Privacy and Information Value in Adverse Selection Markets.

Transcription

1 Prvacy and Informaton Value n Adverse Selecton Markets. Jeevan Jasngh and Alok Chaturved Krannert Graduate School of Management Purdue nversty, West afayette, IN {jasngh;alok}@mgmt.purdue.edu Contact Author: Jeevan Jasngh Ph: ( ; Fax: (

2 Abstract In ths paper we study the mpact of genetc testng, and the use of test results n health nsurance markets a market that exhbts adverse selecton. We characterze the exstence and nature of nsurance contracts when ndvduals can reveal genetc nformaton to nsurers but where revelaton of genetc nformaton s assocated wth a loss of prvacy. We then examne the welfare mplcatons of dfferent polcy proposals regardng genetc testng, wth the decson of the consumer to take a genetc test, and to reveal genetc nformaton, beng endogenous. Keywords: Prvacy, Adverse Selecton, Informaton Value, Genetc Testng, Insurance 1

3 Introducton Markets exhbtng adverse selecton 1 are characterzed by asymmetry n nformaton among market partcpants. Examples nclude but are not lmted to credt markets [Townsend, 14], labor markets [Spence, 11] and nsurance markets [Stgltz, 12]. It has been suggested that an effectve way to obtan the frst best outcome n these markets would be to make the nformaton structure more symmetrc by sharng nformaton [Doherty and Thstle, 4; audon, 8]. audon [8] descrbes a Natonal Informaton Market (NIM, where nformaton about ndvduals can be bought and sold at a market-clearng prce. Ths market would provde a constant source of consumer nformaton to the frms. Such a market where consumers can trade n potentally useful personal nformaton, has been termed as an nformaton market [audon, 8]. Companes such as umera ( are creatng technologes that allow consumers to create ther own profles, whch they can share wth marketers for the rght prce. Ths busness model places personal data under the auspces of the ndvdual, whch can then be used as a new form of currency to enable the Identty Commerce (I-Commerce marketplace. An example of such personal data s the vast amounts of genetc nformaton created by the uman Genome Project and Genetc Testng. Genetc tests attempt to detect the presence of genes that are assocated wth dsease or predspose those who nhert the genes to dsease [Mesln et al., 9]. Genetc testng exacerbates the adverse selecton exstng n nsurance markets, f the results of the test are not made accessble to the nsurers. owever the nsurers request for a level playng feld contrasts wth efforts of consumer groups to ncrease the prvacy protecton of genetc nformaton [Subramanam et al., 11. Snce the DNA molecule s stable, once removed from a person s body and stored, t can become the source of an ncreasng amount of nformaton as more s learned about how to read the genetc code [Edwn, 5]. In other words stored genetc samples wll provde more genetc nformaton than was 1 Adverse effect on proftablty of the unnformed due to asymmetrc nformaton. 2

4 magned when the samples were orgnally collected. Threats to ndvdual prvacy may therefore be presented due to secondary use of the collected nformaton 2. In ths paper we study the mpact of genetc testng and the use of test results on health nsurance markets. Consumers who have taken a genetc test, are assumed to be nformed about ther rsk of a genetc dsease. The nformed low rsk consumers have an ncentve to reveal genetc nformaton/test results to the nsurer, so as not to be clubbed wth the hgh rsk types. We characterze the exstence and nature of nsurance contracts when ndvduals can reveal genetc nformaton to nsurers, but where revelaton of genetc nformaton s assocated wth a loss of prvacy. We then examne the welfare mplcatons of dfferent polcy proposals regardng genetc testng, wth the decson of the consumer to take a genetc test and to reveal genetc nformaton, beng endogenous. The rest of the paper s organzed as follows: Secton 1 covers the background lterature on prvacy and genetc testng. Secton 2 covers the assumptons, model framework and the man results. Implcatons of the results obtaned are summarzed, and lmtatons and drectons for future research are dscussed n Secton Background Prvacy s defned as the moral clam of the ndvduals to be left alone and to control the flow of nformaton about themselves [Coase, 1; Westn, 15]. Revealng genetc nformaton to nsurers consttutes a loss of prvacy because of the nherent loss n control over the use of ths nformaton after t s released. It s well known that nsurance markets are characterzed by adverse selecton see [Rothschld and Stgltz, 10; Stgltz, 13] - asymmetry n nformaton on rsk types between the nformed or partally nformed consumers and unnformed nsurers has an adverse mpact on the profts of nsurers. Genetc testng ncreases the asymmetry n nformaton f the results are avalable only to consumers, thus makng the adverse selecton more acute. There s a lot of debate on how and whether the results of the genetc 2 Secondary use of the nformaton could be any use other than the prmary purpose for whch the nformaton was collected. For example the nsurance companes could sell the nformaton to other frms nterested n the nformaton. 3

