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eiaslp.v5b, 8-12-14
Endogenous Information, Adverse Selection, and Prevention:
Implications for Genetic Testing Policy
Richard Peter*, Andreas Richter**, Paul Thistle†
Abstract: We examine the endogenous value of information in an insurance market where
there is potential adverse selection due to individual differences in the efficiency of loss pre-
vention technology. We show that with observable preventive effort for all risk types, classi-
fication risk is alleviated or might even be overcome: If people can adjust their loss prevention
behavior to the information acquired, information might be valuable. We show that the
relevant policy regimes can be Pareto ranked, with full disclosure being the prefered regime
and an information ban the worst regime. This has important public policy implications for the
areas of genetic testing and HIV testing.
Keywords: information value, prevention, adverse selection
JEL-Classification: D11, D82, G22, G28
* Munich Risk and Insurance Center, Ludwig‐Maximilians‐Universitaet Munich, E‐Mail: [email protected], Phone: +49 89 2180 3882 ** Munich Risk and Insurance Center, Ludwig‐Maximilians‐Universitaet Munich E‐Mail: [email protected] Phone: +49 89 2180 2171
† Department of Finance, University of Nevada Las Vegas, E‐Mail: [email protected], Phone: +1 702 895 3856
Endogenous Information, Adverse Selection, and Prevention:
Implications for Genetic Testing Policy
1 Introduction
There are many situations in which individuals must decide whether to learn about the
potential risks they face. Consider, for example, an individual deciding whether to take a
genetic test. Under which conditions will individuals choose to be tested and acquire
information about their risk? Insurance possibilities impact the value of information, i.e., the
extent to which insurance companies utilize potential customers’ information is crucial in
determining whether individuals decide to become informed. In addition, individuals may
adjust their risk mitigation behavior in response to the information acquired, which in turn
has implications for insurance pricing. Put differently, health risks are not only determined by
individuals’ risk types, but also by environmental factors over which individuals have some
control.
In this paper, we examine public policy toward the use of information from genetic tests
by insurers.1 Public policy decisions about the use of test information will affect the markets
for health insurance, life insurance, annuities, and long-term care insurance. Bundorf,
Herring and Pauly’s (2010) and Handel’s (2013) results are consistent with adverse selection in
employer provided health insurance. Finkelstein and Poterba (2002, 2004) and He (2009)
provide evidence of adverse selection in annuity markets and life insurance markets,
respectively. Zick, et. al (2005) find that individuals who had postive predictive tests for
Alzheimer’ disease substantially increased their purchase of long-tem care insurance. Oster, et.
1 In the paper, we focus on the use of genetic tests. The same issues arise for HIV tests, where low cost home and
mail-order tests are readily available. Similar issues also arise in liability insurance. This is particularly the case
for the development of new products and new technologies where the firms must decide whether to determine
the potential risks to consumers and the potential liability, as well as what steps it will take to mitigate those risks.
2
al (2010) report „strong evidence of adverse selection“ (p. 1048). Asymptomatic individuals
who have tested poitive for Huntington’s disease are five times more likely to own long-tem
care insurance as otherwise comparable individuals.2 The increasing availablity of mail-order
genetic tests for a wide range of conditions has the potential to change the distribution of
information in these insurance markets. Public policy can either exacerbate or mitigate
advese selection in these markets.
This paper also extend the literature on the incentives to acquire information in
insurance markets.3 Milgrom and Stokey (1982) show that, if ex-ante efficient contracts are
negotiated in a complete market economy, the social value of subsequently generated
information is zero, as it cannot create new investment opportunities. The question then arises
why individuals should decide to become informed at all. Crocker and Snow (1986) show that,
when it is costless, using categorical variables in pricing insurance increases welfare.
Rothschild (2011) shows that the government can offer partial social insurance such that
lifting a ban on categorical discrimination is weakly welfare increasing, even if categorization
is costly. Garidel-Thoron (2005) argues that, in dynamic insurance markets, allowing insurers
to share loss information decreases welfare. These analyses assume individuals are
exogenously endowed with knowledge of their risk type.
Other researchers have examined environments where individuals are initially
uninformed. Crocker and Snow (1992) demonstrate that if insurers can observe whether
individuals are informed or not and if consumers do not have prior private information, then
the private value of information is negative. This implies that information will not be obtained
and that insurance deters diagnostic testing. Tabarrok (1994) discusses the potential threat of
uninsurability through genetic testing, because insurance coverage for high risk types might be
too expensive. He suggests genetic insurance as a possible solution to the classification risk
2 The broader evidence on adverse selection is mixed. In addition to risk-based selection, there is also evidence
of selection on other dimensions. See Cohen and Siegelman (2010) for a survey of empirical research on adverse
selection in insurance markets.
3 See Crocker and Snow (2013) for a survey of the literature on risk classification and the value of information in
insurance markets.
3
posed by genetic testing. Strohmenger and Wambach (2000) model an insurance market with
state-dependent consumer preferences and treatment costs exceeding the individual’s
willingness to pay. Then additional risk classification can be welfare enhancing under
symmetric information, but there is the threat of complete market failure under asymmetric
information about risk types. Doherty and Thistle (1996) re-analyze the private value of
information and find that it is non-negative only if insurers are unable to observe the
informational status of the consumers or if individuals are able to conceal their informational
status. This demonstrates the crucial role of the regulator when it comes to the question of how
to handle information from genetic tests or from risk classification devices in general for the
purposes of insurance purchasing. In Doherty and Posey (1998) the value of a treatment option
for tested high risks is examined. However, when thinking about health related risks or
liability risks, one observes that uninformed consumers or low risks will also invest in risk
mitigation. Our model will take this into account. The incentive to acquire information
depend on the tradeoff between the gains from reducing the inefficiency due to adverse
selection and cost of classification risk.
The literature has focused mainly on the canonical Rothschild and Stiglitz (1976)
model. However, both heterogeneity of risk types, and heterogeneity of individual measures of
prevention seem to be important, especially in the contexts of health risks.4 In these situations,
information also has clinical value, since it lets individuals choose loss prevention more
efficiently.
