Testing for Asymmetric Information in Tunisian Automobile Insurance Market

Transcription

1 ISSN (onlne) ISSN (prnt) Medterranean Journal of Socal Scences MCSER Publshng, Rome-Italy May 015 Testng for Asymmetrc Informaton n Tunsan Automoble Insurance Market Do: /mjss.015.v6n3s1p455 Abstract Imen Karaa Economc, Management and computer Scences Doctorate School of FSEG Sfax, Unversty of Sfax,Route de l Aéroport Km 4 Sfax 3018 Tunsa Emal:karaaa.men@gmal.com Noureddne Benlagha* Department of Fnance and Investment, College of Economcs and Admnstratve Scences, Al Imam Mohammad Ibn Saud Islamc Unversty (IMSIU), P.O. Box 5701, Ryadh, Saud Araba Emal: blnour00@yahoo.fr Asymmetrc nformaton has become one of the most nfluental theoretcal concepts n explanng compettve nsurance market. In contract theory, asymmetrc nformaton s the stuaton when one party of an economc transacton possesses nformaton that s not avalable to the other contractual party.in ths perspectve, ths paper ams to nvestgate the presence of asymmetrc nformaton n Tunsan automoble nsurance market. Ths nvestgaton s made usng an ndvdual data set durng the year 009. For ths purpose, we employ two emprcal approaches; the bvarate probt model and the two stages approach of Rchaudeau (1999). Hence, results show a strong evdence for the presence of asymmetrc nformaton for the beggng drvers. Inversely, for the experenced drvers, no evdence of asymmetrc nformaton have been detected. Keywords: Asymmetrc Informaton, Tunsan market, automoble nsurance, Negatve Bnomal model, Bvarate Probt model. 1. Introducton Asymmetrc nformaton has become one of the most nfluental theoretcal concepts n explanng compettve nsurance market. In contract theory, asymmetrc nformaton s the stuaton when one party of an economc transacton possesses nformaton that s not avalable to the other contractual party. In fact, Asymmetrc nformaton arses when an nformatonal gap exsts between an nsurer and an nsured. In such stuaton, nsureds are more nformed about ther own characterstcs or actons than ther nsurer. Potentally, ths could be a harmful stuaton because the nsured can take advantage of the nsurer's lack of knowledge. In a nutshell, asymmetrc nformaton can leads to a problematc because t creates opportuntes for lyng and cheatng by nsured, whch by the way can nduce market neffcency or even falure (Arrow 1963). In ths feld, a number of emprcal studes propose to measure the presence of resdual asymmetrc nformaton problems n several automoble nsurance markets. One can refers to Dahlby (1983/199) for Canada, Puelz and Snow (1994) for USA, Rchaudeau (1999) for France, Sato (006) for Japan, Km et al. (009) for Korea, Englund (010) for Denmark, Sh and Valdez (011) for Sngapore, and L et al. (013) for Tawan case. Besdes a recent revew artcle by Donne et al. (013) whch summarzed the theoretcal and the emprcal lterature concernng asymmetrc nformaton n road safety and automoble nsurance market. In the Canadan automoble nsurance market, two ntal studes (Dahlby, 1983 and 199) have estmated the sgn of the correlaton between the level of nsurance coverage and ex-post realzatons of rsk. Puelz and Snow (1994) found postve coverage-rsk correlaton usng ndvdual data obtaned from a Georga nsurer. However, several emprcal studes show no evdence for asymmetrc nformaton. Usng a French data set, Rchaudeau (1999) as well as Chappor and Salané (000) fnd no systematc relatonshp between coverage and rsk. In addton, Donne et al. (001) reach a smlar concluson for the Canadan automoble nsurance market: those who are more lkely to submt clams do not buy more nsurance. Moreover, these researchers crtczed Puelz and Snow (1994) for falng to consder nonlnear effects. 455

