Differences in total factor productivity and the pattern of international trade

Be sa os, Ge assimos; Tsounis, Nicholas
A icle
Di e ences in o al ac o p oduc i i y and he pa e n o
in e na ional ade
Economies
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Sugges ed Ci a ion: Be sa os, Ge assimos; Tsounis, Nicholas (2024) : Di e ences in o al ac o
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Ci a ion: Be sa os, Ge assimos, and
Nicholas Tsounis. 2024. Di e ences in
To al Fac o P oduc i i y and he
Pa e n o In e na ional T ade.
Economies 12: 85. h ps://doi.o g/
10.3390/economies12040085
Academic Edi o : Sajid Anwa
Recei ed: 12 Feb ua y 2024
Re ised: 4 Ap il 2024
Accep ed: 4 Ap il 2024
Published: 9 Ap il 2024
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economies
A icle
Di e ences in To al Fac o P oduc i i y and he Pa e n o
In e na ional T ade
Ge assimos Be sa os 1and Nicholas Tsounis 1,2,3,*
1
Labo a o y o Applied Economics, Depa men o Economics, Uni e si y o Wes e n Macedonia, Fou ka A ea,
52100 Kas o ia, G eece; [email p o ec ed]
2School o Social Sciences, Hellenic Open Uni e si y, 26335 Pa as, G eece
3School o Economics and Managemen , Open Uni e si y o Cyp us, Nicosia 2252, Cyp us
*Co espondence: [email p o ec ed]
Abs ac : In his wo k, we de elop a ade model ha explains he pa e n o ade be ween coun ies
based on di e ences in o al ac o p oduc i i y (TFP) while also accoun ing o di e ences in ela i e
ac o endowmen s. The no el y s ems om he in oduc ion o p oduc ion unc ions de i ed by
combining he Rica dian and Hecksche –Ohlin–Samuelson (H-O-S) heo ies, wi h TFP di e ences
se ing as he basis o compa a i e ad an age. To his end, a es able hypo hesis is de i ed. Fo he
empi ical measu emen o he TFP in each indus y and coun y, a cons an elas ici y o subs i u ion
(CES)- ype p oduc ion unc ion was employed, and he TFP was calcula ed as he Solow esidual
om he p oduc ion unc ion’s ixed e m. To o e a be e unde s anding, he model was es ed o
he bila e al ade be ween Ge many and Russia, and Ge many and he Czech Republic. I was ound
ha TFP di e ences can be used as a basis o explaining compa a i e ad an ages and, consequen ly,
he bila e al pa e n o ade be ween wo coun ies.
Keywo ds: TFP; Rica dian ade model; Hecksche –Ohlin–Samuelson ade model; Ge many; Russia;
ank es
1. In oduc ion
To al ac o p oduc i i y (TFP) ep esen s he po ion o he ou pu ha canno be
desc ibed by he numbe o inpu s u ilised in p oduc ion o he e ec i eness wi h which
hose inpu s a e u ilised. The TFP is a c ucial componen in bo h long- e m and sho - e m
changes in economic g ow h (Tsounis and S eedman 2021). Acco ding o Akkaya and
Gü e cin (2018) and Kim and Loayza (2019), TFP encompasses he e ec s o economies o
scale on he p oduc i i y o capi al, na u al esou ces, and labou as well as ad ancemen s
in he alloca ion o p oduc i e ac o s and ac o -disembodied echnical inno a ion, which
also cons i u e i s h ee pa s. TFP’s elemen s and, he e o e TFP, di e om na ion o
na ion; Lopez-Ca los (2009) and Po e (2003).
Since (Ab amo i z 1956) and (Solow 1956) made hei ini ial measu emen a emp s,
TFP has been ci ed as one o he key ac o s in luencing economic g ow h. Ea ly s udies,
such as hose by (Me cal e 1997;G ossman and Helpman 1991;Aghion and Howi 1992;
Coe and Helpman 1995;Coe e al. 2009), ha e demons a ed ha TFP is in luenced by bo h
domes ic and o eign esea ch and de elopmen (R&D), human capi al, business cycles,
in as uc u e, he openness o he economy, and o eign di ec in es men (FDI) and FDI
om one’s own coun y ab oad. I was also disco e ed in he li e a u e ha he e ec
o R&D on TFP a ies. Ins i u ions play a ole, al hough hey di e o la ge and small
na ions (Acemoglu e al. 2006). Simila ly, (Kim e al. 2016) di ided he ac o s in luencing
p oduc i i y de elopmen in o i e ca ego ies: (1) educa ion, i.e., he abili y o he wo k o ce
o abso b he knowledge o new echnologies; (2) ma ke e iciency, i.e., e icien and
lexible alloca ion o esou ces by sec o and en e p ise; (3) inno a ion and c ea ion o new
echnologies; (4) in as uc u e, especially anspo , elecommunica ions, ene gy, wa e ,
Economies 2024,12, 85. h ps://doi.o g/10.3390/economies12040085 h ps://www.mdpi.com/jou nal/economies
Economies 2024,12, 85 2 o 19
sewage, and sani a ion; and (5) ins i u ions, i.e., egula ion, judicia y, police, p o ec ion o
p ope y igh s, and undamen al ci il igh s, o ensu e social and economic s abili y.
Howe e , in addi ion o being a d i e o g ow h, TFP also shows how e icien ly
inpu s a e used and, he e o e, a ec s he cos o p oduc ion in he a ious sec o s o he
economy. Gi en ha he TFP o he same sec o di e s ac oss coun ies, i is also ob ious
ha i should a ec he compa a i e ad an ages o a coun y and, he e o e, i s pa e n o
in e na ional ade.
The Rica dian and Hecksche –Ohlin models a e he ounda ion o in e na ional ade
heo y bu e isi ing hem is essen ial due o he apid echnological ad ancemen s and
changing global economic dynamics. These ad ancemen s ha e al e ed he na u e o
compa a i e ad an age by a ec ing p oduc i i y, inno a ion, and p oduc ion p ocesses.
T adi ional models may no ully cap u e he complexi ies o mode n p oduc ion ne wo ks.
New ade models ha inco po a e he e ogeneous i ms p o ide insigh s in o how p oduc-
i i y a ia ions wi hin indus ies shape compa a i e ad an age and ade ou comes.
