Wi kie man, A iel
A icle
Concep ualising p oduc i i y measu emen om a
classical pe spec i e
PSL Qua e ly Re iew
P o ided in Coope a ion wi h:
Associazione Economia ci ile, Rome
Sugges ed Ci a ion: Wi kie man, A iel (2024) : Concep ualising p oduc i i y measu emen om a
classical pe spec i e, PSL Qua e ly Re iew, ISSN 2037-3643, Associazione Economia ci ile, Rome,
Vol. 77, Iss. 309, pp. 145-172,
h ps://doi.o g/10.13133/2037-3643/18513
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ol. 77 n. 309 (June 2024)
Concep ualising p oduc i i y measu emen
om a classical pe spec i e
ARIEL L. WIRKIERMAN
Abs ac :
P oduc i i y seems an ob ious concep : ou pu pe uni o
inpu . Ye , when con ex ualised wi hin al e na i e iews
o p oduc ion and dis ibu ion, challenges ac oss
a emp s a measu ing i a e a om i ial. The aim o
his pape is o p esen and discuss some ounda ional
concep s o measu ing p oduc i i y om a classical
pe spec i e, as opposed o a mo e adi ional s andpoin .
A key dis inc ion is made be ween measu ing p oduc i i y
om he expendi u e (o physical quan i ies) side and
quan i ying p o i abili y om he alue added (o income)
side. P oduc i i y is opposed o p oduc i eness and
commodi y educ ion is con as ed o p ice agg ega ion.
A e c i ically discussing he adi ional s andpoin o
o al ac o p oduc i i y g ow h, his pape concep ually
discusses he me hod o (g owing) subsys ems and he
compu a ion o p oduc ion p ices as analy ical and
empi ical de ices o measu ing p oduc i i y and
p o i abili y in a mul isec o al economy.
Ins i u e o Managemen S udies (IMS), Goldsmi hs, Uni e si y o
London, UK
email: a.wi ki[email p o ec ed]c.uk
How o ci e his a icle:
Wi kie man A.L. (2024), “Concep ualising p oduc i i y
measu emen om a classical pe spec i e”, PSL Qua e ly
Re iew, 77 (309), pp. 145-172.
DOI: h ps://doi.o g/10.13133/2037-3643/18513
JEL codes:
O4, C67, B51
Keywo ds:
p oduc i i y measu emen , inpu -ou pu analysis, e ical
(hype -)in eg a ion, p ices o p oduc ion
Jou nal homepage:
h p: //www.pslqua e ly e iew.in o
P oduc i i y has been a majo ideology o ins i u ions e e since
medie al sal a ionis ideals ceded o mode nis a ionali y.
Reich (2001, p. 40)
1. In oduc ion: why p oduc i i y?
Being apped in his o y makes ou analyses, in appea ance, less gene al, less ‘scien i ic’, mo e
specula i e, ull o coun e ac uals, emp y o imeless s a emen s. Case-by-case de ailed ac ual
desc ip ion o abs ac econs uc ion o he mos emo e pas o he p esen day may appea as
he only way o o e come he c uel y o he his o ical na u e o economic phenomena.
The las couple o hund ed yea s had been so li le in compa ison wi h housands o yea s o
man as a p oduce . Hence, poli ical economy could be hough o be no e y ambi ious. I s objec
Special issue on he Solow-Pasine i deba e on p oduc i i y measu emen
146 Concep ualising p oduc i i y measu emen om a classical pe spec i e
PSL Qua e ly Re iew
o s udy has been qui e easily ci cumsc ibed o he analysis o phenomena o p oduc ion and
dis ibu ion in socie ies a e he appea ance o he capi alis mode o p oduc ion.
1
I s heo ies a e
qui e es ic ed in hei imespan, and so a e hei p ojec ion on o he u u e.
By obse ing egula i ies, we look o p inciples. The o ganisa ion o collec i e labou is one
o hese. In his sense, he passage om alue o ep oduc ion p ices can be analysed as a
de elopmen in economic his o y, as a passage om simple o ex ended ep oduc ion.
2
Bu in
essence, I belie e he c ucial cha ac e isa ion is he passage om an ‘u ban’ o a ‘capi alis ’ mode
o p oduc ion.
The ‘u ban e olu ion’
3
o he ou h millennium B.C. and he ‘capi alis e olu ion’ o he XVIII
cen u y a e wo o he mos impo an ans o ma ions in he mode o p oduc ion o human
his o y. They bo h had, as a c ucial de e minan , he change in he social o ganiza ion o collec i e
labou and he speci ic use o he su plus p oduced by he communi y as a whole.
4
Hence, he human de e mina ion o ans o m he o ganisa ion o collec i e labou is a deep
cause in he appea ance o he capi alis mode o p oduc ion. As ega ds i s en o cemen , he
delica e in e play wi h p imi i e accumula ion
5
should be acknowledged. Howe e , deep
unde s anding is a om mechanical, as he laws o which he capi alis mode o p oduc ion obey
change con inuously in hei de ails, because he changing o ganisa ion o human labou in socie y
eeds back in o he oo o he mode o p oduc ion i sel .
Wage labou , and indi idual owne ship o he means o p oduc ion, a e p obably he wo main
ins i u ional mechanisms o he en o cemen o a pa icula way o o ganising collec i e labou .
And his is a gene al p inciple. Bu he de ails ge con inuously al e ed. And one o he de ails ha
changes in i s long-pe iod ends ac oss ime and space is he hy hm o su plus gene a ing
capaci y o di e en socie ies, o , wha amoun s o he same hing, hei p oduc i i y inc eases.
Bu p oduc i i y is an elusi e concep . The e abound meanings and uses (some imes abuses)
ha place i as bo h cause and e ec o economic g ow h and composi ional changes in economic
s uc u e. I is my con ic ion ha concep ual cla i ica ion can come abou only by looking a he
no ion o p oduc i i y as a piece inside a comp ehensi e iew o he p ocess o p oduc ion and
dis ibu ion. As such, p oduc i i y analysis canno be ee o alue judgemen . No e en physical
p oduc i i y, and clea ly e en less when su plus gene a ing capaci y is hough o in e ms o
p o i abili y.
The aim o his pape is o p o ide a concep ual o e iew and discussion o al e na i e
amewo ks o de ine and measu e p oduc i i y changes. Th oughou , I adop a classical
pe spec i e o economic analysis, ying o es ablish clea di e ences wi h adi ional iews as
ega ds bo h heo y and measu emen . Hence, cla i ying he meaning I a ach o he ‘classical’
pe spec i e is he place o s a .
1
Though no necessa ily being cu en ly unde he capi alis mode o p oduc ion.
2
As s a ed by B ódy (1970, p. 94): “The di e en p ice sys ems belonged o di e en his o ical laye s o Ma x”.
3
O cou se he e m ‘ e olu ion’ is clea ly a me apho , i s o iginal meaning being “comple e o e u n o he ela i e
posi ions o he a ious elemen s ha cons i u e a sys em” (Li e ani, 1998, p. 3). P ocesses o social and echnological
change a e slow and g adual.
4
Fo a de elopmen o he a gumen , see Gilibe (2010).
5
In ac , “[ ]he necessi y o a p imi i e accumula ion o capi al, which socie y could in es in he s uc u al con e sion
o i s mode o p oduc ion, was no only a Ma xis heo y. I was a gene al p esupposi ion a he basis o ‘classical’
poli ical economy” (Li e ani, 1998, p. 7).
A.L. Wi kie man 147
PSL Qua e ly Re iew
2. Wha do I mean by ‘classical’ pe spec i e?
The classical s andpoin o economic analysis has i s oo s in he wo ks o he ‘old classical
economis s’, as in ended by S a a (1960, Appendix D), wi h Quesnay’s Tableau Economique as i s
i s comp ehensi e scheme, ollowed by Ma x’s ([1885] 1978) schemes o ‘Simple Rep oduc ion’
and ‘Rep oduc ion on an Expanded Scale’, and ex ending in o Leon ie ’s (1937) inpu -ou pu
amewo k and S a a’s (1960) sys em o p oduc ion.
6
The connec ions and in e play be ween hese wo ks a e subjec o long-s anding deba es,
which shall no be deal wi h he e. Ins ead, he aim is o highligh only some ea u es o a (mode n)
classical app oach.
Fi s and o emos , he cha ac e ising p inciple is he iew o he economy as a ci cula
p ocess based on he no ion o physical eal cos s, i.e., inpu s a e physically consumed in he
p ocess o gene a ing he ou pu s ha econs i u e he capaci y o es a he e y same p ocess
as inpu s a he same (o enla ged) scale.
Essen ially, “ci cula i y s ands he e o epe i i eness” (Gilibe , 2006, p. 41, n. 16).
Rep oduc ion begins and e u ns o he same poin , pic u ing he whole p ocess as an ascending
spi al whose diame e expands o con ac s. In ac , as S a a would ph ase i : “in a ci cula low
scheme ‘The p oduc ion o a hing has no eal de ini e beginning – he inqui y leads us in o in ini e
ime backwa ds’ (D3/12/7: 27)” (Ku z and Sal ado i, 2005a, p. 497). Wi hin he language o
ma hema ics, ci cula i y can be ep esen ed by eigensys ems, which de ine p ices and quan i ies
in e ms o hemsel es.
