The Solow-Pasinetti debate on the measurement of productivity in the light of modern growth theory

Sember, Florencia R. Article The Solow-Pasinetti debate on the measurement of productivity in the light of modern growth theory PSL Quarterly Review Provided in Cooperation with: Associazione Economia civile, Rome Suggested Citation: Sember, Florencia R. (2024) : The Solow-Pasinetti debate on the measurement of productivity in the light of modern growth theory, PSL Quarterly Review, ISSN 2037-3643, Associazione Economia civile, Rome, Vol. 77, Iss. 309, pp. 127-143, https://doi.org/10.13133/2037-3643/18492 This Version is available at: https://hdl.handle.net/10419/324105 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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To view a copy of this license visit http://creativecommons.org/licenses/by-nc-nd/4.0/ vol. 77 n. 309 (June 2024) The Solow-Pasinetti debate on the measurement of productivity in the light of modern growth theory FLORENCIA R. SEMBER* Abstract: This article aims to study the Solow-Pasinetti debate on the aggregate production function and technical progress as an event that anticipated a divide in the subsequent theories of economic growth and technical change. Ultimately, the debate manifests two completely different approaches, not only to the particular question of technical change but also to political economy tout court. Pasinetti gave paramount importance to the fact that the factors of production could not be treated as symmetrical, as the neoclassical theory treated them. Related to this is Pasinetti’s dismissal of the distinction neoclassical economics made between shifts in the production function to evaluate technical change and movements along it. In fact, he dismissed the neoclassical production function altogether. University of Buenos Aires and CONICET, Argentina email: [email protected] How to cite this article: Sember F.R. (2024), “The Solow-Pasinetti debate on the measurement of productivity in the light of modern growth theory”, PSL Quarterly Review, 77 (309), pp. 127-143. DOI: https://doi.org/10.13133/2037-3643/18492 JEL codes: B22, B41, O40 Keywords: Solow, Pasinetti, production function, productivity measurement Journal homepage: http: //www.pslquarterlyreview.info Luigi Pasinetti’s works cover various topics, such as economic growth, income distribution, structural change, and international economic relations. 1 In particular, he was a great critic of neoclassical economics, which led him to build an alternative system to understand the main problems of industrial economies. This criticism of neoclassical economic theory, simultaneously with his own alternative theoretical construction, led him to propose a dynamic model for an industrial economic system in Structural Change and Economic Growth (Pasinetti, 1981). In his book Keynes and the Cambridge Keynesians, Pasinetti affirmed that all economic theories since Adam Smith could be associated with two main paradigms. The marginalism and neoclassical theories could be associated with the paradigm focusing on exchange, utility and subjective value, and the Classical and Keynesian approaches could be associated with a paradigm focusing on production, labour and objective value (Pasinetti, 2007, pp.18-21). Pasinetti associated these two paradigms with two different phases of economic history. The phase of commercial capitalism, when countries begin to exchange available products and thus * I am grateful to the participants of the AISPE-SISE 2023 Conference in Palermo, where I benefited from very interesting and stimulating discussions, and the two anonymous referees for their helpful suggestions. All remaining errors are my own responsibility. 1 For a general survey of Pasinetti’s trajectory, see Halevi (2016). Special issue on the Solow-Pasinetti debate on productivity measurement 128 The Solow-Pasinetti debate on the measurement of productivity in the light of modern growth theory PSL Quarterly Review increase their material well-being, can be associated with the “exchange paradigm” and the emergence of mercantilist economic theories. The phase of industrial capitalism, when wealth increases progressively with technological and organisational improvements in production, can be associated with the emergence of the “production paradigm”; this began with the Physiocrats, followed by Petty and then Classical Political Economy. Industry and its continuous and cumulative technological changes become the permanent cause of the increase in society’s wealth. According to Pasinetti, the concept of trade is static by nature: it is about allocating existing resources in the best possible way. When the economy moves from a phase in which countries do not trade with each other to a new phase in which they exchange the goods they possess, each country experiences a once and for all improvement in its welfare. Mathematically, the problem is about maximising a