Operating efficiency in the capital-intensive semiconductor industry: A nonparametric frontier approach

Qiao, Guangshun; Lu, Yulin
A icle
Ope a ing e iciency in he capi al-in ensi e semiconduc o
indus y: A nonpa ame ic on ie app oach
Economics: The Open-Access, Open-Assessmen Jou nal
P o ided in Coope a ion wi h:
De G uy e B ill
Sugges ed Ci a ion: Qiao, Guangshun; Lu, Yulin (2024) : Ope a ing e iciency in he capi al-in ensi e
semiconduc o indus y: A nonpa ame ic on ie app oach, Economics: The Open-Access, Open-
Assessmen Jou nal, ISSN 1864-6042, De G uy e , Be lin, Vol. 18, Iss. 1, pp. 1-17,
h ps://doi.o g/10.1515/econ-2022-0050
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Resea ch A icle
Guangshun Qiao* and Yulin Lu
Ope a ing Efficiency in he Capi al-In ensi e
Semiconduc o Indus y: A Nonpa ame ic
F on ie App oach
h ps://doi.o g/10.1515/econ-2022-0050
ecei ed Janua y 31, 2023; accep ed Oc obe 05, 2023
Abs ac : This a icle uses a nonpa ame ic p oduc ion
on ie app oach o in es iga e he ope a ing efficiency
diffe ences by he impac s o capi al expendi u e and busi-
ness model in he global semiconduc o indus y. Handling
he impac o capi al expendi u e as a fixed inpu by he
di ec ional dis ance es ima o , his s udy compa es he ope -
a ing efficiencies in he global semiconduc o indus y be ween
he in eg a ed de ice manu ac u e s and he abless and
ound y fi ms o e 1999–2018. The es ima ion esul s indica e
ha he ope a ing efficiencies do a y in he semiconduc o by
he business model. The e ically in eg a ed manu ac u e s
domina e he semiconduc o indus y, and he capi al-in en-
si e manu ac u e s ope a e mo e efficien ly han he asse -
ligh abless fi ms on a e age.
Keywo ds: semiconduc o indus y, CAPEX, in eg a ed de ice
manu ac u e , nonpa ame ic on ie , di ec ional dis ance
es ima o
1 In oduc ion
In eg a ed ci cui s (ICs) a e essen ial componen s o i -
ually all mode n elec onic de ices. Since Bell labo a o ies
in en ed he ansis o s in 1947 and Texas Ins umen s
eleased he fi s wo king IC in 1958, he semiconduc o
indus y, which is he agg ega e o companies engaged in
he design and ab ica ion o semiconduc o de ices o IC
chips, has been a he o e on o he digi al economy o
decades. F om lap op o sma phone and a ificial in elligence
(AI), semiconduc o de ices a e p esen in nea ly all aspec s o
mode n echnology. The pe sonal compu e e olu ion in he
1970–1980s was a esul o ad ances in semiconduc o ech-
nology, such as he In el 8,008 mic op ocesso (Ce uzzi, 1996).
In he de elopmen and expansion o he Wo ld Wide Web
e olu ion in he 1990s, applica ion-specific in eg a ed ci cui s
played a significan ole in enabling as and efficien ne -
wo king and da a p ocessing, con ibu ing o he g ow h o
web-based echnologies and consume elec onics (Makimo o,
2002).The iseo hesma phonein he2010swassuppo ed
by highe -pe o mance sys em-on-a-chip (SoC), such as he
Apple A se ies and Qualcomm Snapd agon se ies. Cha GPT,
la e ly he mos popula deep lea ning wo kload, equi ed
significan compu a ional powe and was ained on N idia
1
g aphics p ocessing uni s (GPUs).
Due o he g ow h in eme ging echnologies such as AI,
cloud compu ing, In e ne o Things, 5G ne wo ks, au ono-
mous ehicles, indus ial au oma ion, and enewable ene gy
sys ems, he needs o mo e powe ul, ene gy-efficien , and
minia u ized semiconduc o de ices ha e been consis en ly
inc easing. The 2023 Semiconduc o Indus y Associa ion
(SIA) ac book epo ed ha he global semiconduc o sales
eached he highes -e e annual o al o $574 million in
2022.
2
McKinsey’s p elimina y o ecas shows ha he global
semiconduc o indus y is poised o become a illion-dolla
indus y by 2030 (Bu kacky e al., 2022).
1.1 S uc u al Change His o y in he
Semiconduc o Indus y
The semiconduc o indus y has a long his o y o s uc-
u al change. P io o he 1980s, a ew in eg a ed de ice

* Co esponding au ho : Guangshun Qiao, School o Finance and
T ade, Wenzhou Business College, Wenzhou, 325035, China,
e-mail: [email p o ec ed]
Yulin Lu: School o Accoun ing, Jilin Business and Technology College,
Jilin, 130507, China

