Credibility for Classification Ratemaking via the Hierarchical Normal Linear Model

In the past twenty years there has been ever increasing improvement in the techniques of classification ratemaking. Most of this has centered around improvements incredibility procedures and most of the improvements have been due to incorporating aspects of Bayesian analysis. In this paper, I attempt to take this trend to its (perhaps) final stage by developing a true Bayesian approach to the classification ratemaking credibility problem. The opening section will provide the rationale for the Bayesian approach. I will argue that a hierarchical model with a noninformative prior is the most appropriate general framework. I will argue further that a normal model is a reasonable choice, and this model will provide results at least as good as those currently available. An indication of how the normality condition can be relaxed will also be presented. The second section contains a general description and analysis of the hierarchical normal linear model (HNLM). Included are point estimation, estimation of the error in the estimator, and prediction intervals for future losses. The last two items are of special interest since current credibility procedures provide little insight with respect to variation. The next two sections discuss the special case of the one-way model. This is the most common ratemaking model and is the simplest case of HNLM. In Section 3, the formulas from Section 2 are evaluated for this model. In Section 4, two data sets are analyzed. The first set provides an indication of the computational work required to use the HNLM. The second set provides a comparison of this method with two other ratemaking approaches. The final section contains a discussion of the more complex models that can be handled with the HNLM.