Sunday, March 22, 2015

Wren-Lewis Takes a Stab at It

Simon Wren-Lewis will unfortunately have to join Brad DeLong and Nick Rowe in the ranks of not-ready-for-prime-time monetary economists. There is always hope, though. We can allow him a retake of the David Levine's Keynesian economics exam. He could even attempt the same problem, if he wants. Quoting yours truly from my previous post:
If Levine's piece were a prelim question, I'm afraid we would have to fail both Brad and Nick. Brad can't quite get off the ground, as he doesn't understand that Levine's model is indeed a monetary economy and not a barter economy. Nick achieves liftoff, and we can give him points for recognizing the double coincidence problem and that the phone is commodity money. But then he stalls and crashes, walking off in a huff complaining that Levine doesn't know what he's talking about. Levine has posted an addendum to his original post, which I think demonstrates that he does in fact have a clue.
Simon says:
When we allow for the existence of money, it becomes quite clear how the ‘wrong’ real interest rate can lead to a demand deficient outcome. Brad DeLong takes Levine to task for trying to use a barter economy and Say’s Law to refute Keynesian ideas, and Nick Rowe turns the knife.
So, Simon compared notes with Brad and Nick after the exam. Bad idea. Everyone knows that talking to the guys who failed isn't going to help you pass the retake.

What did Simon do on his exam? He followed the time-honored approach of not answering the question he was asked, but answering one he thought he knew the answer to instead. What he gives us is not a critique of what Levine did, but a discussion of New Keynesian (NK) vs. RBC models. To summarize his discussion, Simon thinks that people who work with competitive equilibrium business cycle models (RBC for example) are contradicting themselves. According to him, their models are supposed to be microfounded, but prices are set by some Walrasian auctioneer. That's pretty silly, he thinks. He argues that NK models are superior in this respect, as the suppliers of goods actually set prices in an NK model, just as suppliers do in the real world. He elaborates by saying that NK models
...replace the auctioneer with a more modern macroeconomics - a macroeconomics where firms set prices and central banks change interest rates to achieve a target.
As well, repeating from above:
When we allow for the existence of money, it becomes quite clear how the ‘wrong’ real interest rate can lead to a demand deficient outcome.

First, as I explain in my last post, monetary exchange - whether it's commodity money or fiat money - is critical to how Levine's example works. That's how the "demand shock" propagates itself, and where the big multiplier comes from. Further, in Levine's sticky-price equilibrium, that the real interest rate is wrong is exactly the problem. In fact, the real interest rate is constrained to be zero in the sticky price equilibrium, when efficiency dictates that it should be lower. If you want to call that a "demand deficiency," I guess you can, but part of the point is that that terminology isn't actually descriptive of the basic inefficiency.

Since Simon brought up NK and RBC models, let's discuss that. First, there is in fact no Walrasian auctioneer in a competitive equilibrium. The Walrasian auction was a story thought up by someone (no idea who - anyone know?) to justify focusing attention on equilibrium outcomes - it's entirely outside the model. In a competitive equilibrium, everyone optimizes, markets clear, and that's it. But, does dropping competitive equilibrium make much difference? Well, not really. If we take Prescott's RBC model, and add Dixit-Stiglitz monopolistic competition, what do we get? The model behaves in roughly the same way, except there are some monopoly rents in the production of goods. For a lot of problems, we're not going to care about the difference between monopolistic competition and competitive equilibrium, so we might as well take the easy route, and use competitive pricing. But for Woodford's problem, he can't do that, because he is concerned with sticky prices and relative price distortions. You can't do that in competitive equilibrium, so he needs a technical device, and Dixit-Stiglitz works. He doesn't do that because it's somehow more realistic.

Further, if monetary exchange and central banking are so important to Simon, I'm not sure why he likes NK so much. A Woodford "cashless" model is just that. There's no money in sight, except that people quote prices in terms of some virtual unit of account, and the central bank determines an interest rate in terms of that unit of account. If this is realism, I'm confused. Actual central banks issue some liabilities, hold some assets, and their key policy actions involve swapping some of their liabilities for assets. I don't see that happening in an NK model. What I see is an assumption that the central bank can set a price. I have no idea why this central bank can do that - the model certainly doesn't tell me anything about it.

