Tuesday, March 17, 2015

Nominal rigidity is an entropic force

Commenter pjz brings up transaction costs as a source of nominal rigidity on this post from a couple months ago. In responding, I found a great old post by Mark Thoma about some issues with macro modeling of nominal rigidity.

Basically there are two major mainstream micro approaches to achieve macro nominal rigidity that have observational consequences:

  • Transaction (menu) costs: there is a cost to change the price. Price changes should be observed to infrequent and biased towards large changes (frequent small changes would be penalized).
  • Calvo pricing: only a sample of firms can change their prices in any one period. Price changes would be observed to be infrequent.

What does the data show? [Pictures from Thoma's post]

Oh ...

Nothing seems to be stopping those prices from changing. Essentially among the 60,000 prices observed, prices are sticky in aggregate but not individually. The two mainstream approaches above imply that prices are sticky both individually and in aggregate, something that is flatly contradicted by data.

How do you get sticky aggregate prices with flexible individual prices? Well, one way is entropy as I show in the post from a couple of months ago linked above. The picture in your head should be much like this one (it shows something different, but the concept is the same):

... thousands of prices fluctuating wildly, with the aggregate level barely moving.

One consequence of this would be that there is no microeconomic explanation of nominal rigidity ... flying in the face of the microfoundations approach to the Lucas critique.


  1. I think that most people think that the main source of microfounded price stickiness should be in implicit and explicit wage contracts for the labor market. the big criticism of taylor contracts I think was that they didn't generate enough aggregate nominal rigidity...but with this emergent price stickiness you have here, I think it could go a long way into rehabilitating a micro-emphasis on such contracts...I also remember Harald Uhlig making a presentation where he presents similar evidence...cant remember where though...

    1. Hi LAL,

      Interesting -- I would imagine that you could combine contracts (or menu costs, etc) with an emergent stickiness so that in a more detailed model:

      observed nominal rigidity ≈ entropy + smaller effects + ...

      where contracts and other effects are sub-leading terms. I should investigate how big the entropy terms would be relative to other effects. My initial guess is that it would be suppressed by 1/log N where N is the number of agents. [Entropy goes as N log N and any particular micro effect would be at most proportional to N, so N/(N log N) = 1/log N.] Numerically for 100 million agents this would be a factor of 20 or about 5%. But that's just a guess.

    2. I think a complexity agents approach could essentially involve making a microfounded model and then making a whole bunch of them to recover the entropy effect either by hand or through simulation to make sure it matches up with observed entropy...

      adjusted wage share is something like 65% of income...so i see how labor's share of income is proportional to N but it is also proportional to wages, which could be a higher order function than constant... I think even a small amount of marginal stickiness could have a large average effect...

    3. ughh this stuff confuses me, do I have an entropic force just in the wage market also that is dominating any micro-effects there?

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    5. The entropic forces play the biggest role where something is trying to change the distribution of prices (or wages). The best example is in the labor market where there is a shock to AD that would require the distribution of wage changes to over-represent the negative changes. There would be an entropic force pushing against that change in the distribution.

      Now maybe changes in the price change distributions aren't as important in goods markets -- the changes are to the mean, simply shifting the distribution around. In that case, entropic forces wouldn't be as important in goods markets. However wage stickiness could still impact the goods markets as a higher order effect.

  2. I'm also not so sure everyone sees the above micro data as not sticky...if keeps going back to basically the same top price with strategic price drops presumably through coupons and discounts...I think Uhlig argued that this is not the usual stickiness story...but we could still infer an average welfare loss to such inefficient Nash Equilibria...

    I definitely agree though the kind of "stickiness" we see in micro data is not the same as at the aggregate level

    1. I agree -- the view in Romer's macro text and in the Thoma blog post seems to be that prices are anchored at particular values with frequent "sale" prices in the above examples. But yes, that is definitely different stickiness than is observed in aggregate.

      That's why I think the entropy view is good model -- it is pretty much agnostic about the kinds of fluctuations that are happening at the micro level. All that's needed is that they have some sort of stochastic process (a hidden semi-Markov model seems like a good fit to the above) that isn't broadly coordinated across the economy (except by monetary policy, which acts like a measure of temperature here).

      And if that is the only contribution of information equilibrium, that's a pretty good one.


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