2 ISSN (onlne) ISSN (prnt) Medterranean Journal of Socal Scences MCSER Publshng, Rome-Italy May 015 On the other hand, Cohen (005) dd not fnd any correlaton for begnnng drvers1, she founds a strong correlaton for experenced drvers. Although, the study suggested the mportance of learnng n ths market. Sato (006) used an ndvdual data from the Japanese auto nsurance market, where nsurance rates are strctly regulated. Frst, he found a postve but not statstcally sgnfcant correlaton between the crash rsk and the purchase of own-vehcle coverage, even under the control of all varables observed by the nsurer. Second, he concluded that there was a sgnfcant and negatve correlaton between coverage and rsk when they are defned as the purchase of a zerodeductble polcy and a crash rsk. Recent emprcal studes n the compettve nsurance market show a presence of asymmetrc nformaton n these markets. To take some of the outstandng studes, Grun-Rehomme and Benlagha (007) examned the choce between basc thrd party coverage and deductble varable for begnnng and experenced drvers. Ther study used 4 guarantees types concernng the year 004, ths was made after the new crculaton securty measures mplementaton and the decrease of mortals accdents road. Usng a bvarate ordered model, the researchers fnd a sgnfcant postve correlaton rsk-coverage for begnnng drvers whch choce the thrd party nsurance plus deductble varable for French data. We can notce that most of the prevous emprcal focuses on the coverage-rsk correlaton. Ths paper contrbutes to the lterature by reexamnng whether such coverage-rsk correlaton exsts. The am of ths paper s to nvestgate on resdual asymmetrc nformaton n the Tunsan automoble nsurance market and to fnd ways to mprove and reduce the negatve mpact of asymmetrc nformaton on resource allocaton. Hence, the objectves of ths research proposal are to test the presence of the adverse selecton n the Tunsan nsurance market and to determne varous factors affectng the contact choce and accdent occurrence n the studed nsurance market. For ths purpose, we use a data set that ncludes all nformaton that an nsurer had about ts polcyholders for the 009 year. Our paper dffers from earler studes n two ponts; Frst, we use a recent data from the Tunsan nsurance market, whch s not nvestgated n the emprcal lterature. Ths data s concernng the year 009, after the mplementaton of the new no-clams bonus class. Second, we use the two-stage regresson analyss developed by Rchaudeau (1999) where the probt model s used for coverage choce equaton (frst stage) and the negatve bnomal model for the accdent frequency equaton (second stage). The remander of ths paper s organzed as follows. The next secton presents brefly the Tunsan automoble nsurance market. Then, secton 3 presents the models used and the emprcal test for the presence of asymmetrc nformaton. Secton 4 descrbes the data and reports a descrptve statstcs analyss of the data set. Secton 5 analyses and dscusses the emprcal results. The last secton concludes and dscusses possble future work.. The Tunsan Automoble Insurance Market In Tunsa, the nsurance sector plays an mportant role n the development of the prvate sector and the modernzaton of the securtes markets. For nstance, the Tunsan market characterzed by the presence of nsurance companes operatng n 4 regons. We fnd 1 of these companes engage n mult-branch operatons, 6 are sngle branch companes (3 specalze n lfe nsurance, 1 n expert nsurance, 1 n credt nsurance and 1 n rensurance) and 4 are offshore companes authorzed to conduct operatons wth nonresdents. The nsurance ndustry s domnated by the prvate sector, wth 61.7% n 010. The level of average premum has ncreased from 98,355 TND (n 