5 tests should be used see [Tabarrok, 14]. There are four broad polcy proposals regardng the use of genetc tests for nsurance purposes. nder the frst proposal, nsurers do not nqure, and are not permtted to nqure, whether applcants have been tested. In the second proposal, genetc nformaton s revealed to the nsurer only wth the consent of the consumer. The thrd polcy alternatve s to permt nsurers to nqure whether applcants have been tested and to get genetc nformaton/test results wth the consent of the consumer. The fourth polcy alternatve s to requre, or permt nsurers to requre that applcants be tested, and allow nsurers to use the test results-.e. mandatory release of genetc nformaton for nsurance purposes [Doherty and Thstle, 4]. rshlefer [6] dstngushes between prvate nformaton (avalable only to a sngle ndvdual and publc nformaton (avalable to everyone. Our work s closer to the prvate nformaton stream of lterature Cremer and Khall [2], Crocker and Snow [3] and Doherty and Thstle [4]. Agents receve a prvate sgnal n our model and they choose whether to make the sgnal publc or not 3. Crocker and Snow [3] have shown that f the nsurers know whether the consumers are nformed or unnformed about ther rsk type, then the prvate value of nformaton to unnformed consumers, s negatve. Doherty and Thstle [4] have looked at the case where nsurers cannot dstngush between nformed and unnformed agents and the case where nformaton on rsk type can be concealed or revealed to the nsurers. In ther settng unnformed can take a test (both costless and costly to get nformed about ther rsk type, and can reveal nformaton to nsurers are zero cost. The polcy holders knowledge of ther rsk type s therefore endogenous. They characterze the nature of equlbrum n all these cases, and fnd prmarly that wth costly nformaton, some unnformed may choose to reman unnformed. They also examne the welfare mplcatons of the endogenous nformaton model for publc polcy regardng genetc testng. In our settng, revelaton of nformaton has postve costs assocated wth t as n Jasngh and Chaturved [7] and n contrast to Doherty and Thstle [4]. The dfference between our settng and that of Jasngh and Chaturved [7] s that, the nsurance market settng s compettve n ther case and 3 We also consder a purely publc sgnal n last secton. 4

6 monopolstc n ours 4. We characterze the cost to revealng nformaton to be the loss of prvacy the fear of dscrmnaton because of beng classfed as a hgh-rsk type n a later perod, due to better genetc tests or just the dsutlty due to loosng control over personal nformaton. All genetc testng polcy proposals except the frst one where nsurers are nether permtted to nqure nor use genetc nformaton are affected f the loss of prvacy s taken nto account. As far as the mpact on consent law (Proposal 2, we need not consder the prvacy concerns of the hgh rsk type snce presumably only the low rsk types are affected. owever n the case of mandatory testng and revelaton of nformaton, the loss n prvacy of the hgh rsk type s also taken nto account. 2. Model The nsurance market settng s monopolstc. There s a contnuum of rsk-averse consumers, dentcal n all respects except for accdent probabltes, and a rsk neutral nsurer. All consumers possess dentcal von Neumann-Morgenstern state ndependent utlty functons (., whch are twce contnuously dfferentable and strctly concave. Ther wealth s W n state 1 (no loss and W D n the loss state 2, where W > D. π ; = are the probabltes of accdent of the hgh and low rsk, consumers. We also assume that π > π and 0 < π, π < 1, and that these probabltes are out of the agent s control, so that no moral hazard problem arses 5. We assume that each agent knows her rsk type 6. The proporton of low rsk (hgh rsk consumers n the economy s θ ( θ. If agents do not purchase nsurance they obtan expected utlty, V 0, π for =, ; where ( V ( 0, π = π ( W D + (1 π ( W ; = (1, 4 Insurance markets are monopolstc n several envronments and hence there s a motvaton to study the settng, separately from the compettve settng. There s a also the added motvaton to look at the monopoly settng from a benchmarkng perspectve and to compare the results wth the compettve settng. 5 Moral hazard problem arses due to the fact that nsurers cannot observe the consumers actons how much care she takes to avod a loss. By assumng that consumers cannot affect the probablty of an accdent by ther actons we assume away the moral hazard. 6 Informed consumers can be justfed by the fact that they could have taken a genetc test prevously for some other purpose and hence are fully aware of ther rsk of loss. 5

7 The nsurance contract specfes the premum P and the net ndemnty I 7 pad ncase of a loss. The use of consurance rates and/or deductbles s not permtted. We use the notaton δ = { P, I } to denote the sngle perod nsurance contract offered to type probablty of loss π, under the nsurance polcy δ, s =,. The expected utlty of a consumer wth the V( δ, π = π( W D+ I + (1 π ( W P; =, If consumer releases genetc nformaton to the nsurer, then the consumer faces a loss γ (2 due to loss of prvacy. The loss of prvacy could be the fear of secondary use of the nformaton revealed or the fear of dscrmnaton at a later date due to some nformaton present n the genetc nformaton, whch the consumer s not aware of currently or just the dsutlty at loosng control over the personal nformaton. Ths loss s thus a non-monetary loss and s separable from the utlty from the nsurance contract. The net utlty s V ( δ, π γ (3 Intally let us assume that consumers cannot reveal nformaton to the nsurers,.e. γ = 0. Insurer chooses contracts that maxmze profts. In the frst best case (no asymmetry n nformaton on rsk types, the nsurer chooses contracts that extract the entre surplus of both types of consumers. Both rsk types get complete nsurance. The contract n the frst best case are ( δ, δ (see Fg. 1, and satsfy the constrants V ( δ, π V(0, π = (4 I = D P =, (5 The frst constrant equaton (4 - specfes that the consumers are left ndfferent between buyng and not buyng nsurance, and the second constrant (5 specfes that both agents get complete nsurance. 7 Net Indemnty s the payment made to the consumer n case of loss, mnus the premum 6

