# The Long Swing Hypothesis and the Growth Trend

## The long swing hypothesis

There have been recurrent suggestions in the literature on business cycles that as well as minor and major cycles, there may exist longer swings or waves. Long waves are usually investigated using an economic historical analysis of a few series that display only a small number of complete cycles.13

The long swing hypothesis is that long waves flow through economic life with shorter waves, including business cycles, superimposed upon them. As noted in the previous section, Schumpeter (1939) postulated the existence of numerous cycles but adopted a three-cycle schema, involving Kitchen (minor), Juglar (major) and Kondratieff (long) cycles, as an approximation. Using US data, Adelman (1965) undertook a statistical test for the existence of long swings. The question raised by Adelman was whether these cycles were independent of, though perhaps interacted with, the business cycle. The answer, Adelman observed, hinges on two issues: the cause of long swings, and the extent to which smoothing procedures themselves are responsible for the cycles.

As far as statistical backing for the various approaches is concerned, Adelman refers to her own work on the shocked Klein-Goldberger (K-G) model, which was found to perform quite well for long cycles.14 The implication is that the lead-lag structure imposed by the model weights the shocks to produce long cycles in the manner suggested by the Frisch I hypothesis. Adelman draws attention to another possible interpretation, namely that the lead-lag relations are accidental or reflective of shorter cycles and that random causes explain the long cycle. In addition, smoothing to eliminate short cycles, which is common in the analysis of long cycles, may introduce systematic bias via the Slutsky-Yule effect so that the long cycles might be illusory.

Adelman tries to determine whether smoothing biases are sufficient to explain the existence of long cycles. Spectral analysis is used because it enables the simultaneous determination of cycles of all durations without the need to eliminate shorter cycles. The traditional approach to analysis of cycles of ten to twenty years, as exemplified by Kuznets (1937) and Burns (1934), has been to use moving averages to smooth shorter cycles. Adelman points out that unless the period chosen for the moving average (MA) corresponds to the frequency of the short cycle exactly, spurious cycles will be introduced. This is, of course, likely since the short (business) cycles do not display regular period or amplitude. It is evident from Slutsky (1937) that the spurious cycles are likely to be of longer duration (see section 1.4).

Adelman (1965) calculated power spectra for detrended consumption, investment, output, employment, labour productivity, productivity of capital, and the wholesale price index, with many series being used for each variable. The filtered spectra displayed no evidence of long swings since 1890. Adelman claims that the entire variance in the long swing frequencies is attributable to leakages from power at low frequencies. When the effects of random fluctuations are smoothed out, using spectral techniques, the power that remains in the long swing domain appears to be traceable to the difficulty of removing the entire trend from the data. An alternative view is that the difficulty of removing the 'entire' trend implies long-run structural or systematic change or a stochastic trend (see section 4.3.2). Adelman seems, therefore, to have shown that the trend is unlikely to be cyclical and if it is, the cycle is weak. It is also possible that the trend removal may have eliminated more than just the trend. It is consequently necessary to look at Adelman's method of deriving deviations from trend. Adelman used deviations from log linear rather than MA trends. There seems to be little danger, therefore, that non-trend variation was removed but still the data could have been distorted.

Adelman concludes that long cycles have largely been introduced by smoothing techniques, although large exogenous shocks, and possibly structural shifts, have led to changes in trend which have not been adequately allowed for. To the extent that it exists, the long swing is not endogenously determined but is the result of exogenous shocks.

Howrey (1968) tests the hypothesis that there are swings of between fifteen and twenty-five years, a period which covers various versions of the long swing hypothesis. He first examines the effects of filtering on time series and then applies spectral analysis to various economic time series. He notes that the method commonly used to isolate long swings is to filter the data with an MA process to attenuate short-term fluctuations. The chronology of peaks and troughs is then used to test whether the original series contains a long swing component. Howrey notes that this method is subjective and arbitrary and demonstrates that inference about the original series from filtered series can be misleading. He finds that a major cycle of eight to eleven years in the original series could be converted to a cycle of fifteen to twenty-five years by use of an MA filter, giving further confirmation of the Slutsky-Yule effect.