Here's something Simon says of Levine:
He does not talk about central banks, or monetary policy. If he had, he would have to explain why most of the people working for them seem to believe that New Keynesian type models are helpful in their job of managing the economy.
I work for one of these institutions, and I have a hard time answering that question, so it's not clear why Simon wants David to answer it. Simon posed the question, so I think he should answer it.

49 comments:

  1. according to the articles "Auctioneer" and "Tatonnement and Recontracting" in the General Equilibrium volume of the New Palgrave: Walras is not responsible for the auctioneer, though his process of tatonnement is formally equivalent to an auctioneer who plays similar strategies...naturally there is little indication of who thought up the auctioneer...

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    1. Franklin M. Fisher writes in "Adjustment Processes and Stability" in the same volume as above: "[the auctioneer] does not appear in Walras [..] but may have been invented by Schumpeter in lectures and introduced into the literature by Samuelson [...]".

      Fisher furthers the origin story of the idea with a quote from Edgeworth presumably from a series of disagreements between Edgeworth and Walras over tatonnement vs recontracting.

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  2. "A Woodford "cashless" model is just that. There's no money in sight,..."

    Woodford is wrong about that.

    Let there be green bits of paper, and red bits of paper. Only the central bank is allowed to create green bits of paper. Only the central bank is allowed to destroy red bits of paper. You are not allowed to take green notes from someone without his consent, and you are not allowed to give someone your red notes without his consent. If you ask, the central bank will create one green note plus one red note and give them to you. And if you give the central bank one green note and one red note it will destroy both. There is an equal number of green and red notes in circulation. Green notes have positive value of $1, and red notes have negative value of $1. There is a cash in advance constraint. The central bank pays interest r on your green and red notes. (For every 100 green notes you hold, the central bank pays you 100r green notes per year. For every 100 red notes you hold, the central bank pays you 100r red notes per year).

    For convenience, everyone keeps their green and red notes in a shoe box with their name on it at the central bank. And the central bank keeps a ledger just in case there's a fire. There is a fire, in which all the green and red notes get burned, but the ledger is rescued, so it doesn't matter.

    We now have Woodford's model of a "cashless" economy.

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    1. "There is a cash in advance constraint."

      But Woodford doesn't have one. And he's not wrong. Prices in his model are quoted in terms of something that plays no other role in his model. It's a barter economy where the barter exchange takes place in markets where some prices are fixed.

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    2. Steve; that's where I disagree. Woodford's model implicitly assumes a CIA constraint, whether he realises it or not. Either the buyer must pay for goods by giving the seller green notes, or else the buyer must accept red notes from the seller of goods.

      For simplicity, take a limiting case of Woodford's model, where it goes towards perfect competition, and where Calvo's fairy gets very lazy. And assume all firms are really self-employed workers.

      If there have been no monetary shocks since the beginning of time, the economy starts in competitive equilibrium. Suddenly and unexpectedly the central bank raises the rate of interest r it pays on green and red notes. Calvo's fairy hasn't woken up yet, so all prices stay fixed. Woodford says every individual will want to increase his stock of green notes or reduce his stock of red notes, so there will be a drop in demand for goods and so a drop in sales of goods and a drop in employment.

      But if barter were easy, the unemployed would do a mutually beneficial n-person barter deal at the existing relative prices and barter their way straight back to the competitive equilibrium level of employment.

      (Plus even if there were monopolistic competition, an n-person barter deal bringing everyone back to the competitive equilibrium would be mutually beneficial. Two monopolists with equal markups of price over marginal cost would willingly barter each other's goods to get to the competitive equilibrium.)

      Woodford's model makes no sense as a model of a barter economy. It's a monetary exchange economy, whether Woodford realises it or not.

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    3. You're not making any sense. Woodford is just a Prescott economy with multiple goods, and the relative prices of those goods are messed up. It's clever, but sorry, no money.

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    4. Start in competitive equilibrium, where all prices are right. Assume all agents have the same time preference, and there are no real shocks, so nobody borrows or lends in equilibrium. Now assume all prices are fixed forever. The central bank raises the rate of interest it pays on green and red money balances. The consumption Euler equation tells us that output can't stay at competitive equilibrium. But if barter were possible, output would stay at competitive equilibrium, because relative prices are still correct. It only makes sense if all saving is saving in the medium of exchange. There is an excess demand for the medium of exchange when the central bank raises the rate of interest it pays for holding the medium of exchange. But the net value of the stock of the medium of exchange is zero, because there are equal numbers of red and green notes in circulation, and the red notes have negative value.

