Wednesday, March 4, 2015

The hot potato effect is an entropic force

According to an oft-repeated but probably embellished account, when Laplace gave a copy of Mécanique Céleste to his physics-literate friend Napoleon Bonaparte, Napoleon asked him what role God played in the construction and regulation of the heavens. "Sire," Laplace replied, "I have no need of that hypothesis."
Neil deGrasse Tyson 
The "hot potato effect" describes how injections of so-called high powered money, like cash or monetary base reserves, are like hot potatoes. Individuals are already holding as much money as they want in equilibrium at a given price level, so the additional cash is 'sold' to re-balance their portfolios. That ends up in a cascade of exchanges until everyone is back in equilibrium at a new higher price level.

Scott Sumner wrote a post about this effect awhile ago, calling it the sine qua non of monetary economics. He said something remarkable in that post:
"[people] want explanations they can understand at the individual behavior level.  But that just won’t work in this case."
Something that doesn't exist at the individual behavior level? Sounds like an entropic force! Here's Sumner from the same post explaining the hot potato effect using a parable with gold:
Because before the discovery [of additional gold] people were already in equilibrium, they held as much gold as they wanted to hold at existing prices.  The extra gold is a sort of “hot potato” that people try to get rid of.  But obviously not by throwing it away!  They get rid of it by selling it.  But notice that while that works at the individual level, it doesn’t work in aggregate.  Now someone else has the extra gold. (That’s why attempts to understand money at the level of the representative consumer fail.)  The only way for society as a whole to get rid of the extra gold is by driving down the price of gold [i.e. driving up the price level] until people want to hold the new and larger quantity.
The thing is that this explanation doesn't really explain why the price level goes up. I may have more gold than I want to hold, but I don't want to give it away or get a bad deal. It seems like Sumner is implying that the price level just happens to rise over the course of several 'mistakes' (the price of bacon is too high at this store, but I have the money, i.e. extra gold, and I'm too lazy to go to the other store so I'll buy it anyway even though its not optimal). This is remarkably close to the entropic force view.

The entropic force view would say that the additional 'gold' (high powered money) randomly moves around (and prices randomly fluctuate) until the new most likely configuration (of prices and gold held) with the new larger amount of gold is happened upon by chance. In the simplest case that new most likely configuration is a uniform distribution across the agents. The new most likely price level is also higher since people will randomly accept both high and low prices, but more high prices (bad deals) will be accepted than were accepted before the additional gold was added because those 'mistakes' were made possible (the state space was opened up) by the additional gold in the market.

In the language of thermodynamics, if you add energy to a system, that opens up new parts of phase space with higher momentum states, raising the temperature of the system.

I made a short animation showing how a large injection of high powered money into a segment of the economy eventually finds its way across the entire economy through random exchanges. You can imagine each vertical light blue (well, purplish in the compressed youtube version) bar is an agent, firm or market sector (e.g. imagine the injection happens in the banking sector). The horizontal blue line is the average and median before the injection, the horizontal red dashed line is the average after the injection.



The solid red line is the median level; 50% of the agents are holding high powered money above this level and 50% below. When the median meets the average, that means the typical agent won't make a biased 'mistake', i.e. randomly accept a price that is too high more often than one that is too low. If the median is below the average -- as it is when the high powered money is injected -- then more than half of the agents will tend to increase their holdings since they have below the average level [1].

Effectively, the injection of high powered money is "thermalized" and heads toward a new equilibrium (uniform) distribution at the new average. We see the median (solid red line) rise from the previous average (blue line) to the new average (dashed red line).

The difference here is that there is no real requirement for human behavior in the explanation -- even at the macro level. Agents aren't thrown off of their original "desired" equilibrium and don't "want" to get rid of excess holdings of high powered money. The new equilibrium is just the new most likely state and the agents, if they have more than the average, just tend to reduce their holdings by random exchanges.

Utility maximizing agents? I have no need of that hypothesis.

Footnotes:

[1] This assumes non-preferential attachment -- i.e. all agents are equal. This illustration selects which agents trade money from a uniform distribution. A different mechanism leads to different distributions. See e.g. Bouchaud and Mezard http://arxiv.org/abs/cond-mat/0002374.



9 comments:

  1. except of course without utility maximizing agents there is no good reason for them to enter into costly exchanges at all ....

    ReplyDelete
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    1. Just because agents need food and housing that have some utility value to them does not mean they are maximizing that utility ... max(u) is a different condition from u > 0.

