Saini, Swa i; Meh a, Mee a
A icle
Quali y o schooling, e ili y and economic g ow h
Re iew o Economic Analysis (REA)
P o ided in Coope a ion wi h:
In e na ional Cen e o Economic Analysis (ICEA), Wa e loo, On a io
Sugges ed Ci a ion: Saini, Swa i; Meh a, Mee a (2024) : Quali y o schooling, e ili y and economic
g ow h, Re iew o Economic Analysis (REA), ISSN 1973-3909, In e na ional Cen e o Economic
Analysis (ICEA), Wa e loo (On a io), Vol. 16, Iss. 2, pp. 175-220,
h ps://doi.o g/10.15353/ ea. 16i2.5180
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Re iew o Economic Analysis 16 (2024) 175–220 1973-3909/2024175
Quali y o Schooling, Fe ili y and Economic G ow h
SWATI SAINI*†
Depa men o Economics, Delhi School o Economics, Uni e si y o Delhi
MEETA KESWANI MEHRA
Cen e o In e na ional T ade and De elopmen , Jawaha lal Neh u Uni e si y
The exis ing body o li e a u e unde sco es he c ucial ole o echnology, d i en by bo h
inno a ion and imi a ion, in os e ing economic g ow h. Human capi al eme ges as a key
ac o in luencing echnology adop ion and inno a ion.We conside a R&D-based g ow h
model o analyze how imp o emen in schooling quali y impac s echnical p og ess ( ia
he win channels o imi a ion and inno a ion) and he e o e, long- un economic g ow h
o an economy by wo king h ough he in luence o e ili y a es and educa ion decisions
a household le el. The esul s indica e ha imp o emen in schooling quali y igge s a
child quan i y-quali y ade-o a he household le el when quali y o schooling exceeds
an endogenously de e mined h eshold. A household le el, pa en s in es mo e in he
educa ion o hei child en and ha e lesse numbe o child en. This mic o-le el ade-o
has wo opposing e ec s on agg ega e human capi al accumula ion a he mac oeconomy
wide le el. A highe in es men in educa ion o a child s imula es he accumula ion o
human capi al, which os e s echnical p og ess, bu he simul aneous decline in e ili y
a e educes o al ac o p oduc i i y g ow h by con ac ing he s ock o human capi al.
The o me e ec p e ails o e he la e only when quali y o schooling is highe han
he h eshold and he e o e, economic g ow h is d i en by a e o agg ega e human capi al
accumula ion unde bo h inno a ion and imi a ion egimes. Howe e , when he quali y
o schooling is lowe han his h eshold, pa en s do no in es in he educa ion and ocus
on maximizing e ili y. The e o e, he economy g ows a he a e o popula ion g ow h
a he mac o le el unde he wo egimes. Also, i is ad an ageous o an economy o
inno a e upon he local echnology on ie ins ead o imi a ing om he wo ld echnology
on ie i he a e o human capi al accumula ion is highe han he g ow h a e o wo ld
echnology on ie in he p esence o cons an o diminishing e u ns o R&D sec o .
*This pape is based on one o he essays om he PhD hesis o Swa i Saini. We g a e ully acknowledge
he in aluable commen s and sugges ions ecei ed om Debasis Mondal and Mausumi Das on he ea lie
e sion o he pape . We hank he pa icipan s o he 4 h In e na ional Con e ence on Sou h Asian Eco-
nomic De elopmen , Sou h Asian Uni e si y, New Delhi, CoRe: IGIDR PhD Colloquium, Indi a Gandhi
Ins i u e o De elopmen Resea ch, Mumbai, DAAD wo kshop on “Compa a i e Economic De elopmen
Issues”, Cen e o In e na ional T ade and De elopmen , SIS, JNU, New Delhi, IMR Doc o al Con e -
ence, Indian Ins i u e o Managemen , Bengalu u o hei aluable commen s and sugges ions on ea lie
e sion o he pape . We a e g a e ul o he edi o , Je zy (Ju ek) Konieczny and he anonymous e e ee
o hei commen s and sugges ions.
†Co esponding au ho : [email p o ec ed]
©2024 Swa i Saini and Mee a Keswani Meh a. Licenced unde he C ea i e Commons A ibu ion-
Noncomme cial 3.0 Licence (h p://c ea i ecommons.o g/licenses/by-nc/3.0/). A ailable a
h p:// o ea.o g.
175
Re iew o Economic Analysis 16 (2024) 175–220
Keywo ds: e ili y, quali y o schooling, economic g ow h, inno a ion, imi a ion
JEL Classi ica ions: J13, J11, O11, O30
1 In oduc ion
Acco ding o Ba o & Lee (2013) es ima es, he sha e o popula ion wi hou any o mal school-
ing in de eloping coun ies has declined om 54.6 pe cen in 1960 o app oxima ely 17.4 pe -
cen in 2010. Howe e , me ely expanding access o educa ion does no ensu e ha child en
ac ually lea n in schools. The lea ning ou comes in schools closely hinge upon he quali y o
schooling, which has been gi en inadequa e a en ion in he de elopmen policy pa adigms o
mos de eloping coun ies un il now. Bu mo e ecen ly, de elopmen policies o mos coun ies
a e making a shi owa ds imp o ing lea ning quali y in schools han me ely expanding access
o educa ion.
This policy pa adigm shi in educa ion policy is also e lec ed in he pos -2015 de elopmen
agenda. Impa ing quali y educa ion ea u es as he ou h Sus ainable De elopmen Goal se
by he Uni ed Na ions. This shi is mo i a ed by wo ac o s. Fi s , he e is g owing empi ical
e idence ha quali y o schooling ma e s mo e o economic g ow h. Se e al s udies ha e
ound ha human capi al quali y has a signi ican posi i e impac on g ow h (Hanushek &
Kimko 2000, Hanushek & Woessmann 2012, Ciccone & Papaioannou 2009, Islam e al. 2014,
Neyche a 2016, Al inok & Aydemi 2017, Campbell & ¨
Ung¨
o 2020). Second, poo quali y o
schooling emains a dismal eali y in de eloping coun ies. Acco ding o he Annual S a us
o Educa ion Repo (ASER) (2019) su ey i led ’Ea ly Yea s’, a leas 25 pe cen o Indian
school child en in he ou -eigh age g oup do no ha e age-app op ia e cogni i e and nume acy
skills, making o a massi e lea ning de ici a an ea ly age. Simila ly, Glewwe e al. (2010)
epo ha eache s om u al schools in Kenya we e absen 20 pe cen o he ime; while, in
Zambia and Pakis an, eache s we e absen , espec i ely, 18 pe cen and 10 pe cen o he ime
(Das e al. 2004, Reime s 1993).
In addi ion o hese obse a ions abou quali y o schooling, ce ain demog aphic changes
ha e been obse ed in he wo ld since pas ew decades. The o al e ili y a e has declined
ma kedly in many egions o he wo ld o e he las ew decades.1The a e age e ili y has
declined in sub-Saha an A ica om 6.3 bi hs pe woman in 1990 o 4.6 in 2019. O he egions
ha e also wi nessed a e ili y decline o e he same pe iod - No he n A ica and Wes e n Asia
( om 4.4 o 2.9), Cen al and Sou he n Asia (4.3 o 2.4), Eas e n and Sou h-Eas e n Asia (2.5
o 1.8), La in Ame ican and he Ca ibean (3.3 o 2.0) and he Oceania (4.5 o 3.4)2(Uni ed
Na ions, Depa men o Economic and Social A ai s, Popula ion Di ision 2019). A ound 40
pe cen o he wo ld’s popula ion li es in in e media e- e ili y coun ies and close o 50 pe cen
1To al e ili y a e is de ined as he a e age numbe o child en bo n o women o e a li e ime.
2The egion o Oceania excludes New Zealand and Aus alia in he UN Repo .
176
SAINI, MEHRA Quali y o Schooling, Fe ili y and Economic G ow h
o he global popula ion li es in low- e ili y coun ies.3I is expec ed ha sligh ly less han 30
pe cen o he wo ld popula ion will li e in in e media e- e ili y coun ies and 70 pe cen o he
o al popula ion will li e in low- e ili y coun ies in 2050.
Human capi al is a di ec ac o o p oduc ion, which is posi i ely ela ed o ou pu g ow h
jus like o he ac o s, such as physical capi al and labo (Lucas J 1988, Rebelo 1991, Mankiw
e al. 1992). Addi ionally, human capi al acili a es he adop ion and de elopmen o echnol-
ogy (some imes di e en ia ed by imi a ion and inno a ion ac i i y as wo dis inc ou es o
echnological p og ess) (Nelson & Phelps 1966, Benhabib & Spiegel 1994). Using a ho izon al
R&D-based g ow h model ´
a la Rome (1990) wi h endogenous human capi al supply, Boikos
e al. (2022) model leisu e ex e nali ies in R&D ac i i y and examine hei impac on inno a-
ion a e when in e ac ed wi h echnological spillo e s. They show ha ce e is pa ibus, leisu e
has a posi i e in luence on inno a ion ac i i y i he e a e weak in e empo al spillo e e ec s
a ising om exis ing ideas. Howe e , i he e exis s s ong in e empo al spillo e e ec s, hen,
leisu e has a nega i e in luence on inno a ion ac i i y. As i is e iden om his endogenous
g ow h li e a u e, human capi al is a majo de e minan o economic g ow h. A decline in pop-
ula ion implies a decline in human capi al which can lead o a decline in economic g ow h as
human capi al is he d i ing o ce o R&D ac i i ies. Thus, declining e ili y a e can s angle
economic g ow h.
Howe e , empi ical li e a u e inds ha popula ion g ow h and economic g ow h a e nega-
i ely co ela ed (Kelley & Schmid 1994, B ande & Dow ick 1994, Li & Zhang 2007, He ze
e al. 2012, P e ne e al. 2013). Boikos e al. (2013) in es iga es he ela ionship be ween he
e ili y a e and pe capi a human capi al in es men . Using a heo e ical amewo k, hey show
ha bi h a e has a mono onically nega i e impac on economic g ow h a e when bi h a e is
exogenously gi en and i is assumed ha i s impac on pe capi a human capi al in es men is
linea and mono onically nega i e. In he absence o any speci ic assump ion ega ding impac
on pe capi a human capi al in es men and a e endogenizing bi h a e, hey show ha o-
al impac o popula ion g ow h on economic g ow h is non-mono onic which con o ms wi h
he possibili y ha impac o popula ion g ow h on economic g ow h may di e (in sign and
magni ude) ac oss coun ies cha ac e ized by di e en bi h a es.
The e exis s a s and o heo e ical li e a u e linking R&D based g ow h wi h endogenous
e ili y and educa ion decisions (S ulik 2005, S ulik e al. 2013, Hashimo o & Taba a 2016,
Bucci e al. 2020) ha p o ides an explana ion o why empi ical li e a u e inds no suppo i e
e idence o he pessimis ic p edic ion ha declining e ili y can s angle economic g ow h. The
child quan i y-quali y ade-o a he mic o le el is posi ed as one o he plausible explana ions.
3In e media e- e ili y coun ies a e coun ies (such as India, Indonesia, Pakis an, he Philippines and
Egyp ) whe e women ha e an a e age li e ime e ili y ha anges be ween 2.1 and 4 li e bi hs. Low-
e ili y coun ies a e hose coun ies whe e e ili y is below 2.1 li e bi hs pe woman. I includes almos
all o Eu ope, No he n Ame ica, Aus alia and New Zealand.
177
Re iew o Economic Analysis 16 (2024) 175–220
This mic o le el ade-o ensu es ha declining e ili y is accompanied by highe human cap-
i al endowmen pe pe son in e ms o educa ion and heal h. As a esul , al hough, declining
e ili y educes wo k o ce size bu , also, leads o highe human capi al endowmen pe pe son.
This highe human capi al accumula ion a e s he nega i e economic impac o declining e -
ili y. Gi en ha human capi al is he d i ing o ce o R&D, his en ails a highe R&D ou pu
and highe R&D-based g ow h.
This s and o li e a u e uses disc e e- ime o e lapping gene a ions amewo k o analyze
he e ec o child quan i y-quali y ade-o on economic g ow h. Rise in li e expec ancy o
pa en s (Hashimo o & Taba a 2016),inc ease in heal h in es men o child en (Baldanzi e al.
2021), ising wages (S ulik e al. 2013) a e some o he common mechanisms used o explain
child quan i y-quali y ade-o a he household le el and i s consequen impac on R&D-based
economic g ow h.4In a sligh de ia ion om he usual mechanism o child quan i y-quali y
ade-o adop ed by mos o he s udies in his a ea, Ce ella i e al. (2023) u ilize a wo-
sec o amewo k o show how complemen a i ies be ween human and physical capi al yield
endogenous dynamics o popula ion, physical capi al, and human capi al. Ou wo k is ela ed
o his s and o li e a u e linking R&D based g ow h wi h endogenous e ili y and educa ion
decisions and a emp s a showing quali y o schooling can be ano he mechanism ha can
igge child quan i y-quali y ade-o a he household le el.
The e exis s ano he s and o heo e ical li e a u e ha analyzes he linkages be ween qual-
i y o schooling and economic g ow h. Many exis ing s udies (Tamu a 2001, Gilpin & Kagano ich
2012) on quali y o schooling and economic g ow h ocus on explaining how de e minan s
o quali y o schooling, such as eache -s uden a io and eache quali y oge he , impac he
lea ning p ocess, and he consequen human capi al o ma ion and, he e o e, economic g ow h.
Howe e , mos o hese s udies assume exogenously de e mined popula ion g ow h and also do
no conside echnical p og ess in hei models. Consequen ly, hese s udies a e unable o ana-
lyze he impac o schooling quali y and he esul ing demog aphic change on R&D ac i i ies,
which a e majo de e minan s o echnological de elopmen in he eal wo ld. We imp o e
upon hese pape s by endogenizing bo h - popula ion g ow h and echnical change.
The concep ha he echnology di usion plays a c ucial ole in economic g ow h has a ich
his o ical backg ound. Nelson & Phelps (1966) was one o he i s s udies o highligh he
4In gene al, his child quan i y-quali y ade-o be ween e ili y and educa ion is a c ucial componen
o uni ied g ow h heo y, which models he ansi ion om Mal husian s a e o sus ained g ow h o an
economy. The genesis o his s and o li e a u e can be aced back o he seminal wo k o Becke (1960).
Galo & Weil (2000) pos ula e ha a highe a e o echnical p og ess igge s a child quan i y-quali y
ade-o which induces a demog aphic ansi ion in which e ili y a es decline and in es men s in human
capi al o child en inc ease. This, e en ually, pa es way o he pe iod o sus ained economic g ow h o
an economy. Besides echnical p og ess, declining child mo ali y (Soa es 2005), ise in li e expec ancy
o pa en s (Boucekkine e al. 2002, 2003, Kalemli-Ozcan 2002, 2003), and decline in gende wage gap
(Galo & Weil 1996) a e o he mechanisms o explain child quan i y-quali y ade-o a he household
le el and he consequen long- un de elopmen om s agna ion o mode n g ow h o economies.
178
SAINI, MEHRA Quali y o Schooling, Fe ili y and Economic G ow h
ole o human capi al in acili a ing echnology di usion. Jo ano ic & Rob (1989) o mula e
an agg ega e model ea u ing di e se agen s, whe e in e ac ions gene a ed bo h no el ideas and
he eplica ion o ideas—a p ocess o di usion om ini ially mo e p oduc i e agen s o less
p oduc i e ones. Jo ano ic & MacDonald (1994) del ed in o inno a ion and di usion wi hin a
compe i i e indus y, explo ing how i m-le el incen i es we e in luenced by he dis ibu ion o
echnologies among hei compe i o s. Ko um (1997) in oduced he concep o a echnology
on ie o desc ibe he knowledge s a e wi hin a socie y. Lucas J (2009, 2015) de eloped
models whe e his on ie e ol ed h ough in e ac ions among agen s, leading o he ans e o
knowledge. Lucas J & Moll (2014) expanded on hese models, allowing agen s o alloca e hei
ime be ween p oduc ion and acqui ing knowledge. Pe la & Tone i (2014) show ha g ow h
is gene a ed as a posi i e ex e nali y om isk- aking by less p oduc i e i ms imi a ing mo e
p oduc i e i ms, leading o echnology di usion and sus ained g ow h. Benhabib e al. (2014)
de elop amewo ks in which agen s op imally choose he amoun o in es in imp o ing g ow h
h ough inno a ion as well as h ough echnology di usion. Benhabib e al. (2021) ex end he
analysis u he and show how inno a ion and echnology di usion in e ac o endogenously
de e mine he shape o he p oduc i i y dis ibu ion and gene a e agg ega e g ow h. S okey
(2021) look a echnology-skill complemen a i y and explain how he in e play be ween skill
acquisi ion and echnology d i es economic g ow h in a s ylized economy.
The empi ical li e a u e on echnology di usion employs a ious me hodologies, examin-
ing geog aphic di usion wi hin a coun y, di usion among i ms wi hin an indus y, and c oss-
coun y di usion espec i ely. G iliches (1957) is an ea ly s udy on hyb id co n adop ion in
U.S. ha inds hyb id adop ion ac oss geog aphic egions is well explained by hei ela i e
p o i abili y ac oss egions. Fos e & Rosenzweig (1996) and Fos e & Rosenzweig (2010)
looks a in oduc ion o high-yielding a ie ies in India and ac oss mul iple coun ies espec-
i ely and ind ha schooling played a c ucial ole in explaining a ia ions. Along simila
lines, Manuelli & Seshad i (2014) s udied he g adual di usion o ac o s in U.S. ag icul u e.
Comin & Hobijn (2004) explo e he c oss-coun y di usion o speci ic echnologies o e wo
cen u ies, analyzing 23 indus ial economies and Comin & Hobijn (2010) expand hei s udy o
166 coun ies encompassing he en i e spec um o income le els.In he o me in es iga ion,
hey iden i y human capi al as a c ucial ac o in luencing he speed o adop ion. Building upon
his, Comin & Mes ie i (2018) del e in o adop ion lags and he in ensi y o echnology use. The
indings sugges ha a ia ions in adop ion lags played a signi ican ole in he c oss-coun y
income dispa i ies du ing he nine een h cen u y, while dis inc ions in in ensi y o use u he
con ibu ed o di e gence in he wen ie h cen u y.
As i is e iden om he li e a u e, human capi al plays a pi o al ole in acili a ing ech-
nology di usion. In an in luen ial empi ical s udy, K uege & Lindahl (2001) obse e ha
human capi al enhances g ow h only o he coun ies wi h he lowes le el o educa ion. Tha
is, educa ion ma e s only o ca ching up bu no o inno a ion a he on ie . In an a emp
179
Re iew o Economic Analysis 16 (2024) 175–220
o esol e his K uege -Lindahl puzzle, Vandenbussche e al. (2006) a gue ha human capi al
does no a ec inno a ion and imi a ion uni o mly. They de elop an endogenous g ow h model,
whe e inno a ion makes ela i ely mo e in ensi e use o skilled labo and imi a i e ac i i ies
make ela i ely in ensi e use o unskilled labo and show ha skilled labo has a highe g ow h-
enhancing e ec close o he echnological on ie . Using a panel da ase co e ing 19 OECD
coun ies o pe iod 1960-2000, hey ind e idence in suppo o hei heo e ical indings.5Ang
e al. (2011) empi ically in es iga e he p edic ions o he heo e ical model o Vandenbussche
e al. (2006) o de eloping coun ies. Thei esul s show ha he g ow h enhancing e ec s o
e ia y educa ion a ainmen o skilled human capi al inc ease when high and medium income
coun ies mo e close o he echnology on ie . Human capi al is no con ibu ing o g ow h
in low income coun ies, sugges ing ha hey nei he inno a e no imi a e.
Thus, i can be concluded om he ex an li e a u e ha echnology ( ia he win channels
o inno a ion and imi a ion) is a pi o al d i e o economic g ow h and human capi al plays a
undamen al ole in echnology adop ion and inno a ion in he p ocess o echnical p og ess.
The endogenous e ili y and educa ion decisions a he household le el can in luence human
capi al accumula ion a he agg ega e le el, which in u n, can a ec he economic g ow h ia
i s impac on echnical p og ess. Howe e , impac on economic g ow h can di e depending
upon whe he inno a ion o echnology adop ion is d i ing echnical p og ess.
We y o in eg a e hese di e en s ands o li e a u e by building an o e lapping gene a-
ions e sion o an R&D-based g ow h model ´
a la Diamond (1965) and Jones (1995) o examine
he impac o a child quan i y-quali y ade-o igge ed by imp o emen in quali y o schooling
on echnical p og ess and economic g ow h. We ocus on cha ac e izing wo cases o high and
low quali y o schooling o an economy and examine he co esponding d i e s o economic
g ow h - a e o human capi al accumula ion and popula ion g ow h in hese wo cases unde
wo dis inc egimes o echnological imp o emen - inno a ion and imi a ion. Unde he inno-
a ion egime, echnological imp o emen s occu by inno a ing upon local echnology on ie ,
whe eas echnological p og ess occu s by imi a ing exis ing o eign echnologies unde imi a-
ion egime. We de i e he condi ion unde which i will be ad an ageous o an economy o
inno a e on local echnology on ie . In his espec as well, his wo k is an imp o emen o e
exis ing esea ch in his a ea.
We ind ha he quali y o schooling igge s a child quan i y-quali y ade-o a he mic o
5They show ha human capi al a ec s he a e o echnical p og ess ia a le el e ec and a composi ion
e ec . Holding he composi ion o human capi al cons an , an inc ease in he s ock o human capi al
is always g ow h-enhancing. Howe e , holding i s le el cons an , he g ow h-enhancing p ope ies o
human capi al depend on bo h i s composi ion and he dis ance o he echnological on ie . The g ow h-
enhancing impac o skilled labo inc eases wi h a coun y’s p oximi y o he wo ld echnology on ie ,
whe e p oximi y is measu ed by he a io be ween he o al ac o p oduc i i y in he coun y and he
co esponding a iable o a on ie economy such as US. Con e sely, he g ow h-enhancing impac o
unskilled labo dec eases wi h he p oximi y o he wo ld echnology on ie .
180
SAINI, MEHRA Quali y o Schooling, Fe ili y and Economic G ow h
le el when quali y o schooling su passes an endogenously de e mined h eshold unde bo h
he echnology egimes. When quali y o schooling su passes he h eshold, pa en s in es in
educa ion o hei child en and bea ewe numbe o child en. This mic o-le el ade-o has
wo opposing e ec s on agg ega e human capi al accumula ion a he mac o le el. A highe
in es men in he educa ion o a child s imula es he accumula ion o human capi al, which
os e s echnical p og ess, bu he simul aneous decline in e ili y a e educes he o al ac o
p oduc i i y g ow h and economic g ow h by con ac ing he pool o a ailable esea che s. The
i s e ec p e ails o e la e only when quali y o schooling is highe han he h eshold. When
quali y o schooling is less han he h eshold, pa en s do no educa e hei child en and ocus on
maximizing e ili y. In such a scena io, economic g ow h is solely d i en by popula ion g ow h
unde bo h inno a ion and imi a ion egimes.Dis ance om echnology on ie is ano he d i e
o g ow h unde imi a ion egime.
Ou esul s show ha i is ad an ageous o an economy o inno a e upon he local ech-
nology on ie ins ead o imi a ing om he wo ld echnology on ie i he a e o human
capi al accumula ion is highe han he g ow h a e o wo ld echnology on ie in he p es-
ence o cons an o diminishing e u ns o R&D sec o . Fu he mo e, a me e su passing o he
h eshold le el o quali y schooling is no su icien enough o an economy o expe ience a
highe economic g ow h a e as compa ed o an economy wi h quali y o schooling lowe han
he h eshold le el. Unde he wo echnology egimes, quali y o schooling should be high
enough such ha i leads o high enough in es men s in educa ion o child en, en ailing ha he
g ow h-s imula ing e ec domina es he g ow h-impeding e ec o quali y o schooling.
The es o he pape is o ganized as ollows. Sec ion 2 discusses he basic s uc u e o he
model. Sec ions 3 and 4 discuss he ma ke clea ing condi ion and he key analy ical esul s o
a decen alized economy, which p o ide he key p oposi ions o his s udy. Sec ion 5 concludes.
2 The Model and Equilib ium Solu ions
2.1 The Economic En i onmen
We conside a model economy popula ed by o e lapping gene a ions o people, each o whom
li es o wo pe iods: adul hood and old age. Time is disc e e and spans om 0 o ∞. Du -
ing childhood, which is no modeled explici ly, indi iduals a e ea ed and educa ed by hei
pa en s. All he decisions a e made a he beginning o adul hood. Adul s a e iden ical in
all aspec s.They inelas ically supply hei skills in he labo ma ke . Adul s ca e abou he
consump ion o a homogeneous inal good, numbe and human capi al le el o hei child en.
Du ing old age, indi iduals consume hei sa ings plus in e es ea ned on hese. Abs ac ing
om gende di e ences, each household has a single pa en . Fo a oiding he indi isibili y
p oblem, we assume ha child en a e bo ne in con inuous numbe . All indi iduals su i e up
o adul hood. The educa ion o cu en pe iod’s child en ( hough childhood is no modeled
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Re iew o Economic Analysis 16 (2024) 175–220
explici ly) de e mines human capi al endowmen o nex pe iod’s adul gene a ion. Akin o
Cas ell´
o-Climen & Hidalgo-Cab illana (2012), human capi al accumula ion unc ion depends
on an exogenously gi en quali y o educa ion, pa en al in es men in educa ion and human cap-
i al o pa en . Pa en al in es men in educa ion is a ac ion o income spen on educa ion o
each child.
The p oduc ion s uc u e o he economy closely ollows Rome (1990) and Jones (1995).
The economy consis s o h ee sec o s: inal goods, in e media e goods and R&D. Pe ec com-
pe i ion p e ails in he inal goods and R&D sec o s whe eas monopoly p e ails in he in e me-
dia e goods sec o . The in e media e goods a e ho izon ally di e en ia ed, each p oduced wi h
he help o a bluep in design de eloped in he R&D sec o . The en i e ange o in e media e
goods cons i u es as an inpu in he inal goods sec o .
2.2 Indi iduals
Indi iduals de i e u ili y om c1, , hei own consump ion o he inal good du ing adul hood;
c2, +1, hei own consump ion du ing old age; n , numbe o child en bo ne and h +1, human
capi al pe child. Pa en s’ mo i a ion o in es in human capi al o child en by spending on
child en’s educa ion is d i en by a ‘wa m glow’ o gi ing (And eoni 1989) o p e e ence o
ha ing ‘highe -quali y’ child en (Becke 1960). The li e ime expec ed u ili y o indi iduals in
gene a ion is gi en by:
u =log c1, +β1log c2, +1+β2log(h +1n ),(1)
whe e posi i e weigh s β1and β2measu e he weigh s on u u e consump ion, c2, +1, child quan-
i y, n and quali y, h +1 ela i e o cu en consump ion, c , in he u ili y unc ion. Al e na i ely,
ollowing De la C oix & Doepke (2004), β2can be in e p e ed as an “al uism” ac o .
An indi idual’s embodied human capi al is deno ed by h and he wage pe uni o human
capi al is w . Young adul s spend hei income on cu en consump ion, sa ings o old-age
consump ion and child’s educa ion expendi u e. Rea ing a child necessa ily akes ac ion τ∈
(0,1) o an adul ’s ime, which is gi en exogenously. Acco dingly, he budge cons ain s o
he adul s and old indi iduals a e gi en by:
w h (1 −τn )=c1, +s +e (w h )n ; (2)
c2, +1=(1 + +1)s ,(3)
whe e e is he ac ion o income pe child spen on educa ion, s is sa ings and +1is in e es
a e. Non-nega i i y cons ain s apply o all he a iables.
The human capi al o child en, h +1, depends on human capi al o pa en s, h , pa en al in-
es men in educa ion pe child, e , and quali y o educa ion sys em, θ, which is exogenously
gi en.
h +1=(µ+θe )h .(4)
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SAINI, MEHRA Quali y o Schooling, Fe ili y and Economic G ow h
compe i ion among mul iple R&D i ms o become he i s o succeed in c ea ing and pa en ing
a new bluep in and/o p ocess. 7
I all o he ac o s a e held cons an , an inc ease in R&D ac i i y will induce inc eased du-
plica ion o esea ch e o leading o s epping-on- oes e ec . Addi ionally, R&D p oduc i i y
depends on a ca ch-up e m, ¯
A
A
unde he imi a ion egime. Akin o Nelson & Phelps (1966),
¯
A
A
is he ca ch-up e m, which signi ies he ac ha g ea e he echnological gap be ween
leade and ollowe economy, highe he po en ial o he ollowe economy o ca ch up h ough
imi a ion o exis ing echnologies. Since all R&D i ms end up in a symme ic equilib ium, he
p oduc ion unc ion o echnology unde inno a ion egime a he agg ega e le el educes o:
A +1−A =¯
δ(HA
)λAφ
.(25)
Unde he imi a ion egime, he agg ega e p oduc ion unc ion educes o:
A +1−A =¯
δ(HA
)λAφ
"¯
A
A #.(26)
The ca ch-up e ec is speci ic o he imi a ion egime only. Each i m in he R&D sec o maxi-
mizes p o i s, gi en by:
π ,A=pA
(A +1−A )−wAHA
,
whe e pA
is p ice o a bluep in , A +1−A a e numbe o new bluep in s disco e ed and wAis
he wage a e. Unde bo h imi a ion and inno a ion egimes, using eq. (23), he p o i unc ion
o R&D i m can be exp essed as:
π ,A=pA
δ (HA
)−wAHA
.(27)
In case o bo h he echnology egimes, maximiza ion o p o i s would lead o he ollowing
op imali y condi ion:
wA=pA
δ .(28)
Subs i u ing o δ om eq. (24), he wage a e unde inno a ion egime is now gi en by:
win
A=pA
¯
δ(HA
)λ−1Aφ
=
pA
¯
δ(HA
)λAφ
HA
,(29)
Simila ly, wage a e unde imi a ion egime is exp essed as:
wim
A=
pA
¯
δ(HA
)λAφ
¯
A
A
HA
,(30)
7The e m, (HA
)λ−1in eq (24) cap u es he s epping-on-e ec . The e exis s diminishing e u ns o R&D
e o as 0 <λ<1. The s anding-on-shoulde s e ec is cap u ed by Aφ
in eq. (24).
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Re iew o Economic Analysis 16 (2024) 175–220
whe e supe sc ip s ’in’ and ’im’ e e o a iables unde he inno a ion and imi a ion egimes.
Using eqs. (25) and (26), he wage a e unde bo h he echnology egimes simpli ies o:
wA="pA
(A +1−A )
HA
#.(31)
whe e wages o esea che s a e inc easing in he p ice o bluep in (p ice o pa en ) and numbe
o bluep in s disco e ed.
We, nex , conside he esea ch a bi age condi ion. Sha eholde s o in e media e i ms
ace wo op ions. Fi s , hey can make an in es men o pA
in a isk- ee asse and ea n he
ma ke a e o in e es , which is exogenously gi en. Al e na i ely, hey can pu chase sha es
o in e media e i ms in pe iod and ecei e π +1as di idend in pe iod +1 and can sell hese
sha es o nex gene a ion o ea n capi al gain/loss esul ing om he change in p ice o pa en s
o e ime. In equilib ium, he a e o e u n om bo h hese in es men s should be he same.
Tha is,
+1pA
=π +1+(pA
+1−pA
).
The le hand side o his equa ion is he in e es ea ned om in es ing in a isk- ee asse . The
igh hand side is he sum o he di idend ea ned and he capi al gain/loss.
3 Ma ke clea ing condi ion and Dynamics o he Sys em
Human capi al is used o p oduc ion o inal good, in e media e inpu s and R&D ac i i ies.
Now, in equilib ium, he demand o human capi al in R&D sec o , in e media e inpu s sec o
and inal good sec o should add up o:
HA
+HY
+HI
=H .(32)
This gi es he labo ma ke clea ing condi ion.
Nex , we conside he equilib ium condi ion o inal goods ma ke . Final good is used
o consump ion and o incu ing educa ion expendi u e on child en. The inal goods ma ke
clea ing condi ion is gi en by:
Y =c1, N +c2, N −1+E (33)
whe e E =e w h n N is he o al educa ion expendi u e incu ed on nex gene a ion by he
p esen gene a ion.
Fu he mo e, he agg ega e sa ings o young adul s in pe iod mus be used o ne in es -
men in R&D ac i i ies i.e.
pA
(A +1−A )=s N −pA
A
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SAINI, MEHRA Quali y o Schooling, Fe ili y and Economic G ow h
The e m on le -hand side is he ne in es men in R&D ac i i ies and he i s e m on igh -
hand side is agg ega e sa ings o young adul s and second e m is he dissa ings o he old and
he wo e ms oge he on he igh -hand side ep esen he ne sa ings. Elimina ing pA
A om
bo h he sides yields he ollowing asse ma ke clea ing condi ion8:
pA
A +1=s N (34)
In equilib ium, wages in inal good, in e media es and R&D sec o s should equalize, ha is,
wY=wA=wI. Le ha equalized wage a e be w . Subs i u ing o wYand wI om eqs. (14)
and (22), we ge ha :
HI
HY
=α2
1−α(35)
Now, HY
+HI
=H −HA
.Subs i u ing o HY
om eq.(35), we de i e he human capi al s ock
engaged in in e media es sec o as:
HI
=α2
1−α+α2[H −HA
] (36)
Nex , we subs i u e o s om eq.(6) and pA
om eq. (28) in he asse ma ke clea ing
condi ion and use he ac ha wY=wA=wI=w a equilibi um and ha he size o he
wo k o ce o supply o labo is gi en by L =(1 −τn )N o ge 9:
A +1=ζδ H (37)
whe e ζ=β1
1+β1+β2(1−τn ). Now, we ge he ollowing exp ession o A +1unde he wo echnol-
ogy egimes a e subs i u ing o δ om eq. (24):
Inno a ion egime : A +1=ζ¯
δ(HA
)λAφ
H
HA
; (38)
Imi a ion egime : A +1=ζ¯
δ(HA
)λAφ
"¯
A
A #H
HA
.
which a e subs i u ing om eqs. (25) and (26), simpli ies o a single exp ession o bo h he
egimes:
HA
H
A +1=ζ(A +1−A )
8De ailed de i a ion o asse ma ke clea ing condi ion is p o ided in Appendix B
9We can ea n as a cons an as we know om eq. (8) ha e ili y a e is cons an o e ime
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Re iew o Economic Analysis 16 (2024) 175–220
We ge he employmen sha e in R&D sec o o bo h echnology egimes a e di iding bo h
sides by A as
HA
H
=ζgA,
1+gA,
(39)
Acco dingly, he equilib ium wage a e in he h ee sec o s is gi en by:
wA=wY=wI=(1 −α)Y
HY
.(40)
We, nex , examine he dynamic p ope ies o ou s ylized economy. Fi s , we discuss he
dynamics o physical ac o s o p oduc ion. The agg ega e popula ion, N , g ows a he e ili y
a e, n as ollows:
N +1=n N ,(41)
whe e n is cons an and endogenously gi en by eq. (8).
Taking child ea ing ime in o accoun , he size o he wo k o ce o supply o labo is gi en
by L =(1 −τn )N . Since child ea ing cos s a e cons an o e ime, and om eq. (8) we know
ha e ili y a e is also cons an o e ime, he wo k o ce g ows a he e ili y a e as:
L +1=n L .(42)
Nex , we discuss he dynamics o agg ega e human capi al, H ≡h L . The dynamics o pe
capi a human capi al a e gi en by eq. (9). Using eqs. (9) and (42), he equa ion o agg ega e
human capi al accumula ion can be w i en as:
H +1
H
=
µn ,i θ≤µ
τ ;
(τθ −µ)
(1 −)
n ,o he wise.
(43)
The dynamics o o al ac o p oduc i i y a e gi en by eq.(38) as:
Inno a ion egime:
A +1=ζ¯
δ(HA
)λAφ
H
HA
.(44)
Imi a ion egime:
A +1=ζ¯
δ(HA
)λAφ
"¯
A
A #H
HA
.(45)
Using eqs.(19),(35) and (36), he dynamics o agg ega e ou pu can be w i en as:
Y =(1 −α)1−αα2
α2(1−α)(1 −α+α2)A1−α
"1−HA
H #H (46)
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SAINI, MEHRA Quali y o Schooling, Fe ili y and Economic G ow h
The sys em o equa ions,(eqs. (41)-(46)) ully desc ibes he equilib ium dynamics o ou
model economy o all he plausible cases. The nex sec ion cha ac e izes he balanced g ow h
pa hs o an economy o wo cases - a) when he economy’s quali y o educa ion sys em is
su icien ly high, ha is, θ > µ
τ , and b) when quali y o schooling is less han he h eshold, o ,
θ≤µ
τ .
4 Balanced G ow h Pa h and S eady-S a e P ope ies o he S ylized Econ-
omy
4.1 Cha ac e izing he Balanced G ow h Pa h
We deno e he g ow h a e o xalong he balanced g ow h pa h by gx, ha is, by omi ing he
ime index o b e i y. 10
We, i s , conside he g ow h a e o human capi al accumula ion. The p opo ion o wo k-
o ce employed in inal goods, in e media es and R&D sec o s, (gi en by eqs. (35),(36), (39)
espec i ely) a e cons an as gA, is cons an along he balanced g ow h pa h. The e o e, along
he balanced g ow h pa h, we ha e:
HY
+1
HY
=HA
+1
HA
=HI
+1
HI
=H +1
H
=(1 +gH).(47)
Thus, he human capi al s ocks in he inal good, in e media es and he R&D sec o s g ow a
he a e o o al human capi al accumula ion along he balanced g ow h pa h.
Nex , we conside he g ow h a e o o al ac o p oduc i i y. Unde inno a ion egime, we
obse e om eq. (44) ha :
(1 +gA, )=ζ¯
δH (HA
)λ−1
A1−φ
;
Since along balanced g ow h pa h, he le hand side is cons an , he e o e, igh hand side mus
also be cons an and his holds ue when
(1 +gA)=[(1 +gh)n]λ
1−φ.(48)
The igh hand side ollows om he de ini ion o agg ega e human capi al H =h L and om
eq. (47). Fu he , we obse e om eq. (45) ha he a e o echnical p og ess unde he imi a ion
egime can be w i en as:
(1 +gA, )=ζ¯
δH ¯
A (HA
)λ−1
A2−φ
.
10A balanced g ow h pa h is a long un equilib ium o he economy, also de ined as he s eady s a e, along
which g ow h a e o a iables is ei he ze o o cons an o e ime. Fo any a iable x, he g ow h a e is
deno ed by gx, =(x +1−x )/x , and i s a e o change by ˜gx, =(gx, +1−gx, )/gx, . The balanced g ow h,
hus, equi es ˜gx, =0.
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Re iew o Economic Analysis 16 (2024) 175–220
Simila ly, using he de ini ion o he balanced g ow h pa h, we de i e he long- un a e o ech-
nological p og ess unde imi a ion egime as:
(1 +gA)=(1 +gH)λ
2−φ(1 +g¯
A)1
2−φ=[(1 +gh)n]λ
2−φ(1 +g¯
A)1
2−φ.(49)
Thus, in ui i ely, unde bo h imi a ion and inno a ion egimes, echnological p og ess is d i en
by g ow h in agg ega e human capi al. Human capi al accumula ion imp o es p oduc i i y o
esea che s, which os e s echnological p og ess. Besides agg ega e human capi al, he g ow h
o wo ld echnology on ie is also a d i e o g ow h, bu only in case o imi a ion egime.
The ollowe economy akes ad an age o exis ing echnologies h ough echnology adop ion.
The e o e, as he wo ld echnology on ie g ows, i enhances he po en ial o he ollowe
coun y o ca ch up h ough imi a ion.
Nex , we asce ain he g ow h a es o agg ega e ou pu and pe capi a consump ion along
he balanced g ow h pa h. F om eq. (46) we obse e ha :
(1 +gY)=(1 +gA)1−α(1 +gH).(50)
Along he balanced g ow h pa h, g ow h a e o agg ega e ou pu depends on g ow h a e o
human capi al and o al ac o p oduc i i y.
F om eqs. (48), (49) and (50), we de i e he balanced g ow h pa h o he s ylized economy
unde he wo echnology egimes as:
Inno a ion egime:
(1 +gY)=[(1 +gh)n]1−φ+λ(1−α)
1−φ; (51)
Imi a ion egime:
(1 +gY)=[(1 +gh)n]2−φ+λ(1−α)
2−φ(1 +g¯
A)1
2−φ,(52)
whe e
[(1 +gh)n]=(1 +gH)=
β2θ
(1 +β1+β2)µ1−,i θ < µ
τ ;
β2µ
(1 +β1+β2)τ,i θ=µ
τ ;
β2θ(1 −)1−
(1 +β1+β2)(τθ −µ)1−,o he wise.
This ollows a e subs i u ing he alue o n om eq. (8) in o eq. (43). Thus, along he
s eady s a e, he g ow h a es o agg ega e ou pu a e de e mined by he a e o human capi al
accumula ion unde bo h he egimes o echnical imp o emen .
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SAINI, MEHRA Quali y o Schooling, Fe ili y and Economic G ow h
Fu he mo e, we obse e om he consume ’s op imiza ion exe cise ha he Eule equa ion
has he ollowing s anda d o m:
c +1
c
=β1(1 + +1).(53)
The igh hand side ollows om subs i u ing alues o c and s om eqs. (5) and (6) in eq. (3).
Along he balanced g ow h pa h, pe capi a consump ion g ows a a cons an a e unde bo h he
echnology egimes as is exogenously gi en.
We nex compa e he economic g ow h a es unde he wo echnology egimes. We deno e
he economic g ow h a e unde inno a ion egime by ginn
Yand unde imi a ion egime by gimi
Y.
The inno a ion economy will g ow a a highe a e i
ginn
Y>gimi
Y.
Subs i u ing o ginn
Yand gimi
Y om eqs. (51) and (52), we ge :
(1 +gH)1−φ+λ(1−α)
1−φ>(1 +gH)2−φ+λ(1−α)
2−φ(1 +g¯
A)1
2−φ
which on simpli ica ion yields:11
(1 +gH)λ(1−α)
1−φ>(1 +g¯
A).
Thus, we ha e,
P oposi ion 4.1 (i) Unde inno a ion egime, o al ac o p oduc i i y, agg ega e ou pu
and pe capi a consump ion g ow a a cons an a e along he balanced g ow h pa h
cha ac e ized by eqs. (48), (51) and (53).
(ii) Unde imi a ion egime, o al ac o p oduc i i y, agg ega e ou pu and pe capi a con-
sump ion g ow a a cons an a e along he balanced g ow h pa h cha ac e ized by eqs.
(49), (52) and (53).
(iii) Along he balanced g ow h pa h, he economy unde inno a ion egime exhibi s a highe
economic g ow h a e as compa ed o imi a ion egime i
gH>g¯
A, λ +φ≤1
In ui i ely, unde bo h he echnology egimes, he sel -sus aining endogenous g ow h pa h is
d i en by human capi al accumula ion when quali y o schooling exceeds he h eshold, θ > µ
τ .
In his case, a he mic o le el, pa en s decide o ha e ewe numbe o child en and in es mo e
11We ge he same condi ion i we compa e pe capi a economic g ow h a es unde he wo echnology
egimes.
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Re iew o Economic Analysis 16 (2024) 175–220
in hei educa ion. This ollows om Lemma 1. A he mac o le el, his ade-o aises he a e
o human capi al accumula ion, which encou ages as e echnological p og ess and, he e o e,
economic g ow h. Besides human capi al, g ow h o wo ld echnology on ie is an addi ional
d i e o g ow h unde he imi a ion egime ia he ca ch-up e ec .
Al e na i ely, when quali y o schooling is less han he h eshold, θ≤µ
τ , pa en s do no
in es in he educa ion o child en and ins ead, maximize e ili y. In his case, he balanced
g ow h pa h o he economy is d i en only by popula ion g ow h, which in u n, is de e mined
by he e ili y a e. This esul is simila o he indings o neo-classical models o Solow-
Swan and Cass-Koopmans-Ramsey. The only di e ence is ha popula ion g ow h and echnical
p og ess a e endogenously de e mined in ou model s uc u e.
Thus, he d i e s o economic g ow h di e depending upon he le el o quali y o schooling.
When quali y o schooling su passes he h eshold le el, economic g ow h is d i en by human
capi al accumula ion whe eas i is d i en by popula ion g ow h when quali y o schooling is
less han he h eshold. In a simila con ex , while Ecks ein & Zilcha (1994) do no speci ically
model he quali y o schooling in hei OLG amewo k, hey show he e ec o compulso y
educa ion on economic g ow h and dis ibu ion. Thei analysis e eals ha compulso y school-
ing inanced by p opo ional axes on income inc eases economic g ow h, and makes income
dis ibu ion mo e equi able in he long- un. Simila ly, Tamu a (2001) explici ly model qual-
i y o schooling in hei model o human capi al accumula ion bu does no conside echnical
p og ess. He shows ha quali y o educa ion os e s human capi al o ma ion and, he e o e,
economic g ow h.
Also, i is ad an ageous o an economy o inno a e upon he local echnology on ie in-
s ead o imi a ing om he wo ld echnology on ie i he a e o human capi al accumula ion
is highe han he g ow h a e o wo ld echnology on ie in he p esence o cons an o dimin-
ishing e u ns o R&D sec o (i.e. λ+φ≤1). This implies ha an economy has he po en ial
o become he new wo ld echnology on ie i quali y o schooling should be su icien ly high
such ha i leads o high enough in es men in he educa ion o child en so ha human capi al
accumula ion eme ges as a d i e o economic g ow h.
We nex u n o cha ac e izing he e olu ion o wage a e along he s eady s a e. I is known
om eq. (40) ha wage a e can be exp essed as:
wA=wY=wI=(1 −α)Y
HY
.
Fu he , om eq. (51), unde he inno a ion egime:
(1 +gY)=[(1 +gh)n]1−φ+λ(1−α)
1−φ,and
om eq. (52), unde imi a ion egime, we ha e:
(1 +gY)=[(1 +gh)n]2−φ+λ(1−α)
2−φ(1 +g¯
A)1
2−φ.
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Eqs. (40), (47), (51) and (52) oge he imply ha , along balanced g ow h pa h, wage a e unde
inno a ion egime g ows as ollows:
(1 +gw)=[(1 +gh)n]λ(1−α)
1−φ; (54)
And he wage a e unde imi a ion egime g ows a he a e:
(1 +gw)=[(1 +gh)n]λ(1−α)
2−φ(1 +g¯
A)1
2−φ,(55)
whe e
[(1 +gh)n]=(1 +gH)=
β2θ
(1 +β1+β2)µ1−,i θ < µ
τ ;
β2µ
(1 +β1+β2)τ,i θ=µ
τ ;
β2θ(1 −)1−
(1 +β1+β2)(τθ −µ)1−,o he wise .
In ui i ely, he wage a e depends on agg ega e ou pu and human capi al as exp essed by eq.
(40). I is known om eq. (50) ha g ow h a e o agg ega e ou pu o GDP depends on g ow h
a e o human capi al and o al ac o p oduc i i y along he balanced g ow h pa h. The e o e,
he wage a e g ows a he a e o echnical p og ess along he balanced g ow h pa h unde bo h
he egimes o echnological imp o emen .
Nex , we compa e he wo cases o high and low quali y o schooling and de e mine he
condi ion unde which he economy exhibi s highe g ow h a e o pe capi a income unde he
case o highe quali y o schooling, θ > µ
τ , as compa ed o he case o low quali y o schooling,
θ≤µ
τ , unde he wo echnology egimes.
4.2 Compa a i e Analysis o Pe Capi a Economic G ow h Ra es o Economies wi h
Highe and Lowe Quali y o Schooling
We assume ha when θ > µ
τ , quali y o schooling is deno ed by θh o ha pa icula economy
whe eas quali y o schooling is deno ed by θl o an economy wi h quali y o schooling less han
he h eshold, θ≤µ
τ . De i a ions p o ided in Appendix C show ha an economy wi h highe
quali y o schooling, θh, will expe ience a highe pe capi a income g ow h a e as compa ed
o an economy wi h a lowe quali y o schooling, θl, i he ollowing condi ions hold unde he
indi idual echnology egimes.
Inno a ion egime:
θh> θl"(τθh−µ)
µ(1 −)#λ(1−α)−(1−φ+λ(1−α))
λ(1−α)
; (56)
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Imi a ion egime:
θh> θl"(τθh−µ)
µ(1 −)#λ(1−α)−(2−φ+λ(1−α))
λ(1−α)
.(57)
Thus, we ha e,
P oposi ion 4.2 An economy wi h highe quali y o schooling, θh>µ
τ , will expe ience a
highe pe capi a income g ow h a e as compa ed o an economy wi h lowe quali y o school-
ing, θl≤µ
τ i he quali y o schooling, θh, is su icien ly high cap u ed by he ollowing pa a-
me ic es ic ion:
Inno a ion egime: θh> θl"(τθh−µ)
µ(1 −)#λ(1−α)−(1−φ+λ(1−α))
λ(1−α)
> θl; (58)
Imi a ion egime: θh> θl"(τθh−µ)
µ(1 −)#λ(1−α)−(2−φ+λ(1−α))
λ(1−α)
> θl.
In ui i ely, a me e su passing o he h eshold le el o quali y schooling is no su icien enough
o an economy o expe ience a highe g ow h a e o pe capi a ou pu as compa ed o an
economy wi h quali y o schooling lowe han he h eshold le el. Unde he wo echnology
egimes, quali y o schooling should be su icien ly high as indica ed by he eq. (58) such
ha i leads o high enough in es men in he educa ion o child en, en ailing ha he g ow h-
s imula ing e ec o e powe s he g ow h-impeding e ec o quali y o schooling.
O he wise, he possibili y ha an economy wi h lowe quali y o schooling expe iences a
highe pe capi a economic g ow h a e han an economy wi h highe quali y o schooling is no
uled ou , especially o la ge enough alues o child ea ing cos s, τo o small enough alue
o in e -gene a ional human capi al spillo e s, µand e u ns o educa ion, espec i ely. This
ollows di ec ly om eq. (58). I can be obse ed ha he exp ession, (τθh−µ)
µ(1 −)is inc easing
in τ. In his pa icula case, when he alue o τis su icien ly high, popula ion g ow h a e may
u n ou o be a mo e e ec i e d i e o economic g ow h as he h eshold alue o quali y o
schooling o highe economic g ow h is so high ha an economy may ind no in es ing a all
in educa ion o he u u e gene a ion as a ela i ely mo e bene icial ou come. Simila ly, i can
be shown ha :
∂
∂µ
(τθh−µ)
µ=−τθh
µ2<0;
∂
∂
1−=−1
(1 −)2<0.
These imply ha he h eshold alue o quali y o schooling o highe pe capi a economic
g ow h is dec easing in he alue o µand espec i ely. Thus, his h eshold alue o quali y
o schooling can be high enough o su icien ly small µand such ha popula ion g ow h a e
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is dec easing in he alue o . This implies ha , ce e is pa ibus, his c i ical h eshold alue
dec eases as e u ns o schooling inc ease when quali y o schooling exceeds he h eshold.
The e o e, ce e is pa ibus, pa en s educa e hei child en and bea lesse numbe o child en in
esponse o an inc ease in e u ns o educa ion. Simila o he impac o quali y o schooling,
his mic o le el ade-o gene a es a g ow h-s imula ing e ec and a g ow h-impeding e ec a
he mac o le el.
∂gH
∂ =(1 +gh)n
"1
(1 −)+log(τθ −µ)
1−#
| {z }
G ow h-s imula ing e ec
−1
1−
|{z}
G ow h-impeding e ec
.
The g ow h-s imula ing e ec o e powe s he g ow h-impeding e ec o a change in e u ns o
educa ion when quali y o schooling exceeds he h eshold as shown by eq. (70). Resul an ly,
an inc ease in e u ns o educa ion yields highe a e o echnical p og ess unde bo h inno a ion
and imi a ion egimes.
Also, he g ow h a e o pe capi a income ises as e u ns o educa ion inc ease unde bo h
he echnology egimes when quali y o schooling exceeds he h eshold. The in ui i e ex-
planan ion o his e ec is simila as he explanan ion o a ise in g ow h a e o pe capi a
income as quali y o schooling imp o es unde he wo egimes. The economic g ow h a e, gY,
is inc easing in as he g ow h-s imula ing e ec o e powe s he g ow h-impeding e ec o a
change in e u ns o educa ion. Also, i is known om Lemma 2 ha he popula ion g ow h a e
is dec easing in e u ns o educa ion, . The e o e, he g ow h a e o pe capi a income ises as
e u ns o educa ion inc ease.
When quali y o schooling is s ic ly lowe han he h eshold, pa en s make ze o in es men
in educa ion o hei child en and ocus on ha ing mo e child en. Thus, highe popula ion
g ow h d i es economic g ow h in his case. Addi ionally, i can be obse ed om eq. (9) ha
in e -gene a ional human capi al spillo e s become mo e p oduc i e and spu g ow h a e o
pe capi a human capi al as e u ns o educa ion inc ease whe eas when θ=µ
τ , an inc ease
in e u ns o educa ion yield highe a e o echnical p og ess and, he e o e, economic g ow h
unde bo h he egimes due o highe in e -gene a ional human capi al spillo e s as e ili y a e
and he e o e, popula ion g ow h a e does no depend on e u ns o educa ion in his case.
Simila o he e ec o quali y o schooling, i can be obse ed om eqs. (63) and (64)
ha e u ns o educa ion aise popula ion g ow h a e by a lesse p opo ion as compa ed o
he p opo iona e ise in g ow h a e o agg ega e ou pu unde bo h he echnology egimes.
The e o e, g ow h a e o pe capi a income ises as e u ns o educa ion ises.
This comple es he cha ac e iza ion o he balanced g ow h pa h o ou decen alized econ-
omy.
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5 Discussion
This pape o mula es an analy ical amewo k o examine he impac o quali y o schooling
on echnical p og ess and he e o e, economic g ow h o an economy. Since echnical ad ance-
men s can happen h ough inno a ion and echnology adop ion (imi a ion), one can obse e
a ying impac on economic g ow h depending upon whe he inno a ion o echnology adop-
ion is d i ing echnical p og ess. The e o e, we cha ac e ize wo ypes o economies. The i s
is an inno a ion economy whe e echnological imp o emen s occu by inno a ing upon he
local echnology on ie . The second is an imi a ion economy whe e echnological p og ess
occu s by imi a ing exis ing o eign echnologies. We examine how he endogenous e ili y
and educa ion decisions a he household le el ( igge ed by schooling quali y) in luence hu-
man capi al accumula ion a he agg ega e le el, which in u n, a ec he economic g ow h
unde he wo echnology egimes.
We ind ha he quali y o schooling igge s a child quan i y-quali y ade-o a he mic o
le el when quali y o schooling su passes an endogenously de e mined h eshold unde bo h
he echnology egimes. When quali y o schooling su passes he h eshold, pa en s in es in
he educa ion o hei child en and bea lesse numbe o child en. Howe e , pa en s ocus on
maximizing e ili y and do no educa e hei child en when quali y o schooling is less han he
h eshold. This mic o-le el ade-o gene a es wo ypes o e ec s on economic g ow h a he
mac o le el - a g ow h-s imula ing e ec and a g ow h-impeding e ec . Ou esul s show ha
he o me e ec domina es o e la e only when he quali y o schooling is highe han he
h eshold, and he economy is on a sel -sus aining g ow h pa h. Al e na i ely, when he quali y
o schooling is less han he h eshold, pa en s do no educa e hei child en and ocus, ins ead
on maximizing e ili y. Highe e ili y a e leads o highe popula ion g ow h, which p opels
economic g ow h a e unde bo h inno a ion and imi a ion egimes.
Fu he mo e, i is ad an ageous o an economy o inno a e upon he local echnology on-
ie ins ead o imi a ing om he wo ld echnology on ie i he a e o human capi al accu-
mula ion is highe han he g ow h a e o wo ld echnology on ie in he p esence o cons an
o diminishing e u ns o R&D sec o . Also, a me e su passing o he h eshold le el o quali y
schooling is no su icien enough o an economy o expe ience a highe g ow h a e o pe
capi a ou pu as compa ed o an economy wi h quali y o schooling lowe han he h eshold
le el. Unde he wo echnology egimes, quali y o schooling should be high enough such
ha i leads o high enough in es men s in educa ion o child en, en ailing ha he g ow h-
s imula ing e ec domina es he g ow h-impeding e ec o quali y o schooling.
This esea ch can be ex ended in se e al di ec ions in u u e. Fi s , i is assumed ha quali y
o schooling is exogenous in ou analy ical amewo k. One possible ex ension can be en-
dogenizing quali y o schooling. Quali y o schooling can be endogenized by in oducing an
educa ion sec o in which eache -pupil a io and eache quali y de e mine he quali y o educa-
ion sys em o he economy. I will be in e es ing o examine how he dynamics o he economy
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SAINI, MEHRA Quali y o Schooling, Fe ili y and Economic G ow h
change when an addi ional educa ion sec o is in oduced. In oduc ion o educa ion sec o can
lead o compe i ion be ween R&D and educa ion sec o s o hi ing skilled labo , which may in
u n, in luence he g ow h dynamics o he economy. Second, we ha e ocused only on skilled
labo . Unskilled labo can also be in oduced in he p esen heo e ical s uc u e o de e mine
he impac o quali y o schooling on he dis ibu ion o income be ween skilled and unskilled
wo ke s in he long- un. Thi d, he e exis s a possibili y ha human capi al accumula ion can
be in luenced by echnological p og ess as shown by Bucci (2008). This possibili y can be
explo ed in he u u e by including echnological p og ess in he human capi al accumula ion
unc ion. Fou h, we ha e cha ac e ized inno a ion-only and imi a ion-only egimes. Akin o
Vandenbussche e al. (2006) and Basu & Meh a (2014), a di e si ied egime can be in oduced
whe e bo h inno a ion and imi a ion ac i i ies (wi h unskilled and skilled labo o ce) lead o
echnological imp o emen s.
Appendix A Solu ion o Household’s Op imiza ion Exe cise
The u ili y unc ion is desc ibed as ollows:
Maximize
u =log c1, +β1log c2, +1+β2log(h +1n )
subjec o
w h (1 −τn )=c1, +s +e (w h )n
c2, +1=(1 + +1)s
h +1=(µ+θe )h , < 1
A e subs i u ing o c2, +1and h +1, he lag angian o his p oblem is o mula ed as :
L=log c1, +β1log[(1 + +1)s ]+β2log n +β2log(µ+θe )+β2log h
+ψ[w h (1 −τn )−c1, −s −e n (w h )]
The choice a iables a e c1, ,s ,e and n .The i s -o de condi ions a e:
∂L
∂c1,
=0⇔1
c1,
−ψ=0⇔c1, =1
ψ.(A.1)
∂L
∂s
=0⇔β1
s
−ψ=0⇔s =β1
ψ.(A.2)
∂L
∂n
=0⇔β2
n
−ψτw h −ψe w h =0⇔β2
n
=ψ[τ+e ]w h ⇔n =β2
ψ[τ+e ]w h
.(A.3)
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∂L
∂e
=0⇔β2θ
µ+θe
−ψn w h =0⇔n =β2θ
ψ[µ+θe ]w h
.(A.4)
F om eqs. (A.3) and (A.4), he le hand side can be equa ed o yield:
µ+θe =θ[τ+e ]⇔µ−θτ =e θ[−1]
e =µ−θτ
θ(−1) =θτ −µ
θ(1 −)
Hence, we ha e:
e =
0,i θ≤µ
τ ;
τθ −µ
θ(1 −),o he wise.(A.5)
Nex , we know ha he budge cons ain is gi en by:
w h (1 −τn )=c1, +s +e (w h )n .
F om eq. (A.3), e n (w h ) can be exp essed as:
e n (w h )=β2
ψ−τn w h .(A.6)
Subs i u ing om eqs. (A.1), (A.2) and (A.6), he budge cons ain can be exp essed as:
w h −τn w h =1
ψ+β1
ψ+β2
ψ−τn w h
which on simpli ying leads o:
ψ=1+β1+β2
w h
(A.7)
whose subs i u ion in o eqs. (A.1) and (A.2) yields:
c1, =w h
1+β1+β2
;
s =β1w h
1+β1+β2
,
Subs i u ing o e om eq. (A.5) and o ψ om eq. (A.7) in eq. (A.4), yields:
n =
β2θ
(1 +β1+β2)µ,i θ < µ
τ ;
β2
(1 +β1+β2)τ,i θ=µ
τ ;
β2θ(1 −)
(1 +β1+β2)(τθ −µ),o he wise.
This comple es he solu ion o he u ili y maximiza ion exe cise o households.
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SAINI, MEHRA Quali y o Schooling, Fe ili y and Economic G ow h
Appendix B De i a ion o Asse ma ke clea ing condi ion
I is known om eq.(33) ha inal goods ma ke clea ing condi ion is gi en by:
Y =c1, N +c2, N −1+E
We know om na ional accoun ing ha GNP can be calcula ed using he inal use app oach o
he income app oach. Le GNP be deno ed by Z . F om he inal use side, i is known ha Z is
used o consump ion, in es men in R&D ac i i ies and o incu ing educa ion expendi u e on
child en, i.e.,
Z =c1, N +c2, N −1+E +pA
(A +1−A )=Y +pA
(A +1−A ).(B.1)
F om he income side, g oss na ional income (GNI) is gi en by
GNI =wYHY
+wAHA
+wIHI
+A π (B.2)
Subs i u ing om eqs. (14), (20), (22) and (31), i can be obse ed ha
GNI =Y +pA
(A +1−A )=Z
Thus, he alue o GNI is equi alen o alue o GNP. Equa ing eqs.(B.1) and (B.2), we ha e
c1, N +c2, N −1+E +pA
(A +1−A )=wYHY
+wAHA
+wIHI
+A π (B.3)
=w H +A π
whe e he las e m on he igh -hand side is de i ed using eq.(32) and wY=wA=wI=w
a equilibi um. Now, i is known om he household’s budge cons ain ha w h (1 −τn )=
c1, +s +e (w h )n . Mul iplying bo h sides o he household’s budge cons ain by N , we ge
w H =c1, N +s N +E
whe e E =e (w h )n N .Subs i u ing back in eq.(B.3), we deduce
pA
(A +1−A )=s N +A π −c2, N −1(B.4)
I is known om he esea ch a bi age condi ion ha A π =(1 + )pA
−1A −pA
A .Subs i u ing
o A π and using ha c2, N −1=(1 + )s −1N −1, we ge ha
pA
A +1=s N +(1 + )pA
−1A −c2, N −1=s N +(1 + )(pA
−1A −s −1N −1).(B.5)
Since ini ial asse s a e gi en by pA
−1A0−s−1N−1a =0, we ge he ollowing asse ma ke
clea ing condi ion o any pe iod >0,
pA
A +1=s N .
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Appendix C De i a ions o Eqs. (56) and (57)
We de i e he condi ions when an economy wi h high quali y o schooling θ > µ
τ exhibi s a
highe pe capi a ou pu g ow h a e as compa ed o an economy wi h lowe quali y o schooling
θ≤µ
τ . We assume ha when θ > µ
τ , quali y o schooling is deno ed by θh o ha pa icula
economy whe eas quali y o schooling is deno ed by θl o an economy wi h quali y o schooling
less han he h eshold θ≤µ
τ . An economy wi h highe schooling quali y (θh) will g ow a a
highe a e as compa ed o an economy wi h lowe quali y o schooling (θl) when he ollowing
condi ion holds ue unde bo h he echnology egimes:
gy,θh>gy,θl(C.1)
We i s , de i e he condi ion o inno a ion economy. A s eady s a e, g ow h a e o pe capi a
ou pu unde inno a ion egime is gi en by:
gy=(1 +gh)1−φ+λ(1−α)
1−φnλ(1−α)
1−φ−1.
Thus, we ha e
(1 +gh,θh)1−φ+λ(1−α)
1−φ(nθh)λ(1−α)
1−φ>(1 +gh,θl)1−φ+λ(1−α)
1−φ(nθl)λ(1−α)
1−φ,(C.2)
whe e gh,θhand gh,θla e pe capi a human capi al accumula ion a es when θ > µ
τ and θ≤
µ
τ espec i ely and nθhand nθla e he e ili y a es when θ > µ
τ and θ≤µ
τ espec i ely.
Subs i u ing om eqs. (9) and (8) o (1 +gh,θh), (1 +gh,θl), nθhand nθl o ge :
"(τθh−µ)
1−#(1−φ+λ(1−α)) "θh(1 −)
(τθh−µ)#λ(1−α)
> µ(1−φ+λ(1−α)"θl
µ#λ(1−α)
which on simpli ica ion, yields:
θh> θl"(τθh−µ)
µ(1 −)#λ(1−α)−(1−φ+λ(1−α))
λ(1−α)
.(C.3)
Simila ly, we de i e he condi ion o imi a ion economy. Unde imi a ion egime, he g ow h
a e o pe capi a ou pu gi en by:
gy=(1 +g¯
A)1
2−φ(1 +gh)2−φ+λ(1−α)
2−φnλ(1−α)
2−φ−1.
Thus, we ha e
(1 +g¯
A)1
2−φ(1 +gh,θh)2−φ+λ(1−α)
2−φ(nθh)λ(1−α)
2−φ>(1 +g¯
A)1
2−φ(1 +gh,θl)2−φ+λ(1−α)
1−φ(nθl)λ(1−α)
2−φ.
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Subs i u ing om eqs. (9) and (8) o (1 +gh,θh), (1 +gh,θl), nθhand nθl, we de i e:
"(τθh−µ)
1−#(2−φ+λ(1−α)) "θh(1 −)
(τθh−µ)#λ(1−α)
> µ(2−φ+λ(1−α)) "θl
µ#λ(1−α)
,
which simpli ies o:
θh> θl"(τθh−µ)
µ(1 −)#λ(1−α)−(2−φ+λ(1−α))
λ(1−α)
.(C.4)
This comple es de i a ions o eqs. (56) and (57). To p o e ha hese wo condi ions hold ue
unde he wo echnology egimes, we pos ula e ha ,
λ(1 −α)−(1 −φ+λ(1 −α))
λ(1 −α)>1,and λ(1 −α)−(2 −φ+λ(1 −α))
λ(1 −α)>1.
which can be simpli ied o yield he ollowing exp essions:
−(1 −φ+λ(1 −α))
λ(1 −α)>0,and −(2 −φ+λ(1 −α))
λ(1 −α)>0.
This is a con adic ion as φ < 1, λ < 1, α < 1 and < 1. The e o e,
λ(1 −α)−(1 −φ+λ(1 −α))
λ(1 −α)<1,and λ(1 −α)−(2 −φ+λ(1 −α))
λ(1 −α)<1.(C.5)
Fu he , we know ha θ > µ
τ . Mul iplying bo h sides by τand hen, sub ac ing µ om bo h
sides yields
(τθ −µ)
1−> µ,
Since µ≥1, we ha e:
(τθ −µ)
1−>1.(C.6)
Thus, "(τθh−µ)
µ(1 −)#>1. The e o e, eqs. (C.5) and (C.6) oge he imply ha
"(τθh−µ)
µ(1 −)#λ(1−α)−(1−φ+λ(1−α))
λ(1−α)
>1,and "(τθh−µ)
µ(1 −)#λ(1−α)−(2−φ+λ(1−α))
λ(1−α)
>1.(C.7)
Appendix D De i a ions o Eq. (60)
We know ha (1 +gH)=(1 +gh).n.Di e en ia ing bo h he sides w. . θyields:
∂gH
∂θ =(1 +gh)∂n
∂θ +n∂gh
∂θ .(D.1)
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When θ > µ
τ , we know om Lemma 1 ha ∂n
∂θ =−µβ2(1−)
(1+β1+β2)(τθ−µ)2and i is gi en ha (1 +gh)=
(τθ −µ)
(1 −)
om eq (9). Di e en ia ing ghw. . θ, we ge ha :
∂gh
∂θ ="(τθ −)
1−#
.τ
τθ −µ=(1 +gh)τ
τθ −µ.(D.2)
Subs i u ing his in o eq. (D.1), we ge ha :
∂gH
∂θ =(1 +gh)−µβ2(1 −)
(1 +β1+β2)(τθ −µ)2+(1 +gh)τ
τθ −µ∗n,
Subs i u ing o n om eq. (8),
∂gH
∂θ =(1 +gh)"τβ2θ(1 −)
(1 +β1+β2)(τθ −µ)2−µβ2(1 −)
(1 +β1+β2)(τθ −µ)2#
=(1 +gh)[τθ −µ]β2(1 −)
(1 +β1+β2)(τθ −µ)2.
This comple es de i a ion o eq. (60).
Appendix E De i a ions o Eqs. (65), (66), (67) and (68)
The g ow h a e o pe capi a income can be exp essed as:
(1 +gy)=(1 +gY)
n.(E.1)
Unde inno a ion egime, subs i u ing o (1 +gY) om eq. (51) and simpli ying, we ge :
(1 +gy)=(1 +gh)1−φ+λ(1−α)
1−φnλ(1−α)
1−φ.(E.2)
Taking log on bo h sides and di e en ia ing w. . θ, yields,
1
1+gy
∂gy
∂θ =1−φ+λ(1 −α)
(1 +gh)1 −φ
∂gh
∂θ +λ(1 −α)
(1 −φ)n
∂n
∂θ ,(E.3)
When θ > µ
τ , subs i u ing o n om eq. (8), ∂n
∂θ om Lemma 1 and ∂gh
∂θ om eq. (D.2) yields:
∂gy
∂θ =1+gy
1−φ"(1 −φ+λ(1 −α))τ
τθ −µ−µλ(1 −α)
θ(τθ −µ)#.
I can be obse ed ha ∂gy
∂θ >0, i
(1 −φ+λ(1 −α))τ
(τθ −µ)>µλ(1 −α)
θ(τθ −µ)⇔θ > µλ(1 −α)
τ(1 −φ+λ(1 −α)).
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SAINI, MEHRA Quali y o Schooling, Fe ili y and Economic G ow h
This holds ue as θ > µ
τ ,λ < 1 and φ < 1. Thus, ∂gy
∂θ >0.
Nex , we conside he case when θ < µ
τ . Subs i u ing o n om eq. (8), ∂gh
∂θ om eq.(61) and
∂n
∂θ om Lemma 1 in eq. (E.3), we deduce:
∂gy
∂θ ="λ(1 −α)(1 +gy)
θ(1 −φ)#.
We now, conside he imi a ion egime. Subs i u ing o (1 +gY) om eq. (52) and simpli ying,
we ge :
(1 +gy)=(1 +g¯
A)1
2−φ(1 +gh)2−φ+λ(1−α)
2−φnλ(1−α)
2−φ.(E.4)
Taking log on bo h sides and di e en ia ing w. . θ, we ge :
1
1+gy
∂gy
∂θ =2−φ+λ(1 −α)
2−φ(1 +gh)
∂gh
∂θ +λ(1 −α)
(2 −φ)n
∂n
∂θ .(E.5)
When θ > µ
τ , subs i u ing o n om eq. (8), ∂n
∂θ om Lemma 1 and ∂gh
∂θ om eq. (D.2), we
ha e:
∂gy
∂θ =1+gy
2−φ"(2 −φ+λ(1 −α))τ
τθ −µ−µλ(1 −α)
θ(τθ −µ)#.
Now, ∂gy
∂θ >0 i
(2 −φ+λ(1 −α))τ
τθ −µ>µλ(1 −α)
θ(τθ −µ)⇔θ > µλ(1 −α)
τ(2 −φ+λ(1 −α)).
This also holds ue as θ > µ
τ ,λ < 1 and φ < 2. The e o e, ∂gy
∂θ >0.
We nex , conside he case when θ < µ
τ . When θ < µ
τ , subs i u ing o n om eq. (8), ∂gh
∂θ
om eq.(61) and ∂n
∂θ om Lemma 1 in eq. (E.5) yields:
∂gy
∂θ ="λ(1 −α)(1 +gy)
θ(2 −φ)#.
This comple es de i a ions o eqs. (65), (66), (67) and (68).
Appendix F De i a ions o Eqs. (70) and (71)
We know ha :(1 +gH)=(1 +gh).n. Di e en ia ing bo h he sides w. . , we ge ha :
∂gH
∂ =(1 +gh)∂n
∂ +n∂gh
∂ (F.1)
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Re iew o Economic Analysis 16 (2024) 175–220
When θ > µ
τ , we know om he in e io solu ion o eq. (9) ha (1+gh)=(τθ −µ)
(1 −)
. Taking
log on bo h sides and di e en ia ing w. . , we ge he ollowing exp ession:
1
1+gh
∂gh
∂ =1+log+log(τθ −µ)+
1−−log(1 −)
=(1 +gh)"1
(1 −)+log "(τθ −µ)
1−##.(F.2)
Also, om Lemma 2, we ha e ∂n
∂ =−β2θ
(1 +β1+β2)(τθ −µ). Subs i u ing o ∂n
∂ om Lemma
2 and ∂gh
∂ om eq. (F.2) in o eq. (F.1), we de i e ha :
∂gH
∂ =−β2θ(1 +gh)
(1 +β1+β2)(τθ −µ)+(1 +gh)n"1
(1 −)+log(τθ −µ)
1−#
Subs i u ing o β2θ
(1 +β1+β2)(τθ −µ) om eq. (8), yields:
=(1 +gh)"n"1
(1 −)+log(τθ −µ)
1−#−n
1−#=(1 +gH)log "(τθ −µ)
1−#.
We nex de i e he exp ession o ∂gH
∂ when θ≤µ
τ . When θ≤µ
τ , i is known om eq. (9)
ha :(1 +gh)=µ. Taking log on bo h sides and di e en ia ing ghw. . yields:
∂gh
∂ =(1 +gh)logµ. (F.3)
Subs i u ing o ∂n
∂ and ∂gh
∂ om Lemma 2 and eq. (F.3) in o eq. (F.1), we deduce ha :
∂gH
∂ =
(1 +gH)h1
+logµi>0,i θ < µ
τ ,
(1 +gH)logµ>0, θ =µ
τ .
(F.4)
This comple es he de i a ions o eqs. (70) and (71).
Appendix G De i a ions o Eqs. (72), (73), (74) and (75)
I is known om eq. (E.2) ha he g ow h a e o pe capi a income unde inno a ion egime is
gi en by:
(1 +gy)=(1 +gh)1−φ+λ(1−α)
1−φnλ(1−α)
1−φ.(G.1)
Taking log on bo h sides and di e en ia ing w. . yields:
1
1+gy
∂gy
∂ =1−φ+λ(1 −α)
(1 +gh)1 −φ
∂gh
∂ +λ(1 −α)
(1 −φ)n
∂n
∂ .(G.2)
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