K ause, Melanie; K ip ganz, Sebas ian
A icle — Published Ve sion
Regional Dependencies and Local Spillo e s: Insigh s F om
Commu e Flows
Jou nal o Regional Science
P o ided in Coope a ion wi h:
John Wiley & Sons
Sugges ed Ci a ion: K ause, Melanie; K ip ganz, Sebas ian (2025) : Regional Dependencies and Local
Spillo e s: Insigh s F om Commu e Flows, Jou nal o Regional Science, ISSN 1467-9787, Wiley,
Hoboken, NJ, Vol. 65, Iss. 3, pp. 565-585,
h ps://doi.o g/10.1111/jo s.12752
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Jou nal o Regional Science
RESEARCH ARTICLE
Regional Dependencies and Local Spillo e s: Insigh s
F om Commu e Flows
Melanie K ause
1
| Sebas ian K ip ganz
2
1
Facul y o Economics and Managemen Sciences, Leipzig Uni e si y, Leipzig, Ge many |
2
Depa men o Economics, Uni e si y o Exe e Business School,
Exe e , UK
Co espondence: Melanie K ause ([email p o ec ed])
Recei ed: 14 Augus 2023 | Re ised: 17 Sep embe 2024 | Accep ed: 16 Decembe 2024
Keywo ds: commu ing | shock p opaga ion | spa ial mul iplie | spa ial weigh ma ix
ABSTRACT
A egion's g ow h ajec o y is in luenced by he economic ci cums ances o o he egions in i s p oximi y. While p oximi y is
o en unde s ood in a geog aphic sense, economic connec i i y can ake many di e en o ms. In pa icula , shock ansmission
p ocesses be ween egions a e inhe en ly asymme ic and he e ogeneous, which is no cap u ed by geog aphic p oximi y
measu es. As a po en ial channel o economic dependencies, we conside c oss‐ egional commu e lows. Commu e s, who
spend a subs an ial po ion o hei income in a di e en place om whe e hey ea n i , connec pe iphe al egions o economic
cen e s. In an econome ic amewo k, we es ima e ime‐space dynamic panel models wi h Ge man coun y‐le el da a. Gi en
hose es ima es, we demons a e a conside able a ia ion in he spa ial dis ibu ion o shock esponses om using al e na i e
p oxies o spa ial dependency, which is hidden by he adi ional ocus on a e age ma ginal e ec s. Local spa ial mul iplie s
di e depending on he na u e and o igin o he shock and he assumed ne wo k s uc u e.
JEL Classi ica ion: R12, C23, J61
1 | In oduc ion
Economic di e ences can pe sis o e a long ime, no jus
ac oss coun ies, bu also wi hin coun ies. An impo an aspec
o economic de elopmen is ha egions a e o en closely in-
e connec ed in a ious ways, and he e o e hei de elopmen
is no independen om one ano he . In he ex book Solow–
Swan neoclassical g ow h model—and many o i s ex ensions—
hese dependencies a e le aside. The speed o con e gence is
pu ely de e mined by a egion's dis ance om i s own s eady‐
s a e equilib ium.
In ecen yea s, a s onge ocus has been placed on c oss‐
sec ional dependencies in he o m o local and global ex-
e nali ies. The sou ce o hese spillo e s can be in he accu-
mula ion o physical and human capi al in neighbo ing egions
(Ca ing on 2003), in di ec con ibu ions o each o he 's o al
ac o p oduc i i y (Egge and P a e may 2006), in
echnological in e dependence (E u and Koch 2007), o in
ac o mobili y (P a e may 2012). Economic adjus men p o-
cesses a e hen de e mined by he loca ion in space and he
s eng h o he in e egional linkages. Howe e , hese spa ial
Solow models emain silen abou he de e mina ion o he
spa ial ne wo k s uc u e. In he empi ical li e a u e, he con-
nec i i y be ween spa ial uni s is o en modeled in an ad hoc way
as a unc ion o hei geog aphic dis ance, some imes limi ed o
uni s sha ing a common bo de (Anselin 1988; Anselin and Be a
1998). This is based on he a ionale ha geog aphic dis ance is
an accep able p oxy o unde lying economic linkages.
Howe e , geog aphic connec i i y measu es canno accoun o
he he e ogenei y in he economic ela ionships. Economic
ac i i y is o en geog aphically clus e ed due o compa a i e
ad an ages o a ce ain egion—such as he a ailabili y o
skilled wo ke s, a business‐ iendly egula o y amewo k, and
exis ing in as uc u e. Some egions a e g a i a ional cen e s
This is an open access a icle unde he e ms o he C ea i e Commons A ibu ion 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.
© 2025 The Au ho (s). Jou nal o Regional Science published by Wiley Pe iodicals LLC.
565 o 886Jou nal o Regional Science, 2025; 65:565–585
h ps://doi.o g/10.1111/jo s.12752
which subs an ially in luence he su ounding sa elli e egions,
wi hou much eedback in he opposi e di ec ion. Va ious
s udies ha e ound empi ical e idence ha spa ial spillo e e -
ec s may be asymme ic; echnologically ad anced a eas
in luence hose wi h lowe human capi al (Benhabib and
Spiegel 1994) o lowe o al ac o p oduc i i y (Sille e al.
2021), bu ha dly ice e sa. Such an asymme y o egional
spillo e e ec s canno be cap u ed by geog aphic con igui y.
Ins ead, connec i i y measu es should e lec he g a i a ional
o ces. While hose o ces a e inhe en ly la en , i is o en pos-
sible o ind economic o socioeconomic p oxies o hem.
In his pape , we in es iga e in he con ex o an econome ic
amewo k how app oxima ing he egional linkages by com-
mu e lows as an al e na i e o geog aphic dis ance a ec s he
es ima ion o dynamic adjus men p ocesses. Simila o he as-
sump ions made by Benhabib and Spiegel (1994) and Sille e al.
(2021), commu e lows c ea e asymme ic dependencies
be ween economic “leade s”and “ ollowe s.”Ra he han
de eloping a ull‐ ledged s uc u al model, we conside an
empi ical case s udy and highligh subs an ial di e ences
depending on he assump ions abou he spa ial ne wo k. Using
he bias‐co ec ed maximum likelihood es ima o o Yu, de
Jong, and Lee (2008), we es ima e a ime–space dynamic g ow h
con e gence model wi h spa ial weigh ma ices based on ei he
commu e lows o geog aphic connec i i y. Subsequen ly, we
compu e spa ial mul iplie s o coun e ac ual scena ios in
which we assign ea men —a hypo he ical shock o policy
in e en ion— o small g oups o coun ies. Ou analysis dem-
ons a es ha he dis ibu ional e ec s o a shock o in e en-
ion depend conside ably on which coun ies ecei e he
ea men and on he assumed ne wo k s uc u e. When spil-
lo e s a e ealized h ough commu e connec ions, he s on-
ges e ec s a e achie ed by assigning ea men o coun ies
which ac as g a i a ional cen e s. In con as , wi h geog aphic
spa ial weigh s he economic cha ac e is ics o he ea ed
coun ies a e i ele an ; and he s eng h o he mul iplie e ec s
is solely de e mined by he loca ion and p oximi y o he ea ed
coun ies.
Impo an ly, we do no claim ha commu e lows a e neces-
sa ily a be e p oxy o egional dependencies han geog aphic
dis ance. Since he ue linkages a e unobse ed, he empi ical
model will be misspeci ied in ei he case. Con en ional s an-
da d e o s and con idence in e als only e lec sampling
unce ain y, bu hey do no accoun o he model unce ain y
ega ding he co ec spa ial ne wo k s uc u e. We he e o e
ad oca e o a compa ison o esul s ob ained wi h di e en
spa ial weigh s, o g asp he ange o possible e ec s. In his
ega d, al e na i e ne wo k speci ica ions can be seen as com-
plemen s a he han subs i u es.
We cons uc a spa ial weigh ma ix based on commu e da a
because commu e lows a e a na u al choice o measu ing
in e egional connec i i y a he local le el. In e egional com-
mu e s ea n hei money in one place and spend a signi ican
po ion o i in ano he place, he eby con ibu ing o impo an
links be ween egions. P oos and Thisse (2019) p o ide an
o e iew on he ole ha commu ing plays in u ban economics
and egional science. The classical case is commu ing wi hin
ci ies in he canonical Alonso–Mills–Mu h model (Alonso 1964;
Mills 1967; Mu h 1969) and i s ex ensions (Du an on and
Tu ne 2011; Ahl eld e al. 2015). Ye , commu ing ac oss
egions is also inc easingly becoming he subjec o he heo-
e ical li e a u e. In models o he New Economic Geog aphy
li e a u e, egions a e no only connec ed by ade lows and
spa ial knowledge spillo e s, bu also by commu e lows
(Allen, A kolakis, and Li 2015). Mon e, Redding, and Rossi‐
Hansbe g (2018) demons a e ha spa ial in e ac ions h ough
commu ing can de e mine local economic e ec s o labo
ma ke shocks. In undamen al con as o geog aphic dis ance,
a commu e low ne wo k implies a shock ansmission
mechanism which is p edominan ly one‐way, while allowing
o subs an ial geog aphic he e ogenei y.
