HARVARD John M. Olin Center for Law, Economics, and Business

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1 HARVARD John M. Oln Center for Law, Economcs, and Busness ISSN ASYMMETRIC INFORMATION AND LEARNING IN THE AUTOMOBILE INSURANCE MARKET Alma Cohen Dscusson Paper No /2002 Harvard Law School Cambrdge, MA Ths paper can be downloaded wthout charge from: The Harvard John M. Oln Dscusson Paper Seres: The Socal Scence Research Network Electronc Paper Collecton:

2 Asymmetrc Informaton and Learnng n the Automoble Insurance Market Alma Cohen Abstract Ths paper tests the predctons of adverse selecton models usng data from the automoble nsurance market. In contrast to what recent research has suggested, I fnd that the evdence s consstent wth the presence of nformatonal asymmetres n ths market: hgher nsurance coverage s correlated wth more accdents. Consstent wth the presence of learnng by polcyholders about ther rsk type, such a coverage correlaton exsts only for polcyholders who have had three or more years of drvng experence pror to jonng ther nsurer. Consstent wth the presence of learnng by nsurers about repeat customers, I fnd that, as the experence of the nsurer wth a group of polcyholders ncreases, the coverageaccdents correlaton declnes n magntude and eventually dsappears. Fnally, consstent wth nsurers havng more nformaton about ther repeat customers than would be avalable to other nsurers, I fnd that polcyholders who leave the nsurer are dsproportonately ones wth a poor clams hstory wth the nsurer, and that nsurers make hgher profts on repeat customers than on new customers. JEL classfcaton: D40, D80, D82, D83, L10, G22. Keywords: Asymmetrc nformaton, adverse selecton, screenng, sortng, moral hazard, nsurance, deductble, learnng, nformaton transmsson, repeat customers. Copyrght 2002 Alma Cohen all rghts reserved. Postdoctoral Fellow, Natonal Bureau of Economc Research; John M. Oln Research Fellow n Law, Economcs, and Busness Ths paper s based on a chapter of my doctoral dssertaton at Harvard Unversty. I gratefully acknowledge the valuable comments of Lucan Bebchuk, Gary Chamberlan, Davd Cutler, Rajeev Deheja, Rchard Derrg, George Donne, Lran Enav, Shgeo Hrano, Carolne Hoxby, Tore Nlssen, Arel Pakes, Danel Paserman, Jack Porter, Robert Puelz, Arthur Snow, Manuel Trajtenberg, Rchard Zeckhauser, Davd Wse, and partcpants n semnars at Harvard, Hebrew Unversty, the Herzla Interdscplnary Center, Tel-Avv Unversty, the NBER, and the annual meetng of the Rsk

3 1 Introducton Ever snce the semnal works of Akerlof (1970) and Rothschld and Stgltz (1976), economc theorsts have devoted much effort to developng models of adverse selecton. Ths paper seeks to test the predctons of these models usng data from the market for automoble nsurance. The paper uses a unque and rch data set that I obtaned from an nsurer operatng n the automoble nsurance market n Israel. Because the data ncludes all the nformaton known by the nsurer about ts polcyholders, t s especally fttng for studyng adverse selecton. The data ncludes the nsurer s nformaton about more than 200,000 polces ssued durng a fve-year perod. In partcular, the data contans () all the characterstcs (ncludng past clams hstory) of polcyholders known to the nsurer, () the prce-deductble menus offered to polcyholders and the choces made by them, and () the clams and payments resultng from each polcy. When polcyholders have prvate nformaton about ther rsk type, adverse selecton models predct that hgh-rsk types wll purchase hgher nsurance coverage. Consstent wth ths predcton, I fnd that polcyholders wth low deductbles are assocated wth more accdents and hgher total losses to the nsurer. I also fnd that subsets of the pool of all polces dffer systematcally n how strong the correlaton s (or even n whether t exsts). The dentfed dfferences are consstent wth the presence of learnng by polcyholders and by nsurers. As to the learnng by polcyholders, I fnd that, for polcyholders wth lttle or no drvng experence, low deductbles are not assocated wth more accdents. Such polcyholders mght have had relatvely lttle opportunty to obtan prvate nformaton about ther rsk type and thereby to gan an nformatonal advantage over the nsurer. However, such an assocaton does exst for polcyholders that have suffcent drvng experence. Furthermore, drvng experence pror to jonng the nsurer mght be especally helpful n provdng polcyholders wth an nformatonal advantage over the nsurer; consstent wth ths possblty, I fnd that the coverage-accdents correlaton exsts only for polcyholders who had three or more years of drvng experence pror to jonng the nsurer. As to the learnng by the nsurer, I fnd evdence that the correlaton between low deductbles and more accdents s especally strong for new customers or ones who have been wth the nsurer for a relatvely short perod. For repeat customers, ths correlaton dmnshes n magntude over tme and eventually dsappears. Theory Socety. I also wsh to thank the IDI Company for the data and Sha Fogel, ts CEO, for very helpful dscussons about the company and ts market. 1

