Lesson 5 of 8
The plucking model
In US unemployment data a contraction predicts the recovery that follows, while an expansion predicts nothing. That runs the wrong way for this theory.
By Javier Sanz
Founder of ValueScreener. Built Ninety Nine, a securities services provider, and sold it to a tier-one global bank; ran operations and internationalization at Alpaca, the brokerage API.
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In one minute
- Friedman's image is a string glued under a board, plucked down at random intervals. Output runs along a ceiling and is pulled below it, rather than oscillating around a middle.
- The testable implication: a contraction should predict the following expansion, while an expansion should not predict the next contraction.
- In post-war US unemployment data the first relationship is close to one for one, and the second is not there. A theory in which the boom sizes the bust predicts the opposite pattern.
This is the only lesson in the course built on a data series rather than on an argument, and it is the objection that is hardest to talk your way around, because the pattern it reports is simple enough to check.
Which half of the cycle predicts the other
- Expansion explained by the contraction before it · coefficient 1.120.59
- Contraction explained by the expansion before it · coefficient -0.380.22
What Friedman proposed
The plucking model appears in Friedman's work in 1964 and is revisited by him in Economic Inquiry in 1993. The picture is a taut string glued along the underside of a board, plucked downward at points chosen more or less at random and with random force.
The board is the economy's maximum feasible output. The string is actual output. On this view a contraction is not a swing below an average that a previous boom pushed above; it is a departure from a ceiling, followed by a return to it.
That has a sharp implication, and Friedman drew it. The depth of a contraction should tell you the size of the recovery that follows, because the economy is climbing back to the same ceiling. The length or strength of an expansion should tell you nothing about the next contraction, because each pluck is a new event.
What the data show
Dupraz, Nakamura and Steinsson tested exactly that on the US unemployment rate from January 1948 to the onset of the 2020 recession, taking the amplitude of each contraction and each expansion between turning points.
Regressing the size of an expansion on the size of the contraction before it gives a coefficient of 1.12, with 0.33 reported beneath it, and an R-squared of 0.59. The authors call that relationship highly statistically significant. Regressing the size of a contraction on the expansion before it gives minus 0.38, with 0.27 beneath it, and an R-squared of 0.22, with the sign pointing the wrong way for any story in which a long expansion builds up trouble.
Their own reading is that the evidence strongly favours the plucking view, and their paper goes on to build a model with downward nominal wage rigidity that reproduces it. That modelling is not the point here. The two regressions are.
Why it is awkward for this theory
The Austrian account makes the size of the bust a function of the boom: the longer and larger the credit-driven expansion, the larger the accumulated malinvestment and the deeper the necessary correction. That is a claim about the second regression, and the second regression is close to empty.
Three honest qualifications. The measure is the unemployment rate rather than the structure of production, and a defender can say the theory is about the latter. The sample is one country, and the paper identifies ten peaks and ten troughs plus a peak added at the start, so the regressions rest on very few observations. And a credit boom need not coincide with a labour-market expansion of the same length, so the mapping between the theory's boom and the statistical expansion is not exact.
None of those makes the pattern go away. A reply that takes it seriously has to say what the theory predicts about the amplitude relationship and then show it.
Check yourself
What does the plucking image claim about output?
- That it oscillates symmetrically around a trend
- That it runs along a ceiling and is pulled below it, then returns
- That it grows at a constant rate
Show the answer
Answer: B.
Friedman's string is glued under a board and plucked downward at random, so contractions are departures from a maximum rather than swings around a mean.Which relationship is strong in the post-war US data?
- The size of an expansion predicting the next contraction
- The size of a contraction predicting the following expansion
- Neither, both are near zero
Show the answer
Answer: B.
The reported coefficient is 1.12 with an R-squared of 0.59 for contraction predicting expansion, against minus 0.38 and 0.22 the other way.What is the strongest qualification a defender can raise?
- That the data are not published
- That the series is unemployment rather than the structure of production, over one country and few cycles
- That regressions cannot establish direction
Show the answer
Answer: B.
The measure, the sample size and the mapping between a credit boom and a labour-market expansion are all fair points. They qualify the finding rather than removing it.Sources
- Dupraz, Nakamura and Steinsson, 'A Plucking Model of Business Cycles', NBER Working Paper 26351, October 2019, revised June 2021, section two and Table 1: the plucking property, the regressions of amplitude on the previous phase, the coefficients and R-squared values quoted here, and the sample from January 1948 to the onset of the 2020 recession.
- Friedman, 'The Plucking Model of Business Fluctuations Revisited', Economic Inquiry, volume 31, 1993, and his earlier statement of the same analogy in 1964. Cited for the record as the origin of the model; the papers themselves were not obtained for this lesson, and the string and board image is reported as Dupraz, Nakamura and Steinsson describe and cite it.
- Garrison published a comment on Friedman's plucking model in Economic Inquiry, volume 34, 1996. It is named here so a reader can find the reply; it was not obtained, and nothing is claimed about its contents.
What this leaves out
- This is a heterodox tradition. The mainstream account of the same phenomenon differs, and nothing here is a forecast or a view on any security.
- Friedman's own papers were not obtained. The model is described as reported and cited by the authors who tested it, and their description is the only basis for the account given here.
- The figures are one country, one series and about ten complete cycles. They are evidence about the amplitude relationship in US unemployment and not a general law.