Consider, for example, genetic testing for breast cancer risk. A mutation of the genes
BRCA1 and BRCA2 is known to be associated with a higher risk for breast or ovarian cancer
(Thompson et al., 2002). However, since the 1970s substantial medical progress has been made
in therapies for breast cancer, especially when detected early (Goldhirsch, et. al, 2007). It is
a reasonable assumption that a positive result for a BRCA1 or BRCA2 mutation will change
4 In their seminal work, Ehrlich and Becker (1972) distinguish between self-protection, i.e., investments to reduce the probability of loss, and
self-insurance, i.e., investments to reduce the size of a loss. Common in the insurance literature is also the terminology loss prevention for the
former and loss reduction for the latter risk management device. In this paper we focus on loss prevention.
4
individual prevention behavior in terms of the frequency of seeing a doctor to detect
indications of breast cancer as early as possible. But for individuals who might not know their
genetic make-up or those who have tested negative, the interplay between risk relevant factors
and risk type also determines their final probability of disease.5 Similarly, there are genetic test
that indicate an increased risk for heart attack, hypertension and Type 1 and 2 diabetes, as well
as other diseases where lifesytle choices affect the risk of developing the disease. These, and
many other genetic risks, are multifactorial because individuals do not just passively acquire
information, but can adjust their risk-relevant behavior in response to the information.
However, the lifestyle choices of uninformed individuals and individuals with a negative test
result will also matter when it comes to determining the probability of falling ill. Their choices
cannot be ignored. More generally, the interplay between risk type and factors that can at least
partially be controlled by consumers determines the insurable risk. Einav et. al (2013) report
that individual choose insurance, at least in part, based on their anticipated response to
coverage.
These examples demonstrate that focusing only on an exogenously given distribution of
risks in the population is insufficient to judge the incentives to obtain information in an
adverse selection framework. When decision-makers can react to the information acquired by
adjusting loss prevention effort the information has clinical value. This does not only apply to
“bad news”. Consequently, the risks are endogenous for all individuals. The clinical value of
information adds a dimension to the tradeoff between the costs of adverse selection and
classification risk in determining the value of information. We show, for example, that with
symmetric information the value of information can be positive; when loss prevention is not
possible the value of information is unambiguously negative.
The extent of potential adverse selection and classification risk is determined in large
part by regulations governing the use of test results by insurers. Regulation varies widely
5 In the case of breast cancer typical (endogenous) risk factors are nutrition habits, alcohol consumption, smoking before the age of 16 and
exercising habits amongst others (Colditz and Frazier, 1995; Thune et al., 1997). In general, any habits that might disturb the hormonal
balance might lead to moderate increases in breast cancer risk.
5
across juristictions and across insurance markets, ranging from bans on the use of genetic test
results to voluntary restrictions to no regulation.6 In the U.S, the use of genetic information is
governed by the Health Insurance Portability and Accountability Act (HIPAA) of 1966 and
the Genetic Information and Nondiscrimination ACT (GINA) of 2008. Taken together, these
laws effectively prohibit the use of genetic information (including family health history) in
determining coverage or premiums in both group and individual health insurance for
asymptomatic individuals. These laws do not apply to life insurance, annuities or long-term
care insurance. Most U.S. states have enacted similar laws for health insurance, however, 30
states have no legislation regarding the use of genetic information in life insurance, annuities
or long-term care insurance (National Conference of State Legislatures, 2008a, 2008b).
Canada has no specific legislation governing the use of genetic information. While
Canadian insurance companies do not require genetic tests, they may request the results of any
tests that have been performed. The situation is similar in Australia and New Zealand. The
Oviedo Convention, which is binding on the members of the European Community that have
signed it, prohibits discrimination against a person on the basis of their genetic hertiage.
Austria, Belgium, France, Portugal, Sweden and Switzerland have passed legislation that
effectively prohibits the use of genetic tests by insurance companies; Belgium makes an
exception for life insurance policies above approximately $150,000. U.K. insurers have
aggreed a moratorium on the use of genetic tests (except life insurance policies above
£500,00).7 Individuals are allowed to disclose favorable genetic test results to rebut family
hitory information. In South Africa, insurers have agreed to a Code of Conduct under which
they may not require genetic tests. Previous tests, but not their results, must be disclosed to
the insurer. Most Asian and African countries have not enacted legislation regulating the use
of genetic information by insurers.
We consider four possible policy regimes and analyze the incentives for individuals to
6 See Joly, Braker and Le Huynh (2010) and Otlawski, Taylor and Bombard (2012) for surveys of regulatory
regimes regarding the use of genetic information.
7 The U.K. moratorium has been in place since 2001 and has been extended until at least 2017.
6
take genetic tests and analyze insurance market outcomes. We analyze a duty to disclose or
mandatory disclosure regime under which individuals must provide the results of any genetic
tests to insurers. We consider a “code of conduct“ under which the fact that a test has been
taken must be disclosed but the test results cannot be used by the insurer. We also consider a
consent law or voluntary disclosure regime under which individuals can choose whether or
not to reveal test results. Finally, we examine a ban on genetic testing under which neither
the fact that a test has been taken nor the test result can be used by the insurer.
The policy regime is important in detemining the value of information and the resulting
insurance market outcome. If consumers‘ information status is observable, then insurers can
condition the policies they offer on information status. This exacerbates the classification
risk. The value of information is negative unless information has sufficient clinical value. If
consumers‘ information status is not observable, insurers must offer the same policies to
informed and uniformed. Then the value of information is non-negative, regardless of
whether information has clinical value. Based on the resulting insurance market outcomes,
we are able to ex ante Pareto rank (from the point of view of an untested individual) the
different policy regimes. The clinical value of information affects the Pareto ranking, but
ultimately does not affect the policy recommendation.
The paper proceeds as follows. The next section outlines the basic model and introduces
the different prevention technologies. Section 3 introduces adverse selection by allowing for
different assumptions on the observability of informational status and risk type of consumers.
Section 4 analyzes welfare and ranks the policy alternatives and section 5 discusses public
policy implications and concludes.
