Nick Rowe Teaches Us a Lot about Apples and Bananas

Last week I wrote a post responding to a post by Nick Rowe about money and coordination failures. Over the weekend, Nick posted a response to my post (and to one by Brad Delong). Nick’s latest post was all about apples and bananas. It was an interesting post, though for some reason – no doubt unrelated to its form or substance – I found the post difficult to read and think about. But having now read, and I think, understood (more or less), what Nick wrote, I confess to being somewhat underwhelmed. Let me try to explain why I don’t think that Nick has adequately addressed the point that I was raising.

That point being that while coordination failures can indeed be, and frequently are, the result of a monetary disturbance, one that creates an excess demand for money, thereby leading to a contraction of spending, and thus to a reduction of output and employment, it is also possible that a coordination failure can occur independently of a monetary disturbance, at least a disturbance that could be characterized as an excess demand for money that triggers a reduction in spending, income, output, and employment.

Without evaluating his reasoning, I will just restate key elements of Nick’s model – actually two parallel models. There are apple trees and banana trees, and people like to consume both apples and bananas. Some people own apple trees, and some people own banana trees. Owners of apple trees and owners of banana trees trade apples for bananas, so that they can consume a well-balanced diet of both apples and bananas. Oh, and there’s also some gold around. People like gold, but it’s not clear why. In one version of the model, people use it as a medium of exchange, selling bananas for gold and using gold to buy apples or selling apples for gold and using gold to buy bananas. In the other version of the model, people just barter apples for bananas. Nick then proceeds to show that if trade is conducted by barter, an increase in the demand for gold, does not affect the allocation of resources, because agents continue to trade apples for bananas to achieve the desired allocation, even if the value of gold is held fixed. However, if trade is mediated by gold, the increased demand for gold, with prices held fixed, implies corresponding excess supplies of both apples and bananas, preventing the optimal reallocation of apples and bananas through trade, which Nick characterizes as a recession. However, if there is a shift in demand from bananas to apples or vice versa, with prices fixed in either model, there will be an excess demand for bananas and an excess supply of apples (or vice versa). The outcome is suboptimal because Pareto-improving trade is prevented, but there is no recession in Nick’s view because the excess supply of one real good is exactly offset by an excess demand for the other real good. Finally, Nick considers a case in which there is trade in apple trees and banana trees. An increase in the demand for fruit trees, owing to a reduced rate of time preference, causes no problems in the barter model, because there is no impediment to trading apples for bananas. However, in the money model, the reduced rate of time preference causes an increase in the amount of gold people want to hold, the foregone interest from holding more having been reduced, which prevents optimal trade with prices held fixed.

Here are the conclusions that Nick draws from his two models.

Bottom line. My conclusions.

For the second shock (a change in preferences away from apples towards bananas), we get the same reduction in the volume of trade whether we are in a barter or a monetary economy. Monetary coordination failures play no role in this sort of “recession”. But would we call that a “recession”? Well, it doesn’t look like a normal recession, because there is an excess demand for bananas.

For both the first and third shocks, we get a reduction in the volume of trade in a monetary economy, and none in the barter economy. Monetary coordination failures play a decisive role in these sorts of recessions, even though the third shock that caused the recession was not a monetary shock. It was simply an increased demand for fruit trees, because agents became more patient. And these sorts of recessions do look like recessions, because there is an excess supply of both apples and bananas.

Or, to say the same thing another way: if we want to understand a decrease in output and employment caused by structural unemployment, monetary coordination failures don’t matter, and we can ignore money. Everything else is a monetary coordination failure. Even if the original shock was not a monetary shock, that non-monetary shock can cause a recession because it causes a monetary coordination failure.

Why am I underwhelmed by Nick’s conclusions? Well, it just seems that, WADR, he is making a really trivial point. I mean in a two-good world with essentially two representative agents, there is not really that much that can go wrong. To put this model through its limited endowment of possible disturbances, and to show that only an excess demand for money implies a “recession,” doesn’t seem to me to prove a great deal. And I was tempted to say that the main thing that it proves is how minimal is the contribution to macroeconomic understanding that can be derived from a two-good, two-agent model.

But, in fact, even within a two-good, two-agent model, it turns out there is room for a coordination problem, not considered by Nick, to occur. In his very astute comment on Nick’s post, Kevin Donoghue correctly pointed out that even trade between an apple grower and a banana grower depends on the expectations of each that the other will actually have what to sell in the next period. How much each one plants depends on his expectations of how much the other will plant. If neither expects the other to plant, the output of both will fall.

