Risk self-selection and the concept of equilibrium in a competitive insurance market

Ku yłowicz, Łukasz; Śliwiński, Adam A icle Risk sel -selec ion and he concep o equilib ium in a compe i i e insu ance ma ke Risks P o ided in Coope a ion wi h: MDPI – Mul idisciplina y Digi al Publishing Ins i u e, Basel Sugges ed Ci a ion: Ku yłowicz, Łukasz; Śliwiński, Adam (2022) : Risk sel -selec ion and he concep o equilib ium in a compe i i e insu ance ma ke , Risks, ISSN 2227-9091, MDPI, Basel, Vol. 10, Iss. 1, pp. 1-13, h ps://doi.o g/10.3390/ isks10010009 This Ve sion is a ailable a : h ps://hdl.handle.ne /10419/258320 S anda d-Nu zungsbedingungen: Die Dokumen e au EconS o dü en zu eigenen wissenscha lichen Zwecken und zum P i a geb auch gespeiche und kopie we den. Sie dü en die Dokumen e nich ü ö en liche ode komme zielle Zwecke e iel äl igen, ö en lich auss ellen, ö en lich zugänglich machen, e eiben ode ande wei ig nu zen. 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Risks 10: 9. h ps://doi.o g/10.3390/ isks 10010009 Academic Edi o s: Mogens S e ensen and Angelos Dassios Recei ed: 24 No embe 2021 Accep ed: 21 Decembe 2021 Published: 2 Janua y 2022 Publishe ’s No e: MDPI s ays neu al wi h ega d o ju isdic ional claims in published maps and ins i u ional a il- ia ions. Copy igh : © 2022 by he au ho s. Licensee MDPI, Basel, Swi ze land. This a icle is an open access a icle dis ibu ed unde he e ms and condi ions o he C ea i e Commons A ibu ion (CC BY) license (h ps:// c ea i ecommons.o g/licenses/by/ 4.0/). isks A icle Risk Sel -Selec ion and he Concep o Equilib ium in a Compe i i e Insu ance Ma ke Łukasz Ku yłowicz * and Adam ´ Sliwi´nski Depa men o Risk and Insu ance, Collegium o Managemen and Finance, Wa saw School o Economics (SGH), 162 al. Niepodległo´sci, 02-554 Wa saw, Poland; [email p o ec ed].pl *Co espondence: [email p o ec ed].pl Abs ac : The pu pose o his pape is an analysis o he p esence o sel -selec ion mechanisms on he ma ke ha could b ing he ma ke close o he sepa a ing equilib ium s a e, in line wi h he Ro hschild–S igli z equilib ium model and i s subsequen modi ica ions. An example is he Polish ma ke o compulso y hi d-pa y liabili y insu ance o ehicle owne s. This pape desc ibes his ma ke in e ms o bo h i s s uc u e and i s inancial esul s. The main ocus is on desc ibing he assump ions o he Ro hschild–S igli z model o ma ke s ope a ing unde he condi ions o in o ma ion asymme y and based on he sel -selec ion mechanism, allowing o an unequi ocal de e mina ion o he insu ed’s p o ile wi hou he need o ac ually obse e he insu ed’s beha iou . Finally, we show ha hanks o he sel -selec ion induced by he possibili y o d i ing beha iou moni o ing, he indus y can minimise he nega i e e ec in o ma ion asymme y has on he mo o insu ance ma ke . This can be achie ed, o example, by obse ing he choices made by he insu ed a e being o e ed a new olun a y con ac wi h a p emium based on elema ics da a. Ou analysis was ca ied ou wi h he use o h ee selec ed cha ac e is ics ha can de e mine he insu ed’s isk p o ile, i.e., dis ance co e ed, sel -assessmen , and insu ance p emium paid; he signi icance o he la e —al hough i may be in ui i e—is ques ionable a commonly accep ed signi icance le els. The e o e, he main esul is ha al hough he e is some e idence on he dispu ed ma e , he e can be no de ini i e conclusion—especially in e ms o isk as measu ed by insu ance p emium. Keywo ds: insu ance ma ke equilib ium; Ro hschild–S igli z model; mo o insu ance; sel -selec ion mechanism 1. In oduc ion Equilib ium akes place when supply and demand balance one ano he , which esul s in s able p ices. Some scien is s (e.g., A. Smi h) hough ha ee ma ke would na u ally each a s a e o equilib ium. Howe e , he e a e some biases ha cause di icul ies in his p ocess. One o he mos common ea u es o disequilib ium is in o ma ion asymme y. The e ec i eness o po en ial equilib ium in ma ke s wi h asymme