Portal de Periódicos da CAPES

Pasinetti's ‘Structural Change and Economic Growth’: A Conceptual Excursus

2014; Taylor & Francis; Volume: 26; Issue: 2 Linguagem: Inglês

10.1080/09538259.2014.881671

1465-3982

Nadia Garbellini, Ariel Luis Wirkierman,

Economic Theory and Institutions

AbstractA clear and organic exposition of Pasinetti's theoretical framework of Structural Change and Economic Growth has been prevented by misunderstandings and ambiguities concerning basic categories and terminology. The pre-institutional character of the approach, the nature of its equilibrium paths and the significance—and normative character—of the 'natural' economic system are some of the most controversial issues. The aim of this article is to present a conceptual excursus of the model to establish a solid foundation for fruitful discussions to be held with other Classical approaches.View correction statement:Erratum AcknowledgementsWe wish to thank the anonymous referees for their helpful and valuable comments and suggestions to improve this article. The usual disclaimers apply. Special acknowledgement goes to Professor Luigi Pasinetti, for his continuous encouragement and support.NotesThis article was originally published with errors. This version has been corrected. Please see Erratum (http://dx.doi.org/10.1080/09538259.2014.899193)1For example, see: Asimakopulos (Citation1982, p. 1566), Harris (Citation1982, p. 29) and Taylor (Citation1995, p. 699).2For example, see Parrinello (Citation2004).3On this point, see the criticisms put forward by Schefold (Citation1982) and Taylor (Citation1995).4Given that Pasinetti does not conceive capital as time, the term 'capitalistic' in this context does not stand for 'roundaboutness' (as it has been intended by, for example, Wicksell). In Pasinetti's (Citation1981) analysis, it is coexisting and concurrent labour that is applied to any reduction process of heterogeneous capital goods in terms of homogeneous labour for the purpose of summarising the extent and degree of the division of labour.5See the discussion in, for example, Delorme & Dopfer (Citation1994) as well as the summary and comments in Reati (Citation2000).6In this more recent book, Pasinetti (Citation2007) stresses such a distinction in a much sharper way.7 The basic notation can be found in the Appendix.8Hereinafter, unless differently stated, subscript i is intended as .9The concept of vertical hyper-integration is already present in Pasinetti (Citation1981) even though not always explicitly. For a rigorous statement and development of this concept, and of its analytical properties, see Pasinetti (Citation1988).10 and , respectively.11This is a crucial difference between the notion of vertically integrated sectors and that of vertically hyper-integrated sectors (see Pasinetti, Citation1973; Pasinetti, Citation1988).12This is particularly clear when matching the chapters of the book which 'have been almost entirely re-written' (Pasinetti, Citation1981, p. xiv) since the time of his PhD Thesis with the entries in the index concerning vertical hyper-integration.13In fact, direct productive capacity includes capital goods employed for the production of final consumption commodities, while VHI productive capacity also includes capital goods required for the production of other capital goods (i.e. worn out and additional productive capacity). In the present simplified context, however, the last two components are nil by definition given that capital goods are assumed to be produced by means of labour alone, and thus direct and VHI productive capacity are de facto the same.14Given that both the physical quantity and commodity price systems are formulated as sets of 2m+1 linear and homogeneous equations, they have non-trivial solutions if the coefficient matrix built from any of the systems (1) or (2) is singular, i.e. if its determinant is zero. The condition for this to happen is the same for both systems:The three addenda under summation are direct labour, indirect labour (i.e. direct labour necessary for replacing worn out productive capacity) and hyper-indirect labour (i.e. direct labour necessary for the expansion of productive capacity), respectively summing up to VHI labour for each growing subsystem i.15For details, see Pasinetti (Citation1981, pp. 33–34).16This means setting and , respectively, in expressions (1) and (2). The solutions are then given by:Note that, in the solution for , Pasinetti (Citation1981, p. 41) implicitly assumes that . This amounts to assuming that productive capacity available at the beginning of time period t is totally used up. In order to make the formulation as general as possible, we decided not to make such an assumption at this stage.17See Pasinetti (Citation1973, p. 7, section 5) and Pasinetti (Citation1988, p. 130, section 4).18Analytically, this means that .19According to:for . For the sake of simplicity, we are here assuming steady rates of change of the relevant variables, although this is not the procedure adopted by Pasinetti (Citation1981), at least for the rate of change of final demand for consumption commodities (see Pasinetti, Citation1981, p. 82). This is a crude simplification, though it is not possible—according to the authors—to take full advantage of the increasing realism of working with non-steady rates of change if the model is specified in continuous time. For the scope of the present work, moreover, the simplification adopted does not compromise the conclusions to be reached.20Taking expressions (N.2) and (N.3) evaluated at time period t = 0, and inserting the dynamics described in equation (N.4) we obtain the following solutions for physical quantities and commodity prices, respectively:21The set of accounting identities describing capital accumulation is (where, for any variable in the system, . Given that , we obtain . Therefore, the series of coefficients 'is the only one that affects the stocks of the economic system, i.e. productive capacity in each sector; hence it cannot be taken as given from outside' (Pasinetti, Citation1981, p. 85). This opens up the possibility to perform a general dynamic analysis by specifying a law of movement for the level of per capita new investment demand (), allowing for the discrepancy between productive capacity available at the beginning of period t () and the units of productive capacity actually used