Spatial Price Integration and Spillover Linkages Between Regional Grain Markets in Nigeria

Kassou i, Yacouba; Fo ana, N' Zué Felix
A icle — Published Ve sion
Spa ial P ice In eg a ion and Spillo e Linkages Be ween
Regional G ain Ma ke s in Nige ia
Re iew o De elopmen Economics
P o ided in Coope a ion wi h:
John Wiley & Sons
Sugges ed Ci a ion: Kassou i, Yacouba; Fo ana, N' Zué Felix (2025) : Spa ial P ice In eg a ion and
Spillo e Linkages Be ween Regional G ain Ma ke s in Nige ia, Re iew o De elopmen Economics,
ISSN 1467-9361, Wiley, Hoboken, NJ, Vol. 29, Iss. 3, pp. 1849-1862,
h ps://doi.o g/10.1111/ ode.13190
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Re iew o De elopmen Economics, 2025; 29:1849–1862
h ps://doi.o g/10.1111/ ode.13190
1849
Re iew o De elopmen Economics
REGULAR ARTICLE OPEN ACCESS
Spa ial P ice In eg a ion and Spillo e Linkages Be ween
Regional G ain Ma ke s in Nige ia
YacoubaKassou i1,2,3 | N' Zué FelixFo ana4,5
1Biodi e si y Economics G oup, Ge man Cen e o In eg a i e Biodi e si y Resea ch (iDi ) Halle- Jena- Leipzig, Leipzig, Ge many | 2Depa men
o Economics, Leipzig Uni e si y, Leipzig, Ge many | 3P ague Uni e si y o Economics and Business, Facul y o Finance and Accoun ing, P ague,
CzechRepublic | 4Uni e si é Felix Houphoue Boigny, Abidjan, Cô e d'I oi e | 5Economic Communi y o Wes A ican S a es (ECOWAS) Commission,
Abuja, Nige ia
Co espondence: Yacouba Kassou i (yacouba.kassou i@idi .de)
Recei ed: 24 May 2022 | Re ised: 24 Ap il 2024 | Accep ed: 23 Decembe 2024
Keywo ds: g ain ma ke s| law o one p ice| p ice in eg a ion| ola ili y spillo e
ABSTRACT
This pape aims o cha ac e ize he spa ial se - up o Nige ia's g ain ma ke in eg a ion om Janua y 2002 o Decembe 2013
ac oss 19 Nige ian egions. Using ma ke p ice da a o maize, so ghum, and mille , wo hypo heses a e es ed: (i) he law o one
p ice ac oss ma ke pai s, and (ii) he leade ma ke hypo hesis in any ne wo k o ma ke pai s. The esul s sugges ha in eg a-
ion ails o hold in many cases o o e 60% o ma ke pai s, while pe ec in eg a ion is ound o be conside ably s onge o
o ganized local ma ke s such as Abuja and Lagos han o emo e ma ke s. The e is e idence ha No heas e n ma ke s subjec
o he Boko Ha am insu gency a e weakly in eg a ed wi h he o he ma ke s. Only h ee No hwes u al ma ke s exhibi leading
s a us in ola ili y p edic ion in di e en ma ke s. The indings sugges ha maize and mille ma ke s loca ed in Abuja and Lagos
a e he ne ecei e s o p ice ola ili ies, and hey a e mo e exposed o p ice shocks o igina ing om o he ma ke s. The p icing
policy should mainly concen a e on leading ma ke s as i will be e icien ly ansmi ed o he ollowe s.
1 | In oduc ion
S aple ood lows be ween spa ially disconnec ed a eas in e con-
nec egional ma ke s and acili a e he e icien ansmission o
supply/demand shocks in a gi en ma ke o p ices in o he ma -
ke s in he spa ial ne wo k (Mye s and Jayne2012). Resea ch
a en ion on he deg ee o ma ke in eg a ion and he ansmis-
sion o p ice shocks ac oss ma ke s in de eloping coun ies has
inc eased ma kedly since he ood p ice c isis o 2007/2008. The
inc easing in e es in he opic is explained by he isks asso-
cia ed wi h possible ins abili ies in he p ice o s aple oods in
de eloping coun ies (Rlbeh i e al.2013). Fo ins ance, in he
sub- Saha an A ica egion, i is es ablished ha he a ia ion
in s aple ood p ices ends o be highe and mo e pe sis en
han in o he egions, se e ely impac ing he pu chasing powe
and ood secu i y o poo households (Gilbe , Ch is iaensen,
and Kaminski 2017). Unlocking he in a egional ma ke
connec i i y po en ial is a he hea o he solu ion o limi
p ice inc eases (Abdulai and Egge 1992; Jayne and Jones1997).
The e o e, unde s anding he deg ee o spa ial p ice in eg a ion
and ola ili y ansmission ac oss s aple ood ma ke s is a p e-
equisi e o designing and implemen ing ma ke in e en ions
and ood policies.
Agains his backg ound, his pape aims o p esen a comp e-
hensi e e alua ion o he law o one p ice om wo inno a i e
aspec s in Nige ia. Fi s ly, we examine he deg ee o which s a-
ple ood p ices in geog aphically sepa a ed ma ke s o a di -
e en le els o he alue chain sha e common long- e m p ice
in o ma ion. Secondly, we cha ac e ize he ola ili y dynamics
in ol ing all s aple ood ma ke pai s wi hin Nige ia o cap u e
p ice spillo e s among egional ma ke s. To achie e hese ob-
jec i es, we ocus on majo s aple ood commodi ies, includ-
ing so ghum, maize, and mille , which a e a good illus a ion
This is an open access a icle unde he e ms o he C ea i e Commons A ibu ion-NonComme cial License, which pe mi s use, dis ibu ion and ep oduc ion in any medium, p o ided he
o iginal wo k is p ope ly ci ed and is no used o comme cial pu poses.
© 2025 The Au ho (s). Re iew o De elopmen Economics published by John Wiley & Sons L d.
