© 2021 Published by VŠB-TU Os a a. All igh s ese ed. ER-CEREI, Volume 24: 55–68 (2021).
ISSN 1212-3951 (P in ), 1805-9481 (Online)
E iciency compa ison o selec ed OECD li e
insu ance ma ke s using a h ee-s age DEA
model
Biwei GUAN a
a Depa men o Finance, Facul y o Economics, VŠB – Technical Uni e si y o Os a a, Sokolská ř. 33, Os a a
70200, Czech Republic.
Abs ac
This pape compa es he e iciency o 12 selec ed OECD li e insu ance ma ke s om 2013 o 2019 h ough he
h ee-s age DEA model, iden i ies ways o imp o e he e iciency o he po en ially ine icien insu ance ma ke s,
and de e mines how en i onmen al ac o s in luence he e iciency sco e. The majo con ibu ion o his pape is
ha , by using he h ee-s age DEA model and elimina ing he impac o en i onmen al ac o s on e iciency, he
esul s a e mo e accu a e han hose o p e ious s udies. We ind ha he en i onmen al ac o s ha e li le e ec on
he Ge man, I ish, and I alian li e insu ance ma ke s, which pe o m well. Howe e , a e emo ing he in lu-ence
o en i onmen al ac o s, he echnical e iciency o he Belgian, G eek, and Hunga ian ma ke s dec eases signi i-
can ly.
Keywo ds
Panel da a, h ee-s age DEA model, li e-insu ance ma ke , OCED coun ies, e iciency measu emen
JEL Classi ica ion: C67, G15, G22
56 Ekonomická e ue – Cen al Eu opean Re iew o Economic Issues 24, 2021
E iciency compa ison o selec ed OECD li e
insu ance ma ke s using a h ee-s age DEA
model
Biwei GUAN
1. In oduc ion and Li e a u e Re iew
In ecen yea s, e iciency measu emen in he insu -
ance indus y has become popula and has a ac ed he
a en ion o many egula o s and in es o s. Eling and
Luhnen (2010) men ioned ha , om 2000 o 2010,
mo e han 90 s udies ocused on e iciency measu e-
men in he insu ance indus y. Ka ash e al. (2019)
poin ed ou ha , be ween 1993 and 2018, 132 s udies
on he applica ion o da a en elopmen analysis (DEA)
in he insu ance indus y we e pub-lished. Nowadays,
he amoun o esea ch on his opic is con inuing o
g ow.
The e a e wo main me hods o he measu emen
o e iciency: s ochas ic on ie analysis (SFA) and
da a en elopmen analysis (DEA). In p e ious s udies,
DEA and SFA ha e equen ly been used o assess he
e iciency o he insu ance indus y. In he beginning,
SFA had an ad an age o e DEA in ha i can ana-lyse
he in luencing ac o s. Howe e , a e many s udies on
imp o ing and inno a ing he DEA model had been
p oduced, such as hose by Ba os e al. (2010), Kao
and Hwang (2014), and Yang and Polli (2009), his
ad an age weakened conside ably. Ka ash e al.
(2019) men ioned ha , in ecen s udies on he insu -
ance indus y, DEA has been used mo e han SFA. Fa -
ell (1957) in oduced he basic DEA model o e alua e
he e iciency o mode n compa-nies; on his basis,
Cha nes e al. (1978) and Banke e al. (1984) in o-
duced he CCR model and he BCC model, espec-
i ely. La e , some esea che s poin ed ou ha he a-
di ional DEA model igno ed he in lu-ence o en i on-
men al e ec s and s a is ical noise on decision-making
uni s (DMUs). F ied e al. (2002) p oposed a h ee-
s age DEA model o elimina e he in luence o he
abo e wo ac o s.
As an in e na ional economic o ganiza ion, he O -
ganisa ion o Economic Co-ope a ion and De el-op-
men (OECD) cu en ly includes 38 membe s a es. The
au ho s o a la ge numbe o p e ious s udies ha e se-
lec ed OECD insu ance ma ke s as hei esea ch ob-
jec , al hough he ypes and numbe s o he insu ance
ma ke s selec ed ha e di e ed. Donni and Feche
(1997) in es iga ed he li e insu ance and non-li e
insu ance indus ies in 15 OECD coun ies; Da u yan
and Klumpes (2008) su eyed he li e and non-li e in-
su ance indus ies in se en OECD coun ies; Diacon
(2001) applied he DEA model o analyse he echnical
e iciency (TE) o six OECD gene al insu -ance ma -
ke s; and Diacon e al. (2002) s udied he pu e echnical
e iciency (PTE) and scale e iciency (SE) o 15 OECD
li e insu ance ma ke s h ough he DEA model.
In his pape , we calcula e he alue o echnical e -
iciency, pu e echnical e iciency, and scale e i-
ciency o 12 selec ed OECD li e insu ance ma ke s. To
ob ain he ela ed e iciency alue, we spli he panel
da a in o c oss-sec ional da a, calcula e he e iciency
sco es, espec i ely, and summa ize hem.
