Wednesday, October 1, 2014

Wage stickiness is an entropic force

David Glasner has a post up about the hegemony of new classical economics through "microfoundations"; this latest take put the question in an interesting way that goes well with what I've been thinking about lately:
In chapter 19 of the General Theory, Keynes struggled to come up with a convincing general explanation for the failure of nominal-wage reductions to clear the labor market. Instead, he offered an assortment of seemingly ad hoc arguments about why nominal-wage adjustments would not succeed in reducing unemployment, enabling all workers willing to work at the prevailing wage to find employment at that wage. This forced Keynesians into the awkward position of relying on an argument — wages tend to be sticky, especially in the downward direction — that was not really different from one used by the “Classical Economists” excoriated by Keynes to explain high unemployment: that rigidities in the price system – often politically imposed rigidities – prevented wage and price adjustments from equilibrating demand with supply in the textbook fashion.
Why, in a recession, don't people take wage cuts to clear the labor market?

I think I have an answer: entropy. There is nothing stopping anyone from making the adjustments, it's just highly unlikely that the adjustments will be made (or another way, it is highly unlikely for the economy to find itself in a state where the adjustments have been made). People are pushing against the headwind of an entropic force -- an entropic force that is known by its economics discipline name of sticky wages.

That's why it would be hard to come up with a microfounded explanation for the lack of nominal wage reductions -- there is no microeconomic reason. Sticky wages disappear as you get a smaller and smaller economy, going from macro down to the micro level. A single glue molecule is not sticky and individual molecules do not undergo diffusion.

Let me try an explanation. Nominal wages (NW) are remarkably correlated with NGDP -- in fact, NGDP = 2.1 NW to a very good approximation. So lets assume that nominal wage growth in a given industry (or company) is proportional to [the growth of] that industry's contribution to NGDP. We can then borrow the picture from this post to talk about the distribution of wage growth:


The mean and variance of this distribution is set by macroeconomic variables -- like NGDP and the money supply [1].

If one person takes a nominal wage cut, he or she would move along the red arrow to a position on the negative growth side to the left of the vertical line. It doesn't impact the shape of the distribution too much. However, if lots of people do it, you'd end up with a different distribution:


If this were a thermodynamic variable, the particles on the left side would "experience" an entropic force to return to the original distribution .. because that original distribution represented the most likely configuration consistent with the macro scale variables. The individual particles wouldn't actually feel any force, they'd just end up by random chance back in the most likely configuration.

Well, in the information transfer picture, the labor force would experience that same entropic force. That is to say, they wouldn't feel anything themselves -- in aggregate the labor force would just keep the same distribution of nominal wage growth. Some people would move up, some down. The distribution of wages would have a tendency to stay the same since they are set by macro variables, few people end up with negative nominal wage adjustments to an exogenous shock and wages appear to be "sticky" [2].

Right now you might be saying: "Wait, how can a recession happen at all in this picture?" There are two ways. One is to throw people out of this distribution in proportion to the distribution itself (subtracting a Gaussian from a Gaussian with the same mean and variance is just a re-normalized Gaussian with the same mean and variance). In this case unemployment spikes and you get a one time drop in NGDP that reduces the average growth rate going forward (see footnote [1]). This picture is below:


This mechanism predicts that the distribution of the wage growth of the about-to-be unemployed before the layoffs is roughly the same as the wage growth distribution of the employed before the layoffs. That is to say most people laid off would have had the average wage growth of the employed before the layoffs -- that people with low wage growth or high wage growth prior to the layoffs are not over- or under-represented in layoffs.

The second way is for the market to stop transferring information, prices stop detecting the information flow and nominal wage growth freezes (goes to zero -- see e.g. here [link fixed 10/3/2014]). If I(D) is the information source (demand) and I(S) is the information destination (supply), then this represents a case where I(S) < I(D). It could be described as a coordination failure (the information in peoples' expectations is lost as their inconsistent plans fall apart) or incorrect expectations which lead to information loss.

