Jewczak, Maciej
A icle
De e minan s o Spa ial Loca ion o Pha macies
Compa a i e Economic Resea ch. Cen al and Eas e n Eu ope
P o ided in Coope a ion wi h:
Ins i u e o Economics, Uni e si y o Łódź
Sugges ed Ci a ion: Jewczak, Maciej (2012) : De e minan s o Spa ial Loca ion o Pha macies,
Compa a i e Economic Resea ch. Cen al and Eas e n Eu ope, ISSN 2082-6737, Łodz Uni e si y
P ess, Łodz, Vol. 15, Iss. 4, pp. 87-103,
h ps://doi.o g/10.2478/ 10103-012-0028-4
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10.2478/ 10103-012-0028-4
MACIEJ JEWCZAK*
De e minan s o Spa ial Loca ion o Pha macies
Abs ac
The opic o d ug eimbu semen is an impo an subjec when one makes
a decision on he cons uc ion o he e o m o he heal h sec o . Any change in
he eimbu semen lis ends wi h a ho deba e in he media and in e e yday li e.
Incomp ehensible p icing s a egies used by pha macies, o ce pa ien s o seek
hose places ha o e he necessa y medica ion a he lowes possible p ice.
Recognizing he economic oppo uni ies o a p o i able business, in ecen yea s,
a signi ican inc ease in he numbe o pha macies is obse ed, and he e o e, he
numbe o hese en i ies makes he p ocess o selling d ugs, especially hose om
he eimbu semen lis , almos impossible o con ol.
The a icle aims o e eal he spa ial dependence o he pha maceu ical
ma ke on he example o pha macies in po ia dis ic s o Poland. An a emp is
made o assess he p e alence o spa ial dependence be ween he numbe o
pha macies and o he de e minan s indica ing heal h ca e esou ces, ageing
p ocess and he s a e o heal h o Poles. The summa y o he s udy is o build
a spa ial model wi h i s diagnosis o he numbe o pha macies acco ding o
a ious socio-economic ac o s.
1. In oduc ion
In ecen s udies, bo h heo e ical and empi ical, he dis inguishing
be ween heal h economics and heal h ca e economics should be conside ed. As
a as he heal h economics a e conce ned i is he scien i ic discipline ha ea s
*Uni e si y o Łódź
88 Maciej Jewczak
heal h as an economic issue. Following ha de ini ion, heal h economics ela es
o he p ocess o manu ac u ing, exchange and consump ion o heal h se ices.
The issues o heal h economics con inuously e ol e unde he in luence o bo h
in e nal and ex e nal su oundings o heal h ca e sys em and he heal h
conside a ion o he popula ion. On he o he hand, he heal h ca e economics
in e es s in he analyses o he heal h ca e unc ioning and he manne o
inancing o he heal h se ices in di e en o ganiza ional heal h ca e sys em
ypes. Con empo a y esea ch in he ield o heal h ca e economics, in majo
pa , conside s mos ly he cha ac e is ics o he connec ion be ween he
condi ion o na ional economy o /and he a ea o heal h ca e and heal h
(in a b oad meaning). Due o he di e si y o he heal h ca e sys em p oblems he
need o he in e disciplina y esea ch and he use o app op ia e esea ch
ins umen s induces.
The heal h economics is he science o alloca ing esou ces o he heal h
sys em and wi hin he sys em. In ano he wo ds, heal h economics de e mines
he subjec o in e es o economis s wo king in his ield, as well as, he
me hods o applica ion o economic p inciples in heal h ca e.
In p ac ice, se e al cha ac e is ic app oaches o analysis can be used. One
can highligh many impo an a ibu es o he economy, bu in heal h economics
h ee should be no ed.
