Concentration, market imperfections, and interbranch organization in the Italian processed tomato supply chain

Čechu a, Lukáš; Samoggia, An onella; Jamali Jaghdani, Tinoush
A icle — Published Ve sion
Concen a ion, ma ke impe ec ions, and in e b anch
o ganiza ion in he I alian p ocessed oma o supply chain
Ag icul u al Economics
P o ided in Coope a ion wi h:
Leibniz Ins i u e o Ag icul u al De elopmen in T ansi ion Economies (IAMO), Halle (Saale)
Sugges ed Ci a ion: Čechu a, Lukáš; Samoggia, An onella; Jamali Jaghdani, Tinoush (2024) :
Concen a ion, ma ke impe ec ions, and in e b anch o ganiza ion in he I alian p ocessed oma o
supply chain, Ag icul u al Economics, ISSN 1574-0862, Wiley, Hoboken, NJ, Vol. 55, Iss. 4, pp.
603-620,
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DOI: 10.1111/agec.12835
ORIGINAL ARTICLE
Concen a ion, ma ke impe ec ions, and in e b anch
o ganiza ion in he I alian p ocessed oma o supply chain
Lukáš Čechu a1An onella Samoggia2Tinoush Jamali Jaghdani3
1Depa men o Economics, Facul y o
Economics and Managemen , Czech
Uni e si y o Li e Sciences P ague,
P ague, Czech Republic
2Depa men o Ag icul u e and Food
Sciences, Uni e si y o Bologna, Bologna,
I aly
3Depa men o Ag icul u al Ma ke s,
Leibniz Ins i u e o Ag icul u al
De elopmen in T ansi ion Economies
(IAMO), Halle (Saale), Sachsen-Anhal ,
Ge many
Co espondence
Tinoush Jamali Jaghdani, Depa men o
Ag icul u al Ma ke s, Leibniz Ins i u e o
Ag icul u al De elopmen in T ansi ion
Economies (IAMO), Halle (Saale),
Ge many.
Email: [email p o ec ed]
Funding in o ma ion
Eu opean Union’s Ho izon 2020 esea ch
and inno a ion p og amme, G an /Awa d
Numbe : 727243
Abs ac
The inc ease in ma ke concen a ion and ma ke powe in he ood supply
chain is an issue o conce n globally. This s udy ocuses on an analysis o ma ke
impe ec ions in he I alian p ocessed oma o ood supply chain by conside ing
changes in i s supply chain go e nance om 2006–2018. The iden i ica ion o
he deg ee o non-compe i i e beha io is based on he de i ed ma k-down and
ma k-up models using he la es de elopmen s in s ochas ic on ie me hodol-
ogy. The es ima ed models e eal some deg ee o non-compe i i e beha io in
he inpu as well as in he ou pu p ocessing ma ke . Howe e , in conside a ion
o he esul s on he supply chain go e nance du ing he s udy pe iod, we a gue
ha he es ablishmen o an In e b anch O ganiza ion (IBO) could c ea e ai ly
s able long- e m ood supply chain ela ionships bene i ing all IBO membe s
and in pa icula a me s despi e he signi ican change in concen a ion le els
in he I alian oma o p ocessing sec o a e 2015.
KEYWORDS
concen a ion a e, ood chain, in e b anch o ganiza ions, I aly, ma ke impe ec ions, s ochas-
ic on ie analysis, oma oes
JEL CLASSIFICATION
D43, D71, L11, L13, Q13
1 INTRODUCTION
Fa m inpu ma ke s, ag icul u al commodi y ading, p o-
cessing segmen s, and he e ail ne wo k o ood supply
chains ha e wi nessed an inc easing concen a ion ac oss
he globe (Clapp, 2021). The eme gence o powe ul ood
e aile s, along wi h con inued inc eases in concen a-
ion among ood manu ac u e s, aises issues o bila e al
oligopolies and coun e ailing powe in wholesale ma ke s
(Sex on & Xia, 2018). Al hough inc ease in concen a ion
does no necessa ily lead o an exe cising o ma ke powe
(C espi & MacDonald, 2022; Deconinck, 2021), he con-
This is an open access a icle unde he e ms o he C ea i e Commons A ibu ion License, which pe mi s use, dis ibu ion and ep oduc ion in any medium, p o ided he
o iginal wo k is p ope ly ci ed.
© 2024 The Au ho s. Ag icul u al Economics published by Wiley Pe iodicals LLC on behal o In e na ional Associa ion o Ag icul u al Economis s.
ce n is ha ups eam ma ke powe in ood alue chain
can c ea e highe cos s o downs eam i ms and down-
s eam ma ke powe can c ea e lowe p ices ecei ed o
ups eam i ms. Fu he mo e, he inc easing concen a-
ion and consolida ion among ood manu ac u e s and
e aile s educes he po en ial ading pa ne s o many
a me s o only one o a ew (Fałkowski e al., 2017, ch1),
which can po en ially educe he ba gaining powe o he
p oduce s.
The c ea ion o P oduce s’ O ganiza ions (POs) is one
o he possible ways o inc ease he ba gaining powe o
sca e ed p ima y ag icul u al p oduce s, as POs make
Ag icul u al Economics. 2024;55:603–620. wileyonlinelib a y.com/jou nal/agec 603
604 ČECHURA e al.
bulk pu chases o ag icul u al commodi ies, gi e echnical
assis ance and ad ice o hei membe s, and sell collec-
i ely o p ocessing indus ies unde Eu opean Union (EU)
Regula ion 1308/2013 (Samoggia e al., 2022). This Reg-
ula ion, which is also known as he “Common Ma ke
O ganisa ion (CMO) Regula ion”, add esses he lack o
ba gaining powe o a omized p ima y ag icul u al p o-
duce s and also ies o deal wi h ag icul u al p oduc ion
c ises. When a me s and p ocesso s o ade s in he
supply chain join oge he , hey can o m In e b anch
O ganiza ions (IBOs). IBOs a e o ganiza ions o go e n-
ing he supply chain wi hou being in ol ed in p oduc ion,
p ocessing o ade hemsel es. They p omo e dialogue,
ma ke anspa ency and a e e ence p ice s eamlining
p ocess in hei ood indus y.
The abo e-men ioned discussion makes he measu ing
o he le el o his concen a ion an impo an issue. The e-
o e, by ocusing on oma o p ocessing in I aly, we ha e
decided o es hese concen a ion changes in his ood
supply chain.1I aly was he hi d la ges p oduce o p o-
cessed oma oes wo ldwide in 2020 (wi h 5166 million ons
and +7.6% compa ed o 2019) a e he USA (in pa icula
Cali o nia, wi h 10,258 million ons), and China (5800 mil-
lion ons) (Toma o News, 2021b). In Eu ope, I aly (55.4%),
Spain (25%), and Po ugal (12%) a e he Eu opean coun ies
wi h he highes p oduc ion olumes o p ocessed oma-
oes (Eu opean Commission, 2022). I aly is he second
expo ing coun y a he global le el (23.6%) a e China
(26.3%). As such, i is he i s expo ing coun y o inished
p ocessed oma o p oduc s in he EU, ollowed by Spain
(12.5%) and Po ugal (8.2%) (Toma o News, 2021a).
