Genetic Information: Comparing Alternative Regulatory Approaches when Prevention Matters

Barigozzi, Francesca; Henriet, Dominique Working Paper Genetic Information: Comparing Alternative Regulatory Approaches when Prevention Matters Quaderni - Working Paper DSE, No. 657 Provided in Cooperation with: University of Bologna, Department of Economics Suggested Citation: Barigozzi, Francesca; Henriet, Dominique (2009) : Genetic Information: Comparing Alternative Regulatory Approaches when Prevention Matters, Quaderni - Working Paper DSE, No. 657, Alma Mater Studiorum - Università di Bologna, Dipartimento di Scienze Economiche (DSE), Bologna, https://doi.org/10.6092/unibo/amsacta/4589 This Version is available at: https://hdl.handle.net/10419/159498 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc/3.0/ Genetic Information: Comparing Alternative Regulatory Approaches when Prevention Matters∗ Francesca Barigozzi†and Dominique Henriet‡ This version: December 2008 Abstract We compare the alternative approaches for regulating genetic information in the health insurance market when prevention measures are available. In the model, firms offer insurance contracts to consumers who are initially uninformed of their risk type but can obtain such information by performing a costless genetic test. A crucial ingredient of our analysis is that information has decision-making value since it allows for optimal choice of a self-insurance action (secondary prevention). We focus on the welfare properties of market equilibria obtained under the different regulatory schemes and, by using an intuitive graphical analysis, we rank them unambiguously. Our results show that Disclosure Duty weakly dominates the other regulatory schemes and that Strict Prohibition represents the worst regulatory approach. Keywords: health insurance markets, information gathering, discrimination risk, classification risk, self-insurance. JEL classification: D82; D83; G22; L52. 1Introduction Recent developments in medical science make genetic testing for more than 1000 diseases available to consumers. Genes that imply an elevated risk of several types of cancer, cardiovascular diseases, Alzheimer’s and Huntington’s disease, cystic fibrosis, etc. can be detected. Whenever consumers undertake a test they acquire more precise information on the probability that the illness related to ∗The authors are grateful to Giacomo Calzolari, Liqun Liu, Wolf Rogowski, Katharina Fischer and seminar participants in Bologna, Cagliari, London, Milan, Rome and Toulouse for helpful comments and discussions. †Department of Economics, University of Bologna and CHILD, P.zza Scaravilli 2, 40126 Bologna (Italy). E-mail: [email protected] ‡Department of Economics, Ecole Centrale Marseille, GREQAM and IDEP. E-mail: [email protected] 1 the tested gene will occur. This means that individuals can learn information about their risk. If privacy rules are in place to keep such information private, adverse selection can arise endogenously in the health insurance market. In the ongoing debate on the use of genetic information in insurance markets (illustrated, for example, in Hoy and Ruse 2005) insurance firms are worried that adverse selection and related inefficiencies will increase if consumers can secretly take a genetic test and conceal its result. On the other hand, consumers fear that a class of potentially uninsurable individuals, the ”bad genetic risks”, will be created if insurers can oblige consumers to take a genetic test before policy purchase. This problem is generally referred to as the ”discrimination risk”. However, both consumers and insurers agree that individuals should not lose, because of their fear of the discrimination risk, the important prevention opportunities offered by genetic information. As regards prevention opportunities, our model considers secondary prevention measures (early detection of disease). The efficacy of secondary prevention choices is increasing in the precision of information about the risk of illness (the higher the consumers’ risk, the higher the benefits they obtain from prevention). Secondary prevention corresponds to a self-insurance measure because it reduces the health loss when the illness occurs. As an example, we can consider the BRCA1 and BRCA2 genetic mutations which are implicated in many hereditary breast cancer cases and the genetic mutation responsible for hereditary non-polyposis colorectal cancer (HNPCC). An individual who is positive to a genetic test for one of the mentioned mutations should more frequently perform screening measures such as mammography and colonoscopy to detect the illness at an early stage. While some authors have investigated the case of primary prevention, that is the availability of measures reducing the probability of illness (see Doherty and Posey 1998, Strohmenger and Wambach 2000, Hoel and Iversen 2002), no one has analyzed secondary prevention even though an improved efficacy in the use of such a type of prevention probably represents the most important health benefit of genetic testing to consumers. Many elements affect consumer decisions to learn information about their risk of illness. First, as we already mentioned, genetic information has decisionmaking value since it allows secondary prevention measures to be properly targeted to consumer morbidity. In this sense genetic information is beneficial to consumers. Second, when they gather information, consumers face the risk of learning that they are high-risk and thus information brings with it the risk of paying a high premium (classification risk). Since no coverage for the classification risk is available, genetic information is costly for risk-averse consumers.1 Finally, the regulatory scheme for genetic information in place in the health insurance market influences consumer choices, as we will see. Today four major types of market regulation of genetic information exist (see Viswanathan et al. 2007, Hoy and Ruse 2005 and references within both 1In the real world (and in our model as well) the health insurance market is not able to provide policies that cover the classification risk, despite the obvious increase in consumer welfare. We discuss a remedy to this issue in subsection 2.3.1. 