4 When a polcyholder has stayed wth the nsurer for a suffcently long perod, the nsurer s experence wth the polcyholder mght erode whatever nformatonal advantage the polcyholder mght have had when jonng the nsurer. The above fndngs concernng a coverage-accdents correlaton address questons rased by recent research. Chappor and Salane (2000) suggest that the evdence s nconsstent wth a coverage-accdents correlaton n the market for automoble nsurance. Also studyng ths market, Donne, Gouréroux and Vanasse (2001) suggest that the evdence s nconsstent wth resdual adverse selecton n each of the rsk classes formed on the bass of parameters known to the nsurer. The fndngs of these studes have already had a sgnfcant mpact. In the materals accompanyng the award of the Nobel Prze for work on asymmetrc nformaton, the Swedsh Royal Academy of Scence (2001) cted the Chappor - Salane fndngs as a reason for vewng the evdence on the presence of asymmetrc nformaton n markets as mxed. These fndngs also provded motvaton for the recent work of De Meza and Webb (2001), who develop a model of nsurance markets wth asymmetrc nformaton that does not predct an assocaton between nsurance coverage and accdents. In contrast to ths recent emprcal work, usng a data set that s more complete than the data used n pror work, I obtan robust results that are overall consstent wth the coverage-correlaton predcton of classc adverse selecton theory. My fndngs confrm that such correlaton does not exst for the subset of polces on whch the Chappor-Salane study focused those sold to polcyholders wth less than three years of drvng experence. My fndngs, however, also ndcate that ths result does not carry over to polcyholders wth three or more years of drvng experence who account for a substantal majorty of all polcyholders. In addton to nvestgatng nformatonal asymmetres between polcyholders and ther nsurer, I also examne whether nsurers obtan an nformatonal advantage wth respect to ther repeat customers over rval nsurers. In the nsurance market that I study, as s the case n the US, when a polcyholder swtches to a new nsurer, the new nsurer would not receve from the current nsurer nformaton about the pror nsurer s experence. The nformaton that the new nsurer would have from the customer s own reportng, from nferences drawn from the customer s makng a swtch, or from publc sources can be expected to be less complete than the clam hstory nformaton possessed by the current nsurer. I fnd that the evdence s ndeed consstent wth such dfferences n nformaton among nsurers. In partcular, I fnd that the performance of swtchers s worse than what would be predcted f ther self-reports of past clams were assumed to be as relable as the nsurer s records about ts own repeat customers. Also, I fnd that polcyholders 2

5 who leave the nsurer are dsproportonately ones who had a bad record wth the nsurer and who thus could beneft from swtchng to an nsurer that would know less about them. Polcyholders who reman wth the nsurer, n turn, are dsproportonately ones wth a good past clams record and ones that subsequently perform better than new customers. Furthermore, consstent wth nsurers obtanng prvate nformaton and thus market power wth respect to repeat customers wth good records, I fnd that the nsurer makes hgher profts on repeat customers than on new customers. It should be noted that, whle a coverage-accdents correlaton s consstent wth adverse selecton models, t s also consstent wth moral hazard models. Under a moral hazard story, a correlaton between low deductbles and more accdents can be expected because polcyholders wth hgher nsurance coverage wll have lower ncentve to take precautons. Thus, my fndngs concernng the exstence of coverage-accdents correlaton ndcate only that the presence of adverse selecton cannot be rejected. Because adverse selecton and moral hazard both produce a correlaton between coverage and accdents, dsentanglng them emprcally s wdely vewed as dffcult (Royal Academy of Scence (2001)). Puttng asde the coverage-accdents correlaton, whch can be easly explaned under both adverse selecton and moral hazard stores, some of my other fndngs concernng the dynamcs of behavor over tme do not appear readly explanable by a standard moral hazard story. Dsentanglng adverse selecton and moral hazard, however, s beyond the scope of the present study. The analyss of ths paper s organzed as follows. Secton 2 descrbes the predctons of adverse selecton models that I wll test. Secton 3 dscusses pror emprcal work. Secton 4 descrbes the data used for the study. Secton 5 conducts tests concernng the predcton of coverage-accdents correlaton. Secton 6 tests varous predctons concernng learnng and behavor over tme. Fnally, Secton 7 concludes. 2 Tested Predctons 2.1 Coverage-Accdents Correlaton As s common, the nsurer whose data I use offers a menu wth dfferent levels of deductble (and assocated levels of premum). Polcyholders that choose dfferent deductbles must be dfferent. They mght dffer n ther rsk-averson, 1 and such 1 One possble reason for havng deductbles s to elmnate coverage for small clams that would produce admnstratve costs (whch are ultmately borne by polcyholders) but would 3