7
Second, mos o he in e es lies in he analysis o hose economies whose p oduc ion exceeds
i s p oduc i e consump ion, hus gene a ing a su plus p oduc , a se o commodi ies ha mus be
allo ed o di e en g oups o indi iduals (classes) in socie y. Di e en uses o he su plus by he
classes in socie y gene a e he income-expendi u e loops o a ci cula p ocess.
When commodi ies a e p oduced by means o commodi ies, he no ion o ‘cos o p oduc ion’
as well as ha o ‘ ac o o p oduc ion’ may no su i e close sc u iny, as he ci cula na u e o he
p ocess o ep oduc ion implies ha p oduced means o p oduc ion a e bo h inpu s and ou pu s,
whose p ice o quan i y as a ‘cos ’ may no be known in ad ance o i s p ice o quan i y as a
‘p oduc ’.
In ac , his ci cula i y p inciple should no be con used wi h he ma ginalis iew o he low
exchanges be ween ‘p oduc ’ and ‘ ac o ’ ma ke s, a he basis o gene al equilib ium heo y. In
his s ylised iew ci cula i y is no s aigh o wa d, pa icula ly when conside ing he no ion o a
ma ke o ‘capi al’ (o o he ‘se ices o capi al’): he ‘quan i y o capi al’ is supposed o be a
quan i a i e magni ude “ ha can be measu ed independen ly o , and p io o, he de e mina ion
o he p ices o he p oduc s” (S a a, 1960, p. 9), wi h he a e o p o i s (in e es ) being i s p ice.
Hence, no ional supply and demand schedules mee o de e mine he ‘equilib ium’ p ice and
quan i y o his ‘ ac o ’, hus egula ing – acco ding o i s ‘ ela i e sca ci y’ – income dis ibu ion
be ween labou and capi al (wages and p o i s).
Bu wi hin he ma ginalis sys em, a clea ing in he ma ke s o ‘ ac o s’ is c ucial o he
ma ke s o ‘p oduc s’ as well, as “a demand schedule can only a ec he p ice o he
co esponding p oduc o he ex en o which i a ec s dis ibu ion” (Ga egnani, 1983, p. 310).
This is so because he unc ional ela ionship be ween commodi y p ices and inal demand
c ucially depends on ela i e ac o p ices adjus ing o he p opo ion o hei employmen as
6
In no way does his b ie commen aim o make an exhaus i e enume a ion o he wo ks ‘belonging’ o he classical
adi ion o hough , which ex ends o e cen u ies o his day.
7
See B ódy (1970, pp. 84-94) o de ails.
148 Concep ualising p oduc i i y measu emen om a classical pe spec i e
PSL Qua e ly Re iew
inpu s when demand o inal ou pu changes, i.e., he whole sys em depends on he mechanism
o ac o subs i u ion.
I is, howe e , a well-es ablished ac ha he ac o subs i u ion mechanism canno be
sus ained unde easonable assump ions o he ep esen a ion o economic p oduc ion.
8
In con adis inc ion, when ‘capi al’ is conside ed as a se o p oduced means o p oduc ion –
as i is om a classical pe spec i e – i eme ges ha capi al goods become pa o he ci cula
p ocess o ep oduc ion, so he iew o hem as an agg ega e quan i y measu able be o e he
de e mina ion o p ices is clea ly un enable.
Fu he mo e, he a e o p o i s is no he ‘p ice’ o he ‘quan i y o capi al’. By ollowing
S a a’s in e p e a ion o Rica do ([1817] 1951):
A me hod de ised by Rica do […] is ha o singling ou co n as he one p oduc which is equi ed
bo h o i s p oduc ion and o he p oduc ion o e e y o he commodi y. As a esul , he a e o
p o i s o he g owe o co n is de e mined independen ly o alue, me ely by compa ing he
physical quan i y on he side o he means o p oduc ion o ha on he side o he p oduc , bo h o
which consis o he same commodi y (S a a, 1960, p. 93).
The di icul ies o gene alising his line o hough a e deal wi h by S a a (1960, pp. 22-23). The
(uni o m) a e o p o i s e lec s a (possible) ule o dis ibu ion o he su plus p oduc o he
sys em. Wha should be clea is ha , wi hin he logical s uc u e o classical analysis, he
dis ibu ion o income be ween wages and p o i s has a ‘deg ee o eedom’, as has been ende ed
‘ anspa en ’ in S a a’s (1960, Chap e IV) s anda d sys em.
Finally, when he demand and supply equilib ium heo y o dis ibu ion is abandoned, e en
in he p esence o a iable e u ns, he de e mina ion o ou pu s en ails hem o be ea ed as
independen a iables when de e mining ela i e p ices, and ice- e sa ( o de ails, see Ga egnani,
1987).
Hence, ano he cha ac e ising ea u e o classical analysis is he sepa a ion be ween p ices
and quan i ies, i.e., be ween he alue added and he expendi u e side o he sys em. In ac , his
aspec ex ends o empi ical s uc u es (inpu -ou pu schemes, in pa icula ) as well:
Bo h he ep oduc ion o quan i y and g ow h aspec and he p ice and dis ibu ion aspec a e deal
wi h, and i is made clea ha inpu -ou pu analysis is i mly oo ed in he ‘classical’ adi ion o
economic hough (Ku z e al., 1998, p. xi ).
In his sense, om a classical pe spec i e, ela i e p ices “ ep esen he exchange condi ions
be ween physical goods ha make ep oduc ion wi hin a gi en echnical (me hods o p oduc ion)
and social (dis ibu ion) amewo k possible” (Sche old, 1989, p. 292).
9
Mo eo e , “wi h a su plus,
p ices a e in luenced by i s dis ibu ion” (Gilibe , 2003, p. 34). The e o e, e en an ‘objec i e’
heo y o ela i e p ices based on he echnical condi ions ensuing ep oduc ion has a deg ee o
eedom coming om ou side he p ice equa ions, ep esen ed by he gi en ule o dis ibu ion o
he su plus.
F om he s andpoin o classical analysis, i is possible o a gue ha he de e mina ion o
ela i e physical ou pu s, i.e., he p opo ions o he sys em, s a s om he conside a ion o a
8
The ma ginalis p ocess o ‘inpu subs i u ion’ s a es ha he e exis s “an in e se mono onic ela ion be ween he
p opo ions o any wo inpu s and hei ela i e p ices” (Pasine i, 1977, p. 390). Fo an explana ion and c i ique, see
Pasine i (1977) bu also Mas-Colell (1989, p. 505).
9
Clea ly, his concep ion o ela i e p ices is in s iking con as wi h ha o ma ginalis heo y. P ices a e no indices
e lec ing subjec i e indi idual p e e ences on he desi abili y o commodi ies in e ms o hei ela i e sca ci ies.
A.L. Wi kie man 149
PSL Qua e ly Re iew
gi en (and measu able) se o commodi y balances. Howe e , i s in e p e a ion in e ms o
me hods o p oduc ion and ac i i y le els o di e en p ocesses is no unique.
10
The e o e, om gi en empi ical s uc u es, di e en mappings o heo e ical magni udes can
be a emp ed.
As o he p esen pape , he a gumen es s on he concep ion ha obse ed abula ions o
physical ou pu s in nominal e ms con ain bo h a sel - eplacemen componen and an
expansion/con ac ion componen , which need o be sepa a ed in some cases ( hough no in
o he s).
Wha , in any case, should be clea is he ole o he quan i y sys em in he dis inc ion o wha
e-en e s he ci cula low (and al e s he p oduc i e capaci y o he sys em) om wha does no
(and cons i u es a uly inal use). In his sense, we endo se he iew ha p oduced means o
p oduc ion a e induced by he e ec i e demand exe ed o inal ‘consump ion’ commodi ies.
11
In
o he wo ds, we concei e he ‘accele a o ’ ela ion – he induced cha ac e o in es men demand
– as a mechanism a he basis o ou pu de e mina ion. In ac , “[i] is his de i ed demand aspec
o in es men goods, due o hei being used as means o p oduc ion, ha is new and ypical o
p oduc ion sys ems” (Pasine i, 1981, p. 176).
Howe e , his conside a ion o in es men as induced by he g ow h end o inal e ec i e
demand should no be con used wi h he neoclassical ‘inducemen o in es ’. In he la e case,
demand o in es men is made equal o he supply o sa ings h ough changes in he a e o
in e es . Unde his iew, cu en in es men is seen as u u e consump ion, so he in e es a e is
an equilib a ing in e empo al p ice emune a ing he consump ion o gone oday. Hence, he
inducemen o in es is he emune a ion o he ‘sac i ice’ o wai ing. Abs ac ‘wai ing’ becomes
a ‘ ac o ’ o p oduc ion.
This neoclassical iew aises h ee poin s o discussion. Fi s , whe he he in e es a e
egula es a long-pe iod ade-o be ween p esen and u u e consump ion (cu en in es men ).
