Testing Adverse Selection with Two-Dimensional Information: Evidence from the Singapore Auto Insurance Market

ABSTRACT This article examines adverse selection in insurance markets with two-dimensional information: policyholders' riskiness and degree of risk aversion. We build a theoretical model to make equilibrium predictions on competitive insurance screening. We study several variations on the pattern of information asymmetry. The outcomes range from full separation to partial separation, and complete pooling of risk types. Next, we propose a copula approach to jointly examine policyholders' coverage choice and accident occurrence in the Singapore automobile insurance market. Furthermore, we invoke the theory to identify subgroups of policyholders for whom one may expect the risk-coverage correlation and adverse selection to arise. INTRODUCTION Adverse selection in an insurance market--a stylized situation of asymmetric information--describes the fact that buyers of insurance possess residual private information about their risk that insurers lack even after risk classification. The riskiness of an insurance policyholder is reflected by the probability of a loss, the size of a loss in the event that it occurs, or both. Thus, policyholders of idiosyncratic risks represent different expected indemnity and profitability to insurers, which gives them motivation to try to distinguish or "screen" different types of buyers. The theory of adverse selection in insurance, set forth by Rothschild and Stiglitz (1976), Stiglitz (1977), and Wilson (1977), derives an intuitively appealing outcome: insurers use deductibles as a screening device to induce customers to reveal their private information. In equilibrium, low-risk individuals withstand higher deductibles (or less coverage) in order to distinguish themselves from high-risk individuals and hence to pay a lower premium. The conclusion relies on a condition to align the incentives, typically called the single-crossing property, that is someone with higher risk has a higher marginal cost in deductibles. Since the seminal work of Rothschild and Stiglitz, the theory of adverse selection has been extended in many significant ways. We refer to the excellent survey articles by Dionne and Doherty (1992) and Dionne, Doherty, and Fombaron (2000) and the literature therein for these contributions. Much of the empirical literature on adverse selection in insurance markets has been seeking to test the above theoretical prediction on the correlation of risk and coverage: namely, it is the riskier individuals who purchase more insurance coverage. According to Chiappori et al. (2006), the risk-coverage relationship is quite a robust testable implication in a variety of markets. A recent review article by Cohen and Siegelman (2010) summarizes the empirical tests on different types of insurance market, including auto insurance, annuities, life insurance, reverse mortgages, health insurance, long-term care, and crop insurance. In particular, studies of the auto insurance market present mixed evidence for the theoretical prediction. Puelz and Snow (1994) find a strong positive risk--coverage correlation, though Dionne, Gourieroux, and Vanasse (2001) point out that the presence of adverse selection vanishes when the nonlinearity of the risk classification variables are taken into account. Using a portfolio of contracts from a French insurer, Chiappori and Salanie (2000) also find no evidence of asymmetric information, and the results are robust to both parametric and nonparametric testing methods. The bivariate model proposed by Chiappori and Salanie (1997, 2000) is also employed by Cohen (2005) and Saito (2006) when analyzing Israel and Japanese auto insurance markets, respectively. Supplementing the findings in Chiappori and Salanie (2000), Cohen (2005) conclude with evidence of information asymmetry for the group of experienced drivers but no coverage--risk correlation for beginning drivers. Saito (2006) finds no advantageous information for policyholders when examining the effects of extensive deregulation in the Japanese auto insurance market. …