8 owever under asymmetrc nformaton (Consumers have a pror knowledge of rsk types whle nsurers don t, the frst best contract can t be acheved [Stgltz, 13]. The second best contract satsfes the constrants V ( δ, π V ( δ, π ; = (,, j (6 j V ( δ, π V (0, π ; = (7, Equaton 6 s the ncentve compatblty constrant, whle equaton (7 s the ndvdual ratonalty constrant. The separatng contracts are { δ, δ } (see Fg. 1. The hgh rsk consumers get complete nsurance and are better off than n the full nformaton case, whle the low rsk agent get less than full nsurance. We now assume that a proporton λ 0 < λ 1 of the consumers does not have a pror knowledge of ts rsk type. Out of these unnformed consumers a proporton p (p are hgh rsk (low rsk. The proporton of nformed hgh rsk type (low rsk types s λ (λ, 0 λ, λ < 1 8. Informed < consumers n our settng are consumers who have taken a genetc test n a prevous perod for some nonnsurance related reason e.g. job screenng. θ = λ + p λ (8 θ = λ + p λ (9 All these proportons are assumed to be common knowledge. The pror probablty of loss for the unnformed s π = =, p π (10 The tmng s as follows, the nsurer frst chooses the set of contracts to offer, based on her belefs on the actons by the unnformed (take genetc test or not and the nformed low rsk (reveal nformaton or not. The unnformed then decde whether to take a genetc test or not, and the nformed consumer decde whether to reveal nformaton to the nsurer or not. The choce at each node affects the payoffs of 8 Strct nequaltes are assumed here for smplcty. Thus there are always nformed hgh and low rsk consumers. 7

9 all agents. We denote the aggregate proft of the monopolst f she offers the menu of contracts ( δ, δ, δ Π( δ, δ, δ, to the hgh rsk nformed, the unnformed and the low rsk nformed respectvely, by. If the nsurer does not desgn a contract for a specfc type of consumer for e.g. f the nsurer wants to offer nsurance only to the nformed hgh rsk consumers then the menu of contracts she offers s denoted by ( δ,.,.. The nsurers proft n ths case s denoted by Π( δ,.,.. Smlarly f the nsurer desgns contracts only for the nformed hgh rsk and the unnformed the correspondng notaton for the menu of contracts and profts are ( δ, δ,. and Π ( δ, δ,. Insurance contracts for the dfferent rsk types under dfferent nformaton structures are shown n Fg. 1. W and W are the wealth n the no loss and loss state respectvely. The lne s the complete nsurance lne. V, V, and V are the ndfference curves for the hgh rsk, unnformed and the low rsk agents respectvely that pass through the ntal endowment pont E 9. V and V are ndfference curves ( δ, δ are,δ. nder asymmetrc nformaton, wth no unnformed the contracts are ( δ, δ, whle of the hgh rsk and the unnformed consumer respectvely where they are left wth a postve surplus. V s the shfted ndfference curve of the low rsk consumer - nsurer gves a surplus to the low rsk consumer so as to compensate her for her loss of prvacy. nder full nformaton the contracts offered wth unnformed consumers the contracts are ( δ, δ, δ " ". Wth asymmetrc nformaton, only the hgh rsk consumers get full nsurance. It s easy to see that the followng constrants should be satsfed (see Fg. for an ntutve understandng. V " " ( δ, π V( δ, π > (11 " V( δ, π > V( δ, π (12 9 The slope of the ndfference curves of low rsk, unnformed and hgh rsk consumers at the full nsurance lne are (1 π (1 π (1 π > > π π π 8

10 V " " ( δ, π V( δ, π = (13 " V( δ, π > V( δ, π (14 " V( δ, π = V( δ, π (15 " V( δ, π > V( δ, π (16 V( δ, π = V( δ, π (17 V( δ, π > V( δ, π (18 In our model we model the loss of prvacy due to revelaton of nformaton to nsurer, and ths dfferentates our work from Crocker and Snow [3] and Doherty and Thstle [4] so from now onγ > 0. The fact that we look at a monopolstc settng dfferentates our work from Jasngh and Chaturved [7]. In secton 3.1 we consder the case where all consumers are nformed and low rsk consumers have an ncentve to reveal genetc nformaton to nsurers. Then n secton 3.2, we look at the case where unnformed consumers are present, the nformaton status s not drectly observable, there s an ncentve for consumers to reveal verfable nformaton (negatve test result or genetc nformaton that reveals that the consumer s a low rsk consumer and testng s costly for the unnformed. The observable nformaton status case wth costly revelaton and costly testng s consdered n secton 3.3. The mandatory testng and revelaton of genetc nformaton s consdered n secton nreported postves, verfable negatves, costly revelaton and unobservable nformaton status. We frst consder the case where all consumers are nformed about ther rsk type.e. consent law, the consumers can choose who gets to see the results of the test. It s clear that only the low rsk agents have an ncentve to release nformaton to the nsurers. We look at the case where all low rsk consumers are expected to reveal nformaton. λ = 0. By 9

11 The nsurer would desgn the contracts to maxmze her expected profts subject to the Indvdual Ratonalty (IR constrants of the agents. Thus the problem for the nsurance company s: Max. θ[(1 π P πi] + θ[(1 π P πi] w.r.t. ( P, I,( P, I s.t. V( δ, π γ V(0, π V( δ, π V(0, π We need not worry about the ncentve compatblty constrants, snce for the low type they would not be bndng, and for the hgh rsk type she would not be able to pass off as a low rsk type, f she reveals nformaton to the nsurer. The ndvdual ratonalty constrants of both consumers would bnd. emma 1: Assumng all consumers are nformed about ther rsk types, nsurer cannot observe rsk type and nsurer expects all low rsk consumers to report verfable nformaton to the nsurer at non-zero cost γ then n equlbrum, (a ow rsk and gh Rsk types obtan full nsurance, and (b the unque equlbrum contract s { δ, δ } Proof See Appendx Stgltz [13] has ruled out the possblty of the exstence of a poolng equlbrum because the monopolst can always get a hgher proft by offerng a separatng contract. Keepng ths property n mnd we obtan the followng result. 10

