Brief Overview of Cycle Modelling

Like Marx, Keynes failed to formalise a complete theory of dynamic economic development or of its components, growth and business cycles. It is a testament to the magnitude of the problem that these two great economic and social thinkers were unable to formulate such a theory.

The consequence has been numerous attempts by their disciples to complete their work. Keynesians have tended to seek separate theories of growth and the business cycle while Marxians have attempted to move beyond their initial preoccupation with crises towards an integrated theory of cycles and growth, but they have failed to agree on a common theory.

Meanwhile the work of Schumpeter (1934, 1939), who came much closer to developing a complete theory of dynamic economic development, has largely been ignored in post-war business cycle literature. It has not, however, been ignored in the long-cycle literature that proliferated since the early 1970s. There is no space to review this literature here, but Schumpeter’s contribution will be discussed in the next section and Shackle’s related work will be discussed in section: Shackle on the Business Cycle. Both of these great economists stressed the role of innovations in the generation of business cycles.

Having seen early drafts of Keynes’s General Theory, Harrod (1936) produced a Keynesian theory of the trade cycle in the same year as Keynes’s book was published. His theory was based on multiplier-accelerator interaction. Harrod (1948) went on to concentrate on growth theory but his work on cycles was developed by Samuelson (1939), who demonstrated the various dynamic paths that could be derived from a linear deterministic multiplier-accelerator model.

Earlier work by Frisch (1933) and Slutsky (1937) had shown the possibility of converting a series of random shocks, or impulses, into a cycle using a linear propagation model that displayed a damped monotonic or cyclical path in response to a single disturbance (see section: The Frisch-Slutsky Hypothesis ). If linear stochastic models are to be employed, the basic choice is between Frisch-Slutsky models and explosive paths constrained by ceilings and floors, such as Hicks (1950), which also employed multiplier-accelerator interaction to give the essential dynamics.

In the 1950s a number of nonlinear deterministic models were developed. Goodwin (1951), for example, employed a nonlinear accelerator to generate a limit cycle solution (see section: Nonlinear Cycle Theory, on limit cycles). The Hicks (1950) model can also be regarded as a nonlinear model which incorporates what Samuelson (1947) dubbed ‘billiard table’ nonlinearities and what we have called ‘type I’ nonlinearities.

Other examples of such models are Smithies (1957) and Minsky (1959), which employ Duesenberry-type ratchet effects (Duesenberry 1949) on consumption expenditure within a basic multiplier-accelerator framework. Goodwin (1951), however, employed a nonlinear accelerator function, or ‘type II’ nonlinearity to generate cycles.

These nonlinear models were capable of producing cycles that repeated themselves in the absence of shocks and consequently introduced the possibility of developing models in which the cycle was endogenously generated. They also allowed for the possibility of asymmetric expansionary and contractionary phases, which are not permitted in linear formulations (see section: Are Business Cycles Symmetric? ). Further, in the case of stable limit cycle solutions, shocks can be added to explain the observed irregularity in business cycles.

Also in the 1950s, Goodwin (1955) and Kaldor (1954), among others, became concerned about the separation of cycle and growth theory. The Hicks (1950) assumption of a trend in autonomous investment seemed artificial. They felt that the role of innovation in stimulating growth, as stressed by Schumpeter (1934, 1935, 1939), had been overlooked and that undue stress had been placed on investment induced via the accelerator process.

The Schumpeterian bunching of innovatory investment had been ignored. Goodwin and Kaldor expressed the view that a theory of dynamic economic development was required and that it was incorrect to decompose economic time series into a linear trend and cyclical fluctuations and to try to explain them separately, because they were part of the same process.

The Keynesian structural econometric models built between the late 1950s and the early 1970s tended to display extreme monotonic, rather than cyclical, dampening. Adelman and Adelman (1959) found that autocorrelated, rather than random, shocks were required to generate realistic cycles.6 ‘Type I’ and ‘type II’ nonlinearities were largely ignored in these models and by the end of the 1960s the very existence of business cycles was being questioned.7 Others, following Fisher (1925) (see section: The Monte Carlo Hypothesis ) argued that it had never really existed because it represented the summation of random events with no propagation model transforming them into regular and repeated cycles.

Interest in the business cycle was rekindled as a result of the response of OECD countries to the 1973 oil price shock and in the mid-1970s two papers were published, Nordhaus (1975) and Lucas (1975),8 which stimulated renewed academic interest in the subject. Lucas’s work seems to have had the more lasting impact and has led to numerous attempts to model the cycle as an equilibrium phenomenon.

Most of the work is in the Frisch-Slutsky tradition with a linear model propagating cycles in response to a series of random shocks. The cycle so formulated is, therefore, not endogenous and self-sustaining. This period also saw a resurgence of interest in long waves with speculation that the long post-war upswing had given way to the downswing of the long wave in the 1970s - see Mandel (1980) and Van Duijn (1983).

The major debate in the 1980s was not over whether the Frisch-Slutsky modelling strategy was correct, but over the most important sources of shocks. Lucas (1975) had stressed the importance of monetary shocks but in the 1980s attention turned to real shocks as the major source of impulses. Lucas (1987) suggested a synthesis of the real and monetary equilibrium business cycle approaches which he feels should build on the Kydland and Prescott (1982) contribution. The latter generates cycles using a stochastic derivative of the neoclassical growth model and as such marks a renewed attempt to integrate cycle and growth theory.

A parallel development in the 1980s was the attempt by New Keynesians to derive microeconomic theories to explain wage stickiness and the various other planks on which Keynesian macroeconomic theory was built and, in so doing, to provide a rationalisation for disequilibrium theories of the cycle inspired by Keynes. Greenwald and Stiglitz (1987) assess the progress of the New Keynesian approach to business cycle modelling, which they note is in the Frisch-Slutsky tradition.

External and internal shocks, in the form of shifts in Keynesian ‘animal spirits’ that arise from modelling under uncertainty rather than risk,10 drive the cycle, which is propagated by a Keynesian disequilibrium model with wage and price stickiness and information imperfections. No endogenous theory of the cycle has been developed and no theory of cyclical growth or dynamic economic development is presented in line with the theory towards which Keynes was groping.