Howrey estimates the spectral density functions of a number of economic time series. To abide by the stationarity assumption in applying the spectrum analysis, the growth rates are used. The trend introduces nonstationarity and so the growth rate sequence is more likely to be stationary. Adelman used deviations from log linear trends to test the long swing hypothesis. Howrey points out that the series used by Adelman display nonstationarity and so the applicability of spectral analysis and the validity of Adelman's results are questionable. Howrey notes that nonstationarity in the growth rates series is less conspicuous in most instances, but perhaps no less real.

The long swing hypothesis is interpreted as stating that the contribution of the band of frequencies corresponding to the average period of twenty years is significantly greater than that of neighboring bands. The hypothesis would be rejected if no peak in the spectrum occurs near the long swing frequency. Howrey finds that the long swing seems to be absent from the production series while five to nine and three to five year cycles are present. Two of the consumption series show a peak in the long swing band but the peak is not significant. Investment series show no peak in the long swing frequencies but a significant peak in the five to nine year band. A long cycle is found in nonfarm residential construction, indicating a building cycle of eleven to twelve years, which is shorter than previous estimates. Inventories show a significant peak indicating a four year period, which is about half a year longer than in other series showing peaks in the three to five year period. This is interesting in view of the association of inventories with minor cycles. He notes that the result may be due to the inadequacy of the series.

Howrey finds that his results are inconclusive but they do nothing to dispel skepticism about the existence of a Kuznets cycle. The spectrum peaks that occur in long wave frequency bands are in most cases weak and in no case statistically significant. The results indicate relatively regular fluctuations which are longer than the three to five year, approximately forty month, average of NBER cycles and which fit conveniently into the major cycle category of nine to fifteen years. Howrey's results imply that by virtue of Burns and Mitchell's (1946) definition of business cycles as being of one to ten or twelve years in duration, the NBER may be missing some of the major cycles and that a better test of the Monte Carlo hypothesis (see section 1.2) may be derived by splitting reference cycles into major and minor categories. Nevertheless, this is a strong set of evidence contradicting the Monte Carlo hypothesis.

Burns and Mitchell (1946, Ch. 11) also tested for the significance of the long swing hypothesis. They were aware that the hypothesis that business cycles are subdivisions of longer cycles raises some fundamental questions about their use of averages to expose the typical characteristics of cyclical behaviour and to establish a base from which wide variations in duration can be explained. If the business cycle differed radically according to its position in a long swing then, Burns and Mitchell acknowledge, they would not be justified in using simple averages. In comparing cycles of different activities it would be essential to ensure that they covered like periods within long swings; otherwise bias would occur. The problem, for Burns and Mitchell, was not so much to decide whether or not long cycles exist but whether they are strong enough to command attention at the early stage of the study of business cycles that they felt they were in.

To test the importance of the long swings, seven US series,15 with their accompanying NBER measures, were used. Little indication is given as to why these series were chosen. Burns and Mitchell's procedure was to test a number of hypotheses regarding long swings in order to gauge whether there was any marked change in cycles during the periods indicated. They found that building activity displayed a remarkably regular cycle, with duration between fifteen and twenty years and large amplitudes. They investigate whether business cycles vary in intensity according to whether the economy is experiencing an upswing or a downswing in a building cycle. The averages of reference and specific cycles during the upswing of a building cycle are compared with those occurring in a downswing. Little difference is found and their variance ratio tests show that any differences are not significant. Tests were made for variability in duration and amplitude.

Burns and Mitchell next explore the hypotheses of Wardwell (1927) (major cycles), Kuznets (1930) (secondary secular variations), Kon-dratieff (1935) (long waves) and Burns (1934) (trend cycles). The general approach of these studies was to fit lines of intermediate trend (usually moving averages) that are supposed to eliminate specific cycles. The deviations of these intermediate trends from the primary trend are supposed to expose long cycles. The studies of Kuznets and Burns are most extensive but the cycles cannot be tested directly because their chronology is either non-existent or too coarse for NBER monthly analysis. Similarly Wardwell's annual chronology is not sufficiently accurate.

Burns and Mitchell first test for Kondratieff waves of fifty to sixty years, pointing out that long waves in prices had been frequently postulated. Since NBER data is post-1850, no serious test of the hypothesis, as it stands, can be made since only two complete cycles are observable. Burns and Mitchell therefore consider a simpler question: is there evidence that business cycles in the upswings of long cycles (waves) in commodity prices differ substantially from those occurring in down-swings? They find no significant difference. They then test whether cycle measures vary during periods of opposite price trends. They find a significant difference in the case of durations but not amplitudes. They reserve judgment on the direction of causation.