Second, whe he his long-pe iod ade-o ac ually exis s. And hi d, whe he abs ac wai ing can
be conside ed a ‘p ima y ac o ’ o p oduc ion on he same g ound as labou .
The i s poin can be quickly add essed by no ing ha i p esupposes he ope a ion o he
subs i u ion mechanism (bu om he dual quan i y side). In ac :
he s anda d one capi al good case displays a mono onically dec easing ela ionship be ween
consump ion le els and he a e o in e es […]. This does no gene alize and i is now well
unde s ood ha e en wi h only wo capi al goods, a non-mono one associa ion […] is possible
(Mas-Colell, 1989, p. 506).
Hence, he in e es a e canno be seen as a egula o o in e empo al consump ion le els, as i
simply does no p o ide unambiguous ‘p ice’ signals.
The second poin conce ns whe he highe in es men demand necessa ily implies lowe
consump ion le els. This can be answe ed by no ing ha , om a mode n classical pe spec i e,
capaci y adjus s o demand, and in es men gene a es he sa ings equi ed by he sys em (no
necessa ily h ough a change in income dis ibu ion be ween wages and p o i s), so ha an
10
As a gued in Ga bellini and Wi kie man (2014), empi ical ma ices o in e media e consump ion and g oss ixed
capi al o ma ion con ain implici expansion and con ac ion a es, because p oduc ion equi es ime. Hence, he
sepa a ion be ween ac i i y le els and echniques is no always s aigh o wa d.
11
This poin is c ucial. A capi al good is no s ic ly de e mined on he basis o which indus y is p oducing i , bu also
on he use ha is made o i , i.e., on whe he i e-en e s he ci cula low. The e o e, a machine ha is expo ed is
conside ed a inal consump ion commodi y, while s ocks o ci cula ing capi al p oduced in excess o sel - eplacemen
equi emen s ha a e de o ed o expanding p oduc i e capaci y in he ollowing pe iods a e conside ed new
in es men demand.
150 Concep ualising p oduc i i y measu emen om a classical pe spec i e
PSL Qua e ly Re iew
expansion o in es men does no imply a necessa y dec ease in he le el o consump ion ( hough
i will clea ly al e i s sha e in g oss ou pu ).
As o he hi d poin , i is pa icula ly in e es ing ha e en some app oaches ha claim o be
c i ical o ma ginal p oduc i i y heo y endo se he iew o ‘wai ing’ as a p ima y ac o o
p oduc ion:
Because capi al inpu s a e p oduced means o p oduc ion, inc eases in e iciency due o ad ances
in knowledge o inc easing e u ns o scale will b ing abou inc eases in he ou pu , inpu , and
s ocks o such capi al inpu s e en when p ima y inpu lows emain cons an [...] The ques ion ha
hen a ises is: Wha is (a e) he p ima y inpu (s) ha is (a e) behind he p oduced means o
p oduc ion? This is he ques ion a he hea o he Camb idge capi al con o e sy and has no hing
o do wi h he ques ion o he need o he easibili y o consis en agg ega ion (Cas and Rymes,
1991, pp. 8-9).
The answe o he ques ion sugges ed by hese au ho s eads:
Indi iduals, supplying labou ime, gi e up he immedia e consump ion o such ime in exchange
o he indi ec consump ion ha he selling o nonimmedia e consump ion o such ime a ails
hem. Labou ime sold is he measu e o he labou inpu in p oduc i i y measu es. Indi iduals, by
o going p esen consump ion and accumula ing capi al di ec ly o indi ec ly h ough he bond and
s ock exchanges, a e exchanging p esen o pe manen consump ion. The accumula ion o capi al
is he embodimen o he wai ing indi iduals ha e done. Wi h echnical p og ess, a gi en low o
wai ing (o he o going o a gi en low o p esen consump ion) may be embodied in an inc easing
accumula ion o capi al ha e lec s he e e -inc easing e iciency o wai ing and esul s in highe
le els o pe manen consump ion (Cas and Rymes, 1991, p. 11, emphasis added).
Wha his answe in ends o do is exhaus alue added (in his s ylised case consis ing o
p o i s and wages) in o as many ‘p ima y’ ac o s as he e a e componen s in i , and so jus i y
claims o sha es o alue added on he basis o he subjec i e ‘sac i ices’ o wo king and wai ing.
The e is again a p ecise a emp o es ablish a ‘na u al’ connec ion be ween an ins i u ional
phenomenon ( he dis ibu ion o income) and a physical phenomenon ( he accumula ion o
p oduced means o p oduc ion). Bu , e en mo e, his a emp is pe o med a he indi idual le el
(i is he single indi idual who wo ks and wai s).
Hence, he in e se mono onic ela ion be ween he eal wage a e and he a e o p o i s is he
ade-o be ween wo king (wi h he ensuing consump ion) and wai ing (wi h consequen
sa ing). The social dimension o income dis ibu ion has disappea ed (p o i s and wages a e
equally pe cei ed by single indi iduals), and in e pe sonal income dis ibu ion comes o he o e,
a guing ha he dis ibu ion be ween wages and p o i s is no e lec ing he dynamics o social
classes bu he in e io s uggle each indi idual has in deciding whe he o wo k and consume o
o wai and sa e esou ces.
The no ion o physical eal cos – ha eme ges om S a a’s (1960) sys em o p oduc ion –
aims a es ablishing a sha p b eak wi h any no ion o ‘cos ’ concei ed as he inducemen o
o e come he sac i ice o ende ing esou ces a ailable o hei p oduc i e use. In his sense, he
iew o ‘wai ing’ as a p ima y ‘ ac o ’ se es he same pu pose as he iew o he endowmen o a
‘quan i y o capi al’ (i jus eplaces s ocks wi h lows, ‘capi al’ by he ‘use o capi al’).
12
F om a classical pe spec i e his iew is un enable: long- un accumula ion is induced
p ecisely by he g ow h o consump ion and no by he abs inence om consuming and, while i
12
In ac , in hese analyses, he labou equi ed o he expansion o p oduc i e capaci y is conside ed as ‘capi al
p oduc i i y’ ha acc ues o ‘wai ing’ ( o example, see Gowdy and Mille , 1990, p. 594).
A.L. Wi kie man 151
PSL Qua e ly Re iew
is co ec ha p oduc ion akes ime, his by no means en ails ha sa ing beha iou in he pu sui
o in e es ewa ded as p o i has a ‘na u al’ igh o become a ‘p ima y’ ac o .
This heme leads o he ole o he quan i y o labou as an inpu in p oduc ion. On his issue
he e a e disag eemen s wi hin he classical adi ion, so hese conside a ions canno bu be
conside ed as highly pe sonal. I belie e one should ca e ully dis inguish be ween labou inpu s in
he sys em o p ices (i.e., he alue added side) and he ole o quan i ies o labou wi hin he
sys em o physical ou pu s (i.e., he expendi u e side).
In a sys em o p ice equa ions, quan i ies o labou a e explici ly conside ed as a componen
o p ices h ough wage paymen s. In his sense, by using ei he a uni o m wage a e o a ec o o
indus y wage a es, he sepa a ion be ween quan i ies o labou and hei a e o emune a ion
is an analy ical cons uc .
In his con ex , as done by S a a (1960, p. 10), wage a e di e en ials could be applied o
quan i ies o labou employed in e e y indus y in o de o ende hem homogeneous as ega ds
he p ocess o p icing (i.e., in o de o be able o emune a e each uni o labou wi h a uni o m
wage a e w). Bu his should no be in e p e ed as a p ocess ha ende s di e ing ‘p oduc i i ies’
o labou homogeneous. P oduc i i y plays absolu ely no ole in he applica ion o wage a e
di e en ials o quan i ies o employmen .
In con adis inc ion, as ega ds physical ou pu s (i.e., in a se o commodi y balances),
quan i ies o labou do no explici ly appea in he sys em o equa ions. Thei ole in he analysis
comes in when we acknowledge he necessa y link be ween o al employmen and g oss ou pu
( he human labou cu en ly employed in all indus ies adds up o he o al labou equi ed o
p oduce he g oss ou pu o he economy).
Bu i is possible o g adually modi y he disagg ega ion o o al g oss ou pu , s a ing om
he sum o g oss ou pu by indus y, hen ecognising indi ec equi emen s o sel - eplace
p oduc i e capaci y (and so de ining ne ou pu as he sum o new in es men and inal uses), un il
we accoun o he indi ec equi emen s o expand p oduc i e capaci y (and so de ining ne
ou pu consis ing only o commodi ies o inal uses). In each s ep, labou inpu s by indus y
applied o hese di e en di ec and indi ec commodi y equi emen s edis ibu e o al co-
exis ing employmen in o as many pa s as he e a e p oduc s, unde each de ini ion o ne ou pu .
Each o hese (logical) pa s cons i u es a subsys em – in he sense o S a a (1960, Appendix
A, p. 89) – and is iden i ied by he single componen o he ne p oduc o which i e e s.