6 dfferences would not affect the costs of ther polces to the nsurer. They also mght dffer n the rsks that they face; such dfferences n rsk, of course, would affect the costs of ther polces to the nsurer. The coverage choces made by ndvduals that have prvate nformaton about ther rsk type have been studed by the semnal work of Rothschld-Stgltz (1976) and subsequent work (e.g., Rley (1979), Spence (1978), Myazak (1977), Wlson (1977), and Grossman (1979)). 2 One basc predcton of these models s that, n the presence of such prvate nformaton, a menu of dfferent deductbles wll result n sortng, wth hgh-rsk polcyholders more lkely to choose low deductbles. 3 I therefore wll test the followng hypothess: H1: Polcyholders that choose lower deductbles wll be assocated wth more accdents. 2.2 Learnng and Polcyholders Informatonal Advantage over the Insurer The predcton of a coverage-accdents correlaton arses from models that assume that polcyholders have an nformatonal advantage over the nsurer wth respect to the polcyholders rsk type. Whether and to what extent such nformatonal asymmetres exst mght well depend on the learnng of nformaton by the polcyholder and by the nsurer over tme. One type of possble learnng s by polcyholders. Whle nature accurately knows any ndvdual s rsk-type, the ndvdual mght well be mperfectly nformed about ths rsk-type when gettng a drvng lcense. It s plausble to assume that there s a lmt to how much an ndvdual can learn about the ndvdual s rsk-type by mere ntrospecton,.e., wthout actual experence wth drvng. Thus, the more drvng experence a polcyholder has, the more nformaton the polcyholder s lkely to obtan about the polcyholder's rsk type. Thus, other thngs equal (ncludng how long polcyholders have been wth the nsurer), the more drvng experence a group of polcyholders has, the more lkely t s that the group wll exhbt a coverageaccdents correlaton. provde only mnmal beneft n terms of savng rsk-bearng costs to the polcyholder. Focusng solely on consderatons of rsk-bearng costs and admnstratve costs, the greater an ndvdual s degree of rsk-averson, the lower the optmal deductble for ths ndvdual. 2 For excellent recent surveys of adverse selecton models, see Rley (2001), who surveys such models n general, and Donne, Doherty, and Fombaron (2000), who focus on adverse selecton models of nsurance markets. 3 These models also analyze the optmal choces of menus that nsurers wll make n equlbrum. The predcton that a menu wll result n hgh-rsk types choosng more coverage wll arse, however, even f the menus offered are not optmally set. 4

7 I just dscussed the potental effect of the polcyholder s drvng experence holdng constant other varables ncludng the experence of the nsurer wth the polcyholder. Ths suggests that t s useful to dstngush, as s done n the dagram below, between two perods: () the perod (f any) durng whch a polcyholder was drvng pror to jonng the nsurer.e., durng whch the polcyholder ganed experence wth drvng but wthout the nsurer ganng experence wth the polcyholder, and () the perod (f any) durng whch the polcyholder has been wth the nsurer.e., durng whch both the polcyholder has been ganng drvng experence and the nsurer has been obtanng experence wth the polcyholder. Polcyholder gets drvng lcense Polcyholder jons the studed Tme of observaton Tme Learnng by polcyholder Learnng by polcyholder and studed nsurer Durng the frst perod () n whch the polcyholder drove pror to jonng the nsurer, the realzaton of rsks produced by the polcyholder s drvng was observed by the polcyholder and often also by the polcyholder s nsurer at the tme (as wll be presently dscussed) but not by the studed nsurer. As wll be dscussed below, n the market I study (and often n other nsurance markets as well), nsurers generally do not get ether from pror nsurers of new customers or from self-reportng by such customers a complete and accurate pcture of the past clams hstory of these customers. Thus, drvng experence durng the perod pror to jonng the nsurer mght provde the polcyholder wth an nformatonal advantage over the nsurer. The more drvng experence a new polcyholder had before jonng the nsurer, the greater the lkely asymmetry of nformaton between the polcyholder and the nsurer. Accordngly, the hypothess that I wll test s: H2: The more experence a group of polcyholders had pror to jonng the nsurer, the stronger (or more lkely to exst) the correlaton n ths group between low deductbles and more accdents. Durng the second perod the perod f any between the tme n whch the polcyholder joned the nsurer and the tme of observaton -- nformaton about the 5

8 realzaton of rsks has flown to both the polcyholder and the nsurer. Although there mght be some prvate nformaton receved by the polcyholder even durng ths perod, exstng models have assumed that new nformaton arrvng durng ths perod has been by and large observed by both the polcyholder and the exstng nsurer (see, e.g., Kunreuther and Pauly (1985), Watt and Vazquez (1997)). Under ths assumpton, the Bayesan updatng that each sde wll do wll work to reduce whatever nformatonal asymmetry the polcyholder had when jonng the nsurer. The reason for ths s that, when a polcyholder has an nformatonal advantage when jonng the nsurer, the nformatonal beneft from observng the subsequent realzaton of rsks wll be greater for the nsurer than for the polcyholder. Indeed, assumng that after a polcyholder jons an nsurer they both observe all realzaton of rsks, Watt and Vazquez (1997) prove that, for any gven nformatonal asymmetry that the polcyholder has when jonng, the asymmetry wll go to zero after a suffcently long perod wth the nsurer. Thus, under the consdered story, the longer the perod that a group of polcyholders has been wth the nsurer, the less lkely t s that polcyholders wll have an nformatonal advantage over the nsurer even f they had such an advantage when jonng the nsurer. Accordngly, the hypothess that I wll test s: H3: The more experence the nsurer has had wth a group of polcyholders, the weaker (or less lkely to exst) the correlaton n ths group between low deductbles and more accdents. 2.3 Learnng and Dfferences n Informaton among Insurers The nformaton that an nsurer learns about ts repeat customers mght create a dfference n nformaton between the nsurer and other nsurers to whch these customers mght subsequently turn. Of course, f the repeat customer does turn to another nsurer, ths other nsurer wll ask the customer to report past clam hstory. However, there s evdence that such self-reportng s often substantally ncomplete or naccurate (Insurance Research Councl (1991)). Furthermore, there s evdence that most of the accdents for whch clams are submtted do not appear n publc records and new nsurers thus cannot learn about them from nspectng publc records (Insurance Research Councl (1991)). Fnally, n the Israel market I study, as n the US market, nsurers do not provde nformaton about ther experence wth polcyholders to other nsurers. 4 Therefore, a new nsurer would lkely have an 4 Fombaron (1997b) and de Gardel (1997) study the dfference between the cases n whch nsurers are and are not requred to provde a new nsurer wth all the nformaton that they have wth respect to departng customers, and they also examne the desrablty of requrng 6