The stochastic linear multiplier-accelerator, the linear equilibrium business cycle and the emerging New Keynesian models are all, therefore, based on the Frisch-Slutsky approach and do not attempt to provide an endogenous theory of the cycle. They all utilise essentially linear propagation models to convert random or serially correlated shocks into cycles. Nonlinearities can, however, be used to generate endogenous cycles which can be regarded as the equilibrium motion of the economy.

Recent demonstrations of this fact are due to Chiarella (1986) and Grandmont (1985), who uses nonlinearity to derive a truly equilibrium, in the sense that the cycle is the equilibrium motion and markets clear continuously, theory of the cycle. Normally, however, the nonlinear models employ time trends to explain the movement of the point around which the limit cycle occurs.

Even with nonlinear models, the full integration of cycles and growth remains a problem. In an attempt to achieve such an integration, numerous economists have extended the Goodwin (1967) predator-prey model, which relied on trends in technical progress and the working population to generate growth. Some have, for example, tried to introduce endogenous technical progress. Goodwin stressed the need for a more disaggregated approach and in section: Goodwin’s Macrodynamics his recent work, published in Goodwin and Punzo (1987), will be discussed.

In order to develop an integrated theory of cycles and growth it may be necessary to look to Schumpeter for inspiration, as Goodwin and Kaldor suggested in the 1950s and as long-cycle theorists have done since the early 1970s. Shackle (1938) had already developed a theory which integrated Keynesian and Schumpeterian ideas with a Duesenberry-type ‘ratchet effect’ on consumption. Shackle’s work on the cycle has been largely neglected. In order to rectify this, his work on the business cycle will be reviewed in section: Shackle on the Business Cycle. First, however, Schumpeter’s contribution to business cycle theory will be briefly discussed to provide a background for the discussion of Shackle’s work and the subsequent contribution of Goodwin (section Goodwin’s Macrodynamics).

Schumpeter on Economic Evolution

No attempt is made here to survey in depth Schumpeter’s work on business cycles. Fels (1964) provides a short summary and cites references to other surveys, and innovatory assessments of Schumpeter’s work continue to be produced. Instead, a brief sketch of the essentials will be provided to form a background to subsequent sections of this chapter. Schumpeter (1934, Ch. II) distils the essential features of his theory of capitalist economic development and explains why innovations might be expected to occur in ‘swarms’.

This theory is embellished in Schumpeter (1934, Ch. VI) in an attempt to explain the Juglar, or business cycle, rather than minor, or Kitchen cycles and long, or Kondratieff waves. The embellishment includes discussion of secondary expansionary waves, which spread as a result of the burst of innovatory investment that sets the cycle in motion. Schumpeter (1939, Chs. III and IV) reconsiders the previous analysis and presents three approximations to a theory of the business cycle.

The first approximation is a two-phase cycle which is the result of stripping the Schumpeter (1934, Ch. VI) model back to basics, by ignoring the secondary wave of expansion and developing the ideas of Schumpeter (1934, Ch. II) to explain the fundamental cause of capitalism’s cyclical evolution. The second approximation involves the examination of the effects of introducing the secondary wave of expansion and consists of a four-phase cycle in which financial crises and depressions become possibilities.

Concluding his analysis of the secondary approximation, Schumpeter acknowledges that due to their historical uniqueness, observed cycles will be irregular in period and amplitude. The third approximation postulates that the process of evolution may well give rise to more than one wavelike motion. A three-cycle schema is adopted to facilitate theoretical, statistical and historical analysis of cycles of various lengths.

The basic idea is, however, that innovations may vary in importance and that the more important they are the longer the periods of gestation and absorption are likely to be. This reflects a relaxing of the assumption that swarms of innovatory investment can only occur once the economy has completed its adjustment to a new equilibrium following a previous burst of innovatory investment.

Schumpeter (1939, Ch. VI) concludes his theoretical analysis by considering the impact and causes of external shocks and special cycles, such as agricultural and ‘hog’ cycles. He argues that external shocks elicit a responsive adaptation from the economy which is fundamentally different from the evolutionary adaptation that results from internal shocks caused by bursts of innovatory investment.

Schumpeter therefore aims to describe both why the economy evolves cyclically, rather than evenly, and why business, and perhaps other longer and shorter cycles, take their observed form. His first approximation attempts to identify the fundamental cause and nature of dynamic economic development or evolution. His second and third approximations, and the discussion of ‘other fluctuations’, attempt to explain the observed business and other cycles and reconcile them with alternative theories of the business cycle. The latter tend, in his view, to concentrate on secondary aspects rather than on the primary cause of fluctuations, which is the bunching of innovatory investment.

The proposition that the bunching of innovatory investment is the primary cause of the cyclical development of capitalism is utilised by Shackle (1938), whose contribution (discussed in section: Shackle on the Business Cycle) was to employ Keynesian and Myrdallian insights to develop Schumpeter’s analysis of the secondary wave of expansion. Goodwin, like many other economists, remains unconvinced by Schumpeter’s explanation of bunching1’ and prefers to explain the apparent bunching of innovatory investment as a rapid secondary response, illustrated using his multi-sectoral input-output approach, involving what Schumpeter would call induced investment and multiplier-accelerator interaction.

Shackle’s explanation of the bunching is weak and it appears to be used as a deus ex machina. Fels (1964) notes that the clustering of innovations in Schumpeter’s analysis is not due to the rarity of innovatory genius per se. Instead it is a reflection of the fact that innovation is difficult. Untried combinations must be tested and financiers must be persuaded to back the potential new ventures. Not all will get finance and few of those that do will be successful. Once a breakthrough is made, however, other entrepreneurs will copy or improve upon it and the credibility of ventures, in the eyes of banks, will increase. Induced innovatory investment will occur, resulting in clustering.

The point of departure for Schumpeter’s theory of economic development is an equilibrium state in which there may be growth but no evolution, in the sense that no new products are coming on to the markets and no new methods of production are being tried. The underlying cause of growth in equilibrium is not analysed in depth but is attributed to population growth among other things.

The equilibrium is then disturbed by an internal shock in the form of a swarm of new entrepreneurs successfully introducing a cluster of innovations. The result is a bunching of innovatory investment. Even in the absence of secondary effects a new equilibrium must be sought, for which factors of production must be redeployed. The banks are assumed to be the main source of finance for the ‘new combinations’.12 They are seen as venture capitalists which sponsor new combinations, rather than as broking intermediaries.

