Ezzahid, Elhadj; Ra ik, Hamid
A icle
Analyzing he impac o public capi al on p i a e capi al
p oduc i i y in a panel o A ican na ions
Economies
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Ci a ion: Ezzahid, Elhadj, and Hamid
Ra ik. 2024. Analyzing he Impac o
Public Capi al on P i a e Capi al
P oduc i i y in a Panel o A ican
Na ions. Economies 12: 118. h ps://
doi.o g/10.3390/economies12050118
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economies
A icle
Analyzing he Impac o Public Capi al on P i a e Capi al
P oduc i i y in a Panel o A ican Na ions
Elhadj Ezzahid and Hamid Ra ik *
Depa men o Economics, Facul y o Law, Economic and Social Sciences Agdal, Mohammed V Uni e si y,
Raba 6430, Mo occo; [email p o ec ed]
*Co espondence: [email p o ec ed]
Abs ac : This esea ch con ibu es o he ongoing discou se conce ning he e iciency o public capi al
and i s in luence on he p oduc i i y o p i a e capi al and o al ac o p oduc i i y wi hin A ican
economies. Employing he s anda d p oduc ion app oach, we include public capi al as a dis inc
inpu o assess i s speci ic impac on ou pu g ow h and he enhancemen o o al ac o p oduc i i y.
We a gue ha public capi al, p edominan ly mani es ing h ough in as uc u e, cons i u es an
indispensable elemen o os e ing g ow h. Fundamen al o he p oduc i i y o p i a e capi al is
i s eliance on a su icien s ock o public in as uc u e o ope a ional e iciency. Ou empi ical
analysis e eals ha public capi al exhibi s a subs an i e long- e m in luence on ou pu g ow h and
he p oduc i i y o p i a e capi al. Howe e , in he sho e m, he disce nible impac o public capi al
is less p onounced. Mo eo e , while public capi al eme ges as a no iceable ac o in ou pu g ow h,
i s in luence on o al ac o p oduc i i y emains ela i ely subdued.
Keywo ds: public capi al; economic g ow h; o al ac o p oduc i i y; A ica
1. In oduc ion
Assessing he ex en o which public in as uc u es, such as oads, highways, elec-
ici y ne wo ks, ai po s, ailways, and o he acili ies designed o public use can boos
ou pu g ow h and p oduc i i y is o pa amoun impo ance o policy make s. Cen al o
he objec i e o his pape is he sign and magni ude o he elas ici y o ou pu pe uni o
p i a e capi al wi h espec o public capi al and he con ibu ion o he la e o o al ac o
p oduc i i y (hence o h, TFP).1
Undeniably, public in as uc u es play a pi o al ole in suppo ing he p i a e sec o ,
gi en ha he p oduc ion o goods and se ices ypically necessi a es he anspo a ion
o essen ial inpu s such as ene gy, wa e , and o he i al componen s—a ask un easible
o he p i a e sec o o accomplish on i s own.
2
Hence, a logical p esupposi ion a ises
ega ding he indispensabili y o public in as uc u e o os e sus ained economic g ow h.
Ne e heless, go e nmen -p o ided in as uc u e can po en ially c ea e dis o ions i
i s a s o displace p i a e in es men . Ba o (1990)’s endogenous g ow h model posi s ha
as he p opo ion o go e nmen spending in he g oss domes ic p oduc (GDP) expands,
he economy’s g ow h a e also inc eases un il i a ains an op imal poin , beyond which i
begins o decline. Thus, he p o isioning o in as uc u e by he go e nmen in A ican
na ions migh no be op imal due o inadequa e public in es men .
Fo p i a e capi al o be p oduc i e, i needs an e icien and di e si ied in as uc u e.
Tha is, he p oduc i i y o p i a e in es men is con ingen upon he exis ence o a obus
s ock o public capi al su passing a speci ic h eshold.
3
Thus, he p oduc i i y o public
capi al is expec ed upon eaching his h eshold, se ing as an essen ial equi emen o he
ope a ion o he p i a e sec o .
I is c ucial o s udy he e ec o public capi al on p i a e capi al in A ican na ions
o se e al easons. Fi s , public capi al can enhance he p oduc i i y and g ow h o he
Economies 2024,12, 118. h ps://doi.o g/10.3390/economies12050118 h ps://www.mdpi.com/jou nal/economies
Economies 2024,12, 118 2 o 18
p i a e sec o by p o iding essen ial in as uc u e and se ices ha he p i a e sec o
canno o will no p o ide on i s own. Second, public capi al can also a ec he alloca ion
and e iciency o p i a e capi al by c ea ing posi i e o nega i e ex e nali ies, depending on
he quali y and quan i y o public in es men . Thi d, public capi al can ha e implica ions
o he iscal and mac oeconomic s abili y, as i in ol es public spending, bo owing, and
axa ion decisions. The e o e, s udying he e ec o public capi al on p i a e capi al can
help policy-make s design op imal public in es men s a egies ha can maximize he
bene i s and minimize he cos s o public capi al o he p i a e sec o and he economy as
a whole.
This s udy ocuses on A ica o se e al easons. Fi s , in as uc u e in A ica signi i-
can ly lags behind ha o mos o he de eloping na ions (Fos e and B iceño-Ga mendia
2010). Second, in as uc u e is a majo ca alys o economic g ow h, p oduc i i y enhance-
men , and a acili a o o ade (Donaubaue e al. 2018;Aschaue 1989).