9 nformatonal dsadvantage compared wth a repeated customer s ncumbent nsurer. To be sure, a new nsurer could draw nferences from the fact that a new customer has decded to swtch from the customer's pror nsurer. If all swtchers were ones wth a bad record, the nsurer could have nferred that such a swtcher must have such a record. But n a world n whch some polcyholders change nsurers for other reasons (say, relocaton or dssatsfacton wth some servces of the nsurer or the ntermedatng nsurance agent), an nsurer generally would not be able to nfer fully a new customer's past clams record from the customer s decson to swtch. In partcular, when a customer who n fact has a bad past record swtches to another nsurer, ths other nsurer would not be able to tell for sure that whether the swtch has been motvated by the customer's bad past record or by other reason. Ths adverse selecton story wth nformatonal dfferences among nsurers yelds several testable hypotheses. To start, ths story mples that reports of past clams provded by polcyholders swtchng to the nsurer from other nsurers wll be less complete than the records that the nsurer has about the past clams of ts repeat customers. Accordngly, I wll test the followng hypothess: H4: New customers who report a gven past clams hstory wll perform n the future less well than repeat customers for whom the nsurer has observed such a past clams hstory. Furthermore, although some polcyholders wll leave the nsurer each year for reasons that have nothng to do wth ther record wth the nsurer, some wll leave because of the poor record they have wth the nsurer. Because new nsurers wll be unable to tell that a swtch was motvated by such a poor record, customers wth a bad record wth an nsurer mght have somethng to gan from swtchng to a new nsurer. Accordngly, I wll test the followng hypothess: H5: Polcyholders that leave the nsurer wll be dsproportonately ones wth a poor past clams record Learnng and the Prcng of New and Repeat Customers Turnng to the subject of the prcng of customers over tme, note that substantal work has been done on developng mult-perod models of adverse selecton. Some of these models have focused on the optmal desgn of polces that nsurers to do so. In the market under consderaton, such a requrement s not establshed by law or by agreement among nsurers, and nsurers do not share nformaton about customers. 7

10 commt customers to a mult-perod contract (e.g., Donne (1983), Donne and Lasserre (1985), Cooper and Hayes (1987)) or that nvolve a one-sded commtment of the nsurer to offer the polcyholder certan terms n subsequent perods (Donne and Doherty (1994), De Gardel (1997)). Although such polces are observed n certan countres (see, e.g., Donne and Vanasse (1992)), many nsurance markets use only one-perod polces that nvolve no commtments on the part of ether the customer or the nsurer (Kunreuther and Pauly (1985)). In partcular, ths s the case for all the nsurers operatng n the Israel automoble nsurance market, ncludng the nsurer whose data I study. For our purposes, then, the relevant models are the no-commtment models that were developed by Kunreuther and Pauly (1985), Fombaron (1997), and Nlssen (2000). The nformatonal advantage that nsurers obtan over competng nsurers wth respect to ther repeat customers, whch was dscussed earler, plays an mportant role n these models. When an nsurer has an nformatonal advantage over rval nsurers wth respect to the nsurer s repeat customers, the nsurer wll have market power wth respect to repeat customers that the nsurer has dentfed to be low-rsk types. As a result, the nsurer wll be able to charge these customers more than the break-even prce reflectng ther low rsk, as these customers wll be unable to obtan ths break-even prce from other nsurers to whch the customers low-rsk type would not be known for sure. Relatedly, the above dynamc models also predct lowballng wth respect to new customers. When a new customer jons an nsurer, the nsurer wll antcpate the possblty of chargng more than the break-even prce down the road n the event that the customer turns out to be a low-rsk type. Therefore, the nsurer mght be wllng to charge new customers n ther frst perod less than the break-even prce reflectng ther rsk. Insurers thus can be expected to over-charge repeat customers (relatve to the prce that would reflect ther rsk accordng to the nsurer s nformaton) and, furthermore, mght under-charge new customers (compared wth the prce that would reflect ther rsk). Therefore, nsurers can be expected to make hgher profts and therefore have a lower loss rato (.e., rato of nsurance payments to prema) 5 on repeat customers than on new customers. Ths yelds the last hypothess that I wll test: H6: The nsurer s loss rato wll be lower for repeat customers than for new customers. 5 Loss rato s the standard measure of proftablty of polces used by nsurers. The loss rato on a gven polcy s equal to the nsurer s total payments for clams arsng from the polcy dvded by the total premum receved from the polcyholder. (See Appendx II for a formal specfcaton.) 8