In many coun ies, an inc easing numbe o people wo k in a
di e en place om whe e hey li e. La ge numbe s o in e -
egional commu e s a e ound pa icula ly in coun ies whe e
economic ac i i y is ela i ely decen alized, he dis ances a e
no oo la ge, and he in as uc u e is solid. In he EU, on
a e age 6% o he employed wo king‐age (15–64 yea s) popu-
la ion commu ed o a di e en Nomencla u e o Te i o ial
Uni s o S a is ics (NUTS) 2 egion in 2020. Belgium opped he
lis wi h 21% coun ywide, and up o 49% o some Belgian
p o inces.
1
A he smalle coun y le el—NUTS 3 egions—
hese numbe s a e conside ably highe . As he e is no EU‐wide
da a collec ion on commu ing a his le el o disagg ega ion, we
es ic ou a en ion o Ge many, o which su icien ly long
o igin‐des ina ion commu e low ime se ies can be ob ained.
We in es iga e he di e en shock ansmission implica ions o
commu e ‐based and geog aphy‐based spa ial linkages wi h
panel da a on Ge man coun ies, co e ing he ime span om
2002 o 2017. Fo mos o ou sample pe iod, eal GDP pe
capi a shows s a is ically signi ican nega i e spa ial au o-
co ela ion when egional connec i i y is measu ed h ough
asymme ic commu e lows, bu insigni ican spa ial au o-
co ela ion when symme ic geog aphic weigh s a e used.
Ge many is a sui able case in poin o he ole o commu e s in
egional con e gence and economic shock p opaga ion. I is a
e i o ial s a e wi h a numbe o economic cen e s and con-
side able egional a ia ion in e ms o p ospe i y. The eas e n
pa expe ienced s ong ca ch‐up g ow h in he 1990s and
2000s, bu as a whole is s ill lagging behind. Meanwhile, he e
a e bo h economic hubs as well as poo e egions in he sou h
and wes (Kos eld, Eckey, and D ege 2006; Cola ecchio,
Cu an, and Funke 2011). In ou da a se , be ween 3% and 31%
o a coun y's popula ion was commu ing o a di e en coun y.
Fo he mos a ac i e commu e des ina ions, he incoming
commu e numbe s e en o aled up o 78% o hei own pop-
ula ion size.
Wi h ou ocus on commu e lows as p oxies o spa ial
dependence, ou pape is ela ed o he empi ical li e a u e on
egional economic con e gence (see o ins ance Sala‐i‐Ma ín
1996; Badinge , Mülle , and Tondl 2004; Fische and P a e may
2018). The o en a he coa se classi ica ion o egional uni s in
he li e a u e masks a conside able deg ee o he e ogenei y and
in a‐ egional spillo e s. The ies o o he egions ( ela i e o he
size) end o inc ease a a deepe le el o disagg ega ion. This is
also e lec ed in he obse ed commu ing pa e ns. While he e
ha e been con e gence s udies a he coun y le el— o example
566 o 886 Jou nal o Regional Science, 2025
Kos eld, Eckey, and D ege (2006) o Ge many, Young, Higgins,
and Le y (2008) o he US, and Cheong and Wu (2013) o
China— hese ei he did no explici ly model he dependencies
ac oss coun ies, o hey elied on geog aphic p oximi y measu es.
Wi h ou wo k, we aim o b idge he gap be ween di e en
s ands o he li e a u e: We ans e he insigh s on commu ing
om ne wo k and g a i y models in o spa ial econome ics,
whe e spa ial weigh ma ices a e ypically pu ely based on
geog aphic dis ances. G a i y models ha e a long adi ion in
modeling ade, mig a ion, a ic o commu ing lows
(Luke mann and Po e 1960; E lande and S ewa 1990;
McA hu e al. 2011). As Niede co n and Bechdol (1969)
mo i a e om a u ili y maximiza ion amewo k, lows be ween
wo egions in g a i y models inc ease wi h he size o hei
popula ion and dec ease wi h he dis ance be ween hem. Hence,
hey i ally ely on geog aphic dis ance o a ionalize lows in
goods and people. Recen applica ions o g a i y models include
he p edic ion o commu e lows and a el imes in I eland
(Ah ens and Lyons 2021) as well as Mexico (Du an‐Fe nandez
and San os 2014), whe e he la e a gue ha dis ance should
a he be measu ed in a el imes han Euclidean dis ance. In
ac , beyond pu e dis ance, a numbe o o he ac o s ha e been
shown in he li e a u e o ma e o unde s anding commu e
lows. Tho sen and Gi lesen (1998) poin o speci ic labo ma ke
cha ac e is ics; Simini e al. (2021) use a deep lea ning ame-
wo k o elucida e he ole o he oad ne wo k, anspo a ion
acili ies, and land use in p edic ing mobili y lows. Following
hese lines o hough , geog aphic dis ance is only one o he
ele an ac o s which cha ac e ize g a i a ional o ces. Com-
mu e lows a e closely linked o hem as well. Howe e , in
con as o he g a i y model li e a u e, ou goal is no o p edic
commu e lows bu o use hem as a p oxy o he connec i i y
o egions in ou econome ic analysis o shock p opaga ion.
Commu e ne wo ks ha e also been s udied in ne wo k science
(Ba abási 2003;Ama ale al.2000). Fo Ge man commu e da a,
Pa uelli e al. (2010) ind no subs an ial changes o e he 10 yea s
om 1995 o 2005, al hough hey no ice a sligh end owa ds a
mo e dis ibu ed ne wo k s uc u e and inc eased in e -
connec i i y. Reggiani, Bucci, and Russo (2011) con i m he
mul i‐nodal s uc u e as well as he s abili y o he Ge man
commu e low ne wo k wi h da a om 2003 o 2007, also
poin ing ou ha he mos connec ed dis ic s a e la ge cen e s
such as Hambu g, Be lin, F ank u , Munich, and Cologne in
bo h yea s. The au ho s no e a hie a chy o hubs, a phenomenon
unde lining he asymme ic na u e o commu e lows. These a e
i al insigh s o ou cons uc ion o he spa ial weigh ma ix o
cap u e economic shock spillo e s. Ne wo ks based on com-
mu e lows can be asymme ic, in con as o he classical
geog aphy‐based ne wo ks. A he same ime, he ela i e s a-
bili y o commu e lows—which he da a o ou ime pe iods
also sugges —limi s endogenei y conce ns o ou analysis.
In ou econome ic se ing, we analyze c oss‐sec ional spillo e
e ec s a he coun y le el, which is also ele an om a policy
pe spec i e. Go e nmen in e en ions can ha e qui e di e en
local e ec s, depending on he economic condi ions in a coun y
and i s in e connec edness wi h o he coun ies. Fo example,
conside subsidies o i ms in a pa icula sec o ha a e geo-
g aphically clus e ed in ce ain loca ions. The egional gene al‐
equilib ium e ec s will be e y di e en o subsidies o he
ag icul u al sec o compa ed o he inancial o manu ac u ing
sec o ; he p o ision o public goods in a eas o high popula ion
densi y has di e en implica ions han in u al egions. Gene -
ally, he mul iplie e ec s o an in e en ion in an economic
cen e a e s onge due o he spillo e e ec s o economically
dependen coun ies. While i may seem desi able o di ec ly
in e ene in disad an aged a eas, his is unlikely o achie e he
highes alue o axpaye s' money. Con e sely, a ge ing al eady
p ospe ing coun ies—wi h he aim o maximize he agg ega e
e ec o an in e en ion— aises dis ibu ional conce ns. This
di e en ial esponse o an ini ial s imulus is o en o e looked in
econome ic s udies, whe e i is common p ac ice o epo
a e age e ec s. As we show in his pape , hese dis ibu ional
e ec s can di e subs an ially depending on he assumed spa ial
ne wo k. Wi h geog aphy‐based connec i i y, economic cen e s
and hei pe iphe y would be ea ed symme ically. In con as ,
spillo e s gene a ed by commu e lows (o o he measu es o
economic dependence) can be e y he e ogeneous, which we
would expec o be e e lec he economic eali y.
