Consideration in Estimating Loss Cost Trends

The application of loss trends has long been a fundamental part of the ratemaking process. Despite this, the actuarial literature is somewhat lacking in the description of methods by which one can estimate the proper loss trend from empirical data. Linear or exponential least squares regression is widely used in this regard. However, there are problems with the use of least squares regression when applied to insurance loss data. In this paper, some common pitfalls of least squares regression, as it is commonly applied to insured loss data, and two alternative methods of evaluating loss trends will be illustrated. Both methods are based on simple least squares regression, but include modifications designed to account for the characteristics of insurance loss data. The results of various methods are compared using industry loss data. Stochastic simulation is also used as a means of evaluating various trend estimation methods. The concepts presented are not new. They are presented here in the context of analyzing insured loss data to provide actuaries with additional tools for estimating loss trends.