Rega ding he selec ed ma ke s, we choose Bel-
gium, Denma k, Finland, Ge many, G eece, Hunga y,
I eland, I aly, Luxembu g, Poland, Po ugal, and Spain
as he DMUs in his pape . As we men ioned ea lie , he
OECD has 38 membe coun ies, loca ed in di e en
egions, such as Eu ope, Ame ica, and Asia. Thei cul-
u es, economies, and consume habi s a e e y di e -
en , which, o a ce ain ex en , can lead o signi ican
di e ences in he li e insu ance ma ke . To minimize
he gaps in he ex e nal en i onmen o di e en li e in-
su ance ma ke s, we i s selec EU coun ies (22 in o-
al) in he OECD, which, o some ex en , ha e s onge
simila i ies, o example in e ms o he egula ion o
he insu ance indus y. Un o u-na ely, howe e , when
collec ing he da a, we ind ha some coun ies ha e
incomple e da a, such as La ia, he Slo ak Republic,
and Slo enia wi h incomple e da a on g oss p emiums,
he Czech Re-public, F ance, and he Ne he lands wi h
missing da a on o al in es men s, and so on. To main-
ain he consis ency o he da a o he selec ed ma ke s,
we disca d hese coun ies wi h incomple e da a and
he e o e end up wi h 12 li e insu ance ma ke s as he
esea ch objec i es o his pape .
Eling and Luhnen (2010) calcula ed he a e age TE
alue o hese selec ed li e insu ance indus ies as 0.73
(Belgium), 0.89 (Denma k), 0.84 (Finland), 0.79 (Ge -
many), 0.70 (I eland), 0.78 (I aly), 0.89 (Luxem-bu g),
0.63 (Poland), 0.78 (Po ugal), and 0.82 (Spain). I is
wo h men ioning ha , in ou p e ious esea ch, he TE
o he Ge man li e insu ance ma ke was 1 be ween
2013 and 2017, which is qui e di e en om he esul s
B. Guan – E iciency compa ison o selec ed OECD li e insu ance ma ke s using a h ee-s age DEA model
57
o his pape . In his pape , we elimina e he impac o
en i onmen al e ec s and s a is ical noise o see
whe he we can ob ain di e en answe s.
The pu pose o his pape is o compa e he e i-
ciency o he 12 selec ed OECD li e insu ance ma ke s
om 2013 o 2019 h ough he h ee-s age DEA model,
o ind ways o imp o e he e iciency o he po en ially
ine icien insu ance ma ke s, and o de e mine how he
en i onmen al ac o s in luence he e iciency sco e.
The con ibu ion o his pape is ha mos o he p e i-
ous s udies ha selec ed OECD coun ies as hei e-
sea ch objec s used he basic o wo-s age DEA model
and did no conside he impac o en i onmen al ac-
o s. This pape uses he la es da a o he analysis and
elimina es he impac o en i onmen al ac o s. Thus,
he esul s a e mo e accu a e.
This pape is di ided in o i e sec ions. In sec ion
1, we s a wi h a li e a u e e iew o his opic, b ie ly
in oduce he issues, he cu en s a e o hei esolu-
ion, and he pu pose, s uc u es, and main con ibu-
ion o his pape . In sec ion 2, we in oduce he back-
g ound in o ma ion o he selec ed li e insu ance ma -
ke s in de ail. In sec ion 3, we summa ize he ela ed
da a and explain why hey we e chosen. Then, we in-
oduce he speci ic in o ma ion on he h ee-s age
DEA model. In sec ion 4, he e iciency sco e o each
insu ance ma ke is p esen ed as well as a compa ison
o hese esul s. We conside how o imp o e he e i-
ciency sco e by dec easing he ela ed inpu alue and
he in luence o en i onmen al ac o s on he e iciency
sco e. In sec ion 5, we summa ize he pape , including
i s main con ibu ion and key indings.
2. Gene al In o ma ion o he Selec ed Li e Insu -
ance Indus ies
Fi s ly, OECD membe s a es ha e a ela ionship o
mu ual supe ision and p omo ion. They ha e a close
ela ionship in many ields. Compa ed wi h many inde-
penden insu ance ma ke s, hey ha e g ea e esea ch
alue. Secondly, OECD membe s a es include mos o
he coun ies ha occupy a la ge ma ke sha e o he
global insu ance ma ke o an impo an posi ion in he
his o y o insu ance de elopmen . Mo eo e , ele an
da a on he OECD insu ance ma ke s a e easy o collec
and accu a e.
As we men ioned ea lie , in he adi ional DEA
model, he e iciency sco e is a ec ed by en i on-men-
al ac o s and s a is ical noise. Al hough he 12 se-
lec ed li e insu ance ma ke s ha e g ea commonal-
i ies, o unde s and hei espec i e mac oeconomic en-
i onmen and mic o ma ke en i onmen mo e accu-
a ely, we ha e compiled s a is ics and pe - o med sim-
ple calcula ions on he ele an da a. Some o he da a
selec ed in his sec ion a e also used as en i onmen al
a iables in he h ee-s age DEA model.
2.1 Mac oeconomic En i onmen
In his pape , we selec he popula ion and g oss domes-
ic p oduc (GDP) g ow h a es as indica o s o measu e
he mac oeconomic en i onmen . Gene ally speaking,
he e is a posi i e ela ionship be ween he g ow h a e
o he GDP and he e iciency o he li e insu ance ma -
ke , bu i is di icul o judge he impac o he popula-
ion di ec ly. We selec he comple e da a om 2013 o
2019 and p esen i in he o m o a igu e.