1N idia Co po a ion (Nasdaq: NVDA) is a leading echnology com-
pany specializing in he design and de elopmen o GPUs and AI
compu ing solu ions.
2h ps://www.semiconduc o s.o g/ he-2023-sia- ac book-you -sou ce-
o -semiconduc o -indus y-da a/.
Economics 2024; 18: 20220050
Open Access. © 2024 he au ho (s), published by De G uy e . This wo k is licensed unde he C ea i e Commons A ibu ion 4.0 In e na ional License.
manu ac u e s (IDMs), such as In el, Infineon,
3
ST,
4
and
Texas Ins umen s, we e he dominan playe s in he semi-
conduc o indus y. These IDMs ha e in-house capabili ies
o pe o m all o he p oduc ion p ocesses (e.g., esea ch and
design [R&D], on -end ab ica ion, and back-end assembly
and es [A&T]). Fo example, as a leading IC manu ac u e ,
In el has se e al ab p oduc ion si es (loca ed in he US,
I eland, Is ael, e c.), A&T si es (loca ed in he US, China,
Malaysia, Vie nam, e c.), and ens o housands employees
and pa ne s all o e he wo ld. The e ical in eg a ion o
managing he en i e p oduc ion p ocess in e nally allows
In el o ha e g ea e con ol o e quali y, in ellec ual p op-
e y (IP), and he abili y o op imize he manu ac u ing p o-
cess o specific needs (Malone, 2014).
The semiconduc o indus y is enowned o i s apid
echnological ad ancemen s. This dynamic field con inu-
ally pushes he bounda ies o inno a ion, d i ing p og ess
in a eas o minia u iza ion, pe o mance imp o emen s,
powe efficiency, and eme ging echnologies. Fo example,
he semiconduc o indus y had expe ienced significan
sh inks in p ocess echnology nodes,
5
om a ound 130 nm
in 2000, o 32 nm in 2010, and 7 nm in 2020 (Flamm, 2017).
Howe e , due o physical cons ain s, manu ac u ing chal-
lenges, hea dissipa ion, and powe consump ion issues,
semiconduc o s wi h e e -expanding complexi y app oach
he limi s o Moo e’slaw
6
(Mack, 2011). The expenses o
building a semiconduc o ab ica ion acili y had inc eased
om a ound $1 billion in he 2000s o mo e han $10 billion
nowadays (e.g., see Ib ahim e al., 2014; Lamb ech s e al., 2018).
The subs an ial inc ease in ab cons uc ion cos s became p o-
hibi i e o almos all he IC supplie s. I s imula ed business
model inno a ion in he semiconduc o indus y and ga e
bi h o he abless– ound y business model in he mid-1980s
(Sa ma & Sun, 2017).
In he abless– ounda y business model, abless com-
panies dedica e hei ime o IC design and b and ope a-
ion, while pu e-play ound ies de o e hemsel es o on -
end ab ica ion, and a hi d g oup o companies a e allo ed
o back-end ou sou ced semiconduc o assembly and es
(OSAT) ope a ions. By specializing in IC design wi h b and
ope a ion, abless companies can concen a e hei effo s
and esou ces on c ea ing diffe en ia ed and compe i i e
chips whe e echnological inno a ion mee s s a egic ma -
ke ing, le e aging he manu ac u ing capabili ies o semi-
conduc o ound ies and OSATs (Hu a e e al., 2011). A
he same ime, ound ies and OSATs ake ca e o he ac ual
manu ac u ing p ocess, ab ica ion, and quali y con ol,
allowing abless companies o ocus on hei co e compe en-
cies, esul ing in a mo e flexible semiconduc o business
ecosys em.
A miles one o he e ical disin eg a ion in he semi-
conduc o indus y is he es ablishmen o he Taiwan
Semiconduc o Manu ac u ing Company (TSMC) in 1987.
TSMC in oduced he concep o a pu e-play semiconduc o
ound y, specializing solely in he manu ac u ing o ICs and
commi ed o be a long- e m non-compe i i e pa ne wi h
he abless fi ms. By con inuously in es ing in ad anced
p ocess echnologies, TSMC quickly es ablished i sel as a
leade in semiconduc o manu ac u ing. P esen ly, TSMC
is he fi s company o comme cialize he 7nm p ocess ech-
nology
7
and he la ges dedica ed semiconduc o ound y
wo ldwide.
8
I s ad anced p ocess echnologies, highly au o-
ma ed manu ac u ing acili ies, he abili y o scale p oduc-
ion, and a s ong ocus on cus ome sa is ac ion ha e
helped TSMC o build long- e m ela ionships wi h i s cus o-
me s, enabling i o cap u e a significan sha e o he high-
end semiconduc o ma ke and making i a c ucial playe in
he semiconduc o ecosys em (e.g., see Hsieh e al., 2002).
1.2 CAPEX Plays a C ucial Role
The abless– ound y business model has significan ly changed
he s uc u e o he semiconduc o alue chain o e he las

3Infineon Technologies AG (Infineon) is Ge many’s la ges semicon-
duc o manu ac u e . I was es ablished on Ap il 1, 1999, as a spinoff
om Siemens AG, aking o e Siemens’semiconduc o ope a ions
including i s esea ch, de elopmen , manu ac u ing, and sales ac i -
i ies. Infineon has been a leade in de eloping and p oducing high-
quali y powe MOSFETs (me al-oxide-semiconduc o field-effec an-
sis o s) o a ious applica ions.
4STMic oelec onics (ST) is a global semiconduc o company head-
qua e ed in Gene a, Swi ze land. I was o med in 1987 h ough a
me ge be ween he semiconduc o di isions o I aly’s STET (Socie à
Finanzia ia Tele onica) and F ance’s Thomson Semiconduc eu s.
5His o ically, he p ocess echnology node (also p ocess node o
simply node) was named a e he physical ga e leng h o a ansis o .
Sh inks in p ocess node offe nume ous ad an ages, including
inc eased ansis o densi y, imp o ed pe o mance, enhanced powe
efficiency, cos educ ion, minia u iza ion, ad anced unc ionali y,
and manu ac u ing ad ancemen s.
6Moo e’s law was fi s obse ed in 1965 and la e e ised in 1975 by
Go den Moo e, he co- ounde and chai man eme i us o In el.
Moo e’s law s a es ha he numbe o componen s pe IC doubles
abou e e y 2 yea s.