ic in o ma ion has been he subjec o in ensi e esea ch. Thus a , i has been ound ha he s eng h o he impac o in o ma ion asymme y on ma ke equilib ium depends mainly on whe he he sou ce o in o ma ion has a p i a e o a common alue. In hei now-classic pape , Ro hschild and S igli z (1976) analysed he compe i i e ma ke wi h ad e se selec ion, and a gued ha when insu e s o e con ac s o clien s who ha e in o ma ion abou hei isk p o ile (such in o ma ion has a common alue, bo h o insu e s and o hei clien s), equilib ium in pu e s a egies may no be achie able. The esul s o hei delibe a ions and, in pa icula , he hesis conce ning such imbalance, became he impe us o many ea ises on economic heo y. One o aspec o ma ke s wi h asymme ic in o ma ion ha can help hem o achie e equilib ium is sel -selec ion, which e e s o he pa e n o choices made by indi iduals wi h dis inc pe sonal a ibu es when an en i y is acing a se o possible con ac s (Puelz and Snow 1994;Shapi a and Venezia 1999). The main aim o his pape is Risks 2022,10, 9. h ps://doi.o g/10.3390/ isks10010009 h ps://www.mdpi.com/jou nal/ isks Risks 2022,10, 9 2 o 13 o analyse he p esence o sel -selec ion mechanisms on he ma ke ha could b ing he ma ke close o he sepa a ing equilib ium s a e, consis en wi h he assump ions o he Ro hschild–S igli z model (RS). We analysed he mo o insu ance ma ke in Poland as he la ges among o he CEE insu ance ma ke s. Ro hschild and S igli z o mula ed a de ini ion o equilib ium in a compe i i e insu - ance ma ke , assuming ha equilib ium is a menu o con ac s, such ha when he insu ed make choices ha maximise hei expec ed u ili y, he ollowing is ue: •None o i s elemen s make nega i e expec ed p o i s; •Ou side he equilib ium se , no con ac can make a non-nega i e p o i . Acco ding o he abo e de ini ion, he ma ke in Poland does no each a s a e o equilib ium. We can no e ha he long- e m echnical losses eco ded on he Polish ma ke is-à- is he compulso y mo o hi d-pa y liabili y insu ance (MTPL) sugges ha he ma ke does no mee he i s o he condi ions, as a minimum. This may be e lec ed in he sha p inc ease in a e age p emiums ha was no iceable om he second qua e o 2016. In spi e o his, p emiums a e s ill low, and long- e m policies may need o be adop ed o ensu e s abili y and p edic abili y in he ma ke . To achie e his, mo e e o s should be made owa ds he indi idualisa ion o p emiums. 2. Cha ac e is ics o he Polish MTPL Insu ance Ma ke be ween 2007 and 2020 2.1. Ma ke Concen a ion The mo o insu ance ma ke in Poland is cons an ly changing, in e ms o bo h he numbe o insu ance companies ope a ing in his ield and he sha e s uc u e o indi idual insu e s. Since he 1989 sys emic ansi ion, he Polish ma ke has become he bigges among all o he CEE P&C ma ke s (Figu e 1). Acco ding o he Polish Financial Supe ision Au ho i y (UKNF 2021), a he end o Q3 o 2020, 32 domes ic insu ance companies, including 23 companies wi h a pe mi o conduc di ec ac i i y wi hin G oup 10 (liabili y insu ance a ising ou o he possession o sel -p opelled land ehicles), had a pe mi o conduc insu ance ac i i y in Sec ion II (o he pe sonal and p ope y insu ance). A he end o 2020, he la ges sha e in he MTPL ma ke , as measu ed by he amoun o g oss w i en p emium, was held by PZU S.A (28.03%), TUiR WARTA S.A. (19.49%), and STU E go Hes ia S.A. (17.05%). E en hough hese h ee insu e s held a o al o 65% o he ma ke sha e, he alue o he He indahl–Hi schman Index (HHI) can be gi en by he ollowing o mula: HHI =104∑n i=1σ2 i, (1) whe e σi is he sha e o he i h insu ance company in he ma ke measu ed by g oss w i en p emium, amoun ing o 1598 (calcula ed on he basis o UKNF 2021); his ep esen s a mode a e concen a ion. The index le el is g adually educing, which may indica e a decline in he compe i i eness o he mo o insu ance ma ke in Poland. This amoun was mos ly in luenced by he ma ke sha e o PZU S.A. Sha es in he MTPL insu ance ma ke o he main insu e s be ween