In each o hese subsys ems, he employmen o all indus ies ha is used o he p oduc ion
o he iden i ying ne ou pu commodi y cons i u es he labou con en o his p oduc . This is he
logic adop ed behind he no ion o labou con en o commodi ies. And unde his concep ion,
quan i ies o labou employed in each indus y a e all equally necessa y o sa is y o al
ep oduc i e equi emen s. Each indus y is equally necessa y, di ec ly o indi ec ly, o p oduce
each single commodi y. Then, when applied o each decomposi ion o g oss ou pu , he ec o o
labou inpu s (measu ed in uni s o ull- ime employmen equi alen s o o al hou s) is
homogeneous, as ega ds he de e mina ion o he labou con en o commodi ies.
Two poin s dese e cla i ica ion. Fi s , while i is possible o in e p e he no ion o labou
con en as embodied labou , his can be done as long as i is clea ha we always e e o li ing,
co-exis ing, and concu en employmen .
13
The subsys em edis ibu es o al di ec employmen
in o di ec and indi ec labou equi emen s o ep oduce each di e en no ion o ne ou pu , bu
i is always a logical cons uc . In no way do we conside embodied labou as a locked-in subs ance
13
This iew is clea ly no new. In ac , on his speci ic aspec I ollow Hodgskin ([1825] 1969). See also Milga e and
S imson (2009, pp. 225-231).
152 Concep ualising p oduc i i y measu emen om a classical pe spec i e
PSL Qua e ly Re iew
a elling h ough his o ical ime (and me hods o p oduc ion) accumula ed in commodi ies
(du able means o p oduc ion, o example).
The second poin is ha , om he abo e conside a ions, i eme ges ha ze o p o i p oduc ion
p ices in e ms o labou commanded a e no necessa ily equal o labou con en o commodi ies.
While a p ice sys em conside s wage a e di e en ials, impo ed commodi ies, and axes on
p oduc s in he de ini ion o a ‘ze o p o i ’ p ice, he no ion o labou con en conside s only
domes ically p oduced commodi ies (i is g oss ou pu and no o al supply ha is edis ibu ed),
excludes axes on p oduc s, and conside s he ec o o labou inpu s as homogeneous ( he e o e
no allowing o a mul iplica ion by a ma ix o wage a e di e en ials). Hence, in all ci cums ances
conce ning ac ual sys ems (as di e en ly om a heo e ical model), hese wo magni udes will
no coincide.
In connec ion wi h his poin , no e ha nowhe e ha e I e e ed o he concep o ‘labou
alues’. The conside a ions jus made should make appa en ha i would dese e a mo e ca e ul
ea men han is cus oma ily done, hough his is no an aim o his pape .
Howe e , one u he ela ed aspec should be men ioned, and his is he indispensable
cha ac e o labou o he p oduc ion p ocess. In a sys em ha does no admi ull au oma ion,
i.e., labou is equi ed di ec ly o indi ec ly o p oduce a leas one basic commodi y,
14
labou
inpu s a e indispensable.
I would be qui e di icul o ind a sys em whe e comple e au oma ion we e possible. In such
a hypo he ical sys em, he no ion o labou con en would clea ly lose i s a ionale, as he
necessa y link be ween o al employmen and g oss ou pu would be los . As long as his is no
he case, he dis ibu ion o o al employmen in o logical pa s e eals i sel essen ial o assess
he deg ee o specialisa ion wi hin ac ual sys ems.
Gi en ha , in pu ely abs ac e ms, he no ion o physical p oduc i i y consis s o measu ing
he hy hm o ou pu gene a ion pe uni o inpu , i is possible o a ach o each dis ibu ion o
employmen among subsys ems a speci ic pa e n o ne p oduc pe uni o o al (di ec and
indi ec ) subsys em labou , sugges ing a consis en ou e o p oduc i i y analysis om a classical
pe spec i e
Howe e , be o e u he de elopmen o hese ideas, and in connec ion wi h he dual iew o
p ices and quan i ies a he oo o classical analysis, i migh p o e in e es ing o cla i y he
di e ence be ween wo e y simila e ms, wi h qui e dissimila meanings: p oduc i eness and
p oduc i i y.
3. P oduc i eness and p oduc i i y
The idea o p oduc i e, as opposed o unp oduc i e, human labou can be aced back o he
physioc a ic dis inc ion be ween ‘p oduc i e’ and ‘s e ile’ classes in Quesnay’s Tableau
Economique.
15
In Physioc acy, a class was conside ed ‘p oduc i e’ o ‘s e ile’ acco ding o whe he he labou
i employed gene a ed a ne e enue o no .
16
As en was he only ne income o he sys em,
whose o igin was ag icul u al labou , he only ‘p oduc i e’ class was ha o ag icul u al wo ke s.
14
In he sense o S a a (1960, p. 8).
15
See Gilibe (1977, Chap e 4) o a clea exposi ion and discussion.
16
No e he in e es ing meaning o he wo d e enue: “bo h he concep and he wo d came om F ance, whe e e enu
is he pas pa iciple o e eni , o e u n” (Gilibe , 1987, p. 171). He e, e enue means he e u n o he s a ing poin
in a ci cula scheme.
A.L. Wi kie man 159
PSL Qua e ly Re iew
In a mul isec o al economy, alue added is a esidual a he han an independen en i y, bo h
acco ding o su plus heo y and o he Sys em o Na ional Accoun s.
24
F om he equa ions abo e,
when he means o p oduc ion o sel - eplacemen a e deduced om g oss ou pu , an a i icial
sepa a ion be ween a p ice and olume componen is pe o med: 𝑋−𝑈 = pQ. I 𝑋 and 𝑈 a e
di e en composi e commodi ies, hen hei di e ence ( alue added) canno be an independen ly
measu able composi e commodi y o which a p ice index is a ibu ed. Value added is he e ec o
wo causes (𝑋 and 𝑈), so i is di icul o main ain ha i has a physical meaning in i sel .
25
Fu he mo e, aking alue added as a disagg ega ed measu e o ou pu does no gi e a
comp ehensi e pic u e o he p oduc ion p ocess. P oduc ion is ci cula , and commodi ies can be
gi en inal as well as in e media e uses. Fo p oduc i i y measu emen , i is c ucial o know he
a io be ween g oss ou pu and inal uses, as an economy wi h a highe a io would need mo e
g oss ou pu o p oduce he same physical su plus, in he p esence o inpu sa ing due o echnical
change. This is no necessa ily cap u ed a a disagg ega ed le el by a ne income measu e such as
alue added.
26
No e, hen, ha alue added canno be a cohe en disagg ega ed measu e o physical ou pu ,
and he ‘quan i y o capi al’ canno be a cohe en agg ega ed physical measu e o inpu s. Hence,
i is no a ma e o agg ega ion o disagg ega ion ha leads TFP g ow h o un in o ouble.
Bu e en g an ing a physical in e p e a ion o alue added, he common unc ional o ms used
o empi ical measu emen in adi ional analysis a e no exemp om an essen ial
dimensionali y c i ique, as ad anced by B ódy (1970, pp. 95-96). Conside a adi ional unc ion
like: Q = 𝐴𝐾𝛼𝐿1−𝛼, whe e Q is measu ed in low o money (M) pe yea (T), 𝐾 is measu ed as a
s ock o money (M), and 𝐿 is measu ed in man yea s (𝐻 ×𝑇). Then, we ha e: 𝑀/𝑇 = 𝐴×𝑀𝛼×
(𝐻 ×𝑇)1−𝛼.
Now, wha is he dimension o 𝐴 (i.e., he TFP pa ame e )? I 𝛼 = 1, 𝑀/𝑇 = 𝐴×𝑀, so 𝐴 = 1/𝑇
( he ecip ocal o TFP is measu ed in ime uni s, ‘p oduc i i y’ as ime). I 𝛼 = 0, hen 𝐴 = 𝑀/(𝐻 ×
𝑇2), which could be eo de ed o mean money low pe man yea . And wha i 0 < 𝛼 < 1 (which
is he no mally assumed case)? TFP pa ame e 𝐴 does no ha e any de ini e meaning. So, wha is
he dimension o TFP? I emains an open ques ion, unless one abandons i s pu ely physical
in e p e a ion, based on p oduc ion unc ions, and admi s ha TFP is an accoun ing ‘ esidual’,
simply e lec ing ‘ eal cos educ ions’.
27
As wi h he con usion in he dis inc ion be ween mic o/mac o and agg ega e/disagg ega ed,
i is gene ally hough ha TFP is a comple e (‘ o al’) measu e as agains ‘pa ial’ measu es ha
conside only, e.g., labou p oduc i i y. Bu i is pe ec ly possible o de i e measu es o o al
labou p oduc i i y as well.
28
The con usion has i s o igins in he way TFP (o he ‘ esidual’) has
been concei ed:
In whiche e o m, he measu ed esidual ypically accoun ed o an impo an ac ion o he
obse ed ou pu g ow h, qui e o en hal o mo e.
This esul came as a su p ise o he p o ession, hough pe haps less so o hose who eached i , o
some hing e y like i , by an al e na i e ou e. They we e he people who came a he p oblem ou
o a adi ion o measu ing labo p oduc i i y, and a some poin complemen ed ou pu pe wo ke
wi h a measu e o ou pu pe uni o capi al, and inally joined he wo o c ea e a measu e o o al
ac o p oduc i i y (TFP) (Ha be ge , 1998, pp. 1-2, emphasis added).