Fi s o all, he sca ci y o social esou ces. The classical economic
analysis is based on he assump ion ha indi iduals mus esign om a ce ain
pa o one esou ce in exchange o ano he . This means ha on he na ional
le el, he g ow h in heal h expendi u e o GDP esul s in educ ion o o he
expenses. The oppo uni y cos (cos o gi ing up o ge some hing else) o
heal h ca e can be subs an ial. While mos , pay a en ion o he mone a y cos s o
goods and se ices, economis s conside ime as he mos impo an sca ce
esou ce. Indi iduals sell ime in exchange o emune a ion, and mos p obably
would e use o wo k o e ime, e en i o e ed he a e o pay highe han
no mal, because i is no p o i able. In a simila ein, many indi iduals esign
om he use o admission ee heal h ca e se ices because he cos s o a i al a
he heal h es ablishmen and wai ing o he se ice a e oo high.
Ra ional decision-making is ano he impo an a ibu e. Typically,
economis s examine economic p oblems o human beha io , assuming ha he
indi idual makes a a ional decision. While a ionali y is de ined as making he
bes possible choice o mee ing he objec i es o he limi a ions o esou ces,
some o he indi idual’s beha io in he heal h ca e sys em may seem i a ional.
Bu when i comes o dispu es abou he a ional beha io , economis s o en
poin ou ha he so-called i a ional beha io o en makes sense, bu only i he
achie ed bene i s a e p ope ly unde s ood. The impo an cha ac e is ic o ecen
De e minan s o Spa ial Loca ion… 89
esea ch in heal h ca e is he use o models in he analyses. In economics,
models a e de eloped o illus a e he ongoing o u u e possible p ocesses,
hough should be unde s ood as a e lec ion o eali y. Howe e , he models can
be use ul.
This a icle ocuses mainly on he quan i a i e analyses o he heal h ca e
sys em cha ac e is ics and a emp s o apply he spa ial s a is ics and spa ial
model in heal h economics.
2. Me hods
The apid de elopmen o he me hodological p inciples and hei
applica ion enabled he ex ensi e use o he spa ial econome ics me hods and
models in economic esea ch in many o he scien i ic ields, o ins ance: labo
ma ke economic g ow h, social in e ac ions, en i onmen al p o ec ion and
heal h ca e.
In he economical spa ial s udies, he impac o exogenous a iables on
he endogenous a iable mus also include an in e ac i e combina ion be ween
he obse a ions. This ollows om he ac ha space is no consis ing o
mu ually insula ed uni s. The spa ial in e ac ion be ween wo objec s may also
a ec o he objec s. I should be no ed ha acco ding o he Toble ’s law, he
close he objec s a e geog aphically, he spa ial in e ac ions a e mo e
signi ican .
2.1. Tes ing he spa ial dependence
The e m o spa ial au oco ela ions e e s o spa ial clus e ing o simila
alues and hei in e dependence o in e ac ions in e e ence o he geog aphical
loca ion o he objec s. The s udy o in e dependence ela ionships in geog aphic
space equi es he assump ion on he exis ence o he unc ional ela ionship
be ween he alues o obse ed a iables (Anselin 1988, p. 11). By de ini ion,
his means a lack o independence be ween he obse a ions and he di ec
applica ion o he Toble ’s law.
Spa ial au oco ela ion is a deg ee o co ela ion o he obse ed alues o
a iable in a gi en loca ion wi h he alues o he same a iable in ano he
loca ion. This means ha he es ed a iable a he same ime de e mine and is
de e mined by i s implemen a ion in o he loca ions. When es ing o spa ial
dependence, wo ypes o ela ions a e conside ed: posi i e and nega i e
90 Maciej Jewczak
au oco ela ion. Con i ming he posi i e au oco ela ion, means in e ms o
loca ion, he spa ial accumula ion: high o low alues o obse ed a iables. On
he o he hand, nega i e au oco ela ion can be in e p e ed as he e e se o he
posi i e au oco ela ion - high alues o obse ed a iables adjoin o low and
ice e sa (Suchecki 2010,
pp. 103-105).
The e a e se e al ypes o indica o s o es ing he spa ial dependence.
The mos commonly used s a is ic is Mo an’s I
(Cli and O d 1973)
,
I is used o
es he p esence o global spa ial au oco ela ion acco ding o he scheme
desc ibed by s anda dized weigh s ma ix W. Le us conside he a iable x o
obse ed alues x
i
in n di e en egions (i = 1, 2, ..., n). Then he alue o he
Mo an’s I s a is ics can be desc ibe as ollows (Suchecki 2010, p. 113)
.
