A second approach to stability analysis is to construct models that account for the potential instability of real-world economies by relying on weaker concepts of dynamic equilibrium than those underlying the neoclassical tradition. Various approaches have been taken in the attempt to reconcile instability and equilibrium. The first is that of traditional Keynesian growth models based on the notion of steady growth. Another is the restatement of Keynesian views on the basis of non-linear dynamics. A third approach is represented by endogenous growth theory.
Harrod and Keynesian growth theory
In order to assess the traditional Keynesian theory of growth based on the notion of steady state, we shall begin with a brief analysis of macroeconomic debate following the publication of the General Theory. Keynes’s theory was generally considered applicable only to the short run. In fact, his book lacks virtually any reference to long-period analysis in the ‘modern’ sense of the term. Indeed,
the various statements to be found in the General Theory about long-term problems…are not based on any formal analysis of changes that are likely to take place over time. There is no attempt to link a sequence of short periods and to trace the changes from one to the other that lead to growth and to cyclical movements.
(Asimakopulos 1991:121–2) Moreover, Keynes altogether rejected the use of mathematical formulas to account for sequences of short periods, owing mainly to his belief that long-term expectations cannot be modelled on the basis of past data. This view is evident, for example, in his critique of Tinbergen’s study on the statistical testing of business cycle theories.1
In the late thirties, these aspects of Keynes’s analysis were considered to be major flaws. That is why, after the General Theory was published, ‘with the use of modelling as a common language, economists attempted to represent Keynes’s ideas on business cycles in a variety of mathematical forms’ (Jarsulic 1997:377). Many theorists turned to macroeconometric models employing linear stochastic equations; however, in doing so, they tied themselves to a severely limited dynamic framework lacking ‘an endogenous economic account of business cycle behaviour’ (ibid.: 377).
These limitations were eventually overcome by authors such as Harrod and Kalecki (followed later by Joan Robinson, Kaldor, Goodwin and Pasinetti), who sought to extend Keynes’s short-period analysis to consideration of accumulation over time. This they
accomplished by providing a formal account that very much resembles modern growth theory (see e.g. Asimakopulos 1991; King 2002; Thirlwall 2002). Kalecki developed a mathematically determinate business cycle theory drawing on the dual relation between profits and investment and changes in capital stock.2 Harrod, instead, set out to demonstrate that the business cycle is but one aspect of the growth process. His dynamic approach stemmed from the view that positions of static equilibrium cannot be taken as a starting point for the correct analysis of cyclical phenomena but that these phenomena
‘should be regarded as oscillations around a line of steady growth’ (Harrod 1951:261).
Harrod thus criticized the General Theory for being static (as it focuses on levels of income, not on rates of growth) and limited to the short period (it neglects changes in productive capacity), arguing that it needed to be complemented by a dynamic equilibrium theory concerning rates of growth.3
Harrod initially focused on the relationship between the multiplier and the accelerator, a topic which had attracted the interest of various scholars, including Hansen and Samuelson (see e.g. Samuelson’s classic 1939 paper). He then tried to extend Keynes’s static equilibrium analysis by asking the question ‘if the condition of static equilibrium is that plans to invest must equal plans to save, what must be the rate of growth of income for this equilibrium condition to hold in a growing economy through time?’ (Thirlwall 2002:12). Seeking to answer this question, Harrod developed an analysis of moving equilibrium based on his fundamental growth equation describing the normal ‘warranted’
rate of growth (dependent on the saving rate and on a given capital requirement per unit of output). If this rate prevails, aggregate demand equals productive capacity. One of Harrod’s main conclusions is that, even if this growth rate exists, it is not stable. For this reason, he posited an instability principle meant to provide a fundamental explanation for the business cycle: any deviation of the actual rate of growth from the warranted growth path would be accentuated over time, and the system would be cumulatively unstable. In other words, economies appeared to be poised on a ‘knife-edge’. Any departure from equilibrium, rather than self-righting, would be self-aggravating.
The relation between the actual rate and the warranted rate is a short-run problem.
