Evidence for Adverse Selection in the Automobile Insurance Market

Transcription

1 Evdence for Adverse Selecton n te Automoble Insurance Market Racel J. Huang * Assstant Professor, Fnance Department Mng Cuan Unversty, Tape, Tawan Larry Y. Tzeng Professor, Department of Fnance Natonal Tawan Unversty, Tape, Tawan Jennfer L. Wang Assocate Professor, Department of Rsk Management and Insurance Natonal Cengc Unversty, Tape, Tawan Kl C. Wang Instructor, Department of Rsk Management and Insurance S Cen Unversty, Tape, Tawan * Correspondng Autor. Fnance Department, Mng Cuan Unversty, 250 Cung San N. Rd. Sec. 5, Tape, 111, Tawan. E-mal address: racel@mcu.edu.tw; tel: ext 2871.

2 Evdence for Adverse Selecton n te Automoble Insurance Market Abstract Ts paper proposes a new metod to drectly test te exstence of adverse selecton n te automoble nsurance market. By tracng te renewal decsons of te nsured, we fnd tat, n Tawan automoble nsurance market, te coce of nsurance coverage and te prevous-year clam records are postvely correlated, wc can be a result of adverse selecton but not of moral azard. We furter fnd tat te loss rato s postvely correlated to te coce of nsurance coverage. Ts ndcates tat cross-subsdzaton may exst n te market. Te fndng of cross-subsdzaton furter strengtens te evdence to support te exstence of adverse selecton. JEL classfcaton: D80, G22, C30 Keywords: nsurance market, asymmetrc nformaton, adverse selecton. 1

3 1. Introducton Asymmetrc nformaton as been wdely dscussed n te nsurance lterature snce Rotscld and Stgltz (1976) and Savell (1979) frst poneered ts lne of researc. Followng ter footsteps, many researcers (e.g., Stgltz, 1977; Wlson, 1977; Myazak, 1977; Spence, 1978; Donne and Lesserre, 1985, 1987; and Arnott and Stgltz, 1988) ave provded nsgtful teoretcal analyss on te market wt asymmetrc nformaton problems. More recently, several papers ave used emprcal data to furter examne te teoretcal predctons on asymmetrc nformaton n real world. However, te emprcal evdence n te lterature as not yet reaced a determnant concluson on weter asymmetrc nformaton problems do exst n te nsurance market. Some researces (e.g., Puelz and Snow, 1994; Donne and Gagne, 2002; and Fnkelsten and Poterba, 2004) ave found evdence to support te exstence of asymmetrc nformaton n nsurance markets, wereas oter researces (e.g., Cappor and Salane, 1997, 2000; Cawley and Plpson, 1999; Cardon and Hendel, 2001; Donne, Goureroux, and Vanasse, 2001) ave found no suc evdence. It s mportant to fnd out te exstence of asymmetrc nformaton n realty. It s also essental to furter dentfy ts source, f asymmetrc nformaton exsts. Two types of asymmetrc nformaton problems, adverse selecton and moral azard, specfcally 2

4 receved a lot of attenton n te nsurance lterature. Eac of tese problems as a dfferent mpact on nsurance operaton and sould be remeded by a dfferent soluton. Terefore, t s mportant for nsurers to furter dentfy te source of te asymmetrc nformaton. However, t s not an easy task to separate adverse selecton from moral azard. Cappor and Salane (2000) alleged tat bot adverse selecton and moral azard problems would cause te coce of coverage and te occurrence of te clam to be postvely correlated. Tus, tey examned te exstence of asymmetrc nformaton by testng te condtonal dependence between te coce of coverage and te occurrence of te clam. Unfortunately, under ter approac, we cannot furter dentfy weter asymmetrc nformaton s caused by te adverse selecton or by moral azard problem, because bot adverse selecton and moral azard problems would cause te same result. Among tose researcers wo found evdence to support te exstence of asymmetrc nformaton, only a few ave dentfed ts source. Donne and Gagne (2002) separated moral azard from adverse selecton by analyzng te effect of te replacement cost endorsement. Fnkelsten and Poterba (2004) used data n te annuty market to provde a drect test for adverse selecton under te assumpton tat moral azard problems are lmted n tat market. Cappor and Heckman (2000) and Abbrng, Heckman, Cappor and Pquet (2003) proposed employng dynamc data to 3