1850 Re iew o De elopmen Economics, 2025
o hinly (domes ically)- aded ood commodi ies in Nige ia,
unlike adi ional expo commodi ies (cocoa, co on, co ee).
Since he consump ion pa e ns o hese s aples migh a y ac-
co ding o egions wi hin he same coun y, a comp ehensi e
analysis o s aples in ol es in o ma ion on an accep able spa-
ial esolu ion. Thanks o he g anula i y o he da a p o ided
by Po eous(2019), he s udy ocuses on 19 majo s aple ma ke s
o maize, so ghum, and mille in Nige ia om Janua y 2002 o
Decembe 2013.
F om he empi ical e idence, we selec Nige ia o se e al ea-
sons. Fi s ly, due o apid popula ion g ow h, u ban expansion,
and he in e nal con lic igge ed by he insu gency o Boko
Ha am, ood g ain ma ke s a e challenged by inc easing de-
mand, sho supply, and he con e sion o ag icul u al land
in o se lemen a eas (Odozi and Omonona2012). Acco dingly,
domes ic ood g ain ma ke s need o adjus o hese p essu es
by educing he sensi i i y o p oduc ion o un o eseen e en s
in o de o imp o e he e iciency o he coun y's ag icul u al
p oduc ma ke s. Secondly, in line wi h go e nmen policies
on inc easing he compe i i eness o local alue chains, he
Fede al Go e nmen o Nige ia adop ed es ic ion measu es
on impo s o maize and o he g ains. This measu e can se i-
ously al e he local ma ke s uc u e and equilib ium p ices
o wo k agains ood supplies, pa icula ly du ing poo ha es
season (ad e se e ec s o clima e change).1 As he c ucial policy
p esc ip ion o local ag icul u al de elopmen , ma ke in eg a-
ion is a i al p econdi ion o i s e ec i eness (Baulch1997).
Thi dly, he unde lying s aple oods, including maize, so ghum,
and mille , a e among he leading ce eal c ops o he coun y,
and hei p oduc ion co e s mo e han 50% o he cul i a ed
a ea (Geo ge e al.2021; Law ence e al.2015). Despi e adop -
ing p o ec i e ade policies o p io i ize domes ic ood and ag-
icul u al p oduc ion, Nige ia is expec ed o ace dec eases in
g ain supplies due o con lic and economic ac o s. The no h
o Nige ia, pa icula ly s a es like Kano, Kaduna, and Ka sina,
a e known o p oducing g ains such as maize, mille , and so -
ghum. Howe e , in e nal secu i y ac oss he coun y's leading
ag icul u al s a es poses a se ious challenge o g ain p oduc-
ion. The sou h, including egions like Lagos, Po Ha cou ,
and Calaba , is mo e u banized and indus ialized bu has a
high demand o g ains due o i s la ge popula ion. T ade be-
ween he no h and sou h usually ollows seasonal pa e ns
dic a ed by ag icul u al cycles. The low o g ains om he
no h o he sou h inc eases du ing pe iods o sca ci y o when
p ices a e lowe in he no h du ing he ha es ing season
compa ed o he sou h (Sco , 1972; Ukwu, 2000). T ade s play
a c ucial ole in acili a ing he low o g ain ac oss Nige ia.
They ope a e a di e en le els o he alue chain, including
wholesale and e ail ading, anspo a ion, and s o age. These
ade s help balance supply and demand, ensu ing equilib ium
ac oss g ain ma ke s (Se ge, Lenis, and Li e pool- Tasie 2017).
In addi ion, he poo anspo accessibili y o se e al egions
coupled wi h he di e si y o na u al condi ions has limi ed he
in eg a ion p ocess in Nige ia. All hese ea u es make Nige ia
an appealing case s udy, p o iding an essen ial engagemen
wi h he li e a u e on he b oade dynamics o g ain p ices in
de eloping coun ies.2
The law o one p ice cons i u es he p ima y heo e ical back-
g ound o his s udy. This law holds ha , in a compe i i e
ma ke s uc u e, he p ices o iden ical commodi ies aded in
di e en ma ke s will be he same when exp essed in he same
cu ency (Baulch 1997; S ephens e al.2012). Se e al s udies
es ed he law o one p ice by examining spa ial in eg a ion
in di e en commodi y ma ke s. S a ing wi h he pionee ing
esea ch o (P o opapadakis and S oll1986), ew s udies ind
some suppo o he law o one p ice (Goodwin1992; Obs eld
and Taylo 1997; Pippenge and Phillips2008). Ano he s and
o he li e a u e ails o ind signi ican e idence o he law
o one p ice in commodi y ma ke s (Al- Jab i, Boughanmi,
and Omezzine 2003; Edwa ds and Rankin 2016; Góes and
Ma heson 2017). In he li e a u e, mos o he s udies ha
explo e he law o one p ice gene ally use s anda d uni oo
es s (augmen ed Dickey- Fulle , Philips and Pe on), ec o au-
o eg essions o p ices, and coin eg a ion o G ange - causali y
analyses. Fo me s udies ha e iden i ied a ious ma ke in e-
g a ion measu es, including co ela ion coe icien s, long- e m
mul iplie s, and imes o adjus coin eg a ion coe icien s.
Much empi ical li e a u e explo es he law o one p ice in i s
s ic e sion, holding ha he p ice o a adable good should
equalize ac oss egions i he e a e no impedimen s o ade
be ween hem. O he s udies conside a mo e comp ehensi e
analysis o he law o one p ice in i s weak e sion o m, s em-
ming om he ac ha egional ma ke s a e in eg a ed i p ice
di e en ials ac oss egions do no exceed anspo a ion cos s.
In o he wo ds, in i s weak o m, he law akes in o accoun he
possibili y ha na u al ade ba ie s may allow some egional
p ice di e ences o be no g ea e han anspo a ion cos s
(Fackle and Goodwin2001; Gluschenko2011).
In his pape , we adop an app oach ha adds addi ional
lexibili y o he analysis o ma ke in eg a ion o e space.