The first way, we maintain I(S) ≈ I(D); second way is a market failure -- I(S) ≠ I(D). My opinion is that a little of both happens. Its a bit like trying to get the price tag sticker [2] off of birthday card and ripping the card in the process. Your fight with entropy is partially successful and partially system failure. In this analogy, the economy is the card, the soon-to-be unemployed are the price sticker and you are acting as the economic shock to the system.

Footnotes:

[1] In particular, using the partition function approach, the mean of the wage growth distribution is ~ log NGDP/log M and the variance is ~ 1/log M.


[2] An entropic force we experience in our everyday lives is the stickiness of glue. There is literally nothing you are fighting against when you try to peel a price tag off something ... except entropy.

9 comments:

  1. This comment has been removed by the author.

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  2. Perhaps it's a stupid analogy/question, but as N becomes large how does an individual extract from the random movement in prices that they observe a general trend in the price level (i.e. if you are a molecule, how do you separate aggregate movement from Brownian motion)?

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    1. That is a great question, Robert!

      In the case of pollen grains undergoing Brownian motion in, say, water that is slowly flowing, the molecules only "know" about the trend motion (the flow) through conservation laws and the pollen grains only receive that information through the difference in momentum hitting on each side of the particle. In a sense, neither the pollen nor the water molecules are discerning anything -- they are just obeying the laws of physics individually.

      But in a system like an economy that has humans as the "molecules" there is a very real possibility that the humans could sense their environment (the flow) and change their behavior. I believe this "sensory response" leads to e.g. bubbles and maybe recessions.

      People can see price changes themselves and infer an inflation rate. It's really hard to do, though -- the US government agencies usually don't have their measure of inflation out until a month or so later. And people tend to put more weight on prices of things they buy more often (food, gas) and less weight on other things (including rational inattention).

      My hypothesis (at the center of the information transfer model) is that most of the time the sensory response to price changes is random (or rational inattention means there is no sensory response). A price rise can mean inflation, a supply decrease or a demand increase (or a combination) -- and determining which it is (especially in the presence of noise) is hard. Therefore a given human will probably misinterpret a given price signal in a random way. This negates the sensory response most of the time (bubbles and recessions might be exceptions), making humans more like molecules that don't really "know" what they are doing.

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  3. I think you're overcomplicating a simple issue. Change of price is a transaction, and transactions aren't free. Which means the transaction cost always lags, because to change the transaction cost you need another transaction. In a recession, transaction cost are too high compared to the current output, which makes downward adjustments expensive.

    The higher the relative cost of a transaction, the more downward-sticky it is. Wages are one of the most expensive to change. The transaction cost of changing them is ~100% in wages (time spent talking with a manager, time spent changing contracts, maybe talks with a labor union, etc).

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    1. Hi pjz,

      Actually, the transaction cost theory is the more complicated theory. The transaction cost theory is:

      maximization principle + transaction costs → nominal rigidity

      The theory I am describing is:

      maximization principle → nominal rigidity

      Now the maximization principle is different in the two cases (utility in the former vs entropy in the latter), but transaction costs are not a consequence of utility maximization so represent a more complex theory than a maximization principle alone.

      I wouldn't disagree that transaction costs may save the phenomena -- the resulting theory may even be very accurate. However it may be like adding a density dependent diffusion force that mimics the effect of entropy instead of describing diffusion directly with entropy.

      Aside from being more complex, there are a couple of reasons the transaction cost explanation is problematic at the micro level:

      1) I'm not sure the transaction costs associated with lowering my wage are really that high. A request for a salary cut and its implementation could in theory all be carried out with a few keystrokes. The marginal cost of sending a piece of information and changing a number in a computer database is effectively zero.

      2) Wages change all the time. See this graph:

      http://www.federalreserve.gov/newsevents/speech/yellen20120606-slide8.gif

      Only 20% of wages aren't changing. That means 80% of wages are changing (up to +/- 20%). Transaction costs would explain the 20% stuck at zero change but not the 80%.