2 The Basic Model
2.1 General Assumptions
Following the classical insurance demand literature, we consider risk-averse individuals
with utility of final wealth , which is assumed to be strictly monotonic and concave
7
( ′ 0, ′′ 0). Let 0 be initial wealth which is subject to incurring a loss of with
probability . Individuals may choose effort which reduces the probability of loss and
comes at costs of . The cost of effort is increasing and convex ( ′ 0, ′′ 0).8 Also note
that we assume costs to be separable.9
We assume that the probability of loss consists of a component that is exogenous and of a
component over which the individual has some control and which is in that sense endogenous.
For instance the probability of an illness depends on the genetic make-up, e.g., whether one
has a genetic predisposition to heart disease or hypertension, and on behavior regarding other
risk relevant factors, e.g., nutrition, smoking and drinking habits, or lifestyle in general.
Furthermore, as in Doherty and Posey (1998), treatment decisions and their effectiveness will
typically depend on the level of information. In this respect, we mean by preventive action any
behavior by the individual that might decrease the probability of illness.
We assume that individuals are identical except for prevention technology, such that a
fraction of the population is considered high risk and a fraction = 1 – is considered
low risk. High risk individuals have the loss probability while low risks have the loss
probability . We assume and are strictly decreasing and strictly convex. For any
given level of effort, high risks face a higher loss probability than low risks, formally 1
0, for all . However, individuals might not (yet) know to which risk class
they belong and hence assume an average loss probability of due
to rational expectations.10 Subscript U denotes the uninformed individual.
To analyze heterogeneous prevention technologies we introduce the positive difference
function : as in Hoy (1989). Following his terminology we distinguish
between the three cases of constant difference (CD) for which ′ 0 , decreasing
8 Adopting the terminology of Ehrlich and Becker (1972) we consider self-protection only. An analysis of the value of genetic information if
consumers may choose a loss reduction or self-insurance action can be found in Barigozzi and Henriet (2011). 9 We abstract from heterogeneity in the dimension of prevention cost. Separability is sufficient for the first order approach to be valid
(Rogerson, 1985; Jewitt, 1988). 10 We abstract from ambiguity aversion. Formally, being uninformed corresponds to having a lottery between either the high risk or the low
risk probability, which is disliked by ambiguity-averse decision-makers. For a study of effort choices under ambiguity aversion refer to Snow
(2011) and Alary et al. (2013).
8
difference (DD) for which ′ 0, and increasing difference (ID) for which ′ 0. DD
corresponds to a situation where H-types have the more efficient technology compare to the
L-types. For instance, there might be a promising treatment option available that significantly
lowers the probability of a severe case of the disease. The current situation regarding HIV
treatment could be an example for that case. CD resembles a situation where H-types are
equally efficient at loss prevention as L-types, e.g., if there is no effective treatment available
and the detection of a genetic mutation simply means enhanced likelihood of the occurrence
of a specific disease. In the case of ID, H-types are even less efficient than L-types in
prevention meaning that the genetic mutation not only carries with it an elevated probability
of the occurrence of the disease, moreover the means of preventing the occurrence are no
longer efficient compared to healthy people without the mutation. Let us make an important
clarifying remark regarding terminology. We speak of risk type in order to distinguish high
risks with prevention technology from low risks with prevention technology . We
speak of informational status to distinguish uninformed individuals with prevention
technology from informed individuals with prevention technology or .
2.2 Effort Choices Without Insurance
We initially assume that insurance is not available. Then the individual’s expected utility
is given by
1 , ∈ , , ,
with first-order condition
′ ′ ′ 0. (1)
Optimal effort is chosen such that it balances marginal benefit from prevention and
marginal cost. Let denote optimal effort for a type individual. It is straightforward to
show that under CD we have , under DD we have and under ID
we have . This is intuitively plausible as the marginal cost of prevention does
not depend on type. Therefore, in case of CD where marginal benefit from prevention is equal
9
among types everybody choses the same effort level. Under DD H-types have the more
efficient technology so that the optimal effort is higher. This is reversed in the case of ID.11
The value of information is defined as the change in expected utility from acquiring the
information
. (2)
The value of information is zero in the CD case. For the other two cases, we have
0,
where the inequality holds due to the optimality of and , respectively. In the ID and DD
cases, the information has clinical value, as individuals use the information to adjust their
effort levels to their loss prevention technology. As Savage (1954) points out, the individual is
free to ignore the information and hence it cannot be disadvantageous. This option value of
information raises the value of information. We assume throughout that individuals choose
to become informed if the value of information is non-negative.
2.3 Actuarially Fair Insurance Coverage
Now assume that insurance is available in a perfectly competitive market at actuarially
fair prices. We first abstract from informational asymmetries, i.e., the insurer is able to observe
both informational status and risk type. This is a situation in which the insured has a duty to
disclose.
In our example of health risks, this corresponds to a situation where the insurer must be
informed about whether a genetic test has been conducted and, if so, what the results were.
This might be the case if the insurance company paid for the test, perhaps as a part of more
general medical examination. In this case it seems particularly reasonable that the insurance
company has some information on average precautionary measures taken by an average
individual, a low risk individual and a high risk individual, and therefore considerations of
11 Due to the endogeneity of loss prevention effort the indifference curves over final wealth in the two states of the world might not be
convex. They are decreasing in any case due to the envelope theorem, but the curvature reflects effort adjustments. Technical conditions to
ensure convexity are long-winded and not very insightful so that we assume convexity wherever needed.
10
moral hazard can be neglected.
An insurance policy , , consists of a premium, , a coverage level, , and a
level of prevention activity, . Expected utility is then
1 1 .
Since the market is competitive, insuring a proportion of the loss comes at a premium of
for a type individual. We know from classical insurance demand theory that
full insurance coverage will be obtained, see for instance Mossin (1968).12 The objective of a
type individual is therefore to maximize
,
which yields the first-order condition
′ ′ ′ 0,
where the prime denotes differentiation with respect to . We let denote the first-best
effort level for a type individual, and let denote the first-best policy for type .
For the CD case, the H-types and L-types are equally efficient at loss prevention.
