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ensuring a steady-state balanced growth path require equality of natural and warranted growth rates.63 The former is posited as exogenously given by the rate of growth of population,, whereas the latter is given by the growth rate of the capital stock. Since this grows each is output),64 period by (where is the savings rate, which is assumed to be constant, and the rate of growth of the capital stock can be rewritten as, or (where stands for the capital-output ratio). Reformulated in capital per worker terms, output per capita will depend on capital per worker, as specified by the production function for capital per worker,. In order for the economy to satisfy the Harrod-Domar conditions for steady-state balanced growth, it is required that, which can be rewritten as, and, therefore,. This last equation implies that saving/investment per worker must equal the new investment required for new workers in the economy to allow for a constant growth rate with capital and labour remaining in the same proportions over time (Fine, 2003b). As Mirowski (2011, p.71) points out, it is worthwhile to note ‘the extent to which the model was supposedly cast in “materialist” terms, dictated by technology, demographics, depreciation, and the like’, with the ‘phenomenon of economic growth’ understood as a set of ‘timeless physical relations dictating timeless natural growth rates with smooth adjustments to timeless steady state ratios between key variables’.
All savings are assumed to be invested.
It is following from, and as opposed to, this that EGT gets its name, with the “endogenisation” of technology and the savings rate implying that the parameters expressing them in the model are the outcome of the optimising decisions of agents in the model, and, therefore, determined within the model itself.
These are several, and include the assumptions of perfect competition and full employment in and across all markets (albeit mitigated by their validity in an unspecified long run), and the striking neglect of historical experience, which shows that growth is neither steady nor balanced but, rather, part and parcel of processes of structural change and socio-economic development which, by raising productivity across all sectors and shifting the economy from agriculture into manufacturing and then services, involve major transformations in the proportions of economic activity and composition of output (but see Fine, 2000, 2003b, 2006a for more). However, the most devastating limitations of old growth theory (even if assessed on its own terms) stem from its reliance upon the neoclassical production function as representative of the whole economy (one-sector model), which makes it vulnerable to the Cambridge Critique formulated during the Cambridge capital controversies (Fine, 2000, 2003b, 2006a). In particular, for the Cambridge Critique, see Robinson, 1953-1954 and Harcourt, 1972 for classic accounts, and Fine, 1980 (ch.5, 6), 2012a for shorter and more accessible accounts (but see also footnote 68).
(consideration of) non-economic (factors) as supplement to economic theory in explaining growth.67 Thus, while its intrinsic limitations do not make it a complete and all-encompassing theory of economic growth, it must be noted that this was not something that old growth theory itself aspired to be (Fine, 2003b).
However, to reintroduce technical change into the model would prove to be the ‘Revenge of the Repressed’, with ‘the intrinsic reinsertion of the temporal and the social into the explanation of growth’ (Mirowski, 2011, p.71). As is well-known, in attempting to test the model econometrically with U.S. data for the period 1909-1949, Solow (1957) allowed for the possibility that the production function had changed during the period by adding an additional variable to the model. Thus, he redefined the production function as, where the ‘variable for time’ appeared ‘in to allow for technical change’. Incidentally, this was to give birth to the habit of adding variables to the production function, characteristic of EGT.
However, as Solow himself admitted, ‘the phrase “technical change”’ was to be understood as ‘a shorthand expression for any kind of shift in the production function. Thus slowdowns, speedups, improvements in the education of the labor force, and all sorts of things’ would ‘appear as “technical change”’ (Solow, 1957, p.312). Much to his own surprise (Solow, 2005), Solow found that most of the growth experienced during that period could not be explained by the growth of productive factors but, rather, was to be understood as due to shifts in the production function. However, as opposed to rejecting the model altogether (which could have been a reasonable path to take, given that most of the growth was to be explained by … “all sorts of things”), this led Solow to identify “technical change” as the main determinant for growth (Mirowski, 2011). This “discovery” opened the way to “growth accounting”, i.e.
statistical exercises aiming to measure ‘technological progress or the contribution of exogenous productivity increases to increases in output’ (Fine, 2003b, p.205). Thus, ‘the increase in output … minus contribution to output from increase in capital … minus contribution to output from increase in labour’ came to be understood as ‘the output increase that is not explained by increases in inputs’ and, therefore, ‘designated as due to technological progress and named total factor productivity’. Yet, the latter was ‘recognised to be a residual after the contribution of increases in inputs have been netted out from increases in output’, and, although measured, it was left unexplained (Fine, 2003b, p.206). Indeed, and however Solow himself has recalled this intellectual “division of labour” between the old neoclassical theory of economic growth and a broader conception of development, informed by the consideration of socioeconomic processes: ‘in the early 1950s everybody was interested in economic development, for the obvious reason that most of the population of the world was living in poor economies. I was passively interested in economic development, but I have never been actively interested – in a research way – in what happens in underdeveloped countries. But I got to thinking about development issues and I had read Arthur Lewis. I knew I was not going to work on development issues, but it did get me interested in the general area of economic growth’ (Solow, 2005, p.663).
