Endogenous income elasticities

Missio, Fab izio J.
A icle
Endogenous income elas ici ies
PSL Qua e ly Re iew
P o ided in Coope a ion wi h:
Associazione Economia ci ile, Rome
Sugges ed Ci a ion: Missio, Fab izio J. (2025) : Endogenous income elas ici ies, PSL Qua e ly Re iew,
ISSN 2037-3643, Associazione Economia ci ile, Rome, Vol. 78, Iss. 312, pp. 51-66,
h ps://doi.o g/10.13133/2037-3643/18918
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ol. 78 n. 312 (Ma ch 2025)
Endogenous income elas ici ies
FABRICIO J. MISSIO*
Abs ac :
This pape deepens he analysis o he income elas ici ies
o impo and expo demand in ela ion o he eal
exchange a e (RER) wi hin a balance o paymen s
cons ained g ow h amewo k. I iden i ies how he RER
can a ec hese elas ici ies and explo es he esul ing
implica ions. A key highligh is he RER’s abili y o induce
s uc u al changes owa d mo e complex and echnology-
in ensi e sec o s. To illus a e his, a o mal mul isec o al
model is p esen ed, demons a ing he condi ions unde
which a highe RER can alle ia e ex e nal cons ain s.
Finally, se e al ela ed conside a ions a e add essed.
Fede al Uni e si y o Minas Ge ais (CEDEPLAR/UFMG), Belo
Ho izon e, B azil, email: jmis[email p o ec ed]mg.b
How o ci e his a icle:
Missio F.J. (2025), “Endogenous income elas ici ies”, PSL
Qua e ly Re iew, 78 (312), pp. 51-66.
DOI: h ps://doi.o g/10.13133/2037-3643/18918
JEL codes:
O11, E12, F43
Keywo ds:
balance-o -paymen s cons ain , mul i-sec o al Thi lwall’s Law,
income elas ici ies
Jou nal homepage:
h ps:// osa.uni oma1.i / osa04/psl_qua e ly_ e iew
The pionee ing wo k o Thi lwall (1979) in oduced he s anda d balance o paymen s cons ain
g ow h model (BPCG). In his model, he only sa e way o boos a coun y's g ow h a e while
main aining he in e empo al balance o paymen s equilib ium is h ough s uc u al changes ha
inc ease ( educe) he income elas ici ies o he demand o expo s (impo s).
The ques ion, he e o e, becomes how di e ences in elas ici ies cause di e en g ow h a es
and, abo e all, wha ac o s de e mine his. To answe his, esea che s ha e inco po a ed, in o
his se o models, unc ions ha y o cap u e he endogenei y o he income elas ici ies o
in e na ional ade (among o he s: McCombie and Robe s, 2002; Palley, 2003; Bo a, 2009).
My co-au ho s
1
and I ha e a gued ha he eal exchange a e (RER) can a ec he p oduc i e
s uc u e, p omo ing s uc u al change and al e ing income elas ici ies. Mo e speci ically, we
a gue ha main aining a compe i i e RER incen i izes esea ch and inno a ion by enhancing sel -
inancing condi ions and access o c edi . This, in u n, acili a es he mode niza ion and
di e si ica ion o p oduc i e capaci ies, ul ima ely expanding expo capaci y and educing
* I would like o exp ess my g a i ude o he pa icipan s o he CNPq p ojec en i led “New G een De elopmen alism:
Ins i u ions and Public Policies o Reindus ializa ion wi h Social Equi y” (n. 404978/2023-1) o hei aluable
con ibu ions and he FAPEMIG (a esea ch-suppo ing ounda ion o Minas Ge ais s a e) (APQ-01964-18).
1
I especially men ion F ede ico G. Jayme J , Hugo Ca canholo Iasco Pe ei a, Luciano Gab iel, José Luis O ei o, and
Rica do A aújo.
Special issue on p ema u e deindus ializa ion and clima e change: global No h and Sou h pe spec i es
52 Endogenous income elas ici ies
PSL Qua e ly Re iew
impo s in he long un. Fu he mo e, his en i onmen suppo s sec o s cha ac e ized by highe
complexi y, echnological ad ancemen , and p oduc i i y, which ends o ease ex e nal
cons ain s and os e economic g ow h in de eloping coun ies.