However, H-types have a higher premium rate and therefore they will exert more effort to
reduce the premium. For the DD case, the H-types are more efficient at loss prevention than
the L-types, hence again they will exert more effort than L-types. So for the CD and DD cases
we have . For the ID case, there are two competing effects. H-types have a
higher premium rate which induces them to exert more effort than L-types. However, they are
less efficient at loss prevention and this induces them to exert less effort. Therefore, the overall
effect is ambiguous.
The value of information is given by
, 12 Of course, Mossin (1968) abstracts from prevention and considers a fixed premium only, but in case prevention expenditures are observed,
optimality of full insurance coverage still holds.
11
for constants , 0. The risk premia and capture the effect of classification risk on
wealth and the cost of care, respectively. Again, the optimality of and implies that
that is, information has clinical value. However, this is not sufficient to guarantee that the
value of information is positive. Individuals who choose to become informed are exposed to
classification risk, and we cannot unambiguously sign .13 We conclude that the following
two conditions are sufficient for positivity of the value of information,
,
. (3)
If the insurance premium when uninformed exceeds the expected insurance premium when
informed plus a constant accounting for the aversion to classification risk, and if average
prevention effort is sufficiently below the effort of uninformed individuals, consumers will
decide to become informed and learn about their type.
Proposition 1 Let informational status and risk type be observable. The value
of information can be positive or negative. The inequalities in (3) are sufficient
for the value of information to be positive.
In the appendix we parameterize the heterogeneity in prevention technology and
demonstrate that DD tends to enhance the value of information. If high risks have an effective
treatment option, and therefore have the more efficient prevention technology, the “bad
news” from being a high risk is alleviated and information might still be valuable. We also
demonstrate that there are situations in the CD and ID cases where sufficiently efficient
treatment technologies can lead to a positive value of information.
This finding is related to Proposition 2 in Bajtelsmit and Thistle (2013) about the
13 In the absence of prevention, information has no clinical value but individuals are exposed to classification risk. Then the private value of
information with full insurance is given by for a positive risk premium 0, and is therefore negative.
12
incentive to acquire information in a competitive market for liability insurance. However, in
their analysis, heterogeneity in risk type corresponds to heterogeneity in loss size and
prevention technology is homogeneous across agents. Consequently, adverse selection cannot
be addressed as the insurer always observes amounts claimed. Proposition 1 is also related to
Doherty and Posey’s (1998) finding that the value of information can be positive or negative
and that a positive value of information stems from the treatment option for high risks. We
confirm their result and extend it to our more general setting. Even in situations of CD and ID
the opportunity to mitigate the risk can create informational value.
2.4 Level of Coverage and Optimal Effort
It is worthwhile to examine how the level of insurance coverage will influence the
optimal effort. In adverse-selection problems it is well known that the availability of coverage
might be restricted due to the informational asymmetry. This change in the availability of
insurance will typically be accompanied by a change in loss prevention effort.
For the moment, we take insurance coverage as exogenously given. (We relax this
assumption later in the analysis.) Consider an insurance policy with fixed coverage , and
actuarially fair premium . The objective function is then given by
1 1 ,
for ∈ , , . The first-order condition is
1
0,
where and are final wealth levels in the no-loss state and in the loss state, respectively.
Optimal prevention is chosen to balance the marginal benefit from the reduction of the loss
probability and the marginal benefit from reducing the insurance premium, and the marginal
cost of effort.
Let denote the solution of the first-order condition for a type individual with
coverage . Note that is the optimal effort level with full insurance. The implicit
13
function theorem yields
,
hence, sgn sgn . Now,
1 2
1 ′′ ′′ ,
so ∂ / ∂ is negative as long as the loss probability is less than 1/2 and the individual is
prudent.14 Under these circumstances higher insurance coverage induces the agent to exert a
lower prevention effort and substitute insurance for prevention. The marginal benefit from
prevention here consists of two components, the marginal benefit from the reduced loss
probability itself and the marginal benefit from a reduced insurance premium. Raising
insurance coverage has three marginal impacts. The marginal benefit from loss prevention will
be lower due to the increased coverage, but the marginal benefit of a lower insurance premium
is greater at a higher premium. The condition that the loss probability stays below 1/2 is
necessary and sufficient for the first effect to be dominant.15 However, there will also be an
income effect as more insurance coverage alters the wealth distribution which also affects the
marginal benefits regarding the premium reduction. In general, this third effect cannot be
signed unambiguously; prudence is sufficient to ensure it is negative.
3 The Value of Information
3.1 Preliminaries
Let us now assume that the insurer is unable to distinguish agents with respect to their
prevention technology. The insurer is able to monitor prevention effort, , but the efficiency
of prevention is private information. The question arises of how insurance can be offered in
14 Alternatively, a sufficient condition for negativity would be to assume a loss probability above 1/2 and imprudence which seems not
reasonable for the vast majority of applications. 15 As noted by Ehrlich and Becker (1972), the effect that observable prevention effort lowers the insurance premium can lead to comple-
mentarity between both risk mitigation instruments.
14
this set-up. In a Rothschild and Stiglitz (1976) self-selection design, the equilibrium policies
( ∗, ∗ ) maximize expected utility for the low risks, subject to the self-selection constraint
and the individual policies satisfying breakeven (zero expected profit)
constraints. In addition, there is no other policy that, if offered, would earn non-negative
expected profit. The H-types will be offered full insurance, ∗ . The L-types can only be
offered partial insurance such that the H-types are just indifferent between their contract and
the L-type contract, i.e., the self-selection constraint is
. (4)
Since the choice of effort is observable, mimicry by H-types implies that they must
pretend to be L-types in terms of both the policy chosen and the effort level selected.
Therefore, we need to determine such that the H-types are unwilling to mimic the L-types.
Note that for 0 the LHS of (4) offers no insurance, and . For 1 the
left-hand side of (4) offers full coverage at the L-type rate, and . By
continuity there is at least one value of ∈ 0,1 where the self- selection constraint binds.16
Then H-types receive full and fairly priced insurance coverage and L-types obtain partial and
fairly priced insurance coverage that leaves H-types just indifferent between choosing and
choosing the L-type partial insurance contract ∗ and mimicking the L-type effort .
