Wednesday, April 8, 2015

Incentives are an entropic force

The points are not "incentivized" to diffuse themselves uniformly around the roundabout. They just happen to find the uniform distribution through random movements. 
The latest in my series of X is an entropic force, I'd like to propose the idea, meeting the mainstream of economics halfway, that incentives are an attempt at a microscopic description of an entropic force.

I recently re-read my post/discussion with commenter Jamie -- we both have qualms with the mainstream economic view that a fall in price causally leads to ("incentivizes") a rise in consumption. Jamie put it as an analogy with gasoline:
Which of the following statements is more accurate?

1) An increase in fuel [supplied] causes the car to travel further
2) An increase in the use of the car for travel causes an increase in the fuel [used].
And part of my response:
[The mainstream economic] view also says that an increase in the fuel supply (1) lowers its price and that makes more people buy more fuel. Now this idea is not only that more people can afford fuel at a lower price, or finally afford as much as they need, but that lowering the price incentivizes additional consumption ... like a moth to flame. Jamie and I both have a problem with this view. Lowering the gas price doesn't make me want to drive more. ... Despite my problem with this microeconomic view, I still think it gets the result correct, just not for the right reasons. The problem with the micro viewpoint in the previous paragraph is that is tries to assign a microeconomic explanation for an entropic force.
By "gets the result correct" I effectively mean incentives save the phenomena of supply and demand, like how Calvo pricing saves the phenomena of nominal rigidity. Saving the phenomena is a phrase used to contrast with models that offer explanations. Calvo pricing and incentives do no explain economic behavior, they save the observed economic phenomena.

We observe the fact that lowering the price on e.g. bacon generally tends to increase its consumption. Economics does not teach that this effect is dominated by people who are now able to afford the bacon -- in the model, everyone is able to afford the bacon -- their utility is maximized by doing something else with the money.

That makes it weird for people like Jamie and me. At the very least it should be weird for Jews and Muslims who don't eat bacon on religious grounds -- economists are telling them that they would consume more bacon if the price is reduced, ceteris paribus.

It's weird on the supply side too. Shannon may want to be a doctor, but if the price of bacon rises, economists are telling her she now wants to go into pig farming or pork belly futures a little bit more than she did before.

All of this strikes most ordinary people who don't think of life in terms of the pecuniary incentives as freaky (here's a good example). Economists and homo economicus seem like rational aliens. I'm sure that's where the particular non-intuitive explanations in the Freakonomics vein derive their pageviews. It's also behind a phrase I've seen: "thinking like an economist". It's also probably why there are so many heterodox views out there.

The entropic force view of supply and demand dispenses with this freakiness.

Instead of individuals feeling drawn to buying more bacon because the price fell, on average the total amount of bacon consumed per person rises through millions of individual decisions because that is the most likely state among millions of people. In the entropic force view, this consumption increase doesn't even have to happen! It just happens on average -- if you reset and re-ran the world (like a Monte Carlo simulation), you'd get a different result each time. On average, you get an increase, but fluctuations for N agents are on the order of ~ 1/√N. Jamie and I can't feel compelled to consume more gas at a lower price in the realized world because we in fact aren't compelled to consume more gas in most realizations of the world.

Shannon can't feel pulled into pig farming because she doesn't go into pig farming in most re-runs of the world economy. Someone may consume more gas or go into pig farming (or more likely current pig farmers will produce more bacon), but a story can't be told for a representative agent because it doesn't apply to everyone.

No single atom is compelled to diffuse to a region of lower density. They move around randomly, occasionally colliding with the walls of the container or each other. Collectively, there is an entropic force driving the atoms in a gas to an equal (maximum entropy) distribution over the container. And since there are ~ 10^23 atoms in a macroscopic gas sample, the fluctuations around an equal density are ~ 0.0000000003 %.

Economic systems have fewer agents so have much larger fluctuations than a typical macroscopic atomic system. In physics, we'd probably call a macro-economy a meso-economy instead.

Economists came up with the idea of incentives to figure out why people would be pulled into pig farming or driving further ... or how supply can create its own demand [1] ... at the microeconomic level. When the price falls (or a good is subsidized), people are "incentivized" to consume more than they would have otherwise in order to maximize their utility. We're all greedy algorithms sucking up utility however we can.

And to a great extent, models of incentives work at effectively describing the situation after a price drop or a subsidy. Some people really must be buying less bacon when the price rises because overall consumption is observed to decrease when the price rises. Averaging that decrease in consumption across everyone, you have everyone decreasing their consumption a little bit -- incentivized by the price rise.

But it also leads to the weird idea that subsidized health care will lead to people to have more surgeries even if they could have afforded the extra surgeries before the subsidy. Or that lower gas prices make people drive more (I can assure you I do not want to drive around my hometown any more than I have to). Some budget constrained people do drive more because they can afford it when the price falls; some people do get surgeries because they can afford them after the subsidy.

In economics, these would be treated as an exception to incentives (i.e. a more detailed model of incentives) with an ad hoc model for some goods [2].

The entropic approach unifies these the successes and failures of incentives into a single model -- surgeries and driving may be more like a Fermi-Dirac distribution (lower maximum occupation numbers) than a Maxwell-Boltzman distribution. You have people getting the surgeries deemed medically necessary (and no more) or driving as far as they can given the constraints of work and vacation ... and you still have people rushing into the malls on "Black Friday" for the sales. They're all maximum entropy solutions, just over different sets of available states.