Examining he in e ac ion be ween i m-le el p oduc i i y and compa a i e ad an age
en iches ou unde s anding o ade dynamics beyond adi ional models. In ou case,
in eg a ing TFP di e ences in he model allows o a mo e dis inc unde s anding o
he sou ces o compa a i e ad an age, while also ecognising he dynamic cha ac e o
compa a i e ad an age and accommoda ing changes in echnological capabili ies and
ac o endowmen . All sou ces a ec ing TFP, including ex e nal economies o scale, na u al
esou ces, and labou , as well as ad ancemen s in he alloca ion o p oduc i e ac o s
and ac o -disembodied echnical inno a ion, along wi h ela i e ac o endowmen s,
a e implici ly conside ed o a ec compa a i e ad an ages. The app oach o e s a mo e
ealis ic amewo k o policymake s and esea che s o analyse ade pa e ns and make
in o med decisions.
In his wo k we de elop a ade model ha p edic s he pa e n o ade be ween
coun ies based on TFP di e ences ac oss coun ies, accoun ing o di e ences in ela i e
ac o endowmen s. In his sense, i in oduces p oduc ion unc ions ha a e de i ed
by mixing he Rica dian and Hecksche –Ohlin–Samuelson (H-O-S) heo ies, wi h TFP
di e ences se ing as he basis o compa a i e ad an ages; mo eo e , a es able hypo hesis
is de i ed. The s uc u e o his pape is as ollows: Sec ion 2p esen s he li e a u e
e iew o TFP measu emen . In Sec ion 3, he ade model is p esen ed, he pa e n o
ade be ween coun ies is explo ed, and a es able condi ion o he alidi y o he model
o p edic he pa e n o ade is p esen ed. Sec ion 4p o ides empi ical e idence, and
Sec ion 5concludes he pape .
This pape ’s con ibu ions o he li e a u e a e as ollows: (a) i de elops a ade model
based on he combina ion o he classical and H-O-S heo ies o ade using sec o al TFP
di e ences among coun ies o p edic he bila e al pa e n o ade. Fu he , (b) a es
is sugges ed o he empi ical alidi y o he model, and inally, (c) he empi ical es is
pe o med in he ac ual ade lows be ween Ge many and wo o i s ade pa e ns, namely,
Russia and he Czech Republic.
2. Li e a u e Re iew on TFP Measu emen
To al ac o p oduc i i y measu emen s a e c i ical in analysing and unde s anding he
dynamics o in e na ional ade. In he con ex o in e na ional ade, TFP measu emen s aid
in de e mining he o e all p oduc i i y g ow h o a ious coun ies and egions, shedding
ligh on hei compe i i eness and compa a i e ad an ages. TFP measu emen s p o ide
insigh s in o he de e minan s o economic g ow h and allow o c oss-coun y compa isons
o p oduc i i y le els. Th oughou he yea s, nume ous a emp s o measu e o es ima e
TFP ha e been made. In his sec ion, a selec ion o hose wi h an in e na ional ade ocus
will be p esen ed.
Lipsey and Ca law (2004) p esen ed a no el app oach o measu ing TFP, which quan-
i ies he con ibu ions o echnological ad ances o economic g ow h. Mo e p ecisely,
he au ho s acknowledge he undamen al di icul y o e ec i ely cap u ing echnological
Economies 2024,12, 85 3 o 19
change, pa icula ly he unobse able ea u es ha a e equen ly neglec ed in ypical
TFP assessmen s. To add ess his issue, a model ha seeks o accoun o bo h obse -
able and unobse able echnological ad ancemen was de eloped. The o iginali y o his
me hod lies in he inclusion o elemen s such as physical capi al in es men s, labou o ce
composi ion, and human capi al accumula ion o accoun o TFP g ow h. Fu he mo e,
by dis inguishing be ween embodied and disembodied echnological change, he model
p esen s a mo e dis inc unde s anding o echnological ad ancemen s. This dis inc ion
is c i ical because i enables a ull assessmen o how echnology a ec s p oduc i i y di -
e en ly in di e en sec o s o he economy. Howe e , he e a e ce ain d awbacks o his
s a egy. Inco po a ing addi ional componen s and dis inguishing be ween di e en o ms
o echnological de elopmen migh make he model mo e complex and di icul o apply
in p ac ice.
In he con ex o he OECD coun ies, (Mendi 2007) in es iga ed he e ec s o dis-
embodied echnology ade on TFP. The s udy explo es how c oss-coun y echnological
knowledge exchange migh a ec a coun y’s economic pe o mance and echnological
g ow h. In e ms o empi ical analysis, his s udy seeks o in es iga e he ela ionship
be ween disembodied echnology ade and TFP by iden i ying and measu ing he low
o disembodied echnology in OECD coun ies and assessing how his ade in e ac s
wi h changes in TFP. The indings sugges ha ade in disembodied echnology has a
conside able impac on TFP g ow h, especially in he G7 coun ies. This esul is signi ican
since i calls in o ques ion he no ion ha physical capi al goods ade is he majo d i e o
economic g ow h.
The complexi ies o es ima ing TFP g ow h in he con ex o he Chinese economy
we e analysed by (Heshma i and Kumbhaka 2011). Mo e pa icula ly, he wo k was
conce ned wi h echnical change equi emen s and es ima ion using obse able in e nal and
ex e nal causes o echnological change. TFP g ow h was es ima ed and decomposed in o
echnological change, economies o scale, and echnology index componen s. To in es iga e
he ela ionship be ween echnical change and TFP g ow h in a ious Chinese egions, he
anslog p oduc ion unc ion and he echnological index we e compu ed using da a om
30 p o inces be ween 1993 and 2003. The au ho s’ analysis unde lined he need o p ecisely
calcula e TFP g ow h o assess he economic success o China’s p o inces. They highligh
he di icul ies in a ibu ing TFP de elopmen pu ely o echnological imp o emen , as well
as o he ac o s, such as human capi al and in o ma ion and communica ion echnology,
he low o o eign di ec in es men , and s a e-ini ia ed e o m p og ams.
