- Información
- Chat IA
Cesaratto, S. (1999). Savings and Economic Growth in Neoclassical Theory
Historia y Literatura (Hist0)
Universidad de la Sabana
Comentarios
Vista previa del texto
Cambridge Journal of Economics 1999, 23, 771–
CRITICAL SURVEY
This is the latest in our series of Critical Survey articles. The aim of the series is to report on recent developments, to provide an assessment of alternative approaches and to suggest lines of future enquiry. The intention is that the articles should be accessible not only to other academic researchers but also to students and others more practically involved in the economy. Earlier Survey articles include Chris Freeman on ‘The Economics of Technical Change’, Allin Cottrell on ‘Post-Keynesian Monetary Economics’, Herbert Hovenkamp on ‘Law and Economics in the United States’, Warren Samuels on ‘Institutional Economics’, Philip Arestis on ‘Post-Keynesian Economics’, Geoff Ingham on ‘Economics and Sociology’, Sheila Dow on ‘Mainstream Economic Methodology’, Lionel Orchard and Hugh Stretton on ‘Public Choice’, Andrew Glyn on ‘Does Profitability Really Matter?’, and Ron Martin on ‘The New “Geographical Turn” in Economics’.
Savings and economic growth in
neoclassical theory
Sergio Cesaratto*
In neoclassical economics economic growth depends upon savings. The paper dis- cusses problems with this conventional view, and how these have been tackled, from pre-Solowian authors up to the recent New or Endogenous Growth Theory (EGT). These difficulties became particularly clear with the Solow–Swan model of growth in which the savings rate did not affect the rate of growth. In the absence of exogenous circumstances, savings would only depress the marginal productivity of capital forcing the economy towards a stationary state. The paper interprets EGT as an attempt to react to this gloomy theoretical prospect. The paper examines various difficulties with this attempt.
Key words : Economic growth, Technological change, Neoclassical theory JEL classification : O3, O4.
© Cambridge Political Economy Society 1999
Manuscript received 20 December 1996; final version received 28 July 1998. Address for correspondence : Sergio Cesaratto, via di Porta Labicana 43, 00185 Rome, Italy; email cesarat@dep.eco.uniroma1
- University of Rome ‘La Sapienza’. This paper is based on notes prepared for a seminar given at the Faculty of Economics and Politics, University of Cambridge in May 1996. I should like to thank, with the usual disclaimers, Augusto Graziani, Antonella Palumbo, Fabio Ravagnani, Anna Simonazzi, Robert Solow, Serena Sordi, Antonella Stirati, the participants of seminars in Cambridge, Rome and Rio de Janeiro, and three referees for useful comments. Special thanks are due to Professor Solow for permission to quote some of his written comments. Financial support by the Ministry of University and Scientific Research is gratefully acknowledged.
772 S. Cesaratto
1. Introduction
The publication of the seminal papers by Romer (1986) and Lucas (1988) which launched the so-called New or Endogenous Growth Theory (EGT) witnessed a renewed interest from mainstream economists in the theory of economic growth. The present paper analyses one specific issue in mainstream growth theory, namely the relationship between the saving decisions of the community and the rate of economic growth. How this issue is handled is discussed from the pre-Solowian years up to the recent EGT. This subject has been selected in view of what is generally considered the conventional wisdom about economic growth: the idea that thrift is the main determinant of economic growth and, associated with this, that in the long run there is a positive rate of profits, equal in equilibrium to the marginal productivity of capital, regarded as the reward for parsimony. Paradoxically, the neoclassical models of economic growth of Solow (1956) and Swan (1956) weakened the conventional view by showing that ( i ) in the long run, a positive marginal productivity of capital, net of depreciation, was dependent on a sufficient exogenous growth of the cooperating factors, and ( ii ) the saving decisions of the com- munity were irrelevant for the determination of the rate of growth. The latter depended instead on the exogenous rates of growth of the labour force and of labour efficiency. The reduced role assigned to the preferences of the community between saving and con- sumption and the reliance of the conventional view on exogenous factors was ‘hardly intellectually satisfactory’ (Arrow, 1962, p. 155). Indeed, the central theoretical purpose of EGT appears precisely to build a neoclassical model of economic growth in which ( i ) there are positive (marginal) returns to capital, and ( ii ) the rate of growth is dependent on the preferences of the community between present and future consumption and is, therefore, ‘endogenous’. One main conclusion of this paper is that, from the point of view of economic theory, the recent revival of neoclassical growth theory can be interpreted as an attempt to restore the traditional view. 1 The paper will assess the success of this effort in view of the work already done in the same direction by neoclassical economists, particularly in the 1960s. As such, the paper serves as a critical introduction to the recent revival of neoclassical growth theory. 2 Section 2 discusses the meaning of ‘endogenous growth’ in neoclassical theory, and examines the way in which the relation between saving and economic growth was dealt with in the years preceding the Solow–Swan model. The rather unconventional dis- cussion of the pros and cons of the Harrod–Domar growth equation for the neoclassical view will play a particularly important role in the paper. Section 3 recalls the impact of the Solow–Swan model and reviews the state-of-the-art positions of the 1960s. Section 4 examines the modern revival of neoclassical growth theory, focusing on two main groups of models that will respectively be called ‘pseudo-Harrod–Domar’ and ‘neo-exogenous’
1 As such, the ‘traditional vision’ is not an analytical proposition but is part of the pre-analytical views of neoclassical theory in the sense given to the term by Schumpeter (1954, pp. 41–2). 2 Surveys of EGT have appeared in: Revue Economique , vol. 44, 1993; Economic Journal , vol. 102, 1992; Journal of Economic Perspectives , vol. 8, 1994; Scandinavian Journal, vol. 95, 1993; Oxford Review of Political Economy , vol. 8, 1992. A new journal entirely devoted to this approach has been launched: Journal of Economic Growth. A textbook on EGT was written by Barro and Sala-i-Martin (1995). The contributions by Solow (1992), Parrinello (1993) and Kurz and Salvadori (1997) are more critical. Growth models are currently formulated in the context of dynamic optimisation models, which regard the saving decisions as taken by a representative agent in an intertemporal context. Chiang (1992) is a useful introduction to these models. Fortunately, the fundamental issues concerning neoclassical growth theory can be dealt with by taking the saving decisions as given.
