of multiple goods in this case would be second-order small). Unsurprisingly, monetary shocks have no effect on a barter economy (no demand for money), and little-to-no effect on a monetary-then-barter economy, and so I presume that this wasn’t the point you were intending to make!”
The shock was a monetary shock.
Is it unsurprising that monetary shocks have no effect when barter is allowed?
I get two different reactions:
1. “It’s unsurprising. It’s totally obvious”
2. “It’s totally wrong”
Take your pick!
I’m still not following the rest of your comment.
“A real shock must affect prices, and there is only one price to affect here, so how do labor wages, or the price of fruit, remain sticky?”
There are n different kinds of fruit. They are not identical. They are imperfect substitutes. But the equilibrium is perfectly symmetric, so all fruits will have the same prices in equilibrium.
The price of each fruit is fixed in terms of money.
The labour market is suppressed in my model. Each firm is owned by the one person who works there. If I made the labour market explicit, the money and real wage would be perfectly flexible.
No, you’re removing money. You are requiring that everybody have a zero balance of credits at the end of the barter auction. There’s no reason for anyone who desires to save to have a zero balance of credits, so they won’t do this on their own. You can impose this on a monetary economy, too, and achieve the same result of no excess demand for money and no excess supply of anything else.
There are n different kinds of fruit. They are not identical. They are imperfect substitutes. But the equilibrium is perfectly symmetric, so all fruits will have the same prices in equilibrium.
The price of each fruit is fixed in terms of money.
The labour market is suppressed in my model. Each firm is owned by the one person who works there. If I made the labour market explicit, the money and real wage would be perfectly flexible.
All right, so there are multiple fruit with identical prices. People are endowed with assorted fruit, which they use to buy other fruit, at a sticky price that is the same among all fruit. So there’s still only one relative price: one to one. Either a real shock is impossible, or some prices are flexible.
You need at least three goods with three different prices to have two different relative prices, one of which can be sticky and the other not. Even then, the degree to which excess demand can be moved to and fro depends on elasticities. Modeling money here as a tradable good with independent real value is an obvious next step.
Nick, in the interest of re-engaging with you, I do feel a bit bad about how rude I’ve been getting in this thread, let me go back to this comment of yours:
Let me try another tack.
The optimal allocation of resources is the competitive equilibrium C^, The monopolistic competition natural rate, C* is worse for everyone. And the equilibrium in a recession, Ci, is worse still. Ci is less than C*, which is less than C^. But all firms have a real (relative) price of 1 in all three equilibria.
If we found ourselves in Ci, what would Coase say? Coase would say “OK, if we all increase output by 1%, and all increase consumption by 1%, we would all be better off; so why don’t we all agree to this deal?” (Notice, by the way, that this Coasian deal respects the assumption that all relative prices are 1.)
Under monetary exchange, each individual would want to accept the deal, but would cheat on it. If everyone else followed the deal, and increased their consumption by 1%, his income would rise by 1%, but he gets that income in the form of money, and would save part of that income (he keeps some of the money, then buys bonds with it), and increases his consumption by less than 1%. So under monetary exchange, where each swaps goods for credits, the Coasian deal is unenforceable. So accepting the Coasian deal is not a Nash Equilibrium.
But in a barter exchange, the Coasian deal is enforceable. You don’t get income in the form of money; you get it in fruit. So accepting the Coasian deal is a Nash Equilibrium.
I have two points.
Point 1) In the NK model you can buy bonds for fruit. It’s an economy that does not have money but does have bonds, ergo whoever buys bonds does so in exchange for goods.
This seems to be where we’ve been talking past each other. You say, the possibility of saving is still there but you can only buy your bonds out of the monetary market. I say that even in the barter market people will attempt to save and you have the same problem. Effectively what will happen in the barter market is the apple producer shows up saying “I’ll give you apples today in exchange for bananas tomorrow” and the banana producer repsonds “No, I want apples tomorrow, not today, and I’m willing to give extra bananas today for it. However, I’m not willing to give extra bananas tomorrow for it.” (People want bonds, not futures trades).
Point 2) Even if I agreed with what you said here you’d have already lost the argument in a certain sense. Even in your argument money’s medium of exchange properties are not the cause of the recession. It is an excess demand for saving that is the problem, money only enters because you’ve mysteriously made money the only way to get a bond.
PS: in point 1 above the reason people in the barter market prefer to save is the same as in the cash market. The real rate of interest on the bonds are the same in both markets.
If you allow the real rate to be flexible in the barter market then you’ve departed from your central assumption.
Adam: you have definitely succeeded in re-engaging me in those last two comments.
I agree a lot with what you say here. You very definitely have a point. It’s a valid criticism. I see (OK, I’m pretty sure I see) where you are coming from.