B and e al. (2012) epo a comp ehensi e collec ion o i m-le el TFP es ima es o
China’s manu ac u ing sec o , spanning China’s WTO accession. The s udy’s cen al ocus
is on de e mining whe he epo ed p oduc i i y g ow h in Chinese manu ac u ing i ms is
genuine, i.e., due o c ea i e des uc ion, which ep esen s eal imp o emen s in e iciency,
o po en ially a i icial, i.e., due o c ea i e accoun ing, which includes ac o s such as da a
manipula ion. The au ho s examine whe he epo ed TFP gains uly indica e inc easing
ope a ional e iciency o i hey a e impac ed by ac o s using i m-le el da a om 1988 o
2007. Acco ding o he indings, di e en sec o s o Chinese manu ac u ing demons a e
dis inc pa e ns o p oduc i i y inc ease. Speci ically, some indus ies epo p oduc i i y
gains as a esul o echnology b eak h oughs, while o he s appea o be in luenced by
accoun ing p ac ices. Howe e , his explana ion appea s o be highly a iable ac oss i ms.
Based on he I alian manu ac u ing sec o , An onelli and Scella o (2013) s udied
i m-le el complexi y, social in e ac ions, and TFP. Acco ding o he au ho s, he le el o
complexi y wi hin a co po a ion, pa icula ly in e ms o social in e ac ions and in o ma ion
lows, has a subs an ial e ec on echnical change. They con end ha i ms in ol ed in
mo e complica ed knowledge a e mo e likely o bene i om echnological b eak h oughs
as a esul o he spillo e e ec . In e ms o da a, he au ho s used i m-le el TFP om 1996
o 2005 o a sample o 7020 I alian manu ac u ing i ms. This enables hem o highligh
he dis inc i e ole o egional, in e egional, and localised in a-indus ial knowledge
Economies 2024,12, 85 4 o 19
in e ac ions as dis inc and majo causes o changes in i m-le el TFP, alongside in e nal
esea ch and inno a ion ini ia i es.
A c oss-coun y panel i m-le el da abase was employed by (Gal 2013) o in es iga e
he measu emen o TFP a he indi idual i m le el using da a om he OECD-ORBIS
da abase. The pape indica ed ha no all p oduc i i y indica o s o all na ions can be
calcula ed using eadily a ailable da a, and al e na i e solu ions o his p oblem can be
sugges ed by applying impu a ions o speci ic a iables. Fu he mo e, he pape assessed
he accu acy o hese impu a ions ac oss a se o na ions whe e he a ailable da a in he
ORBIS include a wide ange o TFP measu es. In e ms o he empi ical esul s, he
es ima ion-based app oaches p oduced TFP es ima es ha we e e y close o each o he ,
whe eas he index numbe s we e lowe . The s udy assessed p oduc i i y using al e na i e
me hodologies o coun ies wi h consis en da a co e age as a con ibu ion o he li e a u e
on p oduc i i y assessmen s.
In he con ex o he Ko ean manu ac u ing sec o , Oh e al. (2014) es ima ed TFP
g ow h, echnological change, and ela ed measu es using i m-le el panel da a om
7462 Ko ean manu ac u ing i ms om 1987 o 2007. The au ho s es ima ed wo di e -
en o mula ions o echnological change measu ed by ime ends and he gene al index
app oach. Se e al ex ensions o each s a egy we e also assessed, along wi h hei ad an-
ages and limi a ions. The s udy compa ed he pa ame ic TFP g ow h measu e o he
nonpa ame ic Solow esidual in addi ion o es ima ing and decons uc ing TFP g ow h.
The indings we e mixed, wi h no no iceable di e ences in empo al pa e ns o echnical
change based on company size and simila o e all a e age a es o TFP g ow h ac oss
all models.
Sa pa hy e al. (2017) in es iga ed he measu emen o TFP and a emp ed o disco e
i m-speci ic de e minan s in luencing p oduc i i y in Indian manu ac u ing i ms om
1997 o 2013. The au ho s pa icula ly used he Le insohn and Pe in (L-P) me hod o assess
TFP and he ully modi ied o dina y leas squa es (FMOLS) app oach o s udy i m-speci ic
de e minan s o TFP. The au ho s disco e ed ha disembodied and embodied echnologies
play a signi ican ole in de e mining TFP ac oss subindus ies and all i ms. Acco ding o
he indings, he key sou ces o p oduc i i y o Indian manu ac u ing i ms a e echnology,
size, and i al y in he o m o aw ma e ial impo s. This conclusion is consis en wi h he
indings in he li e a u e ha echnology is c i ical o inc easing co po a e p oduc i i y.
In his wo k, o he empi ical es ima ion o TFP, a cons an elas ici y o subs i u ion
(CES)- ype p oduc ion unc ion, wi h labou and capi al as i s p ima y inpu s, will be used
o measu ing he TFP in each sec o , and he TFP will be es ima ed as he amous Solow
esidual om he ixed e m o he p oduc ion unc ion, accoun ing o all causes o he
TFP, as discussed in he in oduc ion sec ion.
3. The TFP-Based T ade Model
In e na ional ade models a e as old as he science o economics and ha e hei
o igins in he ea ly w i ings o (Smi h 1776;Rica do 1817), wi h he o me o mula ing
he i s model o in e na ional ade based on compa a i e p oduc ion cos s, he so-called
compa a i e ad an ages. A majo handicap o he classical heo y is ha i is based
on he classical labou heo y o alue, assuming he exis ence o one p ima y ac o
o p oduc ion, an assump ion ha is un ealis ic in he p esen wo ld. Ano he c i ical
assump ion o Rica do’s heo y is ha p oduc ion echnologies in he same indus y di e
ac oss coun ies, and his assump ion is he basis o compa a i e ad an ages. On he o he
hand, he Hecksche –Ohlin–Samuelson (H-O-S) (Hecksche 1919;Ohlin 1933;Samuelson
1948,1949,1953,1954) heo y o ade conside s he same p oduc ion echnologies o he
same indus ies ac oss coun ies and de i es compa a i e ad an ages on ela i e ac o
abundances be ween coun ies.
This wo k adap s he assump ions o he Rica dian heo y ega ding p oduc ion
echnologies and he numbe o ac o s in ol ed in p oduc ion by mixing he Rica dian and
Hecksche –Ohlin–Samuelson (H-O-S) heo ies o ade o de i e an app oach ha explains

Economies 2024,12, 85 5 o 19
he bila e al pa e n o ade be ween coun ies based on TFP di e ences and accoun s o
di e ences in ela i e ac o endowmen s ac oss coun ies.
