Heiland, Inga; Š áb, Pa ik
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Es ima ing g a i y equa ions o ade in alue added: A
s uc u al pe spec i e
Economics Le e s
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Sugges ed Ci a ion: Heiland, Inga; Š áb, Pa ik (2025) : Es ima ing g a i y equa ions o ade in alue
added: A s uc u al pe spec i e, Economics Le e s, ISSN 1873-7374, Else ie , Ams e dam, Vol. 254,
pp. 1-5,
h ps://doi.o g/10.1016/j.econle .2025.112476
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h ps://hdl.handle.ne /10419/330838
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Es ima ing g a i y equa ions o ade in alue added: A s uc u al
pe spec i e
Inga Heilanda,b,c,∗, Pa ik Š áb d
aNo wegian Uni e si y o Science and Technology T ondheim, Klæbu eien 72, 7030 T ondheim, No way
bUni e si y o Oslo, No way
cKiel Ins i u e o he Wo ld Economy, Kiellinie 66, 24105 Kiel, Ge many
dFacul y o In e na ional Rela ions, P ague Uni e si y o Economics and Business, nám. Wins ona Chu chilla 1938/4, 130 67 P ague 3, Czech Republic
A R T I C L E I N F O
Da ase link: eplica ion package (O iginal da a
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JEL classi ica ion:
F12
F15
Keywo ds:
S uc u al g a i y
T ade in alue added
A B S T R A C T
A la ge numbe o ecen pape s employ alue-added ade da a alongside adi ional g oss measu es o ade
o es ima e he impac o a ious ade cos s on bila e al ade. Value-added g a i y equa ions a e ypically
jus i ied by e e encing he heo e ical and empi ical me i s o adi ional g a i y equa ions o g oss ade.
Con adic ing his no ion, we use heo y and simula ions o show ha alue-added g a i y equa ions a e
misspeci ied when he g oss ade g a i y equa ion is co ec . Consequen ly, es ima es om alue-added g a i y
equa ions a e di icul o in e p e and p one o omi ed a iables bias.
1. In oduc ion
Many ecen pape s employ alue-added (VA) ade da a along-
side wi h adi ional g oss measu es o ade o es ima e he impac
o a ious ade cos s on bila e al ade.1 VA g a i y equa ions a e
ypically jus i ied by ci ing he heo e ical and empi ical me i s o
adi ional g a i y equa ions o g oss ade. Con adic ing his iew,
we demons a e ha i bila e al g oss ade ollows g a i y, he bila e al
VA ade g a i y equa ions a e misspeci ied.
We employ a simple model o g oss ade and VA ade o pinpoin
he o igin o he misspeci ica ion and conduc simula ion exe cises o
assess he impo ance o he issues in a con olled se ing. Ou esul s
indica e ha bo h he ex e nal and in e nal alidi y o pa ial ade
cos elas ici ies es ima ed wi h educed- o m VA g a i y equa ions a e
limi ed.
Speci ically, we poin ou h ee issues. We use indica o s o egional
ade ag eemen s (RTAs) o illus a e hem, bu ou indings apply o
any ade cos a iable. Fi s , he heo e ical gene al g a i y equa ion
o VA ade, which we de i e om a s uc u al g a i y model o
∗Co esponding au ho a : No wegian Uni e si y o Science and Technology T ondheim, Klæbu eien 72, 7030 T ondheim, No way.
E-mail add ess: [email p o ec ed] (I. Heiland).
1Ou sea ch o he Web o Science and he OECD iLib a y e u ned 35 published academic pape s and 4 policy epo s (lis ed in he Appendix) ha employ
educed- o m g a i y equa ions wi h measu es o bila e al VA ade lows as he le -hand-side a iable.
2Ou de ini ion o gene al and s uc u al g a i y equa ions ollows Head and Maye (2014).
3In se e al o hese pape s, he issue o hi d-coun y e ec s is discussed, hough only a ew pape s a emp o ackle he misspeci ica ion p oblem, using
ei he he me hodology p oposed by Nogue a (2012) (see Lage e al., 2020; Kang and Gapay, 2024) o non-s uc u ally mo i a ed in e ac ion e ms (Mulabdic
e al., 2017; Bo a e al., 2019; Sanguine e al., 2022).
g oss ade2, implies ha he pa ial e ec s o RTAs a e no compa able
ac oss samples, ag eemen s, and ime pe iods, and a e no in o ma i e
o u u e ag eemen s.