      (Many New Keynesians don't get this either. Simon Wren-Lewis does get it.)

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    5. "Simon Wren-Lewis does get it."

      Somehow that's not reassuring. Do the comparative static experiment you're suggesting. NK model, equilibrium quantities and prices. Now increase the nominal interest rate (in one period, once and for all, whatever). By changing the nominal interest rate, the central bank has changed the relative prices. That's the way the model works. So, given the old equilibrum prices of goods in terms of money, we're not in equilibrium any more. Some of the prices have to change - the ones that can - and some of the quantities have to change. This is just about finding the relative prices (including intertemporal relative prices) such that an equilibrium holds, given the price stickiness, and the central bank's control over nominal intertemporal relative prices.

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    6. OK. Suppose the only price that changes is the nominal (and real) interest rate paid on (red and green) money balances, because all other prices are fixed forever.

      If this is an economy where goods can only be traded for (red and green) money, we get a recession. Each individual wants to sell more goods and buy less goods, to accumulate green money and get rid of red money. The short side rule Q=min{Qd,Qs} tells us that the quantity of goods traded falls.

      But if this is an economy where barter is possible, we get exactly the same quantity of trade in goods. Each individual wants to sell goods for money, but can only find willing partners to trade goods for goods.

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    7. "But if this is an economy where barter is possible, we get exactly the same quantity of trade in goods. Each individual wants to sell goods for money, but can only find willing partners to trade goods for goods."

      Not correct.

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  3. Nick,

    What you are describing is very much what I had in mind in my comment on the previous post. And I was aware of the connection to Woodford.

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    1. Yikes. It seems like what you had in mind in the previous post was credit. Woodford doesn't admit credit as there's a representative agent in his basic model. That's what the bond market is about. If there's not government debt, Bonds are priced so the representative agent is indifferent between lending and borrowing. But of course the bond market actually plays no role. There are many other assets that we can price in that model, that also play no role, and are in zero net supply. Money is just another one of those.

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    2. I thought I saw a parallel with Woodford, but I wasn't trying to describe that specifically. I was trying to build something as a variation on Levine's model or possibly yours. But the point was to have a situation where we are restricting the bilateral trades that can take place (to ones involving money) which is preventing otherwise efficient exchanges taking place. I think this is in line with what Nick is getting at (but mayI've misunderstood ).

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    3. Put another way, I was trying to describe a situation where (given the restriction on what type of transactions could take place ) there was a set of transactions which taken together was Pareto efficient, but which could not be arrived at by individual transactions which were all Pareto efficient themselves. I find this more interesting than Levine's scenario.

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    4. Nick E: yep. I think you understand me right.

      Steve: If I issue an IOU, it's credit, but nobody will use it as money. If the Bank of Montreal (or the Bank of Canada) issues an IOU, it can be both credit and used as money.

      The way I read New Keynesian models, individual agents have accounts at the central bank, which can be positive or negative for each individual, but sum to zero, and are used as money. It's functionally the same as the central bank issuing green notes worth +$1 and an equal quantity of red notes worth -$1, setting a rate of interest it will pay on those notes, and people using those notes as currency.

      If all individuals are identical, and payments are perfectly synchronised with receipts, the net and gross demand for money would be zero in equilibrium. But output adjusts to ensure the net demand for money is zero.

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    5. To be specific, we're discussing a model in which there is no capital, and there are monopolistically competitive firms, and a representative consumer. For the sake of argument, suppose there is a continuum of consumers with unit mass, and they are all the same. Each period, the consumers are going to work for the firms, they will earn wage income, and they are going to buy the whole array of goods. Now tell me exactly the sequence of transactions that happens during a period. What assets do the consumers and the firms have when a period starts, and the who interacts with who, and what do they trade?

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    6. Steve: I think that's exactly the right question to ask. But I would rephrase it slightly. How would we need to answer that question so that the New Keynesian model actually makes sense?

      All the produced goods are services. The only asset that individuals and firms have is a chequing account at the central bank. For any individual, the balance in that account can be positive or negative, but the balances net to zero, because the central bank has zero assets. The central bank sets an interest rate on those balances.

      Individuals must pay by cheque (or Interac). And the firms must pay wages (and profits) by cheque. The direct barter of goods for labour, or goods for goods, is impossible.