In his a icle, we ocus on he analysis o ma ke impe -
ec ions in he I alian p ocessed oma o supply chain om
2006 o 2018. Ou aim is o iden i y he deg ee o ma ke
impe ec ions in he inpu and ou pu oma o p ocess-
ing ma ke , conduc a concen a ion analysis o he main
companies o oma o p ocesso s and/o p ocessing asso-
cia ions, and e alua e he manage ial go e nance o he
oma o supply chain ega ding he sus ainabili y, in eg i y
and esilience om a s a ic as well as dynamic pe spec i e.
By ocusing on he imeline o changes du ing 2006–2018
in he I alian oma o supply chain, we es he e ec s o
highe coo dina ion and highe consolida ion on ma ke
impe ec ion. The shaping o an IBO in No h I aly, which
was s a ed in 2007 and was o icially ecognized in 2011
a he egional le el and in 2012 a he Eu opean le el,
is a sign o highe coo dina ion and inc eased ba gaining
powe . Fu he mo e, inc ease in he Concen a ion Ra e
(CR) o he oma o p ocessing indus y a e 2014 is also
a sign o highe consolida ion. In ligh o hese wo ac-
1This selec ion has been done unde he amewo k o he EU Ho izon
2020, VALUMICS p ojec wi h g an ag eemen No. 727243.
o s, his s udy ex ends he esea ch on he analysis o
ma ke impe ec ions. In pa icula , in o de o ill he
esea ch gap iden i ied by explo ing he e ec s o he IBOs,
his a icle add esses he ollowing esea ch ques ions: (1)
wha deg ee o non-compe i i e beha io o he ood p o-
cesso s wi h espec o a me s and/o e aile s could be
obse ed? (2) can we obse e he links be ween ma ke
ailu es and chain go e nance? and (3) is he supply chain
becoming inc easingly compe i i e o can an idiosync a ic
de elopmen be obse ed?
Ou iden i ica ion o he deg ee o non-compe i i e
beha io is based on he de i ed ma k-down and ma k-
up models using he la es de elopmen s in s ochas ic
on ie me hodology. Using a s ochas ic on ie analy-
sis (SFA) o de ec he deg ee o ma ke powe was i s
applied by Kumbhaka e al. (2012) o ma k-up models.
Ano he no el y o ou s udy is he applica ion o his
app oach in he analysis o a oma o supply chain h ough
he decomposi ion o he one-sided e o e m in he ma k-
up and ma k-down models wi hin bo h he ansien and
pe sis en componen s along wi h he ela ion o ela i e
ma k-up and ma k-down o he ma ke powe . In pa icu-
la , we assume ha ma ke powe comes om a company’s
s a egy and hus only he ime-in a ian (pe sis en ) com-
ponen o he ma k-up and ma k-down models can be
associa ed wi h he ba gaining powe . We hen p o ide he
di ec ela ionship be ween he ela i e ma k-up/ ela i e
ma k-down and he deg ee o ma ke powe .
In Sec ions 2and 3, we will analyze he p ocessed oma o
sec o in I aly, in addi ion o IBOs and he le el o con-
cen a ion. A li e a u e e iew on ma ke concen a ion
and coo dina ion is p esen ed in Sec ion 4, while he da a
and me hodology a e desc ibed in sec ion 5and sec ion 6
p esen s he main esul s. We p o ide a discussion and
d aw conclusions in he las wo sec ions.
2 ITALY’S PROCESSED TOMATO
SECTOR AND INTERBRANCH
ORGANIZATION (IBO)
P oduc ion o oma oes o p ocessing in I aly, as well as
in Spain and Po ugal, is locally concen a ed. In I aly,
he oma o p ocessing sec o is di ided be ween a No h-
e n p oduc ion a ea (mainly he Emilia-Romagna egion)
wi h app oxima ely 35% o o al na ional p oduc ion, and
a Sou he n p oduc ion a ea (mainly Campania and Apu-
lia), which comp ises app oxima ely 30% o o al na ional
p oduc ion (see Figu e 1). In I aly in 2020, a o al o 65,634
ha (+2% compa ed o 2019) we e dedica ed o he p oduc-
ion o oma oes o p ocessing. Abou 2.74 million ons
(53.1%) o p ocessed oma oes we e p oduced in he No h-
e n p oduc ion a ea, and 2.42 million ons (46.9%) in he
15740862, 2024, 4, Downloaded om h ps://onlinelib a y.wiley.com/doi/10.1111/agec.12835, Wiley Online Lib a y on [05/07/2024]. See he Te ms and Condi ions (h ps://onlinelib a y.wiley.com/ e ms-and-condi ions) on Wiley Online Lib a y o ules o use; OA a icles a e go e ned by he applicable C ea i e Commons License
ČECHURA e al. 605
FIGURE 1 Map o majo oma o p oducing egions o I aly (Emilia-Romagna in he no h and Apulia in he sou h).
Sou ce: Own elabo a ions, made wi h ggplo 2 (Wickham, 2016), shape ile om GADM2, and oma o p oduc ion da a acqui ed om he I alian S a is ics O ice
(ISTAT3).
Cen e-Sou h p oduc ion a ea (ANICAV, 2020). In pa ic-
ula , I aly is he leading expo e o canned oma oes in
he wo ld, accoun ing o 76% o he global ma ke sha e o
he en main expo ing coun ies o he 2021/2022 season
(Toma o News, 2021a).
In 2007, Emilia-Romagna s akeholde s encou aged he
c ea ion o he “Dis ic o Indus ial Toma oes” in o de o
p epa e o he educ ion in he le els o Common Ag icul-
u al Policy (CAP) suppo as pa o he EU’s CAP e o ms.
The s akeholde s ac i e in his p ocess we e POs, p oces-
so s, esea ch cen e s and o he local ins i u ions (Dona i
e al., 2019; Man ino & Fo cina, 2018). The e i o ial a ea
o he dis ic expanded o include o he a eas dedica ed o
he p ocessing o oma oes.
2Sou ce: h ps://gadm.o g/download_coun y.h ml.
3Sou ce: h ps://www.is a .i /en/.
The IBO was es ablished and in 2011 i was o icially
ecognized by he Emilia-Romagna Regional go e nmen ,
by EU au ho i ies in 2012 and by he I alian Ag icul u e
Minis y in 2017 (NIPTIO,42021b). Thus, he IBO is ully
ac i e only s a ing om 2011. The No h o I aly p og ess
in his ega d led s akeholde s in he Sou h o I aly o es ab-
lish an IBO o Sou he n I aly Toma o P ocessing in 2018,
whichwasalsoe en ually ecognized by I alian au ho i ies
(NIPTIO, 2020).
In No he n I aly a ound 20 oma o p ocessing com-
panies p ocess 98.9% o he oma oes p oduced in he
a ea o he IBO o No he n I aly Toma o P ocessing
(NIPTIO, 2021b). Toma o p ocessing is concen a ed
4NIPTIO e e s o “OI Pomodo o da Indus ia No d I alia” which
can be ansla ed as “No h o I aly P ocessed Toma o In e b anch
O ganiza ion”.