Second, he heo y implies ha ade cos changes ha e he e oge-
neous e ec s on bila e al VA ade be ween hi d coun ies. This implies
ha he es ima ed pa ial elas ici ies o RTAs o membe coun ies a e
con ounded by indi ec e ec s on non-membe coun ies.
Thi d, changes in o he de e minan s o ade be ween hi d coun-
ies happening elsewhe e in he wo ld will bias he RTA es ima e
unless bo h membe s’ and non-membe s’ GVCs a e equally exposed o
he hi d-coun y shock. Gi en ha coun ies’ GVCs a e e y di e en ,
such biases a e gene ally likely and ambiguous in di ec ion.
We a e no he i s o poin ou ha ade cos elas ici ies ob-
ained om educed- o m VA g a i y equa ions a e p oblema ic om
a s uc u al poin o iew; Nogue a (2012) de i ed a heo y-g ounded
log-linea VA g a i y equa ion wi h con ol e ms o indi ec ade
cos e ec s. Howe e , he majo i y o empi ical s udies ha e con inued
o use simple log-linea es ima ion models.3 Mo eo e , we show ha
h ps://doi.o g/10.1016/j.econle .2025.112476
Recei ed 26 Ma ch 2025; Recei ed in e ised o m 26 June 2025; Accep ed 27 June 2025
Economics Le e s 254 (2025) 112476
A ailable online 9 July 2025
0165-1765/© 2025 The Au ho s. Published by Else ie B.V. This is an open access a icle unde he CC BY license ( h p://c ea i ecommons.o g/licenses/by/4.0/ ).
I. Heiland and P. Š áb
he indi ec e ec s o a po en ially p ohibi i ely la ge se o o he
hi d-coun y shocks – including coun y-speci ic ones like p oduc i i y
g ow h and in as uc u e de elopmen – also con ound es ima es o he
pa ial e ec s o ade cos shocks on VA ade.
2. A gene al g a i y equa ion o alue added
2.1. The heo e ical model
We se up a model o bila e al ade be ween 𝑁 coun ies, indexed
by 𝑖, 𝑗, 𝑘, 𝑛, ℎ. Ou analysis es s on wo co e assump ions.
(A1). Final goods ade 𝐶𝑖𝑛 and in e media e goods ade 𝐴𝑖𝑛 om
coun y 𝑖 o coun y 𝑛 ollow gene al g a i y equa ions, espec i ely
gi en by
𝐶𝑖𝑛 =𝜋𝑖𝑛𝐶𝑛and 𝐴𝑖𝑛 =𝜋𝑖𝑛𝐴𝑛wi h
𝜋𝑖𝑛 =𝜏−𝜀
𝑖𝑛
𝛹𝑖𝛷𝑛
𝛷𝑛=
𝑁
∑
ℎ=1
𝜏−𝜀
ℎ𝑛
𝛹ℎ
,
whe e 𝐴𝑛=∑𝑖𝐴𝑖𝑛 and 𝐶𝑛=∑𝑖𝐶𝑖𝑛.4
A1 s ipula es ha ade sha es 𝜋𝑖𝑛 a e iden ical o inal and in e -
media e goods, implying ha o al ade also ollows a gene al g a i y
equa ion:
𝑋𝑖𝑛 =𝜏−𝜀
𝑖𝑛
𝑋𝑛
𝛹𝑖𝛷𝑛
,(1)
whe e 𝑋𝑛=𝐴𝑛+𝐶𝑛.
(A2). Fo e e y coun y 𝑛, he a io o VA o ou pu , deno ed by 𝑣𝑛, is
cons an .
A2 implies ha he a io o expenses o in e media es o coun y
𝑛’s ou pu is (1 − 𝑣𝑛) and A1 and A2 oge he imply ha he sha e o
in e media es sou ced di ec ly om 𝑖 in ou pu o 𝑛 is 𝑎𝑖𝑛 =𝜋𝑖𝑛(1 − 𝑣𝑛).