You have now put your finger on the point where my argument is most vulnerable, and where I am least sure that I am right, and least clear in my own mind.
I am going to argue against you on this point. But I will fully understand if you find my counter-argument less than 100% clear, and less than 100% convincing. It’s because my own head is not 100% clear on it either.
Give me some time to try to marshall my counter as best I can.
Some minor preliminaries:
“Point 1) In the NK model you can buy bonds for fruit. It’s an economy that does not have money but does have bonds, ergo whoever buys bonds does so in exchange for goods.”
Yes, it does have bonds, and the “barter” market doesn’t. We acn interpret the “trading credits” that people may hold between periods as “bonds”. Whether it does or does not have money is the point I need to argue about. Because it is definitely “cashless” in some sense.
“It is an excess demand for saving that is the problem, money only enters because you’ve mysteriously made money the only way to get a bond.”
I need to be clearer on the “mysteriously” bit. I can understand why it appears mysterious.
“PS: in point 1 above the reason people in the barter market prefer to save is the same as in the cash market. The real rate of interest on the bonds are the same in both markets.
If you allow the real rate to be flexible in the barter market then you’ve departed from your central assumption.”
Agreed.
Will be back later, to do my best.
Oh, and yes, if there’s a real shock, after prices have been set, even barter (at those fixed relative prices) won’t get the economy to the competitive equilibrium. Agreed.
Adam:
To summarise your critique (as I understand it)
I have two trading systems (auctioneers). The two trading systems are identical, except: in the first one you can buy bonds; in the second one buying bonds is prohibited. And that is what is driving the results. That’s why adding the second trading system gets the economy out of the recession.
(Agreed with all of the above).
Which raises the question: why do I call the first one “monetary” and the second one “barter”; and what’s that got to do with the prohibition on buying bonds?
Here’s my best shot at the answer:
I’m the apple producer. If I buy bananas for money, I can’t control what the banana producer spends that money on. I can’t prohibit him from spending some or all of it on bonds. If I buy bananas in barter for my apples, I can prohibit him from buying bonds with the proceeds from his sale of bananas. I prohibit him from buying anything with the proceeds, except my apples. It is as if I gave him $100 for his bananas at the posted price, but added a rider in the contract that says he must immediately spend the whole of that $100 on buying my apples at my posted price.
My prohibition on buying bonds in the second trading system was my attempt to model that difference between monetary and barter exchange.
Given the setup in my model, people will accept those riders against buying bonds with the proceeds, even though they would prefer to break those riders if they could get away with it.
I don’t know if this is clear, or convincing, or if it even misses your criticisms completely. It’s about the best i can do.
(But what I may have failed to model correctly, and what I can’t quite get my head around, is the difference between bilateral barter of 2 fruits vs multilateral barter of n fruits. I can’t get my head clear on whether this matters.)
For some reason, this reminds me of Joan Robinson noting that the Walrasian analysis applies pretty well in only one case, that of a prisoner of war camp (a pure, closed barter system), mainly because two characteristics of industrial capitalism are missing in the POW case (and from the Walrasian model): 1) the distinction between income from work and income from property and 2) investments made with uncertain expectations from a long future. Both seem key features of Keynes’ model. Perhaps I read through this too quickly and missed them. If I’m right and they are not there, then can this be a truly Keynesian model, I wonder? Maybe someone has already raised this and I missed it. If so, I apologize for appearing to belabor a point already made.
Maxine: There’s a good reason it reminds you of that. It’s because it shares the belief that trading systems matter.
But I think Joan Robinson was wrong. As in Frances’ Nov 11th post, on the POW camp, they did use money, both as medium of account and medium of exchange. Prices were measured in cigarettes, and people, even non-smokers, traded other goods for cigs. Cigs were money. And you can build uncertain investment into the Walrasian model (OK, Arrow-Debreu). And there is one difference between income from work and income from renting out other property in the Walrasian system: the first gives disutility at the margin. (Of course, Joan Robinson had some beliefs that income from property was different from wages in more ways than that.)
Adam: (Yes, I’m beginning to think that there is an important difference between pairwise and multilateral barter. When I swap you my apples for your bananas, I not only prohibit you from buying bonds with the proceeds, I prohibit you from buying dates with the proceeds. And I wouldn’t buy your bananas if I thought you were going to spend the money on dates, or bonds. I think I should have built this in explicitly in my “barter” market(s).)
Damn!
Well I think we’re comunicating now! But I think we’re drifting away from the original argument.
We’ve agreed that what’s driving the results is whether or not agents can buy bonds, it’s not a money/no money distinction. So then, going back to the first parargraph of the post where you say:
All Keynesian macroeconomics, either explicitly or implicitly, assumes monetary exchange. It’s not just sticky prices that generate Keynesian results. It’s sticky prices plus monetary exchange.