5 verfy te moral azard problem. By adoptng dynamc data, Abbrng, Heckman, Cappor and Pquet (2003) dd not fnd strong evdence of moral azard n France s automoble nsurance market. Ts paper ntends to propose a new approac to drectly trace adverse selecton by usng te nsured s renewal decsons. We frst use prevous-year clam records as a proxy to classfy te nsured s rsk type. We ten examne weter te prevous-year clam records are related to te coce of nsurance coverage n te followng year. Snce te prevous-year clams appened pror to te nsured coosng ter nsurance coverage, only adverse selecton, as argued by Abbrng, Heckman, Cappor and Pquet (2003), can explan te relatonsp between te prevous-year clam records and te nsurance coverage coces. Terefore, we can examne te exstence of adverse selecton by testng te correlaton between te coce of nsurance coverage and te prevous-year clam records for te contnung renewal contracts. 1 Furtermore, we ntend to test weter cross-subsdzaton exsts n te market. Unlke most papers n te lterature generatng ter emprcal ypoteses by Rotscld and Stgltz (1976), we test weter te market equlbrum s separatng equlbrum wt cross-subsdzaton as proposed by Myazak (1977) and Spence (1978). 2 It sould 1 Ts argument rests on te assumpton tat an ndvdual s rsk preference does not cange because of an accdent. If te ndvdual becomes more rsk averse after experencng an accdent, e/se wll coose a polcy wt ger coverage n te renewal decson, no matter wc rsk type te nsured belongs to. 2 Only a few of te researces support cross-subsdzaton. By analyzng te U.S. crop nsurance market, Makk and Somwaru (2001) fnd tat g rsks are under carged wereas low rsks are over carged. 4

6 be noted tat bot Rotscld and Stgltz (1976) and cross-subsdzaton equlbrum proposed by Myazak (1977) and Spence (1978) predct separatng equlbrum, tat g rsks coose g coverage and low rsks coose low coverage. On te oter and, Rotscld and Stgltz (1976) predct tat bot g rsks and low rsks are carged on bass of ter own loss probabltes, wereas cross-subsdzaton equlbrum proposed by Myazak (1977) and Spence (1978) predct tat g rsks receve subsdzaton from low rsks. To provde evdence for te cross-subsdzaton ypotess, 3 we furter test weter te loss rato s related to te coce of coverage. Wen facng te adverse selecton problem descrbed by Rotscld and Stgltz (1976), an nsurer could desgn break-even polces wt dfferent ranges of coverage n a compettve nsurance market. Te nsured would ten self-select nsurance polces accordng to ter own rsk types. Te g-rsk nsured wll coose g coverage and be carged a g premum rate, wle te low-rsk nsured wll coose low coverage and be carged a low premum rate. Tus, n Rotscld and Stgltz s separatng equlbrum, te expected loss rato s not related to te coce of nsurance coverage, as sown n appendx A. On te oter and, te loss rato could be postvely correlated to te coce of nsurance coverage f tere s a cross-subsdzaton n te market, as sown n Appendx B. It s mportant to note 3 Accordng to Crocker and Snow (1985), te consumers welfare can be mproved f cross-subsdzaton s allowed n te nsurance market wt adverse selecton. 5

7 tat te loss rato could be unrelated to te coce of nsurance coverage f only a moral azard problem exsts n te market, as sown n Appendx C. Tus, we may use cross-subsdzaton evdence to furter separate adverse selecton from moral azard. Our emprcal results fnd strong evdence to support tat asymmetrc nformaton problems do exst n Tawan s market. Second, we fnd a postve relatonsp between te coce of nsurance coverage and te prevous-year clam records, wc ndcates te exstence of adverse selecton. Furtermore, we fnd tat te loss rato s sgnfcantly postvely correlated to te coce of nsurance coverage, wc ndcates te exstence of cross-subsdzaton. Tus, our emprcal results support tat adverse selecton problems exst n Tawan s automoble nsurance market and te market equlbrum s a separatng equlbrum wt cross-subsdzaton. Te rest of ts paper s organzed as follows: Sectons 2 ntroduce te automoble nsurance n Tawan and explan wy contracts wt dfferent features could screen ndvduals. Secton 3 descrbes te data and te summary statstcs. Secton 4 provdes evdence for asymmetrc nformaton. Secton 5 confrms tat adverse selecton exsts n Tawan automoble nsurance market. Secton 6 furter demonstrates te evdence of cross-subsdzaton. Secton 7 concludes and suggests some furter extenson. 2. Automoble nsurance n Tawan and te contract screenng 6