They play a key role by expanding credit and creating new purchasing power to meet the additional demands of the new enterprises. In the first approximation, the entrepreneurial function is completely separated from the capitalist function, which is performed by banks. Entrepreneurs are not capitalists; they are innovators who draw on the stock of new possibilities being offered as a result of additions to the stock of knowledge resulting from inventions and other discoveries. Clearly, in a modern financial system entrepreneurs often need to look to specialist venture capitalists, rather than banks, for start-up and development capital.

The swarm-like appearance of entrepreneurs necessitates a special and distinctive process of absorption, which involves incorporating new products and technologies and adapting systems to them, and also a process of liquidation of outmoded enterprises, which must make way for the new. This process is the essence of Schumpeter’s recessions, in which the economy struggles towards a new equilibrium.

The disturbance, to which old enterprises must react, manifests itself in various ways. As the new enterprises bid for means of production, their price is bid up and this raises the cost of the old enterprises. As the new products enter the market to compete with old ones, the old enterprises face a fall in demand for their products and a decline in revenue. The seeds of recession are sown. The length of time between the formation of new enterprises and the appearance of new products, also en masse, is a fundamental determinant of the length of the boom in Schumpeter’s model.

As new enterprises begin to receive revenue, they begin to extinguish debts, and the purchasing power created by banks begins to disappear. The reduced profitability of the old enterprises and the increased uncertainty that follows rapid change will make banks wary about diverting credit to old enterprises. The new enterprises enter a highly competitive environment with differentiated products and earn monopoly profit for a period, but it is gradually eroded by competition.

Eventually the period of prosperity gives way to a recession. Businessmen must learn to adapt to the new situation in which new competitors have become established, old customers and lines of credit cannot be relied upon, and production levels must be adjusted to prevent the accumulation of stocks of commodities that have become more difficult to sell. Schumpeter therefore regards the recession as a process of adjustment and ‘resorption’. Old businesses must adjust and new ones must survive their first test.

The next boom cannot start until the adjustment is nearly complete and a new equilibrium is approached. This is because the high level of uncertainty that is present while adjustment is taking place discourages new investment. Given the assumed separation of the entrepreneurial and capitalist functions, this must be due to the unwillingness of banks to lend.

The fundamental process of economic development described above is embellished in Schumpeter (1934, Ch. VI and 1939, Ch. IV) by the introduction of a secondary wave of expansion. The banking sector also plays a key role in the financing of the secondary wave, which is based on a sort of multiplier-accelerator expansion. As a result of the secondary wave, excesses can occur and there is likely to be significant overshooting of the new equilibrium.

Financial crises can occur as a consequence and the ensuing recession can develop into a depression if overshooting in the downward direction results. A problem of explaining the lower turning point then arises and Schumpeter argues that government economic policy should aim to terminate depressions because, unlike recessions which entail a movement towards a new equilibrium, they serve no useful purpose. Policy-makers are not told, however, how to identify the point at which recession turns into depression and the new equilibrium is overshot. Once terminated, the depression gives way to a recovery or revival, which is also a motion towards equilibrium.

The new equilibrium is unstable in an upward direction and following another burst of innovatory investment, a new expansionary phase, with its primary and secondary waves, begins. The depression phase, it is argued, is not a necessary part of economic development but may feature in some business cycles and so too might financial crises. Institutional reform and macroeconomic policy should, therefore, concentrate on the elimination of depressions and financial crises, but it should be accepted that cyclical evolution is the norm for capitalist economies. By deciding which innovations to sponsor and, in pursuit of profit, allocating capital as efficiently as they can, banks in capitalist economies essentially play the role that the planning agency plays in centrally planned economies.

Each cycle, Schumpeter argues, is a historical individual in the sense that it will depend on the nature of the particular innovations that provide the initial shock starting the cycle and the prevailing structure of the economy and the financial system. These factors are in turn clearly influenced by the evolution that has preceded the cycle in question. Given the uniqueness of each cycle, there is no need to expect regularity of period or amplitude. Further, Schumpeter argues in his third approximation, there is no reason to expect that the cyclical evolution will consist of only one wavelike motion because innovations have different periods of gestation and absorption. It is more likely, he concludes, that there is a multiplicity of cycles which may or may not be related in some way.

The internal shocks caused by the bunching of innovatory investment, Schumpeter argues, give rise to a primary tendency to cyclical evolution, which is the manifestation of the economy’s adjustment to these shocks and which Schumpeter calls economic development. Because of the diverse nature of the shocks, the primary cycles can vary in period and amplitude.

The capitalist economic system is organised in such a way that these internal shocks are likely to be amplified by secondary waves of expansion which give rise to the possibility of financial crises and depressions. The government’s role should be to regulate the capitalist system to prevent excesses leading to crises and to utilise monetary and fiscal policy to attenuate depressions.

The economic system is also hit by external shocks which will themselves create a need for economic adjustment. This is not regarded by Schumpeter as being part of the development process, but it will clearly add to the irregularity of cycles and assure their historical uniqueness. The shocks are also likely to add to the amplitude of cycles in the way that the secondary waves of expansion and other factors, discussed in Schumpeter (1939, Ch. IV), are assumed to do. Before a discussion of the related work of Shackle (1938), the next section will consider the hypothesis that there are longer cycles than the business cycle, and related issues.

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.

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. 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 neighbouring 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 scepticism 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 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 judgement 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: A Brief Overview of Cycle Modelling. 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.

The growth trend

Anticipating the contribution of Nelson and Plosser (1982), discussed below, Blatt (1980) points out that the Frisch-Slutsky hypothesis implies that business cycles are caused by shocks and that any attempt to include business cycle-like oscillations as part of the trend curve produced by the model runs directly counter to the Frischian view. Nevertheless, he notes that the trend does not have to be strictly linear to be consistent with the Frisch-Slutsky hypothesis.

If nonlinear, however, it should be stable with smooth curvature. It should not itself display fluctuations in the business cycle time-scale because otherwise detrending would remove part of the business cycle phenomena to be explained. In the light of the discussion of section: The Long Swing Hypothesis and the Growth Trend, it should be added that the trend should not display regular cycles of longer duration either, because these would instead be consistent with the various long swing hypotheses.

