1. INTRODUCTION

This paper, a shorter version of a previously published one² with which it largely overlaps at least in the theme, tells the story of how it came about that growth theory of the Neoclassical brand (NC, associated with Robert Solow and Trevor Swan) was born out of some logical difficulties of the classical Macro-dynamic theory of fluctuations (associated with the names of Michal Kalecki, Nicholas Kaldor, John R. Hicks and, finally, with Richard M. Goodwin).

A reconstruction of the evolution of the mathematized theories (models) of fluctuations is offered in the way it led to the macroeconomic theory of growth³. In particular, a reason will be suggested for why the driver of growth, technological progress (henceforth, TP), was left exogenous; in other words, how it was eventually accepted that the explanation of growth be left outside the theory that was built to account for it. This generated a conundrum that explains much of the subsequent evolution of the growth approach and the continuing survival of the exogenous approach.

My main thesis is that Neoclassical modelling of the growth phenomenon was born from the failed attempt of classical Macro-dynamics to construct a continuous-time theory jointly explaining, from a unique set of principles, fluctuations and growth. Such a failure left unexplained the driver of the latter. It was to accomplish such an ambitious project, that the marriage of Macro-dynamics with Keynes’ aggregative style of analysis had been thought, at the time, useful. The marriage ended up in an almost disaster, questioning the very empirical foundations of the approach, justifying the exit towards Neoclassical axiomatic.

As ^{Solow was later (1994)} to say [and, perhaps, Giambattista Vico (1668-1744) said, too, well before him], the “same perennial issues seem to come back”. So far, the emergence and often re-emergence of a variety of theories of economic fluctuations has been witnessed, and three peaks of interest in growth, suggesting a peculiar association that demands explanation. To find one, we looked at a common path leading back to the origins of formal dynamics. In our “nonlinear view of history”, some interpretive models often re-appear until certain theoretical issues remain unsolved, though each time they might receive a distinct answer. By mid-1960s growth theorizing seemed to have reached the end of its fruitful years (^{Hahn and Matthews, 1964}). As expectations turned out to be ill founded, we might again be in the middle of another swing. I address one of the unsolved issues that generate these sorts of swings.

2. Waves of growth theory

Hahn and Matthews’s classical review of growth theories begins with ^{Harrod’s 1939} book and ^{Domar’s 1946} article. Although important differences between them are often recalled, probably a universal consensus treats them as basically a single model, which would mark the birth of the formal theory of growth. Rarely is it recalled that Harrod’s 1939 Essay was preceded by his 1936 The Trade Cycle, a book generally considered an unsuccessful and short-lived dash into the theory of fluctuations (see e.g.^{Hansen, 1937}; ^{Solow, 1988}). The book seems to have only left Harrodian knife-edge to ponder on. The Harrod-Domar model would, on the other hand, be the ancestor of NC growth theory, as with the latter it focuses on proving the existence of a full employment equilibrium path.

Naturally, to be practically relevant as a predictor, an equilibrium has to be (at least, locally) unique and the economy must be shown to be stable towards it. That’s precisely what Solow successfully set out to do. His neoclassical growth theory (“the neoclassical response to the Harrod-Domar impulse”, ^{Solow (1994)} would be the successful end of a long term quest: Conventional history inserts the episode of the birth of NC theory into the process that produced the modern General Equilibrium program⁴.

The new perspective I offer hereafter, indicates that episode as a temporary station of a longer intellectual process, and points to a new genealogical thread. To follow such thread, entering an unexpected theoretical scenario, we need to go back to ^{Harrod of the Trade Cycle 1936} (TC). The latter represents the conceptual distillate of a broad reflection on how to theorize economic dynamics⁵; it is at the crossroad of different strands of thought (the Keynesian being just one of them), largely in the making. It was for the latter reason that Harrod could swiftly switch from his general dynamics of 1936, to the theory of growth of the 1939 Essay, and later (1948) to his new book.

TC claimed to offer a “new theory” with a “precise and definite diagnosis” of dynamics of a system out of its equilibrium path. There, we find probably the earliest conscious attempt to analyse both growth and business cycle within a Keynesian framework, along with some mostly intuitions as to how they were to interact. Harrod’s own aim there was to deal with a something much more complex than the mere (knife-edge) stability issue that was going to be read in it, later. The difficulty in the search for an altogether new approach and a definitely poor command of the required mathematics did not help to attain such ambitious goals. The propositions in TC are exactly dual to those of Neoclassical growth theory⁶. With the hindsight of the modern theory of dynamic complexity (that we have been taught by the chaos literature of the 90s), in the TC the issue is not the instability of an equilibrium path⁷. The capitalist system is simply not capable of being stable⁸.

