Saturday, October 11, 2014

Entropy, in three pieces

Entropy. Picture from askamathematician.com.

I. 

Noah Smith thinks that the Efficient Markets Hypothesis has something to do with information theory:
This is because the EMH doesn't emerge from any peculiarity of the way our market system is set up, or the way human beings behave. The EMH comes from something much deeper than that, something that probably has to do with information theory. It comes from the fact that when you exploit information to make a profit in a financial market, you decrease the amount that others can exploit that information. In other words, the financial value of information gets used up [emphasis in original].

One way to see biology is as a process by which living things intercept entropy (free energy) flows. An autotroph converts low entropy high energy photons into high entropy waste (heat, low energy photons); a heterotroph converts low entropy organisms into high entropy waste (heat, poop). Economic agents intercept entropy (information) flows: they convert low entropy money into high entropy goods and services. 
In living things, the free energy in the photons or sugars is converted into lower free energy products and the information in their original structure is lost. The information in the market (e.g. prices of goods) is converted in to quantities of goods where the prices they were bought at no longer matter (according to the EMH). This information is consumed by the market in the same way free energy is consumed by organisms [emphasis mine].
Actually, the main thrust of this blog is that supply and demand are a manifestation of information theory, and market forces are entropic forces. The EMH itself is the analog of the fundamental postulate of statistical mechanics.

II. 

Mark Buchanan defends his view that energy consumption rises with GDP, contra Paul Krugman who says it doesn't have to. Buchanan says that his view was that energy rising with GDP was not an inevitable law of nature, but rather pessimism about our ability to conserve energy (with which I agree). But Buchanan does seem to want to hold on to his point by citing a paper which shows that power use per capita is related via a power law to real GDP per capita. The paper makes the claim that it may not be a coincidence that the power law has an exponent of 0.76, close to the 3/4 power law relationship between mass and energy consumption for organisms. I have two issues with this. One, the units seem all wrong. the relationship for economies is in Watts per capita while GDP is in year-2000 dollars per capita per year -- GDP is not "mass" but rather a growth rate (mass would seem more likely proportional to the value of all goods and services in existence ... the computer I'm using right now still consumes a few hundred Watts of power, but no longer contributes to GDP as I already purchased it). Two, the financial sector is now 10% of US GDP but is a tiny fraction of total US power consumption while the transportation sector is about the same fraction of GDP but uses a large portion of the total energy.

I also think the calculation E ~ GDP is all wrong in general (the economy is not an engine), and showed in this post (in a footnote) that the fundamental physical (computational) limits of the economy as an information processing system required only about 1 red visible light photon per day to produce the entropy change going from 2013 to 2014. Here's more:
Based on this measure (comment) of the number of states in the economic system in the US the amount of energy that would need to be supplied to change the entropy of the US economy from 2013 to 2014 (at 290 K) comes out to be about 6 x 10^-17 Joules or about 400 eV, or about the energy equivalent of 1 red photon per day. 
Now our conversion factor from information to energy is not as good as Nature's kB = 1.38 x 10^-23 J/K -- in fact, given the US energy consumption of ~100 quadrillion BTUs, I'd estimate [the economic Boltzmann constant at] kE ~ 2.5 x 10^13 J/K, or off by a factor of 10^36 from the fundamental limit (kB). That leaves a lot of room for improvement! 
Now if kE doesn't change, you could make an argument that limits to energy consumption (and conservation) are limits to growth [that go as GDP log GDP]. However, in 1960, kE ~ 100 x 10^13, or about a factor of 40 higher (based on ~ 50 quadrillion BTU energy consumption). Assuming we could get another factor of 40, the nominal economy could grow by about 2.5 times and use the same amount of energy.
The survival of biological organisms depends on the consumption of free energy, which is a change in entropy (at constant temperature and pressure), not mechanical power (as is measured by the energy consumption statistics). It is also worth noting that dollars are units we as humans invented. They lack the fundamental heft of "mass" or "energy" (analogs of which would like exist on alien worlds). There is no reason why there should be a decades-long stable relationship between dollars and energy.

III.

David Glasner has another great post on coordination failures and "sticky prices" where he gives two sticky prices (the real wage and the real rate of interest) and two separate human-behavior mechanisms for why they do not fall far enough during a recession (no one worker accepting a lower wage can ameliorate the fact that wages are too high and entrepreneurial pessimism, respectively).

These mechanisms are only unified in the sense that they are coordination failures -- they involve completely different sets of human behaviors and expectations. They also strike me as just-so stories. Reading through Glasner's discussion, you ask yourself questions. If an employer only had a few employees, wouldn't the effect of the reduction in one employee's wages on the business's bottom line be comparable to the few percent slowdown that happens during a recession? If faced with a choice between a layoff or a wage cut, I think I would take the wage cut (I happen to like my job). Employers say they don't cut wages because it hurts morale. However, employers frequently reduce hours -- wouldn't that reduce morale as well? Why more in one case, but not the other? Also, wouldn't some entrepreneurial optimist clean up during a recession with all that free money?

That's why I'm glad Glasner doesn't put too much stock in the specific explanations, but instead says:
It is not obvious what sequence of transactions would result in an increase in output and employment when the real wage is above the equilibrium level. There are complex feedback effects from a change, so that the net effect of making those changes in a piecemeal fashion is unpredictable, even though there is a possible full-employment equilibrium ...
 ... [the explanations leave out] coordination problems that might arise in a multi-product, multi-factor, intertemporal model in which total output depends in a meaningful way on the meshing of the interdependent plans, independently formulated by decentralized decision-makers, contingent on possibly inconsistent expectations of the future.
I think at the heart of these coordination problems lies entropy. Sticky wages or prices are the result of an entropic force -- a (minimally informative, i.e. equilibrium) distribution of wages does not spontaneously arrange (coordinate) itself so that everyone is still employed at the new (lower) wage. Instead you likely get a break-down of the information transfer system of the market (I once looked at the possibility that the information received by the supply was less than the information source information in the demand and that the difference was about the same across employment and interest rate markets).

But one difference between my view and Glasner's is that there really isn't any coordination in the first place. People's plans are randomly sufficiently consistent (or not seriously inconsistent) with each other to keep the economy going most of the time -- the economy is in a random configuration that is consistent with NGDP. The problem seems to be that, occasionally, humans coordinate themselves (mass panic) and the coordination required to undo the damage done by that spontaneous coordination does not happen spontaneously (much like entropy doesn't spontaneously decrease). For example, Vulcans might not have recessions in their economy (were it to have money) because the coordination in the initial mass panic (or just mass pessimism) that triggers layoffs and the fall in NGDP would not occur. No coordination required to undo the (non-existent) damage.

You can imagine a mass panic due to someone yelling fire in a movie theater; the coordination required to undo the spontaneous coordination that happens when someone yells "fire" does not happen spontaneously. Sometimes humans can spontaneously coordinate to increase economic output -- unfortunately the examples seem to be wars and market bubbles.

If you yell "fire" at a bunch of methane molecules in air, they don't spontaneously change their velocity to avoid combustion. But if they did, that would be a spontaneous decrease in entropy as well as lower the free energy of the gas -- meaning the new equilibrium energy is lower. You can't get that free energy back unless you coordinate the methane molecules to return to their original distribution (you might have to coordinate some of the molecules in the air as well) -- which would cost about as much free energy as the original loss [1].

In economic terms, the spontaneous coordination in a recession costs GDP (economic entropy is a function of GDP) that doesn't come back without government coordination (monetary and/or fiscal) or a long wait for GDP growth.

Footnotes:

[1] I'm thinking there's a good analogy with fiscal stimulus and the output gap here.

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