In section: The Monte Carlo Hypothesis it was noted that there is a growing tendency, even at the NBER, to analyse cycles using detrended data.16 In many analyses (log) linear trends are assumed and elsewhere moving average trends are estimated. The presumption in favour of (log) linear trends is a natural extension of the linearity hypothesis, but the data should at least be examined to see if it is appropriate; otherwise detrending will distort the series. It was noted in section: The Long Swing Hypothesis and the Growth Trend, however, that the more sophisticated approach of estimating a moving average trend introduces its own distortions which often show up as spurious cycles of longer duration than the business cycle, as defined by the NBER.

Detrended data used for business cycle analysis is, therefore, highly likely to be distorted and in the absence of better methods of trend estimation, which take account perhaps of the structural changes that occur during long runs of data, it is hard to escape Burns and Mitchell’s (1946) conclusion that it is better to work with non-detrended data.

Nelson and Plosser (1982) challenge the Frischian view, as expressed by Blatt (1980), that macroeconomic time series are best characterised as stationary fluctuations around a deterministic trend. They argue instead that they should be viewed as nonstationary processes that have no tendency to return to a deterministic (trend) path. They see no reason why the secular movement in economic time series should not itself be stochastic and observe that if it is, then models based on deterministic time trend residuals will be misspecified.

They illustrate the types of misspecification that can arise from inappropriate detrending by considering the properties of residuals from a random walk on time, which are known to display drift, similar to secular movements, which is stochastic rather than deterministic in nature (see section: Rational Speculative Bubbles ). They show that the autocorrelation function of the deterministic time trend residuals is a statistical artifact which is determined entirely by sample size. The autocorrelation function displays strong autocorrelation at low lags and pseudo-periodic behaviour at long lags.

Empirical investigations that ignore the possibility that a stochastic trend is the source of the autocorrelation might, therefore, be led to overestimate both the persistence and variance of the business cycle. Further, to the extent that the stochastic nature of the trend can be associated with real shocks, the use of a deterministic trend will underestimate the influence of real shocks.Since the basic statistical issue is the appropriate representation of nonstationary economic time series, Nelson and Plosser (1982) consider two fundamentally different classes of nonstationary processes as alternative hypotheses. One class consists of deterministic function of time plus a stationary stochastic process with zero mean, referred to as the trend-stationary (TS) process.

It is judged that such processes are most appropriately applied to the natural logs of economic time series, and deviations from trend, the so-called cyclical components of the series, are represented as invertible ARIMA processes.

The second class of nonstationary process considered is that in which first, or higher order differences, are a stationary and invertible ARIMA process. This is referred to as a difference-stationary (DS) process and the first order case is used to explain the natural logs of the economic time series examined. The DS class is purely stochastic and the TS class is fundamentally deterministic.

Various historical time series from the United States, including measures of output, spending, money, prices and interest rates, are examined and the relationship of the analysis to McCulloch’s test of the Monte Carlo hypothesis is noted. In particular McCulloch (1975) finds some evidence of periodicity in the logs of real income, investment and consumption after fitting a linear trend but finds no periodicity in their first differences, a finding consistent with their results.

The sample autocorrelation structures for the series are found to be consistent with those expected from a random walk.17 The exception is the unemployment rate series, which exhibits autocorrelation properties consistent with a stationary series. The autocorrelation structures of real, nominal and per capita GNP, real and nominal wages and common stock prices display positive autocorrelation at lag one only. This is characteristic of first order MA processes and inconsistent with the TS model.

The GNP deflator, consumer prices, the money stock and the bond yield exhibit more persistent autocorrelation in first differences but do not show evidence of having been generated by a differenced TS process. In sum, Nelson and Plosser find their evidence to be consistent with the DS representation of nonstationary economic time series.

They do, however, recognise that their tests have little power against the alternative hypothesis of a TS process with an AR root close to unity. This alternative implies little tendency to return to trend and could be indicative of a stable limit cycle produced by a nonlinear model.

Their results, therefore, suggest that economic time series contain stochastic trends of the DS type rather than deterministic time trends. In this case, if (the log of) output is viewed as the sum of a secular or growth component and a cyclical component, and the latter is assumed to be transitory (stationary), then any underlying nonstationarity must be attributed to the secular component. Thus if actual output is in the DS class then so too must be the secular component.

The separation of the secular component from the observed data can, they note, be thought of as a problem of signal extraction when only the information in observed series itself is used. Using, as an example, Friedman’s permanent income model they show that it is not always possible to identify the cyclical and secular components. However, if the cyclical component is stationary and, as they discover, the autocorrelations in the first differences of output are positive at lag one and zero elsewhere, then they demonstrate that the variation in actual output changes will be dominated by changes in the secular, rather than the cyclical, component.

They acknowledge that they cannot prove empirically that cyclical fluctuations are stationary or transitory but feel that their evidence is strongly supportive of the hypothesis that the business cycle is a stochastic process of the DS class.

The hypothesis that the cycle is stationary is implicit in the Frisch 1 hypothesis, which assumes that cyclical fluctuations dissipate over time and the cycle is the result of hitting the propagation model with repeated random shocks. Long-run or permanent movements (nonstationarities) are attributed to the secular (trend) component and are the result of real factors.

Nelson and Plosser believe most economists accept both the Frisch I hypothesis and this view of the trend and, therefore, that the cyclical component is stationary. Finally, they observe that assigning a major portion of the variance in output to innovations in the nonstationary component gives an important role to real factors in output fluctuations and places limits on theories of the business cycle that stress the importance of unanticipated monetary disturbances, such as the Lucas (1975) model. The debate between proponents of real and monetary causes of the business cycle is reviewed in section: Equilibrium Business Cycle (EBC) Modelling.

Nelson and Plosser (1982) therefore provide another strong warning against using residuals from fitted deterministic trend lines for the empirical analysis of business cycles. If the trend follows a nonstationary stochastic process, a possibility that cannot be discounted, then the residuals will contain both cyclical and stochastic trend variation and the magnitude and duration of the supposedly cyclical component will be overstated.

They also warn that first differencing will not remove the stochastic growth component but may render the time series stationary, and the problem of inferring the behaviour of each unobserved component from the observed sum, the signal extraction problem, will remain.

Shackle on the Business Cycle

Shackle (1938) regards his cycle theory as being more like the one Keynes was moving towards than the ‘Keynesesque’ neoclassical multiplier-accelerator interaction models (see Shackle 1967, p.266). He attempted to provide an integrated theory of the multiplier and the investment process in a model with interdependent markets and sectors. Shackle (1967, Ch. 14) later drew a strict distinction between the income-expenditure (Kahn) multiplier, the accelerator and the input-output multiplier. He stressed that underlying the Kahn multiplier is the interdependence of all sectors and components of the economy and that this entails a less mechanical multiplier-accelerator interaction than that expounded in Keynesesque models.

