Fos e -McG ego , Neil; Nomale , Önde ; Ve spagen, Ba
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The Inno a ion and S uc u al T ans o ma ion Da abase: A
Guide
UNU-MERIT Wo king Pape s, No. 2024-027
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The Inno a ion and S uc u al T ans o ma ion Da abase: A Guide
Neil Fos e -McG ego , Önde Nomale & Ba Ve spagen
Published 22 Oc obe 2024
Maas ich Economic and social Resea ch ins i u e on Inno a ion and Technology (UNU-MERIT)
email: in o@me i .unu.edu | websi e: h p://www.me i .unu.edu
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1
The Inno a ion and S uc u al T ans o ma ion Da abase: A
Guide
Oc obe 2024
Neil Fos e -McG ego , Önde Nomale & Ba Ve spagen
Abs ac
This documen summa izes he con en o he Inno a ion and S uc u al T ans o ma ion da abase
p o ides a collec ion o indica o s o he global economy, emphasizing he dynamic na u e o
de elopmen and economic g ow h. The da abase is publicly a ailable om he web (see link in
he main ex ). This documen summa izes he con en o he da abase, u he p o iding
in o ma ion on he da a sou ces and he cons uc ion o he a iables included in he da abase.
Keywo ds: S uc u al change, inno a ion, economic de elopmen , economic g ow h.
JEL Codes: O14, O30, O40, O50, O53
The Inno a ion and S uc u al T ans o ma ion Da abase and his guide a e p o ided unde a
C ea i e Commons BY 4.0 license. This license allows use s o dis ibu e, emix, adap , and
build upon he ma e ial in any medium o o ma , so long as a ibu ion is gi en o he
c ea o . The license allows o comme cial use.
2
1. In oduc ion
The Inno a ion and S uc u al T ans o ma ion da abase p o ides a collec ion o indica o s o he
global economy, emphasizing he dynamic na u e o de elopmen and economic g ow h. This
documen summa izes he con en o he da abase, u he p o iding in o ma ion on he da a
sou ces and he cons uc ion o he a iables included in he da abase. The da abase is publicly
a ailable om he web a
h ps://da a e se.nl/da a e se/inno a ion_and_s uc u al_ ans o ma ion_da abase/
Any u u e upda es o he da abase will be a ailable a he same link. The da abase and his
documen a e p o ided unde a CC BY 4.0 license. This means ha he da abase can be used eely,
as long as app op ia e c edi s a e gi en.1 This c edi can be gi en by ci ing he o hcoming book
ha illus a es he use o he da abase:
Felipe, J., Fos e -McG ego , N., Nomale , Ö and B. Ve spagen, 2025, Inno a ion and
S uc u al T ans o ma ion in Asia, Abingdon (UK): Taylo & F ancis.
The aim o he da abase is o p o ide a esou ce o esea che s, policymake s and o he s ha
p o ides in o ma ion on a se o a iables and indica o s ha a e undamen al o unde s and long-
un g ow h and de elopmen . These indica o s e ol e a ound he opic o s uc u al
ans o ma ion, de elopmen , and in e na ional compe i i eness. Unde lying he da abase is he
p emise ha de elopmen is a p ocess o s uc u al ans o ma ion, i.e., ha inc easing he s anda d
o li ing in an economy in ol es changing wha he economy p oduces and consumes and in ol es
changes in he way ac o s in he economy in e ac . T adi ionally, his p ocess o s uc u al
ans o ma ion was conside ed o in ol e a mo emen o p oduc ion (and consump ion) ac oss
b oad sec o s (e.g., om ag icul u e o indus y o se ices). Wi h he a ailabili y o new da a,
howe e , a mo e nuanced pe spec i e has eme ged. One dimension o his is he obse a ion ha
much s uc u al ans o ma ion is occu ing wi hin sec o s, h ough o example he changing
s uc u e o occupa ions and unc ions wi hin sec o s, as well as changes in he composi ion o
p oduc ion and ac i i ies wi hin sec o s.
Rela ed o hese changes ha e been de elopmen s o he global s uc u e o p oduc ion, wi h
s uc u al ans o ma ion depending o a g ea ex en on he way he economy in e ac s wi h
o eign ma ke s in oday’s global economy. The posi ion o an economy in he in e na ional
s uc u e o p oduc ion depends on he compe i i eness o i ms and o he ac o s in he economy.
In his con ex , compe i i eness, o compa a i e ad an age, de e mines whe e economies, o a he
1 Fo de ails o his license see h ps://c ea i ecommons.o g/licenses/by/4.0/.
3
he i ms loca ed in economies, can con ibu e alue added in global p oduc ion ne wo ks, which
in u n will help de e mine o e all le els o well-being in he economy.
The compe i i eness, o compa a i e ad an age, o an economy is u he a unc ion o he
capabili ies ha exis in he economy. De elopmen can u he be seen as a p ocess o de eloping
compe i i eness in a b oade ange o p oduc s (i.e., di e si ica ion), including a mo e in o mo e
complex p oduc s wi hin and ac oss sec o s (i.e., upg ading). An impo an dimension o an
economy’s capabili ies ela es o i s pe o mance in inno a ion. In his con ex , he e has been a
huge amoun o in e es in ecen yea s in he de elopmen o digi al echnologies and how
inno a ion in hese echnologies is changing he na u e o p oduc ion and wo k.
Based upon hese a gumen s, he da abase is o med a ound ou main pilla s. The i s pilla co e s
da a on s uc u al change and p oduc i i y, p esen ing indica o s ha documen how as , and in o
which di ec ion he s uc u e o he economy changes and he esul ing impac o hese changes
on p oduc i i y g ow h. The second pilla ocuses on compe i i eness and compa a i e ad an age,
which is app oached h ough he no ion o p oduc complexi y, and which in u n can be seen as
a measu e o de elopmen po en ial. This pilla ocuses on de eloping a de ailed pic u e o he so-
called p oduc space and how he economies in he da abase occupy his space. The app oach
in ol es a la ge da a se o expo ed p oduc s and shows how economies a e specialized in hese
di e en p oduc s. The hi d pilla o he da abase is conce ned wi h inno a ion, wi h he da abase
making use o pa en da a o iden i y he ex en o inno a ion as well as he di ec ion o ha
inno a ion, u he p o iding an o e all pic u e o pa en ed in en ions and how hey ela e o he
economy, as well as an o e iew o ends in echnologies ela ed o he so-called ou h indus ial
e olu ion. The inal pilla conside s he global economy and he ole o indi idual economies in
he global s uc u e o p oduc ion h ough an examina ion o so-called Global Value Chains
(GVCs), which highligh ha p oduc ion is agmen ed geog aphically and i ms may con ibu e
(small) pa s o o al alue added o a a ie y o GVCs. The da a o his inal pilla is hea ily based
on global inpu -ou pu ables. The emainde o his documen desc ibes in u n he indica o s ha
all unde each o he ou pilla s, along wi h he da a sou ces used o cons uc hem.
2. Pilla 1: S uc u al Change
2.1. Basic s uc u al change indica o s
The basic indica o s o s uc u al change conside he sec o al composi ion o he economy, as
well as he s uc u e o in e na ional ade (expo s and impo s). Fo he sec o al s uc u e o he
economy, he da abase conside s he s uc u e o alue added, household consump ion demand
and o al demand, all in cons an 2010 US$. These da a a e d awn om he ADB inpu ou pu
ables. The ollowing a iables a e de ined:
4
𝜎𝜎𝑡𝑡𝑡𝑡𝑡𝑡
𝑉𝑉𝑉𝑉=𝑉𝑉𝐴𝐴𝑡𝑡𝑡𝑡𝑡𝑡
∑𝑉𝑉𝐴𝐴𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡
𝜎𝜎𝑡𝑡𝑡𝑡𝑡𝑡
𝐻𝐻𝐻𝐻=𝐻𝐻𝐻𝐻𝑡𝑡𝑡𝑡𝑡𝑡
∑𝐻𝐻𝐻𝐻𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡
𝜎𝜎𝑡𝑡𝑡𝑡𝑡𝑡
𝑇𝑇𝑇𝑇=𝑇𝑇𝑇𝑇𝑡𝑡𝑡𝑡𝑡𝑡
∑𝑇𝑇𝑇𝑇𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡
whe e he indices 𝑖𝑖, 𝑗𝑗, and 𝑡𝑡 deno e economy, sec o and ime pe iod, espec i ely, 𝑉𝑉𝐴𝐴 is alue
added p oduced in he sec o /economy, 𝐻𝐻𝐻𝐻 is inal consump ion by households in economy 𝑖𝑖 o
p oduc s p oduced by sec o 𝑗𝑗 (ei he impo ed o p oduced domes ically), and TD is he sum o
household consump ion, go e nmen consump ion and g oss ixed capi al o ma ion by esiden s
o economy 𝑖𝑖 aimed a p oduc s p oduced by sec o j (again domes ically o impo ed).
These sha es a e used o p oduce an indica o o s uc u al change, which is e med he 𝑁𝑁𝐴𝐴𝑉𝑉
indica o (No m o Absolu e Value changes). This is de ined as ollows:
𝑁𝑁𝐴𝐴𝑉𝑉𝑡𝑡𝐾𝐾=∑�𝜎𝜎𝑇𝑇𝑡𝑡𝑡𝑡
𝐾𝐾−𝜎𝜎0𝑡𝑡𝑡𝑡
𝐾𝐾�
𝑡𝑡2𝑇𝑇
whe e 𝐾𝐾∈{𝑉𝑉𝐴𝐴,𝐻𝐻𝐻𝐻,𝑇𝑇𝑇𝑇} is an index ha e e s o he pa icula indica o o s uc u e being
conside ed and T is he numbe o yea s conside ed. The g ea e he deg ee o s uc u al change
be ween pe iod 0 and 𝑇𝑇, he highe he alue o he 𝑁𝑁𝐴𝐴𝑉𝑉 indica o .
Figu e 1 shows he sec o al sha es o o al demand (𝑇𝑇𝑇𝑇) and he associa ed 𝑁𝑁𝐴𝐴𝑉𝑉 indica o o
Nepal.2 No e ha he da abase does no ha e da a o he yea s 2001-2006, so he pe iod be ween
2000 and 2007 is in e pola ed. We see ha he ecen pe iod 2015-19 is one o ela i ely apid
s uc u al change in o al demand in Nepal.