2 of them).2They are listed below from no-regulation to the most strict regulatory scheme. (i) ”Under a Laissez-Faire approach insurers have full freedom to request new tests and the disclosure of existing tests, and to incorporate test results in underwriting and rating”. The previous and the following quoted sentences are taken from Viswanathan et al. (2007), page 68. Laissez-faire is practiced in Australia, Canada, China, Japan, Korea, Ireland, Portugal, Russia, Singapore, Spain and South Africa. (ii) Under the Disclosure Duty approach consumers ”have to disclose the results of existing tests, at the insurers’ request, but cannot be required to take additional tests”. This is true in Germany, New Zealand, and the UK. (iii) Under the Consent Law approach consumers ”are not required to divulge genetic tests results. If they do, insurers may use this information”, as in the Netherlands and in Switzerland. Finally, (iv) under Strict Prohibition, ”insurers cannot request genetic tests, cannot require applicant to provide existing tests results, and cannot use any genetic information in underwriting and rating”, as in Austria, Belgium, Denmark, France, Israel, Italy and Norway. In the U.S., the Genetic Information Non-discrimination Act (GINA) was signed into law in May 2008. The bill places restrictions on insurers, banning the use of genetic information in underwriting health insurance policies.3 Thus, we can now equate the U.S. approach to Strict Prohibition. The question of genetic privacy is still hotly debated in many countries, as documented by the recent adoption of GINA in the U.S. and by the ongoing discussion (fall 2008) in Germany where a new law aiming at full prohibition of the use of genetic test results in health insurance has been proposed.4More- over, most countries seem to converge towards assigning consumers full privacy on genetic information and banning information transmission to insurers (Strict Prohibition). Also, being aware of the current public perception that genetic information is somehow different from other health information5, in some countries insurance firms have signed a voluntary moratorium on the use of genetic information in health insurance policies (e.g. in the U.K. and in France). In this paper we consider a simple model which enables us to analyze and compare the previously mentioned regulatory approaches for genetic information when secondary prevention is available. We characterize market outcomes under the different regulatory structures and derive a complete ranking. We believe such a welfare analysis is worthwhile in the debate on genetic testing to understand which regulatory approach is preferable from a social welfare point of view and whether protecting consumers’ privacy on genetic information really 2A similar list appears in Doherty and Thistle (1996) as regards regulatory schemes concerning HIV testing and insurance. 3In general, regulation of genetic information is much stricter in the health than in the life insurance market. The implicit reason is that health insurance is considered a priority for consumers whereas life insurance is not. 4This means that Germany is moving from the Disclosure Duty to the Strict Prohibition approach. 5This is called ”genetic exceptionalism” and is due to many reasons. Among them are historical reasons (eugenetics), the potential loss of control over samples and the predominance of predictive genetic tests for monogenetic, very serious diseases (e.g. Huntington’s disease). See the European Commission (2004). 3 increases consumers’ welfare and really avoids the discrimination risk. To the best of our knowledge this type of analysis is missing in the literature on genetic testing. In the model we consider the following timing of actions (in all the regulatory approaches, except in the Laissez-Faire where the order of the first two actions is reversed). First, insurance firms propose contracts to consumers. Second, consumers decide whether to perform a costless genetic test and, possibly, whether to show its result to the insurers. Then consumers accept a contract and, finally, they choose prevention taking as given the insurance policy. Our results show that from a social welfare point of view, the Disclosure Duty approach weakly dominates all the other regulatory schemes. The Laissez- Faire and the Consent Law approaches lead to the same equilibrium allocation. The equilibrium allocation under Strict Prohibition is dominated by all other regulatory schemes. Under Consent Law and Strict Prohibition information always has positive private value, whereas Disclosure Duty leads to information gathering only when the benefit of better prevention choices prevails over the cost raised by the classificationrisk. ThisispreciselywhyDisclosureDuty maximizes consumers’ welfare. When, under Disclosure Duty, information has positive value, this regulatory scheme leads to the same equilibrium allocation as Consent Law and Laissez-Faire. In all the regulatory approaches, when the test is performed, information is disclosed at the equilibrium. Under Consent Law, information is certifiable and it is transmitted at no cost by low-risk consumers showing insurers the test result whereas under Strict Prohibition, screening is obtained through the Rothschild-Stiglitz separating allocation, thus the equilibrium implies a welfare loss since the low-risks receive partial insurance. Strict Prohibition is the only regulatory scheme that endogenously generates adverse selection. As regards prevention choices, when information always has positive private value, that is with Laissez-Faire, Consent Law and Strict Prohibition, choices are always efficient (in a sense that will be specified in the paper) whereas under Disclosure Duty, they are efficient only when consumers learn information. As is discussed in the concluding section, our results have important policy implications since the most commonly adopted regulatory scheme turns out to be the least efficient one. As regards the related literature, all the papers dealing with genetic testing are clearly relevant.6However, the papers most closely related to our study analyze endogenous information in insurance markets and are mentioned below. Crocker and Snow (1992) first showed that, if coverage against the classification risk is not available and if insurers can observe both whether consumers performed the test and the test result itself, the private value of information 6For example, in Hoel and Iversen (2002) genetic information allows better primary prevention measures to be taken and the health insurance market is characterized by a mix of compulsory and voluntary insurance. Hoel et al. (2006) analyze a model where consumers are characterized by preferences for late resolution of uncertainty concerning their health risk. Strohmenger and Wambach (2000) analyze a model with state contingent utility functions. Hoy and Polborn (2000) consider a life insurance model. Interesting empirical analysis can be found in Hoy and Witt (2007), Viswanathan et al. (2007). 