Friday, March 20, 2015

No One Expects the Spanish Inquisition: More on D.K. Levine and J.M Keynes

I guess I shouldn't be surprised. David Levine's piece on Keynesian economics appears to have generated plenty of heat. See for example the comments section in my post linking to Levine. I'm imagining an angry mob dressed like the Pythons, as in the photo above, running through the streets of Florence looking for Levine. Each has a copy of the General Theory, and they're aiming to inflict torture by taking turns reciting it to David, until he renounces his heretical writings.

What drew my attention to Levine's piece initially were blog posts by Brad DeLong and Nick Rowe. 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.

In any case, I thought Levine's example was interesting, and I'd like to follow John Cochrane's suggestion of filling in some of the spaces, which will require some notation, and a little algebra. First, adding to David's addendum, let's generalize what he wrote down. This is just a version of an economy with an absence of double coincidence of wants. If any two people in this world meet, it will never be the case that each can produce what the other wants. It's roughly like Kiyotaki and Wright (1989), except with 4 goods instead of 3. And of course there are some very old versions of the double coincidence problem in the work of Jevons and Wicksell, for example. Brad DeLong, who reads the old stuff assiduously, perhaps missed those things.

Commodity Money
Let's first imagine a world with T types of people, indexed by i = 1,2, ..., T. There are many people of each type. Indeed, for convenience assume that there is a continuum of each type with mass 1. A person of type i can produce one indivisible unit of good i at a utility cost c, and receives utility u from consuming one indivisible unit of good i + 1 (mod T) (i.e. T + 1 (mod T) = 1 ). We need n >= 3 for a double coincidence problem, and n will matter for some elements of the problem, as we'll see. A key feature of the problem will be that each person can meet only one other person at a time to trade - that's a crude way to capture the costs of search and exchange. We could allow for directed search, and I think that would make no difference, but we'll just cut to the chase and assume that each person of type 1 meets with a type 2, each type 2 meets with a type 3, etc., until the type T - 1 people meet with the type Ts. Further, we'll suppose that, as in David's example, good 1 is perfectly durable and costless to store, while all the other goods are perishable - they have infinite storage costs. Assume that u - c > 0 (with some modifications later).

A key element of the problem is that the indivisibility of goods fixes the prices - indeed, in a Keynesian fashion - so long as we only permit these people to trade using pure strategies. That is, David assumes that when two people meet they both agree to exchange one unit of a good for one unit of some other good, or exchange does not take place. But let's do something more general. Suppose that 2 people who meet can engage in lotteries. That is, what they agree to is an exchange where a good is transferred with some probability, in exchange for the other good with some probability. Then, the probabilities play the role of prices. That is, with indivisible goods, we can think about an equilibrium with lotteries as a flexible price equilibrium, and the Levine equilibrium, where one thing always trades for one other thing, as a sticky price equilibrium.

This sounds like it's going to be hard, but it's actually very easy. Work backwards, starting with a meeting between a type T - 1 and a type T. Trade can only happen if type T-1 has good 1, which is what type T consumes, so suppose that's the case. We have to assume something about how these two would-be trading partners bargain. The simplest bargaining setup is a take-it-or-leave-it offer by the "buyer," i.e. the person who is going to exchange something he or she doesn't want for something the "seller" produces. The buyer has one unit of good 1, which is of no value to him/her, so the buyer is willing to give this up with probability one. Since u > c, the seller is willing to produce one unit of good T in exchange, so the optimal offer for the seller is in fact the Levine contract - one unit of good 1 in exchange for one unit of good T. And the same applies to the meetings where types 2, 3, ..., T-1 are the buyers.

But, the type 1 people - these are the producers of the commodity money in this economy - are different. Unlike the buyers in the other meetings, they have to produce on the spot. And, since they make a take-it-or-leave it offer, they are in a position to extract surplus from sellers - and they do it. So, the trade they agree to is an exchange where each type 2 person produces one unit of good 2 and gives it to a type 1 person, and the type 1 person agrees to produce good 1 with probability p(1), where
So, in equilibrium, only a fraction c/u of each of types 2, 3,..., T gets to consume, and all the type 1s - the money producers - consume. There is a welfare loss from this commodity money system, in that the money producers are extracting seignorage from everyone else. In the fixed price equilibrium, where everyone has to trade one unit of a good for one unit of another good, the type 1s are worse off, and everyone else is better off.