774 S. Cesaratto
economic growth and that of profits as the reward for parsimony both depended on circumstances, such as the growth of the labour supply, outside the control of the theory. Mainstream economists reacted to this disappointing situation in two different ways. One answer consisted of the ‘labour-saving inventions’ introduced by Hicks (1932, pp. 124–5). By increasing the labour supply in efficiency units, a constant flow of this class of innovations preserves a balance between the quantities of factors, averts the stationary state, and maintains the positive role of saving. In turn, this constant flow was granted as long as any relative abundance of capital with respect to labour manifested itself in higher real wages and in an incentive for entrepreneurs to introduce this class of ‘induced innovations’. 1 Alternatively, increasing returns to scale were proposed. For instance, Abramowitz (1952, p. 154) argued that capital accumulation, by bringing about a larger output, would at the same time determine a greater efficiency of the given quantities of the other resources so that, as a result, the relative proportions between the quantity of capital and the amount of the cooperating ‘factors’, the latter measured in ‘efficiency units’, were not changed. 2 This approach had Marshallian origins as it relies on the concept of externalities (in modern jargon ‘spill-overs’) which, as they are not appropriable by the single firm, have the advantage of preserving perfect competition. Marshall interpreted the increasing returns as the result of a proportional growth of all factors, produced and non-produced, in one industry, and regarded them as internal to the industry but external to the firm (cf., Sraffa, 1925, 1926). Abramowitz and, as we shall see, modern EGT, see them from a different angle, as the result of a larger scale of the economy brought about by the larger use of a produced factor (capital). In this case, increasing returns are revealed in the greater efficiency of the given quantities of the remaining non-produced factors. In this way the increasing returns counteract the decreasing (marginal) returns to the accumulable factor. As in the case of the Hicksian ‘induced labour-saving inventions’, the externality from capital accumulation allows the economy to grow with a constant proportion of factors averting the stationary state. Both approaches point to a theory of endogenous growth in so far as capital accumu- lation, which is endogenous, generates a greater efficiency of the other factors, either by spurring Hicksian ‘inventions’ or through Marshallian ‘spill-overs’. The theory of induced innovations received some attention in the 1960s (see Ferguson, 1979, ch. 16 for a survey) but very little, as yet, in recent EGT (see, however, Romer, 1987). For this reason we do not discuss it here. More attention has been given to increasing returns both in the 1960s and in recent discussions. Before illustrating these developments, an uncon- ventional look will be taken at the role played by the Harrod–Domar model in the course of events.
1 ‘A change in the relative prices of the factors of production’, Hicks wrote, ‘is itself a spur to invention and to invention of a particular kind—directed at economising the use of a factor which has become relatively expensive. The general tendency to a more rapid increase of capital than labour... has naturally provided a stimulus to labour-saving invention’ (Hicks, 1932, pp. 124–25). 2 The increasing efficiency of the cooperating resources, for example, labour, brought about by the externality that follows capital accumulation, should be distinguished from the increase of per-worker output ( y 5 Y / L ) that follows a progressive rise of per capita capital ( k 5 K / L ). As a glance at a standard ‘well- behaved’ per capita production function shows, d y /d k is nil for k tending to infinity, precisely as a con- sequence of the falling marginal productivity of capital. The externality intervenes in impeding this fall. Because of the externality, the level of efficiency of labour ( H ) grows at the same rate as the stock of capital. In this case d y /d k ’, where k ’ 5 K / HL , is constant although k tends to infinity. Per capita capital and output steadily increase as before with respect to physical labour, but the relative proportion between the capital stock and efficiency labour does not change, leaving the marginal productivity of capital unaffected.