•
Popula ion
The main unc ion o insu ance is o ans e isk.
Di e en om o he ypes o insu ance, li e insu ance
ans e s he isk o su i al o dea h o he insu ed. A
i s , li e insu ance was only used o p o ec he eco-
nomic bu den caused by unp edic able dea h. La e , li e
insu ance in oduced he elemen o sa ing, and g adu-
ally i became an in es men ool wi h bo h insu ance
and sa ing unc ions. The popula ion is an impo an
index ha is closely ela ed o he li e insu ance ma ke .
I we wan o s udy he ela ionship be ween he popu-
la ion and he li e insu ance ma ke ca e ully, we need
o analyse i acco ding o age, gende , u ban/ u al loca-
ion, educa ion le el, and o he aspec s. The cu en o-
cus o his pape is no on hese aspec s, so, in his sec-
ion, we only compa e he o al popula ion o di e en
ma ke s. The esul s a e shown in Figu e 2-1.
Figu e 2-1 The Popula ion o he Selec ed Li e Insu -
ance Ma ke s
Acco ding o he popula ion da a, om 2013 o
2019, no ma e which insu ance ma ke is a ge ed, he
popula ion has no luc ua ion and main ains a s able
le el. Thus, we only show he esul s o 2019. Gene -
ally speaking, coun ies wi h a less se ious aging
0
10
20
30
40
50
60
70
80
90
million people
Popula ion-2019
58 Ekonomická e ue – Cen al Eu opean Re iew o Economic Issues 24, 2021
p oblem will ha e a mo e s able popula ion. A e he
ou b eak o COVID-19 in 2020, he popula ion may
change conside ably, bu we do no ha e he ele an
da a ye . Ge many has he la ges popula ion, ol-lowed
by I aly, Spain, and Poland. The popula ion o Luxem-
bou g is e y small compa ed wi h ha o he o he
coun ies, bu he densi y o i s li e insu ance ma ke is
e y la ge, and we will in oduce i in he nex sec ion.
•
GDP G ow h (%)
The GDP g ow h a e is one o he ou impo an
mac oeconomic indica o s ( he o he h ee a e he un-
employmen a e, in la ion a e, and balance o pay-
men s). I usually e lec s he economic g ow h le el o
a coun y o egion. The de elopmen o he insu ance
indus y and economic g ow h a e closely ela ed and
in e ac wi h each o he (Enz, 2000). On he whole, he
insu ance indus y will de elop be e and as e in
coun ies wi h as economic de elop-men ; he insu -
ance ma ke ac i i ies also ha e a causal ela ionship
wi h economic g ow h. A ena (2008) ound ha bo h
li e insu ance and non-li e insu ance ha e a posi i e
and signi ican causal e ec on economic g ow h. The
esul s a e shown in Figu e 2-2.
Figu e 2-2 GDP G ow h Ra e o he Selec ed Li e In-
su ance Ma ke s
F om Figu e 2-2, we can see ha , di e en om he
popula ion, he GDP g ow h a e luc ua es g ea ly
om 2013 o 2019. Belgium, Denma k, Ge many,
Hunga y, Luxembou g, and Poland all ha e posi i e
GDP g ow h du ing his pe iod, and he luc ua ion is
ela i ely small. Howe e , i is wo h no ing ha I e-
land’s GDP g ow h a e is also posi i e, bu i has a e y
signi ican su ge in 2015, as high as 25%. In ecen
yea s, he de elopmen o I eland’s eme ging indus ies
has been apid, and i has been gi en he i le o he
“Eu opean Silicon Valley.” I has kep pace wi h he
de elopmen o he in o ma ion and com-munica ions
echnology (ICT) indus y, he apid de elopmen o
he in o ma ion indus y helping o inc ease i s GDP.
Finland, G eece, I aly, Po ugal, and Spain some imes
show nega i e GDP g ow h in he pas se en yea s.
Among hem, G eece has he wo s economic g ow h,
expe iencing h ee imes nega i e g ow h, and he low-
es GDP g ow h a e is abou -3%. Gene ally speaking,
in ecen yea s, he GDP g ow h a e o hese coun ies
ollows a downwa d end, and only Denma k and Bel-
gium main ain hei g ow h a he p e ious le el.
2.2 Li e Insu ance Indus y En i onmen
Rega ding he en i onmen o he li e insu ance ma -
ke , we choose ou indica o s, he o al g oss p emi-
ums, densi y, ma ke sha e in he OECD, and pene a-
ion. Di e en om he p e ious sec ion, in his sec ion,
we calcula e he a i hme ic mean o ele an da a o
each li e insu ance ma ke om 2013 o 2019 o anal-
ysis and compa ison. To com-pa e di e en ma ke s
mo e in ui i ely and clea ly, we do no use panel da a
in his sec ion.
•
To al G oss P emiums
To a ce ain ex en , he o al g oss p emium can e-
lec he scale o he whole insu ance ma ke . Usually,
a highe o al g oss p emium means a g ea e ma ke
sha e and a la ge ma ke scale. Figu e 2-3 shows he
o al g oss p emiums.
