Prvacy, Drvng Data and Automoble Insurance: An Economc Analyss Adan Holls Deartment of Economcs, Unversty of Calgary Jason Strauss Deartment of Rsk Management and Insurance, Georga State Unversty November 6, 2007 Abstract Wth new technologes that enable nsurers to electroncally montor vehcles and drvers, nsurers should be able to rce automoble nsurance more accurately, creatng ndvdualzed rces for consumers. The welfare effects of lower rces are straghtforward, but we also consder that consumers have heterogeneous valuatons of rvacy that they may lose f they adot the montorng technologes. We examne the voluntary market adoton of these montorng technologes and ts effect on equlbrum rces and welfare. We fnd a welfare effect equal to the loss n rvacy, but conclude that the overall effect s ambguous wthout consderng moral hazard. aholls@ucalgary.ca; jstrauss2@student.gsu.edu
Introducton Event-data-recorders (EDRs) and telematcs technology ncludng GPS unts (we smly refer to them collectvely as EDRs) rovde a means for automoble nsurance comanes to dscover effcent estmates of the exected losses that automoble drvers wll ncur. Instead of solely relyng on less refned ratng varables such as age, gender, and martal status, nsurers can use EDR technologes to mrove ther estmates. These technologes may also comromse rvacy n qute mortant ways, snce they rovde otentally comrehensve nformaton not only on how ndvduals drve ther vehcles, but also where and when. Not everyone values ths loss of rvacy the same, creatng some nterestng trade-offs whch ths aer exlores. EDRs are caable of generatng, transmttng, analyzng, and storng senstve data relatng to the drvng habts (an ndcator of exected loss) of the ndvdual automoble drver. EDRs rovde data that can be a owerful redctor of the frequency and severty of automoble accdents. Wthout them, nsurance frms must rely on less refned estmates of exected losses whch are based on age, gender, and other characterstcs. Wth EDRs, nsurers can have access to extremely good nformaton about the drvng characterstcs of nsured drvers. In the Unted States, Progressve Casualty Insurance Comany nsttuted a voluntary rogram n 2004 n whch the comany gves drvers an EDR system. Users may receve a reducton n ther nsurance remum based on when, how much and how fast they drve. 2 EDRs can also be used to nform the nsurer of where the drver goes. In the Unted Kngdom, 2 James Warden, North Dakota, other states debate rvacy safeguards on vehcle black boxes. Assocated Press Archve, Fortwayne.com, March 25, 2005.
Norwch Unon offers a rogram for young drvers whch rces ther nsurance based on how frequently and where they drve. 3 Users who drve at less congested and therefore less dangerous tmes ay lower nsurance remums. The rvacy ramfcatons of such technology are consderable. Data from EDRs has been used n court to determne lablty n car accdents 4, for survellance by olce 5, and by car rental agences to determne sulementary charges 6, as well as by nsurers. The same technologes are beng marketed to arents, who can use EDR to tell whether teenagers are drvng recklessly, whether they're wearng seat belts and whether they are just gong to the lbrary as they romsed. 7 Adotng EDR, artcularly for the urose of demonstratng that a drver s safe through dentfyng when and where a car s drven, automatcally creates ntrusons nto rvacy whch may not be desrable for some ndvduals. An nsurer who knows where a car has been drven (for the uroses of determnng an nsurance remum) also has the ablty to determne whether t has been drven reeatedly through a red-lght dstrct, for examle. Thus an mortant feature of the data avalable to nsurers through EDR and assocated technologes s that t reveals much more about the drver than just the level of rsks beng nsured. Stgler (98) onts out that an ndvdual wll be wllng to gve u rvacy that s, to reveal ersonal nformaton when t s effcent to do so. For examle, an ndvdual may wsh to establsh a credt record to obtan a lower nterest rate. Posner (98) observes that ncreased rvacy tends to reduce effcency n transactng, snce t forces relance on nferor sources of 3 Danel Thomas, Norwch Unon offers ay-as-you-drve nsurance. Comutng, 27 January 2005. 4 See Green and McClafferty (2004), Aendx III, for many examles of court cases n whch EDR data has fgured romnently. 5 The Comany v. USA, US Court of Aeals for the Nnth Crcut, No. 02-5635, November 8, 2005. 6 Amercan Car Rental, Inc,. v. Commssoner of Consumer Protecton, Connectcut Sureme Court, 273 Conn. 296 (2005). 7 Mchelle Hggns, A Back-Seat Drver for your Teen s Car. Wall Street Journal, 23 February 2005. 2
