Reply to Parrinello

First of all, we sincerely thank Sergio Parrinello for his detailed comments and criticisms about our book and essay. Parrinello's notes allowed us to critically explore several issues related to the topics covered in the book and possibly clarify our point of view. In this note, we try to offer some replies to keep the debate open and push our understanding a little further. Since many (although not all) of the comments concern Pasinetti's work, it seems convenient to start this note by presenting our understanding of Pasinetti's analysis and explaining how Sergio's comments and criticism may be placed in the context of our reading of Pasinetti's work.

It seems to us that many of the questions posed by Parrinello are better understood if we recall, first of all, that the model of structural dynamics, fully developed by Pasinetti in his (1981, 1993) books, basically represents a normative type of analysis. Like Joan Robinson's ‘Golden Age’ dynamics (1956), Pasinetti's model serves as a benchmark that defines the conditions for the system to grow in full employment equilibrium.

The interest and originality of this model are due to its ability to study the dynamic of the overall economic system by an analytical framework disaggregated at the sectoral level. In this way, it is easy to understand how the different trends of technological progress and labour productivity, spending habits and consumer behaviour, and the allocation of profits and investments between different sectors (essential features of modern capitalist societies) are unlikely to satisfy (if not by chance) the requirements of full employment growth. On the contrary, they tend to produce significant phenomena of technological unemployment and/or Keynesian unemployment (due to a lack of effective demand). For Pasinetti, bolstered by the 1960s critique of the neoclassical theory of capital, these imbalances cannot be resolved through automatic adjustments based on appropriate changes in factor prices. Therefore, moving to an ‘institutional’ level of analysis, a more comprehensive set of adjustment mechanisms is required to bring the actual economic system closer to the level of full employment and adapt it to the evolution of the forces that guide structural dynamics. They must, in the first place, be based on measures aimed at accelerating the processes of reallocation of work among the various productive sectors, training workers and making them capable of adapting to innovations and technological change; secondly, deliberate interventions by policymakers must be aimed at directing the flows of income between the various sectors and filling the gaps in effective demand at an aggregate level.

In this reference model that he called ‘natural system’ (1981, 1993, 2007), there is no room for a concept of causality understood as ‘perturbation of a normal state’ or as ‘deliberate manipulation’ in view of specific policy objectives (Woodward, 2003). Nonetheless, on several occasions, Pasinetti recommended to younger economists engaged at different levels of theoretical investigation to build models able to cope with the phenomena of endogenous causality by adopting formal structures that should be at least partially decomposable.

In this paper, we will go through Parrinello's arguments in a partially different order from the one he followed. In Section 2, we will recall the skeleton of the static version of Pasinetti's model, which stands at the basis of many of the points raised in this discussion. The supposed ‘over-determinacy’ of Pasinetti's model will be analysed in Section 3, and its economic consequences in Section 4. The relation between the problem of the choice of techniques and the analysis of technical progress will be dealt with in Section 5. Some considerations concerning the contraposition ‘causality versus interdependence’ will be presented in Section 6. The rationale for the use of the vertically integrated approach to tackle technical progress is explained in Section 7. The possible opportunity to set macroeconomics before microeconomics is discussed in Section 8. Finally, in Section 9, we will reply to Parrinello's short annotations at the margin of Pasinetti's nine ‘canons’.

Magnitudes c_c, j_c, δ_c, $l_c$, λ_c and π_c are taken as given; magnitudes q_c, q_N, k_c, p_c, z_c and w are unknowns.

Beyond this punctuation, it is probably condition (4) that is considered the cause of the ‘over-determination’ of the model since it involves only parameters. This would bring to the conclusion that this condition may be satisfied only by a fluke (a similar conclusion can be drawn for condition (3) of the closed Leontief system).1 Normally, this outcome is interpreted by observing that both conditions (3) and (4) contain not only technical magnitudes but also consumption coefficients, the last column of matrix A in system (1a-1b) and coefficients c_c in system (-2b′). And precisely these coefficients will have to adapt to the technical coefficients to ensure the fulfilment of condition (3) or (4).