8 In 2003, approxmately 5.6 mllon car owners purcased automoble nsurance from 25 nsurance companes n Tawan. Automoble nsurance accounts for about 50 percent of te nsurance premum volume n most property-lablty nsurance companes and as occuped te largest market sare of te property-lablty nsurance market. Tree types of automoble nsurance ave been observed n te market: compulsory lablty, supplementary lablty, and compreensve coverage for damage. Compulsory lablty covers only te njures to a trd party, no matter f te nsured s responsble. Supplementary lablty, wc s purcased voluntarly, covers bot property damage and bodly njury. Compreensve coverage, wc s also purcased voluntarly, provdes coverage for property damage to te drver's automoble. In 2003, te total premums pad for compreensve coverage nsurance were about US$0.37 bllon and te ncurred losses were about US$0.23 bllon. Tere are tree types of contracts n compreensve coverage nsurance: Type A, B and C. Type A coverage covers all rsks, ncludng all knds of collson and non-collson losses, wc may be caused by mssles or fallng objects, fre, exploson, wndstorm, ntentonal body damage, malcous mscef, and any undentfed reasons oter tan te exclusons n te polcy. Type B coverage selected rsks. It also covers collson and non-collson losses as Type A does. However, te non-collson losses 7

9 caused by ntentonal body damage, malcous mscef, and te undentfed reasons covered under type A are specfcally excluded from type B. Type C covers only damage n a collson nvolvng two or more vecles. Collson losses caused by ttng oter objects suc as a telepone pole, a tree, or a buldng and non-collson losses tat used to be covered under types A and B are specfcally excluded from type C. To examne te asymmetrc nformaton problems n Tawan s automoble nsurance market, we focus on compreensve coverage nsurance. Most of te emprcal papers examne asymmetrc nformaton problem n nsurance market by lmtng ter focus to weter ndvduals purcase greater payment exbt ger rsk. From a dfferent angle to provde evdence of asymmetrc nformaton, Fnkelstan and Poterba s (2004) paper ndcates tat nsurance contracts wt dfferent features could screen ndvduals drectly. For example, an ndvdual wt a ger lfe expectaton wll purcase back-loaded annuty, wc as a ger payment n later perods tan an annuty wt flate payment. An ndvdual wt a lower lfe expectaton wll demand an annuty wt guarantee perod. Followng ter paper, we argue tat dfferent rsk types of ndvduals wll self-select among te tree types of compreensve coverage nsurance. In te present of adverse selecton, tere wll be two types of ndvduals: g rsk type and low rsk type. In automoble nsurance, a g rsk drver as a ger 8

10 probablty causng a car accdent, no matter te accdent nvolves oter vecles. Tus, type A and B contracts could be referred as g coverage contracts, and type C could be referred as a low coverage contract. Terefore, n te present of adverse selecton, g rsk ndvduals wll purcase type A or B contracts and ave a ger probablty to fle a clam, were as low rsk ndvduals wll purcase type C contract and ave a lower probablty to fle a clam. However, types A and B cover more rsks tan type C and obvously could ave more clams. To control te effect caused by te broader coverage of types A and B, we use only clam data of collson losses wt more tan two cars nvolved, 4 snce non-collson losses covered under types A and B are specfcally excluded from type C. It s wort notng tat te above predcton s also observable n te present of moral azard. Wen a market suffers moral azard problem, te ndvduals covered by ger coverage wll be less careful. Tus, f an ndvdual purcase type A or B, e or se wll drve less carefully because tat te contract covers any damage tat caused by any dentfed reason. Meanwle, a drver becomes more careless wll smultaneously ncrease bot te probablty of ttng anoter vecle and oter objects. Terefore, we predct tat te ndvduals wt type A or B contracts wll ave a ger probablty to fle collson losses wt more tan two cars nvolved. 4 Altoug types A, B, and C all cover collson losses wt more tan two cars nvolved, te polcyolders of types A and B are more lkely to be g rsk drvers and could more lkely cause collson losses wt more tan two cars nvolved. 9

11 3. Data and summary statstcs Our data come from a large nsurance company tat controls over 30 percent of te market sare n Tawan s automoble nsurance market. Tus, we beleve tat te data sould be representatve for te entre automoble nsurance market n Tawan. In total, we assemble 185,704 observatons, wc can be dstrbuted as 59,186, 61,627, and 64,891 observatons n 1999, 2000, and 2001, respectvely. 5 Te dataset also ncludes nformaton about age, gender, and marrage status for te nsured s caracters and age of car, brand, and regstered locaton for te car s caracters. Te defntons of all te varables are dsplayed n Tables D1 n Appendx D. Te summary statstcs of all te varables for te wole sample are dsplayed n Table D2 n Appendx D. To track te exstence of adverse selecton, we furter use a sub-sample n wc te nsured purcased nsurance n year t and renewed te polcy n year t + 1. In te sub-sample, tere are 26,420, 28,986, and 31,305 observatons n 1999, 2000, and 2001, respectvely. Te summary statstcs of te renewal decson and all te oter varables for te sub-sample are dsplayed n Table D3 n Appendx D. To track cross-subsdzaton, we nvestgate weter te loss rato of te ndvdual wo purcases types A and B s larger tan tat of te ndvdual wo purcases type C. Te loss rato of te ndvdual s defned as te amount of te clam te ndvdual fles 5 We start from year 1999, because tat type C s launced from tat year. 10

