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On Concepts and Measures of Changes in

Productivity — A reformulation∗

Nadia Garbellini†and

Ariel Luis Wirkierman‡

April 17, 2012

Abstract There exists a vast literature on the measurement of productivitychanges, reflecting a wide range of theoretical approaches to economic analysis.The present paper departs from Pasinetti’s (1959) critique to Solow’s (1957) semi-nal paper, and advances a novel reformulation of Pasinetti’s (1959) original physicalproductivity measures in an Input-Output framework, considering the reproduciblecharacter of intermediate commodities and fixed capital goods.

By reclassifying industry magnitudes in terms of vertically (hyper-) integratedsectors, it is possible to change the unit of analysis and devise sectoral measuresof total labour productivity changes, which account for the input requirements ofall supporting industries participating in the production of each final commodity.Moreover, by measuring composite capital goods in terms of units of productivecapacity we distinguish the analysis of technical change from the pace of accumu-lation.

The correspondence between empirical magnitudes and theoretical categoriesof Pasinetti (1973, 1988) is established by departing from a set of square commodity× activity Supply-Use Tables (SUT) and associated capital coefficient matrices,acknowledging the difference between depreciation, retirements and replacementsof fixed capital in observed given structures.

In order to empirically quantify the dynamics of employment and technicalchange, the productivity measures derived have been applied to the case of Italyduring the period 1999-2007.

Complementarily, in the light of the ‘yeast vs. mushrooms’ debate initiated

by Harberger (1998), the pattern of concentration of disaggregated total labour

∗Paper prepared for the 20th. International Input-Output Conference, Bratislava (Slo-vakia), June 26-29, 2012. Draft version, please do not quote without permission of theauthors.†Facolta di Economia, Universita degli Studi di Pavia (Via San Felice, 7, 27100, Pavia,

Italy), [email protected]‡Facolta di Economia, Universita Cattolica del Sacro Cuore (Via Necchi, 5, 20123,

Milano, Italy), [email protected]

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productivity changes by subsystem is compared to traditional Input-Output TFP

growth measures by industry, allowing to uncover methodological differences im-

plied by each approach.

Keywords Labour Productivity, Vertically (hyper-) integrated sectors, Total Fac-tor Productivity, Input-Output Analysis.

JEL classification C67, B51, D24, O14, O41

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1 Concepts and measures of changes in productivity in historicalperspective

“In this day of rationally designed econometric studies and super-input-

output tables, it takes something more than the usual “willing suspension of

disbelief” to talk seriously of the aggregate production function” (Solow 1957,

p. 312)

“In a production system, saving labour is the ultimate meaning of tech-

nical progress” (Pasinetti 1981, p. 207)

1 Concepts and measures of changes in productivityin historical perspective

The literature concerning technical progress and (changes in) productivitymeasurement is very vast and long-standing, proceeding from many, and verydifferent, theoretical and empirical approaches. A comprehensive review ofsuch a literature is out of the scope of the present paper; however, it is worthdevoting some time to one specific debate which is exactly the starting pointand the inspiration of this paper.

At the end of the 1950s, Robert Solow published his famous paper ‘Tech-nical Change and the Aggregate Production Function’ (1957), in which hedescribed “an elementary way of segregating variations in output per headdue to technical change from those due to the availability of capital per head”(Solow 1957, p. 312). The paper was an attempt to make an explicit dis-tinction between shifts in the aggregate production function and movementsalong it, also providing an empirical application for the US economy between1909 and 1949.

Based on Hicks’ classification, Solow considered “[s]hifts in the produc-tion function [. . . ] as neutral if they leave marginal rates of substitution un-touched [. . . ], simply increas[ing] or decreas[ing] the output attainable fromgiven inputs” (Solow 1957, p. 312). His conclusions were that in the periodconsidered shifts in the production function had been almost neutral, withan acceleration of technical change after 1929. More precisely, over the wholeperiod output per man hours doubled, with 12.5% of this increase due to ahigher capital-labour ratio and 87.5% due to ‘technical change’ — the wellknown Solow’s residual.

Pasinetti’s comment on Solow’s argument came two years later in theReview of Economics and Statistics (Pasinetti 1959, ‘On Concepts and Mea-sures of Changes in Productivity’), criticising Solow’s attempt to evaluatetechnical change “and to introduce capital into the picture by making useof theoretical notions like the production function”, since “these attempts[. . . ] have neglected an important characteristic of capital — that it is repro-

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ducible and that its process of production is also subject to technical change”(Pasinetti 1959, p. 270).

But Pasinetti did not limit himself to criticise Solow’s theoretical ap-proach, clearly in sharp contrast with his own. He also put forward a method-ological proposal for dealing with the issue of technical change in a morecomplete and consistent way, and then implemented it for the case of the USeconomy between 1929 and 1950 — i.e. the period in which Solow recognisedan acceleration of technical progress accompanied by an increase in capitalintensity.

More specifically, Pasinetti considered not only the process of producingfinal (consumption) commodities, but also that of producing the correspond-ing productive capacity. In this way, he derived a simple index of the directionof technical change by computing the variation in the ratio of output per manhours in the consumption goods sector to the hypothetical output per manhours that would be necessary to reproduce the corresponding productivecapacity. When such a ratio is constant through time technical progress isneutral in the sense of Harrod.1 On the contrary, changes in such a ratioreflect capital or labour saving technical progress, according to their sign.

We can notice that Pasinetti adopted Harrod’s — and not Hicks’ as Solowdid — classification of technical progress. As he pointed out, the latter crite-rion “only conveys the information that technical progress takes place exclu-sively in the capital goods producing sector. [. . . ] The richest [. . . ] [criterion]for ‘neutrality’ — in terms of information content — seems therefore to be thefirst one [. . . ] which conveys information on the effects of technical progresson capital-intensity, i.e. on the proportion between the labour which mustbe locked-up in the means of production and the labour which is currentlyrequired” (Pasinetti 1981, p. 214).

Moreover, Solow identified capital intensity with the capital-labour ratio,which Pasinetti calls ‘degree of mechanisation’, while for Pasinetti capital in-tensity is given by the capital-net output ratio. In fact, when this distinctionis recognised:

Solow’s conclusions are therefore ambiguous and contradictory. Whatone can simply say is that the technological change that took place in theU.S. economy, from 1909 to 1949, was accompanied by an increase in thedegree of mechanisation (and not in capital intensity), and by a decrease(not an increase!) in capital intensity.

(Pasinetti 1981, p. 184n)

Solow’s reply and Pasinetti’s rejoinder appeared on the very same issueof the Review of Economics and Statistics.

1See the discussion in Harrod (1973, pp. 52-57).

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Solow argued that Pasinetti’s method cannot be accurate in general, theonly exception being the irrelevant case “when Q is produced by K and L infixed proportions, and no one ever wastes any K or L” (Pasinetti 1959, p. 283,Solow’s Comment). Moreover, he pointed out that Pasinetti’s “doubling thenumber of the commodities in the model increases its realism by 100 per cent[. . . ] [I]f there are really 1,000 commodities worth distinguishing we onlydecrease the unrealism by about one-tenth of one per cent” (Pasinetti 1959,p. 283, Solow’s Comment).

However, in explicitly considering productive capacity, Pasinetti is notgoing from a one- to a two-sector model, but rather accounting for the factthat technical change takes place also in the production of capital goods, andthat this has implications that must be acknowledged:

My position on this issue is not one of more or less aggregation [. . . ]What I do say is that, at whatever level of aggregation our analysis maybe carried on, [. . . ] an evaluation of changes in productivity cannot leavewithout an explicit consideration the technical change which may occur inthe production process of capital”.

(Pasinetti 1959, pp. 285-6)

Solow also rejects Pasinetti’s statement that technical change in the cap-ital goods industry is always capital-saving for the consumption goods in-dustry. In fact, his idea on this issue is the traditional neoclassical one,i.e. technical progress in the production of productive capacity does not savelabour:

[w]hat it saves is an abstract “waiting”. It now takes less saving to adda robot to the stock of capital than it did before.

(Pasinetti 1959, p. 284, Solow’s Comment)

It is our contention that one of the main drawbacks of many — bothmarginalist and other — analyses of technical change is that they fail inrecognising changes in productivity as a physical, technological, phenomenon.Interestingly enough, Solow’s comment to the quotation above is that it “isa true statement and an interesting statement. But it mixes up, as suchstatement must, technological and non-technological facts” (Pasinetti 1959,p. 284). Solow is referring to the fact that changes in the composition ofdemand influence Pasinetti’s aggregate measure of technical change, and alsothat changes in the rate of profit result in non-neutral changes.

What Solow points out is of course true: any aggregate measure is influ-enced by changes in the sectoral composition of the economic system — fromhere the necessity of moving to sectoral measures. Moreover, changes in therate of profit of course cause changes in capital intensity. However, Pasinetti’s

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idea of measuring and classifying technical progress is strongly based, as wewill see below, on the evolution of physical quantities. This point is raisedin a very effective way in Pasinetti’s reply to Solow’s Comment:

[A]part from short-run fluctuations, by far the largest part of changesin productivity over time have been shown to be due to technical changeand only to a minor extent to changes in income distribution. I have simplysuggested, therefore, an approach that focuses the investigation on the firstcause, as opposed to the neo-classical analysis which focuses it on the second.

(Pasinetti 1959, p. 285)

As will be seen in more detail, Pasinetti’s (1959) paper, and the followingdebate with Solow, already contains, though sometimes in a still naive andembryonic way, many ideas and insights that will be further developed andincorporated in his approach to the analysis of structural economic dynamicsand technical progress (Pasinetti 1973, Pasinetti 1981, Pasinetti 1988).

The 1959 paper came back to the fore again forty years later, in 1998,when a note written by Richard Stone in 1960 was posthumously publishedin Structural Change and Economic Dynamics. Stone’s note starts fromPasinetti’s (1959) original measure of productivity, setting it up in input-output terms. The last paragraph of such a note is particularly relevant forour purposes:

In this analysis consumption and assets used up are reduced to theirlabour content and in this way made comparable. Technical progress is saidto be capital saving, neutral or labour saving according as β1/β0 ≷ 1. Thepoint of this note is that such statements can be based on data which areactually being provided by input-output analysts without any reference tothe form of production functions except at the specific points of time undercomparison.

(Stone 1998[1960], p. 231)

The publication of Stone’s (1998[1960]) note caused a further exchangebetween Pasinetti and Solow, showing that the original sources of disagree-ment had not disappeared in the course of those 40 years. But there clearlyemerges that Pasinetti’s (1959) paper has been written in the very same pe-riod in which he was working on his PhD Thesis, the first elaboration of hisvertically hyper-integrated framework. Far away from being two indepen-dent works, they are two faces of the same coin, reflecting the intellectualturmoil that would have led to the formulation of the idea of vertical hyper-integration itself. Richard Stone, in 1960, had perfectly foreseen the naturaldevelopment of Pasinetti’s (1959) analytical apparatus: setting it up intoinput-output terms.

It is also quite clear that writing this paper has been a very importantstep in the genesis of Pasinetti’s approach to economic analysis:

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My 1959 paper [. . . ] originated as a paper for a seminar at the HarvardEconomic Research Project, directed by Wassily Leontief, who was one of mysupervisors while I was at Harvard University.


Leontief’s legacy, as well as Sraffa’s, is absolutely evident when carefullyanalysing Pasinetti’s work.

1.1 Pasinetti’s original measure

Pasinetti’s (1959) analysis — as hinted at above — departs from Solow’s(1957) paper, precisely from an analysis of technical progress “along tradi-tional lines”. Solow is criticised for not having considered the reproduciblecharacter of capital, and therefore the fact that technical progress can takeplace in its production too.

Thus, Pasinetti provides an extension of the analysis also including theproduction of productive capacity. He abandons a ‘real’ measure of capital,defining it in terms of capacity, i.e. with reference to the final (consumption)commodity for whose production process it is employed. First of all, “[t]heunit of measurement with which capital is [usually] measured is itself notindependent of the rate of profit” (Pasinetti 1959, p. 271). But more im-portantly, this redefinition allows to focus attention, when dealing with theproblem of measuring productivity changes, on the evolution of three ratios:Q/L, C/N and C/Q, where C is the capacity necessary for reproducing Q,Q is the quantity of the consumption commodity which is actually produced,L is the (direct) labour employed in its production process and N is thequantity of labour which would be necessary in order to reproduce the wholeexisting productive capacity.

Pasinetti (1959, p. 273) proposes to evaluate the direction of technicalchange by analysing the (relative) movements through time of Q/L and C/N ,i.e. by computing the ratio:

β =Q/L

C/N(1.1)

If a unit of capacity is defined as the composite commodity requiredexactly to reproduce one unit of the consumption commodity at the timeobservations are made, then there will be as many units of capacity as thereare units of the consumption good in the net output. Therefore Q = C, thelast ratio, Q/C, is constant through time and equal to unity, and β becomes:

β =Q/L

C/N

∣∣∣∣Q=C

=N

L(1.2)

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According as to whether d ln β T 0, technical change is labour-saving,

neutral or capital-saving, respectively. Pasinetti (1959) bases his notion ofneutrality on Harrod’s conception (Pasinetti 1959, p. 274). To see this, hederives an equation for the value at current (production) prices of outputof consumption goods and an equation for the value at current prices ofproductive capacity:

pqQ = (τ + r)pcC + waqQ (1.3)

pcC = wakC (1.4)

where aq = L/Q, ak = N/C and τ (assuming linear depreciation) stands forthe reciprocal of the length of life of the capital good.2

According to Harrod, in fact, the direction of technical progress can beclassified on the basis of the movements of the capital/net output ratio for aconstant profit rate:

κ =pcC

pqQ=

akC

(τ + r)akC + aqQ=

N

(τ + r)N + L(1.5)

Notice that when r is constant through time:

d lnκ =κ

βd ln β (1.6)

i.e., the direction of changes in the capital/net output ratio κ always corre-sponds to the direction of movement of the index of technical change β.

1.2 Shortcomings of the original measure

The original index β proposed and measured by Pasinetti suffers from someshortcomings due to both the simplifying assumptions he adopted and thekind of data used for its computation.

First of all, it must be stressed that Pasinetti chose not to use Input-Output data, but rather aggregate figures from National Accounts. This isquite understandable given the aim of the paper, which was basically intendedto be a critique of Solow’s (neoclassical) approach to the study of technicalprogress, and not an empirical analysis of the phenomenon. Since the aim wastheoretical, rather than specifically empirical, it was much more convenient

2These equations can be derived either within a traditional neoclassical framework,using an aggregate production function whose factors are paid their marginal products,or, “perhaps much better, in other theoretical frameworks, such as the Leontief modelsor the dynamic growth models which pay more attention to fixed coefficients and to idlecapacity” (Pasinetti 1959, p. 275).

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to use as manageable data as possible and to accordingly choose consistentsimplifying assumptions.

Pasinetti assumes that all industries in the economic system produce ei-ther a capital or a consumption commodity. Moreover, he also implicitlyassumes that capital goods are produced by means of labour alone — infact, these are the very same assumptions that Pasinetti adopted in his doc-toral thesis and in his 1981 book. The analogy becomes clearer when wecompare equations (1.3) and (1.4) with the price equations of a growing sub-system with the technology of Pasinetti (1981): they share exactly the samecharacteristics.3

Clearly, while these assumptions can be accepted within a work aimingat reaching theoretical conclusions, when adopted in an empirical analysisthey lead to results which are crude approximations of the magnitudes thatare to be computed.

Moreover, and closely connected to the kind of data used for computa-tions, the analysis carried out in Pasinetti’s (1959) paper is an aggregateone. No sectoral measures are proposed or computed. This choice is not ofcourse due to Pasinetti’s denial of the importance of multisectoral analyses,but to the fact that performing an analysis of that kind was beyond the aimand scope of the paper — as stressed by Pasinetti himself in the quotationprovided at page 5: “My position on this issue is not one of more or lessaggregation” (Pasinetti 1959, p. 285). Nonetheless, it is clear — especiallywhen one considers Pasinetti’s more recent scientific production — that go-ing from an aggregate to a multi-sectoral analysis is the natural developmentof the approach suggested in the paper we are discussing. And it is also clear— especially when one reads Stone’s (1998[1960]) paper — that translatingPasinetti’s (1959) framework into input-output terms is the way of improvingit and giving it new life.

Finally, Pasinetti’s original index of technical change mainly depends onnominal, rather than physical, magnitudes — quite obviously, given the re-strictions imposed by the kind of data used for the estimation of β. Theamount of labour that would be necessary for the reproduction of the exist-ing capital stock (N) is estimated as the ratio of the capital stock at current

3In fact, by combining the equation sets (II.5.4) and (II.6.3) in Pasinetti (1981, pp. 39-41), the price equations for a growing subsystem i are:

piXi = (1/Ti + πi)pkiXki + waniXi (1.7)

pkiXki = wankiXki (1.8)

with τi = 1/Ti (the reciprocal of the length of life of the subsystem-specific capital goodi). The parallel with equations 1.3 and 1.4 becomes apparent.

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prices to the average wage in the capital-producing sector. The latter is ob-tained as the ratio of the wage bill in the capital-producing industries to thecorresponding labour force.

By calling K the value at current prices of the existing stock of capital;W and WM the total wage bill and the wage bill in the capital goods sector,respectively; with w and wM the corresponding average wage rates; and Mthe employment in the capital goods sector, one can write:

wM =WM

M, N =

K

wM= K

M

WM

and therefore

β =N

L=K

L

M

WM

=K

W

(M

L

W

WM

)Therefore, when computed in this way, β is given by the product of twocomponents: the capital/wages ratio and a scale factor. Looking at this scalefactor more in detail, we see that in its turn is the product of two components:the ratio of employment in investment goods industry to employment in theconsumption goods industry, and the ratio of overall wage bill to the wagebill of the capital goods industry. In this way, not only β strongly dependson nominal magnitudes, but it is also going to show a co-movement with thecapital/wages ratio.

In fact, by reproducing Pasinetti’s (1959) original empirical exercise forthe Italian economy between 1980 and 2007, this co-movement clearly ap-pears, as displayed by figure 1.

The solid line representing the fixed-capital-net-output ratio (K/Q) expe-riences only mild changes (less than ± 5 p.p. from 1985 onwards), while thefixed-capital-wages ratio (the dashed line K/W ) increases until mid 1980s,remains nearly constant until the beginning of 1990s, and sharply increasesafterwards. As to β (the two-dashed line), though being close to K/Q dur-ing the first ten years, this is no longer so afterwards and, in fact, β clearlyco-moves with K/W during the whole period.

1.3 Towards a reformulation

The above mentioned shortcomings are basically connected with Pasinetti’s(1959) empirical implementation of his theoretical ideas. The necessity ofusing manageable data in order to get ready estimates also compelled thechoice of the simplifying assumptions and forced the computation of roughapproximations of the theoretical magnitudes.

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Figure 1: Dynamics of Fixed Capital to Wages (K/W), Fixed Capital toNet-Output (K/Q) and β (beta) for Italy 1980-2007

It is our contention, however, that the ideas at the basis of Pasinetti’s(1959) theoretical proposal are correct and worth being developed with theaid of the theoretical developments that followed on the one hand, and input-output data and techniques, on the other.