In Harrod’s international intellectual milieu, the Classics were thought to have already provided an acceptable explanation of the long run (this was what really equilibrium analysis was about). The explanation of the “shorter than long run” of economies was still amiss. This did not look at all like equilibrium. All in such varied milieu set out looking for explanations of the more complex dynamics exhibited by “reality”. This might lead either to discontinuities and structural changes⁹, or else it had to have some self-limiting behaviour. Pessimistically, they surmised that the economy would run into the former, if the latter failed to set in. Ragnar ^{Frisch’s (1933)} Manifesto for an empirically founded Macro-dynamics¹⁰ was well aware of the drama of the alternative; even Solow saw it in his celebrated growth paper.

Macro-dynamics placed its hopes in finding self-limiting kinds of unstable dynamics. Doing so, it swept under the theoretical carpet the issue of structural change.

3. Harrod’s TC and macro-dynamics

Macrodynamic formalism had two simple ingredients: A given empirical structure and the dual notion that dynamics was generated by exogenous impulse(s) activating a propagation mechanism, i.e. by the system own structure. Such scheme placed greater weight onto the exogenous impulse, the real engine of dynamics, and relatively less onto propagation, basically seen as a damping mechanism, to be repeatedly re-initialised in order to generate oscillations at finite frequencies. Any motion, including exponential growth, has both its cause and the cause of its persistence in some specifically assumed, often ad hoc, impulse profile. For our history, the project of classical Macro-dynamics could be usefully read against the backdrop of Keynes’s attack against the Classical Stability Postulate, a postulate said to imply the view that an economy is a naturally stable system that, unless disturbed from outside, always lingers around a (possibly, locally unique) equilibrium state. The Classical Stability Postulate was implicit in Frisch’s view of a damping propagation mechanism: His analysis of dynamics had oscillations on the forefront, but a stable, though possibly moving, equilibrium lied at its core.

However, such scheme could be easily reverted by exchanging relative weights: The propagation mechanism being the dynamic engine and the impulse a mere disturbance. This, I believe, is the key to really understand ^{Harrod’s 1936} book, its distance from classical Macro-dynamics (and perhaps Keynes). Still, the notion of a given system (macro-) structure made a marriage with Keynesian analysis of real variables relatively easy. It only needed the simplest structure, with the lowest dimension of one state variable.

Therefore, the simultaneous presence of growth and fluctuations places ^{Harrod’s (1936)} contribution within the research program of Macro-dynamics. However, his rejection of global stability is the basic reason behind the view of the trade cycle as an explosive but time over recurrent path systematically away from equilibrium, the warranted growth path. If intellectual history can at times be told as a spy story, Roy Harrod was the man who really tried to resolve the ambiguity in the classical Macro-dynamics program and to attack that stability postulate head on. The result of such attack was the earliest programmatic attempt at founding an endogenous theory of economic dynamics, but also its temporary failure. Armed with the intuition that an economy should be conceived as an autonomous system (^{Punzo, 2006}) and that, therefore, the propagation mechanism embedded in its own structure would be capable, alone, of sustained fluctuations, Harrod launched a wave of business cycle analysis.

Voicing a latent demand, with perhaps a bad book and the poor mathematics he commanded, he put an intellectual generation to work.

4. A Project

Thus, Harrod did try to formulate his view of system instability but could not handle the complications. Perhaps realising his personal inadequacy to the new standards of mathematization (but also due to other events), he gave up his attempt. According to my story, it was disappointment that produced the 1939 Essay and later work¹¹.

How to solve his problem, i.e. how to get growth and fluctuations together, became the core issue in the thinking of a whole generation: The mathematical problem inadequately dealt with in the TC seems to have been the fundamental motivation leading certain people to move on to a nonlinear formulation of business cycles (bcs) and in continuous time (respecting Harrod’s strong argument against the ad hoc use of lags).

Ironically, while Harrod was looking to save himself with that theory of growth which made him famous, he had contributed to shape the research agenda of the nonlinear endogenous approach to business cycle and other oscillations¹².

Classical business cycle analysis generated a family of models trying to address and to give analytical answers to questions such as: Can self-sustained fluctuations be the generic motions whose explanation is buried deep in the structure of the economy? Non-linear mathematics was the adequate tool to represent such persistent “disequilibrium”.

