Insurance, Consumer Search, and Equilibrium Price Distributions

ABSTRACT We examine a service market with two frictions: search is required to obtain 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 insurer will exacerbate the moral hazard by offering full insurance. A competitive 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. (1) In 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 incentive 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 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. We decompose 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 regardless 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. (2) Thus, the general equilibrium feedback is a much larger concern in the incentive problem. We also 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 insurer has the most ability to promote competition among service firms, it has no incentive to do so. Instead, it offers full insurance, 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 uninsured. 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. …