2 This igu e, as hose below, is copied om he g aphical in e ace on he websi e. In his in e ace, use s can selec
speci ic (combina ions o ) indica o s, economies and sec o s o be displayed. These igu es a e o en linked o each
o he , e.g., clicking/selec ing an obse a ion in one igu e p o ides mo e de ailed in o ma ion o his obse a ion in
a ela ed igu e. All igu es can be sa ed and used in p op ie a y documen s.
5
Figu e 1. S uc u al change in o al demand – he case o Nepal
The sec o s ha a e a ailable in his pilla o he da abase a e iden ical o he sec o s used in he
GVC pilla , wi h a selec ion o hese sec o s also used in o he sec ions o he da abase. These
sec o s a e documen ed in Table 1.
6
Table 1. Sec o s used in basic s uc u al change and GVC sec ions
Sec
num
ISIC Re . 4
Desc ip ion
1
A
Ag icul u e, hun ing, o es y, and ishing
2
B
Mining and qua ying
3
C10-C12
Food, be e ages, and obacco
4
C13, C14
Tex iles and ex ile p oduc s
5
C15
Lea he , lea he p oduc s, and oo wea
6
C16
Wood and p oduc s o wood and co k
7
C17, C18, J58
Pulp, pape , pape p oduc s, p in ing, and publishing
8
C19
Coke, e ined pe oleum, and nuclea uel
9
C20, C21
Chemicals and chemical p oduc s
10
C22
Rubbe and plas ics
11
C23
O he nonme allic mine als
12
C24, C25
Basic me als and ab ica ed me al
13
C28, C33
Machine y, nec
14
C26, C27
Elec ical and op ical equipmen
15
C29, C30
T anspo equipmen
16
C31, C32
Manu ac u ing, nec; ecycling
17
D, E36
Elec ici y, gas, and wa e supply
18
F
Cons uc ion
19
G45
Sale, main enance, and epai o mo o ehicles and
mo o cycles; e ail sale o uel
20
G46
Wholesale ade and commission ade, excep o mo o
ehicles and mo o cycles
21
G47
Re ail ade, excep o mo o ehicles and mo o cycles; epai
o household goods
22
I
Ho els and es au an s
23
H49
Inland anspo
24
H50
Wa e anspo
25
H51
Ai anspo
26
H52, N79
O he suppo ing and auxilia y anspo ac i i ies; ac i i ies
o a el agencies
27
H53, J61
Pos and elecommunica ions
28
K
Financial in e media ion
29
L
Real es a e ac i i ies
30
J58-J60, J62-J63, M, N77-
N78, N80-N82
Ren ing o M&Eq and o he business ac i i ies
31
O
Public adminis a ion and de ense; compulso y social secu i y
32
P
Educa ion
33
Q
Heal h and social wo k
34
E37-E39, R, S
O he communi y, social, and pe sonal se ices
35
T
P i a e households wi h employed pe sons
Tu ning o indica o s o he s uc u e o in e na ional ade (bo h expo s and impo s), he
da abase includes wo g oups o indica o s. The i s is ela ed o global alue chains (GVCs), while
he o he e e s o inno a ion, and in pa icula he g oup o echnologies ha is e e ed o as 4 h
indus ial e olu ion (4IR) echnologies. The indica o s on GVCs dis inguish be ween di e en
ypes o p oduc s, namely consump ion goods, in e media e goods and capi al goods. Acco ding
o his dis inc ion, consump ion goods and capi al goods a e conside ed as he ou pu s o a alue
13
In he case o employmen da a, i is e y di icul o ob ain ac ual da a o many (mos ) o he
economies in he da abase. To o e come his cons ain , he e o e, es ima ed da a om he
In e na ional Labo O ganiza ion was used. This da a is p esen ed in hei online ILOSTAT
da abase6, speci ically he sec ion en i led ILOEST (ILO modelled es ima es and p ojec ions). The
da a used a e om he able called Employmen by sex and economic ac i i y, which p esen s employmen
in 1,000 pe sons a he ISIC Re 4 sec o al b eakdown.
Value added a he sec o al le el is d awn om a da abase on na ional accoun s held a he UN-
DESA S a is ical Di ision.7 Da a on alue added by economic ac i i y p o ided by his da abase is
used, wi h he da a measu ed in cons an 2015 p ices and US dolla s. The da abase uses ma ke
exchange a es, i.e., i makes no a emp o ake in o accoun eal exchange a es ha “co ec ” o
p ice di e en ials be ween economies. Al hough using eal exchange a es (o pu chasing powe
pa i y exchange a es, PPP) is cus oma y o compa ing li ing s anda ds based on agg ega e GDP,
co ec ing o p ice di e en ials a he sec o al le el is impossible due o a lack o da a. Value added
da a a e exp essed in billions o US$.
The da a on alue added a e colla ed acco ding o he ISIC Re . 3 classi ica ion, whe eas he
employmen da a a e epo ed acco ding o he ISIC Re . 4 classi ica ion. A he agg ega ion le el
used in he cons uc ion o he da abase (i.e., he se en sec o s), hese sec o s a e compa able ac oss
he wo e isions howe e . Table 4 documen s he se en sec o s.
Table 4. Sec o al b eakdown in he s uc u al change and p oduc i i y g ow h sec ion
o he da abase
Sec o
numbe
Desc ip ion
ISIC codes
Re . 4
Re . 3
1
Ag icul u e; o es y and ishing
A
A, B
2
Mining, U ili ies
B, D, E
C, E
3
Manu ac u ing
C
D
4
Cons uc ion
F
F
5
T ade; Ho els and es au an s
G, I
G, H
6
T anspo , S o age, Communica ion
H, J
I
7
All o he ac i i ies
K – U
J – P
These da a a e used o cons uc se e al indica o s. The i s is he NAV indica o ha was al eady
de ined abo e o he case o alue-added. In his case i is calcula ed using employmen sha es and
de ined as:
6 h ps://ilos a .ilo.o g/da a/
7 h ps://uns a s.un.o g/unsd/snaama/Downloads
14
𝑁𝑁𝐴𝐴𝑉𝑉𝑡𝑡=∑�𝑆𝑆𝑇𝑇𝑡𝑡𝑡𝑡−𝑆𝑆0𝑡𝑡𝑡𝑡�
𝑡𝑡2𝑇𝑇
whe e 𝑖𝑖 e e s o economies and 𝑆𝑆𝑡𝑡𝑡𝑡𝑡𝑡 is he sha e o sec o 𝑗𝑗 in o al employmen in pe iod 𝑡𝑡 in
economy 𝑖𝑖.
Labo p oduc i i y is he main ocus o he o he indica o s in his second se o indica o s. Labo
p oduc i i y is de ined a he sec o al as well as he agg ega e le el and is calcula ed as alue added
(GDP) di ided by employmen . We p o ide he end o bo h o e all labo p oduc i i y, as well
as he wo componen s, alue added (GDP) and employmen , wi h he end de ined as a se ies o
index numbe s wi h base yea 2015 (2015 = 100). This index is cons uc ed simply as 100 imes he
alue in a pa icula yea di ided by he 2015 alue.
The indica o s o he impac o s uc u al change on labo p oduc i i y g ow h a e based on a
decomposi ion o labo p oduc i i y g ow h. This can be ep esen ed as ollows (we d op he
economy subsc ip i):
𝑃𝑃�𝑇𝑇=𝑃𝑃𝑇𝑇−𝑃𝑃0
𝑇𝑇𝑃𝑃0=∑𝑆𝑆𝑇𝑇𝑡𝑡𝑃𝑃𝑇𝑇𝑡𝑡𝑡𝑡−∑𝑆𝑆0𝑡𝑡𝑃𝑃0𝑡𝑡𝑡𝑡
𝑇𝑇∑𝑆𝑆0𝑡𝑡𝑃𝑃0𝑡𝑡𝑡𝑡 =
∑𝑃𝑃0𝑡𝑡�𝑆𝑆𝑇𝑇𝑡𝑡−𝑆𝑆0𝑡𝑡�
𝑡𝑡𝑇𝑇𝑃𝑃0+∑�𝑃𝑃𝑇𝑇𝑡𝑡−𝑃𝑃0𝑡𝑡��𝑆𝑆𝑇𝑇𝑡𝑡−𝑆𝑆0𝑡𝑡�
𝑡𝑡𝑇𝑇𝑃𝑃0+∑𝑆𝑆0𝑡𝑡�𝑃𝑃𝑇𝑇𝑡𝑡−𝑃𝑃0𝑡𝑡�
𝑡𝑡𝑇𝑇𝑃𝑃0
SSRE DSRE WS
whe e 𝑃𝑃𝑇𝑇 and 𝑃𝑃0 a e agg ega e (labo ) p oduc i i y in yea T and 0, espec i ely, and 𝑃𝑃𝑡𝑡𝑡𝑡 is labo
p oduc i i y in pe iod 𝑡𝑡 and sec o 𝑗𝑗. The h ee e ms in o which o al p oduc i i y g ow h (be ween
yea s T and 0) is decomposed a e on he igh hand side o his exp ession, and a e labelled SSRE
o S a ic S uc u al Realloca ion E ec , DSRE o Dynamic S uc u al Realloca ion E ec and
WS o Wi hin Sec o . SSRE measu es he e ec on p oduc i i y g ow h o ealloca ing esou ces
(i.e., labo ) o sec o s wi h highe p oduc i i y le els a he s a o he pe iod (yea 0), DSRE
measu es he e ec o ealloca ing esou ces o sec o s wi h a as e g ow h a e o p oduc i i y
be ween yea s T and 0, and WS measu es he con ibu ion o p oduc i i y g ow h ha occu s
wi hin sec o s.
Figu e 4 shows a se o diag ams ha illus a e he s uc u al change indica o s o Indonesia. The
op pa o he diag am shows he alue o he NAV indica o o a ious pe iods, which a e
displayed on he ho izon al axis. We see ha s uc u al change in Indonesia was s onges du ing
he 1991-1995 pe iod, and weakes du ing he 2001-05 pe iod. No e ha no all pe iods on he
ho izon al axis a e equal in leng h, bu he NAV indica o is scaled o yea ly changes, i.e., i is
compa able be ween pe iods o unequal leng h.
15
The bo om pa o he igu e shows he p oduc i i y decomposi ions, again o di e en pe iods
on he ho izon al axis (whe e again he e ec s a e scaled o di e ences in pe iod leng h). He e he
black line indica es o al labo p oduc i i y g ow h o e he di e en ime pe iods. This g ow h
a e is equal o he sum o he s acked ba s, which ep esen he h ee e ec s in oduced abo e.