We use 𝐚 o deno e he 𝑁×𝑁 ma ix o di ec inpu coe icien s 𝑎𝑖𝑛 and
𝐁= (𝐈−𝐚)−1 o deno e he co esponding Leon ie in e se wi h ypical
elemen 𝑏𝑖𝑛.
De ini ion 1. VA expo s om 𝑖 o 𝑛, 𝑉 𝐴𝑖𝑛, a e de ined as VA ha
o igina es in 𝑖 and is consumed in 𝑛.
This de ini ion ollows Johnson and Nogue a (2012) and leads us o
he ollowing esul :
P oposi ion 1. Unde A1 and A2, bila e al VA expo s a e gi en by
𝑉 𝐴𝑖𝑛 =𝑣𝑖𝐶𝑛
𝛷𝑛(𝑁
∑
ℎ
𝑏𝑖ℎ𝜏−𝜀
ℎ𝑛
𝛹ℎ),(2)
whe e 𝑏𝑖ℎ =𝑓[{𝜏𝑗𝑘, 𝛹𝑗, 𝛷𝑘, 𝜈𝑘}𝑁
𝑗,𝑘=1 , 𝜀].
P oo . I ollows om 𝐴2 and De ini ion 1 ha 𝑉 𝐴𝑖𝑛 =𝑣𝑖(∑𝑁
ℎ𝑏𝑖ℎ𝐶ℎ𝑛).
Subs i u ing 𝐶ℎ𝑛 and 𝜋ℎ𝑛 om A1 yields (2). The dependency o 𝑏𝑖ℎ on
he ade cos , mul ila e al esis ance e ms, and alue added coe i-
cien s o o he coun ies is due o he ac ha 𝑏𝑖ℎ is a unc ion o all
inpu coe icien s in 𝐚.
P oposi ion 1 has wo impo an implica ions. Fi s , 𝑉 𝐴𝑖𝑛 is no
log-p opo ional o 𝜏𝑖𝑛. Second, 𝑉 𝐴𝑖𝑛 depends in a non- i ial way on
he de e minan s o ade be ween hi d coun ies. In ui i ely, his is
because VA om 𝑖 eaches 𝑛 embodied in goods p ocessed elsewhe e.
The indi ec na u e o VA lows is, o cou se, well known and a ian s
4T ade sha es 𝜋 o his o m a e implied, e.g., by he model o Ea on and
Ko um (2002) o he A ming on model o Ande son and Van Wincoop (2003)
o (2) ha e been employed o quan i y he impac o ade cos changes
on VA ade in compu able gene al equilib ium models.5 The pu pose o
de i ing (2) is o enable a s uc u al in e p e a ion o he coe icien s
ha a e es ima ed by ad-hoc VA g a i y equa ions. This allows us o
pinpoin a se o p oblema ic issues ha a ise unde he commonly
employed educed- o m app oach.6
2.2. Es ima ing he impac o RTAs on (VA) ade
To map ou se up di ec ly in o commonly used panel es ima ion
amewo ks, we add a ime dimension indexed by 𝑡 and employ wo
addi ional assump ions:
(A3). Bila e al ade cos s depend on RTAs and a ec o o o he
obse able ade ba ie s 𝑍𝑖𝑛𝑡 acco ding o
𝜏𝑖𝑛𝑡 = exp {𝛿𝑅𝑇 𝐴𝑖𝑛𝑡 +𝜈𝑍𝑖𝑛𝑡}.(3)
Combining (4) and (3), we de i e he empi ical g a i y equa ion o
g oss ade
ln 𝑋𝑖𝑛𝑡 =𝛽𝑋𝑅𝑇 𝐴𝑖𝑛𝑡 +𝜈𝑍𝑖𝑛𝑡 +𝛾𝑖𝑡 +𝛾𝑛𝑡 +𝛾𝑖𝑛 +𝑢𝑖𝑛𝑡.(4)
whe e 𝛾𝑖𝑡, 𝛾𝑛𝑡, 𝛾𝑖𝑛 a e ixed e ec s. Hence o h, we use 𝜻𝒊𝒏𝒕 o deno e he
ec o o co a ia es in (4).