7The 7 nm p ocess has helped TSMC win majo cus ome s such as
Apple (A se ies Bionic chips), Qualcomm (Snapd agon 800-se ies chip-
se s), and N idia (RTX 30 se ies GPUs).
8TSMC had in es ed mo e han $16 Billion a i s Fab 18, a new ab in
he Sou he n Taiwan Science Pa k o p oducing 5nm and 3nm p o-
cess echnology.
2Guangshun Qiao and Yulin Lu
ew decades and has been a opic o wide in e es (e.g., see
Adne & Kapoo , 2010; Mache e al., 2007; Sa ma & Sun, 2017).
Many ac o s migh affec p oduc ion cos s and p oduc i i y in
he inno a ion-d i ing IC indus y, such as capi al alloca ion
(B own e al., 2005), echnological capabili y (Pa k e al., 2021;
She & Yang, 2005), business model (Shin e al., 2017), de ice
ype (Pa k e al., 2018), ins i u ional ac o (Gugle & Siebe ,
2007; Lu e al., 2013; Walhee & He, 2020), and o eign compe i-
ion (Hende son & Sco , 2018).
The majo challenges in he capi al-in ensi e semicon-
duc o indus y a e he hea y capi al expendi u e (CAPEX)
o clean oom and cos ly equipmen o on -end ab ica-
ion and back-end A&T p ocedu es. Clean ooms mus be
ee o all ai bo ne pa icles, which equi es ad anced fil-
a ion sys ems, con olled ai flow, and igo ous cleaning
p ocedu es. Addi ionally, due o he complexi y o he man-
u ac u ing p ocesses and he need o p ecision and accu-
acy in he p oduc ion o semiconduc o chips, he equip-
men used in on -end ab ica ion and back-end A&T is
cos ly (Monch e al., 2012). Fo example, ex eme ul a iole
li hog aphy (EUV)
9
is a c i ical echnology o ad anced semi-
conduc o manu ac u ing p ocesses. Each EUV machine made
by ASML
10
cos s a ound $200 million o e en highe . The high
cos s associa ed wi h CAPEX can be a significan ba ie o
new companies looking o en e he semiconduc o indus y,
as well as a challenge o exis ing companies looking o
expand hei manu ac u ing capaci y (Powell e al., 2015).
Ano he challenge in he semiconduc o indus y is he
cyclicali y o demand (Ras ogi e al., 2011; Tan & Ma hews,
2010). The semiconduc o indus y is highly dependen on
end-ma ke demand, which can be ola ile and subjec o
apid shi s. I is difficul o companies o accu a ely o e-
cas demand and plan p oduc ion capaci y, which migh
lead o cos ly o e p oduc ion o unde p oduc ion. In o de
o achie e ull-capaci y u iliza ion, he ound ies and OSATs
seek o op imize p oduc i i y by se ing many abless com-
panies, while e en IDMs a e en ing hei idle capaci y o
compe i o s o educe he financial bu den. I also igge ed
many o he IDMs o s a ou sou cing manu ac u ing pa -
ially om he dedica ed ound ies and became ab-li e
11
(Saha, 2015). In compa ison, he abless companies, mos ly
s a ups o spin-offs ha a e ge ing id o he bu den in
se ing up, main aining, and upg ading abs, a e mo e flex-
ible o in eg a e wi hin local knowledge ne wo ks and ocus
in less c owded niche ma ke s, specialized applica ions, o
inno a i e echnologies o explo e echnological di e si y
and compa a i e ad an age, and compe e wi h he IDMs.
Besides he huge equipmen expendi u es, R&D cos s
o de eloping leading-edge p oduc s such as mic op oces-
so s and adio equency de ices also aise s eadily. Wi h
he sh inking o p ocess node, echnological complexi y
and design complexi y inc ease exponen ially. The slow
p og ess in node echnology equi es con inuous in es -
men s in bo h R&D and ad anced ab ica ion acili ies.
Based on he 2023 SIA ac book, US semiconduc o compa-
nies accoun ed o sales o aling $275 billion in 2022, o 48%
o he global ma ke . A he same ime, US semiconduc o
fi ms also in es ed $58.8 billion in R&D, he highes in
his o y o emain compe i i e in he indus y. The unce -
ain y o R&D in es men s and he IP p o ec ion by incum-
ben s se high ba ie s o en y and a o he success o
la ge IDMs, such as In el, ST, and Texas Ins umen s, which
a e able o make isky in es men s and hus ha e a highe
chance o o esee and lead he echnology e olu ions.
1.3 T ade-offs Be ween Business Models
The e has been a long-las ing deba e on which business
model is ope a ing mo e efficien ly, o which business model
is mo e likely o domina e he semiconduc o indus y. On
he one hand, he educed ba ie s o en y by e ical spe-
cializa ion d as ically educes he bu den o CAPEX and
ensu es he domina ion o new ma ke s by he abless design
houses. The en y o new abless companies, mos o which
a e spinoffs om indus y incumben s, spu inno a ion and
p opel he di e sifica ion o p oduc s in a ious applica ions
(Pellens & Della Mal a, 2018).
Fu he mo e, e ical disin eg a ion in he semicon-
duc o alue chain is accompanied and wis ed by he
end o indus y globaliza ion (B own e al., 2005). Since
he 1990s, abless fi ms ha e had subs an ial sha es o e en
domina ed in mos o he as es -g owing ma ke segmen s
(Balconi & Fon ana, 2011). Found ies a e also becoming
echnology ans e o s a he han me ely manu ac u ing
capaci y p o ide s in he semiconduc o alue chain (Li
e al., 2011). In addi ion, he collabo a ion be ween he
asse -ligh abless and he pu e-play ound y p o ides
mo e obus p o ec ion o IP igh s (Sa ma & Sun, 2017).
When he abless fi ms pass on hei design bluep in s o