12 Proposton 1 Assumng all consumers are nformed about ther rsk types, nsurer cannot observe rsk type, and consumers can report verfable nformaton to the nsurer at non zero cost γ, the equlbrum contracts are ( δ, δ ( δ, δ f Π( δ,. Π( δ, δ (,. f Π ( δ,. > Π( δ, δ Proof. See Appendx δ When low rsk consumers don t reveal nformaton then ether (,. or ( δ, δ can be an δ equlbrum. (,. δ s an equlbrum f the profts from servng the hgh rsk type alone s greater than the profts from offerng nsurance to both types. When the low rsk consumers reveal nformaton the equlbrum s ( δ, δ - both consumer types get complete nsurance and the low rsk type are compensated for ther loss of prvacy. For the case, λ > 0 (unnformed consumers, f we assume that testng s costless, then testng s a weakly domnant strategy for the unnformed snce nformaton status s unobservable. All unnformed consumers would take the test and become nformed. Thus wth costless testng, there s no mpact on the above results f we assume that there are some consumers who are unnformed. 2.2 nreported postves, verfable negatves, costly revelaton, unnformed consumers, costly testng and unobservable nformaton status. nnformed consumers can take a costly test to know ther rsk type. Also by consent law, the consumers can choose who gets to see the results of the test. It s clear that only the low rsk agents have an ncentve to release nformaton to the nsurers. 11

13 emma 2. Assumng that some consumers are unnformed about ther rsk type, nsurers cannot dstngush between nformed and unnformed consumers and also cannot observe the rsk types drectly, then a partal poolng or a poolng contract cannot be an equlbrum 10. Proof: See Appendx emma 2 smplfes the calculaton of all the possble equlbrum by narrowng down the set of possble equlbrum, to separatng contracts. Proposton 2. Assumng unnformed consumers can observe ther rsk type at cost c, nformed and unnformed consumers cannot be dstngushed, rsk type s not drectly observed by nsurer and consumers can report verfable nformaton to nsurers at non-zero cost γ. Denotng contracts are feasble: c p by c, fve ( δ, δ, δ f γ > V( δ, π V( δ, π c and Π( δ, δ, δ Π( δ,., δ ( δ,., δ f γ > V( δ, π V(0, π c and Π ( δ, δ, δ < Π( δ,., δ " " " " " " ( δ, δ, δ f c > V( δ, π V( δ, π, Π ( δ, δ, δ >Π( δ,.,. and Π > Π( δ, δ,. " " ( δ, δ, δ v ( " ",.,. f Π ( δ, δ, δ <Π( δ,.,. and Π ( δ,.,. > Π( δ,,. δ v ( δ, δ,. f c > V(0, π V( δ, π and Π ( δ,.,. < Π( δ, δ,. and δ Π < Π(, δ,. " " ( δ, δ, δ δ Proof. See Appendx 10 Poolng contracts are contracts where all consumer types choose the same contract, whle partal poolng contracts are contracts where at least two types choose the same contract. 12

14 Thus we see that dependng on the profts the nsurer gets from dfferent contracts, whch depends on the relatve number of unnformed consumers, and nformed low and hgh rsk consumers, fve dfferent contracts are feasble. Some of the contracts exst only f the aggregate dsutlty due to loss of prvacy and due to testng s greater than a certan value. For example f we denote V (, V(, δ π δ π = γ andv( δ, π V (0, π = γ, then the contract ( δ, δ, δ only exsts 1 f the aggregate utlty exceeds γ,.e. γ + c > γ. c can be consdered to be a scaled cost of testng. The contract ( δ,., δ exsts forγ + c > γ. If the nformed low rsk consumer decde to reveal nformaton then the contracts that are feasble are ( δ, δ, δ and (δ,., δ - the equlbrum ( δ, δ, δ correspondng to the case where the unnformed don t get nformed, but stll get nsurance whle the equlbrum ( δ,., δ correspondng to the case where the unnformed reman unnformed and unnsured. The other three equlbrum are for the case when the nformed low rsk don t reveal nformaton to the nsurer. In two of these equlbrums (,.,. and ( δ, δ,., the low rsk consumer remans unnsured. The unnformed consumer remans unnsured n the equlbrum δ ( δ,.,. 2.3 nreported postves, verfable negatves, costly revelaton, unnformed consumers and observable nformaton status. Everythng s same as n secton 2.2, except that now the nformaton status can be observed by the nsurers.e. the nsurers know whch consumers are nformed and whch consumers are unnformed about ther rsk type. Proposton 3. Assume unnformed consumers can observe ther rsk type at cost c, nformed and unnformed consumers can be dstngushed, rsk type s not drectly observed by nsurers and consumers can report verfable nformaton to nsurers at non-zero costγ. Denotng c, three contracts are p = c feasble: 13

15 ( δ, δ, δ ( δ, δ, δ f c > V( δ, π V( δ, π c and Π( δ, δ, δ Π( δ,.,. ( δ, δ,. f Π ( δ, δ,. > Π( δ, δ, δ Proof. See Appendx If the nformed low rsk consumers decde to reveal nformaton then the only contract feasble s ( δ, δ, δ, where the unnformed contnue to reman unnformed. Note that all agents receve complete nsurance n ths equlbrum, and the low rsk nformed s compensated for her loss n prvacy. When the nformed low rsk don t reveal nformaton, then two contracts are feasble - ( δ, δ, δ where the low rsk nformed only get partal nsurance and ( δ, δ,. where the low rsk nformed consumer remans unnsured. There are no equlbrum where the unformed become nformed by takng a genetc test. Reason beng that they always prefer the contract δ to a lottery over δ or a lottery overδ, δ become nformed., δ. Thus wth observable nformaton status, unnformed have no ncentve to get tested and 2.4 Mandatory testng and release of nformaton for nsurance All consumers have to take a mandatory test, and then reveal the results of the genetc test to the nsurer, n order to get nsurance. Ths mples that all unnformed have to get nformed n order to get nsurance. We now also need to consder the prvacy loss of the hgh rsk consumer type. The prvacy loss of the hgh rsk (low rsk consumer due to release of nformaton s, γ (γ, where γ > γ. Proposton 4. Assume unnformed consumers can observe ther rsk type at cost c, rsk type s not drectly observed by nsurer and hgh rsk (low rsk consumers can report verfable nformaton to 14