24
See Wi kie man (2022a, p. 496, oo no e 1) and he discussion in Wi kie man (2012, Chap e 3) o de ails.
25
On his poin , see Meade (2010).
26
See Rampa (1981b, p. 111) on his poin .
27
Fo example, see Ha be ge (1998, p. 3).
28
See Wi kie man (2012, Chap e 2) o a discussion and Ga bellini and Wi kie man (2014).
160 Concep ualising p oduc i i y measu emen om a classical pe spec i e
PSL Qua e ly Re iew
The ‘ adi ion o measu ing labou p oduc i i y’ (measu ed as indus y alue added pe uni o
labou ) was concep ually ocused on he p oduc i eness o labou , no on i s physical p oduc i i y.
The ‘ o al’ cha ac e o TFP comes om he concep ion o p oduc ion and dis ibu ion acco ding
o ma ginal p oduc i i y heo y. I capi al and labou a e he wo p ominen non-p oduced
p ima y ac o s, a measu e o p oduc i eness has o accoun o he ne income hey bo h gene a e.
Bu he quali ica ion ‘ o al’ is clea ly con ingen on a pu ely heo e ical choice.
Wha should be clea is ha wha dis inguishes a ‘pa ial’ om a ‘ o al’ physical p oduc i i y
measu e is no he di e en ia ed componen s in ne income bu whe he he gene al
in e dependence o he sys em is being aken in o accoun o no . A o al measu e o labou
p oduc i i y, i.e., he compu a ion o he labou con en o all (di ec and indi ec ) commodi y
equi emen s o ep oduce he ne ou pu (possibly expanding p oduc i e capaci y), conside s
capi al goods as well, accoun ing o hei ci cula ion as inpu s and ou pu s h ough he
‘con olu ed’ ne wo k o inpu -ou pu ansac ions.
And in his sense, he inpu -ou pu li e a u e on TFP g ow h measu emen is bo h ele an
and insigh ul.
29
Ne income and ne p oduc a e, in mos cases, clea ly di e en ia ed, and he
la e is used o de i e agg ega e measu es ( o example, see Wol , 1994, p. 81, eq. 3). Bu , while
in e dependence is accoun ed o as ega ds ci cula ing capi al inpu s, ixed capi al is s ill
concei ed as a p ima y ac o o p oduc ion in mos cases.
30
In any case, I hink he c ux o he ma e boils down o he lack o an explici dis inc ion
be ween physical p oduc i i y and p oduc i eness (i.e., p o i abili y). I he de i a ion o a TFP
igu e (be ha using p oduc ion unc ions o by means o inpu -ou pu schemes) s a s om a
heo y o alue added, i canno lead o adequa e measu emen o disagg ega ed physical
p oduc i i y. In ac , e en abandoning some s ingen assump ions o ma ginalis p oduc ion
heo y, and adop ing a scep ical iew o he esidual simply as a educ ion in eal cos s, he
con usion abou p oduc i eness and p oduc i i y emains:
A simple TFP measu e o i ms wi h mul iple ou pu s and mul iple inpu s is o look a he
p o i abili y o a i m, de ined as he e enue o he i m di ided by i s inpu cos . […] [A] s ic
compa ison […] is di icul since he ou pu and inpu p ices aced by hese i ms a e di e en . The
only op ion he e is o adjus he alue agg ega es […] o di e ences in p ice le els (Coelli e al.,
2005, pp. 62-63, emphasis added).
Howe e , o p i ilege a physical in e p e a ion o p oduc i i y does no mean in he leas o deny
he impo ance o p o i abili y changes in he e alua ion o he e ec s o echnical change in
employmen , ou pu p opo ions, and ela i e p ices. Wha mus be clea is he sepa a ion in
concep s and e minology ha is equi ed o dis inguish cause om e ec .
5. Subsys ems and p ices o p oduc ion
The dis inc ion be ween physical p oduc i i y and p o i abili y is no only es ablished by he
al e na i e e e ence o he expendi u e o alue added side o he economy as a s a ing poin ,
bu also o he uni o analysis o which each no ion e e s.
29
See, o example: Wol (1985), Gala in (1988), Wol (1994), en Raa (1994), Casle and Galla in (1997), as well as
Wi kie man (2012, Chap e 3).
30
See Pe e son (1979, pp. 218-219) and Wol (1994, pp. 84-86) o some excep ions.
A.L. Wi kie man 161
PSL Qua e ly Re iew
In ac , he economic sys em can be disagg ega ed in indus ies, p oducing a p oduc mix o
ou pu s, bu i can also be disagg ega ed in sel - eplacing and g owing subsys ems
31
ha p oduce
a single kind o inal commodi y. While p o i abili y measu es a e compu ed a he indus y le el,
disagg ega ed physical p oduc i i y measu es a e o mula ed wi h he subsys em in mind.
5.1. P oduc ion p ices and eigensys ems
Compu able p oduc ion p ices can be concei ed o as p ices implici in he (medley o )
echnique(s) in use in he economic sys em. They ep esen exchange a ios sa is ying necessa y
condi ions o ep oduc ion unde a gi en ule o dis ibu ion o he su plus (e.g., a uni o m p o i
ac o is compu ed in p opo ion o capi al ad anced).
The echnique in use can be hough o be con ained in measu able empi ical s uc u es, like
inpu -ou pu schemes. And empi ical s uc u es e eal changes in echniques when nominal
igu es can be sepa a ed in o a olume g ow h and a p ice componen . In his way, p oduc ion
p ices unc ion as agg ega o s applied o he quan i ies ac ually p oduced o measu e changes in
inpu s and ou pu s, hus allowing o quan i y he changing su plus (in alue e ms) be ween
e enues and ou lays by indus y (i.e., changes in p o i abili y due o echnical changes o a gi en
dis ibu i e con igu a ion).
An impo an ema k on me hod is in o de . No e ha , by in e p e ing compu able classical
p oduc ion p ices as a possible se o agg ega o s,
32
no p esump ion o desc ip i e o p edic i e
powe is a ibu ed o hem. By so doing, he aim is o sepa a e wo ields o inqui y.
In his sense, compu able p ices could be concei ed as one answe o he ollowing p oblem,
posed by S a a:
The p oblem is ha o asce aining he condi ions o equilib ium o a sys em o p ices and he a e o
p o i s, independen ly o he s udy o he o ces which may b ing abou such a s a e o equilib ium.
Since a solu ion o he second p oblem ca ies wi h i a solu ion o he i s , ha is he cou se usually
adop ed in mode n heo y. The i s p oblem howe e is suscep ible o a mo e gene al ea men ,
independen o he pa icula o ces assumed o he second; and in iew o he unsa is ac o y
cha ac e o he la e , he e is ad an age in main aining i s independence (D3/12/15: 2; emphasis
added) (Ku z and Sal ado i, 2005b, p. 433).
In ac , among he i s compu a ions o p ices o p oduc ion, he wo ks o Hejl e al. (1967), Kyn
e al. (1967) and Seke ka e al. (1970) – wi h an o igin in he dynamic inpu -ou pu p ice model –
had he aim o compa ing di e en p ice no ms applied o he same echnique in use.
Since hen, howe e , compu able p oduc ion p ices ha e been used o mul iple pu poses; o
example, he empi ical assessmen o capi al heo y pa adoxes, going om K elle (1977) o Han
and Sche old (2006). In connec ion wi h his a e he deg ee o (non-) linea i y o wage-p o i
schedules o di e en s anda ds o alue and he s udy o he de ia ion o labou alues
(empi ically de ined in a a ie y o ways) om p oduc ion p ices and ma ke p ices.
33
A ela ed
31
Th oughou he pape , he e ms sel - eplacing subsys em and e ically in eg a ed sec o a e used in e changeably,
and he same applies o he e ms g owing subsys em and e ically hype -in eg a ed sec o . While he no ion o sel -
eplacing subsys em was in oduced by S a a (1960, Appendix A, p. 89), i s compac ep esen a ion as a e ically
in eg a ed sec o was in oduced by Pasine i (1973), and i s ex ension o g owing subsys ems o hype -in eg a ed
sec o s was in oduced by Pasine i (1988). See Ga bellini and Wi kie man (2014) o a de ailed discussion.
32
Compu able p ices may be conside ed o be one among he many possible no ms, in he sense o Pasine i (1981, p.
127n).
33
See Ma zi (1993) o a e iew o hese lines o inqui y. The c ucial poin s unde discussion a e: (a) he empi ical
plausibili y o he neoclassical pa able o a su oga e p oduc ion unc ion, (b) he egula i y in ela i e p ice changes as
162 Concep ualising p oduc i i y measu emen om a classical pe spec i e
PSL Qua e ly Re iew
use has been o s udy compu able p ices unde he assump ion o he e ogeneous a es o p o i s
be ween indus ies ( hough gene ally main aining a ixed ela i e s uc u e o p o i a e
di e en ials).