he yea s 2007 and 2020 a e p esen ed in Table 1. Al hough PZU S.A. con inues o hold he la ges sha e o he mo o insu ance ma ke , hei sha e is sys ema ically dec easing. In 2007, he g oss p emium a ibu able o PZU om he MTPL accoun ed o 43.36% o all p emiums on he ma ke o his insu ance. A e 10 yea s, he sha e o PZU had been educed o less han 31%, while he simul aneous inc ease in he sha es o o he insu e s may indica e an inc ease in compe i ion and an in- c easingly less concen a ed ma ke . By he end o 2020, he sha e o he la ges insu e had allen o jus o e 20%. The change in he sha e o he bigges insu e and he diminishing ma ke concen a ion makes he ma ke mo e compe i i e. Theo e ically, his should esul in he ma ke being close o an equilib ium s a e; howe e , wi hou he ele an da a, we canno conclude ha . Risks 2022,10, 9 3 o 13 Table 1. The sha e o indi idual insu e s in he MTPL ma ke be ween 2007 and 2020 (in %; UKNF 2021). Insu e 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 PZU S.A. 43.36 40.65 36.73 34.41 33.60 33.15 33.39 32.64 32.39 30.93 30.78 30.77 29.75 28.03 TUiR WARTA S.A. 8.76 8.21 7.79 8.41 8.83 15.95 15.36 15.57 15.50 16.34 19.00 18.68 19.59 19.49 STU ERGO HESTIA S.A. 5.22 6.37 7.13 6.56 6.76 7.33 8.23 15.42 15.14 14.02 15.30 15.56 15.96 17.05 GENERALI T.U. S.A. 2.21 3.22 3.44 3.35 3.78 4.09 3.72 3.60 4.00 6.31 4.41 4.08 4.01 4.07 AXA UBEZPIECZENIA TUiR S.A. - - - - - - - - 0.78 4.73 6.83 6.62 6.33 6.74 LINK4 TU S.A. 2.25 1.87 2.05 1.93 2.09 2.55 2.96 3.25 3.93 4.79 5.34 5.13 5.04 5.31 COMPENSA TU S.A. 3.53 3.62 4.06 4.23 4.92 4.92 4.59 4.85 4.98 3.37 3.46 3.74 4.13 4.44 TUW TUW 1.41 1.70 2.09 2.34 2.68 3.02 3.41 3.42 3.42 3.66 3.02 2.49 2.14 2.29 TUiR ALLIANZ POLSKA S.A. 5.41 5.45 5.74 5.98 5.11 4.32 4.65 4.43 4.92 3.51 2.74 3.43 3.19 4.49 UNIQA TU S.A. 4.19 4.11 4.38 4.57 4.59 4.73 4.54 4.22 3.74 3.38 2.70 2.81 2.43 2.20 GOTHAER TU S.A. 13.65 3.58 3.57 3.25 2.76 2.72 2.60 3.17 3.15 2.46 2.02 - - - O he s 20.01 21.22 23.02 24.97 24.88 17.23 16.56 9.42 8.06 6.51 4.41 6.69 7.43 5.89 1: Cu en ly WIENER TU S.A. Risks 2022, 9, x FOR PEER REVIEW 3 o 13 COMPENSA TU S.A. 3.53 3.62 4.06 4.23 4.92 4.92 4.59 4.85 4.98 3.37 3.46 3.74 4.13 4.44 TUW TUW 1.41 1.70 2.09 2.34 2.68 3.02 3.41 3.42 3.42 3.66 3.02 2.49 2.14 2.29 TUiR ALLIANZ POLSKA S.A. 5.41 5.45 5.74 5.98 5.11 4.32 4.65 4.43 4.92 3.51 2.74 3.43 3.19 4.49 UNIQA TU S.A. 4.19 4.11 4.38 4.57 4.59 4.73 4.54 4.22 3.74 3.38 2.70 2.81 2.43 2.20 GOTHAER TU S.A. 1 3.65 3.58 3.57 3.25 2.76 2.72 2.60 3.17 3.15 2.46 2.02 - - - O he s 20.01 21.22 23.02 24.97 24.88 17.23 16.56 9.42 8.06 6.51 4.41 6.69 7.43 5.89 1: Cu en ly WIENER TU S.A. Figu e 1. G oss di ec P&C p emiums w i en on domes ic ma ke s in 2019 (Insu ance Eu ope 2021). Al hough PZU S.A. con inues o hold he la ges sha e o he mo o insu ance ma ke , hei sha e is sys ema ically dec easing. In 2007, he g oss p emium a ibu able o PZU om he MTPL accoun ed o 43.36% o all p emiums on he ma ke o his insu ance. A e 10 yea s, he sha e o PZU had been educed o less han 31%, while he simul aneous inc ease in he sha es o o he insu e s may indica e an inc ease in compe i ion and an inc easingly less concen a ed ma ke . By he end o 2020, he sha e o he la ges insu e had allen o jus o e 20%. The change in he sha e o he bigges insu e and he diminishing ma ke concen a ion makes he ma ke mo e compe i i e. 1 164 171 268 363 491 918 1 083 1 110 1 194 1 240 1 689 1 781 1 969 3 579 3 870 4 307 5 676 5 723 7 705 8 541 8 736 8 994 9 983 14 166 15 626 25 925 31 228 65 794 73 205 Liech ens ein Mal a La ia Es onia Cyp us Iceland C oa ia Slo akia Slo enia Bulga ia Luxembou g G eece Romania Hunga y Po ugal Finland Czech Republic No way Sweden Tu key Denma k Belgium Poland Aus ia Ne he lands Swi ze land Spain I aly F ance Ge many Uni ed Kingdom 103,752 Figu e 1. G oss di ec P&C p emiums w i en on domes ic ma ke s in 2019 (Insu ance Eu ope 2021). 