Facilitating Consumer Learning in Insurance Markets:  What Are the Welfare Effects?

AuthorChristoph Schottmüller, Johan N. M. Lagerlöf
Publication Date01 Apr 2018
©The editors of The Scandinavian Journal of Economics 2017.
Scand. J. of Economics 120(2), 465–502, 2018
DOI: 10.1111/sjoe.12231
Facilitating Consumer Learning in
Insurance Markets: What Are the Welfare
Johan N. M. Lagerof
University of Copenhagen, DK-1353 Copenhagen K, Denmark
Christoph Schottm¨uller
University of Copenhagen, DK-1353 Copenhagen K, Denmark
We model a monopoly insurance market in which consumers can learn their accident
risks at a cost c. We then examine the welfare effects of a policy that reduces c.If
cis sufficiently small (c
Æ), the optimal contract is such that the consumer gathers
information. For c
Æ, both the insurer and the consumer benefit from a policy that
reduces cfurther. For c>c
Æ, marginally reducing churts the insurer and weakly benefits
the consumer. Finally, a reduction in cthat is successful, meaning that the consumer
gathers information after the reduction but not before it, can hurt both parties.
Keywords: Adverse selection; consumer policy; genetic testing; information acquisition;
JEL classification:D82; I13
I. Introduction
What are the welfare effects of public policies that help insurance
customers to learn, privately and covertly, about their accident risks?
Although it might be tempting to presume that such policies are
unambiguously welfare enhancing, the question is not straightforward,
particularly if insurance companies have market power. While it is true that
more accurate information can help consumers choose the most appropriate
insurance policy, a reduction in the information-gathering cost is also
likely to affect the insurer’s optimal design of the policy, possibly in a
way that hurts consumers and overall welfare. In this paper, we study
formally the welfare consequences of an exogenous change in insurance
Also affiliated with TILEC.
*We are grateful for helpful comments from two anonymous referees, and from seminar
participants at the University of Copenhagen.
466 Learning in insurance markets
customers’ cost of learning, privately and covertly, about their accident
risks. We do this by first endogenizing the information structure in the
classic model of Stiglitz (1977) of a monopoly insurance market with
adverse selection. Then, we carry out comparative statics exercises with
respect to the information-gathering cost.
Although our analysis is consistent with many kinds of insurance
problems, our preferred interpretation of the model is in terms of health
insurance. In recent years, genetic tests that detect certain risk factors
have become available to consumers; for example, the companies 23andme
and Genome Liberty offer such tests. The tests allow customers to obtain
private information concerning their health risks. As an illustration, if the
marker rs12425791 equals “A”, this increases the risk of having a stroke
by a factor of 1.3 (see Ikram et al., 2009). These tests are associated with
monetary but also non-monetary costs. Studies have shown that people
often feel anxiety in connection with tests that reveal their true health
risks to them.1In this context, we are interested in the welfare effects of
medical counseling and assistance that are targeted at reducing the test
anxiety. In the case of costs that are monetary, we are interested in the
welfare consequences of subsidizing the tests.
Another example within the health insurance context, which fits our
model, is an individual who has private information about her extended
family’s health history. However, she still needs to learn about how that
information translates into a change in her own health risk. If the individual
indeed gathers the additional information (e.g., spends time reading books
or searching the Internet to learn about inheritance patterns of certain
diseases), she will obtain access to private information about her own
health risk.2Examples of public policies that would facilitate the gathering
of additional information include the funding and launch of a web site
with relevant information, a telephone line with free expert advice, and
an informational campaign.
In our model, there is an insurance company that has a monopoly in
its market.3This company and the consumer initially both know only the
prior distribution of the latter’s accident risk. The company first offers a
1For empirical evidence,see Codori et al. (1994) and Meiser and Dunn (2000). For a theoretical
approach, see Hoy et al. (2014).
2This is true even if the additional information is known by the insurance company, as the
company is not privy to the health history of the individual’s family. Of course, insurers
also have additional (private) information on risk that they can use to sort consumers into
different risk categories. Our analysis should be thought of as being conditional on the insurer’s
information (i.e., within a given risk category).
3The important feature of the insurance market that we want to capture with this assumption is
that the insurer has at least some market power. For empirical evidence suggesting that health
insurance markets are not perfectly competitive, see Dafny (2010). To assume a monopoly is
an extreme but also very tractable way of incorporating this feature into the model. It would
©The editors of The Scandinavian Journal of Economics 2017.
J. N. M. Lagerl¨of and C. Schottm¨uller 467
menu of insurance policies. The consumer then chooses whether or not to
acquire, at a cost c, private information about her accident risk. Thereafter,
either she chooses an insurance policy from the menu or she decides to
remain uninsured. The timing is inspired by health insurance markets in
which insurers offer several standard insurance contracts to choose from
and consumers typically have some time to consider which option to take.
Individualized contracts and renegotiation (after information acquisition)
are not feasible on these mass markets because the resulting transaction
costs would be excessive.
Our analysis shows that if the cost of information acquisition cis
sufficiently small (c
Æ, for a cut-off value cÆ>0), the consumer indeed
gathers information, and thus, at the optimum, is privately informed. In
particular, the qualitative features of the optimal menu of insurance policies
are the same as in the model of Stiglitz (1977). For such values of the
cost c, we can show that the na¨ıve intuition is confirmed: a (fur ther)
reduction in the cost benefits both the insurer and the consumer. In other
words, a policy that facilitates consumer learning is a Pareto improvement
if, already at the outset, the consumer finds it worthwhile to learn about
her risk. In practice, this might be precisely the kind of situation in which
such a policy would not be undertaken, as policymakers would believe
it is not needed.
If the cost of information gathering is very high (c>c
, where c >c
it is common knowledge between the insurer and the consumer that the
latter will never have an incentive to gather information and, therefore,
the cost does not matter for the design of the optimal insurance policy.
More interestingly, however, there are intermediate values of the cost
) for which the consumer does not incur the cost but it does
affect the insurance policy. For this range of cost levels, the insurance
company is always worse off from a local reduction in the cost and the
consumer is, depending on parameter values, either indifferent to a local
cost reduction or better off. That is, for these cost levels, there is much
weaker support for the na¨ıve intuition discussed above: either there is
a conflict of interest concerning the desirability of a cost reduction or
such a reduction would lead to a Pareto inferior outcome (with one party
being unaffected and the other being strictly worse off). Again, however,
in practice, this might be precisely the kind of situation in which a policy
that facilitates consumer learning is indeed undertaken, as policymakers
would believe it is needed.
The comparisons discussed above concern changes in cwithin the range
Æand within the range cÆ
. In both cases, we concluded
be interesting to study the questions that we look at in an oligopoly setting, but that must
await future research.
©The editors of The Scandinavian Journal of Economics 2017.

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