2 | Econome ic Model and Me hods
2.1 | Time–Space Dynamic Panel Da a Model
Spa ial econome ic me hods ha e a long adi ion in egional
science and became es ablished in mains eam empi ical eco-
nomics in ecen decades. Fo he analysis o economic
adjus men p ocesses, he es ima ion o a ime–space dynamic
panel da a model is becoming inc easingly popula . Examples
include s udies o egional g ow h in Eu ope (Fische and
LeSage 2015; Fingle on 2020), I aly (Billé, Tomelle i, and
Ra azzolo 2023), Ko ea (E ans and Kim 2014), and OECD
coun ies linked h ough ade (Ho, Wang, and Yu 2013). In
such a model, he g ow h ajec o y o a egion is de e mined by
i s own his o y and he g ow h pa h o o he egions o which i
is connec ed, e lec ing pe sis ence o e ime and spa ial g ow h
pa e ns. Due o sluggish p oduc ion p ocesses and ine ia in
economic en i onmen s, he impac o a shock is ypically no
ully abso bed immedia ely. This pa ial adjus men p ocess can
be modeled wi h lagged dependen a iables. Besides i s impac
on he egion whe e i o igina es, an economic shock also
sp eads h ough he ne wo k o connec ed egions wi h
dec easing in ensi y, depending on he s eng h and di ec ion o
he linkages. We la gely emain agnos ic abou he ype o
shock. The ollowing econome ic model can be de i ed om a
s anda d g ow h model wi h Cobb–Douglas p oduc ion unc-
ion and spa ial ex e nali ies (E u and Koch 2007):
2
y y Wy Wy Xπι
αε
θλ ρ γln = ln + ln + ln + +
++,
N N N
−1−1(1)
T=1,2,…, , whe e yyy y=( , ,…, )
′
N 12
is a ec o o eal
GDP pe capi a o coun ies
i
N=1,2,…, a ime
. I is s an-
da d p ac ice in he economic g ow h li e a u e o use a loga-
i hmic ans o ma ion o he dependen a iable, which is
consis en wi h he no ion o a balanced g ow h pa h and allows
o in e p e he coe icien s o he co a ia es as (semi‐)
elas ici ies. The
NN
×ma ix
W
N
is a (sui ably no malized)
567 o 886
spa ial weigh ma ix ha go e ns he links be ween coun ies.
The scala coe icien s θλ,, and
ρ
de e mine he s eng h o he
empo al and spa ial dependence.
X
is an
N
K×
ma ix o
co a ia es wi h coe icien ec o π.
ιN
is an
N
×
1
ec o o
ones and he coe icien s
γ
a e common ime e ec s o be es-
ima ed. The coun y‐speci ic e ec s
ααα α=( , ,…, )
′
N12
accoun
o any unobse ed ime‐in a ian cha ac e is ics.
ε
is an
N
×
1
ec o o idiosync a ic shocks.
To acili a e he in e p e a ion o he model's coe icien s, i
migh be p e e able o ew i e i in e ms o GDP g ow h a es
and ini ial GDP le els:
yyWyWy
Xπιαε
θλλρ
γ
Δln = ( −1)ln + Δln + ( + ) ln
++++,
N N
N
−1−
1
(2)
whe e
Δ
is he i s ‐di e encing ope a o . y
Δ
ln
app oxima es
he g ow h a e o eal GDP pe capi a.
3
In he absence o spa ial
spillo e e ec s, a alue o
∈θ(0, 1)
e lec s condi ional con-
e gence; coun ies wi h a lowe ini ial eal GDP pe capi a le el
a e ca ching up wi h weal hie egions by g owing a a as e
pace (condi ional on di e ences in he explana o y a iables
X
and ime‐in a ian coun y‐speci ic di e ences cap u ed by
α
).
Lowe alues o
θ
indica e as e con e gence.
Rega ding he spa ial e ms,
λ
>0 e lec s he co‐mo emen o
connec ed egions; a egion bene i s om being linked o o he
as ‐g owing egions, o is cons ained in i s economic de el-
opmen by being dependen on o he slow‐g owing egions. The
coe icien
ρ
measu es he ex en o which he ini ial condi ions
in connec ed egions ma e o he con e gence p ocess. A
posi i e alue o
ρ
implies a phased esponse o changing eco-
nomic condi ions in o he egions; a nega i e alue o
ρ
indi-
ca es ha any ini ial spillo e e ec s a e (pa ially) o se in he
ollowing pe iod. The la e cha ac e izes a si ua ion in which
he ini ial esponse o a shock in a neighbo ing egion o e -
shoo s, ollowed by a subsequen co ec ion. I his co ec ion is
impe ec ,
ρ
λ>−, hen ha ing s ong ies o o he ich egions
yields an addi ional boos o a egion's ca ch‐up g ow h.
4
Fo ou main es ima ion me hod,weneed oassumes ic exo-
genei y o he co a ia es
X
and he spa ial weigh ma ix
W
N
wi h
espec o he inno a ions
ε
. The la e a e assumed o be inde-
penden and iden ically dis ibu ed wi h mean ze o. The co ela-
ion be ween he obse ed a iables and he unobse ed ime‐
in a ian e ec s
α
i
can be le un es ic ed. We also assume ha
W
N
and all slope coe icien s a e cons an o e ime. In p inciple, i
would be desi able o allow o mo e lexibili y. Howe e , espe-
cially gi en a ela i ely sho ime ho izon, allowing o ime
a ia ionin hee ec sandspa ial ela ionships becomes econo-
me ically challenging. The same applies o he endogenei y o
X
o
W
N
wi h espec o he shocks
ε
. In gene al, he e is a adeo
be ween pa simony/e iciency and easibili y/accu acy. We p o-
ide some discussion o hese issues in he ollowing subsec ions.
2.2 | Spa ial Weigh Ma ices
In a ime–space dynamic panel da a model, he spa ial weigh
ma ix is c ucial o cap u ing he links be ween he uni s. In
ou s udy, we es ima e he model wi h di e en spa ial weigh
ma ices and analyze he esul ing implica ions. Spa ial weigh s
based on geog aphic p oximi y ha e a long his o y in empi ical
spa ial analyses (Anselin 1988; Anselin and Be a 1998; LeSage
and Pace 2009). The leading examples a e he bina y con igui y
ma ix wi h weigh s (in ow
i
and column
j
o ma ix
W
N
)
w
ij
ij
=1, and sha e a common bo de
0, and do no sha e a common bo de
,
ij
(3)
and he in e se dis ance ma ix wi h weigh s
w
d
=1,
ij
ij (4)
which a e he in e se Euclidean dis ances
d
i
j
be ween wo
egions (based on geog aphic cen oids).
5
By con en ion, he
diagonal elemen s a e se o ze o; ha is,
w
=0
ii . No e ha bo h
hese ma ices a e by cons uc ion symme ic, so ha a shock
om egion
i
o
j
has he same impac as he o he way ound.
Ye , al e na i e app oaches o cap u e he spa ial spillo e
e ec s ha e become mo e and mo e p ominen in ecen yea s.
Ba aud (1998) and Co ado and Fingle on (2012) ecognize
ha he e is no one ue spa ial weigh ma ix ha is adequa e
in all si ua ions, and ha spa ial in e ac ions a e o en de e -
mined by ela i e economic dis ances a he han geog aphic
bounda ies o dis ances. An example o such economic
weigh s a e ade lows cap u ing in e na ional in e -
dependencies, as in E u and Koch (2011) and Ho, Wang, and
Yu (2013). Ama asinghe e al. (2018)conside weigh sbased
on socioeconomic dis ance such as e hnic links and oad
ne wo ks, and Incal a au e al. (2021) use a el imes.
Fingle on (2001), Ca ing on (2003), and Zhang and Wang
(2017) combine geog aphic dis ance wi h a measu e o ela i e
economic impo ance.
Ano he idea ha we do no pu sue he e is es ima ing he
spa ial weigh s a he han cons uc ing hem om obse ed
a iables. While his is a seemingly lexible app oach, i also has
i s limi a ions. An un es ic ed es ima ion is gene ally in easible
due o he la ge numbe o elemen s in he spa ial weigh ma-
ix, especially when allowing o asymme ies (Beens ock and
Felsens ein 2012). When he spa ial weigh s a e es ima ed om
empi ical co ela ions (Bha acha jee and Jensen‐Bu le 2013;
Bailey, Holly, and Pesa an 2016), hey a e symme ic by con-
s uc ion. E en wi h a da a‐d i en app oach, imposing some
s uc u e (Ge is and Alds ad 2004) o a spa si y assump ion
(Ah ens and Bha acha jee 2015; Pi ibaue , Glocke , and
K isz in 2023) is una oidable.
6
In u ban and egional economics, commu e lows cons i u e a
pa icula ly impo an ansmission mechanism (Allen,
A kolakis, and Li 2015). Mon e, Redding, and Rossi‐Hansbe g
(2018) model he dependency o egions h ough a combina ion
o ade and commu e lows. Calib a ing hei model o US
egional da a, hey ind ha bo h lows co ela e wi h each
o he , wi h commu e lows esponding mo e o dis ance han
ade lows. In pa icula a mo e disagg ega e le els o analysis,
hey a gue ha commu e lows a e i al o unde s anding he
568 o 886 Jou nal o Regional Science, 2025
connec i i y o egions. Commu ing can be an indi idually
op imal decision when he e a e di e ences in local ameni ies
and job oppo uni ies ac oss coun ies. By ea ning hei income
in one egion and spending a signi ican pa o i in ano he
egion, commu e s cons i u e i al economic linkages be ween
hose egions. A coun y's suscep ibili y o income shocks o ig-
ina ing in ano he coun y can be easonably modeled as an
inc easing unc ion o he sha e o esiden s wo king in ha
o he coun y.