Hence, the amount of insurance for L-types will be endogenously determined via self-selection
to resolve the adverse selection problem.17
3.2 Unobservable Risk Type
We first consider the situation where informational status is observable but risk type is
not. For the health insurance example, this is the case in South Africa where insurers operate
16 In the cases CD and ID H-type indifference curves are flatter than L-type indifference curves, as in the standard model. For DD, where
H-type effort is higher than L-type effort for a given wealth profile, the resulting loss probability of high risks might be lower than the
resulting loss probability of L-types, which seems however an unrealistic case: The treatment option would be so efficient that the resulting
probability of disease is smaller than for healthy people. This can be excluded by assuming that does not decrease too quickly. For the
parameterization presented in the appendix the condition would be that be bounded from below. 17 We do not treat potential problems of equilibrium non-existence due to an insufficient share of high risks in the market in this paper, but
rather assume that all contract menus considered are stable equilibrium configurations.
15
under the Code of Conduct (Chapter 20) and may not ask or coerce the applicant to undergo
any genetic test in order to obtain insurance. However, all previous tests must be disclosed, i.e.,
the insurance company knows whether a test has been taken or not but not the result of the
test. Alternatively, the insurance company might pay for the tests, ans so knows the individual
is informed, but the test results are sent to the individual’s private physician for interpretation.
The insurer is then able to separately identify the informed and uninformed. The insurer
will offer the uninformed individuals full and fair insurance coverage and they choose effort
accordingly. For the informed H-types and L-types a self-selection design will be
implemented. Let ∈ 0,1 be the level of coverage where the self- selection constraint (4)
binds and be the level of effort chosen by an L-type under this policy. The endogenous
value of information is then given by
∗
1
1
.
Comparing this to the situation where both informational status and risk type are observable,
we obtain
∗ 0.
This is positive since expected utility under full insurance and associated effort always exceeds
expected utility in a situation with partial insurance and associated effort. If the insurance
company can observe the consumers’ informational status, the value of information declines if
informed consumers cannot reveal their risk type.
Note also that under the assumptions of prudence and sufficiently small loss
probabilities, there is a substitution effect. The presence of H-types exerts a negative
externality on L-types as the availability of insurance coverage is restricted, which in turn
leads to substitution between insurance and loss prevention. This unambiguously raises
16
expenditures on care for L-types when risk type is not observable.18
Proposition 2 Let informational status be observable, then the value of
information can be posive or negative. The endogenous value of information is
larger if individuals are allowed to reveal their risk type when informed.
In a situation where individuals cannot undertake loss prevention measures, the value of
information when risk type is not observable will also be smaller than under complete
information and hence be negative.19 However, when information has clinical value, may
be positive. Consider for instance a situation where the insureds are highly risk-averse and
therefore place a high value on coverage. Hence, the insurance contract offered to L-types will
entail less than full coverage due to the information asymmetry, however, coverage will be
close to full due to high risk aversion. If in addition prevention is sufficiently effective, the
expected utility loss due to less coverage, which decreases the value of information, can be
partly compensated by investing more in prevention, so that the overall effect is not too strong.
Hence, the possibility that information has clinical value may alleviate the conclusion in the
literature that under this regime the value of information is always negative.
3.3 Unobservable Informational Status
In some situations, informational status is unobservable, but risk type can be credibly
revealed by the consumer. For example, there may be a consent law where results from genetic
testing can only be revealed with the consent of the consumer. Therefore, individuals will only
18 The marginal impact of the structure of prevention technology heterogeneity is difficult to assess. In the case of CD and DD, we still have
, as H-type and U-type utility is unaffected. However, under the conditions derived in section 2.4, L-types will exert more effort
compared to a situation with full insurance coverage. Hence, might no longer hold. 19 It is given by
2 1 1 ,
for the self-separating level of insurance coverage 1. With the same argument as above it will be lower than 1 due to lower expected
utility of L-types because the existence of unidentifiable H-types restricts the available coverage.
17
choose to reveal results if they are favorable.
Since insurers cannot directly observe information status, they need to correctly
anticipate consumers’ decisions. If they expect consumers to become informed, insurers will
offer to consumers who provide verification of a negative test result and to everyone
else. Individuals will choose to be tested since a positive result does not make them worse off
and a negative result makes them better off. The value of information is
0.
If they expect consumers will not become informed, insurers offer . Consumers get
the same policy whether or not they are informed, the value of information is zero and
consumers become informed. Becoming informed is a weakly dominant strategy.
Comparing this to the situation where both informational status and risk type are
observable, we obtain
∗ 0,
since full insurance is always preferred to partial insurance for a given loss probability. We see
that, given that the L-types can credibly reveal test results, moving from a regime where
informational status is observable to a regime where it is not increases the endogenous value of
information. This yields the following Propostion:
Proposition 3 If informational status is not observable but risk type can be
revealed by the consumer then the value of information is positive. The
endogenous value of information is higher if informational status is not
observable but risk type can be revealed by the consumer than when
informational status is observable.
The equilibrium depends on the assumption that individuals become informed if the
value of information is non-negative. If there is a small cost to testing, then there is an
equilibrium in which consumers remain uniformed. We consider this possiblility in the
welfare analysis. The result in the this proposition corresponds to Proposition 2 in Doherty and
18
Thistle (1996) where the value of information is shown to be non-negative if informational
status is unobservable or can be concealed.
3.4 Both Risk Type and Informational Status Unobservable
Finally, we analyze the situation where the insurance company cannot observe the
informational status of its customers and consumers cannot reveal their risk type even if they
wanted. This corresponds to a complete ban of genetic information in insurance. In this case
insurance companies are neither allowed to inquire whether tests have been taken, nor are
they allowed to use existing genetic information for rate-making. In some countries, there are
voluntary moratoria on the use of genetic information and in other countries there are
countries in which there is a government ban in place that completely prohibits the use of
genetic information.