( )
( )
( )
∑
∑∑
=
= =
−
−−
=
n
ii
n
i
n
jjiij
xx
xxxxw
I
1
2
1 1
(1)
whe e: n – numbe o obse a ions, x
i
, x
j
– alues o x a iable in loca ions i and
j,
x
– mean alue o x a iable, w
ij
– elemen s o spa ial weigh s ma ix W.
While es ing o spa ial au oco ela ion, a s uc u e o hypo hesis is
examined, he null hypo hesis o lack o spa ial dependence agains he
al e na i e hypo hesis o occu ence o spa ial dependence. I he adjoined
spa ial objec s a e simila in e e ence o he desc ip i e cha ac e is ics, o ming
spa ial clus e s, hen he alue o Mo an’s I s a is ics is posi i e. I he adjoined
spa ial objec s a e a ied ( he spa ial s uc u e is egula , no clus e s a e o med)
hen he alue o Mo an’s I s a is ics is nega i e. The Mo an’s I s a is ics anges
om (-1) o 1. Fo be e isualizing o he ype o Mo an’s I s a is ics,
sca e plo s a e c ea ed and s a is ical signi icance g aph is analyzed, he
pe cen age o pe mu a ions o spa ially andom layou o a iables is calcula ed.
On his basis, i can be concluded abou he exis ence o absence o spa ial
au oco ela ion. The alue o p obabili y (p- alue) is called he pseudo-
signi icance le el and is he a io o he numbe o pe mu a ions o which I
i
> I
0
o he numbe o all pe mu a ions made plus 1. The g ea e he p- alue is, he
less likely is he ac ual p esence o au oco ela ion.
Apa om he need o s udy global spa ial au oco ela ion, he li e a u e
indica es o ob ain a de ailed pic u e o he phenomenon o spa ial dependence.
The e o e, local indica o s o spa ial associa ion analysis (Anselin 1995,
pp. 93–115) (LISA) should be pe o med. I in ol es he s udy o co ela ion
be ween he alues o he a iable in pa icula loca ion in compa ison o

De e minan s o Spa ial Loca ion… 91
loca ions adjoined. Local Mo an’s I s a is ics I
i
a e calcula ed as ollows
(Suchecki 2010, p. 123):
(
)
( )
( )
∑
∑
=
=
−
−
−
=
n
jjij
n
ii
i
i
xxw
xx
n
xx
I
1
1
2
1
(2)
he e: n – numbe o obse a ions, x
i
, x
j
– alues o x a iable in loca ions i and
j,
x
– mean alue o x a iable, w
ij
– elemen s o spa ial weigh s ma ix W.
2.2. Spa ial weigh s ma ix W
In he cons uc ion o he measu es o he spa ial in e ac ions, he spa ial
weigh s play a undamen al ole. The spa ial weigh s o m he spa ial weigh s
ma ix W and a e calcula ed on he basis o dis ance o neighbo hood ma ices.
The weigh ma ices can be cons uc ed wi h he assump ions o di e en ypes
and o de s o con igui y (Suchecki 2010, pp. 33-34). The weigh ma ices a e
usually symme ic and in he analysis o spa ial in e ac ion, ow s anda diza ion
o he elemen s is assumed. This in ol es c ea ing he ans o med ma ix, in
which he sum o he elemen s in each ow equals o 1. The alues o he ma ix
elemen s a e s anda dized wi h a closed in e al <0,1>. Fo he cons uc ion o
s a is ical measu es, he s anda diza ion o he elemen s o he weigh s ma ix is
highly desi able, because o he possibili ies o compa ing di e en spa ial
p ocesses and di e en models, he e o i is easie o in e p e he p ocesses o
spa ial au oco ela ion and au o eg ession.
