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In es iga ing Ex e nali ies o Knowledge
Spillo e among Selec ed Eu opean Coun ies
Fa emeh Taleghani
1
PhD s uden , College o Managemen and Economics, Shahid
Bahona Uni e si y, Ke man, I an
Seyed Abdolmajid Jalaee Es andabadi
Facul y Membe , College o Managemen and Economics Shahid
Bahona Uni e si y, Ke man, I an
Fa emeh I ani Ke mani
P o esso , College o Managemen and Economics Shahid Bahona
Uni e si y, Ke man, I an
Abs ac
Gene ally, knowledge spillo e s esul in he c ea ion o new knowledge,
inc eased compe i i e ad an ages, and economic coope a ion. Since he
in es iga ion o spillo e lows among coun ies is conside ed o be highly
impo an , in his s udy, knowledge spillo e s and i s esul ing ex e nali ies we e
conside ed among a numbe o selec ed Eu opean coun ies du ing 1995 o 2011
using spa ial econome ic analysis. The esul s indica ed an indi ec e ec and
posi i e eedback caused by changing human de elopmen index, esea ch and
de elopmen expendi u e, and knowledge-bea ing impo s, which con i med he
exis ence o spillo e s and adso p ion capaci y in his egion.
Keywo ds: Ex e nali y, Knowledge Spillo e s, Spa ial Econome ics
Ci e his a icle: Taleghani, F., Jalaee Es andabadi, S. A., & Ke mani, F. I. (2015).
In es iga ing Ex e nali ies o Knowledge Spillo e among Selec ed Eu opean Coun ies.
In e na ional Jou nal o Managemen , Accoun ing and Economics, 2(7), 631-645.
1
Co esponding au ho ’s email: aleghani. [email protected]
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632
In oduc ion
Knowledge and echnical de elopmen a e among he p inciple esou ces o dynamism
in economic g ow h models. The e o e, pa en ac i i ies include use, applica ion, and
ans e o scien i ic and echnical knowledge in p oblem sol ing and his knowledge is
di e en om he in o ma ion which is con en ionally applied. On he o he hand,
knowledge ans e occu s ia mo emen o skilled labo , simula ion and e e se
enginee ing by local i ms, and inc easing compe i ion and comme cial communica ion
be ween domes ic and in e na ional i ms; howe e , such ans e is limi ed by he
adso p ion capaci y o he hos coun y ia a ious channels. This capaci y p o ides an
oppo uni y o lea ning and applying knowledge. Fu he mo e, geog aphical dis ance
can acili a e o limi knowledge ans e ; his dis ance is speci ically impo an in
knowledge ans e , because sou ce coun ies a e looking o he des ina ion coun ies
ha , beside s uc u al simila i y, ha e minimum geog aphical dis ance om hem. Thus,
by he o ma ion o a knowledge li e cycle be ween he sou ce and des ina ion coun ies,
bo h o hem could bene i om his knowledge ans e wi h minimum cos . This cycle
indica es a si ua ion in which a o eign coun y ans e s a less sophis ica ed knowledge
o a domes ic coun y. In his case, o eign and domes ic coun ies a e called sou ce and
des ina ion coun ies, espec i ely. A he nex s age, knowledge o he o eign coun y is
combined wi h he domes ic echnology o gene a e new knowledge; hen, i is e u ned
o he o eign coun y. In his case, posi ions o sou ce and des ina ion coun ies a e
changed. In o he wo ds, domes ic and o eign coun ies a e called sou ce and des ina ion
coun ies, espec i ely.