The Rica dian model emphasises he c ucial ole o compa a i e di e ences in p oduc-
ion unc ions, bu i conside s only one ac o o p oduc ion, usually labou . Howe e , in
he H-O-S model, i is essen ial o he p oduc ion unc ions o he same ac i i y o be he
same in all coun ies. A possible ex ension o he Rica dian one- ac o model is o conside
a p oduc ion unc ion ha would be di e en be ween coun ies o an iden ical ac i i y,
bu i s only di e ence would be a mul iplica i e scala . Consequen ly, he echnology in
ac i i y Iwill be cha ac e ised by a p oduc ion unc ion o he ollowing o m:
Qj
i=γj
i iLj
i,Kj
i; (1)
in Equa ion (1), whe e Qdeno es ou pu , ideno es ac i i y i,jdeno es coun y, j,L,K
deno e he wo p ima y ac o s o p oduc ion, and γis a scala (se ing as he measu e o
sec o ’s iTFP).1
In his s udy on he H-O-S heo y, Minhas (1962) came close o desc ibing a p oduc ion
unc ion o he abo e o m, whe e he i ed homohypallagic p oduc ion unc ions o he
da a o ce ain compa able indus ies in Japan and he Uni ed S a es when he s a ed ha
“ he isoquan s in di e en coun ies, excep o a pu e scale change, look alike, and he
ma ginal a es o subs i u ion a e unchanged a gi en capi al: labou a ios” (Minhas 1962).
Howe e , Minhas does no see he p oduc ion unc ion o he abo e o m as a combina ion
o he Rica dian heo y and he H-O-S heo y bu a he ocuses on he implica ions o such
‘neu al’ di e ences in p oduc ion unc ions o he H-O-S heo em. The e is a ple ho a
o s udies on he Rica dian ade model and H-O-S heo y. A selec ion o ecen su ey
s udies on bo h models includes wo ks by (Min o d e al. 2021;Depoo e e and Ra ix 2015;
Sa a anamu hu 2019;Vlados 2019;Chacholiades 2017;Napoles 2018).
Th oughou he es o he analysis, apa om he assump ions o he ‘s anda d’
H-O-S model,2 he ollowing assump ions a e made:
•
The p oduc ion unc ions o ac i i y iin all coun ies a e o he o m
Qi=γi i(Li,Ki)
,
whe e he only di e ence be ween coun ies is he mul iplica i e γi.
•
To simpli y he analysis, i is also assumed ha he e a e wo coun ies, coun y
H
(home) and coun y
F
( o eign). In each coun y, he e a e only wo ac i i ies p oducing
wo inal commodi ies, commodi y 1 and commodi y 2.
Unde he abo e assump ions, he commodi y ade equalises commodi y p ices. I
is o in e es o de i e, unde he abo e assump ions, he ela ionships among ela i e
commodi y p ices, ela i e ac o p ices, and ac o p opo ions.
This can be seen in Figu e 1. The igh -hand side o he igu e is he same as ha
in he H-O-S case since he p oduc ion unc ions o he wo coun ies a e iden ical, apa
om he mul iplica i e scala
γ
. When he a io
π
(w/ )
(whe e
π
is he ac o in ensi y,
wand a e he p ices o labou and capi al, espec i ely, and P1 and P2 a e he p ices
o commodi ies 1 and 2, espec i ely),
γs
cancels ou because
πi=γiαiL
γiαiK =αiL
αiK
( om
he assump ion o homogenei y in p oduc ion unc ions). Addi ionally,
wi=γi∂ i
∂Li
and
i=γi∂ i
∂Ki
. Consequen ly, when calcula ing he a io
w

,
γ
s cancels ou . The e o e,
π
(w/ )
is independen o γs.
As shown, Figu e 1assumes ha commodi y 1 is mo e labou -in ensi e han com-
modi y 2. The wo cu es do no c oss since i was assumed ha he e a e no ac o
in ensi y e e sals.
The ela ionship be ween he ela i e p ices o commodi ies and ela i e ac o p ices
will now be examined, s a ing wi h he p ices o goods 1and 2:
P1γ1=wα1L+ α1K(2)
Economies 2024,12, 85 6 o 19
And
P2γ2=wα2L+ α2K(3)
whe e wis he wage a e, deno es he in e es a e, and
α
s a e he inpu coe icien s o
p oduc ion ( hey indica e he p oduc ion ac o uni s necessa y o p oduce one uni o inal
ou pu ). F om Equa ions (2) and (3), he p ice a io o he wo commodi ies can be de i ed
as ollows: P1
P2
=γ2(wα1L+ α1K)
γ1(wα2L+ α2K)=γ2
γ1
w
α1L+α1K
w
α2L+α2K
(4)
Di e en ia ing
P1
P2
in (4) wi h espec o
w

, a e se e al calcula ions, he ollowing
is de i ed:
dP1
P2
dw
=γ2
γ1
α1K
α2K
π1−π2
w
π2+12(5)
whe e π1=α1L
α1Kand π2=α2L
α2K.
Rela ionship (5)
3
is always g ea e han ze o since, by assump ion, commodi y 1 is
mo e labou -in ensi e han commodi y 2 (
π1>π2
), and all o he e ms in (5) a e posi i e.
The e o e, he commodi y p ice a io
P1
P2
is a s ic ly inc easing unc ion o he ac o –p ice
a io w
.
Economies 2024, 12, x FOR PEER REVIEW 6 o 21
And
𝑃2 γ2 = 𝑤α2L +𝑟α2K
(3)
whe e w is he wage a e, deno es he in e es a e, and αs a e he inpu coe icien s o
p oduc ion ( hey indica e he p oduc ion ac o uni s necessa y o p oduce one uni o
inal ou pu ). F om Equa ions (2) and (3), he p ice a io o he wo commodi ies can be
de i ed as ollows:
𝑃1
𝑃2=γ2(𝑤α1𝐿+𝑟α1𝐾)
γ1(𝑤α2𝐿+𝑟α2𝐾)=γ2
γ1𝑤𝑟α1𝐿+α1𝐾
𝑤𝑟α2𝐿+α2𝐾
(4)
Di e en ia ing (𝑃1
𝑃2) in (4) wi h espec o (𝑤
𝑟), a e se e al calcula ions, he ollow-
ing is de i ed:
𝑑(𝑃1
𝑃2)
𝑑(𝑤𝑟)=γ2
γ1α1𝐾
α2𝐾 π1−π2
(𝑤𝑟π2+1)2
(5)
whe e π1=α1𝐿
α1𝐾 and π2=α2𝐿
α2𝐾.