The twenty-year time interval between TC and the birth of neoclassical growth theory saw the development of such a research programme. Practically the totality of such models were aggregate, the off-springs of that marriage of convenience between classical Macro-dynamics and Keynesian analysis. What at the time appeared to be reciprocal convenience was the fact that the one-dimensional Keynesian model was a mathematically simpler version of the n-dimensional Tableau Economique envisaged in Frisch’s article. A whole group of researchers conspired in arranging for such a marriage. Unfortunately, the two frameworks eventually came to be identified¹³.

Classical business cycle analysis was basically about a thought experiment: Trying to construct a wholly endogenous explanation of dynamics as if an economy could be observed in vitro, insulated from all sorts of exogenous, even stochastic impulses. There was no clear predictive content in its models. This lack was felt to be one of its weakest points in an intellectual atmosphere where growing familiarity with modelling raised increasing expectations and demand for testable hypotheses.

Its models, on the other hand, were all deterministic, built around a common set of properties that could only be represented in nonlinear formulations more adequate than Harrod’s own. Equilibrium growth (e.g. steady state) paths were considered to be empirically irrelevant, rarely or never actually observed, and had to be understood as some of the modes in the complicated modal interlocking typical of large systems. They could be intellectual constructs, or be caused by long run forces exogenous to the natural mechanics of the economy. The task of explaining them, therefore, would be well beyond the realm of theory, as not having any intrinsic interest (^{Goodwin, 1951b}). At times, reference was eclectically made to Harrod’s full employment path, sometimes to Schumpeter’s view of innovation swarms (as e.g. in ^{Kaldor, 1954}), or else to autonomous investment expenditure, perhaps linked to technological progress (^{Hicks, 1950}). Observed fluctuations, instead, were interpreted as the visible manifestation of an inherent tendency to dis-equilibrium, their causes being ingrained into the internal wiring of an economic system. In other words, this approach to business cycle coordinated an endogenous explanation of fluctuations with an exogenous explanation of growth.

However, the relationship between growth as a trend and fluctuation was left unclear¹⁴. Nonlinearity per se was not adequate to the task, for a single state-variable model simply cannot yield at the same time fluctuations and exponential growth. Thus, it cannot solve the problem that haunted the key argument in the TC. Sticking to nonlinearity only for mathematical convenience, eventually led to focus on fluctuations and to give up all attempts to explain (empirically irrelevant, as they thought) equilibrium growth paths. The approach of a whole generation failed to reach the objective it had set to itself, a unified theory of dynamics. A generation’s disillusion, though not the only one! Such was the costs of the initially promising marriage of convenience.

This left a hole in the theory of economic dynamics, and somebody was to look into it.

The failure in addressing satisfactorily Harrod’s issue is, therefore, the first key to understand subsequent developments, among them the birth of growth theory as a dedicated, separate dynamic theory. On the other hand, even mathematically more robust formulations eventually elaborated by e.g. Goodwin, only produced regular, symmetric oscillations, which in fact still represented some sort of equilibrium. Thus, although looking for a disequilibrium theory, the fluctuations that were obtained were far too regular and did not look like the real ones. The explanation of their irregularity was missing, at times receiving ad hoc and unconvincing treatment. Finally, the difficulties associated with nonlinear formulations led to the introduction of qualitative analysis (in the style of Poincaré, Andronov et al.). Important as it was in the history of economic analysis, such a passage was perceived as the abandonment of a quantitative approach, the divorce of theory and econometrics.

Thus, the project of a theory of a self-sustained, endogenously generated or structural dynamics proved to be impossible to realise. At the same time, also the aim of a quantitative theory proved to be unreachable with the mathematics then familiar to most economists.

Two facts that jointly declared the (temporary) end of classical business cycle analysis, and thus liberated growth from the embrace with fluctuations. The awareness of that double failure contributed to the intellectual atmosphere in which was to see the light a theory of growth as an exogenously driven phenomenon.

5. A place for equilibrium growth

Recalling the relevance of the full employment equilibrium path as a predictor, one can appreciate how far neoclassical growth went from classical business cycle theory. The latter did not deny the possibility of equilibrium, but it assigned to it the much limited role of a reference or benchmark behaviour. In fact, there was no obstacle to make it fit into its framework, e.g. keeping self-sustained fluctuations coupled with exogenously-driven growth (in other words, using the model of a nonlinear forced instead of a free oscillator). This would simply require assuming an unstable equilibrium, which could be Harrod’s own path (^{Kaldor, 1940}; ^{Goodwin, 1953}, ¹⁹⁵⁵), a response to some other exogenously given forcing function (e.g. Hicks’ autonomous demand trend), or else having the full employment path acting as a ceiling (^{Hicks, 1950}; ^{Goodwin 1951a}). Not everybody, at the time, found this solution satisfactory (e.g.^{Goodwin, 1950}), but apparently there was no other. There was, in fact, a mathematical problem in endogenizing growth¹⁵. Still, the conceptual question remains: Why was the explanation of growth placed outside dynamic theory?