On he o he hand, no only knowledge spillo e s a e no di ec ly obse able, bu also
hei ans e is accompanied by some ex e nali ies which migh ha e posi i e o nega i e
e ec s on he economic g ow h and de elopmen . This a icle was aimed o in es iga e
he na u e o hese ex e nali ies using in a- and in e - egional pa en esponses o he
changes in he inpu s o knowledge p oduc ion unc ion. The e o e, i is necessa y o
s udy he pa en esponse o each egion and o he egions o changes in inpu s o e e y
egion and he neighbo ing a eas. This esponse indica es Ma shall-A ow-Rome (MAR)
ex e nali ies. Based on MAR pe spec i e, spillo e s occu among simila uni s wi h
sha ing common knowledge; ye , on he opposi e side, he e a e Jacob's ex e nali ies
among complemen a y uni s. The e o e, he egions wi h a ious p oduc s mus c ea e
mo e pa en s. Fu he mo e, Jacob's ex e nali ies a e dec eased wi h mo e inc eased
dis ance compa ed wi h MAR ex e nali ies (Au an -Be na d and LeSage, 2011). Thus, in
his s udy, di ec and indi ec e ec s on pa en we e in es iga ed, which esul ed om
changing he inpu s o knowledge p oduc ion. The e o e, in o de o in es iga e he
ex e nali ies esul ing om knowledge p oduc ion inpu s, esea ch li e a u e and model
desc ip ion a e p esen ed in Sec ions 2 and 3, espec i ely. In addi ion, model es ima ion
is p esen ed in Sec ion 4 and conclusions a e deli e ed in he inal sec ion.
Li e a u e
Conside ing he impo ance o echnology spillo e in in e na ional economy,
nume ous s udies ha e been conduc ed on he p esence and e icacy o echnology
spillo e s in di e en ime pe iods and using di e en me hods. In his sec ion, a quick
e iew o he a ailable esea ch on echnology spillo e is p esen ed. In his ega d,
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633
Anselin e al. (1997) in es iga ed spa ial spillo e s among academic esea ch and pa en
and used da a om 29 s a es in he USA in 1982. They concluded ha he e was weak
e idence on spillo e s among uni e si ies and esea ch ins i u es inside he s a es; bu ,
he esul ed ex e nali ies wen beyond he bo de s. Also, hey ound a co ela ion be ween
academic s udies and pa en ac i i ies in he p i a e sec o along wi h ex e nali ies. Paci
and Usai (2000) s udied knowledge spillo e s and geog aphical dis ibu ion o pa en
using da a om 85 indus ial sec o s in I aly be ween 1990 and 1991. Resul s
demons a ed spa ial co ela ion in he dis ibu ion o pa en ac i i ies and posi i e
in luence o indus ial sec o s om simila indus ial sec o s in he neighbo ing egions.
Thei analysis showed wo ex e nali ies in his s udy. Fische and Va ga (2003) analyzed
knowledge spillo e s om esea ch ac i i ies in scien i ic cen e s o high- echnology
indus ies in 72 egions inside Aus alia and used da a ela ed o 1991. The esul s
indica ed he p esence o in a- egional spillo e s; howe e , some ex e nali ies we e
p oduced which we e smalle han MAR ones. Mo eno e al. (2003) conduc ed a s udy
en i led "Spa ial spillo e , pa en ac i i y, and ole o knowledge p oduc ion p ocess"
using da a om 138 egions in 17 Eu opean coun ies be ween 1978 and 1997. They
ound a signi ican ly posi i e spa ial au o-co ela ion in pa en ; i.e. knowledge p oduc ion
in he s udied egion was in luenced by spa ial spillo e s which esul ed in inc eased
pa en ac i i y in o he egions. The mos impo an e ec i e ac o s o pa en gene a ion
we e in e na ional esea ch and de elopmen expendi u e. D i ield and Lo e (2003)
s udied di ec o eign in es men , echnology sou ce, and e e se spillo e s in UK
indus ies; by ocusing on 1984-1992, hey ound ha he echnology made by spillo e s
in domes ic i ms spil o e o o eign i ms; bu , e ec o hese spillo e s was limi ed o
de eloped sec o s. None heless, bo h sides bene i ed om hese spillo e s. Also, hey
ound ha echnology spillo e s we e in luenced by spa ial concen a ion o indus ies.
Be na d and LeSage (2011) in es iga ed knowledge spillo e s using spa ial econome ic
analysis models and da a om 1992 o 2000. They s a ed ha es ima ing spillo e s,
ega dless o spa ial dimension, can be biased and inconsis en ; acco dingly, hey applied
spa ial TOBIT me hod and concluded ha he bigges di ec and indi ec e ec s o
echnology spillo e s in 94 Asian egions we e ela ed o esea ch and de elopmen
ac i i ies o p i a e sec o ; hese ex e nali ies dec eased wi h dis ance om he sou ce
and he esul s e e ed o op imal egional s a egies.