fraught with conceptual mistakes and inconsistencies, even on its own terms, the measurement of total factor productivity (Fine, 2003b, 2006a),68 all of this testifies to what old growth theory saw as its own limits and theoretical ambitions.69 Incidentally, the lack of any pretence within old growth theory to explain the origins of technical progress went well with Arrow’s (1962a) and Nelson’s (1959) characterisation of knowledge, innovation and research as public goods, on the one hand, and with the faith in the linear model of innovation within U.S. public and science policy circles, on the other (Mirowski, 2011). Thus, ‘[b]y the 1960s, the combination of the linear model, the public good, and Solow-defined technical change became cemented together in the’ U.S. ‘science policy community as the Cold War explanation of choice’ to be used in justifying ‘the continuation of the largesse of government subsidy of science in that era’ (Mirowski, 2011, p.73).
These descend from the vulnerability of old growth theory to the Cambridge Critique. In a one-sector model, represented by the production function in per capita terms, distribution between capital and labour is determined by appeal to their respective marginal products, with the rate of profit equalling and the wage rate equalling. Following from this, the relations between profits, wages and the capital stock in per capita terms are set algebraically, with profit falling as grows because of diminishing marginal returns of. However, by taking into consideration the existence of more than one sector, these results do not hold. ‘First of all, capital as such cannot be measured and placed within a production function with the properties required. Essentially, capital now has both a physical aspect (quantities of machines) and a price aspect – at the very least where is price and quantity of physical capital. The quantity depends on, and this cannot be derived from within the one-sector model, as there is only one good and so no (relative) prices’ (Fine, 2003b, p.205). This invalidates measurements of total factor productivity, since ‘changes in are a combination of changes in both the evaluation and the quantity of capital’, but the measure of total factor productivity stemming from the one-sector old growth theory treats all changes in as if they were changes in physical quantity (Fine, 2003b, p.206).
Solow himself has clarified various time what he took “exogenous” to mean. For example, he has affirmed: ‘When I say that in my work in the 1950s I treated technical change as exogenous, that does not mean that I really believed at the time that it had no internal economic causes. In the very same papers I always treated population growth as exogenous, but I did know about Malthus, and there is clearly a connection between economic development and demographic patterns. What I meant by saying something is exogenous was that I do not pretend to understand this; I have nothing worthwhile to say on this so I might as well take technical change as given … I do not know what the determinants of technical change are in any useful detail’ (Solow, 2005, p.668; similarly, Solow, 1994). This conception of the analytical task of the neoclassical old growth model and the analytical questions it could address are at the basis of Solow’s antipathy towards EGT and its empirics based on multivariable cross-country regressions (see, for example, Solow, 2001), and of Solow’s concern with how ‘the long run in which so much is taken as given or in which the grandly endogenous, such as stages of capitalism and shifting social institutions, are tied’, in EGT models, ‘exclusively to the most simplistic optimising behaviour’ (Fine, 2000, p.261) (see below). Unfortunately, such ‘cautionary notes, even if within the neoclassical paradigm’, have been ignored in EGT, ‘as models based on simple intuitions are worked out mathematically and tested empirically against the conveniently available large data sets across regions and time’ (Fine, 2000, p.261). Incidentally, this, in itself, is exemplary of the relevance of Boulding’s (1966, p.10) prescient concern with the dangers that advances in computing represent for the development of abstract thought in general and economic theory in particular: ‘I confess I am a little worried about one aspect of this movement, fruitful as it undoubtedly is. The very power of the computer to simulate complex systems by very high-speed arithmetic may prevent search for those simplified formulations which are the essence of progress in theory’. Nonetheless, as Solow himself laments, there is still no understanding, in EGT, of the (socio-economic) determinants of technical change (despite claims to the contrary from within EGT).
But the old growth theory ended up running into a series of paradoxes of its own. Of these, the most “striking” (that is, for mainstream economists) was that, despite obvious differences in economic and growth performances across developed and developing countries, the full implications of the Solow model were that, given a common production function (and, therefore, exogenous technology), as well as free mobility of capital, knowledge and technology, the marginal rate of return to investment in developing countries (where capital is scarce) should be much higher than that in developed countries (where capital is abundant).
Further, this should lead to overall convergence across developing and developed economies, with the former converging at faster rates of growth than the latter. But none of this was to be found in reality (Lucas, 1990). However, while this lack of realism was perceived as having brought research within old growth theory to a dead end, it also proved key in pushing mainstream economists to believe that ‘physical capital accumulation alone’ could not ‘account for either continuous growth of per capita income over long periods of time or the enormous geographical disparities in living standards’ observed across national economies (Snowdon, Vane, 2005, p.624, emphasis added) (as well as generating interest for testing conditional convergence, thus setting the bases for the empirics of EGT). Therefore, after two decades of stagnation, the “new” research programme in neoclassical growth theory saw the light in the 1990s, following the impulse of seminal contributions by Lucas (1988) and Romer (1986, 1990a). From these origins, EGT has expanded enormously in both theoretical and empirical content. However, despite the wide variety and mathematical sophistication of EGT models, these ‘have settled down to have common theoretical elements’ (Fine, 2003b, p.207).