15740862, 2024, 4, Downloaded om h ps://onlinelib a y.wiley.com/doi/10.1111/agec.12835, Wiley Online Lib a y on [05/07/2024]. See he Te ms and Condi ions (h ps://onlinelib a y.wiley.com/ e ms-and-condi ions) on Wiley Online Lib a y o ules o use; OA a icles a e go e ned by he applicable C ea i e Commons License
606 ČECHURA e al.
in he p o ince o Pa ma, wi h mo e han hal o he
p i a e p ocessing companies and hal o he p ocessing
p oduce s’ coope a i es loca ed he e (Man ino & Fo cina,
2018). Toma o p ocessing is ca ied ou by bo h p i a e
companies (66% o p ocessed oma oes) and p oduce s’
coope a i es (34% o p ocessed oma oes). The la ges
p i a e p ocessing companies a e loca ed in Pa ma and
Piacenza, such as Mu i, Rodol i, G eci Alimen a i, and
Emiliana Conse e. Some o hese p i a e companies s ill
belong o he ounding amilies (Man ino & Fo cina, 2018).
On he dis ibu ion side, a ound hal o he p ocessed
oma oes a e sold o he ood indus y (47%), 36% o e ail
dis ibu ion, and 18% o HORECA5(NIPTIO, 2021a). The
p ocessing oma o supply chain o he IBO o No he n
I aly Toma o P ocessing s i es o a s ong e ical and
ho izon al coope a ion, bo h in e nally among IBO ac o s
and wi h o he supply chain s akeholde s.
Annual p ocessed oma oes a e p oduced on a con-
ac ual basis ag eed upon by IBO s akeholde s a he
beginning o he ag onomic yea . Mo eo e , he IBO s ake-
holde s ag ee on he gene al ules ha o m he basis o
a amewo k con ac , which se s he oma o p oduc ion
and comme cial ela ionships wi hin he IBO o No he n
I aly Toma o P ocessing, be ween p oduce s, p ocesso s,
and sel -p ocessing coope a i es. The amewo k con ac
includes an app oxima e and p oposed p ice ha is hen
enego ia ed bila e ally by he chain ac o s, in pa icula
he p oduce o ganiza ions and p ocessing indus ies.
The IBO allows o bo h e ical and ho izon al in e-
g a ion in he oma o p ocessing indus y. I wo ks as a
neu al space whe e ade-o s be ween he clashing in e -
es s o p oduce s and p ocesso s can be ound. The IBO
s eamlines he nego ia ion o a e e ence p ice be ween
p oduce s and p ocesso s, helps he coo dina ion o p o-
duc ion planning in o de o sol e con lic ing in e es s, and
hus s abilizes he ma ke . I also impac s he ood chain
bo h ups eam (in luencing policies and inancing) and
downs eam (a ec ing c op planning).
The p ice s eamlining is a key aspec o IBO. The nego-
ia ion o he e e ence p ice o aw oma o o be p ocessed
and paid o p oduce s by p ocesso s can ake up o some
mon hs. The e e ence p ice is no a se minimum p ice,
bu a e e ence p ice ag eed, mainly based on he his o ical
p ices paid in he pas and h ough he analysis o pas con-
ac s. The e e ence p ice a ies acco ding o quali a i e
pa ame e s speci ied in he amewo k con ac , as ag eed
by all IBO’s companies.
The wo pa ame e s a ec ing he inal p ice a e he
le el o “BRIX”, and he pe cen age o majo and mino
de ec s o he oma o o be p ocessed. BRIX is a measu e
o he suga con en o a oma o. The highe he BRIX,
5HORECA e e s o ho el, es au an and ca è.
he swee e he oma o. Majo de ec s a e de ec s ha sig-
ni ican ly a ec he quali y o he oma o, such as b uises
o o . Mino de ec s a e de ec s ha do no signi ican ly
a ec he quali y o he oma o, such as small blemishes
(Samoggia e al., 2022).
3 CONCENTRATION
Ano he de elopmen in he I alian oma o p ocessing sec-
o has been he inc ease in he Concen a ion Ra e (CR)
a e 2012. Table 1shows he op eigh I alian i ms and
hei sha e and concen a ion le el in oma o p ocessing
in he las yea o his s udy (2018).
As can be obse ed, he CR o he op 1, 4, and 8 i ms
(CR1,CR4,andCR8) in 2018 was 11.6%, 39.8%, and 56.4%,
espec i ely, al hough his pic u e was di e en be o e
2015. Figu e 2shows he de elopmen o he CR o he
op1,2,and4 i ms(CR1,CR2and CR4) o he 2006–2020
pe iod. As can be seen, he CR d ama ically changed a e
2014. Du ing his pe iod, he annual amoun o oma o p o-
cessing did no a y a lo in I aly and he a e age annual
oma o p ocessing was 4.9 million ons wi h a coe icien
o a ia ion o 9.28% (Toma o News, 2021c).
Acco ding o a ailable in o ma ion, in 2015, Ag icol o i
Riuni i Piacen ini (A.R.P) me ged wi h Casalasco; in 2017
COPADOR was aken o e by Mu i (Toma o News, 2017);
andin2018Fe a aFoodswaspu chasedbyI al om
(Toma o News, 2018), which we e some o he main me ges
since 2014. I mus be men ioned ha highe le el o con-
cen a ion in he ood supply chain does no necessa ily
mean highe ma ke powe o p ice change (Dong e al.,
2023).
4POS, IBOS, BARGAINING POWER
AND MARKET IMPERFECTION
The e ha e been subs an ial amoun s o esea ch con-
duc ed on he p esence o ma ke powe and a de ia ion
om compe i i eness. A gene al o e iew on hese s udies
canbe oundinC espiandMacDonald(2022), Decon-
inck (2021), and Sex on and Xia (2018). By conside ing
he cu en go e nance o he I alian oma o p ocessing
supply chain, we ocus on hose s udies ha ha e ana-
lyzed he ole o POs on inc easing he ba gaining powe
be ween ac o s o he supply chain and hei e ec on
ma ke impe ec ion.
The e is a gene al pe cep ion among bo h he public
and policymake s ha a me s’ sha e o he o e all ood
alue is un ai ly low (Busch & Spille , 2016; Samoggia e al.,
2021) and he collec i e decisions o a me s in o gani-
za ions such as POs can imp o e bo h ma ke e iciency
15740862, 2024, 4, Downloaded om h ps://onlinelib a y.wiley.com/doi/10.1111/agec.12835, Wiley Online Lib a y on [05/07/2024]. See he Te ms and Condi ions (h ps://onlinelib a y.wiley.com/ e ms-and-condi ions) on Wiley Online Lib a y o ules o use; OA a icles a e go e ned by he applicable C ea i e Commons License

ČECHURA e al. 607
TABLE 1 The op eigh I alian i ms and hei sha e and concen a ion le el in oma o p ocessing in 2018.
Rank Fi m name
F esh
oma oes
(1000 Tons)
Fi m
sha e
(%)
Cumula i e
oma oes
p ocessed
(1000 Tons)
Concen a ion
a e (%)
1 Mu i 540 11.61 540 11.61
2I al om 471 10.13 1,011 21.74
3 Conzo zio Casalasco 463 9.96 1,474 31.70
4Conse e I alia 377 8.11 1,851 39.81
5 La Do ia 241 5.18 2,092 44.99
6Rodol i Mansue o 220 4.73 2,312 49.72
7 P inces Indus ie Alimen a i 186 4.00 2,498 53.72
8Solana 125 2.69 2,623 56.41
Res o I aly 2,027
To al I aly 4,650
Sou ce: Conse e I alia, La Do ia and Toma o News.