2.2. P emiums and Compensa ion Compulso y mo o hi d-pa y liabili y insu ance is he mos equen ly pu chased insu ance in Poland. Acco ding o esea ch, as many as 83.8% o indi idual clien s ha e MTPL (Nowo a ska-Romaniak 2014). This, he e o e, also ep esen s he la ges sha e o he Risks 2022,10, 9 4 o 13 o al insu ance non-li e p emiums. Almos con inuously (excep 2014 and 2015), he sha e o MTPL in o al non-li e p emiums has emained abo e 33%, as can be seen in Figu e 2. Risks 2022, 9, x FOR PEER REVIEW 4 o 13 Theo e ically, his should esul in he ma ke being close o an equilib ium s a e; howe e , wi hou he ele an da a, we canno conclude ha . 2.2. P emiums and Compensa ion Compulso y mo o hi d-pa y liabili y insu ance is he mos equen ly pu chased insu ance in Poland. Acco ding o esea ch, as many as 83.8% o indi idual clien s ha e MTPL (Nowo a ska-Romaniak 2014). This, he e o e, also ep esen s he la ges sha e o he o al insu ance non-li e p emiums. Almos con inuously (excep 2014 and 2015), he sha e o MTPL in o al non-li e p emiums has emained abo e 33%, as can be seen in Figu e 2. Figu e 2. MTPL sha e in non-li e p emiums be ween 2007 and 2020 (UKNF 2021). Table 2 p esen s basic da a on he ac i i y in he MTPL ma ke be ween 2007 and 2020 o he en i e insu ance sec o . Table 2. Technical esul s o he MTPL ma ke in Poland be ween 2007 and 2020 (PLN million; UKNF 2021). Ca ego y 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 G oss assigned p emium 6205 7010 7135 7528 8600 8931 8465 8071 8158 11,655 14,810 14,799 14,924 14,631 G oss compensa ion and bene i s 3906 4383 6161 5284 5465 5447 5512 5895 6826 7980 8553 8764 9452 9002 Technical esul −149 −709 −963 −891 −640 −472 −330 −796 −1056 −1093 483 447 904 521 In 2020, he g oss w i en p emium o MTPL in Poland amoun ed o PLN 14.631 million, and i had dec eased by 2% y/y. A e a pe iod cha ac e ised by apid accele a ion in p emium dynamics (2016), s agna ion has been he case since 2018, wi h a sligh downwa d end. In 2020, g oss claims and bene i s paid unde MTPL amoun ed o PLN 9.002 million. As is he case wi h g oss w i en p emium, he e was a dec ease, compa ed o 2019, o less han 5% y/y. An upwa d end has been obse ed since 2007, bu in 2020 he e was a decline—p obably due pandemic- ela ed a ic es ic ions. 2.3. Technical Resul Be ween 2007 and 2016, he echnical esul s o MTPL insu ance we e nega i e. Technical loss a he end o 2016 amoun ed o PLN 1.093 million, bu had inc eased in compa ison wi h he same pe iod o he p e ious yea , when i amoun ed o PLN 1.056 million PLN. The echnical loss in his insu ance segmen has con inued since 2007, when i amoun ed o PLN 148.770.000. I has long been indica ed ha nega i e inancial ou comes in MTPL can be he esul o he p emiums se a an unde es ima ed le el. This is, among o he hings, he consequence o he p ice wa obse ed in Poland, which is pa icula ly e iden in he mo o insu ance ield, and which has led o a signi ican 34.4% 33.5% 33.1% 34.0% 34.0% 34.0% 30.7% 30.4% 36.2% 39.2% 39.8%37.6% 34.3% 20% 24% 28% 32% 36% 40% 44% 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 Figu e 2. MTPL sha e in non-li e p emiums be ween 2007 and 2020 (UKNF 2021). Table 2p esen s basic da a on he ac i i y in he MTPL ma ke be ween 2007 and 2020 o he en i e insu ance sec o . Table 2. Technical esul s o he MTPL ma ke in Poland be ween 2007 and 2020 (PLN million; UKNF 2021). Ca ego y 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 G oss assigned p emium 6205 7010 7135 7528 8600 8931 8465 8071 8158 11,655 14,810 14,799 14,924 14,631 G oss compensa ion and bene i s 3906 4383 6161 5284 5465 5447 5512 5895 6826 7980 8553 8764 9452 9002 Technical esul −149 −709 −963 −891 −640 −472 −330 −796 −1056 −1093 483 447 904 521 In 2020, he g oss w i en p emium o MTPL in Poland amoun ed o PLN 14.631 mil- lion, and i had dec eased by 2% y/y. A e a pe iod cha ac e ised by apid accele a ion in p emium dynamics (2016), s agna ion has been he case since 2018, wi h a sligh downwa