1 Thanks to Carlos Medeiro for his suggestion to view equation (1) in this way.
2 The impact of the Harrod–Domar model and the received view Unexpected support for the conventional wisdom that an increase in the savings rate will increase the rate of growth of the economy came from one of the most relevant develop- ments of the Keynesian revolution. This is paradoxical to an extent, as the main critical objective of The General Theory was to invert the traditional causal relationship between saving and investment, at least in the short run. As is well known, the earliest attempt to extend the Keynesian theory to the long run, bringing together the double role of investment as one of the determinants of effective demand and as capacity creating, was made by Harrod (1939) and Domar (1946). Harrod’s contribution, which is the more theoretical of the two, shows that, given the marginal propensity to save ( s ) and the desired or normal capital/output ratio ( v ), an economy in which consumption and investment are the only components of effective demand will grow at a rate consistent with normal capacity utilisation if, and only if, the actual growth rate coincides with the ‘warranted rate’ given by the well-known formula
gw 5 s / v (1)
Harrod defines the warranted rate as the ‘rate of growth which, if it occurs, will leave all parties satisfied that they have produced neither more nor less than the right amount. Or, in other words, it will put them into a frame of mind which will cause them to give such orders as will maintain the same rate of growth’ (Harrod, 1939, p. 45). Harrod empha- sised the difficulties surrounding the formation of correct expectations, suggesting that he was more interested in the instability properties of his model than in the steady-state path (which he dismissed as an ‘equilibrium rate’, Harrod, 1939, pp. 45–6). However, in spite of the original instability implications that Harrod envisaged for his model, the major impact of his and Domar’s model had more to do with the characteristics of the warranted rate. It is this particular reception of Harrod–Domar’s results which is of most interest (the ‘Harrod–Domar Weltanschauung ’, as it has been named, cf., Hamberg, 1971, p. 169). This specific reception is based on one agreeable feature of equation (1) for the conventional view of growth, which is the positive relation between the propensity to save and the growth rate. Of course, equation (1) does not imply that a rise in the propensity to save leads to an increase in g (given the instability problems). What the equation does imply, however, is that if a community wants to raise g it must first increase s. 1 According to many commentators, the Harrod–Domar model was, in the 1950s and later, the actual carrier of the traditional prescription that growth depended on the savings rate in development theory and policy (e., Hamberg, 1971, p. 141; Stern, 1991, p. 124; Shaw, 1992, p. 611). One may wonder why there is such a strong similarity between equation (1) and the conventional view of saving as the trigger of growth. A possible interpretation is that equation (1) represents a ‘dynamic’ version of Say’s Law. The latter describes a one- period equilibrium between aggregate demand and supply on the assumption that all saving corresponding to a normal degree of utilisation of productive capacity is invested. Equation (1) extends this approach to a sequence of equilibria and can be thus reinterpreted: should entrepreneurs be so bold as to invest all savings, or were the public authorities able to adopt policies suitable to translate savings into investment, the economy would then grow according to equation (1). The consequent policy prescription is that a higher growth rate hinges upon a higher savings rate. Thus, in spite of the
Savings and economic growth in neoclassical theory 775
Savings and economic growth in neoclassical theory 777
length of this transition period and, therefore, on whether the effects of a higher savings rate on the rate of growth are short-lived or spread over long periods of time (Sato, 1966; King and Rebelo, 1993; Barro and Sala-i-Martin, 1995). Finally, the savings rate may be so low and the technology so backward that no balanced growth equilibrium exists and per capita income tends to fall (cf., e., Solow, 1956, p. 73). This case, however, con- cerns only very poor countries. 1 The exogeneity of technical progress was not felt to be an unfounded assumption in the years of big science. 2 Moreover, the dependence of technical change on the progress of science could well explain the lack of convergence of productivity growth among countries. More likely, the exogeneity of technical progress started to be felt as a problem once it was seen in connection with the lack of influence of the saving decisions on the secular growth rate—which became apparent with Solow’s model—making the role of individual saving decisions—and the policies aimed to stimulate them—ineffectual with respect to the growth rate. The irrelevance of the savings rate with regard to the rate of growth, determined by exogenous causes, merged with the pre-Solowian problem of the negative effects of net capital accumulation on growth in the absence of exogenous forces of growth as two sides of the same coin. If the ‘exogenous factors’, those that are ‘non reproducible’ on the basis of the choices of the community, do not grow, net saving leads the economy towards the stationary state. But if they do grow, then thrift is not a determinant of the accumulation rate. The principle of relative scarcity of the factors of production, as long as there are ‘non reproducible factors’, results in too shaky a foundation for the marginalist view of thrift as the long-run cause of economic growth and, associated with this, for a positive rate of return to capital as the reward of parsimony. It is this theoretical contingency that spurred the beginnings of an ‘endogenous growth’ literature in the early 1960s.
3. The state of the art in the 1960s 3 Three approaches are particularly relevant for an appreciation of the most recent neo- classical analysis of economic growth: the less-well-known Frankel ‘modifier’, vintage models and Arrow’s learning-by-doing model. A fourth approach, proposed by Uzawa (1965) and others, will be mentioned later in the context of recent EGT. Frankel’s ‘modifier’. Frankel’s model (1962) is particularly relevant because it sum- marises quite effectively much of the meaning of both early and recent EGT. In particular, he presents an explicit formulation of the by now famous endogenous ‘ AK growth model’ by Rebelo (1991). Frankel points out that two ‘production functions’ were particularly popular at that time, the Cobb–Douglas function in distribution theory, and the ‘more elementary’
1 Professor Graziani reminded me that in this fourth case, according to the marginalist principles, an increase in the savings rate would exert the positive role of helping the economy to establish a balanced growth equilibrium with a constant per capita income. 2 Consider this quotation from an influential book published in 1947, significantly titled Endless Horizons : ‘Basic research leads to new knowledge. It provides scientific capital. It creates the fund from which the practical applications of knowledge must be drawn. New products and new processes do not appear full- grown. They are founded on new principles and new conceptions, which in turn are painstakingly developed by research in the purest realms of science’ (Vannevar Bush, 1947, pp. 52–3, quoted by Layton, 1974, p. 34). I shall argue below that what I define as the ‘neo-exogenous’ endogenous growth models do not really break with this description of technical change. 3 Useful surveys of 1960s growth models include: Allen (1967), Burmeister and Dobell (1970), Hamberg (1971), Jones (1975), Ramanathan (1982). The best introduction is still Solow (1970).
778 S. Cesaratto
Y 5 aK in the Harrod–Domar types of model. The limitations of the former production function in a growth setting are ‘weighty’, since ‘the resulting long-term rate of growth in output turns out to equal the rate of growth in the labor force. Growth in output per worker, commonly regarded as the essence of development, is zero, and the rate of invest- ment exerts no effect!’ (Frankel, 1962, p. 996). Exogenous technical change can take care of productivity growth, but ‘this approach leads to the unhappy consequence that growth in productivity takes place independently of growth in the capital stock’, so that the ‘adaptation of the Cobb–Douglas function to a growth setting entails... the sacrifice of a satisfactory explanation of growth itself’ (Frankel, 1962, p. 997). What is sacrificed, of course, is the ‘ Weltanschauung’ of the Harrod–Domar models that the economists ‘have found... attractive because of their relatively simple structure, because of the emphasis they give to capital accumulation as an “engine of growth”—an emphasis with deep roots in economic thought... In consequence they have played a central role during recent years in theories of growth and development’ (Frankel, 1962, p. 996). ‘Unfortunately’, he concludes, ‘the production function Y 5 aK (adopted by those models) has nothing interesting to say about resource allocation or income distribution.’ 1 After this description of ‘intellectual discomfort’ (Frankel, 1962, p. 997), Frankel advanced a solution to reconcile the two production functions in order to retain ‘the desirable properties’ of each and to dispose of the ‘limitations’. At this point, the elementary neoclassical model presented by Frankel (1962, p. 1009) aides in the argument.