FIGURE 2 Concen a ion a e o op he 1, 2, and 4 i ms
(CR1,CR2 and CR4) o he pe iod 2006–2018.
Sou ce o da a: Toma o News, La Do ia annual epo s, Mu i, Conse e I alia.
and ba gaining powe (So en ino e al., 2018). The condi-
ion o a omized ups eam supplie s o he supply chain
and downs eam concen a ed o limi ed buye s o supply
chains a e discussed heo e ically and h ough simula ion
by Mé el (2011) and Mé el and Sex on (2017). Fo ins ance,
by conside ing he F ench Com é cheese ma ke , Mé el
(2011) a gues ha encou aging indus y coo dina ion may
be socially desi able.
The dai y a m coope a i es a e one o he majo ag i-
ood POs ha ha e been s udied. By using he egional da a
o U.S. dai y coope a i es o he 2000–2007 pe iod, Caki
and Balag as (2012) ha e shown ha coope a i es use he
ede al milk ma ke o de ing egula ions o exe cise hei
ma ke powe by ha ing 9% ma k-ups on a m milk p ices.
When such a coope a i e is no a ailable, he possibili y
o ma ke powe o be exe cised by p i a ely owned dai y
p ocesso s is e y high.
The e ec o coope a i es on ma ke powe in he I al-
ian ui and ege able (F&V) and dai y supply chains
ha e been es ed by Lee and Van Cayseele (2022) o he
2007–2014 pe iod. Compa ed o non-coope a i es, hey
ound highe ma k-ups o F&V p ocesso coope a i es
and lowe ma k-ups o F&V a me and dai y p ocessing
coope a i es.
To ou knowledge, he e ec s o IBOs on ba gaining
powe and ma ke impe ec ion ha e no been empi ically
es ed. The c ea ion o IBOs can be jus i ied by Sex on’s
(2013) Mode n Ag icul u al Ma ke (MAM) concep . He
a gues ha ood p ocessing i ms conside hei long- e m
ela ionship wi h ag icul u al p oduce s (such as oma o
o dai y a me s). F om his poin o iew, be o e exe cising
ma ke powe , p ocessing i ms conside hei capi al cos
in es men , inelas ic demand o ag icul u al p oduc s and
ansac ion cos s. Sex on a gues ha he p ocessing i ms
need a eliable supply o ag icul u al p oduc s wi h ce ain
cha ac e is ics o ul il hei ou pu obliga ions (Sex on,
2013). The e o e, he a gues ha he coo dina ion be ween
ag icul u al p oduce s and p ocesso s is bene icial o bo h
and ha IBOs a e an example o such coo dina ion.
In his s udy, we look o he e ec o he IBOs and, a he
same ime, he inc easing concen a ion on ma ke impe -
ec ion. Gi en he ac ha ma ke powe comes om a
company’s s a egy ha ing a long- e m na u e as Sex on
a gues, hus only he ime-in a ian (pe sis en ) one-sided
componen o he ma k-up and ma k-down model can be
associa ed wi h he ba gaining powe .
F om he empi ical poin o iew, we ha e decomposed
he one-sided e o e m in he ma k-up and ma k-down
model wi hin bo h he ansien and pe sis en compo-
nen s o a oid upwa d biases o ma k-up and ma k-down
componen s. Mo eo e , we use an es ima ion p ocedu e
ha add esses h ee sou ces o po en ial endogenei y ha
15740862, 2024, 4, Downloaded om h ps://onlinelib a y.wiley.com/doi/10.1111/agec.12835, Wiley Online Lib a y on [05/07/2024]. See he Te ms and Condi ions (h ps://onlinelib a y.wiley.com/ e ms-and-condi ions) on Wiley Online Lib a y o ules o use; OA a icles a e go e ned by he applicable C ea i e Commons License
608 ČECHURA e al.
a e highly p obable o ou models: (i) unobse ed he e o-
genei y; (ii) simul anei y o eg esso s wi h pe sis en and
ansien componen s; and (iii) co ela ion o eg esso s
wi h he noise e m. Finally, we p o ide a di ec ela ion-
ship be ween ma k-up and ma k-down componen s wi h
a ma ke powe indica o .
5DATA AND METHODOLOGY
5.1 Da a
The da a we use in he analysis is d awn om he Amadeus
da abase,6c ea ed and p oduced by Bu eau an Dijk.
The da abase con ains inancial in o ma ion o p i a e
companies ac oss Eu ope and p o ides de ailed in o -
ma ion abou (s anda dized) annual accoun s, inancial
a ios, sec o al ac i i ies and owne ship in o ma ion. The
panel da ase ha we use in ou analysis con ains com-
panies whose main ac i i ies a e oma o ood p ocessing
acco ding o he NACE classi ica ion and desk esea ch
o each o he company websi es. I is a panel da ase
ha ep esen s he pe iod om 2006 o 2018 and con-
ains 97 companies ha p ocess only oma oes o mainly
oma oes.
The ollowing a iables a e used in he analysis:
Ma k-down model: consis s o cos sha e =ma e ial
cos s/ e enue as a dependen a iable and ma e ial cos s,
capi al and labo as co a ia es. Ma e ial cos s a e used in
he o m o he o al cos o ma e ials and ene gy consump-
ion pe company. Re enue is ep esen ed as he ope a ing
e enue ( u no e ) o he companies and ma e ials is he
o al cos s o ma e ials and ene gy de la ed by he index
o p oduce p ices in he indus y (2010 =100). This indi-
ca o is a ela i e ough app oxima ion o he expendi u e
o aw ag icul u al ma e ials. Howe e , he ac ha we
a e analyzing he oma o p ocessing indus y whe e ag i-
cul u al aw ma e ials cons i u e he bulk o he ma e ial
cos s, we assume ha he app oxima ion is accep able.
Labo is ep esen ed by he cos o employees de la ed by
consume p ice index (2010 =100). Capi al is he book
alue o ixed asse s de la ed by he index o p oduce
p ices in he indus y (2010 =100).
Ma k-up model: consis s o e enue sha e = e -
enue/cos s as he dependen a iable and ou pu , no mal-
ized ma e ial cos s and labo as co a ia es, while e enue
is ep esen ed by he ope a ing e enue ( u no e ) o a
company and cos s a e he sum o he labo cos s, ma e-
ials cos s and capi al cos s. Labo cos s a e ep esen ed by
6Mo e in o ma ion on he Amadeus da abase (since 2021 O bis Eu ope)
is p o ided a : h p://www.b din o.com.
he cos s o employees, ma e ial cos s a e he o al cos s o
ma e ials and ene gy consump ion pe company, and cap-
i al cos s a e calcula ed as he book alue o ixed asse s
mul iplied by he in e es a e acco ding o con e gence
c i e ia.