Since insurers cannot directly observe information status, they again need to correctly
anticipate consumers‘ decisions. Under the ban consumers cannot provide verification of
their risk type. If they expect consumers to become informed, insurers offer and *LC ,
where *LC satisfies the self selection constraint VH( ) ≥ VH( *
LC ). Informed high risks
purchase , informed low risks purchase *LC and the uninformed also purchase *
LC . Then
the value of information is
∗ ∗ 0
since the self-selection constraint is binding and .
Individuals become informed since the value of informtion is non-negative. If they expect
onsumers will not become informed, insurers offer to everyone and the value of
information is again zero.
Proposition 4 Let informational status and risk type both be unobservable,
then the endogenous value of information zero.
19
Again, the equilibrium depends on the assumption that individuals become informed if
the value of information is non-negative. If there is a small cost to testing, then the
equilibrium in which consumers remain uniformed. We consider this possiblility in the
welfare analysis.
4 Welfare Implications
As shown in the last two sections, how policyholders’ information is used for
rate-making in insurance crucially impacts the value of information. After analyzing
informational incentives as implied by the contracts offered in equilibrium and the actions
taken by the individuals, we now focus on welfare implications of the different regulatory
regimes. When there is a duty to disclose the fact that a test has been taken and the test result,
the value of information is . When there is a code of conduct, so that the fact a test has been
taken, but not its results, must be revealed, then the value of information is . The value of
information is under a consent law, where test results can be credibly revealed, and is
under a ban on the use of any testing information.
The different policy regimes can be Pareto ranked. The welfare comparisons are ex
ante, that is, from the perspective of an uninformed individual. Consider, for example, the
comparison of the duty to disclose, where the value of information is I1, with the code of
conduct, where the value of information is I2. There are four cases, depending on whether
the value of information is positive or negative under each regime. The cases are summarized
in Table 1. In Case A, the value of information is negative in both regimes. In Case A both
regimes yield the same expected utility. In Case B, I1 < 0 while I2 >0. The fact that I1 < 0
implies that VU( UC ) > θHVH( HC ) + θLVL( LC ) > θHVH( HC ) + θLVL(CL*), so that individuals are
better off under the duty to disclose. In Case C, I1 > 0 implies the first inequality is reversed,
VU( UC ) < θHVH( HC ) + θLVL( LC ) so that individuals are better off under the duty to disclose.
Under Case D, since *LC provides partial coverage, we have θHVH( HC ) + θLVL( LC ) > θHVH( HC
20
) + θLVL( *LC ), so that individuals are again better off under the duty to disclose.
Table 1. Comparison of Duty to Disclose and Code of Conduct
Case Duty to Disclose Code of Conduct Policy
A I1 < 0, I2 < 0 VU( UC ) VU( UC ) Duty to Disclose
B I1 < 0, I2 > 0 VU( UC ) VH( HC ),VL( *LC ) Duty to Disclose
C I1 > 0, I2 < 0 VH( HC ),VL( LC ) VU( UC ) Duty to Disclose
D I1 > 0, I2 > 0 VH( HC ),VL( LC ) VH( HC ),VL( *LC ) Duty to Disclose
Proposition 5. The policy regimes can be ex ante Pareto ranked, with the duty
to disclose preferred to the code of conduct and consent regimes which are in
turn preferred to the ban on the use of information. The code of conduct and
consent regimes are non-comparable.
The remainder of the proof, which consists of case-by-case analyses of the pairwise
comparisons of the policy alternatives, is given in the Appendix.
The result in Proposition 5 can be compared to the outcome when information has no
clinical value (pH and pL are fixed). From Crocker and Snow (1992) and Doherty and Thistle
(1996), we know that the observability of consumer’s information status is critical in
determining the value of information. Under the duty to disclose and code of conduct
regimes, consumers‘ information status is observable. Under both of these regimes, the value
of information is negative (I1 < I2 < 0), so that individuals receive expected utility VU( UC ).
Under the voluntary discolsure and ban regimes, consumers‘ information status in not
observable. Under the voluntary disclosure regime, the value of information is positive (I3 >
0), and individuals receive expected utility of either VH( HC ) orVL( LC ). Finally, under a ban
on the use of genetic tests, the value of information is zero (I4 = 0). Assuming individuals
21
become informed, they receive either VH( HC ) orVL(CL*). Since I1 < I2 < 0 and *LC offers
partial coverage, the duty to disclose and code of conduct regimes are Pareto superior to the
consent law, which in turn is Pareto superior to the ban.
5 Discussion and Conclusion
We analyze alternative public polices toward insurers use of genetic tests. The
increasing availability and falling cost of genetic tests for a wide variety of different conditions
will change the informational environment within which insurance markets operate. Some
fear widepread “genetic discrimination“ if insurance companies are allowed to use genetic test
results to underwrite policies. On the other hand, insurance companies fear “regulatory
adverse selection“ if they cannot use genetic information but individuals can make insurance
purchase decisions based on genetic test results. There is some evidence that both
phenomena are occuring. There is a wide variety of regulatory regimes regarding the use of
genetic test information depending on the juristiction and on the insurance market. We
consider four policy alternatives, a duty to disclose, a code of conduct, consent law and an
information ban. All of these regulatory alternatives are in use in at least some insurance
markets in some juristictions.
We assume there is heterogeneity in loss prevention technology and individuals may or
may not be informed about their technology. This implies there is the potential for adverse
selection along the efficiency dimension of prevention. The inclusion of loss prevention seems
natural in many circumstances. If a genetic test reveals positive or negative results regarding a
specific mutation, individuals will adjust their lifestyle to the information acquired. There are
a large number of genetic tests that indicate an increased risk for diseases such as heart attack,
hypertenion and diabetes where lifestyle has an important role in determining whether the
individual will become symptomatic.
We find that there are two main factors that determine the value of information and
22
thereby insurance market outcomes. These factors are the observability of consumers‘
information status and the clinical value of information. If information status is observable,
then insurance companies can condition their policy offerings based on whether the consumer
is informed or not. This exacerbates the problem of classification risk. Then the value of
information is negative unless the information has sufficent clinical value. The regulatory
regimes where insurers can observe information status are the duty to disclose and the code of
conduct. If information status is not observable, insurers cannot condition their policy
offerings based on whether the individual is informed or not but must offer the same policies
to all. Then the value of information is non-negative whether or not informtion has clinical
value. The regulatory regimes where insurers cannot observe information status are the
consent law and the information ban These regimes provide incentives for, or at least do not
discourage, testing.