Model desc ip ion
In his s udy, endogenous g ow h model was used ins ead o exogenous g ow h model,
since heo y o exogenous g ow h model s a es ha capi al lows om coun ies wi h low
e iciency o hose wi h high e iciency; howe e , s udies ha e shown such a low and
con i m capi al ans e om poo o de eloped coun ies. In ac , he eason can be ound
in endogenous g ow h models. In endogenous g ow h models, he unanimous iew is ha
accumula ion o physical capi al does no make coun ies iche , bu human capi al is
placed beside physical capi al and a g ound is de eloped o he echnology o ma ion
and i s abso p ion capaci y ia esea ch and de elopmen depa men . In his ega d,
Mingyong e al. (2006) applied Rome 's (1990) model o s udy echnology spillo e s and
s a ed ha p oduc ion was made using a la ge numbe o incomple e al e na i e inpu s,
since echnical p ocess is o igina ed om he in en ion o new inpu s ia esea ch and
de elopmen ac i i ies. Two o eign and domes ic coun ies a e hus conside ed. In he
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634
domes ic coun y, economy is composed o h ee pa s o esea ch and de elopmen ,
in e media e goods, and inal goods.
Fo inal goods, good y is p oduced unde pe ec compe i ion and he p oduc ion
unc ion is as ollows:
𝑌=𝐴 𝐻𝑦
𝛼[∫𝑥𝑖𝛽
𝑁
0𝑑𝑖+∫𝑥𝑖∗
∗𝛽
𝑁∗
0𝑑𝑖∗] 𝛼,𝛽>0 ,𝛼+ 𝛽=1 (1)
whe e A, Hy, xi, and 𝑥𝑖∗ a e o al p oduc i i y le el, human capi al used o inal goods,
and numbe s o N in e media e domes ic and o eign inpu s deno ed by i, espec i ely. N
and 𝑁∗ indica e he numbe o domes ic and o eign in e media e inpu s, espec i ely.
In e media e goods a e in en ed o comple ed in esea ch and de elopmen depa men
and a e hen pu chased om wo domes ic and o eign p oduce s. P oduc ion in esea ch
and de elopmen depa men depends on in e na ional spillo e s o esea ch and
de elopmen h ough comme ce, human capi al in es men in his depa men , and
echnical knowledge o domes ic coun y. Since echnical knowledge is shown by
di e en a iables o capi al goods, de eloping plans o answe ing new needs o
domes ic coun y can be de ined as:
𝑁•= 𝛿 𝐻N [N+G(D,H)𝑁∗] (2)
whe e 𝛿, 𝐻N , and H a e a p oduc i i y cons an , amoun o human capi al used in
esea ch and de elopmen depa men , and o al amoun o human capi al, espec i ely,
which indica es he cons an amoun o knowledge and skill in economy (H=HN+Hy).
Also, G(D,H) shows adso p ion capaci y, which is de e mined by o al domes ic human
capi al and ex en o economy openness so ha 𝐷𝜖(0,∞). Fo in e media e goods, a e
he de elopmen o in en ion o a p ojec , an in e media e i m buys he p ojec and
p oduces he inpu s unde pe ec compe i ion. Fo he sake o simplici y, i is assumed
ha in e media e inpu s a e spen on he p oduc ion o a uni o Y.
