Adverse selection is potentially present in many markets. In automobile insurance, it is often documented that insured drivers have information not available to the insurer about their individual risks. This explains the presence of many instruments like risk classification based on observable characteristics (Hoy, 1982 and Crocker and Snow, 1985, 1986), deductibles (Rothschild and Stieglitz, 1976 and Wilson, 1977) and bonus-mauls schemes (Dionne and Lasers, 1985; Dionne and Vanessa, 1992 and Piquet, 1998).
But the presence of deductibles can also be documented by moral hazard (Winter, 1992) or simply by transaction costs proportional to the actuarial premium, and the bonus-mauls scheme is often referred to moral hazard. It is then difficult to isolate a pure adverse selection effect from the data. However, the presence of adverse selection is necessary to obtain certain predictions that would not be obtained with only transaction costs and moral hazard.
ADVERSE SELECTION AND OPTIMAL CHOICE OF INSURANCE
Let us first consider the economy described by Rothschild and Stieglitz (1976) (see Karloff, 1970, for an earlier contribution). There are two types of individuals (i = H,L) representing different probabilities of accidents with pH> jig-. We assume that at most one accident may arrive during the period. Without insurance their level of welfare is given by.
Introduction of different accident costs
f now we take into account different accident costs in the basic Rothschild and Stieglitz model, the optimal choice of deductible may be affected by the distributions of costs conditional to the risk classes (or types). Flute (1994) and Fluet and Mannequin (1994) obtained that a constant deductible will be optimal only when the conditional likelihood.
Adverse selection with moral hazard
Adverse selection with moral hazard The research on adverse selection with moral hazard is starting (see however Dionne and Lasers 1988). We know that a constant deductible may be optimal under moral hazard if the individual can modify the occurrence of accidents but not the severity (winter, 1992). Here to keep matters simple we assume that an insured can affect his probability.
Cross-subsidization between different risk types
One difficulty with the pure Cornet-Nash strategy lies in the fact that a pooling equilibrium is not possible. Wilson (1977) proposed the anticipatory equilibrium concept that always results in an equilibrium (pooling or separation). When the proportion of high risk individuals is sufficiently high, a Wilson equilibrium coincides with a Restate equilibrium. Moreover, welfare of both risk classes can be increased by allowing subsidization: low risk individuals can buy more insurance coverage by subsidizing the high risks (see Crocker and Snow, 1985 and Bombardon, 1997, for more details).
Different risk aversions
The possibility that different risk types may also differ in risk aversion was considered in detail by Villeneuve (1996). It is then necessary to control for risk aversion when we test for the presence of residual adverse selection. We will see that the risk classification variables do, indeed, capture some information on risk aversion. In other words, we can also test for the presence of residual risk aversion in risk classes.
This result suggests that a test for the presence of adverse selection should be applied inside different risk classes or by introducing categorization variables in the model. It is known that the presence of adverse selection is sufficient to justify risk classification when risk classification variables are costless to observe. Now the empirical question becomes.