In particular, we want to stress four theoretical features of Pasinetti’s(1959) proposal which deserve particular attention — and which have thenbeen further developed by Pasinetti himself.

First of all, an analysis of technical change cannot deny the fact thatprogress does not only take place in the production of consumption commodi-ties, but also affects the process of (re)production of capital goods. Stressingthe importance of this phenomenon — in sharp contrast with the neoclassicalapproach followed by Solow (1957) — was the principal aim of Pasinetti’s(1959) paper.

Secondly, and closely connected to the previous point, Pasinetti (1959)uses a definition of net output different from the traditional one, includingonly consumption commodities.4 New investments, together with replace-

4In fact, note that when he computes the ‘capital-output’ ratio in Pasinetti (1959,p. 277, Table 2) the values 3.125595 (for 1929) and 2.6574374 (for 1950) are computedwith Q (net output) taken to be real consumption goods production, and not consumptionplus gross investment demand.

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2 A reformulation of Pasinetti’s original measure

ments, are part of the means of production and not of the net product. Thisidea has been very important in the elaboration of the concept of growingsubsystems, and allowed Pasinetti to go into dynamic analysis and studyingthe problem of capital accumulation.

Another feature which has been introduced in the 1959 article, thoughpresent throughout Pasinetti’s works, is that of measuring the stock of capi-tal in terms of units of productive capacity, rather than in ordinary physicalunits. In this way, it is possible to study the problem of capital accumu-lation separately from that of the composition of the stock of capital itself,and in close connection with the evolution of final demand for consumptioncommodities.

Finally, and most importantly, productivity accounting must be based onthe evolution of physical, and not nominal, magnitudes. In fact, the conceptof productivity is a purely physical-technical one, and the measurement of itsevolution through time has nothing to do with changes in income distributionand market prices.

In order to develop this ideas and implement them empirically, we aregoing to reformulate the analytical apparatus incorporating more recent the-oretical developments and taking into account the intrinsically multisectoralnature of productivity measures.

First, we are going to change the kind of data used for computing produc-tivity measures. In particular, we will use input-output data. More specifi-cally, in order to incorporate pure joint production from the very beginning,we will use the set of Supply-Use Tables (SUT) instead of single-productInput-Output Tables.

Second, we will change the unit of analysis: our sectoral measures willnot be computed at the single-industry level, but will refer to growing sub-systems, i.e. to vertically hyper-integrated sectors (see Pasinetti 1988). Thisstep is the analytical counterpart of incorporating the above mentioned re-definition of the concept of net output: as will be seen in section 2.1, in fact,this very redefinition is at the basis of the hyper-integrated repartition ofeconomic activities leading to the — analytical — construction of growingsubsystems.


Before going into the details of the present reformulation, it is worth spend-ing a few lines for introducing the basic notation. The choice was that ofkeeping as close as possible to the standard notation used in Input-Outputliterature when referring to magnitudes coming from the System of National

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Accounts. While presenting, in section 2.1, the method of (growing) sub-systems, the correspondences with respect to the original notation used byPasinetti (1973) and Pasinetti (1988) — i.e. the two articles in which he devel-oped the concepts of vertical integration and hyper-integration, respectively— will be detailed.

In order not to make notation too heavy, we are going to distinguish aphysical-quantity matrix from the corresponding one in nominal terms simplyby adding the subscript q; moreover, in general, almost all magnitudes willrefer to time period t; in case of exceptions, the time lag i with respect totime period t will be indicated with the subscript ±i. So, for example, whilematrix U will denote the stock of circulating capital, evaluated at currentprices, in time period t, matrix Uq(−1) will denote the stock of circulatingcapital, in physical terms, referring to time period t−1. In the same way, allmagnitudes without different specification will be intended as domesticallyproduced ones; in all cases in which it will be necessary to refer to theimported part or to the total, i.e. the sum of domestically produced andimported part, of any magnitude, we will do it by means of the superscriptsm and ∗, respectively.

The accounting framework representing our point of departure can there-fore be set up in terms of the following magnitudes — all matrices being(commodity × activity) square ones:

U: matrix of circulating capital inputs;V: matrix of gross outputs;Fk: matrix of gross fixed capital formation;fc: final consumption in nominal terms. It is the sum of three components:

private consumption (fcp), public expenditure (fg), and exports (fx);c: final consumption in physical terms;e: vector of activity intensities, in our case a sum vector, i.e. a vector of

ones;ei: vector with a 1 in the i-th position, all other elements being zeros;l: vector of total employment;

K: matrix of gross stocks of fixed capital;Jk: matrix new investment in fixed capital;J: matrix of new investment in circulating capital;

ps: vector of statistical basic prices;R: matrix of retirements of fixed capital inputs.

2.1 The method of (growing) subsystems

In this section, we compute vertically integrated and vertically hyper-integratedsectors, respectively, starting from a set of Supply-Use Tables.

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In order to do so, we start from the material product balances. Grossoutputs are identically equal to:

Vqe ≡ Uqe + Fkqe + c (2.1)

while the stock of fixed capital, both domestically produced and imported,is identically equal to:

Kq ≡ Kq(−1) + Fkq − Rq (2.2)

Kmq ≡ Km

q(−1) + Fmkq − Rm

q

i.e. to the stock inherited from the previous period plus gross investmentsundertaken in the present period minus retirements. To put it in anotherway, the increase in the stock of fixed capital is given by gross investmentsnet of retirements:

Kq − Kq(−1) ≡ Fkq − Rq (2.3)

Kmq − Km

q(−1) ≡ Fmkq − Rm

q

Vertically integrated sectors

Establishing a correspondence between the theoretical magnitudes appearingin Pasinetti’s (1973) article on vertical integration is not a straightforwardtask due to complications implied by the presence of imported commodi-ties (including capital goods), and by the treatment of fixed capital, whichalso involves the distinction between retirements and replacements and theseparation between the latter and new investments.

It is however possible to set up an initial correspondence by neglectingfor a moment the role of imported commodities5 and assuming, as Pasinetti(1973) does, that replacements are constant through time.

In this way, the material product balance (2.1) can be written as:

Vqe = Uqe − Uq(−1)e + Uq(−1)e + Rqe + Jkqe + c =

= Jqe + Uq(−1)e + Rqe + Jkqe + c (2.4)

5Removing this assumption will entail difficulties only as regards fixed capital, since thetreatment of circulating capital is not complicated by the presence of imports. In fact, thestock of circulating capital at the beginning of each productive period is simply given bythe quantity of circulating capital bought by each industry in the previous one. NationalAccounts always separate domestic purchases from imports, and domestic commoditybalances have to take into account circulating capital goods which have actually beenproduced for intermediate uses.

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from which we get:

(Vq − Uq(−1) − Rq)e = Jqe + Jkqe + c (2.5)

We can now compare expression (2.5) with the original system appearingin Pasinetti (1973).6

The first apparent difference is a consequence of introducing pure jointproduction. Specifically, the original vector of gross quantities, X(t), is herereplaced by the unitary vector of activity intensities e. Accordingly, theoriginal identity matrix — in (I − A) — is here replaced by the matrix ofgross outputs.

Matrix A := (A(C)+A(F )δ), “representing that part of the initial stocksof capital goods that are actually used up each year by the production pro-cess” (Pasinetti 1973, p. 4) is given, in our formulation, by (Uq(−1) + Rq).

Here we come to an important point. Matrix Uq is not the same as matrixA(C) of input requirements of circulating capital per unit of gross output. Infact, the Use Table collected by statistical institutes “includes all non-durablegoods and services with an expected life of less than one year which are usedup in the process of production by industries” (EUROSTAT 2008, p. 146),and is obtained by measuring the transactions effectively carried out duringthe accounting period net of changes in inventories of circulating capital.Thus, it cannot be taken to represent the nominal counterpart of a matrix oftechnical coefficients, as growth is implicitly contained in it. It is not possibleto separate the unitary input requirements from the level of operation of eachindustry in observed empirical structures.

Therefore, such transactions include both the circulating capital that goesto replace the commodities actually used up, and those intermediate inputsthat are purchased in order to expand production in the following period.This means that:

Uq = A(C)X(t) + Jq

6 The original expression is (see Pasinetti 1973, expression (2.1), p. 4):(I − A

)X(t) = Y(t)

where:

A := A(C) + A(F )

A := A(C) + A(F )δ

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and therefore:

Uq(−1) = A(C)(−1)X(t− 1) + Jq(−1) = A(C)X(t)

Before removing the above mentioned simplifications and going back tothe general case, it is worth devoting a few lines to the explanation of ourchoice not to consider depreciation as a measure of replacements.

Depreciation is a book-keeping concept, belonging to the value-added sideof the economy. As such, it does not have a physical counterpart. Accordingto book-keeping (linear) depreciation schemes, when a new machine is boughtand enters productive capacity, in order not to alter the cost/profits relationin the corresponding accounting period, an estimate of its life-time is made.The value of the machine is then split into as many parts as its estimatedlife-time, and thus spread over the whole period, in order to smooth theassociated increase of the costs of production. This has nothing to do withthe purely physical concept of replacements, which instead pertain exclusivelyto the expenditure side of the system, having as physical counterpart thematerial product balance equations.7

Expressions (2.2) and (2.3), are important in order to understand theconceptual distinction between retirements and replacements.

Current retirements, contrary to replacements, do not affect the magni-tude of gross investments; they emerge at the end of the production period,after investments have been undertaken, but before determining the compo-sition of the stock of fixed capital available at the end of the period.

In other words, at the beginning of the production period, the availablestock of fixed capital is given by Kq(−1), i.e. by the stock of capital measuredat the end of the previous period after accounting for retirements. Then, grossinvestments are undertaken, and go to increase the initial stock. At the endof the time period, before measuring the final stock, obsolete machines areretired and thus retirements accounted for in the determination of the finalstock of fixed capital.

Replacements, on the contrary, do determine the amount of gross invest-ment, being one of its components. From an empirical point of view, wemight say that replacements are given by retirements measured at the end ofperiod t − 1, i.e. Rq(−1).

8 In this way, current total (domestically produced

7In his 1959 paper, Pasinetti had already noticed that “[a]ll quantities could be inter-preted in net terms but, since depreciation allowances always contain elements of arbi-trariness, it is better to work with gross quantities” (Pasinetti 1959, p. 275). This issuebecomes even more crucial in the discussion of vertical hyper-integration, as will be madeclear below.

8It could be objected that this amounts to assuming continuous full utilisation of pro-

16


plus imported) gross investments can be written as:

F∗kq = R∗q(−1) + J∗kq (2.6)

However, the problem is that, while in the case of retirements — i.e. ofexpressions (2.2) and (2.3) — it is perfectly possible to separate domesti-cally produced from imported components, in the case of replacements —i.e. of expression (2.6) for gross investments — there is a lagged variable,and therefore this separation is not possible anymore.

In fact, with reference to period t − 1, we can separate the retirementsof domestically produced machines (Rq(−1)) from those of imported ones(Rm

q(−1)), but we cannot consistently state that these retirements correspondto replacements of domestically produced and imported machines in the fol-lowing, i.e. the current, period. It might well be that part of the retiredmachines previously domestically produced are now imported, and vice versa.

In passing from a period to the following one, therefore, the correspon-dence between retirements in t− 1 and replacements in t can be establishedonly for the total stock of fixed capital, without distinction.9

In analytical terms, when talking about retirements in period t − 1 wewould consistently write:

R∗q(−1) ≡ Rq(−1) + Rmq(−1)

while, when talking of replacements in period t, we would ideally write:

R∗q(−1) ≡ Θ ⊗ R∗q(−1) + (I − Θ) ⊗ R∗q(−1)

where ⊗ indicates element-wise matrix multiplication.The elements of Θ and of I − Θ are the proportions of all the machines

retired in t − 1 that will be replaced in t by domestically produced and by

ductive capacity. However, to conceive a self-replacement situation as one in which ob-solete machines become replaced by new ones automatically translates into negative newinvestment, if not enough capacity is being created.

9We are implicitly assuming that all gestation periods correspond to one production pe-riod. This is not a realistic assumption. Removing it would imply a series of complicationsregarding the analytical formulation and the data requirements for estimates. Moreover,the column of gross fixed capital formation of the Use Table — as empirically imple-mented — contains only acquisition less disposal of fixed assets, while work-in-progress(which constitute production during the current accounting period in need of further pro-cessing to be sellable) are instead included in the vector of changes in inventories (fordetails, see EUROSTAT 2008, pp. 154-6). Hence, applying uniform gestation period databy commodity on gross fixed capital formation would not be an accurate procedure.

17


imported machines, respectively. However, matrix Θ is seldom ever avail-able in empirical terms, so that actually we cannot separate domestic fromimported replacements.

This represents a problem when operating at the vertically integratedlevel, since the construction of self-replacing subsystems requires to be ableto isolate the net product, which is given by the final demand for consumptioncommodities and domestically produced new investments.

In order to overcome this difficulty, we make an assumption that, thoughbeing in some respects arbitrary, is in our opinion better than assumingthat retirements — and thus replacements — are constant through time,both as regards the domestically produced as well as the imported stock offixed capital. More precisely, we will assume that, for each commodity, theproportion of imported (domestic) replacements to total retirements of theprevious period is the same as the proportion of imported (domestic) to totalfixed capital gross investment. Thus, we estimate a diagonal replacement-proportions matrix θ as follows:

θ = fkq

(f∗kq

)−1

(I − θ) = fmkq

(f∗kq

)−1

where:

fkq = Fkqe; fmkq = Fmkqe; f∗kq = F∗kqe

and, therefore, domestically produced and imported gross investment matri-ces are given by:

Fkq = θR∗q(−1) + Jkq (2.7)

Fmkq = (I − θ)R∗q(−1) + Jmkq

We can now go back to expression (2.4) and, using expression (2.7), writeit as:

Vqe = Uq(−1)e + Jqe + Jkqe + θR∗q(−1)e + c

which, rearranging, leads to:

e =(Vq − Uq(−1) − θR∗q(−1)

)−1 (Jqe + Jkqe + c

)(2.8)

It is now possible to define, by taking advantage of expression (2.8), theconcepts of vertically integrated productive capacity and labour, respectively:

S∗kqe =(K∗q(−1) + U∗q(−1)

)e =

=(K∗q(−1) + U∗q(−1)

) (Vq − Uq(−1) − θR∗q(−1)


)=

= H(Jqe + Jkqe + c

)18


and

L = lTe =

= lT(Vq − Uq(−1) − θR∗q(−1)


)=

= νT(Jqe + Jkqe + c

)where:

H :=(K∗q(−1) + U∗q(−1)

) (Vq − Uq(−1) − θR∗q(−1)

)−1(2.9)

is the matrix of vertically integrated productive capacity, and:

νT := lT(Vq − Uq(−1) − θR∗q(−1)

)−1(2.10)

is the vector of vertically integrated labour coefficients.Let us also define the total quantity of labour employed in each vertically

integrated sector i as:L(i)ν = νT yei = νiyi (2.11)

where y = Jqe + Jkqe + c is the net product vector.Note that the units of productive capacity (the columns of H = [hi]) con-

sist of both domestically produced and imported stock matrices of circulatingand fixed capital inputs. This will also hold in the vertically hyper-integratedcase.

Clearly, National Accounts do not include physical, but only nominalmagnitudes. This means that our actual commodity balance is

Ve = U(−1)e + Je + Jke + θR∗(−1)e + fc

i.e.

psVqe = ps(Uq(−1)e + Jqe + Jkqe + θR∗q(−1)e + c

)Therefore, the absolute magnitudes we can actually compute depend on

statistical prices:

psHp−1s = ps

(K∗q(−1) + U∗q(−1)

) (Vq − Uq(−1) − θR∗q(−1)

)−1p−1s

νT p−1s = lT

(Vq − Uq(−1) − θR∗q(−1)

)−1p−1s

But this is not so for variations through time of the vector of verticallyintegrated labour coefficients and of the units of vertically integrated pro-ductive capacity — i.e. of the columns of matrix H. In fact, since data allow

19


us to express all periods’ magnitudes at constant prices, when computingvariations through time the effect of prices vanishes:(

νT p−1s − νT

(−1)p−1s

)ps(ν(−1))

−1 =(νT − νT

(−1)

)(ν(−1))

−1

pj(hj(−1))−1p−1

s

(pshjp

−1j − pshj(−1)p

−1j

)= (hj(−1))

−1(hj − hj(−1)

)Vertically hyper-integrated sectors

Recovering data for building vertically hyper-integrated sectors is much eas-ier, in empirical terms, than for vertically integrated ones. In fact, buildinggrowing sub-systems requires first of all a redefinition of the concept of netoutput, involving demand for final consumption commodity only; all invest-ments, and not only replacements, are part of the means of production, andtherefore there is no need to estimate the current replacements matrix inorder to separate the two components of gross investment as we did in ex-pression (2.7).

In order to arrive to the vertically hyper-integrated formulation, we canstart straightforwardly from expression (2.1), i.e. from our initial materialproduct balance:

Vqe ≡ Uqe + Fkqe + c (2.1)

To find a correspondence between our formulation and Pasinetti’s (1988)original one, it is necessary to take into account that Pasinetti treated fixedcapital as a joint product, in the tradition of Sraffa (1960).10 Instead, weadopt an empirically more tractable procedure, working with gross fixedcapital formation and fixed capital stock matrices, though incorporating purejoint production.

As we stressed at the beginning of the section devoted to vertical integra-tion, matrix Uq — and also Fkq — already include growth; i.e. they involveboth replacements and new investments. Therefore, our statistical outlay— based, it is worth stressing the point again, on transactions that actu-ally took place during the whole accounting period — is much more suitablefor vertically hyper-integrated analyses than for vertically integrated ones.The separation between replacements and new investments, which alwayshas to be estimated and therefore is always somewhat artificial, is not at allnecessary here. In fact:

10The original expression is (see Pasinetti 1989, expression (2.1a), p. 479):

AX(t) + gAX(t) + C(t) + A∑

riX(i)(t) = BX(t)

20


[w]ith technical change going on, each machine is never replaced by anexact similar physical machine, and this makes it impossible to say what isthat is replaced and kept intact. Measurement in terms of units of [hyper-integrated] productive capacity overcomes this possibility.


Therefore, the vector of operation intensities X(t) is here replaced by theunitary vector e and B corresponds to Vq. The most apparent differenceis represented by the fact that it is not possible to find a one-to-one corre-spondence between Pasinetti’s (1989) matrices A, gA, A

∑riX

(i)(t) and ourmatrices Uq and Fkq , but rather:

Uqe + Fkqe = AX(t) + gAX(t) + A∑

riX(i)(t)

Once this correspondence has been established, we can directly write:

e =(Vq − Uq − Fkq

)−1c

S∗kqe =(K∗q(−1) + U∗q(−1)

) (Vq − Uq − Fkq

)−1c = Mc (2.12)

L = lT(Vq − Uq − Fkq

)−1c = ηTc (2.13)

where:

M :=(K∗q(−1) + U∗q(−1)


)−1(2.14)

is the matrix of vertically hyper-integrated productive capacities, and

ηT := lT(Vq − Uq − Fkq

)−1(2.15)

is the vector of vertically hyper-integrated labour coefficients.Let us also define the total quantity of labour employed in each vertically

hyper-integrated sector i as:

L(i)η = ηT cei = ηici (2.16)

Moreover, note that:

n∑i=1

L(i)η =

n∑i=1

ηT cei = ηT cn∑i=1

ei = ηT ce = ηTc = L (2.17)

i.e. growing subsystems exhaust total employment of the economy.11

11It is straightforward to see that this also holds for self-replacing subsystems, i.e. ver-tically integrated sectors.