Howe e , I belie e i is essen ial o cla i y he ansmission mechanisms ha unde lie he
hypo hesis o income elas ici y endogenei y. This is p ecisely he objec i e o his a icle. Mo e
speci ically, I p opose o de elop he ansmission mechanisms be ween he RER and income
elas ici ies o in e na ional ade u he , showing how he RER can a ec nonp ice
compe i i eness h ough s uc u al change and, hus, elax ex e nal cons ain s.
Following his, I p esen a simpli ied and didac ic ex ension o he mul isec o al BPCG
amewo k, in eg a ing he h ee main ansmission mechanisms discussed h oughou he
a icle. I hen explo e he condi ions unde which he RER can elax ex e nal cons ain s.
In summa y, he p ima y heo e ical con ibu ion o his pape is o suppo he hypo hesis
ha he income elas ici ies o impo and expo demand a e endogenous o RER wi hin a BPCG
amewo k.
This wo k is no in ended o be an exhaus i e e iew o he en i e li e a u e, as he opic o
he e ec s o he RER on he economy is as and mul i ace ed. Reade s a e encou aged o engage
mo e deeply wi h he exis ing li e a u e, including he wo ks o Razmi e al. (2012), Blecke
(2016), Rape i (2020), Demi and Razmi (2022), Palazzo and Rape i (2023); hese o e aluable
insigh s. Addi ionally, his s udy can be seen as a complemen o p e ious wo ks de eloped by
mysel and co-au ho s. Na u ally, I ha e bene i ed g ea ly om hese discussions, and I am
g a e ul o my colleagues o hei consis en ly ui ul con ibu ions.
1. Theo e ical aspec s
In pos -Keynesian li e a u e, he RER has been somewha neglec ed. In he con ex o he so-called
BPCG models, he long- e m equilib ium g ow h a e depends on he a io be ween he income
elas ici ies o expo s and impo s. Changes in he RER a e conside ed i ele an o long- e m
g ow h, ei he because o empi ical e idence ha p ice elas ici ies o expo s and impo s a e low
(so ha he impac o an RER dep ecia ion on he g ow h a e o expo s and impo s is limi ed)
o because e ms o ade do no show a sys ema ic end owa d app ecia ion o dep ecia ion in
he long un (McCombie and Robe s, 2002, p. 92).
Acco ding o Thi lwall (2002, p. 69), achie ing a highe g ow h a e o e he long e m while
adhe ing o he in e empo al balance o paymen s equilib ium equi es s uc u al changes ha
boos he income elas ici y o expo s and educe i o impo s. In Thi lwall’s model, he di ec ion
o causa ion lows om elas ici ies, which e lec he p oduc ion s uc u e, o g ow h. As he
au ho poin s ou , his is he basic assump ion o all classic co e-pe iphe y models, such as hose
o P ebisch (1950), My dal (1957), See s (1962), and Kaldo (1970).
Pasine i’s (1981, 1993) wo k on s uc u al economic dynamics ad ances his discussion. The
au ho demons a es ha changes in he p oduc ion s uc u e lead o al e a ions in g ow h, gi en
he di e en a es o sec o al demand expansion. In o he wo ds, each sec o has a pa icula
capaci y (a di e en elas ici y) o bene i om inc eases in ou pu . This idea, along wi h he
ope a ion o an ex e nal cons ain on g ow h, was inco po a ed by A aújo and Lima (2007) in o
a o mal model, analogous o Thi lwall’s, which e ains Pasine i’s mul isec o al dynamics. The
inal esul , exp essed in he equa ion known as he Mul isec o al Thi lwall’s Law, shows ha a
coun y’s pe capi a income g ow h a e is di ec ly p opo ional o he g ow h a e o i s expo s
(gi en by he sec o al income elas ici y o demand mul iplied by he wo ld economy’s g ow h
F.J. Missio 53
PSL Qua e ly Re iew
a e) and in e sely ela ed o he income elas ici y o he sec o al impo demand, wi h bo h
elas ici ies weigh ed by he ela i e sha es o he sec o s in he ade composi ion.