4 is negative and consumers prefer to remain uninformed. Doherty and Thistle (1996) developed a model where some consumers are initially informed on their risk type and others are not. They showed that information has positive private value only when insurers cannot observe consumers’ information status, that is if consumers can conceal not only the test result but also the fact that they performed the test. Both when information provided by the test is not verifiable and when the test result is certifiable (that is under Strict Prohibition and Consent Law respectively), at the equilibrium all consumers perform the test. In Doherty and Posey (1998) information has decision-making value. However, as already noted, the latter authors analyze the case of self-protection; we instead consider the case of self-insurance. Moreover, all the previously mentioned authors analyze one or two information structures at most, we instead compare all the alternative regulatory approaches and we are able to rank them unambiguously. Finally our paper is also related to the more general literature on information gathering before contracting (among others Hirshleifer 1971 and Khalil and Cremer 1992)7and, more closely, to the literature on the economics of privacy. In line with the Chicago School approach to the latter issue (for example Stigler 1980 and Posner 1981), our results show that privacy is not welfare improving. In our model this happens because, if privacy is assigned to consumers on their information status and on test results, consumers decide to learn information also when it is inefficient to do so. Our paper is organized as follows. Section 2 introduces the model set-up and analyses the decision-maker’s problem without insurance. Subsection 2.2 describes how insurance coverage affects consumer choices in terms of prevention and defines the interim optimal allocation. Subsection 2.3 shows the ex-ante optimal allocation and discusses how to decentralize such allocation in the market. Both the interim optimal and the ex-ante optimal allocations will be used to rank market outcomes in the subsequent sections. In section 3 market equilibria are obtained and characterized under the different regulatory schemes. In Section 4 we compare the alternative regulatory structures and derive a complete ranking. Section 5 provides some final remarks and discusses policy implications. We relegate almost all the proofs to the appendix. 2 The model Decision-makers are endowed with a fixed amount of wealth w, and are characterized by the von Neumann-Morgenstern utility function u(w),increasing and concave. They face the risk of a monetary loss L(a),where 0<L(a)<w. The action ais a self-insurance measure. By interpreting L(.)as the monetary equivalent of a negative health shock, the action arefers to secondary prevention or early detection of disease. The action can take only two values, 0and 1 (either decision-makers perform prevention or not) with L(1) = l<L(0) = L. Moreover, the action ais taken before the realization of the risk and implies a 7See Bennardo (2008) for a recent analysis along these lines. 5 utility cost Ψ(a),withΨ(0) = 0 and Ψ(1) = Ψ.In the real world secondary prevention which allows early curative action is generally observable and certifiable; thus, we assume that insurers observe the action a. As a consequence, all the insurance contracts analyzed in the paper are contingent on the level of secondary prevention. We consider two decision-maker types, the high- and the low-risks, respectively characterized by the probability pLand pHof incurring the loss, with 0<p L<p H<1.We assume that pLand pHare fixed, so that no ex-ante moral hazard problem exists. The proportion of high- and low-risk types in the population is λand (1 −λ)respectively. These parameters are assumed to be common knowledge. Consumers do not know their type ex-ante, they perceive their loss probability as pU=λpH+(1−λ)pL.Information can be gathered without cost by performing a genetic test. Risk neutral insurance companies propose contracts to consumers. The insurance market is characterized by free entry such that insurance firms earn zero profits in equilibrium. This is why, in our analysis, social welfare corresponds to consumer welfare. 2.1 The decision-maker’s problem without insurance In this subsection we focus on the decision whether to gather information when insurance is not available. Consumers decide whether to learn information or not by anticipating that, in the subsequent stage, they will choose whether to perform prevention given the information they may have acquired. Proceeding backward, let’s consider the second stage, that is the choice of the preventative action. An individual characterized by loss probability pi∈ {pL,p U,p H}who chooses action aachieves the following expected utility level: V(pi,a)=piu(w−L(a)) + (1 −pi)u(w)−Ψ(a) The decision-maker chooses a positive amount of prevention if V(pi,1) ≥ V(pi,0),that is if piu(w−l)+(1−pi)u(w)−Ψ≥piu(w−L)+(1−pi)u(w), or: pi≥Ψ u(w−l)−u(w−L)=Ψ ∆0 (1) The term ∆0is positive and measures the benefit from prevention. When this term is large and/or the cost of prevention Ψis low, inequality (1) is easily verified. Put differently, inequality (1) shows that decision-makers choose to perform prevention when their loss probability is sufficiently high. Remark 1 The uninsured decision-makers choose prevention if inequality (1) holds. This implies that incentives to perform prevention are increasing in the decision-makers’ risk. 6 Let’s define ba(pi)the action chosen by an individual characterized by probability of loss piand b V(pi)the individual’s indirect expected utility when the probability is piand the chosen action is ba(pi). In the first stage, uninformed decision-makers compare utility when they remain uninformed to expected utility when they gather information, that is ˆ V(pU)to λb V(pH)+(1−λ)b V(pL).The following remark illustrates consumer choices about information when insurance is not available. Remark 2 Without