This is linked, I surmise, to the attitude of business cycle theorists of the time towards “relevant” exogenous impulses. These and generally any forces exerting effects onto equilibrium were deemed to have also other major effects. Even with greater determination than in Macro-dynamics, classical business cycle theory was looking for structural explanations referring to basic mechanisms supposedly regulating system functioning. Thus, consistently, it was thought that, behind any long run tendency, there would be processes slowly shaping and most likely also changing the very economic structure. Demographic movements, structural change (of resource re-allocation type, and/or sectoral capital accumulation), technological progress and innovation were conceptualizations of such forces, which would interact with one another in a complicated way (a notion very close to Schumpeter’s view, see ^{Kaldor, 1954}). Though with different formulations, various models put forward the view that all those were discontinuous processes, possibly of a stochastic nature. At any rate, their interaction would produce complicated outcomes: e.g. deforming an otherwise regular fluctuation: Shifting equilibrium in unpredictable directions (^{Goodwin, 1946}), bringing about abrupt or catastrophic changes, and the like. All such non-systematic forces at work, most unlikely would produce anything similar to an equilibrium or a smooth trend. Structural and technological change was the only explanation for irregularity left to classical business cycle analysis. On the other hand, realism seemed to be justification for leaving them outside a theory of systematic dynamics.

Thus, shortly before the appearance of neoclassical theory, for theorists and theories in the business cycle program the issue was not to explain growth but, rather, how to combine an accepted though unexplained growth driver with seemingly better understood endogenous oscillations. One way to go about it was to make also growth look endogenous, i.e. by identifying it with a statistical average over actual oscillations. Alternatively, to this practical answer, it could be argued, à la Schumpeter, that it was the oscillation that generated growth (^{Kaldor, 1954}). Neither of these solutions was really available for formal analysis, the former being premature, the latter implying formidable mathematical complications¹⁶.

A third conceivable solution was to have an economy switch frequency, from fluctuation to growth, and thus simply get rid of fluctuations from then onwards. This was impossible when structural change was not contemplated or even methodologically conceivable, as it was the case in classical Macro-dynamics, but it was the only alternative left. It implied a mechanism by which an explosive motion (e.g. an oscillation) would be converted into smooth growth (for example, growth along the full employment path) -an explosive growth limited by Hicks’ and Goodwin’s ceiling. Designing and embedding a new mechanism of structural adjustment was required.

6. The Neoclassical Revolution: continuous technological progress

Seen from the point of view of the classical business cycle program, this was the true innovation of neoclassical growth theory: introducing exogenous but continuous Technological Progress. Classical business cycle program had it exogenous but discontinuous, hence could only generate pulses, not continuous growth. NC proved to propose a relatively simple solution, with far reaching consequences, though. Seen against the relatively poor performance of the agenda of classical business cycle, the equilibrium path had suddenly become worth to have a closer look at.

A silent paradigm shift took place launching the creation of modern Macro-dynamics endowed with what later, after a process of further enrichment, was to be called the “choice theoretical framework”. The interpretation of the formal model was altered accordingly. With the introduction of a production function, the structure upon which a Macro-dynamic model was to be constructed would no longer be an observed set of relations and realized values for variables and structural parameters. It became founded upon realizable values of an ex-ante functional approach. This produced the well-known analysis of the dynamical properties around that equilibrium. It also proved that, under the assumed conditions and in a time horizon sufficiently long to be called long run, certain key variables of Harrod and the then contemporary business cycle research would cease to play a role, and be replaced by other “determinants” of growth. In particular, the self-feeding process of capital accumulation was superseded by exogenous technical progress as the explanation of growth performance. The divorce (of TP from capital accumulation) was a surprising consequence.

As said, that Technical Progress could be a driving force of long run equilibrium was not foreign to people in business cycle research. However, they were inclined to think that it induced an irregularly fluctuating path, hard to distinguish from endogenously driven oscillations (as in Schumpeter’s theory, formalised in e.g.^{Goodwin, 1946}; ^{Kaldor, 1954}). Only a steady and continuous process (at a positive rate) of productivity enhancement is compatible with smooth growth, though. It is this assumption that generates the steady state path associated with the neoclassical predictions. The basic difference of neoclassical growth theory from classical business cycle analysis, therefore, is in its treatment of exogenous technical progress as a continuous process.

Such hypothesis appears hardly consistent with the exogeneity assumed, but is also necessary to support the other hardly intuitive but logical implication of the neoclassical model: That the pace of capital accumulation does not contribute to shape long run growth. With this move, a whole tradition of thought, which had Schumpeter as perhaps its most prominent representative, was buried.