16 nsurer at non-zero cost γ (γ where γ γ and reportng nformaton s mandatory for nsurance, then denotng V = V ( δ, π γ and V = V (0,π =,, > If V < V and V < V nobody buys nsurance. If V < V ; V V and pv + pv c< V, unnformed reman unnformed, only nformed low rsk buy nsurance and the only contract offered s δ. If V < V ; V V and pv + pv c> V, then unnformed become nformed and the low rsk buy the only contract offered δ. v If V V and V V and pv + pv c< V, then unnformed reman unnformed and reman unnsured, both hgh rsk and low rsk reveal nformaton and are offered the contracts ( δ, δ. v If If V V and V V and, pv + pv c V then unnformed become nformed, both hgh rsk and low rsk reveal nformaton and are offered the contracts ( δ, δ Proof: Straghtforward comparson of the utltes of each type of agent wth or wthout nsurance wth the clause that nsurance requres mandatory testng leads to above results. The menu of contracts ( δ, δ, compensates both the hgh rsk and low rsk for the loss of prvacy. Mandatory testng and release on nformaton mposes addtonal costs on all agents n some cases. The monopolst may be worse off f there are a large number of unnformed who decde to reman unnformed and unnsured. 15

17 3. Dscusson In ths paper we have looked at the tradeoff between the value of nformaton and the value of prvacy n a market exhbtng adverse selecton health nsurance market. Nature of nsurance contracts under each of the polcy proposals has been summarzed n the propostons. nder the frst proposal, where nsurers are nether permtted to ask whether the consumer has undergone any test nor ask for test results, the contracts offered are - full nsurance for the hgh rsk, and ncomplete nsurance for the unnformed and the low rsk. These contracts rely on pure self-selecton a la Stgltz. Contracts of ths form mpose a sgnalng cost on the unnformed and the nformed low rsk type they have to sgnal ther type by acceptng less then full nsurance. If release of nformaton s allowed by consent law, and nsurers cannot observe the nformaton status (Proposton 2, then there are a number of possble canddate equlbrums. These equlbrums depend on the relatve proftablty of the menu of contracts, whch n turn depends on the relatve number of nformed low rsk, nformed hgh rsk and unnformed consumers. Some of these equlbrums only exst f the aggregate dsutltes due to testng and loss of prvacy are above a certan value. One of these equlbrums s the separatng menu of contract offered under proposal 1. From a welfare perspectve, we look at the mpact on the welfare of agents ndvdually. It would be dffcult to get a measure of overall socal welfare wthout specfc numbers on the number of agents of each type. We frst do a welfare comparson of proposal 1 and 2. The monopolst nsurer s always weakly better off under proposal 2, snce she always has the opton of offerng the separatng contract under proposal 1. She can do no worse than the proft that she get under proposal 1. The low rsk consumer s better off n some of the equlbrums under proposal 2, than under proposal 1, snce she gets complete nsurance as opposed to partal nsurance under proposal 1. owever n some other equlbrum, she s ndfferent between the two proposals. Proposal 1 s favorable to the hgh rsk type snce she s always left wth a postve surplus. nder proposal 2 she stll contnues to get complete nsurance but n some equlbrum s left wth zero surplus. Smlarly, the unformed consumer s better off under some equlbrums under 16

18 proposal 2, whle she s ndfferent n some other equlbrums compared to the contract she obtans under proposal 1. The results of Proposton 3 are relevant to Proposal 3, where the nsurer always knows the nformaton status of the consumers. The results suggest that the unnformed can also get full nsurance. The key dfference between proposals 2 and 3 s that the nsurers can dentfy the nformed hgh rsk from the unnformed. Snce ths nformaton s conveyed to the nsurers wthout any nherent loss to the consumers of any type, from a welfare perspectve Proposal 3 domnates Proposal 2 addtonal nformaton s avalable wthout a cost. The addtonal nformaton on the nformaton status also reduces the number of possble canddate equlbrums to three. Snce the nsurer can desgn nsurance contracts based on the nformaton status, none of the unnformed take a genetc test and prefer to reman unnformed. Ths s a result of the rsk averseness of the consumers because of whch they prefer the frst best contract desgned for the unnformed, over a lottery of the frst best contracts desgned for the nformed low rsk and nformed hgh rsk types. Now comparng proposal 1 and proposal 3, we fnd that of the three canddate equlbrums under proposal 3, the low rsk consumer s better off n one, and ndfferent n the other two, compared to her contract n proposal 1. The hgh rsk consumer s worse off n two of the equlbrums under proposal 3 and ndfferent n the other compared to her contract n proposal 1. The unnformed consumer gets the frst best contract n all the equlbrums under proposal 3. Snce the frst best contract leaves her wth zero surplus, she ends up beng worse off then than under proposal 1, where she s left a postve surplus. Mandatory testng and mandatory revelaton of nformaton does the worst n terms of socal welfare, snce t mposes addtonal costs on the hgh rsk and unnformed agents wthout provdng any benefts to the hgh rsk, and provdng benefts to the unnformed only n some cases. In ths paper we make the smplstc assumpton that there are only two rsk types. Extenson to a contnuum of rsk types s a possble drecton of future research. It s possble that some of the Nash equlbrums that we have calculated can be elmnated based on some refnement crtera, however we refran from addressng refnement ssues n ths paper. The nsurance settng s monopolstc, and the 17

