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Wednesday, October 16, 2019

Should We Care About Plucking Models?

Milton Friedman suggested a description of the business cycle in the 1960s: the "Plucking Model." The analogy is of a string stretched tight across a board: you can pluck the string away from the board, but tension will pull the string back quickly, and then slam into the board.

Importantly, there needs to be a board stopping the string. This is different than a normal pluck of a guitar string, where the string will overshoot its steady state on the return, and then oscillate.
Figure: Canadian Real GDP and Recessions

We can sort-of see this in Canadian real GDP data (U.S. GDP data are smoothed more, and so it might look better.) Most of the time, real annual GDP growth bounces around an average that looks to be around 2.5%. This was punctuated by two deep contractions that match the recessions as defined by the C.D. Howe Business Cycle Council. (There was a bit of a surge in the late 1990s that somewhat messes up the story, although some of it could be explained by the dip around 1996.)

There are two main predictions of the model.
  1. Growth will "normally" bounce around some trend level, with relatively small deviations.
  2. Recessions are "abnormal" and involve a large downward deviation in real GDP, followed by a rapid reversion to trend.
"Mainstream" economists (particularly fans of Milton Friedman) find this quite a useful concept. From my perspective, this is just an alternative way of observing that recessions are qualitatively a deviation from the typical behaviour seen in an expansion. Since slumps had already been a topic of intense interest by earlier economists (notably Keynes), I see limited academic novelty in this model.

Mainstream Context

Within the context of neoclassical models, the plucking model description is of more interest. It suggests a different observed set of dynamics, with recessions being distinctive. Workhorse (simplified) models suggest that fluctuations are random around a steady state, which suggests that real GDP growth rates shooting up to 6% from a 2% "steady state" should happen as often as falling to -2% from 2%. We generally do not see that (although the Canadian 2000 surge kind of fits that description).

As such, mainstream economists have an interest in generating models that look closer to the Plucking Model than a model with symmetric steady state behaviour. A recent working paper by Dupraz, Nakamura, and Steinsson (URL: is an example of generating a model that has similar behaviour. (I have not read the article in depth, I am noting this now as a marker for myself to return to this for Volume II of my book on recessions.)

Post-Keynesians: Yawn

Volume I of my book on recessions (still in editing) focuses mainly on the Post-Keynesian theory of recessions. The second volume will look at mainstream theory, and the Plucking Model will get a look-in there. The only question for me now is whether I need to add a discussion of it as part of the descriptive part of the book. My feeling is that I can largely defer the discussion, although I worked in a quick description in a sub-section.

The interesting thing about the Plucking Model is that the Post-Keynesians -- who obsessively attack every aspect of neoclassical economics, particularly Monetarism -- don't waste any ammunition on it. It is largely forgotten (including by myself, until recently...), other than by a few loyal Friedmanites.

I would guess that if you did want to hear a Post-Keynesian critique of the Plucking Model, the bulk of the complaints would be the assumption of a a steady state growth rate that cannot be overshot. What economic force corresponds to the "board" stopping overshoot of "maximum GDP"? Although one could point to full employment (which was a plausible story in the hot 1960s labour markets), we have seen persistent underemployment since the early 1990s. 

Meanwhile, the argument is that a hot economy leads to higher productivity growth (Verdoorn's Law). There is no "law of nature" determining the path of maximum output; the decision to keep resources underemployed (to fight inflation) lowers the path of future trend growth.

The fact that there is a rapid re-acceleration after a recession trough is not exactly a surprise given how automatic stabilisers work, and the tendency for a policy response to occur with a lag. 

Figure: Greek Nominal GDP

The idiotic step of dismantling the automatic stabilisers in Greece led to a very distinct "non-plucking" outcome. (Figure above is an out-of-date chart of nominal GDP that I had lying around; no time to dig up real GDP data right now.) Output dropped, and stayed down. The "plucking" effect is not a natural law, it is the result of post-war Keynesians getting some things right. However, given enough neoliberal economics Ph.D.'s, it is possible to blow up Friedman's "model."

The main issue I have is that it is purely descriptive: it tells us that "plucks" happen, but not why they happen. If we can determine the dynamics behind a recession, we might be able to generate model output that looks like "plucking."

In summary, I am not sure that this matters for anyone other than neoclassical economists who want to come up with a reason to cite Milton Friedman.

(c) Brian Romanchuk 2019

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