009 to 106,195 TND n 010). Lookng to ther products dstrbuton n 008, nsurance companes use about 697 ntermedares (614 nsurance agents, 55 brokers and 8 agents authorzed to sell lfe nsurance) formng a network makng nsurance polces presents n all dfferent regons. They employ also about 10 actuares and 1008 experts and commssoners of damage authorzed to assess and evaluate the losses and damages. In 010, the Tunsan market structure has not changed; the automoble nsurance contrbutes to total busness wth 46.18% of the market. The lfe nsurance branch, wth 14.45%, follows t. The group health nsurance, varous rsks, transport and fre nsurance branches experenced the hghest growth rates, wth 13.05%, 11.%, 6.76% and 5.65%, respectvely. 1 Begnnng drvers are those havng less than 3 years drvng experence before contractng wth the nsurer. The descrpton of the nsurance market n ths secton s based on the notes of the F.T.U.S.A. (010) 456

3 ISSN (onlne) ISSN (prnt) Medterranean Journal of Socal Scences MCSER Publshng, Rome-Italy May Methodology To nvestgate the presence of adverse selecton n the Tunsan automoble nsurance market, we employ two models: the two-stage regresson analyss developed by Rchaudeau (1999) and the bvaat bvarate probt model ntroduced by Chappor and Salané (000) and Donne et al. (001). 3.1 The two-stage regresson analyss of Rchaudeau (1999) In ths modelng, the frst stage ams to estmate the coverage choce and the second stage estmates the accdent occurrence Choce of a coverage equaton (frst stage) In ths stage, the coverage choce can be defned as a dchotomous varable: * 1 f C = βx + ε 0, C = 0 otherwse, A maxmum lkelhood probt regresson s employed to estmate the deductble choce equaton. Then, the generalzed resdual s gven by: φ( X ˆ 1β1) ˆ ε [ ˆ = C Φ( X1 β1) ], Φ( X ˆ ˆ 1β1)(1 Φ( X1 β1)) (3) Where (.) and (.) are, respectvely, the densty and cumulatve dstrbuton functons of the standard normal dstrbuton, and 1 ˆβ s an estmated coeffcent vector. If the εˆ s postve (negatve), then the polcyholder has subscrbed a thrd party coverage polcy The accdent Frequency equaton (second stage) In the second stage, we estmate the probablty of accdent usng a count data model, and more precsely, a negatve bnomal model of the number of accdents. To test for asymmetrc nformaton, the resdual obtaned from the bnary choce coverage model n equaton (3) s used as nput when estmatng the negatve bnomal model3. The probablty of havng y accdents s gven by: P( Y = y ) = σ (4) Where (.) s the Gamma functon, ˆβ βˆ and ε are estmated coeffcents vectors. The regresson coeffcent βˆε captures the correlaton between the nsurance coverage and the frequency of accdents, condtonal on the effects of all observables on both the coverage choce and the accdent frequency. If βˆε s postve and statstcally sgnfcant, we conclude the exstence of asymmetrc nformaton. Ths wll be our test of the effcency n the Tunsan automoble nsurance market. The Rchaudeau's test may nduce an estmaton bas n the second-stage equaton. Usng the result of Murphy and Topel (1985), we correct ths bas by testng the statstcal sgnfcance of βˆε. In ths last test, the asymptotc varance-covarance matrx for two-stage maxmum lkelhood model s defned as: 1 1 ' 1 ' 1 ' 1 1 = R + R [ R3R R3 R4 R R3 R3R R4 ] R (5) Where, 1 Γ y + σ Γ 1 Γ 1 1 R1 = E β1 β1 R3 = E β1 β [ σ exp( X ˆ β + ˆ ε ˆ β )] 1 y + ( y + 1) [ 1 + σ + exp( X ˆ β + ˆ ε ˆ β )] σ R = E β β 1 R4 = E. β1 β ε y ε 3 Based on the Akake s Informaton Crteron (AIC) statstc, the negatve bnomal regresson fts our data better than the Posson regresson (see statstcs for dsperson parameters n Table 4). See also Km et al. (009) who show smlar results for Korean data and Donne and Vanasse (199) for Canadan data. 457