Now, consider a "demand shock." That is, suppose that all the type T people receive utility u* from consuming, where u* < c, and everyone else is the same as before. A point I want to make here is that the Keynesian failure can come from anywhere in the chain - it need not come from the money producers. If we consider the flexible price, or lottery, equilibrium, now the type T - 1 buyers have to do something different in order to get the type T sellers to produce. It is still best for the buyers in these meetings to offer their commodity money (good 1) with certainty, but the take-it-or-leave-it offer the buyer makes involves the seller producing with probability
Further, now it is possible that, because the type T - 1 buyers get a bad deal, they won't be so willing to work when they are trading with T - 2 buyers. Indeed, in this equilibrium (if there is one - more about that later), we can work backward to determine that a type i person will produce with probability
What the type 1 and type 2 people do is potentially a little different, because this involves the behavior of the type 1s, who are the commodity money suppliers. Again, working backward, we can show that an equilibrium will exist if and only if
If that inequality does not hold, then there is not enough total surplus in this economy to support trade, and everything shuts down. But, if (4) holds, then the solutions for p(1) and p(2) are:
So, the effects of the "demand shock" could be transmitted back in the chain, even to the commodity money supplier if the problem is severe enough, i.e. if u*/c is very small. This is quite interesting, as what is going on is that financial arrangements (albeit crude ones - this is just a commodity money system) propagate "shocks." A decline in demand in one sector gets transmitted to others. And all this interconnection and specialization could in fact shut the economy down - even without sticky prices.

Note that I'm putting "demand shock" in scare quotes. Why? Because, in spite of the fact that the comparative static experiment involved a decline in the utility type Ts receive from consuming, it affects everything a type T does, in particular his or her labor supply. Why work if you don't like to eat? This illustrates why terms like "demand shock" and "demand deficiency" have no meaning in a properly specified general equilibrium model. This is a standard criticism of IS/LM models that goes back to at least the mid-1970s. For example, the IS curve is shifting because the behavior of some consumers changed, but those consumers are the same people who are supplying labor in the labor market, and holding money in the money market. Why don't we take account of that? Why indeed. Spelling these things out in the model means you don't miss that, which could be very important.

The next step is easy, as Levine already did it. If prices are fixed (all trade is one thing for one other thing), then the "demand shock" will shut everything down. The flexible price lottery equilibrium is, as far as I can tell, Pareto efficient, so that's a useful benchmark. So note first that having this economy shut down - in this extreme example - will sometimes be efficient, if (4) does not hold. Thus, in that case, the fixed price equilibrium is actually OK. But that's not what interests us. Suppose u* < c, but (4) holds. Then clearly the fixed price equilibrium is not Pareto efficient. But how would we fix it? David goes through some possibilities, but the key message is that, if the government is going to intervene in this world in a good way, it has to redistribute. Somehow the government has to move surplus to type Ts from everyone else, so that the type T's are willing to trade. If the shocks are causing some inefficiency, we can't correct the problem through some blunt policy which says the government should just buy some stuff, and it really doesn't matter what. Indeed, it does matter, and this crude model is an illustration of that fact.

As well, note that a typical justification for thinking about the sticky price equilibrium rather than the flexible price equilibrium, is that pricing is hard for the people in the model to figure out. Indeed, that's the case here. People sometimes argue that mixed strategies (as in the flexible price equilibrium) are very difficult to implement in practice. But that doesn't let the government off the hook. If it wants to correct the incorrect pricing - the prices are the wrong ones in the sticky price equilibrium - they have to do so by replicating the flexible price equilibrium, and that involves lotteries. That's just an example of a general problem in Keynesian economics.

Fiat Money
So, you might wonder why we would worry about a commodity money economy, if that's not the type of world we currently live in. Well, it's not so hard to extend the idea to a fiat money economy. Some things change in an interesting way, but the basic idea stays intact. We're going to work in an overlapping generations framework. Samuelson's OG model is not used so much anymore, but it was a standard workhorse for monetary economics at the University of Minnesota until about the mid-1980s. For this example, it works nicely.

The people that live in this world look much like the people in the commodity money economy, except they each live for two periods. They can produce an indivisible unit of the current perishable consumption good when young at a cost c, and receive utility u from consuming an indivisible unit of consumption good when old. Each period, a continuum of two-period-lived people with unit mass are born. In period 1, there is a continuum of old people who live only one period. The initial old each receive utility u from consumption of one unit of the consumption good, and each has one unit of indivisible fiat money. We'll make the bold assumptions that fiat money cannot be counterfeited, and that it is perfectly durable. Each period, each young person is matched with one old person.

We'll suppose, as in the commodity money economy, that in a meeting between a young person and an old person with money, the old person makes a take-it-or-leave-it lottery offer to the young person. This is actually easier to analyze than the commodity money equilibrium, as the initial old people want to give up their money no matter what - they're not like the commodity money producers who have a cost of producing money. So, here the flexible price equilibrium and the fixed-price equilibrium are the same thing. Each period, every old person exchanges one unit of money for one good produced by a young person, every young person receives utility -c + u > 0, every initial old person receives utility u, and money circulates forever.

Now, suppose that sometime in the future, in period T, utility from consuming is lower for all the people who are born that period, i.e. they receive u* from consuming when old, and u* < c, just as before. Again, this is easier than in the commodity money case, as this economy will not shut down under flexible pricing. Letting p(i) denote the probability a young person produces in a trade with an old person, we get
which should look familiar from the commodity money case, but now this holds for all t = 1,2,...,T. But for t = T+1, T+2, p(i) = 1 as before. So now we get a temporal interpretation of the idea. Future anticipated shocks propagate backward in time.