This wo k aims o shed ligh on he con ibu ion o public capi al o he p oduc i i y
o p i a e capi al in A ican economies, using he s anda d p oduc ion unc ion app oach
and da a om 1960 o 2017. The es o his pape is o ganized as ollows. Sec ion 2deals
e iewis he li e a u e on he nexus be ween public capi al and g ow h. Sec ion 3ou lines
he channels h ough which public in as uc u e a ec s ou pu and p oduc i i y. Sec ion 4
de ails he empi ical app oach. Sec ion 4p esen s he model. Sec ion 5discusses he da a
and s ylized ac s. Sec ion 6p esen s he esul s. Finally, Sec ion 7concludes.
2. Public Capi al and G ow h
The po en ial ole o public capi al in enhancing economic g ow h and p oduc i i y
poses a challenging ela ionship o measu e empi ically. This s ems om he di icul ies in
es ima ing he s ock o public capi al, equi ing assump ions abou i s ini ial alue, dep eci-
a ion a e, and he p ice de la o o public in es men (E e ha and Sumlinski 2001).
While i is he case ha he s ock o public capi al is he sum o public in es men s
made each yea minus he dep ecia ion a e, s udying he impac o public capi al ins ead
o in es men is mo e ele an due o he ac ha i akes a long ime o public p ojec s o
ha e a posi i e e u n mani es ed h ough he enhanced p oduc i i y o he p i a e sec o .
While he e is abundan esea ch s udying empi ically public capi al in ela ion o
ou pu g ow h and p i a e capi al, he e is, howe e , none o he case o A ican economies.
Thus, u he esea ch is impe a i e o assess he in luence o public capi al on g ow h. Such
ask is no only o g ea impo ance om an academic pe spec i e, bu i can also guide
policy making by shi ing a en ion on he likely equal impo ance o public capi al as, in
ecen yea s, he e has been inc eased in e es in he p imo dial ole o he p i a e sec o .
4
Es ima es o capi al s ock, bo h public and p i a e, a e p edica ed on assump ions
ela ed o ini ial s ock le els and dep ecia ion a es, po en ially leading o inaccu acies. Con-
sequen ly, empi ical s udies could exhibi biases in de e mining he ex en o public capi al’s
con ibu ion o g ow h, pa icula ly in coun ies wi h unsa is ac o y s a is ical sys ems.
Go e nmen in es men migh no e ec i ely ansla e in o in ended in as uc u e
like oads, b idges, o public buildings due o ine iciencies. Ine icien go e nmen in-
es men s migh be cos ly due o co up ion and he en -seeking beha io o poli icians
and bu eauc a s (Kee e and Knack 2007). Indeed, he agg ega e da a used by expe s o
es ima e public capi al s ock migh no accu a ely e lec he eal physical capi al a ailable.
Signi ican in as uc u e gaps a e obse ed in A ican coun ies. Inc eases in ac o
inpu s a he ini ial s ages o de elopmen a e assumed o gene a e high e u ns due o
high ma ginal p oduc i i y. Acco dingly, we should expec o ind elas ici ies o ou pu
wi h espec o public capi al o be ela i ely highe in A ican economies compa ed o
ad anced and middle-income economies. The main a ionale o his assump ion is he
obse ed gaps o public in as uc u es in A ica, especially in sub-Saha an coun ies.
The empi ical li e a u e p esen s a a ied spec um ega ding he impac o public
capi al on economic g ow h. Some s udies ind a nega i e con ibu ion, while o he s high-
ligh i s signi icance in os e ing g ow h (Lig ha and Suá ez 2011). In hese s udies, public
Economies 2024,12, 118 3 o 18
capi al is ypically in eg a ed as a ac o inpu alongside labo and p i a e capi al wi hin
p oduc ion unc ions.
5
Bom and Lig ha ’s (2014) me a- eg ession analysis, examining
578 es ima es om 68 s udies be ween 1983 and 2008, e ealed sho - un ou pu elas ici ies
o abou 0.083, long- un elas ici ies a ound 0.122, wi h an a e age ou pu elas ici y o
app oxima ely 0.106, signi ying i s subs an ial con ibu ion o g ow h.
In con as , Aschaue (1989), in a seminal pape which aimed o in es iga e he 1970s
p oduc i i y decline in he U.S, inds a ema kable 0.39% inc ease in ou pu pe uni o
p i a e capi al a e a 1% ise in he public–p i a e capi al a io. This elas ici y s a kly
con as s wi h he a e age 0.106 ound in Bom and Lig ha ’s me a-analysis. Howe e ,
c i iques om au ho s like Munnell (1990) challenged he c edibili y o Aschaue ’s esul s,
conside ing hem disp opo iona ely high ela i e o common indings in he li e a u e.
Ouéd aogo e al. (2019) es ima ed he impac o public in es men on p i a e in-
es men in sub-Saha an A ican coun ies, e ealing an o e all posi i e e ec o public
in es men on i s p i a e coun e pa . Simila ly, Hende son and Kumbhaka (2006) ex-
plo ed a panel encompassing 48 s a es,
6
es ima ing a posi i e and signi ican e u n on
public capi al.
Lig ha (2000) es ima ed he e ec o public capi al on ou pu g ow h in Po ugal.
Employing he p oduc ion unc ion app oach and he un es ic ed ec o au o eg essi e
model (VAR) wi h yea ly da a spanning om 1965 o 1995, he s udy un eiled public capi-
al’s c ucial ole as a de e minan o long- e m g ow h. The elas ici y o ou pu conce ning
public capi al in his analysis aligned wi h p io li e a u e, s anding a 0.19.
A slanalp e al. (2010) examined he impac o public capi al ac oss OECD (O ganisa-
ion o Economic Co-ope a ion and De elopmen ) and de eloping coun ies, using da a
om 1960 o 2001. Thei indings indica ed a posi i e elas ici y o ou pu wi h espec o
public capi al. No ably, o non-OECD na ions, he elas ici y was ela i ely highe , wi h
a public capi al coe icien a 0.13, while de eloping coun ies exhibi ed an insigni ican
coe icien o public capi al.