We a gue ha geog aphic spa ial weigh ma ices ail o cap u e
hese dependencies because hey do no accoun o he he -
e ogenei y o he coun ies. Economic ac i i y is o en clus e ed
in ce ain egions. A h i ing economy in hese coun ies adi-
a es o a la ge a ea depending on he s eng h o he linkages.
Con e sely, he economic cen e is o en la gely insula ed
agains ad e se de elopmen s in su ounding coun ies. This
means ha economic spillo e e ec s can be e y he e ogenous
ac oss egions, as documen ed, in e alia, by Des e anis, Di
Se io, and F age a (2022) o I aly and So i ou and Tsiapa
(2015) o G eece. They can also be asymme ic, wi h a s onge
dependence o lagging egions on echnologically ad anced
leade s (Benhabib and Spiegel 1994; Sille e al. 2021). Such an
asymme ic dependence canno be cha ac e ized by geog aphic
measu es, bu i is an inhe en cha ac e is ic o commu e
lows.
While commu ing is a signi ican phenomenon in small‐scale
egions, we do no claim ha commu e lows a e a pe ec
p oxy o economic in e ‐coun y links. The e a e ce ainly o he
c oss‐coun y in e connec ions along he alue chain. Ye , i can
be e y di icul o e en impossible o ob ain al e na i e mea-
su es o economic connec i i y—such as ade low da a—a a
e y disagg ega ed geog aphical le el. Commu e lows migh
hus be he bes a ailable p oxy o he economic ne wo k
s uc u e. In applica ions wi h a di e en egional scope, o he
measu es—i a ailable—migh be mo e sui able.
7
The in ui i e idea o why commu e lows can cap u e depen-
dencies be ween egions and ma e o shock p opaga ion is
ha commu e s ea n hei income in one egion and spend a
ce ain pa o i in ano he egion. This channel is independen
o whe he people physically lea e hei home and ge in o hei
place o wo k e e y day, o whe he hey (pa ially) wo k om
home. Telecommu ing has g own in impo ance in he wake o
he COVID‐19 pandemic and has added o u he de‐coupling
employees' place o esidence om hei employe 's wo k si e,
as documen ed, among o he s by Dingel and Neiman (2020)
and Ba e o, Bloom, and Da is (2021). Consequen ly, e en long‐
dis ance commu e linkages can be po en ially ele an o he
shock ansmission in he ne wo k. Since ou measu e o
commu e lows elies on indi iduals' and employe s'
loca ions— a he han physical commu ing— he commu e ‐
based weigh ma ix con inues o cap u e hese linkages in a
changing wo king wo ld.
No e ha in con as o he li e a u e on g a i y models and
ne wo k science men ioned ea lie , we do no aim o explain o
p edic commu e lows in his pape ; we a he use hem as a
desc ip i e ne wo k measu e in ou econome ic shock p opa-
ga ion analysis. We ini ially cons uc he commu e weigh s as
he commu e ou low
C
i
j
om coun y
i
o coun y
j
ela i e o
he popula ion size
P
i
o coun y
i
:
≠
w
C
Pij
ij
=,
0, =
.
ij
ij
i
Asymme y o W
N
hus ollows om di e en absolu e com-
mu e le els ≠CC
ij j
i
o di e en popula ion sizes ≠
P
P
ij
.
Le us illus a e he implica ions o di e en weigh ma ices
based on a minimal ex ac om ou Ge man coun y‐le el da a
se , as shown in Figu e 1. The i s coun y in his example is he
ci y o F ank u am Main, a la ge inancial cen e in a densely
popula ed a ea. I sha es i s no hwes e n and wes e n bo de s
wi h he u al dis ic s Hoch aunusk eis and Main‐Taunus‐
K eis (o de ed second and hi d in he ollowing ma ices).
Fu he wes , he ci y o Wiesbaden connec s o he Main‐
Taunus‐K eis, bu wi hou a di ec bo de o ei he o he i s
wo coun ies. We igno e all o he coun ies o his illus a ion.
The bina y‐con igui y and he in e se‐dis ance spa ial weigh
ma ices (be o e any s anda diza ion) look as ollows:
W
W=
0110
1010
1101
0010
,=
0 0.05 0.07 0.04
0.05 0 0.05 0.04
0.07 0.05 0 0.08
0.04 0.04 0.08 0
NN,con . ,in .dis .
The i s ow/column in he con igui y ma ix indica es ha
F ank u sha es a bo de wi h he wo u al coun ies, bu no
bo de wi h he ou h coun y (Wiesbaden). The u al dis ic s
a e neighbo s hemsel es, bu only one o hem (Main‐Taunus‐
K eis) is also connec ed o Wiesbaden. The la e s ill expe i-
ences spa ial spillo e s om he i s wo coun ies (and
ice e sa), bu only indi ec ly h ough he in e media y Main‐
Taunus‐K eis. In con as , he in e se‐dis ance weigh s allow
o immedia e spillo e s among all coun ies, wi h di e en
in ensi ies acco ding o he in e se dis ance o hei geog aphic
FIGURE 1 | Shape, loca ion, and geog aphic cen oids o ou
selec ed Ge man coun ies.
569 o 886
cen oids. We see ha mo e dis an coun y pai s ha e smalle
en ies. Bu due o he i egula shapes o he coun y a eas, he
connec ion be ween F ank u and Wiesbaden is o simila
s eng h as he connec ion be ween F ank u and he Hoch-
aunusk eis, despi e only he second pai sha ing a bo de .
Impo an ly, bo h ma ices imply symme ic shock ansmis-
sions, igno ing he ac ha he coun ies' economic s uc u e is
undamen ally di e en . F om he wo u al commu e bel
dis ic s, a signi ican sha e o he popula ion wo ks in he
economic cen e F ank u , while he e is e y limi ed com-
mu ing in he opposi e di ec ion. E en hough i is loca ed
u hes away, Wiesbaden is s ill an a ac i e place o li e o
commu e s o F ank u — hanks o i s u ban cha ac e and
ameni ies. This is e lec ed in he commu e ‐based spa ial
weigh ma ix ( ounded o 2 decimals):
W
=
0 0.01 0.02 0
0.11 0 0.02 0
0.15 0.02 0 0.02
0.03 0 0.01 0
N, comm.
The en ies in he i s column highligh ha F ank u a ac s
a ela i ely high sha e o he o he coun ies' popula ion, while
commu ing in he e e se di ec ion is limi ed ( i s ow). This
asymme y is cha ac e is ic o ne wo ks wi h a s ong cen e ‐
pe iphe y s uc u e.
When cons uc ing hese ma ices o ou econome ic es ima-
ion, we apply a spec al s anda diza ion; ha is a di ision o all
weigh s by he absolu e alue o he la ges eigen alue o
W
N
.
This is a s anda d p ocedu e o ensu e ha he spa ial lag
coe icien
λ
in ou econome ic model (Equa ion 2)isona
simila scale i espec i e o he spa ial weigh s. I implies a
con enien uppe bound on he pa ame e space,
λ
<1
, o
IWλ−
NN
o be in e ible. The la e is a s abili y equi emen
o he dynamic sys em de ined by Equa ion (1).
8
We apply he
same spec al s anda diza ion also o he adi ional geog aphy‐
based spa ial weigh ma ices. I is impo an o no e in his
con ex ha he spa ial weigh s cap u e ela i e di e ences in
he s eng h o he ne wo k connec ions. The absolu e magni-
ude is i ele an . Fo example, i commu e lows we e wice as
la ge e e ywhe e, his would be exac ly o se by he employed
s anda diza ion. I is o his eason ha he esul s om di -
e en ypes o weigh s—measu ed a di e en scales—a e
compa able.
I is wo h keeping in mind ha all spa ial weigh ma ices ha e
hei ad an ages and disad an ages. The simple geog aphy‐
based ma ices do no equi e any economic da a, elying on he
assump ion ha geog aphic closeness is a sui able p oxy o
economic connec ions. The in e se‐dis ance ma ix inco po-
a es his logic in i s pu e o m, whe eas he bina y‐con igui y
ma ix uses he idea ha neighbo ing egions a e closely in-
e linked. Ye , hese ma ices unde es ima e he links be ween
egions i a sizeable numbe o he wo k o ce commu es o a
la ge economic cen e ha is no di ec neighbo and a signi -
ican dis ance away. The p oposed commu e ma ix comes
wi h he d awback o equi ing de ailed da a o commu ing low
da a. Ye , once his da a has been ob ained, i a guably cap u es
ac ual economic beha io mo e accu a ely.