function under certain restrictions. The concept of industry, on the contrary, is dynamic by its nature, since it is implicit that new methods are discovered through industrial production. Thus, there is a continuous learning process. In this case, any mathematical formulation must be a function of time, since the learning process is cumulative and involves a rate of change. Pasinetti stressed his differences with the neoclassical theory of growth on several occasions (Pasinetti, 1981, 2000, 2007) but, at the same time, he admitted that neoclassical theory had a unifying principle that the alternative theories did not achieve. The theories belonging to the production paradigm – among which Pasinetti placed the Keynesian and Kaleckian short-run theories, Leontief’s input-output analysis, Sraffa’s production of commodities scheme, the theories of the behaviour of the firm, 2 the Harrod-Domar and other post-Keynesian theories of growth and distribution – all presented their contributions independently of one another. They lacked a unifying principle analogous to the marginal principle. To this, Pasinetti added that postKeynesian economics did not fight back hard enough at the first attempts to absorb Keynes’s approach into mainstream theory. Although the Cambridge Keynesians contributed significantly in the 1950s and 1960s in several fields of study, the spread of the Cambridge School of postKeynesian economics came to a halt. One of the causes, as stated by Pasinetti, was that there was much criticism of mainstream economics but the amount of work necessary to build an alternative paradigm of a monetary theory of production had been underestimated. Additionally, the Cambridge post-Keynesians failed to leave a younger generation of academics following in their tracks. In this way, a concrete possibility of bringing back the production paradigm failed. In the modern theory of economic growth, the divide described by Pasinetti started as soon as Solow and Swan absorbed the seminal contributions by Harrod and Domar into neoclassical economics. Harrod presented his dynamic theory as “a marriage of the ‘acceleration principle’ and the ‘multiplier’ theory” (Harrod, 1939, p. 14). Harrod’s warranted rate of growth, 𝐺𝑊=𝑠𝑣 ⁄, is determined by the propensity to save, 𝑠, and the capital/output ratio, 𝑣. This line traced by 𝐺𝑊 “represents the one level of output at which producers will feel in the upshot that they have done the right thing, and which will induce them to continue in the same line of advance” (Harrod, 1939, p. 22). Harrod also introduced the notion of the natural rate of growth,𝐺𝑁, which is the maximum rate of growth allowed by the increase in population and technological improvement. Harrod showed that, when the rate of growth actually produced is different from the warranted rate, disequilibrium is self-aggravating. Additionally, there is no inherent tendency for warranted and natural rates to coincide. If the warranted rate is above the natural rate, the economy will tend to depression and unemployment, 2 Pasinetti refers to the theories of the firm developed after Sraffa’s criticism of Marshall, followed by Robinson’s and Chamberlin’s theories of imperfect competition, the formulation of the full-cost principle and managerial theories of the 1960s. F.R. Sember 129 PSL Quarterly Review and, in the opposite case, it will tend to exhibit successions of profit booms. Thus, the capitalist economy is highly unstable. Mainstream economics incorporated Harrod’s contribution in the framework of neoclassical production functions, interpreting Harrod’s case as the particular case of production with fixed coefficients and proposing production functions where the technological magnitude, 𝑣, was variable. The economy can adapt to the natural growth rate through the perfect substitutability of capital and labour. Conversely, post-Keynesians built theories in which the propensity to save varies and the distributive shares, 𝑃/𝑌 and 𝑊/𝑌, are determined sequentially. The Solow-Pasinetti debate on the aggregate production function that is the object of this article took place in the Review of Economics and Statistics between 1957, when Solow’s article “Technical change and the aggregate production function” was published, and 1959, when Pasinetti responded with his article “On concepts and measures of changes in productivity”. Pasinetti’s response motivated a rejoinder from Solow and, in turn, a new response from Pasinetti (Pasinetti, 1959; Solow, 1957, 1959). Forty years later, in 1998, the publication of an article by Richard Stone triggered another exchange between the two authors, showing that the disagreements expressed in the fifties persisted (Stone, 1998; Solow, 1998; Pasinetti, 1998). This is not surprising since, in the end, both theories are embedded in different paradigms, i.e., neoclassical theory is embedded in what Pasinetti called the exchange paradigm and Pasinetti’s theory is embedded in the production paradigm. This article presents the Solow-Pasinetti debate of the end of the fifties as an episode that, for the first time, manifests the two different directions the theory of economic growth was beginning to take. Later, the most known manifestation of this divide was the Two Cambridges controversy. However, the germ of this difference can already be found in the Pasinetti-Solow debate, which was not given much importance in the literature. 