Speci ically, we explo e he issue o ma ke in eg a ion by
conside ing di e en g ades o in eg a ion, which can be clas-
si ied in o (i) he pe ec in eg a ion o ma ke pai s based
on he assump ion o he s ic law o one p ice, (ii) he con-
di ional in eg a ion o ma ke pai s assuming a weak law o
one p ice, (iii) he in e media e g ade be ween in eg a ion
and non- in eg a ion ela ed o ma ke pai s ending owa ds
in eg a ion, (i ) he g ade o nei he in eg a ed no ending-
owa ds- in eg a ion consis ing o ma ke pai s ollowing an-
dom walk p ocess. A simila classi ica ion o di e en deg ees
o in eg a ion has been used ecen ly (Gluschenko 2021) o
p o ide a comp ehensi e analysis o he le el o in eg a ion
o Russian ma ke s. In addi ion, we o e u he insigh s in o
ola ili y spillo e s among egional s aple ood ma ke s o
gauge ma ke in e connec edness and p o ide esh pe spec-
i es on he po en ial isks posed by i egula i ies in con lic -
a ec ed a eas o o he ma ke s.
The cu en s udy con ibu es o he exis ing li e a u e in wo
di ec ions. Fi s , we allow o a mo e lexible analysis o he
deg ee o spa ial in eg a ion by conside ing di e en dimen-
sions o spa ial in eg a ion ac oss pai wise ma ke s. P e ious
s udies mainly examine he deg ee o in eg a ion in i s s ic
e sion, whe e he e is no oom o a bi age ac oss ma ke s.
As discussed p e iously, conside ing di e en g ades o in e-
g a ion allows us o accommoda e he complex s uc u e o
local ma ke s in a de eloping coun y like Nige ia, cha ac e -
ized by liquidi y and a ailabili y cons ain s, high ansac ion
cos s, and inadequa e p o ision o ma ke in as uc u es.
1851
These ac o s may yield di e en g ades o spa ial in eg a ion,
which should be aken in o accoun in o de o p o ide mo e
eliable ou comes. Secondly, we add o he exis ing li e a u e
on local ma ke linkages and p omp egional p ice shock
p opaga ion ac oss pai wise ma ke s by conside ing majo
subsis ence c ops widely consumed. This is qui e appealing in
Nige ia, subjec o he Boko Ha am insu gency, whe e s aple
ood ma ke s in he a ec ed egion a e likely o be less con-
nec ed o o he egions due o he des uc ion o oads and
communica ion acili ies (Adelaja and Geo ge 2019). Thi dly,
we examine he s eng h o p ice co- mo emen be ween each
pai o p o inces o p o ide insigh in o which local g ain
ma ke s a e mos closely linked by accoun ing o ola ili y
spillo e s. To he bes o ou knowledge, his wo k is he i s
o explici ly allow o ola ili y spillo e s in he nexus be ween
local ma ke s.
2 | Da a, Model, and Es ima ion S a egy
2.1 | Da a
The empi ical analysis elies on mon hly da a om Janua y
2002 o Decembe 2013 collec ed om 19 ma ke s in all e-
gions o Nige ia. We ocus on he coun y's majo s aple c op
ma ke s, ha is, Abuja, Aku e, Benin ci y, Calaba , Enugu,
Gombe, Ibadan, Ilo in, Jos, Kaduna, Kano, Ka sina, Lagos,
Lokoja, Maidugu i, Maku di, Po ha cou , Soko o, Yola.
The o al numbe o egion pai s o be examined is gi en by
N(N−1)∕2
, which is
19 ×18∕2=171
local g ain ma ke s
wi hin Nige ia.
Unlike p e ious s udies conside ing speci ic ma ke s due o
da a a ailabili y (Adewopo e al.2021), i is essen ial o no e
ha all Nige ian egions a e ep esen ed in he sample. This
allows us o ha e a clea o e iew o he pa e n o c op p ices
o he whole coun y. The local ma ke da a we e aken om
(Po eous2019) and encompassed mon hly maize, mille , and
so ghum p ices o each ma ke - ca chmen geog aphy. The au-
ho iden i ies a ma ke ca chmen geog aphy using he min-
imum a el- ime app oach, and i is conside ed as he egion
o which he minimum a el ime o he ma ke is smalle
han he minimum a el ime o any o he ma ke (i.e., he
egion o which he ma ke is he “closes ” in e ms o a el
ime). Following his de ini ion, Po eous(2019) iden i ies 19
ma ke s, no ably Abuja, Aku e, Beninci y, Calaba , Enugu,
Gombe, Ibadan, Ilo in, Jos, Kaduna, Kano, Ka sina, Lagos,
Lokoja, Maidugu i, Maku di, Po ha cou , Soko o, Yola.
G ain p ices a e collec ed om a a ie y o sou ces, includ-
ing he Li ing S anda ds Measu emen S udy (LSMS- ISA), he
Wo ld Food P og am's VAM uni and FAO's GIEWS p ojec ,
USAID's FEWS NET p ojec , nongo e nmen al o ganiza ions,
and o he esea che s. P ices a e measu ed in US dolla s pe
kilog am, ensu ing ha p ice obse a ions a e s anda dized
ac oss each c op ma ke .3
Basic desc ip i e s a is ics a e epo ed in Table 1 o each
c op. The a e age so ghum and mille p ices a e sligh ly
highe han maize p ices. When we look a he ku osis and
skewness esul s, we can make he ollowing poin s: (i) all
p ices a e posi i ely skewed, (ii) p ice changes o so ghum
and mille a e no no mally dis ibu ed, which is o mally
con i med by he Ja que- Be a es s a is ics. The a iabili y
o p ices gi en by he s anda d de ia ion is ela i ely highe
o so ghum and mille ela i e o maize p ices. Since we a e
in e es ed in unde s anding p ice in eg a ion and ansmis-
sion ac oss local ma ke s, we also p o ide in o ma ion on he
mean and s anda d de ia ion o he p ice di e en ials o each
c op o e he sample pe iod in Figu es1–3.4 We speci y he
mean (
cp
) and s anda d de ia ion (
𝜎
) o he p ice di e en-
ials (
E s
) in ma ke s
and
s
as ollows:
The s a is ics depic ed in Figu es 1–3 p o ide in o ma ion
on he espec i e mean and s anda d de ia ion o he p ice
di e en ials o maize, so ghum, and mille . An inspec ion
o he p ice dispe sion shows ha p ices a e highly ola ile
wi h d ama ic luc ua ions, he maximum and minimum a io
equals almos 4.5, 5.5, and 5.3 o bo h mean and s anda d de-
ia ion o he absolu e di e en ial p ices o maize, so ghum,
and mille , espec i ely. The highe di e ences be ween max-
imum and minimum p ice alues can be explained by bo h
supply and demand- side shocks, such as clima ic and egional
in la ion. Ano he impo an obse a ion is ha he mean
and s anda d de ia ion o he absolu e p ice di e en ial ol-
low simila mo emen s o e he esea ch pe iod. Howe e ,
he mean absolu e p ice di e en ial is ela i ely highe han
he s anda d de ia ion. As epo ed in Table1, e idence o he
ARCH e ec a he selec ed lags 1 and 3 mo i a es us o ac-
coun o ola ili y spillo e in he ma ke p ice ansmission
mechanism.