19 study of ths settng s mportant not only because some nsurance markets are domnated by a sngle nsurer, but also because t s a benchmark settng to be compared wth the compettve settng [Jasngh and Chaturved, 7]. We could have consdered better posterors on the probabltes of losses nstead of consderng perfect nformaton, from takng a genetc test. owever as Doherty and Thstle [4] have shown n ther settng, the results don t change by assumng better posterors. We expect our results to hold true even after modfyng the settng to one wth better posterors. 18

20 References [1] Coase, R.. (1960. The problem of socal cost, Journal of aw and Economcs, pp [2] Cremer, J. and Khall, F. (1992. Gatherng Informaton before Sgnng a Contract, Amercan Economc Revew, 82(3, pp [3] Crocker, K.J., and Snow, A. (1992, The socal values of hdden nformaton n adverse selecton economes, Journal of Publc Economcs, 48, pp [4] Doherty, N.A. and Thstle, P.D. (1996, Adverse selecton wth endogenous nformaton n nsurance markets, Journal of Publc Economcs, 63, pp [5] Edwn S. Flores Troy, (1997. "The Genetc Prvacy Act: An Analyss of Prvacy and Research Concerns", Journal of aw, Medcne & Ethcs, 25(4, pp [6] rshlefer, J. (1971. The prvate and socal value of Informaton and the reward to ncentve actvty, Amercan Economc Revew, 61, pp [7] Jasngh, J. and Chaturved, A. (2002. On Prvacy, Adverse Selecton and Genetc Databases, Workng paper, Krannert Graduate School of Management. [8] audon, K.C. (1996. Markets and Prvacy, Communcatons of the ACM, Vol 39 (9, pp [9] Mesln, E.M., Thomson, E.J. and Boyer, J.T. (1997. The ethcal, legal, and socal mplcatons research program at the Natonal uman Genome Research Insttute, Kennedy Insttute of Ethcs Journal, 7(3, pp [10] Rothschld, M. and Stgltz, J. (1976. Equlbrum n Compettve Insurance Markets: An Essay on the Economcs of Imperfect Informaton, Quarterly Journal of Economcs, pp [11] Subramanam, K., emare, J., ershey, J.C., Pauly, M.V., Armstrong, K. and Asch, D.A. (1999. Estmatng Adverse Selecton Costs form Genetc Testng for Breast and Ovaran Cancer: The Case of fe Insurance, The Journal of Rsk and Insurance, 66(4, pp [12] Spence, M. (1973. Job Market Sgnalng, Quarterly Journal of Economcs, 87, pp [13] Stgltz J. (1977, Monopoly, Non-near Prcng and Imperfect Informaton: The Insurance Market, The Revew of Economc Studes, 44(3, pp

21 [14] Tabarrok, A. (1994. Genetc testng: an economc and contractaran analyss, Journal of ealth Economcs, 13, pp [15] Townsend, R. (1999, Optmal Contract and Compettve Markets wth Costly State Verfcaton, Journal of Economc Theory, 21, pp [16] Westn, A.F. (1967. Prvacy and Freedom, Atheneum, New York. 20

22 APPENDIX W V V V V V V δ δ δ δ δ δ " δ δ " δ E W 1 Fg. 1. Insurance Contracts 21

23 W 2 V V F V 0 45 V V F δ δ δ δ = δ " P δ " E W 1 Fg 2 Non Exstence of Poolng or Partal Poolng Contracts Proof of emma 1 Settng up the agrangan for maxmzng the proft of the monopolst, wth λ and µ as the multplers for the IR constrants for the low rsk type and hgh rsk types respectvely and takng the frst order condtons, we obtan. θ θ λ= = ( W P ( W D+ I θ θ µ= = ( W P ( W D+ I (A1 (A2 I = D P ; Snce (. > 0, λ > 0 and µ > 0, ( W P = ( W D + I, whch mples that =,. Both rsk types get complete nsurance.e. they have the same wealth n both states. 22

24 The equlbrum contracts are the pont of ntersecton of the ndfference curves wth the equal wealth lne. Snce the ndvdual ratonalty constrant of the hgh rsk type bnds, she gets the same contract δ as n the full nformaton case. The low rsk agent s compensated for her loss of prvacy and so her ndfference curve shfts up. The pont of ntersecton of ths shfted ndfference curve wth the equal wealth lne s the contract δ (Fg Proof of Proposton 1. We verfy that t s an equlbrum for the low rsk consumers to reveal nformaton and get the contract δ, and then show that not revealng nformaton can also be an equlbrum. If nsurer expects the low rsk to reveal nformaton, then, she offers the contracts ( δ, δ (See emma 1. The value of revealng nformaton to the low rsk s Snce V( δ, π γ = V(0, π, I = 0. We wll make the assumpton that the low rsk consumer wll buy If the nsurer expects the low rsk not to reveal nformaton, then she offers the contracts ( δ, δ or she rsk type s always an equlbrum, f the profts to the monopolst from offerng (,. s greater than the proft offerng ( δ, δ.e. = [ ( δ, π γ] (0, π I V V nsurance by revealng nformaton, when I = 0. wll provde nsurance to only the hgh rsk types by offerng the contract δ ( δ,. ( δ, δ Π >Π.. Offerng nsurance only to the hgh δ ( δ, δ can be an equlbrum f the nsurers proft under ths menu of contracts s hgher than the proft under δ. Π( δ, δ Π ( δ,. The value of revealng nformaton for the low rsk types s I = [ V( δ, π γ] V( δ, π = γ 23