Bleaney e al. (2001) uses a panel da a model o in es iga e he e ec s o dis o iona y
axes, ha is, axes ha cause ine iciencies in he economy by discou aging consump ion
and sa ing, and go e nmen expendi u es o OECD coun ies. Thei esul s aligned wi h
he p edic ions o Ba o’s endogenous g ow h model. Likewise, Rami ez (2002) analyzed
he co ela ion be ween public spending on in as uc u e and labo p oduc i i y in Mexico.
Th ough coin eg a ion analysis, hei s udy concluded ha go e nmen spending on
in as uc u e, a he han o e all go e nmen in es men , signi ican ly in luenced he
g ow h o labo p oduc i i y.
Ram (1996) conduc ed an es ima ion in which ou pu is a unc ion o he sha es o
p i a e and public in es men s in GDP, along wi h he annual g ow h a e o expo s. The
indings e ealed ha public in es men exhibi ed no ably highe p oduc i i y compa ed
o i s p i a e coun e pa .
Examining he ole o public capi al accumula ion in ou pu g ow h o 28 de eloping
coun ies be ween 1981 and 1991, Dessus and He e a (2000) employed a simul aneous
equa ions model. Thei conclusion poin ed owa ds he posi i e impac o public capi al
accumula ion on long- e m g ow h. Howe e , hey highligh ed an indi ec c owding-ou
e ec o p i a e capi al accumula ion esul ing om public capi al o ma ion.
In his ega d, Hol z-Eakin (1992) a gued ha i is coun e -in ui i e o sugges ha
he public p o ision o oads, b idges, wa e , sewage acili ies, and o he componen s o
in as uc u e do no a ec p oduc ion di ec ly. Howe e , he s udy acknowledged ha
ce ain public p ojec s migh no be subjec o cos –bene i cons ain s and could su i e
despi e being unp oduc i e. Consequen ly, he s udy emphasized he limi a ions o using
agg ega e da a o con incingly es ablish public capi al as he sole d i e o imp o emen s
in p i a e p oduc i i y.
Compa ed o he ci ed li e a u e (see Table 1), his s udy is an empi ical con ibu ion
ega ding he e ec o public capi al, i s ly on ou pu in he sho - and long- e m; secondly,
on he p oduc i i y o p i a e capi al; hi dly, on he o al ac o p oduc i i y in he con ex
Economies 2024,12, 118 4 o 18
o A ican economies. In his con ex , his s udy seeks o ill he gap ega ding empi ical
s udies assessing he elas ici y o ou pu wi h espec o public capi al.
Table 1. A summa y o he li e a u e on he e iciency o public capi al.
S udy Focus Key Findings
Ram (1996)Ou pu es ima ion based on p i a e and
public in es men s
Public in es men has a highe
p oduc i i y compa ed o p i a e
in es men .
Dessus and He e a (2000) Role o public capi al in ou pu g ow h
Posi i e impac o public capi al
accumula ion on long- e m g ow h, ye
no ed indi ec c owding-ou e ec on
p i a e capi al.
Hol z-Eakin (1992)Public in as uc u e’s impac on
p oduc ion
Dispu es coun e -in ui i e idea o no
di ec impac bu acknowledges some
unp oduc i e public p ojec s due o
cos –bene i cons ain s.
Lig ha (2000)E ec o public capi al on ou pu g ow h
in Po ugal
Public capi al ound as a c ucial
de e minan o long- e m g ow h,
showing a ce ain elas ici y o ou pu
conce ning public capi al.
A slanalp e al. (2010)
Impac o public capi al ac oss OECD and
de eloping coun ies
Posi i e elas ici y o ou pu conce ning
public capi al, wi h ela i ely highe
impac o non-OECD na ions, while
de eloping coun ies exhibi ed an
insigni ican coe icien .
Bleaney e al. (2001)E ec s o dis o iona y axes and
go e nmen expendi u es
Aligns wi h p edic ions o Ba o’s
endogenous g ow h model, explo ing he
impac on OECD coun ies.
Hende son and Kumbhaka (2006)Re u n on public capi al o a panel o
48 s a es
Shows a posi i e and signi ican e u n
on public capi al.
Rami ez (2002)Co ela ion be ween public spending on
in as uc u e and g ow h
Go e nmen spending on in as uc u e,
a he han o e all go e nmen
in es men , signi ican ly in luences he
g ow h o labo p oduc i i y.
Aschaue (1989)1970s p oduc i i y decline and
public–p i a e capi al a io
Indica es a subs an ial inc ease in ou pu
pe uni o p i a e capi al wi h a ise in
he public–p i a e capi al a io, a inding
challenged due o disp opo iona ely
high esul s.
Sou ce: au ho s.
The Dynamics o Public Capi al, P i a e Capi al, and Ou pu
Exogenous g ow h models place signi ican emphasis on in es men o ansi ional
dynamics and achie ing s eady-s a e g ow h. Howe e , ea lie models like ha o Solow
(1956) did no di e en ia e be ween he impac s o p i a e and public capi al on hese
dynamics. P i a e capi al no ably enhances ou pu di ec ly by bols e ing he economy’s
p oduc i e esou ces and indi ec ly by os e ing echnological ad ancemen s, he eby
enhancing o e all e iciency.
Con e sely, public capi al, la gely ep esen ed by in as uc u e, does no di ec ly
impac p oduc ion. Ins ead, i s ole lies in enhancing he e icacy o p i a e capi al and
labo p oduc i i y, acili a ing he adop ion o new echnologies and modes o p oduc ion.
Ye , due o he absence o a di ec p icing mechanism o go e nmen se ices, which a e
p ima ily inanced h ough axes o bo owing, he alloca ion o public capi al migh no
always be op imally managed.