Y 5 aK b( HL )1 – b (3)
S 5 sY (4)
I 5 d K /d t 5 K· (5)
S 5 I (6)
L 5 Loe λ t (7)
H 5 Hoe μ t (8)
(Observe that, for simplicity, this model assumes that Y is the full-employment income, and that investment is equal to the savings supply corresponding to the full-employment income. The existence of diminishing demand curves for both labour and ‘capital’ in their respective markets justifies these assumptions.) On the basis of this standard model, Solow obtained the secular growth rate given by equation (2). If equation (3) is replaced by Y 5 aK , using equations (4), (5), and (6), and neglecting equations (7) and (8), the warranted-growth equation (1) is obtained (with v 5 1/ a ). In order to retain equation (3), while still obtaining equation (1) (a savings-rate depen- dent growth rate), Frankel proposes the following procedure: assume the economy to be made up of n small and identical firms, each characterised by a production function
Yi 5 aK b i ( HLi )1–b (9)
1 With respect to Frankel’s ‘deep roots in economic thought’ of the idea of ‘capital accumulation as an “engine of growth”’, it should be noted that the theoretical association between the saving and investment decisions in neoclassical theory, to which Frankel refers, should not be confused with that found in the classical economists (cf., Garegnani, 1983, p. 26, n. 4 and the references there provided).
780 S. Cesaratto
‘Investment has been married to Technology’ (Phelps, 1962, p. 549). The idea was that a higher savings rate leads not only to higher per capita capital endowment, but also to the ‘modernisation’ of the capital stock. However, in spite of the hypothesis of ‘embodied technical change’, the equilibrium growth rate remained stubbornly exogenous. It was, in fact, the same as that of the disem- bodied model, equal to the exogenous rate of growth of the labour force in efficiency units (see, e., Allen, 1967, ch. 15). Moreover, Phelps (1962) also disposed of the ‘moderni- sation’ effect, showing that the average age of capital was independent of the type of technical change, and he concluded that ‘in the long run, any increase in thrift must rely for its effectiveness upon the prosaic mechanism of capital deepening’ (p. 557). 1 Arrow’s failure. Arrow also starts from a dissatisfaction with the exogenous nature of productivity growth in Solow’s model (Arrow, 1962, p. 155). Although better known than Frankel’s ‘modifier’, Arrow’s learning-by-doing model was less effective in obtaining an endogenous growth rate. Arrow’s original model was of a ‘clay-clay’ type, but it has usually been examined in the simpler ‘putty-putty’ version proposed by Sheshinsky (1967). Arrow’s seminal contribution is probably the main inspiration of EGT. There- fore, it is important to understand what went wrong with it. According to Arrow, investment is not only the carrier of technical change, as in the vintage models, but it represents its source. Frankel asserted that the accumulation of capital was the source of increasing returns at the aggregate level. Arrow was perhaps more convincing by linking increasing returns to the empirical evidence of learning pro- cesses. The specification chosen by Arrow to substitute equation (8), similar to Frankel’s equation (10), is:
H 5 K α (11)
with 0 ,α,1. Labour-augmenting technical progress is then a social externality of the process of capital accumulation which takes place at the firm level. Much as in Frankel, the single firm cannot appropriate the externality as this is the involuntary collective result of indi- vidual actions. The externality consists of a learning process derived from the cumulating of experience acquired by using the preceding vintages. This process leads to an improve- ment of the design of the newest generations of equipment. Substituting equation (11) in equation (3) we get Y 5 aK b+ a(1 – b) L 1 – b. Observe that this equation implies increasing returns to scale (the sum of the exponents is larger than one). In terms of rates of growth, the expression gy 5 [(b1a(1 – b)] gk + (1 – b)lcan be obtained. In the steady state gy 5 gk 5 g , so that the steady-state aggregate and per capita
growth rates are g 5 l and g 95 al , respectively (cf., e., Ferguson, 1979, ch. 14). 1 – a 1 – a None of the terms is related to the endogenous decisions to accumulate capital and, in spite of the assumption of increasing returns to scale, the rate of growth is still determined by the exogenous variables aandl. Economic reasoning shows us why Arrow failed to relate g to the savings rate. The
1 The intuition is that the more frugal community will have more equipment of any age, but the average age of the capital stock is the same as that of the more profligate one. The discussion was initially based on the Solow–Swan ‘putty-putty’ model. Subsequent models based on more rigid assumptions concerning the degree of substitutability between production factors left unscathed the independence of the growth rate from thrift. However, they conceded some effects of a higher savings rate on the average age of the capital stock (Allen, 1967, ch. 15; Solow, 1970, ch. 3).