insurance, (i) when prevention is optimal for low-risks (pL≥Ψ ∆0)or when no-prevention is optimal for high-risks (pH≤Ψ ∆0),decisionmakers are indifferent between remaining uninformed and gathering information. (ii) When pL<Ψ ∆0<p Huninformed decision-makers acquire information on their risk-type. Proof. See Appendix 6.1. From 1, when prevention costs are such that the optimal action for informed low-risks is a positive level of prevention, prevention is optimal also for uninformed and informed high-risks. Thus, uninformed individuals are indifferent between acquiring and not acquiring information. The same reasoning applies when informed high-risks choose no-prevention.8On the contrary, when pL<Ψ ∆0<p H,positive prevention is optimal for high-risks whereas no-prevention is the optimal choice for low-risks. Intuitively, here information is useful for appropriate prevention decisions so that acquiring information is welfare improving. Note that, since no insurance is available, when deciding whether to gather information individuals do not face the classification risk, they simply anticipate the positive effect of information in terms of better prevention choices. Social welfare when insurance is not available, W0,is represented in Figure 1 as a function of prevention cost Ψ.Notethat,for0≤Ψ≤∆0pL,both types perform prevention; for ∆0pL<Ψ<∆0pHhigh-types only perform prevention; for Ψ≥∆0pHno one performs prevention. We conclude this section by observing that, without insurance, the private and social value of information is positive for ∆0pL<Ψ<∆0pH.9In all the other cases the private and social value of information is zero and decisionmakers are indifferent between remaining uninformed and gathering information. 2.2 Interim optimal insurance We analyze here optimal insurance contracts from an interim perspective, that is when decision-makers perform the test and the test result is public informa- 8Note that, when the action ais not available, uninsured decision-makers are always indifferent between remaining uninformed and learning their type. In other words, without insurance and considering decision-makers uniquely concerned with information gathering, V(pU)is always equivalent to λV (pH)+(1−λ)V(pL). 9Note that, under the Law of Large Number, consumers’ expected utility and social welfare are the same such that the private and social value of information are equivalent. 7 tion. In the next sub-paragraph we will analyze the ex-ante optimal allocation. Both the ex-ante optimal and the interim optimal allocation will be used to characterize and rank market outcomes under the different regulatory schemes. In the following Piindicates the insurance premium and Iithe indemnity reimbursed in the event of the loss occurring. The optimal contract is hence the solution of the following program: (max Pi,Ii,ai piu(w−Pi−L(ai)+Ii)+(1−pi)u(w−Pi)−Ψ(ai) s.t.: Pi≥piIi where i=L, H. Obviously the optimal contract provides full-insurance: Ii= L(ai)at a fair premium. Assuming full information, risk neutral insurance firms and free entry, the interim optimal allocation can be decentralized in the market. In such a case consumers choose prevention given the full-insurance contract (piL(ai),L(ai)). The level W(pi,a)of utility achieved by a decision-maker characterized by risk piand action ais: W(pi,a)=u(w−piL(a)) −Ψ(a) Prevention is positive if W(pi,1) ≥W(pi,0): u(w−pil)−Ψ≥u(w−piL) or: ∆(pi)=u(w−pil)−u(w−piL)≥Ψ(2) Remark 3 In the interim optimal allocation: (i) prevention is performed if inequality (2) holds; (ii) incentives to perform prevention are increasing in the decision-maker’s risk; (iii) given a risk pi,incentives to perform prevention are lower than without insurance. Proof. See Appendix 6.2. Note that, if ∆(pi)<Ψ≤pi∆0,type-pidoes not exert prevention when fully insured whereas he chooses positive prevention when uninsured. In fact, insurance reduces the benefits from the preventative action and discourages prevention for a given risk. Total welfare in the interim optimal allocation is: W∗ I=λu(w−pHL(˜a(pH)))+(1−λ)u(w−pLL(˜a(pL)))−λΨ(˜a(pH))−(1−λ)Ψ(˜a(pL)) (3) where ˜a(pi), the action chosen by an individual characterized by risk pi,is 1if inequality (2) holds and 0otherwise. From Remark 3: Definition 1 (Interim optimal allocation) The interim optimal allocation W∗ Iis the allocation such that decision-makers are informed and fully insured. Premium is type-dependent and equal to ˜ Pi=piL(˜a(pi)).Moreover: •when 0≤Ψ≤∆(pL),˜a(pL)=˜a(pH)=1. 8 values of prevention cost consumers may prefer to acquire information. In fact, when prevention cost is close to ∆(pU)ignorance can make decision-makers’ prevention choices very inefficient: for Ψ3≤Ψ≤∆(pU)uninformed low-types perform prevention despite prevention cost being too high given their risk and, for ∆(pU)≤Ψ≤Ψ4,uninformed high-types do not perform prevention despite prevention cost being sufficiently low given their risk. The following corollary summarizes the welfare properties of the equilibrium allocations described in Lemma 1. Corollary 1 (Welfare properties of equilibrium allocations under Disclosure Duty)When insurance against classification risk is not available and a Disclosure Duty rule is in place: (i) in Type 1 Equilibrium social welfare is WU:with respect to the first-best over-prevention arises for Ψ1<Ψ≤∆(pU) whereas under-prevention arises for ∆(pU)<Ψ<Ψ2.(ii) in Type 2 Equilibrium, in the interval Ψ3≤Ψ≤Ψ4the interim optimal allocation W∗ Iis reached and prevention choices are interim efficient whereas for Ψ<Ψ3and Ψ>Ψ4social welfare is WUwith over-prevention arising for Ψ1<Ψ<Ψ3and under-prevention arising for Ψ4<Ψ<Ψ2. (iii) Welfare losses (with respect to the first-best)arelowerinType2EquilibriumthaninthatofType1. Inboth equilibria first-best is reached for Ψ≤Ψ1and Ψ≥Ψ2. Proof. (i) The welfare comparison between WUand W∗ EA can be easily obtained from Figure 2. (ii) The welfare comparison between Equilibrium of type 2 and first-best can be performed by comparing W∗ EA in Figure 2 with the kinked bold line in Figure 3 and noting that Ψ1<Ψ3<Ψ4<Ψ2. As a final observation, in our graphical analysis the vertical distance between the kinked lines W∗ Iand WUfor Ψ=0describes the welfare loss that decisionmakers incur when they face the classification risk (see Figure 3). In this last paragraph we consider the private and social value of information under Disclosure Duty. For the Law of Large Numbers, W∗ Iand WUrepresent both consumers’ (expected) utility and social welfare. Moreover, given the informational structure characterizing Disclosure Duty, the private and social value of information are equivalent. Corollary 2 (The value of information under Disclosure Duty) Under Disclosure Duty, the private and social value of information are the same. In Equilibrium of Type 1 the value of information is always negative. In Equilibrium of Type 2 the value of information is positive for Ψ3<Ψ<Ψ4and negative for Ψ<Ψ3and Ψ>Ψ4. 