Ou pu s a e ep esen ed by he ope a ing e enue
( u no e ) o a company and a e de la ed by he sec o al
index o oma o p ocessing p ices (2010 =100). Ma e ial
and labo a e no malized by capi al. Fo he case o he
ma k-down model, ma e ials is he o al cos s o ma e i-
als and ene gy de la ed by he index o p oduce p ices in
he indus y (2010 =100); labo is ep esen ed by he cos s
o employees de la ed by he consume p ice index (2010 =
100); and capi al is he book alue o ixed asse s de la ed by
he index o p oduce p ices in he indus y (2010 =100).
We ejec p oduce s wi h ewe han ou obse a-
ions (on a e age) o comply wi h he equi emen s o
he Gene alized Me hod o Momen s (GMM) es ima o .
Fu he mo e, we dec ease he p oblem wi h he use o
unbalanced panel da a his way. Finally, he GMM model
es ima es used inpu a iables as ins umen s lagged up
o wo pe iods o he equa ion in le els and up o h ee
pe iods o he equa ion in di e ences. We hen use yea
dummies and he size a iable o he ma k-down model
and yea dummies o he ma k-up model as addi ional
ins umen s. Summa y s a is ics o he main a iables a e
p o ided in Table 2. Finally, he dependen a iable and he
co a ia es a e loga i hmically ans o med and no malized
by hei mean in bo h models.
5.2 Theo e ical models
The ma k-down and ma k-up models a e de i ed using
he conjec u al a ia ion app oach (e.g., B esnahan, 1982;
Mu h & Wohlgenan , 1999). We ollow he s anda d beha -
io al assump ion abou p o i maximiza ion. In his case,
he Op imiza ion P oblem (OP) can be app oached ei he
as inpu - o ou pu -ma ke o ien ed.
Inpu ma ke -o ien ed OP—ma k-down model
𝜋𝑖=𝑅(𝒑, 𝑥𝑖,𝒛
𝒊,𝑡
)−𝑤
𝑥.𝑥𝑖−𝒘
′
𝐳.𝒛𝒊(1)
whe e 𝜋𝑖is he p o i o i h p ocesso , 𝑅(𝒑, 𝑥𝑖,𝒛
𝒊,𝑡) ep-
esen s he e enue unc ion depending on he ec o o
p oduc p ices (p), ag icul u al aw ma e ials (𝑥𝑖), k h
o he inpu s (𝑧𝑖,𝑘) and a ime end (𝑡) as an indica o o
echnical change. The symbol 𝑤𝑥and 𝒘𝒛a e used o he
co esponding ac o p ices, and he supply unc ion o aw
ma e ials is:
𝑥=𝑔(𝑤𝑥,𝒔
)o 𝑤𝑥=𝑔
−1 (𝑥,𝒔)(2)
15740862, 2024, 4, Downloaded om h ps://onlinelib a y.wiley.com/doi/10.1111/agec.12835, Wiley Online Lib a y on [05/07/2024]. See he Te ms and Condi ions (h ps://onlinelib a y.wiley.com/ e ms-and-condi ions) on Wiley Online Lib a y o ules o use; OA a icles a e go e ned by he applicable C ea i e Commons License
ČECHURA e al. 609
TABLE 2 Summa y s a is ics o main a iables ( housands o Eu os).
Va iable Mean S anda d de ia ion Minimum Maximum
Ope a ing e enue (Tu no e ) (R) 33,401.5 113,028.0 135.0 1,052,047.0
To al cos s o ma e ials and ene gy (M) 20,507.7 65,504.6 57.8 542,232.8
Cos s o employees (L) 3112.2 12,024.1 .6 121,197.7
Book alue o ixed asse s (C) 12,025.4 46,711.2 1.3 465,413.9
Sou ce: Own calcula ion om Amadeus da a.
whe e sis a ec o o supply shi e s and 𝑥=
∑𝐼
𝑖=1 𝑥𝑖
is he o al supply o aw ma e ial (summing o e I
p ocesso s), o in e ms o he in e se supply unc ion
𝑤𝑥=𝑔
−1 (𝑥, 𝒔). Then, he i s o de condi ion o p o i
maximisa ion is:
𝜕𝑅 (𝒑, 𝑥𝑖,𝒛, 𝑡)
𝜕𝑥𝑖
−𝑤
𝑥−𝜕𝑔−1 (𝑥,𝒔)
𝜕𝑥
𝜕𝑥
𝜕𝑥𝑖
𝑥𝑖=0 (3)
and a e ea angemen :
𝑤𝑥(1+ Θ
𝜀𝑥)=𝜕𝑅 (𝒑, 𝑥, 𝒛, 𝑡)
𝜕𝑥 , whe e (4)
𝜀𝑥=𝜕𝑥
𝜕𝑔−1 (𝑥,𝒔)
𝑔−1 (𝑥,𝒔)
𝑥=𝜕lnx
𝜕ln𝑤𝑥
>0
In Equa ion (4), 𝜀𝑥deno es he p ice elas ici y o he aw
oma o supply and Θ=𝜕𝑥
𝜕𝑥𝑖
𝑥𝑖
𝑥is a conjec u al elas ici y
cap u ing he deg ee o oligopsonis ic ma ke powe (B es-
nahan, 1989). The pa ame e ange is 0 <Θ<1. Θ =0
co esponding o pe ec compe i ion, while Θ =1 cha ac-
e izes a monopsonis ic ma ke .7Using Equa ion (4)and
he ela i e ma k-down measu e (σ), we de i e a di ec
ela ion be ween conjec u al elas ici y and ela i e ma k-
down. In pa icula , he ma k-down measu es he pe cen
de ia ion o ac o p ices om hei Ma ginal Re enue
P oduc (MRP)8as 𝜎=𝑀𝑅𝑃𝑥−𝑤𝑥
𝑀𝑅𝑃𝑥
. Subs i u ing he ac o
cos wi h ma ke powe (𝑀𝑅𝑃𝑀𝑃
𝑥)and he ac o cos
unde pe ec compe i ion (𝑀𝑅𝑃𝐶
𝑥=𝑤
𝐶
𝑥)in o he ela i e
7Since p ices o o he inpu s a e assumed o be cons an , hei op imal
le el is gi en when he ac o p ice is equal o he alue o Ma ginal
Re enue P oduc (MRP):𝑾𝒛=𝜕𝑹(𝒑,𝑥,𝒛,𝑡)
𝜕𝒛 .
8The ela i e ma k-down is analogously de ined o he Le ne index
(Le ne , 1934) which measu es he deg ee o oligopolis ic powe . The
Le ne index gi es he pe cen o he p ices ha a e abo e ma ginal
cos . The ela i e ma k-down is co espondingly he pe cen age he ac o
p ice is below he alue o he ma ginal e enue p oduc .
ma k-down esul s in:
𝜎𝑀𝑃_𝐶=𝑀𝑅𝑃𝑀𝑃
𝑥−𝑤
𝐶
𝑥
𝑀𝑅𝑃𝑀𝑃
𝑥
=
1
(1+ Θ
𝜀𝑥)
𝜕𝑅
𝜕𝑥 −𝜕𝑅
𝜕𝑥
1
(1+ Θ
𝜀𝑥)
𝜕𝑅
𝜕𝑥
=
1
(1+ Θ
𝜀𝑥)−1
1
(1+ Θ
𝜀𝑥)
=−Θ
𝜀𝑥
(5)
Tha is, ela i e ma k-down (𝜎𝑀𝑃_𝐶) is p opo ional (in
absolu e alue) o he indica o o ma ke powe and can be
di ec ly compu ed when he supply elas ici y (𝜀𝑥) and con-
jec u al elas ici y (Θ) a e known. O , i we know ela i e
ma k-down and supply elas ici y, we may calcula e conjec-
u al elas ici y. Finally, i he supply elas ici y is unknown
bu supposed o be cons an in he long un, we may use
Equa ion (5) o in es iga e dynamics in conjec u al elas ic-
i y in case ha ela i e ma k-down is es ima ed and ice
e sa.
