  This paper addresses the identification of insurance models with
multidimensional screening where insurees have private information about their
risk and risk aversion. The model includes a random damage and the possibility
of several claims. Screening of insurees relies on their certainty equivalence.
The paper then investigates how data availability on the number of offered
coverages and reported claims affects the identification of the model
primitives under four different scenarios. We show that the model structure is
identified despite bunching due to multidimensional screening and/or a finite
number of offered coverages. The observed number of claims plays a key role in
the identification of the joint distribution of risk and risk aversion. In
addition, the paper derives all the restrictions imposed by the model on
observables. Our results are constructive with explicit equations for
estimation and model testing.