(A4). Exogenei y o he co a ia es
E[𝑢𝑖𝑛𝑠|𝜻𝑖𝑛𝑡]= 0 o 𝑠, 𝑡 = 1,…, 𝑇 .
Unde A4, (1) and (4) imply ha he elas ici y o g oss ade o a
ade cos change ha is due o a change in RTA membe ship is
𝛽𝑋=𝜕E[ln 𝑋𝑖𝑛𝑡|𝜻𝒊𝒏𝒕]
𝜕𝑅𝑇 𝐴𝑖𝑛𝑡
= −𝜀𝛿. (5)
In analogy o (4), VA g a i y equa ions employ ( a ian s o ) he
empi ical model
ln 𝑉 𝐴𝑖𝑛𝑡 =𝛽𝑉 𝐴𝑅𝑇 𝐴𝑖𝑛𝑡 +𝜈𝑉 𝐴𝑍𝑖𝑛𝑡 +𝛾𝑖𝑡 +𝛾𝑛𝑡 +𝛾𝑖𝑛 +𝜖𝑖𝑛𝑡 (6)
o es ima e 𝛽𝑉 𝐴 =𝜕E[ln 𝑉 𝐴𝑖𝑛𝑡|𝜻𝒊𝒏𝒕]
𝜕𝑅𝑇 𝐴𝑖𝑛𝑡 . Howe e , he heo e ical VA g a i y
Eq. (2) implies se e al issues ha complica e he es ima ion o (6).
Issue (1): Coe icien he e ogenei y. Acco ding o (2) and (3), he elas-
ici y o VA ade o a change in RTA membe ship is
𝜕ln 𝑉 𝐴𝑖𝑛𝑡
𝜕𝑅𝑇 𝐴𝑖𝑛𝑡
=𝜕ln 𝑉 𝐴𝑖𝑛𝑡
𝜕(ln 𝜏−𝜀
𝑖𝑛𝑡 )(−𝜀𝛿)(7)
whe e
𝜕ln 𝑉 𝐴𝑖𝑛𝑡
𝜕(ln 𝜏−𝜀
𝑖𝑛𝑡 )=𝜕(ln 𝐶𝑛𝑡∕𝛷𝑛𝑡)
𝜕(ln 𝜏−𝜀
𝑖𝑛𝑡 )+𝜔𝑖𝑖𝑛𝑡 +∑
ℎ
𝜔𝑖ℎ𝑛𝑡 (𝜕ln 𝑏𝑖ℎ𝑡
𝜕(ln 𝜏−𝜀
𝑖𝑛𝑡 )−𝜕ln 𝛹ℎ𝑡
𝜕(ln 𝜏−𝜀
𝑖𝑛𝑡 ))
and 𝜔𝑖ℎ𝑛𝑡 =𝑏𝑖ℎ𝑡𝜏−𝜀
ℎ𝑛𝑡𝛹−1
ℎ𝑡
∑𝑗𝑏𝑖𝑗𝑡𝜏−𝜀
𝑗𝑛𝑡𝛹−1
𝑗𝑡
. No e ha 𝜕ln 𝑉 𝐴𝑖𝑛𝑡
𝜕𝑅𝑇 𝐴𝑖𝑛𝑡
depends on cha ac e is ics
o he pai 𝑖, 𝑛. Thus, he bes we can aim o by es ima ing (6) is he
sample a e age o 𝜕E[ln 𝑉 𝐴𝑖𝑛𝑡|𝜻𝑖𝑛𝑡]
𝜕𝑅𝑇 𝐴𝑖𝑛𝑡
o he pai s whose RTA s a us changes.
The magni ude o his a e age e ec , which we deno e wi h
𝛽𝑉 𝐴,𝑡𝑟𝑒𝑎𝑡𝑒𝑑, will depend on he se o coun y pai s and he ime pe iod
included in he es ima ion, e en i he ac ual da a we e gene a ed by
a p ocess consis en wi h A1–A4. In con as ,
𝛽𝑋,𝑡𝑟𝑒𝑎𝑡𝑒𝑑 es ima es −𝜀𝛿
unde A1–A4, independen o he sample composi ion.