3.2 The Consent Law approach Under Consent Law decision-makers can secretly take the test before insurance purchase and are then free to show the test result or to conceal it. If they transmit the information provided by the test to insurers, the latter can use such information for rating. Thus, insurers offer contracts contingent on information 15 Figure 4: consumers’ decision-tree under Consent Law. that may have been disclosed by consumers. Figure 4 shows the decision-makers’ decision tree under Consent Law. Informed individuals who learn that they are low-types have incentives to show the test result to insurers to buy the policy at a low premium. Individuals who receive bad news, on the other hand, prefer to conceal the test result by pretending to be uninformed. Since insurers are not able to separate (ex-ante) the informed high-risks from the uninformed, they must offer the same contract to both of them (see Figure 4). In this situation, if decision-makers choose to perform the test, insurance firms can easily screen consumer types by offering full insurance at a fair premium to low-risks who show the test result. Decision-makers pretending to be uninformed are necessarily high-risks and, at the equilibrium, they also receive full insurance at a fair premium. This screening mechanism works only if performing the test is a dominant strategy for uninformed consumers. We show in the proof of the following lemma that decision-makers do prefer to acquire information if firms offer to uninformed individuals a (partial) insurance contract such that informed high-risks, by accepting such a policy, receive the same utility as they would by showing insurers the test result. The intuition is that, by performing the test, decision-makers can always obtain the same utility as uninformed (when they learn they are high-risk) or they may be able to choose a policy that is strictly preferred (when they learn that they are low-risk). Lemma 2 (Equilibrium allocation under Consent Law)UndertheConsent Law approach, at the equilibrium decision-makers perform the test and show the test result to insurers when they learn that they are low-risk. Both types receive full insurance at a fair premium.13 13The described equilibrium is unique. In fact, no other equilibrium exists where consumers learn information, nor an equilibrium where decision-makers remain uninformed. To see the latter point note that fair full insurance contracts must be offered to people showing the test result, since otherwise new firms would enter the market and make positive profits on low- 16 Proof. See the Appendix 6.5. Lemma 2 extends Doherty and Thistle’s Proposition 2 (1996) to the case of secondary prevention. Our proof is different, however, since Doherty and Thistle consider a game with simultaneous moves, whereas we assign the first move to insurers. Moreover, in Doherty andThistlesomeconsumersknowtheir risk ex-ante, whereas here all consumers are ex-ante uninformed. From the previous discussion:14 Corollary 3 (Welfare properties of the equilibrium allocation under Consent Law) When insurance against the classification risk is not available and Consent Law is in place, the equilibrium allocation corresponds to the interim optimal allocation and prevention choices are interim efficient. Since, under Consent Law, acquiring information is a dominant strategy for decision-makers, the private value of information is positive. As for the social value of information, it corresponds to the difference between welfare in the equilibrium allocation W∗ Iand welfare in the allocation that would emerge when consumers remain uninformed WU.15 The following corollary can be stated: Corollary 4 (The value of information under Consent Law) Under Consent Law (i) the private value of information is positive; (ii) when condition (9) holds, the social value of information is always negative. When the opposite of condition (9) holds, the social value of information is positive for Ψ3<Ψ<Ψ4and negative for Ψ<Ψ3and Ψ>Ψ4. 3.3 The Strict Prohibition approach Under Strict Prohibition insurers cannot request any genetic test and cannot use genetic information for rating. This implies that, as under Consent Law, privacy risks. Moreover,wehavealreadyobservedthatthesamepolicymustbeoffered to informed consumers not showing the test result and to the uninformed. Thus, remaining uninformed can never be a dominant strategy. 14Note that, when the information structure is such that insurers observe decision-makers’ information status but not the test result, a different equilibrium allocation arises. In fact, in such a case, different contracts can be offered to informed high-risks and to uninformed decision-makers. Moreover, informed consumers not showing the test result are necessarily high-risks. Thus, both uninformed and informed high-risk consumers receive full coverage at a fair premium (respectively pUL(aU)and pHL(aH)). As a consequence, when deciding whether to learn their type, decision-makers must choose between the allocation for uninformed consumers WUand the interim optimal allocation W∗ Iso that we are back to the equilibria obtained under the Disclosure Duty approach. This proves that, from a social welfare point of view, Disclosure Duty is equivalent to a regulatory scheme assigning privacy to the test result but not to consumers’ information status and allowing information transmission on test results from consumers to insurers. 15To calculate the social value of information we do not compare the market outcome under Consent Law with the ex-ante optimal allocation. In fact, since the classification risk is not covered in our market (compulsory genetic insurance is not enforced), first-best can never be reached. 