The igu e e eals ha labo p oduc i i y g ow h in Indonesia was nega i e du ing he pe iod 1996-
2000, which encompasses he “Asian c isis”. The WS e ec domina es in mos pe iods, while he
DSRE is always nega i e. The SSRE peaks in he pe iod jus be o e he Asian c isis (1991-95).
Figu e 4. S uc u al change and labo p oduc i i y g ow h in Indonesia
Figu e 5 shows a u he ea u e o he websi e, wi h he igu e epo ing a b eakdown o he h ee
e ec s in he decomposi ion (WS, SSRE and DSRE) in o hei componen s a he sec o al le el.
This uses he ollowing de ini ions (we omi he ime scaling a iable 𝑇𝑇):
𝑀𝑀ℎ𝑖𝑖𝑐𝑐𝑀𝑀𝑖𝑖 𝑖𝑖𝑐𝑐 𝑐𝑐𝑖𝑖𝑅𝑅𝑐𝑐𝑖𝑖 𝑐𝑐𝑖𝑖𝑐𝑐𝑖𝑖𝑐𝑐𝑀𝑀𝑡𝑡𝑖𝑖𝑀𝑀𝑖𝑖𝑡𝑡𝑝𝑝𝑡𝑡= 𝑃𝑃𝑇𝑇𝑡𝑡−𝑃𝑃0𝑡𝑡
𝑃𝑃0
𝑖𝑖𝑐𝑐𝑖𝑖𝑡𝑡𝑖𝑖𝑖𝑖𝑐𝑐 𝑖𝑖𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑝𝑝𝑐𝑐𝑖𝑖𝑐𝑐𝑡𝑡 𝑐𝑐ℎ𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡= 𝑆𝑆0𝑡𝑡
𝑀𝑀ℎ𝑖𝑖𝑐𝑐𝑀𝑀𝑖𝑖 𝑖𝑖𝑐𝑐 𝑖𝑖𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑝𝑝𝑐𝑐𝑖𝑖𝑐𝑐𝑡𝑡 𝑐𝑐ℎ𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡=𝑆𝑆𝑇𝑇𝑡𝑡−𝑆𝑆0𝑡𝑡
16
𝑖𝑖𝑐𝑐𝑖𝑖𝑡𝑡𝑖𝑖𝑖𝑖𝑐𝑐 𝑖𝑖𝑖𝑖𝑐𝑐𝑖𝑖𝑡𝑡𝑖𝑖𝑀𝑀𝑖𝑖 𝑐𝑐𝑖𝑖𝑐𝑐𝑖𝑖𝑐𝑐𝑀𝑀𝑡𝑡𝑖𝑖𝑀𝑀𝑖𝑖𝑡𝑡𝑝𝑝𝑡𝑡=𝑃𝑃0𝑡𝑡
𝑃𝑃0
I is easily seen ha hese ou componen s can be used o cons uc he h ee e ec s in he
decomposi ion:
• SSRE is he sum ac oss sec o s o 𝑖𝑖𝑐𝑐𝑖𝑖𝑡𝑡𝑖𝑖𝑖𝑖𝑐𝑐 𝑖𝑖𝑖𝑖𝑐𝑐𝑖𝑖𝑡𝑡𝑖𝑖𝑀𝑀𝑖𝑖 𝑐𝑐𝑖𝑖𝑐𝑐𝑖𝑖𝑐𝑐𝑀𝑀𝑡𝑡𝑖𝑖𝑀𝑀𝑖𝑖𝑡𝑡𝑝𝑝𝑡𝑡×
𝑀𝑀ℎ𝑖𝑖𝑐𝑐𝑀𝑀𝑖𝑖 𝑐𝑐𝑠𝑠 𝑖𝑖𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑝𝑝𝑐𝑐𝑖𝑖𝑐𝑐𝑡𝑡 𝑐𝑐ℎ𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡
• DSRE is he sum ac oss sec o s o 𝑀𝑀ℎ𝑖𝑖𝑐𝑐𝑀𝑀𝑖𝑖 𝑐𝑐𝑠𝑠 𝑐𝑐𝑖𝑖𝑐𝑐𝑖𝑖𝑐𝑐𝑀𝑀𝑡𝑡𝑖𝑖𝑀𝑀𝑖𝑖𝑡𝑡𝑝𝑝𝑡𝑡×
𝑀𝑀ℎ𝑖𝑖𝑐𝑐𝑀𝑀𝑖𝑖 𝑐𝑐𝑠𝑠 𝑖𝑖𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑝𝑝𝑐𝑐𝑖𝑖𝑐𝑐𝑡𝑡 𝑐𝑐ℎ𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡
• WS e ec is he sum ac oss sec o s o 𝑖𝑖𝑐𝑐𝑖𝑖𝑡𝑡𝑖𝑖𝑖𝑖𝑐𝑐 𝑖𝑖𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑝𝑝𝑐𝑐𝑖𝑖𝑐𝑐𝑡𝑡 𝑐𝑐ℎ𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡×
𝑀𝑀ℎ𝑖𝑖𝑐𝑐𝑀𝑀𝑖𝑖 𝑐𝑐𝑠𝑠 𝑐𝑐𝑖𝑖𝑐𝑐𝑖𝑖𝑐𝑐𝑀𝑀𝑡𝑡𝑖𝑖𝑀𝑀𝑖𝑖𝑡𝑡𝑝𝑝𝑡𝑡
Using he example o Indonesia, Figu e 5 plo s o each o he h ee decomposi ion e ms he wo
cons i uen pa s o he decomposi ion e m o each sec o agains each o he . E ec s ha a e
posi i e a e plo ed in blue and nega i e con ibu ions a e plo ed in ed, while he size o he
bubbles indica es he magni ude o he absolu e alue o he e ec . In he case o Indonesia, and
ocusing on he pe iod 1991-2000, i can be seen ha he Mining & u ili ies sec o makes a s ong
con ibu ion o he WS e ec , which a ises la gely due o apid p oduc i i y change, despi e he
ela i ely small employmen sha e. Simila conclusions can be d awn o he o he wo e ec s,
DSRE and SSRE.
17
Figu e 5. Sec o labo p oduc i i y decomposi ions iew in he da abase
18
The da abase u he epo s ela i e p oduc i i y le els o pai s o economies. An example o his
is p o ided in Figu e 6 o Japan and India. These ela i e p oduc i i y indica o s pe sec o a e
calcula ed as ollows:
𝑅𝑅𝑖𝑖𝑐𝑐𝑃𝑃𝑡𝑡𝑘𝑘𝑡𝑡𝑡𝑡=𝑃𝑃𝑡𝑡𝑡𝑡𝑡𝑡𝑋𝑋𝑅𝑅𝑡𝑡
𝑃𝑃𝑘𝑘𝑡𝑡𝑡𝑡𝑋𝑋𝑅𝑅𝑘𝑘
whe e 𝑃𝑃 is labo p oduc i i y as be o e (measu ed in 2015 US$ pe wo ke ), 𝑋𝑋𝑅𝑅 is a eal exchange
a e ac o , and he subsc ip s 𝑘𝑘, 𝑐𝑐, and 𝑗𝑗 deno e wo coun ies and a sec o espec i ely (𝑗𝑗 can also
deno e he o al economy). The eal exchange a e ac o XR is he a io be ween he Wo ld Bank’s
PPP exchange a e o in e na ional $ and he ma ke exchange a e o US$, bo h in 2015 ( he base
yea o he p ice index used in he p oduc i i y calcula ions). No e ha XR con e s he
p oduc i i y da a in o uni s ha e lec domes ic pu chasing powe . In he g aph we see ha ela i e
p oduc i i y in Japan compa ed o India is g adually alling o e he pe iod 1991-2019.
Figu e 6. ela i e labo p oduc i i y iew in he da abase
Table 5 documen s he a iables ha a e a ailable in he s uc u al change pa o he da abase.
19
Table 5. Indica o s in s uc u al change and p oduc i i y sec ion
Index (2015=100) o employmen , by sec o and o o al economy
Index (2015=100) o alue added (GDP), by sec o and o o al economy
Index (2015=100) o labo p oduc i i y, by sec o and o o al economy
Sec o al sha es o employmen
Sec o al sha es o alue added (GDP)
Agg ega e labo p oduc i i y g ow h o a ious (sub)pe iods
Wi hin Sec o (WS) e ec in agg ega e labo p oduc i i y g ow h o a ious (sub)pe iods
S a ic S uc u al Realloca ion E ec (SSRE) in agg ega e labo p oduc i i y g ow h o a ious
(sub)pe iods
Dynamic S uc u al Realloca ion E ec (DSRE) in agg ega e labo p oduc i i y g ow h o
a ious (sub)pe iods
𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄 𝒐𝒐𝒐𝒐 𝒑𝒑𝒑𝒑𝒐𝒐𝒑𝒑𝒑𝒑𝒄𝒄𝒑𝒑𝒑𝒑𝒑𝒑𝒑𝒑𝒑𝒑𝒑𝒑
𝒋𝒋
con ibu ion o he decomposi ion e ec in he sec o
𝒑𝒑𝒄𝒄𝒑𝒑𝒑𝒑𝒑𝒑𝒄𝒄𝒊𝒊 𝒄𝒄𝒆𝒆𝒑𝒑𝒊𝒊𝒐𝒐𝒑𝒑𝒆𝒆𝒄𝒄𝒄𝒄𝒑𝒑 𝒔𝒔𝒄𝒄𝒄𝒄𝒑𝒑𝒄𝒄
𝒋𝒋
con ibu ion o he decomposi ion e ec in he sec o
𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄 𝒐𝒐𝒐𝒐 𝒄𝒄𝒆𝒆𝒑𝒑𝒊𝒊𝒐𝒐𝒑𝒑𝒆𝒆𝒄𝒄𝒄𝒄𝒑𝒑 𝒔𝒔𝒄𝒄𝒄𝒄𝒑𝒑𝒄𝒄
𝒋𝒋
con ibu ion o he decomposi ion e ec in he sec o
𝒑𝒑𝒄𝒄𝒑𝒑𝒑𝒑𝒑𝒑𝒄𝒄𝒊𝒊 𝒑𝒑𝒄𝒄𝒊𝒊𝒄𝒄𝒑𝒑𝒑𝒑𝒑𝒑𝒄𝒄 𝒑𝒑𝒑𝒑𝒐𝒐𝒑𝒑𝒑𝒑𝒄𝒄𝒑𝒑𝒑𝒑𝒑𝒑𝒑𝒑𝒑𝒑𝒑𝒑
𝒋𝒋
con ibu ion o he decomposi ion e ec in he sec o
3. Pilla 2: P oduc Complexi y
The pilla on p oduc complexi y builds on he idea ha he pe o mance o economies in
in e na ional ade is de e mined by p oduc i e capabili ies, and ha de ailed da a on expo s can
he e o e p o ide an indica ion o he capabili ies ha a e p esen in he p oduc i e s uc u e o an
economy. The s a ing poin o he cons uc ion o mos o he indica o s in his pilla is
in o ma ion on whe he wo (expo ed) p oduc s a e join ly p oduced wi h compa a i e ad an age
by a single economy, in o ma ion ha is aken as an indica ion ha he p oduc ion o hese wo
p oduc s sha e ce ain capabili ies.