We are able to ex ante Pareto rank the policy regimes based on the insurance market
outcomes that they lead to. When information has no clinical value, the duty to disclose and
code of conduct produce the outcome where individuals choose not to take tests and purchase
the pooled full coverage policy. This outcome is Pareto superior to that of the consent law,
where individuals choose to be tested and purchase risk-type specific full coverage policies.
The consent law is in turn Pareto superior to the information ban, which leads to an outcome
where individuals choose to be tested and choose from a separating menu of insurance policies.
When information has clinical value, the duty to disclose is ex ante Pareto superior to the code
of conduct and consent law. The code of conduct and consent law are Pareto
non-comparable, but both are preferred to the information ban. The clinical value of
information does have an effect on the Pareto ranking of the policies. But regardless of
whether information has clinical value or not, the duty to disclose is at least weakly Pareto
superior to the other policy alternatives. Regardless of whether information has clincal value
or not, the information ban is Pareto inferior to all of the other policies and is the least
desireable policy alternative.
23
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27
Appendix
6 Value of Information without Insurance
Let us assume for simplicity that ′ for a constant ∈ . 0 resembles the
case CD, 0 the case ID, and 0 the case DD. Integration yields
′ 0 0 .
Taking as given, we obtain
0 0 ,
0 0 .
Rearranging (2) yields
∗ ∗ ∗
∗ ∗ ∗ .
Denoting by the value of information if ′ , we know that 0 0 .
Furthermore, as prevention is optimal and satisfies (1), we can exploit the envelope theorem to
obtain
∗
0,
∗
∗ ,
∗
∗ .
Therefore, the marginal effect of a variation of on the value of information is given by
∗ ∗ ,
which is zero for 0, positive for 0, and negative for 0. Applying the implicit
function theorem, we can also calculate the second derivative to find that
∗ ∗
∗ ∗ .
For the special case of CD, i.e., 0, we find that
′′ ∗ 0, (5)
confirming that 0 0 is a local minimum. It is also a global minimum, as there are no
28
zeros of ∂ / ∂ except 0. The following picture illustrates a possible shape of .
Figure 1: Shape of the value of information function without insurance
Hence, it is clear that information about type is always valuable, as it allows individuals to
adjust their behavior in terms of risk management to the information acquired.
7 Value of Information with Full Information
Again, we choose the specification ′ to facilitate the calculation of marginal
effects of altering the structure of prevention technology heterogeneity. Prevention
technologies are as before. By use of the envelope theorem, we obtain
0,
′ ,
′ ,
Hence, we obtain for the endogenous value of information
29
′ ′
Under CD and DD, we have that , hence and therefore
∂ / ∂ is negative. Due to continuity, it will also be negative for a range ∈ 0, . Hence,
the value of information increases when moving from ID over CD to DD. Let us illustrate a
possible shape of in the following figure.
Figure 2: Shape of the value of information function with full insurance
The solid line represents a scenario where the value of information is always negative. Here
classification risk prevails and insurance deters information acquisition which is due to rather
inefficient prevention opportunities. The dotted line represents a situation where for some low
values of information is valuable and for high values it is not. This is a situation where
efficient prevention opportunities for high risks improve on the value of information and help
to overcome the deterring effect of classification risk. The dashed line represents a situation
where even for some positive values of information is valuable. Efficient risk mitigation
opportunities can alleviate classification risk up to the point that the private value of
information becomes positive, even if high risk individuals are equipped with the less
30
favorable prevention technology.
8 Numerical Example for a Positive Value of Information in the
Benchmark Case
In this section we provide a numerical example for a positive value of information if both
informational status and risk type are observable. We introduce quadratic loss prevention
technologies, discuss the case of risk neutrality with linear prevention costs and show how it
extends to the general set-up introduced above.
8.1 Quadratic Loss Preventione Technology
For analytical convenience we standardize effort to the unit interval ∈ 0,1 . Let loss
probability be given by with ∈ 0,1 , ∈ 1 , 2 and
∈ ,1 . Hereby 0 ensures that ′′ 2 0∀ and 1 entails that
the interval for is nonempty. 1 renders the parameter region for
nonempty and 2 lets ′ 2 0∀ . Finally, and 1
ascertain that 1 0 and 0 1 respectively.
We now incorporate prevention technology heterogeneity by specifying
and ,
with 0 1. Furthermore, shall be picked from the interval 1 , 2
and from the interval ,1 . We impose the condition 2 1 to ensure
that the first interval will be nonempty.20 For ease of exposition we define :
and then .
8.2 The Value of Information under Risk Neutrality and Linear Prevention Cost
Let us assume that utility is given by resembling risk neutral decision making
20 The second is nonempty in any case then.
31
and that prevention cost be given by for ∈ 0,1 . In this tractable case we obtain
for the endogenous value of information if both informational status and risk type are
observable.
The optimal effort levels maximize and
therefore satisfy the first order conditions 2 1 0.21 They are given by
. Let be contained in the open interval , , which is nonempty in
any case. This ensures that we only consider interior maxima and the first order approach is
legitimate.
Plugging the effort levels into the expression for , we obtain
⋅
⋅
⋅
⋅
0.
Hence, in this case the endogenous value of information is always positive which means that
uninformed individuals will from an ex-ante perspective always prefer to obtain information
and to adjust effort accordingly to staying uninformed and exerting effort based on average
prevention technology. The reason is that risk-neutral agents are not affected by classification
risk.
21 The second order conditions are satisfied, 2 0.
32
8.3 Extension to the General Model
In order to construct a numerical example with risk aversion and convex prevention cost
we use a parameterization that nests risk neutrality and linear cost of effort. Therefore let
and with 0 and 1 . The case above corresponds to the
choice , 0,1 . Now we can express the value of information as a function of these new
variables, , , and it is straightforward that is a continuous function of , .
