Conceptualising productivity measurement from a classical perspective

Wirkierman, Ariel Article Conceptualising productivity measurement from a classical perspective PSL Quarterly Review Provided in Cooperation with: Associazione Economia civile, Rome Suggested Citation: Wirkierman, Ariel (2024) : Conceptualising productivity measurement from a classical perspective, PSL Quarterly Review, ISSN 2037-3643, Associazione Economia civile, Rome, Vol. 77, Iss. 309, pp. 145-172, https://doi.org/10.13133/2037-3643/18513 This Version is available at: https://hdl.handle.net/10419/324106 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) Conceptualising productivity measurement from a classical perspective ARIEL L. WIRKIERMAN Abstract: Productivity seems an obvious concept: output per unit of input. Yet, when contextualised within alternative views of production and distribution, challenges across attempts at measuring it are far from trivial. The aim of this paper is to present and discuss some foundational concepts for measuring productivity from a classical perspective, as opposed to a more traditional standpoint. A key distinction is made between measuring productivity from the expenditure (or physical quantities) side and quantifying profitability from the value added (or income) side. Productivity is opposed to productiveness and commodity reduction is contrasted to price aggregation. After critically discussing the traditional standpoint of total factor productivity growth, this paper conceptually discusses the method of (growing) subsystems and the computation of production prices as analytical and empirical devices for measuring productivity and profitability in a multisectoral economy. Institute of Management Studies (IMS), Goldsmiths, University of London, UK email: a.wirki[email protected]c.uk How to cite this article: Wirkierman A.L. (2024), “Conceptualising productivity measurement from a classical perspective”, PSL Quarterly Review, 77 (309), pp. 145-172. DOI: https://doi.org/10.13133/2037-3643/18513 JEL codes: O4, C67, B51 Keywords: productivity measurement, input-output analysis, vertical (hyper-)integration, prices of production Journal homepage: http: //www.pslquarterlyreview.info Productivity has been a major ideology of institutions ever since medieval salvationist ideals ceded to modernist rationality. Reich (2001, p. 40) 1. Introduction: why productivity? Being trapped in history makes our analyses, in appearance, less general, less ‘scientific’, more speculative, full of counterfactuals, empty of timeless statements. Case-by-case detailed factual description or abstract reconstruction of the most remote past to the present day may appear as the only way to overcome the cruelty of the historical nature of economic phenomena. The last couple of hundred years had been so little in comparison with thousands of years of man as a producer. Hence, political economy could be thought to be not very ambitious. Its object Special issue on the Solow-Pasinetti debate on productivity measurement 146 Conceptualising productivity measurement from a classical perspective PSL Quarterly Review of study has been quite easily circumscribed to the analysis of phenomena of production and distribution in societies after the appearance of the capitalist mode of production. 1 Its theories are quite restricted in their timespan, and so are their projection onto the future. By observing regularities, we look for principles. The organisation of collective labour is one of these. In this sense, the passage from value to reproduction prices can be analysed as a development in economic history, as a passage from simple to extended reproduction. 2 But in essence, I believe the crucial characterisation is the passage from an ‘urban’ to a ‘capitalist’ mode of production. The ‘urban revolution’ 3 of the fourth millennium B.C. and the ‘capitalist revolution’ of the XVIII century are two of the most important transformations in the mode of production of human history. They both had, as a crucial determinant, the change in the social organization of collective labour and the specific use of the surplus produced by the community as a whole. 4 Hence, the human determination to transform the organisation of collective labour is a deep cause in the appearance of the capitalist mode of production. As regards its enforcement, the delicate interplay with primitive accumulation 5 should be acknowledged. However, deep understanding is far from mechanical, as the laws to which the capitalist mode of production obey change continuously in their details, because the changing organisation of human labour in society feeds back into the root of the mode of production itself. Wage labour, and individual ownership of the means of production, are probably the two main institutional mechanisms for the enforcement of a particular way of organising collective labour. And this is a general principle. But the details get continuously altered. And one of the details that changes in its long-period trends across time and space is the rhythm of surplus generating capacity of different societies, or, what amounts to the same thing, their productivity increases. But productivity is an elusive concept. There abound meanings and uses (sometimes abuses) that place it as both cause and effect of economic growth and compositional changes in economic structure. It is my conviction that conceptual clarification can come about only by looking at the notion of productivity as a piece inside a comprehensive view of the process of production and distribution. As such, productivity analysis cannot be free of value judgement. Not even physical productivity, and clearly even less when surplus generating capacity is thought of in terms of profitability. The aim of this paper is to provide a conceptual overview and discussion of alternative frameworks to define and measure productivity changes. Throughout, I adopt a classical perspective to economic analysis, trying to establish clear differences with traditional views as regards both theory and measurement. Hence, clarifying the meaning I attach to the ‘classical’ perspective is the place to start. 1 Though not necessarily being currently under the capitalist mode of production. 2 As stated by Bródy (1970, p. 94): “The different price systems belonged to different historical layers for Marx”. 3 Of course the term ‘revolution’ is clearly a metaphor, its original meaning being “complete overturn of the relative positions of the various elements that constitute a system” (Liverani, 1998, p. 3). Processes of social and technological change are slow and gradual. 4 For a development of the argument, see Gilibert (2010). 5 In fact, “[t]he necessity of a primitive accumulation of capital, which society could invest in the structural conversion of its mode of production, was not only a Marxist theory. It was a general presupposition at the basis of ‘classical’ political economy” (Liverani, 1998, p. 7). A.L. Wirkierman 147 PSL Quarterly Review 2. What do I mean by ‘classical’ perspective? The classical standpoint to economic analysis has its roots in the works of the ‘old classical economists’, as intended by Sraffa (1960, Appendix D), with Quesnay’s Tableau Economique as its first comprehensive scheme, followed by Marx’s ([1885] 1978) schemes of ‘Simple Reproduction’ and ‘Reproduction on an Expanded Scale’, and extending into Leontief’s (1937) input-output framework and Sraffa’s (1960) system of production. 6 The connections and interplay between these works are subject to long-standing debates, which shall not be dealt with here. Instead, the aim is to highlight only some features of a (modern) classical approach. First and foremost, the characterising principle is the view of the economy as a circular process based on the notion of physical real costs, i.e., inputs are physically consumed in the process of generating the outputs that reconstitute the capacity to restart the very same process as inputs at the same (or enlarged) scale. Essentially, “circularity stands here for repetitiveness” (Gilibert, 2006, p. 41, n. 16). Reproduction begins and returns to the same point, picturing the whole process as an ascending spiral whose diameter expands or contracts. In fact, as Sraffa would phrase it: “in a circular flow scheme ‘The production of a thing has no real definite beginning – the inquiry leads us into infinite time backwards’ (D3/12/7: 27)” (Kurz and Salvadori, 2005a, p. 497). Within the language of mathematics, circularity can be represented by eigensystems, which define prices and quantities in terms of themselves. 