A Copula-Based Panel Data Model for Pricing Insurance Contracts with Endogenous Deductibles

Abstract

Insurers adjust premiums for renewing policyholders based on past claims, a practice known as experience rating. This paper examines experience rating in insurance contracts with deductibles, a key instrument for mitigating inefficiencies arising from information asymmetry between policyholders and insurers. We propose a copula-based panel data model that accounts for the endogeneity of deductible choice, particularly when the assumption of contemporaneous exogeneity is violated-consistent with theories of adverse selection and moral hazard. We also introduce a computationally efficient algorithm for inference and prediction. The framework accommodates various types of non-Gaussian outcomes and is well-suited for predictive applications. We apply the method to a government property insurance program, using historical claims data to develop an experience rating scheme. Results reveal a negative relationship between deductible choice and underlying risk, providing empirical support for endogenous selection behavior. Compared to standard approaches that treat deductibles as exogenous, our model enables more refined risk segmentation and improved identification of profitable business.