As in the commodity money economy, everything shuts down if everyone has to trade at fixed prices. In period T, the young will not accept money, and so by induction no one will. Here, just as with commodity money, the problem in the fixed-price economy is not a monetary problem - it's that the prices are wrong. It's always puzzled me, for example, why Mike Woodford thinks of his models as prescriptions for how central banks should behave, as the relative price distortions that exist in those models look like problems for the fiscal authority to work on. I haven't worked out the details, but I think that a policy that would work in the fixed price equilibrium is to simply replicate the flexible price equilibrium with a sequence of taxes on old agents (random confiscations of money) and subsidies for the young (random transfers of money). You can do something similar in a Woodford model with consumption taxes (see this paper by Correia et al.).

We could also think about unanticipated preference shocks in this model. For example, suppose the utility of consumption for old persons is a random draw, which they learn when they are young. With probability q they receive u*, and with probability 1 - q, they receive u. Then, we can construct an equilibrium in which the young produce with probability s* when their utility when old will be u*, and produce with probability s when their utility from consuming when old will be u. For an equilibrium to exist requires
So the economy shuts down unless the unconditional expected utility of a given agent who always receives his or her consumption good when old is not negative. If an equilibrium exists, then s = 1, and
Therefore, the random preference shocks produce random business cycles in which production and consumption are low in bad states and high in good states. But these cycles are efficient. Low demand for goods means low willingness to work, but note that this doesn't mean that the person with the "demand shock" consumes less. They work less and supply less consumption goods.

As in all the previous cases, if prices are fixed, then this economy shuts down because of these demand shocks. There is always a positive probability that the young next period will not accept money, so it is not valued in equilibrium and there is no trade. Again, the problem is that the prices are wrong. A fix for this is for the government to step in, if it can, and replicate the allocation that was achieved under flexible prices. What should work is that, when a bad shock is realized (the young learn that their utility from consumption when old is u*), the government taxes money away from old people, at random, and gives it to young people, again at random. Note that this doesn't involve running a deficit - it's a tax/transfer scheme with taxes = transfers. Again, the cure is redistribution. Further, note that an optimal allocation has cycles - it's not optimal to smooth the cycle completely, even if that were possible (and I'm not sure it is).

So, I think this is an interesting example. It's obviously special, and we wouldn't take it to the U.S. Treasury and tell them about it, hoping to influence their decisions. The message is that whatever anyone thinks they know about "Keynesian" ideas, and the "Keynesian" policies derived from those ideas, they should reconsider. There's nothing obvious about that stuff. We can write down coherent models in which Keynesian phenomena occur, and the optimal policies don't seem to look like anything like that Paul Krugman recommends. And it's not because his IS/LM model is "right." Far from it. We understood that long ago.


  1. This column appeared on 16 March:

    There's a lot of Keynesian macroeconomics in modern research, but it suits the political agenda of Krugman and de Long to ignore it. They are not interested in economics but political persuasion.

    1. "They are not interested in economics but political persuasion."

      Seems misdirected. Why do they need to discredit the economics profession to further their political ends?

  2. Very nice.

    One thing strikes me in your fiat money version. You are considering a scenario where there is a fall in the expected relative utility from future consumption. However, I think the typical Keynesian scenario would be one where there is a rise in the relative expected utility of future consumption, i.e. where people decide to consume less today and more tomorrow.

    This seems to be just a consequence of your set-up where agents consume only when old. The choice for agents then, whilst appearing to be an intertemporal one is really just a choice between leisure and consumption. Which, may indeed be an issue, but it doesn't strike me as being the issue that Keynesians tend to be concerned with.

    It would be interesting to know what would happen if you extended your model, in line with Samuelson, so that agents consumed in their first year of life as well. To analyse Keynesian arguments, you could then look at what happens when there is a shift in preference between current and later consumption. (Ideally this would be done so as to eliminate any substitution effects between consumption and leisure, so as to isolate the relevant effects.)

    I think that would then be getting closer to the sort of issues that Keynesians have in mind.

    1. Basically what matters is that people work, earn money, and spend it on consumption goods. We could add intertemporal choice in consumption plans and I don't think it would make a lot of difference to the basic idea. What "Keynesians have in mind" are many things. And for every person with a "Keynesian" idea, there is another who claims the idea is "not Keynesian." "Interest and Prices" is definitely not what Keynes had on his mind.

    2. Yes, Leijonhufvud and Clower argued in the 1960s that the economics of Keynes is not the same thing as Keynesian economics. Sticky prices/wages was what Robinson called "bastard Keynesianism". Krugman and de Long are bastards. Cooper, Diamond, Bryant, Angeletos are more the real descendants.

    3. "And for every person with a "Keynesian" idea, there is another who claims the idea is "not Keynesian." "

      This is true. And I have no interest in arguing over what "Keynesian" really means.