Rela ionship (5)3 is always g ea e han ze o since, by assump ion, commodi y 1 is
mo e labou -in ensi e han commodi y 2 (π1>π2), and all o he e ms in (5) a e posi i e.
The e o e, he commodi y p ice a io (𝑃1
𝑃2) is a s ic ly inc easing unc ion o he ac o –
p ice a io (𝑤
𝑟).
Figu e 1. TFP di e ences, ela i e commodi y p ices, ela i e ac o p ices, and ac o p opo ions.
Howe e , he ela ionship be ween ela i e commodi y p ices and ela i e ac o
p ices is no independen o 𝛾s. Since 𝛾s di e s be ween coun ies, i is expec ed ha ,
unlike in he case o he H-O-S heo y, he ela ion be ween (𝑃1
𝑃2) and (𝑤
𝑟) in he wo
coun ies is ep esen ed by di e en cu es. The e o e, he le -hand side o Figu e 1 will
gene ally be di e en om ha in he H-O-S heo y and will depend on he alue o he
𝛾s.
Figu e 1. TFP di e ences, ela i e commodi y p ices, ela i e ac o p ices, and ac o p opo ions.
Howe e , he ela ionship be ween ela i e commodi y p ices and ela i e ac o p ices
is no independen o
γ
s. Since
γ
s di e s be ween coun ies, i is expec ed ha , unlike in
he case o he H-O-S heo y, he ela ion be ween
P1
P2
and
w

in he wo coun ies is
ep esen ed by di e en cu es. The e o e, he le -hand side o Figu e 1will gene ally be
di e en om ha in he H-O-S heo y and will depend on he alue o he γs.
Th ee cases can be dis inguished in his simple wo-coun y, wo-commodi y, wo-
ac o model:
•γH
1
γH
2
<γF
1
γF
2
, whe e he supe sc ip s Hand Fdeno e he home coun y and he o eign
coun y, espec i ely. This case is shown in Figu e 1. F om ela ionship (4), we ha e
he ollowing:
Economies 2024,12, 85 7 o 19
P1
P2H
=γH
2
γH
1
w
α1L+α1K
w
α2L+α2K
(6)
o coun y Hand
P1
P2F
=γF
2
γF
1
w
α1L+α1K
w
α2L+α2K
(7)
o coun y F. Now,
γH
1
γH
2
<γF
1
γF
2
⇔γH
2
γH
1
>γF
2
γF
1
,
whe e, a he same ela i e ac o –p ice a io, coun y H’s commodi y p ice a io
P1
P2H
will be g ea e han ha o coun y F’s
P1
P2F
(since he
α
coe icien s a e he same o he
wo coun ies by assump ion), o , because commodi y p ices equalise a e he in oduc ion
o ade, a he same commodi y p ice a io, coun y F’s ela i e ac o –p ice a io is g ea e
han ha o coun y H. F om ela ionship (5), in he case whe e
γH
1
γH
2
<γF
1
γF
2
, he ollowing
is de i ed:


dP1
P2
dw


H
>

dP1
P2
dw


F
which implies ha he cu e deno ing he ela ionship be ween
P1
P2
and
w

, as shown
in Figu e 1, o coun y F, will be s eepe han ha o coun y H. In Figu e 1, he cu e
FF deno es he ela ionship be ween he commodi y p ice a io and ac o p ice a io in
coun y Fand he cu e HH in coun y H. The wo cu es (HH and FF) do no in e sec
because ela ionships (6) and (7) ensu e ha o he same commodi y p ice a io, he ac o
p ice a io in coun y Fwill always be highe , in a ixed p opo ion, han ha in coun y H.
•γH
1
γH
2
>γF
1
γF
2
; his is he same as in he i s case, wi h he only di e ence being ha in
Figu e 1, he cu e FF will now ep esen coun y H, and he cu e HH will ep esen
coun y F.
•γH
1
γH
2
=γF
1
γF
2
; in his case, HH and FF on he le -hand side o Figu e 1will coincide, and
he igu e will be he same as ha o he H-O-S heo y case. In his case, Samuelson’s
ac o p ice equaliza ion heo em (Samuelson 1949) holds; Samuelson (1948,1949).
3.1. The Pa e n o T ade wi h Iden ical Rela i e Fac o Endowmen s
We will now examine wha can be p edic ed o he pa e n o ade be ween he coun-
ies i p oduc ion unc ions a e o he o m desc ibed by (1). Le us conside wo coun ies,
Hand F, unde he assump ions se o h in Sec ion 2. To de e mine he p oduc ion possibil-
i y on ie s o he wo economies, we can examine coun y Ha wo di e en ime poin s,
in oducing he cha ac e is ic di e ences o coun y F a he second ime poin . The e o e,
assume ha he p oduc ion unc ions o he wo ac i i ies a ime a e
Q1=γ1 1(K1,L1)
and
Q2=γ2 2(K2,L2)
,
γ1=γ2
, and ha commodi y 1is he labou -in ensi e commodi y.
A ime
+
1, he e is a change in he p oduc ion unc ion, and
γ2
becomes g ea e han
γ1
. The e ec s in indus y 2would ha e been he same as hose in indus y 2 had hey
expe ienced Hicks’ neu al echnical p og ess.
Wi h he expe ience o such echnical p og ess, indus y 2’s isoquan s will be enum-
be ed, wi h each isoquan co esponding o a highe ou pu a e he change han be o e.
The p oduc ion possibili y on ie will shi ou wa d, as illus a ed in Figu e 2. Cu e AB
is he coun y’s p oduc ion possibili y on ie a ime , and cu e AC is he p oduc ion
possibili y on ie a e he change a ime +1.
Economies 2024,12, 85 8 o 19
Economies 2024, 12, x FOR PEER REVIEW 8 o 21
becomes g ea e han 𝛾1. The e ec s in indus y 2 would ha e been he same as hose in
indus y 2 had hey expe ienced Hicks’ neu al echnical p og ess.
Wi h he expe ience o such echnical p og ess, indus y 2’s isoquan s will be enum-
be ed, wi h each isoquan co esponding o a highe ou pu a e he change han be o e.
