The Theory of Risk Classification

1 8.1 INTRODUCTION The efficiency and equity effects of risk classification in insurance markets have been a source of substantial debate, both amongst economists and in the public policy arena. 1 The primary concerns have been the adverse equity consequences for individuals who are categorized unfavorably, and the extent to which risk classification enhances efficiency in insurance contracting. While equity effects are endemic to any classification scheme that results in heterogeneous consumers being charged actuarially fair premiums, whether such classification enhances market efficiency depends on specific characteristics of the informational environment. In this contribution we set out the theory of risk classification in insurance markets and explore its implications for efficiency and equity in insurance contracting. Our primary concern is with economic efficiency and the role of risk classification in mitigating the adverse selection that arises when insurance applicants are better informed about their riskiness than insurers. We are also interested in the role of classification risk, that is, uncertainty about the outcome of a classification procedure. This uncertainty imposes a cost on risk averse consumers and is thus a potential cause of divergence between the private and social value of information gathering. In addition, the adverse equity consequences of risk classification bear directly on economic efficiency as they contribute to the social cost of classification risk. We begin by considering as a benchmark the case in which both insurers and insurance applicants are symmetrically uninformed about the applicants' propensities for suffering an insurable loss. 2 8.2.1 Homogeneous Agents Formally, the insurance environment consists of a continuum of risk averse consumers, each of whom possesses an initial wealth W and may suffer a (publicly-observed) loss D with known probability p. Each consumer's preferences are represented by the von Neumann-Morgenstern utility function U(W), which is assumed to be strictly increasing and strictly concave, reflecting risk aversion. A consumer may purchase insurance against the loss by entering into a contract) , (I m C ! , which specifies the premium m paid to the insurer and the indemnification I received by the insured when the loss occurs. A consumer's expected utility under the insurance contract C is given by) () 1 () () , (N D W U p W U p C p V ! + " , (1) where m W W I D m W W N D ! " + ! ! " and denote the consumer's state-contingent …