Goodwin’s work, which develops these ideas, is discussed in the next section. By combining the Kahn multiplier with a Schumpeter-like clustering of innovations and a Duesenberry-type consumption ratchet effect, Shackle (1938) is able to derive an essentially endogenous theory of the cycle.

Like many other cycle theorists, Shackle was primarily concerned with explaining the major or Juglar cycle, which seemed to be prevalent in the United Kingdom, and implicitly accepted that the minor or Kitchen cycle was an inventory cycle. At the outset he makes it clear that economic decisions are made under uncertainty, rather than risk, in the sense of Keynes (1936) and Knight (1921). Consequently economic conduct is not completely rational but, he argues, this does not imply that economists cannot theorise rationally about it.

Nevertheless, he notes that there is a tendency to draw the opposite conclusion and that this has led to a preference for the Walrasian equilibrium framework. We might add that latterly it has led to the widespread adoption of the rational expectations hypothesis and equilibrium business cycle modelling. In the Shackle tradition, the New Keynesian school is making renewed efforts to develop disequilibrium business cycle models in which decisions are made under uncertainty.

Shackle (1938) in fact presented two theories of the cycle. One is a theory, closely related to the work of Schumpeter, in which a bunching of innovatory investment initiates a cycle in which the income-expenditure multiplier and induced investment also figure prominently as a result of the interdependence of sectors of the economy. The other is an attempt to develop the General Theory’s insights using what Shackle calls Swedish sequence analysis.

The General Theory had concentrated on explaining underfull employment equilibrium. It had not proceeded to develop a dynamic theory of the cycle, though Keynes believed that he had laid the foundations for one by developing Kahn’s income-expenditure multiplier idea.

In 1936, fired by the Myrdallian idea of ex ante and ex post and a belief in the vital role of expectations, Shackle tore up a year’s work on the Austrian theory of capital and began to study the new (post-General Theory) Keynesianism in the light of the new Wicksellianism. The resulting doctoral thesis formed the basis of Shackle (1938). Shackle did not regard the two theories contained therein as being mutually exclusive.

Shackle viewed Keynesesque multiplier-accelerator theory as retrograde because it incorrectly attempted to replace the concept of an equilibrium point with an equilibrium trend or cycle and to dispense with the use of outside influences to explain the cycle. However, in a stochastic world, which Shackle clearly believed in, nonlinearities are required to generate an endogenous cycle. What Shackle was probably trying to highlight was that the essence of the General Theory was the instability of investment that resulted from its dependence on unexplainable expectational variables.

He stressed that Keynes’s system was essentially open in the sense that it was subject to both exogenous shocks and internal shocks which affected functions and parameters. The investment decision was regarded as nonrational (not irrational) because of its dependence on expected profits and the unknowable future, even to the extent that investment can be expressed as a function of the interest rate.

Shackle noted that the rate of interest itself is a function of the expected interest rate (1967, p.247) because of the speculative motive for holding money. The General Theory itself, Shackle observed, has little to say about how expectations are formed under uncertainty, regarding them as a free autonomous variable.

Shackle concentrates on investment as the key to understanding the business cycle and stresses the importance of expectations formation under uncertainty as an influence on investment decisions. In this respect his work is consistently Myrdallian. It is a world where:

People must find out, compare and decide before they act; then register results and make fresh plans and decisions. (1967, p.270)

Shackle’s Schumpeterian theory is based on the bunching of inno-vations and its impact via the income-expenditure multiplier. Shackle observes that businessmen are less confident and exact in their expectations following a large scale change wrought by a major investment. Past experience provides little guidance and consequently, following a new investment, businessmen need a learning period to explain new possibilities and develop new plans.

In this period they are essentially involved in ensuring that the new system is managed efficiently. Monetary influences are also important. Having undertaken new investment, firms will be highly geared and face financial constraints on further expansion. Individual businesses are, therefore, likely to show alternating periods of growth and constancy of physical equipment, an improvement phase being followed by a testing phase. If the phases of the majority of businesses ‘cluster’ then cyclical variation of aggregate investment will follow.

To explain the clustering, Shackle invokes the interaction of multiplier and induced investment. The latter is not based on a fixed coefficient accelerator, which Shackle rejects as unrealistic, but is influenced by input-output interaction. The clustering of investment activity leads to a rise in construction costs and the price of capital which eventually chokes off the boom.

Shackle believed his Myrdallian theory to be more interesting. Following a rise in autonomous investment, perhaps due to a burst of innovatory investment, there is a multiplier-based expansion leading to induced investment which has further multiplier effects and so on.

The process can only continue, Shackle argues, as long as the multiplier effect is unexpected, for once it comes to be expected net investment will have reached a maximum because there will be no further unexpected increase in aggregate income to induce an increase in it. The failure of net investment to accelerate will eliminate the multiplier effect and, with growth reduced, investment will fall and a downswing will ensue. The whole cycle is explained by changes in expectations which are generated continuously by the effects of former changes. Investment is again the key variable.

The multiplier-induced expansion, which follows the rise in autonomous investment, causes an unexpected improvement in business outlook and induces a further increase in investment. The accelerator effect therefore does not mechanistically depend on the capital-output ratio, as did Harrod’s (1936) ‘Relation’, but is the consequence of business psychology.

Even though Shackle is not seeking a fully endogenous theory of the cycle, he states:

The business cycle is much more akin to fatigue than to disease in that it is not an exceptional or accidental occurrence but part of the nature of a modern industrial economy. (1938, p.5)

The theory is, however, endogenous in the sense that the most important shocks are the internal ones that lead to shifts in businessmen’s psychology, rather than the external or exogenous shocks that drive Frisch-Slutsky-type cycle models.

Shackle’s Schumpeterian theory is based on the idea that there is a ‘leaping fountain’ of investment opportunities due to a continuous stream of inventions which provide innovatory opportunities. At some point some entrepreneurs will act to take advantage of these opportunities because of a shift in their expected profitability.