The indica o s in his g oup a e based on de ailed p oduc le el expo da a (wi h in o ma ion on
mo e han 5,000 p oduc s). Using his da a an es ablished me hod om he exis ing li e a u e,
known as he ECI (Economic Complexi y Index) me hod, is adop ed o calcula e an indica o o
p oduc quali y om he p oduc -le el expo da a (Hidalgo and Hausmann, 2009; Hidalgo, 2021).
This indica o o p oduc quali y is e e ed o as p oduc complexi y in he da abase. Concep ually,
p oduc complexi y is an indica o o he p oduc ion capabili ies ha a e needed o sell he p oduc
wi h compa a i e ad an age in in e na ional ma ke s. Thus, each o he 5,000+ p oduc s in he
da abase has i s own alue o p oduc complexi y, wi h he complexi y o he p oduc s ha an
economy expo s wi h compa a i e ad an age u he being an indica o o he capabili ies o i ms
loca ed in a pa icula economy. The o mal de ini ion o he p oduc complexi y indica o is
p o ided in he annex.
20
3.1. Basic p oduc complexi y indica o s and upg ading
In his pa o he da abase, a numbe o basic indica o s o p oduc complexi y a e p esen ed,
along wi h in o ma ion on he way in which complexi y is dis ibu ed o e economies and how his
dis ibu ion a ec s he upg ading po en ial o economies. The basic idea behind he upg ading
po en ial is ha i is gene ally ad an ageous o mo e in o p oduc s wi h highe complexi y because
hese ma ke s a e gene ally mo e exclusi e and equi e highe capabili ies, and hence o e a highe
po en ial o c ea ing alue added.
P oduc complexi y indica o s a e based on he no ion o compa a i e ad an age, which is
calcula ed as ollows
𝑀𝑀𝑡𝑡𝑡𝑡= 1 𝑖𝑖𝑠𝑠 𝑚𝑚𝑡𝑡𝑡𝑡∑𝑚𝑚𝑞𝑞𝑡𝑡𝑞𝑞
�
∑𝑚𝑚𝑡𝑡𝑖𝑖𝑖𝑖∑∑𝑚𝑚𝑞𝑞𝑖𝑖𝑖𝑖𝑞𝑞
�> 1 𝑖𝑖𝑐𝑐𝑖𝑖 0 𝑐𝑐𝑡𝑡ℎ𝑖𝑖𝑖𝑖𝑤𝑤𝑖𝑖𝑐𝑐𝑖𝑖
whe e 𝑀𝑀𝑡𝑡𝑡𝑡 is he (bina y) compa a i e ad an age o economy 𝑖𝑖 in p oduc 𝑗𝑗, and 𝑚𝑚𝑡𝑡𝑡𝑡 is he alue o
expo s o economy 𝑖𝑖 in p oduc 𝑗𝑗. In wo ds, he indica o o compa a i e ad an age is one (i.e.,
he economy has a compa a i e ad an age in p oduc 𝑗𝑗) i he economy’s sha e in o al expo s o
he p oduc is la ge han i s sha e in expo s o all p oduc s oge he , and ze o o he wise.8 The
alues o compa a i e ad an age 𝑀𝑀𝑡𝑡𝑡𝑡 can be a anged in a ma ix, R, wi h each ow ep esen ing a
p oduc , and each column an economy. The sum o e ows in a column is he numbe o p oduc s
in which he economy has compa a i e ad an age, and we e e o his as he di e si ica ion le el
o he economy:
𝑖𝑖𝑖𝑖𝑀𝑀𝑖𝑖𝑖𝑖𝑐𝑐𝑖𝑖𝑠𝑠𝑖𝑖𝑀𝑀𝑖𝑖𝑡𝑡𝑖𝑖𝑐𝑐𝑐𝑐𝑡𝑡=1
𝑐𝑐�𝑀𝑀𝑡𝑡𝑞𝑞
𝑞𝑞
whe e 𝑐𝑐 is he numbe o p oduc s in he da abase, such ha he di e si ica ion index ep esen s
he sha e o all p oduc s in which economy 𝑖𝑖 has compa a i e ad an age. Simila ly, he ubiqui y o
a p oduc is de ined as: 𝑐𝑐𝑅𝑅𝑖𝑖𝑢𝑢𝑐𝑐𝑖𝑖𝑡𝑡𝑝𝑝𝑡𝑡=�𝑀𝑀𝑖𝑖𝑡𝑡
𝑖𝑖
Which is simply he numbe o economies ha expo a pa icula good, 𝑗𝑗, wi h compa a i e
ad an age. Using he di e si ica ion and ubiqui y indica o s, we ollow Hidalgo and Hausmann
(2009) in de ining a measu e called s anda dness:
8 An equi alen de ini ion o compa a i e ad an age would be ha he expo sha e o p oduc 𝑗𝑗 in coun y 𝑖𝑖 is
g ea e han he expo sha e o p oduc 𝑗𝑗 ac oss all coun ies (i.e., he wo ld).
21
𝑐𝑐𝑡𝑡𝑖𝑖𝑐𝑐𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑐𝑐𝑖𝑖𝑐𝑐𝑐𝑐𝑡𝑡=∑𝑀𝑀𝑡𝑡𝑞𝑞𝑐𝑐𝑅𝑅𝑖𝑖𝑢𝑢𝑐𝑐𝑖𝑖𝑡𝑡𝑝𝑝𝑞𝑞𝑞𝑞
𝑐𝑐×𝑖𝑖𝑖𝑖𝑀𝑀𝑖𝑖𝑖𝑖𝑐𝑐𝑖𝑖𝑠𝑠𝑖𝑖𝑀𝑀𝑖𝑖𝑡𝑡𝑖𝑖𝑐𝑐𝑐𝑐𝑡𝑡𝑀𝑀𝑖𝑖𝑚𝑚𝑞𝑞�𝑐𝑐𝑅𝑅𝑖𝑖𝑢𝑢𝑐𝑐𝑖𝑖𝑡𝑡𝑝𝑝𝑞𝑞�
�
No e ha he exp ession in he nume a o is he a e age ubiqui y o he p oduc s in which he
economy has compa a i e ad an age. The denomina o is he maximum alue o ubiqui y o e all
p oduc s, which we use (con a y o he de ini ion in Hidalgo and Hausmann, 2009) o scale he
s anda dness measu e (which is hus bound by ⟨0. .1]).
The da abase also con ains sec o al e sions o s anda dness and di e si ica ion. Fo his, we assign
each o he p oduc s in he expo da abase o an economic sec o .9 This implies ha his pa o
he da abase is limi ed o sec o s ha p oduce adeable goods, which ules ou , o example, many
o he se ices sec o s.10 The sec o s o which we p esen indica o s a e lis ed in Table 6 below.
The indica o s a e calcula ed by summing o e he p oduc s ha belong o a sec o :
𝑖𝑖𝑖𝑖𝑀𝑀𝑖𝑖𝑖𝑖𝑐𝑐𝑖𝑖𝑠𝑠𝑖𝑖𝑀𝑀𝑖𝑖𝑡𝑡𝑖𝑖𝑐𝑐𝑐𝑐𝑡𝑡𝑡𝑡=1
𝑐𝑐𝑡𝑡� 𝑀𝑀𝑡𝑡𝑞𝑞
𝑞𝑞∈𝑡𝑡
and
𝑐𝑐𝑡𝑡𝑖𝑖𝑐𝑐𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑐𝑐𝑖𝑖𝑐𝑐𝑐𝑐𝑡𝑡𝑡𝑡=∑𝑀𝑀𝑡𝑡𝑞𝑞𝑐𝑐𝑅𝑅𝑖𝑖𝑢𝑢𝑐𝑐𝑖𝑖𝑡𝑡𝑝𝑝𝑞𝑞𝑞𝑞∈𝑡𝑡
𝑐𝑐𝑡𝑡×𝑖𝑖𝑖𝑖𝑀𝑀𝑖𝑖𝑖𝑖𝑐𝑐𝑖𝑖𝑠𝑠𝑖𝑖𝑀𝑀𝑖𝑖𝑡𝑡𝑖𝑖𝑐𝑐𝑐𝑐𝑡𝑡𝑡𝑡𝑀𝑀𝑖𝑖𝑚𝑚𝑞𝑞∈𝑡𝑡�𝑐𝑐𝑅𝑅𝑖𝑖𝑢𝑢𝑐𝑐𝑖𝑖𝑡𝑡𝑝𝑝𝑞𝑞�
�
whe e k indica es a sec o , and 𝑐𝑐𝑡𝑡 is he numbe o p oduc s in he sec o .
The calcula ion o p oduc complexi y ollows he ECI me hod o Hidalgo (2021). Fo his, we
i s c ea e a ow-no malized and a column-no malized e sion o he compa a i e ad an age
ma ix R. The ow-no malized e sion is c ea ed by di iding each elemen o he ma ix by di e si y
o he column, and he column-no malized e sion is c ea ed by di iding each elemen by ubiqui y
o he ow. We hen c ea e a new ma ix by p e-mul iplying he column-no malized e sion o he
ma ix by he anspose o he ow-no malized e sion. P oduc complexi y is equal o he
eigen ec o ha belongs o he second-dominan eigen alue o his ma ix.11
Based upon he cons uc ed indica o o p oduc complexi y, economy i ness le els a e calcula ed
as he a e age alue o p oduc complexi y o he p oduc s ha he economy has compa a i e
ad an age in:
9 This assignmen is done using conco dances be ween ISIC ( o he inpu -ou pu sec o s) and he Ha monised
Sys em (HS) o he expo da abase, o , as in oduced below, conco dances be ween HS and BEC. These
conco dances a e a ailable on he Wo ld Bank’s WITS se e h ps://wi s.wo ldbank.o g/.