d end. In 2020, g oss claims and bene i s paid unde MTPL amoun ed o PLN 9.002 million. As is he case wi h g oss w i en p emium, he e was a dec ease, compa ed o 2019, o less han 5% y/y. An upwa d end has been obse ed since 2007, bu in 2020 he e was a decline—p obably due pandemic- ela ed a ic es ic ions. 2.3. Technical Resul Be ween 2007 and 2016, he echnical esul s o MTPL insu ance we e nega i e. Technical loss a he end o 2016 amoun ed o PLN 1.093 million, bu had inc eased in compa ison wi h he same pe iod o he p e ious yea , when i amoun ed o PLN 1.056 million PLN. The echnical loss in his insu ance segmen has con inued since 2007, when i amoun ed o PLN 148.770.000. I has long been indica ed ha nega i e inancial ou comes in MTPL can be he esul o he p emiums se a an unde es ima ed le el. This is, among o he hings, he consequence o he p ice wa obse ed in Poland, which is pa icula ly e iden in he mo o insu ance ield, and which has led o a signi ican dec ease in he amoun o insu ance p emiums (Tomaszewska 2017). Rega dless o an inc ease in he MTPL p emiums, be ween 2016 and 2017, he ollowing was he case: •Vehicle epai cos s we e cons an ly ising, as we e he cos s o medical p ocedu es; • Cos s incu ed by insu e s we e g owing, in connec ion wi h he guidelines o claims se lemen in oduced by he Polish Financial Supe ision Au ho i y; • Changes in he legal en i onmen we e p oli e a ing, such as he endency o cou s o awa d e e -highe compensa ion o acciden ic ims and hei ela i es; • The axa ion ules ega ding, o example, he inclusion o VAT in he claims se lemen p ocess, we e being amended; • Changes in socie al income, leading o an inc ease in u u e compensa o y pensions and o inc eased needs, we e also on he inc ease. Risks 2022,10, 9 5 o 13 This esul ed, in 2016, in he losses o MTPL emaining a a le el simila o ha o 2015, while 2017 was he i s yea in which he echnical esul eached a posi i e alue, amoun ing only o PLN 482.6 million. A simila si ua ion occu ed in 2018, when he echnical p o i was PLN 447 million. A posi i e echnical esul also occu ed a he end o 2019 and in 2020. In 2020, he echnical esul ell by jus o e 42% y/y. Undoub edly, one o he easons o he imp o emen in he echnical e iciency o he MTPL ma ke was he decline in he alue o g oss claims and claims ela ed o he COVID-19 pandemic, which has o ced many d i e s o change hei habi s, and led o a ewe ehicles being on he oads. I should be bo ne in mind ha he global pandemic and lockdown no only had a posi i e impac on he numbe o claims—which was a consequence o he economic slowdown and he ac ha people we e o ced o immedia ely ans e hei ac i i ies o an In e ne en i onmen (G˛ebski 2021)—bu also caused nega i e o undesi able e ec s o appea . Due o he limi a ion o income, some o he insu ed esigned om insu ance (in- cluding compulso y insu ance), while o he s decided no o p o ide insu e s wi h eliable in o ma ion abou hei isk—leading in u n o an unde es ima ion o hei insu ance p emiums. A sepa a e g oup is also made up o he insu ed who decided o ex o compen- sa ion in o de o p o ec hei own budge s. All o hese ac ions had un o eseen e ec s on bo h he pe o mance o indi idual insu e s and he o e all ma ke equilib ium. 3. The RS Model and he MTPL Insu ance Ma ke in Poland Conside ing he ma ke and legal condi ions o mo o hi d-pa y liabili y insu ance in Poland, we concluded ha he RS model o compe i i e ma ke s wi h asymme ic in o ma ion is su icien o he co ec desc ip ion o he si ua ion o he MTPL ma ke . This model mos accu a ely e lec s he condi ions o he unc ioning o he ma ke , and he ollowing a gumen s should be men ioned among he p emises behind he choice o he abo e model: • The RS model, unlike i s la e modi ica ions, does no allow con ac s o be cancelled once o e ed, meaning ha he e a e signi ican ba ie s o exi ing he ma ke ; his is in line wi h he compulso y na u e o MTPL insu ance; • The MTPL ma ke in Poland can be conside ed