However, Harrod also considered the problem of long-run instability in terms of the relationship between the actual rate and the ‘natural’ rate of growth, as determined by the rate of growth of the labour force and the rate of growth of output per worker, which represents the potential rate of growth of the economy. Thus, if all labour is to be employed, the actual growth rate must match the natural rate. Again, this equilibrium too turns out to be unstable (see e.g. Asimakopulos 1991:138, 165; Ruttan 2001:24; King 2002:56–8; Thirlwall 2002:14–15).4
As Jarsulic pointed out, one of the key implications of Harrod’s theory is that
‘investment should be self-reinforcing and that this would produce instability in any aggregate demand system’ (Jarsulic 1997:338). Moreover, Harrod’s theory indicates that the accelerator may be somewhat weakened by the presence of a substantial level of autonomous investment, unrelated to the current level or rate of change of income.
Monetary policy and a programme of public works, while perhaps of some help, may still prove inadequate in offsetting the effects of a relatively high warranted rate and the resulting tendency for the system to relapse into depression before full employment is reached in a boom: ‘Stagnation might therefore be the normal state for mature capitalism’
(King 2002:59).
Instability and dynamic equilibrium 23
The neo-Ricardians
For the sake of brevity, we will not provide a detailed account of the debate following Harrod’s contribution to Keynesian growth theory as to how to overcome the problem of the knife edge (i.e. the Cambridge, UK, flexible saving-ratio model versus the Cambridge, US, variable capital-ratio model) or the capital theory debate.5 However, we shall outline the major developments of the Keynesian stance.
On the one hand, some Keynesians followed the neo-Ricardian tradition based on
‘real’ analysis without money, rejection of the neoclassical value and distribution theory and reliance on alternative models of income distribution, especially the classical surplus approach. These theorists insisted that the principle of effective demand should be coupled with a relatively strong notion of long-run equilibrium, which was regarded as the centre of gravitation (e.g. Eatwell and Milgate 1983; Garegnani 1983; Bortis 1996).
Neo-Ricardians ‘…stress the importance of long-period analysis. Normal prices are supposed to be stable in the long run and are consequently seen as centres of gravity, around which short-period or temporary market prices fluctuate’ (Eatwell and Milgate 1983:5). Uncertainty and money are not considered significant in the long run, where normal prices are determined by the technological and institutional environment instead.
For neo-Ricardians, one implication of this view is that ‘it is not sufficient to develop a theory of fluctuations. A theory of the long-term trend is also required’ (ibid.). Such a theory is necessary for the analysis of stability ‘since it matters whether fluctuations are around trends implying lower or, in contrast, higher level of persistent unemployment’
(ibid.).
A distinguishing characteristic of this approach is that it is able to account for structural change. This is especially apparent in Pasinetti’s contributions to the theory of growth in a multi-sector economy (e.g. Pasinetti 1981). Whereas Harrodian models imply a form of equilibrium over time in terms of steady-state balanced growth, with the economy changing only in terms of increased size, Pasinetti presents a model of equilibrium over time coexisting with continuous structural change brought about by differences in the rate of technological change and the income elasticities of demand in the various sectors.
Kaldor, Robinson and Minsky
In juxtaposition with the neo-Ricardian tradition, post-Keynesian theorists such as Kaldor and Robinson progressively abandoned steady growth theory as the foundation for discussing stability issues. At first, these authors insisted
upon defining as a basis of their argument a steady growth process and elucidating the circumstances under which this process can be maintained.
They also conclude, more or less in passing, that the maintenance of steady growth is difficult if not impossible under capitalist processes.
(Minsky 1975, quoted in King 2002:113)
Later, however, these theorists were to drastically modify their views. As noted by King,
‘Robinson and Kaldor began their career as equilibrium economists. They ended up as severe critics of both the concept itself and of its relevance to any actual capitalist economies’ (King 2002:77). Equilibrium analysis, in their view, was best replaced by historical analysis, where history is taken to be a sequence of short-term events. This implies that the long run has no independent existence (Harcourt 1981:5).
In line with this view, Minsky, another important post-Keynesian figure, took no interest in the analysis of production, the operation of product markets, pricing theory or Sraffa’s critique of neoclassical theory, all of which had attracted the attention of the Cambridge Keynesians instead. In particular, Minsky believed that ‘Growth without cycles…was simply impossible, “real” analysis without money was futile, paradoxes in capital theory and alternative models of income distribution were at best amusing academic games’ (King 2002:113). On the grounds of his financial instability hypothesis (see e.g. Tvede 2001:205–10 and Chapter 18), he even suggested that
once you define the financial institutions of capitalism in any precise form then the normal path of the economy is intractably cyclical and the problems…of macroeconomic theory is to spell out the properties of the cyclical process…within a cyclical perspective uncertainty becomes operational… without a cyclical perspective uncertainty is more or less an empty bag.