      Now why is barter impossible in this model? You could think up a better answer to that question than I could. Maybe the services must be consumed at the point of production, firms are physically separated, and individuals are anonymous so nobody trusts an individual's IOU? Something like that.

      But unless we interpret the NK model something like I have sketched above, it makes no sense at all. Monetary exchange is implicit in that model, despite what Woodford says about a "cashless" economy. And the rate of interest set by the central bank is the rate of interest it pays on money balances.

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    7. You could introduce shocks to preferences for different varieties, if you like, so that some individuals will have positive and some negative balances in equilibrium, depending on how much they earn as wages+profits. Then take the limit as those shocks go to zero, so all are identical.

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    8. Sorry, you didn't answer the question. Make it really simple. No shocks to start with. All the consumers are identical, and there's a continuum of them. Suppose their period utility is u(c) - v(n), where c is the utility from consuming (aggregate consumption), n is labor supply, and everyone has discount factor B. There are monopolistically competitive firms a la Dixit and Stiglitz. Each firm produces output of its product using a linear technology: y = an, where a is productivity and y is output. Now, tell me exactly what happens during a period. Consumers and firms enter the period with some assets. What are they? Then, what happens? I want to know exactly how output gets produced, who trades what with who, in what sequence, and finish off at the end of the period, with something that makes sense so we can start up in the next period, etc.

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    9. At the beginning of the period all agents have $0 balance in their chequing accounts at the central bank. They are permitted to have either positive or negative balances at the end of the period, but the central bank enforces the no-ponzi condition (somehow). There are no other assets or liabilities that carry over from one period to the next.

      Firms announce their prices.

      The central bank announces the nominal interest rate.

      Consumers then mail cheques to all the firms, and place binding orders for the consumption goods.

      Consumers turn into workers, go to the firms to work, and produce the goods that have been ordered that morning. Each customer's order is put in a special box to which only the customer has the password to prevent theft. The worker then deposits the cheques in his account at the central bank. Firms are worker-owned cooperatives, so we don't need to distinguish wages from profits.

      Workers turn back into consumers, and visit all the firms and consume the goods they have ordered on the spot. Goods cannot be transported, and can't be stored until the next period.

      The day ends.

      If all agents are identical, each will end the day with a $0 balance in his chequing account.

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    10. Maybe the firms should deposit the cheques *before* they produce the goods and put them in the customer's box, to make sure the cheques won't be bounced by the central bank enforcing a no-ponzi condition on a consumer who has gone beyond his credit limit. Firms have names and reputations, so won't rip off customers. Customers are anonymous, except for their secret passwords they write on their cheques.

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    11. "They are permitted to have either positive or negative balances at the end of the period, but the central bank enforces the no-ponzi condition (somehow)."

      The consumers are all identical. How would one have positive balance and the other a negative balance at the end of the period? And if everyone begins the period with zero balances, what happened to the balances between periods. A no-Ponzi-scheme condition is something that prevents economic agents in our models from borrowing infinite amounts. What's that got to do with it?

      "Each customer's order is put in a special box to which only the customer has the password to prevent theft."

      Now you have introduced theft. That wasn't in the specification of the environment we started with.

      "Firms have names and reputations, so won't rip off customers."

      Sounds like limited commitment. That wasn't in there either.

      Seems you're introducing some stuff that we worry about in monetary models, but which isn't in Woodford's model. To demonstrate what you want, you can't alter his environment.

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    12. "Seems you're introducing some stuff that we worry about in monetary models, but which isn't in Woodford's model."

      I agree. That stuff needs to be introduced to explain why people need to use monetary exchange in Woodford's model, so we can make sense of NK model's results. That's what I'm saying.

      "The consumers are all identical. How would one have positive balance and the other a negative balance at the end of the period?"

      In symmetric Nash equilibrium, all will choose the same amount of consumption and so have zero balances at the end of the period. But in order to solve for that Nash Equilibrium, we have to solve for each agent's reaction function, where they consider what would happen if they acted differently from everyone else. Just like Prisoner's Dilemma.

      "And if everyone begins the period with zero balances, what happened to the balances between periods."

      If an agent ends the period with $M balances, he begins the next period with $M(1+r) balances. So if M=0, he begins the next period with 0 balance too.

      "A no-Ponzi-scheme condition is something that prevents economic agents in our models from borrowing infinite amounts. What's that got to do with it?"