12 dvded by te amount of te nsurance premum te ndvdual pays. Te summary statstcs of te loss rato (LR) for te wole sample and for te renewal sample are respectvely dsplayed n Tables D2 and D3 n Appendx D. 4. Evdence for asymmetrc nformaton Our emprcal analyss begns by testng te exstence of asymmetrc nformaton n Tawan s automoble nsurance market. We follow te emprcal model suggested by Cappor and Salane (2000), wc used a par of probt models to test te condtonal dependence between te coce of coverage and te occurrence of te clam. Te probt models are as te follows: Prob( y = 1) = Φ( β ), and (1) X a Prob( z = 1) = Φ( β ), (2) X b were X s te varable for ndvdual s nformaton, β a and β b are te coeffcent vectors of te regressor, and Φ s te cumulatve dstrbuton functon of N (0,1). y s a dummy varable tat ndcates ndvdual cooses g-coverage polces. Snce bot types A and B cover non-collson clams and type C covers only collson clams, we classfy types A and B as g coverage and type C as low coverage. Tus, wen an ndvdual cooses compreensve automoble nsurance coverage of type A or B, ten y = 1; oterwse y = 0. z s anoter dummy varable tat marks 11

13 a clam. In ts paper we do not use all te clams wen defnng te varable z. Instead, we employ only tose clams tat nvolve a collson wt at least two cars. To avod a potental bas caused by unobservable accdents n type C, we employ te same crtera to dentfy a clam for all polces,.e., z = 1 wen an ndvdual fles a clam caused by a collson wt at least two cars; oterwse z = 0. Te estmated resduals of te above two probts can be calculated as follows: εˆ ηˆ φ( X βa) φ( X βa) = E( ε y) = y (1 y ), (3) Φ( X β ) Φ( X β ) a φ( X βb) φ( X βb ) = E( η z) = z (1 z), (4) Φ( X β ) Φ( X β ) b b a were φ s te densty dstrbuton functon of N (0,1), respectvely. To test te condtonal dependent of εˆ and ηˆ, we follow Cappor and Salane (2000) and use a test statstc W 6 : W ( n = 1 = n = 1 εˆ ηˆ ) 2 εˆ ηˆ 2 2. (5) W s dstrbuted asymptotcally as a χ 2 (1). We test ts sgnfcance under te null ypotess of cov( ε, ) = 0. If tere s asymmetrc nformaton, te condtonal η dependence between te coce of coverage and te occurrence of te clam sould be sgnfcantly postve. 6 In Cappor and Salane (2000) emprcal dataset, te dfference of te lengt of te polces comes from te msmatc of year and calendar year, so te W -statstc n ter researc needs a wegt. Because our data are calculated on a calendar year bass, our W -statstc does not need te wegt factor. 12

14 Usng te wole sample, we report te condtonal correlatons between coverage and clam for eac year n Table 1. Consstent wt our ypotess, we fnd tat te correlaton coeffcents ( ρ ) between ε and η n ts table are all postve. Furtermore, te statstcs (W ) sow tat te correlatons between te coce of coverage and te occurrence of a clam are sgnfcantly dfferent from zero. Tus, te emprcal evdence mples tat asymmetrc nformaton problems do exst n Tawan s automoble nsurance market. [Insert Table 1 about ere] It sould be noted tat many of te clams are generated by new cars and many new cars owners wo purcased te compreensve nsurance do not renew ter polces for te followng year. Te means of z (te average clam frequency) for te sub-sample are 9.94%, 11.55%, and 4.65% n 1999, 2000, and 2001, respectvely. However, te means of z for te entre sample are 27.44%, 31.01%, and 32.41% n 1999, 2000, and 2001, respectvely. On te oter and, te means of carage 0 (te proporton of new cars) for te sub-sample are 1.25%, 1.04%, and 0.83% n 1999, 2000, and 2001, respectvely, wereas, te means of carage 0 for te entre sample are 43.03%, 39.06%, and 31.24% n 1999, 2000, and 2001, respectvely. It s generally beleved n te nsurance ndustry tat new cars could contrbute most of te asymmetrc nformaton problems. By comparng te emprcal results from te entre 13