34
Fo he pu pose o his pape , he in e es lies in he use o compu able p ices o measu e he
e ec s o echnological p og ess on he dis ibu i e possibili ies o he sys em, i.e., compu a ion
o changes in p o i abili y induced by changes in he echnique in use, o each gi en dis ibu i e
con igu a ion. Ope a ionally, his akes place by assessing he shape o ‘wage-p o i cu es’.
Among empi ical wo ks wi h his aim, i is possible o men ion:
1. The s udies o Ma zi and Va i (1977) (using only ci cula ing capi al) and Ma zi (1982)
(including also ixed capi al) o he I alian economy, assessing he Ha od-neu al cha ac e
o changes in echniques.
2. The wo ks o Ozol (1984, 1991) o Canada and he US, concluding on he ‘cos educing
au oma ion’ cha ac e o echnical change.
3. The s udy o Leon ie (1986) o he US, in oducing a linea p og am o ind he mos
p o i able ( o a gi en eal wage a e) echnique, a each easible alue o he a e o p o i s.
4. The s udy by Ma zi (1994) o he I alian economy (using only ci cula ing capi al), which
ela es he con exi y o he wage-p o i schedule (as each inal commodi y al e na i ely
becomes he s anda d o alue) o he capi al in ensi y o he (balanced) g ow h subsys em
associa ed wi h each inal p oduc .
5. The wo k o Degaspe i and F edholm (2010), p oposing he a ea unde al e na i e wage-
p o i schedules ( o a common numé ai e commodi y) as an indica o o he deg ee o
echnical p og ess ac oss ime and space, wi h an applica ion (using only ci cula ing capi al)
o selec ed OECD economies.
All o he abo e-men ioned s udies ha e in common a classical awa eness ha is applied o inpu -
ou pu da a. Some ela ed s udies analyse echnical change by means o wage-p o i cu es, which
a e buil only wi h na ional accoun s da a by indus y ( o example, see Michl, 1991; Fe e i,
2008).
When Leon ie (1951) no iced ha , by consolida ing inpu -ou pu accoun s, i was possible o
ob ain ze o ne income, he connec ed each income sou ce wi h a speci ic use o expendi u e.
Clea ly, he iew o an economy wi h bo h ze o ne income and ze o su plus p oduc co esponds
o a closed sys em, whe e all income-expendi u e loops a e endogenous.
In such sys ems, he e is comple e duali y be ween p ices and quan i ies and be ween income
and expendi u e ( he e a e no inal uses), and he no ions o p oduc i i y and p o i abili y acqui e
a dual cha ac e as well. Ma hema ically, he s uc u e o closed sys ems is usually o mula ed as
an eigen-p oblem, whe e he maximum (in modulus) eigen alue summa ises he sys em’s su plus
bo h in physical and alue e ms.
S a ing om he seminal wo k o B ódy (1970), di e en s udies ha e concep ualised he
measu emen o p oduc i i y inc eases as an eigenp oblem.
35
Though e y appealing om an
income dis ibu ion is al e ed, and (c) he empi ical plausibili y o a pu e labou heo y o alue. No e ha all h ee cases
imply a desc ip i e/p edic i e ole o he no ion o classical p oduc ion p ice.
34
See Flaschel (2010, Pa II, Chap e 8, sec ion 8.5) o de ails.
35
Fo example, Buccella o (1990) has used he le and igh eigen ec o s associa ed wi h he maximum eigen alue o
compu e sha es in p oduc ion acco ding o ‘s anda d p opo ions’ o e alue indus ies acco ding o hei associa ed
‘s anda d p ices’, in o de o de ec ma ke o e - and unde - alua ion. In ano he s udy, Aulin-Ahma aa a (1999, p.
358) de elops (only in heo e ical e ms) he ‘ ully e ec i e a e’ o p oduc i i y change, by assuming ha all inpu s a e
( e)p oduced (including labou ).
A.L. Wi kie man 163
PSL Qua e ly Re iew
analy ical poin o iew, i s empi ical implemen a ion is no s aigh o wa d. To adequa ely
sepa a e (s a is ical) p ices om olume g ow h, i is necessa y o neglec he p esence o
impo ed commodi ies (which ep esen a ull ma ix as opposed o a single column ec o o
expo s) as well as he p esence o axes on p oduc s and p oduc ion. Mo eo e , i is necessa y o
deal wi h an essen ial empi ical disa ay in bo h wages ≡ consump ion and p o i s ≡ in es men
heo e ical iden i ies.
In any case, he o mula ion o an eigensys em o he comple e ‘augmen ed’ ma ix and he
s udy o i s spec al p ope ies should no be con used wi h he compu a ion o he maximum
eigen alue o in e -indus y low ma ices o assess he in ensi y o use o in e media e inpu s
(gene ally ci cula ing capi al).
36
In hese cases, he spec al p ope ies se e as a summa ising
de ice (wi h eigen ec o s as a pa icula sys em o weigh s o agg ega ing ows and columns)
and no as a comp ehensi e measu e o su plus o sel -con ained closed sys ems.
5.2. Subsys ems
The measu emen o disagg ega ed physical p oduc i i y o labou wi h e e ence o he
subsys em as a uni o analysis has i s o igin in conside ing join ly Leon ie ’s (1953) compu a ions
o “ he oundabou , as compa ed wi h he di ec , e ec s which he changes in he inpu s uc u es
o a ious indus ies ha e on he o e -all p oduc i i y o labou ” (Leon ie , 1953, p. 39; emphasis
added), and S a a’s (1960, Appendix A, p. 89) cons uc i e algo i hm o build he logical de ice o
a subsys em.
37
E en be o e he appea ance o he subsys em, Pasine i (1959) (in eply o Solow’s (1957)
con ibu ion) had al eady no iced he need o accoun o he ep oducible cha ac e o capi al
goods, measu ing hem in e ms o inal commodi y-speci ic uni s o capaci y, in o de o de i e
physical measu es o p oduc i i y changes.
38
A e he subsys em had been de ised, Pasine i
(1963, Chap e V) in oduced he i s algeb aic and concep ual ela ions connec ing indus ies
wi h e ically in eg a ed sec o s (i.e., sel - eplacing subsys ems) o he s udy o echnical
p og ess.
Mo eo e , Gossling and Do ing (1966) p esen ed he i s empi ical applica ion o
p oduc i i y measu emen adop ing he subsys em as a uni o analysis. Gossling (1972) p o ided
a comp ehensi e empi ical s udy o p oduc i i y g ow h by subsys em, including a compa ison
wi h adi ional ‘pa ial’ and ‘ o al’ ac o measu es.
39
The c ucial idea behind he subsys em is i s deg ee o au onomy. By epa i ioning he whole
ow ec o o g oss ou pu s and he ma ix o in e media e uses by indus y in o as many logical
pa s as he e a e componen s in he column ec o o inal uses by commodi y, all means o
p oduc ion, labou , and ou pu s a e edis ibu ed in o each o hese pa s, acco ding o hei
con ibu ion as a suppo ing indus y o he ac i i y which p oduces he inal commodi y.
36
See, o example, Rampa and Rampa (1982) (including also ixed capi al and impo ed commodi ies) and Ma engo
(1992).
37
A ela ed app oach o he measu emen o di ec and indi ec labou equi emen s, explici ly ecognising i s meaning
as a ‘p oduc i i y’ index, has been ad anced by Vincen (1962), who sugges ed he e m “p oduc i i é in ég ale du
a ail” ( o al p oduc i i y o labou ). See Gossling (1972, pp. 52-54) o a discussion.
38
See Ga bellini and Wi kie man (2023) o an exposi ion o he deba e be ween Solow and Pasine i.
39
In a ela ed a icle, Gossling (1974) complemen ed his s udy conside ing he open economy, i.e., di ec and indi ec
equi emen s o impo ed commodi ies.
164 Concep ualising p oduc i i y measu emen om a classical pe spec i e
PSL Qua e ly Re iew
The edis ibu ion o commodi ies in associa ion wi h o he s, as an al e na i e o he
agg ega ion o indus ies, is ho oughly discussed by Leon ie (1967), who no iced ha
agg ega ion and educ ion we e wo s a egies o deal wi h oo de ailed empi ical s uc u es:
Agg ega ion, i.e. summa ion o essen ially he e ogeneous quan i ies, is one o he wo de ices ha
he economis uses o limi he numbe o a iables and unc ional ela ionships in e ms o which
he desc ibes wha he obse es. The o he is educ ion, ha is, elimina ion o ce ain goods and
p ocesses (Leon ie , 1967, p. 419).
In a undamen al con ibu ion, Pasine i (1973) es ablished explici connec ions be ween he
subsys em and he logical de ice o e ical in eg a ion, i.e., he educ ion o some commodi ies in
e ms o o he s. By in oducing a compac algeb aic ep esen a ion o a sel - eplacing subsys em,
as he esul o e ically in eg a ing co-exis ing o al employmen and capi al goods, i became
possible o wo k wi h al e na i e ep esen a ions o he same echnique in use, ei he in di ec
e ms (di ec labou and di ec p oduc i e capaci y) o in e ically in eg a ed e ms ( e ically
in eg a ed labou and p oduc i e capaci y).