      Nothing. I just stuck it in there for completeness. Otherwise every agent will want to borrow infinite amounts, and we don't get a sensible equilibrium.

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    13. Though the practical difficulties of enforcing the no-ponzi condition probably explains why central banks issue currency, and don't let everyone have a chequing account that can have a negative balance. That's why the real world doesn't look exactly like Woodford's model of what central banks do. Whether that difference is big enough to matter,....I think maybe it is. But that's another question.

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    14. "I agree. That stuff needs to be introduced to explain why people need to use monetary exchange in Woodford's model, so we can make sense of NK model's results. That's what I'm saying."

      I thought you were telling me Woodford was wrong. How can we say he's wrong about his model if you're talking about a different one?

      "In symmetric Nash equilibrium..."

      Why is this Nash? I thought the labor market was competitive and there is monopolistic competition. Dixit-Stiglitz involves some strategic play, but that doesn't seem to be what you're getting at.

      "Prisoner's Dilemma"

      Whoa. What's that about?

      "Otherwise every agent will want to borrow infinite amounts..."

      From who? On what market?

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    15. Woodford is wrong about his model being a non-monetary exchange model. He implicitly assumes that barter is ruled out when he uses the consumption-Euler equation to say the central bank sets the rate of interest and that affects consumption.

      Firms play Bertrand-Nash when setting prices (if Calvo's fairy lets them). Consumers play Cournot Nash when choosing consumption, because they take their current period income from others' consumption as given.

      Prisoner's Dilemma is a simple example of a symmetric game where all players make the same choice in equilibrium, but where to solve for that equilibrium we have to ask what would happen to an individual player's utility if he chose an action different from the other players.

      Borrow infinite amounts from the central bank, by consuming an infinite amount so the balance in his chequing account at the central bank goes to minus infinity.

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    16. And I have deleted the competitive labour market for simplicity, and replaced it with worker-owned firms. It doesn't make any difference to anything.

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    17. "He implicitly assumes that barter is ruled out when he uses the consumption-Euler equation to say the central bank sets the rate of interest and that affects consumption."

      That statement makes no sense. The Euler equation comes from the consumer's optimization problem. The central bank's setting for the nominal interest rate affects relative prices, which affects consumption, and then the Euler equation tells you how, in part. That's got nothing at all to do with barter exchange or the lack of it.

      "Consumers play Cournot Nash when choosing consumption, because they take their current period income from others' consumption as given."

      Wrong again. In Woodford's model, the consumers optimize by choosing quantities, treating prices as given.

      "Prisoner's Dilemma is a simple example of a symmetric game where all players make the same choice in equilibrium, but where to solve for that equilibrium we have to ask what would happen to an individual player's utility if he chose an action different from the other players."

      A prisoner's dilemma is a particular two-by-two game. Look it up.

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    18. "The central bank's setting for the nominal interest rate affects relative prices, which affects consumption, and then the Euler equation tells you how, in part. That's got nothing at all to do with barter exchange or the lack of it."

      For simplicity, hold all firms nominal prices fixed at competitive equilibrium relative prices forever. Then the central bank raises the nominal (and real) interest rate above the natural rate for one period. Woodford and the Euler equation say that consumption and employment will drop. But if it does drop, underemployed individuals would all gain from a barter deal where they all agree to increase consumption back to the original amount.

      "In Woodford's model, the consumers optimize by choosing quantities, treating prices as given."

      Agreed. But it's a Nash equilibrium. Each individual consumer chooses quantity of consumption taking other consumers quantities of consumption as given.

      "A prisoner's dilemma is a particular two-by-two game. Look it up."

      I know that. I was using it as an example of a symmetric game with identical players. Woodford's game is also symmetric with identical players, though it's not 2x2.

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    19. "But if it does drop, underemployed individuals would all gain from a barter deal where they all agree to increase consumption back to the original amount."

      That's just it. They can only make Barter deals at Woodford prices.

      "Each individual consumer chooses quantity of consumption taking other consumers quantities of consumption as given."

      Wrong. Other consumers' consumption quantities have no bearing in that model on an individual consumer's decisions. They optimize given prices.

      "Woodford's game is also symmetric with identical players, though it's not 2x2."

      The Nash game that firms are playing is not a prisoner's dilemma.