9EUV uses ex eme ul a iole ligh wi h a wa eleng h o nea
13.5 nm o c ea e in ica e pa e ns on silicon wa e s, allowing o
he p oduc ion o smalle and mo e complex ICs.
10 Ad anced semiconduc o ma e ial li hog aphy (ASML) is a Du ch
mul ina ional co po a ion and he sole supplie in he wo ld o EUV
pho oli hog aphy machines used o manu ac u e he mos ad anced
chips, a ge ing 5 and 3 nm p ocess nodes.
11 Fab-li e, also called ab-ligh , e e s o a semiconduc o company
ha e ains some in-house ab ica ion acili ies bu also elies on ou -
sou cing a la ge po ion o i s p oduc ion o ex e nal ound ies.
Ope a ing Efficiency in he Capi al-In ensi e Semiconduc o Indus y 3
pu e-play ound ies, he h ea s o eplica ion and he isk
o IP he a e ela i ely low, compa ing wi h he ea ly
yea s when abless fi ms’ICs could only be manu ac u ed
by hei i al IDMs.
On he o he hand, despi e a end owa d e ical
specializa ion d i en by he en y o abless fi ms, he e -
ically in eg a ed IDMs ha e con inued o pe sis and
coexis wi h he abless en an s in he semiconduc o
indus y. Dibiaggio (2007) and Mon e e de (1995) c edi
he efficiency o IDMs o he in e naliza ion o ansac ion
cos s. E ns (2005), Mache (2006), and Kapoo and Adne
(2012) hold he knowledge-based iew ha he IDMs achie e
pe o mance ad an ages when echnological de elopmen s
in ol e complex p oblems. Kapoo (2013) p oposed and
ound ha he incumben s who pe sis wi h e ical in eg a-
ion inc ease hei emphasis on sys emic inno a ions. Due o
he inhe en ly inc easing complexi y o he semiconduc o
supply chain, cu en ly he e does no exis an adequa e e e -
ence model o he semiconduc o indus y, and mo e app o-
p ia e and s a e-o - he-a models a e in g ea demand o ana-
lyze he semiconduc o supplychain(Monche al.,2012).
The semiconduc o indus y is commonly cha ac e -
ized as bo h echnology-in ensi e and capi al-in ensi e.
Much esea ch on he opic o s uc u al change in he
semiconduc o indus y emphasizes he e olu ion o ech-
nology (Chen e al., 2019; Cho, 2020; Hwang & Choung, 2014;
Shin e al., 2017). The impac s o capi al in es men s in he
semiconduc o indus y ha e no been discussed adequa ely.
Besides he esea ch shown ea lie ha ocus on analyzing
he impac s o echnology e olu ion in he semiconduc o
indus y, his s udy plans o emphasize he ea u e o capi al
in ensi e in compa ing he ade-offs o business model in he
semiconduc o indus y. This s udy applies up- o-da e econo-
me ic me hods o handle he impac s o CAPEX as a lump
sum fixedinpu andexplo es hediffe ences o ope a ing
efficiency by business model in he highly dynamic semicon-
duc o indus y in he pas wo decades. The me hodolo-
gical con ibu ions o a icle will be discussed in he nex
subsec ions.
1.4 B ie Li e a u e Re iew
Taking ad an age o a flexible unc ional o m, da a en elop-
men analysis (DEA) is one o he mos popula app oaches
o efficiency es ima ion. The e a e ich eco ds o pe o -
mance e alua ion in he semiconduc o indus y using he
DEA app oach. Fo ins ance, Kozme sky and Yue (1998)exam-
ined he cos efficiency o 56 IC companies wo ldwide and
showed ha US, Japanese, Sou h Ko ean, and Taiwanese IC
companies had become he majo pa icipan s in he global
semiconduc o indus y in he ea ly 1990s. Lu and Hung
(2010) compa ed he manage ial pe o mance efficiency o
48 leading e ically disin eg a ed fi ms in Taiwan’sIC alue
chain and no ed ha abless companies pe o m be e han
ound ies and OSATs. Jang e al. (2016) measu ed he cumu-
la i e change in R&D efficiency o 49 global leading abless
companies and no ed ha du ing he pe iod 2007–2013, he
o e all R&D efficiency declined sligh ly. Li e al. (2019)
explo ed 64 majo Chinese en e p ises in he semiconduc o
indus y and ound ha he mos significan ac o limi ing
u u e imp o emen s o inno a ion efficiency was a low
le el o scale efficiency.
One common p oblem o hese s udies, among o he s,
such as Lu e al. (2013), Hsu (2015), Hung e al. (2014), and
Tsai e al. (2017), is he slow con e gence a e o he non-
pa ame ic DEA es ima o .
12
Accompanied by he inc easing
numbe s o inpu and ou pu dimensions, he con e gence
a e in DEA es ima ion is dec easing sha ply. In cases when
he obse a ions a e es ic ed o a small numbe ei he by
geog aphic bounda y o by business model bounda y, he
issue o slow con e gence a e in DEA es ima ion may
become se e e and c i ical. Fo example, he esea ch o
Kuo and Yang (2012), Lu and Hung (2010), and Wu e al.
(2006) used a small numbe o 38–39 companies o e alua e
he pe o mance o he abless co po a ions in Taiwan,
while in some ex eme cases, such as Chen and Chen
(2011), Hung and Lu (2008), Lin e al. (2019), and Liu and
Wang (2008), he s udies con ained only 10–25 companies.
The effec i e pa ame ic sample size o he DEA es ima o s
in hese app oaches was e y small, which migh lead o
uncon incing esul s.
13
1.5 Me hodological Fea u es
The main me hodological ea u e in his s udy, a e high-
ligh ing he slow con e gence a e in DEA es ima ion, is o
p o ide an empi ical example o choosing he app op ia e
es ima ion me hods in analyzing he ope a ional efficiencies
o he semiconduc o indus y, aiming o gain a as e con-
e gence a e and hence a lowe o de o es ima ion e o .

12 The con e gence a e quan ifies how as he es ima ion e o
dec eases when inc easing he sample size
n
. Gene ally, he con e -
gence a e in a linea eg ession is −
n
1
2, while he con e gence a e o a
nonpa ame ic es ima o is slowe han i s pa ame ic coun e pa .
13 Fo example, Hung and Lu (2008) used he DEA o es ima e effi-
ciencies o 25 companies by 4 inpu and 3 ou pu a iables. The effec-
i e pa ame ic sample size o Hung and Lu (2008) was only ≈
+
25 3
2
43 .
Appendix A explains how o calcula e he effec i e pa ame ic
sample size.
4Guangshun Qiao and Yulin Lu

