Jean Pinquet

ADVERSE SELECTION AND MORAL HAZARD IN INSURANCE: CAN DYNAMIC DATA HELP TO DISTINGUISH?

A standard problem of applied contracts theory is to empirically distinguish between adverse selection and moral hazard. We show that dynamic insurance data allow to distinguish moral hazard from dynamic selection on unobservables. In the presence of moral hazard, experience rating implies negative occurrence dependence: individual claim intensities decrease with the number of past claims. We discuss econometric tests for the various types of data that are typically available. Finally, we argue that dynamic data also allow to test for adverse selection, even if it is based on asymmetric learning. (JEL: D82, G22, C41, C14)

Experience rating through heterogeneous models

This paper presents statistical models which lead to experience rating in insurance. Serial correlation for risk variables can receive endogeneous or exogeneous explanations. The paper recalls that the main interpretation for automobile insurance is exogeneous, since positive contagion is always observed for the number of claims reported and since true contagion should be negative. This positive contagion can be explained by the revelation throughout time of a hidden features in the risk distributions. These features are represented by heterogeneity components in a heterogeneous model. Prediction on longitudinal data can be performed through the heterogeneous model, and the paper provides consistent estimators for models related to number and cost of claims. Examples are given for count data models with a constant or time-varying heterogeneity components, one or several equations, and for a cost-number model on events. Empirical results are presented, which are drawn from the analysis of a French data base of automobile insurance contracts.

Allowance for the Age of Claims in Bonus-Malus Systems

The purpose of the paper is to use the age of claims in the prediction of risks. A dynamic random effects model on longitudinal count data is presented, and estimated on the portfolio of a major Spanish insurance company. The estimated autocorrelation coefficients of stationary random effects are decreasing. A consequence is that the predictive ability of a claim decreases with the lag between the period of risk prediction and the period of occurrence. There is a wide gap between the long term properties of actuarial and real-world experience rating schemes. This gap can be partly filled if the age of claims is taken into account in the actuarial model.

Designing optimal bonus-malus systems from different types of claims

This paper provides bonus-malus systems which rest on different types of claims. Consistent estimators are given for some moments of the mixing distribution of a multi equation Poisson model with random effects. Bonus-malus coefficients are then obtained with the expected value principle, and from linear credibility predictors. Empirical results are presented for two types of claims, namely claims at fault and not at fault with respect to a third party.

Time-varying credibility for frequency risk models: estimation and tests for autoregressive specifications on the random effects

Abstract This paper estimates and tests autoregressive specifications for dynamic random effects in a frequency risk model. Linear credibility predictors are derived from the estimators. Examples are provided from the automobile portfolio of a Spanish insurance company.

Commitment and Lapse Behavior in Long‐Term Insurance: A Case Study

This paper presents a case study of a portfolio of individual long-term insurance contracts sold by a Spanish mutual company. We describe the risk levels, the rating structure and the implied cross-subsidies on a portfolio of policies providing health, life and long-term care insurance. We show evidence of reclassification risk through the history of disability spells. We also analyze the lapse behavior and seek to provide a rationale for the portfolios dynamics. Lastly, we draw conclusions regarding the design of such contracts.

The Role of Memory in Long-Term Contracting with Moral Hazard: Empirical Evidence in Automobile Insurance

This paper tests the efficiency associated with the role of memory in long-term contracting. Bonus-malus schemes in automobile insurance are examples of contracts that use memory. During the eighties different contributors (Lambert, 1983, Rogerson, 1985, Boyer, and Dionne, 1989) showed how multi-period contracting under moral hazard improves resource allocation. In particular, it was demonstrated that multi-period contracts with memory outperform those without memory under full commitment.

Selection bias and auditing policies for insurance claims

Selection bias results from a discrepancy between the range of estimation of a statistical model and its range of application. This is the case for fraud risk models, which are estimated on audited claims but applied on incoming claims in the design of auditing strategies. Now audited claims are a minority within the parent sample since they are chosen after a severe selection performed by claims adjusters. This paper presents a statistical approach which counteracts selection bias without using a random auditing strategy. A two equation model on audit and fraud (a bivariate probit model with censoring) is estimated on a sample of claims where the experts are left free to take the audit decision. The expected overestimation of fraud risk derived from a single equation model is corrected. Results are rather close to those obtained with a random auditing strategy, at the expense of some instability with respect to the regression components set. Then we compare auditing policies derived from the different approaches.

Experience rating schemes for fleets of vehicles

This paper proposes bonus-malus systems for fleets of vehicles, by using the individual characteristics of both the vehicles and the carriers. Bonus-malus coefficients are computed from the history of claims or from the history of safety offences of the carriers and the drivers. The empirical results are derived from a data set obtained from the Societe de l’Assurance Automobile du Quebec, the public insurer for bodily injuries and the regulator of road safety.

Experience rating in non-life insurance

This paper presents statistical models which lead to experience rating in insurance. Serial correlation for risk variables can receive endogeneous or exogeneous explanations. The interpretation retained by actuarial models is exogeneous and reflects the positive contagion usually observed for the number of claims. This positive contagion can be explained by the revelation throughout time of a hidden features in the risk distributions. These features are represented by fixed effects which are predicted with a random effects model. This article discusses identification issues on the nature of the dynamics of non-life insurance data. Example of predictions are given for count data models with a constant or time-varying random effects, one or several equations, and for cost-number models on events.