3 The debate manifests two completely different approaches, not only to the particular question of technical change but also to political economy tout court. In section 1, we present the Solow-Pasinetti debate on the measurement of productivity, which anticipates already the main differences between neoclassical and alternative theories of economic growth. Here, we find a first outline of what will later be Pasinetti’s main criticisms of the neoclassical theories of growth and technological change, as well as some elements that will play an important role in constructing his theory of structural change and economic growth. In the following sections, we present two aspects that condense the main points of the divide between post-Keynesian theories and neoclassical theories of economic growth and their implications. In section 2, we discuss the question of the asymmetry of the factors of production. Pasinetti contended that the theories of classical inspiration were well aware of the different natures of land, labour and capital. Neoclassical economics, on the other hand, treated all factors of production as symmetrical, which has consequences on the explanation of income distribution as well. Section 3 presents the debate over the relevance (or not) of distinguishing between movements along the production function and shifts in the production function when discussing technical change. Pasinetti considered this distinction irrelevant. On the other hand, this distinction is the core of the explanation of technological change for neoclassical economics. Finally, in section 4, we draw some conclusions. 3 For a review of the debate and a reformulation of Pasinetti’s formula, see Garbellini and Wirkierman (2023). 130 The Solow-Pasinetti debate on the measurement of productivity in the light of modern growth theory PSL Quarterly Review 1. The Solow-Pasinetti debate on the measurement of productivity Solow’s 1957 article aimed to describe “an elementary way of segregating variations in output per head due to technical change from those due to changes in the availability of capital per head” (Solow, 1957, p. 312). This was equivalent to distinguishing between shifts in the production function and movements along it. In order to do this, Solow assumed that factors of production are paid their marginal products and there is neutral technical change, defined as a shift in the production function that leaves the marginal rates of substitution unchanged. 4 He defines the production function as: 𝑄=𝐴(𝑡)𝑓(𝐾,𝐿) (1) where 𝑄 represents output, 𝐾 and 𝐿 represent capital and labour in physical units, and 𝑡 appears to allow for technical change. The function 𝐴(𝑡) measures the accumulated effects of shifts over time. Solow proceeded to show that, if all the factors of production can be classified as capital or labour, the sum of the relative shares of capital and labour, 𝑤𝐾 and 𝑤𝐿, is equal to one. Assuming that 𝑓 is homogeneous of degree one and defining 𝑞=𝑄𝐿 ⁄,𝑘=𝐾𝐿 ⁄, Solow obtained the equation: 𝑞󰇗𝑞=𝐴󰇗 𝐴+𝑤𝐾𝑘󰇗𝑘 (2) In this case, from the series of output per man-hour, capital per man-hour, and the share of capital, it is possible to estimate the technical change index, 𝐴(𝑡). 5 Solow presented his estimate of technical change for the US economy for the period 1909-1949. Setting 𝐴(1909)=1, he obtained 𝐴(1949)= 1.809. From this and the time series utilised, he concluded that productivity per manhour almost doubled, and that 12.5% of that change corresponded to increased capital per manhour 6 (𝐾/𝐿) and the remainder 87.5% to technical change. In his response, Pasinetti stated that this type of analysis “although satisfactory for land and labor, is still incomplete with respect to capital, because it does not take into account the characteristic that capital is not something which comes from heaven, or from outside, but from the production process itself: it is reproducible” (Pasinetti, 1959, p. 272). This might seem an obvious assertion, but it has consequences because it implies that capital production is also subject to technical change. To show why Solow’s treatment is misleading, Pasinetti began treating the problem along traditional lines. He assumed at time 𝑡 the production function 𝑄=𝑓(𝐿,𝐾) and at time 𝑡+𝜙 the production function 𝑄=𝜙(𝐿,𝐾), where: 4 This is the concept of neutrality proposed by Hicks: technical change is neutral if it increases the output attainable from given inputs, leaving the marginal rates of substitution unchanged. Pasinetti uses, instead, neutrality in the sense of Harrod, which considers technical change neutral if labour productivity in the consumption goods sector changes in the same proportion as overall capital productivity does. Pasinetti does not use neoclassical production functions, so the concept of the marginal rate of substitution makes no sense to him in this context. 