11 3 Pror Emprcal Work 3.1 Exstence of Asymmetrc Informaton Evdence consstent wth adverse selecton and coverage-rsk correlaton has been found n some studes of nsurance markets. Surveyng the evdence on the health nsurance market, Cutler and Zeckhauser (2000) conclude that, n ths market, adverse selecton s present and quanttatvely large. 6 Furthermore, Fredman and Warshawsky (1990), Bruggavn (1993) and, most recently, Fnkelsten and Poterba (2000) have found evdence consstent wth adverse selecton n the annuty market. However, wth respect to the market for automoble nsurance, recent work has argued that the evdence s nconsstent wth the presence of adverse selecton. 7 A man focus of pror work about the automoble nsurance market has been on testng the predcton that hgher nsurance coverage s correlated wth more accdents. Three ntal studes suggested the presence of adverse selecton, but ther fndngs were crtczed by subsequent research as unrelable. Dahlby (1983) and Dahlby (1992), the frst two studes on the subject, dd not have ndvdual data on coverage. Puelz and Snow (1994) dd use ndvdual data obtaned from a Georga nsurer, but subsequent work questoned ther results. Although Puelz and Snow had ndvdual data, they dd not have some of the varables affectng rsk type such as the polcyholder s years of drvng experence and the polcyholder s past clam hstory that the nsurer had. In contrast, my data ncludes all the nformaton about ndvdual polcyholders known to the nsurer. Donne, Gouréroux, and Vanasse (2001) recently rased another objecton to the Puelz-Snow study. They suggest that the nsurer s rsk classfcaton s suffcent (n the sense that there s no resdual adverse selecton n each rsk class n the nsurer s portfolo) once nonlnear effects, not consdered by Puelz and Snow, are taken nto account. To address the problem suggested by these authors, I checked the robustness of my results by controllng for the suggested non-lnearty bas n unreported regressons, and I obtaned the same robust results throughout. 6 One notable excepton n ths area s Cardon and Hendel (2001), who fnd no evdence of adverse selecton n ther study of the health nsurance market. 7 Recent work (Cawley and Phlpson (1999)) has also questoned whether adverse selecton exsts n the market for lfe nsurance. 9

12 Chappor and Salane (1997, 2000) suggest that the correlaton between deductble choce and rsk type should be tested usng bvarate probt. Chappor and Salane (2000) apply ths test to French data. Two knds of nsurance coverage are offered n France, and the authors tested whether ndvduals who bought hgher coverage turned out to be rsker. Fndng no such correlaton, they nferred that the exstence of adverse selecton n ths market can be rejected. The testng done by ths study, however, was lmted to polcyholders wth no more than two years of drvng experence. Thus, the study tested the exstence of coverage-correlaton correlaton only among begnnng drvers who consttute a small subset of all polcyholders. The absence of such correlaton n the case of such drvers, who have had lttle opportunty to develop through drvng experence an nformatonal advantage over the nsurer, does not necessarly mply that such correlaton does not exst among other drvers. In my analyss I conduct tests wth respect to the whole pool of polces as well as separately for begnnng and more experenced drvers. As wll be dscussed n detal later, my analyss confrms the Chappor-Salane fndng that correlaton between coverage and accdents does not exst for begnnng drvers. The analyss ndcates, however, that such correlaton does exst wth respect to polcyholders drvers wth more than two years of drvng experence and, because such polcyholders consttute a very large majorty, also for the pool of all polces. 3.2 Learnng There has been relatvely less emprcal work on learnng over tme about polcyholders rsk type. 8 The studes that conducted testng for the presence of coverage-accdents correlaton n a large pool of polces have commonly not broken the pool nto subsets based on the experence of the nsurer wth the customer or on the drvng experence of the nsurer. For example, Puelz and Snow (1994) and Donne, Gouréroux, and Vanasse (2001), whch have reached opposte results concernng the exstence of correlaton n a general pool of polces, have not examned how ther results hold for subsets of the pool defned by nsurer or polcyholder experence. As wll be seen, n the data that I examne, such subsets dffer n whether and to what extent a coverage-accdents correlaton exsts. There has been some work on the temporal pattern of profts on new and repeat customers n ths market. The two studes that consdered t (D Arcy and Doherty 8 Because my focus s on asymmetrc nformaton about polcyholders rsk type, the learnng on whch I focus concerns nformaton about customers rsk type. Another type of learnng that mght go on when polcyholders stay wth the same nsurer concerns learnng by polcyholders about the qualty of the nsurer s servces (Israel (2001)). 10

13 (1990) and Donne and Doherty (1994)) reached opposte conclusons (one suggestng lowballng wth respect to new customers and one suggestng hghballng wth respect to such customers). In contrast to ths paper, these two studes reled on aggregate data. As dscussed, one of the elements that I wll study s the possblty that durng the perod n whch a polcyholder stays wth an nsurer, the nsurer and the polcyholder wll by and large receve the same nformaton about accdents occurrng n that perod. It s worth notng n ths connecton the recent work by Hendel and Lzzer (2001) about the market for lfe nsurance. They fnd evdence that s consstent wth symmetrc learnng takng place after a polcyholder jons an nsurer. 9 4 The Data 4.1 The Insurer and ts Records The paper s based on data that I receved from an nsurer that operates n the market for automoble nsurance n Israel. The nsurer started sellng nsurance polces n November 1994, and the data I receved covers the subsequent fve years of operaton. The nsurer s share of the total market of automoble nsurance n Israel durng ths perod was on the order of 5%. The data contans nformaton about 216,524 polces and about 111,138 dfferent polcyholders (some polcyholders bought polces n two or more years). The data ncludes all the nformaton that the nsurer had about each of these polces. Each observaton has the followng varables wth respect to the polcyholder: (the lst of all varables appears n Appendx I): (1) Polcyholder s demographc characterstcs: age, educaton, gender, famly status, place of brth, mmgraton year, and place of resdence; (2) Polcyholder s car characterstcs: sze of engne, model year, value of the car, value of the rado, commercal vehcle or not, man vehcle or not, type of protecton aganst theft; (3) Polcyholder s drvng characterstcs: years snce gettng drvng lcense, number of clams n the past three years, young drver or not, age of young drver, 9 In contrast to the automoble nsurance market that I study, the lfe nsurance market commonly nvolves one-sded commtment by nsurers, whch commt to the level of prema n the event that the polcyholder wll elect to stay n future perods. Hendel and Lzzer fnd evdence that actual contract have front loadng, whch s what s predcted for contracts wth one-sded commtment and learnng over tme. Because the market I study nvolves one-perod contracts wth no commtment, learnng n ths market has dfferent mplcatons. 11