      Nevertheless, I do think there are scenarios in which I think a deficit would be welfare improving. And I do think that can illustrated in set-ups similar to yours. (I'm pretty sure what I described would do that.)

      I think your model and Levine's are very interesting, but it looks to me that you are deliberately only considering scenarios where deficits are (fairly obviously) not going to be effective.

    4. A good question to ask is why we should care whether any piece of research captures "what is on the minds of Keynesians." Surely that's not helpful if you want science to move forward.

    5. " are deliberately only considering scenarios where deficits are (fairly obviously) not going to be effective."

      The only thing I'm deliberately doing is trying to make sense out of Levine's example. I have papers (published and unpublished) in which government debt matters, and running a deficit can be a good idea. There are old tax-rate-smoothing arguments for running deficits and surpluses. None of those things has anything to do with sticky prices, sunspot equilibria, or other such "Keynesian" ideas.

    6. OK, fair enough. Maybe my comment should have been directed at Levine only.

      I was thinking about your commodity money set-up and how this might be tweaked into a fiat money version. I wondered whether you'd think the following made sense.

      Take your basic scenario (without the lotteries for the moment), but make all goods perishable. However, we provide for all agents to have an account with a central registry. The registry records a number of units for each agent, which may be a positive or negative number. The aggregate number of units is zero.

      Exchange is carried out against these units, one unit for each good, with the registry recording the transfer.

      Rather than producing in each period, each agent has a random chance of being able to produce with a given probability. If the agent is able to produce, they can choose whether or not to produce their good at cost c. Otherwise, they do not produce and there is no cost.

      As agents do not produce in each period, they cannot consume in every period, so they have to choose which periods to consume in. They will not necessarily consume in the same periods in which they produce. Any difference is carried forward in the holding of units at the registry.

      Units are the only way of storing value from one period to the next, as indeed they are the only way of storing value between meetings within the same period.

      I think this set up allows for an interesting co-ordination failure. Let's define m as the value that agents place on the holding of their marginal unit, based on how they expect to use that for future consumption (or future leisure). Then it seems we may find ourselves in a position where m > u > c. In this situation, there would be a clear benefit in production and consumption within the same period, provided that could be co-ordinated. However, in separate individual exchanges, no-one is prepared to part with units in exchange for goods.

      Do you think there is anything in this?

    7. Yes. Let me put it another way. It's well-known that, in models like this, we don't need money if recordkeeping is sufficiently good. That's Kocherlakota (1998) "Money is Memory." So, consider the overlapping generations economy in the "fiat money" section, but take the money out. Now, think of this as a dynamic game. Each period, old people are matched with young people. And a young person can produce one good for an old person, or not (rule out the lotteries, to keep it simple). There's always an equilibrium where the economy shuts down. If each young person thinks that they will get nothing from the young person in the next generation, he or she will not produce anything. But suppose that every young person believes that, if they produce today for an old person, then in the next period an old person will produce for them. But, if they fail to produce today, everyone knows that, and no one will produce for them tomorrow. There are then implicit "punishments" that enforce good behavior. It's a kind of credit system, and it depends on memory, i.e. the knowledge of the past bad behavior of others.

      A nice model for handling things like that is the Lagos-Wright construct, where everyone lives forever (instead of 2 periods, as in an OG model). That allows you to mix money and credit, have banks in the model, etc.

  3. As I puzzled through your post, trying to put meaning (to me) with your words, I tried allowing Type 1 to make inexpensive 'silver spoons'. Silver spoons worked well as 'money' but soon everyone had silver spoons. This was also good, as silver spoons could be the plus-or-minus for every trade of fixed value (three things were traded at each exchange (two items and silver spoons)).

    I have not yet figured out how to make the probability equations work. I understand that utility will always be greater than cost (c), with utility (u) always in the mind of the buyer. Using your formula p(1) = c/u, we would notice that no trade would happen unless the probability was less than one.

    Perhaps the potential for three-item exchanges is the source of my incomprehension. It seems like the probability should equal near one for every three-item exchange.

    1. 1. There are no three-item exchanges. In the commodity money economy, there are only exchanges in which one person has the commodity money (or can produce it, in the case of type 1), and the other can produce the good the person with the money wants. In the exchange between a type 1 and type 2, the type 1 makes a take it or leave it offer, and chooses p(1) and p(2), which are the probabilities that she hands over a silver spoon to the type 2, and the probability that type 2 hands over the type 2 good to the type 1 person. Type 1's utility from the trade is:

      (1) - p(1)c + p(2)u

      and type 2's utility is:

      -p(2)c + p(1)p(3)u

      But we already know (from working backward) that p(3)=1. Now note that

      (2) -p(2)c + p(1)u = 0,

      since if this were not the case, either type 2 would not want to produce, or type 1 could lower p(1) and make herself better off. So, subsitute for p(2) in equation (1) using (2), and the problem of type 1 is to choose p(1) to maximize

      p(1)c[-1 + u/c]

      Now note that (2) implies p(2) < p(1). And p(1) is a probability, so p(1)<=1. The objective function tells us that p(1) is chosen to be as large as possible, so p(1) = 1 and p(2) = c/u. This makes the type 2 indifferent to trading, and minimizes work effort for the type 1.