7 Second, most of the interest lies in the analysis of those economies whose production exceeds its productive consumption, thus generating a surplus product, a set of commodities that must be allotted to different groups of individuals (classes) in society. Different uses of the surplus by the classes in society generate the income-expenditure loops of a circular process. When commodities are produced by means of commodities, the notion of ‘cost of production’ as well as that of ‘factor of production’ may not survive close scrutiny, as the circular nature of the process of reproduction implies that produced means of production are both inputs and outputs, whose price or quantity as a ‘cost’ may not be known in advance of its price or quantity as a ‘product’. In fact, this circularity principle should not be confused with the marginalist view of the flow exchanges between ‘product’ and ‘factor’ markets, at the basis of general equilibrium theory. In this stylised view circularity is not straightforward, particularly when considering the notion of a market for ‘capital’ (or for the ‘services of capital’): the ‘quantity of capital’ is supposed to be a quantitative magnitude “that can be measured independently of, and prior to, the determination of the prices of the products” (Sraffa, 1960, p. 9), with the rate of profits (interest) being its price. Hence, notional supply and demand schedules meet to determine the ‘equilibrium’ price and quantity of this ‘factor’, thus regulating – according to its ‘relative scarcity’ – income distribution between labour and capital (wages and profits). But within the marginalist system, a clearing in the markets for ‘factors’ is crucial to the markets for ‘products’ as well, as “a demand schedule can only affect the price of the corresponding product to the extent to which it affects distribution” (Garegnani, 1983, p. 310). This is so because the functional relationship between commodity prices and final demand crucially depends on relative factor prices adjusting to the proportion of their employment as 6 In no way does this brief comment aim to make an exhaustive enumeration of the works ‘belonging’ to the classical tradition of thought, which extends over centuries to this day. 7 See Bródy (1970, pp. 84-94) for details. 148 Conceptualising productivity measurement from a classical perspective PSL Quarterly Review inputs when demand for final output changes, i.e., the whole system depends on the mechanism of factor substitution. It is, however, a well-established fact that the factor substitution mechanism cannot be sustained under reasonable assumptions for the representation of economic production. 8 In contradistinction, when ‘capital’ is considered as a set of produced means of production – as it is from a classical perspective – it emerges that capital goods become part of the circular process of reproduction, so the view of them as an aggregate quantity measurable before the determination of prices is clearly untenable. Furthermore, the rate of profits is not the ‘price’ for the ‘quantity of capital’. By following Sraffa’s interpretation of Ricardo ([1817] 1951): A method devised by Ricardo […] is that of singling out corn as the one product which is required both for its production and for the production of every other commodity. As a result, the rate of profits of the grower of corn is determined independently of value, merely by comparing the physical quantity on the side of the means of production to that on the side of the product, both of which consist of the same commodity (Sraffa, 1960, p. 93). The difficulties of generalising this line of thought are dealt with by Sraffa (1960, pp. 22-23). The (uniform) rate of profits reflects a (possible) rule of distribution for the surplus product of the system. What should be clear is that, within the logical structure of classical analysis, the distribution of income between wages and profits has a ‘degree of freedom’, as has been rendered ‘transparent’ in Sraffa’s (1960, Chapter IV) standard system. Finally, when the demand and supply equilibrium theory of distribution is abandoned, even in the presence of variable returns, the determination of outputs entails them to be treated as independent variables when determining relative prices, and vice-versa (for details, see Garegnani, 1987). Hence, another characterising feature of classical analysis is the separation between prices and quantities, i.e., between the value added and the expenditure side of the system. In fact, this aspect extends to empirical structures (input-output schemes, in particular) as well: Both the reproduction or quantity and growth aspect and the price and distribution aspect are dealt with, and it is made clear that input-output analysis is firmly rooted in the ‘classical’ tradition of economic thought (Kurz et al., 1998, p. xiv). In this sense, from a classical perspective, relative prices “represent the exchange conditions between physical goods that make reproduction within a given technical (methods of production) and social (distribution) framework possible” (Schefold, 1989, p. 292). 9 Moreover, “with a surplus, prices are influenced by its distribution” (Gilibert, 2003, p. 34). Therefore, even an ‘objective’ theory of relative prices based on the technical conditions ensuing reproduction has a degree of freedom coming from outside the price equations, represented by the given rule of distribution of the surplus. From the standpoint of classical analysis, it is possible to argue that the determination of relative physical outputs, i.e., the proportions of the system, starts from the consideration of a 8 The marginalist process of ‘input substitution’ states that there exists “an inverse monotonic relation between the proportions of any two inputs and their relative prices” (Pasinetti, 1977, p. 390). For an explanation and critique, see Pasinetti (1977) but also Mas-Colell (1989, p. 505). 9 Clearly, this conception of relative prices is in striking contrast with that of marginalist theory. Prices are not indices reflecting subjective individual preferences on the desirability of commodities in terms of their relative scarcities. A.L. Wirkierman 149 PSL Quarterly Review given (and measurable) set of commodity balances. However, its interpretation in terms of methods of production and activity levels of different processes is not unique. 10 Therefore, from given empirical structures, different mappings to theoretical magnitudes can be attempted. As to the present paper, the argument rests on the conception that observed tabulations of physical outputs in nominal terms contain both a self-replacement component and an expansion/contraction component, which need to be separated in some cases (though not in others). What, in any case, should be clear is the role of the quantity system in the distinction of what re-enters the circular flow (and alters the productive capacity of the system) from what does not (and constitutes a truly final use). In this sense, we endorse the view that produced means of production are induced by the effective demand exerted for final ‘consumption’ commodities. 11 In other words, we conceive the ‘accelerator’ relation – the induced character of investment demand – as a mechanism at the basis of output determination. In fact, “[i]t is this derived demand aspect of investment goods, due to their being used as means of production, that is new and typical of production systems” (Pasinetti, 1981, p. 176). However, this consideration of investment as induced by the growth trend of final effective demand should not be confused with the neoclassical ‘inducement to invest’. In the latter case, demand for investment is made equal to the supply of savings through changes in the rate of interest. Under this view, current investment is seen as future consumption, so the interest rate is an equilibrating intertemporal price remunerating the consumption forgone today. Hence, the inducement to invest is the remuneration for the ‘sacrifice’ of waiting. Abstract ‘waiting’ becomes a ‘factor’ of production. This neoclassical view raises three points for discussion. First, whether the interest rate regulates a long-period trade-off between present and future consumption (current investment). Second, whether this long-period trade-off actually exists. And third, whether abstract waiting can be considered a ‘primary factor’ of production on the same ground as labour. The first point can be quickly addressed by noting that it presupposes the operation of the substitution mechanism (but from the dual quantity side). In fact: the standard one capital good case displays a monotonically decreasing relationship between consumption levels and the rate of interest […]. This does not generalize and it is now well understood that even with only two capital goods, a non-monotone association […] is possible (Mas-Colell, 1989, p. 506). Hence, the interest rate cannot be seen as a regulator of intertemporal consumption levels, as it simply does not provide unambiguous ‘price’ signals. The second point concerns whether higher investment demand necessarily implies lower consumption levels. This can be answered by noting that, from a modern classical perspective, capacity adjusts to demand, and investment generates the savings required by the system (not necessarily through a change in income distribution between wages and profits), so that an 10 As argued in Garbellini and Wirkierman (2014), empirical matrices of intermediate consumption and gross fixed capital formation contain implicit expansion and contraction rates, because production requires time. Hence, the separation between activity levels and techniques is not always straightforward. 