In synthesis, model (-2b′) is not over-determined; in particular, the inclusion of condition (5) does not induce any over-determinacy of the model. The impression that the model is over-determined can arise from the fact that, in order to exclude trivial solutions, condition (4) involves only magnitudes that enter the model as parameters. However, this does not entail that they must be treated as unmodifiable magnitudes.

But ‘what to do’ depends on the purpose for which the model is built. In a static analytical framework the purpose could be of highlighting the absence of any automatisms for the fulfilment of full employment when output levels are determined according to the first 2C equations of system (2a), that is, according to the principle of effective demand expressed, in this case, at the level of each sector. In particular, system (-2b′) highlights an aspect that the closed Leontief model leaves in the shadows: the failure in satisfying condition (4) does not prevent the satisfaction of the first 2C equations of system (2a). This means that we can have equilibrium at the level of each sector (where the first 2C equations are satisfied) while having disequilibrium at the macroeconomic level. From a static viewpoint, this is what the model aims to say, besides the (probably) unfortunate title of Pasinetti's seventh methodological issue or canon: ‘Disequilibrium and instability (not equilibrium) as the normal state of industrial economies’. It is a relevant result: it provides a multisectoral version of the notion of ‘under-employment equilibrium’. Beyond the existence or the possibility of imagining an adjustment process of quantities and/or prices, such an analysis aims to outline a situation of under-employment equilibrium for a multisectoral economy.

In paragraph 2.3, Parrinello observes that a comparative dynamic analysis involving the problem of the choice of techniques has yet to be developed in the vertically integrated approach. His contention is certainly correct. Yet, the analysis of structural change developed by Pasinetti has the purpose of studying the effects of technical progress and the evolution of final demand2; hence, the time horizon in consideration is the medium-long run, where the changes observed in the techniques adopted are mainly constituted by the switches between known and new techniques. Along this horizon, the existence of a plurality of techniques at a given moment in time, and thus the choice among them, is less relevant than the introduction of new techniques to which the analysis is devoted.

The term ‘causality’ is probably a little pretentious. In fact, throughout our essay included in the volume (see Bellino and Nerozzi, 2021), we alternate it with the term ‘sequentiality’. The latter reflects better our understanding and probably Pasinetti's too. Sequentiality indicates a specific order in which the endogenous variables of a model (or, at least, some of them) are determined instead of being determined simultaneously. Thus the ‘right’ contraposition is between ‘sequentiality versus simultaneity’. The latter terminology may also clarify how we cope with Hoover's statement, according to which a sequential system can be transformed into a simultaneous one (and vice versa) though a linear combination of equations. Hoover's statement is obviously true. Yet, we can find a logical-mathematical criterion to distinguish between a sequential and a simultaneous determination of endogenous variables: we have sequentiality when the structural form of the model is decomposable; otherwise, we have simultaneity. The two examples quoted by Parrinello (the non-substitution theorem and Sraffa's distinction between basics and non-basics) perfectly fit our logical-mathematical criterion.

In the Walrasian model, ‘simultaneity’ applies to endogenous variables, again understood formally rather than ontologically. On this point, we aim to stress the difference between a general equilibrium model (but also between a partial equilibrium model), where prices and quantities are determined simultaneously, and a Keynesian model, where investments must be determined before consumption, savings, and national income; indeed, the latter variables are simultaneously determined once a certain level of investments is established; the same can be said for a production price system, where one distributive variable has to be determined outside the system, while prices are determined simultaneously. We can agree that this difference may be qualified using terms like simultaneity and sequentiality instead of interdependence and causality. While appropriate lexical clarifications can undoubtedly improve our exposition of Pasinetti's thought, we think that the abovementioned analytical difference is meaningful from the economic point of view.