10 The da a used o cons uc he a ious indica o s in his pilla is he UN Com ade da abase, which epo s
in o ma ion on goods ade only. Da a on se ices ade does exis – and is also a ailable om he UN – bu
consis en da a ac oss economies is only a ailable a a much highe le el o agg ega ion.
11 The eigen ec o s ha e ambiguous sign, and we choose he sign such ha p oduc s wi h low ubiqui y end o ha e
high complexi y.
22
𝑠𝑠𝑖𝑖𝑡𝑡𝑐𝑐𝑖𝑖𝑐𝑐𝑐𝑐𝑡𝑡=∑𝑀𝑀𝑡𝑡𝑞𝑞𝐻𝐻𝑞𝑞𝑞𝑞
𝑐𝑐×𝑖𝑖𝑖𝑖𝑀𝑀𝑖𝑖𝑖𝑖𝑐𝑐𝑖𝑖𝑠𝑠𝑖𝑖𝑀𝑀𝑖𝑖𝑡𝑡𝑖𝑖𝑐𝑐𝑐𝑐𝑡𝑡
The sec o al e sion o i ness is
𝑠𝑠𝑖𝑖𝑡𝑡𝑐𝑐𝑖𝑖𝑐𝑐𝑐𝑐𝑡𝑡𝑡𝑡=∑𝑀𝑀𝑡𝑡𝑞𝑞𝐻𝐻𝑞𝑞𝑞𝑞∈𝑡𝑡
𝑐𝑐𝑡𝑡×𝑖𝑖𝑖𝑖𝑀𝑀𝑖𝑖𝑖𝑖𝑐𝑐𝑖𝑖𝑠𝑠𝑖𝑖𝑀𝑀𝑖𝑖𝑡𝑡𝑖𝑖𝑐𝑐𝑐𝑐𝑡𝑡𝑡𝑡
Figu e 7 p o ides an illus a ion o he indica o s desc ibed abo e, wi h da a epo ed on he Basic
me als and ab ica ed me al sec o in 2019. Economies’ i ness in he sec o is on he ho izon al
axis, while di e si ica ion is epo ed on he e ical axis. The size o he bubbles in his igu e is
p opo ional o he le el o s anda dness. We obse e a gene ally posi i e associa ion be ween he
wo indica o s, bu his is no a linea ela ion. A i s , di e si ica ion inc eases along wi h i ness,
bu a a ce ain h eshold alue, i ness does no inc ease any u he . We also see ha economies
wi h high di e si ica ion and high i ness end o be he ones wi h low s anda dness, while
economies wi h low i ness and low di e si ica ion also ha e high s anda dness.
Figu e 7. Di e si ica ion and i ness in basic me als and ab ica ed me al, 2019
29
𝑊𝑊𝑡𝑡𝑑𝑑𝑑𝑑𝑑𝑑=�𝑀𝑀𝑡𝑡𝑡𝑡
∑𝑀𝑀𝑡𝑡𝑡𝑡𝑡𝑡∈𝑑𝑑𝑑𝑑𝑑𝑑 𝐻𝐻𝑡𝑡𝐹𝐹
𝑡𝑡∈𝑑𝑑𝑑𝑑𝑑𝑑
𝑊𝑊𝑡𝑡𝑓𝑓𝑑𝑑𝑖𝑖=�𝑀𝑀𝑡𝑡𝑡𝑡
∑𝑀𝑀𝑡𝑡𝑡𝑡𝑡𝑡∈𝑓𝑓𝑑𝑑𝑖𝑖 𝐻𝐻𝑡𝑡𝐹𝐹
𝑡𝑡∈𝑓𝑓𝑑𝑑𝑖𝑖
Whe e he supe sc ip s 𝑖𝑖𝑐𝑐𝑐𝑐 and 𝑠𝑠𝑐𝑐𝑖𝑖 deno es domes ic and o eign, o he se o domes ic o
o eign inpu sec o s o he chain, espec i ely. In addi ion o inpu complexi y o he alue chain,
ou pu complexi y o he alue chain can simply be de ined as 𝐻𝐻𝑡𝑡𝐹𝐹.
Figu e 11 documen s inpu complexi y e sus ou pu complexi y in he Food and be e ages sec o ,
o 2019. We see a clea posi i e ela ionship: economies wi h highe inpu complexi y also end o
ha e highe ou pu complexi y. Howe e , he e a e some economies ha a e clea ly abo e (o
below) he line ha summa izes his ela ionship (i.e., he line o bes i ). Those economies ha
a e signi ican ly abo e (below) he line can be conside ed o add compa a i ely much (li le)
complexi y o he ou pu o he alue chain.
Table 8 p o ides he lis o indica o s ha a e a ailable in he sec ion o he da abase on p oduc
complexi y in global alue chains. The lis o sec o s ha is included in he calcula ions, and o
which da a on inpu - and ou pu complexi y a e a ailable is documen ed in Table 6 abo e.13
13 Though he sec o “all o he sec o s” is excluded om he analysis he e.
30
Figu e 11. Inpu and ou pu complexi y o in e media es in he Food, be e ages and
obacco sec o in 2019
Table 8. Indica o s in he p oduc complexi y in global alue chains sec ion
Ou pu complexi y o he chain ( inal goods)
Complexi y o in e media e goods o he sec o (ou pu )
Complexi y o all goods ( inal and in e media e) o he sec o (ou pu )
Inpu complexi y all domes ic and o eign alue ( o al) in o he chain
Inpu complexi y o domes ic alue in o he chain
Inpu complexi y o o eign alue in o he chain
4. Pilla 3: Inno a ion
Inno a ion is a mul i- ace ed p ocess, in which many di e en kinds o inpu s and ou pu s can be
ound. Technology is an impo an inpu in o he inno a ion p ocess, bu inno a ion can also be
o ganiza ional, o be ela ed o ma ke ing and design, among o he hings. In ou da abase, we
31
conside only indica o s ela ed o echnological inno a ion, and wi hin his es ic ion we co e
only pa en ed in en ions. The e a e many well-known d awbacks o pa en s as indica o s o
( echnological) inno a ion, such as he ac ha no all pa en ed in en ions lead o ac ual
inno a ions ha appea in he ma ke . Also, he p opensi y o pa en s in en ions di e s g ea ly by
indus y. The alue o pa en s also di e s widely, wi h a majo i y o pa en s being o e y li le
alue, and a ew pa en s accoun ing o he la ge majo i y o o al alue o pa en s. In spi e o all
hese d awbacks, pa en indica o s a e de eloped and used in he da abase since hey a e a ailable
o a la ge numbe o economies and can be used o cons uc indica o s ha ha e a high deg ee
o compa abili y be ween economies.
The pa en indica o s used in he da abase a e cons uc ed using he PATSTAT da abase. This is a
da abase wi h in o ma ion on indi idual pa en applica ions om a a ie y o pa en o ices a ound
he wo ld. PATSTAT is p o ided by he Eu opean Pa en O ice (EPO), and con ains, among
o he hings, in o ma ion on so-called pa en amilies. A pa en amily is de ined as a se o ela ed
pa en documen s (applica ions and g an s) ha o igina e om di e en pa en o ices a ound he
wo ld bu co e a single in en ion. Each o he di e en documen s, o amily membe s, p o ide
p o ec ion in a speci ic geog aphical ju isdic ion, which is o en an economy, bu can also be
mul iple economies. The pa en amily is he basic uni ha is used o cons uc he pa en
indica o s in he da abase, pa icula ly he use o he so-called DOCDB de ini ion o amilies.
The basic app oach o cons uc ing he indica o s in ol es coun ing pa en amilies, whe e only
amilies ha ha e membe s in a leas wo pa en ju isdic ions (a eas whe e p o ec ion is sough )
o a a egional pa en o ice such as he EPO a e conside ed. By elimina ing pa en amilies wi h
jus one ju isdic ion, he in en ion is o include only pa en s abo e a ce ain h eshold o o iginali y
and expec ed economic alue. When cons uc ing he indica o s, all membe s o pa en amilies –
whe he hey be pa en applica ions o g an s – a e included.
PATSTAT also p o ides an indica ion o he mos likely indus y o o igin o he pa en applica ion.
This is based on a conco dance be ween he pa en class (a classi ica ion o pa en s in o
echnological domains) and he NACE indus y classi ica ion. This in o ma ion is used o link
some he pa en indica o s o he inpu -ou pu ables ha a e used in he global alue chain sec ion
o he da abase. Loca ion o pa en amilies (i.e., he o igin o he in en ion co e ed by he pa en
amily) is de e mined in a ac ional way on he basis o he loca ion o in en o s.
4.1. Pa en indica o s o 4 h indus ial e olu ion echnologies
The e m 4 h indus ial e olu ion has been used o desc ibe a se o eme ging echnologies in which
digi al connec i i y, au oma ion and a i icial in elligence play a cen al ole. These echnologies a e
applied o a ange o echnological domains and p oduc i e sec o (in o he wo ds, hey a e
32
pe asi e). I is gene ally belie ed ha hese echnologies ha e g ea economic po en ial bu will
also ans o m he wo kplace and socie y mo e gene ally.
Using he PATSTAT da abase 4 h indus ial e olu ion (4IR) pa en s a e iden i ied, wi h he
da abase p o iding coun s o he pa en amilies ha a e conside ed o be 4IR, u he
dis inguishing be ween a numbe o echnological ields in which hese pa en amilies a e classi ied.
In o de o iden i y 4IR pa en s, a me hodology p oposed by he Eu opean Pa en o ice (EPO,
2020) is applied. The app oach adop ed does no ollow he exac EPO me hodology, bu his
app oach is app oxima ed h ough he PATSTAT da abase que y ha was designed o ex ac
in o ma ion on 4IR pa en s.14
Because he e a e ela i ely ew 4IR pa en amilies de ined in his way (in o al, he e a e abou
200,000 4IR pa en amilies), he da abase uses 10-yea cumula i e numbe s. Thus, he da a
documen ed in he da abase o yea 𝑇𝑇 always include he numbe s o pa en s amilies om yea
𝑇𝑇−9 o 𝑇𝑇.