11 This point is crucial. A capital good is not strictly determined on the basis of which industry is producing it, but also on the use that is made of it, i.e., on whether it re-enters the circular flow. Therefore, a machine that is exported is considered a final consumption commodity, while stocks of circulating capital produced in excess of self-replacement requirements that are devoted to expanding productive capacity in the following periods are considered new investment demand. 150 Conceptualising productivity measurement from a classical perspective PSL Quarterly Review expansion of investment does not imply a necessary decrease in the level of consumption (though it will clearly alter its share in gross output). As to the third point, it is particularly interesting that even some approaches that claim to be critical of marginal productivity theory endorse the view of ‘waiting’ as a primary factor of production: Because capital inputs are produced means of production, increases in efficiency due to advances in knowledge or increasing returns to scale will bring about increases in the output, input, and stocks of such capital inputs even when primary input flows remain constant [...] The question that then arises is: What is (are) the primary input(s) that is (are) behind the produced means of production? This is the question at the heart of the Cambridge capital controversy and has nothing to do with the question of the need or the feasibility of consistent aggregation (Cas and Rymes, 1991, pp. 8-9). The answer to the question suggested by these authors reads: Individuals, supplying labour time, give up the immediate consumption of such time in exchange for the indirect consumption that the selling or nonimmediate consumption of such time avails them. Labour time sold is the measure of the labour input in productivity measures. Individuals, by forgoing present consumption and accumulating capital directly or indirectly through the bond and stock exchanges, are exchanging present for permanent consumption. The accumulation of capital is the embodiment of the waiting individuals have done. With technical progress, a given flow of waiting (or the forgoing of a given flow of present consumption) may be embodied in an increasing accumulation of capital that reflects the ever-increasing efficiency of waiting and results in higher levels of permanent consumption (Cas and Rymes, 1991, p. 11, emphasis added). What this answer intends to do is exhaust value added (in this stylised case consisting of profits and wages) into as many ‘primary’ factors as there are components in it, and so justify claims to shares of value added on the basis of the subjective ‘sacrifices’ of working and waiting. There is again a precise attempt to establish a ‘natural’ connection between an institutional phenomenon (the distribution of income) and a physical phenomenon (the accumulation of produced means of production). But, even more, this attempt is performed at the individual level (it is the single individual who works and waits). Hence, the inverse monotonic relation between the real wage rate and the rate of profits is the trade-off between working (with the ensuing consumption) and waiting (with consequent saving). The social dimension of income distribution has disappeared (profits and wages are equally perceived by single individuals), and interpersonal income distribution comes to the fore, arguing that the distribution between wages and profits is not reflecting the dynamics of social classes but the interior struggle each individual has in deciding whether to work and consume or to wait and save resources. The notion of physical real cost – that emerges from Sraffa’s (1960) system of production – aims at establishing a sharp break with any notion of ‘cost’ conceived as the inducement to overcome the sacrifice of rendering resources available for their productive use. In this sense, the view of ‘waiting’ as a primary ‘factor’ serves the same purpose as the view of the endowment of a ‘quantity of capital’ (it just replaces stocks with flows, ‘capital’ by the ‘use of capital’). 12 From a classical perspective this view is untenable: long-run accumulation is induced precisely by the growth of consumption and not by the abstinence from consuming and, while it 12 In fact, in these analyses, the labour required for the expansion of productive capacity is considered as ‘capital productivity’ that accrues to ‘waiting’ (for example, see Gowdy and Miller, 1990, p. 594). A.L. Wirkierman 151 PSL Quarterly Review is correct that production takes time, this by no means entails that saving behaviour in the pursuit of interest rewarded as profit has a ‘natural’ right to become a ‘primary’ factor. This theme leads to the role of the quantity of labour as an input in production. On this issue there are disagreements within the classical tradition, so these considerations cannot but be considered as highly personal. I believe one should carefully distinguish between labour inputs in the system of prices (i.e., the value added side) and the role of quantities of labour within the system of physical outputs (i.e., the expenditure side). In a system of price equations, quantities of labour are explicitly considered as a component of prices through wage payments. In this sense, by using either a uniform wage rate or a vector of industry wage rates, the separation between quantities of labour and their rate of remuneration is an analytical construct. In this context, as done by Sraffa (1960, p. 10), wage rate differentials could be applied to quantities of labour employed in every industry in order to render them homogeneous as regards the process of pricing (i.e., in order to be able to remunerate each unit of labour with a uniform wage rate w). But this should not be interpreted as a process that renders differing ‘productivities’ of labour homogeneous. Productivity plays absolutely no role in the application of wage rate differentials to quantities of employment. In contradistinction, as regards physical outputs (i.e., in a set of commodity balances), quantities of labour do not explicitly appear in the system of equations. Their role in the analysis comes in when we acknowledge the necessary link between total employment and gross output (the human labour currently employed in all industries adds up to the total labour required to produce the gross output of the economy). But it is possible to gradually modify the disaggregation of total gross output, starting from the sum of gross output by industry, then recognising indirect requirements to self-replace productive capacity (and so defining net output as the sum of new investment and final uses), until we account for the indirect requirements to expand productive capacity (and so defining net output consisting only of commodities for final uses). In each step, labour inputs by industry applied to these different direct and indirect commodity requirements redistribute total coexisting employment into as many parts as there are products, under each definition of net output. Each of these (logical) parts constitutes a subsystem – in the sense of Sraffa (1960, Appendix A, p. 89) – and is identified by the single component of the net product to which it refers. In each of these subsystems, the employment of all industries that is used for the production of the identifying net output commodity constitutes the labour content of this product. This is the logic adopted behind the notion of labour content of commodities. And under this conception, quantities of labour employed in each industry are all equally necessary to satisfy total reproductive requirements. Each industry is equally necessary, directly or indirectly, to produce each single commodity. Then, when applied to each decomposition of gross output, the vector of labour inputs (measured in units of full-time employment equivalents or total hours) is homogeneous, as regards the determination of the labour content of commodities. Two points deserve clarification. First, while it is possible to interpret the notion of labour content as embodied labour, this can be done as long as it is clear that we always refer to living, co-existing, and concurrent employment. 