In he con ex o ou econome ic amewo k, i could be a -
gued ha commu e lows migh eac endogenously o eco-
nomic shocks. As a mi iga ion—and because ou main
es ima ion me hod equi es cons an spa ial weigh s—we
cons uc he commu e low ma ix wi h da a om he
ini ial yea in ou sample. In Sec ion 3.2,wedemons a e ha
he commu e lows emain easonably s able o e ime. In
his con ex , i is impo an o ecognize ha —in he absence
o s ong p io in o ma ion abou he ue spa ial dependence
s uc u e—model misspeci ica ion is una oidable. I he ue
linkages a e close o hose implied by a commu e ne wo k,
hen he po en ial endogenei y o slowly changing commu e
lows is expec ed o be a lesse p oblem han he mis-
speci ica ion bias esul ing om geog aphic weigh s. Because
o his inhe en unce ain y abou he co ec speci ica ion o
W
N
, we ad oca e o he es ima ion o model (Equa ion 1)wi h
al e na i e weigh ma ices, o ge an idea abou he ange o
plausible e ec s.
2.3 | Pa ial E ec s and Spa ial Mul iplie s
The spa ial lag
W
yln
N induces con empo aneous spillo e e -
ec s among coun ies. Thus, he pa ial e ec o a change in he
exogenous eg esso s
X
on he ec o y
l
n
(condi ional on he
ini ial s a e y
l
n −
1
) is no jus gi en by πbu
Sπ
λ()
N, whe e
S
IWλλ()=( −)
NNN
−
1
is he sho ‐ un spa ial mul iplie ma-
ix. The esul ing e ec s will be he e ogeneous ac oss coun ies.
As summa y measu es, i is common p ac ice o epo a e age
pa ial e ec s, di e en ia ed be ween di ec , indi ec , and o al
e ec s (LeSage and Pace 2009). The di ec e ec s a e go e ned
by he main‐diagonal elemen s o he spa ial mul iplie ma ix.
They cap u e he esponse o a shock o igina ing in he same
coun y, aking in o accoun he eedback e ec s while he shock
p opaga es h ough he ne wo k. The a e age sho ‐ un di ec
spa ial mul iplie is
sS s S
s
λNλNλ
¯()=1′() =1 ( ) ,
d
i
N
iNi N
=1
whe e siis a selec ion ec o wi h 1 as he
i
‐ h elemen and 0
elsewhe e.
The o ‐diagonal elemen s o he spa ial mul iplie ma ix cap-
u e he indi ec e ec s; hese a e he esponses o shocks
o igina ing in ano he coun y
j
. The a e age sho ‐ un indi ec
spa ial mul iplie is de ined as
sS s s S ssλNλNλ
¯()=1′() =1′()
,
i
N
iN−i
i
N
iNi
ind
=1 =1
−
whe e sιs=−
−iN i
is a ec o wi h 0 as he
i
‐ h elemen and 1
elsewhe e. Thus, he a e age indi ec e ec can ei he be seen
as he a e age esponse o a shock o equal size in all o he
coun ies, o as he a e age o he cumula i e e ec s on all o he
coun ies, depending on whe he we i s sum ac oss ows o
columns o he spa ial mul iplie ma ix. The a e age sho ‐ un
o al spa ial mul iplie is hen he sum o he di ec and indi ec
mul iplie s:
570 o 886 Jou nal o Regional Science, 2025
sS ι
ιSιSι
sλsλsλNλ
NλNλs
¯()=¯()+¯()=1′()
=1′() =1′() .
d
i
N
iN
N
i
N
NNi NNN
o ind
=1
=1
When he pa ial e ec s a e e y he e ogeneous ac oss coun ies,
a e aging hem p o ides only li le insigh . Fo ou coun e -
ac ual analyses, we a e in e es ed in he impac o a shock ha
o igina es in a selec ed subse o
N
coun ies ha sha e some
common cha ac e is ics. These a e he ea ed coun ies. Le
ζ
be
he ea men ec o which con ains elemen s 1 o all ea ed
and 0 o all un ea ed coun ies, and ζι
ζ
=−
N
− he selec ion
ec o o he un ea ed coun ies. We de ine he a e age sho ‐
un mul iplie o he ea ed coun ies as
ζSζsλNλ
¯()= 1′(),
N
and he a e age sho ‐ un mul iplie o he un ea ed coun-
ies as
ζSζsλNN λ
¯()= 1
−′().
N
un
−
Ins ead o a e ages, we can also compu e speci ic quan iles and
o he quan i ies o in e es om he dis ibu ion o mul iplie s
collec ed in he
N
×
1
ec o
Sζ
λ()
N.
These sho ‐ un e ec s gene ally do no p o ide a comple e
pic u e i he e a e signi ican adjus men e ec s o e ime. I
θ
o
ρ
a e nonze o, hen he e is only a pa ial con empo aneous
adjus men o he dependen a iable. The e can be a sho ‐ un
o e shoo ing ha is co ec ed in he ollowing pe iods, o a
g adual build‐up o he e ec s o e ime. I is hus o en mo e
in e es ing o analyze he e ec s on he long‐ un equilib ium.
The long‐ un spa ial mul iplie ma ix is gi en by
LIWθλρ θ λ ρ(, , )=((1−)−(+) )
NNN
−
1
. The a e age long‐
un mul iplie s
l
θλρ lθλρ lθλρ lθλρ
¯(, , ),
¯(, , ),
¯(, , ),
¯(, ,
)
dind o
,
and
l
θλρ
¯(, , )
un a e de ined analogously o hei sho ‐ un
coun e pa s abo e.
2.4 | Es ima ion Me hods
T ea ing
α
in he econome ic model (Equa ion 1) as a ec o o
ixed e ec s causes an inciden al‐pa ame e s p oblem since he
ime dimension in ou da a se is ela i ely sho (
T=15
). A e
applying a sui able ans o ma ion o emo e hese ime‐
in a ian e ec s om he model, such as de ia ions om
wi hin‐g oup means, he ans o med lagged dependen a ia-
ble will be co ela ed wi h he idiosync a ic e o e m (Nickell
1981). To adjus he es ima es o he esul ing bias, we apply
he Yu, de Jong, and Lee (2008) bias‐co ec ed QML es ima o ,
which also accoun s o he endogenei y o he spa ial lag in he
o mula ion o he likelihood unc ion. Yu, de Jong, and Lee
(2008) i s apply a wi hin‐g oup ans o ma ion o model
(Equa ion 1) o emo e he inciden al pa ame e s
α
, hen es i-
ma e he ans o med model by QML condi ional on he ini ial
obse a ions y
l
n
0
, and inally apply an analy ical bias co ec ion
o he coe icien es ima es.
9
A sho coming o he QML es i-
ma o is he equi emen o a cons an spa ial weigh ma ix
o e ime. O he wise, he bias co ec ion would become
un easible. In p inciple, allowing o ime‐ a ying spa ial
weigh s and explici ly modeling eedback om economic
g ow h o commu e lows would be desi able. In he cu en
con ex , howe e , he limi a ions o he da a p e en a mo e
sophis ica ed app oach. Impo an ly, as we emphasize in Sec-
ion 3.2, he obse ed a ia ion in he commu e lows o e ime
is much less ele an han he undamen al choice o he ype o
spa ial weigh s.
As an al e na i e o QML es ima ion, he coe icien s in model
(Equa ion 1) could be es ima ed by he gene alized me hod o
momen s (GMM), as discussed by Lee and Yu (2014), among
o he s. The ad an age o he GMM app oach is i s lexibili y o
accommoda e di e en assump ions ega ding he exogenei y o
X
. I also allows o ime‐ a ying spa ial weigh s. On he o he
hand, GMM es ima ion is ela i ely ine icien and he po en ial
weakness o he ins umen s poses iden i ica ion challenges, in
pa icula o highly pe sis en p ocesses as in ou applica ion.
Because o a lack o in e nal obus ness, we decided no o use
GMM as ou main es ima ion echnique, and elega e i o he
Suppo ing In o ma ion.
3 | Da a
Fo ou analysis, we combine da a om se e al sou ces. Mos
mac oeconomic da a a e a ailable in GENESIS‐Online and he
Regionalda enbank Deu schland, wo da a bases hos ed by
Ge many's ede al and egional s a is ical o ices. Da a on em-
ployees and commu e s has been ob ained om he ede al
employmen agency. The geoda a used o isualiza ion pu -
poses and he cons uc ion o he geog aphy‐based spa ial
weigh s is p o ided by he geoda a cen e o he ede al agency
o ca og aphy and geodesy. Fo a ull desc ip ion o he da a
sou ces and necessa y da a adjus men s, as well as summa y
s a is ics, see he Suppo ing In o ma ion.