Howe e , analyses o how a ia ions in exchange a e policy can d i e s uc u al changes
2
in
economies a e s ill in hei ea ly s ages. Fo example, wi hin he BPCG amewo k, his dimension
is o en unde explo ed o insu icien ly add essed. In hese models, he income elas ici ies
associa ed wi h o eign ade se e a dual pu pose: hey no only de e mine agg ega e demand
bu also e lec a ange o supply-side ac o s ha in luence he economy’s s uc u al
compe i i eness. Then, he ex e nal cons ain de e mined by income elas ici ies can be
in luenced only by changes in RER le els i he economy unde goes pe manen RER dep ecia ion
o app ecia ion. This is alid because he di ec e ec s o exchange a e policy a ia ions on
g ow h a e conside ed, while he po en ial e ec s on echnological p og ess, capi al accumula ion,
and p oduc i e he e ogenei y – and consequen ly on he elas ici ies hemsel es – a e o e looked.
The e o e, u he analysis is needed o deepen he unde s anding o he connec ion be ween he
RER and income elas ici y.
In o he wo ds, exis ing analyses assume ha he channels a ec ing he p oduc i e s uc u e
ope a e h ough he s imuli exe ed by RER a ia ions on demand and/o he wage s uc u e.
Howe e , while hese a e impo an , i is acknowledged ha hey do no cap u e he ull ange o
e ec s. Fo example, a compe i i e RER can in luence he supply side o he economy by inducing
an inc ease in he indus y’s sha e o he p oduc (see O onello e al., 2024). Since his sec o
exhibi s a highe a e age p oduc i i y compa ed o o he s, his change ends o enhance he
e iciency o he en i e economy. The e o e, he s a ing poin o add essing his gap is he
unde s anding ha he RER le el can in luence p oduc i i y and he economy’s p oduc i e
s uc u e, d i ing changes in pa e ns o specializa ion and compe i i eness h ough o he
mechanisms as well.
The hypo hesis o endogenous income elas ici ies o o eign ade expands he analysis by
allowing o he examina ion o addi ional e ec s o he exchange a e on g ow h. Fu he mo e, i
enhances ou unde s anding o he ac o s ha de e mine hese elas ici ies.
3
Some s udies ha e inco po a ed unc ions in o BPCG models o cap u e he endogenei y o
elas ici ies. McCombie and Robe s (2002) in eg a e s uc u al change in o Thi lwall’s Law by
in oducing hys e esis in he pa ame e s ha de e mine he economy’s long- e m g ow h a e. In
his scena io, he a io o he income elas ici ies o demand o expo s and impo s is speci ied as
a nonlinea unc ion o pas g ow h a es. Palley (2003) sugges s ha he income elas ici y o
impo demand is a nega i e unc ion o excess capaci y. The a ionale behind his app oach is
ha impo s a e ela ed o economic “bo lenecks”. As excess capaci y and unemploymen
dec ease, hese bo lenecks become mo e signi ican , he eby inc easing he sha e o impo s in
income g ow h. Bo a (2009) a gues ha , in de eloping coun ies, he income elas ici ies o expo
(impo ) demand a e a posi i e (nega i e) unc ion o he sha e o manu ac u ing in domes ic
ou pu .
I is also acknowledged ha he income elas ici ies o impo and expo demand a e
endogenous o he RER le el (Ba bosa-Filho, 2006; Missio and Jayme J ., 2012; Fe a i e al., 2013;
O ei o e al., 2015; Missio e al., 2017).
Acco ding o Missio and Jayme J . (2012), he s a ing poin is o obse e ha he e a e o he
mechanisms (no explo ed by he li e a u e) h ough which he RER le el in luences p oduc i i y
2
S uc u al change is unde s ood as he eo ganiza ion o he p oduc i e s uc u e, e lec ed in a coun y’s ade
specializa ion pa e n.
3
In summa y, i is assumed ha changes in he p oduc i e s uc u e, which e lec modi ica ions in elas ici ies, al e he
ex e nal cons ain s and, he e o e, ha policies ha p omo e such s uc u al changes ha e e ec s on g ow h.