Ma ke balance
P ice o p oduc Y is conside ed one. 𝑊Hy and W𝐻N a e he paymen s o human capi als
in esea ch and de elopmen along wi h inal goods depa men s, espec i ely. Also,
𝑃xiand 𝑃xi a e he p ice o domes ic and o eign in e media e inpu s. Since in e media e
goods a e con e ed in o capi al, capi al p ice is also conside ed one uni and in e es a e
( ) is de e mined in a pe ec inancial ma ke . I is also assumed ha ma ke s Y and H
a e compe i i e o Y p oduc ion i ms. Two c i e ia exis o in e media e goods: i s , i
is assumed ha in en o s a e ee o en e he business and, second, each in e media e
good is p oduced by a monopoly on he sale. The e o e, he p oblem can be p esen ed as
ollows o a inal p oduce :
𝑀𝑎𝑥 𝜋=𝑌{𝐻𝑦 ,𝑥𝑖,𝑥𝑖∗
∗} − 𝑊Hy𝐻𝑦−∫𝑃𝑥𝑖𝑥𝑖
𝑁
0𝑑𝑖−∫𝑃𝑥𝑖∗
∗𝑥𝑖∗
𝑁∗
0𝑑𝑖 ∗ (3)
By adop ing he equi ed i s -o de condi ions o he abo e maximiza ion p oblem,
we ha e:
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𝑊Hy=αY 𝐻𝑦
⁄ (4)
𝑥i=𝐻𝑦 [A𝛽 𝑃xi]
⁄1
α , i.e. 𝑃xi=A𝛽𝐻𝑦𝛼x−𝛼 (5)
𝑥𝑖∗
∗=𝐻𝑦 [A𝛽 𝑃x𝑖∗
∗]⁄ 1
α , i.e. 𝑃𝑥∗=A𝛽𝐻𝑦𝛼𝑥∗ −𝛼 (6)
Acco ding o he abo e equa ions, i is clea ha all he in e media e goods a e
employed o he p oduc ion o inal goods; he e o e, he same demand unc ion is
sha ed. P oduce s in in e media e inpu depa men use p ice 𝑃𝑥 o maximize cu en
p o i a any gi en ime.
𝑉(𝑡)=∫ (
∞
𝑡𝑃 x .x − 1 .x) e−
(s , )(s− )𝑑𝑠
X is o al in e media e inpu s which a e p oduced by demand unc ion a any ime and
(s , )=[1 𝑠−𝑡
⁄ ]∫𝑟(𝑣)𝑑𝑣
∞
𝑡 indica es a e age in e es a e be ween imes and s.
The e o e, by assuming a cons an alue o in e es a e, he p oblem o in e media e
i ms o selec ing a p ice which could maximize p o i is gi en as ollows:
max
𝑃 x 𝜋𝑚=𝑃 x .(x − 1) .x (7)
The solu ion o p ice o monopoly on he sale is p esen ed below:
𝑃 xi =𝑃 x =1 𝛽
⁄ (8)
A simila me hod o ob aining he p ice o o eign in e media e inpu s is:
𝑃x𝑖∗
∗= 𝑃x∗
Since domes ic economy could be comple ely combined wi h global economy, deg ee
o economy openness is used so ha , o ob ain e e y X uni om a o eign in e media y,
x 𝑒D uni s should be sen . The e o e, op imum p ice o a o eign monopoly can be
ob ained.
𝑃x𝑖∗
∗= 𝑃x∗=𝑒𝐷𝛽
⁄ (9)
By inse ing Equa ions 8 and 9 in Equa ions 5 and 6, balances alue o xi and xi∗ a e
ob ained.
𝑥i=x=A1α
⁄𝛽2α
⁄𝐻𝑦 (10)
𝑥𝑖∗=𝑥∗=A1α
⁄𝛽2α
⁄𝐻𝑦𝑒−𝐷 α
⁄ (11)
Using Equa ions 1, 10, and 11, balance le el o he p oduc is de e mined as:
𝑌=𝐴𝐻𝑦𝛼(𝑁𝑥𝛽+𝑁∗𝑥∗𝛽)=A1α
⁄𝐻𝑦 𝛽2𝛽 α
⁄(N+𝑁∗𝑒−𝐷𝛽 α
⁄)=
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A1α
⁄𝐻𝑦 𝛽2𝛽 α
⁄[𝑁+𝐹(𝐷)𝑁∗] (12)
In his case, 𝐹(𝐷)=𝑒−𝐷𝛽 α
⁄ , 𝐹(0)=1, 𝐹(∞)=0, and 𝜕𝐹 𝜕𝐷
⁄<0 and PN is he
pa en p ice o he in e media e p oduc . By gua an eeing ee en y in o he in e media e
depa men , he educed alue o p o i would be equal o he pa en p ice.