(Minsky 1975, quoted in King 2002:113)
Non-linear dynamics
Building on the seminal contributions of Keynes, Schumpeter, Harrod, Kaldor and Goodwin, a more recent class of models (e.g. Goodwin 1990, see also for reference Vercelli 1991; Jarsulic 1997) refute the view typically emphasized by neoclassical economists (see e.g. Samuelson 1939) that the structure of the economy is linear and invariant. For example, as Vercelli pointed out (1991:38), economic systems are non- linear and cannot be safely approximated by linear models. A number of theorists have suggested that recent developments in natural sciences and mathematics (e.g. chaos theory and other forms of non-linear dynamics),6 according to which the universe is becoming more complex and potentially more unstable (see e.g. Prigogine and Nicolis 1989), may also be applicable to economic systems. In fact, both chaos theory and Keynesian theory are anti-determinist and anti-reductionist, revealing an important link.
In other words, both hold that you cannot analyse non-linear system as you do with linear ones, by breaking the system into details which are analysed one at a time. Non-linear systems have to be understood in their entirety (Tvede 2001:198; see also Vercelli 1997:288).
In order to understand the connection between these new formal tools and growth theory, it should be noted that it was immediately clear to some Keynesians, such as Kaldor, that the language of linear dynamic systems underlying Harrod’s work was inadequate to the tasks he had undertaken. Kaldor (1940) produced a synthesis of Harrod and Kalecki’s ideas, introducing non-linear methods into Keynesian cyclical analysis.
Instability and dynamic equilibrium 25
Other important models, such as Goodwin’s (1951), were also produced along these lines. The usefulness of such models is that
they show that the positive feedbacks generated by aggregate demand, represented by an investment accelerator, can easily produce unstable aggregate equilibria under economically reasonable assumptions. When the dynamics of the system are constrained by non-linearities, which in the Goodwin case stand for ‘floors’ and ‘ceilings’ to investment demand, self-sustaining cycles are the outcome. Thus the models suggest that empirically reasonable depictions of economic behaviour can produce, independent of external shocks, at least part of business cycle dynamics.
(Jarsulic 1997:380) Several versions of such Kaldor-Goodwin models were developed, based on various specifications of the investment function, time lags and, more recently, the introduction of financial factors affecting investment decisions (e.g. interest rates or liquidity constraints). Although these models have been successful in demonstrating that instability usually results from multiplier-accelerator sources and that there are many instances in which endogenous cycles result, they are fraught with serious limitations; in particular, their behaviour is too regular, when there are no external shocks.
Recent developments in the mathematics of non-linear dynamics may offer new insights into such problems, however (see e.g. Vercelli 1991, 1997; Jarsulic 1997; Tvede 2001). The discovery that simple, deterministic non-linear systems are ‘messy’, that is, capable of producing extremely complex dynamics, is seen by many as having important implications for stability analysis and for economics in general. For example, chaotic, dynamical systems show sensitive dependence on initial conditions, that is, the so-called butterfly effect. This implies unpredictability about dynamical paths (see e.g. Jarsulic 1997; Tvede 2001:188–9).7 Moreover, these systems defy classic determinism, in the sense that ‘the property of chaotic systems imposes the use of stochastic methods for analysing and forecasting their dynamics’ (Vercelli 1997:288). They may eventually prove to have multiple, alternative, dynamic equilibria, the so-called ‘attractors’, or in other words, competing gravity centres which could exert pull in a system (Tvede 2001:192).8
However, this does not mean that the study of business cycles is an inherently futile task. On the contrary, while these approaches do imply that the system cannot be understood according to a few, simple rules and that ‘the behaviour of the system when you start to combine your rules could be much more complicated than formerly anticipated’ (Tvede 2001:200), they also suggest that mechanisms penetrating the complexity of many feed back systems can be found. One example is mode-locking, a phenomenon that
happens when a number of initially uncorrelated processes lock into each other’s rhythm to create a strong, aggregate movement. Given a vast multitude of processes in the economy that can contribute to instability, you would end up with something very similar to random noise, if it were not for mode-locking. Because of mode-locking, a boom can spread from
one sector to many…the business cycle is a movement in the aggregate;
when the economy moves, almost everything moves in the same direction because of mode-locking…
(ibid.: 201) Although non-linear dynamics ‘is unlikely to produce many practical tools for economic and financial forecasting’ (ibid.: 199), it does increase our understanding of the nature of some economic and financial systems. As noted by Freeman and Louça for example,
Nonlinear systems and models question the traditional definition of endogenous and exogenous variables, differentiate the impact of external perturbation according to the state of the system, produce mode-locking behaviours, model structural instability and dynamic stability in the same context, and interpret complexity.