Mo eo e , he Equa ion (4) implies ha : 𝑤𝑥=MR𝑃𝑥=
𝜕𝑅
𝜕𝑥 unde pe ec compe i ion. This ela ion can u he be
exp essed expanding bo h sides by 𝑥
𝑅as:
𝑤𝑥
𝑥
𝑅≤𝑀𝑅𝑃𝑥
𝑥
𝑅=𝜕𝑅
𝜕𝑥
𝑥
𝑅=𝜕𝑙𝑛𝑅
𝜕𝑙𝑛𝑥 =𝜕𝑙𝑛𝐷0
𝜕𝑙𝑛𝑥 (6)
whe e he las equali y comes om he duali y o he e -
enue (R) and ou pu dis ance (Do) unc ions (Shepha d,
1970) and he inequali y occu s when conjec u al elas ici y
(Θ) is nonze o, ha is, he si ua ion wi h a ce ain deg ee
o ma ke impe ec ions.
Ou pu ma ke -o ien ed OP—ma k-up model
The op imiza ion p oblem can be in oduced o he ou -
pu ma ke in he analogical way. In his case, he p o i
unc ion o p ocesso (i)isgi enby:
𝜋𝑖=𝑝.𝑦
𝑖−𝐶(𝒘, 𝑦𝑖,𝑡
)(7)
whe e pis a p ice o ou pu , yiis he ou pu o i h p ocesso ,
wis a ec o o inpu p ices, and C(w,yi, ) is a cos unc ion
o p ocesso (i) and ime end ( ) o cap u ing echnical
change. The co esponding i s -o de condi ion o p o i
maximiza ion is:
𝜕𝑓−1 (𝑦,𝒅)
𝜕𝑦 .𝜕𝑦
𝜕𝑦𝑖
.𝑦𝑖+𝑝−𝜕𝐶 (𝒘, 𝑦𝑖,𝑡)
𝜕𝑦𝑖
=0o (8)
15740862, 2024, 4, Downloaded om h ps://onlinelib a y.wiley.com/doi/10.1111/agec.12835, Wiley Online Lib a y on [05/07/2024]. See he Te ms and Condi ions (h ps://onlinelib a y.wiley.com/ e ms-and-condi ions) on Wiley Online Lib a y o ules o use; OA a icles a e go e ned by he applicable C ea i e Commons License
610 ČECHURA e al.
𝑝. (1+ Ω
𝜀𝑝)=𝜕𝐶 (𝒘, 𝑦𝑖,𝑡)
𝜕𝑦𝑖
(9)
whe e dis a ec o o demand shi e s, 𝜀𝑝=𝜕𝑦
𝜕𝑓−1(𝑦,𝑑)
𝑝
𝑦<0
s ands o a demand elas ici y o he inal p oduc and
Ω= 𝜕𝑦
𝜕𝑦𝑖
.𝑦𝑖
𝑦is a conjec u al elas ici y. This conjec u al
elas ici y p o ides in o ma ion abou he he deg ee o
oligopolis ic ma ke powe . In pa icula , he elas ici y is in
he in e al Ω∈[0,1]whe e Ω =0 indica es compe i i e
beha io and Ω =1 cha ac e izes monopolis ic powe .
Analogically o inpu ma ke , Equa ion (9)canbeused
o de i e he ela ion be ween conjec u al elas ici y and he
ela i e ma k-up (φ) measu ed as he pe cen de ia ion o
p oduc p ice om he ma ginal cos : φ=
𝑃−𝑀𝐶
𝑀𝐶 (Kumb-
haka e al., 2012).9Tha is, subs i u ing he p oduc p ice
wi h ma ke powe (𝑝𝑀𝑃) and ma ginal cos unde pe ec
compe i ion (𝑝𝐶=𝑀𝐶
𝐶) in o he ela i e ma k-up esul s
in:
𝜑𝐶_𝑀𝑃 =𝑝𝐶−𝑀𝐶
𝑀𝑃
𝑀𝐶𝑀𝑃 =
𝜕𝐶
𝜕𝑦 −1
(1+ Ω
𝜀𝑝)
𝜕𝐶
𝜕𝑦
1
(1+ Ω
𝜀𝑝)
𝜕𝐶
𝜕𝑦
=
1− 1
(1+ Ω
𝜀𝑝)
1
(1+ Ω
𝜀𝑝)
=Ω
𝜀𝑝
(10)
Equa ion (10)10 shows ha he ela i e ma k-up (𝜑𝐶_𝑀𝑃)
is p opo ional (in absolu e alue) o he indica o o ma -
ke powe and can be di ec ly compu ed when he demand
elas ici y and conjec u al elas ici y a e known. On he con-
a y, i he ela i e ma k-up and demand elas ici y a e
known, we may calcula e conjec u al elas ici y. Finally, i
he demand elas ici y is supposed o be cons an in he long
un, we may use Equa ion (10) o s udy dynamics in con-
jec u al elas ici y in case ha ela i e ma k-up is es ima ed
and ice e sa.
Mo eo e , i ollows om Equa ion (9) ha : 𝑝≥
𝜕𝐶(𝒘, 𝑦𝑖,𝑡)
𝜕𝑦𝑖
o Ω ∈ [0, 1], which can be exp essed expand-
ingbo hsidesby 𝑦
𝐶as:
𝑝.𝑦
𝐶≥𝜕𝐶 (𝒘, 𝑦𝑖,𝑡)
𝜕𝑦𝑖
.𝑦
𝐶=𝜕𝑙𝑛𝐶
𝜕𝑙𝑛𝑦 =𝜕𝑙𝑛𝐷𝐼
𝜕𝑙𝑛𝑦 (11)
whe e he las equali y comes om he duali y o he cos
(C) and inpu dis ance (DI) unc ions (Shepha d, 1970).
9The ela ion o he ela i e ma k-up and Le ne index is: 𝐿=𝑃−𝑀𝐶
𝑃=
𝜑
1+𝜑 .
10 No e: using Le ne index in Equa ion (10) ins ead o ela i e ma k-up
esul s in: 𝐿𝐶_𝑀𝑃 =Ω
𝜀𝑝+Ω .
5.3 Es ima ion s a egy
The inequali ies in (6)and(11) can be ans o med o he
equali ies by adding a non-nega i e one-sided e o e ms,
u o he ma k-down model and ε o he ma k-up model
(see Kumbhaka e al., 2012 o he ma k-up model):
𝑤𝑥.𝑥
𝑅=𝜕ln𝐷𝑜
𝜕lnx −𝑢, 𝑢≥0and (12)
𝑝.𝑦
𝐶=𝜕𝑙𝑛𝐷𝐼
𝜕𝑙𝑛𝑦 +𝜀, 𝜀≥0
In Equa ion (12), ucap u es he ma k-down and ε he
ma k-up. To es ima e ma k-down and ma k-up o each
i m we use s ochas ic on ie me hodology om he
e iciency li e a u e (e.g., Kumbhaka & Lo ell, 2000).