21


Also in this case, since we are starting from a nominal product balance,we cannot compute M and ηT , but rather:

psMp−1s = ps

(K∗q(−1) + U∗q(−1)


)−1p−1s

ηT p−1s = lT

(Vq − Uq − Fkq

)−1p−1s

However, as in the previous case, computing changes through time allowsto get rid of the price effects:(

ηT p−1s − ηT(−1)p

−1s

)ps(η(−1))

−1 =(ηT − ηT(−1)

)(η(−1))

−1

pj(mj(−1))−1p−1

s

(psmjp

−1j − psmj(−1)p

−1j

)= (mj(−1))

−1(mj − mj(−1)

)where mj is the j-th column of matrix M.

2.2 Measures of changes in productivity

On the basis of the methods described in section 2.1, we are therefore goingto compute a series of vertically (hyper-)integrated measures of changes inlabour productivity — both at the sectoral level and for the economic systemas a whole — and a sectoral and an aggregate index of the direction oftechnical change.

In order to ease exposition, we will give the analytical formulation of theabove mentioned measures of labour productivity in absolute terms. We havealready shown, in the previous section, that computing variations make theinfluence of prices to disappear, so that it is not necessary to repeat the proofhere.

The labour productivity of each vertically integrated sector i is given bythe ratio of the net product — in this case given by consumption and newinvestments: yi = eTi Jqe + eTi Jkqe + ci — to total labour force employed inthe vertically integrated sector itself:

α(i)ν =

yi

L(i)ν

=yiνiyi

=1

νi=(lT(Vq − Uq(−1) − θR∗q(−1)

)−1ei

)−1

In the same way, labour productivity in each vertically hyper-integratedsector i is given by the ratio of the net product, which in this case consistsof final consumption only, to the total labour force employed in the sector asa whole:

α(i)η =

ci

L(i)η

=ciηici

=1

ηi=(lT(Vq − Uq − Fkq

)−1ei

)−1

22


Another sectoral measure of labour productivity, which we compute invertically hyper-integrated terms only, is

N (i)η = ηTmici (2.18)

i.e. the quantity of co-existing vertically hyper-integrated labour that wouldbe necessary for the reproduction of the existing productive capacity withthe technique actually in use.

The last measure of labour productivity is an aggregate one, i.e. Pasinetti’s(1981) standard rate of growth of productivity, though computed in verticallyhyper integrated terms and within a complete inter-industry relations frame-work:

ρ∗ =

∑ni=1 L

(i)η dlnα

(i)η∑n

i=1 L(i)η

=n∑i=1

L(i)η

Ldlnα(i)

η (2.19)

The standard rate of growth of productivity is therefore given by the weightedaverage of the rate of growth of labour productivity in the different verticallyhyper-integrated sectors, the weights being the ratio of total labour employedin the corresponding growing subsystem to total labour in the economicsystem as a whole.

Finally, we are going to compute an aggregate index and a set of sectoralindexes of the direction of technical change, both being re-elaborations ofPasinetti’s (1959) original index β. As we are going to see in a moment, in thiscase it is possible to compute absolute levels rather than variations throughtime. In fact, all these indexes are ratios of vertically hyper-integrated labournecessary for the production of the net output, i.e. of final consumption, tovertically hyper-integrated co-existing labour for the reproduction of the ex-isting productive capacity, either aggregate or sectoral, as given by expression(2.18).

In particular, the economy-wide index is given by:

β∗ =Q/L

C/N=N

L=

∑iN

(i)η∑

i L(i)η

=ηTMc

ηTc(2.20)

while the disaggregated index for each vertically hyper-integrated sector i

23


is:12

β(i) =ci/L

(i)η

ci/N(i)η

=N

(i)η

L(i)η

=ηTmiciηici

=ηTmi

ηi(2.21)

The aggregate measure is obtained starting from Pasinetti’s (1959) orig-inal formulation, but computing N and L consistently with the verticallyhyper-integrated framework exposed above. In this way, the major short-coming of the original measure — i.e. that of depending on nominal, ratherthan physical, magnitudes — is overcome. The fact of co-moving with thecapital/wages — rather than with the capital/output — ratio was a directconsequence on the way in which N and L were estimated, and therefore thisshortcoming is overcome by the present formulation too.

As to the sectoral indexes, their formulation is the obvious extensionof the aggregate one. Clearly, this extension is straightforward once input-output data are used. Moreover, it is worth stressing that while the aggregatemeasure also depends on the composition of demand, and thus its movementsthrough time also depend on changes in such a composition, the sectoralindexes are intrinsically technical, since they are independent of the structureof consumption.

12 It is straightforward to show that the absolute level of both measures can be computedstarting from nominal magnitudes, since the effect of prices cancels out:

ηT p−1s psMp−1s psc

ηT p−1s psc=

ηTMc

ηTc= β∗

ηT p−1s psmip−1i

ηip−1i

=ηTmi

ηi= β(i)

24

3 An empirical exploration


Having derived a set of sectoral and aggregate computable measures of pro-ductivity increase and direction of technical change, this section reports theresults of their empirical application to study the Italian economy during1999-2007. Data has been obtained from the Italian National Institute ofStatistics (ISTAT).

In particular, after singling out some aggregate features of the processof technological development (section 3.1), a more detailed analysis at thesectoral level is performed (sections 3.2 and 3.3) and, finally, a comparisonbetween hyper-integrated labour productivity changes and (Input-Output)Total Factor Productivity Growth (TFPG) is reported (section 3.4).

3.1 Aggregate Trends

Tables 2 and 3 display levels and rates of change, respectively, of selectedaggregate variables for the period 1999-2007. Their description is given inTable 1.

For the aim of analysing co-movement trends among variables, the fullperiod 1999-2007 is divided into three sub-periods: 1999-2000, 2000-2003 and2003-2007. The first two years are presumably the end of a trend that comesfrom previous years, the 2000-2003 sub-period is characterised by negativeproductivity growth (as measured by ρ∗, and computed according to (2.19)),while the contrary occurs in the final 2003-2007 sub-period.

The transition between 1999 and 2000 is characterised by the highestvalues for ρ∗ (2.46 p.p.) and ρtfp (1.76 p.p.) of the whole period, i.e. highproductivity growth and increasing surplus from the value added side. Thishas been accompanied by a mild decrease in the wage share ΩW and realwage rate w/c∗p, together with the highest increase in employment (1.80 p.p.)between 1999 and 2007.

Moreover, note that the ratio of the money wage rate to the price ofthe average consumption basket (w/c∗p) experiences a decrease (from 1.88 to1.83). Thus, given that the money wage rate and employment are increasing,this must be due to the rising consumption per-capita.

The sub-period 2000-2003 is characterised by negative productivity growthas well as a decrease in the real wage rate though accompanied by a mild in-crease in the wage share. The ratio of the money wage to average per-capitaconsumption remains constant with a rising money wage rate and employ-ment, indicating an increase in nominal per-capita (average) consumption.

25

3 An empirical explorationT

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(mln

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/th

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620.8

621.5

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(%)

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60.3

30.1

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(pp

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26


Between 2000 and 2003, capital intensity of the system shows the high-est increase of the whole period, either measured at current statistical prices(S∗/C) or by using vertically hyper-integrated labour coefficients as aggrega-tors (β∗), so the direction of technical change has clearly been non-neutral.

The negative trend of productivity growth is reverted in the 2003-2007sub-period, though experiencing continuous decline. The rhythm of employ-ment creation has also been reduced though the real wage rate has experi-enced the highest increase of the whole 1999-2007 period during 2003-2006.Real wage increase with mild wage share increase have been accompanied bya rising trend in the ratio of money wage rate to per-capita average consump-tion. Technical change has been capital intensity-increasing (both S∗/C andβ∗ have risen), though to a lesser extent than during 2000-2003.

It is interesting to ask to what extent productivity increases (as measuredby ρ∗) have accrued to real wage growth (as measured by ∆%(w/c∗p)). Forthe whole 1999-2007 period, ρ∗ has exceeded ∆%(w/c∗p) by a yearly averageof 0.25 p.p., though it is interesting to notice that when productivity is falling(2000-2003), the real wage decreases to a lesser extent (their yearly averagedifference is -0.53 p.p.). Hence, productivity movements amplify those of thereal wage rate in both directions, though the overall trend suggests that only60% of productivity growth accrues to wages, on average.

Finally, it emerges from Table 3 that when Pasinetti’s (1959) originalmeasure β is replaced by β∗ (as defined in (2.20)), its co-movement and orderof magnitude clearly resembles the ratio S∗/C of total capacity (domesticallyproduced plus imported) to net output (of the growing subsystem).13

3.2 Industry/Subsystem Trends

The structure of the economic system by industry, vertically inte-grated and vertically hyper-integrated sectors

Tables 16, 17 and 18 in Appendix A display the percentage distribution oflabour by industry, vertically integrated (VI, hereinafter) sector and verti-cally hyper-integrated (VHI, hereinafter) sector, respectively. The first con-clusion that can be drawn by looking at these tables is that, whatever therepartition of economic activities, the structure of employment (at this aggre-gation level) has not undergone radical changes. Therefore, Table 4 reportsthe average values (across years) for the whole 1999-2007 period.

It is interesting to compare the distribution of labour among different ac-tivities when industries, VI sectors and VHI sectors are alternatively adoptedas the unit of analysis, as displayed in columns (1), (2) and (3) of Table 4.

13Their correlation coefficient between 2000 and 2007 is 0.978.

27


Table 4: Employment/Labour (re)distribution by Industry/Subsystem, Italy(average 1999-2007), (1)-(3) in average % and (4) in yearly average percentagepoints (p.p.)

Lj/L L(i)ν /L L

(i)η /L L

(i)η /L− Lj/L

(1) (2) (3) (4)

AA:Agriculture 5.65 1.49 1.92 −3.73BB:Fishing 0.24 0.19 0.19 −0.05CB:Mining non-energy 0.14 0.03 0.03 −0.10DA:Food-Tobacco 1.92 5.35 5.72 3.80DB:Textiles 2.48 3.62 3.75 1.27DC:Leather 0.80 1.24 1.32 0.52DD:Wood 0.75 0.19 0.19 −0.56DE:Paper-Printing 1.11 0.88 0.98 −0.13DF:Coke-Petroleum 0.11 0.21 0.29 0.18DG:Chemicals 0.86 1.30 1.43 0.57DH:Plastics 0.86 0.59 0.67 −0.19DI:Non-met. minerals 1.06 0.67 0.70 −0.36DJ:Metals 3.52 1.78 1.78 −1.73DK:Machinery n.e.c. 2.50 4.18 3.87 1.36DL:Electr. Machinery 1.88 1.81 1.54 −0.33DM:Transport Equip. 1.12 1.79 1.84 0.72DN:Manufacture n.e.c. 1.31 1.85 1.92 0.60EE:Energy 0.56 0.58 0.73 0.17FF:Construction 7.38 7.97 0.63 −6.75GG:Trade 14.48 15.41 16.03 1.55HH:Hotel-Restaurant 5.69 7.28 7.87 2.19II:Transport-Comm. 6.52 4.94 5.42 −1.10JJ:Finance 2.49 1.51 1.58 −0.91KK:Business Services 10.73 6.90 8.81 −1.92LL:Public Admin. 5.85 7.69 9.20 3.35MM:Education 6.54 6.56 6.76 0.23NN:Health 6.10 7.45 7.91 1.80OO:Personal Services 4.07 3.27 3.64 −0.44PP:Household Services 3.28 3.26 3.28 0.00

Source: Own computation based on Supply-Use Tables (SUT) and National Accounts Data, ISTAT

In doing so, it is important to keep in mind that in the first case we areconsidering as output those composite commodities jointly produced by thevarious industries, while in the latter two cases we are considering the singlecommodities produced as the main output by the corresponding industry.

In all three cases, it is possible to note that six industries/subsystemsaccount for about 50% of total labour. The results are summarised in thefirst part of Table 5.

On a first inspection of Table 5, we can see that the concentration oflabour in the first six activities is higher at the VI sector- rather than at the

28


Table 5: Labour distribution: Industry-level, VIS-level and VHIS-level (Italy,average 1999-2007)

Pos. Industry Cum. % VI sector Cum. % VHI sector Cum. %1 GG:Trade 14.48 GG:Trade 15.41 GG:Trade 16.032 KK:Business

Services25.21 FF:Construction 23.38 LL:Public

Admin.25.23

3 FF:Construction 32.59 LL:PublicAdmin.

31.07 KK:BusinessServices

34.04

4 MM:Education 39.13 NN:Health 38.52 NN:Health 41.955 II:Transport-

Comm.45.65 HH:Hotel-

Restaurant45.80 HH:Hotel-

Restaurant49.82

6 NN:Health 51.75 KK:BusinessServices

52.70 MM:Education 56.58

Source: Table 4.

Activity % as Industry % as VI sector % as VHI sectorFF:Construction 7.38 7.97 0.63DA:Food-Tobacco 1.92 5.35 5.36AA:Agriculture 5.65 1.49 1.92

Source: Table 4.

industry-level, and further increases when VHI sectors are chosen as unit ofanalysis.

Activities GG:Trade, KK:Business Services and NN:Health are present inall three cases, though in different positions (with the exception of GG:Tradewhich is always the most important activity). If we extended our table toinclude the first eight — rather than six — positions, LL:Public Admin.,HH:Hotels-Restaurant and MM:Education would also be among the mostimportant activities in all three cases.

The only, though very sharp, difference is represented by FF:Construction,which is one of the main industries as well as VI sectors (with a very similarrelative importance). However, when looking at Table 4, we can see that itis a very small VHI sector, employing only 0.63% of total labour. From thiswe infer that FF:Construction is an activity employing mostly direct labour,which explains the similarity when looked at as an industry and as a VI sec-tor, and that almost all of its output consists of means of production used byother activities. This result is particularly interesting. Were we to use thepresent analysis to evaluate, for example, the opportunity of public invest-ment aiming at sustaining employment in the economic system, a traditionalinter-industry analysis would lead us to conclude that by investing in thissector it would be possible to give rise to a number of backward linkages inthe economic system as a whole. On the contrary, stating the analysis inVHI terms allows us to see that this would not be an adequate conclusion.

29


Moreover, there are two further activities characterised by a relevantchange in their relative position when the unit of analysis is changed (ascan be seen in the second part of Table 5). The first one is DA:Food-Tobacco,which increases considerably its labour participation when seen as a (grow-ing) subsystem instead of as an industry. This clearly means that it is asubsystem which absorbs labour from other activities, and thus has a strongindirect labour component.14

The second one is AA:Agriculture, which is in an opposite situation: itis much more important when looked at as an industry than as a (grow-ing) subsystem. This means that a considerable part of the gross outputof the corresponding industry is used as intermediate commodities by otheractivities (e.g. DA:Food-Tobacco).

Finally, there are three VHI sectors that changed in an apparent waytheir relative weight in labour distribution during the period as a whole:KK:Business Services (increasing from 7.91 to 9.62%); DB:Textiles (decreas-ing from 4.19 to 3.11%); and DN:Manufacture n.e.c. (declining from 2.19 to1.63%).

Redistribution of labour between industry and growing subsystem

Table 19 in Appendix A reports the yearly redistribution of labour that takesplace when the unit of analysis is switched from the industry to the growingsubsystem. Moreover, column (4) of Table 4 displays the mean value forthe whole 1999-2007 period. Due to the stable character of redistributionpatterns through time, we focus on the average value across years.

Given the different output concept to which industry and subsystemlabour refer to, the same total employment L is redistributed in the logicaloperation of hyper-integration, partitioning the system into as many parts asthere are final commodities. Hence, L

(i)η reflects the total labour required to

reproduce a unit of commodity i for final uses, this labour coming both fromthe industries directly producing it and from all the supporting industriesproviding inputs for them.

Redistribution patterns allow to identify which growing subsystems mainlyprovide (L

(i)η − Lj < 0, j = i) or absorb (L

(i)η − Lj > 0, j = i) labour, as well

as to see the importance of backward linkages exerted by final industries toall their supporting industries.

As can be read from column (4) of Table 4, the transformation of nat-ural resources and primary products into manufactured commodities im-plies a crucial absorption of labour by subsystems like DA:Food-Tobacco and

14See below, at the end of this section, the analysis of labour redistribution betweenindustries and subsystems, focusing on column (4) of Table 4.

30


DB:Textiles. Moreover, note the dimension of subsystem LL:Public Admin.as a demander of commodities through its backward linkages.

Three important service subsystems (HH:Hotel-Restaurant, NN:Healthand GG:Trade) are among those with highest absorption of labour (togetheradding to 5.54 p.p.). As to manufacturing, DK:Machinery n.e.c. (mainlymechanical machinery), DM:Transport Equip. (the automobile complex),DN:Manufacture n.e.c. (which includes furniture) and DG:Chemicals (whichincludes pharmaceutical products) are among the most relevant growing sub-systems as regards labour absorption.

In contradistinction, the most important provider of labour is clearlyFF:Construction, given that (almost) all its output goes to increase the pro-ductive capacity of the different growing subsystems. As a reflection of theindustrialization of primary products AA:Agriculture is a crucial provider oflabour.

More interesting is the case of service subsystems like KK:Business Ser-vices, II:Transport-Comm. and JJ:Finance, which together add to -3.93 p.p.,and suggests that the demand they exert through backwards linkages toother industries is offset by their role as provider of standardised services toall other industries (including themselves). Moreover, among manufacturingsubsystems DJ:Metals is the most important provider of labour through theintermediate (circulating and fixed) capital inputs it sells to other industries,assuming a role of crucial provider of intermediate inputs economy-wide.

Employment and gross output dynamics by industry

Table 20 in Appendix A reports year-by-year industry employment dynamics(∆%Lj) and gross output growth by commodity (∆%qi) during the consid-ered period. Moreover, columns (1)-(2) of Table 6 display yearly averagevalues for these variables across years.

On a yearly average basis, the five industries with highest increase inemployment are KK:Business Services (3.70 p.p.), FF:Construction (2.98p.p.), PP:Household services (2.86 p.p.), HH:Hotel-Restaurant (2.50 p.p.)and OO:Personal Services (1.97 p.p.).