The p oduc ion possibili y on ie will shi ou wa d, as illus a ed in Figu e 2. Cu e AB
is he coun y’s p oduc ion possibili y on ie a ime , and cu e AC is he p oduc ion
possibili y on ie a e he change a ime 𝑡+1.
Figu e 2. The Rybczynski e ec o he TFP di e ences.
I he commodi y–p ice a io is gi en by he slope o he coun y’s p e- ade p oduc-
ion possibili y on ie a poin D, hen he p ice a io will be assumed o emain he same
a e he change, wi h he new p oduc ion poin being poin E. A poin E, he ou pu o
commodi y 1 has allen absolu ely, and he ou pu o 2 has inc eased.
On he o he hand, i he ac o ‒p ice a io is kep cons an a he p e-change le el,
he p oduc ion poin would shi om D o F. Howe e , a F, he slope o he p oduc ion
possibili y on ie is s eepe han he slope a D; he e o e, a any gi en ac o p ice, com-
modi y 2 becomes ela i ely cheape a e he change in indus y 2.
F om he abo e analysis, he ela i e supply cu es o he coun y be o e and a e
he change in indus y 2 can be de i ed ( he ela i e supply cu e shows how ela i e
ou pu , wi h ull employmen o bo h ac o s, a ies wi h ela i e commodi y p ices). Be-
o e he change, he ela i e supply cu e is depic ed by he HH cu e (Figu e 3). In he
abo e discussion, i has been shown ha a e he change, he ou pu o commodi y 1 will
all, and he ou pu o 2 will inc ease i he ela i e commodi y p ices emain he same (a
he same (𝑃1
𝑃2), he a io will co espond o a lowe (𝑄1
𝑄2) a io); al e na i ely, i p ices a e
allowed o change commodi y 2, hey will become cheape ela i e o commodi y 1 ( o he
same (𝑄1
𝑄2), he a io will co espond o a highe (𝑃1
𝑃2) a io). This means ha he ela i e
supply cu e mus mo e o he le o cu e HH in Figu e 3.
Ins ead o conside ing he same economy a wo di e en ime poin s, we conside
wo di e en coun ies, 𝐻 and 𝐹, whe e coun y 𝐹 has he cha ac e is ics o coun y 𝐻
a ime 𝑡+1 (a e he change); hen, he ela i e supply cu es o he wo coun ies a e
depic ed by he cu es HH and FF in Figu e 3. A his poin , he only di e ence be ween
he wo economies is hei desc ibed di e ence in p oduc ion unc ions. The wo econo-
mies a e assumed o ha e iden ical o e all ac o - o-endowmen a ios, as p esen ed in
Figu e 3.
Figu e 2. The Rybczynski e ec o he TFP di e ences.
I he commodi y–p ice a io is gi en by he slope o he coun y’s p e- ade p oduc ion
possibili y on ie a poin D, hen he p ice a io will be assumed o emain he same
a e he change, wi h he new p oduc ion poin being poin E. A poin E, he ou pu o
commodi y 1has allen absolu ely, and he ou pu o 2has inc eased.
On he o he hand, i he ac o –p ice a io is kep cons an a he p e-change le el,
he p oduc ion poin would shi om D o F. Howe e , a F, he slope o he p oduc ion
possibili y on ie is s eepe han he slope a D; he e o e, a any gi en ac o p ice,
commodi y 2becomes ela i ely cheape a e he change in indus y 2.
F om he abo e analysis, he ela i e supply cu es o he coun y be o e and a e he
change in indus y 2can be de i ed ( he ela i e supply cu e shows how ela i e ou pu ,
wi h ull employmen o bo h ac o s, a ies wi h ela i e commodi y p ices). Be o e he
change, he ela i e supply cu e is depic ed by he HH cu e (Figu e 3). In he abo e
discussion, i has been shown ha a e he change, he ou pu o commodi y 1will all, and
he ou pu o 2will inc ease i he ela i e commodi y p ices emain he same (a he same
P1
P2
, he a io will co espond o a lowe
Q1
Q2
a io); al e na i ely, i p ices a e allowed o
change commodi y 2, hey will become cheape ela i e o commodi y 1( o he same
Q1
Q2
,
he a io will co espond o a highe
P1
P2
a io). This means ha he ela i e supply cu e
mus mo e o he le o cu e HH in Figu e 3.
Ins ead o conside ing he same economy a wo di e en ime poin s, we conside
wo di e en coun ies,
H
and
F
, whe e coun y
F
has he cha ac e is ics o coun y
H
a ime
+
1 (a e he change); hen, he ela i e supply cu es o he wo coun ies a e
depic ed by he cu es HH and FF in Figu e 3. A his poin , he only di e ence be ween he
wo economies is hei desc ibed di e ence in p oduc ion unc ions. The wo economies
a e assumed o ha e iden ical o e all ac o - o-endowmen a ios, as p esen ed in Figu e 3.
I he ela i e demand cu e, DD, which ep esen s he p opo ion o commodi ies
consumed as a unc ion o ela i e p ice, is in oduced in his igu e, and unde he as-
sump ion ha he ela i e demand cu e is he same o he wo coun ies ( he ypical
assump ion o demand in he neoclassical ade model), he p e- ade p ice a ios in he
wo coun ies can be ound. In Figu e 3, he equilib ium p e- ade p ice a io o coun y
H
is PH, and ha o coun y Fis PF.
T ade can only occu a a p ice a io lying in he in e al
PHPF
, because a any o he
p ice a io, he wo coun ies will ha e an excess supply o he same commodi y (a a p ice
a io g ea e han
PF
, he e will be an excess supply o commodi y 1a p ices lowe han
Economies 2024,12, 85 15 o 19
Table 4. Spea man ank co ela ion es be ween γ- a ios and X/M a ios o each coun y.
