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

• Published date: 01 April 2018
• Date: 01 April 2018
• DOI: http://doi.org/10.1111/sjoe.12231

©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

Effects?*

Johan N. M. Lagerl¨of

University of Copenhagen, DK-1353 Copenhagen K, Denmark

johan.lagerlof@econ.ku.dk

Christoph Schottm¨uller†

University of Copenhagen, DK-1353 Copenhagen K, Denmark

christoph.schottmueller@econ.ku.dk

Abstract

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;

insurance

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

Æ),

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

(cÆ

) 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

0

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.