54 Endogenous income elas ici ies
PSL Qua e ly Re iew
and he p oduc i e s uc u e o he economy, he eby al e ing he pa e n o specializa ion and
compe i i eness.
These “new” mechanisms a e associa ed wi h he possibili y ha main aining a compe i i e
RER
4
can es ablish incen i es o , o example, echnological p og ess. Mo e speci ically, cu ency
dep ecia ion – inc easing i ms’ p o i s and hei capaci y o sel - inancing – a ec s he unds ha
a e a ailable o hese i ms o unde ake in es men p ojec s ela ed o esea ch and inno a ion.
5
RER app ecia ion p omo es a edis ibu ion o income om p o i s o wages, which implies a
educ ion in i ms’ abili y o sel - inance. This leads o dec eased a ailabili y o in e nal unds o
acqui ing new echnologies. Addi ionally, i ms ace inc eased di icul ies in accessing ex e nal
inancing due o in o ma ion asymme ies in inancial ma ke s, esul ing in c edi a ioning.
Consequen ly, e en wi h he po en ial o acqui e inexpensi e echnology om ab oad, a ious
p oduc i e sec o s may emain unable o in es in mode nizing hei p oduc i e capaci y.
On he o he hand, wi h a compe i i e RER, i is expec ed ha i ms will unde ake inno a i e
ac i i ies, leading o g ea e p oduc i e he e ogenei y ( o example, a la ge a ie y o goods
p oduced) and s uc u al homogeniza ion, as echnological p og ess is now a ained by sec o s
no adi ionally linked o ex e nal ma ke s. In he mo e backwa d sec o s, whe e he e u ns on
inno a i e ac i i ies a e highe , i is expec ed ha discon inui ies will be swi ly o e come.
6
An inc ease in p oduc i e he e ogenei y, especially in adable sec o s, unde sco es he
Kaldo ian insigh s om “Ve doo n’s Law”, which highligh s a posi i e link be ween indus ial
ou pu g ow h and p oduc i i y. This g ow h leads o ans o ma i e changes in p oduc i e
s uc u es and demand composi ion, which, in u n, p omo e new p ocesses and p oduc
inno a ions in he indus ial sec o . Such g ow h suppo s he expansion o business ope a ions
and he adop ion o mode n echnology, enhancing p oduc i i y. This shi no only d i es in e nal
sec o al inno a ion bu also lays he g oundwo k o inc eased ex e nal economic in e ac ions.
Addi ionally, a compe i i e RER boos s ex e nal demand, os e ing ou pu g ow h and
cumula i e p oduc i i y gains, pa icula ly h ough dynamic economies o scale, whe e
echnological changes become i e e sible. This cycle o g ow h and inc easing e u ns
accele a es p oduc i i y and echnological ad ancemen , enhancing compe i i eness in ex e nal
ma ke s h ough mechanisms such as lea ning by doing, using, in e ac ing, and expo ing.
7
In sho , sus aining a compe i i e RER os e s g ea e p oduc i e he e ogenei y, ad ances
echnological p og ess, enhances he capaci y o inance in es men s, and inc eases o e all labou
p oduc i i y. This ensu es, o e ime, a highe income elas ici y o demand o expo s. Simila ly,
he income elas ici y o demand o impo s dec eases as domes ic manu ac u ing di e si ies and
4
Discussing a compe i i e RER equi es conside ing i s le el. Achie ing a compe i i e a e equi es implemen ing
policies o e a ce ain pe iod ha lead o a signi ican and sus ained de alua ion. The impac o he RER on he
p oduc i e s uc u e is pa ly due o his change in i s le el. The e o e, he e ms compe i i e RER, RER de alua ion,
and RER unde alua ion a e o en used in e changeably.
5
The empi ical li e a u e shows ha he main de e minan s o R&D spending and physical capi al in es men a e cash
low and sales olume (Hall, 1992; Himmelbe g and Pe e sen, 1994; Bond e al., 1999). These a e wo a iables ha a e
posi i ely a ec ed by dep ecia ions in he RER le el. See also Dao e al. (2021).