𝑃𝑁=𝑉(𝑡)=∫𝜋𝑚(𝑠)
∞
𝑡 e−
(s , )(s− )𝑑𝑠 (13)
Assuming a cons an alue o in e es a e, a speci ic solu ion can be ob ained owing
o he cons an alue o PN. In his case, he ollowing equa ion is ob ained:
𝑃𝑁=𝑉(𝑡)=1
𝑟𝜋𝑚(𝑡)=1
𝑟(𝑃𝑥−1)x=1
𝑟(1
𝛽−1)x=1
𝑟(𝛼
𝛽)x (14)
In he esea ch and de elopmen depa men , o al income o esea ch and
de elopmen ac i i ies is as ollows:
𝑇𝑅=𝑃𝑁𝑁•=𝑃𝑁𝛿𝐻𝑁[𝑁+𝐺(𝐷 ,𝐻)𝑁∗]
And o al cos s a e as ollows:
𝑇𝐶=W𝐻N.𝐻𝑁
The e o e, ee en y in o esea ch and de elopmen depa men is gua an eed and he
paymen o human capi als in he esea ch and de elopmen depa men would be:
W𝐻N=𝛿𝑃𝑁[𝑁+𝐺(𝐷 ,𝐻)𝑁∗] (15)
Below, Rome assumes ha human capi al mo es be ween depa men s. Fu he mo e,
by de e mining he balance condi ion and alloca ing human capi al o depa men s o
inal p oduc ion and esea ch and de elopmen , Rome s a es ha paymen s o human
capi al mus be equal in all he depa men s:
W𝐻N=W𝐻y (16)
Conside ing Equa ions 4, 12, 14, and 15, Equa ion 16 can be ew i en as ollows:
α 𝐴1α
⁄ β2β α
⁄[𝑁+𝐹(𝐷 )𝑁∗]=𝛿(α
𝑟βx) [𝑁+𝐺(𝐷 ,𝐻)𝑁∗]
By inse ing Equa ion 10 in 𝑥 in he abo e equa ion, he ollowing equa ion is
ob ained:
𝐻y𝛿
𝑟[𝑁+𝐺(𝐷 ,𝐻)𝑁∗]=1
β[𝑁+𝐹(𝐷 )𝑁∗]
Consequen ly, he abo e equa ion can be simpli ied as Equa ion 17.
𝐻y=𝑟[𝑁+𝐹(𝐷 )𝑁∗]
𝛿β[𝑁+𝐺(𝐷 ,𝐻)𝑁∗] (17)
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Conside ing Hy, o calcula ion simplici y, i is assumed ha :
𝑁𝑤𝑜𝑟𝑙𝑑 =𝑁+𝑁∗ , 𝑁∗
𝑁=𝑢 (18)
I 𝑢≥0, hen he e is echnology gap be ween o eign and domes ic coun ies.
𝑁= 1
1+𝑢𝑁𝑤𝑜𝑟𝑙𝑑,𝑁∗=𝑢
1+𝑢𝑁𝑤𝑜𝑟𝑙𝑑 (19)
By inse ing Equa ion 19 in Equa ion 17, he ollowing ela ion is ob ained:
𝐻y=𝑟[1+𝑢 𝐹(𝐷 )]
𝛿β[1+𝑢 𝐺(𝐷 ,𝐻)] (20)
Since 𝐻N=H−𝐻y, Equa ions 2 and 19 can be used o calcula e echnology g ow h
a e:
𝑔𝑁=𝑁•
𝑁=𝛿𝐻N[1 + 𝑢 𝐺(𝐷 ,𝐻)]=𝛿(𝐻−𝐻y)[1 + 𝑢 𝐺(𝐷 ,𝐻)]
By inse ing Equa ion 18 in Equa ion 12, he ollowing ela ion is ob ained:
𝑌= 𝐴1α
⁄ 𝐻yβ2β α
⁄[1 + 𝑢 𝐹(𝐷 )]𝑁 (21)
I is cons an , Equa ion 20 indica es ha Hy is also cons an ; also, 𝑥 is cons an
acco ding o Equa ion 10. In his economy, using capi al and p oduc , o al p oduc ion
g ows a an equal a e N. G ow h a e 𝑔 o achie ing a s a ic balance g ow h pa h o all
he a iables can be w i en as:
𝑔=𝑔𝑦=𝑔𝐶=𝑔𝑁=𝛿𝐻N[1 + 𝑢 𝐺(𝐷 ,𝐻)]=𝛿(𝐻−𝐻y)[1 + 𝑢 𝐺(𝐷 ,𝐻)] (22)
Equa ion 22 shows a posi i e co ela ion be ween g ow h a e wi h economic s abili y
g, human capi al in esea ch and de elopmen HN, and adso p ion capaci y 𝐺(𝐷,𝐻) so
ha , wi h inc easing human capi al in esea ch and de elopmen depa men and
imp o ing domes ic adso p ion capabili y, g ow h a e wi h economic s abili y is
inc eased. I 𝐻N=0, he e is no long- e m g ow h; i 𝐻N is posi i e and less han H, hen
g would be posi i e.