Then, assuming ha bo h he ou pu and inpu dis ance
unc ionsha e anslog o m, he esul ingma k-down(13)
and ma k-up (14) models, espec i ely, o one ou pu is as
ollows11:
𝑤𝑥𝑥
𝑅=𝛽
𝑥+𝛽
x 𝑡+𝛽
xxlnx +𝜷
′
𝒛𝑥ln𝒛−𝑢and (13)
py
𝐶=𝛼
𝑦+𝛼
y 𝑡+𝛼
yylny +𝜶
′
𝒙𝑦ln ∼
𝒙+𝜀, whe e (14)
˜
𝑥𝑗=𝑥
𝑗∕𝑥𝐽 o j=1,...,J.
The coe icien s 𝜶and 𝜷in Equa ions (13)and(14)a e
ac ually he coe icien s o he i s o de de i a ion o
anslog ou pu and inpu dis ance unc ions, espec i ely,
which is he eason o he no a ion s uc u e o he coe i-
cien s. Kumbhaka e al. (2012) i s applied he s ochas ic
on ie app oach in he es ima ion o he deg ee o ma -
ke powe in Equa ion (9). In ou s udy, we adjus his
app oach in he ollowing way: we use a sys em GMM es i-
ma o o add ess he endogenei y p oblem and o ob ain
unbiased pa ame e s as well as e o componen s. Then,
we decompose a non-nega i e one-sided e o e m o
he ansien ( ime a ian ) and pe sis en ( ime-in a ian )
pa s, ha is, ui, =μi, +ηi o he ma k-down model and
εi, =ςi, +ψi o he ma k-up model. Mo eo e , he in e -
cep e ms will be ela ed o he e ogenei y componen s o
espec he di e en i m’s echnologies. This concep ual
dis inc ion o he ou componen s12 allows ge ing unbi-
ased es ima es o he one-sided e o e ms. In pa icula ,
since he ma ke powe is a p oduc o i m s a egy ha
11 The de ail in o ma ion on ou pu and inpu dis ance unc ions and he
de i a ion o models (13) and (14) a e p o ided in he Appendix.
12 The model speci ica ion is an analogy o he 4-componen s ochas ic
on ie model (Tsionas & Kumbhaka , 2014).
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h ps://doi.o g/10.1111/agec.12835
APPENDIX A1: OUTPUT DISTANCE FUNCTION
AND MARK-DOWN MODEL SPECIFICATION
I we assume a join -p oduc ion p ocess wi h he inpu ec-
o 𝒙∈ℜ
𝐽
+ o p oduce he ou pu ec o 𝒚∈ℜ
𝑀
+, hen
he p oduc ion echnology can be exp essed by he ou pu
possibili y se 𝑃(𝒙)={𝒚∶𝒙can p oduce (𝒚)} . The ou -
pu possibili y se is supposed o be closed, con ex and
bounded by he ou pu isoquan Isoq 𝑃 (𝒙) = {𝒚 ∶ 𝒚 ∈
𝑃(𝒙), 𝜆(𝒚) ∉ 𝑃(𝒙),𝜆 > 1} and he inpu s as well as ou -
pu s a e supposed o be s ongly, o eely, disposable ( o
mo e e e ence see Kumbhaka & Lo ell, 2000). Then,
Shepha d’s ou pu dis ance unc ion (Shepha d, 1970)isa
adial measu e o he dis ance om ou pu ec o y o Isoq
P(x):
𝐷𝑂(𝒙, 𝒚)=in {𝜃>0∶(𝒚∕𝜃)∈𝑃(𝒙)} ,(A.1)
whe e 𝜃measu es he maximum deg ee o he p opo -
ional inc ease o y o gi en x(Zhou e al., 2014).
I we assume ha he ou pu dis ance unc ion has a
anslog o m, we can w i e20:
ln 𝐷0=𝛽
0+𝛽
𝑡𝑡+1
2𝛽 𝑡+𝛽
𝑥lnx +𝛽
x lnx +1
2𝛽xx(lnx)2
+𝜷
′
𝒛ln𝒛+𝜷
′
𝒛𝑡ln𝒛𝑡 + 1
2ln𝒛′𝑩𝒛𝒛ln𝒛+ln𝒛′𝜷𝒛𝑥lnx
+𝜷
′
𝒚ln𝒚+𝜷
′
𝒚𝑡ln𝒚𝑡 + 1
2ln𝒚′𝑩𝒚𝒚ln𝒚+ln𝒚′𝜷𝒚𝑥lnx
+ln𝒚′𝑩𝒚𝒛ln𝒛
(A.2)
The i s de i a i e o Equa ion (A.2) wi h espec o
ma e ial inpu s is:
𝜕ln𝐷0
𝜕lnx =𝛽
𝑥+𝛽
x 𝑡+𝛽
xx ln 𝑥 + 𝜷′
𝒛𝑥 ln𝒛+𝜷
′
𝒚𝑥 ln 𝒚 (A.3)
Using Equa ions (A.3)in ela ion(6)21 we ge :
𝑤𝑥𝑥
𝑅≤𝛽𝑥+𝛽
x 𝑡+𝛽
xx ln 𝑥 + 𝜷′
𝒛𝑥 ln𝒛+𝜷
′
𝒚𝑥 ln 𝒚 (A.4)
The ou pu dis ance unc ion is homogenous o deg ee
1 in ou pu s. The e o e, we impose homogenei y es ic-
ion by no malising all he ou pu s by one ou pu o ge he
empi ical ep esen a ion o Equa ion (4) obees ima ed:
𝑤𝑥𝑥
𝑅≤𝛽𝑥+𝛽
x 𝑡+𝛽
xx ln 𝑥 + 𝜷′
𝒛𝑥 ln𝒛+𝜷
′
𝒚𝑥 ln ∼
𝒚(A.5)
whe e 
𝑦𝑚=𝑦
𝑚∕𝑦𝑀 o m=1,...,M.
20 To ollow he main body o he a icle, we spli he ec o o inpu x
in o: ag icul u al aw ma e ials (x) and ec o o o he inpu s (z).
21 To ecall ela ion (6) om a main body o he a icle:
𝑤𝑥
𝑥
𝑅≤MR𝑃𝑥
𝑥
𝑅=𝜕𝑅
𝜕𝑥
𝑥
𝑅=𝜕lnR
𝜕lnx =𝜕ln𝐷0
𝜕lnx
15740862, 2024, 4, Downloaded om h ps://onlinelib a y.wiley.com/doi/10.1111/agec.12835, Wiley Online Lib a y on [05/07/2024]. See he Te ms and Condi ions (h ps://onlinelib a y.wiley.com/ e ms-and-condi ions) on Wiley Online Lib a y o ules o use; OA a icles a e go e ned by he applicable C ea i e Commons License
ČECHURA e al. 619
Fo one ou pu , (A.5) educes o (homogenei y o deg ee
1 in ou pu s equi es ha βyx=0):
𝑤𝑥𝑥
𝑅≤𝛽𝑥+𝛽
x 𝑡+𝛽
xx ln 𝑥 + 𝜷′
𝒛𝑥 ln 𝒛 (A.6)
The inequali y in (A.5) can be ans o med o he
equali y adding a non-nega i e one-sided e o e m u:
𝑤𝑥𝑥
𝑅=𝛽
𝑥+𝛽
x 𝑡+𝛽
xx ln 𝑥 + 𝜷′
𝒛𝑥 ln𝒛−𝑢, 𝑢≥0,
(A.7)
which is a ep esen a ion o he ma k-down model in
Equa ion (13) in he main body o he a icle.