By looking more in detail the year-by-year performance of the threemain activities (as displayed in Table 20 of Appendix A), it emerges thatKK:Business Services started from an important increase in the first period(1999-2000, 7.17 p.p.), progressively slowed down up to 2004-2005 (1.34 p.p.)and then accelerated again until the end of the period, though being far awayfrom the initial value (2.98 p.p. in 2006-2007). Employment in HH:Hotel-Restaurant also increased considerably in the first period (7.75 p.p.), thenslowed down, though being still quite sustained, up to 2003-2004, experienc-

31


ing very modest increases (around 0.30 p.p. yearly) in the last four years.Finally, FF:Construction did not show a definite trend, with employment dis-playing an oscillating behaviour, with its minimum in 2005-2006 (1.20 p.p.)and its maximum in 2000-2001 (2.98 p.p.).

The five industries that, on the contrary, saw the greatest decline intheir employment on a yearly average basis are DC:Leather (-2.87 p.p.),DB:Textiles (-2.47 p.p.), AA:Agriculture (-1.70 p.p.), DD:Wood (-1.51 p.p.)and DH:Plastics (-1.37 p.p.).

Column (2) of Table 6 conveys information about changes in gross out-put by commodity, which can be compared to that regarding employmentdynamics. The result is that PP:Household services is the only industry thatis among the five most dynamics activities as regards both employment andoutput growth; on the contrary, four of the industries with worst employ-ment performance are also among the five industries whose output declinedthe most: DC:Leather (-2.87 p.p.), DB:Textiles (-2.47 p.p.), AA:Agriculture(-1.70 p.p.) and DH:Plastics (-1.37 p.p.).

VI and VHI labour productivity dynamics

Tables 21 and 22 in Appendix A report year-by-year dynamics of VI andVHI labour productivity (∆%α

(i)ν and ∆%α

(i)η , respectively) together with the

corresponding net output growth (∆%yi and ∆%ci, respectively). Moreover,Tables 23 and 24 in Appendix A report changes in total labour at the VIand VHI sector level (∆%L

(i)ν and ∆%L

(i)η , respectively). Additionally, mean

values across years for each of these variables are reported in columns (3)-(8) of Table 6. When looking at year-by-year changes, recall that for eachVI/VHI sector i, respectively:

∆%L(i)ν = ∆%yi − ∆%α(i)

ν (3.1)

∆%L(i)η = ∆%ci − ∆%α(i)

η (3.2)

Expression (3.1) is a ‘spurious’ decomposition: changes in yi are due tochanges in both final demand for consumption commodities and for newinvestment goods. But the process of reproduction of capital goods is it-self subject to technical change, so that changes in vertically integrated netoutput are also influenced by changes in productivity, i.e. by the second ad-dendum of the decomposition. On the contrary, expression (3.2) correctlyseparates the effect of changes in the composition of effective demand forfinal uses from the effects of technical progress on total subsystem employ-ment, thereby separating what re-enters from what does not re-enter thecircular flow. Hence, it is ∆%L

(i)η that displays the structural dynamics of

employment as intended by Pasinetti (1981, pp. 94-7).

32


able

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33


Given that VI and VHI labour productivity changes crucially depend onemployment trends, it is useful to draw conclusions on the basis of the jointdynamics of labour productivity and total labour by VI and VHI sector,respectively. By combining positive and negative values for each variable,four typologies can be distinguished. The results of such an inspection aresummarised in Table 7.

Table 7: Activity classification by the joint dynamics of labour productivityand total labour by VI and VHI sectors (average values for 1999-2007)

Vertically integrated (VI) sectors

∆%L(i)ν > 0 ∆%L

(i)ν < 0

∆%α(i)ν > 0 DG, DH, DJ, DK, JJ, LL, MM,

NN, PPDB, DC, DD, DI, DL

∆%α(i)ν < 0 BB, CB, DA, DE, DF, EE, FF,

GG, HH, KK, OOAA, DM, DN

Vertically hyper-integrated (VHI) sectors

∆%L(i)η > 0 ∆%L

(i)η < 0

∆%α(i)η > 0 AA, CB, DA, DE, DG, DH, DJ,

DK, DM, GG, II, JJ, MM, NN,PP

DB, DC, DD, DI, DL, DN, LL

∆%α(i)η < 0 BB, DF, EE, HH, KK, OO FF

Source: Table 6.

The activities in the upper-left quadrant in each tabulation of the Tablecorrespond to ‘virtuous’ sectors: they are characterised by increasing labourproductivity and employment. The ones in the bottom-left quadrant, onthe contrary, are ‘vicious’ sectors: they saw a decrease of both labour pro-ductivity and employment. Then, we have those activities which increasedproductivity but decreased employment, at the bottom-right quadrant, andthose where the opposite has occurred, in the upper-left one.

Let us start by analysing the dynamics of vertically integrated labour pro-ductivity. As can be seen from Table 7, there are nine ‘virtuous’ and three‘vicious’ VI sectors. The virtuous ones include diffused intermediate inputslike DG:Chemicals and DH:Plastics, as well as the metals-mechanical machin-ery complex (DJ:Metals and DK:Machinery n.e.c.). As to services, we haveJJ:Finance, LL:Public Admin., MM:Education, NN:Health and PP:HouseholdsServices, two of which (LL:Public Admin. and NN:Health) are also amongthe most important as to their share in total employment. Altogether,on average, these nine subsystems account for 34.68% (37.25% in 2000,38.17% in 2006) of total employment. Instead, the three vicious sectors areAA:Agriculture, DM:Transport Equip. and DN:Manufacture n.e.c., which,on average, account for 5.13% of total employment (5.50% in 2000, 3.82% in

34


2006).Let us now look at vertically hyper-integrated labour productivity (sec-

ond tabulation of Table 7). In this case, there is only one vicious sector(FF:Construction) and 15 virtuous ones, which altogether accounted for63.95% (in 1999) and 63.05% (in 2007) of total employment (62.97% onaverage). Some virtuous growing subsystems are virtuous in VI terms aswell (DG, DH, DJ, DK, JJ, MM, NN and PP); while AA:Agriculture andDM:Transport Equip. are instead classified as vicious VI sectors. This sug-gests that the increase in employment and productivity in the productionof new investment goods in these growing subsystems was strong enough asto counterbalance the opposite trend in the reproduction of the verticallyintegrated net product.

However, besides looking at the dynamics of labour productivity as asingle magnitude, it would also be informative to decompose each verticallyhyper-integrated labour coefficient into a direct and an (hyper-) indirect com-ponent. In order to do so, note that from the definition of ηT in (2.13), it ispossible to obtain for each final commodity i:

ηi = ηTei = lTV−1q ei + lTV−1

q (Uq + Fkq)(Vq − Uq − Fkq)−1ei (3.3)

where each addendum in the RHS of the equation may be defined as:

η(i)d ≡ lTV−1

q ei

η(i)hy ≡ lTV−1

q (Uq + Fkq)(Vq − Uq − Fkq)−1ei

The first addendum (η(i)d ) represents the direct labour employed by all

industries producing commodity i, while the second addendum (η(i)hy) stands

for the indirect and hyper-indirect labour requirements to reproduce a unitof commodity i for final uses.

Accordingly, define α(i)η,d = 1/η

(i)d and α

(i)η,hy = 1/η

(i)hy , and by noting that

α(i)η = 1/ηi so that d lnα

(i)η = −d ln ηi = −d ln(η

(i)d + η

(i)hy) it is possible to

write for each growing subsystem i:

d lnα(i)η = ωη,dd lnα

(i)η,d + (1 − ωη,d)d lnα

(i)η,hy (3.4)

where ωη,d = η(i)d /ηi, i.e. the share of direct labour in total vertically hyper-

integrated labour per unit of net output.In terms of a first order approximation, expression (3.4) becomes:

∆%α(i)η = ωη,d∆%α

(i)η,d + (1 − ωη,d)∆%α

(i)η,hy (3.5)

35


Hence, it is possible to explore to what extent the total change in hyper-integrated labour productivity (∆%α

(i)η ) is due to a direct labour saving

effect (∆%α(i)η,d) or to an (hyper-) indirect effect (∆%α

(i)η,hy), weighted by the

importance of direct labour within each growing subsystem (ωη,d).Table 25 in Appendix A reports the decomposition of hyper-integrated

labour productivity changes into its direct and (hyper-) indirect components,together with the share ωη,d, for selected years (1999-2000, 2003-2004, and2006-2007). Additionally, columns (8)-(11) of Table 6 display the mean valuesacross years of these variables.

By using this information, it is possible to classify sectors according tothe joint dynamics of these variables, as reported by Table 8.

Table 8: Activity classification by the joint dynamics of direct and (hyper-)indirect components of productivity changes (average values for 1999-2007)

∆ω(i)η,d > 0 ∆ω

(i)η,d < 0

∆%α(i)η,d > 0 ∆%α

(i)η,d < 0 ∆%α

(i)η,d > 0 ∆%α

(i)η,d < 0

∆%α(i)η,hy > 0 DG, DD, DA,

DL, DK, DB,DN, DE, MM

FF,HH DC, DH, JJ, II,DM, LL, DI, DJ

∆%α(i)η,hy < 0 BB, KK, OO AA, NN, CB,

GG, EEDF

Source: Table 25 in Appendix A.

Among sectors with an increasing direct component, nine had an overallincrease in productivity, i.e. both their direct and the indirect componentsgrew. As to the two subsystems with increasing indirect and decreasing di-rect productivity (FF:Construction and HH:Hotel-Restaurant), in both casesthe negative direct effect prevailed, so that total VHI labour productivitywas decreasing. The last three sectors with increasing direct componenthad a decreasing VHI productivity (BB:Fishing, KK:Business Services andOO:Personal Services). No sector was characterised by an increasing directproductivity together with a decreasing indirect one.

Among sectors with a decreasing direct component, eight saw an overallincrease in VHI productivity, and only one (DF:Coke-Petroleum) a decrease.No sector is characterised by decreasing direct productivity and increasingindirect one. On the contrary, five sectors behaved in the opposite way.Among them, four (AA:Agriculture, NN:Health, CB:Mining non-energy andGG:Trade) had an increasing overall productivity, and only EE:Energy adecreasing one.

36


3.3 Capital intensity and direction of technical change

As has been emphasized by Pasinetti himself “[i]ndirectness or roundabout-ness of a production process clearly refers to a relation between stocks andflows” (Pasinetti 1981, p. 180). In this sense, capital intensity, as given byβ∗ (computed according to (2.20)) for the economy as a whole or by β(i)

(computed according to (2.21)) for each growing subsystem, is the proposedmeasure to analyse the direction of technical change.15

Table 10 reports year-by-year levels of β(i) for each growing subsystem,together with the mean value across years and the absolute difference betweenthe first (2000) and last (2007) year.

It is interesting to analyse data on capital intensity jointly with VHIlabour productivity. A subdivision into four typologies according to the signof their joint dynamics is displayed in Table 9.

Table 9: Activity classification according to capital intensity and productivitychanges.

∆β(i) > 0 ∆β(i) < 0

∆%α(i)η > 0 AA, CB, DA, DB, DC, DD, DE,

DG, DH, DI, DJ, DK, DL, DM,DN, GG, II, JJ, LL, MM, NN

∆%α(i)η < 0 DF, FF, HH, OO BB, EE, KK

Source: Tables 6 and 10.

As to the direction of technical change, by inspecting Table 9, we no-tice that only three sectors experienced a decrease in capital intensity —i.e. capital saving technical change16 — namely BB:Fishing, EE:Energy andKK:Business Services. The remaining 26 sectors saw an increase in β(i), rang-ing from +0.03 (OO:Personal Services) to +3.29 (DF:Coke-Petroleum).17

Moreover, the three sectors with decreasing capital intensity also saw adecrease in VHI labour productivity. On the contrary, only four of the sectorswith an increasing β(i) had a decreasing productivity — namely, DF:Coke-Petroleum, FF:Construction, HH:Hotel-Restaurant and OO:Personal Ser-vices. All the others have been characterised by increasing capital intensityand VHI labour productivity.

15Instead, the capital labour ratio cannot be taken as an index of capital intensity giventhat, for example, it depends on the standard of value chosen to close the price systemwith which capital inputs are aggregated (for details, see Pasinetti 1981, p. 182).

16By capital saving we mean that the vertically hyper-integrated labour required toreproduce the stock of productive capacity decreases relatively to that required to repro-duce the net output, consistently with our contention that technical progress is ultimatelyalways labour saving.

17Excluding PP:Household services which only employs direct labour.

37


able

10:

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ital

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nsi

ty,

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(i)

act

2000

2001

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38


Given that 22 out of 29 growing subsystems are characterised by in-creasing productivity and capital intensity, it is interesting to classify sectorsaccording to their average performance in terms of productivity and meanlevel of capital intensity with respect to their respective aggregate values.Such classification is reported in Table 11.

Table 11: Activity classification according to capital intensity levels andproductivity changes.

β(i) > β∗ β(i) ≤ β∗

∆%α(i)η > ρ∗ DA, DE, DG, DH, DI, DM, II,

LLAA, DB, DC, DD, DJ, DK, DL,DN, JJ, NN

∆%α(i)η ≤ ρ∗ CB, DF, EE, KK BB, FF, GG, HH, MM, OO, PP

Source: Tables 2, 3, 6, and 10.

Among the most dynamic subsystems (i.e. with both changes in pro-ductivity and level of capital intensity greater than the corresponding aggre-gates) we find a most important Italian traditional manufacturing subsystem(DA:Food-Tobacco), the Chemical-Pharmaceutical cluster (DG:Chemicals),the transport equipment cluster (DH:Plastics, which includes rubber tiresand DM:Transport Equip.) and the information, communication and logis-tics complex (DE:Paper-Printing, II:Transport-Comm.).

As to the least dynamic subsystems (i.e. with both changes in produc-tivity and level of capital intensity lower than the corresponding aggregates)we have FF:Construction, and an important groups of traditional privateservices among which the most important is, of course, GG:Trade.

As to subsystems with higher than average capital intensity and slowerthan average productivity dynamics, we have the mining-energy industries(CB:Mining non-energy, DF:Coke-Petroleum and EE:Energy), as well asKK:Business Services.

Finally, by considering those subsystems with greater than average pro-ductivity growth but lower than average capital intensity, we find a groupof natural resources-based sectors (AA:Agriculture, DB:Textiles, DC:Leather,DD:Wood and DN:Manufacture n.e.c., which mainly includes furniture), rela-tively direct labour intensive service subsystems (JJ:Finance and NN:Health)and the metals-machinery complex (DJ:Metals, DK:Machinery n.e.c. andDL:Electr. Machinery).

At first sight, the metals-machinery complex might seem to be an ex-ception with respect to the other two groups, which are basically employingdirect labour. The reason is that the output of this complex (i.e. the denom-inator of capital intensity) consist itself of capital goods. Moreover, we cannotice that, restricting our attention to the machinery complex, productivity

39


growth (2.03 p.p. for DK:Machinery n.e.c. and 2.07 p.p. for DL:Elctr. Ma-chinery) is much higher than both the standard rate (ρ∗ = 0.62) and theyearly average real wage rate growth (∆(w/c∗p) = 0.37). This confirms that18

if, in any production process, at a certain point of time, machines aresubstituted for labour, the reason simply is that productivity in the machineproducing sector is increasing faster than the over-all wage rate. This process,again, is entirely independent of any change in the rate of profit.


3.4 Yeast and Mushrooms: hyper-integrated productivity andTFP

From the aggregate dynamics of Table 3 it can be inferred that there existdifferences between the standard rate of productivity growth (ρ∗) and (Input-Output) TFP Growth (ρtfp).Clearly, each of these measures comes from adifferent theoretical approach to productivity measurement.

In fact, ρ∗ is an aggregate measure of physical productivity changes ob-tained from the system of expenditure (i.e. from the nominal counterpart of aset of material product balances), having vertically hyper-integrated labourcontent at its root. Being derived from a system of physical quantities itonly considers commodities domestically produced, as it aims to measurethe degree of the division of labour required to reproduce the net output ofthe system. At its disaggregated level, it refers to the growing subsystem asits unit of analysis.

Instead, ρtfp is an aggregate measure of the monetary surplus (evalu-ated in terms of a standard of value) obtained from the value added side ofan Input-Output system, which considers only circulating capital inputs asreproducible, with fixed capital being a non-produced primary factor. It con-siders both domestically produced and imported commodities, as it simplymeasures the excess of returns over all costs (included that of imports). Atits disaggregated level, it refers to the industry as its unit of analysis.

Given that traditional ‘growth accounting’ exercises are performed interms of TFP Growth19 it is relevant to make a comparison — at a dis-aggregated level — between the results obtained by alternative methods.

Consider first Table 12 reporting the absolute difference (i.e. in percentagepoints) between industry TFP Growth rate (ρtfp,j) and subsystem rate of

18See page 49 in section 4 for a discussion of this point.19Note, however, that most treatments do not even consider the reproducible character of

intermediate (circulating capital) inputs, given that they depart from a national accountingnet income identity, considering industry value added (instead of gross output) as a physicalmeasure of disaggregated net product (for details, see Wolff 1994, pp. 77-80).

40


hyper-integrated labour productivity change (∆%α(j)η ). Results should be

interpreted with care given that the unit of analysis in each case differs.