6
I is implici ly assumed ha echnology is one o he essen ial elemen s in long- e m g ow h, as imp o emen s in
p oduc ion echniques lead o inc eases in p oduc i i y and an accele a ion o he g ow h a e, allowing o he
inco po a ion o excess labou and a educ ion in s uc u al he e ogenei y. Mo eo e , i is acknowledged ha s uc u al
change can be p omo ed by he e y accumula ion o capi al, which leads o a educ ion in he echnological gap, as new
echnologies a e ypically embodied in new machine y and equipmen (Fage be g, 1994). Thus, since bo h capi al
accumula ion and echnological inno a ion a e in luenced by he le el o he RER, i is e iden ha he RER also has
e ec s on g ow h om he supply side o he economy.
7
The inc ease in p oduc i e he e ogenei y in a “dual” economy à la Lewis allows o an inc ease in labou p oduc i i y
h ough he ealloca ion o labou om lagging non adable sec o s o ad anced adable sec o s.

F.J. Missio 55
PSL Qua e ly Re iew
he echnology inco po a ed in hese p oduc s ad ances. The e o e, a dep ecia ed RER enhances
p oduc i e di e si y and he echnological sophis ica ion o domes ic goods, educing eliance on
impo s and subsequen ly lowe ing he income elas ici y o demand o impo s.
2. RER, s uc u al change, and he endogenous income elas ici ies
The main a gumen in suppo o he hypo hesis o endogenous income elas ici ies o o eign
ade, ela i e o he RER le el, is ha he exchange a e can induce s uc u al change and,
consequen ly, modi y a egion’s o coun y’s economic s uc u e, he eby imp o ing i s
pe o mance in in e na ional ade in a sus ained manne o e ime (Missio and Jayme J ., 2012;
B esse -Pe ei a e al., 2015; Ma coni e al., 2021).
Thus, o cla i y hese poin s, i is assumed ha s uc u al change occu s because he RER le el
in luences he p oduc i e s uc u e in h ee dimensions:
i) he sha e o each sec o /p oduc in o al impo s and expo s (composi ion e ec );
ii) he numbe o sec o s (p oduc s) exis ing (p oduced) in he economy (specializa ion e ec );
and
iii) he a ac i eness o p oduc s and/o he in ensi y o echnological p og ess embodied in he
p oduc s (sophis ica ion e ec ).
The key ques ion now is o iden i y he mechanisms h ough which he RER can gene a e
composi ion, specializa ion, and sophis ica ion e ec s (which a e no necessa ily independen o
one ano he ). In gene al, hese mechanisms can be iden i ied as ollows:
a) Composi ion e ec : he RER is a c ucial ool o p omo ing g ow h h ough empo a y, ye
su icien ly p olonged, changes in he ela i e p ices o adable and non adable goods.
Sus aining a s able and compe i i e RER can ealign he p oduc i e s uc u e owa ds
echnologically ad anced adable goods, enabling sho - e m impac s on agg ega e demand
om in e na ional ade o acili a e long- e m economic g ow h. The acili a ion o access o
in e na ional ma ke s s imula es p oduc ion in expo sec o s, gene a ing posi i e dynamic
ex e nali ies ac oss he economy, such as lea ning om compe i ion in ex e nal ma ke s and
a ac ing o eign di ec in es men . This enhances he p oduc i i y and compe i i eness o
domes ic p oduc s. Fo de eloping coun ies ha ha e p og essed in hei indus ializa ion,
main aining a compe i i e RER pa icula ly bene i s he indus ial sec o by acili a ing he
accep ance o he Kaldo ian implica ions o Ve doo n’s Law, which links indus ial ou pu
g ow h o p oduc i i y g ow h. As indus ial p oduc ion expands, new p ocesses a e adop ed,
new businesses eme ge, and exis ing i ms g ow, enabling he adop ion o mode n equipmen
and hus inc easing o e all economic p oduc i i y. Some s udies in he li e a u e ha add ess
hese links a e Ba bosa-Filho (2006), Cimoli e al. (2013), Fe a i e al. (2013), Missio e al.