APPENDIX A2: INPUT DISTANCE FUNCTION AND
MARK-UP MODEL SPECIFICATION
The p oduc ion echnology can be al e na i ely
exp essed by he inpu equi emen se 𝐿(𝒚)={𝒙∶
𝒙can p oduce 𝒚} , wi h he inpu ec o 𝒙∈ℜ
𝐽
+ o p o-
duce he ou pu ec o 𝒚∈ℜ
𝑀
+. The inpu equi emen se
is supposed o be closed, con ex and bounded by he inpu
isoquan Isoq 𝐿 (𝒚) = {𝒙 ∶ 𝒙 ∈ 𝐿(𝒚), 𝜆(𝒙) ∉ 𝐿(𝒚), 𝜆 <
1} and he inpu s as well as ou pu s a e supposed o be
s ongly, o eely, disposable ( o mo e e e ence see again
Kumbhaka & Lo ell, 2000). Shepha d’s inpu dis ance
unc ion (Shepha d, 1970) is hen a adial measu e o he
dis ance om ou pu ec o y o Isoq L(y):
𝐷𝐼(𝒚, 𝒙)=sup
{𝜇>0∶(𝒚∕𝜇)∈𝐿(𝒚)} ,(A.8)
whe e 𝜇measu es he maximum deg ee o p opo ional
educ ion o x o gi en y(Zhou e al., 2014).
Assuming ha he inpu dis ance unc ion wi h one
ou pu has a anslog o m:
ln 𝐷𝐼=𝛼
0+𝛼
𝑡𝑡+1
2𝛼 𝑡2+𝛼
𝑦lny +𝛼
y lny +1
2𝛼yy(lny)2
+𝜶
′
𝒙ln 𝒙 + 𝜶′𝒙𝑡 ln 𝒙𝑡 + 1
2ln𝒙′𝑨𝒙𝒙ln𝒙
+ln𝒙′𝑨𝒙𝑦lny,
(A.9)
he i s de i a i e o equa ion (A.9) wi h espec o ou pu
is:
𝜕ln𝐷
𝐼
𝜕ln𝑦 =𝛼
𝑦+𝛼
y 𝑡+𝛼
yy ln 𝑦 + 𝜶′
𝒙𝑦 ln𝒙(A.10)
Consequen ly, using Equa ion (A.10)in ela ion(11)22
22 To ecall ela ion (11) om a main body o he a icle:
𝑝.𝑦
𝐶≥𝜕𝐶(𝒘,𝑦𝑖,𝑡)
𝜕𝑦𝑖
.𝑦
𝐶=𝜕lnC
𝜕lny =𝜕ln𝐷𝐼
𝜕lny
we ge :
𝑝⋅𝑦
𝐶≥𝛼𝑦+𝛼
y 𝑡+𝛼
yy ln 𝑦 + 𝜶′
𝒙𝑦 ln𝒙(A.11)
The inpu dis ance unc ion is homogenous o deg ee 1
in inpu s. Homogenei y is imposed by no malising all he
inpu s by one inpu . The e o e, he empi ical ep esen a-
ion o (A.11)is:
𝑝⋅𝑦
𝐶≥𝛼𝑦+𝛼
y 𝑡+𝛼
yy ln 𝑦 + 𝜶′
𝒙𝑦 ln ∼
𝒙(A.12)
whe e 
𝑥𝑗=𝑥
𝑗∕𝑥𝐽 o j=1,...,J.
T ans o ming inequali y (A.12) o he equali y by adding
a non-nega i e one-sided e o e m 𝜀we ge :
𝑝⋅𝑦
𝐶=𝛼
𝑦+𝛼
y 𝑡+𝛼
yy ln 𝑦 + 𝜶′
𝒙𝑦ln ∼
𝒙+𝜀, 𝜀 ≥0,
(A.13)
which is a ep esen a ion o he ma k-up model in Equa-
ion (14) in he main body o he a icle.
APPENDIX A3: MARK-DOWN AND MARK-UP
ESTIMATION WITHOUT COOPERATIVES
Tables A3.1 and A3.2 p o ide he pa ame e es ima es
o he ma k-down and ma k-up models o he I alian
oma o ood p ocessing sec o wi hou conside ing he
coope a i es. Table A3.3 p o ides s a is ical cha ac e is ics
o he ela i e ma k-down and ela i e ma k-up. The
esul s o hese es ima ions a e app oxima ely simila o
he ull models.
TABLE A3.1 Ma k- down model wi hou coope a i es.
Va iable Coe icien
S anda d
de ia ion P- alue
.000 .001 .577
ln_M .085 .011 .000
ln_L −.043 .012 .001
ln_C −.023 .009 .013
Cons an .351 .028 .000
P- alue
AR(2) .04 .965
Hansen es o o e id. es ic ions: chi2(63) 69.53 .267
Numbe o obse a ions: 893
Sou ce: Own calcula ions.
15740862, 2024, 4, Downloaded om h ps://onlinelib a y.wiley.com/doi/10.1111/agec.12835, Wiley Online Lib a y on [05/07/2024]. See he Te ms and Condi ions (h ps://onlinelib a y.wiley.com/ e ms-and-condi ions) on Wiley Online Lib a y o ules o use; OA a icles a e go e ned by he applicable C ea i e Commons License
620 ČECHURA e al.
TABLE A3.2 Ma k-up model wi hou coope a i es.
Va iable Coe icien
S anda d
de ia ion P- alue
.004 .002 .054
ln_y −.041 .015 .006
ln_nL .053 .034 .123
ln_nM −.069 .036 .056
Cons an −1.871 .121 .000
P- alue
AR(2) .30 .766
Hansen es o o e id. es ic ions: chi2(96) 89.04 .680
Numbe o obse a ions: 955
Sou ce: Own calcula ions.
TABLE A3.3 Summa y s a is ics o ma k-down and ma k-up
es ima ions wi hou coope a i es.
Mean
S anda d
de ia ion Minimum Maximum
Rela i e
ma k-down
.217 .003 .000 .476
Rela i e
ma k-up
.164 .003 .000 .619
Sou ce: Own calcula ions.
15740862, 2024, 4, Downloaded om h ps://onlinelib a y.wiley.com/doi/10.1111/agec.12835, Wiley Online Lib a y on [05/07/2024]. See he Te ms and Condi ions (h ps://onlinelib a y.wiley.com/ e ms-and-condi ions) on Wiley Online Lib a y o ules o use; OA a icles a e go e ned by he applicable C ea i e Commons License