nformaton. However, f rvacy tself s a good, as dscussed by Hrshlefer (98) and Murhy (996), then gvng t u creates a loss. Of course, the valuaton of rvacy by ndvduals s not lkely to be smlar. Some eole value t hghly and guard t jealously, and some may have much lghter concerns about revealng ersonal nformaton (Archer [980], Culnan [995], and Nowak and Phels [992]). Our analyss therefore ncludes a heterogeneously-valued loss of rvacy for drvers who adot EDR n lne wth Hu and Png (2006) who assert that consumers do value rvacy and that they value t dfferently. Flova and Welzel (2005) nvestgate adverse selecton, moral hazard and rvacy wth EDR-generated nformaton whch s accessed after an accdent and rovdes hgh or low ndemnty based on the revealed rsk-tye of the drver or the revealed effort level of the drver. In ther scenaro, the ntroducton of EDR technology enhances welfare unless there s ntal cross-subsdzaton of rsks. Our analyss dffers n a number of resects, most notably n the modelng and conceton of rvacy. Strauss and Holls (2007) have analyzed the ntroducton of EDR technology f only one frm has access to the technology, and shown, n the absence of rvacy concerns, that the welfare effect deends on whether comettve nsurers are able to searate consumers through a menu of contracts. The result from Strauss and Holls (2007) dffers from that of Crocker and Snow (986) because Crocker and Snow assume that all frms are symmetrcally nformed. 3
Ths aer follows the same reasonng as Strauss and Holls (2007) but dffers n three resects: we ncororate rvacy, consumers know ther rsk-tye 8, and we allow for the comettve use of EDR technology (.e. we allow for symmetrc nformaton across nsurers). The welfare effects, however, stll deend on whether nsurers can ool or searate consumers. Our analyss offers two ossble scenaros: consumers are requred to have full nsurance, or they may urchase artal nsurance. Gven a requrement to have full nsurance, consumers have no way of sgnalng ther rsk-tye, and so n the absence of EDR technologes, all consumers are ooled. Analyzng ths stuaton allows us to focus on the nteracton between nsurance remums and rvacy. We also beleve that ths aroach of examnng the two extremes s valuable snce realty lkely les somewhere n-between. In many stuatons, there are regulatons whch lmt the extent to whch consumers can use artal nsurance to sgnal ther tye (as llustrated n Tables and 2). The tycal mnmum automoble nsurance regulaton (whch vares from state to state and rovnce to rovnce) requres consumers to have a mnmum amount of thrd-arty lablty nsurance whle some requre mandatory no-fault accdent-benefts coverage as well (rmarly n Canada). Table shows summary statstcs for mnmum automoble nsurance requrements n the US as of 2007 for those states that had mnmum automoble nsurance requrements. Table 2 shows summary statstcs for Canada. 8 Note that f we assume that consumers do not know ther rsk tye and that they are not requred to urchase full nsurance, we end u wth the same result as that examned here n the model wth full nsurance, f consumers exerment wth new technologes. 4
Table, Summary Statstcs of US Automoble Insurance Thrd-Party- Lablty Mnmums by State, US $ B.I./erson B.I./Total P.D. Mean $23,098 $46,333 $4,620 Std. Dev. $7,40 $4,939 $6,92 Mn. $0,000 $20,000 $5,000 Max $50,000 $00,000 $25,000 Obs. 46 45 46 Retreved from: htt://www.dmv.org/ on November 5, 2007 B.I.=Bodly Injury, P.D.