Figu e 2-3 To al G oss P emiums o he Selec ed Li e
Insu ance Ma ke s
-4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12
Belgium
Denma k
Finland
Ge many
G eece
Hunga y
I eland
I aly
Luxembou g
Poland
Po ugal
Spain
GDP G ow h (%)
2019 2018 2017 2016 2015 2014 2013
B. Guan – E iciency compa ison o selec ed OECD li e insu ance ma ke s using a h ee-s age DEA model
59
F om Figu e 2-3, i is no di icul o see ha he
I alian li e insu ance ma ke has he la ges o al g oss
p emium, while he Ge man li e insu ance ma ke anks
second wi h a small gap, which is somewha su p ising.
Ge many’s insu ance ma ke is supposed o be he la g-
es in e ms o scale, a la ge han o he insu ance
ma ke s. I is appa en ha he Ge man li e insu ance
ma ke no longe has ob ious ad an ages his yea . In
addi ion, we can see ha he o al g oss p emiums o
G eece and Hunga y a e he lowes . Wha is in e es ing
he e is ha , al hough Luxembou g has he smalles pop-
ula ion, i s o al g oss p emiums a e in he middle o he
12 li e insu ance ma ke s. Luxembou g’s pe capi a
wage is e y high, he unemploymen a e is e y low,
and i s medical insu ance sys em is pe ec , he a e age
li e expec an-cy being as high as 83 yea s. These could
be he easons o i s high o al g oss p emium.
•
Densi y
The densi y is ob ained by di iding he di ec g oss
p emium by he popula ion, which can e lec he de-
elopmen deg ee o he insu ance business and he
s eng h o people’s insu ance consciousness. The e-
sul s a e shown in Figu e 2-4.
Figu e 2-4 Densi y o he Selec ed Li e Insu ance Ma -
ke s
Al hough he o al g oss p emiums o each ma ke
a e qui e di e en , when we compa e he densi y o he
ma ke s, we ind ha i is e y simila , excep in Den-
ma k, I eland, and Luxembou g. In pa icula , he den-
si y o he li e insu ance ma ke in Luxembou g is much
highe han ha o o he li e insu ance ma ke s. To a
ce ain ex en , his shows ha he insu ance indus y in
Luxembou g has a high deg ee o de el-opmen and
people ha e a s ong sense o insu ance. As we
men ioned ea lie , Luxembou g’s medical insu ance
sys em is pe ec , and he s a u o y heal h sys em is e-
sponsible o 99% o esiden s’ heal h ca e.
•
Ma ke Sha e in he OECD
Gene ally, he la ge he ma ke sha e, he s onge
he compe i i eness. Howe e , a la ge ma ke sha e
does no mean a high p o i as i is only one o he ac-
o s a ec ing p o i abili y. The e a e se e al ways o
calcula e he ma ke sha e; he e, we use he di ec g oss
p emium basis. The esul s a e shown in Figu e 2-5.
Figu e 2-5 Ma ke Sha e o he Selec ed Li e Insu ance
Ma ke s
The ma ke sha e o he I alian li e insu ance ma ke
is he la ges . As we men ioned ea lie , he e is a posi-
i e ela ionship be ween he o al g oss p emi-um and
he ma ke sha e, which is con i med he e. The G eek
li e insu ance ma ke and he Hunga ian li e insu ance
ma ke a e anked second o las and las , espec i ely.
I we compa e Figu e 2-5 wi h Figu e 2-3, we ind ha
he ankings o each ma ke a e almos he same.
•
Pene a ion
The pene a ion is ob ained by di iding he di ec
g oss p emium by he GDP, which e lec s he posi ion
o he insu ance indus y in he whole na ional econ-
omy. Pene a ion usually depends on a coun y’s o e -
all economic de elopmen le el and he de el-opmen
speed o he insu ance indus y. Pene a ion can also be
used o judge he de elopmen po en ial o he insu -
ance ma ke . The esul s a e shown in Figu e 2-6.
0
5
10
15
20
25
30
35
40
Densi y ( housands o US Dolla )
0,745
2,076
0,256
4,348
0,087
0,070
1,537
4,947
0,908
0,2880,381
1,316
0,0
0,5
1,0
1,5
2,0
2,5
3,0
3,5
4,0
4,5
5,0
(%)

60 Ekonomická e ue – Cen al Eu opean Re iew o Economic Issues 24, 2021
Figu e 2-6 Pene a ion o he Selec ed Li e Insu ance
Ma ke s
F om Figu e 2-6, we can see ha he pene a ion o
he li e insu ance ma ke in Luxembou g is he highes ,
close o 35%. The second is he pene a ion in he li e
insu ance ma ke in I eland, which is abou 12.5%. Ge -
many and I aly ha e he op wo li e insu ance ma ke s
in e ms o he o al p emium and ma ke sha e, bu
hei pene a ion is no high, wi h 2.86% and 6.057%,
espec i ely. The las wo a e s ill he Hunga ian li e
insu ance ma ke and he G eek li e insu ance ma ke .