cp
=2
N(N−1)
N−1
∑
=1
N
∑
s= +1||
E s
||
𝜎
=
(
2
N(N−1)
N−1
∑
=1
N
∑
s= +1
(||
E s
||
−cp
)
2
)1∕2
TABLE 1 | Summa y s a is ics.
Maize So ghum Mille
Mean 0.327 0.343 0.349
Median 0.322 0.334 0.331
Maximum 0.510 0.589 0.587
Minimum 0.212 0.225 0.249
S d. De . 0.076 0.095 0.089
Skewness 0.717 1.077 1.287
Ku osis 2.935 3.499 3.816
Ja que- Be a 4.128 9.792*** 14.597***
P obabili y 0.126 0.007 0.000
ARCH(1) 115.326*** 120.36*** 233.89***
ARCH(3) 271.96*** 189.63*** 144.69***
***Indica es signi icance a 1% le el.
1852 Re iew o De elopmen Economics, 2025
2.2 | Model and Es ima ion S a egy
As in Gluschenko(2011), he p ice di e en ials (
E s
) ac oss ma -
ke s can be exp essed as ollows:
whe e
G
and
Gs
ep esen g ain p ices in egions
and
s
(
,s=1…,N
) a pe iod
. The economic model o he s ic law
o one p ice can be se as ollows:
I
E s
is s a iona y, hen he p ices in he ma ke s can be in equi-
lib ium in he long un, and sa is y he law o one p ice hypo h-
esis. Empi ically, he law o one p ice can be es ed using he
ollowing AR(1) model wi h no cons an :
whe e,
Δ
s ands o he i s di e ence ope a o . The s a ion-
a i y o
E s
implies he alidi y o he law o one p ice. In his
si ua ion, ma ke s and s, a e pe ec ly in eg a ed. As dis-
cussed ea lie , one can model he law o one p ice in i s weak
o m by es ing whe he
E s
is s a iona y a ound a non- ze o
cons an . To do so, we can e- speci y p ice di e en ials ac oss
ma ke s as
G ∕Gs =1+q s
o
E s
≡
ln(1
+
q s)
, whe e
q s
ep-
esen s ime- in a ian a bi age ansac ion cos s in pe cen -
age e ms. We e- speci y Equa ion(3) by including a cons an
e m
𝛼=−𝜑q s
:
The s a iona i y o
E s
a ound a non- ze o cons an sugges s ha
he weak law o one p ice is e i ied wi h ma ke s and s being
condi ionally in eg a ed. The condi ionali y o he in eg a ion
comes om he p ice dispa i y
q s
s ems om anspo a ion
cos s. Ano he concep o ma ke in eg a ion ha is di e en
om he law o one p ice can be es ed by conside ing whe he
he e could be a ca ching- up e ec ac oss ma ke s. In his si u-
a ion, he e is a mo emen owa ds in eg a ion wi h an asymp-
o ically decaying end (
q s( )
), and he p ice di e en ials a e
gi en by
G ∕Gs =1+q s( )
o
E s
≡ln
(
1+q
s
( )
)
, whe e
q s( )
app oaches ze o when
goes o in ini y and
d∣q s( )∣∕d <0
.
The concep o con e gence p ocess can be seen as a supe posi-
ion o wo long un p ocesses o de e minis ic con e gence and
sho - un o s ochas ic con e gence, which can be w i en as:
The di e ence be ween equa ions(3) and (4) and equa ion(5)
is ha he long- un pa hs a e ime- in a ian
q s( )=0
in equa-
ion (3) and
q s( )=−
𝛼
∕𝜑
in equa ion(4). Consequen ly, he
con e gence o he law o one p ice o simply con e gence om
equa ions (3 & 4) is based only on sho - un ea u es o adjus -
men owa ds he long- un pa h. We p o ide a g aphical isual-
iza ion o he di e en p ope ies o con e gence in Figu e4a–c.
Besides he conside a ion o di e en ypes o con e gence,
we also accoun o h ee modes o he con e gence end,
including he exponen ial end (
Q( )=𝛼e𝛿 ,𝛿<0
), he log-
exponen ial end
Q
( )=ln
(
1+𝛼e𝛿
)
,𝛿<
0
, and he ac ional
end
Q( )=
𝛼
∕(1+
𝛿
),
𝛿<
0
. Equa ions (3–5) can be mod-
i ied o include he ollowing end when es ing he law o
one p ice.