=Proerty Damage Table 2, Summary Statstcs of Canadan Automoble Insurance Mnmum Requrements by Provnce, CDN $ Mn. Lablty Total A.B. A.B./ Person Alberta $200,000 $50,000 n/a Brtsh Columba $200,000 n/a $50,000 Mantoba $200,000 no lmt no lmt New Brunswck $200,000 n/a $50,000 New Found Land and Labrador $200,000 n/a n/a Nova Scota $500,000 n/a $25,000 Ontaro $200,000 n/a $00,000 Prnce Edward Island $200,000 n/a $25,000 Quebec $50,000 n/a n/a Saskatchewan $200,000 n/a $5,502,000 Retreved from: htt://www.bc.ca/en/car_insurance and htt://www.saaq.gouv.qc.ca/en/ndex.h on November 5, 2007. Mn. Lablty=mnmum total thrd arty lablty nsurance coverage requred A.B. = Accdent Benefts (no fault nsurance coverage akn to ersonal njury rotecton n the US). Saskatchewan also mandatorly requres collson and comrehensve coverage wth a $700 deductble. The two requrements of mnmum nsurance and mandatory artcaton n no-fault accdent-benefts coverage are restrctons that are akn to requrng full nsurance. By restrctng the ablty of the consumer to choose lower levels of thrd-arty coverage and lower 5
levels of no-fault accdent-benefts coverage, the regulator lmts the ablty of the consumer to sgnal her rsk-tye to the nsurer through artal nsurance urchasng. Whle these mnmum restrctons would not bnd on all consumers, we susect t lkely that they bnd on some. We analyze those stuatons here. A Model wth Full Insurance Rsk-averse consumers urchase nsurance so as to alter ther attern of ncome across states of the world. Each consumer has a unque robablty of havng an accdent. For smlcty, we normalze the cost of an accdent to equal one. The exected loss s then the robablty of an accdent. Let W denote the consumer s wealth f there s no accdent and W2 hs wealth f there s an accdent. Let Π 0 be an endowment of rvacy that s equal across all ndvduals. EDR technology erfectly reveals the rsk of the consumer to the nsurer, but at a cost of less rvacy. Let π be the amount of rvacy that ndvduals must gve-u n order to use EDR technology, 0 < π < Π. Let β 0 be an ndvdual s valuaton of rvacy; rvacy valuatons are heterogeneous whereas the quanttes of rvacy endowed, and lost through EDR technology, are homogenous. 9 The consumer s exected utlty (equaton(.)) s then the standard exected utlty functon lus addtonal terms for the valuatons of rvacy. U (, W, W, β ) = (- ) u( W ) + u( W ) + β Π β π (.) 2 2 9 Note that U ( ) s a functon of π = 0. β and not Π orπ. If a consumer does not choose EDR technology, 6
Equaton (.) s normally behaved so that the utlty of wealth n both states of the world s ncreasng wth wealth and the margnal utlty s decreasng wth wealth. The utlty from rvacy s ncreasng n rvacy and the rvacy valuaton. Every consumer s ndfferent between states of the world because of the full nsurance requrement. Let be the cost of nsurance for ndvdual. Let Wɶ = W be the consumer s wealth n all states of the world once fully nsured. Because each consumer receves full nsurance and s ndfferent between states of the world, the consumer s exected utlty functon n equaton (.) can be rewrtten as t s n equaton (.2) snce the robabltes across states of the world must sum to one. U (, Wɶ, β ) = (- ) u( Wɶ ) + u( Wɶ ) + βπ βπ = u( Wɶ ) + β Π β π (.2) = u( W ) + β Π β π Notce that the rsk of an accdent does not now drectly enter the utlty functon snce all consumers have full nsurance. It s straghtforward to see that utlty-maxmzng consumers wll trade ther rvacy for gans n wealth (through a reducton n nsurance rces ) when t s n ther nterest to do so. In addton to that, t s also nterestng to thnk about the externalty that the consumers who adot EDR (and trade rvacy for lower rces) wll have on the consumers who do not adot EDR. Indeed, we wll show that the consumers who are most lkely to adot EDR are those wth relatvely low rsk; as they accet EDR and remove themselves from the ool, the rces that the remanng ooled consumers must ay wll rse. 7
We assume that and β have jont dstrbuton F( β ), and we make no artcular assumtons over ths dstrbuton. The nsurance remum ad by the consumer deends on whether the consumer adots EDR technology or not. In a comettve market n the absence of EDR technology, the ooled remum for the grou s (, ) f β d dβ 0 0 where each consumer has an exected loss of. The suerscrt n denotes the ooled remum before the ntroducton of EDR technology. The nsurance frms offer the oolng rce of wthout knowng any ndvdual s actual rsk. There s no loss n rvacy. When EDR technology s ntroduced, consumers have a choce between usng the technology and not usng the technology; they can urchase nsurance whch requres montorng by an EDR devce or they can urchase nsurance that does not requre an EDR devce. Consumers who do not use EDR wll contnue to ay a oolng rce. Consumers who use EDR wll ay an actuarally far remum for ther nsurance snce ther drvng rsks ncludng how, where, and when they drve are assumed to be erfectly revealed to the nsurer. When EDR s ntroduced, those consumers who adot t face a loss n rvacy but ay a remum based on ther true rsk rather than one based on the average rsk n the ool. Thus, those consumers for whom ( ) ( ) u W u W > β π wll adot EDR, snce ther utlty from nsurance cost savngs outwegh ther loss n utlty from ther loss n rvacy. 8