Once autonomous investment increases the multiplier comes into play and causes bunching and the cycle follows. There does seem to be a risk that the cycle could stick at the floor for some time if expectations concerning profitability remain depressed. The Wicksellian theory requires an initial rise in autonomous investment and, to the extent that this is a result of a burst of innovatory investment, the two theories can be integrated. Shackle is more optimistic than Keynes, who sees a ‘stagnating pool’ of investment opportunities (Keynes 1936, Ch.17). There may, however, be some stagnation in times of recession, when pessimism prevails, and this may lead to a protracted depression.

Expanding on his theory, Shackle identifies two types of industry: one producing consumption goods and the other investment equipment. The expansion phase is initiated by a shift in expectations leading to investment. Workers are taken on, consumption expenditure rises and there is a multiplier effect. This leads to induced investment by the consumption industries and a secondary multiplier effect and then to increased demand for the products of the equipment industries and induced investment by them.

A third multiplier effect results and so on. In the Schumpeterian theory the upswing ends when the price of capital rises as a result of bunching and the process goes into reverse, causing a downswing. Alternatively the multiplier loses its impact once it comes to be expected, as in the Wicksellian theory.

Shackle postulates that the downswing is unlikely to witness an equiproportional decrease in the activity of the equipment and consumption industries because a Duesenberry-type ratchet effect will prevent consumption falling as fast as income. Investment will, therefore, fall more rapidly than consumption. He notes that because of the ratchet effect the expansion and contraction phases are likely to be asymmetric. Shackle therefore identified, at an early stage, the importance of nonlinearities for explaining the observed asymmetry of business cycles.

As the recession persists two processes are ongoing. Entrepreneurs are gradually overcoming the disappointment of their expectations in previous crises, and foreseen and unforeseen events are changing their economic outlook. To the extent that they influence business outlook, the unforeseen events or external shocks play a role in Shackle’s theory. With the accumulation of new apparent opportunities and the return of the desire to exploit them there is an increase in investment and the recovery gets under way.

The foreseeable events include demographic changes, improvements in infrastructure, and innovation. The unforeseeable events include political crises, disasters and windfalls, and inventions. Inventions are seen as the primary source of the fountain of continually changing opportunities. Shackle identifies two types of invention: new consumables and technology changes.

Shackle’s integrated Schumpeterian-Wicksellian theory, therefore, consists of a boom generated by the interaction of induced investment with the income-expenditure multiplier and the clustering of inventions. It comes to an end as the price of capital rises due to the clustering, the most profitable investment opportunities are exhausted, and the multiplier comes to be expected.

The interaction of the multiplier and induced investment, through input-output interaction, can explain the clustering. The Wicksellian theory, Shackle feels, needs help to explain the upturn, while the Schumpeterian theory may need help to explain the downturn. The integration of theories helps to overcome their weaknesses.

Shackle concludes by presenting a number of alternative (to the consumer-expenditure ratchet effect) explanations of asymmetry. One is based on the idea that the marginal propensity to consume will decline during the boom and that as the peak approaches the multiplier will be small for increases in income but large for decreases, with the reverse holding in the trough. Another explanation revolves around the behaviour of the banking system which will have a strong incentive to reduce its outstanding loans when the boom busts.

As a consequence banks are likely to raise their interest rates and put pressure on debtors to reduce their expenditure. This will further discourage investment. The boom starts with a return of courage and desire for entrepreneurial activity. During the depression, technical progress will have rendered some capital obsolescent.

The equipment industries will initially have spare capacity and the supply of capital goods will be elastic. Individuals will have increased their monetary balances as a result of the speculative motive and banks will be looking for lending opportunities. Credit will, therefore, be cheap and the price of capital will be low and expected to remain so, at least in the short run, and modernisation will be required. Cumulative recovery and boom, based initially on cheap bank credit pending the issue of new securities, can therefore be expected.

Goodwin’s Macrodynamics

Goodwin explores similar ground to Shackle (1938). In so doing he employs modern mathematical techniques to develop ideas which he had previously explored20 using more primitive mathematical tools. Influences on Goodwin’s work include Keynes, Harrod, Schumpeter, Sraffa, von Neumann, Kalecki and Marx. The result is a magisterial attempt to analyse the process of capitalist economic development.

Goodwin adopts a multi-sectoral approach in order to emphasise the high degree of interdependence of various sectors of the economy, which he views as a ‘system’ in the sense that it is a structure in which the interaction of the parts is as important as the nature of each part. Further, it is a system which is continuously changing, although not at a uniform rate, and which is inherently nonlinear.

This creates a problem because it is not currently possible to solve a general n-equation system of nonlinear equations. It is difficult enough to solve systems of two or three nonlinear equations and Goodwin notes that limit cycle theorems cease to hold when there are more than two equations. Linear approximations must therefore be employed, but this need not be too damaging if linearisation is done with caution, Goodwin argues.

He is not therefore advocating general linearisation and accepts that, as a result of the approximation, his results have limited validity. They will only be applicable in the short run, rather than the long run: which, in the tradition of Keynes and Kalecki, is regarded as a series of short runs.

Goodwin draws attention to the inability of linear models to explain the generation of limit cycles. In spite of this, he demonstrates that piecewise linear analysis can be employed to explain the existence and persistence of oscillations. He provides an illustrative example in which a two-sector model has two distinct regimes, one stable and one unstable, and shows that such a system can generate a limit cycle.21 Although piecewise linear, the overall model essentially contains type I nonlinearities22 because there are bifurcation points at which qualitative changes in economic behaviour occur with movements from stable to unstable regimes.

Goodwin’s method of analysis is then to apply systems theory to multi-sectoral macroeconomic models to facilitate analysis of qualitative changes in the behaviour of economic models. Catastrophe theory and the theory of bifurcations23 are employed to explain why the economy moves between qualitatively different regimes and to examine the effects of moving backwards and forwards between such regimes. To make use of catastrophe theory, the piecewise linear systems include variables with fast and slow adjustment speeds.

The general objective of Goodwin’s analysis is to develop the observation of Marx and Schumpeter that capitalism grows in fits and starts. He argues that the driving force of the evolutionary dynamics of the capitalist economic system is the relentless search for profit. The Schumpeterian view that innovation is the root cause of cyclical growth is viewed as central to the understanding of dynamic economic development or the evolution of the economy. The continuous drive for profits forces technical change but the morphology is not smooth. Rather than through steady growth, the economy evolves by way of a series of rapid expansions followed by recessions, and occasionally depressions.