(1)
E s
=ln
(
G
∕G
s )
(2)
G ∕Gs =1 o E s =0 o =0, . …,Tand a egion pai ( , s)
(3)
ΔE s =𝜑E s, −1+
(4)
ΔE s =𝛼+𝜑E s, −1+
(5)
ΔE s =q s( )−(𝜑+1)×q s( −1)+𝜑E s, −1+
(6a)
E s
=ln
(
1+𝛼e
𝛿 )
−(𝜑+1)⋅ln
(
1+𝛼e
𝛿( −1))
+𝜑E
s, −1
+
FIGURE 1 | Summa y s a is ics o he absolu e p ice di e en ials o
maize. [Colou igu e can be iewed a wileyonlinelib a y.com]
FIGURE 2 | Summa y s a is ics o he absolu e p ice di e en ials o
so ghum. [Colou igu e can be iewed a wileyonlinelib a y.com]
FIGURE 3 | Summa y s a is ics o he absolu e p ice di e en ials o
mille . [Colou igu e can be iewed a wileyonlinelib a y.com]

1853
Conside ing he gene al speci ica ion displays in (6- a), (6- b),
and (6- c), one can conclude ha g ain p ice con e gence holds
i ime se ies
E s
is s a iona y abou one o mo e o hese end
models and pa ame e
𝛿
is well signed. Howe e , a w ong sign
o
𝛿
indica es de e minis ic di e gence. I should be no ed ha
all h ee e sions o Equa ion (6) a e es ima ed o each ma -
ke pai , and he mos sui able model is selec ed ollowing he
bes i ( he minimal sum o squa ed esiduals) i hey u n ou
o be comple i e. Ano he impo an ea u e o he co-
mo emen be ween he se ies is he du a ion o he de ia ion
(
𝜋
) o he p ice gap om i s long- un pa h, which can be iden-
i ied as he ime i akes o he dispa i y o hal e. In he case
o log- exponen ial end,
𝜋=ln(0.5)∕𝛿
; o he exponen ial
end
𝜋
=1
𝛿ln
(
ln(0.5(ⅇ𝛼+1))
𝛼
)
; and o he ac ional
end
𝜋
=1
𝛿
ln
(
𝛼
ln(0.5(
ⅇ𝛼
+1))
−1
)
.
Fo he sake o obus ness, we employ he augmen ed Dickey-
Fulle (ADF) and Phillips- Pe on (P.P.) uni oo es s o es he
null hypo hesis o uni oo (
H0:𝜑=0
) agains he al e na i e o
s a iona i y (
H1:𝜑<0
). Despi e a la ge se o uni oo es s, he
ADF and P.P. uni oo es s a e mo e se e e in ejec ing he null
hypo hesis.
We also in es iga e ola ili y ansmission be ween g ain
ma ke s by employing a modi ied- e sion o he Lag ange
(6b)
Δ
E
s
=𝛼e
𝛿
−(𝜑+1)𝛼e
𝛿( −1)
+𝜑E
s, −1
+
(6c)
Δ
E s =𝛼
1+𝛿
−
(𝜑+1)𝛼
1+𝛿
+E s, −1+
FIGURE 4 | Di e en pa e ns o in eg a ion ac oss pai wise g ain ma ke s in Nige ia. [Colou igu e can be iewed a wileyonlinelib a y.com]
1854 Re iew o De elopmen Economics, 2025
Mul iplie (L.M.) ola ili y spillo e es de eloped by Ha ne
and He wa z(2006). The app oach is commonly used o es i-
ma e he spillo e e ec s in a iance ac oss ma ke s based on
he uni a ia e GARCH model app oach (A uke en, Çe ik, and
Ko kmaz2021; Nazlioglu, E dem, and Soy as2013). Ha ne and
He wa z(2006) conside he ollowing speci ica ion:
whe e condi ional a iance
𝜎2
i
=w
i
+𝜕
i
2
ⅈ −1
+𝛽
i
𝜎
2
ⅈ −1
and
𝜉i
ep-
esen s he s anda dized esiduals o GARCH model. The null
hypo hesis o non- ola ili y ansmission (
H0:Ψ=0
) is es ed
agains he al e na i e hypo hesis o ola ili y ansmission
(
H1:Ψ
≠
0
). The au ho s p opose he ollowing L.M. s a is ic o
es he ola ili y ansmission be ween wo- g ain ma ke s.
whe e
V�
𝜃i
�
=k
4T
�∑
T
=1zj z�
j −
∑
T
=1zj x�
i
�∑
T
=1xj x�
j
�−1∑
T
=1xⅈ z�
j
�
and k =1
T
∑
T
=1
�
𝜉2
ⅈ −1
�2
.
The es ima ion p ocedu e can be summa ized as ollows:
i. Es ima e a GARCH(1, 1) model o he esidual
ⅈ
and
j
and ob ain he s anda dized esiduals
𝜉i
, pa ial de i a-
i es
xⅈ
, and he ola ili y p ocess
𝜎2
j
en e ing
zj
.
ii. Reg ess
(
𝜉
2
ⅈ
−1
)
on
x′
i
and
z′
j
.
iii.
𝜆LM
is equal o
T
imes he coe icien o explana ion R-
squa ed o he la e eg ession.
3 | Empi ical Findings
This sec ion es ima es and discusses he empi ical indings. I
is di ided in o wo pa s. Fi s , we epo he pai wise c oss-
ma ke in eg a ion esul s and discuss Nige ia's g ain ma ke
in eg a ion pa e n. Second, we epo he esul s on ola il-
i y p ice ansmission ac oss ma ke s o cha ac e ize whe he
ma ke s a e in eg a ed in e ms o ansmission o p ice
luc ua ions.
3.1 | Spa ial In eg a ion o Nige ian G ain Ma ke s
Based on Pai wise Co- Mo emen Analysis
Be o e in e p e ing he esul s, i should be no ed ha i is ha dly
possible o p esen he speci ic es ima ion o each egion pai .
We summa ize he esul s ob ained by displaying he pe cen age
o egional ma ke s wi h which a gi en indi idual ma ke is in e-
g a ed, con e ging, and di e ging in Table2. These pe cen ages
a e ob ained as he a io o he numbe o egion pai s belong-
ing o a speci ic ype o in eg a ion o he o al numbe o pai s.