Economies 2024,12, 118 5 o 18
In a neoclassical amewo k o economic g ow h, posi i e echnological shocks a e
p esumed o be he p ima y ca alys o long- e m g ow h. Eas e ly and Le ine (2001)
ound empi ical e idence ha co obo a es his asse ion, sugges ing ha TFP s ands as a
signi ican d i e o economic g ow h. Wi hou he p oduc i i y gains, he g ow h o pe
capi a income would ha e been subs an ially lowe in indus ialized economies. Addi ion-
ally, wi hin Solow’s g ow h model, he accumula ion o physical capi al con ibu es o pe
capi a ou pu g ow h only un il he s eady s a e is eached. Subsequen ly, sus ained g ow h
is p edominan ly de i ed om exogenous echnological changes.7
In ligh o wha p ecedes, we belie e ha he absence o obus public in as uc u e
hinde s he p i a e sec o om p opelling p oduc i i y, e en in he p esence o o he g ow h
ca alys s such as echnology, physical and human capi al, and well-es ablished ins i u ions.
Fo ins ance, i we conside a se s ock o p i a e inpu s—whe e kis a b oad concep
o capi al, co e ing bo h human and physical capi al—alongside ins i u ions ensu ing
p ope y igh s, law en o cemen , and con ac en o cemen , he p i a e sec o ’s inabili y
o access c ucial elemen s like oads, ene gy, o wa e di ec ly impedes ou pu gene a ion.
To illus a e, assuming Cobb–Douglass echnology,
y=A·kαg1−α
, wi h low le els o
g, ou pu will be low despi e su icien endowmen s o k. The e o e, i ollows ha public
in as uc u e is necessa y o spu he eme gence o g ow h in he p i a e sec o .
Boos ing he s ock o public capi al necessi a es public in es men which can be unded
h ough axes o bo owing. Howe e , axes, once hey exceed a ce ain h eshold, can
in oduce dis o ions,
8
hinde ing g ow h a he han acili a ing i . Al hough ex e nal
bo owing can be e ec i e, i is no a sus ainable s a egy when he social a e o e u n o
public in es men alls below he cos o bo owing.
Despi e public capi al being a majo inpu in he p oduc ion unc ion besides p i a e
inpu s, i does no necessa ily con ibu e signi ican ly o g ow h. One o he easons why
public in es men does no con ibu e o he g ow h o p i a e p oduc ion is i s c owding
ou e ec o p i a e in es men (see, Sunda a ajan and Thaku 1980;Higgins and Link
1981, among o he s). This was one o he chie coun e a gumen s o public spending since
i was i s ad oca ed by Keynes. Financing public spending h ough axes educes he
esou ces a ailable o he p i a e sec o , esul ing in dec eased p i a e in es men and,
consequen ly, educed o e all g ow h.9
Al e na i ely, when public spending is unded h ough bo owing, he heigh ened
demand o loanable unds aises in e es a es, making i cos lie o he p i a e sec o
o in es , he eby supp essing p i a e p oduc ion. Ine icien public in es men u he
complica es he inancing o public p ojec s h ough axes o ex e nal bo owing, as in es o
us co ela es closely wi h he economy’s iscal posi ion. P oponen s o de ici spending
con end ha judicious public bo owing, in es ed in p ojec s s imula ing p i a e in es -
men , can indi ec ly enable new channels o p oduc ion and di ec ly bols e agg ega e
demand h ough classical Keynesian channels.
Ba o’s seminal wo k in 1990 delinea es wo ca ego ies o public expendi u es. The i s
pe ains o p oduc i e in es men s ha signi ican ly con ibu e o long- e m g ow h, while
he second ca ego y in ol es expendi u es deemed i ele an o g ow h, such as spending
on social se ices. Tax educ ions on in es men s imula e g ow h by incen i izing he
p i a e sec o o in es , much like public spending aimed a en o cing p ope y igh s
and main aining law and o de , which, in u n, enhances he e u ns on p i a e capi al.
Con e sely, dis o iona y axes impede p i a e in es men , he eby diminishing long-
e m g ow h. Building upon his, he Ba o and Sala-i-Ma in (1992) model assumes n
p oduce s gene a ing ou pu y(whe e he agg ega e ou pu is ep esen ed as Y = ny) using
he Cobb–Douglas echnology:
y=Ak1−αgα,
whe e Ais echnology, k ep esen s a b oad concep o capi al
10
pe p oduce (k = K/n), g
ep esen s he go e nmen -p o ided se ices pe p oduce (g = G/n); Gand K ep esen s
agg ega e public and p i a e capi als. Go e nmen inances i s se ices h ough a p opo -
Economies 2024,12, 118 6 o 18
ional ax on ou pu
τ
and le ies a lump-sum ax L.
11
The go e nmen is subjec o he
ollowing cons ain :
ng +C=L+τny,
whe e C ep esen s go e nmen consump ion, i.e., non-in es men goods ha a e no
included in he p oduc ion unc ion. They showed ha he g ow h a e ∅is as ollows:
∅=λ(1−τ)(1−α)A1
1−α(g
y)α/(1−α)−µ,
whe e
λ
and
µ
a e pa ame e s in he u ili y unc ion. This equa ion illus a es ha dis o -
iona y axes diminish he g ow h a e, whe eas go e nmen -p o ided se ices deno ed by
‘g’ augmen g ow h. Non-dis o iona y axes, speci ically L, exhibi no impac on g ow h.
I is no ewo hy ha go e nmen consump ion does no a ec he g ow h a e. Howe e ,
wi hin he model, he e is he assump ion ha he go e nmen main ains a balanced bud-
ge , he eby a oiding su pluses o de ici s. Bleaney e al. (2001) conduc ed a es on he
a o emen ioned model, yielding obus esul s ha a i m i s asse ions—highligh ing he
endu ing impac o iscal policy on economic g ow h.