4 ISSN (onlne) ISSN (prnt) Medterranean Journal of Socal Scences MCSER Publshng, Rome-Italy May Bvarate probt model To test the condtonal ndependence between the contract choce and the accdent occurrence, we follow the emprcal approach proposed by Chappor and Salané (000). In fact, they use a bvarate probt model to examne the coveragersk correlaton. In ths modelng, the accdent occurrence Y s presented as follows: 1 f the drver ncurs at least one accdent durng the calandar year Y = 0 Otherwse Hence, the bvarate model s composed by two equatons: - The equaton of the deductble Choce * 1 f C = βx + ε 0, C = 0 otherwse, (6) - The equaton of accdent Occurrence * 1 f Y = γ X + η 0, Y = 0 otherwse, (7) In ths specfcaton, β γ X and are coeffcents to be estmated. represents the matrx of observable ndependent varables. The two error terms, ε and satsfy the followng standard condtons: E[ ε ] = E[ η ] = 0, Var[ ε ] = Var[ η ] = 1 and Cov[ ε, η ] = ρ. In ths model, ρ measures the correlaton between coverage and rsk and allow as to conclude about the presence of resdual adverse selecton n the portfolo. 4. Emprcal Methodology 4.1 Data To nvestgate the asymmetrc nformaton, we consder a portfolo of polces that contans nformaton for 3115 polcyholders In ths emprcal study, we employ 11 varables, consstng of the polcyholder s car s and accdent s characterstcs. The descrpton of dfferent varables are presented n the appendx (1). In our analyss, the coverage choce measured by thrd party coverage versus comprehensve coverage rather than low premum versus hgh premum. Thus, we defne t as follows: 1 f the contract corresponds to a Thrd Party Lablty CoverageChoce = 0 otherwse, 4. Summary statstcs To begn wth, let us gve an overvew of our data set. The fle contans 5301 women (17.03% of total populaton) and 584 males (8.97%) of whch 1574 leadng vehcle for commutng and famly use and drvng vehcles for commercal use. The average premum s 314TND and the maxmum premum that the nsurer receves s 5909 TND. The number of accdents stretches from no accdents up to 8 accdents, where the mean value s 0.0 ndcatng a low frequency of accdents. Most vehcles are of French brand (or 58.81% of all cars), wth 916 cars for prvate use and 9090 cars for commercal use, and whch are respectvely 50.34% and 49.66%. Moreover, about 30% of the drvers lve n the Coast of Tunsa especally n the governorate of Sousse. It s very eventful on the economc, admnstratve and socal captal. Concernng the job of the polcyholders varable, employees represent about 50% of the populaton and 1% are functonares whereas 1% are artsan. In our sample of 3115 contracts, we have nformaton on the number of responsble accdents reported by the nsured to hs nsurer n 009. Our data ncludes 8 contracts (1176 contracts) that have at least one accdent durng the contract year for the begnnng drvers (experenced drvers), 60 (745) contracts clamed two accdents, 114 (161) contracts made 3 accdents and 73 (13) contracts clamed more than three accdents (See table1). No sngle polcyholder n our portfolo ncurred more than eght accdents durng the year. 458

5 ISSN (onlne) ISSN (prnt) Medterranean Journal of Socal Scences MCSER Publshng, Rome-Italy May 015 Table 1. Dstrbuton of number of accdents Number of accdents Total Begnners drvers Experenced drvers Number Percent Number Percent Number Percent Total Results 5.1 The choce of coverage Table presents the estmaton results of the probt modelng that s the frst step regresson analyss of Rchaudeau (1999). The left-hand sde of ths table suggests the estmaton for the begnnng drvers whereas the rght-hand sde presents the estmaton for the experenced drvers. For the begnnng