Savings and economic growth in neoclassical theory 781
problem of endogenous growth is to show that there can be a constant rate of growth without an exogenous growth of the labour force or exogenous technical change. Suppose that l50. Equation (11) suggests that with a,1, the growth rate of labour efficiency is less than proportional to the growth of the capital stock. Analytically this is shown by the logarithmic derivatives, H· / H 5a K· / K. Therefore, endogenous capital accumulation is not capable of bringing about a proportional increase in the labour force in efficiency units, arresting the decreasing marginal returns to capital. The only thing that equation (11) can do is expand the growth effects of the exogenous growth rate of the labour force. On the one hand, this was a remarkable advance with respect to the original Solow–Swan contri- bution, as productivity growth became independent of exogenous technical change (Hamberg, 1971, p. 53). On the other hand, however, productivity growth becomes dependent on the exogenous growth of the labour force, confirming the latter in its essential role. One obvious solution is to assume that the growth rate of labour efficiency is pro- portional to that of the capital stock (that is a51), so that the economy can progress, fuelled by capital accumulation with a constant proportion of capital and labour in efficiency units, finally free from any ‘manna from heaven’, either in the form of additional cohorts of workers or of exogenous technical change. Why did Arrow not introduce this assumption? One reason is that the empirical evidence suggested to Arrow that technical progress was not an endless cumulative process and that some external engine, such as population growth, was necessary (Arrow, 1962, p. 166). Another possible deeper reason relates to the inconsistency between this stronger assumption concerning technical change and the role of labour in the theory of distribution and employment as traditionally envisaged by marginalist economists. Since this strong assumption is the starting point of the recent revival of Arrow’s model, this question will be discussed later in a new context.
4. Romer, Lucas and the second generation of endogenous growth models
An intergenerational comparison. During the 1960s the mainstream discussion on growth theory had a distinctly abstract flavour. The ‘neoclassical synthesis’ was indeed con- sidered to be empirically relevant for the management of industrialised countries, whereas the Harrod–Domar model was perfectly suited as a policy guide for developing countries. At the beginning of the 1970s, interest in the theory of economic growth temporarily faded as the monetarist criticism of the neoclassical synthesis took centre stage. 1 Later, as a result of the progressive restoration of pre-Keynesian views, the long-run implications of neoclassical theory were no longer looked at from the Keynesian point of view as a ‘special case’, not very relevant for the actual management of the economy, but taken literally as a source of policy prescriptions. 2 This renewed interest may explain the urgency of mending its less satisfactory implications. In particular, as long as thrift is not restored as a deter- minant of the rate of growth, there is less scope for the orthodox policy prescriptions aimed at raising the savings rate. The diversity in the growth experiences and, in particular, the rapid development of the South-east Asian economies also stimulated new research on economic growth. One clear 1 Malinvaud (1993) recognises that the results of the capital controversy also contributed to the fall of interest in neoclassical growth theory. 2 Up-to-date macroeconomics textbooks (e., Romer, D., 1996) illustrate the neoclassical growth model and its recent developments in the first chapters. By contrast, the standard textbooks written by the authors of the neoclassical synthesis dealt with growth at the end of the book (e., Ackley, 1961) and in many cases growth coincided with the Harrod–Domar model and not with that by Solow and Swan.
Savings and economic growth in neoclassical theory 783
productivity and the choices of the community between present and future consumption. These choices affect labour productivity via the resources devoted to R&D, education, infrastructures and the like.
4. Pseudo-Harrod–Domar models The one-sector or ‘AK’ model. Reviving Arrow’s approach (1962), this first group of models relates the growth of labour productivity to capital accumulation, a process described by equation (11). In his seminal paper, Paul Romer (1986) makes an assumption about technical change that is much stronger than that made by Arrow, with a>1 instead of a ,1 as proposed by Arrow. Let us discuss the milder assumption, a51. In this case, the growth of the capital stock induces a proportional growth of labour productivity so that the economy can grow independently of the exogenous growth of the labour force (which is assumed to be constant in natural units). Romer seems to be reviving Abramowitz’s suggestion of increasing returns brought about by the increase in the supply of a single factor (see above Section 2). EGT literature expresses this in saying that there are constant returns to the ‘produced factor’. More precisely, the externality that springs from capital accumulation permits a proportional growth of all factors in efficiency units, so that the marginal returns to the accumulable factor are constant along the secular growth path. If a, the externality is so strong that the growth rate is increasing with time (this has attracted some criticism and will be discussed below in Section 5). By contrast, as shown by the Arrow model discussed above, the mere existence of increasing returns to scale is not enough to generate endogenous growth. However, even with the assumption a51, Romer’s model runs into trouble if it attempts to accommodate the full employment of a growing labour force: the increasing returns are sufficient to generate a growth of the labour force in efficiency units pro- portional to capital accumulation. Should the model also try to accommodate the growth of population in natural units, the economy would find itself off the balanced growth path (Hamberg, 1971, pp. 52–5; Ramanathan, 1982, p. 97; Giannini, 1996; D. Romer, 1996, p. 103). This difficulty suggests an explanation as to why Arrow considered a ,1 as the most sensible assumption. Romer’s road to endogenous growth was already open to theoretical economists in the 1960s, but was dismissed because it led to undesirable results. Let us now go back to Romer’s argument in order to draw on its ultimate implications. Assume that in Arrow’s equation (11) a 51, that is
H 5 K (12)
so that the rate of technical change is proportional to the rate of growth of the capital stock. Assume also that there is a constant labour force L that can be normalised to 1. Substituting (12) in (3), with L 5 1, the expression Y 5 aK b K 1 –bis obtained, which simplified gives
Y 5 aK (13)