14 gender of young drver, lcense years of young drver, whether the polcyholder had nsurance n the past, addtonal drvers (f any); (4) Menu of contract terms offered: the company offered four deductble-premum alternatves low-deductble, regular-deductble, hgh-deductble, and very-hghdeductble contracts -- whch wll be descrbed n detal n subsecton 4.2 below; (5) Deductble choce: what deductble (and accompanyng premum) was chosen by the polcyholder; (6) Perod covered: the length of the perod covered by the purchased polcy (whch was usually one year); and (7) Realzaton of rsks covered by the polcy: the number of clams submtted by the polcyholder and a descrpton of each submtted clam, ncludng the amount of damages reported and the amount that the nsurer pad or was expected to pay. Table 1 dsplays descrptve statstcs of the varables. I also receved from the nsurer the estmate that, when calculatng ts costs, the nsurer used for the average admnstratve costs nvolved n processng a clam. In testng for dfferences n profts on new and repeat customers, I ncluded these estmated costs of processng clams n calculatng the nsurer s total costs. Because these processng costs were estmates and not hard number lke the other varables, I checked n all cases whether the reported results hold gnorng these estmated costs and I found that the results dd hold The Deductble-Premum Menu Israel nsurers are allowed to develop ther own formula for determnng nsurance prema, provded that they submt them for approval by the nsurance regulator. The factors that the regulator does not allow nsurers to use n settng the premum are place of brth, place of resdence, occupaton, and educaton. The nsurer under study attempted to take nto account n ts prcng decsons all the nformaton that t was permtted to use. The nsurer offered ts potental customers a menu of contract choces after frst obtanng from them all the nformaton descrbed n subsecton 4.1. The potental customer was then gven a menu of four premum-deductble contracts. One opton, whch was labeled regular by the company, offered a regular deductble and a regular premum. The term "regular" was used for ths deductble level both because t was relatvely smlar to the deductble levels offered by other nsurers and because t was chosen by most polcyholders. The regular premum was a functon of all the characterstcs of the polcyholder used n the nsurer's formula. The regular deductble was set at the level of 50% of the (regular) premum that was 12

15 assocated wth the regular deductble, except that the regular deductble was capped at 1400 New Israel Shekels (NIS) (about $350 durng the consdered perod). The three other prce-deductble contracts ncluded n the menu offered to potental customers were: 1) a low deductble, set at 60% of the level of the regular deductble, comng wth a premum equal to 1.3 tmes the level of the regular premum; 2) a hgh deductble, set at a level equal to 1.8 tmes the level of the regular deductble, comng wth a premum equal to 0.7 tmes the regular premum; and 3) a very hgh deductble, set a level equal to 2.6 tmes the level of the regular deductble, and comng wth a premum equal to tmes the regular premum. Because I dd not have an access to the company s formula for determnng prema, I regressed the regular premum quoted to each customer on all the customer s characterstcs that the company was allowed to use n ts formula to test how well a lnear regresson can explan the premum. The regresson, whch appears n Table 2, has an R 2 of 0.71, whch ndcates that a lnear model can be used nstead of the actual formula Summary Statstcs Table 3 provdes summary statstcs for the whole perod covered by the data. The table ndcates that, compared wth regular-deductble polcyholders, lowdeductble polcyholders have hgher clam frequency and loss rato, and polcyholders wth hgh or very hgh deductbles have lower clam frequency and loss rato. Snce only a very small fracton of the customers chose hgh or very hgh deductbles (apparently the company dd not prce them low enough to make them attractve), my focus below wll be on dfferences between low-deductble and regular-deductble polcyholders. Polcyholders who chose low deductbles had a larger ncdence of one or more clams durng the lfe of the polcy. For example, 28% of low-deductble polcyholders had at least one clam, whereas only 21% percentage of regular-deductble polcyholders had at least one clam. Note that low-deductble polcyholders were able to fle clams also for accdents whose damages were too small to clam under polces wth a regular, hgh, or very hgh level of deductble. Thus, t s useful to compare low-deductble and regular-deductble polcyholders n terms of the number of clams of a type that can be submtted by both groups of polcyholders. The data ndcates that, countng 10 Most of the regressons below use all the characterstcs of the polcy as covarants. For robustness check, n unreported regressons I used the regular premum nstead of the characterstcs of the polcy, and I obtaned results that were smlar n terms of both sgnfcance and magntude throughout. 13