(2017), Libman e al. (2019) and Palazzo (2024a, 2024b).
b) Di e si ica ion e ec : his e e s o he changes p oduced by RER on he a ie y o goods
(sec o s) ha make up he expo and impo baske s. F om he pe spec i e o expo s, he
a gumen has wo main poin s. i) A compe i i e RER encou ages expo -o ien ed in es men s
by acili a ing domes ic i ms’ access o ex e nal ma ke s. This sugges s ha economic
de elopmen is shaped by he in es men a e, which is, in u n, in luenced by he exchange
a e, especially conce ning expo -d i en in es men s. These in es men s esul in
di e si ica ion o p oduc ion. ii) Gi en ha echnological p og ess la gely s ems om capi al
accumula ion – whe e new echnologies a e ypically embedded in new machine y and
56 Endogenous income elas ici ies
PSL Qua e ly Re iew
equipmen – i is easonable o expec he addi ion o new p oduc s o he expo baske
(Missio and Jayme J ., 2012; O ei o e al., 2015). Fu he mo e, a a ian o his e ec can be
obse ed in how he RER in luences he unc ional dis ibu ion o income. Speci ically,
changes in income dis ibu ion, which a e impac ed by a ia ions in he RER, a ec he
p oduc i e s uc u e, ul ima ely de e mining he deg ee o specializa ion in p oduc ion (Dosi
e al., 1990; Missio and Jayme J ., 2012). Rega ding impo s, he compe i i e RER educes he
a ie y o impo ed goods, concen a ing impo s on essen ial goods necessa y o he
unc ioning o he economy. As he le el o economic de elopmen inc eases, he eliance on
hese goods diminishes, as domes ic p oduc ion begins o mee local ma ke demand.
c) Sophis ica ion e ec : he RER can subs an ially impac echnological p og ess embedded in
p oduc s. Speci ically, cu ency de alua ion boos s co po a e p o i s and enhances i ms’
capaci y o sel - inancing, he eby inc easing a ailable unds o in es men in esea ch and
inno a ion p ojec s. This leads o a g ea e a ailabili y o in e nal unds o acqui ing new
echnologies, and i educes i ms’ eliance on ex e nal inancing, pa icula ly since c edi
ma ke s o en ace a ioning due o in o ma ion asymme ies. Consequen ly, unde a
compe i i e exchange a e, companies a e mo e likely o engage in inno a i e ac i i ies ha
inco po a e highe le els o echnology in o hei p oduc s, enhancing hei quali y and appeal
in in e na ional ma ke s.
8
See Missio and Jayme J . (2012), Caglayan and Demi (2019) and
Ma coni e al. (2020).
Iden i ying hese mechanisms is c ucial; howe e , ha alone does no clea ly demons a e
hei e ec s on income elas ici ies. To p og ess in his a ea, applying sec o al models can be an
e ec i e app oach. To illus a e his, we no e ha he agg ega e income elas ici ies o expo s can
be iewed as a weigh ed a e age o sec o al elas ici ies. Fo mally, his can be exp essed as:
𝜀 =∑𝜔𝑋𝑖𝜀𝑖
𝑘
𝑖=1 (1)
whe e 𝜀 is he agg ega e income elas ici y, 𝜔𝑋𝑖 ep esen s he sha e o sec o 𝑖 in he expo baske ,
𝜀𝑖 is he income elas ici y o sec o 𝑖, and 𝑘 is he numbe o p oduc s/sec o s expo ed.
This weigh ed o mula cap u es he in luence o sec o al elas ici ies on he agg ega e
elas ici y, e lec ing he di e en con ibu ions o each sec o . Equa ion (1) o malizes he idea
ha a coun y’s expo p o ile is composed o 𝑘 goods, each wi h a speci ic income elas ici y 𝜀𝑖,
whose con ibu ion o he de e mina ion o 𝜀 depends on i s sha e in ha p o ile, 𝜔𝑋𝑖.
