Multidimensional Screening in Insurance Markets with Adverse Selection

ABSTRACT Bundled coverage of different losses and distinct perils, along with differential deductibles and policy limits, are common features of insurance contracts. We show that, through these practices, insurers can implement multidimensional screening of insurance applicants who possess hidden knowledge of their risks, and thereby reduce the externality cost of adverse selection. Competitive forces drive insurers to exploit multidimensional screening, enhancing the efficiency of insurance contracting. Moreover, multidimensional screening allows competitive insurance markets to attain pure strategy Nash equilibria over a wider range of applicant pools, resolving completely the Rothschild-Stiglitz nonexistence puzzle in markets where the perils space is sufficiently divisible. INTRODUCTION When insurance applicants possess hidden knowledge of their risks of incurring a loss, as in the seminal model of insurance contracting with adverse selection analyzed by Rothschild and Stiglitz (1976), the market is driven by competition for those in the low-risk class. These applicants wish to distinguish themselves from high- risk applicants in order to obtain insurance coverage at terms more favorable than would be made available if they were pooled with the high risks. The desired separation is attained through a screening mechanism whereby insurers offer applicants their choice from a menu of contracts, one of which provides high risks with full and fair insurance, while the other incorporates a lower average price for coverage but also includes a deductible that is unacceptable to high risks. In this article, we show that separation of this sort is accomplished most effectively by multidimensional screening implemented through the contractual bundling of different perils and different losses. Bundled coverage, with differential deductibles and policy limits, allows insurers to screen applicants in several dimensions, thereby reducing the externality cost that low-risk applicants must bear to distinguish themselves from high risks. As a consequence, insurers can compete most effectively for the low-risk applicants by offering contracts that exploit efficient multidimensional screening. (1) The prediction that insurance markets will offer contracts with differential coverage for alternative losses and distinct perils is confirmed by commonly observed practices. (2) For example, a typical homeowner's policy provides bundled indemnification for both liability and property losses, with different policy limits for these losses. Furthermore, within each category of loss, a homeowner faces different levels of coverage for distinct perils that cause the same damage, or different losses caused by the same peril. Generally, there is a deductible for the home being destroyed by fire, but if the same home is destroyed by flood, the deductible is 100%, as the policy explicitly provides no coverage for this peril. Moreover, losses of specific types of property, such as jewelry, rugs, or antiques, are also subject to specific (lower) sublimits. Similarly, automobile insurance typically bundles different levels of coverage, such as losses resulting from collision, personal injury, uninsured motorists, and medical bills, into the same policy with different sublimits depending on the peril or category of loss. It is also common to observe different deductibles for alternative perils causing the same loss. For example, an automobile lost through theft or fire is typically subject to a lower deductible through the "comprehensive" portion of the policy than would be the case were the loss a result of an accident and therefore covered by the "collision" part of the policy. Coverage limitations are also commonly observed in commercial insurance, where sublimits, coinsurance provisions, deductibles, and exclusions often vary according to the peril or type of loss. (3) Our analysis not only shows that multidimensional screening is efficient but also shows that multidimensional screening provides an avenue for insurance markets to circumvent the nonexistence problem identified by Rothschild and Stiglitz. …