up during period t (). The specification of the dynamics of investment is a degree of freedom that, once closed, allows us to perform an institutional analysis of different theories of capital accumulation. Another degree of freedom can be opened by changing the last equation of both the physical quantity and the commodity price systems, in order to explicitly allow for the possibility of flow-disequilibrium, for example, by writing:meaning that macroeconomic condition (N.1) is not satisfied if . For a hint at different cases that can occur as a consequence of flow and stock disequilibria, see Pasinetti (Citation1981, pp. 47–48).22In particular, we can get the condition for keeping flow-equilibrium by inserting equation (N.4) into equation (N.1):It can be noted that the demand coefficients for new investment are still taken as exogenously given, their specification being the subject of the following few paragraphs.23Mathematically, since and, in stock equilibrium, , we have that . As the growth of final demand is given by , the following set of sectoral capital accumulation conditions must be satisfied:24Analytically:where the 's are sectoral capital/output ratios.25In Pasinetti (Citation1981), as each capital goods-producing industry is specific to each consumption goods-producing one, it is the second aspect that is emphasised, although the framework allows for further generalisation to reflect also the first one. See Pasinetti (Citation1988).26By substituting capital accumulation conditions (N.6) into the macroeconomic condition (N.5) and writing it as follows:Note that the two addenda distribute total labour of the system between the labour requirements of final consumption commodities and the labour requirements of equilibrium gross investments.27The left-hand side of equation (N.8) stands for the size of per-capita total effective demand in time period t.28In order to define them, we shall start from the full-employment macroeconomic condition for flow-equilibrium. By inserting equations (N.6) into (N.5) and rearranging, we get:which, defining , can be written as:29The three components are given by , , and , respectively. For details, see Pasinetti (Citation1981, p. 102).30The rate of growth of , which we may denote by , is the rate of growth of VHI labour productivity of sector i, given by the weighted average of the rates of growth of direct, indirect and hyper-indirect labour productivity, the weights being the proportions of the three kinds of labour to total labour employed in VHI sector i, respectively:Note that, within the Classical tradition, system measures of labour productivity have always relied on vertical integration rather than hyper-integration to assess productivity changes. See, for example, Gupta & Steedman (Citation1971) and De Juan & Febrero (Citation2000).31If 'we choose to reckon prices in terms of Classical "labour commanded"' (Pasinetti, Citation1981, p. 99), the wage rate still being the basis for the price system, we set . Hence, the equilibrium dynamic path of relative physical quantities, sectoral employment and commodity prices is given by, respectively:In what follows, whenever a nominal magnitude has a letter in brackets as a superscript, that letter will indicate the numéraire commodity adopted. Therefore, indicates the price of commodity i when the numéraire of the price system is the wage rate. For a complete analysis of the equilibrium structural dynamics of a growing economic system, see Pasinetti (Citation1981, pp. 91–99).32In fact, we have:33In this case, we have:34It is given by:35In this case, we have:where is the rate of change of the relative price of commodity i when the numéraire is the wage rate.36Since in equilibrium , this follows from:37In fact, from condition (N.13) and from the expression for natural prices of consumption commodities (4), respectively, it follows that:As a consequence, the value, at current prices, of total quantities, net of replacements, produced in each sector equals the total income it generates, i.e.:38In fact, any commodity or composite commodity can be chosen as the numéraire of the price system; analytically, this amounts to setting its price equal to unity, and keeping it constant through time. For example, if commodity h is chosen as the numéraire, we set and . Symmetrically to , which is the rate of change of the relative price of commodity i when the numéraire is the wage rate, is the rate of change of the relative price of commodity h when the numéraire is the price of commodity h itself. Once the numéraire is specified, the wage rate has to be expressed in terms of it; this again means closing two degrees of freedom, i.e. we have to set both the wage rate at time zero and its rate of change in terms of the chosen numéraire. Within the 'natural' economic system, again taking commodity h as the numéraire, this means setting , from where we obtain and therefore:the rate of change of the price of any consumption commodity i being given by:The rate of change of the wage rate in terms of the chosen numéraire—the real wage rate—is thus given by the rate of increase of labour productivity in the corresponding sector, whereas the rate of change of the price of commodity i, in terms of the chosen numéraire, is given by the difference of the rate of change of labour productivity in the corresponding sector with respect to the rate of change in VHI labour productivity in the sector producing the numéraire commodity.39When the hypothesis of steady rate of change of per capita demand for consumption commodity i is removed, the natural rates of profit are no more exactly constant through time, but shall exhibit a roughly constant trend.40See Pasinetti (Citation1981, pp. 71–77).41Amongst these, see Asimakopulos (Citation1982), Eltis (Citation1982), Kregel (Citation1982), Schefold (Citation1982), Rymes (Citation1984), Shapiro (Citation1984), and Taylor (Citation1995).42The development of the concept of vertical hyper-integration went through different stages. Pasinetti's (Citation1981) book was the final result of a process that began with his Doctoral dissertation at the University of Cambridge (Pasinetti, Citation1962), which was partially published in Pasinetti (Citation1965), and was itself an intermediate step towards the analytical elaboration of vertical hyper-integration, accomplished in Pasinetti (Citation1988).