When we compa ed he GDP g ow h a e ea lie , we
ound ha G eece’s economic g ow h is he wo s ,
which is one o he easons o he poo de elopmen o
i s li e insu ance ma ke .
3. Da a and Me hodology
In he second s age o he DEA model, in addi ion o
he inpu and ou pu a iables equi ed in he adi-
ional model, we need o selec en i onmen al a ia-
bles. These a iables mus no be con olled pe sonal-
ly bu also need o a ec he e iciency sco e. In his
pape , we conside he insu ance ma ke en i onmen
and he mac oeconomic en i onmen . Thus, we choose
he insu ance densi y, ma ke sha e, and g ow h o he
GPD as he ele an indica o s. Huang and Eling (2013)
also selec ed he a io o sha eholde equi y o asse s,
liabili ies o liquid asse s a io, and p emiums o su plus
a io as indica o s o he insu -ance ma ke ’s egula o y
en i onmen .
In he exis ing esea ch, he choice o inpu a ia-
bles and ou pu a iables has also been e y di e en .
Ka ash e al. (2019) ound ha , as ou pu a iables,
“p emiums” accoun ed o 50.82%, “losses and
incu ed losses” accoun ed o 22.13%, and “in es -
men income” accoun ed o 21.31%, while, as inpu
a iables, “ he numbe o employees”, “capi al deb ”,
“equi y capi al”, and “ma e ials and business se - ices”
accoun ed o 60.72%, 49.18%, 37.7%, and 32.79%, e-
spec i ely. The a iables ha we selec ed a e sligh ly
di e en om he abo e a iables, which we will ex-
plain in de ail in he nex sec ion.
3.1 Da a
This pape selec s he ele an da a o 12 OECD li e
insu ance ma ke s om 2013 o 2019, mainly om he
OECD (2014–2020). When using he h ee-s age DEA
model, i is e y impo an o de ine he inpu , ou pu ,
and en i onmen al a iables easonably. Di e en om
o he manu ac u ing indus ies, he p oduc s o he in-
su ance indus y a e in isible, which makes i mo e di -
icul o de ine and e alua e inpu and ou pu a iables
han in o he indus ies. The a ionali y o he en i on-
men al a iables will also a ec he signi icance o he
exis ence o he second s age.
•
Inpu Va iables
The inpu a iables ha ha e gene ally been used in
he p e ious s udies can mainly be di ided in o h ee
ca ego ies, namely labou inpu , capi al inpu , and o he
ma e ial inpu (Eling and Jia, 2019; Eling and Luhnen,
2010; Eling and Schape , 2017). How-e e , we could
no ind he numbe o employees in only he li e insu -
ance ma ke ; hus, in his pape , he numbe o compa-
nies, deb capi al, and equi y capi al a e chosen as he
inpu indica o s. Many p e ious s udies ha e used he
p ice o labou o ep esen he labou inpu (Cummins
e al., 2004; Huang and Eling, 2013), choosing he em-
ployee wages in he inancial and insu ance se ices as
one o he inpu a iables. In his pape , we do no apply
his app oach because hese employee wages do no ac-
cu a ely ep esen he labou p ice o he li e insu ance
indus y. The numbe o companies can ep esen he
compe i i e abili y o he insu ance indus y; he o he
wo indica o s can ep esen he capi al inpu and ope -
a ional si ua ion o he indus y.
•
Ou pu Va iables
Rega ding he ou pu a iables, we can conside he
social unc ions o he insu ance indus y. One o he
e y impo an unc ions unde aken by insu ance is
isk p o ec ion. The non-insu ance indus y is mo e
conce ned abou he claims, while he li e insu ance in-
dus y is mo e conce ned abou he bene i s. The e-
o e, in his pape , o he li e insu ance indus y, we
choose he sum o he ne income plus g oss echnical
p o isions and he o al in es men s as he ou pu a i-
ables.
•
En i onmen al Va iables
3,626
7,473
2,4452,860
1,015
1,238
12,505
6,057
34,503
1,360
4,263
2,441
0,00
5,00
10,00
15,00
20,00
25,00
30,00
35,00
(%)
B. Guan – E iciency compa ison o selec ed OECD li e insu ance ma ke s using a h ee-s age DEA model
61
In he selec ion o en i onmen al a iables, we con-
side he mac oeconomic en i onmen o he whole
ma ke and he indus y en i onmen o he li e insu -
ance ma ke i sel . We choose he g ow h o he GDP
( ela ed o he o e all economy), he insu ance densi y
( ela ed o he insu ance ma ke ), and he ma ke sha e
( ela ed o he insu ance ma ke ) as ela ed a iables.
The g ow h o he GDP can show us he quali y o he
mac oeconomic en i onmen in which he ma ke is lo-
ca ed. Gene ally, apid GDP g ow h is mo e conduci e
o an e icien s a e o he insu ance indus y. Th ough
he insu ance densi y and ma ke sha e, we can unde -
s and he impo ance and de elopmen o each indi id-
ual insu ance ma ke in he whole indus y. Acco ding
o ou p e ious e-sea ch, he e ec i e alue o an in-
su ance ma ke wi h a la ge ma ke sha e o highe in-
su ance densi y is usually highe . These en i onmen al
a iables will e en ually ha e a g ea e impac on he
e iciency sco e. Table 3-1 p esen s he sample sum-
ma y s a is- ics.