      I think we should stop here. You make bold statements about Woodford being wrong, Levine not knowing what he's doing, and some other people you think should go back to school. But, from what I've seen, I'd say you don't know your economics very well. You're also incredibly stubborn, and I think I'm probably wasting my time on this.

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    20. OK. Thanks for the discussion.

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  4. Kaput toys
    Comment on Nick Rowe on ‘Wren-Lewis Takes a Stab at It’

    You write: “Firms are worker-owned cooperatives, so we don't need to distinguish wages from profits.”

    That is, of course, a fatal error/mistake. You have to distinguish between wage income, distributed profit and profit. These are quite different things. It is irrelevant whether the firm is a cooperative or a joint-stock company. Your error/mistake, though, is pardonable because the profit theory is false since Adam Smith and the models of Stephen, Simon, Nick E. and all the rest are not one iota better in this respect. Time to realize that RBC, NK and NC models are logically defect.

    For the correct profit theory see first
    http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2575110

    and for the correct theory of money see then
    http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2569663

    Egmont Kakarot-Handtke

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    1. Tell me -- does your tinfoil hat burn your scalp when you go out in the sun?

      Inquiring minds want to know.

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  5. Ah but de Long has slain Levine via picador Krugman & matador Sims:
    http://www.bradford-delong.com/2015/03/on-the-stupidity-of-anti-monetarist-economics-david-k-levine-vs-chris-sims-as-refereed-by-paul-krugman-with-additional-th.html
    Though you may think of other bull-related concepts when reading de Long

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    1. I would like to see DeLong and Levine in a room together. Krugman and Levine would also be good.

      Unfortunately, Krugman is no better than DeLong at figuring out what Levine is up to. As usual of course, it's always possible that Krugman understands but doesn't want to admit it.

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  6. I'm sorry to come back rather late on this - I was travelling and my question was too long to tap out on my phone.

    I don't really understand the point you are making about Woodford's model being equivalent to a barter economy. This may well be because I don't understand the model well enough, but when I work through what I think it is doing, it seems fairly critical to me that certain barter exchanges are disallowed.

    Starting from your outline of the model, I imagine that what is going on is something like the following:

    All agents have an account with a central registry (the Bank). The account balances can be positive or negative. All agents start with a zero balance. At the start of the period therefore, there are no assets (or liabilities).

    Firms set prices and determine how much they expect to sell. They hire labour and pay wages. Payment of wages involves firms instructing the Bank to debit their accounts and credit those of households. This gives households a positive balance on their accounts and firms a negative balance, i.e. firms are overdrawn. In the simplest case, we are assuming no constraint on the amount to which they can be overdrawn.

    Households then buy goods from firms. Payment is effected the same way. This results in firms having a positive balance, with households being overdrawn.

    Firms distribute profit to households (with payment effected the same way), leaving all balances at zero for the end of the period. In principle, any household could carry a positive balance to the next period, thereby deferring consumption, but they can only do so if some other household runs a negative balance and, as we are assuming identical households, this does not occur.

    There is an equilibrium set of prices (and wages) which achieves the optimal relative consumption between periods and balance between consumption and leisure within each period.

    We now want to consider a change in B, resulting in future consumption being valued more highly, whilst holding the set of prices and wages fixed. It is convenient to specifically consider that, at the start of period t, there is a change in the value of B that applies for discounting from period t+1 to period t, but there is no change in the value of B for discounting from all subsequent periods back to period t+1. In the limited scenario we have here, I think this implies there is no impact beyond the current period.

    In equilibrium, current consumption is given both by the Euler equation: u'(c) = u'(c*)Bp/p*, and by the balance between consumption and leisure: u'(c) = v'(n)w/p where w and p are wages and prices and * indicates the value for the next period (I'm assuming nominal interest of zero). With no change in the set of wages and prices, when B rises one of these conditions for current consumption must fail.

    If we allow households and firms to trade labour for goods, they will do so up to the point where u'(c)=v'(n)w/p. At this point, we have u'(c) < u'(c*)Bp/p*. Households would like to sell some of their current goods in return for a positive balance at the bank, thereby deferring consumption. But they will find no takers at the fixed price, because everyone is on the same side of the trade.

    If we disallow the barter exchange of labour for goods, households can only obtain goods through monetary exchange (that is through the process of credits and debits at the Bank). Since this now involves them giving up future consumption, they will only do so to the point where u'(c) = u'(c*)Bp/p*. This obviously involves a higher rate of consumption than in the barter case.