This app oach allows us o iden i y egions s ongly (o weakly)
in eg a ed wi h he es o he coun y's egions. Fo he sake o
b e i y, we also p o ide an emblema ic g aphical isualiza ion o
he i e possible in eg a ion pa e ns o some egions in Figu e4.
Figu e4 shows ha he e idence o di e en deg ees o in e-
g a ion seems ob ious ac oss ma ke pai s, exempli ying he
econome ic conside a ion ollowed in he s udy. As discussed
ea lie , one can disen angle i e pa e ns o p ice di e en ials
ac oss ma ke pai s. Figu e 4a g aphically illus a es he pa -
e n o pe ec in eg a ion ac oss ma ke pai s. As can be seen,
he p ice di e en ial be ween Lagos and Abuja has a mean
a ound ze o (p ice pa i y), and he se ies luc ua es wi hin a
band, which is consis en wi h a co a iance s a iona y p ocess.
The s ong e sion o he ma ke in eg a ion hypo hesis implies
he da a- gene a ing p ocess o he p ice di e en ial se ies o be
co a iance s a iona y as illus a ed in Figu e 4a. De ia ions
om he p ice pa i y ake a ound 12.5 mon hs o die ou . The
g aphical illus a ion o he condi ional in eg a ion is depic ed
in Figu e4b. The analysis indica es ha Lagos and Beninci y
ma ke s a e condi ionally in eg a ed, wi h he p ice di e en ial
luc ua ing a ound 1% wi h
𝜋=27.3 mon hs
. The e is e idence
owa d in eg a ion in he long- un, as shown in Figu e4c. P ice
di e en ials in Ibadan and Kano g ain ma ke s display a non-
linea dec easing pa e n, suppo ing he e idence o in eg a-
ion in he long un. The mean- e e ing p ocess owa ds he
long- un pa h occu s a e 11.56 mon hs. Figu es4d,e display
he non- in eg a ion cases, whe e he beha io o he p ice di -
e en ial ollows a andom walk p ocess in Figu e4d, whe eas
he p esence o de e minis ic p ice di e gence d i es he non-
in eg a ion p ocess obse ed in Figu e4e.
Table2 summa izes he pe cen age o egion pai s wi hin Nige ia
ha a e pe ec ly in eg a ed (P.I.), condi ionally in eg a ed (CI),
con e ging (CONV), di e ging (DIV), and no in eg a ed (N.I.).
S a ing wi h all maize ma ke pai s, he indings e eal ha , on
a e age, 30.47% (14.15% + 16.62%) a e pe ec ly o condi ionally
in eg a ed (see las ow o Table2). Accoun ing o he ma ke
pai s mo ing owa ds con e gence, a o al o 37.85% is obse ed.
In e es ingly, a ela i ely high numbe o local ma ke s end o
be pe ec ly in eg a ed wi h he Abuja and Lagos maize ma -
ke s. The da a e eal ha , on a e age, 30% o he coun y's ma -
ke s a e pe ec ly in eg a ed wi h Abuja and Lagos. Al hough
maize ma ke s loca ed in Gombe, Maidugu i, and Yola a e less
in eg a ed unde he pe ec in eg a ion hypo hesis, he e is e -
idence o condi ional con e gence and mo emen owa ds con-
e gence wi h he local ma ke s. We show ha non- in eg a ion
pa e ns a e epo ed in nea ly 61.48% o ma ke pai s. Thus,
one can in e ha Nige ian maize ma ke s display a high deg ee
o non- in eg a ion, p o iding li le e idence a o ing he law o
one p ice.
Conce ning Nige ian so ghum ma ke s, we epo ha 20.61%
o ma ke pai s a e pe ec ly o condi ionally in eg a ed on a e -
age. Adding ma ke pai s mo ing owa ds con e gence, we ha e
a o al o 25.22%. Among indi idual ma ke s, he local ma ke
o Kano seems o be highly in eg a ed ma ke wi h a pe ec in-
eg a ion a e equal o 46.78%. Ano he impo an obse a ion
is ha he e a e no signi ican pa e ns o pe ec in eg a ion
wi h he ollowing ma ke s: Gombe, Ilo in, Ka sina, Maidugu i,
and Yola, gi en ha hey a e no pe ec ly in eg a ed wi h any
ma ke s. Howe e , indings suppo e idence ha condi ional
and mo emen owa ds con e gence, in he long un, can be e-
po ed in hese ma ke s. Again, i could be obse ed ha he e
a e mo e di e ging ma ke s, as nea ly 74.75% o he so ghum
p ice di e en ials a e di e ging and no in eg a ed. The highe
pe cen age a es o non- in eg a ion and di e gence pa e ns
ac oss ma ke pai s imply ha he law o one p ice is no enable
(7)
ⅈ =𝜉i
√
𝜎2
i , =1+z�
j Ψ,z�
j =
(
2
j −1,𝜎2
j −1
)
(8)
𝜆
LM =1
4T
[T
∑
=1(
𝜉2
ⅈ −1
)
z�
j
]
V
(
𝜃i
)
−1
[T
∑
=1(
𝜉2
ⅈ −1
)
zj
]
∼𝜒2(2
)
1855
TABLE 2 | Summa y o he spa ial in eg a ion esul s.