The e o e, s able g ow h a e would be equal o:
𝑔=𝜎𝐻[1+𝑢𝐺(𝐷,𝐻)−(𝜌 β)[1+u F(D)]
⁄
1+(𝜎 β)[1+u F(D)]
⁄ (23)
Below, in o de o s udy ex e nali ies in he knowledge p oduc ion unc ion, spa ial
econome ic is used so as o ob ain in a- and in e - egional ex e nali ies. Acco ding o
he s udies by LeSage and Pace (2009), when da a samples ha e a spa ial componen , wo
cases would occu : 1) spa ial dependence be ween obse a ions, and 2) spa ial
he e ogenei y (spa ial s uc u e).
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Con en ional econome ic analysis igno es hese wo issues o a g ea ex en , which
could be due o he iola ion o Gauss-Ma ko 's assump ions used in eg ession models.
The e o e, in o de o apply his me hod, i s concep s should be unde s ood. Below, a
b ie desc ip ion o spa ial he e ogenei y and dependence and he way o de e mining
loca ion and spa ial lags is p esen ed.
Spa ial dependence
Spa ial dependence in a se o sample da a means ha obse a ions in loca ion i depend
on o he obse a ions in loca ion j. In o he wo ds:
𝑌𝑖=𝑓(𝑌𝑗), 𝑖=1,2,…,𝑛 𝑖 ≠𝑗 (24)
This dependence may exis among di e en obse a ions and dis u bing componen s
and mus co espond wi h undamen al heo ems o egional science; i.e. close
obse a ions mus e lec a highe deg ee o spa ial dependence han he ones which a e
dis an om each o he . In o he wo ds, spa ial dependence and i s e ec s on obse a ions
mus dec ease wi h inc easing dis ance be ween obse a ions.
Spa ial he e ogenei y
The e m spa ial he e ogenei y e e s o de ia ion in ela ions be ween obse a ions a
he le el o geog aphical loca ions. In mos cases, di e en ela ions a e expec ed o each
poin in he space. In o he wo ds, linea ela ion is exp essed as ollows:
𝑌𝑖= 𝑋𝑖𝛽𝑖+ 𝜀𝑖 (25)
whe e i, Xi, Yi, and 𝜀𝑖 indica e he ob ained obse a ions a poin s i=1,2,3,…,n in he
space, 𝑋𝑖 shows n×k ec o o desc ip i e a iables along wi h i s ela ed 𝛽𝑖 pa ame e
se , 𝑌𝑖 is dependen a iable in obse a ion o loca ion i, and 𝜀𝑖 is andom e o in he
abo e ela ion. A mo e complex p esen a ion o his concep is as ollows:
𝑌𝑖=𝑓(𝑋𝑖𝛽𝑖+ 𝜀𝑖) (26)
Conside ing Equa ion 15, i is no expec ed o es ima e a se o n pa ame e s om
ec o 𝛽𝑖 conside ing one sample o obse a ions and unique es ima ion o each poin in
he space. Gene ally, spa ial he e ogenei y also iola es he Gauss-Ma ko 's assump ion
which sugges s only one de ini e linea ela ionship wi h cons an a iance be ween
sample obse a ions. The e o e, a e ejec ing he null hypo hesis, which s a es lack o
any spa ial au o-co ela ion among dis u bing componen s, spa ial e o model (SEM),
simul aneous au o- eg ession- eg ession (SAR) model, gene al spa ial model, o spa ial
Du bin model can be u ilized.