Commenting on an excellent paper by Backhouse and Laidler about the promising developments in macroeconomics that were cut short because of the IS-LM revolution, I made reference to a passage quoted by Backhouse and Laidler from Bjorn Hansson about the Stockholm School. It was the Stockholm School along with Hayek who really began to think deeply about the relationship between expectations and coordination failures. Keynes also thought about that, but didn’t grasp the point as deeply as did the Swedes and the Austrians. Sorry to quote myself, but it’s already late and I’m getting tired. I think the quote explains what I think is so lacking in a lot of modern macroeconomics, and, I am sorry to say, in Nick’s discussion of apples and bananas.

Backhouse and Laidler go on to cite the Stockholm School (of which Ohlin was a leading figure) as an example of explicitly dynamic analysis.

As Bjorn Hansson (1982) has shown, this group developed an explicit method, using the idea of a succession of “unit periods,” in which each period began with agents having plans based on newly formed expectations about the outcome of executing them, and ended with the economy in some new situation that was the outcome of executing them, and ended with the economy in some new situation that was the outcome of market processes set in motion by the incompatibility of those plans, and in which expectations had been reformulated, too, in the light of experience. They applied this method to the construction of a wide variety of what they called “model sequences,” many of which involved downward spirals in economic activity at whose very heart lay rising unemployment. This is not the place to discuss the vexed question of the extent to which some of this work anticipated the Keynesian multiplier process, but it should be noted that, in IS-LM, it is the limit to which such processes move, rather than the time path they follow to get there, that is emphasized.

The Stockholm method seems to me exactly the right way to explain business-cycle downturns. In normal times, there is a rough – certainly not perfect, but good enough — correspondence of expectations among agents. That correspondence of expectations implies that the individual plans contingent on those expectations will be more or less compatible with one another. Surprises happen; here and there people are disappointed and regret past decisions, but, on the whole, they are able to adjust as needed to muddle through. There is usually enough flexibility in a system to allow most people to adjust their plans in response to unforeseen circumstances, so that the disappointment of some expectations doesn’t become contagious, causing a systemic crisis.

But when there is some sort of major shock – and it can only be a shock if it is unforeseen – the system may not be able to adjust. Instead, the disappointment of expectations becomes contagious. If my customers aren’t able to sell their products, I may not be able to sell mine. Expectations are like networks. If there is a breakdown at some point in the network, the whole network may collapse or malfunction. Because expectations and plans fit together in interlocking networks, it is possible that even a disturbance at one point in the network can cascade over an increasingly wide group of agents, leading to something like a system-wide breakdown, a financial crisis or a depression.

But the “problem” with the Stockholm method was that it was open-ended. It could offer only “a wide variety” of “model sequences,” without specifying a determinate solution. It was just this gap in the Stockholm approach that Keynes was able to fill. He provided a determinate equilibrium, “the limit to which the Stockholm model sequences would move, rather than the time path they follow to get there.” A messy, but insightful, approach to explaining the phenomenon of downward spirals in economic activity coupled with rising unemployment was cast aside in favor of the neater, simpler approach of Keynes. No wonder Ohlin sounds annoyed in his comment, quoted by Backhouse and Laidler, about Keynes. Tractability trumped insight.

Unfortunately, that is still the case today. Open-ended models of the sort that the Stockholm School tried to develop still cannot compete with the RBC and DSGE models that have displaced IS-LM and now dominate modern macroeconomics. The basic idea that modern economies form networks, and that networks have properties that are not reducible to just the nodes forming them has yet to penetrate the trained intuition of modern macroeconomists. Otherwise, how would it have been possible to imagine that a macroeconomic model could consist of a single representative agent? And just because modern macroeconomists have expanded their models to include more than a single representative agent doesn’t mean that the intellectual gap evidenced by the introduction of representative-agent models into macroeconomic discourse has been closed.

13 Responses to “Nick Rowe Teaches Us a Lot about Apples and Bananas”

  1. 1 Nick Rowe September 18, 2014 at 1:48 am

    Thanks David. Yes, I ducked the whole “Stockholm problem” in this post. I jumped straight to the “fix-price quantity equilibrium”, with no discussion of how the economy actually got there. This is equivalent to Old Keynesians jumping straight to the point where the AE curve cuts the 45 degree line, with no discussion of changing expectations of Y when AE =/= Ye. It’s equivalent to Old Monetarists jumping straight to Md=Ms with no discussion of the hot potato process.