5E.g., Johnson and Nogue a (2017) and Felbe may e al. (2022) employ
quan i a i e ade models ea u ing g a i y in in e media e and inal goods
ade o s uc u ally es ima e he pa ial e ec o RTAs on g oss ade and
hen calcula e he co esponding changes in he wo ld inpu –ou pu ma ix
and he new VA ade lows.
6While ou ocus is on VA expo s, he logic we ou line ex ends o ela ed
measu es such as he domes ic VA con en o expo s o impo s o he ca bon
con en o ade.
Economics Le e s 254 (2025) 112476
2
I. Heiland and P. Š áb
Issue (2): Lack o con ol g oup. Unde A2, VA expo s om 𝑗 each 𝑘
ia e e y possible ou e. This implies ha a educ ion in 𝜏𝑖𝑛, e.g., due
o a bila e al RTA be ween 𝑖 and 𝑛 also bene i s VA ade om 𝑗 o 𝑘
ha a els ia 𝑖 and 𝑛. Fo mally, excep o kni e-edge cases,
𝜕ln 𝑉 𝐴𝑗𝑘𝑡
𝜕ln(𝜏−𝜀
𝑖𝑛𝑡 )≠0 ∀ 𝑖, 𝑛, 𝑗, 𝑘. (8)
Fo example, o wo coun ies 𝑗, 𝑘, which a e no pa o he RTA, he
e ec is
𝜕ln 𝑉 𝐴𝑗𝑘𝑡
𝜕(ln 𝜏−𝜀
𝑖𝑛𝑡 )=𝜕ln(𝐶𝑘𝑡∕𝛷𝑘𝑡)
𝜕(ln 𝜏−𝜀
𝑖𝑛𝑡 )+∑
ℎ
𝜔𝑗ℎ𝑘𝑡 (𝜕ln 𝑏𝑗ℎ𝑡
𝜕(ln 𝜏−𝜀
𝑖𝑛𝑡 )−𝜕ln 𝛹ℎ𝑡
𝜕(ln 𝜏−𝜀
𝑖𝑛𝑡 ))
Like he pa ial e ec on he ‘‘ ea ed’’ coun y pai s, he e ec on
‘‘un ea ed’’ pai s is he e ogeneous. Issue 2 implies ha , unde A1–A4,
we will ne e be able o eco e he (sample-dependen ) 𝛽𝑉 𝐴,𝑡𝑟𝑒𝑎𝑡𝑒𝑑 .
Hence, we will a bes be able o iden i y he di e ence be ween he
a e age e ec o he RTA on membe s’ VA ade wi h each o he and
he a e age e ec on all o he , indi ec ly a ec ed pai s:
𝛽𝑉 𝐴 =
𝛽𝑉 𝐴,𝑡𝑟𝑒𝑎𝑡𝑒𝑑 −
𝛽𝑉 𝐴,𝑢𝑛𝑡𝑟𝑒𝑎𝑡𝑒𝑑.(9)
Issue (3): Omi ed a iables bias. The non-ze o c oss de i a i es in
(8) imply mo e gene ally ha he e ec o a gi en RTA canno be
iden i ied sepa a ely om any ade cos change happening elsewhe e
in he wo ld. Since 𝜕ln 𝑉 𝐴𝑖𝑛𝑡
𝜕ln(𝜏−𝜀
𝑗𝑘𝑡) is non-ze o and pai speci ic, i.e., no
abso bed by expo e and impo e ixed e ec s, any ade cos change
ac oss he wo ld ha coincides wi h he change in 𝑅𝑇 𝐴𝑖𝑛 will bias he
coe icien
𝛽𝑉 𝐴, excep in special cases. Mo eo e , omi ed a iables
bias is no limi ed o ade cos . In ac , e en changes in he coun y-
speci ic pa ame e s 𝛹ℎ and 𝑣ℎ, ha in luence 𝑉 𝐴𝑖𝑛𝑡 h ough he Leon ie
coe icien s in (2), will bias he coe icien i hey coincide wi h he
o ma ion o he RTA.