      3) Prices of goods are incredibly volatile on very short time scales:

      http://economistsview.typepad.com/economistsview/2008/03/the-evidence-on.html

      If transaction costs mattered here, then prices wouldn't fluctuate from week to week.

      Basically prices are sticky in aggregate, but not individually. Entropy is one possible explanation. Transaction costs imply prices are sticky individually and in aggregate, something that is not observed.

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    2. >The theory I am describing is: maximization principle → nominal rigidity

      It's not a different theory because transaction costs are necessarily a part of entropy maximization.
      Entropy maximization is a phenomenological law describing result of many local processes.
      Because it loses information, to describe a specific case you have to add additional complexity.
      Like "throw people out of this distribution in proportion to the distribution itself".

      >I'm not sure the transaction costs associated with lowering my wage are really that high. A request for a salary cut and its implementation could in theory all be carried out with a few keystrokes.

      By few keystrokes? I find that hard to imagine, outside of some form of forced labor. Many people have severance pay and required notice period. Firing an employee with these can incur costs up to one year of pay, and that's all you can do if they don't agree to a pay cut. In the case of unionized labor you run into risk of a strike.

      Workers without any of these protections obviously exist, but how many? Out of those, low-skilled ones work for near or at to minimum wage, so no reduction is possible.

      Additionally people handling all that are probably paid too much, because due to a recession there's bigger supply of potential replacements.

      Compare that to rising the pay. Now you can indeed do that by a few keystrokes (a bonus), which would result in happy and surprised people. A base pay increase would be a bit more complex, but still drastically cheaper and easier than reduction. If the economy is growing, it's even cheaper (as % of output) because wages were negototiated sometime in the past when it was smaller.

      >Transaction costs would explain the 20% stuck at zero change but not the 80%.

      Why? It seems consistent to me. Many workers who are worth less than they currently earn, but the high transaction costs of reduction prevent reducing the pay, so they are stuck at 0.

      >If transaction costs mattered here, then prices wouldn't fluctuate from week to week

      The cost of changing commodity prices is very close to zero.


      >Transaction costs imply prices are sticky individually and in aggregate, something that is not observed.

      Why do they imply that?
      "Aggregate stickiness" sounds like slowly changing money supply.

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    3. Hi pjz,

      The idea that one model of price adjustments fails to describe the empirical microeconomic data is not controversial; for example here is David Romer's Advanced Macroeconomics (p 338):

      "Thus the microeconomic evidence does not show clearly what assumptions about price adjustment we should use in building a macroeconomic model."

      It is doubtful Romer was unaware of transaction costs. Also, when you say: "The cost of changing commodity prices is very close to zero." this is actually pointed out as false a few lines later in the same textbook from the above quote -- costs to change all the prices in a store are remarkably high: on the order of 1% of revenues.

      You also said:

      It's not a different theory because transaction costs are necessarily a part of entropy maximization. Entropy maximization is a phenomenological law describing result of many local processes.
      Because it loses information, to describe a specific case you have to add additional complexity. Like "throw people out of this distribution in proportion to the distribution itself".

      I don't quite understand this.

      Once you have nominal rigidity, the mechanisms are the same in both models:

      nominal rigidity + economic shock → unemployment

      This is either:

      (maximization principle + transaction costs) + economic shock → unemployment

      or

      (maximization principle) + economic shock → unemployment

      "throwing people out of the distribution in proportion to that distribution" is throwing people out at random. Essentially all of the processes are random.

      Transaction costs are not necessarily a part of entropy maximization because entropy maximization applies to many physical systems like ideal gasses ... and atoms don't exchange money, and there isn't a penalty for exchanging energy.

      Actually -- that's a really good analogy. Energy is conserved for individual atoms, but for macroscopic systems, you can lose energy as waste heat. In this entropy model of nominal rigidity (that may or may not be correct) individual prices and wages aren't sticky, but there is stickiness at the macro level.

      Delete

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