13 The subsystem redistributes total direct employment into direct and indirect labour requirements to reproduce each different notion of net output, but it is always a logical construct. In no way do we consider embodied labour as a locked-in substance 13 This view is clearly not new. In fact, on this specific aspect I follow Hodgskin ([1825] 1969). See also Milgate and Stimson (2009, pp. 225-231). 152 Conceptualising productivity measurement from a classical perspective PSL Quarterly Review travelling through historical time (and methods of production) accumulated in commodities (durable means of production, for example). The second point is that, from the above considerations, it emerges that zero profit production prices in terms of labour commanded are not necessarily equal to labour content of commodities. While a price system considers wage rate differentials, imported commodities, and taxes on products in the definition of a ‘zero profit’ price, the notion of labour content considers only domestically produced commodities (it is gross output and not total supply that is redistributed), excludes taxes on products, and considers the vector of labour inputs as homogeneous (therefore not allowing for a multiplication by a matrix of wage rate differentials). Hence, in all circumstances concerning actual systems (as differently from a theoretical model), these two magnitudes will not coincide. In connection with this point, note that nowhere have I referred to the concept of ‘labour values’. The considerations just made should make apparent that it would deserve a more careful treatment than is customarily done, though this is not an aim of this paper. However, one further related aspect should be mentioned, and this is the indispensable character of labour for the production process. In a system that does not admit full automation, i.e., labour is required directly or indirectly to produce at least one basic commodity, 14 labour inputs are indispensable. It would be quite difficult to find a system where complete automation were possible. In such a hypothetical system, the notion of labour content would clearly lose its rationale, as the necessary link between total employment and gross output would be lost. As long as this is not the case, the distribution of total employment into logical parts reveals itself essential to assess the degree of specialisation within actual systems. Given that, in purely abstract terms, the notion of physical productivity consists of measuring the rhythm of output generation per unit of input, it is possible to attach to each distribution of employment among subsystems a specific pattern of net product per unit of total (direct and indirect) subsystem labour, suggesting a consistent route for productivity analysis from a classical perspective However, before further development of these ideas, and in connection with the dual view of prices and quantities at the root of classical analysis, it might prove interesting to clarify the difference between two very similar terms, with quite dissimilar meanings: productiveness and productivity. 3. Productiveness and productivity The idea of productive, as opposed to unproductive, human labour can be traced back to the physiocratic distinction between ‘productive’ and ‘sterile’ classes in Quesnay’s Tableau Economique. 15 In Physiocracy, a class was considered ‘productive’ or ‘sterile’ according to whether the labour it employed generated a net revenue or not. 16 As rent was the only net income of the system, whose origin was agricultural labour, the only ‘productive’ class was that of agricultural workers. 14 In the sense of Sraffa (1960, p. 8). 15 See Gilibert (1977, Chapter 4) for a clear exposition and discussion. 16 Note the interesting meaning of the word revenue: “both the concept and the word came from France, where revenu is the past participle of revenir, to return” (Gilibert, 1987, p. 171). Here, revenue means the return to the starting point in a circular scheme. A.L. Wirkierman 159 PSL Quarterly Review In a multisectoral economy, value added is a residual rather than an independent entity, both according to surplus theory and to the System of National Accounts. 24 From the equations above, when the means of production for self-replacement are deduced from gross output, an artificial separation between a price and volume component is performed: 𝑋−𝑈 = pQ. If 𝑋 and 𝑈 are different composite commodities, then their difference (value added) cannot be an independently measurable composite commodity to which a price index is attributed. Value added is the effect of two causes (𝑋 and 𝑈), so it is difficult to maintain that it has a physical meaning in itself. 25 Furthermore, taking value added as a disaggregated measure of output does not give a comprehensive picture of the production process. Production is circular, and commodities can be given final as well as intermediate uses. For productivity measurement, it is crucial to know the ratio between gross output and final uses, as an economy with a higher ratio would need more gross output to produce the same physical surplus, in the presence of input saving due to technical change. This is not necessarily captured at a disaggregated level by a net income measure such as value added. 26 Note, then, that value added cannot be a coherent disaggregated measure of physical output, and the ‘quantity of capital’ cannot be a coherent aggregated physical measure of inputs. Hence, it is not a matter of aggregation or disaggregation that leads TFP growth to run into trouble. But even granting a physical interpretation to value added, the common functional forms used for empirical measurement in traditional analysis are not exempt from an essential dimensionality critique, as advanced by Bródy (1970, pp. 95-96). Consider a traditional function like: Q = 𝐴𝐾𝛼𝐿1−𝛼, where Q is measured in flow of money (M) per year (T), 𝐾 is measured as a stock of money (M), and 𝐿 is measured in man years (𝐻 ×𝑇). Then, we have: 𝑀/𝑇 = 𝐴×𝑀𝛼× (𝐻 ×𝑇)1−𝛼. Now, what is the dimension of 𝐴 (i.e., the TFP parameter)? If 𝛼 = 1, 𝑀/𝑇 = 𝐴×𝑀, so 𝐴 = 1/𝑇 (the reciprocal of TFP is measured in time units, ‘productivity’ as time). If 𝛼 = 0, then 𝐴 = 𝑀/(𝐻 × 𝑇2), which could be reordered to mean money flow per man year. And what if 0 < 𝛼 < 1 (which is the normally assumed case)? TFP parameter 𝐴 does not have any definite meaning. So, what is the dimension of TFP? It remains an open question, unless one abandons its purely physical interpretation, based on production functions, and admits that TFP is an accounting ‘residual’, simply reflecting ‘real cost reductions’. 27 As with the confusion in the distinction between micro/macro and aggregate/disaggregated, it is generally thought that TFP is a complete (‘total’) measure as against ‘partial’ measures that consider only, e.g., labour productivity. But it is perfectly possible to derive measures of total labour productivity as well. 28 The confusion has its origins in the way TFP (or the ‘residual’) has been conceived: In whichever form, the measured residual typically accounted for an important fraction of the observed output growth, quite often half or more. This result came as a surprise to the profession, though perhaps less so to those who reached it, or something very like it, by an alternative route. They were the people who came at the problem out of a tradition of measuring labor productivity, and at some point complemented output per worker with a measure of output per unit of capital, and finally joined the two to create a measure of total factor productivity (TFP) (Harberger, 1998, pp. 1-2, emphasis added). 