    The apple producers’ demand for bananas depends on their expected sales of apples. The banana producers’ demand for apples depends on their expected sales of bananas. What process ensures that one sides’ expectations matches the other sides’ plans? How long will that process take, and is it likely to get to that “semi-equilibrium”?

    You and David Laidler are right that this problem has been pretty much forgotten, especially in representative agent models. But I haven’t forgotten it. I have done a few posts on this, and in a couple of posts actually used that period analysis Stockholm method (though I didn’t know it was called that). (I called it “the very short run”, or “monetary disequilibrium theory”.)

    To my mind, the problem with representative agent models is this: the representative agent can not be assumed to know that he is the representative agent. (Just like the agent with the average height cannot be assumed to know his height is average, unless he knows the height of every agent in the population.) So that, even though each agent knows his own plans and expectations, we cannot assume that the representative agent knows the representative agent’s plans and expectations. Which means, paradoxically, that the representative agent does not always know his own plans and expectations!

  2. 2 Tom Brown September 18, 2014 at 9:52 am

    David, I look forward to digging in when I get the chance, but I just have to say I loved the title:

    “Nick Rowe Teaches Us a Lot about Apples and Bananas”


  3. 3 Frank Restly September 18, 2014 at 10:27 am


    “Because expectations and plans fit together in interlocking networks, it is possible that even a disturbance at one point in the network can cascade over an increasingly wide group of agents, leading to something like a system-wide breakdown, a financial crisis or a depression.”

    That is the reason you have legally protected contracts, so that two parties can agree to meet each other’s expectations ahead of time and each party has recourse if the other fails.

    A breakdown in those legal protections would result in a recession.

  4. 4 charlie September 18, 2014 at 11:26 am

    I think modern macro is starting to address these issues of expectations co-ordination and networks. Cooper and John did a book about this almost 20 years ago! I do think you and Nick are a bit behind the curve here

  5. 5 Nick Rowe September 18, 2014 at 12:38 pm

    charlie: I didn’t know about Cooper and John’s book, but I did read their related article, maybe late 1980’s. It influenced my thinking too. But the major influences were David Laidler, 30 years ago, and Hayek too.

  6. 6 Nick Rowe September 18, 2014 at 12:40 pm

    Plus other inter-war UK monetary economists, like Hawtrey, Robertson etc. But unlike David I get them all muddled, which is why I can’t do history of thought.

  7. 7 charlie September 18, 2014 at 12:59 pm

    and also there is that whole literature on “global games” like Morris and Shin. Have you checked that out ? Although the price of entry is formidable and I cannot pretend to say I get it fully but it does seem to speak to David and Nick’s complaints.

  8. 8 Nick Rowe September 18, 2014 at 2:34 pm

    charlie: I just checked out the first hit on Google. I was doing OK with their first example (the Staghunt game) until the bottom of the 4th page, then they lost me.

    My impression: yep, games like staghunt (JJ Rousseau) are very much relevant to this sort of question. But my brain is now too old to follow them in the very fine details of equilibrium selection. All I can do is write stuff like this:

  9. 9 David Glasner September 18, 2014 at 2:36 pm

    Nick, You are so welcome.

    You said:

    “I jumped straight to the “fix-price quantity equilibrium”, with no discussion of how the economy actually got there.”

    Are you saying that you didn’t explicitly list all the steps of your argument, but that the steps could be filled in? Or are you open to the possibility that there might not be a path by which the equilibrium would be reached?
    I will try to have a look at your posts on the subject, and then we can continue the discussion.

    On representative agents, it doesn’t seem to me that representative agents have even the slightest degree of self-consciousness that you are attributing to them. If they did, they would go insane.

    Tom, You are a good audience.

    Frank, Contracts rarely are so explicit that all the terms of the contract are spelled out and all contingencies fully anticipated.

    charlie, I remember the article by Cooper and John “Coordinating Coordination Failures in Keynesian Economics.” I don’t remember much about it, and probably didn’t read it. What’s the title of their book? Do you think that article has had much influencel on the development of macro? Thanks for the reference to Morris and Shin.

  10. 10 Nick Rowe September 18, 2014 at 4:58 pm

    David: “Are you saying that you didn’t explicitly list all the steps of your argument, but that the steps could be filled in? Or are you open to the possibility that there might not be a path by which the equilibrium would be reached?”