2.3. Spa ial modeling
Spa ial modeling imp o es he cons uc ion o he econome ic model. I
he analysis s a s om he simple linea eg ession model, he applica ion o
c oss-sec ional sample as a localized da a equi es aking in o accoun he spa ial
in e ac ions ha may occu be ween he s udied uni s, which a e exp essed
h ough he in oduc ion o he model ma ix o weigh s W. The in e ac ions
may ela e o he endogenous a iables – spa ial au o eg ession is assumed,
exogenous a iables – c oss spa ial eg ession is assumed and andom
componen – spa ial au oco ela ion o e o s is assumed (Suchecki 2010,
92 Maciej Jewczak
p. 239). Fo he pu pose o his a icle Spa ial Au o eg essi e and Spa ial E o
Model a e u he desc ibed.
Spa ial Au o eg essi e Model (o Spa ial Lag Model) (A bia 2006)
assumes ha he alues o he endogenous a iable in one loca ion a e dependen
on spa ially lagged mean alues o he endogenous a iable in adjoin loca ions.
Fo mally, SLM model can be desc ibed as ollows (Suchecki 2010, pp. 248-
250):
2
, :N( , )
ρ σ
+ +y = Wy X
β ε ε 0 I
(3)
whe e: y – endogenous a iable, X – exogenous a iables ma ix, β – ec o o
s uc u al pa ame e s, W – spa ial weigh s ma ix, ρ – spa ial au o eg ession
pa ame e , Wy – spa ially lag endogenous a iable, ε – independen andom
componen . In SLM models he signi icance o ρ pa ame e is es ed.
Spa ial E o Model can be es ed, when in eg ession an au oco ela ion
in linea andom componen is assumed:
2
, ~ N( , )
λ σ
+ +y = X
β ξ ξ= Wξ ε,ε0 I
(4)
whe e: y – endogenous a iable, X – exogenous a iables ma ix, β – ec o o
s uc u al pa ame e s, W – spa ial weigh s ma ix, λ – spa ial au oco ela ion
pa ame e , Wξ – spa ially lag e o (mean e o om adjoin loca ions),
ε – independen andom componen . In SEM models he signi icance o λ
pa ame e is e i ied. SEM model assumes he exis ence o spa ial in e ac ions
(au oco ela ion), caused by andom ac o s (no included in modeling) o
measu emen e o s (Suchecki 2010, p. 250).
3. Da a se and esea ch assump ions
3.1. Da a sou ce and speci ica ion
The sou ce o da a o he analysis is Local Da a Bank o Cen al
S a is ical O ice
1
. A he ime o cons uc ing he esea ch he mos cu en da a
was da ed o 2010. The da a used in he analysis was ga he ed on he NUTS 4
2
1
h p://www.s a .go .pl/bdlen/app/s ona.h ml?p_name=indeks [day o access 14.07.2012].
2
In acco dance o he Nomencla u e o Uni s o Te i o ial S a is ics.
De e minan s o Spa ial Loca ion… 93
le el – o 379 Polish po ia s. As a subjec o he esea ch he numbe o
pha macies in Poland was accep ed and a da a se o po en ial explana o y
a iables was conside ed. The i s g oup o explana o y a iables was
connec ed s ic ly wi h he heal h ca e and included:
• numbe o medical es ablishmen s,
• numbe o doc o s, pha macis s.
The second g oup o explana o y a iables included:
• g oss mon hly a e age income,
• numbe o people a age:
o wo king,
o p e-wo king,
o pos -wo king,
• numbe o people h ea ened wi h:
o wo k en i onmen ,
o wo k nuisance,
o mechanical ac o s.
3.2. Main and speci ic objec i es
The main objec i e o he a icle was o iden i y he spa ial dependence on
he example o he numbe o pha macies in Polish dis ic s. Apa om he
main objec i e, some speci ic objec i es we e assumed as well. An a emp o
e i y he p esence o spa ial dependence be ween he numbe o pha macies
and explana o y a iables
3
was made. As a summa y o he esea ch a spa ial
model o he numbe o pha macies was designed and speci ied, depending on
a ious ac o s.
