Preprint A110/2001
Non-Monotone Insurance Contracts and their Empirical Consequences

Humberto Moreira | Araujo, Aloisio

**Keywords: **
Non-monotone contracts; correlation between coverage and risk; omitted variable

The goal of this paper is to build a hidden information model showing how omitted variables (asymmetric information) can bias the sign of the correlation of equilibrium variables conditioning on all observable variables. We show that this may be the case when the omitted variables have a non-monotonic relation with the observable ones. Moreover, because this non-monotonic relation is deeply related with the failure of the single crossing property (SCP) in one-dimensional screening problems, the existing literature on asymmetric information does not capture this feature. Therefore, our main result is to point out the importance of the SCP in testing predictions of the hidden information models. For concreteness, we present an insurance model where the insured agents have heterogeneity in risk aversion and in lenience (a prevention cost parameter). Risk aversion is described by a continuous parameter which is correlated with lenience and, for the sake of simplicity, we assume perfect correlation. In the case of positive correlation, the more risk averse agent has higher cost of prevention leading to a higher demand for coverage. Equivalently, the SCP of the Rothschild and Stiglitz model is valid and implies a positive correlation between coverage and risk in equilibrium. On the other hand, if the correlation between risk aversion and lenience is negative, not only may the SCP be broken, but also the monotonicity of contracts, i.e., the prediction that high (low) risk averse types choose full (partial) insurance. In both cases riskiness is monotonic in risk aversion, but in the last case there are some coverage levels associated with two different risks (low and high), which implies that the ex-ante (with respect to the risk aversion distribution) correlation between coverage and riskiness may have every sign (even though the \QTR{it}{ex-post} correlation is always positive). Moreover, using another instrument (a proxy for riskiness), we give a testable implication to disentangle single crossing and non single crossing under a zero correlation result: the monotonicity of coverage as a function of riskiness. Since by controlling for risk aversion (no asymmetric information), coverage is a monotone function of riskiness, this also gives a test for asymmetric information.