Table 12: Difference between Industry TFPG and Hyper-Subsystem LabourProductivity Growth, Italy - ρtfp,j − ∆%α

(j)η (pp)

act 99-00 00-01 01-02 02-03 03-04 04-05 05-06 06-07 meanDF:Coke-Petroleum 0.06 −12.74 6.90 19.29 29.21 7.96 9.31 −16.92 5.38KK:Business Services 2.08 2.90 2.21 −0.15 0.82 1.81 0.24 0.53 1.30EE:Energy −1.18 6.09 2.28 5.22 −12.34 −3.32 0.39 5.36 0.31PP:Household Services 0.07 0.17 0.06 −0.01 0.26 0.21 0.19 0.21 0.14OO:Personal Services 0.77 3.05 1.07 −0.27 −5.13 1.08 0.82 −0.26 0.14FF:Construction −1.15 0.17 0.81 0.40 −1.21 0.85 −0.68 0.88 0.01BB:Fishing −2.09 1.81 1.51 −3.27 1.30 −1.28 0.44 0.68 −0.11HH:Hotel-Restaurant −1.23 −0.10 1.52 2.09 0.25 −1.44 −0.64 −1.53 −0.13JJ:Finance −1.82 −2.33 1.68 −0.94 1.40 −0.32 0.92 −0.59 −0.25NN:Health −0.85 −0.45 −0.51 0.14 0.36 0.24 −0.58 −0.76 −0.30GG:Trade −0.53 1.33 0.66 −0.29 −1.09 −2.30 0.12 −0.67 −0.35MM:Education 0.49 −2.36 −0.19 −0.82 0.08 −0.61 0.15 0.02 −0.41CB:Mining non-energy −6.03 −5.13 5.83 −0.63 4.25 1.74 −6.20 1.65 −0.57DJ:Metals −3.47 −0.85 1.69 −0.59 −4.50 −0.12 1.51 1.46 −0.61II:Transport-Comm. −2.12 −0.42 −1.35 0.43 −0.77 −0.66 −0.45 −0.40 −0.72AA:Agriculture −0.12 −0.28 0.24 −2.44 2.89 −5.05 0.11 −1.51 −0.77DI:Non-met. minerals −4.59 1.98 2.62 0.08 −2.43 −3.89 −3.12 1.35 −1.00LL:Public Admin. −0.87 0.21 0.00 −0.25 −1.42 −2.31 −1.96 −1.69 −1.04DN:Manufacture n.e.c. −6.30 −0.42 2.24 0.38 −4.13 0.74 −2.18 −0.82 −1.31DE:Paper-Printing −1.36 −2.49 −1.12 −0.48 −2.91 −1.43 −0.52 −0.87 −1.40DM:Transport Equip. −6.85 −1.17 −0.95 −0.75 1.80 −0.03 0.01 −3.40 −1.42DK:Machinery n.e.c. −4.58 −1.49 2.85 −0.42 −4.46 −1.28 −2.65 −0.19 −1.53DL:Electr. Machinery −5.34 0.96 −0.32 0.87 −4.23 −4.09 −1.80 0.01 −1.74DC:Leather −9.73 −0.49 4.00 0.83 −5.28 −1.08 −4.03 1.51 −1.78DB:Textiles −4.64 0.36 −0.55 −0.24 −2.90 −1.71 −5.32 0.53 −1.81DA:Food-Tobacco −4.43 0.30 −1.64 −0.26 −3.08 −3.78 −0.31 −1.35 −1.82DH:Plastics −3.38 −1.46 1.27 −1.08 −6.21 −2.04 −1.55 −2.00 −2.06DD:Wood −5.63 −3.43 3.17 −0.41 −4.99 −4.36 −2.68 −2.34 −2.58DG:Chemicals −8.58 −2.60 7.20 −7.38 −5.40 −2.28 −7.24 0.52 −3.22


On average, with the exception of the first 6 sectors, hyper-integratedlabour productivity changes exceeds TFP Growth. Interestingly though,exceptions are not unrelated: KK:Business Services, OO:Personal Servicesand PP:Household Services represent the core of private service subsystems,EE:Energy and DF:Coke-Petroleum are the two most important energy sec-tors and, finally, FF:Construction is quite special given that when shift-ing from industry to growing subsystem its net product almost vanishes.Moreover, this pattern of differences is not uniform across years, and it canbe noticed that most sign changes agglomerate in particular combinationsof sectors and years (e.g. 2001-2002, and BB:Fishing, HH:Hotel-Restaurant,JJ:Finance, NN:Health in 2003-2004).

The different unit of analysis (industry versus growing subsystem), thecontrasting treatment of produced means of production (fixed capital, inparticular), the dependence on a standard of value in the case of TFPG,

41


the different consideration of imported commodities and, most fundamen-tally, the fact that hyper-integrated labour productivity departs from theexpenditure system rather than from the system of revenue outlay relations(i.e. from a theory of value added), explain the sharp disagreement in theresults obtained.

Thus, rather than focusing on absolute differences in growth rates of iso-lated industries or individual subsystems, it would be desirable to comparethe whole sectoral distribution behind aggregate growth within each alterna-tive method, expecting to see differences in the complete sectoral pattern ofproductivity changes. In order to do so, we follow a methodology introducedby Harberger (1998) for the study of traditional TFP Growth, which consistsin computing the absolute real cost reductions due to productivity increases.

The crucial point in Harberger’s (1998) argument consists in recognisingthe additive nature of TFP improvements, once turned into monetary unitsat base-year prices. Hence, he computed the absolute value added of theinitial year that can be saved by means of proportional increases in TFP.

In our case, instead of measuring real cost reductions in terms of initialvalue added, these will be measured in terms of industry’s gross output val-ued at base year prices (for Input-Output TFP) and in terms of quantitiesof labour (for hyper-integrated labour productivity). Thus, under the sec-ond method real cost reductions translate into an absolute saving of labourrequirements.

Therefore, for TFPG, if Gj(0) = pT

(0)Vqej represents current gross output

of industry j valued at base year (t = 0) Input-Output pricespT

(0), then, thereal cost reduction due to TFP increases is given by:

CStfp,j = Gj(0)

(1 − e−ρtfp,j

), j = 1, . . . , n (3.6)

In contradistinction, if L(i)η represents the total labour of growing subsystem

i and α(i)η is the corresponding level of hyper-integrated labour productivity,

then the absolute saving of labour requirements due to productivity increasesis given by:

LS(i)η = L(i)

η

(1 − e−d lnα

(i)η), i = 1, . . . , n (3.7)

Tables 13 and 14 display real cost reductions (in millions of monetaryunits at base-year prices per year) and absolute saving of labour requirements(in thousand of employment units per year) for Italy (1999-2007) due toincreases in TFP and hyper-integrated productivity growth, respectively.

42


able

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B:F

ish

ing

243.4

6−

287.2

2−

80.3

288.5

0−

150.0

2−

122.8

961.3

1−

38.3

8−

35.7

0D

H:P

last

ics

−210.8

7−

264.0

6530.8

3−

506.9

6281.1

9−

233.9

4118.9

1−

97.8

3−

47.8

4D

E:P

ap

er-P

rinti

ng

137.9

1−

80.2

6−

445.9

1−

506.3

2226.4

5−

59.9

2114.0

881.7

0−

66.5

3F

F:C

on

stru

ctio

n803.8

3229.2

9−

247.9

94.3

362.8

1−

754.0

4269.8

3−

1173.6

5−

100.7

0E

E:E

ner

gy

−1363.5

5561.2

9365.3

4−

174.4

1−

156.8

5−

159.0

0143.4

4−

261.2

2−

130.6

2D

F:C

oke-

Pet

role

um

−328.7

533.8

6254.9

5−

396.9

2−

464.8

5−

298.3

0−

225.5

2129.4

5−

162.0

1H

H:H

ote

l-R

esta

ura

nt

834.2

1−

845.7

5−

3081.6

9−

1828.2

5−

579.8

8214.4

6978.0

8672.8

9−

454.4

9G

G:T

rad

e2138.5

0−

161.4

4−

5317.5

0−

4232.4

21478.8

4789.4

7−

540.0

3519.9

3−

665.5

8K

K:B

usi

nes

sS

ervic

es3061.1

81660.2

03033.0

9−

202.1

8−

4529.3

4−

4531.9

5−

75.9

1−

4436.4

7−

752.6

7O

O:P

erso

nal

Ser

vic

es−

1770.9

8−

1352.1

5−

1612.6

1−

1514.4

21534.3

4−

1750.0

0−

395.3

567.5

0−

849.2

1

Sou

rce:

Ow

nco

mp

uta

tion

base

don

Su

pp

ly-U

seT

ab

les

(SU

T)

an

dN

ati

on

al

Acc

ou

nts

Data

,IS

TA

T

43


able

14:

Abso

lute

lab

our

savin

gin

the

grow

ing

subsy

stem

,It

aly

-LS

(i)

η(t

h.U

LE

per

year

)

act

99-0

000-0

101-0

202-0

303-0

404-0

505-0

606-0

7m

ean

LL

:Pu

blic

Ad

min

.16.6

712.7

411.2

027.6

951.3

464.7

131.7

335.6

631.4

7D

A:F

ood

-Tob

acc

o91.1

7−

19.0

823.6

9−

3.2

735.4

964.5

410.5

324.7

828.4

8II

:Tra

nsp

ort

-Com

m.

60.7

531.2

231.7

5−

7.7

88.8

223.2

3−

3.6

97.8

119.0

1D

K:M

ach

iner

yn

.e.c

.55.3

29.2

3−

38.3

23.2

453.0

012.6

837.0

89.8

917.7

6D

B:T

exti

les

64.1

2−

4.4

3−

6.2

0−

14.5

826.5

816.3

550.9

9−

5.6

015.9

0N

N:H

ealt

h20.7

223.6

33.8

1−

10.6

810.6

122.9

427.5

619.8

614.8

1D

G:C

hem

icals

25.3

96.3

8−

25.0

525.9

822.3

06.7

726.5

1−

1.1

710.8

9M

M:E

du

cati

on

−14.1

733.7

325.6

018.9

57.6

6−

9.4

7−

9.3

57.2

67.5

3D

L:E

lect

r.M

ach

iner

y23.6

9−

1.7

0−

4.3

3−

8.5

520.2

815.4

79.0

02.7

27.0

7D

M:T

ransp

ort

Equ

ip.

35.3

60.5

00.1

00.6

8−

7.4

4−

4.0

48.3

320.0

96.7

0JJ:F

inan

ce16.6

76.9

4−

15.8

12.1

01.2

39.8

25.7

022.7

76.1

8D

N:M

anu

fact

ure

n.e

.c.

37.9

0−

4.2

7−

13.4

9−

8.3

020.1

2−

0.7

013.7

53.9

36.1

2D

C:L

eath

er37.8

04.9

6−

20.4

6−

6.5

816.2

55.6

714.4

1−

3.7

16.0

4G

G:T

rad

e51.8

1−

52.7

7−

100.1

7−

48.9

963.7

199.8

5−

12.2

033.7

14.3

7A

A:A

gri

cult

ure

−9.0

3−

7.0

2−

3.2

75.3

422.8

715.8

8−

8.6

412.7

73.6

1D

H:P

last

ics

4.1

50.9

40.8

9−

0.8

111.3

92.1

33.0

52.6

73.0

5D

J:M

etals

14.6

44.7

8−

6.7

12.2

815.5

21.5

5−

3.0

9−

4.9

23.0

1D

E:P

ap

er-P

rinti

ng

4.1

85.3

4−

0.2

0−

2.1

38.4

52.9

21.9

32.5

02.8

7D

I:N

on

-met

.m

iner

als

9.8

4−

3.5

6−

3.5

6−

3.0

24.4

96.3

65.0

8−

2.7

71.6

1D

D:W

ood

3.6

22.4

2−

2.9

2−

0.1

62.4

21.5

81.3

51.2

81.2

0C

B:M

inin

gn

on

-en

ergy

0.3

50.6

3−

0.4

4−

0.1

3−

0.4

80.1

60.4

5−

0.2

80.0

3P

P:H

ou

seh

old

Ser

vic

es0.6

42.0

3−

0.4

7−

0.2

1−

0.8

2−

0.4

8−

0.2

6−

0.1

80.0

3F

F:C

on

stru

ctio

n2.9

20.0

2−

1.6

2−

0.6

21.9

4−

2.0

41.1

9−

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2−

0.0

8B

B:F

ish

ing

6.0

7−

6.4

6−

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53.2

5−

3.5

4−

2.0

61.2

3−

1.1

7−

0.6

2E

E:E

ner

gy

−3.8

4−

7.3

4−

2.2

1−

10.0

321.8

75.4

2−

0.1

2−

10.8

7−

0.8

9D

F:C

oke-

Pet

role

um

−2.2

97.5

8−

2.4

5−

14.4

9−

26.5

2−

9.3

2−

10.1

713.7

6−

5.4

9H

H:H

ote

l-R

esta

ura

nt

38.6

3−

16.6

1−

97.9

8−

84.4

0−

19.1

833.8

836.5

346.8

9−

7.7

8O

O:P

erso

nal

Ser

vic

es−

27.9

5−

44.2

1−

33.5

7−

21.3

170.3

4−

35.1

1−

13.9

03.5

6−

12.7

7K

K:B

usi

nes

sS

ervic

es−

19.4

4−

46.0

0−

26.1

52.0

2−

44.2

1−

68.1

2−

6.0

5−

40.9

0−

31.1

1

Sou

rce:

Ow

nco

mp

uta

tion

base

don

Su

pp

ly-U

seT

ab

les

(SU

T)

an

dN

ati

on

al

Acc

ou

nts

Data

,IS

TA

T

44


A positive figure in Table 13 means a reduction in real costs, while inTable 14 indicates a saving of labour requirements induced by productivityincreases. Given that total employment has increased, labour saving trendshave been offset by the dynamics of final effective demand by commodity.

It is noticeable that by looking at the top nine and bottom eight indus-tries/subsystems in each Table, there is great similarity as to the sectors withhighest and lowest real cost reductions and absolute labour saving trends.

Among the common industries/subsystems with highest absolute cost im-provements/productivity increases we find II:Transport-Comm., NN:Health,LL:Public Admin. among services, and DA:Food-Tobacco, DK:Machineryn.e.c., DL:Electr. Machinery among manufacturing. As to the sectors withworst performance we find the energy complex (CA:Mining energy, DF:Coke-Petroleum, EE:Energy) and a core of private services (KK:Business Services,OO:Personal Services, HH:Hotel-Restaurant).

A more subtle point is related to the volatility of real cost reductionsacross industries. If, on the basis of Table 13, we compute the coefficient ofvariation (cv)20 across years for each industry, we find that those activitieswith highest (on average) cost reductions have the lowest volatility (as mea-sured by the cv). This suggests that cost-reducing industries have been morepersistent in their performance during the whole 1999-2007 period. A simi-lar point can be made for absolute labour saving across growing subsystems,though to a lesser extent, as there is less dispersion between sectors in thecoefficients of variation across time periods.

This last observation suggests that it would be interesting to study thedegree of concentration of sectoral productivity increases.

To that end, Harberger (1998) introduced a particular Lorenz-curve typeof diagram (a Harberger diagram, hereinafter), that displays the cumulatedabsolute contribution to aggregate growth of each sector (on the y-axis),according to its cumulated share of the initial level variable (on the x-axis).By rescaling the y-axis in such a way that the y-value corresponding tothe x-value of 100% equals the aggregate growth rate, and ordering sectors(in a decreasing order) according to their growth rate, a concave diagramobtains, displaying the disaggregated pattern of absolute contributions tooverall absolute labour saving or real cost reduction.

Harberger diagrams of average trends for both hyper-integrated labourproductivity changes and Input-Output TFP Growth are built using theinformation of Tables 14 and 13, respectively, together with data on pro-ductivity growth rates. Figure 2 displays the respective diagrams for bothhyper-integrated labour productivity changes (VHILPC) and Input-Output

20The coefficient of variation is the ratio between the standard deviation and the mean.

45


TFP Growth (TFPG).Complementarily, in order to characterise the pervasiveness and curvature

of each diagram in Figure 2, two summary statistics due to Inklaar & Timmer(2007, p. 178) are reported in Table 15.21

Table 15: Yeast vs. Mushrooms Patterns, Italy, (average 1999-2007)

Concept ρ Pervasiveness CurvatureVHILPC (ρ∗) 0.62 77.84 0.53TFPG (ρtfp) 0.11 54.88 0.85


Figure 2: Harberger diagrams of Italy for ρ∗ and ρtfp, 1999-2007

It clearly emerges that the pattern depicted by hyper-integrated produc-tivity growth shows a more diffused and balanced character than that of TFPGrowth. The fact that all industries participate in each growing subsystem(though in different proportions) provides a first intuition for this result.However, the contrast is due not only to a change in the unit of analysis, but

21Pervasiveness is measured by the cumulative share of sectors with positive contribu-tions, while the curvature is measured by the ratio A/B, where A is the area betweenthe curve and a straight line connecting the origin with the y-value corresponding to theaggregate growth rate (ρ), and B is the area below the curve. In this way the resultingstatistic is contained between zero and one.

46

4 Summary of findings and concluding remarks

also to the fact that while hyper-integrated productivity growth is a physicalmeasure of labour saving trends, TFPG is defined with reference to a systemof relative prices and captures surplus/deficit conditions in value added perunit of gross output.

Not only ρ∗ is much higher than ρtfp, but also the pervasiveness of hyper-integrated labour productivity is higher than that of TFP Growth, i.e. thecumulative share of sectors increasing labour productivity in total employ-ment is almost 78%, while the cumulative share of industries increasing TFPin gross output at constant prices is only around 55%.

The higher curvature of TFPG suggests a clearly ‘mushroom’ like pattern,where few industries account for the greatest part of overall TFP Growth,while in the VHILPC case the pattern is more ‘yeast’ like. This last featurecan be better illustrated by referring to the two diagrams in Figure 2. Thedashed line splits the curve into two parts. To the left we can see thosesectors/industries whose positive contribution to productivity changes is notcounterbalanced by the negative contributions. In other words, these activ-ities alone could account for the whole aggregate productivity growth. Onthe x-axis, in correspondence to the intersection with the dashed line, we canread the importance of such activities — in terms of the cumulated share ineither total labour or gross output. In the VHILPC case, there are manysectors appearing to the left of the intersection, thus contributing to the pro-ductivity performance of the whole system, and accounting for more than30% of total employment. On the contrary, in the TFPG case, one industryonly — accounting for less than 6% of total gross output — appears to theleft of the intersection (JJ:Finance).


The aim of the present paper has been that of formulating in input-outputterms Pasinetti’s (1959) ideas on the measurement of productivity growth(and the evaluation of technical change), making their vertically hyper-integrated nature explicit.

More efficient computation techniques, data availability allowing for atrue separation between price and volume growth (by means of series of squarecommodity × activity Supply-Use Tables at current and past-year-prices),and the theoretical refinements that Pasinetti himself put forward after hisDoctoral Thesis, have allowed us to compute his original 1959 measure, giveempirical content to his 1981 ‘standard rate of growth of productivity’, aswell as to a set of sectoral measures of capital intensity and vertically (hyper-)integrated labour productivity changes.

47


The analytical operation of vertical hyper-integration aims at separatingthat part of gross output which re-enters the circular flow, i.e. replacementsand new investments of both circulating and fixed capital inputs, from thatwhich does not. Shifting the unit of analysis from industries or verticallyintegrated (VI) sectors to vertically hyper-integrated (VHI) sectors has al-lowed us to reach novel results from both a methodological and an empiricalpoint of view.

An example of such a shift of perspective is represented by the analysis ofVHI employment dynamics, which allows to consistently separate the effectsof changes in the composition of final consumption demand from those oftechnical change (for details see section 3.2, page 32, and Table 6).

Vertical hyper-integration sheds light on the effects of growth on the net-work of inter-industry relations, and unfolds truly comprehensive backwardlinkages in a way which is unattainable not only within industry-level anal-ysis, but also by means of traditional subsystems.

As to the identification of backward linkages, we computed the labour ab-sorption exerted by each growing subsystem from its supporting industries(see column (4) of Table 4). Such a measure allows to quantify employmentcreation that might be stimulated by increases in final demand for differentconsumption commodities.22 Interestingly, we found LL:Public Administra-tion among one of the most important sectors as to hyper-integrated labourabsorption.23

Another outcome of this shift of perspective concerns the quantificationof activities’ relative importance in terms of their share in total employment:activities mainly providing fixed capital inputs see their relative importancesharply reduced when considered as growing subsystems. An example, inthe case analysed by the present paper, is represented by the subsystemFF:Construction (see section 3.2, page 29).

As to the interpretation of the empirical results, the multidimensionalcharacter of the effects of technical change prevents us from finding a uniquescalar synthetic indicator that captures them all. For this reason, differenttypologies have been put forward to study the joint dynamics of the variousmeasures computed.

A first typology was built according to the joint dynamics of VHI em-ployment and labour productivity. In fact, labour saving trends induced by

22Note that final demand for consumption commodities includes private consumptionas well as public consumption and exports.