    2. Thanks for the detailed answer. I need to do additional thinking and relating to make this all jell together cohesively.

  4. "I'm imagining an angry mob dressed like the Pythons, as in the photo above, running through the streets of Florence looking for Levine."

    This is just sad. It's stated quite clearly at the beginning of the famous sketch that the action begins in Jarrow, on New Year's Eve 1911. Your reluctance to study the classics will get you into trouble some day.

    1. But they won't find Levine in Jarrow. They have to go to Florence.

    2. I should add, for people who can't figure this out, that Kevin is referring to the Jarrow march against unemployment:

      I don't think that Levine has got something against the unemployed, which brings up another issue. A common tactic of Keynesians is to counterattack against objections to Keynesian economics by inferring, or stating outright, that if you object to Keynesian economics, you must hate the unemployed. That's nonsense.

    3. Apologies. I hadn't realized Levine is based in Florence. No, I wasn't referring to the Jarrow march, though for all I know that might have inspired the Monty Python sketch. It begins with a caption (implausible given the background) indicating that we are in Jarrow, in the dying moments of 1911 (see link below). Nor do I suppose Levine has anything against the unemployed themselves, as opposed to the concept of involuntary unemployment, which evidently does bug him.

    4. Incidentally I agree that one shouldn't make inferences about political leanings from attitudes to Keynes. Greg Mankiw can fairly be called a Keynesian, whereas I don't see anything especially Keynesian in the writings of Amartya Sen or Thomas Piketty. But you won't see Sen or Piketty advising a Republican president. Probably the simplest way to identify a Keynesian is to pose the question: do the notions of (a) aggregate demand deficiency, and (b) involuntary unemployment, make sense to you? There's a correlation between reactionary politics and hostility to Keynes, but partly that's thanks to various confounding variables like hostility to FDR, devotion to Hayek etc. The antagonism of Bob Lucas to Keynesian ideas seems to be more aesthetic than political.

    5. We are constantly asking questions about everything. That's how any science sorts things out. I wouldn't characterize it as "hostility" to question Keynesian ideas. I also wouldn't characterize Lucas as objecting to the aesthetics. There's a well-reasoned scientific objection there.

    6. "Probably the simplest way to identify a Keynesian is to pose the question: do the notions of (a) aggregate demand deficiency, and (b) involuntary unemployment, make sense to you?"

      Then, I guess a Keynesian is someone who is:

      (a) wedded to a particular model. "Demand deficiency" and "involuntary unemployment" have a particular meaning in terms of a particular model or models. We can write down models of Keynesian-like phenomena in which those terms have no meaning. A true Keynesian is not willing to think about anything but IS-LM, or some such, so they are going to reject it out of hand.

      (b) Not scientific: "Demand deficiency" is not something I can objectively observe. Like the Holy Ghost, I can claim its existence, but I can't show it to you. Similarly, "involuntary" is not scientifically useful in economics. It seems that what Keynesians mean when they say "involuntary unemployment" is that a person is in a state in which they are inefficiently unemployed. But that doesn't have anything to do with what the person who is unemployed will tell you. I could tell you that I am unemployed and would like to be employed, that I am working half-time and would like to work full-time, that I would really like to live in a better house. But that doesn't tell an economist anything he or she needs to know about whether government policy can improve the aggregate state of the world.

  5. This *is* an interesting post Steve. I'm getting more out of it than David Levine's post. But I *think* (I'm not sure, because I'm not sure I understand it) there's a big empirical problem with it.

    Good 1 is gold, and all the other goods are services. Type T people want gold to fix their teeth, and everybody else only wants gold to use as money. u* is the utility type T people get from having their teeth fixed. As u* falls, the price of gold falls. If u* falls too far, gold producers stop producing gold, so there is no gold, so all trade stops.

    If we measure all prices in gold, a fall in the price of gold means a rise in the price of all other goods. Recessions would be associated with inflation, or even hyperinflation. And gold producers stop producing gold in recessions because it doesn't cover the cost of production, and that's what causes the recession. Money disappears.

    It's the same problem with your fiat money example. People fear that paper money will become worthless in future, so it becomes worthless today, so trade stops because money is essential to trade, and the only good that can serve as money becomes worthless.

    I think that works fine for the Zimbabwean recession, where trade became very hard because the Zim dollar became worthless, but we normally associate recessions with disinflation or deflation.

    1. Nick

      I'd be interested in your view on the variation I outlined above at 2.07. Maybe closer to how you'd see it?

    2. Nick E: If you add interest on balances at the central registry (central bank) to your 2.07 model, and allow the central bank to choose that rate of interest, I think you now have Woodford's model. See my comment on Steve's next post. (It's my red and green money example, where red notes have negative value.)