3. The Channels h ough Which Public In as uc u e A ec Ou pu and P oduc i i y
The e a e many channels h ough which public in es men can a ec ou pu and TFP
(see Figu e 1). One ype o public in es men migh no be enough o encou age g ow h
because he p i a e sec o needs many in as uc u es in o de o unc ion e icien ly. The
ollowing igu e is a lis o he main componen s o public capi al and how hey con ibu e
o imp o ing ou pu and TFP.
Economies 2024, 12, x FOR PEER REVIEW 6 o 19
+
=
+
,
whe e C ep esen s go e nmen consump ion, i.e., non-in es men goods ha a e no in-
cluded in he p oduc ion unc ion. They showed ha he g ow h a e ∅ is as ollows:
∅
=
(
1
−
)
(
1
−
)
(
)
/
(
)
−
,
whe e and a e pa ame e s in he u ili y unc ion. This equa ion illus a es ha dis o -
iona y axes diminish he g ow h a e, whe eas go e nmen -p o ided se ices deno ed
by ‘g’ augmen g ow h. Non-dis o iona y axes, speci ically L, exhibi no impac on
g ow h. I is no ewo hy ha go e nmen consump ion does no a ec he g ow h a e.
Howe e , wi hin he model, he e is he assump ion ha he go e nmen main ains a bal-
anced budge , he eby a oiding su pluses o de ici s. Bleaney e al. (2001) conduc ed a es
on he a o emen ioned model, yielding obus esul s ha a i m i s asse ions—highligh -
ing he endu ing impac o iscal policy on economic g ow h.
3. The Channels h ough Which Public In as uc u e A ec Ou pu and P oduc i i y
The e a e many channels h ough which public in es men can a ec ou pu and TFP
(see Figu e 1). One ype o public in es men migh no be enough o encou age g ow h
because he p i a e sec o needs many in as uc u es in o de o unc ion e icien ly. The
ollowing igu e is a lis o he main componen s o public capi al and how hey con ibu e
o imp o ing ou pu and TFP.
Roads play a p imo dial ole in bols e ing p i a e sec o p oduc i i y by signi ican ly
educing ansac ion cos s. Ag awal e al. (2017) conduc ed a s udy u ilizing da a on high-
ways, ail oads, and ou es, aiming o un eil he impac o in e -s a e anspo a ion on
egional inno a ion. Thei empi ical indings e ealed ha a 10% inc ease in he s ock o
highways co ela es wi h a 1.7% su ge in egis e ed pa en s. Mo eo e , hey highligh ed
he unde es ima ed in luence o anspo a ion in as uc u e on economic g ow h. In e -
connec ing egions h ough oads yields a dual bene i —i allows egions o le e age hei
specialized p oduc ion by ading su plus goods and os e s in e dependence, enabling
egional specializa ion.
Figu e 1. The channels h ough which public capi al in luences ou pu and p oduc i i y. Sou ce:
au ho s.
Figu e 1. The channels h ough which public capi al in luences ou pu and p oduc i i y. Sou ce:
au ho s.
Roads play a p imo dial ole in bols e ing p i a e sec o p oduc i i y by signi ican ly
educing ansac ion cos s. Ag awal e al. (2017) conduc ed a s udy u ilizing da a on
highways, ail oads, and ou es, aiming o un eil he impac o in e -s a e anspo a ion
on egional inno a ion. Thei empi ical indings e ealed ha a 10% inc ease in he
s ock o highways co ela es wi h a 1.7% su ge in egis e ed pa en s. Mo eo e , hey
highligh ed he unde es ima ed in luence o anspo a ion in as uc u e on economic
Economies 2024,12, 118 7 o 18
g ow h. In e connec ing egions h ough oads yields a dual bene i —i allows egions o
le e age hei specialized p oduc ion by ading su plus goods and os e s in e dependence,
enabling egional specializa ion.
In he con ex o he A ican con inen , he expansion o oad ne wo ks is poised
o signi ican ly enhance con inen al and global ade. The expansion and c ea ion o
anspo a ion channels ac oss A ican coun ies will likely s eamline he mo emen o
goods, os e ing inc eased ade links. Impo an ly, anspo a ion in as uc u e no only
eases he mo emen o goods bu also acili a es he mobili y o ac o s o p oduc ion (Buys
e al. 2006;A is e al. 2007).
F om a mic oeconomic pe spec i e, a i m endowed wi h speci ic ac o inpu s expe i-
ences enhanced p oduc i i y due o educed ansac ion cos s s emming om ei he he
cons uc ion o new public oads o he enhancemen o exis ing ones. This imp o emen
enables he i m o gene a e mo e ou pu using he same inpu le els, e ec i ely ele a ing
he o al ac o p oduc i i y. An essen ial cha ac e is ic o publicly p o ided in as uc u es
is hei b oad- eaching bene i o nume ous p i a e agen s. This easoning ex ends o
a ious public in as uc u es ha acili a e anspo a ion. Suppo ing his asse ion, in
he case o manu ac u ing es ablishmen s in India du ing he pe iod 1998–2012, Kail hya
and Kambhampa i (2022) ound ha a 1% inc ease in oad densi y co ela es wi h a 0.25%
ise in TFP.
Conside ing he a o emen ioned poin s, he ine iciency o public in es men in an
en i onmen ma ked by a limi ed s ock o anspo a ion in as uc u e does no s em
om he inhe en ine ec i eness o public capi al i sel . Ins ead, i o en ela es o he
challenges in implemen ing and managing public p ojec s, issues like co up ion, and he
ele a ed cos s o public in es men . Dzhumashe (2014) illus a es ha , a lowe le els o
he go e nmen ’s sha e in GDP, co up ion signi ican ly hampe s he e iciency o public
spending, consequen ly impac ing o e all g ow h.