As for the existence of a ‘simultaneous causality’, this concept was not questioned by Pasinetti and is, indeed, compatible with Simon causality (see Bellino & Nerozzi, 2017, fn. 10). Pasinetti himself also admits that within a decomposable system there can be simultaneously determined subsystems and illustrates their possible structure (Bellino & Nerozzi, 2017, p. 1659).

We agree. In particular, we would say that in the von Neumann model the quantity variables (output levels and the rate of growth) and the value variables (the prices and the rate of profits) are determined simultaneously. Also in the closed Leontief model, again, the quantity variables, as well as the value variables, are determined simultaneously, provided the consumption coefficients adjust to exclude trivial solutions.

As far as the von Neumann model is concerned, the balancing and absence of net forces that become difference-makers in the steady state of growth of the economy derive, if we grasp the point correctly, from the assumption that Walras' law always applies and that there is market clearing equilibrium in all markets. Assuming the above definition of ‘normal state’ and ‘cause’ as a deviation from the ‘normal state’, then effective demand or structural dynamics, to the extent that they produce an imbalance in the forces driving steady-state growth, ‘cause’ a departure from the full-employment growth path.

In paragraph 3.3, Parrinello raises a difficulty concerning the possibility of arguing in causal terms within the vertically integrated framework in which Pasinetti carries out his analysis.

Parrinello observes that Pasinetti describes technical progress directly through a change (a reduction) of vertically integrated labour coefficients. Yet, since vertically integrated labour coefficients are derived from original input-output coefficients, Parrinello writes: ‘[s]uch property has negative implications if the approach with integrated sectors is applied to a theory of causality based on the notions of control, manipulability, interventions […] because its parameters cannot be controlled independently each from another: they are said to be not variation - free’. However, this point does not seem to apply here, where Pasinetti's aim is to introduce technical progress within an input-output framework. Input-output matrices are constructed from a given set of commodities and industries so that technical progress can only take the form of a reduction in the use of these commodities. Anyway, technical progress is a much more complicated phenomenon since it consists of a new way of doing things (new processes, new means of production, new final goods) rather than a thriftier way of using the same inputs (on this, see Pasinetti, 1981, chap. VI, in particular, § 3). All these reasons explain the choice to represent technical progress at the vertically integrated level.3

In general terms, we can agree with Parrinello's suggestion advanced in his paragraph 3.4. However, we do not think Parrinello's interpretation adequately reflects the mainstream notion of ‘micro-foundations’. Micro-foundation is often presented as the method by which genuine macroeconomic analyses must be derived from the aggregation of myriads of choices by individuals that are often deemed homogeneous so that the set of behavioural rules and rational criteria adopted by a representative agent may plot how the whole economy would behave when faced with the same shocks and opportunities as the individual. With the sole exception of network analysis and certain families of agent-based models, where the relationship structure among agents may be crucial to determining macroeconomic processes, micro-foundation is always intended as a substitute for macroeconomics so that eventually, the latter may lose its autonomy as a discipline. The alternative idea of a macro-foundation of microeconomics is by no means to be intended as the opposite (and equally undue) resolution of micro into macro but as the careful consideration of the fact that individual behaviour is bounded by equilibrium or disequilibrium conditions which are determined at the macroeconomic level, and are crucial to incomes, prices, factor supply, and demand. When effective demand is inadequate or excessive, individuals' consumption or saving plans cannot be fulfiled, and rational economic agents cannot pursue any kind of microeconomic optimisation.

Moreover, some basic notions shared by the classical-Keynesian school themselves impose the logical priority of a macro-over a micro-approach: for example, the very notion of ‘surplus’, that is, the excess of produced quantities over the quantities of the same commodities that have been employed for their production. If this difference has to be intended (correctly) in physical terms it pertains to the system as a whole, not to industries or, even less, to firms.

In this last Section, we give a short reply/comment to the other annotation made by Parrinello in his Section I to the nine methodological issues (or canons) considered by Pasinetti as qualifying the classical-Keynesian approach. For the reader's convenience, we reproduce as a quotation Parrinello's annotation for each canon.