Romer’s model can therefore be regarded as a new version of Frankel’s ‘ AK model’ which, as we have seen, easily gives rise to a pseudo-Harrod–Domar warranted rate of growth. To grasp the dynamics of Romer’s model, note that in equation (13) K can be regarded as having two components, one physical and the other ‘human’, which is the result of the spill-over from capital accumulation entailed by equation (12) (e., Barro and Sala-i-Martin, 1995, p. 39). The community’s savings rate directly affects the
784 S. Cesaratto
accumulation of the physical component, and indirectly affects, via equation (12), the ‘human capital’ component. Solow suggests that the essence of these models is that ‘there is no primary factor, labor has disappeared’ (1992, p. 32). Solow’s statement may appear too drastic. After all, labour still appears as ‘human capital’. However, Solow is correct in the sense that labour, as traditionally understood in economic analysis, has disappeared. It only vaguely reappears, merged and blurred, as the ‘human’ component of the social capital stock. These models are known in literature as ‘ AK ’ or linear growth models (Rebelo, 1991; Barro and Sala-i-Martin, 1995, ch. 1; D. Romer, 1996, p. 104). They are often thought of as encapsulating the essential message of EGT. Their message is that endogenous growth comes from a sector of the economy that produces without using non-reproducible resources, but only a ‘reproducible factor’, the accumulation of which hinges on the saving preferences of the community. Rebelo, for instance, argues that ‘all that is required to assure the flexibility of perpetual growth is the existence of a “core” of capital goods that is produced with constant returns technologies and without the direct or indirect use of non reproducible factors’ (Rebelo, 1991, p. 502). 1 In Romer’s version of the AK model, the sector that produces without using non- reproducible resources is a ‘virtual’ sector, represented by equation (12), in which capital exhibits an externality which gives rise to the production of ‘human capital’. In the most simple AK model, corn is produced by using only corn (e., Rebelo, 1991, p. 507). 2 In other models, physical or human capital is produced in a separate industry without employing non-reproducible resources. Barro and Sala-i-Martin (1995, pp. 179–82), for example, following Rebelo (1991), describe a two-sector economy (such as corn and education) in which the final output Y , used both as consumption and capital goods, and the intermediate good H , also defined as human capital, are both produced through a constant return technology that makes use of both the resources. Notably, labour, as traditionally understood, does not appear in the production functions. 3 Some ambiguities in the theoretical status of ‘pseudo-Harrod–Domar’ models. An obvious way to look at what, above, has been called the Solowian paradox is that, by its very nature, the requirement of full employment requires that the natural growth rate coincides with that of the labour force and cannot depend on other parameters, namely on the savings rate. Not surprisingly, then, one price which must be paid in order to make the rate of growth endogenous is the sacrifice of the constraint of full employment by eliminating labour from the production function. By cancelling the role of labour (and of
1 In terms of policy prescriptions, Rebelo concludes that ‘an increase in the income tax rate decreases the rate of return to the investment activities of the private sector and leads to a permanent decline in the rate of capital accumulation and in the rate of growth’ (Rebelo, 1991, p. 501). 2 In a similar fashion, EGT authors have rediscovered how to dismiss the role of labour by adopting the CES production function. Barro and Sala-i-Martin (1995, pp. 42–6, 164–7) argue that for particularly high degrees of substitution between labour and capital, and for high values of the savings rate, a CES production function can generate endogenous growth. The idea is that, in spite of becoming progressively abundant with respect to labour, capital is now highly substitutable for labour, so that net saving, in the absence of efficiency– labour growth, does not translate into a falling marginal productivity of capital but into endless growth of per capita output (Grossman and Helpman, 1994, p. 25). Ça va sans dire that this result was clearly exposed by Solow (1956, pp. 70–1), and discussed later by other authors (e., Brown, 1966, p. 50, quoted by Ferguson, 1979, p. 105; Allen, 1967, p. 54). The hypothesis was probably dismissed after the early warning by Arrow et al. (1961, p. 231) that high substitutability was not ‘the empirically relevant case’ (cf., also Hamberg, 1971, p. 165). 3 According to Barro and Sala-i-Martin (1995) the two-sector model presents stability problems. Future work should explore the nature of these problems in the light of the well-known difficulties met by the traditional neoclassical two-sector models (cf., Solow, 1961, for a simple introduction).
786 S. Cesaratto
K b( uHL )1 – b. The term u represents the share of labour time employed in the production of corn. He then modifies equation (8) by writing:
H
.
5 H zd[1 – u ] (14)
where 1 – u is the share of labour time diverted, on the basis of the preferences of the community between present and future consumption, from the production of corn to educational activities that will increase the efficiency of the forthcoming generations of labourers. In order to obtain a constant growth rate, Lucas assumes z51. It may be noted that Lucas’s model merely consists of a modification of equation (8) of the standard neoclassical growth model—the solution of equation (14), with z51, is indeed H 5 e d[1 – u ] t. Therefore, contrary to the AK models, the second strand of EGT models initiated by Lucas do not break with neoclassical principles. As Lucas put it: ‘[a]side from these changes in the technology... to incorporate human capital and its accumulation, the model... is identical to the Solow model’ (1988, pp. 19–20). The difference is, of course, that the term 1 – u allows us to regard the rate of change of labour efficiency as dependent on the saving decisions of the community. 1 Neo-vintage models. In another seminal paper, Paul Romer (1990) moves from a pro- duction function that represents the final corn sector:
A
Y 5 HY a L b( xi 1 – a– b (15)
i 51
in which ‘capital’ appears as the sum of A different ‘types’ of capital goods xi , L is the stock of ‘ordinary’ labour, and HY the amount of ‘human capital’ devoted to the production of Y. The xi are produced in an intermediate-goods sector by using ‘foregone output’, that is, saved corn, and the designs are produced by a third sector called the research sector. Each capital good has the same production cost consisting of hunits of output (corn), and since they present the same marginal productivity the same amount of each, x ̄, is produced. The research sector produces ‘designs’ of new capital goods by using a constant amount of ‘human capital’ HR , which is subtracted from the direct production of corn which uses the remaining HY , plus the existing stock of knowledge A , measured by the number of already available designs. Equation (8) now takes the following endogenous shape:
A· 5d HRA (16)
Since A types of capital goods exist at any time, it follows that (
A xi 5 Ax ̄ , and equation (15) can be written i 51
Y 5 A [ HY a L b x ̄ 1 – a– b].