a compe i i e ma ke , despi e he dominan ole o one o he ma ke playe s; e idence o his may be ound in he en y o new playe s in o he ma ke , based on hei eedom o p o ide insu ance and e- insu ance se ices; mo eo e , he HHI alue o 1683 shows a mode a e concen a ion; • Insu e s ope a ing on he ma ke y o selec he isk and di e en ia e insu ance p emiums— o example, h ough he widesp ead use o no-claims bonuses—due o which he ma ke s i es o achie e a sepa a ing a he han a pooling equilib ium; • Al hough insu e s seek o maximize p o i s, hey mus ollow he p emium–compensa ion balance p inciple, which equi es he insu ance und and expec ed compensa ions o be balanced; his is di ec ly e lec ed in he de ini ion o equilib ium, assuming no long- e m p o i s a he echnical le el; • The insu ed a e in possession o p i a e in o ma ion o a common alue, especially e- ga ding he way in which he ehicle is used, which esul s in in o ma ion asymme y on he ma ke , possibly esul ing in ad e se selec ion; • The RS model is based on wo a iables— he p emium, and he alue o he po en- ial compensa ion—igno ing he issue o p oduc di e en ia ion h ough addi ional se ices. In addi ion, he p esence o a nega i e echnical esul in he Polish ma ke may sugges ma ke imbalance caused by he ollowing: • The in oduc ion by some ma ke playe s o c eam-skimming con ac s, causing losses among o he insu e s; • High- isk insu ed pe sons wi hholding in o ma ion ele an o he co ec p emium calcula ion, and hei pu chase o con ac s dedica ed o low- isk g oups. Risks 2022,10, 9 6 o 13 Bo h si ua ions a e consis en wi h he consequences o he model assump ions adop ed, making he achie emen o a s a e o sepa a ing equilib ium dependen on he na owing o he scope o co e o e ed o low- isk insu ed pe sons, as well as he impossibili y o in oducing c eam-skimming con ac s by one o mo e ma ke pa icipan s. This con i ms he co ec selec ion o he model o desc ibe he si ua ion o he Polish mo o hi d-pa y liabili y insu ance ma ke . Howe e , unde asymme ic in o ma ion, wi h he assump ions o he RS model ha ing been adop ed, he ma ke canno each he pooling equilib ium, while he exis ence o a sepa a ing equilib ium is also no gua an eed. Ha ing ull knowledge o he insu ed’s isk ype, he insu e could achie e inancial balance by o e ing hem con ac s ha p o ide ull co e age. The monopolis can also achie e ull p emium ex ac ion om each isk class. This e iciency canno be achie ed when in o ma ion is asymme ic (Snow 2015). The consequences o in o ma ion asymme y p ima ily a ec low- isk insu ed pe sons who expe ience loss o u ili y due o a p emium ha is oo high, in ela ion o hei p obabili y o loss incu ence, o in connec ion wi h pa ial insu ance. The Nash equilib ium concep , which does no allow a con ac ha can gene a e a non-nega i e p o i o exis ou side an equilib ium se , is he e o e insu icien o he co ec desc ip ion o he mo o insu ance ma ke in he RS model ( he condi ions o he Nash equilib ium may no be me once he ma ke has o e ed a C P con ac ). Au ho s such as Wilson (1977); Janes (1978); Beli eau (1984); Dionne and Dohe y (1991); and Donnelly e al. (2014) ha e indica ed ha ad e se selec ion can be educed by using sc eening. This can be done when he insu ed a e o e ed a menu o al e na i e con ac s in o de o induce sel -selec ion. The ques ion emains as o whe he he e a e e ec i e ools o he applica ion o he selec ion mechanism, which allows o he co ec ca ego isa ion o insu ed pe sons. 4. Resea ch Assump ions and Design 4.1. Resea ch Ques ion As pa o he discussion on he insu ance ma ke equilib ium, he ques ion a ises as o whe he he use o ools by insu e s o moni o he d i ing s yle o he insu ed will ac i a e he sel -selec ion mechanism, which would allow o an unequi ocal de e mina ion o he insu ed’s p o ile wi hou he need o ac ually obse e hei beha iou —especially hose who do no allow o hei d i ing pa e ns o be moni o ed. The ques ion comes down o assessing he