Identification of Insurance Models with Multidimensional Screening

TL;DR

This paper explores how to identify insurance models with multidimensional screening, considering private information on risk and risk aversion, and examines the impact of data availability on model identification.

Contribution

It provides explicit equations for estimation and testing, demonstrating that the model is identifiable despite bunching and finite coverages.

Findings

Model structure is identifiable despite bunching.

Number of claims is crucial for identifying risk and risk aversion.

Explicit restrictions on observables are derived for testing.

Abstract

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.