Simul aneous au o- eg ession- eg ession model
This model explains y a ia ions as a linea combina ion o neighbo ing coun ies like
au o- eg essi e ime se ies and emphasizes on wha occu s in hese coun ies, because
knowledge p oduc ion in e e y coun y can be a ec ed by a ia ions in knowledge
p oduc ion and spillo e s o neighbo ing coun ies. In his ega d, me hod o maximum
In e na ional Jou nal o Managemen , Accoun ing and Economics
Vol. 2, No. 7, July, 2015
ISSN 2383-2126 (Online)
© IJMAE, All Righ s Rese ed www.ijmae.com
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likelihood can be used o es ima e pa ame e s o his model. The abo e men ioned model
is as ollows:
𝑦i=ρ∑Wijyj+∑𝛽𝑘𝑥𝑘𝑖
𝑘
𝑘=1 +εi=
n
j=1 ρW y + Xβ+εi (27)
εi~N(0,σ2In)
Spa ial e o model
In spa ial econome ic analysis, a model is spa ial e o model, in which knowledge
p oduc ion is in luenced by shock c ea ion in neighbo ing coun ies. This model can be
p esen ed as:
𝑦i=∑𝛽𝑘𝑥𝑘𝑖
𝑘
𝑘=1 +εi=Xβ+ui (28)
ui=λWui+εi , εi~N(0,σ2In)
Spa ial Du bin model
This model which has he spa ial coe icien o dependen a iable and desc ip i e is
w i en as ollows:
𝑦i=ρWy+Xβ+𝑊Xθ+εi (29)
εi~N(0,σ2In)
I mus be men ioned ha spa ial Du bin model is p e e ed o simul aneous spa ial
eg ession-au o- eg ession and spa ial e o models, because when 𝜃=0, SDM is
con e ed in o simul aneous spa ial eg ession-au o- eg ession model, and when 𝜃=
−𝛽𝜌, his model is changed o spa ial Du bin model. In addi ion o simul aneous spa ial
eg ession-au o- eg ession model, in spa ial Du bin model, di ec e ec s can be also
dis inguished om indi ec ones. I is wo h men ioning ha spa ial Du bin model is less
biased han simul aneous spa ial eg ession-au o- eg ession model; also, spa ial e o
model esul s in he elimina ion o spa ial spillo e s.
Technology pa en s esul ed om spa ial knowledge spillo e s om neighbo ing
egions a e examples o posi i e ex e nali ies o posi i e spillo e s. A la ge pa o
knowledge is implici and i s ans e equi es coope a ion and common ac i i ies. On he
o he hand, he e is explici knowledge, since conduc ing ideas o echnological pa en s
ensu es he exis ence o people who ha e ela ionship wi h in en o s' expe ience. This
knowledge exis ence inc eases and is o en ans e ed as a esul o disco e ing new ideas
in a egion. Knowledge o a pa icula egion and i s neighbo ing egions is a good gene al
commodi y, which p o okes spa ial explana ion o knowledge. Spa ial eg ession
models can be used o de e mine spa ial ex en o spillo e s h ough in es iga ing indi ec
e ec s using expanded se ies 𝐼𝑛+𝜌𝑊+𝜌2𝑊2+⋯. Gene ally, in o de o ob ain di ec
e ec s, i s , e ec o inc easing desc ip i e a iable in coun y i on dependen a iable
in coun y i is calcula ed (i.e. own-pa ial de i a i e is equal o 𝜕𝑦𝑖
𝜕𝑥𝑖) and since i=1,2,3,…,n,
all he e ec s in he en i e egion is a e aged. To calcula e indi ec accumula i e e ec ,