The semiconduc o indus y is, indeed, a highly globalized
indus y. Fo example, Silicon Valley, loca ed in he sou he n
San F ancisco Bay A ea o Cali o nia, US, enowned o i s
collabo a i e ecosys em ha os e s en ep eneu ship and
inno a ion, has a ac ed a clus e o amous abless semicon-
duc o companies, such as N idia, Qualcomm,
14
AMD,
15
and
Xilinx.
16
While he US has a s ong p esence in he abless
semiconduc o sec o , he e a e also abless companies based
in o he coun ies such as he UK, Is ael, Japan, and China. In
o de o suppo he g ow h o he abless semiconduc o
indus y on a global scale, ound ies and OSATs a e loca ed
in a ious egions a ound he wo ld o ca e o he global
demand o semiconduc o p oduc ion and ensu e a di e se
supply chain o semiconduc o manu ac u ing. Hence, his
s udy conside s he deeply globalized semiconduc o alue
chain as an agg ega ed indus y and collec s da a on 470
semiconduc o companiesallo e hewo ldwi h5,136obse -
a ions in 1999–2018. The global da abase no only p o ides a
wo ldwide pe spec i e o he semiconduc o indus y, bu
also gains a as e con e gence a e in DEA es ima ion.
Fu he mo e, his s udy uses a dimensionali y educ ion ech-
nique o u he imp o e hecon e gence a e.
Ano he me hodological ea u e in his a icle is o
ea he CAPEX as a fixed inpu by using he di ec ional
dis ance measu e. CAPEX is a kind o lump sum in es -
men , which in ol es significan up on expenses ha
a e expec ed o yield long- e m benefi s. By alloca ing
unds owa d acqui ing new echnology, upg ading in a-
s uc u e, and expanding acili ies, companies can enhance
p oduc i i y, imp o e ope a ional efficiency, and le e age he
la es echnological ad ancemen s o s ay compe i i e in he
ma ke . Al hough CAPEX decisionsplayac ucial oleinde e -
mining he le el o p oduc i i y and echnology wi hin an
o ganiza ion, in he sho un, CAPEX is no unde manage s’
di ec con ol. The di ec ional dis ance es ima o p o ides a
con enien me hod o dis inguish he non-disc e iona y fixed
inpu CAPEX wi h o he a iables. The se ing o his me hod
will be discussed u he in he nex sec ion.
Ano he me hodological ea u e in his a icle is o
in es iga e he impac s o he business model in he semi-
conduc o indus y h ough a condi ional nonpa ame ic
on ie app oach. Recen de elopmen s in nonpa ame ic
on ie es ima ion (Da aio & Sima , 2014; Da aio e al.,
2020) p o ide ools o analyze he ope a ing efficiencies
in he semiconduc o indus y unde a ious ypes o con-
s ain s such as capi al in es men s and he business model.
While he he e ogenei y by CAPEX is ea ed as a fixed inpu
a iable by he di ec ional dis ance es ima o (Da aio e al.,
2020), he he e ogenei y by he business model is handled by
he condi ional efficiency es ima o s (Da aio & Sima , 2007). In
addi ion, sepa abili y es ecommended by Sima and Wilson
(2020) is applied o choose he op imal condi ions conside ing
bo h he he e ogenei ies by he business model and ime.
1.6 Findings and O ganiza ion
This a icle aims o ollow he Da aio e al.'s (2020)app oach
o shed ligh on disen angling he impac o capi al in es -
men s and compa ing he echnical efficiencies be ween
IDMs and e ically disin eg a ed abless and ound y fi ms
in he semiconduc o indus y. The es ima ion esul s indi-
ca e ha CAPEX plays a c ucial ole in he semiconduc o
indus y and e ically in eg a ed manu ac u e s domina e
he indus y. Since semiconduc o companies hea ily ely
on CAPEX o acqui e ad anced equipmen , o es ablish and
upg ade manu ac u ing acili ies, and o de elop cu ing-
edge echnologies, he capi al-in ensi e IDMs and OSATs
ope a e mo e efficien ly han he asse -ligh abless fi ms on
a e age. I is wo h no ing ha such kind o ope a ing effi-
ciency is p obably no a ibu ed o managemen imp o e-
men , bu gene a ed om subsidies o M&A (Ve Wey, 2019).
In os e ing a heal hy and compe i i e semiconduc o eco-
sys em, we sugges o il he subsidies o he semiconduc o
indus y owa ds he abless sec o o encou age mo e inno a-
ion and di e sifica ion.
This a icle is o ganized as ollows. Sec ion 2 explains
he nonpa ame ic on ie amewo k and discusses he
diagnos ics and es s a is ics o choose a sui able es ima o
in his esea ch. Sec ion 3 in oduces he da a and defines
he a iables. Sec ion 4 p esen s he empi ical esul s and
discusses he effec o capi al in es men and business
model in he semiconduc o indus y. Sec ion 5 concludes.
2 Me hodology
2.1 DEA App oach
The economic heo y o efficiency in p oduc ion can be
aced o Fa ell (1957). A ibu ed by i s flexibili y and
adap abili y, DEA (Cha nes e al., 1978) is conside ed he

14 Qualcomm holds significan IPs and pa en s ela ed o Code
Di ision Mul iple Access (CDMA) echnology and has es ablished i sel
as a leade in mobile echnology wi h i s Snapd agon p ocesso s.
15 Ad anced Mic o De ices, Inc. (AMD), headqua e ed in San a
Cla a, is a majo abless semiconduc o company known o i s
CPUs. AMD compe es wi h In el in he compu e p ocesso ma ke .
16 Xilinx, Inc., loca ed in San Jose, is a well-known abless company
specializing in field-p og ammable ga e a ays (FPGAs) and SoCs.
Ope a ing Efficiency in he Capi al-In ensi e Semiconduc o Indus y 5
mains eam app oach in on ie analysis o assessing
echnical efficiency.
17
A la ge and g owing li e a u e has
de eloped on he applica ion o he DEA app oach in he
semiconduc o indus y (e.g., see Jang e al., 2016; Li e al.,
2019; Sueyoshi & Ryu, 2020; Tsai e al., 2017; Zhou e al.,
2020). This a icle ollows he DEA app oach and applies
he la es me hodological ad ancemen s o Bădin e al.
(2012), Da aio e al. (2020), and Sima and Wilson (2020)
o add ess he impac s o CAPEX, business model, and
ime in he e e -e ol ing semiconduc o indus y.
P oduc ion heo y p ima ily examines how he p o-
duc ion p ocess wo ks wi hin a fi m o combine
p
inpu s
o achie e he desi ed le el o
q
ou pu s and analyzes he
ac o s ha affec p oduc ion decisions. The idea in he DEA
app oach is o es ima e he efficiency sco e o a p oduc ion
plan (
x
y,), o he dis ance om (
x
y,) o he bounda y o he
p oduc ion se
=
Ψ

{
() ∣ }∈
++
xy x y,can p oduce
pq
.Asa
nonpa ame ic app oach, DEA does no equi e explici
assump ions abou he unde lying p oduc ion unc ion,
allowing o a flexible da a-d i en analysis. Hence, we
selec he DEA app oach in handling he efficiency es ima-
ion o he semiconduc o indus y.
2.2 Di ec ional Dis ance Measu e
The e a e ou kinds o commonly used efficiency measu es
in he DEA app oach, namely, inpu -o ien ed Deb eu–Fa el
measu e, ou -o ien ed Deb eu–Fa el measu e, hype bolic
measu e (Wilson, 2012), and di ec ional dis ance measu e
(Chambe s e al., 1998). The inpu -, ou pu -, and hype bolic
o ien ed measu es a e adial measu es ha allow o only
nonnega i e alues. In con as , he di ec ional dis ance
measu e is an addi i e measu e. The di ec ional dis ance
measu e is gi en by:
(∣ ) {∣( )}=−+∈
β
xyd d βx βd y βd,,,Ψsup , Ψ,
xy x y
(2.1)
which p ojec s (
x
,
y
) on o he echnology in a specified di ec ion
(
−
d
x
,
d
y
). The di ec ional dis ance measu e (‖ )
β
xyd d,,,Ψ
xy
nes s he inpu - and ou pu -o ien ed measu e as a special
case by se ing he di ec ion ec o (
d
d,
xy
)as(
x
,0)and
(
y0,
), espec i ely.
The di ec ional dis ance measu e allows o nega i e
alues o
x
and
y
, as i adds he easible quan i ies o a
uni ’s ou pu and simul aneously sub ac s p opo ional
quan i ies om i s inpu . The choices o he di ec ions
d
x
and
d
y
a e also flexible. Some di ec ion can be se equal o
ze o o ep esen a non-disc e iona y inpu o ou pu
(Sima & Vanhems, 2012). This ea u e is used o p oxy
CAPEX in he semiconduc o indus y in his s udy, by
ca ego izing CAPEX in o a fixed inpu ha is no unde
manage s’di ec con ol in he sho un.
2.3 Es ima ion o he F on ie
The a ainable se
Ψ
is unobse ed. Nonpa ame ic me hods
such as DEA and ee disposal hull (FDH) a e de eloped o
es ima e he unobse able p oduc ion se
Ψ
. The FDH es i-
ma o