    I apologise if you feel that you have already addressed this in your exchange with Nick Rowe and I understand if you don't wish to go into it again. It's just that I've read through your comments and I just don't see it, so I feel I must be missing something fundamental.

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    1. "higher" in the last sentence of the penultimate paragraph should read "lower".

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    2. There are no exchanges disallowed in Woodford's model. What is going on is that the firms are sometimes constrained in the prices they set. He's got a story in there about prices being set in terms of money, and the central bank affecting the relative prices, but that's not relevant for thinking about how the exchange actually takes place, which is the same as it would be if we just took the baseline stochastic growth model with monopolistically competitive producers. Consumers are trading subject to their budget constraints, and firms sell their output and pay their workers, with some profits that need to somehow be rebated to consumers (they own shares in the firms, say). Just as in standard GE, it's not critical exactly how the exchange takes place, and there can be different ways to describe it. Typically we don't describe it - because it doesn't matter. Everyone is optimizing, there's an equilibrium concept, and that's all we care about. You can think of everything happening simultaneously, with workers paying for their consumption goods with their wages and share income, which are paid in goods - which of course are the revenues the firms receive from the consumers. If you don't like that, think of the consumers paying for the goods with IOUs, which the firms use to pay their workers, and then all the IOUs are settled at the end of the period. You don't need money to execute any transactions in Woodford's world, and no one ever holds the stuff.

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    3. I appreciate that in a state of general equilibrium it's probably not going to make any difference what individual exchanges take place. But what about the situation where some or all prices are stuck so that not all markets clear? Can it then be possible that the outcome depends on which exchanges are permitted? In my description, whether households end up long leisure / short future consumption or long current consumption / short future consumption depends on whether the direct leisure / goods trade is permitted.

      Or maybe the answer is that my scenario makes sense, but just that it's not a good reflection of Woodford's model. Quite possible.

      Whether there is actually any money in my set-up is an interesting question and maybe just down to interpretation. I described it in a way that implied non-zero intra-period balances. But imagine each period is a day and the guy who does the ledgers at the bank doesn't get round to doing the books till after close of business. He just collects up all the payment instructions and makes the entries which always cancel out. There's no time stamp on the payments - only the day is relevant, so there is never a non-zero balance existing for any meaningful period of time. I don't think it's obvious that there is any actual money in this situation. It still relies on the third party entity (the Bank) though, rather than bilateral credit as with the IOUs.

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    4. "But what about the situation where some or all prices are stuck so that not all markets clear?"

      In Woodford's model, the prices are not going to be market clearing prices in terms of the equilibrium concept that is used, say, in the underlying model with flexible prices. So Woodford needs another equilibrium concept. He assumes that a firm that cannot change its price in the current period has to serve all the consumers that want to purchase the firm's good at the fixed price. So, that's just another kind of equilibrium. Any fixed-price or fixed-wage model has to deal with the problem of how to redefine equilibrium. But this has nothing to do with the process of exchange. Money in Woodford's model is not money as we know it - it's not a medium of exchange. It's just a unit of account relative to which we can define what price stickiness means. In actually monetary models, it's critical how exchange takes place, and the role money and other assets play in exchange. But that's not what Woodford is about. What he wrote down is not a monetary model.

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    5. I'm grateful to you for taking the time to engage on this - I'm finding it extremely informative. I think it has also finally clicked why it has taken me so long to understand your point.

      It strikes me that it makes quite a bit of difference here exactly what price inflexibility we are talking about. If we assume, say, staggered price setting, but fully flexible wages, then we will always have a situation where both the Euler equation and the equation relating labour and consumption hold. In that case, there is no arbitrage in a barter trade between labour and consumption, so it makes no difference whether we assume barter or monetary exchange. The same applies if we assume sticky wages, but fully flexible prices.

      In the scenario I had been describing, both wages and prices were independently sticky. In that case, you can't have both marginal conditions fulfilled at the same time, so there needs to be something that determines which one holds. This is where I believe it matters whether or not it is assumed that barter exchange is possible, but I don't think Woodford goes into this.

      Beyond the unit of account, this is the only way in which monetary exchange has any role in the model. Therefore, as we move towards the limiting case of fully flexible wages (or prices), then any distinction between a barter economy and a monetary economy disappears. Money becomes, as you say, like stardust - just a reference price.