5 Solow also considers the case of non-neutral technical change but arrives at equivalent conclusions. In this article, we will limit the study to the simpler cases, since it does not affect the essence of the discussions. 6 Solow calls the capital per man-hour capital intensity. Instead, Pasinetti calls this the degree of mechanisation and defines capital intensity as the capital-output ratio. This is important, because capital intensity and the degree of mechanisation do not necessarily have to vary in the same direction. Hence, variations in the degree of mechanisation are not, in general, an indicator of the variation of capital intensity (for more details, see Pasinetti, 1981, pp. 180-184). F.R. Sember 131 PSL Quarterly Review 𝑄: number of pieces (one piece being the quantity which was sold in the base year at $1 million) 𝐿: man-years 𝐾: tons of steel (one ton being equal to the quantity that was bought in the base year at $1 million) As mentioned above, Pasinetti remarked that Solow’s analysis was incomplete because, besides the production function of the consumption goods industry, it is necessary to consider the production function of the capital goods industry. Technical change might take place in either of the two sectors. If there is technical change in the capital goods industry, the same quantity of tons of steel of capital does not have the same meaning in time 𝑡 or in time 𝑡+  , if at 𝑡+  the same capital can be obtained from smaller quantities of capital or labour. This implies that, for the purpose of evaluating changes in productivity, measuring capital in physical units is misleading. Additionally, Pasinetti stresses that it is important to consider that both industries are not symmetrical, because whatever form technical change takes in the capital goods industry (neutral, labour-saving or capital-saving), its effect is always capital-saving for the consumption goods industry. In the first simplified case he presented, Pasinetti assumed that the production of capital uses only labour and that capital lasts forever. Now, to compare productivity between two different equilibrium situations, it is necessary to consider, besides 𝑄/𝐾 and 𝑄/𝐿, the changes in the productivity of the capital goods industry, that is, 𝐾/𝑁 (where 𝑁 is the quantity of labour that would be necessary to reproduce the stock of capital). To avoid the difficulties associated with the fact that the conditions of production of 𝐾 in the past may have been different from the conditions at the present time, Pasinetti chose to redefine capital, 𝐾, in terms of its capacity, 𝐶. 7 Now, 𝑁 is the labour required to reproduce the existing productive capacity with the technique available when observations are made. The three variables that must be explained are 𝑄/𝐿, 𝑄/𝐶 and 𝐶/𝑁. In the case considered by Pasinetti at this stage, in a neo-classical framework with full employment, the output, 𝑄, coincides with the productive capacity of capital, 𝐶, since, in equilibrium, capital is fully employed. In this case, 𝑄 = 𝐶 and only 𝑄/𝐿 and 𝐶/𝑁 are left. The first represents labour productivity in the consumption goods sector, and the second is overall capital productivity. Pasinetti presented the following directional index of change: 𝑄𝐿 ⁄ 𝐶𝑁 ⁄ (3) The index will remain constant in time if labour productivity in the consumption goods sector changes in the same proportion as overall capital productivity. If the index increases, this means that labour productivity has increased more than overall capital productivity and technical change has been labour-saving; if the index decreases, it means that overall capital productivity has increased more than labour productivity, so the change has been capital-saving. 8 It is interesting to note that, when 𝐶 = 𝑄, the index (3) becomes 𝑁/𝐿, that is, the ratio between the quantity of labour needed to reproduce the stock of capital and the quantity of labour used to produce consumption goods. 7 This will later be at the base of his analysis in terms of vertically integrated sectors. 8 This is neutrality in the sense of Harrod (see footnote 4, above). 