The goal of this paper is to show the possibility of a non-monotone relation between coverage and risk which has been considered in the literature of insurance models since the work of Rothschild and Stiglitz (1976). More generally, we 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 SCP in one-dimensional screening problems, the existing literature on asymmetric information does not capture this feature. Hence, our main result is to point out the importance of the SCP in testing predictions of the hidden information models.