From above we know that 0,1 0 and therefore we find an open neighborhood of 0,1
where it is still positive. Picking parameters 0 and 1 from that open environment
we obtain the example.
Appendix 9 Proof of Propostion 5
Recall that under the duty to disclose the value of information is I1, under the code of conduct,
value of information is , under the consent law the value of information is , and under a
ban on the use of test information the value of information is .
Table A1 compares the duty to disclose with the consent law. In Case A, the fact that I1 < 0
implies VU( UC ) > HVH( HC ) + LVL( LC ). This implies the the duty to disclose regime is
preferred. In Case B, where I1 > 0, the insurance market outcomes are the same under both
regimes and individuals not worse off under the duty to disclose.
Table A1. Comparison of Duty to Disclose and Consent Law
Case Duty to Disclose Consent Law Policy
A I1 < 0, I3 > 0 VU( UC ) VH( HC ),VL( LC ) Duty to Disclose
B I1 > 0, I3 > 0 VH( HC ),VL( LC ) VH( HC ),VL( LC ) Duty to Disclose
Table A2 compares the duty to disclose and the ban. In Case A, the fact that I1 < 0 implies that
VU( UC ) > HVH( HC ) + LVL( LC ) > HVH( HC ) + LVL(CL*), so that individuals are better off
33
under the duty to disclose. In Case B, the fact that LC offers full coverage while CL* offers
partial coverage implies that individuals are better off under the duty to disclose.
Table A2. Comparison of Duty to Disclose and Ban
Case Duty to Disclose Ban Policy
A I1 < 0, I4 = 0 VU( UC ) VH( HC ),VL(CL*) Duty to Disclose
B I1 > 0, I4 = 0 VH( HC ),VL( LC ) VH( HC ),VL(CL*) Duty to Disclose
Table A3 compares the code of conduct and the consent law. In Case A, I2 < 0 implies that VU(
UC ) > HVH( HC ) + LVL(CL*) and I3 > 0 implies that HVH( HC ) + LVL( LC ) > VU(CU*).
However, it cannot be determined whether VU( UC ) or HVH( HC ) + LVL( LC ) is larger.
Which policy is preferred depends on the underlying parameters. In Case B, VL( LC ) > VL(CL*)
implies that the Consent law is preferred. The code of conduct and the consent law are Pareto
non-comparable.
Table A3. Comparison of Code of Conduct and Consent Law
Case Code of Conduct Consent Law Policy
A I2 < 0, I3 > 0 VU( UC ) VH( HC ),VL( LC ) Indeterminate
B I2 > 0, I3 > 0 VH( HC ),VL(CL*) VH( HC ),VL( LC ) Consent Law
Table A4 compares the code of conduct and the ban. In Case A, the fact that I2 < 0 implies VU(
UC ) > HVH( HC ) + LVL( LC ) > HVH( HC ) + LVL(CL**), so that individuals are better off under
the duty to disclose. In Case B, individuals are not worse off under the code of conduct than
the ban.
Table A4. Comparison Code of Conduct and Ban
34
Case Code of Conduct Ban Policy
A I2 < 0, I4 = 0 VU( UC ) VH( HC ),VL(CL*) Code of Conduct
B I2 > 0, I4 = 0 VH( HC ),VL(CL*) VH( HC ),VL(CL*) Code of Conduct
Table A5 compares the consent law and the ban. In the only case, the fact that LC provides
full coverage while CL** provides partial coverage implies the consent law is preferred.
Table A5. Comparison of Consent Law and Ban
Case Consent Law Ban Policy
A I3 > 0, I4 = 0 VH( HC ),VL( LC ) VH( HC ),VL(CL*) Consent Law
Taken together, the results from the text and the analyses of Tables A1 and A2 imply the
duty to disclose is Pareto superior to the other policy regimes. The results in the text and the
analyses of Tables A3 and A4 imply that the other policies are Pareto superior to the ban on the
use of information.
The equilibria under the consent law and under the ban depend on the assumption that
individuals become informed if the cost of information is zero. We now consider the
outcome when there are small information costs. This implies that, under the consent law,
there is a second equilibrium where individuals remain uninformed. Under the ban the
unique equilibium is for individuals to remain uninformed. In both cases, individuals receive
expected utility VU( UC ).
First, consider the comparison of the consent law with the duty to disclose. If I1 < 0,
then the consent law and duty to disclose yield the same expected utlity. If I1 > 0, individuals
receive either VH( HC ) or VL( LC ). Then I1 > 0 implies HVH( HC ) + LVL( LC ) > VU( UC ), and
the duty to disclose is preferred. Now consider the comparison of the consent law with the
code of conduct. If I2 < 0, then the code of conduct and the consent law both yield expected
35
utility VU( UC )> If I2 > 0 individuals receive either VH( HC ) orVL(CL*). Again, I2 > 0 imples
HVH( HC ) + LVL(CL*) > VU( UC ) and the code of conduct is preferred. The comparison of the
duty to disclose and the code of conduct with the ban yields the same results, both are
preferred to the ban. The welfare analysis is not sensitive to the assumption that individuals
become informed if the value of information is non-negative.
36
Acknowledgment
We would like to thank Shinichi Kamiya, Jana Mühlnickel and Jörg Schiller for their
helpful comments on earlier versions of this article. We also thank participants at the Research
Seminar of Riskcenter at the University of Barcelona, the Hamburg-München-Hohenheimer
Insurance Economics Colloquium 2012, the American Risk and Insurance Association Annual
Meeting 2012, the Jahrestagung des Vereins für Socialpolitik 2012, the 39th Seminar of the
European Group of Risk and Insurance Economists, the 3rd CEQURA Conference on
Advances in Financial and Insurance Risk Management, the Western Risk and Insurance
Association Annual Meeting 2013, the Allied Social Science Associations Annual Meeting
2013, the Annual Meeting of the Deutscher Verein für Versicherungswissenschaft 2013 and
the 2013 Risk Theory Society Annual Meeting for valuable comments, which led to significant
improvements. Any remaining errors are, of course, our own.