16 only clams for damages exceedng the level of the regular deductble (clams that could be submtted by both low-deductble and regular-deductble polcyholders), the percentage of polcyholders flng such clams s sgnfcantly hgher for lowdeductble polcyholders than for regular-deductble polcyholders. Smlarly, countng only clams for damages exceedng 1.5 and 2 tmes the level of the regular deductble, the percentage of polcyholders flng such clams s also sgnfcantly hgher for low-deductble polcyholders than for regular-deductble polcyholders. 5 Are Lower Deductbles Correlated wth Hgher Rsks? The summary statstcs presented n secton 4 are consstent wth the predcton that low-deductble polcyholders are assocated wth hgher clam frequences and hgher losses for the nsurer (hypothess H1). Ths secton tests ths predcton. I contnue to focus on dfferences between low-deductble and regular-deductble polcyholders because, as noted, the overwhelmng majorty of polcyholders n the data belong to these two groups, wth less than 2% choosng hgh or very hgh deductbles. 5.1 Testng for Coverage-Accdents Correlaton I start by comparng low-deductble and regular-deductble polcyholders n terms of the number of clams submtted. As noted earler, ths comparson should focus on clams that can be submtted by both types of polcyholders. If we were to count all clams reported by low-deductble polcyholders, then we would expect to fnd more clams submtted by low-deductble polcyholders even f the two groups dd not at all dffer n ther rsk type; ths would happen because low-deductble polcyholders can submt clams wth respect to a larger range of accdents. Below I therefore compare these two groups n terms of clams that exceed the level of regular deductbles and thus can be submtted by polcyholders n both groups. As wll be noted below, the results hold also when makng the comparsons n terms of clams exceedng certan hgher thresholds. I frst tested for a correlaton between low deductbles and more accdents usng OLS specfcaton. For the set of all the polcyholders choosng ether low or regular deductble, I regressed the number of clams exceedng the regular deductble on all the characterstcs of the polcyholder and the vehcle and on a dummy varable representng whether a regular or a low deductble was chosen. I ran ths regresson for the whole pool of polces and also separately for the polces n each of the nsurer s fve years of operaton. 14

17 The results, whch are dsplayed n Table 4, ndcate that the number of clams exceedng the regular deductble s hgher (at the 1% confdence level) for lowdeductble polcyholders than for regular-deductble polcyholders. Ths s the case both for the whole pool and for each of the fve years of operatons. For the whole pool, low-deductble polcyholders had on average 0.03 clams more than regulardeductble polcyholders (at the 1% confdence level). Ths dfference s sgnfcant relatve to the average number of clams that exceeded the regular deductble for ether low- or regular-deductble polces. The average number of clams exceedng the regular deductble was 0.23 for low-deductble polcyholders and 0.18 for regular-deductble polcyholders (see Table 1). Low-deductble polcyholders have about 20% more such clams than regular-deductble polcyholders n each of the fve years ncluded n the data. The second test that I used s the bvarate probt recommended and used by Chappor and Salane (2000). The bvarate probt estmates the correlaton ρ between the error terms of two bnary equatons. These two equatons are the choce of the deductble on the polcyholder s characterstcs and the occurrence of at least one clam on the polcyholder s characterstcs. If the error terms of the two equatons are ndependent, then ρ wll be equal to 0. The results, whch are shown n Table 5, provde an estmate for ρ that s negatve, statstcally sgnfcant (at the 1% confdence level) and equal to Thus, the hypothess that the two equatons are ndependent can be rejected. In addton to the above two tests, I also used other specfcatons. In partcular, I used Posson dstrbuton for the number of accdents, a logt dstrbuton for a varable that was equal to 1 f the polcyholder had an accdent and 0 otherwse, and a smlar probt test. In all cases, the results were smlar both n drecton and n magntude. Fnally, t mght be argued that regular-deductble polcyholders mght sometmes be reluctant to submt clams for accdents whose damage exceeds the regular deductble but just barely. They mght elect not to submt such clams, so the argument goes, n order to avod the transacton costs nvolved n submttng a clam and/or to avod havng a clam n ther record that mght lead to an ncrease n the premum n subsequent years (see Hosos and Peters (1989)). To ensure that the above results are not vulnerable to ths problem, I dd the tests dscussed above also for clams exceedng 1.5 tmes the level of the regular deductble as well as for clams exceedng 2 tmes the level of the regular deductble. In both cases I obtaned smlar results, namely that the number of clams exceedng the used threshold s hgher (at the 1% confdence level) for low-deductble polcyholders than for hghdeductble polcyholders. It s worth notng that I followed a smlar procedure of usng alternatve, hgher thresholds also for all the other tests n ths paper that 15

18 nvolve the number of clams, and I obtaned smlar results throughout; all of the results reported below are thus robust to ths problem. 5.2 Losses from Accdents I now turn to comparng low-deductble and regular-deductble polcyholders n terms of the costs to the nsurer produced by clams exceedng the regular deductble. I regressed the total nsurance payments made by the nsurer n connecton wth such clams on all the characterstcs of the polcyholder and on a dummy varable reflectng whether a regular or low deductble was chosen. The regressons, whch are dsplayed n Table 4, ndcate that such total nsurance payments are hgher (at the 1% confdence level) for low-deductble polcyholders. Ths result holds for the whole pool and for each of the fve years n the data. The regresson ndcates that the nsurer s total nsurance payments n connecton wth clams exceedng the regular deductble was hgher (at the 1% confdence level) for low-deductble polcyholders than for regular-deductble polcyholders by NIS (~$58-$78). Ths ncrease s roughly equal to 20% of the average level of total nsurance payments among regular-deductble polcyholders. 5.3 Begnnng vs. Experenced Drvers As dscussed earler, Chappor and Salane (2000), studyng the performance of polcyholders wth less than three years of drvng experence, found no coverageaccdents correlaton for such polcyholders. Below I explore source for the dfference between ths result and the results obtaned above for the pool of all polcyholders. In partcular, I examne whether n my data the results are dfferent for the relatvely small subset of polcyholders wth lttle drvng experence. To examne ths possblty, I frst regressed (n unreported regressons) the number of clams on the deductble level controllng for all the other varables separately for polcyholders wth less than three years of drvng experence and for polcyholders wth three or more years of such experence. I found that the coeffcent of the deductble was not sgnfcant for the frst group of begnnng drvers but was negatve and sgnfcant (at the 1% confdence level) for the second group of more experenced drvers. I also ran the bvarate probt test used by Chappor and Salane (2000) separately for polcyholders wth less than three years of drvng experence and for polcyholders wth three or more years of such experence. For polcyholders wth less than three years of drvng experence, I found (see Table 6, columns 1 and 2) 16