17 is assigned to consumer information status and to the test result; however, unlike Consent Law, a ban is imposed on information transmission and use.16 We prove that, as under the Consent Law approach, information gathering is a dominant strategy for decision-makers. However, here the equilibrium corresponds to the Rothschild-Stiglitz separating allocation. As before, insurers are able to screen consumer types and the information acquired is disclosed at the equilibrium. Unlike the previous case, informed low-risks receive partial insurance. The Rothschild-Stiglitz separating contracts work as a screening mechanism only if performing the test is a dominant strategy for uninformed consumers. We show in the following lemma that, if firms offer consumers a set of selfselective contracts involving partial insurance at a fair premium, decision-makers will indeed choose to acquire information. In particular, as under Disclosure Duty, insurance firms offer three different types of contract: one for uninformed consumers, one for informed high-risks and one for informed low-risks. However, since the consumers’ informational status is private information, here contracts must be self-selecting. Lemma 3 (Equilibrium allocation under Strict Prohibition)Underthe Strict Prohibition approach, decision-makers perform the test. The equilibrium corresponds to the Rothschild-Stiglitz separating allocation. Proof. See Appendix 6.6. This result extends Doherty and Thistle’s Proposition 1 (1996) to the case of secondary prevention. Again our proof is different since in our model choices are sequential and all decision-makers are ex-ante uninformed.17 As regards market outcome under Strict Prohibition we can say the following:18 16The same information structure can also describe a situation where insurers’ associations adopt a voluntary moratorium on the use of genetic tests. 17The existence of an equilibrium requires the usual Rothschild-Stiglitz condition on the number of low-risks, which must be sufficiently high (Rothschild and Stiglitz 1976). If such condition is not verified we can use different equilibrium concepts such as the Wilson or the Miyazaki equilibrium (see Wilson 1977 and Miyazaki 1977). Both equilibria emerge when the Rothschild-Stiglitz one does not exist. The Wilson equilibrium occurs when insurers can withdraw contracts making negative profits, whereas the Miyazaki equilibrium occurs when insurance companies can offer several contracts involving cross-subsidization. Note that whatever concept of equilibrium we use, the proof in Appendix 6.6 still holds and information gathering remains the consumers’ dominant strategy. 18Note that, when information structure is such that insurers observe decision-makers’ information status but not the test result and a ban on information transmission exists, a different equilibrium occurs. Since contracts can be contingent on consumers’ information status, uninformed individuals receive full coverage at a fair premium whereas informed ones receive self-selective (Rothschild-Stliglitz) contracts. As a consequence, when deciding whether to learn information, decision-makers must choose between the allocation for uninformed consumers WUand the lottery assigning full coverage at a high premium with probability λand partial coverage at a low premium with probability 1−λ. This leads to equilibria similar to the ones we obtained with Consent Law under the same informational structure (see footnote 14). However, in the present case, consumers will prefer to remain uninformed more often since here information gathering leads to the Rothschild-Stliglitz equilibrium, that is to a lower welfare. 18 Corollary 5 (Welfare properties of the equilibrium allocation under Strict Prohibition) When insurance against the classification risk is not available and Strict Prohibition is in place, the equilibrium allocation is such that high-risks receive full insurance at a fair premium, whereas low-risks receive partial insurance at a fair premium. Prevention choices are interim efficient for high-risks, whereas low-risks perform prevention more often than in the interim efficient allocation. Proof. The first sentence comes directly from Lemma 3. For the last sentence see Appendix 6.7. We have shown that under Strict Prohibition decision-makers perform the test. Again this implies that the private value of information is positive. As regards the social value of information, we compare the Rothschild-Stiglitz separating allocation and WU. The following corollary can be stated: Corollary 6 (The value of information under Strict Prohibition) Under Strict Prohibition (i) the private value of information is positive; (ii) when condition (9) holds, the social value of information is always negative. When the opposite of condition (9) holds, the social value of information is negative for Ψ<Ψ3and Ψ>Ψ4and is lower than under consent law for Ψ3<Ψ<Ψ4.19 We saw that under Consent Law the equilibrium allocation W∗ Idominates WUonly if the opposite of condition (9) holds and prevention costs belong to the interval [Ψ3,Ψ4]. Under Strict Prohibition and when the previous conditions are verified, social welfare is lower than under Consent Law because of the welfare cost paid by (partially insured) low-risks in the Rothschild-Stiglitz equilibrium. This explains the second part of point (ii) in Corollary 6. 3.4 The Laissez-Faire approach Under the Laissez-Faire approach insurers can request the disclosure of existing tests (as under Disclosure Duty) and they can also request new tests to be performed (and disclosed). Since in our setting consumers are ex-ante uninformed, this regulatory approach implies that insurers decide whether consumers should perform the test or not. Given that the test is costless and useful for rating, insurers will always ask consumers to perform the test. Like disclosure duty, the Laissez-Faire approach implies symmetric information between consumers and insurance firms. A natural interpretation of the first actions in the timing is the following: insurers ask potential consumers to perform the test and then the test result 19Contrary to us, Doherty and Posey (1998) find that the social value of information is always positive when information structure corresponds to Strict Prohibition. This difference essentially depends on the fact that, in their model, part of the consumers are ex-ante informed. Thus, to evaluate the social value of information, they compare the equilibrium allocation (where all consumers become informed) with the allocation that would arise without information gathering (where the uninformed remain uninformed and informed consumers receive the Rothschild-Stiglitz separating contracts). 