Next Burns and Mitchell consider Schumpeter's (1939) hypothesis, that Juglar cycles (nine to ten year major cycles) contain three (minor) cycles of approximately forty months. Howrey's (1968) results seem to support this hypothesis. A test is performed by grouping the first and third cycles, according to their position in the alleged Juglar cycles. One would expect the rise in the first cycle to be larger, and the fall smaller, than that in the third cycle. Evidence is favourable towards the hypothesis but Burns and Mitchell note that the trough dates of Juglars correspond to severe depressions so that one would expect a substantial difference between cycles occupying opposite ends of the particular Juglar periods examined. If some internal regularity characterised cycles separated by troughs of severe depressions the hypothesis would be on sounder footing, they argue. They find no support for this, however, but do regard Schumpeter's suggestion as a valuable one warranting further research.

Burns and Mitchell next examine the Kitchen (1923) hypothesis. Kitchen's major cycles are aggregates of two, and sometimes three, minor cycles each lasting forty months on average. The limit of each major cycle is distinguished by a maximum of exceptional height, by a high bank rate and sometimes by a panic. Kitchen's chronology of cycles differs markedly from the NBER chronology. Burns and Mitchell believe that this is due to Kitchen's concentration on financial variables, which show extra cycles. Kitchen's chronology is closest to that of the NBER for US data. Burns and Mitchell explore the possibility of differences between first and last business (minor) cycles occurring within Kitchen's major cycles. The two groups of cycles, they find, are basically the same although the average duration of the first group of cycles is greater. This difference is not significant and, in fact, of the five major cycles explored, three of the first cycle groups were shorter. One would also expect smaller amplitude for the first group than the second group of cycles. This was true for eleven out of eighteen cases but the difference was found not to be significant. Burns and Mitchell feel that major cycles may exist but their existence does not produce systematic bias to business cycles and so the averaging procedure used in their work is an acceptable approximation.

Burns and Mitchell observe that trends make it easier to mark off depressions than booms. They therefore rerun the above tests, but with major cycles marked off by severe depressions, due to the unsatisfactory chronology provided by Kitchen's work. This also provides a test of the Schumpeter and Wardwell hypotheses that major cycle troughs coincide with major depressions. Burns and Mitchell mark out a list of major depressions, which they regard as highly tentative. The cycles are distributed into three groups: reference cycles marked by troughs just following a severe depression; reference cycles within which a major depression falls; and the rest of the cycles. Specific cycles are grouped in a similar manner. Tests for differences in duration and amplitude were made. They found no significant difference in duration, but a significant difference in amplitude was discovered. This is attributed to the method of classification. They conclude that the hypotheses need further investigation, but there is insufficient evidence to accept the major cycle marked off by severe depression hypothesis. Their tests are to be understood in the light of the tentative datings of severe depressions.

In summarising their results, Burns and Mitchell draw attention to the fact that they used only a small sample of series (seven in all). In addition, these series are not the ones normally chosen by long-cycle theorists to demonstrate their theories. Further, they have made no allowance for leads and lags and their significance tests are approximate at best. They regard themselves as being in no position to say whether cycles have varied systematically but they are satisfied that these long-run effects are sufficiently small to allow them to use their averages as a first approximation.

The tests of the various hypotheses usually proceed by dividing cycles into groups and using F-tests to determine whether there is a significant difference, either in measures of average duration or average amplitude, between groups of cycles. The probability tables used in the F-tests are derived from a theoretical population distributed according to the normal curve. Burns and Mitchell point out that because definite evidence exists that the frequency distribution of their cycle measures is often skewed, the tests they make are in some degree inexact. A second problem is that the probability tables are based on the assumption that the observations entering the sample are independent. Burns and Mitchell feel reasonably sure that cyclical measures do not fulfil this condition, although they come closer to doing so than the original time series data. Thus there is a second source of bias to the tests. They feel that these biases in the testing procedure have not seriously hampered their analysis since they are only interested in testing whether the effects of cyclical changes in cycles are substantial, rather than whether they exist.

The renewed interest in long cycles since the early 1970s was noted in section 4.1. There is no space to review this literature here. If, however, cycles with periods longer than that normally associated with the business cycle exist, then (log) linear trend removal will not isolate the business cycle. Instead it will be necessary to remove the influence of the long swing on the data. This presents a difficult problem, given the risk that moving average smoothing will severely distort the data.