132 The Solow-Pasinetti debate on the measurement of productivity in the light of modern growth theory PSL Quarterly Review After this simplified presentation, Pasinetti introduced a numéraire in order to obtain a way to be able to estimate technical change. The price of output is set at 𝑃𝑞=1. Supposing equilibrium 9 from the production function 𝑄 = 𝑓 (𝐿,𝐾) and calling: 𝑟=𝜕𝑄 𝜕𝐾𝐾1 𝑃𝑐𝐶 the rate of profit, where 𝑃𝐶 is the price of one unit of capacity, 𝑎𝑞=𝐿𝑄 ⁄ the input of labour in one unit of output, 𝑎𝑘=𝑁𝐶 ⁄ the input of labour in one unit of capacity, Pasinetti obtained the ratio between capital and output: 10 𝛽= 𝑎𝑘 𝑟𝑎𝑘+𝑎𝑞 (4) The term 𝑟𝑎𝑘 is the only difference with equation (3), and, since 𝑟 tends to be constant over time, 𝑟𝑎𝑘 does not modify the direction of change. As in the case of equation (3), technical change is neutral if 𝛽 remains constant, labour-saving if 𝛽 increases, and capital-saving if 𝛽 decreases. Using the index 𝛽, Pasinetti extended his analysis to the same period used by Solow and reached opposite results. While, to Solow capital intensity had increased by 12.5%, to Pasinetti capital intensity had decreased by 20%. Note that capital intensity is measured as the capitaloutput ratio and not as the capital-labour ratio, as in Solow. The capital-labour ratio can be considered an indicator of technical change only if 𝐶/𝑁 (overall capital productivity) changes in the same proportion (Pasinetti, 1959, p. 273). Changes in productivity cannot be measured by changes in the productivity of labour alone, since capital also intervenes in production. Solow’s comment on Pasinetti’s critique and Pasinetti’s response shows that they had completely different views on the relevant factors to consider when dealing with the problem of technical change. To Solow, the traditional treatment of technical change is based on the distinction between shifts in the production functions and movements along it. Dismissing this distinction means abandoning the possibility of dealing with technical change. The notion of a production function “is meant to express the fact (if it is a fact) that any time a firm or industry or economic system faces a range of technological alternatives anyone of which might be chosen, and that given enough time 11 any previously made choice can be changed without appealing to new knowledge” (Solow, 1959, p. 283). To Solow, Pasinetti’s coefficient gives accurate results only in the case of fixed proportions because he abandoned the possibility of substituting labour for capital at a given technical knowledge. Solow took Pasinetti’s proposal of considering the production of capital goods as a mere question of less aggregation. This doubling the number of commodities in the model increases its realism by 100 per cent. […] It is not quite true to say that by failing to distinguish between consumables and capital goods I ignore 9 This means that the cost of production of capital is equal to its market evaluation. 10 For details, see Pasinetti (1959, pp. 273-274). 11 The expression “given enough time” will be discussed by Pasinetti when he will examine the problems of choice of techniques and change of techniques. F.R. Sember 133 PSL Quarterly Review that capital is in fact produced. At best, we are dealing with simplified models (Solow, 1959, pp. 283-84). Pasinetti stressed that the matter is not one of more or less aggregation but that, at any level of aggregation, evaluation of productivity cannot be made independently of the technical changes in the production of capital. Both types of technical change, in the consumption or capital goods, have different impacts on the economic system. In his response, Solow made some examples to show that Pasinetti’s measurement of technical change can vary even if there is no technical change. The first of these examples is a case where consumer goods are produced by robots alone and the robots are produced by labour alone. If, with a new method, the same quantity of robots can be produced more cheaply, then there is a labour-saving invention in the capital sector, but it is not clear why this represents a capital-saving improvement in the consumer sector. It does not save robots; it just saves abstract “waiting”. 12 Solow also drew attention to the fact that Pasinetti’s coefficient will change with a change in the rate of profit or with changes in savings or demand, even if there has been no technical change. Pasinetti recognised that this was true, but he started his reasoning by appealing to the fact that statistics show that the rate of profit in capitalistic economies has remained almost constant. Apart from short-run fluctuations, the largest part of changes in productivity over time are due to technical changes and not to changes in income distribution. To Solow, the difference between both approaches was not related to capital being produced or not but to the worthiness of distinguishing between reversible substitution of the factors of production given a state of technology and shifts in technology. Pasinetti claimed that he was not denying the existence of different possible production techniques but that, once the choice has been made, the options not chosen are irrelevant and cannot be observed. 