u h ulness o he s a emen ha he insu ed disclose hei isk p o ile when deciding on he ype o insu ance con ac hey wan o pu chase. Fo he pu poses o u he analysis, he o iginal RS model was modi ied by assuming ha he insu e s, in addi ion o he o iginal sepa a ing con ac s C H (q H , H )iC L ’(q L ’, L ’), decide o in oduce an addi ional con ac C D wi h a a i using in o ma ion abou he insu ed’s d i ing s yle, whe e qis he alue o po en ial compensa ion and is he amoun o he p emium o low (L)- and high (H) isk g oups, espec i ely. This con ac , g aphically p esen ed in Figu e 3, p o ides ull q D co e age wi h he p emium L i he insu ed uses he ehicle esponsibly and sa ely, o wi h he p emium H i hey a e assigned o he Hg oup; i p o ides ull co e age q D =q L =q H =dwi h he ollowing p emium: D= L, o L g oup H, o H g oup (2) whe e L< H. Risks 2022,10, 9 7 o 13 Risks 2022, 9, x FOR PEER REVIEW 7 o 13 abou he insu ed’s d i ing s yle, whe e q is he alue o po en ial compensa ion and is he amoun o he p emium o low (L)- and high (H) isk g oups, espec i ely. This con ac , g aphically p esen ed in Figu e 3, p o ides ull q D co e age wi h he p emium L i he insu ed uses he ehicle esponsibly and sa ely, o wi h he p emium H i hey a e assigned o he H g oup; i p o ides ull co e age q D = q L = q H = d wi h he ol- lowing p emium: 𝑟=𝑟, o L g oup 𝑟, o H g oup (2) whe e L < H . Figu e 3. Ma ke equilib ium a e he in oduc ion o he C D con ac . As can be in e ed om he ma ke model, when selec ing a speci ic ype o insu ance con ac om he se o possible ypes o con ac s, he ollowing is ue: • G oup L ha e an incen i e o p o ide he insu e wi h da a on hei d i ing s yle, as his would enable hem o choose he con ac on he highe indi e ence cu e. A he same ime, hey will no su e he limi a ion o use ulness due o in o ma ion asymme y. Thus, hey e eal hei isk g oup o he insu e , and in e u n ecei e ull co e age wi h a s ill-low p emium; • G oup H a e indi e en o he con ac s o e ed, as bo h he dedica ed con ac wi h he adi ional a i and he insu ance con ac using da a on hei beha iou p o ide ull co e age. Insu ed pe sons a e also awa e ha he lowe p emium, in he e en o concluding a C D con ac , will only be a ailable i hey change hei d i ing s yle and use he ehicle sa ely. I can be expec ed ha a leas some o he insu ed—awa e o he consequences o in oducing he possibili y o he insu e moni o ing hei be- ha iou , and encou aged by he ision o a lowe p emium—will e i y hei d i ing s yle and conclude a C D con ac ; o he s, who do no see he need o change hei d i ing s yle, will emain wi h he adi ional con ac . As can be seen in Table 3, high- isk insu ed pe sons who conclude a con ac wi h he adi ional a i will unambiguously disclose hei p o ile o he insu e wi hou he insu e ha ing o e i y i wi h moni o ing de ices. 45° w1 w2 E CH C L πH=0 πL=0 ūH ūL CL’ CD Figu e 3. Ma ke equilib ium a e he in oduc ion o he CDcon ac . As can be in e ed om he ma ke model, when selec ing a speci ic ype o insu ance con ac om he se o possible ypes o con ac s, he ollowing is ue: • G oup L ha e an incen i e o p o ide he insu e wi h da a on hei d i ing s yle, as his would enable hem o choose he con ac on he highe indi e ence cu e. A he same ime, hey will no su e he limi a ion o use ulness due o in o ma ion asymme y. Thus, hey e eal hei isk g oup o he insu e , and in e u n ecei e ull co e age wi h a s ill-low p emium; • G oup H a e indi e en o he con ac s o e ed, as bo h he dedica ed con ac wi h he adi ional a i and he insu ance con ac using da a on hei beha iou p o ide ull co e age. Insu ed pe sons a e also awa e ha he lowe p emium, in he e en o concluding a C D con ac , will only be a ailable i hey change hei d i ing s yle and use he ehicle sa ely. I can be expec ed ha a leas some o he insu ed—awa e o he consequences o in oducing he possibili y o he insu e moni o ing hei beha iou , and encou aged by he ision o a lowe p emium—will e i y hei d i ing s yle and