      So I think I would agree with you that, at least in the benchmark fully flexible wage version, that monetary exchange is irrelevant in the Woodford model.

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  7. Yes, but Woodford's model does exclude barter in the sense that it requires exchanges to take place through a common standard, a medium of account. Agents cannot directly negotiate quantities and bypass the MOA in their exchanges, which is why relative price distortions can cause dislocations. Nick Rowe above is right that if barter, defined as directly negotiating exchanges without reference to some MOA was possible, the NK recession goes away. This is not like the old Fama Accounting System of Exchange where it truly is a non-monetary system equivalent to barter; exchanges here must take place through MOA prices and thus bypassing the price system through direct barter is not allowed in the model. The mechanics of the exchanges don't seem to matter but they do in the sense that they must happen through the MOA standard for the NK model to mean anything.

    This doesn't necessarily mean that Nick Rowe is right that a MOE is hiding in the cashless model as bonds. It is at least possible that the MOA in the cashless version is what Buiter called phlogiston, i.e. a mere government definition that cannot by owned (and cannot be an MOE), but happens by some focal-point magic to successfully select a determinate, non-explosive price level equilibrium. Woodford is not entirely clear in his responses to these criticisms as he seems to conflate those that accuse him of leaving the money supply out of the explicit equations in the standard model with those who focus on the cashless version where no reserve balances or currency exist at all.

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    1. "Agents cannot directly negotiate quantities and bypass the MOA in their exchanges, which is why relative price distortions can cause dislocations."

      I don't entirely agree with this. I think relative prices distortions give you dislocations (demand / supply mismatches?) whether you have barter or not - it's just you get different ones (and less optimal ones) if you restrict the ways exchange can take places.

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    2. "it requires exchanges to take place through a common standard, a medium of account."

      No, that's just how prices are defined (see my reply above). Nothing to do with what is exchanged for what - just the terms of exchange.

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    3. To make this clearer (hopefully): In any general equilibrium model in which money plays no role, for example an Arrow-Debreu model, which is the most general, all that matters are relative prices. So, in writing the theory down, I could for example define any good to be the numeraire, and define all prices and quantities in terms of that numeraire. But it doesn't matter how I choose the numeraire - the equilibrium relative prices don't change as a result. In fact, I could choose some extraneous object to be the numeraire if I wanted to. This would be an object that plays no role in the model - it doesn't enter preferences or technology. Call it stardust, say, define all other prices in terms of stardust, and it doesn't matter. The equilibrium relative price of peaches today in terms of oranges tomorrow is still the same. To start with, that's what Woodford does. He says, basically, that stardust is the numeraire, then expresses all prices and quantities in terms of stardust. If that's as far as he went, it would not matter. But, he also says that it may be costly (in fact infinitely costly in some specifications) to change a price in terms of stardust. Not only that, he says that there is a central bank, and the central bank has the power to set the price of stardust tomorrow in terms of stardust today. But that's all he does. This doesn't mean that stardust is a medium of exchange. It's not. Stardust is a unit of account - it's the numeraire. And that matters because changing a price in terms of the numeraire - so defined - is costly. How does exchange take place? Exactly as it does in the economy in which we never bother to think about stardust. But our stardust economy is different because the relative prices can be messed up, and the central bank has the power to fix that problem.

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    4. wow, a model of clarity. But kudos to Nick Rowe whose nonsense and limited competence was actually helpful in elucidating the Woodford model. Actually Mr Rowe plays this role many, many times, so thanks to him for being brave enough be the student who asks dumb questions so others can understand.

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    5. Yes, you'll see I got a little snippy with poor Nick. This was certainly not a waste of time, at least for me, as I think I better understand exactly what is going on in these models.

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  8. Indeed, you should use David Levine's take-down of all the nonsense Keynes/Hicks/Samuelson/Krugman have been peddling for years. Thus you can fail out anyone with heretical views. I love it when you convincingly repudiate the idiocy of the likes of know-nothing hicks like Hicks and Paul Samuelson, and show that you've discovered that these Nobel Laureates have all be repeatedly making a very basic error, and that there is no such thing as demand shortfalls.

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    1. I'm not sure how Hicks and Samuelson entered the discussion. Obviously you think there is such a thing as a demand shortfall. So tell me exactly what it is so that I can understand it.

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