13 To constrain the alternative bygone possibilities in a function that cannot but be arbitrary because non-observable is of no use for our purpose if, “given enough time [for] any previously made choice to be changed”, the firm or the industry or the economic system will be faced with the same rate of interest but with an entirely new set of technical choices (Pasinetti, 1959, p. 285). In summary, Pasinetti stated, “The contention has been that, since capital comes from the production process itself, on which technical change operates, it cannot be dealt with in the same way as labor and land” (Pasinetti, 1959, p. 281). Technological change cannot be measured by labour productivity alone, neglecting the other factors of production. Moreover, the attempts to evaluate technological change with models based on the production function of neo-classical inspiration need a physical or real notion of capital. However, the same physical unit of capital can have different meanings, according to the technical knowledge that prevails. That is the reason for redefining capital in units of productive capacity. In this way, the two ratios, 𝑄/𝐿 and 𝐶/𝑁, can give a complete evaluation of the nature of technical change. 12 To Pasinetti, this is a change in 𝑁, so that the ratio of labour locked up in the production of capital to the labour used in the production of consumption goods decreases, that is, there is an overall increase in overall capital productivity. To Pasinetti, there is nothing abstract about the increase in productivity; it is a physical notion. 13 This will be treated in section 3. 134 The Solow-Pasinetti debate on the measurement of productivity in the light of modern growth theory PSL Quarterly Review 2. The treatment of the factors of production One of the big differences between growth models of classical or Keynesian inspiration and neoclassical models is their treatment of production factors and the explanation of distribution derived from them. The first kind of growth model takes into account the different nature of the factors of production, which allows an explanation of the distribution related to the explanation of growth. On the contrary, neoclassical models consider production factors symmetrically, as variables of production functions with certain mathematical properties. The distribution ends up being explained with the resolution of some system of simultaneous equations rather than as a process. The importance of distinguishing between the different nature of the factors of production was clear since Ricardo: The produce of the earth – all that is derived from its surface by the united application of labour, machinery, and capital, is divided among three classes of the community, namely, the proprietor of the land, the owner of the stock or capital necessary for its cultivation, and the labourers by whose industry it is cultivated. […] To determine the laws which regulate this distribution, is the principal problem in Political Economy […] (Ricardo, 1981, p. 5). In Ricardo’s explanation, capitalists save and invest out of their profits, and, in so doing, they set up a process of capital accumulation and increased demand for workers. In the long run, as a consequence of diminishing marginal returns to land, the rate of profit will decrease until there are no more savings or investments. The way to avoid this outcome is international trade (which allows food to be imported without having to resort to less fertile lands) or a technological improvement that increases the productivity of the land. In this explanation, the marginal principle is applied only to land, a non-produced factor of production. Labour and capital, instead, were associated with different social classes: wages had an explanation and profits a different one, related to the role of workers and capitalists in society. Moreover, the explanation of the growth of the economy was deeply linked to the theory of distribution. Marginalism in the 1870s, by focusing on the problems of demand, brought back the exchange paradigm to economic theory. The basic model presupposes a set of utility-maximising individuals endowed with a set of given resources and finds the prices that lead to an optimum allocation of resources through exchange. The marginal utility approach was then extended to production, considering land, labour and capital on the same footing. The marginal utility scheme was duplicated to treat production, introducing the well-behaved production function, linear and homogeneous, with marginal productivities equating to the factor prices. The extension of the marginal principle to capital implies that capital is formally treated like a non-produced factor: neoclassical theory treats all the factors of production as if they were land (Pasinetti, 2000, p. 389). Hence, as an extension of the marginal utility functions, production functions were set out as convex and differentiable. Moreover, marginal productivities had to be such that they could be substitutes for the factor prices, making the production function linear and homogeneous. There is no recognition that the nature of each factor is different