The "Plucking Model" of Business Fluctuations Revisited

By Friedman, Milton | Economic Inquiry, April 1993 | Go to article overview

The "Plucking Model" of Business Fluctuations Revisited


Friedman, Milton, Economic Inquiry


The recent surge of renewed interest in business cycles in general, and real business cycles in particular, brought to mind a "plucking model" of business fluctuations that I suggested some twenty-five years ago but that has since sunk into complete oblivion.(1) I was led to the model in the course of investigating the direction of influence between money and income. Did the common cyclical fluctuations in money and income reflect primarily the influence of money on income or of income on money? One of the five kinds of evidence that I examined was the "serial correlation of amplitudes of cycle phases.(2)

As I wrote, "Is the magnitude of an expansion related systematically to the magnitude of the succeeding contraction? Does a boom tend on the average to be followed by a large contraction?" (p. 271). To find out, I calculated rank difference correlations between measures of the amplitudes of expansions and successive contractions in three different series for the period 1879 to 1961. The three series were rate of change of the stock of money, a physical index of general business, and clearing-debits as an indicator of dollar value change in general business.

Similarly, I asked the same question, except starting with a contraction in the given series and correlating its amplitude with the amplitude of the succeeding expansion.(3)

The results were striking. For all three series the correlation was trivial between the amplitude of an expansion and the amplitude of the succeeding contraction. On the other hand, for both the rate of change of the money stock, and the physical index of general business, the correlation was high and statistically significant between the amplitude of a contraction and the amplitude of the succeeding expansion. For clearing-debits, this correlation too was low.

I concluded, "There appears to be no systematic connection between the size of an expansion and of the succeeding contraction, whether size is measured by physical volume or by dollar value" (pp. 272-73). On the other hand, a "large contraction in output tends to be followed on the average by a large business expansion; a mild contraction, by a mild expansion," (p. 273) though that is not so for the dollar value of the expansion and contraction.

I went on,

This phenomenon, if it should be confirmed by a fuller analysis of data for the United States and other countries, would have important implications for the analysis of business cycles in general, not solely for our monetary studies. For one thing, it would cast grave doubt on those theories that see as the source of a deep depression the excesses of the prior expansion |the Mises cycle theory is a clear example~.(4) For another, it would raise serious questions about both the analytical models, in terms of which most of us have come to approach the analysis of cycles, and the statistical methods we use to analyze them.

Our analytical models generally involve a conception of a self-generating cycle, in which each phase gives rise to the next, and which may be kept going by a sequence of random shocks, each giving rise to a series of damped perturbations. The corresponding physical analogy is of an electrical network in which responses are described by sine waves. The asymmetric serial correlation patter suggests that this analogy may be misleading, that a better one is what can be termed a plucking model. Consider an elastic string stretched taut between two points on the underside of a rigid horizontal board and glued lightly to the board. Let the string be plucked at a number of points chosen more or less at random with a force that varies at random, and then held down at the lowest point reached. The result will be to produce a succession of apparent cycles in the string whose amplitudes depend on the force used in plucking the string. The cycles are symmetrical about their troughs; each contraction is of the same amplitude as the succeeding expansion. …

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