19 that the correlaton between the error terms of the two bnary equatons, ρ, has a postve value of that s not statstcally sgnfcant (wth a standard error of 0.059). The non-exstence of statstcally sgnfcant correlaton for ths subset of my data s consstent, of course, wth the fndngs of Chappor and Salane who studed polcyholders wth less than three years of drvng experence. 11 However, for the group of polcyholders wth three or more years of drvng experence, a correlaton between low deductbles and more accdents does exst. For ths group, the results ndcate (see Table 6 columns 3 and 4) that ρ has a negatve value of that s statstcally sgnfcant (at the 1% confdence level). Ths enables rejectng the ndependence of the two equatons. Thus, although the Chappor-Salane fndngs of statstcal nsgnfcance of ρ are confrmed for polcyholders wth less than three years of drvng experence n my data, they do not carry over to polces purchased by polcyholders wth more drvng experence. The latter polces purchased by drvers wth such experence account for a very substantal majorty of the polces sold by the consdered nsurer and n the Israel automoble nsurance market n general (as well as n the French market consdered by Chappor and Salane). Because of the numercal domnance of polces purchased by experenced drvers, the pool of all polces s also characterzed (as dentfed earler) by a correlaton between low deductbles and more accdents. The dentfed dfference between young and experenced drvers hghlghts the possble mportance of learnng of nformaton n ths market. The next secton wll study the subject of learnng more systematcally. 6 Learnng 6.1 Learnng by Polcyholders I start by testng the predcton concernng learnng by polcyholders and, n partcular, concernng the effects of drvng experence that polcyholders had before 11 Note that the results reported above are ones that do not exclude the nformaton I have n my data on past clams hstory, whereas the Chappor-Salane fndngs were reached usng data that dd not nclude nformaton on past clams hstory whch they dd not have. To duplcate wth my data exactly what these authors dd, I excluded the nformaton that I have on the past clams hstory of polcyholders and then dd the bvarate probt test on polcyholders wth less than three years of experence. Agan, I found that ρ, the correlaton between of the error terms of the two equaton, s very close to zero (0.0023) and the 95 percent nterval s equal to [-0.111, 0.116]. Ths s smlar to the Chappor-Salane fndng that zero falls wthn the 95 percent confdence nterval for ρ. 17

20 jonng the nsurer (hypothess H2). Accordng to ths hypothess, a coverage - accdents correlaton s more lkely to exst for groups of polcyholders wth more drvng experence pror to jonng the nsurer. To test ths hypothess, I dvded all the polces n the data nto 5 sub-groups made of the polcyholders that have respectvely 0, 1, 2, 3, or 4 or more years of drvng experence not wth the nsurer. I then tested the presence of coverageaccdents correlaton for each sub-group separately. The results, whch are reported n Table 7, ndcate that a coverage-accdents correlaton does not exst for the groups of polcyholders wth only 0,1, or 2 years of drvng experence pror to jonng the nsurer. Such correlaton does exst, however, for the two groups of polcyholders who have 3 years or 4 or more years of drvng experence not wth the nsurer. Thus, the results are consstent wth the story that, the longer the drvng experence pror to jonng the nsurer of a group of polcyholders, the more lkely ts members to have an nformatonal advantage over the nsurer, and thus the more lkely to exst a coverage-accdents correlaton. Interestngly, fndng that a coverage-accdents correlaton does not exst for polcyholders wth no or lttle drvng experence, I am able to reject the possblty that polcyholders can obtan sgnfcant prvate nformaton about ther rsk type n connecton wth automoble accdents from mere ntrospecton or from observng ther performance n other dmensons of lfe. The data s consstent wth sgnfcant prvate nformaton about ths rsk type comng only from actual experence wth one's own drvng. 6.2 Learnng by Insurers I now turn to testng the predcton that, as the experence of the nsurer wth a polcyholder ncreases, the polcyholder s ntal nformatonal advantage over the nsurer (f any) can be expected to dmnsh and ultmately dsappear (hypothess H3). To examne ths ssue, I test whether the coverage-accdents correlaton declnes or dsappears for groups of polcyholders wth whom the nsurer has had long experence. To ths end, I dvded all the polces n the data nto 5 sub-groups those n whch the nsurer has had respectvely 0, 1, 2, 3, or 4 years of pror experence wth the polcyholder. For each group, I regressed the number of clams exceedng the regular deductble on the choce of the deductble and all of the polcyholder s characterstcs. As Table 8 shows, the coeffcent on the deductble choce decreases wth the length of the nsurer s experence wth the polcyholder. For example, for the group of polcyholders wth zero years of company experence, the coeffcent on the deductble choce s equal to and s 18

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