15 sample and te sub-sample, we are able to furter analyze weter te asymmetrc nformaton problems preval n te market, no matter wc polces result from new cars. In Table 2, we perform Cappor and Salane s test by usng te sub-sample data for te nsured wo contnue to renew ter polces n te followng year. Consstent wt te results n Table 1, all of te correlaton coeffcents ( ρ ) n Table 2 are stll postve. Te result once agan confrms te exstence of asymmetrc nformaton n te sub-sample group of te contnung renewal nsured. However, we fnd all of te correlaton coeffcents ( ρ ) n Table 2 are respectvely smaller tan tose n Table 1. It sould be noted tat te sub-sample conssts of fewer new cars, wereas te entre sample ncludes many new cars. Tus, combng te results of Tales 1 and 2, our emprcal evdence ndcates tat te nsurance markets for bot new cars and old cars could suffer from asymmetrc nformaton problems, altoug te nsurance market for new cars could suffer more severe problems. [Insert Table 2 about ere] 5. Evdence for adverse selecton In ts secton, we drectly track te exstence of adverse selecton. We use a sub-sample were te nsured purcased nsurance n year t 1 and renewed ter polcy n te followng year t. In year t, te nsurer could observe weter te 14

16 ndvduals fle a clam n te prevous year t 1. Tus, ts record could be ndcated as a proxy of ndvdual s rsk type. Te ndvdual s contract coce at year t wll be affected by all of te observable varables at year t and s or er rsk type. To test weter a g rsk type wll coose g coverage, we use a probt model as te follows: Prob( yt = 1) = Φ( X tβ c + β dzt 1 ), (6) were y t s as defned n te prevous secton, X t s te varable for ndvdual s nformaton at year t, and β c and β d are te coeffcent vectors of te regressor. Wen ndvdual fles a clam caused by a collson wt at least two cars n year t 1, ten z 1; oterwse z 0. t 1 = = t 1 In Equaton (6), z t 1 s now as a proxy of ndvdual s rsk type. It does not mean tat te ndvdual s rsk type s observable at year t. Te nsurer could only conclude tat te nsured as a g probablty of beng a g rsk type wen te nsured fles a clam at year t 1. If te sample of z 1 contans more g rsk drvers, ten te t 1 = teory of adverse selecton would predct a postve β d. However, t s very mportant to recognze tat tere exsts anoter force wc could drve β d beng negatve: experence ratng. If te nsured fles a clam at year t 1, ten e or se wll face an ncrease of premum for all coce of contracts at year t. A g coverage contract would become less affordable to te nsured wo ever fled a clam n te prevous year. 15

17 Tus, te effect of experence ratng would lead te nsured wt prevous clam records to coose a contract wt less coverage at year t. Terefore, β d would be negatve. In Table 3, we report te estmator between te coce of te renewal decson and te prevous-year clam records. We fnd all te coeffcents are sgnfcantly postve. Ts result confrms tat a g rsk type nsured wll coose g coverage contract. Our result support tat te effect of experence ratng s domnated by adverse selecton. Combnng te fndngs n Tables 2 and 3, our emprcal results provde evdence to support tat adverse selecton contrbutes to asymmetrc nformaton problems n Tawan s automoble nsurance market. [Insert Table 3 about ere] It sould be noted tat te evdence from Tables 1 and 2 supports te exstence of asymmetrc nformaton problem n te nsurance market, were evdence from Table 3 ndcates tat asymmetrc nformaton problems could be caused by adverse selecton. However, we cannot exclude te possblty of te exstence of moral azard, snce t s possble tat bot adverse selecton and moral azard mgt co-exst n te market. 6. Evdence for cross-subsdzaton Fnally, to track te exstence of cross-subsdzaton, we construct a Tobt regresson as follows: 16

18 LR = X β + β y + υ, (7) e f were LR s te total clam amount dvded by te premum for eac ndvdual. X and y are as defned above. It s mportant to recognze tat LR as a mass on zero snce most ndvduals do not fle a clam. Tus, we use a Tobt regresson to estmate te parameters n Equaton (7). Accordng to our model n Appendx B, we predct tat β f, te coeffcent of y n Equaton (7), sould be sgnfcantly postve f cross-subsdzaton exsts. In Table 4, be usng te renewal sample, we report β f n te Tobt regresson. If tere s adverse selecton but no cross-subsdzaton n te market, te coce of polcy sould not correlate to te loss rato as sown n Appendx A. From Table 4, we fnd tat all te coeffcents are sgnfcantly postve, wc mples tat te nsured wo buy g coverage polces tend to ave g loss ratos. Te evdence from Tables 3 and 4 togeter mply tat te nsurance market may exst bot adverse selecton and cross-subsdzaton. Moreover, snce moral azard can not make ndvdual s coce of te polcy and te ndvdual s loss rato correlated as sown by Appendx C, evdence from Table 4 could furter support te exstence of adverse selecton. [Insert Table 4 about ere] 7. Concluson Identfyng te source of asymmetrc nformaton s an mportant ssue n te 17