Bu , e en hough i deal wi h he case o balanced g ow h, Pasine i’s (1973) cons uc
emained essen ially s a ic, in he sense o ep esen ing only sel - eplacing subsys ems. New
in es men s we e s ill included in he ne ou pu , so pa o he physical su plus o indus ies
p oducing capi al goods s ill needed o be exchanged be ween (o edis ibu ed among) hese sel -
eplacing sec o s, in o de o each o hem o expand hei commodi y-speci ic p oduc i e
capaci y. This clea ly posed di icul ies o he deg ee o au onomy o he sel - eplacing
subsys em.
40
Thus, in he con ex o a dynamic economy, Pasine i (1988) in oduced he logical de ice o
e ical hype -in eg a ion in explici associa ion wi h he no ion o a g owing subsys em. The key
di e ence is ha g oss in es men o sel - eplace and expand commodi y-speci ic p oduc i e
capaci ies is edis ibu ed among indus ies acco ding o hei ep oduc ion equi emen s (which
now include expansion/con ac ion) when he educ ion p ocess is pe o med. The e o e,
in es men becomes ully induced by he g ow h o e ec i e demand o inal uses.
41
Among he di e en wo ks ei he applying he concep o o al labou equi emen s o
explici ly adop ing a sel - eplacing subsys em pe spec i e, i is possible o men ion:
1. The s udy by Gup a and S eedman (1971) o he UK, in which di ec and o al labou
equi emen s a e compu ed, leading he au ho s o conclude ha “ o al (o sys em) labou use
alls bu less apidly han di ec labou use” (Gup a and S eedman, 1971, p. 32).
2. The empi ical s udies by Rampa (1981a) and Rampa and Rampa (1982), he heo e ical
conside a ions o Siniscalco (1982), and he wo k by F edholm and Zambelli (2009), which
explici ly adop Gossling’s (1972) ope a o o map be ween indus ies and sel - eplacing
subsys ems.
3. The s udies by Ochoa (1986), De Juan and Feb e o (2000), and Flaschel (2010, Pa I, Chap e
3, pp. 63-68), connec ing o al labou p oduc i i y o labou con en o commodi ies h ough
labou alues.
4. The heo e ical conside a ions by Sey ied (1988), who explici ly sepa a es e ically
in eg a ed labou p oduc i i y om e ically in eg a ed labou en abili y, his la e concep
measu ing “how much labou mus be disposed o p oduce one uni o ou pu […] i beside he
40
The idea o his sub le bu essen ial poin is due o Ga bellini (2010, pp. 48-51). The eade is e e ed o his sou ce
o a clea exposi ion and discussion.
41
See Ga bellini and Wi kie man (2014) o a de ailed exposi ion.
A.L. Wi kie man 165
PSL Qua e ly Re iew
ep oduc ion o capi al he capi al owne s can claim pa o he p oduc as p o i ” (Sey ied,
1988, p. 172).
5. The s udies by Milbe g and Elmslie (1992), Elmslie and Milbe g (1996), and Die zenbache e
al. (2000), which adop an inpu -ou pu app oach o s udy c oss-coun y con e gence o
labou p oduc i i y a he e ically in eg a ed le el.
Fu he de elopmen s o his line o esea ch ha e de ised, discussed, and empi ically
implemen ed sec o al (and agg ega e) p oduc i i y measu es in e ms o g owing subsys ems (o
e ically hype -in eg a ed sec o s):
1. The s udy by Ga bellini and Wi kie man (2014), es ablishing a di ec co espondence
be ween Supply-Use Tables and Pasine i’s (1973, 1988) heo e ical magni udes, making an
explici p ice- olume sepa a ion and explo ing he possibili y o empi ically sepa a ing
g ow h om he echnique in use.
2. The con ibu ion by B ondino (2019), applying he (hype -)subsys em app oach o he
Chinese economy, inding ha subsys ems wi h he highes p oduc i i y pe o mance had
been a ge ed by indus ial policy.
3. The wo k by Wi kie man (2022a), compa ing hype -in eg a ed p oduc i i y dynamics
amongs ad anced indus ial economies, inding ha p oduc i i y gains acc uing o wages
we e amongs he lowes in he economies wi h he highes o e all hype -in eg a ed labou
p oduc i i y g ow h.
4. The s udy by Ga bellini and Wi kie man (2023), o e ing a concep ual, analy ical, and
empi ical econs uc ion o he deba e be ween Solow (1957) and Pasine i (1959) on
p oduc i i y measu emen .
The idea o using he subsys em (o e ically in eg a ed sec o ) as a uni o analysis o he s udy
o echnical change has o en been c i icised (see, e.g., Sche old, 1982, p. 549, and Hagemann, 1987,
p. 346). I belie e his is mainly due o wo misunde s andings.
Fi s , e ical in eg a ion is some imes conside ed going backwa ds in ime, in a so o ‘neo-
Aus ian’ pe spec i e. I hink he o igin o his con usion comes om placing he gene al analy ical
de ice o e ical in eg a ion in he con ex o a speci ic join p oduc ion model ( he ‘pu e ixed-
capi al sys em’), in which machines o di e en yea s a e consolida ed – h ough a discoun ing
p ocedu e applied o he p ice equa ions – in o de o ob ain a single-p oduc sys em:
We may call his ope a ion ‘ e ical in eg a ion in a empo al sense’ o he ac i i ies employing he
machine in i s a ious yea s o age; i allows us o o mally elimina e he join -p oduc ion
componen and b ing he analysis back o he o ms o single p oduc ion wi h only ci cula ing
capi al (Baldone, 1980, p. 96).
Second, i is some imes main ained ha a es o p oduc i i y g ow h a he e ically in eg a ed
le el a e exogenous da a o he analysis:
The indus y-speci ic na u e o echnical change also implies ha , con a y o Pasine i’s
assump ion, a es o p oduc i i y g ow h in he di e en e ically in eg a ed sec o s canno be
hough o as being independen o each o he (Hagemann, 1987, p. 346).
166 Concep ualising p oduc i i y measu emen om a classical pe spec i e
PSL Qua e ly Re iew
In his case, I hink he o igin o he con usion comes om aking a speci ic desc ip ion o he
echnique in use p esen in Pasine i’s (1981) model – in which capi al goods a e p oduced by
labou alone – and assigning o i a gene al in e p e a ion o e ically in eg a ed magni udes.
42
Pasine i’s (1981) ‘in e media e case’ (i.e., a desc ip ion o echnology wi hou basic
commodi ies) was hough o as a pu ely exposi o y heo e ical de ice. In his pa icula case, he
a es o g ow h o di ec labou coe icien s coincide wi h hose o e ically (hype -) in eg a ed
labou coe icien s. Bu his is clea ly a om being a gene al p inciple.
In ac , i is appa en ha e ically (hype -) in eg a ed magni udes a e de i ed om indus y
le el ones, claiming no logical p imacy o independence.
43
In any gene al empi ical applica ion,
e ical in eg a ion is a de ice applied o exis ing di ec (indus y) magni udes o ob ain de i ed
( e ically in eg a ed) p oduc i i y g ow h a es.
This second sou ce o misunde s anding wa ns, howe e , o he impo ance o making a clea
s a emen as ega ds he aims and pu poses o p oduc i i y analysis om he pe spec i e o
subsys ems. As s a ed by Pasine i himsel :
he analy ical de ice o e ical in eg a ion is no mean o ca ch he de ailed and localized sou ces
o echnical change; on he con a y, i is mean o syn hesize he o e all e ec o echnical change
(wha e e i s sou ces, o na u e, o emo e localiza ion in he economic sys em) on he inal s age
o p oduc ion, o p ices and o employmen (Pasine i, 1990, p. 258, emphasis in he o iginal).
Thus, he ocus is on measu ing he e ec s o echnical change on p opo ions, p ices, and
employmen and no o s udy he causes behind changing p oduc i i ies.
5.3. Measu ing p oduc i e capaci y
In a mul isec o al economy, a scala o subsys em measu e o physical inpu pe uni o ou pu is
no s aigh o wa d o ob ain, gi en he mul i ude o ou pu -inpu p oduc i i y a ios p esen in
he economy. I is necessa y o sol e he agg ega ion o commodi ies, o he educ ion o some o
hem in e ms o o he s.
This is pa icula ly di icul o capi al goods, which, by being ep oducible, a e hemsel es
subjec o p oduc i i y imp o emen s. In ac , in he summa y eco d o he deba e a he 1958
Con e ence on he Theo y o Capi al, Kaldo no iced wo adically di e en posi ions on his issue:
One ex eme case was o assume ha he e was no echnical p og ess in he p oduc ion o capi al
goods bu ha hese always equi ed he same amoun o eal esou ces. This was ob iously qui e
un ealis ic. A he o he ex eme, one could say ha a uni o capi al was wha e e uni was capable
o p oducing a gi en ou pu in a gi en yea – igno ing bo h longe and sho e ou pu s eams. He e
any dis inc ion be ween he quan i y o capi al and i s p oduc i i y was washed away by he
de ini ion i sel . Any idea ha capi al migh ha e a ying p oduc i i ies was los ; i s ou pu was
always cons an (Hague, 1961, p. 304, emphasis added).