Ψ
FDH
is defined as:


{( ) ∣ }=⋃ ∈ ≥ ≤
∈++
xy x Xy Y
Ψ
,,
,
XY
pq iiFDH ,
ii n (2.2)
whe e

{( )
}
=XY,
nii
. FDH es ima o

(∣
)β
xyd d,,,Ψ
xy
FDH is
ob ained by eplacing
Ψ
wi h

Ψ
FDH
. DEA es ima o

Ψ
DE
A
is
he con ex hull o

Ψ
FDH
(Banke e al., 1984).
18
The ade-offbe ween FDH and DEA is no i ial.
Sima and Wilson (2015) summa ized ha he FDH and
DEA es ima o s con e ge o limi ing dis ibu ions a a es
o
+
n
pq
1
and ++
n
pq
21, espec i ely. The con e gence a e o he
FDH and he DEA es ima o slows down wi h he inc easing
o dimensionali y
+
p
q
.
19
To minimize he es ima ion e o
empi ically, we can ei he inc ease he sample size
n
o
dec ease he o al dimensions o
+
p
q
. I he sample size
n
is es ic ed o a small numbe by eal-wo ld cons ain s,
including he ma ke scale o scope o he indus y, geog a-
phical o poli ical es ic ions, and he high cos o da a
collec ion, dimension educ ion such as he p incipal com-
ponen analysis (PCA) may become an a ac i e solu ion.
Appendix A p o ides an in oduc ion o PCA.
A e he diagnos ics o dimension educ ion, a es o
con exi y is ecommended o he ade-offbe ween

Ψ
FDH
and

Ψ
DE
A
(Kneip e al., 2015). I he null hypo hesis o con-
exi y is ejec ed, he FDH es ima o is he only consis en
es ima o . Al e na i ely, i he null hypo hesis is no ejec ed,
he DEA es ima o migh be p e e ed. Howe e , he es o
con exi y (Kneip e al., 2015; Kneip e al., 2016) depends on
andomly spli he o iginal sample in o wo independen sub-
samples o he bias e m calcula ions. This s udy applies a

17 Lampe and Hilge s (2015) su eyed 4,782 publica ions on pe o -
mance measu emen in 1978–2012 and ound ha 4,021 we e o DEA,
and 761 we e o s ochas ic on ie analysis (SFA).

18 To be mo e p ecise, he no a ion DEA is o he a iable- e u ns- o-
scale DEA in his s udy.
19 The es ima ion e o will inc ease wi h he slowdown o con e -
gence a e. This is known as he cu se o dimensionali y in nonpa a-
me ic es ima ion.
6Guangshun Qiao and Yulin Lu
boo s ap algo i hm (Sima & Wilson, 2020) o he con exi y
es o o e come his issue.
2.4 Condi ional Efficiency Measu es
The e exis ac o s such as he business model, cons ain s
o echnology and egula o y, and diffe ences in owne ship,
which a e beyond con ol o he manage bu may influence
he p oduc ion p ocess. These ac o s a e deno ed as en i -
onmen al ac o s ∈
Z
. Da aio and Sima (2005) p oposed
o in es iga e he join beha io o (
)
XYZ,, in p obabili y
e ms by defining he condi ional a ainable se as =
Ψ
z

{
() ∣
}
∈=
++
xy x y Z z, can p oduce when
pq . No e ha
=⋃
∈
Ψ
Ψ
zZ z. The p obabili y dis ibu ion o (
X
Y,) condi-
ional on
=
Z
z
can be w i en as:
(∣) ( ∣ )=≤≥=
∣
H
xyz X xY yZ z,P ob,
.
XYZ,
(2.3)
A condi ional di ec ional dis ance measu e is gi en by:
(∣ ) {∣ ( ∣)
}
=−+
>
∣
β
xyd d z βH x βd y βdz,,, sup ,
0.
xy XYZ x y,(2.4)
Plugging a nonpa ame ic es ima o o (
)
⋅
∣
H
XYZ,in o equa-
ion (2.4) can de i e he es ima ion o he condi ional effi-
ciency sco e acco dingly.
20
2.5 Second S age Analysis
In a pa icula case,
Z
has no impac on he bounda ies o
he
Ψz
and
=
ΨΨ
z
. Sima and Wilson (2007, 2011) called i
he sepa abili y condi ion and a gued ha i he sepa abili y
condi ion is no hold, nai e eg ession in a second-s age
analysis may p o ide inconsis en es ima ion. Al e na i ely,
Bădin e al. (2012, 2014) sugges ed a flexible nonpa ame ic
loca ion-scale model
(∣)==
β
XYZ z,
() ()+μz σzεin a second-
s age eg ession, whe e
(
)
μz
measu es he a e age effec o
z
and (
)
σzp o ides addi ional in o ma ion on he dispe sion o
he efficiency dis ibu ion.
Bădin e al. (2012) de i ed he pu e efficiency om he
loca ion-scale model as:
() (∣)()
()
=−
ε
zβxyz μz
σz
,
.
(2.5)
The pu e efficiency in equa ion (2.5)p o idesameasu eo
inefficiency whi ened om he main effec o he en i onmen al
ac o s. This a icle uses he pu e efficiency o measu e he
impac s o business model and ime in he semiconduc o
indus y.
3 Da a and Va iable Specifica ion
The da a a e collec ed om he Sub-Indus y o Semiconduc o s
in he Compus a da abase. In o de o p o ide a global
pe spec i e o he semiconduc o alue chain, we com-
bined da a om bo h he Compus a No h Ame ica da a-
base and he Compus a Global da abase o co e companies
in he indus y wo ldwide. As he semiconduc o indus y is
amous o being a cyclical indus y (e.g., see Ras ogi e al.,
2011; Tan & Ma hews, 2010), we ga he 20 yea s o da a in
1999–2018 o co e a sufficien pe iod wi h mul iple business
cycles in he indus y. We exclude liquid c ys al display
manu ac u e s, ligh -emi ing diode manu ac u e s, and
pho o ol aic p oduce s om he da ase , limi ing he sample
o only IC manu ac u e s in a na ow sense. Hence, he
panel da a include 5,136 obse a ions om 470 unique com-
panies in he global semiconduc o indus y in 1999–2018.
The eason o he da a o begin in 1999 is wo old.
Fi s , he global semiconduc o alue chain has been p e-
limina ily es ablished in he la e 1990s since he incep ion
o he abless– ound y business model in he la e 1980s.
Since 1999, he e a e plen y o a ailable annual epo s o
he abless and ound y fi ms on he open ma ke . Second,
he yea 1999 is a sui able s a ing poin o obse e he
de elopmen end in he global semiconduc o indus y.
Two yea s a e he 1997 Asian financial c isis, he semicon-
duc o indus y is in a golden decade wi hou massi e exo-
genous shocks un il he 2008 financial c isis.
Iden i ying he inpu s and ou pu s o he p oduc ion
unc ion has always been a subjec o con o e sy, ei he
in pa ame ic o in nonpa ame ic on ie es ima ions,
wi hou excep ion in he semiconduc o indus y. Hence,
we so he mos commonly used a iables in 37 empi ical
s udies, which apply he DEA app oach in he semicon-
duc o indus y. Besides a ew a iables chosen o specific
opics, he commonly used a iables in hese a icles a e
highly concen a ed in o wo inpu and wo ou pu ca e-
go ies. The fi s inpu ca ego y measu es a iable inpu s,
including labo , aw ma e ial, R&D, sales, and ma ke ing
expendi u e, while he second inpu ca ego y measu es
fixed asse s. The e o e, we speci y
p
=5 inpu s (labo , mea-
su ed by he numbe o employees [
X
1
]; COGS [
X
2
]; R&D
expendi u e [
X
3]; sales and ma ke ing expendi u e [
X
4];
and fixed asse s, measu ed by p ope y, plan , and equip-
men [PP&E] [
X
]). No e ha we dis inguish he no a ion o

