A Critique of Credibility Tables

Abstract

Insurance rate revision involves the treatment of experience data acquired since the current rate was adopted. Credibility tables assign factors to varying quantities of experience data which indicate how weights should be assigned to the data utilized in the rate revision process. The statistical basis of these tables is discussed and the underlying rationale is examined as it pertains to standards for full and to the assignment of partial credibilities. It is concluded that the factors which appear in currently used tables are based on highly judgmental assumptions and are not an objective approach to the weighting of experience data. A more economically sound approach based on modern statistical decision theory is suggested. The treatment of loss data by casualty insurers, as it pertains to the rate-making or rate revision process, has been a subject of controversy for some time. A desirable criterion for an insurance rate is that it reflect current loss conditions, however practical considerations mitigate against too frequent rate revisions. Insurance rates should be revised when loss data indicate that the loss parameter upon which the current rate has been based has changed. The determination of when, or more to the point, whether that parameter has indeed changed, must be based on a statistical treatment of loss data, the mechanics of which are not the subject of this article. However, assuming that a rate revision is deemed to be in order, the problem of the believability of the available data becomes paramount. Jerome D. Braverman, Ph.D., is Senior Staff Engineer for Hughes Aircraft Company. Dr. Braverman has had over 15 years of experience in the application of statistical and operations research techniques to both business and engineering problems in the capacity of both employee and independent consultant. He has been Lecturer in Statistics at the San Fernando Valley State College. This article was submitted for publication in September, 1966. The term credibility was introduced into the field of actuarial science as a measure of the believability that can be attached to a particular volume of data. To be more accurate, it is a measure of the believability or reliability than can be attached to an estimate of a parameter that is derived from some particular volume of data. The Statistical Basis Intuition generally tells us that a lot of data are better than a little, or that an estimate computed from a large volume of experience data is more reliable or believable than one computed from a very small amount of data. And if, for the sake of this discussion, one ignores those problems associated with method of data collection and analysis, data sources, etc. by inserting the qualifying statement that all else is equal, this intuitive conclusion is statistically correct. Therefore, having set in motion the rate revision process, the larger the amount of experience data available for the estimation of the new loss parameter, the more believable that estimate will be. It should follow that for some very large amount