24 See Wirkierman (2022a, p. 496, footnote 1) and the discussion in Wirkierman (2012, Chapter 3) for details. 25 On this point, see Meade (2010). 26 See Rampa (1981b, p. 111) on this point. 27 For example, see Harberger (1998, p. 3). 28 See Wirkierman (2012, Chapter 2) for a discussion and Garbellini and Wirkierman (2014). 160 Conceptualising productivity measurement from a classical perspective PSL Quarterly Review The ‘tradition of measuring labour productivity’ (measured as industry value added per unit of labour) was conceptually focused on the productiveness of labour, not on its physical productivity. The ‘total’ character of TFP comes from the conception of production and distribution according to marginal productivity theory. If capital and labour are the two prominent non-produced primary factors, a measure of productiveness has to account for the net income they both generate. But the qualification ‘total’ is clearly contingent on a purely theoretical choice. What should be clear is that what distinguishes a ‘partial’ from a ‘total’ physical productivity measure is not the differentiated components in net income but whether the general interdependence of the system is being taken into account or not. A total measure of labour productivity, i.e., the computation of the labour content of all (direct and indirect) commodity requirements to reproduce the net output (possibly expanding productive capacity), considers capital goods as well, accounting for their circulation as inputs and outputs through the ‘convoluted’ network of input-output transactions. And in this sense, the input-output literature on TFP growth measurement is both relevant and insightful. 29 Net income and net product are, in most cases, clearly differentiated, and the latter is used to derive aggregate measures (for example, see Wolff, 1994, p. 81, eq. 3). But, while interdependence is accounted for as regards circulating capital inputs, fixed capital is still conceived as a primary factor of production in most cases. 30 In any case, I think the crux of the matter boils down to the lack of an explicit distinction between physical productivity and productiveness (i.e., profitability). If the derivation of a TFP figure (be that using production functions or by means of input-output schemes) starts from a theory of value added, it cannot lead to adequate measurement of disaggregated physical productivity. In fact, even abandoning some stringent assumptions of marginalist production theory, and adopting a sceptical view of the residual simply as a reduction in real costs, the confusion about productiveness and productivity remains: A simple TFP measure for firms with multiple outputs and multiple inputs is to look at the profitability of a firm, defined as the revenue of the firm divided by its input cost. […] [A] strict comparison […] is difficult since the output and input prices faced by these firms are different. The only option here is to adjust the value aggregates […] for differences in price levels (Coelli et al., 2005, pp. 62-63, emphasis added). However, to privilege a physical interpretation of productivity does not mean in the least to deny the importance of profitability changes in the evaluation of the effects of technical change in employment, output proportions, and relative prices. What must be clear is the separation in concepts and terminology that is required to distinguish cause from effect. 5. Subsystems and prices of production The distinction between physical productivity and profitability is not only established by the alternative reference to the expenditure or value added side of the economy as a starting point, but also to the unit of analysis to which each notion refers. 29 See, for example: Wolff (1985), Galatin (1988), Wolff (1994), ten Raa (1994), Casler and Gallatin (1997), as well as Wirkierman (2012, Chapter 3). 30 See Peterson (1979, pp. 218-219) and Wolff (1994, pp. 84-86) for some exceptions. A.L. Wirkierman 161 PSL Quarterly Review In fact, the economic system can be disaggregated in industries, producing a product mix of outputs, but it can also be disaggregated in self-replacing and growing subsystems 31 that produce a single kind of final commodity. While profitability measures are computed at the industry level, disaggregated physical productivity measures are formulated with the subsystem in mind. 5.1. Production prices and eigensystems Computable production prices can be conceived of as prices implicit in the (medley of) technique(s) in use in the economic system. They represent exchange ratios satisfying necessary conditions for reproduction under a given rule of distribution of the surplus (e.g., a uniform profit factor is computed in proportion to capital advanced). The technique in use can be thought to be contained in measurable empirical structures, like input-output schemes. And empirical structures reveal changes in techniques when nominal figures can be separated into a volume growth and a price component. In this way, production prices function as aggregators applied to the quantities actually produced to measure changes in inputs and outputs, thus allowing to quantify the changing surplus (in value terms) between revenues and outlays by industry (i.e., changes in profitability due to technical changes for a given distributive configuration). An important remark on method is in order. Note that, by interpreting computable classical production prices as a possible set of aggregators, 32 no presumption of descriptive or predictive power is attributed to them. By so doing, the aim is to separate two fields of inquiry. In this sense, computable prices could be conceived as one answer to the following problem, posed by Sraffa: The problem is that of ascertaining the conditions of equilibrium of a system of prices and the rate of profits, independently of the study of the forces which may bring about such a state of equilibrium. Since a solution of the second problem carries with it a solution of the first, that is the course usually adopted in modern theory. The first problem however is susceptible of a more general treatment, independent of the particular forces assumed for the second; and in view of the unsatisfactory character of the latter, there is advantage in maintaining its independence (D3/12/15: 2; emphasis added) (Kurz and Salvadori, 2005b, p. 433). In fact, among the first computations of prices of production, the works of Hejl et al. (1967), Kyn et al. (1967) and Sekerka et al. (1970) – with an origin in the dynamic input-output price model – had the aim of comparing different price norms applied to the same technique in use. Since then, however, computable production prices have been used for multiple purposes; for example, the empirical assessment of capital theory paradoxes, going from Krelle (1977) to Han and Schefold (2006). In connection with this are the degree of (non-) linearity of wage-profit schedules for different standards of value and the study of the deviation of labour values (empirically defined in a variety of ways) from production prices and market prices. 33 A related 31 Throughout the paper, the terms self-replacing subsystem and vertically integrated sector are used interchangeably, and the same applies for the terms growing subsystem and vertically hyper-integrated sector. While the notion of selfreplacing subsystem was introduced by Sraffa (1960, Appendix A, p. 89), its compact representation as a vertically integrated sector was introduced by Pasinetti (1973), and its extension to growing subsystems or hyper-integrated sectors was introduced by Pasinetti (1988). See Garbellini and Wirkierman (2014) for a detailed discussion. 32 Computable prices may be considered to be one among the many possible norms, in the sense of Pasinetti (1981, p. 127n). 33 See Marzi (1993) for a review of these lines of inquiry. The crucial points under discussion are: (a) the empirical plausibility of the neoclassical parable of a surrogate production function, (b) the regularity in relative price changes as 162 Conceptualising productivity measurement from a classical perspective PSL Quarterly Review use has been to study computable prices under the assumption of heterogeneous rates of profits between industries (though generally maintaining a fixed relative structure of profit rate differentials). 