Goodwin argues that the major constraints on economic growth are the inputs that cannot be produced by the economy, namely ‘labour’ and ‘land’, and that until now the ‘land’ constraint has not been binding. The rate of extraction of raw materials has proved to be fairly elastic, and synthetic substitutes have often been produced as part of the innovatory process.

The binding constraint has usually, therefore, been the size of the working population. Goodwin discusses the possibility that the land constraint may become binding in the future if a concerted attempt is made to eliminate the unemployment that has persisted in the 1980s by stimulating significantly faster growth. In his model this could be brought about by an increase in government expenditure.

The sustained high level of unemployment might reflect, he feels, the widespread adoption of computer- and robot-based technology. In the same way that innovatory investment has enabled production of synthetic substitutes for raw materials, it has now made a major breakthrough in replacing human brain and muscle power and co-ordination.

The coefficients of the technology matrix employed in his multi-sectoral analysis may have changed substantially from those prevailing in previous periods, to which his analysis is perhaps more applicable. An alternative view is that Goodwin’s assumption that the growth of the working population is steady is unrealistic and that a fluctuation in population growth contributed significantly to the rise in unemployment in the 1970s and 1980s.

Under this view it is perfectly possible that the labour constraint will reassert itself, as it appeared to be doing, especially where skilled labour is concerned, in a number of OECD countries towards the end of the 1980s following a sustained period of growth. It is also likely that population growth itself is influenced by economic growth.

Goodwin’s analysis is based on the assumption that growth is unstable in an upward direction in the sense that, once started, the expansion phase develops into a boom period of exponential growth. The exponential growth reduces the reserve army of the unemployed, which is the available trained and disciplined workforce not currently employed. The fall in unemployment leads to an excess demand for labour, which encourages firms to bid up wages and bestows greater bargaining power upon the trade unions.

Once the labour constraint begins to bite, the rise in real wages will lead to a reduction in profits. Firms will explore cost reducing, labour saving innovatory investment opportunities. Nevertheless, growth will eventually slow and the optimistic expectations, on the basis of which the investment was undertaken, will be disappointed. The upper turning point will have been reached and declining aggregate demand and output will lead to recession and a decline in employment. The boom is thus terminated as the growing economy bumps up against a Hicksian ceiling imposed by labour shortages (see Hicks 1950).

The rise in unemployment leads to a reduction in the rate of growth of wages and it is assumed that labour saving investment will continue in an effort to reduce labour inputs and restore profitability. The possibility of getting stuck in a depression is acknowledged and it is stressed that the problem of explaining the lower turning point is harder than that of explaining the upper one.

But if the stimulus of autonomous innovatory investment proves insufficient to lead the economy out of the depression, then Goodwin feels that the government has the option of expanding autonomous expenditure by increasing its own expenditure. Goodwin does, however, assume that autonomous innovatory investment will generally lead the economy out of a recession and essentially provide a Hicksian floor (Hicks 1950).

The cycle model described is clearly also related to the Goodwin (1967) model, which examines the symbiosis of capital and labour, and to the Kalecki (1943) model, which has spawned a literature on political business cycles.24 Kalecki considers how the state might be expected to behave in a capitalist system. In Kalecki’s model its role is essentially to ensure that the ‘reserve army’ remains disciplined and prepared for work.

This is done by allowing booms to be terminated, rather than sustaining them using Keynesian policies, and attenuating slumps by stimulating demand. Developing these ideas, Boddy and Crotty (1975) have pointed out that periodic employment of members of the reserve army is essential to prevent loss of skills, just as periodic unemployment is necessary to maintain discipline. This would imply that the long-term unemployed of the 1980s have effectively ceased to be members of the reserve army and have become an ‘underclass’ of unemployables instead.

This may explain why high unemployment levels appear to have little influence on wage bargaining while the rate of change of unemployment has a more significant impact. According to this view, governments may have found it necessary to encourage a sustained increase in unemployment to discipline workers after the excesses of the 1970s and now need to introduce retraining schemes to bring the long-term unemployed back into the reserve army.

In Goodwin’s model, the lower turning point occurs because even though profits are low and there is abundant excess capacity, innovatory investment will be spurred by the ceaseless search for increased profitability. He suggests that rather than being lumpy, as postulated by Schumpeter and Shackle, technical change may in fact progress fairly smoothly by virtue of being the result of many small independent events. Nevertheless, it is capable of giving rise to cyclical output growth. Innovatory investment in the slump may not be directed towards labour saving, as it is in the boom, but towards cost reduction and the creation of new products.

Innovatory investment is regarded as the source of autonomous as opposed to induced investment; and because it is assumed to grow relatively smoothly, it effectively establishes a floor, in the Hicksian manner, and helps to explain the lower turning point. The size of the ensuing expansion will depend on the technological significance of the innovations. If they are of major importance, Goodwin postulates, then long waves may be generated. If they are of lesser importance, then they will not give such a large impetus to growth.

Thus Goodwin employs what he regards as Schumpeter’s key insight: that new processes lower costs and restore profitability, even in conditions of excess capacity. He attaches less importance to the bunching of innovations, which Schumpeter and Shackle regard as so important. He attributes the apparent bunching to multiplier-accelerator interaction, which is analysed using a multi-sectoral model.

The trend increase in autonomous innovatory investment leads to a change in the parameters of the technology matrix as well as an increase in the level of investment. Via input-output relationships and the interaction between consumption and investment, a matrix multiplier-accelerator interaction generates exponential growth. Using the multi-sectoral approach, he is able to formalise ideas that seem to underlie Shackle’s (1938) description of the multiplier-accelerator interaction process.

The multi-sectoral approach employed by Goodwin is a stark contrast to the market islands scenario discussed in section: Equilibrium Business Cycle (EBC) Modelling , but Goodwin does employ a Lucasian limited information assumption. Producers are assumed only to observe information in their own markets. Each market or sector, however, directly or indirectly depends on every other; therefore shocks to one sector will eventually affect all other sectors in the system.

The transmission mechanism described by the input-output relationships can be regarded as fixed in the short run. All sectors will nevertheless change at different rates, though normally in the same direction, Goodwin argues. Because shocks are unlikely to hit the same set of sectors with the same magnitude twice and technological events will have changed in the improbable event that they do, economic development is likely to be highly irregular and historically unique. Thus the problem for analysts of economic dynamics is, Goodwin argues, to discover the response of a slowly changing structural system to a series of external shocks. This makes it particularly intractable and suggests that catastrophe theory might be a useful tool for the analysis of economic systems.