Russia-Ge many Czech Republic-Ge many
Sec o s
Ra io Ra io Ra io Rank
γX/M γ
X/M
γX/M γ
X/M
Ag icul u e
Ag icul u e, o es y, and ishing 3.961 0.462 19 12 30.54 3.80 4 22
Mining and qua ying o non-ene gy-p oducing p oduc s
6.848 4.523 21 18 567.59 0.753 22 9
Ene gy
Mining and ex ac ion o ene gy-p oducing p oduc s 19,630.6 56,726.1 24 24 240.92
154.75
14 24
Coke and e ined pe oleum p oduc s 0.751 12.662 12 21 21,992.4 0.544 24 4
Elec ici y, gas, wa e supply, sewe age, was e, and
emedia ion se ices 303.3 2934.4 23 23 37.031 1.273 5 14
Manu ac u ing
Food p oduc s, be e ages, and obacco 1.306 0.112 13 5 273.97 0.033 17 2
Tex iles, wea ing appa el, lea he , and ela ed p oduc s 0.295 0.102 7 4 74.20 0.990 9 11
Wood and p oduc s o wood and co k 0.152 2.549 3 17 231.04 2.843 13 21
Pape p oduc s and p in ing 0.302 0.260 8 11 122.17 0.598 10 5
Chemicals and pha maceu ical p oduc s 2.329 0.126 15 7 271.03 0.624 16 6
Rubbe and plas ic p oduc s 1.757 0.147 14 8 336.23 1.045 19 12
O he non-me allic mine al p oduc s 0.409 0.161 9 9 56.91 1.484 8 15
Basic me als 0.480 4.586 10 19 411.18 0.633 21 7
Compu e , elec onics, and op ical equipmen 4.356 13.106 20 22 260.86 1.878 15 16
Machine y and equipmen , NEC. 0.143 0.073 2 3 198.22 0.941 12 10
Mo o ehicles, aile s, and semi- aile s 0.293 0.049 6 2 1214.21 1.965 23 17
O he manu ac u ing; epai and ins alla ion o machine y
and equipmen 3.571 0.028 18 1 167.33 2.649 11 20
Cons uc ion 0.286 0.189 5 10 373.25 0.011 20 1
Se ices
Wholesale and e ail ade; epai o mo o ehicles 3.201 1.313 17 15 44.80 2.089 7 18
T anspo a ion and s o age 0.010 1.821 1 16 11.61 2.412 3 19
Telecommunica ions 0.650 1.186 11 14 37.64 1.120 6 13
Financial and insu ance ac i i ies 3.021 0.116 16 6 286.27 0.488 18 3
Public admin. and de ence; compulso y social secu i y 219.3 0.542 22 13 0.606 4.600 1 23
A s, en e ainmen , ec ea ion, and o he se ice
ac i i ies 0.251 5.001 4 20 4.776 0.731 2 8
Spea man Rank Co ela ion Tes
Spea man ank coe icien ( s) 0.301 0.495
Numbe o obse a ions (n) 24 24
T-s a is ic 1.479 2.676
Deg ees o eedom (DF) 22 22
p- alue 0.047 ** 0.013 **
Sou ce: Au ho s’ calcula ions; ** indica es p< 0.05.
As men ioned in Sec ion 3abo e, he anking o commodi ies acco ding o hei
γ
- a io
is no su icien o p edic ing he pa e n o ade. Thus, he ankings acco ding o ac o
in ensi y and ankings acco ding o ela i e ac o endowmen mus be examined.
Acco ding o he null hypo hesis (H0) in he Spea man ank co ela ion es , he e is no
mono onic ela ionship be ween he wo se s o a iables examined, while he al e na i e
hypo hesis (H1) sugges s ha he e is a signi ican mono onic ela ionship. Fo he case
o he Czech Republic and Ge many, Table 3shows ha he alue o he Spea man ank
co ela ion coe icien is equal o 0.401, indica ing a mode a e o high posi i e co ela ion
be ween
γ
- and he
α
- a io. Finally, o he case o Russia, he esul s show ha he
Spea man co ela ion coe icien is equal o 0.62, indica ing a high co ela ion be ween
γ
-

Economies 2024,12, 85 16 o 19
and he
α
- a io. The esul s o he ac o in ensi ies o he
γ
- a io ank es , i.e., he necessa y
condi ion, alida e ha we p oceed wi h he ade pa e n ank es o each coun y case.
In Table 4, he co ela ion coe icien s be ween
γ
- and he expo - o-impo a io a e
p esen ed. The co ela ion coe icien o he case o he Czech Republic and Ge many was
equal o 0.495 and s a is ically signi ican a he 5% le el. On he o he hand, he co ela ion
coe icien o Russia is equal o 0.301 and i is s a is ically signi ican a he 5% le el. We
conclude ha TFP di e ences can be used as a basis o explaining compa a i e ad an ages
and, he e o e, he pa e n o ade exhibi ed be ween wo coun ies.
In he con ex o he Czech Republic and Ge many, he Spea man co ela ion coe icien
explains a la ge sha e o ade dynamics compa ed o he case wi h Russia, indica i e o
educed anspo a ion cos s a ibu ed o he geog aphical p oximi y o he wo coun ies
and he absence o ade impedimen s ha allow commodi y–p ice equalisa ion. Con-
e sely, he co ela ion coe icien obse ed be ween Russia and Ge many egis e s as
lowe , p ima ily a ibu able o he EU sanc ions imposed on Russia o he annexa ion o
C imea in 2014.
5. Conclusions and Policy Implica ions
In his pape , we ha e shown ha in he case whe e p oduc ion unc ions a e desc ibed
by ela ionship (1), and unde he assump ion ha he wo coun ies ha e iden ical ac o –
endowmen a ios, di e ences in TFP a he indus y le el be ween coun ies can be used
o p edic he pa e n o ade. Fu he mo e, we ound ha i coun ies ha e di e en
ac o - o-endowmen a ios, a u he condi ion is equi ed, i.e., he indus y TFP a ios (i.e.,
γ a ios) mus p edic he pa e n o ade acco ding o hei anking by ac o in ensi ies.
Mo e speci ically, he Spea man ank co ela ion coe icien was used o es he ela-
ionship be ween he
γ
- and
α
- a ios, as well as he
γ
- a ios and he impo - o-expo a io.
Addi ionally, wo Spea man ank co ela ion coe icien s we e calcula ed. The i s es was
used o assess he easibili y o using he ank es o he di ec ion o ade ( ank es be ween
γ
- and he
α
- a io); as soon as his es yielded alid esul s, he s eng h o he ade pa e n
be ween he
γ
- a io and he impo - o-expo a io could be measu ed o he bila e al ade
ela ionship be ween Russia and he Czech Republic, wi h Ge many as hei ading pa ne .