drvers, commutng and famly use cars are more lkely to be nsured by comprehensve nsurance than commercal use cars. In addton, we note that females have a greater probablty of choosng a comprehensve coverage than males, ndcatng perhaps that ther rsk-averson s greater. The probablty of buyng thrd party nsurance s hgher for the polcyholders who have age between 56 and 75 years. For the experenced drvers, the probablty of choosng thrd party coverage s more mportant for female and for the polcyholders who are older than 31 years. Prmary use cars are more lkely to be nsured by comprehensve coverage than commercal use cars. One nterestng pont to note s that the jobs of the polcyholders also have a role n the choce of coverage. The probablty of choosng thrd party coverage decreases wth the senor executve, the artsan, the employee and the unemployed. Table. Probt model results Independent varables Begnnng drvers Experenced drvers Coeffcent p-value Coeffcent p-value Female Prmary use Age Age Age Age Job Job Job Job Job Job Orgn Orgn Orgn Orgn Orgn Orgn Zone Zone

6 ISSN (onlne) ISSN (prnt) Medterranean Journal of Socal Scences MCSER Publshng, Rome-Italy May 015 Zone Zone Zone Constant Number of obs Log lkelhood The probablty of havng an accdent Accordng to the estmated parameters n the second equaton related to the occurrence of accdents (the second part of table 4), the probablty of makng at least one accdent at the nsurer ncreases accordng to female and to the agent lves n bg Tuns. Furthermore, ths probablty decreases wth job of the drvers. Partcularly, the accdent occurrence s negatvely related to the unemployed person, the employee and the retred person. Table 3 shows that many exogenous varables have a sgnfcant effect on accdents frequency for both begnnng and experence drvers. A specal note s the need for some exogenous varables. Frst, we examne the frequency of accdents for begnnng drvers. The postve sgn for the coeffcents of gender and the resdence area that suggests that female and polcyholders lve n bg Tuns have a hgher chance to ncur accdents. In addton, we observe a postve effect of vehcle's use on the probablty of accdent. The polcyholder specfes the prmary use of the nsured car as for commercal use that has a hgher chance of accdents. Second, we move to examne the accdent frequences for experenced drvers. We observe that the accdent frequency s postvely related to the job and the resdence area of polcyholders. Ths probablty decreases accordng to the age of drvers. Table 3. Negatve Bnomal model Results Begnnng drvers Experenced drvers Independent varables Mtopel Mtopel Coeffcent Std.Err. p-value Coeffcent Std. Err. p-value Accdent frequences equaton Female Prmary use Age Age Age Age Job Job Job Job Job Job Orgn Orgn Orgn Orgn Orgn Orgn Zone Zone Zone Zone Zone Constant RESIDU Lnalpha cons Number of obs Log lkelhood

7 ISSN (onlne) ISSN (prnt) Medterranean Journal of Socal Scences MCSER Publshng, Rome-Italy May Testng for asymmetrc nformaton Accordng to table 4, the frst estmaton results show that the correlaton between the error terms of the two bnary equatons s postve. Thus, the estmated value of s 0.16 for begnnng drvers. Ths assocaton s strong and sgnfcant wth a p-value of Hence, we fnd that polcyholders who purchase better coverage tend to be more prone to make clams. We therefore, fnd an evdence of asymmetrc nformaton, ether wth reference to adverse selecton or wth reference to moral hazard, especally when the observed varables are takng nto account The second estmaton results show that we agan fnd a postve correlaton between coverage-rsk for experenced drvers. The estmates value of s The p-value of, however, suggests that ths assocaton s not