Footnotes:

[1] Say's law in mainstream macroeconomics isn't considered true (partially because of the existence of money), but one description of the role of a central bank is to make Say's law true in practice via monetary policy.

[2] Footnote added 4/16/2015: Per LAL in comments below, this would be the inclusion of satiation points. However, that breaks the fundamental theorem of welfare economics -- that market outcomes (Walrasian equilibrium) are Pareto efficient -- which requires local non-satiation. This is interesting because it kicks out one of the legs in favor of utility in the first place: to have something that can be maximized defining a Pareto efficient allocation. If we're not maximizing utility, then why worry about the utility maximizing solution? Why not work with the entropy maximizing solution?

7 comments:

  1. "In economics, these would be treated as an exception to incentives (i.e. a more detailed model of incentives) with an ad hoc model for some goods."

    in the above stand-alone paragraph, what is "these"? and what is the meaning of the above paragraph?

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    1. Hi LAL,

      "These" refers to the two scenarios -- driving more or having more surgeries. I was only making the point that some kinds of goods are necessary, but more is not necessarily better, so the straightforward application of incentives does not apply to a reduced price.

      I used to live in Washington DC and no drop in the price of gas would make me consume more gas -- it may be the worst place to drive in the US. Although some people love to drive even in traffic.

      So a blanket application of the idea that price reductions incentivizes additional consumption isn't a uniform model and scenarios such as surgery and fuel consumption may require modifications to the idea of incentives.

      The thing is that it may well be that a drop in the price of gas or medical care does effectively "incentivize" additional consumption even in the case of unpleasant consumption that could have been afforded even before the price drop. This is weird to many people and describing it as an incentive is strange because it's not something people want to do!

      However, if you describe it in terms of entropy, people can be pulled in to additional consumption of medical care even if they aren't actively trying to maximize utility by having more surgeries than necessary.

      In short, entropy can answer the question of why people on average would consume more of a good that doesn't make sense for them to consume more of in terms of individual actions.

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    2. I see yes, in order to aggregate preferences we usually need monotonicity...at least it is the easiest route, but many goods today make more sense with a satiation point(s)...there is probably a really nice connection between satiation points and entropic forces...

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    3. I'm thinking more now that goods with satiation points is not the best way to try and make the point I was trying to make ... that most people don't feel like they are rationally maximizing utility.

      A better way might be that humans don't need to devote their brains' computational resources in the grocery store in the entropic force view ... they could run on their own heuristics and the maximum entropy solution would still result. This isn't so much "rational inattention" as "rational heuristic attention".

      Some more thinking to do in any case.

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  2. you might be trying to only talk about representative agent models...in which case ignore the following...

    you not wanting more bacon is irrelevant and perfectly in line with the demand theory of slutsky and/or hicks...however, lowering the gas price does make you wealthier so to prove your point you need to burn an equivalent amount of money (if you spend it you look a lot like a rational consumer)...now that i've biased you by pointing this out i dont want you to derive utility from burning money to spite me...instead we should see if muslims and jews burn the additional money they get now that their neither jewish nor muslim customers are wealthier and purchasing more of their wares (ironically and sadly the answer might be yes if we actually look at current political actions) ...anyway this is undergraduate level stuff at Rice and the U of C for sure

    on the point of firm entry...quantity and market entry are separate though related questions...why would we expect someone in a completely different field to suddenly become a pig farmer based on a marginal rise in price? instead i think we might expect someone already producing pigs to produce a marginal pig...this is somewhere between undergraduate and graduate level work...

    there are a lot of good criticisms of current micro theory...but i dont think you have found them...maybe focus on the good parts of your theory and hold off on the criticisms until you have a firmer grasp of models that are not new by this point...

    i recommend hick's "a revision of demand theory"...slutsky is good too but i only find sporadic papers in english...

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    1. after several re-readings of your post i notice that you actually realize the difference between producing a marginal unit of pigs being done by current farmers rather than doctors building or buying a farm...but the point i am reaching for there is that the incentive model tells us when a doctor should or shouldn't enter the pig farming industry and when current farmers should just produce an additional slice of bacon...this story of re-running the economy basically side steps the whole issue...why are there on average more states where pig farmers produce more bacon than states in which doctors producing more bacon? that is the question an economist is supposed to answer...

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    2. I was mostly referring to representative agent theories ... I also realize I was being somewhat provocative. Of course there are excellent arguments to understand the kinds of issues I bring up.

      People who might have been doctors really were drawn into finance in the 2000s in a manner well-described by incentives -- I myself almost went to work on both wall street and at a big bank developing mortgage risk models (ha!) back in the apparently crazy 'quant' days.

      My point was directed at two kinds of people:

      1. Non-economists and others around in the econoblogosphere who think that the whole general "homo economicus" approach is morally distasteful, counterintuitive or politically right wing. In a sense, I am trying to present an interpretation that is largely divorced from politics or specific views of human behavior -- but is fully consistent with "incentives".

      2. Economists who see the world in terms of incentives -- I hoped to show that the basic concept of incentives can effectively be interpreted as an entropic force.

      Writing something for those two very different audiences was probably an impossible task -- but that's what blogs are for ... experimental writing!

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