Elec ici y ne wo ks s and as a i al componen o in as uc u e, ac ing as he li eblood
o economic p oduc ion in de eloped economies. In ac , elec ici y in as uc u e is in-
dispensable o echnology-in ensi e machine y and high-end de ices, acknowledged in
li e a u e as pi o al d i e s o p oduc i i y. Lowe ing ene gy cos s o es ablished busi-
nesses can subs an ially educe hei o e all expenses and bols e hei ou pu . Ex ending
elec ici y ne wo ks o p e iously unelec i ied u al a eas o e s households he capaci y
o ope a e elec ic appliances o household asks, ha e access o illumina ion du ing nigh
hou s, acili a e asks like well-digging and ins alling wa e pumps, ul ima ely leading
o inc eased ag icul u al p oduc ion. Se e al s udies demons a e he posi i e impac o
ene gy consump ion on economic g ow h (e.g., S e n e al. 2019;Bane jee e al. 2017;Saidi
and Hammami 2015).
While he p i a e sec o can supply elec ici y, he ini ial phases o es ablishing la ge-
scale ene gy in as uc u es in impo e ished na ions o en demand subs an ial in es men s,
making hem mo e easible by he go e nmen . Con e sely, la ge-scale in as uc u es
ha migh no yield immedia e o medium- e m p o i s migh no a ac p i a e sec-
o in ol emen .
In es men s in heal hca e and educa ion play a pi o al ole in enhancing he quali y
o human capi al, a well-explo ed concep in he li e a u e. Alongside hese, he p o ision
o essen ial in as uc u es is indispensable o os e ing skilled human capi al, especially
o i ms engaged in echnology-in ensi e goods.
Tsau ai and Ndou (2019) conduc ed an analysis on he in luence o in as uc u e and
human capi al de elopmen on economic g ow h in ansi ional economies. Employing
dynamic panel and gene alized me hods o momen s es ima o s (GMMs), he s udy spans
25 ansi ional economies om 1995 o 2015. The indings unde sco e he impo ance o he
in e ac ion be ween in as uc u e and human capi al de elopmen in bols e ing economic
g ow h in ansi ional economies. This s udy ecommends policies ocusing on augmen ing
human capi al de elopmen o ampli y he capaci y o in as uc u e de elopmen in
in luencing economic g ow h.
Economies 2024,12, 118 8 o 18
Finally, Canning and Benna han (2000) explo e he impac s o in as uc u e and hu-
man capi al on economic de elopmen u ilizing c oss-coun y da a spanning om 1950
o 1992. Thei esea ch es ima es a p oduc ion unc ion encompassing in as uc u e and
human capi al as inpu s while con olling o geog aphical, ins i u ional, and openness
ac o s. The s udy a i ms he signi ican and posi i e e ec s o bo h in as uc u e and hu-
man capi al on ou pu pe wo ke . Fu he mo e, i highligh s ha , in coun ies wi h highe
le els o human capi al, he ma ginal p oduc o in as uc u e is p opo ionally highe .
While each public in as uc u e componen independen ly in luences ou pu , he col-
lec i e execu ion o mul iple public p ojec s—such as oads, highways, elec ici y ne wo ks,
elecommunica ion in as uc u es, dams, and sewe acili ies—yields a cumula i e and
ampli ied e ec on o e all g ow h. A synch onized inc ease in hese a ied in as uc u e
componen s signi ican ly con ibu es o economic de elopmen . Con e sely, an isola ed
su ge in one aspec , like public in es men in oads wi hou a concu en de elopmen
o o he public acili ies, is unlikely o mani es no iceable impac s on ou pu g ow h.
This unde s anding, al hough challenging o empi ically es , s ongly ad oca es o a
comp ehensi e expansion o a ious public in as uc u e componen s h oughou he
A ican con inen .
4. Model
To es ima e he elas ici y o ou pu wi h espec o he public capi al s ock, we use a
s anda d Cobb–Douglas p oduc ion unc ion, such as ha in Aschaue (1989):
Yi =F(Ni ,Ki ,Gi )=Ai NeN
i KeK
i GeG
i (1)
whe e Y
i
is ou pu , A
i
is he le el o p oduc i i y, N
i
is labo , K
i
is p i a e capi al, and G
i
is he public capi al s ock.
eN,eK
, and
eG
a e he elas ici y o ou pu wi h espec o labo ,
p i a e and public capi al, espec i ely. The subsc ip s iand ep esen he coun y and
ime a iables, espec i ely. I is possible o include o he kinds o capi al such as human
and ins i u ional capi al, bu we assume ha hey indi ec ly a ec he g ow h a e ia hei
impac on he p oduc i i y measu e Ai .
Following he wo k o Aschaue (1989), we in oduce na u al loga i hms which yield
he ollowing equa ion:
yi =ai +eN·ni +eK·ki +eG·gi , (2)
This equa ion does no assume any es ic ions on he pa ame e s, assuming ha
compe i i e ma ke s p i a e inpu s will be paid hei ma ginal p oduc s. I is assumed
ha go e nmen se ices make p i a e inpu s mo e p oduc i e and allow o inc easing
e u ns o e all inpu s. I is assumed ha he e a e cons an e u ns o scale o e p i a e
inpu s bu inc easing e u ns o scale o e all inpu s, i.e.,
eN+eK=
1. Thus, we ob ain he
ollowing equa ion:
yi =ai +eN·ni +(1−eN)·ki +eG·gi (3)
Simpli ying yields he ollowing:
yi =ai +eN·ni +ki −eN·ki +eG·gi (4)
The e o e:
yi −ki =ai +eN·(ni −ki )+eG·gi (5)
Addi ionally, p oduc i i y is gi en by:
pi =yi −sN·ni −sk·ki =ai +eG·gi (6)
Equa ion (5) exp esses ou pu pe uni o capi al as a unc ion o p oduc i i y, he
labo –capi al a io, and he s ock o public capi al, while Equa ion (6) exp esses o al
ac o p oduc i i y as a unc ion o echnical p og ess and he low o go e nmen se ices
assuming i is ela ed o he s ock o public capi al, whe e sNand ska e ac o sha es.