19 is disclosed to both consumers and insurers.20 The consequence is that, under Laissez-Faire,insurersoffer full insurance contracts at a fair premium to high- and low-types. Lemma 4 (Equilibrium allocation under Laissez-Faire)UndertheLaissez- Faire approach the equilibrium allocation corresponds to the interim efficient allocation and prevention actions are interim efficient. Since under Laissez-Faire insurance firms require consumers to perform the test, the private value of information has no meaning. As regards the social value of information, as under Consent Law, we must compare allocations W∗ Iand WU.Thus, part (ii) in Corollary 4 also applies to the Laissez-Faire approach. 4 A comparison of the alternative regulatory approaches We now compare the different regulatory approaches analyzed before and derive a complete ranking. From the four previous lemmas we can state the following: Proposition 1 (Welfare comparison of the alternative regulatory approaches) From a social welfare point of view the Disclosure Duty approach weakly dominates all the other regulatory schemes. The Laissez-Faire and the Consent Law approaches lead to the same equilibrium allocation. The equilibrium allocation under Strict Prohibition is dominated by all the other regulatory schemes. In the rest of this section first we summarize our results as regards prevention choices and then as regards information disclosure at the different equilibria. Under the Laissez-Faire and the Consent Law approaches prevention choices are interim efficient. With Strict Prohibition they are interim efficient for highrisks, whereas low-risks choose prevention under partial insurance. This implies that low-risks perform prevention more often under Strict Prohibition than in the interim efficient allocation. Under Disclosure Duty prevention choices are interim efficient only in Equilibrium of Type 2 for prevention costs belonging to the interval [Ψ3,Ψ4].Importantlyinsuchaspecific case, Disclosure Duty, Laissez-Faire and Consent Law all lead to the same equilibrium allocation and therefore to the same social welfare, whereas in all the other cases disclosure duty strongly dominates the other regulatory schemes even though it leads to less efficient prevention choices. Note that the effectiveness of secondary prevention, the magnitude of the classification risk as well as the cost of prevention all 20Note that, if the order of the first two actions in the timing were the same as before (first insurers offer contracts, then they ask consumers to perform the test and the test result is disclosed), the first best allocation would be obtained. In fact, in such a case the insurance contract offered by insurers would also cover the classification risk. However, since in the real world the classification risk is not covered, we exclude such a sequence of actions. 20 affect the decision to gather information under Disclosure Duty and therefore the possibility of Equilibrium of Type 2 occurring.21 As a final observation Laissez-Faire, Consent Law and Strict Prohibition always lead to information disclosure at the equilibrium. Disclosure Duty, again, leads to information disclosure only in Equilibrium of Type 2 and for intermediate values of prevention costs. In general, either the informational structure is such that insurers observe the test result, if any (as in the Laissez-Faire and in the Disclosure Duty approach), or insurers learn information on consumer risks ex-post by using self-selective contracts. Basically, under Consent Law information is transmitted at no cost by low-risks showing insurers the test result. Under Strict Prohibition, on the other hand, screening requires a welfare cost since self-selecting contracts provide partial insurance to the low-risks. Put differently, Strict Prohibition is the only regulatory scheme which endogenously produces standard adverse selection. 5Conclusion In this paper we contribute to the literature on genetic testing by (i) introducing secondary prevention measures which assign decision-making value to genetic information and by (ii) providing a welfare analysis of the alternative schemes used to regulate genetic information. In particular, we investigate the four main regulatory approaches we find today in health insurance markets: Laissez-Faire, Disclosure Duty, Consent Law and Strict Prohibition. Our simple and tractable model allows for unambiguous ranking. In our model consumers may gather information on their risk of illness before insurance policy purchase. Insurance firms offer policies covering the risk of the monetary loss associated with the illness but not the classification risk. We put ourselves in a context which seems more natural when considering information provided by genetic testing: we assume that all consumers are ex-ante uninformed and that information allows better choices as regards secondary prevention. Our model makes some assumptions that could be worth relaxing in the future. Genetic tests have no cost and consumer prevention choices are observable by insurance firms. However, the first assumption is common to almost all the literature on genetic testing22 and the second one is plausible for secondary prevention, which indicates a certifiable medical procedure. 21For example we expect Equilibrium of Type 1 to occur under Disclosure Duty in the case of genetic test for Huntington’s disease since, for such an illness, classification risk is high and early detection of disease is ineffective. Thus, Disclosure Duty should strongly dominate the other regulatory schemes as regards testing for Huntington’s disease whereas Equilibrium of Type 2 could occur under Disclosure Duty in the case of tests detecting BRCA1, BRCA2 or HNPCC genetic mutations since, for the illnesses related to those mutations, effective secondary prevention exists. Thus, for those tests and for some values of prevention costs, Disclosure Duty could be equivalent to Consent Law and Laissez-Faire. 22An exception is Doherty and Thistle (1996). 