low However, the consumers who adot EDR are those wth relatvely low β and relatvely snce for them the gan from a reducton n remums exceeds ther loss n utlty from a reducton n rvacy. 0 For ths reason, the oolng rce must ncrease followng the ntroducton of EDR technology. The average ooled rsk for the remanng grou ncreases to 2 where 2 >. The new average ooled rsk can be wrtten as a functon of the average ooled rce 2 from before the ntroducton of EDR technology, ( ) 0 P β π 0 P βπ (, β ) f d dβ (, β ) f d dβ. For clarty, ( ) 2 > 0 snce the hgher the orgnal rsk, the hgher the resultng ooled rce after EDR has been ntroduced. Gven the ncreased average rsk-level n the ool, comettve nsurers would requre a hgher remum. The new, hgher ooled remum wll lead to further defectons from the ool. As the teratve rocess contnues, the oolng rce ncreases and alters the oortunty set for the consumers who are ooled. An equlbrum s a set of contracts * (, ) * (where s the equlbrum oolng rce for all consumers remanng n the ool and s the vector of ndvdual s actuarally-far EDR 0 Consder that for any two consumers wth dentcal rvacy valuatons, the consumer wth a lower robablty of an accdent wll be more wllng to use EDR. Also consder that for any two consumers wth dentcal robabltes of accdents, the consumer wth a lower rvacy valuaton wll be more wllng to use EDR. 9
contracts) such that no nsurer can roftably devate by offerng any other contract or contract set and all consumers choose ther most referred contract from among those offered. Gven * (, ) *, all consumers for whom ( ) ( ) u W u W > β π have adoted the EDR technology. Furthermore, all consumers remanng n the ool do not wsh to devate from the ooled rce snce t s not n ther utlty maxmzng nterest to do so snce they receve more utlty from ther rvacy than they do from the cost savngs that EDR rovdes. In equlbrum, EDR contracts must be rced such that the remum s equal to the robablty of an accdent for that ndvdual. A oolng contract must be rced to be equal to the average rsk of all those consumers n the ool. It s straghtforward to show the exstence of the oolng equlbrum f the dstrbuton functon (, ) F β s contnuous: a comettve equlbrum requres that the oolng rce be equal to the average rsk of those n the ool, whch s between 0 and. The average rsk of those n the ool s an ncreasng functon of the oolng rce. As the oolng rce ncreases, more consumers devate to the EDR contract. Fgure llustrates the exstence of such an equlbrum. 2 The curved lne reresents the average rsk ( ) of those n the ool for any gven oolng rce. A comettve equlbrum must be on the dagonal so that the oolng rce earns zero rofts. If the dagonal s only crossed once, that would be the equlbrum. Wth multle crossngs, as n Fgure, the lowest crossng ont (whch occurs at * ) s the equlbrum. * Evdently, a lower rce than would result n losses to any frm whch offered t, whle a hgher rce would attract no customers. 0
To show the exstence of ths equlbrum t s ntutve to consder the oolng rce at the extremes: when the oolng rce s equal to zero and when the oolng rce s equal to one. If the oolng rce was zero, every drver would enter the ool because t would be n ther nterest to receve free nsurance. The average rsk n the ool would then necessarly be above the offered rce of zero, as n Fgure. If the oolng rce was (the hghest rce ossble), the average rsk n the ool would necessarly be below the oolng rce of snce some consumers wth an exected loss below the hghest ossble cost would devate and use EDR technology nstead. The combnaton of these two scenaros gves us the exstence of at least one crossng ont as shown n Fgure.