    For this particular little model (at least, the simplest version where they cannot buy or sell fruit trees) I *think* that, under any reasonable assumptions about learning, I could fill in the steps that would get the agents to that fixed-price equilibrium. For example, assume the apple producer expects to be able to sell this period the number of apples he actually sold last period.

    But more generally, I am more than open to the possibility that for some models there might not be a path by which an equilibrium would be reached (except under daft assumptions about learning or knowledge). The Steve Williamson controversy was about this.

    One of the things I like about NGDPLT is that I *think* it would be easier for agents to learn the new equilibrium path. And when central banks are seen as setting a nominal interest rate it becomes very hard to learn the new equilibrium path, and the economy can get stuck at the ZLB.

    My old posts didn’t get very far. This was one attempt:

  11. 11 David Glasner September 19, 2014 at 10:38 am

    Nick, So, do you claim that whenever an economy is not on a path from one equilibrium to another, there must be an excess demand for money in that economy? Which Williamson controversy are you referring to?

    I do agree with you that NGDPT is that it would tend to anchor expectations in a useful way, and thanks for the link to your old post. I will try to have a look.

  12. 12 Nick Rowe September 19, 2014 at 5:15 pm

    David: “Nick, So, do you claim that whenever an economy is not on a path from one equilibrium to another, there must be an excess demand for money in that economy?”

    I don’t think I would claim that is always the case. And at the micro-level we may see coordination failures that have little to do with money. But those things we call “recessions” do seem to have the symptoms that would fit with the hypothesis of an excess demand for money.

    “Which Williamson controversy are you referring to?”

    The one where he said that if the Fed raised the nominal interest rate this would cause inflation to rise, via the Fisher effect. (I should have called it the Kocherlakota controversy.)

  13. 13 Chase September 21, 2014 at 6:54 pm

    David & Nick. I am definitely not an economist, but I like to observe and find out where logic makes my opinions land. So, I have been trying to figure out why I am not convinced on NGDP targeting (growth or level). There are a couple reasons, but I think the main one is a concern over the possibility for long-term unemployment driven by stringent adherence to an NGDP growth or level target. I will try to explain what I mean by this and you both may say this is crazy or stupid (or too unlikely to care about), but it tracks along the lines of why I don’t like EVA for internal business evaluation. I work in the call center finance industry. Let’s say there is a technology introduced that dramatically reduces the number of call center agents needed to service all the customers at all the companies that have call centers. We can call this an IVR or interactive voice response system if we want to. This cuts employment in this sector substantially almost over night. However, because this are B to B contracts that are likely 3 years or more in length, the benefit of this accrues to the BPO provider’s investors or management instead of resulting in reduced pricing ultimately to customers. We could also say this doesn’t pass to customers because efficiencies gained by BPO are to the benefit of the BPO and many companies allow for that as long as they are getting the best rate that BPO offers to anyone else (or think they are).

    I believe in this example we have a situation where employment is reduced while NGDP is unchanged, not because the fed has targeted NGDP and labor is reallocated to new uses and output remained the same, but because prices were not reduced and the wages went to increased rents instead. Under NGDP I believe the Fed would do nothing and the unemployment rate would tick up relatively. Over a one-time event this may not sound like much, but if we believe this isn’t a one-time event (and I don’t think it is) then this could add up to long-term stagnation in the labor market.. At the same time, even if prices reduce we could see the savings rate reduce as demand for this product at this price is higher and it seems to me that if the labor gets reallocated at the same time that the savings rate declines we will end up with higher NGDP than the target and tighter money to offset it that will end in less employment instead of less consumption.

    Under the current mandate, the Fed would appropriately react to the lowering of unemployment without the added inflation (assuming the Fed cared to hit its unemployment mandate) with a loosening of money. If we looked back in time would we see an NGDP growth path that is higher than the Fed would have targeted and what would have happened to employment if that excess NGDP growth was the result of unanticipated levels of productivity growth?

    Sorry, very long and sorry if it makes zero economic sense at all.

    P.S. great posts by all. Fun for a non-econ observer to follow as far as we are able.


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About Me

David Glasner
Washington, DC

I am an economist in the Washington DC area. My research and writing has been mostly on monetary economics and policy and the history of economics. In my book Free Banking and Monetary Reform, I argued for a non-Monetarist non-Keynesian approach to monetary policy, based on a theory of a competitive supply of money. Over the years, I have become increasingly impressed by the similarities between my approach and that of R. G. Hawtrey and hope to bring Hawtrey's unduly neglected contributions to the attention of a wider audience.

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