3. Quan i ica ion o he e ogenei y and bias
3.1. Me hodology
In his sec ion, we demons a e he quan i a i e impo ance o
he abo emen ioned issues in a con olled simula ion se ing whe e
A1–A4 hold. We use a a ian o he model o Aichele and Heiland
(2018) o simula e he exac pa ial and gene al equilib ium e ec s o
a hypo he ical RTA on g oss ade and VA ade.7 The model sa is ies
A1 and A2, and we simula e ade cos shocks ha sa is y A3 and A4.
Speci ically, we assume ha he se o coun ies 𝐵 ⊂ 𝑁 o ms an
RTA ha educes ade cos among membe s by 10% (𝛿=.9) and
a ade elas ici y 𝜀= −5. The model yields coun e ac ual changes
𝑋𝑖𝑛 =𝑋′
𝑖𝑛∕𝑋0
𝑖𝑛, whe e 𝑋0
𝑖𝑛 (𝑋′
𝑖𝑛) is g oss bila e al ade in he baseline
(coun e ac ual) equilib ium, and, analogously, coun e ac ual changes
in VA ade,
𝑉 𝐴𝑖𝑛 =𝑉 𝐴′
𝑖𝑛∕𝑉 𝐴0
𝑖𝑛 o 𝑖, 𝑛 ∈𝑁. Ou assump ions imply
ha we can eco e he pa ial e ec o he RTA on g oss ade om
he eg ession
ln
𝑋𝑖𝑛 =𝛽𝑋𝑅𝑇 𝐴𝑖𝑛 +𝜇𝑖+𝜇𝑛+𝑢𝑖𝑛,(10)
whe e 𝑅𝑇 𝐴𝑖𝑛 equals one o 𝑛, 𝑖 ∈𝐵, 𝑛 ≠𝑖 and ze o o he wise. 𝛽𝑋
obse es 𝑒𝛽𝑋=𝛿𝜀.
In analogy o (10), we se up he ad-hoc log linea es ima ion
equa ion
ln
𝑉 𝐴𝑖𝑛 =𝛽𝑉 𝐴𝑅𝑇 𝐴𝑖𝑛 +𝜇𝑖+𝜇𝑛+𝜀𝑖𝑛 (11)
o s udy he p ope ies o
𝛽𝑉 𝐴.
7The model baseline is calib a ed o ma ch p oduc ion and bila e al ade
o 65 coun ies and he es o he wo ld in he OECD ICIO da abase in 2018.
Fig. 1. BRICS, e ec s on RTA-membe s s. Non-membe s.
3.2. Resul s
Fi s , we ocus on he ex en o he e ogenei y ha is concealed
by he a e age pa ial e ec (issue 1). To ha end, we simula e he
ollowing scena io:
Scena io 1 (‘‘𝐵𝑅𝐼𝐶𝑆’’). We assume ha he BRICS coun ies (B azil,
Russia, India, China, and Sou h A ica) o m an RTA ha educes ade
cos s be ween RTA membe s by 10%.
To quan i y he he e ogenei y, we calcula e he dis ibu ion o he
pa ial VA ade e ec s o he RTA ac oss all possible quad uples wi h
one ea ed pai . S a ing wi h g oss ade as a e e ence poin , A1
implies
ln (
𝑋𝑖𝑛∕
𝑋𝑖𝑗
𝑋𝑘𝑛∕
𝑋𝑘𝑗 )=𝛽𝑋i 𝑅𝑇 𝐴𝑖𝑛 = 1, 𝑅𝑇 𝐴𝑖𝑗 , 𝑅𝑇 𝐴𝑘𝑛, 𝑅𝑇 𝐴𝑘𝑗 ≠1.