Table 3-1 Summa y o he Sample S a is ics o he 12
Li e Insu ance Ma ke s
Uni
Min
Mean
Max
S d. de .
Panel A: Inpu a iables
Numbe o
companies
1
2
35.10
93
24.61
Deb capi al
Million
US
dolla s
2761
215989
126429
0
329010
Equi y capi-
al
Million
US
dolla s
167
6927.70
25254
7321.54
Panel B: Ou pu a iables
To al in es-
men s
Million
US
dolla s
1407
197433
142791
3
341112
Ne income
+ Technical
p o isions
Million
US
dolla s
2225
194739
120690
3
304032
Panel C: En i onmen al a iables
Densi y
US
dolla s
141
4953.74
48768
10536
Ma ke
sha e
%
0.10
1.41
8.40
1.74
G ow h o
GDP
%
-
3.241
2.556
25.163
3.203
Numbe o obse a ions 672
F om Table 3-1, we can see ha , o he inpu a i-
ables, he deg ee o dispe sion o he deb capi al is e y
la ge; he deg ee o dispe sion o bo h he ou pu a ia-
bles is e y la ge; and, in he en i onmen a ia-bles,
he deg ee o dispe sion o insu ance densi y is he la g-
es . Th ough he obse a ion o he esul s in Table 3-
1, i is no di icul o ind ha he maximum alues o
mos o he indica o s a e a highe han hei a e age
alues. Looking a he o iginal da a, we can see ha his
is because he inpu and ou pu alues o he Ge man
li e insu ance ma ke a e much highe han hose o he
o he ma ke s, which is also he main eason o he
wide dispe sion o a ious indica o s. A he same ime,
we ind ha equi y capi al is much lowe han deb cap-
i al, while he wo ou pu a iables a e close.
3.2 Th ee-S age DEA Model
Da a en elopmen analysis is sui able o he e alua-
ion o complex mul i-ou pu and mul i-inpu p ob-
lems. We can use he DEA model o calcula e many
kinds o e iciency sco es. In his pape , we mainly o-
cus on he TE, PTE, and SE o he li e insu ance indus-
y. Table 3-2 desc ibes hese h ee kinds o e iciency
in de ail.
Table 3-2 DEA E iciency Te ms
Te m
Desc ip ion
Decomposi-
ion
Technical
E i-
ciency
TE e lec s he abili y o a manu ac-
u e o maximize ou pu unde a
gi en inpu , he e u ns o scale a e
ixed. (
θ
om CCR model)
TE=SE×PTE
Pu e
Technical
E i-
ciency
PTE e lec s he p oduc ion e i-
ciency o he inpu s o he DMU a
he op imal scale, he e u ns o scale
can be changed. (
θ
om BCC model)
PTE=TE/SE
Scale
E i-
ciency
SE e lec s he gap be ween he ac-
ual scale and he op imal p oduc ion
scale.
SE=TE/PTE
•
The Fi s S age: Calcula e E iciency using Un-
adjus ed Inpu o Ou pu Va iables
In his pape , we selec he inpu -o ien ed BCC
model (Banke e al., 1984) and he inpu -o ien ed CCR
model (Cha nes e al., 1978) o calcula e he equi ed
e iciency. The assump ion o he CCR model is ha ,
in he p oduc ion p ocess, he scale e u n is ixed.
When he inpu changes in p opo ion, he ou pu
should also change in p opo ion. Fo he inpu -o ien ed
CCR model, he op imiza ion model is as ollows:
min θ (1)
s. .
∑
λjxij ≤ θxi0
n
j=1 (2)
∑λjy j ≥ y 0
n
j=1 (3)
λj ≥ 0, i = 1, 2
,
..., n; j = 1, 2,
..., n; = 1, 2,
..., n (4)
whe e xij ep esen s he i- h inpu s o he j- h DMU and
y j ep esen s he - h ou pu s o he j- h DMU; he e,
he e a e h ee inpu s, wo ou pu s, and 12 DMUs. λj is
a scala , and θ is an inpu adial measu e o echnical
e iciency. Among hem, he op imal solu ion is θ *,
and 1-θ * ep esen s he maximum inpu ha can be e-
duced wi hou educing he ou pu le el a he cu en
echnical le el. A la ge θ * means ha a smalle
amoun o inpu can be educed, ep esen ing g ea e
e iciency. When θ * = 1, i means ha he DMU is
cu en ly in a echnical e ec i e s a e.
The BCC model has almos he same cons ain s as
he CCR model. The only di e ence is ha , in he BCC
model, he e is also a cons ain on λ, which can
62 Ekonomická e ue – Cen al Eu opean Re iew o Economic Issues 24, 2021
basically ensu e ha manu ac u e s o a simila size a e
compa ed wi h manu ac u e s ha a e no alid a he
han manu ac u e s wi h la ge gaps. The cons ain is as
ollows: ∑𝜆𝑗=1
𝑛
𝑗=1 (5)
•
Second S age: Adjus ing he Inpu o Ou pu
Va ia-bles wi h SFA Slack Reg ession
When using SFA slack eg ession o eg ess he
slack a iables in he i s s age, we need o conside
whe he o adjus he inpu and ou pu a iables a he
same ime o o adjus only one o hem. F ied e al.
