A Theory of the Demand for Underwriting

ABSTRACT We examine the demand for underwriting and its effect on equilibrium in an insurance market in which insureds know their risk type, but insurers do not. Our analysis indicates that a set of policies including one that requires buyers to take an underwriting test can constitute a full coverage Nash equilibrium when perfect classification is possible. We also find that underwriting equilibria, in which low risks obtain greater coverage than they would without underwriting, widely exist in a Wilsonian market with nonmyopic insurers. Our findings provide a potential explanation for why empirical evidence on adverse selection is mixed. INTRODUCTION Transfer of risk in a private market inevitably entails underwriting in some form. (1) In practice, the ability to underwrite well is one of the cornerstones of a successful insurance operation. Poor risk selection, in contrast, can result in significant losses and insurer failure. While some forms of risk classification are prohibited by law, underwriting on the basis of race, for example; insurers have significant leeway to incorporate information that they feel, is necessary in risk selection and pricing. (2) The purpose of this article is to investigate the demand for underwriting and its impact on equilibrium in insurance markets. Particularly, we examine the conditions under which underwriting tests, which we define by the accuracy and the cost of the tests, lead to equilibrium where low-risk (LR) consumers obtain greater coverage than they would in self-selection partial coverage equilibrium. Thus, we argue that many underwriting techniques are financially advantageous to insureds whose costs of coverage are lowered by the exclusion of higher risks from insurance pools and show that underwriting contributes to reducing adverse selection in insurance markets. To underscore the significance of underwriting techniques in insurance markets, it may be helpful to borrow the remark by Dionne, Gourieroux, and Vanasse (2001) who study the Quebec auto insurance market: ... by an appropriate risk classification procedure, the insurer is able to control for adverse selection and does not need any additional self-selection mechanism. The prior literature has considered the bookends of our analysis. At one extreme, if an insurer's underwriting has zero probability to reveal an insured's true risk type, a Rothschild-Stiglitz (RS, hereafter) separating equilibrium may hold (Rothschild and Stiglitz, 1976). (3) Alternatively, depending on the ratio of LRs to high risks (HRs) in the market, there may either be no equilibrium (Rothschild and Stiglitz, 1976) or a pooling equilibrium in which HRs are subsidized by LRs (Wilson, 1977). At the opposite extreme, perfectly accurate underwriting at zero cost results in a first-best equilibrium, full coverage for each risk type at actuarially fair premiums (e.g., Mossin, 1968). Between these extremes are the more likely actual market cases in which underwriting is neither costless nor perfectly accurate and self-selection does not perfectly reveal a consumer's risk type. Our model is different from prior studies on information acquisition (see, e.g., Crocker and Snow, 1992; Doherty and Thistle, 1996; Hoy and Polborn, 2000) in several respects. Most fundamentally, these studies assume that consumers are unaware of their risk type ex ante and invest in learning their risk type. In contrast, consistent with the literature on adverse selection, we assume that individuals know their risk type, but insurers do not. Second, we consider underwriting as a part of the process of insurance purchasing. Information gained through underwriting becomes known to both the potential purchaser and the insurer. This setting is consistent with the ordinary insurance purchasing process. For instance, when a consumer wants to purchase life insurance, he or she typically needs to provide personal information to an insurer to obtain a rate. …