(12)
The pa ial ade e ec is cons an ac oss membe s o he RTA and
independen o he composi ion o he con ol g oup. In con as , e e y
RTA membe expe iences a di e en pa ial VA ade e ec , and so does
e e y non-membe . Hence, he dis ibu ion o
ln (
𝑉 𝐴𝑖𝑛∕
𝑉 𝐴𝑖𝑗
𝑉 𝐴𝑘𝑛∕
𝑉 𝐴𝑘𝑗 ) o 𝑅𝑇 𝐴𝑖𝑛 = 1, 𝑅𝑇 𝐴𝑖𝑗 , 𝑅𝑇 𝐴𝑘𝑛, 𝑅𝑇 𝐴𝑘𝑗 ≠1
(13)
is non-degene a e. Fig. 1 (dashed blue line) shows he dis ibu ion o
he RTA e ec s ac oss quad uples. The pa ial VA e ec s a e smalle
han he pa ial e ec on g oss ade on a e age, bu span a wide ange.
Fig. 2 plo s he dis ibu ion o he RTA e ec s on he con ol g oups,
calcula ed as
ln (
𝑉 𝐴𝑖𝑛∕
𝑉 𝐴𝑖𝑗
𝑉 𝐴𝑘𝑛∕
𝑉 𝐴𝑘𝑗 ) o 𝑅𝑇 𝐴𝑖𝑛, 𝑅𝑇 𝐴𝑖𝑗 , 𝑅𝑇 𝐴𝑘𝑛, 𝑅𝑇 𝐴𝑘𝑗 ≠1.(14)
As implied by (8), he e ec s a e non-ze o and he e ogeneous ac oss
pai s.
Table 1 shows he es ima e o 𝛽𝑉 𝐴 om (11) in column 1. The
implied a e age pa ial VA ade change is (𝑒𝛽𝑉 𝐴 − 1) ∗ 100% = 54.97%.
To illus a e ha he es ima e o he VA ade cos elas ici y depends
on he composi ion o he es ima ion sample, we analyze wo addi ional
scena ios:
Scena io 2: ‘‘𝐵𝑅𝐼𝐶𝑆 +𝑇 𝑇 𝐼𝑃 ’’. In pa allel wi h he o ma ion o he
𝐵𝑅𝐼𝐶𝑆 ag eemen as de ined in Scena io 1, ano he RTA (called
‘‘TTIP’’) is o med be ween he U.S. and all EU27 membe s, which also
educes ade cos s be ween membe s by 10%.
Economics Le e s 254 (2025) 112476
3
I. Heiland and P. Š áb
Fig. 2. BRICS, e ec s on Non-membe s.
Table 1
Pa ial VA ade e ec s unde di e en scena ios.
1.𝐵𝑅𝐼𝐶𝑆 2.𝐵𝑅𝐼𝐶𝑆 +𝑇 𝑇 𝐼𝑃 3.𝐵𝑅𝐼𝐶𝑆2001 4.𝐵𝑅𝐼𝐶𝑆 +𝑈𝑆
𝛽𝑉 𝐴 0.4381 0.4474 0.4476 0.4402
No e: In all ou scena ios, he pa ial ade e ec on g oss ade is 𝛽𝑋= 0.5268.
Scena io 3: ‘‘𝐵𝑅𝐼𝐶𝑆2001’’. Like in Scena io 1, he BRICS coun ies o m
an RTA, bu now we calib a e he model baseline wi h da a om 2001
ins ead o 2018.
In bo h new scena ios, we ind pa ial a e age VA e ec s ha
a e app oxima ely 1.5 pe cen age poin s la ge han in he baseline
scena io (see columns 2, 3). By cons uc ion, he pa ial e ec on g oss
ade a e iden ical.
To demons a e he issue o omi ed a iables bias, we s udy he
ollowing scena io:
Scena io 4: ‘‘𝐵𝑅𝐼𝐶𝑆 +𝑈𝑆’’. In addi ion o he BRICS ag eemen as
in Scena io 1, a posi i e in as uc u e shock occu s in he USA which
educes ade cos s be ween he U.S. and all des ina ions (including he
U.S. i sel ) by 50%.
Column 4 shows ha he es ima ed pa ial VA ade e ec o
𝐵𝑅𝐼𝐶𝑆 is a ec ed by he in as uc u e shock occu ing elsewhe e
in he wo ld. This occu s despi e he ac ha he di ec e ec on
BRICS coun ies’ and non-BRICS coun ies’ VA ade wi h he US is
abso bed by he coun y ixed e ec s in (11). In con as , in he g oss
ade eg ession, he coun y ixed e ec s pe ec ly con ol o he
in as uc u e shock.