Economies 2024,12, 118 15 o 18
Table 6. Ou pu pe uni o capi al (y−k).
Equa ion Es ima ion Me hod Cons an Time n−k g −k g k
(13) aFixed e ec s
−5.85 ***
(−8.55)
0.003 ***
(9.87)
0.481 ***
(38.63)
0.133 ***
(8.58)
(14) bFixed e ec s
−15.172 ***
(−5.68)
0.008 ***
(6.00)
0.323 ***
(7.07)
0.128 ***
(8.30)
−0.296 ***
(−6.19)
a
F(3;2118) = 744.85 ***; R
2
: wi hin = 0.50, be ween = 0.50, o e all = 0.48.
b
F(4;2217) = 564.92 ***; R
2
: wi hin = 0.50,
be ween = 0.47, o e all = 0.45. *** signi ican a 5% accep ance h eshold.
Equa ion (14) (Table 6) acili a es sepa a e es ima es o he coe icien s associa ed wi h
public and p i a e capi al. Speci ically, a 1% inc ease in public capi al is associa ed wi h an
app oxima e 0.13% ise in p i a e capi al’s p oduc i i y. This esul unde sco es he pi o al
ole o public capi al in augmen ing he p oduc i i y o he p i a e sec o .
Equa ion (15) (Table 7) shows ha a 1% inc ease in public capi al causes only a 0.053%
inc ease in o al ac o p oduc i i y. Upon including p i a e inpu s, he esponse o o al
ac o p oduc i i y o a 1% inc ease in public capi al ises o 0.128% (Equa ion (16), Table 7),
which indica es he p esence o se ial co ela ion among explana o y a iables. Equa ion
(17) (Table 7) ela es TFP o public capi al and he combina ion o p i a e inpu s. We obse e
ha he combina ion o p i a e inpu s ca ies a nega i e sign, which is in acco dance wi h
he assump ion o cons an e u ns o scale. Equa ion (18) (Table 7) exhibi s he s ong
ela ionship be ween public capi al pe uni o he combina ion o p i a e inpu s and TFP.
A 1% inc ease in he public capi al pe combina ion o p i a e inpu s aises o al ac o
p oduc i i y by 0.13%.
Table 7. To al ac o p oduc i i y (p).
Equa ion Es ima ion Me hod Cons an Time g k n i g −i
(15 aFixed e ec s 3.671 ***
(3.73)
−0.001 ***
(−2.65)
0.053 ***
(4.53) – – – –
(16) bFixed e ec s
−15.172 ***
(−5.68)
0.008 ***
(6.00)
0.128 ***
(8.30)
−
0.104 ***
(−6.72)
−
0.328 ***
(7.19) – –
(17) cFixed e ec s
−7.190
(−4.52)
0.004
(5.03)
0.142
(9.46) – –
−0.266
(−9.22) –
(18) dFixed e ec s 0.820
(1.25)
−0.000
(−0.06) – – – – 0.13
(8.65)
a
F(2;2219) = 11.78 ***; R
2
: wi hin = 0.01, be ween = 0.01, o e all = 0.00.
b
F(4;2217)= 30.96 ***;
R2: wi hin = 0.05
,
be ween = 0.36, o e all = 0.28.
c
F(3;2218) = 36.48 ***; R
2
: wi hin = 0.04, be ween = 0.32, o e all = 0.25.
dF(2;2219) = 38.96 ***
; R
2
: wi hin = 0.03, be ween = 0.31, o e all = 0.25. *** signi ican a 5% accep ance h eshold.
The esul s o ou empi ical es ing show ha public capi al is a signi ican con ibu o
o he p i a e sec o ’s p oduc i i y. Howe e , i s di ec impac on TFP is small. None heless,
upon including p i a e inpu s in he speci ica ion, his impac inc eases signi ican ly due o
he s ong co ela ion be ween public capi al and p i a e inpu s. Mo eo e , ou esul s a e
suppo i e o he assump ion o cons an e u ns o scale. Public capi al seems o ha e a
signi ican impac on ou pu g ow h in he long un. Howe e , in he sho un, i s impac
on g ow h is unno iceable.
7. Conclusions
This s udy is a con ibu ion o he deba e o e he e ec i eness o public capi al and
i s con ibu ion o he g ow h o ou pu and TFP. Indeed, his s udy ad ances he empi ical
li e a u e on public capi al’s impac on ou pu and p i a e capi al p oduc i i y bo h in
he sho and long e m, as well as on o al ac o p oduc i i y in he con ex o A ican
economies. We add ess a signi ican gap in he li e a u e by es ima ing he elas ici y o
Economies 2024,12, 118 16 o 18
ou pu wi h espec o public capi al o he case o A ican economies, highligh ing i s
subs an ial long- e m in luence on ou pu g ow h and he p oduc i i y o p i a e capi al.
Al hough he sho - e m e ec s a e less ma ked, and he impac on o al ac o p oduc i i y
is subdued, ou indings unde sco e he c i ical ole o public capi al in economic g ow h.