3.1 | Da a Assembly
Ou uni o obse a ion is Ge man coun ies ( u al and u ban
dis ic s), equi alen o he NUTS 3 le el o he Nomencla u e o
Te i o ial Uni s o S a is ics. In he pas decades, Ge man
s a es ha e unde gone se e al local go e nmen eo ganiza ions
ha lead o a consolida ion o coun ies o ed awn dis ic
bo de s. These e o ms educed he o al numbe o Ge man
coun ies om 439 o 401, o which he e a e 107 u ban and 294
u al dis ic s. We unde ook subs an ial da a assembly wo k o
ec ea e he ime se ies o all a iables o he dis ic s uc u e
as p esen a he end o ou sample pe iod. De ails on he da a
se cons uc ion can be ound in he Suppo ing In o ma ion.
3.2 | Commu e Flows
Fo ou pu pose, commu e s a e de ined as all employees whose
o icial place o wo k is loca ed in a di e en coun y han hei
571 o 886
main esidence.
10
This includes indi iduals wi h a seconda y
esidence a o nea hei place o wo k, who may no commu e
om hei main esidence on a daily basis. Weekend com-
mu e s migh s ill spend a subs an ial pa o hei income a
hei main esidence, in pa icula i hey a e a amily's main
b eadwinne . This de ini ion also includes elecommu e s, who
do no physically a el o hei employe 's wo k si e, a phe-
nomenon which has inc eased in he wake o he COVID‐19
pandemic.
In 2002, on a e age 12.1% o he esiden s in a coun y we e
commu ing o a di e en coun y. 69.2% o he hese commu e s
li ed in an adjacen coun y o hei place o wo k, and ano he
16.9% had o c oss wo coun y bo de s. Un il 2017, he com-
mu e sha e o he a e age coun y ose o 15.9%, wi h 66.1% o
commu e s wo king in a neighbo ing coun y and ano he 17.4%
ha ing o c oss one addi ional bo de . The e is hus a sligh
endency owa ds inc easing commu e dis ances o e ou
sample pe iod despi e he o e all s abili y.
Commu e lows a e qui e he e ogeneous ac oss Ge many.
Mo eo e , hey a e highly asymme ic. In he wo panels o
Figu e 2, i is appa en ha u ban a eas—iden i iable by hei
compa a i ely small a ea—a ac a la ge numbe o commu e s
ela i e o hei popula ion size om he su ounding u al
a eas, bu less so in he opposi e di ec ion. Ye , he pic u e is no
uni o m ac oss he coun y. As i ms in subu ban a eas o en
ace a cos ad an age bu can s ill access he la ge pool o
wo ke s who p e e li ing in an u ban en i onmen , hese
subu ban coun ies bo h send a lo o commu e s ou o he
u ban cen e and also welcome ela i ely high commu e
numbe s. The la ge he dis ance o he nex u ban cen e , he
smalle he commu e lows in bo h di ec ions. Because he
QML es ima ion o sho ‐
T
ime–space dynamic panel models
equi es a cons an spa ial weigh ma ix o e ime, we popula e
i wi h he ini ial commu e lows in he yea 2002, which also
helps o add ess po en ial endogenei y conce ns. The a iabili y
o commu e lows o e ime is ela i ely low such ha he
po en ial ad e se consequences o using cons an spa ial
weigh s a e expec ed o be small. As a measu e o a iabili y, we
conside he F obenius no m o he ma ix di e ence be ween
2 yea s, ela i e o he F obenius no m o he ini ial‐pe iod
weigh ma ix:
WW
W
ww
w
−=−
,
NN F
NF
i
N
j
Nij ij
i
N
j
Nij
,2002 ,
,2002
=1 =1 ,2002 , 2
=1 =1 ,2002 2
whe e all weigh s ha e been spec ally s anda dized. The ela-
i e F obenius di e ence om 2002 o 2003 is only 2.4%. This
igu e emains ela i ely s able o subsequen 1‐yea di e -
ences. Fo he whole ime span, om 2002 o 2017, he di e -
ence becomes 15.3%. By i sel , his numbe is ha d o in e p e
bu i becomes mo e meaning ul when we compa e he com-
mu e low ma ix o al e na i e spa ial weigh ma ices.
The ela i e F obenius di e ence o he spec ally no malized
con igui y ma ix o he ini ial commu e low ma ix is 90.1%.
Fo he in e se‐dis ance ma ix i is e en highe wi h 128.7%.
FIGURE 2 | Spa ial dis ibu ion o he pe capi a low o commu e s om and o he 401 Ge man coun ies in 2002, g ouped in o qua iles.
572 o 886 Jou nal o Regional Science, 2025
as speed o con e gence would coun e ac he s imulus. Wi h
minimum and maximum o al long‐ un mul iplie s equal o
6.02 and 9.77, espec i ely, we ob ain coun y‐speci ic speeds o
adjus men in he ange om 10.8% o 18.2%. Because he
be ween‐coun y di e ences a e p ima ily d i en by he indi ec
spill‐in mul iplie s, he spa ial dis ibu ion o he speed o
adjus men looks e y simila o Figu e 6, whe e da ke shades
co espond o slowe adjus men speeds.
4.3 | Coun e ac ual Scena ios
To u he unco e he he e ogenei y o he spa ial mul iplie s,
we conside some illus a i e coun e ac ual scena ios. We do
his by assuming ha a ce ain g oup o coun ies is ea ed wi h
a uni shock, while all o he coun ies a e only indi ec ly a ec ed
h ough he cumula i e spillo e e ec s. This app oach could
be easily adjus ed o accommoda e al e na i e scena ios. Fo
example, he ea men in ensi y could be a ied by using a
con inuous ea men indica o
ζ
ins ead o a bina y one. In
each o ou scena ios, 20 coun ies— he op o bo om 5% o he
dis ibu ion acco ding o some ea men indica o —a e di ec ly
a ec ed by he hypo he ical ea men .
In Table 3, we epo he a e age long‐ un spa ial mul iplie s o
ea ed and un ea ed coun ies o each o he se en ea men
scena ios. The o me is concep ually compa able o he con-
en ional a e age o al mul iplie . The wo would be iden ical i
he ea men was applied o all 401 coun ies. The a e age
mul iplie o he un ea ed has a simila in e p e a ion as he
a e age indi ec mul iplie , al hough i applies only o a sub-
sample. Bo h mul iplie s a e necessa ily smalle han hose in
Table 2because he spillo e e ec s o igina e in ewe coun ies.
In ou i s coun e ac ual exe cise, we conside he 20 coun ies
wi h he highes GVA sha e o he inancial sec o (in he yea
2002) as he ea ed coun ies.
21
Six ou o he 20 ea ed coun ies
a e in he Rhein‐Main a ea, wi h F ank u am Main as a cen e
o g a i y. These coun ies a e s ongly in e linked, bo h om a
commu e pe spec i e and in a pu ely geog aphic ne wo k.
They bene i om hei own ea men and he ea men o
hei neighbo ing coun ies. I is he e o e no su p ising o ind
a compa a i ely la ge a e age mul iplie on he ea ed. Gi en
ha no all o he ea ed coun ies a e loca ed in ea men
clus e s, he e is also conside able he e ogenei y wi hin he
ea ed g oup. The s onges long‐ un e ec on he log o eal
GDP pe capi a is close o eigh old he size o he ini ial
ea men , while i is less han six old o mo e isola ed ea ed
coun ies.
The e a e p onounced di e ences be ween he mul iplie s om
he h ee spa ial weigh ma ices. While he lowe bound o he
mul iplie is qui e s able ac oss ne wo k s uc u es and coun-
e ac ual scena ios, he uppe bound a ies subs an ially.
Unde he i s coun e ac ual ea men scena io, he e ec s
a e s onges based on he commu e links, which one may no
ha e expec ed om he es ima ed spa ial lag coe icien s. Fo
he un ea ed coun ies, hose closely linked o clus e s o ea ed
coun ies each a mul iplie o up o 2.3, which is conside able
gi en ha hese a e en i ely indi ec e ec s. This maximum
mul iplie o he un ea ed is oughly hal ed unde he con i-
gui y ne wo k, and i is almos negligible when in e se‐dis ance
weigh s a e used, e en o hose coun ies in close p oximi y o
he ea ed ones. In Figu e 7, i is e iden ha also unde he
mo e a o able ne wo k schemes any no iceable indi ec e ec s
emain local. Fo he majo i y o un ea ed coun ies, he e is
ha dly any measu able esponse.
In ou second coun e ac ual scena io, we apply he ea men
o he 20 coun ies wi h he highes sha e o he indus ial sec o
in hei GVA. While mos o hose coun ies a e loca ed in he
sou h o Ge many, hey a e no s ongly clus e ed and ha dly
any o hem sha es a common bo de wi h ano he ea ed
coun y. Consequen ly, he eedback e ec s a e smalle han in
FIGURE 6 | Indi ec long‐ un spill‐in mul iplie s.