  6. Well, this example wasn't set up to capture all the empirical facts. It's pretty simple, and extreme. But, of course in the fixed price equilibrium, prices are fixed. That's all there is to it. Lower demand enough, and the quantities fall - dramatically. You're not seeing a hyperinflation - you're seeing nothing - no quantities traded, so no prices.

    In the commodity money equilibrium with flexible prices, I think it's pretty nice. The commodity money can be traded even if the person who consumes the commodity does not value it very much. A demand shock anywhere in the chain - not just at the end - will in general lower the price of the commodity in some market or markets. Do you have a problem with the idea that a decrease in the demand for money lowers its price? I don't.

  7. In your fixed price equilibrium, a drop in the industrial demand for gold causes the gold miners to stop producing gold, so all gold is in someone's mouth, and there is no gold to use as money, so trade stops. But recessions don't look like that. Sellers of goods and labour are even more willing than usual to accept gold in exchange for goods and labour. They search harder to find a buyer who will pay gold. They don't refuse to accept gold because the industrial demand for gold has disappeared. The unemployed head off panning for gold, because the opportunity cost of gold mining has fallen.

    With flexible prices, a fall in the industrial demand for gold will reduce the price of gold in terms of other goods. I have no problem with that. But we normally associate gold standard recessions with a rising price of gold in terms of goods. Like in the 1930's. Until Roosevelt raised the price of gold in terms of dollars, which helped end the recession.

    1. "Sellers of goods and labour are even more willing than usual to accept gold in exchange for goods and labour."

      You've read their minds?

    2. "But we normally associate gold standard recessions with a rising price of gold in terms of goods. Like in the 1930's. Until Roosevelt raised the price of gold in terms of dollars, which helped end the recession."

      During the Depression, we weren't trading commodity money. You're getting way too involved with issues this crude little example obviously wasn't set up to deal with.

    3. I can't read their minds, but I have no reason to disbelieve what they tell me. Plus we can observe their increased efforts to find buyers, and buyers' reduced efforts to find sellers.

      In Cuba in the mid-1990's it looked very different. The underemployed did not want money, because there was nothing in the stores they could buy with extra money. I observed line-ups to buy things, and snarly sellers. In a Canadian recession I observe line-ups to sell things, and snarly buyers.

    4. Let me try another approach. Some of what you are talking about - what went on during the gold standard for example - might be explained by a flight to safe assets. That's not in Levine's example of course - he just wants to strip it down so there's no credit, no aggregate risk, etc. You could tie together historical episodes when gold, for example, was more important, with modern episodes in which people flee to government debt they perceive as relatively safe. I've got models of safe asset shortages, if you're interested, and I think those might be used to address these historical episodes.

    5. I see recessions as more of a flight to the medium of exchange. A flight to safe assets might cause that flight to the medium of exchange, but it's the excess demand for the medium of exchange that is the immediate cause of the recession.

      In a recession it takes more effort to sell illiquid goods (like labour and houses) for the medium of exchange, and it takes less effort to buy illiquid goods for the medium of exchange. When keynesians talk about an excess supply of labour and goods in a recession, that's just a crude way of talking about the extra effort required to sell them, and the extra ease of buying them.

      When we talk about some goods being "illiquid", I think we need to distinguish between illiquidity from the seller's point of view, and illiquidity from the buyer's point of view. Because those two types of illiquidity seem to vary inversely over the business cycle, in what looks to me like a systematic way.

    6. Which is one of the main reasons I read you, because you take things like liquidity and monetary exchange seriously, and try to build it into macro models.

  8. My biggest problem with Levine's example is that he uses the wrong shock.

    A reasonable interpretation of Levine's model is that it is a supply shock in a production network. He has a network of producers and suppliers, and there has been a negative supply shock to the producers of a critical component, so that they value consumption (and hence production) less relative to leisure. If prices are allowed to adjust, this isn't a huge problem: the price of the component produced by these suddenly lazy agents would increase, which would induce them to produce more, and induce consumers of their products to substitute away from these. By construction in the example, substitution is impossible, meaning that demand for this input is highly inelastic, and so the reduction in supply would cause prices to move a lot.

    Now if prices cannot adjust, the outcome is much worse: not enough of the critical good is produced, and so overall production plunges. This is a rather extreme form of the negative productivity effects of price dispersion in a sticky price model: here the problem is that RELATIVE prices between different goods are mispriced, resulting in an inefficient productive arrangement.

    Note that it doesn't really matter that this particular good is critical because it can be used as a medium of exchange. It could be any other input into the production network. All that matters is that it is important in the production of other goods, so that if it were unavailable that would make production of other goods impossible, or at least very expensive. Making it important because it is a medium of exchange, rather than (say) a direct input into production, simply means that it enables production by faciliating exchange.

    I would argue that this is very different than what Keynesians have in mind. When Keynesians talk about a demand shock, they usually have in mind something that will requires the real interest rate to fall. For example, instead of shocking the relative preference for leisure over consumption, a very reduced form way of modeling a Keynesian demand shock would be an increase in the discount factor, so that agents become more patient. This would increase agents' demand for future consumption (and leisure), while reducing demand for current consumption (and leisure). Thus agents would like to produce more and consume less, i.e. they want to increase their savings.

