Insurance, Consumer Search, and Equilibrium Price Distributions

• Author: Ş. Nuray Akın,Brennan C. Platt
• Published date: 01 June 2014
• DOI: http://doi.org/10.1111/j.1539-6975.2013.01515.x
• Date: 01 June 2014

©

DOI: 10.1111/j.1539-6975.2013.01515.x

397

INSURANCE,CONSUMER SEARCH,AND EQUILIBRIUM

PRICE DISTRIBUTIONS

S¸. NurayAkın

Brennan C. Platt

ABSTRACT

We examine a service market with two frictions: search is required to ob-

tain price quotes, and insurance coverage for the service reduces household

search effort. While fewer draws from a price distribution will directly raise

a household’s average price, the indirect effect of reduced search on price

competition has a much greater impact, accounting for at least 89 percent

of increased average expenditures. In this environment, a monopolist in-

surer will exacerbate the moral hazard by offering full insurance. A compet-

itive insurance market typically results in partial insurance and significant

price dispersion, yet a second-best contract would offer even less insurance

coverage.

INTRODUCTION

In most markets where insurance plays a prominent role (such as medical services

or auto repairs), the price of a particular service varies significantly from one firm

to another.1In a typical market, consumers respond to price dispersion by obtaining

price quotes from a number of firms and selecting the lowest price. However, when

an insurance company ultimately pays for most of the service, the consumer’s incen-

tive to search is dramatically reduced. This article studies insurance contracts in an

environment with moral hazard due to search.

An insurance contract (or policy) consists of the premium charged to households

as well as a coinsurance rate, defined as the percentage of an insurance claim that

the household pays out-of-pocket. In offering a particular policy, an insurer must

consider the incentives it creates for both households and service providers. We depict

S. Nuray Akın works in the Department of Economics, University of Miami. Brennan C.

Platt works in the Department of Economics, Brigham Young University. We are grate-

ful to Marco Bassetto, Hulya Eraslan, Boyan Jovanovic, David Kelly, Manuel Santos, Alan

Sorensen, and Val Lambson for their valuable comments. All remaining errors are our

own.

1Sorensen (2000) provides an empirical investigation of price dispersion in the prescrip-

tion drug market (pricing the same drug across retailers). He documents that, on aver-

age, the highest posted price is over 50 percent above the lowest available price; fur-

thermore, differences in pharmacy characteristics can account for at most one-third of the

dispersion.

S¸.

The Journal of Risk and Insurance, 2013, Vol. 81, No. 2, 397–429

398 THE JOURNAL OF RISK AND INSURANCE

this in a general equilibrium model in which the interactions between these agents

endogenously determine the insurance policy, the distribution of service prices, and

the search intensity of households.

Moral hazard can be measured as the increase in the expected total cost of the event

due to the presence of a particular insurance contract. Wedecompose two effects that

contribute to this rise in expected cost. First, a direct effect occurs when consumers

request fewer quotes from the same distribution. This was studied in Dionne (1984),

which we extend by identifying a second indirect effect, which happens in equilibrium

because requesting fewer quotes results in less price competition among the service

providers, shifting the distribution toward higher prices. Indeed, we find that regard-

less of parameter values, the latter effect is at least 8.6 times bigger than the former,

or in other words, is responsible for at least 89 percent of the cost increase caused by

moral hazard.2Thus, the general equilibrium feedback is a much larger concern in

the incentive problem.

Wealso characterize the second-best insurance policy, which selects a coinsurance rate

that balances consumption smoothing against incentives to search. This is compared

with the insurance policy from two different insurance market structures: monopoly

and perfect competition.

Surprisingly, even though a monopolist insurerhas the most ability to promote com-

petition among service firms, it has no incentive to do so. Instead, it offers full in-

surance, resulting in no search and a high service price. While this leads to high

expected payouts on insurance, these are passed on to households in their insurance

premium. In addition, households are willing to pay a larger risk premium on top

of it precisely because they face greater variance in wealth should they remain unin-

sured. To the best of our knowledge, we are the first to provide this result in the

literature.