579 o 886
TABLE 3 | A e age coun e ac ual long‐ un spa ial mul iplie s.
Commu e
W
N
Con igui y
W
N
In e se‐dis ance
W
N
T ea ed Un ea ed T ea ed Un ea ed T ea ed Un ea ed
Financial cen e s 6.540*** 0.228** 6.134*** 0.081** 6.024*** 0.050
(0.478) (0.102) (0.366) (0.036) (0.343) (0.094)
[5.86, 7.94] [0.02, 2.31] [5.76, 6.94] [0.00, 1.22] [5.98, 6.10] [0.02, 0.15]
Indus ial cen e s 5.867*** 0.092*** 5.838*** 0.070** 6.004*** 0.051
(0.311) (0.037) (0.308) (0.031) (0.333) (0.097)
[5.81, 6.03] [0.00, 1.79] [5.75, 6.09] [0.00, 0.62] [5.98, 6.02] [0.02, 0.28]
Ag icul u al cen e s 5.908*** 0.022*** 6.274*** 0.076** 6.001*** 0.042
(0.315) (0.009) (0.401) (0.034) (0.330) (0.079)
[5.80, 6.13] [0.00, 0.61] [5.77, 7.05] [0.00, 1.24] [5.98, 6.02] [0.02, 0.20]
High GDP pe capi a 6.171*** 0.311** 5.824*** 0.058** 6.020*** 0.055
(0.376) (0.134) (0.306) (0.026) (0.343) (0.104)
[5.85, 7.76] [0.02, 2.29] [5.73, 6.13] [0.00, 0.62] [5.98, 6.08] [0.02, 0.39]
Low GDP pe capi a 5.877*** 0.024*** 6.008*** 0.094** 6.010*** 0.047
(0.312) (0.009) (0.342) (0.041) (0.335) (0.088)
[5.80, 6.14] [0.00, 0.44] [5.76, 6.43] [0.00, 0.93] [5.98, 6.03] [0.02, 0.15]
High popula ion densi y 6.340*** 0.317** 6.139*** 0.071** 6.077*** 0.054
(0.416) (0.137) (0.369) (0.032) (0.389) (0.102)
[5.89, 7.15] [0.02, 1.92] [5.76, 6.98] [0.00, 1.54] [5.97, 6.18] [0.02, 0.26]
Low popula ion densi y 5.993*** 0.014*** 6.575*** 0.054** 6.012*** 0.036
(0.325) (0.005) (0.493) (0.025) (0.334) (0.067)
[5.81, 6.23] [0.00, 0.55] [6.02, 7.36] [0.00, 1.23] [5.98, 6.03] [0.02, 0.12]
No e: The mul iplie s a e compu ed o he eg essions in columns (3), (6), and (9) o Table 1. S anda d e o s (in pa en heses) a e compu ed wi h he Del a me hod. The
p
‐ alues co espond o a one‐sided es o equali y o uni y o he a e age mul iplie on he ea ed, and a one‐sided es o equali y o ze o o he a e age mul iplie on
he un ea ed. The minimum and maximum mul iplie s a e shown wi hin he squa e b acke s. In each coun e ac ual, he e a e 20 ea ed and 381 un ea ed coun ies.
*p< 0.1
0
;**
p< 0.05; ***p< 0.0
1
.
FIGURE 7 | Coun e ac ual long‐ un spa ial mul iplie s o ea men o inancial cen e s.
580 o 886 Jou nal o Regional Science, 2025
he i s scena io and he e is no much a ia ion o he long‐
un mul iplie e ec on he ea ed, wi h he highes mul iplie
ba ely exceeding six. In he hi d scena io, we use he GVA
sha e o he ag icul u al sec o as an indica o o selec 20
coun ies ha a e p edominan ly u al. These a e la gely clus-
e ed in he no heas o Ge many. The geog aphic p oximi y
yields compa a i ely la ge mul iplie e ec s om a con igui y
ne wo k. In con as , when we use commu e weigh s, he
mul iplie s on he ea ed and un ea ed a e bo h ela i ely low
as he e a e no subs an ial commu e lows be ween hese
coun ies. The long‐ un mul iplie s om he in e se‐dis ance
spa ial weigh s emain small due o he o se ing e ec s o he
con empo aneous and one‐pe iod‐lagged spa ial spillo e s.
In he nex wo scena ios, we conside a ea men o he 20
iches and 20 poo es coun ies (in 2002), espec i ely. The
o me can be mainly ound in he sou h and sou hwes o
Ge many, while many o he la e a e clus e ed in he eas and
along he o me in a‐Ge man bo de . The di e en implica-
ions o commu e ‐based o con igui y‐based spa ial weigh s
become qui e appa en when compa ing hese wo ea men
scena ios. Unde he o me egime, he long‐ un spa ial mul-
iplie s a e highe when he iches coun ies a e ea ed because
he su ounding coun ies end o ha e s ong commu e link-
ages wi h hem. Wi h con igui y weigh s, he ein o cemen o
he spillo e e ec s is s onge om a ea men o he poo es
coun ies, simply because o he geog aphic clus e ing. The
esul ing di e en ial spa ial mul iplie s on he un ea ed a e
appa en in Figu es 8and 9.
22
Finally, he conclusions om ea ing coun ies wi h he highes
o lowes popula ion densi y a e e y simila o hose om
a ge ing inancial cen e s o ag icul u al cen e s, espec i ely.
The e a e impo an policy consequences o hese indings. I i
was he objec i e o a policy make o maximize he o al bene i
o he whole coun y om an in e en ion in a limi ed numbe
o coun ies, a commu e ‐based p opaga ion mechanism would
sugges o a ge weal hy and densely popula ed a eas. Ye , his
would agg a a e exis ing inequali ies, as emo e and poo ly‐
connec ed egions would be le behind e en u he . Con-
e sely, di ec ly a ge ing he poo es egions would equi e a
s onge s imulus o achie e he same agg ega e e ec due o
he small local mul iplie s.
23
On he o he hand, assuming a
pu ely geog aphic shock p opaga ion would lead o e y di -
e en conclusions.
5 | Conclusion and Discussion
This pape demons a es ha al e na i e assump ions on he
spa ial ne wo k s uc u e in he analysis o egional economic
g ow h wi h local spillo e e ec s can esul in signi ican ly
di e en local adjus men dynamics. Impo an ly, he eg es-
sion coe icien s in a ime–space dynamic panel da a model can
be highly misleading abou he magni ude o he e ec s. Local
spa ial mul iplie can be la ge e en wi h ela i ely small spa ial‐
lag coe icien s. Mo eo e , he he e ogenei y o he spa ial
mul iplie e ec s is masked by adi ionally epo ed a e age
e ec s. We highligh ha he p opaga ion o an ini ial s imulus
no only depends on he assumed ne wo k s uc u e, bu also
he place in which i o igina es. The local mul iplie e ec s can
subs an ially a y ac oss coun ies, depending on hei posi ion
in he spa ial ne wo k and he na u e o he conside ed ea -
men o shock.
Unless he e is s ong p io in o ma ion on he ne wo k s uc-
u e, we p opose o compa e he esul s om al e na i e spec-
i ica ions o ob ain an idea abou he ange o plausible e ec s.
We ad oca e o conside ing a b oade ange o measu es o
spa ial dependence in empi ical wo k—depending on he
esea ch con ex , and da a a ailabili y pe mi ing— ha a e no
jus based on geog aphic dis ance bu be e e lec he unde -
lying economic ansmission mechanisms. Commu e lows can
FIGURE 8 | Coun e ac ual long‐ un spa ial mul iplie s o ea men o ich coun ies.
581 o 886
be such a measu e in he analysis o egional economic in e -
dependence when he geog aphic uni s a e su icien ly dis-
agg ega ed. Commu e lows link egions in which employees
ea n hei income—o en compa a i ely ich u ban a eas— o
hose whe e hey spend a subs an ial pa o i —o en com-
pa a i ely poo u al a eas—and hey do so in an asymme ic
way. While commu e lows a e co ela ed wi h geog aphic
p oximi y, hey a e based on wo ke s' obse ed beha io and
hus e lec he economic eali y. In con as , asymme ic shock
p opaga ion mechanisms canno be adequa ely cap u ed when
dependencies a e p oxied me ely by he ela i e geog aphic
loca ion o he egions.
F om a policy pe spec i e, ou esul s emphasize ha he di -
e en ial egional impac s o an in e en ion should be ca e ully
conside ed. In ou coun e ac ual scena ios, di ec ly ea ing he
poo es egions ha dly c ea es any spillo e e ec s unde a
commu e low ne wo k s uc u e, while la ge gains can be
ealized by ea ing he well‐connec ed iche coun ies. This
c ea es a po en ial ade‐o be ween maximizing he agg ega e
wel a e gains om an in e en ion and educing inequali y
ac oss egions.