4. Discussion and conclusions
Be o e concluding, we would like o discuss he assump ions un-
de lying ou amewo k. A3 is a widesp ead and ai ly ha mless log-
linea i y assump ion. A4, in con as , is likely o ail when con on ed
wi h eal-wo ld da a. Howe e , we adop i o p ac ical pu poses only,
because we wan o demons a e he challenges associa ed wi h VA
g a i y es ima es o a iables whose e ec s on g oss ade can be
cleanly iden i ied using OLS wi h ixed e ec s.
A1 and A2 wa an mo e discussion. A2 implies ha he VA com-
posi ion o expo ed goods is iden ical ac oss des ina ions, e ec i ely
uling ou he possibili y ha di e en inpu s a e used o di e en
des ina ion ma ke s. I we had eal da a on alue added con en ,
we could mo e accu a ely measu e coun y-pai speci ic exposu e o
he ea men o con ounding shocks. The empi ical issues caused by
he e ogeneous exposu e, howe e , would pe sis . The same holds o
elaxing A1 by allowing o di e ences be ween ade sha es o inal
and in e media e goods o mul iple sec o s.
Finally, we do no in end o ou analysis o sugges ha g oss ade
g a i y equa ions a e co ec . Ins ead, we wan o poin ou ha he
use o educed- o m VA g a i y equa ions should no be jus i ied by
e e encing he heo e ical and empi ical me i s o g a i y equa ions
o g oss ade. We hink he misspeci ica ion issues ou lined he e a e
ele an beyond ou s ylized amewo k because hey a ise om he
mul ila e al na u e o VA ade and he uniqueness o each coun y’s
GVC, which is an empi ical ac . Consequen ly, we belie e ha he
e ec s o ade cos changes on VA ade a e be e s udied using a
s uc u al model o ade in inal and in e media e goods.
Decla a ion o Gene a i e AI and AI-assis ed echnologies in he
w i ing p ocess
Du ing he p epa a ion o his wo k he au ho s used Cha GPT-4 o
imp o e he language. A e using his ool, he au ho s e iewed and
edi ed he con en as needed and ake ull esponsibili y o he con en
o he published a icle.
Funding
Funded by he Eu opean Commission h ough i s Ho izon Eu ope
esea ch and inno a ion p og amme unde g an ag eemen numbe
101061123. Views and opinions exp essed a e howe e hose o he
au ho s only and do no necessa ily e lec hose o he Eu opean
Union o he Eu opean Resea ch Execu i e Agency (REA), he g an ing
au ho i y. Nei he he Eu opean Union no he g an ing au ho i y can
be held esponsible o hem.
Appendix
Lis o academic pape s and policy epo s es ima ing g a i y equa ions wi h
alue added ade lows
Academic pape s
Blind e al. (2018)Sanguine e al. (2022)
Bo a e al. (2019)Sha ma e al. (2023)
Böhmecke-Schwa e and
Blind (2023)
Sha ma e al. (2024)
Chen e al. (2022)Thang e al. (2021)
Díaz-Mo a e al. (2022)Tokas (2021)
Doan and Le (2021)Tokas (2022)
Fe ő e al. (2024)Wang and Thanga elu
(2021)
Hayakawa and Mukunoki
(2023)
Wolszczak-De lacz and Lu
(2022)
Johnson and Nogue a
(2017)
Yang (2022)
Kang and Gapay (2024)Yang (2023)
Lage e al. (2020)Yang and Liu (2024)
Le e al. (2022)Zanino ić (2022)
Lee (2019)Zanino ić and Buga čić
(2023)
Lu and Wolszczak-De lacz
(2024)
Zanino ić e al. (2024)
Mulabdic e al. (2017)Zhang e al. (2024)
Njike (2021)Zhao (2022)
Olczyk and Ko dalska
(2017)
Zhong e al. (2022)
Pahl and Timme (2019)
Policy epo s
Cades in e al. (2016)
Jouanjean e al. (2017)
Moïsé and So escu (2015)
OECD (2021)
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I. Heiland and P. Š áb
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