23This important role of public expenditure in income generation is amplified if weconsider that hyper-integrated backward linkages translate into a wider tax base (andtherefore, tax revenues), allowing for further public stimulus to final demand, generatingfurther income and so on, in a virtuous expenditure-income circle.

48


productivity increases and technological unemployment are two sides of thesame coin. Thus, when both magnitudes are increasing a subsystem can reallybe defined as ‘virtuous’.

Another typology was built according to the sectoral level of capital in-tensity and labour productivity changes relative to their respective aggregatevalues. This classification allowed us to identify, among the most dynamicsubsystems, complexes of importance for the Italian economy like transportequipment and food products.

The patterns emerging from these two typologies suggest that the link be-tween capital intensity and technological unemployment is subtle and shouldbe treated with care.24 In the first place, the ratio of fixed capital to labourshould not be considered as an index of capital intensity but as indicatorof the degree of mechanisation of the system. Secondly, the substitution ofcapital for labour is not the consequence of changing relative ‘factor’ pricestriggering movements along an isoquant, but is instead a dynamic processintimately connected to the hyper-integrated productivity growth of subsys-tems producing machinery with respect to the standard rate of productivitygrowth and the dynamics of the real wage rate. In fact, the increasing degreeof mechanisation in Italy is confirmed by the finding that in the machinerycomplex productivity grows much more than both ρ∗ and the average realwage rate.

Finally, we compared the outcomes of our approach to that of traditionalTFP Growth measurement. As detailed in section 3.4, changing the unit ofanalysis and recognising the purely physical-technical nature of productivityleads to completely different results and conclusions.

Further lines of research open up for exploration. Our very empiricalanalysis had to be restricted to a small set of results, but the computationsperformed would have allowed us to go deeper into many aspects.

Availability of more disaggregated data covering a longer period of timewould have allowed us to draw more detailed conclusions on structural changeand long-term trends of technical progress.25

Another interesting field of investigation is the juxtaposition of verticalhyper-integration and ‘horizontal’, as we might call it, clustering of indus-tries. This might unfold key properties of convoluted multi-regional struc-

24This is clearly not the case in marginalist analyses of technical change, where thesubstitution mechanism conceives capital as an homogeneous quantity with a ‘factor price’(the rate of profits), and suggests an inverse monotonic relation between the capital labourratio and relative ‘factor’ prices (the ratio of the rate of profits to the real wage rate).

25An example is provided by the analysis of changes in capital intensities, which on sucha short period of time (almost a decade) might simply reflect cyclical movements and thepresence of idle productive capacity.

49


tures, where linkages might spread on a territorial dimension. This approachseems particularly promising for the analysis of the Italian productive system,whose core is represented by regional industrial districts.

50

A Detailed Tables for Industries and (Growing) Subsystems

Appendices

A Detailed Tables for Industries and (Growing) Sub-systems

51

A Detailed Tables for Industries and (Growing) SubsystemsT

able

16:

Indust

ryL

abou

rdis

trib

uti

on,

Ital

y-Lj/L

(%)

act

1999

2000

2001

2002

2003

2004

2005

2006

2007

mea

nG

G:T

rad

e14.6

914.5

914.5

714.4

914.5

614.4

514.

31

14.

38

14.

26

14.

48

KK

:Bu

sin

ess

Ser

vic

es9.3

99.9

110.2

110.7

210.9

711.1

311.

26

11.

37

11.

60

10.

73

FF

:Con

stru

ctio

n6.

786.8

87.1

87.2

47.3

97.4

87.

78

7.75

7.91

7.38

MM

:Ed

uca

tion

6.7

16.6

16.6

06.5

76.6

06.4

86.

45

6.43

6.40

6.54

II:T

ran

spor

t-C

omm

.6.5

16.5

16.4

76.4

86.4

96.4

56.

55

6.60

6.64

6.52

NN

:Hea

lth

6.04

6.0

96.0

96.0

76.1

16.1

76.

19

6.10

6.05

6.10

LL

:Pu

bli

cA

dm

in.

6.3

06.2

26.0

95.9

85.7

85.7

35.

64

5.52

5.41

5.85

HH

:Hot

el-R

esta

ura

nt

5.1

95.5

15.5

35.6

35.8

15.9

25.

93

5.85

5.83

5.69

AA

:Agr

icu

ltu

re6.2

96.1

26.0

75.8

05.5

05.4

65.

28

5.26

5.04

5.65

OO

:Per

son

alS

ervic

es3.

953.9

74.0

44.0

24.0

14.0

74.

09

4.24

4.25

4.07

DJ:M

etal

s3.5

63.4

43.4

43.4

43.5

43.4

63.

48

3.61

3.67

3.52

PP

:Hou

seh

old

Ser

vic

es3.1

13.1

03.1

83.2

03.1

73.3

03.

42

3.48

3.59

3.28

DK

:Mac

hin

ery

n.e

.c.

2.47

2.4

72.4

42.4

42.4

92.5

12.

55

2.59

2.57

2.50

JJ:F

inan

ce2.

562.5

12.5

12.4

72.4

42.4

52.

45

2.47

2.52

2.49

DB

:Tex

tile

s2.7

72.7

02.6

62.6

12.5

82.4

52.

30

2.13

2.09

2.48

DA

:Food

-Tob

acco

2.0

41.9

81.8

71.8

81.8

91.9

41.

89

1.89

1.90

1.92

DL

:Ele

ctr.

Mac

hin

ery

1.91

1.9

01.8

51.8

51.8

61.8

41.

88

1.90

1.91

1.88

DN

:Man

ufa

ctu

ren

.e.c

.1.4

01.3

71.3

31.3

21.3

01.2

91.

30

1.26

1.24

1.31

DM

:Tra

nsp

ort

Equ

ip.

1.2

61.2

21.1

41.1

01.0

01.0

71.

06

1.08

1.12

1.12

DE

:Pap

er-P

rinti

ng

1.1

91.1

41.1

21.1

11.1

01.0

91.

08

1.07

1.04

1.11

DI:

Non

-met

.m

iner

als

1.0

81.0

81.0

91.0

91.0

71.0

31.

04

1.00

1.03

1.06

DG

:Ch

emic

als

0.93

0.9

00.8

70.8

80.8

50.8

30.

84

0.83

0.82

0.86

DH

:Pla

stic

s0.9

30.9

20.9

00.9

00.8

80.8

50.

82

0.78

0.77

0.86

DC

:Lea

ther

0.9

30.9

00.8

70.8

40.8

30.7

70.

70

0.67

0.68

0.80

DD

:Wood

0.8

10.8

00.7

80.7

90.7

60.7

40.

69

0.68

0.66

0.75

EE

:En

ergy

0.6

30.6

10.5

80.5

70.5

40.5

30.

53

0.54

0.52

0.56

BB

:Fis

hin

g0.

260.2

50.2

40.2

40.2

20.2

30.

23

0.23

0.23

0.24

CB

:Min

ing

non

-en

ergy

0.15

0.1

40.1

40.1

40.1

30.1

30.

13

0.12

0.12

0.14

DF

:Cok

e-P

etro

leu

m0.1

10.1

10.1

10.1

00.1

00.1

00.

10

0.10

0.11

0.11

CA

:Min

ing

ener

gy0.

030.0

30.0

30.0

40.0

40.0

40.

04

0.04

0.04

0.03

Sou

rce:

Ow

nco

mp

uta

tion

bas

edon

Su

pply

-Use

Tab

les

(SU

T)

an

dN

ati

onal

Acc

ou

nts

Data

,IS

TA

T

52


able

17:

VI

Lab

our

dis

trib

uti

on,

Ital

y-L

(i)

ν/L

(%)

act

2000

2001

2002

2003

2004

2005

2006

mea

nG

G:T

rad

e15.6

715.1

415.1

715.5

815.4

815.

28

15.

55

15.

41

FF

:Con

stru

ctio

n7.

51

8.0

78.0

18.1

78.1

77.

88

7.99

7.97

LL

:Pu

bli

cA

dm

in.

7.9

07.7

67.7

57.6

27.6

27.

70

7.47

7.69

NN

:Hea

lth

7.27

7.1

77.2

67.4

17.5

47.

74

7.76

7.45

HH

:Hot

el-R

esta

ura

nt

6.8

67.3

07.0

47.3

27.3

87.

41

7.67

7.28

KK

:Bu

sin

ess

Ser

vic

es6.6

66.5

37.1

37.0

06.6

66.

86

7.44

6.90

MM

:Ed

uca

tion

6.6

56.7

76.5

76.6

06.4

76.

41

6.46

6.56

DA

:Food

-Tob

acco

5.7

05.4

05.2

05.4

65.1

05.

05

5.55

5.35

II:T

ran

spor

t-C

omm

.5.1

45.0

64.9

14.7

04.7

45.

13

4.87

4.94

DK

:Mac

hin

ery

n.e

.c.

4.21

4.0

94.1

84.1

64.1

94.

11

4.33

4.18

DB

:Tex

tile

s3.8

63.7

43.9

43.7

63.5

73.

39

3.10

3.62

OO

:Per

son

alS

ervic

es2.

95

3.1

33.2

03.3

43.5

53.

22

3.52

3.27

PP

:Hou

seh

old

Ser

vic

es3.1

03.1

83.2

03.1

73.3

03.

42

3.48

3.26

DN

:Man

ufa

ctu

ren

.e.c

.1.9

82.0

11.9

21.8

11.9

31.

71

1.62

1.85

DL

:Ele

ctr.

Mac

hin

ery

2.01

1.9

51.8

61.6

51.7

71.

77

1.69

1.81

DM

:Tra

nsp

ort

Equ

ip.

2.0

21.8

41.8

51.8

01.6

51.

69

1.71

1.79

DJ:M

etal

s1.5

81.8

81.7

61.7

71.5

91.

77

2.08

1.78

JJ:F

inan

ce1.

52

1.5

21.4

31.4

21.4

21.

51

1.71

1.51

AA

:Agr

icu

ltu

re1.5

01.2

61.6

21.4

11.8

92.

28

0.49

1.49

DG

:Ch

emic

als

1.16

1.2

01.4

41.4

11.4

21.

27

1.19

1.30

DC

:Lea

ther

1.4

11.3

91.2

91.2

41.1

61.

11

1.07

1.24

DE

:Pap

er-P

rinti

ng

0.8

80.9

80.7

90.9

00.9

30.

87

0.83

0.88

DI:

Non

-met

.m

iner

als

0.7

60.8

10.7

20.5

80.6

40.

62

0.54

0.67

DH

:Pla

stic

s0.5

70.5

80.7

10.5

50.5

90.

56

0.59

0.59

EE

:En

ergy

0.4

80.5

10.5

90.5

90.6

60.

64

0.61

0.58

DF

:Cok

e-P

etro

leu

m0.2

00.2

10.2

00.1

80.1

80.

21

0.27

0.21

DD

:Wood

0.2

60.2

00.1

50.2

10.2

20.

15

0.17

0.19

BB

:Fis

hin

g0.

19

0.2

50.1

70.1

70.1

60.

17

0.22

0.19

CB

:Min

ing

non

-en

ergy

0.03

0.0

40.0

50.0

10.0

20.

05

0.03

0.03

Sou

rce:

Ow

nco

mp

uta

tion

bas

edon

Su

pply

-Use

Tab

les

(SU

T)

an

dN

ati

onal

Acc

ou

nts

Data

,IS

TA

T

53


able

18:

VH

IL

abou

rdis

trib

uti

on,

Ital

y-L

(i)

η/L

(%)

act

1999

2000

2001

2002

2003

2004

2005

2006

2007

mea

nG

G:T

rad

e16.3

516.1

515.9

515.9

916.1

016.0

415.

74

16.

05

15.

89

16.

03

LL

:Pu

bli

cA

dm

in.

9.5

39.4

29.3

99.4

09.3

69.2

99.

07

8.79

8.57

9.20

KK

:Bu

sin

ess

Ser

vic

es7.9

18.1

68.4

38.6

48.6

98.9

89.

41

9.45

9.62

8.81

NN

:Hea

lth

7.61

7.6

47.6

47.7

57.9

08.1

08.

27

8.16

8.10

7.91

HH

:Hot

el-R

esta

ura

nt

7.2

57.5

87.6

67.8

18.0

38.2

08.

11

8.17

8.07

7.87

MM

:Ed

uca

tion

7.0

56.9

86.8

56.7

76.7

76.6

26.

67

6.61

6.58

6.76

DA

:Food

-Tob

acco

6.2

05.8

55.7

55.7

45.7

25.7

15.

66

5.51

5.36

5.72

II:T

ran

spor

t-C

omm

.5.4

65.3

95.1

85.0

95.3

55.5

45.

57

5.61

5.60

5.42

DK

:Mac

hin

ery

n.e

.c.

3.79

3.8

03.8

73.8

53.8

43.8

43.

78

3.88

4.14

3.87

DB

:Tex

tile

s4.1

94.0

84.1

83.9

83.9

03.6

83.

47

3.17

3.11

3.75

OO

:Per

son

alS

ervic

es3.

223.4

33.6

33.7

33.8

03.5

63.

73

3.83

3.80

3.64

PP

:Hou

seh

old

Ser

vic

es3.1

13.1

03.1

83.2

03.1

73.3

03.

42

3.48

3.59

3.28

AA

:Agr

icu

ltu

re1.9

92.0

12.0

82.0

81.8

71.8

61.

83

1.80

1.76

1.92

DN

:Man

ufa

ctu

ren

.e.c

.2.1

92.1

12.0

52.0

21.9

21.8

51.

78

1.69

1.63

1.92

DM

:Tra

nsp

ort

Equ

ip.

2.0

32.0

41.7

71.7

91.6

71.7

71.

75

1.84

1.91

1.84

DJ:M

etal

s1.5

41.6

61.6

51.6

21.6

31.7

61.

83

2.09

2.28

1.78

JJ:F

inan

ce1.

401.5

21.6

21.5

81.4

81.4

21.

57

1.77

1.87

1.58

DL

:Ele

ctr.

Mac

hin

ery

1.53

1.6

41.6

91.5

31.5

01.4

81.

49

1.51

1.53

1.54

DG

:Ch

emic

als

1.47

1.4

51.5

01.6

51.4

91.3

71.

40

1.29

1.27

1.43

DC

:Lea

ther

1.5

31.4

91.4

61.3

91.3

31.2

51.

16

1.11

1.12

1.32

DE

:Pap

er-P

rinti

ng

1.0

51.0

21.0

00.9

81.0

00.9

50.

96

0.93

0.92

0.98

EE

:En

ergy

0.7

40.6

60.6

80.7

20.8

00.7

70.

76

0.72

0.72

0.73

DI:

Non

-met

.m

iner

als

0.7

60.7

60.7

60.7

40.7

00.6

90.

64

0.61

0.63

0.70

DH

:Pla

stic

s0.6

80.7

00.6

90.6

90.6

80.6

60.

65

0.65

0.64

0.67

FF

:Con

stru

ctio

n0.

700.6

80.6

80.6

50.6

40.5

90.

56

0.57

0.57

0.63

DF

:Cok

e-P

etro

leu

m0.2

90.2

60.2

40.2

30.2

70.3

30.

33

0.33

0.31

0.29

BB

:Fis

hin

g0.

210.2

00.1

80.1

90.1

70.1

80.

18

0.19

0.18

0.19

DD

:Wood

0.2

20.2

10.2

10.2

00.1

90.1

80.

16

0.15

0.14

0.19

CB

:Min

ing

non

-en

ergy

0.03

0.0

30.0

30.0

30.0

30.0

30.

03

0.03

0.03

0.03

CA

:Min

ing

ener

gy0.

000.0

00.0

00.0

00.0

00.0

00.

00

0.00

0.03

0.00

Sou

rce:

Ow

nco

mp

uta

tion

bas

edon

Su

pply

-Use

Tab

les

(SU

T)

an

dN

ati

onal

Acc

ou

nts

Data

,IS

TA

T

54


able

19:

Lab

our

redis

trib

uti

onb

etw

een

Indust

ryan

dG

row

ing

Subsy

stem

,It

aly

-L

(i)

η/L

−Lj/L

(pp)

act

1999

2000

2001

2002

2003

2004

2005

2006

2007

mea

nD

A:F

ood

-Tob

acco

4.1

63.

87

3.88

3.86

3.83

3.77

3.78

3.62

3.46

3.80

LL

:Pu

bli

cA

dm

in.

3.2

23.

20

3.31

3.42

3.58

3.56

3.44

3.27

3.17

3.35

HH

:Hot

el-R

esta

ura

nt

2.0

62.

07

2.13

2.18

2.22

2.27

2.18

2.31

2.25

2.19

NN

:Hea

lth

1.5

71.

54

1.55

1.68

1.79

1.93

2.07

2.06

2.05

1.80

GG

:Tra

de

1.65

1.55

1.38

1.50

1.54

1.58

1.43

1.67

1.63

1.55

DK

:Mac

hin

ery

n.e

.c.

1.32

1.33

1.43

1.42

1.36

1.33

1.23

1.30

1.57

1.36

DB

:Tex

tile

s1.4

21.

38

1.52

1.36

1.33

1.23

1.17

1.04

1.02

1.27

DM

:Tra

nsp

ort

Equ

ip.

0.7

70.

83

0.62

0.69

0.67

0.71

0.68

0.75

0.80

0.72

DN

:Man

ufa

ctu

ren

.e.c

.0.7

90.

74

0.72

0.69

0.63

0.56

0.48

0.43

0.40

0.60

DG

:Ch

emic

als

0.54

0.55

0.63

0.77

0.64

0.54

0.56

0.46

0.45

0.57

DC

:Lea

ther

0.5

90.

58

0.60

0.55

0.50

0.49

0.46

0.44

0.44

0.52

MM

:Ed

uca

tion

0.3

40.

37

0.24

0.20

0.17

0.14

0.23

0.18

0.18

0.23

DF

:Cok

e-P

etro

leum

0.1

70.

15

0.13

0.13

0.17

0.22

0.23

0.23

0.21

0.18

EE

:En

ergy

0.10

0.05

0.10

0.15

0.25

0.24

0.23

0.18

0.21

0.17

PP

:Hou

seh

old

Ser

vic

es0.0

00.

00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

CA

:Min

ing

ener

gy−

0.03

−0.

03

−0.0

3−

0.04

−0.

04

−0.0

4−

0.04

−0.

04

−0.0

1−

0.03

BB

:Fis

hin

g−

0.06

−0.

05

−0.0

6−

0.05

−0.

05

−0.0

5−

0.04

−0.

05

−0.0

5−

0.05

CB

:Min

ing

non

-en

ergy

−0.

12−

0.11

−0.1

1−

0.11

−0.

11

−0.1

0−

0.10

−0.

09

−0.0

9−

0.10

DE

:Pap

er-P

rinti

ng

−0.

14−

0.13

−0.1

2−

0.14

−0.

10

−0.1

4−

0.11

−0.

14

−0.1

3−

0.13

DH

:Pla

stic

s−

0.25

−0.

23

−0.2

1−

0.21

−0.1

9−

0.18

−0.

16

−0.1

3−

0.13

−0.

19

DL

:Ele

ctr.

Mac

hin

ery

−0.