Ma ke
Maize So ghum Mille
PI CI CONV DIV NI PI CI CONV DIV NI PI CI CONV DIV NI
Abuja 29.23% 17.54% 11.70% 0.00% 41.53% 11.69% 11.69% 0.00% 0.00% 76.62% 35.08% 23.39% 0.00% 0.00% 41.53%
Aku e 5.84% 29.23% 11.70% 0.00% 53.23% 23.39% 5.84% 11.69% 0.00% 59.08% 5.84% 0.00% 0.00% 0.00% 94.16%
Beninci y 5.84% 35.08% 11.70% 0.00% 47.38% 5.84% 5.84% 0.00% 0.00% 88.32% 17.54% 5.84% 0.00% 0.00% 76.62%
Calaba 23.39% 11.70% 0.00% 0.00% 64.91% 17.54% 0.00% 0.00% 0.00% 82.46% 0.00% 0.00% 40.93% 0.00% 59.07%
Enugu 23.39% 17.54% 0.00% 0.00% 59.07% 5.84% 0.00% 0.00% 5.84% 88.32% 0.00% 0.00% 0.00% 0.00% 100%
Gombe 0.00% 29.24% 5.84% 0.00% 64.92% 0.00% 17.54% 0.00% 0.00% 82.16% 5.84% 5.84% 0.00% 0.00% 88.32%
Ibadan 17.54% 29.24% 0.00% 0.00% 53.22% 5.84% 11.69% 29.23% 5.84% 47.4% 5.84% 11.69% 0.00% 0.00% 82.47%
Ilo in 11.70% 23.39% 5.84% 0.00% 59.07% 0.00% 0.00% 0.00% 0.00% 100% 23.39% 17.54% 0.00% 0.00% 59.07%
Jos 17.54% 29.24% 5.84% 0.00% 47.38% 5.84% 23.39% 0.00% 5.84% 64.93% 5.84% 29.23% 0.00% 0.00% 64.93%
Kaduna 11.70% 0.00% 5.84% 0.00% 82.46% 11.69% 40.93% 0.00% 0.00% 47.38% 11.69% 17.54% 0.00% 0.00% 70.77%
Kano 23.39% 0.00% 11.69% 0.00% 64.92% 46.78% 11.69% 11.69% 0.00% 29.84% 11.69% 23.39% 0.00% 0.00% 64.92%
Ka sina 17.54% 0.00% 0.00% 0.00% 82.46% 0.00% 0.00% 0.00% 5.84% 94.16% 0.00% 23.39% 11.69% 0.00% 64.92%
Lagos 29.23% 29.24% 11.69% 0.00% 29.84% 23.39% 5.84% 29.23% 0.00% 41.54% 46.78% 11.69% 0.00% 0.00% 41.53%
Lokoja 5.84% 0.00% 17.54% 0.00% 76.62% 11.69% 11.69% 0.00% 0.00% 76.62% 0.00% 23.39% 0.00% 0.00% 76.61%
Maidugu i 0.00% 0.00% 5.84% 11.69% 82.47% 0.00% 0.00% 0.00% 5.84% 94.16% 0.00% 5.84% 0.00% 0.00% 94.16%
Maku di 5.84% 11.70% 11.70% 0.00% 70.76% 5.84% 5.84% 0.00% 0.00% 88.32% 0.00% 11.69% 0.00% 0.00% 88.31%
Po ha cou 23.39% 29.24% 0.00% 0.00% 52.37% 11.69% 23.39% 0.00% 11.69% 53.23% 5.84% 0.00% 0.00% 0.00% 94.16%
Soko o 17.54% 23.39% 17.54% 0.00% 41.53% 5.84% 23.39% 0.00% 5.84% 64.93% 29.23% 35.08% 23.39% 0.00% 12.3%
Yola 0.00% 0.00% 5.84% 0.00% 94.16% 0.00% 0.00% 5.84% 0.00% 94.16% 0.00% 5.84% 0.00% 0.00% 94.16%
A e age 14.15% 16.62% 7.38% 0.62% 61.48% 10.15% 10.46% 4.61% 2.46% 72.29% 10.77% 13.23% 4.00% 0.00% 72.00%
No e: Each cell in Table2 p esen s he numbe o ma ke s ha ha e a gi en ype o in eg a ion wi h a gi en ma ke di ided by 18, which ep esen s he o al numbe o pai s in which his ma ke pa icipa es. Only he las ow
con ains he a e age pe cen ages o 171 pai s.
Abb e ia ions: CI, condi ional in eg a ion; CONV, mo emen owa ds con e gence; DIV, di e gence; NI, non- in eg a ion; PI, pe ec in eg a ion.
1856 Re iew o De elopmen Economics, 2025
in Nige ian so ghum ma ke s. By looking a he in eg a ion o
he Nige ian mille ma ke , we epo ha 24% o he coun y's
ma ke s a e in eg a ed pe ec ly and condi ionally, while 4% o
he coun y's mille ma ke mo es owa ds con e gence. Mos
ma ke s appea o be pe ec ly in eg a ed wi h Abuja and Lagos,
while weakly in eg a ed ma ke s a e loca ed in Calaba , Enugu,
Ka sina, Lokoja, Maidugu i, Maku di, and Yola. We obse e
ha a signi ican ac ion o ma ke pai s, abou 72%, a e no
in eg a ed, p o iding e idence agains he alidi y o he law o
one p ice in Nige ian mille ma ke s.
O e all, one can ejec he alidi y o he law o one p ice ac oss
Nige ian g ain ma ke s, co obo a ing he low le el o in eg a ion
wi hin A ican coun ies e idenced in p e ious s udies (Jayne,
Mye s, and Nyo o2008; Pie e and Kaminski 2019). Ano he
impo an obse a ion is ha allowing o di e en classes o
in eg a ion (condi ional in eg a ion and mo emen owa ds in-
eg a ion) subs an ially inc eases he pe cen age o in eg a ed
ma ke pai s. This sugges s ha p e ious s udies examining he
law o one p ice in i s s ong e sion (pe ec in eg a ion) may
igno e he possibili y o di e en o ms o con e gence in he
long un. Fu he mo e, we epo ha ma ke s loca ed in no h-
eas Nige ia (Gombe, Maidugu i, Yola), which ha e been in a
s a e o Boko Ha am insu gency, lack in eg a ion wi h he es
o he coun y. In con as , mos egional ma ke s a e likely o be
in eg a ed wi h cen al ma ke s o Abuja and Lagos a e likely as
hey end o be pe ec ly in eg a ed wi h a maximum numbe o
o he egional g ain ma ke s, sugges ing he ela i e impo ance
o he geog aphical loca ion o g ain ma ke s.