However, something was felt to be wrong: Either in the very conception of technical progress and, hence, of its relation with investment and with the role of the latter, or else in the concept of a time horizon long enough to make capital disappear from the growth scenario. The often hot debate following the birth of neoclassical theory shows the varied reactions to those implications, with the appearance of theories of vintage capital goods, the discussion about embodied versus disembodied technical progress, Kaldor’s attempt at formalising a new technical progress (investment) function, finally Arrow’s learning by doing¹⁷.

This debate never really abated. The third and most recent of the waves of interest in growth theory sprung up as a re-definition and re-interpretation of the role of capital accumulation in growth performance.

7. Cycling?

Harrod’s thesis, that growth would arise from the very same endogenous sources of fluctuations, was left unproved. Neoclassical growth theory did not address it nor did it share it. Simply, the profession’s theoretical attention shifted from fluctuations without growth to growth without fluctuation.

Correspondingly, the out-of-equilibrium interpretation of observed dynamics was abandoned in favour of one of equilibrium; and correspondingly the view spread around, according to which economic dynamics, rather than being essentially endogenously-driven, responds to external forces. This opened a new phase in an intellectual cycle that had already started with an early phase with endogeneity (i.e. an endogenous explanation) as the dominating paradigm, followed by the unsatisfactory mix produced by the classical business cycle analysis. The articulation, at about the same time, of the linear econometric methodology associated with the Cowles Commission (^{Morgan, 1990}) and its wide acceptance were the other logical consequences of the same fact. Like in neoclassical growth theory, a similarly exogenous theory of fluctuations was proposed, refreshing a view that has been at the origins of Macro-dynamics. Oscillations would again be transient deviations from a (globally) stable equilibrium, kept alive by an unexplained tendency to be hit by stochastic impulse(s), a view that had been contemplated already but soon dismissed.

The conceptual match with neoclassical theory was practically perfect. The econometric models of the 60s got along very well with a dynamic theory that focussed only upon stable equilibria and therefore guaranteed predictability in econometric models so that they complemented each other. The 1970s and the very early part of the 1980s happily lived in a new, finally unified paradigm of exogeneity. It was a sort of middle season in the nonlinear history of dynamics I am sketching out.

A winter of discontent arrived with a third growth wave, when the so called new theories of endogenous growth became ripe. It was regretted that, in the effort to get rid of fluctuations, neoclassical growth theory had also got rid of capital accumulation, there was no longer such necessity. A search for a novel role for capital accumulation and technological progress in explaining growth performance, also in conjunction with the release of a massive new data bank to tap, ignited the wild fire of the so called theory of endogenous growth. A set of older ideas made a comeback as growth determinants: e.g. in particular, the centrality of investment (though qualified to suit modern times, with education and research and development entering into it), innovation processes, international trade, and many others. What widely different models shared, was their success in bending manifold phenomena, even the vision of the innovation process as essentially discontinuous (as was Schumpeter’s), to fit steady state analysis. They were the product of a discontent with certain, also empirical, implications of the neoclassical theory, more than the product of the search for a new theoretical framework. However, at the peak of a relatively short fashion season, endogenous growth got coupled with the exogenously-driven fluctuations of the still surviving standard or linear econometric model and the new monetarist theory.

Each of these waves or “seasons” of dynamics represented a temporary equilibrium station as they had their own built-in de-stabiliser: The initial one was the search for a unified theory of growth and cycle; the second, the season of the classical analysis of business cycle ended in the failure of dealing with such issue. This last season started from the discontent with the poor relevance given to various forms of investment and to innovation, but it left the same open issue as the second. Giving opposite explanations for the modes of actual dynamics, it did not respond to the apparent demand for a unique dynamic paradigm.

A step further, into a fourth season, and a new brand of Macro-dynamics was produced. This fully adheres to the classical self-regulating principle: According to the real business cycle approach, all sorts of dynamics are taken to be optimal equilibrium responses to exogenous shocks, and explained by the use of the choice theoretic framework. The possibility of dis-equilibrium is not denied but is seen to be just a transient phenomenon.

In this last but one phase, there are many ideas that already belonged to Classical Macro-dynamics, the first one being that the distinction between growth and fluctuations is not really relevant: Both are types of fluctuations with different frequencies. Moreover, just like in the older approach, real business cycle theory promotes a linear view of dynamics, and in its extreme blown version (where growth as well as fluctuations are stochastically induced), the unifying explanatory principle is exogeneity, once again¹⁸.