20 Appendix B in oduces a as and efficien compu a ion o he
di ec ional dis ance measu e.
Ope a ing Efficiency in he Capi al-In ensi e Semiconduc o Indus y 7
he fixed inpu
X
om he o he a iable inpu s
X
1
,
X
2
,
X
3,
and
X
4.
Compa ably, he fi s ou pu ca ego y measu es e -
enue and he second ou pu ca ego y measu es he ma ke
alue o he fi ms. Hence, we speci y
q
=2ou pu s( o al
e enue
[
]Y1
;andsha eholde s’equi y, measu ed by common
o dina y equi y [CEQ]
[
]Y
2
). Fo he ou pu a iable Y
2
,weuse
sha eholde s’equi y ins ead o he ma ke alue o a fi m,
because he a iable o ma ke alue is suffe ing om
missing da a in he Compus a da abase, and he a iable
sha eholde s’equi y is also a widely used p oxy o he alue
o a fi m. The same da ase had been used in Qiao and Wang
(2021), bu in his app oach, we add he a iable
X
o empha-
size he impac o CAPEX, and measu e i as a fixed inpu by
he di ec ional dis ance es ima o o achie e mo e obus
esul s.
Table 1 gi es he summa y s a is ics o he a iables
in 1999–2018 pooled da a. In o de o p o ide a uni o m
s anda d ac oss yea s, all he a iables excep
X
1
a e
exp essed in US
$
millions, and hei alues ha e been
adjus ed o 2018 US dolla by GDP defla o . The dis ibu ion
o all he a iables is hea ily skewed o he igh , owning o
he domina ion o se e al semiconduc o gian s in he
ma ke .
Besides inpu s and ou pu s, we speci y
=2 en i on-
men al a iables (business model [
Z1
]; and ime, measu ed
by he yea s 1999–2018 [
Z2
]). The business model
Z1
is a
disc e e a iable, which ca ego izes he business models o
abless, IDM, ound y, and A&T in o h ee g oups. The fi s
g oup con ains he abless, which a e labo -in ensi e o IC
design. The second g oup con ains ound ies and OSATs,
ha a e capi al-in ensi e o ab ica ion. The hi d g oup
con ains IDMs ha a e bo h labo -in ensi e and capi al-
in ensi e. Al e na i ely,
Z2
can ei he be a con inuous
a iable o a disc e e one. I
Z2
is ea ed as a con inuous
a iable, choosing he op imal ime windown o
Z2
is c i-
ical, which will be discussed u he in he nex sec ion.
Table 2 b eaks down he 5,136 obse a ions by he
business model. I is no su p ise ha o e hal o he com-
panies a e abless. As he ba ie s o en y, which ely
hea ily on CAPEX, a e much lowe o abless han o
he o he s, abless companies sp ing up like he mush-
ooms in he la e 1990s o he ea ly 2000s. A he same
ime, he numbe o fi ms ope a ing in o he kinds o busi-
ness models emains ela i ely s able. A e he golden
decade o as g ow h in he semiconduc o indus y come
o an end in he mid-2000s (e.g., see Flamm, 2017), he p o-
po ions o fi ms in each business model a e g adually fixed.
A ound 60% o he fi ms a e abless, while 20% o he fi ms
a e IDMs and he es 20% a e ei he on -end wa e abs o
back-end OSATs.
4 Empi ical Resul s
Mos nonpa ame ic es ima o s suffe om he cu se o
dimensionali y. Based on he h ee diagnos ics in oduced
in Appendix A, he necessi y o dimension educ ion is
unambiguous. Wi h se en dimensions (
=
p5
and
=
q
2
)in
he o iginal da a, he effec i e pa ame ic sample size m o
annual da a is small, no ma e using FDH o DEA es ima-
o s. We calcula e he alues o he la ges eigen alue o he
momen ma ices o
′XX
and ′
Y
Y o he co esponding sum
o eigen alues o be
=
R
91.19%
xand =
R
98.31%
y,indica ing
high co ela ions among he inpu s and among he ou pu s.
The e o e, dimension educ ion can educe es ima ion e o .
Asligh diffe ence in p ocessing PCA o he di ec ional
Table 1: Summa y s a is ics o 1999–2018 pooled da a
Va iable Min Q1 Median Mean Q3 Max
X1
0.001 0.160 0.486 3.082 2.011 107.600
X
20.001 24.170 88.008 475.252 301.645 18226.000
X
3
0.000 4.302 18.330 160.217 67.001 13543.000
X
40.549 5.885 20.087 125.406 67.185 1982.015
X
0.005 6.065 27.787 554.060 174.405 48976.000
Y
1
0.003 47.283 161.799 1064.110 563.655 70848.000
Y
2
0.175 44.279 151.749 1114.748 487.730 74563.000
Obs. 5,136
Uniq. Obs. 470
No e.
X1
deno es he labo ,
X
2deno es he cos o goods sold (COGS),
X
3
deno es he R&D expendi u e,
X
4deno es he sales and ma ke ing
expendi u e,
X
deno es he fixed asse s, Y
1
deno es he e enue, Y
2
deno es he sha eholde s’equi y, Obs. deno es he obse a ions, and uniq. obs.
deno es he companies. The uni o
X1
is housand employees, and uni s o o he a iables a e US$ million. All alues ha e been adjus ed o 2018 US$
by GDP defla o .
8Guangshun Qiao and Yulin Lu
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Ope a ing Efficiency in he Capi al-In ensi e Semiconduc o Indus y 15