On the other hand, a perfectly competitive (PC) policy includes some coinsurance

but still less than the second-best policy, due to search externalities. The insurer only

optimizes with respect to the policy’s direct effect on its clients, neglecting the indirect

benefits of extra search effort.

In our model, there is a continuum of ex ante identical households and service firms,

and an insurance firm. Households face a random event (such as an auto accident or

health problem)3with some fixed probability. If the event occurs, the household must

2A similar flavor arises in Fershtman and Fishman (1994) and Armstrong, Vickers, and Zhou

(2009). Both articles consider the effect of an exogenous price cap in a market with search

frictions (but no insurance contracts). While the cap necessarily reduces the high end of the

price distribution, it has the unintended consequence of reducing the benefits of search. As

fewer consumers seek additional quotes, retailers compete less vigorously and the low end

of the price distribution will rise; indeed, consumers can be left worse off after the imposition

of the price cap.

3This is purely a monetary loss, and thus assumes away any irreparable damage. Ma and

McGuire (1997) model health shocks as a monetary loss that can be partially recovered de-

pending on the quantity and quality of health care purchased.

INSURANCE, CONSUMER SEARCH, AND EQUILIBRIUM PRICE DISTRIBUTIONS 399

hire a service firm to fully repair4the damage. This service is homogenous across

the service firms, but each firm may charge a different price. Households know the

distribution of offered prices, but can only learn the price charged by a particular firm

through costly search effort.

Households can insure against this event by purchasing a policy offered by the insur-

ance firm. If the event occurs, the policy reimburses a stipulated fraction of the actual

price paid. All service firms are within the insurer’s approved network, meaning they

have agreed not to charge more than a maximum price.

Search is simultaneous, as in Burdett and Judd (1983); that is, a household receives all

quotes at the same time. A simultaneous search environmentcan generate equilibrium

price dispersion even though firms and households are homogeneous.5Our model

extends Burdett and Judd (1983) in threenoteworthy ways: households are risk averse,

insurance contracts are incorporated, and quotes are obtained with a probability that

depends on search effort. The last feature greatly improves tractability and reduces

the number of equilibria.

Our work contributes to a broad literature on moral hazard problems, which occur

whenever the presence of insurance distorts incentives for the insured, causing an

increase in expected payout.6Two other forms of moral hazard are well known.

First, the insured person may exercise less precaution (such as defensive driving),

increasing the probability of loss. Second, the insured person may increase his con-

sumption of the covered service (such as medical appointments), increasing the

size of loss. These have been extensively studied, beginning with the work of Ar-

row (1963), Pauly (1968), Smith (1968), Zeuckhauser (1970), and Ehrlich and Becker

(1972).

However, moral hazard in search has received much less attention, with the only

formal analyses in Dionne (1981, 1984).7In a model where the coinsurance rate is

taken as exogenous and the distribution of prices is fixed regardless of the number

of quotes requested by households, Dionne identifies the negative incentive effect of

insurance on search behavior and hence on expected service prices. However, this

omits a crucial (and, as we show, larger) component of the story: the endogenous

response of firms to household search.

4This indivisibility of repairs eliminates an intensive margin that the household might adjust

(or insurer might limit) in response to the price. This seems reasonable for many urgent

health expenditures (such as unexpected surgery or filling a vital prescription) or major auto

reconstruction, in which the choice is essentially discrete (to do it or not), and search is limited

by the need to choose a provider rather quickly.

5Baye, Morgan, and Scholten (2006) provide a comprehensive and insightful review of models

of search that can produce equilibrium price dispersion. Sequential search can produce price

dispersion with homogeneous buyers if search is nonstationary due to deadlines; see Akin

and Platt (Forthcoming).

6Rowell and Connelly (2012) provides an extensive history on the usage of the term moral

hazard.

7Arrow (1963) mentions the potential problem: “Insurance removes the incentive on the part

of individuals, patients, and physicians to shop around for better prices for hospitalization

and surgical care.”