19 nsurance lterature. Prevous studes ave separated moral azard from adverse selecton by usng eter dynamc data (Cappor and Heckman, 2000) or te partcularty of a sample set (Donne and Gagne, 2002; and Fnkelsten and Poterba, 2004). In ts paper, we propose a new metod to drectly examne te exstence of adverse selecton. Usng tree-year ndvdual data from a large nsurance company n Tawan, ts paper analyzes weter adverse selecton exsts n te nsurance market. We use renewal decsons to track adverse selecton problems. By adoptng clam records as a proxy of te nsured s rsk type, we allege tat only adverse selecton, not moral azard, can explan te relatonsp between te prevous-year clams and te coce of coverage n te followng year. We furter argue tat te ndvdual s loss rato wll be postvely correlated to ndvdual s coce of coverage f tere exst bot adverse selecton and cross-subsdzaton n te market. Applyng te same approac as Cappor and Salane (2000), our emprcal evdence confrms tat asymmetrc nformaton problems do exst n Tawan s compreensve automoble nsurance market. Furtermore, our results make a new contrbuton to te nsurance lterature by furter drectly trackng te exstence of adverse selecton. Our emprcal evdence sows tat te correlaton between te coce of nsurance coverage and te prevous-year clam records s sgnfcantly postve, and te loss rato s also sgnfcantly postvely correlated to te coce of coverage. Tus, 18

20 we conclude tat adverse selecton exsts n Tawan s compreensve automoble nsurance market. It sould be also noted tat our fndngs actually do not refute but rater supplement tose papers tat found no evdence to support te exstence of asymmetrc nformaton. Frst, we employ data from compreensve automoble nsurance, wc was not yet used to examne asymmetrc nformaton problems n te lterature. Second, we use data n te early stage of te developng nsurance market, wle most of te data used n te lterature as come from a well-developed market. It s possble tat asymmetrc nformaton exsts n te early stage of te nsurance market, as descrbed by Rotscld and Stgltz (1976). However, over te years, nsurance companes collect more and more nformaton to screen te nsured and eventually elmnate asymmetrc nformaton problems n te market. Tus, our fndngs suggest tat furter nvestgaton of asymmetrc nformaton problems by comparng dfferent nsurance markets or data from dfferent countres s defntely needed. 19

21 References Abbrng, J.H, P. Cappor, J.J. Heckman, and J. Pnquet, 2003, Adverse Selecton and Moral Hazard n Insurance: Can Dynamc Data Help to Dstngus? Journal of te European Economc Assocaton, 1: Abbrng, J.H. P. Cappor, and J. Pnquet, 2003, Moral Hazard and Dynamc Insurance Data, Journal of te European Economc Assocaton, 1: Arnott, R., and J.E. Stgltz, 1988, Randomzaton wt Asymmetrc Informaton, Rand Journal of Economcs, 19: Cardon, J.H., and I. Hendel, 2001, Asymmetrc Informaton n Healt Insurance: Evdence from te Natonal Medcal Expendture Survey, Rand Journal of Economcs, 32: Cawley, J., and T.J. Plpson, 1999, An Emprcal Examnaton of Informaton Barrers to Trade n Insurance, Amercan Economc Revew, 89: Cappor, P., and J. Heckman, 2000, Testng for Moral Hazard on Dynamc Insurance Data: Teory and Econometrc Tests, workng paper. Cappor, P., and B. Salane, 1997, Emprcal Contract Teory: Te Case of Insurance Data, European Economc Revew, 41: Cappor, P., and B. Salane, 2000, Testng for Asymmetrc Informaton n Insurance Markets, Journal of Poltcal Economy, 108: Crocker, K.J., and A. Snow, 1985, Te Effcency of Compettve Equlbra n Insurance Markets wt Asymmetrc Informaton, Journal of Publc Economcs, 26: Donne, G., and R. Gagne, 2002, Replacement Cost Endorsement and Opportunstc Fraud n Automoble Insurance, Journal of Rsk and Uncertanty, 24: Donne, G., C. Goureroux, and C. Vanasse, 2001, Testng for Evdence of Adverse 20