Appendix
A P incipal Componen Analysis
PCA is a mapping
⟼
++++
RR
Ψ
:
pq 1
1
. In ma ix no a ion,
×
pn
ma ix
X
and
×
qn
ma ix
Y
a e ans o med o
×
n1
ma ices ′
X
Λx1and ′YΛy1by p e-mul iplying he fi s
eigen ec o
Λ
x
1
and Λ
y
1
o he momen ma ices
′XX
and
′
Y
Y, espec i ely. Un o una ely, he e is no heo em ha
p ecisely iden ifies si ua ions whe e dimension educ ion
should be used. Wilson (2018) p o ides h ee diagnos ics
o empi ical esea ch.
The fi s diagnos ic is o compu e he effec i e pa a-
me ic sample size m,incaseo
n
obse a ions in a non-
pa ame ic es ima ion. Se ing =mn
κ
1
2, and hus, ≈⌊ ⌉mn
κ2,
whe e he con e gence a e
=
+
κ
pq
1 o FDH es ima o and
=
++
κ
pq
21 o DEA es ima o , and ⌊⌉adeno es he in ege
nea es
a
. Hence, he c i e ion o judging he minimum
sample size min pa ame ic es ima ion can be used as
e e ence in judging he minimum sample size
n
in non-
pa ame ic es ima ion.
Figu e A1: Op imal ime window o
Z2
by LSCV.
16 Guangshun Qiao and Yulin Lu
A second diagnos ic is o conside he p opo ion o
n
obse a ions ha yield efficiency sco es equal o one. Since
he, FDH es ima o con e ges slowe han he DEA es i-
ma o , a obus diagnos ic o he cu se o dimensionali y
should use he FDH efficiency es ima o . I mo e han
25–50% o he obse a ions yield efficiency sco es equal
o one, he es ima ion esul s a e no con incing.
A hi d diagnos ic is o de e mine he a ios
R
xand
R
y
o he la ges eigen alue o he momen ma ices
′XX
and
′
Y
Y o he co esponding sum o eigen alues o
′XX
and
′
Y
Y. The a ios o
R
xand
R
yp o ide measu es o how close
he co esponding momen ma ices a e o ank-one. Fo
example, i
R
x=0.9, hen he ma ix wi h dimension educ-
ion ′
X
Λx1con ains 90% o he independen linea in o ma-
ion in he o iginal ma ix
X
.
In p ac ice, Wilson (2018) p oposed s anda dizing he
ma ices
X
and
Y
be o e PCA o ensu e ha he inpu s o
ou pu s ha e he same scale, in case o excessi e numbe o
inpu s o ou pu s.
B Compu a ion o he Di ec ional
Dis ance Measu e
This s udy ollows he Da aio e al. (2020) app oach o
compu e he di ec ional dis ance measu e using he FDH
es ima o .
Fi s , use he Hadama d componen -wise di ision o
ec o s
⊘
o do a mono onic ans o ma ion o he da a as:
=⊘ =⊘
X
Xd YYd
*and *
.
xy
Then, he di ec ional dis ance es ima o in equa ion (2.1)
can be exp essed explici ly as:
(∣ ) { ∣ (
∣) }
[{ }]
{∣ }
=> −
+>
=−−
∣
≤
βxyd d β H x βy
βx
xXYy
,, sup 0 *,*
0,
max min **,**,
xy nXYX
iX x ii
,**
i ,
(A1)
whe e
n
is he sample size,
{}∈in1,2, …,
, and
X
is he
fixed inpu .
Simila ly, he condi ional di ec ional dis ance es i-
ma o in equa ion (2.4) can be exp essed as:
(∣ ) [{
}]
{∣ ∣ ∣ }
=
−−
≤−≤
β
xyd d z x
XY y
,,, max min
*
*,**,
xy iX x Z z h
ii
,
i i,(A2)
whe e
Z
deno es a ec o o en i onmen al a iables.
C Ke nel Me hod
A nonpa ame ic es ima o o (
)
⋅
∣
H
XYZ,in equa ion (2.3) can
be ob ained by s anda d ke nel smoo hing, i.e.,

(∣) ()
=
∑≤≥
⎛
⎝⎞
⎠
∑⎛
⎝⎞
⎠
∣
−
−
H
xyz XxYyK
K
I
,,
,
XYZ
i
nii Zz
h
i
nZz
h
,
i
i
whe e ()⋅
K
is a ke nel unc ion and
h
is a ec o o band-
wid hs (
)
=
h
hh,…, 1.Bădin e al. (2010, 2012), Hall e al.
(2004), Jeong e al. (2010), and Li e al. (2013) had discussed
ex ensi ely how o choose he op imal bandwid h
h
by
leas -squa e c oss- alida ion (LSCV).
In his s udy, he op imal bandwid h
h
o he ime
Z2
is
calcula ed by minimizing
()
()
 
 
()()
()
 
 
∑∑⎡
⎣
⎢≤≤≥− ⎤
⎦
⎥
−
=≠
∑≤≤≥
∑
≠
−≠
xxx xyy
nn
I,,
1,
i
nji
ni j i j ij
xxx xyyKzz
Kzz
I
1,,
,, ,
,
2
nki
nkj
k j kj
hik
nki
nhik
1,,
11
whe e
() (
)
=
K
K
hh
h
1. The pa e ns in Figu e A1 ep esen
he op imal ime window by he business model using LSCV.
Ope a ing Efficiency in he Capi al-In ensi e Semiconduc o Indus y 17