21 Our results show that market and health authorities aiming at maximizing consumers’ welfare should implement a mild type of regulation such as the Disclosure Duty scheme. With this regulatory approach consumers are free to decide whether to perform genetic tests but have no privacy rights on information status and on test results. We have proved that only under Disclosure Duty consumers remain uninformed when the cost imposed by the classification risk prevails over the benefit of information in terms of better prevention measures, that is, when gathering information is not efficient. The result that the insurance market performs better under mild regulation than under strong regulation of genetic information is not new. In different models Hoel and Iversen (2002) and Hoel et al. (2006) reached the same conclusion.23 What clearly emerges from our analysis is that Strict Prohibition, the most widespread regulatory approach, adopted with the explicit objective of increasing consumers’ welfare by avoiding genetic discrimination, leads to the worst market outcome from a consumer welfare point of view. Strict Prohibition assigns consumer privacy on information status and test result and bans information transmission from consumers to insurers. Such a ban turns out to be detrimental to consumer welfare because it leads to adverse selection and thus prevents efficient exchange in the health insurance market. Consent Law performs better than Strict Prohibition because it assigns consumers both privacy on genetic information and control rights on information provided by the test. More generally, privacy on genetic information turns out to be of no use in preventing discrimination since under both Consent Law and Strict Prohibition insurance firms adopt screening devices such that information is fully disclosed at the equilibrium. To conclude, governments aiming at protecting ”bad genetic risks” from discrimination should not impose strict regulation of genetic information; they should instead opt for a Disclosure Duty rule and then provide a specific public program, or expand the existing ones, offering (subsidized) insurance coverage for the high-risks.24 Even better, governments should try to create the missing market for ”genetic insurance”, as proposed by Tabarrok (1994). In this regard our model characterizes the welfare loss due to the lack of coverage against the classification risk and clearly states the importance of ”genetic insurance” provision. We believe that it would be interesting to formally investigate reasons why, in the real world, insurance markets are not able to provide coverage for the classification risk. We leave this issue to future research. 23In Hoy and Ruse (2005) the decision whether to gather information is not endogenous, however the authors stress the inefficiencies due to adverse selection arising when privacy on genetic information is assigned to consumers. 24Possible redistributional policies aimed at remedying existing inequality in health risk and in insurance premium produced by genetic testing are analyzed in Rees and Apps (2006). 22 6Appendix 6.1 Proof of Remark 2 (i) When pL≥Ψ ∆0the optimal action for low-type decision-makers corresponds to a positive level of prevention: ba(pL)=1.Given inequality 1, this implies: ba(pU)=ba(pH)=1,and, b V(pU)=λb V(pH)+(1−λ)b V(pL).Whereaswhen pH≤Ψ ∆0the optimal action for high-type decision-makers corresponds to noprevention: ba(pH)=0.Thus, ba(pU)=ba(pL)=0and, again, b V(pU)=λb V(pH)+ (1 −λ)b V(pL).(ii) Suppose first that pL<p U≤Ψ ∆0<p H. When uninformed, decision-makers do not exert prevention such that b V(pU)=pUu(w−L)+(1− pU)u(w).If decision-makers acquire information, given again inequality 1, their expected utility becomes: λb V(pH)+(1−λ)b V(pL)=λ(pHu(w−l)+(1−pH)u(w)−Ψ) +(1−λ)(pLu(w−L)+(1−pL)u(w)) =λpHu(w−l)+(1−λ)pLu(w−L)+(1−pU)u(w)−λΨ Using1itiseasytoverifythatb V(pU)<λ b V(pH)+ (1 −λ)b V(pL).Suppose now that pL<Ψ ∆0≤pU<p H.Here uninformed consumers choose prevention and b V(pU)=pUu(w−l)+(1−pU)u(w)−Ψ.By comparing b V(pU)and λb V(pH)+ (1 −λ)b V(pL)it is easy to verify that, again, b V(pU)<λ b V(pH)+ (1 −λ)b V(pL). 6.2 Proof of Remark 3 (i) It comes directly from the discussion above Remark 3. (ii) It is easy to prove that ∆(pi)is an increasing function. In fact, ∂∆(pi) ∂pi=−lu0(w−pil)+Lu0(w− piL)which is positive since L>l≥0and u0(w−piL)>u 0(w−pil)≥0.(iii) Inequality (1) is the condition for positive prevention without insurance and can be written as pi∆0≥Ψ. We compare inequality (1) with (2), and we prove that ∆(pi)≤pi∆0.The latter inequality can be rewritten as u(w−pil)−piu(w− l)≤u(w−piL)−piu(w−L).Let f(x)=u(w−pix)−piu(w−x).f 0(x)= −piu0(w−pix)+piu0(w−x)be positive as soon as 0≤pi≤1and uconcave. Then fis increasing and u(w−pil)−piu(w−l)=f(l)≤f(L)=u(w−piL) −piu(w−L). 6.3 Proof of Remark 5 We start with the proof of (ii). Functions W∗ Iand WUcross each other twice if W∗ Icalculated in Ψ=∆(pU)is larger than WU=u(w−pUL)(see Figure 3); this writes: λu(w−pHl)+(1−λ)u(w−pLL)−λ∆(pU)>u(w−pUL)(10) Substituting ∆(pU)=u(w−pUl)−u(w−pUL)and rearranging inequality (10), the opposite of condition (9) can be easily found. Ψ3is the value on the left of 23 ∆(pU)such that W∗ I=u(w−pUl)−Ψ,whereas Ψ4is the value on the right of ∆(pU)such that W∗ I=u(w−pUL).(i)Itcomesimmediatelyfrom(ii). 6.4 Proof of Remark 6 Let’s substitute pH−pU=(1−λ)(pH−pL)and pU−pL=λ(pH−pL)in the l.h.s. of (9) and call pH−pL=x. We can therefore rewrite the l.h.s. of (9) as a function of x: Γu(x)= [u(w−pUl)−u(w−pUl−(1−λ)lx)] (1−λ)l [u(w−pUL+λLx)−u(w−pUL)] λL Because of the concavity of u,Γis an increasing function such that: Γu(0) = u0(w−pUl) u0(w−pUL)≤1.(11) Moreover, substituting Γu(x)in condition (9), W∗ Iand WUcross each other if: Γu(pH−pL)≤L l(12) Putting together (11) and (12): 0≤pH−pL≤Γ−1 uµL l¶. 6.5 Proof of Lemma 2 The proof is organized in two steps. First we show that, at the equilibrium, decision-makers perform the test when insurance firms offer full-insurance contracts; we then show that the result does not change when firms are free to offer partial-insurance contracts. (i) Full-insurance contracts. Suppose that firms are constrained to offer full-insurance contracts. Insurers ex-ante propose 4 full-insurance contracts contingent on the decision-maker’s action and on the test result if decision-makers decide to show it, and 2 full-insurance contracts only contingent on the preventative action if decision-makers do not show the test result. The insurance premiums are: with prevention without prevention Show result L πL1=pLl πL0=pLL Show result H πH1=pHl πH0=pHL Don’t show πN1πN0 We are looking for an equilibrium where decision-makers perform the test and show the test result to insurers when the test reveals good news. For this equilibrium to exist, we have necessarily pHl≥πN1≥pLland pHL≥πN0≥ pLL. 24