and that there is a succession by which the distribution is determined. Ricardo had thought of diminishing returns on land because it was a scarce, non-produced factor. The main objects of economic theory, as in Adam Smith, were reproducible goods: F.R. Sember 141 PSL Quarterly Review express the technology actually in use. Instead, it is interpreted as representing other techniques that can be used as alternatives to the one that has already been chosen. Pasinetti remarks that, in this way, the techniques available at a certain point in time (the choice of techniques) come to coincide with the techniques that are relevant to the process of change. This also makes the concept of marginal productivity meaningless, even if we consider different possible interpretations for function (8). First, if function (8) is interpreted as representing the productive structure at one point in time, the derivatives are 0. This is not a particular case, as textbooks say, but the general case. Once technology has been chosen, it cannot be changed. It does not make sense to talk about substitutability at a given point in time. Second, if function (8) is represented as a function for the choice of technique at a certain point in time, the derivatives might not exist. The different techniques have completely different requirements of physical outputs, generating discontinuities. Besides, there is no reason to expect that a change in prices should go in different directions than the changes in quantities. 19 So, in the end, the process of technical change comes forth from the interplay of the production functions and the choice of technique functions. Over time, each choice of technique function is enriched with new options available, with new technical methods, while others can be eliminated because they become obsolete. This does not per se change anything in the production functions. When new techniques are actually incorporated into production in the corresponding economic sector, part of the production process of this sector will change. Consequently, the technical coefficients will change, representing the new methods continually being incorporated. 4. Concluding remarks In this article, we showed that the Solow-Pasinetti debate anticipated many aspects of the different directions taken by the theories of growth and technical change after the foundational works of Harrod and Domar. Economic growth and technical change were largely discussed in the following years, and the Cambridge capital controversy may be the most salient debate. In the following decades, Pasinetti developed his own alternative theory, incorporating vertically integrated sectors and elements from Sraffa and Leontief. Even if, in his critique of Solow, the matter was treated along traditional lines, Pasinetti made it clear that: As a matter of fact, it has been the purpose of the last section to frame the analysis in such a way that it can be interpreted also, perhaps much better, in other theoretical frameworks, such as the Leontief models or the dynamic growth models which pay more attention to fixed coefficients and to idle capacity. […] This is a useful property especially for comparisons of single industries, where the occurrence of fixed coefficients and the notion of capacity acquire much more precise content than for the economy as a whole and can be explicitly accounted for (Pasinetti, 1959, p. 275). In 1998, on the occasion of the publication of an article by Richard Stone called “Changes in productivity”, Pasinetti and Solow had another exchange in the journal Structural Change and Economic Dynamics. In this posthumous article, Stone combined Pasinetti’s 𝛽 coefficient with input-output analysis to obtain a coefficient for the classification of technical progress “based on data which are actually being provided by input-output analysts without any reference to the form of the production functions except at the specific points of time under comparison” (Stone, 1998, p. 231). 19 See also Pasinetti (1977, chapter 6). 142 The Solow-Pasinetti debate on the measurement of productivity in the light of modern growth theory PSL Quarterly Review Pasinetti commented on this short article by repeating some of his concerns with the neoclassical theory of technical change (Pasinetti, 1998). The fact that technical progress takes place not only in the production of final goods but also in the production of the capital goods necessary to make those final goods has important consequences for evaluating technical progress. Thus, it is incorrect to consider both the capital-output ratio and the capital-labour ratio as indices of capital intensity. As we have shown, Pasinetti calls capital intensity the capital-output ratio, and he calls the degree of mechanisation the capital-labour ratio. This distinction was essential. The ratios will move in the same direction only in the absence of technical progress, but they might move in opposite