Basically then, taking away bonds prevents the intertemporal Euler condition from having any effect on behaviour and so goods markets clear. So I agree, no bonds or money (no savings medium of any kind) means no recession.
On the market structure question, I’d have just had the auctioneer in the barter market also auction off the bonds. His job would be to clear all the goods markets and the bond market with the additional proviso that the bond market clear at the interest rate that the central bank wants. That’s what I’ve always understood the NK model to mean.
This would imply that to clear the bond market the Euler condition would have to be satisfied and so if the central bank sets too high a rate then we’d get a recession.
Can we now agree that, at least in principle, an NK model that has no money but does have bonds makes sense, that you can get a recession if the central bank sets the real rate too high? (And perhaps you want to change the second paragraph in the original post?)
Now, as for what your starting to think about in these last few comments I have to think you’re on track for a good point. Notice my understanding of the NK model was multi-lateral barter including bonds. If you restrict to bi-lateral barter then you may well be right, even if I what I want is for someone to sell me a bond, if there’s none to be found I may well settle for utility improving trades that are still second best.
Even this is not obvious though, seems to me there might be search friction that gets in the way of market clearing. If I want a bond but you won’t issue me one perhaps I don’t trade with you, I go on to the next meeting and try to get the next person I meet to issue me a bond.
Thinking more on pairwise vs multilateral barter:
1, In the second market, n(n-1)/2 pairwise barters could get the economy out of the recession. The apple-seller trades some apples for bananas, some apples for carrots….and the banana seller sells some bananas for carrots…etc. That’s a Nash equilibrium to accept.
2. In the second market, one big n-person barter, that all have to sign off on simultaneously, could also get the economy out of the recession. The apple seller produces n more apples, and gets 1 banana, 1 carrot,…etc in return. That’s also a Nash equilibrium to accept.
3. What will NOT work is the mere prohibition on buying bonds with the proceeds of a sale. The apple seller will not spend $n on bananas, because he knows that only $1 will be spent on apples, and the remaining $(n-1) will be spent on other fruit. Escaping the recession that way is not a Nash equilibrium.
Barter is normally 1. Barter can be 2. (though it’s rare). But 3 isn’t barter. It’s more like monetary exchange, rather that barter, with just one restrictive covenant attached about what you can’t spend the proceeds on.
Pure monetary exchange is totally unrestricted on what you can do with the proceeds of sale. Pure barter is totally restricted on what you can do with the proceeds of sale.
“This would imply that to clear the bond market the Euler condition would have to be satisfied and so if the central bank sets too high a rate then we’d get a recession.”
Agreed.
“Can we now agree that, at least in principle, an NK model that has no money but does have bonds makes sense, that you can get a recession if the central bank sets the real rate too high? (And perhaps you want to change the second paragraph in the original post?)”
Not really. The question is not whether it has (a stock of) “money”, but whether it has “monetary exchange”, and what precisely that means. If there are no restrictions on what the seller of goods can do with the proceeds of the sale, then I would want to call it “monetary exchange”. And if there’s monetary exchange in that sense, and the central bank sets the real rate too high, you get a recession. And I would say that “Barter exchange” means that there are total restrictions (no freedom) on what the seller can do with the proceeds of the sale. And with barter exchange, in that sense, there would be no recession even if the central bank set the interest rate too high. There would just be an excess demand for bonds.
One of these days I’m going to re-write my post from scratch. Because I really do think it makes a valid point, but it’s not as clear as it should have been (because I wasn’t as clear in my head as I should have been).
So a NK model that has money regularly exchanged for goods and services, but no bonds or savings, doesn’t have monetary exchange? Mr. Rowe, with all due respect, I think redefining terms that way is potentially misleading (to say the least). How did “monetary exchange” become “restrictions on what your trading partners can do”? If you wanted to remove bonds from the economy, just say a “no-bond economy”.
david. Think about the real world.
When you buy something with money, do you tell the seller what he is allowed to spend his money on? Of course not.
When you buy something with barter, do you tell the seller what he has to buy with the proceeds? Of course you do, by definition. He has to buy your apples if he wants you to buy his bananas.
Considering money is just a bond with a zero maturity, redeemable on demand, whatever redeemable means, I don’t think bonds can be separated from money unless one is willing to impose a redeemable when due or expiry condition on the forward contract. Separating money from bonds is more possible by banning lending and forward contracts, though reciprocal gifting would soon circumvent this, wink wink, nod nod. An investment or speculation in inventory is possible whenever one deems exchange unfavorable, but that would be in a specific good by a specific person. A bubble may form in it if enough do then change their mind, but as with all speculations, prices fluctuate.
No. There’s no restriction on what the seller must buy. You mentioned multilateral barter yourself already.