22 Selecton n te Automoble Insurance Market: A Comment, Journal of Poltcal Economy, 109: Donne, G., and P. Lasserre, 1985, Adverse Selecton, Repeated Insurance Contracts and Announcement Strategy, Revew of Economc Studes, 52: Donne, G., and P. Lasserre, 1987, Adverse Selecton and Fnte-Horzon Insurance Contracts, European Economc Revew, 31: Fnkelsten, A., and J.M. Poterba, 2004, Adverse Selecton n Insurance Markets: Polcyolder Evdence from te U.K. Annuty Market, Journal of Poltcal Economy, 112: Makk, S.S., and A. Somwaru, 2001, Evdence of Adverse Selecton n Crop Insurance Markets, Journal of Rsk and Insurance, 68: Myazak, H., 1977, Te Rate Race and Internal Labour Market, Bell Journal of Economcs, 8: Puelz, R., and A. Snow, 1994, Evdence on Adverse Selecton: Equlbrum Sgnalng and Cross-Subsdzaton n te Insurance Market, Journal of Poltcal Economy, 102: Rotscld, M., and J.E. Stgltz, 1976, Equlbrum n Compettve Insurance Markets: An Essay on te Economcs of Imperfect Informaton, Quarterly Journal of Economcs, 90: Savell, S., 1979, On Moral Hazard and Insurance, Quarterly Journal of Economcs, 93: Spence, M., 1978, product Dfferentaton and Performance n Insurance Markets, Journal of Publc Economcs, 10: Stgltz, J. 1977, Monopoly, Nonlnear Prcng, and Imperfect Informaton: Te Insurance Market, Revew of Economc Studes, 44: Wlson, C.A., 1977, A Model of Insurance Markets wt Incomplete Informaton, 21

23 Journal of Economc Teory, 16: Wnter, R.A., 2000, Optmal Insurance under Moral Hazard, Handbook of Insurance, Edted by G. Donne, Boston, Dordrect and London: Kluwer Academc. 22

24 Table 1 Te Condtonal Correlaton Between Coverage and Clam n Compreensve Automoble Insurance n Years 1999 to 2001 Year ρ W *** *** *** *** *** *** Note: Te sgnfcant level of 99% s denoted by *** Table 2 Te Condtonal Correlaton Between Coverage and Clam n te Same Year (Sub-sample of Contnued Insured) Year ρ W *** *** *** *** *** *** Note: Te sgnfcant level of 99% s denoted by *** Table 3 Te relatonsp Between Coverage and prevous Clam records (Sub-sample of Contnued Insured) Year β d *** *** *** Note: Te sgnfcant level of 99% s denoted by *** Table 4 Te Coeffcent of Rsk Type for Loss Rato n Tobt Regresson Year β f *** *** *** Note: Te sgnfcant level of 99% s denoted by *** 23

25 Appendx A Assume tat ndvduals face a bnomnal property rsk wt eter a fxed loss wt a probablty π or no loss wt1 π, were denotes rsk types n te economy, {, l} and 1 π > π > 0. Let te fracton of rsk type agents sθ. > l Te types are te nsured s prvate nformaton and are unobservable to te nsurer. For te sake of smplcty, assume all ndvduals ave te same ntal wealtw, loss amount L, and utlty functon U wt U > 0 and U 0. On te bass of Rotscld and Stgltz s (1976) separatng equlbrum, a rsk-neutral nsurer wt a cost loadng λ n a compettve nsurance market wll offer two contracts to te market, and eac contract n te equlbrum set makes zero proft. Ponts B and G n Fgure A1 denote te optmal contracts for g and low-rsk type ndvduals, respectvely. A g-rsk type nsured s ndfferent about coosng ponts B or G, wereas a low-rsk type nsured prefers pont G. Zero proft contracts n te equlbrum suggest tat pont B contans g coverage Q for a g nsurance premum ( 1 + λ)π Q, and pont G contans low coverage Q l for a low nsurance premum ( 1 + λ)π Q l. Let E denote te l expectaton operator. Tus, te expected value of loss rato LR for te type nsured wll become. π Q E ( LR) = (1 + λ) π Q 1 =, wc s ndependent of rsk type 1+ λ 24

26 Wealt n te loss state p l 45 0 p U l B G w-l U 0 w Wealt n te no-loss state Fgure A1 Separatng Equlbrum 25

27 Appendx B Based upon te model settng n Appendx A, we now consder Myazak s (1977) separatng equlbrum wt cross-subsdzaton. As proposed by Puelz and Snow (1994), under cross-subsdzaton, te nsurance premum for te type nsured, {, l}, would be [ Q k ] P = ( 1+ λ) π +, (B1) were k s a carge for cross-subsdzaton among contracts. Snce te nsurance market s under perfect competton, te nsurer wll earn zero expected proft, wc mples tat cross-subsdzaton across rsk types wll net out to zero,.e., w = 0, k were w denotes te proposton of te nsured wt rsk type. In Myazak s model, te nsurer wll earn proft on polces purcased by low rsk type nsured but ncur losses on tose purcased by g rsk type nsured. In oter words, k < 0 < k. l Terefore, te expected loss rato of g rsk types wll be greater tan tat of low rsk types, snce E( LR = [ π Q + k ] (1 + λ) [ π Q + k ] [ π Q + k ][ π Q + k ] > 0. ) E( LR ) π Q = (1 + λ) l l l l π Q k π Q k π l Q l l l l (B2) 26