38−

0.2

7−

0.16

−0.

32

−0.3

6−

0.36

−0.

39

−0.3

9−

0.38

−0.

33

DI:

Non

-met

.m

iner

als

−0.

32−

0.3

2−

0.33

−0.

35

−0.3

6−

0.34

−0.

41

−0.3

9−

0.39

−0.

36

OO

:Per

son

alS

ervic

es−

0.73

−0.5

4−

0.40

−0.

29

−0.2

1−

0.50

−0.

36

−0.4

2−

0.46

−0.

44

DD

:Wood

−0.

59−

0.5

8−

0.57

−0.

58

−0.5

8−

0.56

−0.

53

−0.5

3−

0.51

−0.5

6JJ:F

inan

ce−

1.16

−0.9

9−

0.89

−0.

89

−0.

97

−1.

03

−0.8

8−

0.70

−0.

66

−0.9

1II

:Tra

nsp

ort-

Com

m.

−1.0

5−

1.12

−1.

29

−1.3

9−

1.14

−0.

91

−0.9

8−

0.98

−1.

03

−1.1

0D

J:M

etal

s−

2.0

2−

1.78

−1.

79

−1.8

2−

1.91

−1.

71

−1.6

5−

1.51

−1.

38

−1.7

3K

K:B

usi

nes

sS

ervic

es−

1.4

8−

1.75

−1.

78

−2.0

8−

2.28

−2.

15

−1.8

5−

1.92

−1.

98

−1.9

2A

A:A

gric

ult

ure

−4.3

0−

4.11

−3.

99

−3.7

2−

3.63

−3.

61

−3.4

5−

3.46

−3.

28

−3.7

3F

F:C

onst

ruct

ion

−6.0

8−

6.20

−6.

50

−6.5

9−

6.75

−6.

89

−7.2

1−

7.18

−7.

34

−6.7

5

Sou

rce:

Ow

nco

mp

uta

tion

bas

edon

Su

pply

-Use

Tab

les

(SU

T)

an

dN

ati

onal

Acc

ou

nts

Data

,IS

TA

T

55


Tab

le20

:In

dust

ryL

abou

rG

row

than

dC

omm

odit

yG

ross

Outp

ut

Gro

wth

,It

aly

(in

p.p

.)

99-0

000-0

101-0

202-0

303-0

404-0

505-0

606-0

7m

ean

∆%Lj

∆%qi

∆%Lj

∆%qi

∆%Lj

∆%qi

∆%Lj

∆%qi

∆%Lj

∆%qi

∆%Lj

∆%qi

∆%Lj

∆%qi

∆%Lj

∆%qi

∆%Lj

∆%qi

AA

:Agri

cult

ure

−0.8

8−

1.8

60.9

6−

0.6

6−

3.4

0−

1.8

6−

4.6

7−

4.0

3−

0.2

89.4

7−

3.2

0−

2.7

61.0

5−

1.8

0−

3.1

80.1

1−

1.7

0−

0.4

2B

B:F

ishin

g−

4.7

39.2

40.5

2−

9.5

3−

0.3

4−

5.3

6−

7.9

00.7

85.2

8−

2.9

8−

1.2

5−

6.5

93.7

05.8

71.2

0−

1.9

9−

0.4

4−

1.3

2C

A:M

inin

generg

y−

7.5

2−

9.7

1−

4.8

0−

13.5

044.3

017.8

0−

7.6

5−

4.9

21.1

3−

4.9

9−

2.2

73.1

62.2

7−

5.8

62.2

212.0

03.4

6−

0.7

5C

B:M

inin

gnon-e

nerg

y−

2.3

4−

2.1

1−

0.3

02.6

72.6

46.7

1−

5.9

5−

4.9

4−

4.3

9−

3.4

02.5

39.7

9−

4.4

7−

3.6

9−

2.9

9−

8.2

6−

1.9

1−

0.4

0D

A:F

ood-T

obacco

−1.0

95.4

2−

4.0

7−

2.7

21.7

8−

0.7

31.3

82.0

82.9

11.3

7−

2.7

42.0

81.8

1−

0.2

31.3

11.8

50.1

61.1

4D

B:T

exti

les

−0.6

95.8

80.0

80.6

2−

0.4

9−

1.1

2−

0.8

3−

4.6

4−

4.5

3−

4.2

8−

6.2

1−

3.5

0−

5.9

8−

2.8

7−

1.0

6−

1.1

5−

2.4

7−

1.3

8D

C:L

eath

er

−1.6

05.1

4−

2.0

64.6

8−

2.2

0−

6.3

4−

0.8

9−

4.4

8−

7.1

7−

5.7

5−

9.0

1−

3.2

3−

2.1

30.9

12.0

70.6

5−

2.8

7−

1.0

5D

D:W

ood

0.4

34.8

4−

0.2

11.1

31.7

0−

4.7

6−

2.0

80.1

2−

2.4

51.3

5−

6.8

5−

6.3

30.2

4−

0.7

1−

2.8

75.7

7−

1.5

10.1

8D

E:P

ap

er-

Pri

nti

ng

−2.0

03.6

8−

0.3

44.0

70.7

1−

2.6

3−

0.2

21.6

9−

0.7

12.5

0−

1.3

20.5

21.0

21.4

5−

1.4

40.6

3−

0.5

41.4

9D

F:C

oke-P

etr

ole

um

1.8

8−

0.5

1−

1.8

82.3

2−

9.5

7−

1.5

3−

0.4

20.9

33.7

10.7

63.1

9−

1.4

91.5

6−

2.4

31.5

32.0

60.0

00.0

1D

G:C

hem

icals

−1.5

6−

2.6

3−

0.8

6−

1.2

92.3

87.5

0−

3.3

4−

3.0

6−

1.8

13.0

61.1

3−

1.6

21.0

7−

1.2

9−

0.7

30.9

8−

0.4

70.2

1D

H:P

last

ics

0.9

3−

0.4

4−

1.1

6−

1.7

01.2

58.7

4−

1.9

1−

3.8

2−

2.7

70.1

8−

3.6

5−

4.3

4−

3.0

10.8

1−

0.6

2−

0.5

9−

1.3

7−

0.1

5D

I:N

on-m

et.

min

era

ls1.2

85.4

02.8

57.8

50.9

64.0

7−

1.2

7−

3.0

2−

3.5

01.2

91.8

6−

1.0

4−

2.6

2−

1.5

43.3

72.0

40.3

71.8

8D

J:M

eta

ls−

1.4

42.0

31.7

34.2

91.1

32.0

03.4

62.1

3−

1.7

1−

2.1

10.6

40.8

15.0

75.0

12.5

84.9

91.4

32.3

9D

K:M

achin

ery

n.e

.c.

1.7

26.6

20.5

31.6

21.0

30.5

22.6

72.5

51.2

04.2

41.6

40.2

93.1

87.3

00.1

13.1

41.5

13.2

9D

L:E

lectr

.M

achin

ery

1.5

45.1

6−

1.1

35.0

61.2

9−

2.3

71.5

1−

2.6

0−

0.6

43.9

21.9

40.9

52.7

12.8

51.7

34.0

11.1

22.1

2D

M:T

ransp

ort

Equip

.−

1.6

45.2

5−

4.3

1−

2.2

3−

2.5

3−

4.0

5−

8.8

8−

3.6

66.8

31.7

6−

0.2

3−

5.2

23.1

87.8

63.9

56.6

6−

0.4

50.8

0D

N:M

anufa

ctu

ren.e

.c.

−0.6

24.9

7−

0.9

70.3

70.7

90.0

4−

1.2

3−

3.6

3−

0.0

32.4

50.6

0−

1.9

8−

1.5

60.6

0−

1.0

0−

1.5

3−

0.5

00.1

6E

E:E

nerg

y−

1.8

1−

0.4

1−

3.3

52.4

9−

1.0

23.2

3−

3.5

03.7

8−

2.6

93.2

30.9

32.2

92.5

11.4

1−

2.3

6−

0.1

1−

1.4

11.9

9F

F:C

onst

ructi

on

3.2

43.7

86.0

25.1

22.0

73.0

12.7

11.4

31.6

31.1

74.0

22.1

51.2

01.1

92.9

61.0

22.9

82.3

6G

G:T

rade

1.1

44.3

91.6

01.6

20.7

10.0

31.1

3−

0.5

4−

0.3

82.2

2−

0.8

40.7

32.0

43.0

70.0

81.8

90.6

81.6

8H

H:H

ote

l-R

est

aura

nt

7.7

58.9

42.1

32.3

53.0

9−

3.9

33.7

8−

0.4

02.3

00.4

60.2

10.7

20.3

02.9

30.4

71.7

62.5

01.6

0II

:Tra

nsp

ort

-Com

m.

1.8

28.3

21.1

05.5

81.4

94.0

90.7

32.5

9−

0.2

11.2

11.6

83.6

32.2

30.4

71.6

03.4

11.3

13.6

6JJ:F

inance

−0.3

96.4

41.6

73.4

8−

0.0

5−

0.9

8−

0.7

10.1

70.8

23.7

70.1

85.1

62.2

95.9

73.0

24.8

20.8

63.6

0K

K:B

usi

ness

Serv

ices

7.1

75.7

34.7

93.2

66.1

34.0

02.9

12.1

01.8

2−

0.1

61.3

40.2

22.4

92.3

02.9

81.4

83.7

02.3

7L

L:P

ublic

Adm

in.

0.3

81.2

8−

0.3

62.1

5−

0.4

71.8

9−

2.7

81.8

5−

0.5

11.2

7−

1.4

81.0

5−

0.5

9−

0.1

8−

1.0

40.5

3−

0.8

61.2

3M

M:E

ducati

on

0.4

20.5

01.5

81.7

30.7

62.3

01.0

91.3

8−

1.5

0−

0.6

5−

0.3

1−

1.5

71.2

7−

0.0

40.4

40.9

40.4

70.5

7N

N:H

ealt

h2.5

93.0

91.8

12.6

70.9

32.2

71.2

31.5

31.3

03.4

60.5

63.2

90.0

91.1

10.0

91.1

01.0

72.3

2O

O:P

ers

onal

Serv

ices

2.3

2−

1.8

93.3

60.3

20.8

1−

1.0

10.2

9−

2.3

41.9

18.0

90.7

7−

4.8

65.1

52.0

11.1

90.7

31.9

70.1

3P

P:H

ouse

hold

Serv

ices

1.6

81.7

74.1

14.3

91.8

91.8

2−

0.1

9−

0.2

24.3

24.2

23.7

43.6

83.3

93.3

63.9

83.9

52.8

62.8

7

Sourc

e:

Ow

ncom

puta

tion

base

don

Supply

-Use

Table

s(S

UT

)and

Nati

onal

Accounts

Data

,IS

TA

T

56


Tab

le21

:C

omm

odit

yN

etO

utp

ut

Gro

wth

and

VI

Lab

our

Pro

duct

ivit

yG

row

th,

Ital

y(i

np.p

.)

00-0

101-0

202-0

303-0

404-0

505-0

6m

ean

∆%yi

∆%α(i)

ν∆

%yi

∆%α(i)

ν∆

%yi

∆%α(i)

ν∆

%yi

∆%α(i)

ν∆

%yi

∆%α(i)

ν∆

%yi

∆%α(i)

ν∆

%yi

∆%α(i)

νA

A:A

gri

cult

ure

−25.2

4−

11.0

022.2

74.6

3−

14.9

5−

1.0

645.5

511.5

618.2

95.8

6−

165.6

7−

24.5

4−

19.9

6−

2.4

3B

B:F

ishin

g17.0

3−

16.1

4−

35.8

7−

0.2

78.6

45.4

8−

13.9

5−

7.1

711.2

6−

0.6

78.7

6−

14.7

5−

0.6

9−

5.5

9C

B:M

inin

gnon-e

nerg

y45.1

2−

0.4

520.3

34.0

1−

156.1

3−

11.7

960.2

2−

0.8

9127.5

322.4

9−

118.2

0−

41.9

6−

3.5

2−

4.7

6D

A:F

ood-T

obacco

−12.5

9−

9.0

14.0

54.9

46.0

20.5

7−

0.3

46.5

36.3

65.6

6−

2.2

7−

15.3

90.2

1−

1.1

2D

B:T

exti

les

1.9

42.8

92.9

5−

3.7

0−

10.9

6−

6.5

8−

3.2

91.6

6−

1.2

33.7

8−

3.4

23.1

4−

2.3

30.2

0D

C:L

eath

er

2.1

61.8

8−

11.4

0−

5.9

2−

9.3

1−

5.9

1−

5.5

32.8

50.1

34.4

81.3

54.7

1−

3.7

70.3

5D

D:W

ood

−21.2

42.1

7−

34.8

2−

8.2

641.4

65.6

4−

3.1

7−

4.1

4−

39.7

81.9

825.6

37.0

4−

5.3

20.7

4D

E:P

ap

er-

Pri

nti

ng

6.3

5−

5.8

8−

23.8

8−

3.0

517.1

02.4

96.6

52.9

4−

10.0

5−

3.6

32.4

72.6

1−

0.2

3−

0.7

5D

F:C

oke-P

etr

ole

um

−2.9

7−

18.3

4−

12.8

8−

5.1

312.6

816.9

9−

2.8

8−

10.8

30.5

1−

18.7

5−

11.9

8−

30.3

2−

2.9

2−

11.0

7D

G:C

hem

icals

14.4

99.3

818.5

4−

1.8

7−

9.4

6−

9.9

110.1

78.3

5−

10.9

4−

0.7

07.9

312.1

75.1

22.9

0D

H:P

last

ics

5.9

02.4

931.6

49.4

8−

31.7

7−

9.0

713.2

25.8

9−

11.6

3−

6.1

415.2

08.0

23.7

61.7

8D

I:N

on-m

et.

min

era

ls10.0

31.1

0−

5.2

63.3

4−

30.0

8−

10.1

611.6

02.4

9−

3.6

1−

0.1

2−

8.0

83.9

6−

4.2

30.1

0D

J:M

eta

ls20.4

91.1

8−

4.5

8−

0.5

1−

0.9

9−

3.7

2−

8.9

50.6

510.7

51.0

820.3

43.7

46.1

80.4

0D

K:M

achin

ery

n.e

.c.

−2.1

2−

1.0

7−

0.6

5−

4.3

0−

0.5

9−

1.4

35.7

75.2

3−

2.3

8−

0.5

912.1

55.3

82.0

30.5

4D

L:E

lectr

.M

achin

ery

5.1

25.9

7−

10.8

7−

8.1

4−

15.5

4−

5.9

716.0

59.7

2−

0.6

90.6

0−

0.7

43.0

2−

1.1

10.8

6D

M:T

ransp

ort

Equip

.−

17.5

2−

9.3

98.7

87.6

3−

9.2

3−

7.4

0−

4.0

75.3

7−

6.9

8−

9.3

512.6

09.9

2−

2.7

4−

0.5

3D

N:M

anufa

ctu

ren.e

.c.

−5.8

7−

8.8

1−

0.1

92.6

4−

11.4

9−

6.9

18.2

52.7

4−

8.9

63.0

2−

0.3

82.5

1−

3.1

1−

0.8

0E

E:E

nerg

y7.0

2−

2.4

94.1

2−

5.9

66.2

36.7

12.5

5−

8.7

53.0

05.5

10.2

8−

0.7

43.8

7−

0.9

5F

F:C

onst

ructi

on

7.2

1−

1.5

11.6

90.7

9−

1.3

8−

4.1

61.0

70.6

2−

0.8

01.6

9−

1.6

7−

4.3

41.0

2−

1.1

5G

G:T

rade

−1.0

6−

0.1

2−

2.7

0−

3.3

6−

2.3

9−

4.9

03.7

34.0

2−

1.1

0−

0.6

75.8

61.6

20.3

9−

0.5

7H

H:H

ote

l-R

est

aura

nt

0.0

6−

8.2

8−

5.6

8−

3.7

22.9

2−

1.9

00.3

7−

0.4

11.3

70.5

73.4

7−

0.2

10.4

2−

2.3

3II

:Tra

nsp

ort

-Com

m.

0.3

80.6

1−

2.7

0−

0.6

2−

0.8

63.9

10.3

9−

0.5

59.8

22.0

9−

6.9

0−

3.3

10.0

20.3

6JJ:F

inance

−2.5

4−

0.3

6−

6.7

3−

2.8

2−

1.3

2−

2.8

97.2

25.1

33.9

01.9

29.8

32.8

21.7

30.6

3K

K:B

usi

ness

Serv

ices

−3.2

9−

2.5

15.3

9−

3.6

4−

4.0

4−

2.5

6−

6.0

9−

0.9

01.0

2−

2.8

28.1

8−

0.7

20.2

0−

2.1

9L

L:P

ublic

Adm

in.

2.3

12.3

11.8

70.5

91.9

02.6

61.2

81.3

60.9

7−

0.6

4−

0.1

81.3

11.3

61.2

6M

M:E

ducati

on

1.2

6−

2.2

62.4

54.3

60.6

0−

0.4

5−

0.4

71.2

3−

2.5

5−

1.8

42.0

4−

0.1

30.5

60.1

5N

N:H

ealt

h2.4

32.1

22.6

5−

0.1

02.4

3−

0.2

04.1

21.6

93.4

50.8

20.9

3−

0.2

22.6

70.6

8O

O:P

ers

onal

Serv

ices

5.9

9−

1.2

6−

2.1

5−

6.1

2−

1.7

6−

5.8

118.2

49.3

4−

20.0

7−

7.7

311.8

21.3

22.0

1−

1.7

1P

P:H

ouse

hold

Serv

ices

4.3

90.2

81.8

2−

0.0

6−

0.2

2−

0.0

34.2

2−

0.1

13.6

8−

0.0

63.3

6−

0.0

32.8

80.0

0

Sourc

e:

Ow

ncom

puta

tion

base

don

Supply

-Use

Table

s(S

UT

)and

Nati

onal

Accounts

Data

,IS

TA

T

57

Tab

le22

:C

omm

odit

yF

inal

Con

sum

pti

onG

row

than

dV

HI

Lab

our

Pro

duct

ivit

yG

row

th,

Ital

y(i

np.p

.)

