Risk Aversion and the Willingness to Pay for Insurance: A Cautionary Discussion of Adverse Selection

ABSTRACT Textbooks frequently describe adverse selection as an almost inevitable feature of insurance markets with heterogeneous buyers and asymmetric information. But if low-risk applicants are more risk averse than their high-risk counterparts, the former may be as willing or more willing than the latter to purchase insurance at any given price. The present article discusses this possibility in several forms suitable for different levels of instruction, to help bridge the gap between insurance education and current research on this topic. INTRODUCTION Insurance textbooks often present adverse selection as a nearly inescapable problem in markets with heterogeneous buyers and asymmetric information. Vaughan and Vaughan (2001, p. 115), for example, state that "Underwriting . . . is an essential element in the operation of any insurance program, because unless the company selects from among its applicants, the inevitable result will be adverse selection" (emphasis added). Baranoff's (2004, p. 77) position is equally unequivocal: "The business of insurance inherently involves discrimination; otherwise, adverse selection would make insurance unavailable." Similarly, Dorfman (2002, p. 29) remarks, "Adverse selection . . . is an ever present fact in the insurance market," and Rejda (2003, p. 23) writes, "adverse selection can never be completely eliminated."1 But while there is no denying that adverse selection can be a serious problem for insurers, it is not inevitable, either in principle or in practice. Indeed, the empirical evidence is mixed. Studies by Browne (1992), Browne and Doerpinghaus (1993), Cutler and Zeckhauser (1998), and Makki and Somwaru (2001) obtained evidence of adverse selection in health and crop insurance, while D'Arcy and Doherty (1990), Dahlby (1992), and Puelz and Snow (1994) observed it in the U.S. and Canadian auto insurance markets. But the Puelz and Snow (1994) results have been widely criticized as spurious (see especially Dionne et al., 2001), and Chiappori and Salanie (2000), Dionne et al. (2001), and Chiappori et al. (2002) found no evidence of adverse selection in either the Canadian or French automobile insurance markets. Moreover, recent studies by Cawley and Philipson (1999) and Cardon and Hendel (2001) found no adverse selection in the life or health insurance markets, respectively. Thus, despite extensive investigation of adverse selection, no empirical consensus on its importance has yet emerged.2 Given the disparity in empirical findings, it seems appropriate to temper the usual classroom discussion of adverse selection with some caveats and perhaps even some mention of the potential for the opposite phenomenon, advantageous selection. The present article is therefore intended as a supplement to textbook presentations; it should serve as a cautionary note to students (and perhaps a reminder to faculty) that adverse selection is a possible, but not universal, feature of insurance markets characterized by asymmetric information. The next section briefly describes the standard presentation and its implicit assumptions. We then present the argument against adverse selection in several forms appropriate for different levels of instruction-an intuitive exposition, a graphical analysis, and a simple mathematical model. The model derives an explicit condition under which adverse selection will not arise despite asymmetric information regarding loss probabilities, and some simple numerical examples are then provided. The article ends with a brief conclusion. ADVERSE SELECTION AND ADVANTAGEOUS SELECTION Though textbooks differ, the typical presentation runs as follows. Adverse selection arises from asymmetric information: insurance applicants know the probabilities of loss facing them, but insurance companies cannot distinguish high-risk applicants from low-risk applicants. If the insurers charge an average premium rate to all applicants, high-risk individuals will receive a subsidy and purchase more coverage than low-risk individuals, who find the premiums rather expensive relative to their risk exposure. …