Modeling the 'Pseudodeductible' in Insurance Claims Decisions

Abstract

In many different managerial contexts, customers leave money on the table by, for example, their failure to claim rebates, use available coupons, and so on. This project focuses on a related problem faced by homeowners who may be reluctant to file insurance claims despite the fact their losses are covered. I model this consumer decision by introducing the concept of the pseudodeductible, a latent threshold above the policy deductible that governs the homeowner's claim behavior. We show how the observed number of claims can be modeled as the output of three separate stochastic processes: the rate at which losses occur, the choice of the individual to file or not file a claim on that loss and the size of the losses. Furthermore, we demonstrate that allowing for the possibility of pseudodeductibles enables one to sort out (and make accurate inferences about) these three processes.

We test this model using a proprietary dataset provided by State Farm, the largest underwriter of personal lines insurance in the United States. Using Dirichlet process priors to capture heterogeneity and the interplay among the three processes, we uncover several relevant stories that drive the number of claims and use the pseudodeductible to explain several phenomena in observed customer behavior. For instance, some customers have a small number of losses, but all are filed as claims, while others may experience many more losses, but are more selective about which claims they file. These stories explain several observed phenomena regarding the claims decisions that insurance customers make, and have broad implications for customer lifetime value and market segmentation.

Keywords: Duration models, Dirichlet process priors, insurance claims, semiparametric Bayesian statistics, underreporting

JEL Classification: C12, C15, C24, C42, G22, M3