99-0

000-0

101-0

202-0

303-0

404-0

505-0

606-0

7m

ean

∆%ci

∆%α(i)

η∆

%ci

∆%α(i)

η∆

%ci

∆%α(i)

η∆

%ci

∆%α(i)

η∆

%ci

∆%α(i)

η∆

%ci

∆%α(i)

η∆

%ci

∆%α(i)

η∆

%ci

∆%α(i)

η∆

%ci

∆%α(i)

η

AA

:Agri

cult

ure

2.5

2−

1.9

53.1

7−

1.4

8−

1.8

2−

0.6

6−

9.0

61.0

79.4

15.1

84.0

43.5

7−

2.2

6−

1.9

210.0

42.9

02.0

10.8

4B

B:F

ishin

g13.1

913.6

3−

20.4

3−

12.8

9−

1.5

8−

5.1

02.6

57.5

4−

1.0

1−

8.0

6−

3.3

0−

4.4

74.8

32.7

725.3

2−

2.5

22.4

6−

1.1

4C

B:M

inin

gnon-e

nerg

y11.6

44.9

6−

1.7

58.5

23.5

5−

6.1

5−

7.2

3−

1.7

38.8

6−

6.9

21.9

32.0

71.5

45.7

9−

1.9

2−

3.3

42.0

80.4

0D

A:F

ood-T

obacco

3.6

36.6

1−

1.0

4−

1.3

83.8

71.7

4−

0.0

5−

0.2

42.3

52.5

94.2

04.7

52.0

10.7

618.8

51.8

34.2

32.0

8D

B:T

exti

les

5.9

26.8

93.9

8−

0.4

6−

4.0

1−

0.6

2−

2.8

5−

1.5

1−

2.8

82.8

4−

4.0

21.8

4−

0.2

86.2

113.0

8−

0.7

11.1

21.8

1D

C:L

eath

er

8.7

111.3

91.4

71.4

3−

9.5

4−

5.7

0−

5.9

8−

1.9

5−

1.4

15.1

8−

6.2

31.8

71.0

45.2

014.9

3−

1.3

40.3

72.0

1D

D:W

ood

9.4

87.5

67.7

74.9

4−

7.2

6−

5.6

0−

7.6

0−

0.3

11.1

35.4

5−

8.1

33.6

32.1

83.4

46.6

73.4

20.5

32.8

2D

E:P

ap

er-

Pri

nti

ng

5.0

81.7

51.9

52.2

7−

1.4

9−

0.0

83.0

1−

0.9

0−

1.3

63.5

32.8

81.2

71.7

80.8

37.3

21.0

92.4

01.2

2D

F:C

oke-P

etr

ole

um

−4.2

7−

3.4

05.7

713.1

0−

6.0

0−

4.2

46.6

4−

23.4

4−

6.0

4−

34.0

80.8

2−

11.1

2−

13.6

7−

11.7

35.9

118.3

7−

1.3

6−

7.0

7D

G:C

hem

icals

10.7

87.8

26.7

71.9

05.3

2−

6.7

6−

1.1

76.7

6−

0.8

16.3

64.5

72.0

52.7

08.0

87.4

3−

0.3

64.4

53.2

3D

H:P

last

ics

8.3

82.6

81.2

30.5

82.5

90.5

40.5

5−

0.4

95.5

97.1

1−

0.5

21.3

23.1

71.9

310.3

91.6

83.9

21.9

2D

I:N

on-m

et.

min

era

ls6.7

85.8

00.5

6−

1.9

9−

1.2

0−

1.9

4−

5.2

6−

1.6

80.6

42.6

6−

4.1

83.8

70.5

63.3

25.6

1−

1.8

10.4

41.0

3D

J:M

eta

ls12.7

34.2

22.5

11.2

4−

0.2

7−

1.6

93.3

70.5

812.4

24.0

02.9

60.3

612.7

1−

0.6

95.2

6−

0.9

46.4

60.8

9D

K:M

achin

ery

n.e

.c.

8.1

16.5

64.4

01.0

4−

2.5

0−

4.0

71.6

70.3

55.3

35.8

5−

0.4

61.3

68.5

34.1

0−

2.2

51.0

32.8

52.0

3D

L:E

lectr

.M

achin

ery

12.8

46.9

94.8

6−

0.4

4−

8.4

9−

1.0

7−

1.3

1−

2.2

93.7

05.7

23.7

14.3

84.7

12.5

0−

4.4

30.7

31.9

52.0

7D

M:T

ransp

ort

Equip

.10.9

27.8

7−

13.1

20.1

02.0

90.0

2−

6.0

70.1

63.5

3−

1.8

2−

2.7

8−

0.9

38.8

01.9

717.6

94.5

12.6

31.4

9D

N:M

anufa

ctu

ren.e

.c.

5.7

47.8

2−

2.2

9−

0.8

6−

2.2

6−

2.7

3−

5.3

1−

1.6

90.0

34.4

0−

4.3

2−

0.1

50.5

63.2

27.9

00.9

40.0

11.3

7E

E:E

nerg

y−

2.6

8−

2.2

41.5

2−

4.6

44.5

9−

1.3

64.2

2−

5.6

46.1

411.9

72.6

32.9

5−

3.6

0−

0.0

7−

5.2

0−

5.9

40.9

5−

0.6

2F

F:C

onst

ructi

on

2.0

91.8

20.6

50.0

1−

3.3

4−

1.0

0−

1.0

3−

0.4

0−

4.2

01.2

6−

2.2

6−

1.4

02.7

40.8

70.2

2−

1.7

0−

0.6

4−

0.0

7G

G:T

rade

2.9

21.3

9−

0.0

7−

1.3

9−

1.6

9−

2.6

0−

0.8

3−

1.2

61.4

81.6

41.5

42.5

94.2

5−

0.3

21.0

90.8

51.0

90.1

1H

H:H

ote

l-R

est

aura

nt

8.3

92.3

52.4

4−

0.9

3−

1.6

8−

5.2

3−

0.7

3−

4.3

81.0

5−

0.9

80.6

91.7

13.0

21.8

62.2

02.3

41.9

2−

0.4

1II

:Tra

nsp

ort

-Com

m.

6.2

84.9

6−

0.3

32.5

01.7

12.6

03.8

7−

0.6

34.3

70.6

81.9

91.7

42.3

5−

0.2

74.9

20.5

63.1

51.5

2JJ:F

inance

5.1

45.3

16.4

51.9

7−

4.7

5−

4.0

1−

3.8

60.5

50.4

60.3

58.0

32.8

77.1

21.5

09.3

35.3

33.4

91.7

3K

K:B

usi

ness

Serv

ices

2.3

5−

1.0

62.0

9−

2.3

80.8

0−

1.2

90.9

10.1

00.9

6−

2.0

72.5

1−

3.0

60.7

2−

0.2

60.4

4−

1.7

31.3

5−

1.4

7L

L:P

ublic

Adm

in.

1.4

40.7

62.1

30.5

81.9

30.5

01.8

71.2

31.2

02.2

81.0

52.9

0−

0.2

11.4

40.5

21.6

51.2

41.4

2M

M:E

ducati

on

−0.0

9−

0.8

71.8

32.0

81.6

01.5

81.7

61.1

7−

1.5

20.4

70.3

6−

0.5

9−

0.1

3−

0.5

70.7

70.4

40.5

70.4

6N

N:H

ealt

h2.8

71.1

93.0

91.3

33.2

40.2

12.0

6−

0.5

73.6

40.5

53.2

51.1

71.0

31.3

81.0

10.9

92.5

30.7

8O

O:P

ers

onal

Serv

ices

2.4

2−

3.7

01.6

4−

5.3

50.4

1−

3.8

0−

0.4

1−

2.3

45.2

17.9

3−

1.5

5−

3.9

62.7

9−

1.5

11.3

00.3

81.4

8−

1.5

5P

P:H

ouse

hold

Serv

ices

1.7

70.0

94.3

90.2

81.8

2−

0.0

6−

0.2

2−

0.0

34.2

2−

0.1

13.6

8−

0.0

63.3

6−

0.0

33.9

5−

0.0

22.8

70.0

1

Sourc

e:

Ow

ncom

puta

tion

base

don

Supply

-Use

Table

s(S

UT

)and

Nati

onal

Accounts

Data

,IS

TA

T

58


able

23:

Unit

sof

VI

Lab

our

Gro

wth

,It

aly

-∆

%L

(i)

ν(p

p)

act

00-0

101-0

202-0

303-0

404-0

505-0

6m

ean

AA

:Agr

icu

ltu

re−

14.2

417.

64

−13.8

933.

98

12.

43

−141.1

3−

17.

53

BB

:Fis

hin

g33.

18

−35.6

13.

16

−6.

78

11.

93

23.

52

4.90

CB

:Min

ing

non

-en

ergy

45.

57

16.

32

−144.3

461.

11

105.

04

−76.2

41.

24

DA

:Food

-Tob

acco

−3.

58

−0.8

95.

45

−6.

87

0.70

13.

12

1.32

DB

:Tex

tile

s−

0.95

6.65

−4.3

8−

4.95

−5.0

1−

6.5

5−

2.53

DC

:Lea

ther

0.2

7−

5.4

8−

3.4

0−

8.38

−4.3

6−

3.3

6−

4.12

DD

:Wood

−23.4

0−

26.5

635.

82

0.97

−41.7

518.

59

−6.

06

DE

:Pap

er-P

rinti

ng

12.2

4−

20.8

314.

60

3.71

−6.4

2−

0.1

50.

53

DF

:Cok

e-P

etro

leu

m15.3

7−

7.7

5−

4.3

17.

96

19.

26

18.

34

8.15

DG

:Ch

emic

als

5.11

20.

41

0.44

1.82

−10.2

4−

4.2

42.

22

DH

:Pla

stic

s3.

41

22.

16

−22.6

97.

33

−5.4

87.

19

1.99

DI:

Non

-met

.m

iner

als

8.93

−8.6

0−

19.9

39.

11

−3.5

0−

12.0

4−

4.34

DJ:M

etal

s19.3

1−

4.0

72.

73

−9.

61

9.67

16.

60

5.77

DK

:Mac

hin

ery

n.e

.c.

−1.

05

3.65

0.83

0.54

−1.7

96.

77

1.49

DL

:Ele

ctr.

Mac

hin

ery

−0.

85

−2.7

2−

9.5

76.

33

−1.2

9−

3.7

6−

1.98

DM

:Tra

nsp

ort

Equ

ip.

−8.

13

1.15

−1.8

3−

9.45

2.37

2.67

−2.

20

DN

:Man

ufa

ctu

ren

.e.c

.2.

94

−2.8

3−

4.5

85.

51

−11.9

8−

2.8

9−

2.31

EE

:En

ergy

9.51

10.

08

−0.4

911.

30

−2.5

11.

01

4.82

FF

:Con

stru

ctio

n8.7

20.

90

2.78

0.45

−2.4

92.

67

2.17

GG

:Tra

de

−0.

94

0.66

2.52

−0.

30

−0.4

34.

24

0.96

HH

:Hot

el-R

esta

ura

nt

8.3

4−

1.9

64.

82

0.78

0.80

3.68

2.74

II:T

ran

spor

t-C

omm

.−

0.23

−2.0

8−

4.7

70.

94

7.73

−3.5

9−

0.33

JJ:F

inan

ce−

2.18

−3.9

21.

57

2.09

1.98

7.01

1.09

KK

:Bu

sin

ess

Ser

vic

es−

0.78

9.04

−1.4

8−

5.19

3.84

8.90

2.39

LL

:Pu

bli

cA

dm

in.

0.0

01.

28

−0.7

6−

0.07

1.62

−1.4

80.

10

MM

:Ed

uca

tion

3.5

1−

1.9

11.

06

−1.

70

−0.7

12.

16

0.40

NN

:Hea

lth

0.3

12.

75

2.63

2.43

2.63

1.15

1.98

OO

:Per

son

alS

ervic

es7.

24

3.97

4.05

8.90

−12.3

410.

50

3.72

PP

:Hou

seh

old

Ser

vic

es4.1

11.

89

−0.1

94.

32

3.74

3.39

2.88

Sou

rce:

Ow

nco

mp

uta

tion

bas

edon

Su

pply

-Use

Tab

les

(SU

T)

an

dN

ati

onal

Acc

ou

nts

Data

,IS

TA

T

59


able

24:

Unit

sof

VH

IL

abou

rG

row

th,

Ital

y-

∆%L

(i)

η(p

p)

act

99-0

000-0

101-0

202-0

303-0

404-0

505-0

606-0

7m

ean

AA

:Agr

icu

ltu

re4.4

74.

65

−1.

16

−10.1

34.

22

0.47

−0.

34

7.14

1.17

BB

:Fis

hin

g−

0.44

−7.5

43.

52

−4.8

87.

06

1.16

2.06

27.

85

3.60

CB

:Min

ing

non

-en

ergy

6.68

−10.2

79.

71

−5.5

015.

78

−0.1

4−

4.25

1.41

1.68

DA

:Food

-Tob

acco

−2.

980.

34

2.13

0.18

−0.

23

−0.5

51.

25

17.

02

2.14

DB

:Tex

tile

s−

0.97

4.44

−3.

39

−1.3

5−

5.73

−5.8

6−

6.49

13.

79

−0.

69

DC

:Lea

ther

−2.

680.

03

−3.

84

−4.0

3−

6.59

−8.1

0−

4.16

16.

26

−1.

64

DD

:Wood

1.9

12.

83

−1.

66

−7.2

9−

4.33

−11.7

5−

1.26

3.25

−2.

29

DE

:Pap

er-P

rinti

ng

3.3

3−

0.3

2−

1.40

3.91

−4.

89

1.60

0.95

6.23

1.18

DF

:Cok

e-P

etro

leum

−0.

88−

7.3

2−

1.75

30.

07

28.

04

11.

94

−1.

93

−12.4

65.

71

DG

:Ch

emic

als

2.97

4.86

12.

07

−7.9

2−

7.17

2.52

−5.

38

7.80

1.22

DH

:Pla

stic

s5.7

00.

65

2.05

1.04

−1.

51

−1.8

41.

23

8.71

2.00

DI:

Non

-met

.m

iner

als

0.98

2.55

0.74

−3.5

8−

2.02

−8.0

4−

2.76

7.42

−0.

59

DJ:M

etal

s8.5

11.

27

1.42

2.78

8.42

2.60

13.

40

6.20

5.58

DK

:Mac

hin

ery

n.e

.c.

1.55

3.36

1.57

1.32

−0.

52

−1.8

24.

43

−3.2

90.

82

DL

:Ele

ctr.

Mac

hin

ery

5.85

5.30

−7.

42

0.97

−2.

02

−0.6

72.

21

−5.1

6−

0.12

DM

:Tra

nsp

ort

Equ

ip.

3.0

5−

13.2

22.

07

−6.2

35.

35

−1.8

56.

83

13.

18

1.15

DN

:Man

ufa

ctu

ren

.e.c

.−

2.08

−1.4

20.

47

−3.6

2−

4.37

−4.1

7−

2.66

6.96

−1.

36

EE

:En

ergy

−0.

446.

16

5.95

9.86

−5.

84

−0.3

2−

3.53

0.74

1.57

FF

:Con

stru

ctio

n0.2

70.

64

−2.

34

−0.6

3−

5.46

−0.8

61.

87

1.93

−0.

57

GG

:Tra

de

1.53

1.31

0.91

0.43

−0.

16

−1.0

54.

57

0.24

0.97

HH

:Hot

el-R

esta

ura

nt

6.0

43.

38

3.55

3.65

2.03

−1.0

21.

16

−0.1

42.

33

II:T

ran

spor

t-C

omm

.1.3

2−

2.8

3−

0.89

4.50

3.69

0.25

2.62

4.36

1.63

JJ:F

inan

ce−

0.17

4.48

−0.

74

−4.4

20.

12

5.16

5.62

3.99

1.76

KK

:Bu

sin

ess

Ser

vic

es3.4

24.

47

2.09

0.81

3.03

5.57

0.98

2.17

2.82

LL

:Pu

bli

cA

dm

in.

0.6

81.

56

1.43

0.64

−1.

08

−1.8

5−

1.65

−1.1

3−

0.18

MM

:Ed

uca

tion

0.7

9−

0.2

60.

01

0.60

−1.

99

0.94

0.45

0.33

0.11

NN

:Hea

lth

1.6

81.

76

3.04

2.63

3.09

2.09

−0.

35

0.03

1.74

OO

:Per

son

alSer

vic

es6.

127.

00

4.22

1.93

−2.

73

2.41

4.30

0.92

3.02

PP

:Hou

seh

old

Ser

vic

es1.6

84.

11

1.89

−0.1

94.

32

3.74

3.39

3.98

2.86

Sou

rce:

Ow

nco

mp

uta

tion

bas

edon

Su

pply

-Use

Tab

les

(SU

T)

an

dN

ati

onal

Acc

ou

nts

Data

,IS

TA

T

60


Tab

le25

:H

yp

er-i

net

grat

edla

bou

rpro

duct

ivit

ygr

owth

dec

omp

osit

ion,

Ital

y(1

999-

2007

)

99-0

003-0

406-0

7m

ean

∆%α(i)

η∆

%α(i)

η,d

∆%α(i)

η,hy

ω(i)

η,d

∆%α(i)

η∆

%α(i)

η,d

∆%α(i)

η,hy

ω(i)

η,d

∆%α(i)

η∆

%α(i)

η,d

∆%α(i)

η,hy

ω(i)

η,d

∆%α(i)

η∆

%α(i)

η,d

∆%α(i)

η,hy

ω(i)

η,d

DG

:Chem

icals

7.8

2−

0.1

110.6

326.1

66.3

6−

1.3

49.2

627.2

8−

0.3

62.4

4−

1.5

329.4

03.2

31.1

34.0

327.4

0D

D:W

ood

7.5

64.7

310.0

146.3

75.4

52.8

77.7

246.7

33.4

25.0

61.8

548.8

82.8

22.0

23.5

347.7

2D

A:F

ood-T

obacco

6.6

17.1

66.4

918.4

52.5

9−

0.7

93.3

618.6

61.8

31.6

01.8

919.3

02.0

81.3

72.2

518.6

0D

L:E

lectr

.M

achin

ery

6.9

95.6

18.1

645.8

65.7

25.2

86.0

946.1

40.7

33.4

0−

1.6

747.3

22.0

71.4

12.6

446.0

2D

K:M

achin

ery

n.e

.c.

6.5

65.2

27.2

834.9

95.8

53.7

37.0

435.9

91.0

33.3

0−

0.3

337.4

82.0

31.3

22.4

236.1

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61

REFERENCES

References

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Harrod, R.F. (1973). Economic Dynamics. Macmillan, London.

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Pasinetti, L.L. (1959). On Concepts and Measures of Changes in Productiv-ity. The Review of Economics and Statistics, 41(3):270–286.

——— (1973). The Notion of Vertical Integration in Economic Analysis.Metroeconomica, 25:1–29.

——— (1981). Structural Change and Economic Growth — A TheoreticalEssay on the Dynamics of the Wealth of Nations. Cambridge UniversityPress, Cambridge.

——— (1988). Growing subsystems, vertically hyper-integrated sectors andthe labour theory of value. Cambridge Journal of Economics, 12(1):125–34.

——— (1989). Growing subsystems and vertically hyper-integrated sectors:a note of clarification. Cambridge Journal of Economics, 13(3):479–80.

——— (1998). A Note on Richard Stone’s paper on Changes in Productivity.Structural Change and Economic Dynamics, (9):233–5.

Solow, R.M. (1957). Technical Change and the Aggregate Production Func-tion. The Review of Economics and Statistics, 39(3):312–320.

Sraffa, P. (1960). Production of Commodities by Means of Commodities.Cambridge University Press, Cambridge.

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Wolff, E.N. (1994). Productivity measurement within an Input-Outputframework. Regional Science and Urban Economics, 24(1):75–92.

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On Concepts and Measures of Changes in Productivity | A ... · On Concepts and Measures of Changes in Productivity | A reformulation ... irrelevant case \when Qis produced by