3.2 | Spillo e P ice T ansmission Ac oss
Ma ke Pai s
Ha ing es ablished he deg ee o in eg a ion ac oss ma ke
pai s, i is appealing o policy pu poses o isola e indi idual
ma ke (s) ha play(s) leade ship posi ion(s) in he o ma ion and
ansmission o p ices. I is easonable o expec he leading ole
o Abuja and Lagos, gi en ha hese ma ke s a e ully in eg a ed
wi h a ela i ely highe numbe o local ma ke s. To add ess he
leading ma ke possibili ies, we in es iga e whe he he e is a
ola ili y spillo e ac oss ma ke pai s. Tables3–5 epo he ol-
a ili y spillo e esul s ac oss ma ke pai s o maize, so ghum,
and mille , espec i ely.
Table 3 summa izes he es ima ion esul s o he spillo e
p ice ansmission ac oss maize ma ke pai s. The indings
show ha o all ma ke pai s in ol ing Abuja and Lagos, he
null hypo hesis o no ola ili y spillo e canno be ejec ed a
he con en ional signi icance le el. This indica es ha he
causali y is unidi ec ional, wi h p ice ola ili ies in indi idual
ma ke s G ange causing p ices in Abuja and Lagos. The lack
o signi ican e e se causali y om Abuja and Lagos owa ds
he o he ma ke s p o ides e idence agains he leade ship po-
si ion o hese wo ma ke s. Ano he in e es ing inding is ha
he null hypo hesis o no ola ili y is equen ly ejec ed when
conside ing he causali y om Gombe, Kano, Maidugu i, and
Yola o he o he ma ke s. This inding indica es ha shocks o
Gombe, Kano, Maidugu i, and Yola p ices signi ican ly a ec
p ices in all ma ke s. Gi en ha hese ma ke s a e loca ed in he
no heas o Nige ia excep Kano, one migh claim ha he ol-
a ili y o maize p ices in he con lic - a ec ed a eas could ac as
a signal o o he ma ke s. This p o ides co obo a i e e idence
abou he po en ial e ec o con lic on he ansmission o ola-
ili y shocks ac oss ma ke s.
In he case o so ghum p ice ansmission ac oss ma ke s e-
po ed in Table4, he null hypo hesis o no ola ili y spillo e
is signi ican ly ejec ed when conside ing he causa ion om
Kaduna and Soko o o he o he ma ke s. Fo ins ance, he e
is e idence o unidi ec ional ola ili y spillo e s emming om
Kaduna o 12 local ma ke s, including Abuja, Aku e, Beninci y,
Calaba , Enugu, Gombe, Ibadan, Ilo in, Kano, Ka sina, Lokoja,
Maku di. A simila pa e n was obse ed om Soko o o 13
ma ke s, namely Abuja, Aku e, Beninci y, Calaba , Enugu,
Gombe, Ilo in, Kano, Ka sina, Lagos, Maidugu i, Maku di, and
Po ha cou . These indings emphasize he leading ole o he
Kaduna and Soko o so ghum ma ke s in p edic ing ola ili y in
o he ma ke s. Howe e , wo- way ola ili y spillo e causali ies
( eedbacks) a e ound o exis be ween Kaduna and Soko o, indi-
ca ing in e dependence be ween hese wo leading ma ke s. Pu
di e en ly, he p ice in one ma ke eac s o any p ice ola ili y in
he o he ma ke . Fu he mo e, bi- di ec ional spillo e ola ili y
is mo e common ac oss indi idual ma ke s in ol ing Abuja and
Lagos. Fo ins ance, he esul s indica e ha causal eedback in
eigh pai s (i.e., Abuja—Beninci y, Abuja—Kano, Abuja—Lagos,
Aku e—Enugu, Lagos—Aku e, Lagos—Beninci y, Lagos—
Calaba , Lagos—Enugu), which is an indica ion o inc eased in-
e connec edness ac oss so ghum ma ke s.
Conside ing he ola ili y spillo e ac oss mille ma ke s, he
esul s epo ed in Table 5 indica e ha o all pai s, includ-
ing Kaduna and Kano, we epo a signi ican unidi ec ional
spillo e s emming om Kaduna and Kano o mos o he e-
maining ma ke s. Fo ins ance, we obse e subs an ial ola ili y
spillo e s om Kaduna o 13 local ma ke s, including Abuja,
Aku e, Beninci y, Calaba , Enugu, Ibadan, Ilo in, Ka sina,
Lagos, Lokoja, Maidugu i, Maku di, Po ha cou , and Soko o.
Simila ly, unidi ec ional ola ili y was obse ed om Kano o 12
local ma ke s, such as Abuja, Aku e, Beninci y, Calaba , Enugu,
Ibadan, Jos, Ka sina Lagos, Maidugu i, Maku di, and Soko o.
The unidi ec ional ola ili y connec edness om Kaduna and
Kano o he emaining ma ke s indica es he leading ole o
hese ma ke s in p edic ing ola ili y in Nige ian mille ma -
ke s. In e es ingly, he esul s show high bi- di ec ional ola ili y
connec edness among mille p ices in Kano and Kaduna. This
sugges s he in e dependence be ween he wo cen al ma ke s
in e ms o ola ili y in he Nige ian mille ma ke . I is also ex-
pedien o no e ha local ma ke s exe a g ea e in luence on
he ola ili ies o p ices in Abuja and Lagos, gi en he e idence
o he one- way causali y om o he ma ke s o Abuja and Lagos.
This simply communica es ha he mille ma ke in Abuja and
Lagos a e ne ecei e s o p ice ola ili ies and a e mo e exposed
o p ice shocks om o he ma ke s. We also epo bi- di ec ional
ola ili y connec edness among se en ma ke pai s, includ-
ing Aku e—Calaba , Aku e—Ka sina, Beninci y—Calaba ,
Calaba —Po ha cou , Soko o—Ka sina, Soko o—Lokoja, and
Soko o—Maidugu i. The bi- di ec ional ola ili y connec edness
among hese pai s indica es ha no indi idual p ice plays a lead-
e ship ole.