statstcally sgnfcant (= 0.963). Therefore, we fnd no evdence of adverse selecton or moral hazard. Ths result s consstent wth that of Sato (006). Table 3 provdes, also, the estmate of the rsk-coverage correlaton for begnnng drvers and experenced drvers. The negatve bnomal model gves us a smlar result as the probt bvarate model. For the begnnng drvers, the coeffcent of the coverage choce resdual varable s postve and statstcally sgnfcant, ths fndng clearly demonstrates that asymmetrc nformaton s present n the Tunsan automoble nsurance market. However, ths coeffcent becomes negatve and statstcally nsgnfcant for the experenced drvers. To sum up, all these results show no evdence of asymmetrc nformaton for experenced drvers and the exstence of evdence for begnnng drvers. Table 4. Bvarate Probt Estmaton Results Begnnng drvers Experenced drvers Independent Coeffcent p-value Coeffcent p-value Varables Choce of contractequaton Female Commercal use Age Age Age Age Age Job Job Job Job Job Job Orgn Orgn Orgn Orgn Orgn Orgn Zone Zone Zone Zone Zone Constant Accdent occurrenceequaton Female Commercal use Age Age Age Age Age

8 ISSN (onlne) ISSN (prnt) Medterranean Journal of Socal Scences MCSER Publshng, Rome-Italy May 015 Job Job Job Job Job Job Orgn Orgn Orgn Orgn Orgn Orgn Zone Zone Zone Zone Zone Constant Athrho Rho Number of obs Log lkelhood Wald ch(46) Prob>ch Lke lhood-rato test of rho=0 χ 1 = ( P > χ = χ () 1 = 0.00( P > χ = 0.963) () ) 6. Concluson In ths paper, we examned coverage-rsk relatonshp n the Tunsan automoble nsurance market usng a cross sectonal data from a major nsurer. We used the bvarate probt model and the negatve bnomal model to help descrbng any evdence of prvate nformaton. When analyzng the entre portfolo of polcyholders from the nsurer, all our procedures gve the same results. For the begnnng drvers, we found sgnfcant postve relatonshp between polcyholder s coverage choce and the occurrence of accdents, ndcatng the presence of adverse selecton. Ths relatonshp provdes evdence that some unobserved and unobservable factors affects the nsurance contract choce. Therefore, for the experenced drvers, asymmetrc nformaton seems to be at most a neglgble phenomenon n the nsurance automoble market. One major crtcsm of the condtonal correlaton approach wth cross sectonal data s that t does not allow separaton adverse selecton from moral hazard. Our analyss s lmted to a combned result of the two asymmetrc nformaton problems. However, as suggested by Abbrng et al. (003), dynamc data could help dstngush between the adverse selecton and moral hazard. Fnally, we leave ths as one of the future research drectons to pursue. Appendx 1. Characterstcs of the Drver Gender: 1 f the nsured s male (8.97%); 0 f the nsured s female (17.03%). Age: the age of the polcyholder (mean =45.49, std. dev. =13.9, mn= 18, max= 98). Age s categores : we use fve dummy varables Age 1 = 1 f the polcyholder have age between 18 and 1 years (0.47%); 0 otherwse. Age = 1 f the polcyholder have age between and 30 years (11.60%); 0 otherwse. Age 3 = 1 f the polcyholder have age between 31 and 55 years (66.86%); 0 otherwse. Age 4 = 1 f the polcyholder have age between 56 and 75 years (16.65%); 0 otherwse. Age 5 = 1 f the polcyholder s older than 75 years (4.4%); 0 otherwse. Job: For the job of the polcyholder, many possble classfcatons can be used to dstngush between professons for polcyholders. In ths study, we propose seven dchotomous varables defned as follows: 46

