Estimation and Testing for Functional Form in Pure Premium Regression Models

Estimation of pure premiums for alternative rate classes using regression methods requires the choice of a functional form for the statistical model. Common choices include linear and log-linear models. This paper considers maximum likelihood estimation and testing for functional form using the power transformation suggested by Box and Cox. The linear and log-linear models are special cases of this transformation. Application of the procedure is illustrated using auto insurance claims data from the state of Massachusetts and from the United Kingdom. The predictive accuracy of the method compares favorably to that for the linear and log-linear models for both data sets. KEYWORDS pure premium regression models, functional form, maximum likelihood estimation, power transformation.