Chancing an interpretation: Slutsky's random cycles revisited ∗

∗ I am grateful to the comments of two anonymous referees for some suggested improvements and clarifications on an earlier version of this article. One referee's comments were particularly detailed and I thank them especially for their assistance.

Abstract

This article examines Slutsky's 1927 paper ‘The Summation of Random Causes as the Source of Cyclic Processes'. It provides an in-depth analysis of both the content and the reception of Slutsky's groundbreaking contribution by distinguishing between a ‘real' and a ‘statistical' interpretation of Slutsky's two related hypotheses, and also discusses the context of composition of the paper in the Moscow Conjuncture Institute. It then places the 1927 paper in the context of Slutsky's other work in economics and statistics, and highlights some lines of influence that have emanated from it. Various latent ambiguities in Slutsky's ideas are considered.

Keywords:

• Business cycles
• econometrics
• statistics
• Kuznets
• Frisch

Notes

∗ I am grateful to the comments of two anonymous referees for some suggested improvements and clarifications on an earlier version of this article. One referee's comments were particularly detailed and I thank them especially for their assistance.

1 An alternative translation of the Russian title might be ‘The Compounding of Accidental Causes as the Origin of Cyclic Processes’.

2 I am grateful to one of the referees for the basic outline of this summary.

3 Some of the original data series given in the 1927 article were excluded from the 1937 version.

4 For some background information on Slutsky's life, see Barnett (2004).

5 It is necessary to discuss this procedure in some more detail. Presenting a graph that coincides quite accurately with actual business cycles, but is generated by summed random causes, neither proves nor disproves any sort of explanatory link between the two. If the graph coincides better than any other model currently available, it might be accepted as the approach that currently ‘best fits’ the data, but this does not mean for certain that it is completely accurate. At any point in the future an even better model could replace it, or a less accurate model could replace it with a more plausible connection to the actual events being described.

6 In Fourier analysis a waveform is analysed to discover the sine wave frequencies that it contains. Through harmonic analysis it can be shown that periodic non-sinusoidal waveforms are composed of combinations of pure sine waves. One major component, a large amplitude sine wave of the same frequency as the wave under consideration, is called the fundamental. The other components are sine waves with frequencies that are exact multiples of the frequency of the fundamental. These harmonics are numbered according to the ratio between their frequencies and that of the fundamental. See Bell (1981: 17 – 8).

7 Slutsky's model series were taken from NKFin (People's Commissariat of Finance) data obtained in drawing the numbers of a Soviet government lottery loan.

8 In the 1927 article Slutsky did mention Yule's (1926) article on nonsense correlations, and hence Yule's work might have been one of the inspirations for Slutsky's efforts in this respect.

9 George W. Bush should take note.

10 For a discussion of Tugan-Baranovsky's work on fluctuations, see Barnett (2001). For Pervushin, see Barnett (1996).

11 Frisch had contacted Slutsky personally when the idea of creating an econometric society was first proposed, and hence the connection between the two pioneers was direct.

12 Judy Klein has posited that the mental machinations of forming expectations could be a mechanism by which a moving summation of random disturbances was actually achieved in an economy. See Klein (1997: 278).

13 Differencing procedures are not always mentioned in this respect.

14 Marji Lines has suggested that from a methodological point of view, R.E. Lucas's business cycle theory followed more in the spirit of Slutsky than Frisch (Lines 1990: 359). Lines outlined a model in which random monetary shocks were filtered in the process of aggregate expectation formation so as to produce correlated price expectations, which led to the autocorrelated stochastic fluctuations known as business cycles (p. 369). However, Lines has fallen into the trap of attributing the idea of ‘shocks’ to Slutsky rather than to Frisch.

15 I am grateful to Professor Eugen Seneta for assistance in comprehending Slutsky's contribution on this particular topic. The stochastic limit should be distinguished from what is usually called Slutsky's theorem, which states that if X_n is a sequence of random variables that converges in probability to a, then a continuous function of X_n would converge in probability to a continuous function of a. See Davidson (1994: 286).