directions as soon as technical progress comes into the picture. Pasinetti also repeated the importance he placed, in his formulation, on giving up the distinction between shifts in the production function and movements along it and on renouncing assumptions about the production functions that are not observable. Solow’s response again raised this issue: I found it astonishing then and find it astonishing now. […] I would have thought that economics very often proceeds by thinking about the decisions – optimising or not – made by agents like households and firms. We cannot understand a decision without considering the range of choices that were available, or perceived to be available, to the agent when the decision was made (Solow, 1998, p. 238). This assertion reflects a more profound disagreement. To Solow, economics had to understand the decisions made by agents among a range of available choices. This is related to the conception of economics as defined by Lionel Robbins as “the science that studies human behaviour as a relationship between ends and scarce means which have alternative uses” (Robbins, 1932, p. 15). Pasinetti, instead, defended the classical conception of economics as the study of how nations grow and distribute their income. In his last book, Keynes and the Cambridge Keynesians: A ‘Revolution in Economics’, Pasinetti stressed that it was necessary to go back to classical political economy and the Keynesian school, also including some authors less influenced by Keynes, like Sraffa and Kalecki. The aim had to be to build an alternative paradigm from all these contributions, a unifying theoretical scheme under the production paradigm that accounts for growth and distribution. References Domar E.D. (1946), “Capital Expansion, Rate of Growth, and Employment”, Econometrica, 14 (2), pp. 137-147. Garbellini N., Wirkierman A. (2023), “The Solow-Pasinetti debate on productivity measurement: Review and reformulation”, Structural Change and Economic Dynamics, n. 65 (april). Available online. Halevi J. (2016), “Luigi Pasinetti and the Political Economy of Growth and Distribution”, INET Working Paper Series, n. 40, New York: Institute for New Economic Thinking. Available online. Harrod R.F. (1939), “An Essay in Dynamic Theory”. The Economic Journal, 49 (193), pp. 14-33. Kaldor N. (1957), “A Model of Economic Growth”, The Economic Journal, 67 (268), pp. 591-624. Kalecki M. (1942), “A Theory of Profits”, The Economic Journal, 52 (206/207), pp. 258-267. Kalecki M. (1947), “Three Ways to Full Employment”, in Oxford Institute of Statistics (ed.), The Economics of Full Employment: Six Studies in Applied Economics (pp. 39-58), Oxford: Basil Blackwell. Pasinetti L.L. (1959), “On Concepts and Measures of Changes in Productivity”, The Review of Economics and Statistics, 41 (3), pp. 270-286. Pasinetti L.L. (1962), “Rate of Profit and Income Distribution in Relation to the Rate of Economic Growth”, The Review of Economic Studies, 29 (4), pp. 267-279. Pasinetti L.L. (1977), Lectures on the Theory of Production, London: Macmillan. F.R. Sember 143 PSL Quarterly Review Pasinetti L.L (1981), Structural Change and Economic Growth: A Theoretical Essay on the Dynamics of the Wealth of Nations, Cambridge (UK) and New York: Cambridge University Press. Pasinetti L.L (1998), “A note on Richard Stone’s paper on changes in productivity”, Structural Change and Economic Dynamics, 9 (2), pp. 233-235. Pasinetti L.L (2000), “Critique of the Neoclassical Theory of Growth and Distribution”, PSL Quarterly Review, 53 (215), pp. 383-431. Available online. Pasinetti L.L (2007), Keynes and the Cambridge Keynesians: A «Revolution in Economics» to Be Accomplished, Cambridge (UK): Cambridge University Press. Ricardo D. (1981), On the Principles of Political Economy and Taxation, in Sraffa P. and Dobb M. (eds.), The Works and Correspondence of David Ricardo, Vol. 1, New York: Cambridge University Press. Robbins L. (1932), An Essay on the Nature and Significance of Economic Science, London: Macmillan. Robinson J. (1945), “Review of The Economics of Full Employment”, The Economic Journal, 55 (217), pp. 77-82. Solow R.M. (1956), “A Contribution to the Theory of Economic Growth”, The Quarterly Journal of Economics, 70 (1), pp. 65-94. Solow R.M. (1957), “Technical Change and the Aggregate Production Function”, The Review of Economics and Statistics, 39 (3), pp. 312-320. Solow R.M. (1959), “Comment”, The Review of Economics and Statistics, 41(3), pp. 282-285. Solow R.M. (1998), “Comment”, Structural Change and Economic Dynamics, 9 (2), pp. 237-238. Stone R. (1998), “Changes in productivity”, Structural Change and Economic Dynamics, 9 (2), pp. 229-231. Swan T.W. (1956), “Economic Growth and Capital Accumulation”, Economic Record, 32 (2), pp. 334-361. Sylos Labini P. (1995), “Why the interpretation of the Cobb-Douglas production function must be radically changed”, Structural Change and Economic Dynamics, 6 (4), pp. 485-504.