25 Snce value of nformaton s negatve, low rsk do not reveal nformaton. The hgh rsk types are ndfferent between δ and δ, so ( δ, δ s also an equlbrum. Proof of emma 2 Stgltz [13] has ruled out the exstence of poolng contracts. In the Stgltz [13] envronment there are only hgh and low rsk consumers. ere we show graphcally that the result doesn t change when unnformed consumers are present, and also rule out partal poolng contracts usng the same logc The separatng menu of contracts s ( δ, δ, δ " " n Fg. 2. EF and EF are the zero proft curves for the unnformed and hgh rsk consumers. Proft curves of the monopolst from the hgh rsk and the unnformed when the she offers the menu of contracts ( δ, δ, δ " " " are parallel to EF and EF respectvely, and pass through the ponts δ and δ respectvely. " " If the monopolst offers the partal poolng contract ( δ, δ, δ, where δ = δ then there always exsts a P P P separatng contract ( δ, " δ, δ " such that the monopolst makes a hgher proft on the hgh rsk agent. Ths can be seen by lookng at the so-proft lne of the monopolst for the hgh rsk consumer through every possble δ and δ P. The monopolst contnues to make the same proft on the low rsk and the unnformed. The same logc extends to poolng contracts. Thus for every possble partal poolng or poolng contract, there exsts a separatng contract that makes a hgher proft. sng ths fact a partal poolng or poolng contract cannot be an equlbrum. Proof of Proposton 2. There are three players n the game the unnformed consumer, the nformed low rsk type and the nsurer 11. The strategy space for the unnformed s to get nformed or to reman unnformed. The strategy space for the nformed low rsk s to reveal nformaton or not to reveal nformaton. The strategy space for the nsurer s to desgn the set of contracts. We adopt the followng approach to calculate the equlbrums - the nsurer pcks the most proftable menu of contracts gven one of the four possble combnatons of strateges of the other two players. If none of the other two players has an ncentve to devate gven the contract offered by the nsurer and the strategy 11 The nformed hgh rsk consumer always end up wth the contract δ and are not part of the game. 24

26 of the other player, then the contract s an equlbrum. We calculate all the equlbrums n four steps; each step corresponds to the nsurers belef on the four possble strategy combnatons of the other two players. Step 1: Assume that the nsurer expects the nformed low rsk type to reveal nformaton and the unnformed type to become nformed, then t would offer the contracts ( δ, δ. The value of revealng nformaton for the nformed low rsk types s u = [ V( δ, π γ] V(0, π Snce V( δ, π γ = V (0, π, u = 0 and all nformed low rsk types would reveal nformaton. The value of gettng nformed for the unnformed s I = { p V( δ, π + p [ V( δ, π γ] c} V(0, π sng the fact that V ( δ, π (0, π, addng and subtractng (0, and usng the fact that pv(0, π + pv(0, π = V(0, π = V pv π I = p [ V ( δ, π V (0, π γ ] c Snce V( δ, π γ = V(0, π, I = c< 0. Snce the value of nformaton s negatve, all unnformed would reman unnformed and so ( δ, δ cannot be an equlbrum. Step 2: Assume now that the nsurer expects the nformed low rsk not to reveal nformaton, and the unnformed to get nformed. In ths case, the nsurer offers the contracts ( δ, δ or just the contract δ. The nsurer s better off offerng the contract ( δ, δ f Π( δ, δ Π( δ,. and she s better off servng just the hgh rsk by only offerng the contract ( δ,. f Π < Π δ ( δ, δ (,.. We look at the case Π( δ, δ Π( δ,. n step 2.a and the case Π ( δ, δ < Π( δ,. n step 2.b. 2.a Insurer offers ( δ, δ u = [ V( δ, π γ] V( δ, π = γ The value of revealng nformaton for the nformed low rsk s 25

27 Snce the value of revealng nformaton s negatve, the nformed low rsk wll not reveal nformaton. The value of gettng nformed for the unnformed s I = { p V( δ, π + p V( δ, π c} V( δ, π sng the fact that V ( δ, π = V( δ, π and pv pv V ( δ, π + ( δ, π = ( δ, π I = c< 0 Snce I s negatve, unnformed wll not become nformed and ( δ, δ cannot be an equlbrum. 2.b. Insurer offers (,. δ The value of revealng nformaton for the nformed low rsk s u = [ V(0, π γ] V(0, π = γ Snce the value of revealng nformaton s negatve, the nformed low rsk wll not reveal nformaton. The value of gettng nformed for the unnformed s I = { p V( δ, π + p V(0, π c} V(0, π sng V( δ, π = V(0, π and pv (0, π + pv (0, π = V(0, π, I = c< 0. nnformed wll not become nformed and so ( δ,. cannot be an equlbrum. Step 3: Assume now that the nsurers expect the nformed low rsk type to reveal nformaton and the unnformed to reman unnformed. In ths case the, nsurers there can be three possble best strateges for the nsurer. sng emma 2 we can rule out poolng and partal poolng contracts. 3.a. Offer nsurance to all three ( δ, δ, δ 3.b. Offer nsurance to the hgh rsk and low rsk and unnformed reman unnsured ( δ,., δ 3.a Insurers best strategy s ( δ, δ, δ f Π( δ, δ, δ Π( δ,., δ The value of revealng nformaton for the nformed low rsk types s 26