34 For the purpose of this paper, the interest lies in the use of computable prices to measure the effects of technological progress on the distributive possibilities of the system, i.e., computation of changes in profitability induced by changes in the technique in use, for each given distributive configuration. Operationally, this takes place by assessing the shape of ‘wage-profit curves’. Among empirical works with this aim, it is possible to mention: 1. The studies of Marzi and Varri (1977) (using only circulating capital) and Marzi (1982) (including also fixed capital) for the Italian economy, assessing the Harrod-neutral character of changes in techniques. 2. The works of Ozol (1984, 1991) for Canada and the US, concluding on the ‘cost reducing automation’ character of technical change. 3. The study of Leontief (1986) for the US, introducing a linear program to find the most profitable (for a given real wage rate) technique, at each feasible value of the rate of profits. 4. The study by Marzi (1994) for the Italian economy (using only circulating capital), which relates the convexity of the wage-profit schedule (as each final commodity alternatively becomes the standard of value) to the capital intensity of the (balanced) growth subsystem associated with each final product. 5. The work of Degasperi and Fredholm (2010), proposing the area under alternative wageprofit schedules (for a common numéraire commodity) as an indicator of the degree of technical progress across time and space, with an application (using only circulating capital) to selected OECD economies. All of the above-mentioned studies have in common a classical awareness that is applied to inputoutput data. Some related studies analyse technical change by means of wage-profit curves, which are built only with national accounts data by industry (for example, see Michl, 1991; Ferretti, 2008). When Leontief (1951) noticed that, by consolidating input-output accounts, it was possible to obtain zero net income, he connected each income source with a specific use of expenditure. Clearly, the view of an economy with both zero net income and zero surplus product corresponds to a closed system, where all income-expenditure loops are endogenous. In such systems, there is complete duality between prices and quantities and between income and expenditure (there are no final uses), and the notions of productivity and profitability acquire a dual character as well. Mathematically, the structure of closed systems is usually formulated as an eigen-problem, where the maximum (in modulus) eigenvalue summarises the system’s surplus both in physical and value terms. Starting from the seminal work of Bródy (1970), different studies have conceptualised the measurement of productivity increases as an eigenproblem. 35 Though very appealing from an income distribution is altered, and (c) the empirical plausibility of a pure labour theory of value. Note that all three cases imply a descriptive/predictive role for the notion of classical production price. 34 See Flaschel (2010, Part II, Chapter 8, section 8.5) for details. 35 For example, Buccellato (1990) has used the left and right eigenvectors associated with the maximum eigenvalue to compute shares in production according to ‘standard proportions’ or revalue industries according to their associated ‘standard prices’, in order to detect market overand under-valuation. In another study, Aulin-Ahmavaara (1999, p. 358) develops (only in theoretical terms) her ‘fully effective rate’ of productivity change, by assuming that all inputs are (re)produced (including labour). A.L. Wirkierman 163 PSL Quarterly Review analytical point of view, its empirical implementation is not straightforward. To adequately separate (statistical) prices from volume growth, it is necessary to neglect the presence of imported commodities (which represent a full matrix as opposed to a single column vector of exports) as well as the presence of taxes on products and production. Moreover, it is necessary to deal with an essential empirical disarray in both wages ≡ consumption and profits ≡ investment theoretical identities. In any case, the formulation of an eigensystem for the complete ‘augmented’ matrix and the study of its spectral properties should not be confused with the computation of the maximum eigenvalue of inter-industry flow matrices to assess the intensity of use of intermediate inputs (generally circulating capital). 36 In these cases, the spectral properties serve as a summarising device (with eigenvectors as a particular system of weights for aggregating rows and columns) and not as a comprehensive measure of surplus of self-contained closed systems. 5.2. Subsystems The measurement of disaggregated physical productivity of labour with reference to the subsystem as a unit of analysis has its origin in considering jointly Leontief’s (1953) computations of “the roundabout, as compared with the direct, effects which the changes in the input structures of various industries have on the over-all productivity of labour” (Leontief, 1953, p. 39; emphasis added), and Sraffa’s (1960, Appendix A, p. 89) constructive algorithm to build the logical device of a subsystem. 37 Even before the appearance of the subsystem, Pasinetti (1959) (in reply to Solow’s (1957) contribution) had already noticed the need to account for the reproducible character of capital goods, measuring them in terms of final commodity-specific units of capacity, in order to derive physical measures of productivity changes. 38 After the subsystem had been devised, Pasinetti (1963, Chapter V) introduced the first algebraic and conceptual relations connecting industries with vertically integrated sectors (i.e., self-replacing subsystems) for the study of technical progress. Moreover, Gossling and Dovring (1966) presented the first empirical application of productivity measurement adopting the subsystem as a unit of analysis. Gossling (1972) provided a comprehensive empirical study of productivity growth by subsystem, including a comparison with traditional ‘partial’ and ‘total’ factor measures. 39 The crucial idea behind the subsystem is its degree of autonomy. By repartitioning the whole row vector of gross outputs and the matrix of intermediate uses by industry into as many logical parts as there are components in the column vector of final uses by commodity, all means of production, labour, and outputs are redistributed into each of these parts, according to their contribution as a supporting industry to the activity which produces the final commodity. 36 See, for example, Rampa and Rampa (1982) (including also fixed capital and imported commodities) and Marengo (1992). 37 A related approach to the measurement of direct and indirect labour requirements, explicitly recognising its meaning as a ‘productivity’ index, has been advanced by Vincent (1962), who suggested the term “productivité intégrale du travail” (total productivity of labour). See Gossling (1972, pp. 52-54) for a discussion. 38 See Garbellini and Wirkierman (2023) for an exposition of the debate between Solow and Pasinetti. 39 In a related article, Gossling (1974) complemented his study considering the open economy, i.e., direct and indirect requirements of imported commodities. 164 Conceptualising productivity measurement from a classical perspective PSL Quarterly Review The redistribution of commodities in association with others, as an alternative to the aggregation of industries, is thoroughly discussed by Leontief (1967), who noticed that aggregation and reduction were two strategies to deal with too detailed empirical structures: Aggregation, i.e. summation of essentially heterogeneous quantities, is one of the two devices that the economist uses to limit the number of variables and functional relationships in terms of which he describes what he observes. The other is reduction, that is, elimination of certain goods and processes (Leontief, 1967, p. 419). In a fundamental contribution, Pasinetti (1973) established explicit connections between the subsystem and the logical device of vertical integration, i.e., the reduction of some commodities in terms of others. By introducing a compact algebraic representation of a self-replacing subsystem, as the result of vertically integrating co-existing total employment and capital goods, it became possible to work with alternative representations of the same technique in use, either in direct terms (direct labour and direct productive capacity) or in vertically integrated terms (vertically integrated labour and productive capacity). But, even though it dealt with the case of balanced growth, Pasinetti’s (1973) construct remained essentially static, in the sense of representing only self-replacing subsystems. New investments were still included in the net output, so part of the physical surplus of industries producing capital goods still needed to be exchanged between (or redistributed among) these selfreplacing sectors, in order for each of them to expand their commodity-specific productive capacity. This clearly posed difficulties for the degree of autonomy of the self-replacing subsystem. 