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 (see section 2.3). 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 (see section 2.3), 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 (see section 2.3), 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 2.2, 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 to the 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.