The esul s o he i s ank es be ween
γ
- and
α
- a ios indica ed a s a is ically signi ican and
posi i e ela ionship o 0.62 o Russia–Ge many and 0.401 o he Czech Republic–Ge many.
This esul alida ed ou decision o p oceed wi h he ade pa e n ank es . The co ela ion
coe icien be ween he
γ
- and expo - o-impo a ios was ound o be o he co ec sign,
equal o 0.301 o Russia–Ge many and, 0.495 o he Czech Republic–Ge many, implying ha
he model can p edic he di ec ion o ade pa e ns be ween he wo coun ies.
The TFP can be used as an analy ical ool o assessing and desc ibing he compa -
a i e ad an age be ween coun ies. By quan i ying he e iciency wi h which inpu s a e
ans o med in o ou pu s in a coun y, TFP allows o he iden i ica ion o ela i e p oduc-
i i y le els. A highe TFP indica es a compa a i e ad an age in ans o ming p ima y
manu ac u ing inpu s in o goods and se ices. This measu emen aids in iden i ying he
sec o s o indus ies in which he coun y has a compa a i e edge. Based on he s udy’s
esul s, coun ies can use sec o al TFP es ima es o analyse compa a i e ad an ages o
bila e al ade ela ions and di ec esou ces o hese indus ies, he eby inc easing ade
gains. TFP di e ences, on he o he hand, can be used by policymake s o lea n mo e
abou how coun ies can enhance hei economic g ow h by be e unde s anding global
economic dynamics and ade pa e ns. The e o e, a ho ough analysis o TFP di e ences
be ween coun ies can highligh a eas o specialisa ion, which in u n guide ade s a egies
and in o m policy decisions.
The limi a ions o he ade model p esen ed in his pape , as wi h e e y model o
economic heo y, s em om he assump ions adop ed. In ou case, i is assumed ha ade
equalises commodi y p ices; he e o e, he e a e no ade impedimen s o anspo a ion
cos s. Addi ionally, while he p esen ed model implici ly accoun s o he exis ence o
ex e nal economies o scale ( hei e ec s a e inco po a ed in o he
γ
pa ame e o he
Economies 2024,12, 85 17 o 19
p oduc ion unc ions), i does no accoun o he exis ence o in e nal economies o scale
ha a e p esen when he e is monopoly powe in a sec o .
Fu he wo k can be pu sued by wo pa hs: i s , by a emp ing o inco po a e ade
impedimen s and anspo a ion cos s ( hey bo h a ec he commodi y–p ice equalisa ion
assump ion) and second, by conduc ing an empi ical analysis by i ing he new p oduc ion
unc ions o eal-wo ld da a om addi ional coun ies and es ing whe he he pa e n o
ade is compa ible wi h he one p edic ed by he model.
Au ho Con ibu ions: Concep ualiza ion, N.T. and G.B.; me hodology, N.T. and G.B.; w i ing—
o iginal d a p epa a ion, N.T. and G.B.; w i ing— e iew and edi ing, N.T. and G.B. All au ho s
ha e ead and ag eed o he published e sion o he manusc ip .
Funding: This esea ch ecei ed no ex e nal unding.
In o med Consen S a emen : No applicable.
Da a A ailabili y S a emen : All da a sou ces we e app op ia ely sou ced. Howe e , all da ase s
used in he s udy a e a ailable by he au ho s upon easonable eques .
Con lic s o In e es : The au ho s decla e no con lic o in e es .
Appendix A
In Table A1 below, we summa ise all he symbols used in he ex wi h hei de ini ions:
Table A1. Symbols and de ini ions.
Symbol De ini ion
Qj
iOu pu o ac i i y i o coun y j
γj
iMul iplica i e scala (sec o ’s iTFP o coun y j)
Lj
iLabou inpu o ac i i y iand coun y j
Kj
iCapi al inpu o ac i i y iand coun y j
πiFac o in ensi y o commodi y i
wP ice o labou
P ice o capi al
P1 P ice o commodi y 1
P2 P ice o commodi y 2
αiL Inpu coe icien o labou o commodi y i
αiK Inpu coe icien o capi al o commodi y i
HIndica o o he home coun y (Ge many in he Sec ion 4)
FIndica o o a o eign coun y (Russia o he Czech Republic in he Sec ion 4)
PHEquilib ium p e- ade p ice a io o coun y H
PFEquilib ium p e- ade p ice a io o coun y F
zHFac o –p ice a io o coun y H
zFFac o –p ice a io o coun y F
LHLabou endowmen o he home coun y
KHCapi al endowmen o he home coun y
LFLabou endowmen o he o eign coun y
KFCapi al endowmen o he o eign coun y
σSubs i u ion elas ici y pa ame e
Sou ce: Au ho s’ cons uc ion.
Economies 2024,12, 85 18 o 19
No es
1
This no ion is no new; Bhagwa i (1964), in his wo k (Bhagwa i 1964, p. 6), had a simila sugges ion, wi hou pu suing he
analysis o he pa e n o ade c ea ed wi h his combina ion.
2
The assump ions su icien o he logical alidi y o he ‘s anda d’ H-O-S model include he ollowing: (a) wo p ima y,
homogeneous ac o s o p oduc ion (o he same quali y in each coun y), in a gi en supply ha is ully employed, (b) p oduc ion
unc ions ha a e homogeneous o deg ee one, (c) no ac o in ensi y e e sals, (d) no ade impedimen s, such as a i s, quo as,
e c., (e) no anspo cos s, and ( ) i is assumed ha he e is pe ec compe i ion.
3
This ela ionship is alid o bo h cases o ixed and a iable inpu coe icien s o p oduc ion. Howe e , o he es o he analysis,
i will be assumed ha he inpu coe icien s a e a iable, i.e., he
α
s a e unc ions o
w
s
. O he wise, cu es 11 and 22 in Figu e 1
will be e ical and he ange o a ia ion o he ac o –p ice a io will become in ini e.
4This implies ha he coun y wi h he lowe p e- ade wage- o-in e es a e a io will expo he labou -in ensi e commodi y.
5The ba indica es ac o endowmen .
6The mos ecen da a a ailable in he WIOD da abase o each se ies we e om 2014.
7Fo obus ness, bo h measu es o labou inpu s we e used.
8See Sec ion 3.
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