Figu e 12 shows 4IR pa en ing ends o Hong Kong, China. In he uppe panel we see a s eady
ise o he sha e o 4IR pa en ing in o al global pa en ing, agains which we can compa e he sha e
o 4IR pa en ing in Hong Kong, China. We see ha his sha e is highe han he global sha e ( o
he en i e pe iod) and ha i ises mo e s eeply a e 2010, sugges ing ha Hong Kong, China is a
ela i ely in ensi e p oduce o 4IR echnologies. The lowe panel o he igu e epo s in o ma ion
on he pe o mance o Hong Kong, China in o al global pa en ing, wi h he igu e showing ha
he sha e o Hong Kong, China in o al global pa en ing is inc easing o e ime, albei a a slowe
pace a e 2010.
14 The exac EPO que y could no be eplica ed because he Que y language used by EPO is no gene ally a ailable
ou side pa en o ices, and because PATSTAT does no con ain he ull ex o he pa en s. The que y used o he
da abase is ully documen ed in Menéndez e al. (2023).
33
Figu e 12. To al- and 4IR-pa en ing iew in he da abase, Hong Kong, China
Figu e 13 shows he o al numbe o pa en s in 4IR in Hong Kong, China, spli by sub ield. He e
he s eep ise a e 2010 is also isible. We also see ha by he end o he pe iod, connec i i y,
consume goods, da a secu i y, (sma ) home, IT ha dwa e, se ices and so wa e a e he la ges
4IR sub ields in Hong Kong, China pa en ing. The 4IR sub ields ha a e a ailable in he da abase
a e documen ed in Table 9, while Table 10 lis s he indica o s in his pa o he da abase.
34
Figu e 13. 4IR pa en ing by sub ields in Hong Kong, China
35
Table 9. Sub ields o 4IR echnologies
Sub ield #
Desc ip ion
1
3D suppo sys ems
2
Ag icul u e
3
Connec i i y
4
Consume goods
5
Co e a i icial in elligence
6
Da a managemen
7
Da a secu i y
8
Geo posi ioning
9
Heal hca e
10
Home
11
Indus ial
12
In as uc u e
13
IT ha dwa e
14
Powe supply
15
Sa e y
16
Se ices
17
So wa e
18
Use in e aces
19
Vehicles
20
To al
Table 10. Va iables in he 4IR pa en indica o s sec ion
Pa en amilies in all 4IR ields
Pa en amilies by 4IR sub ields
Pa en amilies in all echnology ields
Sha e o 4IR pa en amilies in all pa en amilies, pe economy and globally
Sha e o economy in all pa en amilies
4.2. Pa en indica o s in he con ex o global alue chains
In o de o ela e pa en coun s o global alue chains, a simila app oach o ha used o ela e
p oduc complexi y o global alue chains (sec ion 3.2 o his documen ) is adop ed. Ini ially, an
indica o called he pa en con en o alue added is de ine, wi h his indica o s being de ined a he le el
o sec o s in economies:
𝑄𝑄𝑡𝑡=𝑃𝑃𝑖𝑖𝑡𝑡𝑡𝑡
𝑉𝑉𝐴𝐴𝑡𝑡
whe e 𝑄𝑄𝑡𝑡 is he pa en con en o alue added in sec o 𝑗𝑗 ( emembe ha his is a sec o in a
pa icula economy, e.g., he Japanese basic me als sec o , o he Ge man chemicals sec o ), 𝑉𝑉𝐴𝐴𝑡𝑡 is
alue added in he sec o , and 𝑃𝑃𝑖𝑖𝑡𝑡𝑡𝑡 is he numbe o pa en amilies assigned o he sec o , again
36
cumula ed o e 10 yea s. Two e sions o he pa en con en indica o a e de ined: pa en s in all
echnology ields and pa en s in 4IR echnology ields only, as de ined in he p e ious sec ion.
The indica o s 𝑄𝑄𝑡𝑡 can hus be conside ed analogous o 𝐻𝐻𝑡𝑡𝐹𝐹 in Sec ion 3.1. An analogue o he 𝑊𝑊𝑡𝑡
indica o can u he be de ined as: 𝑂𝑂𝑡𝑡=�𝑀𝑀𝑡𝑡𝑡𝑡
𝑠𝑠𝑡𝑡𝑄𝑄𝑡𝑡
𝑡𝑡
Whe e 𝑂𝑂𝑡𝑡 is he pa en con en o he alue chain o sec o j (whe e again his indica o is
cons uc ed o ei he all echnology ields o 4IR ields only) As in sec ion 3.1, his indica o can
u he be sepa a ed in o wo pa s:
𝑂𝑂𝑡𝑡𝑑𝑑𝑑𝑑𝑑𝑑=�𝑀𝑀𝑡𝑡𝑡𝑡
∑𝑀𝑀𝑡𝑡𝑡𝑡𝑡𝑡∈𝑑𝑑𝑑𝑑𝑑𝑑 𝑄𝑄𝑡𝑡
𝑡𝑡
𝑂𝑂𝑡𝑡𝑓𝑓𝑑𝑑𝑖𝑖=�𝑀𝑀𝑡𝑡𝑡𝑡
∑𝑀𝑀𝑡𝑡𝑡𝑡𝑡𝑡∈𝑓𝑓𝑑𝑑𝑖𝑖 𝑄𝑄𝑡𝑡
𝑡𝑡
Whe e he supe sc ip s 𝑖𝑖𝑐𝑐𝑐𝑐 and 𝑠𝑠𝑐𝑐𝑖𝑖 again e e o domes ic and o eign, espec i ely, o he se
o domes ic o o eign inpu sec o s o he chain. In o he wo ds, 𝑂𝑂𝑡𝑡𝑑𝑑𝑑𝑑𝑑𝑑 cap u es he pa en con en
o he alue chain om domes ic sou ces, while 𝑂𝑂𝑡𝑡𝑓𝑓𝑑𝑑𝑖𝑖 cap u es he pa en con en om o eign
sou ces.
The indica o s 𝑂𝑂𝑡𝑡,𝑂𝑂𝑡𝑡𝑑𝑑𝑑𝑑𝑑𝑑 and 𝑂𝑂𝑡𝑡𝑓𝑓𝑑𝑑𝑖𝑖 ocus on alue chains, i.e., hey ake a p oduc ion poin o
iew. We can also use he pa en con en o alue added o conside inal demand (i.e., consump ion
and in es men ). In his way, we can cons uc he indica o
𝐽𝐽𝑡𝑡=�𝑤𝑤𝑡𝑡𝑡𝑡
𝜓𝜓𝑡𝑡𝑄𝑄𝑡𝑡
𝑡𝑡
whe e 𝑤𝑤𝑡𝑡𝑡𝑡 is he alue-added con ibu ion o sec o 𝑖𝑖 o he inal demand o sec o 𝑗𝑗 p oduc s in
he economy o which 𝑗𝑗 belongs and 𝜓𝜓𝑡𝑡 is o al inal demand o sec o j p oduc s in he economy
o which 𝑗𝑗 belongs. An example o he 𝐽𝐽𝑡𝑡 indica o is ha i could e lec he a e age pa en con en
o alue added deli e ed o inal demand (i.e., consump ion and in es men ) o anspo
equipmen in Vie Nam (in his case, 𝑗𝑗 is he Vie namese anspo equipmen sec o ).
Figu e 14 plo s o all economies in he da abase he pa en in ensi y o own alue added agains
pa en in ensi y o he alue chain (“all alue added used”) o 2015, o he o al economy. We see
a s ong co ela ion be ween hese indica o s: economies ha ha e pa en -in ensi e p oduc ion
also end o use mo e pa en -in ensi e inpu s in hei alue chains. The Asian economies
Tapei,China, Republic o Ko ea and Japan op he lis on bo h indica o s.
37
Figu e 14. Pa en in ensi y o GVCs in 2015
Table 11 lis s he indica o s in his pa o he da abase.
38
Table 11. Indica o s a ailable in inno a ion and global alue chains sec ion
Pa en con en o alue added
Pa en con en o he alue chain
Domes ic pa en con en o he alue chain
Fo eign pa en con en o he alue chain
Pa en con en o inal demand
Pa en con en o alue added, only 4IR pa en s
Pa en con en o he alue chain, only 4IR pa en s
Domes ic pa en con en o he alue chain, only 4IR pa en s
Fo eign pa en con en o he alue chain, only 4IR pa en s
Pa en con en o inal demand, only 4IR pa en s
5. Pilla 4: Indica o s o Global Value Chain pa icipa ion
Indica o s in his pilla a e hea ily based on inpu -ou pu ables, which equi es a amewo k ha
allows o he de ini ion and concep ualiza ion o GVCs using such da a. This in ol es making a
dis inc ion be ween so-called in e media e goods and inal goods. Final goods a e goods ha a e
ei he used o consump ion o in es men (e.g., a ca ), while in e media e goods a e goods ha
a e used in he cons uc ion o inal goods, i.e., s eel ha is used o build a ca .
The dis inc ion be ween inal and in e media e also holds o se ices. Fo example, a hai cu is a
se ice deli e ed o inal demand, while a cou ie se ice deli e ing business documen s is an
in e media e deli e y. Some goods o se ices can ei he be deli e ed as inal o as in e media y
(i.e., elec ici y, insu ance), and hey may appea in wo places in he inpu -ou pu ables ha we
use.
The dis inc ion be ween in e media e and inal is used o concep ualize he alue chain. Value
chains a e ini ially de ined by sec o s o indus ies, e.g., he s eel indus y o he ood indus y.
These sec o s a e u he de ined by he economy in which hey a e loca ed, i.e., we ha e he
Ge man ca indus y as well as he I alian ca indus y, and he Japanese ood sec o as well as he
B azilian ood sec o . The alue chains in each o hose economy-sec o combina ions a e de ined
as he en i e (so-called e ically in eg a ed) chain ha is needed o p oduce he inal ou pu o he
sec o . In he example o a ca sec o , i includes he ca s hemsel es as inal deli e ies, and all he
in e media e deli e ies (goods and se ices) needed o p oduce hese ca s.
In his way, ade, and hence he global dimension o he alue chains appea s in wo o ms. Fi s ,
he e a e expo s (and he associa ed impo s) o he inal good i sel . This is ully in line wi h he
adi ional idea o ade in he economic li e a u e, e.g., exchanging clo h o wine. Second,
in e media e goods a e aded, and hence he e will be an in e na ional componen o he alue
chain in e ms o he inpu s ha a e used in he p oduc ion o inal goods.