Acknowledgmen s
We hank Michael Be lemann, Richa d Bluhm, Jö g B ei ung, Jan
Di zen, Paul Elho s , Michael P a e may , Alexand a Scha a , and he
anonymous e e ees o e y help ul commen s and sugges ions. Fu -
he use ul commen s we e ecei ed om pa icipan s a he SEW in
Pa is, he UEA Eu opean Mee ing in Ams e dam, he IAAE Annual
Con e ence in Nicosia, he IPDC in Vilnius, he ERSA Cong ess in
Lyon, and he i ual ES Wo ld Cong ess, as well as in a ious uni-
e si y semina s. We dedica e his pape o he la e Ho s En o who
encou aged us o wo k on his opic. His suppo in he ea ly s age o
ou ca ee s was in aluable. Open Access unding enabled and o ga-
nized by P ojek DEAL.
Da a A ailabili y S a emen
The da a ha suppo he indings o his s udy a e a ailable om he
au ho s upon eques and will be made publicly a ailable upon accep-
ance o his a icle.
Endno es
1
Sou ce o EU commu ing da a: Eu os a , online da a code
LFST_R_LFE2ECOMM (employmen and commu ing by sex, age
and NUTS 2 egions).
2
Al e na i e model speci ica ions include he spa ial e o model,
whe e he spa ial spillo e e ec s (and he ime dynamics) a e
modeled in he e o e m
ε
ins ead o he dependen a iable. This
would allow o spa ially co ela ed shocks, bu excludes c oss‐
sec ional eedback in esponse o changes in he eg esso s
X
. Ye
ano he al e na i e would be o conside spa ial lags in
X
, leading o
aso‐called spa ial Du bin model. Howe e , i is less s aigh o wa d
o mo i a e and in e p e he e ec s om such speci ica ions in ou
con ex .
3
≡≈
()
yyy gg
Δ
ln ln −ln = ln = ln(1 + )
i i i
y
y
,−1i
i ,−1 o small al-
ues o he g ow h a e g.
4
In line wi h hese a gumen s, esea che s o en ind suppo o he
coe icien ela ionship
ρ
θ
λ
=−in empi ical con e gence s udies
(Pa en and LeSage 2012; Ho, Wang, and Yu 2013; Fische and
LeSage 2015).
5
Common a ia ions a e o also gi e nonze o weigh s o second‐o de
neighbo s in he con igui y ma ix, o o de ine a cu ‐o dis ance in
he in e se‐dis ance ma ix a e which all weigh s a e se o ze o.
He e, we es ic ou sel es o he basic e sions o he geog aphic
spa ial weigh ma ices o keep he analysis pa simonious.
6
No ably, Pi ibaue , Glocke , and K isz in (2023) ind ma kedly di -
e en spill‐in and spill‐ou mul iplie s, e lec ing asymme ic
connec i i y.
7
One migh conside supplemen ing geog aphy‐based weigh ma i-
ces using in o ma ion abou he oad ne wo k o a el imes
be ween coun ies. Ye , in a coun y such as Ge many wi h well‐
de eloped oad and public anspo a ion ne wo ks, such a el
FIGURE 9 | Coun e ac ual long‐ un spa ial mul iplie s o ea men o poo coun ies.
582 o 886 Jou nal o Regional Science, 2025
imes a e closely ela ed o he g ea ‐ci cle dis ance. Mos impo -
an ly, a ne wo k based on a el imes would s ill be symme ic.
Whe e a el imes ma e , his will be e lec ed in di e ences in he
commu e lows ha we obse e.
8
The same uppe bound could be achie ed wi h a ow s anda diza-
ion; ha is a di ision o all weigh s by he espec i e ow sum
w
j
Nij
=1
. Howe e , he la e would no p ese e he unde lying
ne wo k s uc u e. As Kelejian and P ucha (2010) and Neumaye
and Plümpe (2016) poin ou , his would gene ally esul in a
misspeci ied model. In ou case, he weigh s would no longe be
ela i e o he popula ion size
P
i
because he la e is cons an wi hin
each ow. As a consequence, compa a i ely isola ed coun ies wi h
ew commu e links and coun ies ha a e s ongly connec ed o
o he s would appea o ha e simila ly s ong commu e links a e
applying a ow s anda diza ion.
9
While his bias co ec ion was de eloped unde asymp o ics whe e
bo h
T
and
N
go o in ini y, simula ion e idence e eals ha i
wo ks ema kably well e en o sho
T
. I ou ime dimension was
conside ably longe , we should also ea he ime e ec s
γ
as inci-
den al pa ame e s. Lee and Yu (2010) ex end he es ima o o Yu, de
Jong, and Lee (2008) in ha di ec ion.
10
No e ha we only ha e commu e low da a o employees who a e
subjec o social secu i y con ibu ions. This excludes ci il se an s
and sel ‐employed people. I also excludes Ge man esiden s who
commu e o a wo kplace ab oad.
11
De ailed summa y s a is ics a e p o ided in he Suppo ing
In o ma ion.
12
The g ow h a e o eal GDP pe capi a is app oxima ed by he i s
di e ence in he na u al loga i hm.
13
We abula e Mo an's
I
and he espec i e s anda dized z‐sco e o
all yea s and all h ee spa ial weigh ma ices in he Suppo ing
In o ma ion. Ou empi ical esul s a e obus o he choice o he
commu ing base yea .
14
An ex eme example is he Eas Ge man manu ac u ing ligh house
Eisenach, whe e he sha e o he indus ial sec o emained ai ly
s able be ween 51% and 47% be o e he c isis onse , bu hen
plumme ed o 27% in 2008. Since hen, he indus ial sec o e-
co e ed and eached again 43% by 2014.
15
While he s anda diza ion o he spa ial weigh ma ices should
ensu e ha he uppe bound o he spa ial lag coe icien is uni y,
es ima es abo e 1 can occu as an a i ac o he bias co ec ion
p ocedu e, as happened he e in column (7) o Table 1.
16
In he Suppo ing In o ma ion, we p esen GMM es ima ion esul s
ea ing in es men as endogenous. I s coe icien u ns s a is ically
insigni ican . Remo ing in es men om he model ha dly al e s he
esul s p esen ed in his sec ion, bo h quali a i ely and
quan i a i ely.
17
In a model wi hou spa ial spillo e e ec s, he speed o adjus men
can be compu ed as
θ
−
ln(
)
(Islam 1995).
18
LeSage and Fische (2008) and C espo Cua esma and Feldki chne
(2013) add ess his unce ain y abou he spa ial weigh ma ix in a
Bayesian model a e aging amewo k.
19
Fo la ge e ec sizes, he log app oxima ion becomes inaccu a e.
The spillo e e ec in pe cen is calcula ed using he exponen ial
ans o ma ion, o example,
≈e−1 50.2
%
0.407
.
20
The magni ude o he mul iplie ge s smalle in he bo de egions o
Ge many. Especially o dis ic s bo de ing ano he coun y, we
canno cap u e he ull dependencies as we do no obse e he ull
ne wo k. This is he classical bounda y p oblem (G i i h 1983), o
which no simple p ac ical solu ion exis s. In ou applica ion, a el-
a i ely la ge numbe o coun ies lies inland wi h only limi ed c oss‐
coun y commu e links, so ha he a e age mul iplie s would
ha dly be a ec ed. Ne e heless, o hose ew coun ies wi h s ong
c oss‐bo de ies, he p edic ions om ou coun e ac ual analysis
should be aken wi h cau ion. The bounda y p oblem is ela ed o
he modi iable a eal uni p oblem (MAUP), which desc ibes he
phenomenon ha a esul in geo‐spa ial esea ch may a y wi h he
size o shape o he uni o analysis (Fo he ingham and Wong 1991;
Bailey and Ga ell 1995). Impo an ly, bo h issues a ise i espec i e
o he spa ial weigh ma ix used.
21
This exe cise should no be in e p e ed as an analysis o how a shock
is ansmi ed h ough he inancial sys em. I such a shock leads o
an ou pu educ ion in he inancial cen e s, he expec ed mac o-
economic consequences o he eal economy can be s udied wi hin
ou amewo k.
22
Fo he emaining coun e ac ual scena ios, he g aphical illus a-
ion o he long‐ un spa ial mul iplie s on he un ea ed can be ound
in he Suppo ing In o ma ion.
23
Ou analysis assumed local shocks o he log o eal GDP pe capi a
o equal size. Due o he log ans o ma ion, hese shocks will be
la ge in absolu e e ms o iche coun ies. In he Suppo ing
In o ma ion, we conside scena ios wi h equally sized absolu e
shocks. The quali a i e conclusions emain una ec ed.
Re e ences
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Suppo ing In o ma ion
Addi ional suppo ing in o ma ion can be ound online in he
Suppo ing In o ma ion sec ion.
585 o 886