40 Thus, in the context of a dynamic economy, Pasinetti (1988) introduced the logical device of vertical hyper-integration in explicit association with the notion of a growing subsystem. The key difference is that gross investment to self-replace and expand commodity-specific productive capacities is redistributed among industries according to their reproduction requirements (which now include expansion/contraction) when the reduction process is performed. Therefore, investment becomes fully induced by the growth of effective demand for final uses. 41 Among the different works either applying the concept of total labour requirements or explicitly adopting a self-replacing subsystem perspective, it is possible to mention: 1. The study by Gupta and Steedman (1971) for the UK, in which direct and total labour requirements are computed, leading the authors to conclude that “total (or system) labour use falls but less rapidly than direct labour use” (Gupta and Steedman, 1971, p. 32). 2. The empirical studies by Rampa (1981a) and Rampa and Rampa (1982), the theoretical considerations of Siniscalco (1982), and the work by Fredholm and Zambelli (2009), which explicitly adopt Gossling’s (1972) operator to map between industries and self-replacing subsystems. 3. The studies by Ochoa (1986), De Juan and Febrero (2000), and Flaschel (2010, Part I, Chapter 3, pp. 63-68), connecting total labour productivity to labour content of commodities through labour values. 4. The theoretical considerations by Seyfried (1988), who explicitly separates vertically integrated labour productivity from vertically integrated labour rentability, this latter concept measuring “how much labour must be disposed to produce one unit of output […] if beside the 40 The idea of this subtle but essential point is due to Garbellini (2010, pp. 48-51). The reader is referred to this source for a clear exposition and discussion. 41 See Garbellini and Wirkierman (2014) for a detailed exposition. A.L. Wirkierman 165 PSL Quarterly Review reproduction of capital the capital owners can claim part of the product as profit” (Seyfried, 1988, p. 172). 5. The studies by Milberg and Elmslie (1992), Elmslie and Milberg (1996), and Dietzenbacher et al. (2000), which adopt an input-output approach to study cross-country convergence of labour productivity at the vertically integrated level. Further developments of this line of research have devised, discussed, and empirically implemented sectoral (and aggregate) productivity measures in terms of growing subsystems (or vertically hyper-integrated sectors): 1. The study by Garbellini and Wirkierman (2014), establishing a direct correspondence between Supply-Use Tables and Pasinetti’s (1973, 1988) theoretical magnitudes, making an explicit price-volume separation and exploring the possibility of empirically separating growth from the technique in use. 2. The contribution by Brondino (2019), applying the (hyper-)subsystem approach to the Chinese economy, finding that subsystems with the highest productivity performance had been targeted by industrial policy. 3. The work by Wirkierman (2022a), comparing hyper-integrated productivity dynamics amongst advanced industrial economies, finding that productivity gains accruing to wages were amongst the lowest in the economies with the highest overall hyper-integrated labour productivity growth. 4. The study by Garbellini and Wirkierman (2023), offering a conceptual, analytical, and empirical reconstruction of the debate between Solow (1957) and Pasinetti (1959) on productivity measurement. The idea of using the subsystem (or vertically integrated sector) as a unit of analysis for the study of technical change has often been criticised (see, e.g., Schefold, 1982, p. 549, and Hagemann, 1987, p. 346). I believe this is mainly due to two misunderstandings. First, vertical integration is sometimes considered going backwards in time, in a sort of ‘neoAustrian’ perspective. I think the origin of this confusion comes from placing the general analytical device of vertical integration in the context of a specific joint production model (the ‘pure fixedcapital system’), in which machines of different years are consolidated – through a discounting procedure applied to the price equations – in order to obtain a single-product system: We may call this operation ‘vertical integration in a temporal sense’ of the activities employing the machine in its various years of age; it allows us to formally eliminate the joint-production component and bring the analysis back to the forms of single production with only circulating capital (Baldone, 1980, p. 96). Second, it is sometimes maintained that rates of productivity growth at the vertically integrated level are exogenous data of the analysis: The industry-specific nature of technical change also implies that, contrary to Pasinetti’s assumption, rates of productivity growth in the different vertically integrated sectors cannot be thought of as being independent of each other (Hagemann, 1987, p. 346). 166 Conceptualising productivity measurement from a classical perspective PSL Quarterly Review In this case, I think the origin of the confusion comes from taking a specific description of the technique in use present in Pasinetti’s (1981) model – in which capital goods are produced by labour alone – and assigning to it a general interpretation of vertically integrated magnitudes. 42 Pasinetti’s (1981) ‘intermediate case’ (i.e., a description of technology without basic commodities) was thought of as a purely expository theoretical device. In this particular case, the rates of growth of direct labour coefficients coincide with those of vertically (hyper-) integrated labour coefficients. But this is clearly far from being a general principle. In fact, it is apparent that vertically (hyper-) integrated magnitudes are derived from industry level ones, claiming no logical primacy or independence. 43 In any general empirical application, vertical integration is a device applied to existing direct (industry) magnitudes to obtain derived (vertically integrated) productivity growth rates. This second source of misunderstanding warns, however, of the importance of making a clear statement as regards the aims and purposes of productivity analysis from the perspective of subsystems. As stated by Pasinetti himself: the analytical device of vertical integration is not meant to catch the detailed and localized sources of technical change; on the contrary, it is meant to synthesize the overall effect of technical change (whatever its sources, or nature, or remote localization in the economic system) on the final stage of production, of prices and of employment (Pasinetti, 1990, p. 258, emphasis in the original). Thus, the focus is on measuring the effects of technical change on proportions, prices, and employment and not to study the causes behind changing productivities. 5.3. Measuring productive capacity In a multisectoral economy, a scalar or subsystem measure of physical input per unit of output is not straightforward to obtain, given the multitude of output-input productivity ratios present in the economy. It is necessary to solve the aggregation of commodities, or the reduction of some of them in terms of others. This is particularly difficult for capital goods, which, by being reproducible, are themselves subject to productivity improvements. In fact, in the summary record of the debate at the 1958 Conference on the Theory of Capital, Kaldor noticed two radically different positions on this issue: One extreme case was to assume that there was no technical progress in the production of capital goods but that these always required the same amount of real resources. This was obviously quite unrealistic. At the other extreme, one could say that a unit of capital was whatever unit was capable of producing a given output in a given year – ignoring both longer and shorter output streams. Here any distinction between the quantity of capital and its productivity was washed away by the definition itself. Any idea that capital might have varying productivities was lost; its output was always constant (Hague, 1961, p. 304, emphasis added). The first ‘extreme case’ corresponds to the traditional TFP treatment of the ‘quantity of capital’, in which a TFP growth measure is assumed to capture disembodied efficiency changes, independently from capital deepening, which are assumed to require the same amount of real resources (e.g., ‘waiting’) per unit of saving. The second ‘extreme case’ consists in measuring capital goods in ‘units of capacity’, i.e., as a set of composite commodities of heterogeneous physical content, specific for each final product 42 See Garbellini (2010, pp. 152-155) for a development of the argument and Garbellini (2010, pp. 138-164) for a reply to other criticisms of the vertically (hyper-) integrated approach. 