Given HY , L and x ̄ , a constant output growth is clearly generated via equation (16). The similarity between Romer’s (1990) model and Solow’s (1960) vintage model is profound. This is not meant to diminish the novelty of Romer’s contribution, but rather to indicate where real progress has been made. First of all, both models adopt a ‘Cobb– Douglas’ which allows the translation of a form of technical change which superficially concerns the design of capital goods in the ‘labour-augmenting’ form necessary for a steady-state growth path (cf., e., Hamberg, 1971, pp. 148–50).
1 ‘Here at least is a connection between “thriftiness” and “growth”’ is the comment of Lucas (1988, p. 23) on the outcome of his model based on equation (14).
Savings and economic growth in neoclassical theory 787 More importantly, the treatment of heterogeneity in the capital stock is similar. In both authors the capital stock is made up of machines which, in spite of their different ‘design’, are homogeneous in the final product (corn). The defence of this treatment of capital as ‘metaphoric’ (e., by Barro and Sala-i-Martin, 1995, p. 213) is not acceptable. ‘Metaphors’ as well as ‘parables’ are only defensible as didactic devices: the validity of a theory cannot be decided by them. The persistent difficulties of neoclassical economists in dealing with ‘capital’ underlines the enduring relevance of the capital controversy for the current conventional models. 1 Finally, the economics of innovation implicit in both models is not radically different. Technical change is exogenous in Solow’s (1960) vintage model and proceeds according to an exponential equation similar to equation (8). It is endogenous in Romer (1990) and takes place according to equation (16), the solution of which is A 5 e d HRt. Except for the term HR , which represents labour used to produce design instead of corn and establishes the dependence of the rate of technical change on the saving decisions of the community, the description of technical change is similar in both models. In the Lucas and Romer models, a common feature of equations (14) and (16) is found as ‘human capital’ enters as a constant , either in the form of share of time devoted to education, or as a constant amount. The reason for this is clearly to ensure a constant rate of technical change and steady-state growth. Earlier contributors (e., Phelps, 1966; Shell, 1966), who attempted other plausible hypotheses concerning technical progress, e., making it dependent on growing levels of research labour-force or R&D resources, indeed met problems obtaining balanced growth (cf., Cesaratto, 1999). Why neo-exogenous models? It is now time for us to justify the term ‘neo-exogenous’ models. A theory of endogenous growth aims to find an internal mechanism which generates economic growth. Various approaches can be found in the history of economic analysis (Cesaratto, 1996). For instance, the Smithian and Kaldorian traditions interpret endogenous growth as the interaction between the division of labour, inventive activity and market size. Marx and Schumpeter associated endogenous growth with the pressure of competition on the innovative behaviour of the capitalistic and the entrepreneurial classes, respectively. Consistent with an approach that regards thrift as the trigger of economic growth, the neoclassical theory of endogenous growth tries to associate the rate of growth with the saving decisions of the community. This association is direct in the ‘ AK models’, and is postulated through the influence of the savings rate on the pace of technical change, through R&D, education etc., in the ‘neo-exogenous’ models. In the former approaches, the endogenous aspect of economic growth refers to various institutional, social and economic mechanisms that may generate economic change, whereas in EGT these mechanisms remain exogenous. Technical change is generally depicted as a process of self-generation of knowledge, with no interaction with other
1 The literature on the vintage models contributed to the clarification of the limitations that the aggregation of heterogeneous capital goods presents in neoclassical theory (see Fisher, 1965; Harcourt, 1972, p. 74). In models a là Romer (1990) or a là Solow (1960), pieces of equipment belonging to various vintages differ only in the ‘amount’ of technical change they embody, which is exogenously known. As a result, the well-known problem of neoclassical capital theory—the dependence of the ‘value’ of the capital stock on distribution— does not arise. In more analytical terms, both Solow and Romer respected ‘Leontief’s theorem on separable functions’ that Solow (1956), in his reply to Joan Robinson’s objections to the neoclassical notion of capital, had shown to be sufficient for a consistent aggregation of heterogeneous capital goods (cf., e., Ferguson, 1979, p. 274). For instance, equation (15) is written for the purpose of respecting Leontief’s separability conditions. ‘Heterogeneity’ is here quite peculiar, since the capital goods are homogeneous in terms of pro- duction costs, and are actually homogeneous to the consumption good, although they use different quantities of labour to produce a unit of output.
Savings and economic growth in neoclassical theory 789 While these criticisms are well known, it may be useful to emphasise the additional ones proposed in this paper. First, with regard to the pseudo-Harrod–Domar models, we have seen that even with the milder assumption of a51 in equation (11), this class of models cannot accommodate a positive growth rate of a fully employed labour force. Second, the AK models take Say’s Law for granted in assuming that the existing productive capacity is constantly fully utilised, although in a Harrod–Domar framework the translation of full employment saving into investment is not ensured. Finally, in the neo-exogenous model, in order to obtain balanced growth, it is not enough to assume that in technical progress functions the ‘exponents’ are equal to one. To ensure that the rate of endogenous tech- nical change is constant, the economic variables inserted in the functions must also be constant. This is more acceptable when these variables appear as constant ‘shares’ (shares of educational labour in the total labour force, or of R&D in national income etc.); it is less acceptable when they are inserted as constant ‘levels’ (amounts of educational labour or R&D expenditure, etc.). It may be concluded, in agreement with Frank Hahn, that EGT models are charac- terised by ‘backward reasoning’, not from the empirical observation on the sources and patterns of technical change in their modelling, but from the constraints that the theoretical background poses to their modelling. These theories, Hahn writes, ‘are all intent on models which allow equilibrium growth at a constant rate. Hence suitable forms are arrived at by a backward reasoning from this requirement. I am quite unsure that this is a good procedure. Certainly it is uncomfortable to have what after all amounts to a theory of economic history hinge on functional forms for which there is no pretence that they are empirically based’ (Hahn, 1994, p. 1).