By using equa ion (1) and simpli ying i unde he assump ion ha he e ec s a e
independen , we can demons a e he e ec o he RER on he agg ega e elas ici y o he expo s
by conside ing each o he h ee main e ec s discussed abo e.
i) Conside ing he composi ion e ec , we ha e:
𝜀(𝜃)=∑𝜔𝑋𝑖(𝜃).𝜀𝑖
𝑘
𝑖=1 (1.1)
8
The inc ease in R&D ac i i ies (sophis ica ion e ec ), combined wi h he eme gence o new business uni s
(composi ion e ec ), leads o he in oduc ion o new p oduc s, ein o cing he specializa ion e ec . Fu he mo e, i is
impo an o emphasize ha he sec o al sophis ica ion e ec has implica ions o o he sec o s o he p oduc i e
s uc u e, as s uc u al homogeniza ion is expec ed, since echnological p og ess is now also inco po a ed in sec o s
ha a e no linked o he ex e nal ma ke . Gi en ha he e u ns on inno a i e ac i i ies a e highe in he lagging
sec o s, i is expec ed ha he discon inui ies will be quickly o e come.
F.J. Missio 57
PSL Qua e ly Re iew
whe e 𝜃 is he RER le el. A compe i i e RER p omo es a change in he p oduc i e s uc u e in
a ou o high- ech adable goods, which ha e a highe income elas ici y o demand. I is
impo an o no e ha , while he alues o he elas ici ies emain unchanged, he sha e o he
sec o s associa ed wi h highe elas ici ies does change. This implies ha he agg ega e alue o 𝜀
will inc ease.
ii) Conside ing he di e si ica ion e ec , we a gue ha modi ica ions in he long- e m RER
le el impac he quan i y o goods (sec o s) ha make up he expo impo p o ile. In
o mal e ms, k is a unc ion o he RER le el.
𝜀(𝜃)=∑𝜔𝑋𝑖.𝜀𝑖
𝑘(𝜃)
𝑖=1 (1.2)
iii) In he case o he sophis ica ion e ec , since he e is a change in he deg ee o echnology
inco po a ed in o he p oduc s, he income elas ici y associa ed wi h each p oduc
changes:
𝜀(𝜃)=∑𝜔𝑋𝑖.𝜀𝑖
𝑘
𝑖=1 (𝜃) (1.3)
I is assumed ha he i s wo e ec s in luence he agg ega e elas ici y o impo s in opposi e
di ec ions. Speci ically, a compe i i e RER ends o dec ease he sha e o goods wi h a highe
deg ee o echnological in ensi y in he impo po olio and o educe he numbe o impo ed
p oduc s. The sophis ica ion e ec does no apply.
3. Endogenei y in he mul isec o al model
This sec ion aims o p esen a o mal a gumen ha in eg a es he key issues discussed.
Speci ically, he p oposed o maliza ion seeks o accoun o he e ec s o a ia ions in he RER
on he p oduc i e s uc u e (s uc u al change) in he h ee dimensions ou lined in he p e ious
sec ion, while also conside ing he hypo hesis o he endogenei y o elas ici ies.
In o mal e ms, his implies adop ing a modi ied e sion o Thi lwall’s mul isec o al law, ha
is:
𝑦𝑑=(∑𝜌𝑖(𝜃)𝜀𝑖(𝜃)
𝑘(𝜃)
𝑖=1 )/(∑𝜑𝑖(𝜃)𝜋𝑖
𝑛(𝜃)
𝑖=1 )𝑦𝐸 (2)
whe e 𝑦𝑑 is he domes ic income; 𝑦𝐸 is he ex e nal income, 𝜌𝑖 (𝜑𝑖) ep esen s he sha e o sec o
i in expo s (impo s), 𝜀𝑖 (𝜋𝑖) is he income elas ici y o demand o expo s (impo s), 𝑘 (𝑛) is he
numbe o sec o s/p oduc s ha make up he expo s (impo s), and 𝜃 is he RER le el.
Equa ion (2) speci ically inco po a es he idea ha s uc u al change is endogenous o he
RER.
9
E en i he numbe o sec o s emains cons an and he elas ici ies do no change, a ia ions
in he RER can s ill a ec he pa icipa ion o each sec o in he p oduc i e s uc u e and,
consequen ly, can in luence he g ow h a e (composi ion e ec ). Addi ionally, equa ion (2)
9
Equa ion (2) suppo s he indings o he mul isec o al model discussed by A aújo and Lima (2007), indica ing ha ,
e en when elas ici ies emain cons an , s uc u al changes can impac he o e all g ow h a e. These changes o en
esul om shi s in demand composi ion – due no o changes in elas ici ies bu a he o he a ying pa icipa ion o
each sec o in agg ega e expo s o impo s – d i en by e ol ing as es o p e e ences, as sugges ed by Engel’s law.