conclude a C D con ac ; o he s, who do no see he need o change hei d i ing s yle, will emain wi h he adi ional con ac . As can be seen in Table 3, high- isk insu ed pe sons who conclude a con ac wi h he adi ional a i will unambiguously disclose hei p o ile o he insu e wi hou he insu e ha ing o e i y i wi h moni o ing de ices. Table 3. Risk p o iles ha can be obse ed by he insu e a e he insu ed pe son chooses he ype o con ac . Risk G oup o Insu ed (Unobse able by Insu e s)A ailable Con ac s Insu ed’s Willingness o Change Thei D i ing S yle Con ac Chosen Acco ding o he Ma ke Model Risk P o ile Obse able by Insu e s (a e Disclosu e o P e e ences by he Insu ed) Low- isk CL’ CDn/a CDLow- isk High- isk CH CDYes CDLow- isk High- isk CH CDNo CHHigh- isk Risks 2022,10, 9 8 o 13 4.2. Resea ch Me hods and Da a The analysis was based on he da a collec ed h ough a su ey conduc ed in he pe iod om 1 Ap il o 9 July 2018. The insu ance companies’ clien s we e asked o ill in a s anda dised ques ionnai e wi h 8 closed ques ions ega ding hei a i udes and 10 demog aphic ques ions. The ques ions e lec se e al isk ac o s used by insu ance companies in hei p icing and isk assessmen , such as insu ed age, he app oxima e dis ance hey co e annually, o hei place o esidence. In addi ion, some ques ions designed o in es iga e he a i udes o he insu ed o allowing some o m o iola ion o hei p i acy we e included. Pa icipa ion in he s udy was olun a y, ee o cha ge, and he au ho s had no in luence on he selec ion o he esea ch sample. The da a used in he esea ch we e based on he opinions o 624 esponden s. The esponden s g oup was di e se in e ms o sex (women accoun ed o almos hal o he su ey’s pa icipan s—47.76%) and age ( he mos nume ous g oup was be ween 36 and 40 yea s old—20.67%). App oxima ely 7 ou o 10 esponden s we e below 41 yea s old. The mean age was 36.5 yea s. The mos nume ous g oup we e men be ween 31 and 35 yea s old (67 pa icipan s), while he smalles g oup we e women om 56 o 60 yea s old (6 esponden s).1 Pea son’s chi-squa ed es was used in he analysis, allowing he au ho s o es he ela ionship be ween selec ed nominal a iables. In o de o desc ibe he con ingency, coe - icien s such as C amé ’s V, Pea son’s C adj , and Tschup ow’s Twe e used. Addi ionally, a logis ic eg ession model was used o de e mine he di ec ion o he obse ed ela ionships. As pa o he su ey, esponden s we e asked abou hei a i udes o MTPL insu ance wi h a p emium based on hei d i ing-s yle da a. Answe ing he ques ion “Would you be willing o allow o he moni o ing o you d i ing s yle in exchange o a ca insu ance p emium educ ion?”, 56.09% o he pa icipan s ga e one o he possible posi i e esponses (17.95% o hem indica ed “De ini ely Yes”); 15.71% o hem said “De ini ely No ”. In consequence, i can be concluded ha he es will ag ee o some o m o iola ion o hei p i acy, expec ing addi ional inancial incen i es, e.g., an insu ance p emium educ ion. The pa icipan s’ a i udes o d i ing s yle moni o ing a e p esen ed in Table 4. Table 4. Insu ed pe sons’ willingness o consen o he moni o ing o hei d i ing s yle, and he cha ac e is ics analysed. Va iables Consen o Moni o ing o he D i ing S yle (%) To al De ini ely No Ra he No Ra he Yes De ini ely Yes A e age dis ance co e ed (km) ≤5000 8 23 28 10 69 5001–10,000 22 42 63 17 144 10,001–15,000 18 52 80 32 182 15,001–20,000 19 32 39 22 112 >20,000 31 27 28 31 117 P e ious p emium (PLN) ≤400 8 13 9 1 31 401–600 12 36 45 24 117 601–800 28 39 57 33 157 801–1000 14 42 59 21 136 1001–1500 21 26 34 18 99 1501–2000 4 13 19 7 43 >2000 11 7 15 8 41 Sel - epo ed d i ing s yle Bad, qui e bad, o a e age 113 31 45 17 106 Qui e good 40 97 116 31 284 Good 45 48 77 64 234 1 : Due o he small numbe o esponden s wi h “bad” o “qui e bad” sel -assessmen , o he needs o la e calcula ions, a ans o ma ion was made by combining da a ep esen ing “bad” (n = 1), “qui e bad” (n = 6), and “a e age” (n = 99) sel -assessmen .