28 Appendx C In ts appendx, we adopt Wnter s (2000) dden acton model of moral azard to demonstrate tat te expected loss rato s uncorrelated to te nsurance coverage. Assume tat ndvduals face a bnomnal property rsk wt eter a fxed loss L or no loss. Indvduals could employ self-protecton wt cost x to reduce te loss probablty. π (x) wt π ( x) < 0 and π ( x) > 0. Altoug te self-protecton beavor could not be observed by te nsurer, te nsurer could stll estmate te probablty of rsk occurrence. Tus, te rsk neutral nsurer would offer only a coverage Q for premum ( 1 + λ) π (x) Q, were λ denotes te nsurance loadng. Te expected loss rato LR --- nsurance coverage. π( x) Q E( LR) = (1 + λ) π ( x) Q 1 = --- wll be ndependent of te 1+ λ 27

29 Appendx D Table D1 Defntons of te Varables Varables Defnton y a dummy varable equals 1 wen an ndvdual cooses a type A or B polcy, oterwse equals 0 k z a dummy varable equals 1 wen an ndvdual cooses a type A or B polcy n te next year, oterwse equals 0 a dummy varable equals 1 wen an ndvdual s clam s caused by a collson and te clam amount s above te tresold amount, oterwse equals 0 LR loss rato, equals loss amount dvded by te premum carage0 a dummy varable equals 1 wen te car s new, oterwse equals 0 carage1 a dummy varable equals 1 wen te age of te car s one year, oterwse equals 0 carage2 a dummy varable equals 1 wen te age of te car s two years, oterwse equals 0 carage3 a dummy varable equals 1 wen te age of te car s tree years, oterwse equals 0 carage4 a dummy varable equals 1 wen te age of te car s four years, oterwse equals 0 carage5 a dummy varable equals 1 wen te age of te car s fve years, oterwse equals 0 carage6 a dummy varable equals 1 wen te age of te car s sx years, oterwse equals 0 carage7 a dummy varable equals 1 wen te age of te car s seven years, oterwse equals 0 carage8 a dummy varable equals 1 wen te age of te car s egt years, oterwse equals 0 carage9 a dummy varable equals 1 wen te age of te car s nne years, oterwse equals 0 carage10 a dummy varable equals 1 wen te age of te car s ten years, oterwse equals 0 carage11 a dummy varable equals 1 wen te age of te car s eleven years, oterwse equals 0 sexf a dummy varable equals 1 wen te owner of te car s female, oterwse equals 0 marred a dummy varable equals 1 wen te owner of car s marred cty a dummy varable equals 1 wen te owner of te car lves n te cty, oterwse equals 0 arean a dummy varable equals 1 wen te car s regstered n te nort of Tawan, oterwse equals 0 areas a dummy varable equals 1 wen te car s regstered n te sout of Tawan, oterwse equals 0 areaeast a dummy varable equals 1 wen te car s regstered n te east of Tawan, oterwse equals 0 catpcd_1 a dummy varable equals 1 wen te car s a sedan and s for non-commercal or long-term rental purposes, oterwse equals 0 catpcd_2 a dummy varable equals 1 wen te car s a small fregt-truck and s for non-commercal purposes or for busness use, oterwse equals 0 tramak_ =n,f,,t,c, dummy varable equals 1wen te trademark of te car s te assgned brand, oterwse equals 0 age2 a dummy varable equals 1 wen te age of te nsured s between 30 and 25, oterwse equals 0 age3 a dummy varable equals 1wen te age of te nsured s between 60 and 30, oterwse equals 0 age4 a dummy varable equals 1 wen te age of te nsured s above 60, oterwse equals 0 28

30 Table D2 Summary Statstcs for All Sample year Varable Mean Std Dev Mean Std Dev Mean Std Dev z y LR carage carage carage carage carage carage carage carage carage carage carage carage Sexf Marra Cty arean Areas areaeast catpcd_ catpcd_ Tramak_n Tramak_f Tramak_ Tramak_t Tramak_c age age age Numbers of observatons

31 Table D3 Summary Statstcs for Renewal Sample year Varable Mean Std Dev Mean Std Dev Mean Std Dev z y LR carage carage carage carage carage carage carage carage carage carage carage carage Sexf Marra Cty arean Areas areaeast catpcd_ catpcd_ Tramak_n Tramak_f Tramak_ Tramak_t Tramak_c age age age Numbers of observatons