    What happens to the equilibrium? In Levine's model, the only means of saving is to hold onto telephones (I think), since they are the only storable good. The gross real interest rate is then the price of telephones today over the price tomorrow. Assuming these prices are fixed at 1, the real interest rate fails to fall to clear the market. The telephone guy makes his telephone, and instead of using it to buy good 2, he just sits on it. Then production shuts down everywhere else. There's your Keynesian demand shock.

    1. "When Keynesians talk about a demand shock, they usually have in mind something that will requires the real interest rate to fall. For example, instead of shocking the relative preference for leisure over consumption, a very reduced form way of modeling a Keynesian demand shock would be an increase in the discount factor, so that agents become more patient."

      When you say "reduced form" you're telling me that you don't know what this "demand shock" is. How are we supposed to know what "Keynesians have in mind" if they can't articulate it? But, suppose that we take your reduced form approach. In the "fiat money" section, if the young person discounts the future more, that's equivalent to a drop in u.

  9. I'll admit that I find your dynamic model difficult to map onto the real world because it conflates the role of money as a medium of exchange and as a store of value, and because it doesn't distinguish between the intertemporal margin and the labor-leisure margin. Thus by construction it doesn't let us talk about the distinction I brought up in my previous comment. In fact, I can think of at least two interpretations of the model: that it's about a store of value that facilitates intertemporal exchange, and that it's about a medium of exchange that facilitates exchange in a production network.

    However, I will try to engage with the model. If I am interpreting it correctly, you are considering a fall in the marginal utility of consumption below the marginal cost of production for one period. Now in terms of aggregate efficiency, the solution should be to not produce in that period -- there's a dynamic inefficiency. That doesn't happen because this would prevent future exchanges by destroying money -- in effect, the supply of money is inelastic, and so the price falls until all money is bought. The fall in the current price of money implies that the expected return on money rises (since its future price is constant), until the producers decide it is worth it to produce. Further, because the current value of money has fallen, the returns on money in earlier periods fall, and so the returns on production fall, and past production. We get backward propagation of the shock.

    As I said above, I find this model very difficult to interpret. First, the "demand shock" is equivalently a "supply shock", and the optimal moneyless policy would be to not produce at all! This doesn't sound like what Keynesians are talking about. Further, if we are thinking of money in this model as a metaphor for a store of value, a higher return corresponds to a higher interest rate, which is just the opposite of what Keynesians are worried about, and supports the interpretation of the model as capturing a supply shock within a system of decentralized exchange, rather than a Keynesian demand shock.

    But then are we really talking about money at all, rather than (say) bonds? If we are really talking about money, then we can interpret the model as being about the generally small delay between when we produce and when we consume, and we're worried about the return to money during this interval. You could argue that this is a metaphor for a nominal interest rate that is too HIGH, since this would imply a greater cost of carrying money. Though this interpretation is a bit of a stretch, and would require a lot more machinery to explicitly include in the model.

    In short, I'm not convinced that this is the right model for critiquing Keynesian economics. It's an interesting model of exchange and money, but it's not clear that it helps clarify anything about the issues Keynesians are concerned about.

    1. Okay, let me expand somewhat on my comment on the dynamic OLG model. I think I now understand how to fit the Keynesian story into the model.

      My two-sentence version of Keynesian economics is that the real interest rate is too high, so that the good/asset markets don't clear at the optimal level of production. Then there is some rationing process (sometimes involving sticky prices or wages) that reduces output down to the level of demand. Now can the model capture this story?

      First let me modify the model slightly, for ease of exposition and greater flexibility: suppose that output is y(t), utility of the old from consumption is u(y), the cost of production is c(y), and the price of output is p(t) (so now p is the price rather than the probability of a match). Further, suppose that the young and old participate in a Walrasian market, rather than negotiating in bilateral meetings.

      Optimal production satisfies u'(y)=c'(y). Call this level y*. The young produce according to c'(y(t)) = p(t)/p(t+1)*u'(y(t+1)). Since we again have a single unit of money, demand from the old is simply p(t)y(t)=1, or unit elastic demand. The gross real interest rate in this economy is p(t)/p(t+1).

      The optimal production process can be achieved if we set prices p(t)=p(t+1) at the level p*=1/y*, which implies a constant real interest rate R=1. Suppose we are in period t, and that p is fixed at p* in all periods after t. Then the real interest rate stuck "too high" in period t would mean that p(t) > p*. Then y(t) demanded would be yd(t) = 1/p(t) < 1/p* = y*, so we have "deficient demand." Moreover, desired production would satisfy c'(y) > u'(y(t+1)), and since y(t+1) = y*, this implies desired production ys > y*.

      Now the economy is demand rationed: The young want to produce more than the old want to buy, but they can't. We need some rationing mechanism, for instance we can bring back the idea of matching probabilities: say the young sell only a fraction of what they produce.