(2002) p oposed ha his depends on he ype o o ien-
a ion ha we choose in he i s s age. In his pape , we
choose he inpu -o ien ed app oach, so, in he second
s age, we only adjus he inpu a iables. In addi ion,
F ied e al. (2002) men ioned ha we should pe o m a
sepa a e eg ession o each di e -en slack a iable,
which allows he en i onmen al a iables o ha e di -
e en e ec s on di e en slack a iables. We can con-
s uc he ollowing SFA slack eg ession unc ions:
Sni = (Zi; βn) + ni + μni (6)
i = 1, 2, ... , I; n = 1, 2, ... , N (7)
whe e Sni is he slack alue o n- h inpu s on i- h DMU;
Zi ep esen s he en i onmen al a iables, βn ep e-
sen s he coe icien o en i onmen al a iables; ni
ep esen s he s a is ical noise and μni ep esen s he
manage ial ine iciency. ~ N (0, σ 2) is he andom
e o e m, i can ep esen he in luence o s a is ical
noise on inpu slack a iables; μ ~ N+ (0, σμ2) can ep-
esen s he in luence o manage ial ine iciency on in-
pu slack a iables.
As men ioned ea lie , using SFA slack eg ession
helps o elimina e he in luence o s a is ical noise and
en i onmen al e ec s. The e o e, we need o adjus he
inpu a iables. The adjus men o mula is as ollows:
Xni
A = Xni + [ max( (Zi; β
n))- (Zi; β
n) ] + [ max( ni) - ni ] (8)
i = 1, 2, ... , I; n = 1, 2, ... , N (9)
whe e Xni
A ep esen s he adjus ed inpu a iables; Xni is
he o iginal inpu a iables; [ max ( (Zi; β
n)) - (Zi;
β
n) ] ep esen s he adjus men o he inpu a iables
based on he en i onmen al e ec s; is he unc ion
o m; [ max ( ni) - ni ] shows he adjus men o he in-
pu a iables based on he s a is ical noise. To calcula e
he s a is ical noise, we ha e he ollowing o mulas:
𝐸(𝜇|𝜀 ) = 𝜎 ∗ × [ 𝜙(𝜆𝜀
𝜎)
𝛷 (𝜆𝜀
𝜎) + 𝜆𝜀
𝜎 ] (10)
σ*=σμσ
σ (11)
σ=
√
σμ2+σ 2 (12)
λ= σμ
σ (13)
𝐸 [ 𝑣𝑛𝑖|𝑣𝑛𝑖 + 𝜇𝑛𝑖 ] = 𝑆𝑛𝑖 − 𝑓 (𝑍𝑖; 𝛽𝑛) − 𝐸 [ 𝜇𝑛𝑖|𝑣𝑛𝑖 + 𝜇𝑛𝑖 ](14)
We p edic he maximum slack o se up a base
equal o he wo s ex e nal condi ions. When he p e-
dic ed slack is lowe han he maximum p edic ed slack
(among all he DMUs), we inc ease he inpu s; i he
DMU has e y good condi ions, a e he adjus -men ,
i may lowe hei e iciency.
•
Thi d S age: Calcula e he E iciency Using Ad-
jus ed Inpu o Ou pu Va iables
In his s age, he adjus ed inpu a iables a e e-ap-
plied o he DEA model o he i s s age o ob ain a
new e iciency sco e. The adjus ed esul s will be mo e
accu a e han he esul s o he i s s age because all he
DMUs a e adjus ed o he same ex e nal en i on-men ,
and he impac o s a is ical noise is p oposed.
4. Empi ical Resul s
In he i s s age, using DEAP 2.1 can help us o ob ain
he ini ial e iciency sco e o he TE, PTE, and SE; hen,
in he second s age, we can adjus he inpu a iables
wi h F on ie 4.1, using he inpu o ien a ion and selec -
ing he cos unc ion; in he hi d s age, we use he ad-
jus ed inpu a iables and employ DEAP 2.1 o ecal-
cula e he adjus ed e iciency sco e. The e a e 12 li e
insu ance indus ies as DMUs, and he pe iod is se en
yea s, om 2013 o 2019.
When we use DEAP 2.1 o calcula e he e iciency
sco e, we i s need o choose he speci ic model o use.
We selec 12 decision-making uni s o se en yea s.
Unlike he di ec calcula ion o sec ion da a, when we
use panel da a, we ha e wo op ions. We can spli he
panel da a in o c oss-sec ional da a and calcula e he e -
iciency sco es, espec i ely, and summa ize hem o
we can use he Malmquis model, en e ing he panel
da a di ec ly.
The Malmquis model (Fa e e al., 1992) can be
used o measu e he p oduc i i y change, and he
p oduc i i y change can be decomposed in o ech-nical
change and echnical e iciency change. Th ough he
Malmquis model, we can also ob ain he TE and PTE
o each ma ke in e e y yea , and hen we can calcula e
he SE. Howe e , he e is a p oblem: when we use he
h ee-s age DEA model, in he second s age, o adjus
he inpu a iables, we need o use he inpu slacks. The
Malmquis model canno p oduce inpu slacks. Thus,
we choose he i s me hod o dealing wi h he applica-
ion o panel da a in DEAP 2.1.