45
Figu e 17. RCA in g oss and alue-added expo s in Chemicals in 2019
46
Table 12. Indica o s used in GVC posi ioning indica o s sec ion
Backwa d: sha e o own alue added in he alue chain
Backwa d: sha e o domes ic o he sec o s in alue added o he chain
Backwa d: sha e o o eign sec o s in alue added o he chain
Fo wa d: sha e o own alue chain in alue added o he sec o
Fo wa d: sha e o alue deli e ed o o he domes ic alue chains as sha e o alue added o he sec o
Fo wa d: sha e o alue deli e ed o o eign alue chains as sha e o alue added o he sec o
Domes ic backwa d in eg a ion
Domes ic o wa d in eg a ion
Value added expo s o he economy o a speci ic global sec o , RCA
Value added impo s o he economy om a speci ic global sec o , CII
Value added expo s, RCA (o he expo ing sec o )
Value added impo s, CII (o he impo ed sec o )
G oss in e media e expo s o economy o a speci ic global sec o , RCA
G oss in e media e impo s o economy om a speci ic global sec o , CII
G oss in e media e expo s o economy-sec o , RCA
G oss in e media e impo s om economy-sec o , CII
G oss inal demand expo s o economy-sec o , RCA
G oss inal demand impo s om economy-sec o , CII
G oss o al expo s o economy-sec o , RCA
G oss o al impo s o economy-sec o , CII
5.2. Regional and global alue chains
This sec ion o he da abase aims o p o ide an imp ession o how “global” global alue chains
a e. I uses he no ion o geog aphical dis ance o ope a ionalize his. This s a s om a dis ance
ma ix ha was ob ained om CEPII15, and which con ains he geog aphical dis ance in km
be ween he capi als o he economies in he inpu -ou pu da abase. This dis ance is aken as
ep esen a i e o he gene al dis ance be ween economy-pai s. Wi h his dis ance ma ix and he
ma ix 𝑉𝑉 ha was in oduced abo e he ollowing wo basic measu es a e cons uc ed:
𝑅𝑅𝑡𝑡𝑏𝑏𝑏𝑏=∑𝑖𝑖𝑡𝑡𝑡𝑡𝑀𝑀𝑡𝑡𝑡𝑡𝑡𝑡∈𝑓𝑓𝑑𝑑𝑖𝑖
∑𝑀𝑀𝑡𝑡𝑡𝑡𝑡𝑡∈𝑓𝑓𝑑𝑑𝑖𝑖 ∑𝑖𝑖𝑡𝑡𝑡𝑡𝑡𝑡∈𝑓𝑓𝑑𝑑𝑖𝑖
�
𝑅𝑅𝑡𝑡𝑓𝑓𝑏𝑏=∑𝑖𝑖𝑡𝑡𝑡𝑡𝑀𝑀𝑡𝑡𝑡𝑡𝑡𝑡∈𝑓𝑓𝑑𝑑𝑖𝑖
∑𝑀𝑀𝑡𝑡𝑡𝑡𝑡𝑡∈𝑓𝑓𝑑𝑑𝑖𝑖 ∑𝑖𝑖𝑡𝑡𝑡𝑡𝑡𝑡∈𝑓𝑓𝑑𝑑𝑖𝑖
�
whe e 𝑅𝑅𝑡𝑡𝑏𝑏𝑏𝑏 is he backwa d GVC Geo Radius o he sec o 𝑗𝑗, 𝑅𝑅𝑡𝑡𝑓𝑓𝑏𝑏 is he o wa d GVC Geo Radius
o he sec o 𝑗𝑗, and 𝑖𝑖𝑡𝑡𝑡𝑡=𝑖𝑖𝑡𝑡𝑡𝑡 is he dis ance be ween he economy o which sec o 𝑖𝑖 belongs and
he economy o which sec o 𝑗𝑗 belongs. The nume a o in bo h exp essions is he weigh ed a e age
o he dis ance o GVC ading pa ne s o sec o 𝑗𝑗, using ei he backwa d o o wa d o eign
linkages as weigh s (domes ic linkages a e dis ega ded in he cons uc ion o hese indica o s). The
denomina o in bo h exp essions is he unweigh ed dis ance o ading pa ne s. Hence he
15 h p://www.cepii. /CEPII/en/bdd_modele/bdd_modele_i em.asp?id=6
47
indica o is a ela i e dis ance, whe e he GVC-weigh ed dis ance is exp essed ela i e o he
unweigh ed dis ance. A alue smalle (la ge ) han 1 indica es ha GVC ading pa ne s end o
be ela i ely close-by ( a away). As i u ns ou he alues ha we ind in he da abase a e almos
exclusi ely less han one, which is consis en wi h he gene al inding in so-called g a i y ade
models ha ade is mo e in ensi e be ween economies ha a e close o each o he .
Figu e 18. Backwa d and o wa d geo adius in Rubbe and plas ics in 2019
Figu e 18 shows a plo o he backwa d geo adius agains he o wa d geo adius o he Rubbe
and plas ics sec o in 2019. A posi i e co ela ion be ween he wo dimensions exis s. Gene ally,
48
he geo adiuses a e obse ed o be below uni y, which indica es ha ade (wi hin global alue
chains) occu s o e ela i ely sho dis ances. The e a e excep ions o his gene al pa e n, howe e ,
wi h he o wa d adius o Indonesia and India being abo e one, o example.
Figu e 19 shows he ime se ies o he o wa d and backwa d geo adius o Indonesia in he
Rubbe and plas ics sec o . He e i can be obse ed ha bo h o hese indica o s, bu especially he
o wa d adius, a e ising o e ime, wi h a jump a ound 2014-15. Since 2017 he o wa d adius
inc eases o a alue abo e one.
Figu e 19. Sec o al backwa d and o wa d geo adius in Rubbe and plas ics in Indonesia,
2007-2019
The lis o indica o s p o ided in his sec ion a e lis ed in Table 13, while he sec o s o which
hese indica o s a e a ailable a e he same as in p e ious sec ions (Table 1).
Table 13. Indica o s in GVC posi ioning sec ion
Backwa d Geo Radius o GVC in eg a ion
Fo wa d Geo Radius o GVC in eg a ion
49
Re e ences
Acemoglu, D. and P. Res epo, 2018, Demog aphics and au oma ion, NBER Wo king Pape no.
24421, Na ional Bu eau o Economic Resea ch.
EPO (Eu opean Pa en O ice), 2020, Pa en s and he ou h indus ial e olu ion. The global
echnology ends enabling he da a-d i en economy, Munich.
Fos e -McG ego , N., Nomale , Ö. and B. Ve spagen, 2019, Measu ing he c ea ion and
adop ion o new echnologies using ade and pa en da a, UNIDO Wo king Pape
Hidalgo, C.A., 2021, Economic complexi y heo y and applica ions. Na Re Phys 3, 92–113.
h ps://doi.o g/10.1038/s42254-020-00275-1
Hidalgo, C., and R. Hausmann, 2009, The Building Blocks o Economic Complexi y,
P oceedings o he Na ional Academy o Sciences 106(26):10570–75.
Menéndez De Medina , Me cedes, Önde Nomale & Ba Ve spagen, 2023, Iden i ica ion o
Fou h Indus ial Re olu ion echnologies using PATSTAT da a, UNU-MERIT Wo king
Pape 2023-023. h ps://unu-me i .nl/publica ions/wppd /2023/wp2023-023.pd
Nomale , Ö and B. Ve spagen, 2022, Some new iews on p oduc space and ela ed
di e si ica ion, UNU-MERIT Wo king Pape no. 2022/11, UNU-MERIT.
50
Annex
A1. The use o he BEC classi ica ion
The app oach o cons uc he da a on global alue chains in he s uc u al change pilla (sec ion 2
o he main ex ) is based upon he la es e sion o he B oad Economic Ca ego ies (BEC)
classi ica ion, BEC Re . 5.16 This classi ica ion allows o a spli o HS p oduc s in o h ee b oad
end use ca ego ies: in e media e consump ions (in e media es); g oss ixed capi al o ma ion
(capi al); and inal consump ion (consume goods). A co espondence be ween he 2012 e ision
o he HS classi ica ion and BEC Re . 5 has been p o ided by he Uni ed Na ions S a is ics
Di ision.17 In addi ion o hese h ee dimensions, he BEC Re . 5 classi ica ion has a numbe o
mixed ca ego ies (e.g., in e media e/capi al, consume /capi al, e c.). These mixed ca ego ies a e
alloca ed o one o he h ee agg ega es, wi h in e media e/capi al and in e media e/consump ion
being alloca ed o in e media es, consume /capi al and consume /in e media es o consume
goods, and capi al/consume and capi al/in e media es o capi al goods.
In addi ion o he spli be ween he h ee end use ca ego ies, he BEC classi ica ion u he spli s
in e media e and consume goods in o p ima y and p ocessed goods. P ima y goods a e hose wi h
cha ac e is ics o p ima y sec o s o he economy, such as a ming, o es y, ishing, and ex ac i e
indus ies, as well as goods ha unde ake only mino modi ica ions and whose alue is hus s ill
la gely om p ima y sec o s (e.g., ginned co on). P ocessed goods, con e sely, a e hose ha
in ol e ex ensi e p ocessing. This dis inc ion be ween p ima y and p ocessed has been used o
help iden i y global alue chain ade, wi h p oduce s o p ima y goods conside ed highe ups eam
(i.e., s ong o wa d linkages), while p oduce s o p ocessed goods end o be u he downs eam
(i.e., s ong backwa d linkages).
A no el y o BEC Re . 5 o e he ea lie BEC Re . 4 ela es o he conclusion ha he de ini ion
o in e media es – including he p ocessed and p ima y spli – is oo b oad o be use ul in he
con ex o global alue chains. P ocessed in e media e goods, o example, ha e been ound o
comp ise many gene ic p oduc s wi h published e e ence p ices o commonly sold a auc ion as
well as in e media es wi h a mo e speci ic use in a pa icula indus y. BEC Re . 5, he e o e,
in oduces an addi ional spli be ween gene ic and speci ic in e media e goods (as well as capi al
goods) o be e iden i y ade wi hin global alue chains.