Fgure There s a one-to-one relatonsh between the average ooled rsk and the average ooled rce, as shown by the curve. Proft equals zero anywhere on the dagonal lne. The lowest crossng reresents the equlbrum oolng rce. At any rce above ths, a frm would not sell any olces; at any rce below ths, a frm would earn negatve rofts. 2
Welfare equaton (.3). The aggregate overall change n utlty due to the mlementaton of EDR s equal to * β π * ( ( ) ( ) βπ ) β ( ( ) ( )) β (.3) U = u W u W d d + u W u W d d 0 0 0 * βπ The frst ntegral reresents the (ossbly negatve) gans to consumers who swtch to EDR technology. They ay a dfferent remum than orgnally, and gve u ther rvacy. The second ntegral reresents the losses to consumers who reman n the ool, and ay a hgher remum followng the mlementaton of EDR for some consumers. Fgure 2 llustrates the effects of ntroducng EDR. Wthout EDR, there s a oolng rce. Those consumers wth rsks < are subsdzng those wth > and all consumers have no loss n rvacy. When EDR s ntroduced, the consumers n area A adot t ntally, whch forces the oolng rce to ncrease to reflect the new, hgher average rsk n the ool. The new, hgher oolng rce encourages even more consumers to leave the ool, ultmately * resultng n an equlbrum oolng rce of. At that ont, all those consumers n areas A, B and C have adoted EDR, and the others reman ooled because t s n ther nterest not to gve u ther rvacy snce ther cost savngs wll not outwegh ther rvacy losses. 3
Fgure 2 Only the consumers n area A are better off than before the ntroducton of EDR technology. These consumers gve u rvacy (whch they do not hghly value) n exchange for a reducton n ther nsurance remum. Consumers n areas B and C accet the technology because the ncreased oolng rce changes ther oortunty set and makes t benefcal for them to gve u ther rvacy. Consumers n area B ay less than ntally, but the reducton n remum s nsuffcent to comensate them for ther loss n rvacy. Consumers n area B are 4
thus net losers relatve to the orgnal non-edr world. Consumers n area C are worse off n every way, as they forgo rvacy and ay a hgher remum than before the ntroducton of EDR technology. Consumers n areas D, E and F do not adot EDR and so mantan ther rvacy, but they ay a hgher nsurance remum. It s rvately effcent for consumers n area A to gve u ther rvacy, exactly n the way that Stgler (980) suggests; subsequently, t s effcent for consumers n areas B and C to gve u ther rvacy too. However, from a socal welfare ersectve, as equaton (.3) hghlghts n ths model, EDR s lkely to be harmful. The total remums ad wll be the same wth and wthout EDR, although clearly ther dstrbuton changes, as consumers n areas A and B ay less, whle consumers n areas C, D, E and F ay more. The reducton n aggregate welfare arses because consumers n areas A, B and C suffer a reducton n rvacy, whle aggregate remums ad reman unchanged. Searaton through screenng Now suose that artal nsurance s ossble, enablng a searatng equlbrum n the srt of Rothschld and Stgltz (976) and Wlson (977). Suose that there are only two rsk tyes who are contnuously dstrbuted accordng to ther reference for rvacy. In ths case, there s no cross-subsdzaton between rsk tyes, and each consumer receves nsurance based on far odds. However, low-rsk tyes wll only have ncomlete nsurance, whle hgh-rsk tyes wll obtan full nsurance. Wth EDR, low-rsk tyes have the oortunty to obtan full nsurance at actuarally far rces but at the cost of reduced rvacy. Those consumers wth a relatvely low valuaton of rvacy wll adot EDR technology, and they wll be better off. Note that because there s no 5