28 u = [ V( δ, π γ] V(0, π Snce V( δ, π γ = V(0, π, u = 0, and all nformed low rsk reveal nformaton. The value of gettng nformed for the unnformed s I = { p V( δ, π + p [ V( δ, π γ] c} V( δ, π sng the fact that V ( δ, π = V( δ, π, addng and subtractng pv( δ, π and usng pv( δ, π + pv( δ, π = V( δ, π I = p [ V( δ, π V( δ, π γ] c If γ < V( δ, π V( δ, π c, where c = c/ p, then the value of gettng nformaton s postve, the unnformed choose to become nformed and so the contract ( δ, δ, δ cannot be an equlbrum. If γ > V( δ, π V( δ, π c, then unnformed contnue to reman unnformed, and ( δ, δ, δ s an equlbrum. 3.b Insurers best strategy s to offer ( δ,., δ f Π > The value of revealng nformaton for the nformed low rsk types s u = [ V( δ, π γ] V(0, π. I = p [ V( δ, π V(0, π γ] c ( δ,., δ Π( δ, δ, δ By the same argument as n 3a. all low rsk consumers wll reveal nformaton. The value of gettng nformed for the unnformed s I = { p V( δ, π + p [ V( δ, π γ] c} V(0, π It s easy to show that the value of gettng nformed reduces to ( δ,., δ s an equlbrum only f unnformed reman unnformed.e. γ > V( δ, π V(0, π c where c s same as before. 27

29 Step 4: Assume now that the nsurer expects the nformed low rsk type not to reveal nformaton, and the unnformed to reman unnformed. In ths case the possble best strateges for the nsurer could be one of the followng " " 4.a. Insurer offers the separatng menu of contract ( δ, δ, δ. 4.b. Offer nsurance only to the hgh rsk by only offerng the contract ( 4.c. Offer nsurance to only the hgh rsk and the unnformed- ( δ, δ,. δ,.,. We wll only outlne the steps to check whether each of these strateges can be an equlbrum. In each of the followng steps we wll assume that the contract offered by the nsurer s her best strategy.e. the monopolst maxmzes her profts by offerng the contract. 4.a. ( δ, δ, δ " " " " u = [ V( δ, π γ] V( δ, π = γ I = { p V( δ, π + p V( δ, π c} V( δ, π " " " " I = p [ V( δ, π V( δ, π ] c " " " " If c > V ( δ, π V( δ, π, then ( δ, δ, δ s an equlbrum. 4.b. ( δ,.,. u = [ V(0, π γ] V(0, π = γ sng V( δ, π = (0, π (0, (0, (0, V and pv π + pv π = V π I = { p V( δ, π + p V(0, π c} V(0, π = c Snce value of releasng nformaton for the low rsk and the value of gettng nformed for the unnformed s negatve ( δ,.,. s an equlbrum. 28

30 4.c. ( δ, δ,. u = [ V(0, π γ] V(0, π = γ I = { p V( δ, π + p V(0, π c} V( δ, π I = p [ V(0, π V( δ, π ] c If c > V (0, π V( δ, π, then ( δ, δ,. s an equlbrum. Proof of Proposton 3. As before there are three players n the game the unnformed, the nformed low rsk type and the nsurer. The nsurer now can dentfy the nformed consumers from the unnformed. We calculate all the equlbrums n four steps; each step corresponds to the nsurers best response based on belefs on the four possble strategy combnatons of the other two players. Step 1 and Step 2: No unnformed would become nformed when the nsurer can observe the nformaton status. Reason beng that the an unnformed consumer prefers δ, whch s the contract she would get f she remans unnformed, to a lottery over δ and δ. Ths s a result of her rsk averson. Thus there are no equlbrum where the unnformed becomes nformed. Step 3: Assume now that the nsurers expect the nformed low rsk type to reveal nformaton, and the unnformed to reman unnformed. sng emma 2 we can rule out poolng and partal poolng contracts. The best strategy for the nsurer s to offer the menu of contracts for the nformed low rsk types s u = [ V( δ, π γ] V(0, π ( δ, δ, δ The value of revealng nformaton Snce V( δ, π γ = V(0, π, u = 0, and all nformed low rsk reveal nformaton. The value of gettng nformed for the unnformed s I = { p V( δ, π + p [ V( δ, π γ] c} V( δ, π 29

31 sng the fact that V ( δ, π = V(0, π and V ( δ, π = V(0, π, addng and subtractng pv(0, π and usng pv(0, π + pv(0, π = V(0, π I = p [ V( δ, π V(0, π γ] c= c Snce value of releasng nformaton for the low rsk, and the value of gettng nformed for the unnformed s negatve ( δ, δ, δ s an equlbrum. Step 4: Assume now that the nsurer expects the nformed low rsk type not to reveal nformaton, and the unnformed to reman unnformed. In ths case the possble best strateges for the nsurer could be one of the followng 4.a. Insurer offers the separatng menu of contract ( δ, δ, δ f Π( δ, δ, δ Π( δ, δ,.. 4.b. Offer nsurance to only the hgh rsk and the unnformed- ( δ, δ,. f Π ( δ, δ,. > Π( δ, δ, δ We wll only outlne the steps to check whether each of these strateges can be an equlbrum. In each of the followng steps we wll assume that the contract offered by the nsurer s her best strategy.e. the monopolst maxmzes her profts by offerng the contract. 4.a. ( δ, δ, δ u = [ V( δ, π γ] V( δ, π = γ I = { p V( δ, π + p V( δ, π c} V( δ, π sng the fact that V( δ, π = V ( δ, π, V( δ, π = V( δ, π and pv pv V ( δ, π + ( δ, π = ( δ, π I = p [ V( δ, π V( δ, π ] c " If c > V ( δ, π V( δ, π, then ( δ, δ, δ s an equlbrum. 30

32 4.b. ( δ, δ,. u = [ V(0, π γ] V(0, π = γ I = { p V( δ, π + p V(0, π c} V( δ, π sng the fact that V ( δ, π = V (0, π, V ( δ, π = V (0, π and pv(0, π + pv(0, π = V(0, π I = c Snce value of releasng nformaton for the low rsk and the value of gettng nformed for the unnformed s negatve ( δ, δ,. s an equlbrum. 31