      Now observe that this is the opposite of the sort of rationing you talk about above. You talk about a case where future utility of consumption falls. From the supply equation above, this implies that at the original real interest rate R=1, c'(y) = u'(y(t+1)) falls, meaning that y supplied falls. Then the economy is supply rationed: a fraction of the buyers can't make trades with the young producers, but all producers succeed in selling their output. This is because the interest rate is too low.

      So I stand by my contention that what you present about is a model of a supply shock, not a demand shock.

    2. In general equilibrium the distinction is meaningless, as is the concept of "aggregate demand". Why spend all these words to decide if some shock fits into one of two meaningless categories. Just write papers, man, whoever you are. And don't listen to John D, he's bat-poop crazy.

  10. I am trying to connect 'probability' to monetary transactions but without success. I keep coming up with connections to the roll-of-a-dice or flip-of-a-coin for logical bridges. I also considered market share of a brand as a probability in any one transaction. Nothing I can come up with is making that vital connection with cost-and-utility.

    So I am sorry, this probability model seems to be a dead-end for me.

    1. Roger:

      The probabilities are a rationing mechanism. If the economy is supply rationed, there are more buyers than sellers. Think of showing up at the store and the item you want is out of stock, like flashlights during a blackout, or many basic goods in Venezuela or the Soviet Union.

      Demand rationing looks more like: you are looking for a job, but you can't find one. Or, you produce some goods, but nobody shows up at your store to buy them.

    2. The problem you're having is that you don't understand economics. It isn't physics -- particles don't respond to information about where they are going to be.

    3. The probabilities are in there because that's the easiest way to extend Levine's example so I have something that is the equivalent of flexible prices. It's well known in economic theory that indivisibilities present a problem. When goods can't be divided into little pieces, as is the case here, then some of the nice theorems we have don't hold. But, it's straightforward to handle the indivisibilities and still have the nice theorems, which is to allow for lotteries. Instead of trading one thing for one thing, or not trading at all. I can trade a thing with some probability for another thing with some probability, and then exchange is determined by the "roll of a dice" effectively, though it's a funky dice that we set up in advance to deliver outcomes with the right probabilities. We engage in lotteries all the time - that's what insurance is about. And, when we're indifferent, we might flip a coin to make a decision. However, one of the objections to the use of lotteries in economics is that people will in general have a hard to constructing these in practice, which is why this is not observed in a widespread way. However, that's OK for this example, as those are exactly the kinds of objections some people have to flexible prices - it's a typical Keynesian argument.

  11. Sounds a bit like Jennifer L'ao's “A Traffic Jam Theory of Recessions”

    1. That paper didn't really work out.

    2. I hadn't seen it, and now I've just read the abstract. One reaction is that, if I understand what is going on, "traffic jam" is the wrong analogy. Also, in the model above, with lotteries the shock in the chain dissipates - the effect is smaller the further you are from the source. If the abstract accurately reflects the paper, that doesn't seem to be the case in Lao's model. Why do you say it didn't work out?

  12. " There's nothing obvious about that stuff. We can write down coherent models in which Keynesian phenomena occur, and the optimal policies don't seem to look like anything like that Paul Krugman recommends. And it's not because his IS/LM model is "right." Far from it. We understood that long ago."

    Nope. Simple reduced form short-run general equilibrium models like IS-LM and more complex New Keynesians models lead to the same policy conclusions: at the ZLB monetary policy becomes ineffective and you gotta use fiscal policy.
    Keynesian models (meaning models that feature demand shortfalls, not models that have much in common with the General Theory) have performed empirically quite well during the last years. IS-LM predicted that inflation will remain low, that massive QE will not increase inflation and that fiscal policy will not lead to crowding out.
    Whatever model you used on the other hand, if you used any, to make your hyperinflation predictions a few years ago has not. As I am a scientist I roll with the theory that works empirically.

    1. Nope nope.

      "Simple reduced form short-run general equilibrium models like IS-LM and more complex New Keynesians models lead to the same policy conclusions..."

      IS-LM and Woodford NK are entirely different beasts - not the same policy conclusions at all. NK is sometimes dressed up with the same language, but it's different. Actually, we could never say these two models have the same policy conclusions, as we have no idea in IS-LM what the objective function of the policymaker should be. In NK, that's well-defined.

      "IS-LM predicted that inflation will remain low"

      Where's the inflation rate in the IS-LM model. There is IS, there is LM, the two curves intersect to determine r and Y. The price level is fixed.

      "that massive QE will not increase inflation"

      How would I represent QE in IS-LM. I see M in the model, but I don't see mortgage backed securities, or government debt of different maturities. How am I supposed to think about QE?

      "fiscal policy will not lead to crowding out."

      I thought government spending was supposed to have a large multiplier. You would think we would be doing a lot worse given the behavior of government spending in the US.

      "As I am a scientist I roll with the theory that works empirically."

      You seem to have funny ideas about empirical work.