cross-subsdzaton, (hgh rsk tyes have full nsurance and low rsk tyes have artal nsurance at actuarally far rces) ths has no effect on any other consumers. Ths mles an aggregate welfare ncrease from the mlementaton of EDR snce no consumer wll accet t unless hs total ncrease n welfare from lower rces and greater nsurance coverage outweghs hs loss of rvacy. Concluson Wth EDR, low-rsk tyes have the oortunty to obtan full nsurance at actuarally far rces, but at the cost of reduced rvacy. The consumers for whom rvacy valuatons are relatvely low wll adot EDR technology f they are subsdzng other members of the ool they wll be better off because of the cost savngs they realze. The removal of ther subsdy to the ool requres the remanng members of the ool to bear hgher costs whch alter the oortunty sets of those stll remanng n the ool. The dfference between the full nsurance and screenng case llumnates the welfare effects of EDR. The rce of nsurance, n a comettve market, must reflect ts average cost. If EDR does not reduce the average cost of nsurance (whch t cannot f t has no effect on the actual robablty of accdents), ts effects must be on rvacy and on the amount of nsurance urchased. If EDR does affect moral hazard, the overall welfare results are ambguous wthout knowng the magntudes of the two effects. In the model wth mandatory full nsurance and oolng, the reducton n rvacy consttutes the entre aggregate welfare mact. In the screenng case, there s a trade-off that occurs between loss of rvacy and ncreased nsurance coverage for rsk-averse consumers, whch s domnated by the gans from ncreased nsurance coverage. 6
In ths bref note, we have consdered the market mlementaton of event-data-recorders (EDRs), telematcs and related montorng technologes whch allow nsurers to obtan very extensve nformaton about how, when, and where consumers drve. Ths should, n turn, ermt more recse nsurance rcng, whch may allow low-rsk drvers to reduce ther nsurance costs, but at a cost of a loss n rvacy. We have consdered the case of full nsurance wth oolng, and the case of screenng contracts, and shown that the welfare effect deends on whch case holds. We have not drectly consdered the moral hazard mlcatons of EDR technology, whch may be very mortant and could outwegh the losses n rvacy. References Archer, Rchard L. 980. Self-Dsclosure. In The Self n Socal Psychology, edted by Danel M. Wegner and Robn R. Vallacher, 83 204. New York: Oxford Unversty Press. Crocker, K. J., and A. Snow, 986, The Effcency Effects of Categorcal Dscrmnaton n the Insurance Industry, Journal of Poltcal Economy, 94(2): 32-344. Culnan, Mary J. 995. Consumer Awareness of Name Removal Procedures: Imlcatons for Drect Marketng. Journal of Drect Marketng, 9 (Srng): 0 9. Flova, Lla and Peter Welzel, 2005, Reducng Asymmetrc Informaton n Insurance Markets: Cars wth Black Boxes, unublshed workng aer. Green, R. and K. McClafferty, 2004. Revew of Jursrudence Regardng Event Data Recorders: Imlcatons for the Access and Use of Data for Transort Canada Collson Investgaton, Reconstructon, Road Safety Research and Regulaton. Transort Canada, avalable at htt://www.tc.gc.ca/roadsafety/edr/techncalreort/menu.htm, last accessed July 30 2007. Hrshlefer J., 980, Prvacy: Its Orgn, Functon, and Future. Journal of Legal Studes, 9 (4): 649-664. Hu, Ka-Lung, and I.P.L. Png, 2006, The Economcs of Prvacy. Forthcomng n Handbook of Informaton Systems and Economcs, edted by Terry Hendershott, Elsever. 7
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