Goodwin’s adoption of the multi-sectoral approach is enlightening and appears to be consistent with the model Shackle (1938) had in mind. His decision to model innovatory investment as a smooth trend, rather than as appearing in swarms as hypothesised by Schumpeter and Shackle, is consistent with the analysis of Hicks (1950) and Goodwin’s earlier work on the business cycle. This is perhaps the least satisfactory aspect of his important contribution tothe theory of dynamic economic development.

In Shackle (1938), the bunching of innovatory investment is essentially a deus ex machina. Goodwin finds that it is unnecessary to use such a device in his more sophisticated multi-sectoral model. Neither Goodwin nor Shackle appears to get to grips with what Schumpeter was attempting to do. This was to explain how autonomous investment is generated. This, and the wider issue of technological diffusion, is examined in the long swing literature.

There is no space to review this literature here, but clearly the insights employed by Goodwin, that diffusion can be described by changes in the coefficients of the technology matrix, must be developed further. It is simply not sufficient to assume that these changes occur smoothly, as if described by some simple time trend.

Concluding Remarks

Shackle attempted to synthesise Keynes’s insights into the implications of decision-making under uncertainty, especially with regard to investment, with ideas, normally associated with Schumpeter, concerning the effects of the bunching of innovations. He also considered the implications of nonlinearities, in the form of ratchet effects and an implied nonlinear consumption function, for the asymmetry of the cycle. Finally, he considered the implications of introducing a banking system into the model.

His work could be extended using New Keynesian insights, such as wage contracts and implicit price contracts. The mechanism for the diffusion of innovations and the role of input-output interactions clearly require further examination. Long and Plosser (1983), and others working with real business cycle (RBC) models, have also begun to explore the implications of input-output interactions for the business cycle, while work on the diffusion of technical progress has so far been mainly associated with long-cycle analysis.

However, using a multi-sectoral model, Goodwin and Punzo (1987) make a major contribution to the analysis of the role of technical change in dynamic economic development. Goodwin ignores the bunching of innovations stressed by Schumpeter and Shackle in explaining the lower turning point, and also the role of the financial sector in general and the banking sector in particular, although he acknowledges that financial instability may contribute to the upper turning point. There is, therefore, still some way to go, but they point us in the right direction.

By stressing the importance of real as opposed to monetary shocks, the RBC approach has neglected the role of the banking and the wider financial sector in cycle propagation. Lucas (1987) and Eichenbaum and Singleton (1986) have suggested a synthesis of real and monetary shock-induced equilibrium business cycle theories.

The Keynesian econometric models of the 1960s and the early 1970s also tended to have underdeveloped monetary and financial sectors. Further work clearly needed to be done to develop a model in which money and banking played an important part in the propagation of cycles. Some progress has been made in modelling the monetary transmission mechanism since the mid-1970s and numerous non-Keynesian models have been developed, but the essential role of the financial sector in cycle generation is perhaps still not fully understood.

More generally, greater attention needs to be paid to the propagation model. The tendency has been to adopt the Frisch-Slutsky approach without question and, if the propagation model cannot generate realistic cycles from random impulses, to assume that the shocks are themselves serially correlated. Convincing explanations of why shocks should in fact generally be serially correlated have yet to be presented.

This approach begs the question of whether an endogenous theory of the cycle, or a theory which at least relies less heavily on shocks, should be sought. The existing endogenous theories utilise nonlinearities but a systematic attempt to identify the nonlinearities that form the basis of such theories has not been undertaken. As Zarnowitz (1985) concludes, following a sifting of the evidence derived from confronting the various testable hypotheses with economic data, a synthesis of competing business cycle theories is required.

The synthesis model will have to be a structural one. It will, therefore, be necessary to move away from the quasi-reduced form vector-autoregressive models (VAMS) that have been prevalent in the literature since the mid-1970s. More complex econometric models, in the spirit of those abandoned in the face of the ‘Lucas critique’ (Lucas 1976) and Sims’s (1980) warnings concerning ‘incredible identification’ restrictions, will have to be built.

Such models will need to pay more attention to microfoundations than their predecessors and will perhaps incorporate New Keynesian insights and sectoral analysis based on input-output relationships. They will also need to pay more attention to the role of money and the modelling of the banking and wider financial sector and its interaction with the other sectors.

Additionally they should exploit the profession’s improved understanding of time series analysis. The over-identifying exclusion restrictions should be analytically and empirically justified. Finally, the models should aim to explain dynamic economic development as a combined process of growth and the business and perhaps other cycles. In order to take account of the ‘Lucas critique’, the game-theoretic context of economic decision-making will need to be given further consideration and the implications of the uncertain environment for decision-making will have to be considered further. In the presence of uncertainty, as opposed to risk, the rational expectations hypothesis is inadequate and alternative expectations formation mechanisms and their implications must be considered.

Finally, developments in the field of open economy macroeconomics28 must be acknowledged in the modelling of dynamic economic development. It is widely accepted that the world’s economies have become increasingly interdependent and that the greater capital mobility permitted since the early 1970s has accelerated this process.

There seems to be a growing international synchronisation of cycles among OECD countries and this has major implications for North-South relationships. In the pre-war period there was also evidence of an increased synchronisation of cycles. In the post-war period there was little evidence of synchronisation but it has emerged again since the early 1970s29 as globalisation has progressed. The causes and implications of this require further investigation.

Eichengreen and Portes (1987) made a start by attempting to identify the most important international linkages and the major similarities and differences between the 1920s and 1930s and the 1970s and 1980s and ‘global imbalances’ (Rajan, 2010) persist between trade surplus countries, such as China, and trade and fiscal deficit countries, such as the US, were a major cause of the GFC. The global imbalances got worse and persisted in the run up to the 2007-9 Global Financial Crisis and worringly, did not unwind in its aftermath.

The re-emergence of synchronisation appears to have been combined with the return of the ‘classical’ business cycle, in place of the ‘growth cycles’ of the 1960s, and a decline in the growth rate. This suggests a clear link between cycles and growth which requires further investigation. An explanation of why shifts in the revealed statistical growth trend occur from period to period is also required. Students of long cycles may well have a contribution to make here.