Thursday, June 15, 2017

Microfoundations, the Euler Equation, and the Phillips Curve

Late last night (early this morning for everyone in America?) I had a conversation on Twitter with Noah Smith that got a lot of attention, and later turned into a discussion with with Jonathan Hyde about the New Keynesian Phillips Curve.

The actual thread is pretty long and confusing, so I'll just summarize it here. First in a sort of tongue-in-cheek way I asked Noah why economists model agents rationally when they are evidently not rational. He and I then went back and forth about empirical evidence, and I said "Well the Euler equation at least is patently wrong, and the NKPC [New Keynesian Phillips Curve] has trouble explaining inflation since 2008," which led to everyone's favorite tweet of the night (after my joke about how the models in Physics actually work):

 This is where Jonathan came to the defense of the NKPC:

 While his comment is not wrong, I think it points to one of the main problems with macro: insistence on modelling the underlying factors behind observed phenomena like the Phillips Curve, aka obsession with microfoundations.

The expectations augmented Phillips Curve has been around since the late 1960's, but microfoundations meant that economists spent years trying to figure out why rational optimizing firms would not adjust their prices instantly -- for a while the debate was between Taylor contracts and menu costs as a source of nominal rigidity -- but eventually settled with the mathematically tractable hand wave that is Calvo pricing.

The Calvo model basically says that firms face a constant an exogenous probability that they will not be able to change prices in the next period, so they might set their price too high or too low this period so that they won't be stuck with an extremely suboptimal price next period. This obviously doesn't classify as a "microfoundation" in that it doesn't appeal to a friction that actually exists in the real world.

In principle, microfoundations might seem like a good idea since they help deal with the Lucas Critique that relationships that appear in the aggregate data -- like the relation between inflation and unemployment -- might disappear when they are exploited. The problem comes when you realize that models with perfectly rational utility/profit maximizing agents don't work empirically. When that fact becomes clear, there are two options: add a whole bunch of implausible assumptions about agents (like Calvo pricing or habit formation) to make the model fit the data or just go back to modelling things ad hoc.

Economics has mostly gone with the first approach in the last 30 years, adding tons of parameters (e.g., the fraction of firms that cannot change their prices in a given period, the degree of habit formation, the elasticity of demand for individual monopolistically competitive firms, etc.) to a model just so they can come up with models that behave a lot like the old ad hoc models.

I don't think that economic incentives shouldn't be considered when making modelling decisions, but frequently models with completely rational agents and utility maximization produce results that go too far. A key example of this is consumption. In my last post I showed that consumption is pretty much entirely explained by income and wealth, which is a prediction of the Permanent Income Hypothesis (PIH). Essentially, agents try to "smooth" consumption in the face of shocks to income, so they consume out of their wealth when their income falls and save when income is high. A slight amount of consumption smoothing also occurs when people become unemployed. The consumption Euler equation also predicts consumption smoothing, but to an absurd degree. Whereas Jason Smith and I found that consumption is highly receptive to changes in income, the Euler equation predicts complete consumption smoothing.

A more ad hoc consideration of economic incentives and the economic data would lead to a highly qualified version of the PIH that does a much better job empirically than a strict utility maximizing approach. The same thing goes for the Phillips Curve, where assuming rational expectations makes the relationship statistically insignificant (see the t statistic on u_gap, the gap between the unemployment rate and the Congressional Budget Office's estimate of the natural rate of unemployment, in the table below):

Ultimately, in my opinion, the empirical failures of microfounded models show that trying to rigorously model the underlying causes of relationships we see in the aggregate data is a waste of time. Business cycle theory in particular should be more empirically oriented and less focused on logical consistency.

Update: here's a link to the code where I compare the New Keynesian Phillips Curve and a backwards looking Phillips Curve to the data.


  1. Nice post.

    Price stickiness appears in aggregated data, but not disaggregated which makes me think this is not a "microfoundation" (i.e. it doesn't have to do with individual prices and agents, but only appears at the macro scale). Here's a reference and discussion from Thoma:

    The paper also makes an appearance in David Romer's Advanced Macroeconomics textbook.

    Regarding the PIH, I think it's actually shown *not* to be true by the data (i.e. consumption does fluctuate with income). Noah Smith wrote a post on it awhile back and the model you're using is basically the same as the one I used to show that the PIH is a poor approximation.

    1. Forgot the link:

      It contains both the model and link to/discussion of Noah's piece.

      Also, it is true that adding wealth smooths consumption a little bit, but empirically the "elasticity" is low (i.e. instead of perfectly following income, it follows it less because of wealth).

    2. I was trying to make it clear that the data support an extremely qualified version of the PIH where there is a small amount of consumption smoothing (which is why I said the consumption Euler equation predicts smoothing "to an absurd degree", that "consumption is highly receptive to changes in income", and that consumption smoothing during unemployment is "slight").

      The unemployment paper I linked to is actually the one Noah was referring to in his post, which I got the link to by looking at your post, but I felt like linking to the paper directly was better under the circumstances.

      When it comes to price stickiness, I think as long as price stickiness is observable in aggregate data it's not worthwhile to try to model it from "first principles". The idea that the Calvo model doesn't match micro data is not in the least bit surprising, since its assumptions are patently absurd.

      More specifically, I'm interested in what causes the apparent cost stickiness that the paper Thoma refers to, because the authors imply that explains most of the apparent inertia in prices instead of price stickiness itself. The first thing that comes to mind is wage rigidity, but maybe I misunderstood what they mean by "costs".


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