Different tests can be used to verify the presence of adverse selection in a given market and their nature is a function of the available data. If we have access to individual data from the portfolio of an insurer and want to test that high-risk individuals in a given class of risk choose the lower deductible, the test will be a function of the different risk classes used by the insurer, and consequently of the explanatory variables introduced in the model. Intuitively, when the list of explanatory variables is large and the classification is appropriate, the probability to find a residual adverse selection in a portfolio is low.
Very few articles have analyzed the significance of residual adverse selection in insurance markets. Dahl (1983, 1992) reported evidence of some adverse selection in Canadian automobile insurance markets and suggested that his empirical results were in accordance with the Wilson-Miyazaki-Spence model that allows for cross-subsidization between individuals in each segment defined by a categorization variable. His analysis was done with aggregate data. Until recently, the only detailed study with individual data was that of purls and Snow (1994) (see Chipper, 1998, for an overview of the recent papers and Richaudeau, 1997, for a thesis on the subject).
In their analysis they considered four different adverse selection models. They found evidence of adverse selection with market signaling and no-cross-subsidization between the contracts of different risk classes. In other words, they found evidence of separation in the choice of deductible with non-linear insurance pricing and no-cross-subsidization. To obtain their results they estimated two structural equations: a demand equation for a deductible and a premium function that relates different ratifications variables to the observed premix.
The demand equation can be derived from the low-risk individual maximization problem in a pure adverse selection model with a positive loading factor. This yields DL* > D H• > 0 with two types of risk in a given class (Proposition 2). Unfortunately, it cannot be obtained from the first-order condition (4) in Juelz and Snow which corresponds to the first-order condition of the result presented in Proposition 1 above. Another criticism concerns the relationship on non-linear insurance pricing and the Rothschild-Stieglitz model. In fact from the discussion above, the separation result is due to the introduction of a self-selection constraint in the low-risk individual problem and not from the fact that insurance pricing is non-linear. The two problems yield different empirical tests. From Proposition 2, we do not need the non-linearity of the premium schedule to verify that a separating contract is chosen.
A new evaluation of adverse selection in automobile insurance
In this section, we present an econometric model and empirical results on the presence of adverse selection in an automobile insurance market. The data come from a large private insurer in Canada and concern collision insurance since the insured has the choice for a deductible for that type of insurance only. There are no bodily injuries in the data and liability insurance for property damages is compulsory. In that respect, we are close to Juelz and Snow (1994).
In order to perform carefully the analysis of adverse selection in this portfolio from a structural model, it is important to design a basic latent model. The discussion presupposes that two deductibles DI < D2 are available.