Efficiency comparison of selected OECD life insurance markets using a three-stage DEA

© 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