(2001:117) As a result, non-linear approaches are becoming more common in the field of cycle analysis, technological change and the evolution of institutions, and it even seems to encourage reconciliation between alternative heterodox perspectives, such as those by Keynes and Schumpeter (see e.g. Vercelli 1991, 1997). Furthermore, non-linear systems increase the plausibility of active policy moves, because a model that describes an unstable system is useful in explaining the interventions meant to stabilize it (see e.g.
Vercelli 1991:36). Another aspect of this approach is that it contributes to the development of Keynesian theory, for it shows that
simple, deterministic non-linear economic models can produce time series behaviour which is dynamically complex, non-quite-periodic and extraordinarily resistant to prediction. This sounds like the business cycle behaviour with which empirical economists are concerned, and which Keynes was trying to explain. Non-linear Keynesian macroeconomic models can in many cases be shown to produce dynamic complexity. This has been done analytically and by means of computer simulations by several authors…
(Jarsulic 1997:382)
New Growth Theory
Another approach to instability and growth issues is endogenous growth theory, or NGT.
NGT has become popular over the last few decades to account for a number of key phenomena conflicting with the Old Growth Theory (OGT) underlying the neoclassical stance. One example is the lack of convergence between rich and poor countries. The main purpose of NGT is to provide an internal mechanism for long-run growth; in other words, it seeks to endogenize what OGT takes as exogenous. Whereas OGT considers the natural rate of growth to be dependent on the growth of the labour force and labour
Instability and dynamic equilibrium 27
productivity (determined by technical progress), which are both exogenously determined, NGT takes into account other factors involved in growth, such as investment.
Although the literature on endogenous growth includes many different models,9 it can be argued that they all share a shift in focus from a notion of the economy based on a perfectly working market to one riddled with market imperfections. By introducing such imperfections, NGT rules out the neoclassical assumption of diminishing returns to capital which are necessary to OGT’s conclusions concerning the exogenous nature of growth. This step involves some significant methodological divergences from the standard model.
First, it signifies a move away from Becker’s ‘imperialist’ approach to an alternative approach to microfoundations and the relationship between economics and other social sciences. As Fine points out
the new microfoundations treat the economy as subject to imperfections to which non-market responses are a rational, if not necessarily efficient, response. In this light, institutions, norms and customs are seen as the path dependent, collective response to market imperfections. As a result, institutions etc. are neither taken as exogenous nor reduced to an as if market approach characteristic…
(Fine 2003:214) Second, it involves placing the emphasis on such key phenomena as increasing returns to scale (the bigger the economy, the higher the level of productivity) and positive externalities. Emphasis on such microeconomic imperfections is not new. For instance, Marshall chose to treat increasing returns as externalities in order to reconcile competitive equilibrium with dynamic phenomena at the level of industry (Thirlwall 2002:31). However, NGT is unique in that it transforms micro-imperfections into a macro influence on the growth rate.10 By extending Marshallian thinking to the aggregate level, NGT theorists assume that constant returns to scale hold for individual firms, while positive spillover effects—due, for example, to education, invention, learning and networks such as industrial districts—spread individual gains more widely throughout the economy as a whole, eliminate diminishing returns to aggregate capital and account for endogenous growth. In principle, any market imperfection can be used to generate a model for NGT, so long as it generates increasing returns; the analytical highway from market imperfections through increasing returns to endogenous growth has many lanes (Fine 2003; Stiroh 2003:730).
A particularly relevant example for the analysis of the NE can be found in Romer (1986), where research and development (R&D) spillovers are seen to produce this result.
That is
each firm might face constant returns to scale and diminishing returns to capital, but its R&D effort could spill over and affect the aggregate stock of knowledge that is available to all firms. This would endogenize the evolution of the level of technology.
(Stiroh 2003:731)