      One can think of living organisms consuming (available) free energy as an analogy to economic agents 'consuming' utility. Individual species don't maximize free energy consumption -- they're just trying to survive. However the most likely state of all living organisms on the planet is one where they maximize free energy consumption. This isn't achieved by local maximization, but rather by what Jaynes called "dither": random exploration of the available state space:

      http://informationtransfereconomics.blogspot.com/2015/02/jaynes-on-entropy-in-economics.html

      There might not even need to be some reason beyond entropy that sets off exchange in the first place. Maximum entropy production may encourage the emergent formation of dissipative structures -- like an exchange economy itself!

      Delete
  2. Very cool! I'm sure you have seen this already at some point, but I stumbled upon another physicist's description of economic reality via thermodynamics, quite interesting. Turns out most of us live in a Boltzmann-Gibbs economy where we trade bits of paper in thermodynamic equilibrium, but the wealthy exhibit supercritical powerlaw distribution of their income, in that they have "escaped" the rest of us.

    http://arxiv.org/pdf/1204.6483.pdf

    ReplyDelete
    Replies
    1. Hi Todd, Thanks.

      And thanks for the link. The link in the footnote of this post also discusses the power law tail in the distribution in wealth -- and even indicates the possibility of a phase transition where nearly all wealth is held by a finite number of individuals (wealth condensation). I like to think of that as the Feudalism limit ...

      Maybe the reason power laws crop up all the time is because of information equilibrium?

      http://bactra.org/notebooks/power-laws.html

      Delete
  3. Wow Cosma is a very smart guy with strong opinions, and not afraid to put them on the internet. Certainly the subtitle could be "How I learned to stop worrying and love the power law correlations..." In the words of Dr. Fielitz himself:

    The finding that power laws and exponential laws in nature
    can be justified by a general information equilibrium concept releases us from the “pressure”
    to justify a new found power/exponential correlation by any internal assumptions about the
    considered process. The release from this “justification pressure” will enable us to see
    correlations which we would otherwise simply consider as accidental or even as nonsense.

    ReplyDelete
  4. Wow Cosma is a very smart guy with strong opinions, and not afraid to put them on the internet. Certainly the subtitle could be "How I learned to stop worrying and love the power law correlations..." In the words of Dr. Fielitz himself:

    The finding that power laws and exponential laws in nature
    can be justified by a general information equilibrium concept releases us from the “pressure”
    to justify a new found power/exponential correlation by any internal assumptions about the
    considered process. The release from this “justification pressure” will enable us to see
    correlations which we would otherwise simply consider as accidental or even as nonsense.

    ReplyDelete
    Replies
    1. Fielitz and BorchardtMarch 6, 2015 at 1:45 AM

      Todd, we would like to add that this quotation was part of a private communication. For readers of this blog which would like to understand the context of this statement we refer to section II B in http://arxiv.org/abs/0905.0610.
      Peter and Guenter

      Delete
  5. I am a bit late to this party but. . . .

    Sumner: "Because before the discovery [of additional gold] people were already in equilibrium, they held as much gold as they wanted to hold at existing prices. The extra gold is a sort of “hot potato” that people try to get rid of. But obviously not by throwing it away! They get rid of it by selling it. But notice that while that works at the individual level, it doesn’t work in aggregate. Now someone else has the extra gold."

    So far so good.

    Sumner continues: "(That’s why attempts to understand money at the level of the representative consumer fail.) The only way for society as a whole to get rid of the extra gold is by driving down the price of gold [i.e. driving up the price level] until people want to hold the new and larger quantity."

    Beg pardon. By assumption we are in a closed economy, so there is no way for society as a whole to get rid of the "extra" gold.

    Go back to the previous part of Sumner's explanation. Some people have more gold than they want to hold. Therefore they sell it. But they cannot sell it at the old price because nobody wants to buy it at that price; they already have enough. But somebody will be willing to buy it at a lower price. The sale is made. At that point the buyer has the amount of gold he wants. Therefore he does not try to sell it. There is no hot potato effect.

    ReplyDelete
    Replies
    1. I agree -- there cannot be a hot potato effect if there aren't mistakes (or changes in preferences ... how much gold agents want to hold). If your agents are perfect rational agents with stable preferences, there is nowhere for the "excess gold" to go.

      The hot potato effect requires mistakes or changing preferences.

      Delete

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