I is impo an o no e ha economic g ow h in A ica is no ma ching wha we should
expec om a con inen ha is ich wi h na u al esou ces and, on he o he hand, has
an abundan supply, hough unskilled, o labo . Using he s anda d p oduc ion unc ion
app oach, we es ima ed he elas ici y o ou pu wi h espec o public capi al and es ed
he assump ion o cons an e u ns o scale. Ou esul s show ha public capi al is an
impo an con ibu o o ou pu in he long un. We also es ima ed he esponse o p i a e
capi al’s p oduc i i y o changes in public capi al. Ou empi ical model shows ha public
capi al is a signi ican ac o in enhancing p i a e capi al’s p oduc i i y. Howe e , we we e
unable o ind a s ong associa ion be ween public capi al and o al ac o p oduc i i y.
The s udy o he dynamics o economic g ow h assigns a p imo dial ole o ins i u ional
quali y which, h ough i s ole in spu ing a clima e ha a o s p i a e incen i es and
lowe ing ansac ion cos s, is he main d i e o economic g ow h (Acemoglu e al. 2005;
No h 1991). The e o e, o hcoming s udies dealing wi h he same issue should con ol
o he impac o ins i u ions on he e iciency o bo h public and p i a e in es men s. The
magni ude o he impac o public capi al on ou pu in A ican economies is in acco dance
wi h he p eceding li e a u e ha uses panel da a. Consequen ly, ou model is in a o o
mo e public in es men in in as uc u e o boos he p oduc i i y o he p i a e sec o . As
i is well documen ed in he li e a u e, ac o inpu s alone a e no enough o g ow h and
p oduc i i y enhancemen (Eas e ly and Le ine 2001). I is impo an o bea in mind ha
one o he ca ea s in ou da ase is he deg ee o i s accu acy, since he s a is ical sys em in
A ican coun ies is a om being sa is ac o y.
Au ho Con ibu ions: Concep ualiza ion, E.E. and H.R.; me hodology, E.E. and H.R.; so wa e,
H.R.; alida ion, E.E.; o mal analysis, H.R.; in es iga ion, H.R.; esou ces, H.R.; da a cu a ion, H.R.;
w i ing—o iginal d a p epa a ion, H.R.; w i ing— e iew and edi ing, H.R. and E.E.; isualiza ion,
H.R.; supe ision, E.E.; p ojec adminis a ion, E.E.; All au ho s ha e ead and ag eed o he published
e sion o he manusc ip .
Funding: This esea ch ecei ed no ex e nal unding.
Ins i u ional Re iew Boa d S a emen : No applicable.
In o med Consen S a emen : No applicable.
Da a A ailabili y S a emen : Da a used in his s udy can be accessible a : h ps://www. ug.nl/
ggdc/p oduc i i y/pw /pw - eleases/pw 9.1?lang=en and h ps://da a.im .o g/?sk=1ce8a55 -c a7
-4bc0-bce2-256ee65ac0e4 (accessed on 2 May2024).
Con lic s o In e es : The au ho s decla e no con lic o in e es .
No es
1F om a public policy pe spec i e, he highe he elas ici y, he mo e ui ul i is o in es in public acili ies.
2We assume ha he p i a e sec o is unable o p o ide in as uc u e on i s own.
3
Acco ding o Pe ei a and And az (2013), he ou pu elas ici y o public capi al is 0.093 when he public capi al s ock is below he
h eshold le el o 72.4% o GDP and 0.193 when i is o e he h eshold.
4
The Washing on Consensus has placed emphasis on p i a iza ion and he ans e o s a e-owned en e p ises and o he o ms o
public p ope y o he p i a e sec o .
5
Typically, a log-linea ized Cobb–Douglas unc ion is used ei he in le els o in i s di e ences. When es ima ing he elas ici y o
ou pu wi h espec o public capi al in loga i hmic le els, a conce n a ises abou po en ial spu ious eg ession due o he upwa d
sloping end o ac o inpu s. Con e sely, employing es ima ion in i s loga i hmic di e ences add esses his issue, al hough i
comp omises he long- e m ela ionship be ween ou pu and he public capi al s ock.
6Speci ically, 48 Ame ican s a es.
Economies 2024,12, 118 17 o 18
7
Wi hin he well-known neoclassical Solow (1956) g ow h model, an up ick in he sa ing a e ini ially ele a es he capi al s ock o
i s s eady s a e le el. Beyond his poin , addi ional in es men p ima ily se es o o se he pe capi a dep ecia ion o capi al.
Once he economy eaches i s s eady s a e, sus ained g ow h p edominan ly a ises om exogenous echnological shocks.
8Taxes diminish he pool o weal h accessible o he p i a e sec o , he eby exe ing a nega i e in luence on p i a e incen i es.
9
This a ionale holds when ac o accumula ion is conside ed he p ima y g ow h d i e . Howe e , i public expendi u e on
in as uc u e has he capaci y o enhance o al ac o p oduc i i y and o se he loss incu ed om a dec ease in g oss capi al
o ma ion, he likelihood o c owding ou p i a e in es men diminishes.
10 kincludes human and physical capi al.
11
The pa icula i y o lump sum axes is ha hey do no inc ease p opo ionally o he g ow h o ou pu and in his model a e
conside ed o be non-dis o iona y, ha is, hey ha e no e ec on p i a e incen i es o in es in k.
12
Fac o sha es a e de i ed om es ima ing he Cobb–Douglass p oduc ion unc ion whe e he s anda d elas ici ies o labo and
p i a e capi al a e app oxima ions o sKand sN.
13 Be ween pa en heses a e he -S uden s a is ics.
Re e ences
Acemoglu, Da on, Simon Johnson, and James A. Robinson. 2005. Ins i u ions as a undamen al cause o long- un g ow h. Handbook o
Economic G ow h 1: 385–472.
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au ho (s) and con ibu o (s) and no o MDPI and/o he edi o (s). MDPI and/o he edi o (s) disclaim esponsibili y o any inju y o
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