4.1 S age 1
In he i s s age, we choose a mul i-s age DEA model
wi h inpu -o ien ed and a iable scale e u ns. The
B. Guan – E iciency compa ison o selec ed OECD li e insu ance ma ke s using a h ee-s age DEA model
63
mul i-s age model is mo e accu a e han he o he mod-
els.
We calcula e he echnical e iciency, pu e ech-
nical e iciency, and scale e iciency o each ma ke in
each yea and calcula e he a i hme ic mean alue o he
ele an e iciency o each ma ke om 2013 o 2019;
we summa ize all he esul s in Table 4-1. A he same
ime, Figu e 4-1 shows he a e age e icien-cy o each
ma ke o p o ide a clea e compa ison o he e i-
ciency o he di e en ma ke s.
Table 4-1 E iciency Sco e om S age 1
TE
PTE
SE
TE
PTE
SE
Belgium
Denma k
2013
0.933
1
0.933
0.942
0.945
0.997
2014
0.919
0.965
0.952
0.92
0.961
0.957
2015
0.904
1
0.904
0.916
1
0.916
2016
1
1
1
0.944
0.979
0.964
2017
1
1
1
0.966
0.966
1
2018
1
1
1
0.984
0.991
0.993
2019
0.973
0.981
0.992
0.993
1
0.993
Finland
Ge many
2013
1
1
1
1
1
1
2014
1
1
1
1
1
1
2015
1
1
1
1
1
1
2016
0.983
0.996
0.987
1
1
1
2017
0.967
0.975
0.992
1
1
1
2018
1
1
1
1
1
1
2019
0.998
1
0.998
1
1
1
G eece
Hunga y
2013
0.965
0.985
0.98
0.951
1
0.951
2014
0.44
0.927
0.475
0.947
1
0.947
2015
0.448
0.925
0.485
0.952
1
0.952
2016
0.989
1
0.989
1
1
1
2017
1
1
1
1
1
1
2018
0.989
1
0.989
0.999
1
0.999
2019
0.992
1
0.992
1
1
1
I eland
I aly
2013
1
1
1
0.957
0.975
0.982
2014
1
1
1
0.958
0.973
0.984
2015
1
1
1
0.961
0.979
0.982
2016
0.995
0.995
1
1
1
1
2017
0.995
1
0.995
1
1
1
2018
0.987
0.995
0.992
0.919
0.919
1
2019
0.985
0.992
0.993
1
1
1
Luxembou g
Poland
2013
0.958
0.963
0.994
0.958
0.962
0.996
2014
0.963
0.97
0.994
0.953
0.957
0.995
2015
0.954
0.962
0.992
0.967
0.972
0.995
2016
0.999
1
0.999
1
1
1
2017
1
1
1
1
1
1
2018
1
1
1
1
1
1
2019
1
1
1
1
1
1
Po ugal
Spain
2013
0.974
0.977
0.997
0.937
0.989
0.948
2014
0.969
0.972
0.997
0.887
0.941
0.942
2015
0.967
0.97
0.997
0.925
0.982
0.942
2016
0.985
0.985
1
0.938
0.939
0.999
2017
0.985
0.986
1
0.926
0.943
0.981
2018
0.926
0.926
0.999
0.917
0.917
1
2019
0.873
0.877
0.995
1
1
1
F om Table 4-1, we can gain a e y de ailed un-de -
s anding o he ele an e iciency sco e o each li e in-
su ance ma ke in each yea . We obse e ha almos all
he ma ke s each he e ec i e s a e be ween 2013 and
2019, wi h he excep ion o Den-ma k and Po ugal. In
addi ion, we can see ha he e a e mo e e icien ma -
ke s in 2015–2018 han in 2013–2015. As many as
se en li e insu ance ma ke s, mo e han hal o hem,
had eached an e ec i e s a e in 2017.
Figu e 4-1 Compa ison o he Resul s om S age 1
Al hough, in he p e ious chap e , we ound ha he
Ge man li e insu ance ma ke is no he bes in all as-
pec s, i s whole ma ke eached an e ec i e s a e be-
ween 2013 and 2019, which shows ha , in he Ge man
li e insu ance ma ke s, inpu esou ces a e no was ed
and all inpu s a e comple ely and e ec- i ely con e ed
in o ou pu . O he emaining 11 li e insu ance ma ke s,
G eece’s e iciency is he lowes , wi h echnical e i-
ciency o only 0.832 and scale e iciency o only 0.844.
Howe e , he scale e icien-cy o G eece is no he low-
es ; Poland has he lowes SE sco e o only 0.956. The
pu e echnical e iciency sco es o he ma ke s a e no
e y di e en , and one o he easons is ha , when cal-
cula ing he PTE, he e u ns o scale a e a iable. In
addi ion, he TE alue ob ained in he i s s age is
0,00
0,10
0,20
0,30
0,40
0,50
0,60
0,70
0,80
0,90
1,00
TE PTE SE
Belgium Denma k Finland Ge many
G eece Hunga y I eland I aly
Luxembou g Poland Po ugal Spain