The i s ‘ex eme case’ co esponds o he adi ional TFP ea men o he ‘quan i y o capi al’,
in which a TFP g ow h measu e is assumed o cap u e disembodied e iciency changes,
independen ly om capi al deepening, which a e assumed o equi e he same amoun o eal
esou ces (e.g., ‘wai ing’) pe uni o sa ing.
The second ‘ex eme case’ consis s in measu ing capi al goods in ‘uni s o capaci y’, i.e., as a
se o composi e commodi ies o he e ogeneous physical con en , speci ic o each inal p oduc
42
See Ga bellini (2010, pp. 152-155) o a de elopmen o he a gumen and Ga bellini (2010, pp. 138-164) o a eply
o o he c i icisms o he e ically (hype -) in eg a ed app oach.
43
See he ea ly commen s by Pasine i (1963, Chap e V).
A.L. Wi kie man 167
PSL Qua e ly Re iew
o he economy. Bu hen, i capaci y is de ined in e ms o he inal ou pu ac ually p oduced, a
e e y momen he numbe o uni s o commodi y-speci ic capaci y would coincide wi h he
numbe o uni s o each inal p oduc (Kaldo ’s idea o a ‘cons an ou pu coming om capi al’).
Howe e , by adop ing such a measu ing od, he ‘quan i y o capi al’ in eal e ms would no
be needed anymo e, and, a he same ime, each o hese composi e commodi ies would change
hei physical composi ion om one pe iod o he nex , hough e aining hei unc ion as
commodi y-speci ic ‘p oduc i e capaci ies’. This ou e was p ecisely he one aken by Pasine i
(1959) h oughou his app oach o s uc u al economic dynamics.
44
Wha Kaldo obse es is ue,
‘ he di e ence be ween he quan i y o capi al and i s p oduc i i y’ is dispensed wi h. Bu his is
no a p oblem when p oduc i i y measu emen is no concei ed om he alue added side, as
he e is no ne income o dis ibu e among ‘ ac o s’. In ac , he p ocedu e o using a educ ion
( h ough e ical in eg a ion) a he han an agg ega ion o capi al goods is pe ec ly in line wi h
adop ing a subsys em pe spec i e.
6. By way o conclusion
I is o cou se ue ha “ o measu e is no o unde s and” (Sal e , 1966, p. 1), and his is
pa icula ly so as ega ds p oduc i i y analysis:
One o he easons why in e p e a i e analysis o p oduc i i y has been slow o de elop has been
he in e minable con o e sy o e wha is p oduc i i y and wha do we eally wish o measu e. The
wo d now ca ies a mul i ude o meanings; o some i measu es he pe sonal e iciency o labou ;
o o he s, i is he ou pu de i ed om a composi e bundle o esou ces; o he mo e philosophic, i
is almos synonymous wi h wel a e; and in one ex eme case i has been iden i ied wi h ime. I
pe sonally belie e ha much o his discussion has p o ed ui less and only se ed o con use he
issues o measu emen wi h he issues o in e p e a ion. Unless he e is a e olu ion in s a is ical
echniques and in o ma ion, only one ype o p oduc i i y concep is measu able. This is he concep
o ou pu pe uni o inpu (Sal e , 1966, p. 2, emphasis added).
Fa om being a i ial s a emen , he posi ion aken by Sal e (1966) was no he usual one a he
ime o w i ing (and, clea ly, e en less nowadays). Bu i hope ully se es o cla i y he b oad
o e iew p esen ed in he p eceding sec ions. In sum, I belie e ha applied p oduc i i y (and
p o i abili y) analysis om a classical pe spec i e ough o be ca ied ou by measu ing changes in
physical inpu use pe uni o ou pu (as seen om he expendi u e side) using (g owing)
subsys ems, as well as s udying he e ec s ha changes in physical p oduc i i y ha e on he
(p ice) su plus o he sys em (as seen om he alue added side), using p oduc ion p ice sys ems.
Expendi u e depends on commodi y ci cula ion, on ma e ial balances, on p opo ions: g oss
o ne p oduc . In sum, on physical ou pu s. Value added depends on commodi y ci cula ion-cum-
exchange, and exchange implies ela i e p ices (and so s anda ds o alue).
P oduc i eness s a s om he exchange o commodi ies wi hin he capi alis mode o
p oduc ion: ne income and dis ibu i e ules mus be aced. P oduc i eness is mic o-economic;
i can be applied o a single agen , a i m, an indus y. And, o ge o he o e all economy,
agg ega ion is necessa y.
P oduc i i y, ins ead, s a s om he ‘collec i e labou e ’, om he labou con en in he
ci cula ion o commodi ies, e ealing a con inuous and dynamic p ocess o di ision o labou ,
specialisa ion, au oma ion and echnological unemploymen (labou sa ing ends), coun e ac ed
by e ec i e demand. P oduc i i y is mac o-economic; he e is no sense in sea ching o he
44
See Pasine i (1963, 1973, 1981, 1986, 1988). See also Ga bellini and Wi kie man (2023).
168 Concep ualising p oduc i i y measu emen om a classical pe spec i e
PSL Qua e ly Re iew
p oduc i i y o an indi idual, as he c ucial poin o p oduc i i y analysis is gene al
in e dependence. Tha is why p oduc i i y measu es s a om he subsys em, he minimal uni
o analysis, no ma e he le el o agg ega ion chosen. In ac , Pasine i’s (1959) i s a emp a
he concep o p oduc i i y was limi ed o an economy wi h wo subsys ems, bu he wo c ucial
ones: a sec o p oducing he means o p oduc ion, he o he p oducing inal uses. His in ui ions
could la e be gene alised, hanks o educ ion and no agg ega ion.
Reduc ion, o exp essing some commodi ies in e ms o o he s, has u ned ou o be one
impo an analy ical de ice o p oduc i i y measu emen om a classical pe spec i e. Ano he
one has been o measu e capi al goods in ‘capaci y uni s’, i.e., in e ms o he inal commodi ies
ha can be ep oduced wi h hem. Bu hen i is clea ha , o ha e a capaci y-uni o measu emen ,
i becomes necessa y o sepa a e wha e-en e s he p oduc ion p ocess om wha is a uly inal
use. And o his ask i is he expendi u e side, he physical su plus, which needs o be analysed.
I s c ucial componen is in es men : a dual concep in i sel . In es men is a sou ce o demand, o
expendi u e, bu i also gene a es capaci y, al e s he means o p oduc ion ha ha e o be p iced
in he alue added side.
G oss in es men , i.e., ( ixed) capi al accumula ion, plays a c ucial ole in p oduc i i y analysis,
so he mechanism behind i s ea men o p oduc i i y measu emen in he con ex o empi ical
g owing subsys ems should be ende ed explici :
in each yea , he g oss in es men unde aken by each indus y ep esen s he low o capi al goods
equi ed o main ain he indus y on i s cu en g ow h pa h (Pe e son, 1979, p. 220).
In ac , aced wi h mul i-pe iod accoun ing iden i ies om he side o physical ou pu s, we obse e
only quan i ies p oduced. The sepa a ion be ween me hods o p oduc ion and ac i i y le els o
indus ies is analy ical. I we assume uni a y ope a ion in ensi ies, his leads o echnique-cum-
in ensi y le el low ma ices. This obse a ion means ha i is no possible o sepa a e, on en i ely
‘objec i e’ g ounds, g ow h om echnical change in empi ically gi en s uc u es: empi ical
ma ices con ain g ow h a es.
All in all, on p oduc i i y analysis om a classical pe spec i e, almos e e y hing awai s o be
empi ically explo ed. This pape has been only a s uc u ed in i a ion o hink abou ounda ional
concep s and some exis ing li e a u e ha may help i g ow u he .
In his sense, he e a e se e al di ec ions o u he esea ch. Wi h he consolida ion o in e -
coun y p oduc ion ne wo ks and he a ailabili y o global in e - egional inpu -ou pu (IRIO)
da a, i has become possible o measu e p oduc i i y by ep esen ing a global alue chain as an
in e na ional subsys em p oducing a inal p oduc . Bu , while p oduc i i y became an
in e na ional concep , compe i i eness emained a na ional one, so i would be in e es ing o
unde s and hei in e play in a global economy. As ega ds echnological change, new (concep ual
and empi ical) challenges eme ge o measu e p oduc i i y and p o i abili y in an e a o as
au oma ion and indus ial obo isa ion, whe e ixed-capi al becomes e e -inc easingly malleable
(Wi kie man, 2022b, p. 274). I au oma ion was aken o an ex eme, would he indispensable ole
o labou in p oduc ion be a isk? Finally, wi h he inc easing digi alisa ion o p oduc ion
p ocesses, he e is a need o unde s and he nuances o p oduc i i y measu emen when he
di e ences be ween physical and digi al ou pu s (and hei associa ed inpu s) become appa en
(Wi kie man, 2022b, p. 280).