16 h ps://uns a s.un.o g/unsd/ ade/classi ica ions/Se iesM_53_Re .5_17-01722-E-Classi ica ion-by-B oad-
Economic-Ca ego ies_PRINT.pd
17 h p://uns a s.un.o g/unsd/s a com/47 h-session/documen s/BG-2016-11-Manual-o - he-Fi h-Re ision-o - he-
BEC-E.pd
51
A2. P oduc complexi y and upg ading p obabili y
The p obabili y measu e o upg ading is based on he idea ha a coun y’s cu en specializa ion
s uc u e (pa ly) de e mines which p oduc s a e likely a ge s o de eloping new compa a i e
ad an ages. The calcula ions s a by de ining 𝑋𝑋 as he amilia bina y ma ix o e ealed
compa a i e ad an age (RCA), wi h elemen s:
xij = 1 i 𝐸𝐸𝑖𝑖𝑖𝑖𝐸𝐸𝑖𝑖
�
𝐸𝐸𝑖𝑖𝐸𝐸
�≥1 and xij = 0 o he wise,
whe e 𝐸𝐸𝑡𝑡𝑡𝑡 deno es he alue o expo s o p oduc 𝑖𝑖 by coun y 𝑗𝑗 and he absence o a subsc ip
indica es a summa ion o e he ele an dimension. The ma ix 𝑋𝑋 has dimensions 𝑐𝑐×𝑐𝑐, whe e
𝑐𝑐 is he numbe o p oduc s and 𝑐𝑐 is he numbe o coun ies. Typically, 𝑐𝑐 >> 𝑐𝑐. We assume
ha each coun y expo s a leas one p oduc , and each p oduc is expo ed by a leas one coun y.
A gi en 𝑋𝑋 ma ix con ains a o al o 𝑖𝑖=∑ ∑ 𝑚𝑚𝑡𝑡𝑡𝑡∀𝑡𝑡∈{1,2,..𝑛𝑛}∀𝑡𝑡∈{1,2,..𝑑𝑑} e ealed compa a i e
ad an ages.
The so-called densi y me ic o ela ed a ie y (Klinge and Hausman, 2006) d aws on he no ion
o condi ional p obabili y, compu ed on he basis o obse ed co-occu ences. The condi ional
p obabili y cap u es he idea ha ha ing a compa a i e ad an age in one p oduc p o ides
in o ma ion abou he likelihood ha a coun y has a compa a i e ad an age in ano he p oduc .
I he condi ional p obabili y is high (low), he wo p oduc s a e likely o equi e simila capabili ies
o expo hem wi h compa a i e ad an age.
Fo mally, le 𝑘𝑘𝑖𝑖𝑞𝑞 deno e he numbe o coun ies which ha e compa a i e ad an age bo h in
p oduc 𝑢𝑢 and in p oduc 𝑐𝑐, and 𝑐𝑐𝑖𝑖 deno e he numbe o coun ies which ha e compa a i e
ad an age in p oduc 𝑐𝑐 (wha is usually called he ‘ubiqui y’ o a p oduc ). Then 𝑀𝑀𝑞𝑞𝑖𝑖=𝑘𝑘𝑞𝑞𝑖𝑖 𝑐𝑐𝑖𝑖
⁄
deno es he p obabili y ha a coun y has compa a i e ad an age in p oduc 𝑢𝑢, condi ional on he
coun y ha ing compa a i e ad an age in p oduc 𝑐𝑐. In ma ix no a ion, hese condi ional
p obabili ies a e gi en by:
𝐻𝐻=𝑆𝑆−1𝑋𝑋𝑋𝑋𝑇𝑇,
whe e he supe sc ip 𝑇𝑇 indica es a ansposed ma ix and 𝑆𝑆 is he ma ix wi h he co esponding
ow-sums o 𝑋𝑋 on he main diagonal and ze os elsewhe e. No e ha he diagonal o 𝑆𝑆 hus con ains
he ubiqui y o espec i e p oduc s, i.e.,
𝑐𝑐𝑡𝑡𝑡𝑡=�∑𝑚𝑚𝑡𝑡𝑡𝑡∀𝑡𝑡∈{1,2,..𝑛𝑛}𝑖𝑖𝑠𝑠 𝑖𝑖=𝑗𝑗
0𝑐𝑐𝑡𝑡ℎ𝑖𝑖𝑖𝑖𝑤𝑤𝑖𝑖𝑐𝑐𝑖𝑖
52
The da abase in ol es he use o a new measu e ha is also based on he idea o condi ional
p obabili y, bu which di e s om he densi y measu e. Fo his new measu e, a ma ix wi h a
complemen a y condi ional p obabili y measu e is used, which is de ined as:
𝐵𝐵=𝑈𝑈−1𝑍𝑍𝑋𝑋𝑇𝑇,
whe e 𝑍𝑍=𝑂𝑂–𝑋𝑋 and 𝑈𝑈 is a ma ix wi h he ow-sums o 𝑍𝑍 on he main diagonal. Thus, 𝑍𝑍 is a
ma ix o “an i-RCA”, in which he elemen s a e 𝑧𝑧𝑡𝑡𝑡𝑡= 1 i 𝑚𝑚𝑡𝑡𝑡𝑡= 0 and 𝑧𝑧𝑡𝑡𝑡𝑡= 0 i 𝑚𝑚𝑡𝑡𝑡𝑡= 1. The
diagonal elemen s o 𝑈𝑈 a e hen de ined as 𝑐𝑐𝑡𝑡𝑡𝑡=𝑐𝑐−𝑐𝑐𝑡𝑡𝑡𝑡, which is he numbe o coun ies ha
ha e no RCA in p oduc 𝑗𝑗. The elemen s 𝑅𝑅𝑖𝑖𝑞𝑞 o ma ix 𝐵𝐵 e lec he p obabili y ha a coun y has
RCA in p oduc 𝑢𝑢 condi ional on no ha ing RCA in p oduc 𝑐𝑐. We in e p e hese condi ional
p obabili ies as ollows: i 𝑅𝑅𝑖𝑖𝑞𝑞 is low (high), p oduc s 𝑐𝑐 and 𝑢𝑢 a e likely o sha e a high (low) deg ee
o capabili ies needed o expo hem wi h compa a i e ad an age. Thus, he condi ional
p obabili ies 𝑅𝑅𝑖𝑖𝑞𝑞 a e complemen a y o 𝑀𝑀𝑖𝑖𝑞𝑞.
The p oposed measu es a e hen de ined, in ma ix no a ion as:
𝐸𝐸=𝐻𝐻𝑇𝑇𝑋𝑋+𝐵𝐵𝑇𝑇𝑍𝑍
𝑑𝑑,
which is an 𝑐𝑐×𝑐𝑐 ma ix. No e ha o a coun y 𝑗𝑗 ha has ac ual compa a i e ad an age in 𝑠𝑠𝑡𝑡
p oduc s, each en y in he 𝑗𝑗 h column o 𝐻𝐻𝑋𝑋 is he sum o 𝑠𝑠𝑡𝑡 al e na i e condi ional p obabili ies,
while each en y in he
𝑗𝑗 h column o 𝐵𝐵𝑍𝑍 is he sum o 𝑐𝑐−𝑠𝑠𝑡𝑡 o he condi ional p obabili ies. Thus,
h ough he di ision by 𝑐𝑐, each en y in ( he 𝑗𝑗 h column o ) 𝐸𝐸 is he sum o exac ly 𝑐𝑐 al e na i e
condi ional p obabili y es ima ions, which means ha he elemen s o 𝐸𝐸 a e a e age condi ional
p obabili ies.
Ma ix 𝐸𝐸 can be seen as a p obabilis ic es ima ion o 𝑋𝑋. I can be ea anged o ob ain sepa a e
measu es o ela ed and un ela ed a ie y. Fo his, we p oceed as ollows:
𝐸𝐸=𝐻𝐻𝑇𝑇𝑋𝑋+𝐵𝐵𝑇𝑇𝑍𝑍
𝑑𝑑=𝐻𝐻𝑇𝑇𝑋𝑋−𝐵𝐵𝑇𝑇(𝑂𝑂−𝑋𝑋)
𝑑𝑑=𝐵𝐵𝑇𝑇𝑂𝑂+𝐾𝐾𝑇𝑇𝑋𝑋
𝑑𝑑,
whe e 𝐾𝐾 ≡𝐻𝐻–𝐵𝐵 is a ma ix o ma ginal condi ional p obabili ies. W i en his way, he ma ix 𝐸𝐸
has wo cons i uen (addi i e) elemen s. The i s o hese, 𝐸𝐸1≡𝐵𝐵𝑇𝑇𝑂𝑂/𝑐𝑐 is an 𝑐𝑐×𝑐𝑐 ma ix in
which all ows a e equal o each o he , i.e., whe e he e is no coun y- a ia ion. In each o he
coun y-columns o his ma ix, he 𝑖𝑖 h elemen indica es an au onomous p obabili y o being
specialized in p oduc 𝑖𝑖, which we de ine as he p obabili y o a hypo he ical coun y wi hou any
p io compa a i e ad an ages (a coun y ha does no ade and begins expo ing jus p oduc 𝑖𝑖).
53
We cha ac e ize his componen o ma ix 𝐸𝐸 as he pa ha co esponds o un ela ed di e si y.
The componen 𝐸𝐸2≡𝐾𝐾𝑇𝑇𝑋𝑋/𝑐𝑐 (also 𝑐𝑐×𝑐𝑐) esul s om he pa icula specializa ion p o ile o
he coun y in e ms o bo h p oduc ela edness ( e lec ed in 𝐾𝐾) and he ma ix 𝑋𝑋. 𝐸𝐸2 is he induced
pa o 𝐸𝐸 ha co esponds o ela ed di e si y. In he da abase, we use 𝐸𝐸2 as he measu e o
upg ading p obabili ies.
In o de o calcula e p oduc complexi y, we also use he ma ix 𝑋𝑋 ha epo s compa a i e
ad an ages. This ollows he me hod o ECI (Hidalgo, 2021). Fo his, we need he “ aw”
di e si ica ion measu e ha has al eady been de ined in he main ex , and which can be e-de ined
he e as he diagonal ma ix 𝑇𝑇 wi h elemen s:
𝑖𝑖𝑡𝑡=�𝑋𝑋𝑡𝑡𝑖𝑖
𝑖𝑖
on he main diagonal. We hen calcula e a new ma ix as ollows:
(𝑈𝑈−1𝑋𝑋)𝑇𝑇𝑋𝑋𝑇𝑇−1
P oduc complexi y is calcula ed as he eigen ec o ha co esponds o he second la ges
eigen alue o his ma ix.
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