Addi ionally, i aligns wi h he esul s o Missio e al. (2017), demons a ing how RERs a ec echnological p og ess
h ough he mechanism o cumula i e causa ion, known as he sophis ica ion e ec .
58 Endogenous income elas ici ies
PSL Qua e ly Re iew
inco po a es he idea ha he RER can in luence he numbe o sec o s in he economy
(di e si ica ion e ec ), pa icula ly hose linked o he in e na ional ma ke (whe e sophis ica ion
e ec is mos p ominen ).
F om equa ion (2), we can demons a e ha (see appendix):
𝑑𝑦𝑑/𝑑𝜃 =[(∑(𝜌𝑖′(𝜃)𝜀𝑖(𝜃)+𝜌𝑖(𝜃)𝜀𝑖′(𝜃))
𝑘(𝜃)
𝑖=1 )(∑𝜑𝑖(𝜃)𝜋𝑖
𝑛(𝜃)
𝑖=1 )−
(∑𝜌𝑖(𝜃)𝜀𝑖(𝜃)
𝑘(𝜃)
𝑖=1 )(∑𝜑𝑖
′(𝜃)𝜋𝑖
𝑛(𝜃)
𝑖=1 )]/[(∑𝜑𝑖(𝜃)𝜋𝑖
𝑛(𝜃)
𝑖=1 )2]𝑦𝐸 (3)
To ad ance he analysis o he sign o his de i a i e, we no e ha :
i) 𝑑 𝑘
𝑑 θ >0 – Cu ency de alua ions inc ease he numbe o expo sec o s connec ed o
in e na ional ade. Acco ding o B esse -Pe ei a (2012), he RER ac s as a kind o swi ch ha
ei he “ u ns on” o “ u ns o ” i ms ha a e echnologically and adminis a i ely compe en
in ela ion o global demand.
ii) 𝑑 𝑛
𝑑 θ <0 – A compe i i e RER ends o dec ease he di e si y o impo ed p oduc s and he
in ol emen o o eign sec o s in he na ional economy. This happens o wo main easons:
i s , i enables he domes ic economy o ocus on p oducing goods wi h highe echnological
in ensi y ( he sophis ica ion e ec ); second, he p ice e ec edi ec s demand owa ds
impo s. As a esul , domes ically manu ac u ed goods p og essi ely ca e o he demand o
echnologically ad anced p oduc s, whe eas impo s become concen a ed on less
echnologically in ensi e, mo e cos -e ec i e goods.
iii) 𝑑 𝑘
𝑑 θ >𝑑 𝑛
𝑑 θ – Tas es, p e e ences and habi s, along wi h in es men s in ad e ising, ma ke ing,
and he es ablishmen o dis ibu ion channels, c ea e a ce ain igidi y in he declining
demand o impo ed goods. As a esul , he p esence o in e na ional sec o s in he domes ic
economy con ac s mo e slowly han he expansion o domes ic i ms in o in e na ional
ma ke s.
Addi ionally, we can conside ha 𝜌𝑖(𝜃), 𝜀𝑖(𝜃), and 𝜑𝑖(𝜃) a e linea in 𝜃, ha is:
i) 𝜌𝑖(𝜃)=𝑎𝑖(𝜃)+𝑏𝑖 (4)
ii) 𝜑𝑖(𝜃)=−𝑒𝑖(𝜃)+𝑓𝑖 (5)
iii) 𝜀𝑖(𝜃)=𝑐𝑖(𝜃)+𝑑𝑖 (6)
Equa ion (4) illus a es he “composi ion e ec ” on expo s. A compe i i e RER os e s
expo s, in es men , and indus ializa ion, hus enhancing he pa icipa ion o mo e echnology-
in ensi e sec o s. These sec o s end o exhibi highe income elas ici ies. The cons an e m (𝑏𝑖)
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