3.3. Resea ch hypo heses
Fo he pu pose o he esea ch hypo heses we e o med. Fi s ly, i
a pa ien goes o he doc o /medical es ablishmen , hen he pha macy should be
loca ed close o ha doc o /medical es ablishmen . Secondly, people a pos -
3
G oup consis ing o da a o : g oss mon hly a e age income, numbe o doc o s, numbe o
medical es ablishmen s, numbe o people a pos -wo king age, numbe o people a isk because
o he wo k en i onmen .
94 Maciej Jewczak
wo k age need an easy access o medicines. Thi dly, people who wo k and claim
o be h ea ened because o hei wo k en i onmen need access o medicines.
4. Resul s
4.1. Baseline s udy
In he pe iod 2003-2010, an inc ease in he numbe o pha macies and
hei employees has been obse ed. The a e age g ow h a e no ed o he
numbe o pha macies and he numbe o pha macis s amoun ed o 2.38% and
1.03%, espec i ely. The igu e 1 below p esen s he endencies obse ed in
hose ime se ies and indica es ha annually he numbe o pha macies inc eased
by 231,15 objec s on a e age, and he numbe o pha macis s inc eased by
352,14 employees on a e age, ce e is pa ibus. Bo h pa ame e s o he ime
a iable o he linea end unc ions we e signi ican .
Figu e 1. Numbe o pha macis s and pha macies
Sou ce: de eloped by au ho , on he basis o CSO da a in Mic oso Excel So wa e.
Compa ing he anks, a egula i y is obse ed: on a e age, he e a e
2 pha macis s in a pha macy, which is consis en wi h he guidelines o Minis y
o Heal h.
De e minan s o Spa ial Loca ion… 101
Table 5. SEM summa y o ou pu : Spa ial E o Model - Maximum Likelihood Es ima ion
Dependen Va iable : LA Numbe o Obse a ions: 379
Mean dependen a : 29.807388 Numbe o Va iables : 5
S.D. dependen a : 42.894081 Deg ee o F eedom : 374
Lag coe . (Lambda) : 0.443498
R-squa ed : 0.975087 R-squa ed (BUSE) : -
Sq. Co ela ion : - Log likelihood :-1270.366036
Sigma-squa e : 45.836938 Akaike in o c i e ion : 2550.73
S.E o eg ession : 6.7703 Schwa z c i e ion : 2570.419753
REGRESSION DIAGNOSTICS
DIAGNOSTICS FOR HETEROSKEDASTICITY
TEST DF VALUE PROB
B eusch-Pagan es 4 13020.8 0.0000000
DIAGNOSTICS FOR SPATIAL DEPENDENCE
TEST DF VALUE PROB
Likelihood Ra io Tes 1 45.41532 0.0000000
Va iable Coe icien S d.E o z- alue P obabili y
CONSTANT 2,966 0,804 3,687 0,000
LZOZ 0,200 0,022 8,886 0,000
LLEK 0,023 0,003 7,900 0,000
LZSP 0,002 0,000 4,860 0,000
LWPOP 0,001 0,000 12,916 0,000
LAMBDA 0,443 0,061 7,219 0,000
Sou ce: de eloped by au ho , on he basis o CSO da a in GeoDa 0.95.

102 Maciej Jewczak
A e he inal es ima ion, he coe icien s o he explana o y a iables
u ned ou o be signi ican , assuming he 5% le el o e o . The impac o each
exogenous a iable was consis en wi h p e iously made assump ions. The mos
impo an ac was he signi icance o λ pa ame e , which con i med he
exis ence o spa ial dependence and indica ed he in luence o andom ac o s o
measu emen e o s on he numbe o pha macies in Poland. Diagnosis o
spa ial dependence (Likelihood Ra io es ) was signi ican , which indica ed ha
applica ion o SEM model o explaining he changes in he numbe o
pha macies in Poland in 2010 elimina ed he p oblem o spa ial au oco ela ion
in da a, bu did no deal wi h he p oblem o he e ogenei y.