43 See the early comments by Pasinetti (1963, Chapter V). A.L. Wirkierman 167 PSL Quarterly Review of the economy. But then, if capacity is defined in terms of the final output actually produced, at every moment the number of units of commodity-specific capacity would coincide with the number of units of each final product (Kaldor’s idea of a ‘constant output coming from capital’). However, by adopting such a measuring rod, the ‘quantity of capital’ in real terms would not be needed anymore, and, at the same time, each of these composite commodities would change their physical composition from one period to the next, though retaining their function as commodity-specific ‘productive capacities’. This route was precisely the one taken by Pasinetti (1959) throughout his approach to structural economic dynamics. 44 What Kaldor observes is true, ‘the difference between the quantity of capital and its productivity’ is dispensed with. But this is not a problem when productivity measurement is not conceived from the value added side, as there is no net income to distribute among ‘factors’. In fact, the procedure of using a reduction (through vertical integration) rather than an aggregation of capital goods is perfectly in line with adopting a subsystem perspective. 6. By way of conclusion It is of course true that “to measure is not to understand” (Salter, 1966, p. 1), and this is particularly so as regards productivity analysis: One of the reasons why interpretative analysis of productivity has been slow to develop has been the interminable controversy over what is productivity and what do we really wish to measure. The word now carries a multitude of meanings; to some it measures the personal efficiency of labour; to others, it is the output derived from a composite bundle of resources; to the more philosophic, it is almost synonymous with welfare; and in one extreme case it has been identified with time. I personally believe that much of this discussion has proved fruitless and only served to confuse the issues of measurement with the issues of interpretation. Unless there is a revolution in statistical techniques and information, only one type of productivity concept is measurable. This is the concept of output per unit of input (Salter, 1966, p. 2, emphasis added). Far from being a trivial statement, the position taken by Salter (1966) was not the usual one at the time of writing (and, clearly, even less nowadays). But it hopefully serves to clarify the broad overview presented in the preceding sections. In sum, I believe that applied productivity (and profitability) analysis from a classical perspective ought to be carried out by measuring changes in physical input use per unit of output (as seen from the expenditure side) using (growing) subsystems, as well as studying the effects that changes in physical productivity have on the (price) surplus of the system (as seen from the value added side), using production price systems. Expenditure depends on commodity circulation, on material balances, on proportions: gross to net product. In sum, on physical outputs. Value added depends on commodity circulation-cumexchange, and exchange implies relative prices (and so standards of value). Productiveness starts from the exchange of commodities within the capitalist mode of production: net income and distributive rules must be faced. Productiveness is micro-economic; it can be applied to a single agent, a firm, an industry. And, to get to the overall economy, aggregation is necessary. Productivity, instead, starts from the ‘collective labourer’, from the labour content in the circulation of commodities, revealing a continuous and dynamic process of division of labour, specialisation, automation and technological unemployment (labour saving trends), counteracted by effective demand. Productivity is macro-economic; there is no sense in searching for the 44 See Pasinetti (1963, 1973, 1981, 1986, 1988). See also Garbellini and Wirkierman (2023). 168 Conceptualising productivity measurement from a classical perspective PSL Quarterly Review productivity of an individual, as the crucial point for productivity analysis is general interdependence. That is why productivity measures start from the subsystem, the minimal unit of analysis, no matter the level of aggregation chosen. In fact, Pasinetti’s (1959) first attempt at the concept of productivity was limited to an economy with two subsystems, but the two crucial ones: a sector producing the means of production, the other producing final uses. His intuitions could later be generalised, thanks to reduction and not aggregation. Reduction, or expressing some commodities in terms of others, has turned out to be one important analytical device for productivity measurement from a classical perspective. Another one has been to measure capital goods in ‘capacity units’, i.e., in terms of the final commodities that can be reproduced with them. But then it is clear that, to have a capacity-unit of measurement, it becomes necessary to separate what re-enters the production process from what is a truly final use. And for this task it is the expenditure side, the physical surplus, which needs to be analysed. Its crucial component is investment: a dual concept in itself. Investment is a source of demand, of expenditure, but it also generates capacity, alters the means of production that have to be priced in the value added side. Gross investment, i.e., (fixed) capital accumulation, plays a crucial role in productivity analysis, so the mechanism behind its treatment for productivity measurement in the context of empirical growing subsystems should be rendered explicit: in each year, the gross investment undertaken by each industry represents the flow of capital goods required to maintain the industry on its current growth path (Peterson, 1979, p. 220). In fact, faced with multi-period accounting identities from the side of physical outputs, we observe only quantities produced. The separation between methods of production and activity levels of industries is analytical. If we assume unitary operation intensities, this leads to technique-cumintensity level flow matrices. This observation means that it is not possible to separate, on entirely ‘objective’ grounds, growth from technical change in empirically given structures: empirical matrices contain growth rates. All in all, on productivity analysis from a classical perspective, almost everything awaits to be empirically explored. This paper has been only a structured invitation to think about foundational concepts and some existing literature that may help it grow further. In this sense, there are several directions for further research. With the consolidation of intercountry production networks and the availability of global inter-regional input-output (IRIO) data, it has become possible to measure productivity by representing a global value chain as an international subsystem producing a final product. But, while productivity became an international concept, competitiveness remained a national one, so it would be interesting to understand their interplay in a global economy. As regards technological change, new (conceptual and empirical) challenges emerge to measure productivity and profitability in an era of fast automation and industrial robotisation, where fixed-capital becomes ever-increasingly malleable (Wirkierman, 2022b, p. 274). If automation was taken to an extreme, would the indispensable role of labour in production be at risk? Finally, with the increasing digitalisation of production processes, there is a need to understand the nuances of productivity measurement when the differences between physical and digital outputs (and their associated inputs) become apparent (Wirkierman, 2022b, p. 280).