9 ISSN (onlne) ISSN (prnt) Medterranean Journal of Socal Scences MCSER Publshng, Rome-Italy May 015 Job 1 = 1 f the polcyholder s an offcal (1.1%); 0 otherwse. Job = 1 f the polcyholder s a senor executve (.78%); 0 otherwse. Job 3 = 1 f the polcyholder s an unemployed person (8.01%); 0 otherwse. Job 4 = 1 f the polcyholder s a craft (11.96%); 0 otherwse. Job 5 = 1 f the polcyholder s an employee (48.61%); 0 otherwse. Job 6 = 1 f the polcyholder s a retred person (5.49%); 0 otherwse. Job 7 = 1 f the polcyholder s a mddle manager (1.94%); 0 otherwse. - Resdence area varables: we defne 6 dchotomous varables to capture the effect of the mmedate envronment of the ndvdual drver. Zone 1 = 1 f the polcyholder lves n bg Tuns (8.35%); 0 otherwse. Zone = 1 f the polcyholder lves n North (1.45%); 0 otherwse. Zone 3 = 1 f the polcyholder lves n Northwest (10.83%); 0 otherwse. Zone 4 = 1 f the polcyholder lves n Coast (9.90%); 0 otherwse. Zone 5 = 1 f the polcyholder lves n Center (5.71%); 0 otherwse. Zone 6 = 1 f the polcyholder lves n South (1.76%); 0 otherwse. Characterstcs of the car - Use of the car = 1 f the polcyholder specfes the prmary use of the nsured car as for commutng and famly use (50.58%); 0 otherwse (.e., commercal use) (49.4%). Car brand: We defne seven categores that capture the car s country-of-orgn effect. Orgn 1 = 1 f the car made n France (58.81%); 0 otherwse. Orgn = 1 f the car made n Italy (1.6%); 0 otherwse. Orgn 3 = 1 f the car made n German (17.31%); 0 otherwse. Orgn 4 = 1 f the car made n Chna or n Korea or n Japan (9.9%); 0 otherwse. Orgn 5 = 1 f the car made n the USA (0.34%); 0 otherwse. Orgn 6 = 1 f the car made n England (0.8%); 0 otherwse. Orgn 7 = 1 f the car made n other countres (0.70%); 0 otherwse. Past nvolvement n accdents Accdents number: the number of accdent (mean = 0.07, std. dev. = 0.646, mn = 0, max=8). Bonus-malus classes: t s a dscrete varable. There are 8 classes from 1 to 8 (mean =5.845, std. dev. =.75, mn=0, max=8). Indemnty: t s a contnue varable (mean = 163, std. dev. = , mn = 0, max = ). References Abbrng J., Heckman J., Chappor P.A., and Pnquet J. (003): Adverse selecton and moral hazard n nsurance: Can dynamc data help to dstngush? Journal of the European Economc Assocaton, 1(-3), pp Chappor P.A. and Salané B. (000): Testng for Asymmetrc Informaton n Insurance Markets, Journal of Poltcal Economy, 108, pp Cohen A. (005): Asymmetrc nformaton and learnng: evdence from the automoble nsurance market, The Revew of Economcs and Statstcs, 87, pp Cohen A. and Segelman P. (010): Testng for Adverse Selecton n Insurance Markets, Journal of Rsk and Insurance, 77(1), pp Cutler D.M. and Reber S.J. (1998): Payng For Health Insurance: The Trade-Off between Competton and Adverse Selecton, The Quarterly Journal of Economcs, 113, pp Cutler D.M. and Zeckhauser R.J. (1998): Adverse Selecton n Health Insurance, Forum for Health Economcs & Polcy, Vol. 1: (Fronters n Health Polcy Research), Artcle. Dahlby B. (1983): Adverse Selecton and Statstcal Dscrmnaton: An Analyss of Canadan Automoble Insurance, Journal of Publc Economcs, 0, pp Dahlby B. (199): Testng for Asymmetrc Informaton n Canadan Automoble Insurance, Contrbutons to Insurance Economcs (Boston: Kluwer Academc Publshers), pp Donne G. and Ghal O. (005): The (199) Bonus-Malus System n Tunsa: An Emprcal Evaluaton, Journal of Rsk and Insurance, The Amercan Rsk and Insurance Assocaton, 7(4), pp Donne G., Gouréroux C. and Vanasse C. (001): Testng for Evdence of Adverse Selecton n the Automoble Insurance Market: A Comment, Journal of Poltcal Economy, 109, pp Donne G. and Vanasse C. (199): Automoble Insurance Ratemakng n the Presence of Asymmetrcal Informaton, Journal of Appled Econometrcs, 7, pp Donne G., St-Amour P. and Vencatachellum, D. (009): Asymmetrc nformaton and adverse selecton n Maurtan slave auctons, Revew of Economc Studes, 760 (4), pp

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