5. Discussion and Conclusions
The implemen a ion o spa ial in e ac ions imp o ed he i o model:
Table 6. C i e ions o i o OLS and EM
C i e ia
5
OLS
SEM
Log likelihood -1293,07 < -1270,37
Akaike 2596,15 > 2550,73
Schwa z 2615,84 > 2570,42
Sou ce: de eloped by au ho , on he basis o CSO da a in GeoDa 0.95.
All o he c i e ia ecei ed o SEM model indica ed he be e usage o
ha model, compa ing wi h he OLS. Un o una ely, due o he high
he e ogenei y o Polish po ia s i was no possible o deal wi h he p oblem o
he e oskedas ici y. The model adjus ed o spa ial dependence (SEM) –
elimina ed he p oblem o spa ial dependence in he da a.
Apa om he s ic ly echnical esul s and indings o he analyses, i
should be emphasized ha he me hods o spa ial econome ics can be widely
used in heal h ca e analyses, o ins ance, in de eloping a ool/model o
de ining he de e minan s o he numbe o pha macies in Poland. I was
con i med, ha on a e age when i e new medical es ablishmen s a e ound in
a po ia , hen a pha macy appea s in ha egion, as well. The me hods o
e ealing he spa ial dependence allowed o iden i y he a eas o occu ence o
spa ial au oco ela ion o he numbe o pha macies and he numbe o people a
5
I is no possible o compa e he R
2
o OLS and SEM models, ins ead alues o Log
likelihood, Akaike and Schwa z c i e ions a e used. Be e model has highe alues o Log
likelihood, lowe alues o Akaike and Schwa z c i e ions.
De e minan s o Spa ial Loca ion… 103
isk due o he wo k en i onmen . Mo eo e , he esea ch con i med he need o
inco po a e spa ial in e ac ion ac o in he modeling o heal h ca e on he
example o he numbe o pha macies.
Re e ences
Anselin L., (1988), Spa ial Econome ics: Me hods and Models, Kluwe Academic Publishe s,
Do d ech
Anselin L., (1995), Local Indica o s o Spa ial Associa ion – LISA, Geog aphical Analysis 27(2)
A bia G., (2006), Spa ial Econome ics: S a is ical Founda ions and Applica ions o Regional
Con e gence, Sp inge –Ve lag, Be lin
Cli A.D., O d J.K., (1973), Spa ial Au oco ela ion, Pion, London
Suchecki B. (ed.), (2010), Ekonome ia p zes zenna. Me ody i modele analizy danych
p zes zennych, C.H.Beck, Wa szawa
S eszczenie
DETERMINANTY LOKALIZACJI PRZESTRZENNEJ APTEK
Tema yka e undacji leków o is o ne zagadnienie p zy podejmowaniu wszelkich
decyzji do yczących ksz ał u e o m dla sek o a opieki zd owo nej. Każdo azowa zmiana
wykazu leków e undowanych kończy się go ącą deba ą w mediach i w codziennym
życiu. Niez ozumiałe s a egie cenowe, s osowane p zez ap eki, zmuszają pacjen ów do
poszukiwania ych miejsc, k ó e o e ują niezbędny lek w jak najniższej cenie.
Dos zegając możliwości dob ego biznesu ekonomicznego, na p zes zeni os a nich la ,
obse wuje się znaczący wz os liczby ap ek, a w związku z ym, liczebność ych
podmio ów uniemożliwia pełną kon olę w p ocesach sp zedaży leków, zwłaszcza ych
z lis e undowanych.
Celem a ykułu jes wykazanie p zes zennych zależności obse wowanych na
ynku a maceu ycznym na p zykładzie liczby ap ek w powia ach Polski. Podję a zos ała
p óba oceny wys ępowania p zes zennych zależności pomiędzy liczebnością ap ek
a liczbą leka zy, liczbą zakładów opieki zd owo nej, jak ównież innych de e minan
wskazujących na p oces s a zenia się społeczeńs wa i s anu zd owia Polaków.
Podsumowaniem badań jes p óba budowy modelu p zes zennego i jego diagnoza dla
liczby ap ek w zależności od óżnych czynników społeczno-gospoda czych.