6. Final remarks
This paper has argued that recent developments of neoclassical growth theory represent attempts to solve the problem for mainstream economics that without the exogenous growth of non-produced factors, either in physical or in efficiency units, the progressive abundance of capital which results from a net savings rate induces a fall in the marginal productivity of capital and a tendency towards the stationary state. This is an embarrass- ing outcome for neoclassical theory, since the progressive role of thrift in economic growth and a long-run positive reward to parsimony must rely on exogenous circum- stances. Unfortunately, in the most favourable circumstances of a positive long-run growth of non-produced factors, the choices of the community between present and future consumption become irrelevant for the determination of the rate of growth. Although known earlier, these results became particularly apparent with Solow’s (1956) model. We have reviewed some of the early contributions to endogenous growth theory that followed Solow’s model. We have not criticised modern EGT for having taken inspiration from these contributions. Rather, the indictment is the cavalier way in which this inspiration is often dealt with. This is particularly evident in the case of the developers of the ‘pseudo- Harrod–Domar’ models, who pay little attention to the consistency of their approach with neoclassical theory. The previous generations of neoclassical economists paid greater attention to this consistency, as in the case of Frankel and Arrow. In addition, previous generations of neoclassical economists did not attribute too much importance to the kind of results on which the ‘neo-exogenous’ models have built their reputation. EGT emphasises results that were well known, but carefully circumscribed by the older authors (e., by Hahn and Matthews, 1964, pp. 833–4). As Stiglitz puts it (1990, p. 55):
790 S. Cesaratto
We knew how to construct models that ‘worked’, but felt uneasy making these special assumptions. It was one thing to assume that savings rates were constant—that was a behavioral hypothesis that provided a not bad description of the economy over long periods of time, and besides, it was an assumption that could, with some increased complexity to the model, be altered, with only minor consequences for the central results of the model. But it was quite another thing to assume, for instance, that the effects of learning just offset the effects of diminishing returns due to land scarcity! That was a technological assumption, and although we may have agreed with Einstein that God had created a universe of great simplicity, it seemed going too far to assume that he had endowed technology with these special parameters, simply so that we could construct our steady state models. 1
A more radical criticism of both the old and new neoclassical growth theory concerns the exclusive focus on the supply side, that is, on the generation of social resources, guided by the choices of the community between present and future consumption, as the source of income growth. This vision of economic growth has been dramatically weakened both by the Keynesian theory of effective demand and by the Sraffian criticism of neoclassical capital theory. From both these points of view, the idea that a market economy tends to the full employment of social resources is undermined. An increasing amount of social resources, physical and ‘intellectual’, cannot be seen as a sufficient condition for economic growth, and their generation cannot be explained independently of the growth of effective demand. An alternative approach to EGT, based on the theory of effective demand, would not neglect the importance of the supply side (cf., Arestis and Sawyer, 1998, pp. 190–1), for instance of the institutional and educational background of differ- ent countries, but would identify the ultimate relevance of these factors in their capacity either to stimulate effective demand or to respond to it. 2
Bibliography
Abramovitz, M. 1952. Economics of growth, in Haley B. F. (ed.), A Survey of Contemporary Economics , Homewood, Irwin Ackley, G. 1961. Macroeconomic Theory , London, Macmillan Allen, R. G. D. 1967. Macroeconomic Theory , London, Macmillan Arestis, P. and Sawyer, M. 1998. Keynesian economic policies for the new millennium, Economic Journal , vol. 108, 181– Arrow, K. J. 1962. The economic implications of learning by doing, Review of Economic Studies , vol. 29, 155– Arrow, K. J., Chenery, H. B., Minhas, B. S. and Solow, R. M. 1961. Capital–labor substitution and economic efficiency, Review of Economics and Statistics , vol. 43, 225– Barro, R. J. and Sala-i-Martin, X. 1995. Economic Growth , New York, McGraw-Hill Bertola, G. 1994. Wages, profits and theories of growth, in Pasinetti, L. L. and Solow, R. M. (eds), Economic Growth and the Structure of Long-Term Development, New York, St. Martin’s Press Blomstrom, M., Lipsey, R. E. and Zejan, M. 1996. Is fixed investment the key to economic growth? Quarterly Journal of Economics , vol. 61, 269– Bortis, H. 1997. Institutions, Behaviour and Economic Theory—A Contribution to Classical-Keynesian Political Economy , Cambridge, Cambridge University Press 1 In his comments on this paper, Solow reinforced this interpretation. He wrote that while he was pleased with my revival of the work of Marvin Frankel, with whom he had had many discussions, ‘it bothered me then (with Frankel’s model) as it does now, with EGT, that (equation 10) requires g51, and will not work if g. 1 or g,1’ (Solow’s italics). 2 Some recent contributions in this journal have developed this alternative approach: J.-I. You (1994), Targetti, Foti (1997), Setterfield (1997). A recent, promising merger of Kalecki’s (1970) and Kaldor’s (1970) approaches to the theory of accumulation with the Sraffian approach to distribution theory has been advanced by Serrano (1995, 1996) and Bortis (1997).
Cesaratto, S. (1999). Savings and Economic Growth in Neoclassical Theory
Asignatura: Historia y Literatura (Hist0)
Universidad: Universidad de la Sabana
- Descubrir más de:
