Das, Ramesh Chand a
A icle
In e ela ionships among go e nmen pa icipa ion, popula ion and
g ow h o pe capi a income: Inqui y on op wen y income-holding
coun ies in he wo ld
Economies
P o ided in Coope a ion wi h:
MDPI – Mul idisciplina y Digi al Publishing Ins i u e, Basel
Sugges ed Ci a ion: Das, Ramesh Chand a (2025) : In e ela ionships among go e nmen
pa icipa ion, popula ion and g ow h o pe capi a income: Inqui y on op wen y income-holding
coun ies in he wo ld, Economies, ISSN 2227-7099, MDPI, Basel, Vol. 13, Iss. 2, pp. 1-29,
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Published: 12 Feb ua y 2025
Ci a ion: Das, R. C. (2025).
In e ela ionships Among
Go e nmen Pa icipa ion, Popula ion
and G ow h o pe Capi a Income:
Inqui y on Top Twen y Income-
Holding Coun ies in he Wo ld.
Economies,13(2), 46. h ps://doi.o g/
10.3390/economies13020046
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A icle
In e ela ionships Among Go e nmen Pa icipa ion, Popula ion
and G ow h o pe Capi a Income: Inqui y on Top Twen y
Income-Holding Coun ies in he Wo ld
Ramesh Chand a Das
Depa men o Economics, Vidyasaga Uni e si y, Midnapo e 721102, Wes Bengal, India;
[email p o ec ed].ac.in
Abs ac : The li e a u e on g ow h in economics encompasses wo main ace s o hink-
ing: he applicabili y o diminishing p oduc i i y o capi al, as has been in he neoclas-
sical g ow h model wi h exogenous echnological p og ess, and he applicabili y o non-
diminishing p oduc i i y o capi al, as has been in he endogenous g ow h models. The
main conclusion o he o me is he c oss-coun y con e gence o a common s eady s a e
while ha o he la e is non-con e gence. The emendous his o y o he g ow h o
he wo ld’s so-called de eloped economies in he 1980s, di e ging wi h he so-called
backwa d economies, has nulli ied he applicabili y o he neoclassical g ow h model and
jus i ied non-s eady s a e posi i e pe capi a g ow h o income and consump ion h ough
endogenous echnological p og ess in e ms o knowledge capi al, human capi al, good
public ins i u ions, e c. The p esen s udy aims o examine whe he pe capi a income
g ow h is explained by he size o go e nmen in e en ion coupled wi h he wo king
popula ion size in he wo ld’s op wen y coun ies in e ms o agg ega e income. Wi h
he heo e ical se up o he model and using empi ical ools, such as coin eg a ion, e o
co ec ion and causali y in a ec o au o eg ession s uc u e, his s udy e eals ha eigh een
coun ies main ain long- un ela ionships among pe capi a income g ow h, go e nmen
pa icipa ion, popula ion and he in e ac ion ac o s be ween go e nmen in e en ion and
popula ion, excep ing Ge many and Canada. Fu he , in he sho un, o ele en coun ies
on he lis , he e a e ins ances in which public ins i u ions associa ed wi h he popula ion
and he in e ac ion e m ha e a causal in luence on he g ow h o pe capi a income. The
empi ical esul s ela ing o income g ow h, hus, ha e sus ainabili y implica ions.
Keywo ds: public ins i u ion; g ow h; wo king popula ion; PCGDP; consump ion;
sus ainabili y; coin eg a ion; VAR; VECM; causali y
1. In oduc ion
Economis s o en a e engaged in a popula deba e on whe he he go e nmen sec o
should ake pa in economic ac i i ies. I yes, in wha capaci y? The classical (Smi h,1776;
Say,1834, among o he s) and neoclassical economis s (Solow,1956) had ull ai h in he
wo king o a ma ke economy in a compe i i e s uc u e wi h he comple e absence o he
go e nmen sec o as i hampe s economic ac i i y. Only he p i a e buye s and selle s
will be capable o de e mining commodi y and ac o p ices wi h no sunk cos o dead
weigh loss. Bu he my h was b oken in he 1920s when he wo ld’s indus ially de eloped
ma ke economies collapsed and he e was a long ecession in business ac i i ies. Classical
economis s had no solu ion a ha ime. The ailu e o he laissez ai e doc ine o he
capi alis ic economis s in he G ea Dep ession o he 1920s and 1930s has been well known
Economies 2025,13, 46 h ps://doi.o g/10.3390/economies13020046
Economies 2025,13, 46 2 o 29
enough o allow public policymake s o p omo e go e nmen in e en ions in economic
ac i i ies besides i s social and adminis a i e wo ks—a phenomenon suppo ed by he
classical and neoclassical economis s, philosophe s and poli ical scien is s. In his Gene al
Theo y, P o esso J. M. Keynes (1936) ecommended s ong go e nmen in e en ions in
economic ac i i ies, especially in he sho un, o esis dep essiona y si ua ions. La e ,
Robe Ba o (1990) inco po a ed he go e nmen ac o in o he endogenous g ow h
models o jus i y one o he majo causes o why g ow h can be pe pe ual. Bu empi ical
e idence p o es ha go e nmen in e en ions may be good o bad o economies o
di e en s a u es. The good e ec channels a e o wo ca ego ies: i s , he go e nmen
mus ha e a ole in ields like legisla ion, secu i y o p ope y igh s and p o iding a p ope
en i onmen o p i a e in es men and p oduc ion h ough dec easing ansac ion cos s;
second, he go e nmen mus in e ene in o he ields whe e i comes o playing oles
and/o gi ing se ices o sec o s like in as uc u es, human de elopmen , public heal h
and educa ion. The wo al e na i es suppo he o wa d linkage de elopmen policy whe e
posi i e public in es men leads o he expansion in he p i a e sec o and o he associa ed
sec o s, leading o he applicabili y o he c owding-in hypo hesis (Rami ez,1998;E den &
Holcombe,2006;A onso & S . Aubyn,2008;Mahmoudzadeh e al.,2013;Wa ne ,2014;¸Sen
& Kaya,2014;Das e al.,2015,2018;F ancois e al.,2024; among o he s). This hypo hesis
mos ly wo ks in he coun ies o g oups o coun ies om de eloping na ions whe e he
capi al ma ke s a e ela i ely unde de eloped compa ed o de eloped coun ies. The
economic logic o de ending go e nmen in e en ions in economic ac i i ies is ha i
p o ec s he sec o s in which he ma ke mechanism ails o i has a compa a i e ad an age
o e he p i a e sec o .
Howe e , hese in e en ions in ol e cos s as well. Some o he p oposi ions unde
his heading a e as ollows: Fi s , he go e nmen has o a o d i s cos s h ough public bo -
owing and ax e enues. Recei ing axes om economic agen s makes hem discou aged
in ha hey educe hei wo k e o and consume and sa e less, which hu s economic
g ow h. Second, public bo owing also inc eases he a e o in e es and c owds ou p i-
a e in es men and ax inc eases in he u u e (Aschaue ,1989;Fu ce i & Sousa,2009;
Phe sa ong & Ichihashi,2012;¸Sen & Kaya,2014;Das e al.,2015,2018;Nguyen & T inh,
2018;Ben Zee e al.,2023; among o he s). This happens mos ly in he case o de eloped
coun ies whe e capi al ma ke s a e de eloped and ha e sa u a ion le els depending on
he equi emen s o he economies’ necessi ies; any mo e public in es men leads o an
inc ease in he a e o in e es which leads o a educ ion in he demand o in es men s
om p i a e uni s. Thi d, i p oduces ine icien economic ou pu s, unlike he ma ke
o ces ha b ing he economy o op imali y h ough he e ec i e alloca ion o esou ces.
Thus, go e nmen in e en ions, among o he s, can p omo e co up ion and bu eauc a ic
en -seeking ac i i ies. Fou h, cen aliza ion and bu eauc a ic ac i i ies dec ease c ea i i y
in bo h he public and p i a e sec o s. In acco dance wi h ma ke mechanisms, ewa ds
and penal ies o decisions a e di ec ly subjec o wise choices, because hey will appea in
peoples’ weal h and p ope y e y soon. A se ies o posi i e and nega i e e ec s can be
added o his.
Empi ical e idence, including ha p o ided by G ossman (1990), Ghali (1998),
Loizides and Vam oukas (2005), e c., e eals ha he e ec o go e nmen size is he
cause o economic g ow h. On he o he hand, s udies such as hose o Gwa ney e al.
(1998), Fols e and Hen ekson (2001), among o he s, e eal ha he e ec o go e nmen
size on economic g ow h is nega i e. Fu he mo e, he heo e ical wo ks o Robe Ba o
(1990), Mou mou as and Lee (1999), e c., and he empi ical e idence p o ided by Ba o
(1991) and Chiou-Wei e al. (2010) show ha in he lowe le els o go e nmen ac i i ies,
Economies 2025,13, 46 3 o 29
he e ec o go e nmen expendi u es is posi i e, bu is e e sed i i inc eases, which is
shown wi h an in e ed U-shaped cu e.
The e o e, he ac i i ies o he go e nmen ha e bo h posi i e and nega i e e ec s
on economic g ow h. On he one hand, i inc eases economic g ow h by p o iding a
p ope en i onmen o p i a e ac i i ies, legisla ion ega ding p i a e possession and i s
gua an ee, building in as uc u es and public goods, and on he o he hand, i dec eases
economic g ow h h ough bo owing and axa ion policies, dec easing c ea i i y and
inc easing ine iciency, whe e he in ensi y o he nega i e e ec s depends on he amoun
o money spen and how i is spen ( ypes o expendi u es). Thus, he inal e ec o
go e nmen expendi u es depends on he kind o go e nmen expendi u es (p o ec ion
o p ope y igh s, subsidies, in as uc u es, e c.) and i s posi i e o nega i e e ec s on
economic g ow h.
The ole o he go e nmen sec o in e ms o good public ins i u ions ha ing public
good p ope ies in he g ow h o pe capi a income in he coun ies o he Wes du ing he
1980s onwa ds has been jus i ied by an endogenous g ow h heo e ician in he wo ks o
Robe Ba o (1990,1991). The model es ablishes ha he inco po a ion o a good public
ins i u ion unde no ax o a lump sum ax sys em causes he pe pe ual g ow h o pe
capi a income and consump ion and ha hese g ow h a es a e dependen upon he size o
go e nmen in he economy, he popula ion size and he combina ions o he wo. The e o e,
o coun ies, he e should be long- e m ela ionships be ween pe capi a income g ow h,
he size o he go e nmen , popula ion size and hei in e ac ions.
1.1. Objec i e o This S udy
This s udy examines whe he public sec o pa icipa ions in line wi h he endogenous
g ow h model o Robe Ba o ha e long- un ela ions wi h he pe capi a GDP g ow h
a es in he wo ld’s op 20 coun ies in e ms o GDP o he pe iod 1991–2020.
1.2. Con ibu ions o This S udy
This s udy con ibu es o he exis ing li e a u e in he ollowing manne :
•
I examines he endogenous g ow h model in ol ing public ins i u ions o he wo ld’s
op 20 coun ies in GDP
•
I inco po a es he e ec s o popula ion as a scale ac o on g ow h o pe capi a GDP
•
I cap u es he in e ac ion e ec s be ween public pa icipa ion and labo o ces on pe
capi a GDP g ow h a es and shows he ou e owa ds sus ainable de elopmen
The pape is o ganized as ollows: The nex sec ion, Sec ion 2, p esen s he li e a u e
e iew ollowed by he heo e ical model and public sec o linkages wi h sus ainable
de elopmen . Sec ion 3 ocuses on he ma e ials and me hods; Sec ion 4co e s esul s,
analysis and discussion; and inally, Sec ion 5concludes his s udy.
2. Re iew o Rela ed Li e a u e
This s udy has conduc ed a li e a u e e iew o he ex an li e a u e and classi ied i
in o h ee sub-sec ions. Fi s , i co e s he s udies on he linkages be ween public spending
and g ow h; hen, i p esen s he heo e ical model o Robe Ba o (1990) wi h some
modi ica ions in line wi h he equi emen s o his s udy; and hen, i co e s some s udies
on he public sec o ’s linkages wi h sus ainable de elopmen .
2.1. Public Spending and G ow h Linkages
Landau (1983) s udied he ele an da a o 104 coun ies on a c oss-sec ional basis and
ound signi ican ly nega i e ela ions be ween he g ow h a e o eal pe capi a GDP and
he amoun o go e nmen consump ion expendi u e as a a io o GDP. Using da a o each
Economies 2025,13, 46 4 o 29
coun y a e aged o e oughly 20-yea pe iods o 47 coun ies, Ko mendi and Megui e
(1985) ound no signi ican ela ion be ween he a e age g ow h a es o eal GDP and
a e age g ow h a es o le els o he sha e o go e nmen consump ion spending in GDP.
G ie and Tullock (1987) ex ended he Ko mendi–Megui e o m o analysis o 115 coun ies,
using da a on go e nmen consump ion o a pooled c oss-sec ion analysis, and ound
a signi ican ly nega i e ela ion be ween he g ow h o eal GDP and he g ow h o he
go e nmen sha e o GDP. Ba h and B adley (1987) ound a nega i e ela ion be ween
he g ow h a e o eal GDP and he sha e o go e nmen consump ion spending o
16 OECD coun ies o he pe iod 1971–1983. Aschaue (1989) a gued ha he se ices
om go e nmen in as uc u e we e pa icula ly impo an in he con ex o g ow h
whe e he oles o public se ices as an inpu o p i a e p oduc ion we e conside ed. I is
his p oduc i e ole ha c ea es a po en ially posi i e linkage be ween go e nmen and
income g ow h. Ba o (1989) showed ha in he se o 98 coun ies o which go e nmen
consump ion spending o GDP was measu ed, a eg ession o he a e age annual g ow h
a e o eal pe capi a GDP om 1960 o 1985 on a se o explana o y a iables led o
nega i e coe icien s. The e was hus an indica ion ha an inc ease in esou ces de o ed o
nonp oduc i e (bu possibly u ili y-enhancing) go e nmen se ices was associa ed wi h
lowe pe capi a g ow h a es o income. Bu wi h a sepa a e se o 76 coun ies ha ing he
public-in es men - o-GDP a io as he eg esso , he indings showed a posi i e coe icien .
This esul was consis en wi h he hypo hesis ha he ypical coun y came close o he
quan i y o public in es men ha would maximize he income g ow h a e. The ole o
go e nmen ins i u ions, including he ule o law and well- unc ioning p ope y igh s, in
explaining long- un economic pe o mance has eme ged om new ins i u ional economics
pionee ed by No h (1989). De a ajan e al. (1996) ocus on he link be ween he le el o
public expendi u e and g ow h using da a om 43 de eloping coun ies o e 20 yea s
and show ha an inc ease in he sha e o cu en expendi u e has posi i e and s a is ically
signi ican g ow h e ec s. Blankenau and Simpson (2004) explo e his expendi u e–g ow h
ela ionship in he con ex o an endogenous g ow h model in which p i a e and public
in es men a e inpu s o human capi al accumula ion, and he empi ical e idence is mixed
conce ning he e ec s o public educa ion expendi u es on economic g ow h. Bose e al.
(2007) examine he g ow h e ec s o go e nmen expendi u e o a panel o 30 de eloping
coun ies in he 1970s and 1980s in agg ega e and disagg ega ed go e nmen expendi u es.
The esul s show ha he sha e o go e nmen capi al expendi u e in GDP is posi i ely and
signi ican ly co ela ed wi h economic g ow h, and a he disagg ega ed le el, go e nmen
in es men in educa ion and o al expendi u es in educa ion a e signi ican ly associa ed
wi h g ow h. Rajkuma and Swa oop (2008) examined he ole o go e nance in he
e ec i eness o public spending in achie ing social ou comes o a sample o 91 coun ies
and showed ha he quali y o go e nance could la gely explain di e ences in he e icacy o
public spending. A onso and Jalles (2011) conduc ed an empi ical analysis o 108 coun ies
o 1970–2008 on go e nmen size and ins i u ional quali y and ound ha he size o he
go e nmen had an ad e se e ec on economic g ow h while ins i u ional quali y had a
posi i e impac . Wu e al. (2010) examined he causal ela ionship be ween go e nmen
expendi u e and economic g ow h in a panel o 182 coun ies o 1950–2004 and ound ha
he go e nmen played a ole in economic g ow h. A onso and Fu ce i (2010) analyzed he
e ec s in e ms o size and ola ili y o go e nmen spending and e enue on economic
g ow h in OECD and EU coun ies and ound bo h a iables o be de imen al o economic
g ow h. In hei la e s udy, A onso and Jalles (2014) s udied he iscal composi ion–
g ow h nexus o a se o OECD coun ies and ound no signi ican impac o e enues
on g ow h, whe eas expendi u es had nega i e e ec s. In hei wo k, Chak abo y and
K ishnanku y (2012) ocus on he expendi u e on educa ion as a de e minan o economic
Economies 2025,13, 46 5 o 29
g ow h in Indian s a es. Using a panel da a model, hei s udy shows ha expendi u e on
educa ion posi i ely in luences he g ow h o he economy. Ku (2015) in es iga es he
di ec and indi ec e ec s o heal h expendi u es on economic g ow h using he Fede –Ram
model o Tu kiye in mon hly da a o he pe iod 2006–2013 and shows ha he di ec
impac o go e nmen heal h expendi u es on economic g ow h in Tu kiye is posi i e and
signi ican and i s indi ec impac is nega i e and signi ican . Malese ic and Golem (2019)
ob ained he esul s o EU15 coun ies du ing 1995–2014, whe e he single mos impo an
go e nmen expendi u e i em was educa ion among agg ega e expendi u e o economic
g ow h. Pahle i (2017), s udying an Indonesian panel o 33 s a es o he pe iod 2008–
2012, shows ha go e nance and heal h expendi u e a e ound o ha e a posi i e impac
on human de elopmen ; meanwhile, heal h expendi u e is disco e ed o a ec human
de elopmen in a nega i e di ec ion. Chu chill e al. (2015) pe o med a hie a chical me a-
eg ession analysis o e iew 87 empi ical s udies ha epo 769 es ima es o he e ec s
o go e nmen size on economic g ow h, and he indings indica e ha he ela ionship
be ween go e nmen size and g ow h is con ex -speci ic and he exis ing e idence is
insu icien o es ablish a nega i e causal e ec . Bhanumu hy e al. (2016) examined public
expendi u e, good go e nance and human de elopmen in dis ic s o Madhya P adesh
in India, inco po a ing an in e ac ion e m o add ess he linkage e ec o go e nmen
expendi u e; good go e nance was in oduced in addi ion o o he explana o y a iables,
and he esul showed ha good go e nance signi ican ly con ibu ed o be e economic
pe o mance. Liu e al. (2018) conduc ed a s udy on go e nance quali y and economic
g ow h o p o inces in China o he pe iod 2001–2015 in a panel da a model, and his
s udy a i ms ha good go e nance con ibu es o g ow h posi i ely. Olaoye e al. (2019)
es ed o causali y be ween go e nmen expendi u e and economic g ow h, bu hei
esul shows no e idence o a causal ela ionship. A lis o s udies was compiled by Das
(2021) in a olume co e ing he deba e on he op imum size o a go e nmen in e en ion
which shows in gene al ha he impac depends on se e al si ua ions ac oss coun ies
and g oups; howe e , no speci ic conclusion is d awn. Da a and Chak aba i (2021) show
ha a go e nmen ’s budge alloca ion o de elopmen managemen p og ams has an
op imum le el/uppe bound nega ing he con using esul s o he impac s on he size o
he go e nmen in e en ion as e idenced by many s udies in he li e a u e. Sinha e al.
(2021) highligh ha he ex en o FDI in lows is highly in luenced by se e al mac o policies
o go e nmen s o he han subsidies; howe e , go e nmen policies owa ds open economy
mac oeconomic ac o s a e mo e e ec i e. Jain and Nagpal (2021) ha e obse ed ha a ise
in he size o he public spending in a selec ed de eloping coun ies and g oups esul s
in a subs an ial inc ease (dec ease) in he g ow h a e when he public spending is below
(abo e) he op imal h eshold le el, indica ing a non-mono onic associa ion.
2.2. Theo e ical Model
The weak jus i ica ion o neoclassical economis s such as Solow (1956) on he wo king
o c oss-coun y con e gences du ing he 1980s among he de eloped na ions has in lu-
enced he new g ow h heo e icians such as Rebelo (1991), Lucas (1988), Rome (1994),
Ramsey (1928) and Robe Ba o (1990), who explained h ough endogenous g ow h mod-
els how he c oss-coun y con e gences did no wo k. The endogenous g ow h heo ies
conside he wo king o inc easing e u ns o scale whe e he sou ces o such e u ns o
scale a e esea ch and de elopmen ( he Rome Model), human capi al ( he Lucas Model),
one- ac o model ( he Rebelo Model wi h Y = AK ype p oduc ion unc ion) and good
public ins i u ions ( he Ba o Model).
The p esen s udy uses he basic s uc u e o he Robe Ba o (1990) model o endoge-
nous g ow h and makes some simple modi ica ions o he p oduc ion unc ion inco po a -
Economies 2025,13, 46 6 o 29
ing he in e ac ion e ec s be ween go e nmen expendi u e as a a io o agg ega e ou pu
and he wo king popula ion in he economy. This is because a good public ins i u ion (as
measu ed by high G/Y) leads o good-quali y public ins i u ional ou pu s in e ms o good
educa ional a ainmen , heal h bene i s, legal and judicial suppo s, in e nal and ex e nal
secu i y, e c., inc easing he good-quali y popula ion size.
Thus, ollowing he Ba o model, le us suppose ha , in he p oduc ion unc ion,
he e is G as he addi ional inpu ( o ep esen public se ices o public inpu wi hou
conges ion e ec s and use cha ges) wi h L and K (as p i a e inpu s) p oducing ou pu Y.
The Cobb–Douglas- ype p oduc ion unc ion o he whole economy is
Yi= AL1−α. Kα. G1−α(1)
whe e 0 < α< 1.
The p oduc ion unc ion shows he wo king o cons an e u ns o scale (CRS) in
p i a e inpu s, L and K (as he sum o hei powe s is 1), and he inclusion o G as ano he
ac o o p oduc ion leads he o al p oduc ion sys em o inc easing e u ns o scale (IRS)
as he sum o hei powe s is g ea e han 1. ‘A’ s ands o echnology which, among
o he s, cap u es he in e ac ion e ec s be ween go e nmen ’s pa icipa ion in he agg ega e
economy as measu ed by G/Y and L ( he wo king popula ion) which is G/Y
×
L (i.e.,
A = A(G/Y ×L
)). I all o he componen s o A a e ixed, hen he e can be a one- o-one
ela ion be ween A and G/Y
×
L, i.e., A = (G/Y)
×
L. The modi ied model in he p esen
s udy, hus, has mo e lexibili y in analyzing he impac s o se e al componen s o he
public ins i u ional sys em on economic g ow h.
Assume ha he agg ega e labo o ce is cons an . In ha case, i G is cons an , he
e u ns om p i a e capi al (K) will be diminishing. On he o he hand, i G inc eases
along wi h K ( ha means bo h p i a e and public capi als mo e in posi i e di ec ions
simul aneously like c owding-in e ec s), hen diminishing MPk will no a ise. He e, public
capi al is complemen a y o K and L and an inc ease in G leads o an inc ease in he MPL
and MPk ( his is he sou ce o endogenous g ow h).
The p oduc ion unc ion in pe capi a o m is
y=A.kα. G1−α(2)
The o al ou pu o he economy is
Σy=y×L=Y=AL.kα. G1−α= AL. kα. (G/Gα)
O , Gα= (AL. kα. G)/Y = AL. kα. (G/Y)
O . G = (G/Y)1/α. (AL)1/α. k
(3)
The common budge cons ain aced by he agg ega e economy is
dk/d = dm/d = ˙
m= y −c−δk−G/L
whe e G/L is pe capi a consump ion o public goods/se ices. He e, ‘m’ is he s a e
a iable ep esen ing asse alue, and c is he pe capi a consump ion, which is he in e se
o sa ings in an in e empo al in ini e pe iod model.
Following he Ramsey model, we se he cu en alue Hamil onian unc ion o u ili y
maximiza ion wi h espec o c, G and k.
H = u(c ). e−(ρ−n) +β [y −c−δk−G/L]
Economies 2025,13, 46 7 o 29
He e,
β
is he co-s a e a iable,
ρ
is he discoun a e, n is he popula ion g ow h a e
and
δ
is he a e o dep ecia ion. Assuming he popula ion g ow h a e is a n and he con-
s an elas ici y o subs i u ion u ili y unc ion, u = (c
1−σ
/1
−σ
),
σ
being he in e empo al
elas ici y o subs i u ion o cons an elas ici y o ma ginal u ili y o consump ion. Thus, he
Hamil onian is now
H(c, G, k) = (c1−σ/1−σ). e−(ρ−n) +β [y −c−δk−G/L]
o , H(c, G, k) = (c1−σ/1−σ). e−(ρ−n) +β [A. kα. G1−α−c−δk−G/L]
The FOCs a e
δH/δc = 0, >> c−σ. (1−σ)/(1−σ). e−(ρ−n) =β(4)
δH/δG = 0, >>(1−α). β. A. kα. G−α−β/L = 0
o , (1−α). A. kα. G−α= 1/L (5)
δH/δk = −δβ/δ >>β.α. A. kα−1. G1−α−β δ =−δβ/δ (6)
And he ans e sali y condi ion is
lim
→∞(β .m )=0
Now, we ake he de i a i e o βw. . ime om (4) and subs i u e i in o (6).
We ob ain
β(α. A. kα−1. G 1−α−δ) = σ.c−σ. [(δc/δ )/c]. e−(ρ−n)
Now, pu ing he alue o β om (1) in o he abo e ela ion
c−σ. (1−σ)/(1−σ). e−(ρ−n) .(α. A. kα−1. G1−α−δ) = σ.c−σ. [(δc/δ )/c]. e−(ρ−n)
o , α. A. kα−1. G1−α−δ=σ. [(δc/δ )/c]
o , [(δc/δ )/c] = 1/σ[α. A. kα−1. G1−α−n−δ]
(7)
Now, om (2),
(1−α). A. kα. G−α= 1/L
O , (1−α). A. kα. G1−α= 1/L
O , (1−α). A. L. kα. G1−α= 1
O . (1−α). Y = G
O , G/Y = (1 −α)
(8)
This means he go e nmen -expendi u e- o-GDP a io (=G/Y) is cons an whe e G/Y
s ands o he sha e o p oduc i e go e nmen expendi u es in GDP. In o he wo ds, he
op imal condi ion o he go e nmen in a coun y is o main ain a cons an G/Y in he
model wi h a lump sum ax. Howe e , he sha es a y ac oss he coun ies depending
upon he alues o
α
, which measu es he p oduc i i y o public se ices ela i e o p i a e
se ices. I could a y ac oss coun ies o a numbe o easons ela ed o geog aphy, he
sha e o ag icul u al p oduc ion, u ban densi y and so on. Hence, he g ow h a es o
income, consump ion and capi al accumula ion a y ac oss he coun ies. As he alue o
αinc eases, G/Y alls, and as a esul , he g ow h a e alls.
Economies 2025,13, 46 8 o 29
Now, we pu he exp ession o G om (1) in (7)
(δc/δ )/c = 1/σ[α. A. kα−1. G1−α−n−δ]
O , (δc/δ )/c = 1/σ[α. A. kα−1. G1−α−n−δ]
O , (δc/δ )/c = 1/σ[α. A. kα−1. {(G/Y)1/α. (AL)1/α. k}1−α−n−δ]
O , (δc/δ )/c = 1/σ[α. A. kα−1. {(1−α)1−α/α. (AL)1−α/α. k1−α−n−δ]
O , (δc/δ )/c = 1/σ[α. A1/α. (1−α)1−α/α. L1−α/α−n−δ]
(9)
The e o e, he social planne ’s op imum solu ion is iden ical o ha unde a decen al-
ized sys em unde he lump sum ax assump ion.
The op imal a e o g ow h o k, y and c will be he a e [w i ing (
δ
c/
δ
)/c =
.
c
c
], which
is gi en below as
˙
c/c = 1/σ[α.A1/α. (G/Y)1−α/α. L1−α/α−n−δ]
= 1/σ[α.A1/α. (1−α)1−α/α. L1−α/α−n−δ]
Le us eplace he e m A wi h G/Y
×
L = (1
−α
)
×
L (as has been explained in he
in oduc o y pa o he model), and he e ised consump ion g ow h ela ion becomes
˙
c/c = 1/σ[α. {(1−α)×L}1/α. (1−α)1−α/α. L1−α/α−n−δ]
= 1/σ[α. (1−α)(2−α)/α. L(2−α)/α−n−δ](10)
I is clea om he exp ession ha he a e o g ow h o pe capi a consump ion
depends on he ma ginal p oduc i i y o pe capi a capi al which again depends upon
he endogenous g ow h componen , he G/Y a io (=1
−α
), popula ion size (=L) and he
in e ac ions be ween G/Y and popula ion size (cap u ed by A = G/Y
×
L), bu no on pe
capi a capi al accumula ion (=k). The in ui ion behind he e ec s o G/Y on popula ion o
he e e se is ha a good public ins i u ion (as measu ed by high G/Y o high (1
−α
)) leads
o good-quali y public ins i u ional ou pu s in e ms o good educa ional a ainmen , heal h
bene i s, legal and judicial suppo s, in e nal and ex e nal secu i y, e c., inc easing he
good-quali y popula ion size (Lucas,1988;Ba o & Lee,1993;Ba o,2001;Ba o & Lee,2001;
Ve huls ,1838;Das & Mukhe jee,2019;Diebol & Hippe,2019;Das,2020;Hussain & Das,
2024). On he o he hand, in coun ies ha ing good-quali y public ins i u ions, he inc ease
in popula ion size o he coun ies will be able o abso b he good public ins i u ional
amewo ks ha will push up hei p oduc i i y which will hen help in inc easing he
g ow h o pe capi a consump ion. The a e o g ow h o pe capi a income (
.
y
/y) will hen
be posi i e wi h G/Y, popula ion and hei in e ac ion e m (G/Y
×
L). Hence, as he scale
ac o , L, inc eases along wi h G/Y, he ma ginal p oduc i i y o capi al inc eases, b eaks i s
diminishing na u e, and ul ima ely,
.
c
/c and
.
y
/y inc ease in he long un wi hou eaching
any s eady-s a e solu ion.
2.3. Public Sec o Linkages wi h Sus ainable De elopmen
The Uni ed Na ions 17-poin sus ainable de elopmen goals (SDGs) include good
public ins i u ions ha ing he capabili y o making economic g ow h, p omo ing good
heal h and educa ion, educing co up ion, c imes, e c., which is co e ed in Goal Numbe
16. SDG 16 (Global Goal 16) is amed o p omo e peace ul and inclusi e socie ies o
sus ainable de elopmen ; p o ide access o jus ice o all; and build e ec i e, accoun able
and inclusi e ins i u ions a all le els. The goal has 12 a ge s, 23 indica o s and 10 ou come
a ge s. The ou come a ge s ela ed o ou analysis a e o de elop e ec i e, accoun able and
anspa en ins i u ions; ensu e esponsi e, inclusi e and ep esen a i e decision-making;
ensu e public access o in o ma ion; and p o ec undamen al eedoms. The p oposed
Economies 2025,13, 46 15 o 29
Table 1. Con .
ADF S a is ics (P obabili y)
Coun y G/Y Ra io
(Le el)
Popula ion
(Le el)
(G/Y) ×
Popula ion
(Le el)
PCGDP
G ow h
(Le el)
G/Y Ra io (1s
Di .)
Popula ion (1s
Di .)
(G/Y) ×
Popula ion (1s
Di .)
PCGDP
G ow h (1s
Di .)
S. Ko ea −2.3 (0.25) −2.40 (0.18) −2.73 (0.0/) −2.26 (0.21) −4.30 (0.00) −4.4 (0.00) * −4.73 (0.00) −5.26 (0.00)
Aus alia −2.1 (0.27) −1.97 (0.35) −2.00 (0.32) −2.79 (0.09) −5.1 (0.00) −2.97 (0.05) −5.00 (0.00) −3.79 (0.00)
Mexico −1.8 (0.62) −1.25 (0.83) −2.01 (0.44) −2.72 (0.09) −3.79 (0.00) −3.2 (0.03) * −3.01 (0.04) −4.72 (0.00)
Spain −2.1 (0.25) −2.10 (0.24) −1.99 (0.46) −2.85 (0.07) −3.01 (0.05) −3.10 (0.04) −2.99 (0.05) −3.85 (0.00)
Indonesia −2.8 (0.08) −2.38 (0.19) −2.66 (0.09) −2.73 (0.08) −5.80 (0.00) −4.38 (0.00) −5.66 (0.00) −3.73 (0.00)
Ne he lands −2.4 (0.18) −2.21 (0.27) −2.30 (0.26) −2.49 (0.14) −4.34 (0.00) −3.21 (0.03) −4.30 (0.00) −4.49 (0.00)
S. A abia −2.9 (0.07) −2.14 (0.30) −2.71 (0.07) −2.42 (0.15) −4.95 (0.00) −3.14 (0.04) −6.71 (0.00) * −4.42 (0.00)
Tu kiye −2.1 (0.27) −2.81 (0.07) −2.62 (0.09) −2.61 (0.11) −6.09 (0.00) −4.81 (0.00) −5.62 (0.00) −4.61 (0.00)
Swi ze land −2.4 (0.18) −1.98 (0.35) −1.58 (0.41) −2.73 (0.08) −4.24 (0.00) −2.98 (0.05) −3.58 (0.01) −4.73 (0.00)
No e: * ma k indica es I(2) se ies. Sou ce: au ho ’s calcula ions.
4.3. Johansen Coin eg a ion Tes Resul s
As he numbe o endogenous a iables is mo e han wo, we use he VAR model o
iden i y he op imum lag and coin eg a ion among he ou a iables. The op imum lag is
selec ed by looking a he minimum alues o mos o he es ing c i e ia such as LR, inal
p edic ion e o (FPE), Akaike in o ma ion c i e ion (AIC), Schwa z in o ma ion c i e ion
(SIC) and Hannan–Quinn in o ma ion c i e ion (HQIC). In all he cases wi h each o he
ou indica o s playing he ole o dependen a iable in e changeably, he op imum lag
is obse ed o be 2 ( he esul s a e no shown in ables). The Johansen coin eg a ion es
echnique is used, and he esul s a e p esen ed in Table 2. This es is pe o med o see
whe he he lowe -o de alues a e coin eg a ed.
Table 2. Johansen coin eg a ion es esul s.
Coun y Hypo hesized
No. o CEs
T ace S a is ics (P ob)
Rema ks
USA *
None * 69.303 (0.00) The a iables a e
coin eg a ed and he e is
1 coin eg a ing equa ion
a he 0.05 le el
A mos 1 * 23.036 (0.38)
A mos 2 8.0005 (0.13)
A mos 3 2.606 (0.11)
China *
None * 103.4 (0.00) The a iables a e
coin eg a ed and he e
a e 4 coin eg a ing
equa ions a he 0.05 le el
A mos 1 * 42.65 (0.00)
A mos 2 19.96 (0.00)
A mos 3 5.39 (0.02)
Japan
None * 54.209 (0.01) The a iables a e
coin eg a ed and he e is
1 coin eg a ing equa ion
a he 0.05 le el
A mos 1 * 22.017 (0.29)
A mos 2 9.316 (0.33)
A mos 3 2.336 (0.12)
Ge many
None * 43.60 (0.11)
No coin eg a ion
A mos 1 * 21.16 (0.34)
A mos 2 7.25 (0.54)
A mos 3 1.53 (0.21)
Economies 2025,13, 46 16 o 29
Table 2. Con .
Coun y Hypo hesized
No. o CEs
T ace S a is ics (P ob)
Rema ks
India
None * 62.52 (0.00) The a iables a e
coin eg a ed and he e is
1 coin eg a ing equa ion
a he 0.05 le el
A mos 1 * 23.76 (0.21)
A mos 2 11.47 (0.18)
A mos 3 3.04 (0.08)
UK *
None * 49.16 (0.03) The a iables a e
coin eg a ed and he e is
1 coin eg a ing equa ion
a he 0.05 le el
A mos 1 * 19.57 (0.45)
A mos 2 7.54 (0.51)
A mos 3 2.76 (0.09)
F ance
None * 80.95 (0.00) The a iables a e
coin eg a ed and he e
a e 4 coin eg a ing
equa ions a he 0.05 le el
A mos 1 * 43.05 (0.00)
A mos 2 19.18 (0.01)
A mos 3 5.86 (0.01)
I aly
None * 47.56 (0.00) The a iables a e
coin eg a ed and he e is
1 coin eg a ing equa ion
a he 0.05 le el
A mos 1 * 28.79 (0.06)
A mos 2 14.88 (0.06)
A mos 3 4.68 (0.06)
Canada *
None * 38.56 (0.22)
No coin eg a ion
A mos 1 * 27.79 (0.11)
A mos 2 13.88 (0.06)
A mos 3 5.68 (0.06)
B azil
None * 77.33 (0.00) The a iables a e
coin eg a ed and he e
a e 2 coin eg a ing
equa ions a he 0.05 le el
A mos 1 * 38.01 (0.00)
A mos 2 9.86 (0.29)
A mos 3 0.28 (0.59)
Russia *
None * 54.36 (0.01) The a iables a e
coin eg a ed and he e
a e 2 coin eg a ing
equa ions a he 0.05 le el
A mos 1 * 32.37 (0.02)
A mos 2 13.18 (0.10)
A mos 3 3.76 (0.06)
S. Ko ea *
None * 70.63 (0.00) The a iables a e
coin eg a ed and he e
a e 2 coin eg a ing
equa ions a he 0.05 le el
A mos 1 * 38.50 (0.00)
A mos 2 11.51 (0.18)
A mos 3 0.189 (0.66)
Aus alia
None * 59.83 (0.00) The a iables a e
coin eg a ed and he e
a e 2 coin eg a ing
equa ions a he 0.05 le el
A mos 1 * 19.91 (0.43)
A mos 2 4.33 (0.87)
A mos 3 0.15 (0.70)
Mexico *
None * 98.71 (0.00) The a iables a e
coin eg a ed and he e
a e 3 coin eg a ing
equa ions a he 0.05 le el
A mos 1 * 45.36 (0.00)
A mos 2 18.45 (0.01)
A mos 3 1.95 (0.16)
Economies 2025,13, 46 17 o 29
Table 2. Con .
Coun y Hypo hesized
No. o CEs
T ace S a is ics (P ob)
Rema ks
Spain
None * 52.67 (0.00) The a iables a e
coin eg a ed and he e is
1 coin eg a ing equa ion
a he 0.05 le el
A mos 1 * 23.74 (0.20)
A mos 2 12.92 (0.11)
A mos 3 2.59 (0.09)
Indonesia
None * 68.93 (0.00) The a iables a e
coin eg a ed and he e
a e 2 coin eg a ing
equa ions a he 0.05 le el
A mos 1 * 31.05 (0.03)
A mos 2 5.60 (0.74)
A mos 3 3.15 (0.08)
Ne he lands
None * 47.99 (0.04) The a iables a e
coin eg a ed and he e is
1 coin eg a ing equa ion
a he 0.05 le el
A mos 1 * 21.95 (0.29)
A mos 2 11.25 (0.19)
A mos 3 3.45 (0.06)
S. A abia *
None * 56.16 (0.00) The a iables a e
coin eg a ed and he e
a e 4 coin eg a ing
equa ions a he 0.05 le el
A mos 1 * 29.67 (0.01)
A mos 2 15.47 (0.05)
A mos 3 5.45 (0.01)
Tu kiye
None * 55.75 (0.00) The a iables a e
coin eg a ed and he e is
1 coin eg a ing equa ion
a he 0.05 le el
A mos 1 * 28.17 (0.07)
A mos 2 10.89 (0.27)
A mos 3 4.56 (0.03)
Swi ze land
None * 78.83 (0.00) The a iables a e
coin eg a ed and he e is
1 coin eg a ing equa ion
a he 0.05 le el
A mos 1 * 28.87 (0.31)
A mos 2 13.56 (0.10)
A mos 3 0.009 (0.94)
No e: * ma ks in he i s column indica e he se ies o he coun ies ollowing he I(2) ea u e. Again, * ma ks
in he second column deno e ejec ion o he ‘no coin eg a ion’ hypo hesis a he 0.05 le el. Sou ce: au ho ’s
calcula ions.
I is obse ed om he able ha he T ace S a is ics show coin eg a ion esul s among
he a iables in 18 coun ies a he 0.05 le el o signi icance, bu his was no shown o
Ge many and Canada. This means he ou g ow h indica o s as pe he Ba o model a e
coin eg a ed and he e a e long- un ela ionships among hem. This is a alid jus i ica ion
o whe he he go e nmen sec o in e ms o good ins i u ions has good impac s on pe
capi a income g ow h. The leading coun ies in he wo ld in e ms o GDP ha e expe ienced
highe g ow h o ou pu s due o hei s ong public ins i u ions, hei labo o ce and he
coo dina ion be ween public spending and labo o ce.
Now, we es o sho - un dynamics among he ou a iables a ound he equilib ium
ela ions by VECM o see whe he he coin eg a ing ela ions a e s able. Fu he , VECM
analysis is pe o med o hose coun ies ha ha e long- un ela ions among he a iables.
The esul s o VECM a e gi en in Table 3.
Economies 2025,13, 46 18 o 29
Table 3. Long- un causali y es esul s h ough VECM.
Coun y Dependen
Va iables Independen Va iables EC Te m(η) P ob. Rema ks
China
G/Y G/Y ×L, Popula ion, PCGDP 15.59 0.00 No LR causali y
G/Y ×L G/Y, Popula ion, PCGDP 0.0001 0.00 No LR causali y
Popula ion G/Y, G/Y ×L, PCGDP −271,179 0.31 No LR causali y
PCGDP G ow h G/Y, G/Y ×L, Popula ion 579.21 0.26 No LR causali y
Japan
G/Y G/Y ×L, Popula ion, PCGDP −23.59 0.02 G/Y ×L, Popula ion, PCGDP→G/Y
G/Y ×L G/Y, Popula ion, PCGDP −2.0000 0.02 G/Y, Popula ion, PCGDP→G/Y ×L
Popula ion G/Y, G/Y ×L, PCGDP 401,023 0.39 No LR causali y
PCGDP G ow h G/Y, G/Y ×L, Popula ion 37,322 0.00 No LR causali y
India
G/Y G/Y ×L, Popula ion, PCGDP 2.003 0.14 No LR causali y
G/Y ×L G/Y, Popula ion, PCGDP 1,790,000 0.09 No LR causali y
Popula ion G/Y, G/Y ×L, PCGDP −294,086 0.01 G/Y, G/Y ×L, PCGDP→Popula ion
PCGDP G ow h G/Y, G/Y ×L, Popula ion 61.67 0.22 No LR causali y
UK
G/Y G/Y ×L, Popula ion, PCGDP −0.063 0.98 No LR causali y
G/Y ×L G/Y, Popula ion, PCGDP 4,112,746 0.97 No LR causali y
Popula ion G/Y, G/Y ×L, PCGDP 79,800 0.00 No LR causali y
PCGDP G ow h G/Y, G/Y ×L, Popula ion −2353 0.46 No LR causali y
F ance
G/Y G/Y ×L, Popula ion, PCGDP −1.02 0.19 No LR causali y
G/Y ×L G/Y, Popula ion, PCGDP −39,756,754 0.22 No LR causali y
Popula ion G/Y, G/Y ×L, PCGDP 39,862 0.00 No LR causali y
PCGDP G ow h G/Y, G/Y ×L, Popula ion −1219 0.31 No LR causali y
B azil
G/Y G/Y ×L, Popula ion, PCGDP 0.07 0.03 No LR causali y
G/Y ×L G/Y, Popula ion, PCGDP 9,181,923 0.03 No LR causali y
Popula ion G/Y, G/Y ×L, PCGDP −338.3 0.26 No LR causali y
PCGDP G ow h G/Y, G/Y ×L, Popula ion −26.16 0.18 No LR causali y
Russia
G/Y G/Y ×L, Popula ion, PCGDP −23.42 0.00 G/Y ×L, Popula ion, PCGDP→G/Y
G/Y ×L G/Y, Popula ion, PCGDP −23,500,000 0.00 G/Y, Popula ion, PCGDP→G/Y ×L
Popula ion G/Y, G/Y ×L, PCGDP −233,665 0.05 G/Y, G/Y ×L, PCGDP→Popula ion
PCGDP G ow h G/Y, G/Y ×L, Popula ion 3318 0.13 No LR causali y
S. Ko ea
G/Y G/Y ×L, Popula ion, PCGDP −14.58 0.03 G/Y ×L, Popula ion, PCGDP→G/Y
G/Y ×L G/Y, Popula ion, PCGDP −5,040,000 0.03 G/Y, Popula ion, PCGDP→G/Y ×L
Popula ion G/Y, G/Y ×L, PCGDP −64,407 0.70 No LR causali y
PCGDP G ow h G/Y, G/Y ×L, Popula ion −23.39 0.00 G/Y, G/Y ×L, Popula ion→PCGDP
Aus alia
G/Y G/Y×L, Popula ion, PCGDP −0.31 0.03 No LR causali y
G/Y ×L G/Y, Popula ion, PCGDP −2,040,000 0.13 No LR causali y
Popula ion G/Y, G/Y ×L, PCGDP −64,407 0.70 No LR causali y
PCGDP G ow h G/Y, G/Y ×L, Popula ion 0.49 0.01 No LR causali y
Mexico
G/Y G/Y ×L, Popula ion, PCGDP 4.77 0.08 No LR causali y
G/Y ×L G/Y, Popula ion, PCGDP 45,600,000 0.03 No LR causali y
Popula ion G/Y, G/Y ×L, PCGDP −14,147 0.74 No LR causali y
PCGDP G ow h G/Y, G/Y ×L, Popula ion 8.89 0.04 No LR causali y
Spain
G/Y G/Y ×L, Popula ion, PCGDP 6.085 0.00 G/Y ×L, Popula ion, PCGDP→G/Y
G/Y ×L G/Y, Popula ion, PCGDP −17,000,000 0.00 G/Y, Popula ion, PCGDP→G/Y ×L
Popula ion G/Y, G/Y ×L, PCGDP 99,605 0.41 No LR causali y
PCGDP G ow h G/Y, G/Y ×L, Popula ion 6.475 0.00 No LR causali y
Economies 2025,13, 46 19 o 29
Table 3. Con .
Coun y Dependen
Va iables Independen Va iables EC Te m(η) P ob. Rema ks
Indonesia
G/Y G/Y ×L, Popula ion, PCGDP −2.76 0.33 No LR causali y
G/Y ×L G/Y, Popula ion, PCGDP −30,900,000 0.41 No LR causali y
Popula ion G/Y, G/Y ×L, PCGDP 79,385 0.00 No LR causali y
PCGDP G ow h G/Y, G/Y ×L, Popula ion −0.91 0.05 G/Y, G/Y ×L, Popula ion→PCGDP
Ne he lands
G/Y G/Y ×L, Popula ion, PCGDP 3.62 0.55 No LR causali y
G/Y ×L G/Y, Popula ion, PCGDP 41,572,903 0.52 No LR causali y
Popula ion G/Y, G/Y ×L, PCGDP 39,787 0.00 No LR causali y
PCGDP G ow h G/Y, G/Y ×L, Popula ion −0.87 0.77 No LR causali y
S. A abia
G/Y G/Y ×L, Popula ion, PCGDP −4.24 0.00 G/Y ×L, Popula ion, PCGDP→G/Y
G/Y ×L G/Y, Popula ion, PCGDP −87,856,447 0.00 G/Y, Popula ion, PCGDP→G/Y ×L
Popula ion G/Y, G/Y ×L, PCGDP 45,042 0.47 No LR causali y
PCGDP G ow h G/Y, G/Y ×L, Popula ion 0.14 0.00 No LR causali y
Tu kiye
G/Y G/Y ×L, Popula ion, PCGDP −1.44 0.00 G/Y ×L, Popula ion, PCGDP→G/Y
G/Y ×L G/Y, Popula ion, PCGDP −53,429,008 0.01 G/Y, Popula ion, PCGDP→G/Y ×L
Popula ion G/Y, G/Y ×L, PCGDP 32,999 0.03 No LR causali y
PCGDP G ow h G/Y, G/Y ×L, Popula ion −0.46 0.41 No LR causali y
Swi ze land
G/Y G/Y ×L, Popula ion, PCGDP −0.936 0.12 No LR causali y
G/Y ×L G/Y, Popula ion, PCGDP −4,546,936 0.16 No LR causali y
Popula ion G/Y, G/Y ×L, PCGDP −1776 0.36 No LR causali y
PCGDP G ow h G/Y, G/Y ×L, Popula ion −9.91 0.01 G/Y, G/Y ×L, Popula ion→PCGDP
No e: PCGDP in columns 3 and 6 ep esen s he g ow h o PCGDP. Sou ce: au ho ’s own calcula ions.
I is obse ed ha he e o s in maximum o he models a e no co ec ed as he signs o
he e o co ec ion e ms a e no nega i e and signi ican . Though he e a e some nega i e
alues o he said e m, hey a e no s a is ically signi ican in mos o he cases. Only in
he case o h ee coun ies, S. Ko ea, Indonesia and Swi ze land, a e he e signi ican e o
co ec ions when PCGDP G ow h is he endogenous dependen a iable. I can also be
said ha good public ins i u ions, popula ion and hei in e ac ion e ms a ec o a he
ha e a causal in luence on he pe capi a GDP g ow h a e in he long un. On he o he
hand, PCGDP G ow h, popula ion and he in e ac ion e m ha e a causal in luence on
he go e nmen sha e o GDP in he long un in he case o some coun ies such as Japan,
Russia, S. Ko ea, Spain, S. A abia and Tu kiye. Again, popula ion is in luenced by he es
o he ac o s in he long un in he case o India and Russia. This s udy does no ind any
e o co ec ion o long- un causali y in any o he ou combina ions o he a iables in he
case o China, he UK, F ance, I aly, B azil, Aus alia, Mexico and he Ne he lands.
4.4. Sho -Run Causali y Tes Resul s
Al hough he e a e absences in he long- un causal ela ions in mos o he coun ies,
a leas o he occasions whe e PCGDP G ow h is held as an endogenous dependen
a iable, he e may be he possibili ies o sho - un causal in e plays among he a iables.
The Wald es is used o es o sho - un causali y among he a iables. The esul s a e
gi en in Table 4. The decision ule is h ough he alues o Chi-Squa e es s a is ics wi h
p obabili ies less han 0.05.
Economies 2025,13, 46 20 o 29
Table 4. Sho - un causali y es esul s (Wald es ).
Coun y Dependen
Va iables Independen Va iables Chi-Squa e
Value P ob. Rema ks
USA
G/Y G/Y ×L, Popula ion, PCGDP 2.468 0.480 No SR causali y
G/Y ×L G/Y, Popula ion, PCGDP 7.768 0.051 G/Y, Popula ion, PCGDP→G/Y ×L
Popula ion G/Y, G/Y ×L, PCGDP 3.722 0.293 No SR causali y
PCGDP G ow h G/Y, G/Y ×L, Popula ion 4.035 0.257 No SR causali y
China
G/Y G/Y ×L, Popula ion, PCGDP 17.95 0.00 G/Y ×L, Popula ion, PCGDP→G/Y
G/Y ×L G/Y, Popula ion, PCGDP 19.66 0.00 G/Y, Popula ion, PCGDP→G/Y ×L
Popula ion G/Y, G/Y ×L, PCGDP 3.15 0.78 No SR causali y
PCGDP G ow h G/Y, G/Y ×L, Popula ion 6.38 0.38 No SR causali y
Japan
G/Y G/Y ×L, Popula ion, PCGDP 5.28 0.50 No SR causali y
G/Y ×L G/Y, Popula ion, PCGDP 6.078 0.41 No SR causali y
Popula ion G/Y, G/Y ×L, PCGDP 2.27 0.89 No SR causali y
PCGDP G ow h G/Y, G/Y ×L, Popula ion 19.53 0.003 G/Y, G/Y ×L, Popula ion→PCGDP
Ge many
G/Y G/Y ×L, Popula ion, PCGDP 1.38 0.96 No SR causali y
G/Y ×L G/Y, Popula ion, PCGDP 1.53 0.95 No SR causali y
Popula ion G/Y, G/Y ×L, PCGDP 19.60 0.00 G/Y, G/Y ×L, PCGDP→Popula ion
PCGDP G ow h G/Y, G/Y ×L, Popula ion 1.55 0.00 No SR causali y
India
G/Y G/Y ×L, Popula ion, PCGDP 6.48 0.37 No SR causali y
G/Y ×L G/Y, Popula ion, PCGDP 7.64 0.26 No SR causali y
Popula ion G/Y, G/Y ×L, PCGDP 13.06 0.04 G/Y, G/Y ×L, PCGDP→Popula ion
PCGDP G ow h G/Y, G/Y ×L, Popula ion 3.40 0.75 No SR causali y
UK
G/Y G/Y ×L, Popula ion, PCGDP 4.25 0.64 No SR causali y
G/Y ×L G/Y, Popula ion, PCGDP 4.27 0.63 No SR causali y
Popula ion G/Y, G/Y ×L, PCGDP 16.11 0.01 G/Y, G/Y ×L, PCGDP→Popula ion
PCGDP G ow h G/Y, G/Y ×L, Popula ion 15.81 0.05 G/Y, G/Y ×L, Popula ion→PCGDP
F ance
G/Y G/Y ×L, Popula ion, PCGDP 3.11 0.79 No SR causali y
G/Y ×L G/Y, Popula ion, PCGDP 3.95 0.68 No SR causali y
Popula ion G/Y, G/Y ×L, PCGDP 50.40 0.00 G/Y, G/Y ×L, PCGDP→Popula ion
PCGDP G ow h G/Y, G/Y ×L, Popula ion 3.25 0.77 G/Y, G/Y ×L, Popula ion→PCGDP
I aly
G/Y G/Y ×L, Popula ion, PCGDP 13.06 0.04 G/Y ×L, Popula ion, PCGDP→G/Y
G/Y ×L G/Y, Popula ion, PCGDP 12.58 0.05 G/Y, Popula ion, PCGDP→G/Y ×L
Popula ion G/Y, G/Y ×L, PCGDP 3.09 0.79 No SR causali y
PCGDP G ow h G/Y, G/Y ×L, Popula ion 3.12 0.79 No SR causali y
Canada
G/Y G/Y ×L, Popula ion, PCGDP 6.27 0.39 No SR causali y
G/Y ×L G/Y, Popula ion, PCGDP 6.29 0.39 No SR causali y
Popula ion G/Y, G/Y ×L, PCGDP 1.34 0.96 No SR causali y
PCGDP G ow h G/Y, G/Y ×L, Popula ion 8.70 0.19 No SR causali y
B azil
G/Y G/Y ×L, Popula ion, PCGDP 27.10 0.00 G/Y ×L, Popula ion, PCGDP→G/Y
G/Y ×L G/Y, Popula ion, PCGDP 28.22 0.00 G/Y, Popula ion, PCGDP→G/Y ×L
Popula ion G/Y, G/Y ×L, PCGDP 17.08 0.00 G/Y, G/Y ×L, PCGDP→Popula ion
PCGDP G ow h G/Y, G/Y ×L, Popula ion 12.30 0.05 G/Y, G/Y ×L, Popula ion→PCGDP
Russia
G/Y G/Y ×L, Popula ion, PCGDP 9.30 0.15 No SR causali y
G/Y ×L G/Y, Popula ion, PCGDP 9.03 0.17 No SR causali y
Popula ion G/Y, G/Y ×L, PCGDP 19.87 0.00 G/Y, G/Y ×L, PCGDP→Popula ion
PCGDP G ow h G/Y, G/Y ×L, Popula ion 6.68 0.35 G/Y, G/Y ×L, Popula ion→PCGDP
Economies 2025,13, 46 21 o 29
Table 4. Con .
Coun y Dependen
Va iables Independen Va iables Chi-Squa e
Value P ob. Rema ks
S. Ko ea
G/Y G/Y ×L, Popula ion, PCGDP 6.94 0.32 No SR causali y
G/Y ×L G/Y, Popula ion, PCGDP 7.41 0.28 No SR causali y
Popula ion G/Y, G/Y ×L, PCGDP 26.41 0.00 G/Y, G/Y ×L, PCGDP→Popula ion
PCGDP G ow h G/Y, G/Y ×L, Popula ion 27.99 0.00 G/Y, G/Y ×L, Popula ion→PCGDP
Aus alia
G/Y G/Y ×L, Popula ion, PCGDP 4.62 0.59 No SR causali y
G/Y ×L G/Y, Popula ion, PCGDP 6.62 0.35 No SR causali y
Popula ion G/Y, G/Y ×L, PCGDP 4.12 0.66 No SR causali y
PCGDP G ow h G/Y, G/Y ×L, Popula ion 18.59 0.00 G/Y, G/Y ×L, Popula ion→PCGDP
Mexico
G/Y G/Y ×L, Popula ion, PCGDP 10.12 0.12 No SR causali y
G/Y ×L G/Y, Popula ion, PCGDP 11.56 0.07 No SR causali y
Popula ion G/Y, G/Y ×L, PCGDP 18.86 0.00 G/Y, G/Y ×L, PCGDP→Popula ion
PCGDP G ow h G/Y, G/Y ×L, Popula ion 25.025 0.00 G/Y, G/Y ×L, Popula ion→PCGDP
Spain
G/Y G/Y ×L, Popula ion, PCGDP 51.77 0.00 G/Y ×L, Popula ion, PCGDP→G/Y
G/Y ×L G/Y, Popula ion, PCGDP 44.47 0.00 G/Y, Popula ion, PCGDP→G/Y ×L
Popula ion G/Y, G/Y ×L, PCGDP 2.51 0.86 No SR causali y
PCGDP G ow h G/Y, G/Y ×L, Popula ion 22.86 0.00 G/Y, G/Y ×L, Popula ion→PCGDP
Indonesia
G/Y G/Y ×L, Popula ion, PCGDP 7.85 0.24 No SR causali y
G/Y ×L G/Y, Popula ion, PCGDP 8.75 0.19 No SR causali y
Popula ion G/Y, G/Y ×L, PCGDP 15.67 0.01 G/Y, G/Y ×L, PCGDP→Popula ion
PCGDP G ow h G/Y, G/Y ×L, Popula ion 32.92 0.00 G/Y, G/Y ×L, Popula ion→PCGDP
Ne he lands
G/Y G/Y ×L, Popula ion, PCGDP 1.07 0.98 No SR causali y
G/Y ×L G/Y, Popula ion, PCGDP 1.09 0.98 No SR causali y
Popula ion G/Y, G/Y ×L, PCGDP 13.19 0.05 G/Y, G/Y ×L, PCGDP→Popula ion
PCGDP G ow h G/Y, G/Y ×L, Popula ion 0.82 0.99 No SR causali y
S. A abia
G/Y G/Y ×L, Popula ion, PCGDP 19.52 0.00 G/Y ×L, Popula ion, PCGDP→G/Y
G/Y ×L G/Y, Popula ion, PCGDP 15.75 0.01 G/Y, Popula ion, PCGDP→G/Y ×L
Popula ion G/Y, G/Y ×L, PCGDP 2.84 0.83 No SR causali y
PCGDP G ow h G/Y, G/Y ×L, Popula ion 7.77 0.25 No SR causali y
Tu kiye
G/Y G/Y ×L, Popula ion, PCGDP 12.98 0.05 G/Y ×L, Popula ion, PCGDP→G/Y
G/Y ×L G/Y, Popula ion, PCGDP 12.65 0.05 G/Y, Popula ion, PCGDP→G/Y ×L
Popula ion G/Y, G/Y ×L, PCGDP 6.56 0.36 No SR causali y
PCGDP G ow h G/Y, G/Y ×L, Popula ion 5.82 0.44 No SR causali y
Swi ze land
G/Y G/Y ×L, Popula ion, PCGDP 5.44 0.48 No SR causali y
G/Y ×L G/Y, Popula ion, PCGDP 4.95 0.54 No SR causali y
Popula ion G/Y, G/Y ×L, PCGDP 23.66 0.00 G/Y, G/Y ×L, PCGDP→Popula ion
PCGDP G ow h G/Y, G/Y ×L, Popula ion 34.26 0.00 G/Y, G/Y ×L, Popula ion→PCGDP
No e: PCGDP in columns 3 and 6 ep esen s he g ow h o PCGDP. Sou ce: au ho ’s own calcula ions.
In 11 coun ies on he lis , public ins i u ions associa ed wi h popula ion and he
in e ac ion e m ha e a causal in luence on he g ow h o PCGDP. These coun ies a e
Japan, he UK, F ance, B azil, Russia, S. Ko ea, Aus alia, Mexico, Spain, Indonesia and
Swi ze land. Thus, in mos o he coun ies, he g ow h o PCGDP is explained by good
public pa icipa ion coupled wi h i s impac s on he popula ion. In o he wo ds, he Ba o
model o endogenous g ow h inco po a ing public ins i u ions wo ks well in he wo ld’s
leading coun ies in e ms o he g oss domes ic p oduc . I is also obse ed ha he g ow h
o income and popula ion ha e a causal in luence on go e nmen pa icipa ion in coun ies
Economies 2025,13, 46 22 o 29
like China, I aly, B azil, Spain, S. A abia and Tu kiye. On he o he hand, he in e ac ion
ac o is in luenced by income g ow h, labo o ce and go e nmen pa icipa ion in he
coun ies such as he USA, China, I aly, B azil, Spain, S. A abia and Tu kiye. The e a e
common esul s in he case o G/Y and G/Y
×
L o he abo e se s o coun ies. B azil
is he only coun y in he lis whe e all ou occasions o causal in e plays ha e wo ked.
Canada is he only coun y in he lis whe e no causal in e plays among he ou associa ed
a iables a e obse ed.
4.5. Robus ness o he Resul s
To check he obus ness o he esul s o he model, his s udy es s o he no mali y
o he esiduals. Table 5p esen s he esul s o he di e en models speci ied agains he
c i e ia o se ial au oco ela ion, he e oskedas ici y and no mali y checks o he esidu-
als h ough he B eusch–God ey Se ial Co ela ion LM Tes , B eusch–Pagan–God ey
He e oskedas ici y Tes and His og am-No mali y Tes , espec i ely.
Table 5. Residuals’ diagnos ic checking (only p obabili ies a e no ed).
Coun y Dependen
Va iables
B eusch–God ey
Se ial Co ela ion
LM Tes
B eusch–Pagan–
God ey
He e oskedas ici y
Tes
His og am-
No mali y Tes Rema ks
China
G/Y 0.999 0.853 0.934 Model has good i as he e o s
sa is y all he diagnos ic checking
G/Y ×L 0.999 0.838 0.22
Model has pa ially good i as he
e o s do no sa is y he
no mali y p ope y
Popula ion 0.999 0.98 0.037
Model has pa ially good i as he
e o s do no sa is y he
no mali y p ope y
PCGDP G ow h 0.995 0.70 0.72 Model has good i as he e o s
sa is y all he diagnos ic checking
Japan
G/Y 0.992 0.36 0.95 Model has good i as he e o s
sa is y all he diagnos ic checking
G/Y ×L 0.995 0.27 0.96 Model has good i as he e o s
sa is y all he diagnos ic checking
Popula ion 0.99 0.54 0.21
Model has pa ially good i as he
e o s do no sa is y he
no mali y p ope y
PCGDP G ow h 0.99 0.70 0.60 Model has good i as he e o s
sa is y all he diagnos ic checking
India
G/Y 0.20 0.93 0.65 Model has good i as he e o s
sa is y all he diagnos ic checking
G/Y ×L 0.99 0.59 0.005
Model has pa ially good i as he
e o s do no sa is y he
no mali y p ope y
Popula ion 0.89 0.32 0.48 Model has good i as he e o s
sa is y all he diagnos ic checking
PCGDP G ow h 0.98 0.12 0.96 Model has good i as he e o s
sa is y all he diagnos ic checking
UK
G/Y 0.96 0.40 0.50 Model has good i as he e o s
sa is y all he diagnos ic checking
G/Y ×L 0.99 0.65 0.83 Model has good i as he e o s
sa is y all he diagnos ic checking
Popula ion 0.58 0.30 0.54 Model has good i as he e o s
sa is y all he diagnos ic checking
PCGDP G ow h 0.99 0.12 0.96 Model has good i as he e o s
sa is y all he diagnos ic checking
Economies 2025,13, 46 23 o 29
Table 5. Con .
Coun y Dependen
Va iables
B eusch–God ey
Se ial Co ela ion
LM Tes
B eusch–Pagan–
God ey
He e oskedas ici y
Tes
His og am-
No mali y Tes Rema ks
F ance
G/Y 0.98 0.54 0.60 Model has good i as he e o s
sa is y all he diagnos ic checking
G/Y ×L 0.85 0.64 0.72 Model has good i as he e o s
sa is y all he diagnos ic checking
Popula ion 0.78 0.88 0.69 Model has good i as he e o s
sa is y all he diagnos ic checking
PCGDP G ow h 0.84 0.91 0.84 Model has good i as he e o s
sa is y all he diagnos ic checking
B azil
G/Y 0.99 0.88 0.81 Model has good i as he e o s
sa is y all he diagnos ic checking
G/Y ×L 0.85 0.78 0.68 Model has good i as he e o s
sa is y all he diagnos ic checking
Popula ion 0.97 0.83 0.59 Model has good i as he e o s
sa is y all he diagnos ic checking
PCGDP G ow h 0.85 0.78 0.68 Model has good i as he e o s
sa is y all he diagnos ic checking
Russia
G/Y 0.99 0.47 0.41 Model has good i as he e o s
sa is y all he diagnos ic checking
G/Y ×L 0.94 0.58 0.56 Model has good i as he e o s
sa is y all he diagnos ic checking
Popula ion 0.88 0.66 0.60 Model has good i as he e o s
sa is y all he diagnos ic checking
PCGDP G ow h 0.91 0.63 0.55 Model has good i as he e o s
sa is y all he diagnos ic checking
S. Ko ea
G/Y 0.97 0.26 0.72
Model has pa ially good i as he
e o s do no sa is y he
no mali y p ope y
G/Y ×L 0.92 0.48 0.77 Model has good i as he e o s
sa is y all he diagnos ic checking
Popula ion 0.95 0.65 0.66 Model has good i as he e o s
sa is y all he diagnos ic checking
PCGDP G ow h 0.94 0.71 0.58 Model has good i as he e o s
sa is y all he diagnos ic checking
Aus alia
G/Y 0.99 0.80 0.14
Model has pa ially good i as he
e o s do no sa is y he
no mali y p ope y
G/Y ×L 0.98 0.85 0.45 Model has good i as he e o s
sa is y all he diagnos ic checking
Popula ion 0.96 0.86 0.58 Model has good i as he e o s
sa is y all he diagnos ic checking
PCGDP G ow h 0.97 0.91 0.68 Model has good i as he e o s
sa is y all he diagnos ic checking
Mexico
G/Y 0.99 0.57 0.19
Model has pa ially good i as he
e o s do no sa is y he
no mali y p ope y
G/Y ×L 0.88 0.61 0.43 Model has good i as he e o s
sa is y all he diagnos ic checking
Popula ion 0.95 0.64 0.54 Model has good i as he e o s
sa is y all he diagnos ic checking
PCGDP G ow h 0.96 0.75 0.62 Model has good i as he e o s
sa is y all he diagnos ic checking
Economies 2025,13, 46 24 o 29
Table 5. Con .
Coun y Dependen
Va iables
B eusch–God ey
Se ial Co ela ion
LM Tes
B eusch–Pagan–
God ey
He e oskedas ici y
Tes
His og am-
No mali y Tes Rema ks
Spain
G/Y 0.99 0.51 0.007
Model has pa ially good i as he
e o s do no sa is y he
no mali y p ope y
G/Y ×L 0.99 0.60 0.78 Model has good i as he e o s
sa is y all he diagnos ic checking
Popula ion 0.98 0.62 0.71 Model has good i as he e o s
sa is y all he diagnos ic checking
PCGDP G ow h 0.97 0.71 0.65 Model has good i as he e o s
sa is y all he diagnos ic checking
Indonesia
G/Y 0.91 0.69 0.66 Model has good i as he e o s
sa is y all he diagnos ic checking
G/Y ×L 0.97 0.72 0.68 Model has good i as he e o s
sa is y all he diagnos ic checking
Popula ion 0.95 0.75 0.78 Model has good i as he e o s
sa is y all he diagnos ic checking
PCGDP G ow h 0.98 0.82 0.58 Model has good i as he e o s
sa is y all he diagnos ic checking
Ne he lands
G/Y 0.99 0.72 0.012
Model has pa ially good i as he
e o s do no sa is y he
no mali y p ope y
G/Y ×L 0.96 0.81 0.002
Model has pa ially good i as he
e o s do no sa is y he
no mali y p ope y
Popula ion 0.98 0.77 0.15
Model has pa ially good i as he
e o s do no sa is y he
no mali y p ope y
PCGDP G ow h 0.99 0.68 0.22
Model has pa ially good i as he
e o s do no sa is y he
no mali y p ope y
S. A abia
G/Y 0.99 0.87 0.42 Model has good i as he e o s
sa is y all he diagnos ic checking
G/Y ×L 0.98 0.78 0.56 Model has good i as he e o s
sa is y all he diagnos ic checking
Popula ion 0.95 0.88 0.62 Model has good i as he e o s
sa is y all he diagnos ic checking
PCGDP G ow h 0.98 0.74 0.57 Model has good i as he e o s
sa is y all he diagnos ic checking
Tu kiye
G/Y 0.99 0.80 0.51 Model has good i as he e o s
sa is y all he diagnos ic checking
G/Y ×L 0.98 0.74 0.59 Model has good i as he e o s
sa is y all he diagnos ic checking
Popula ion 0.95 0.75 0.65 Model has good i as he e o s
sa is y all he diagnos ic checking
PCGDP G ow h 0.96 0.81 0.71 Model has good i as he e o s
sa is y all he diagnos ic checking
Swi ze land
G/Y 0.97 0.45 0.01
Model has pa ially good i as he
e o s do no sa is y he
no mali y p ope y
G/Y ×L 0.98 0.66 0.62 Model has good i as he e o s
sa is y all he diagnos ic checking
Popula ion 0.99 0.85 0.71 Model has good i as he e o s
sa is y all he diagnos ic checking
PCGDP G ow h 0.88 0.71 0.56 Model has good i as he e o s
sa is y all he diagnos ic checking
No e: PCGDP in columns 3 and 6 ep esen s he g ow h o PCGDP. Sou ce: au ho ’s own calcula ions.
