NCCI Publishes Research on Bayesian Trend Selection

Posted Date: June 15, 2012

Industry InformationResearch

View complete report: Bayesian Trend Selection (PDF)
By Frank Schmid, Chris Laws, and Matthew Montero

Executive Summary

Selecting loss ratio trends is an integral part of NCCI aggregate ratemaking. The trend selection draws on an exponential trend (ET) regression model that is typically applied to the latest 5, 8, and 15 observations; these three alternative regressions are dubbed the 5-point, 8-point, and 15-point ET. Then, using actuarial judgment (which may account for a variety of influences), the three estimates are aggregated into a single forecast. This process of decision making under uncertainty can be formalized using Bayesian model selection.

The Bayesian Trend Selection (BTS) is confined to processing data of past forecast errors, which represents both a strength and a weakness of this model. On one hand, the BTS is not prone to biases in human decision making. On the other hand, the model is not capable of processing information that is not incorporated in the data, such as changes in the economic or legislative environments that occur between the end of the experience period and the time of decision making.

The BTS is validated on data from past ratemaking seasons. Further, the robustness of the model is examined for past ratemaking data and a long series of injury (and illness) incidence rates for the manufacturing industry. In both cases, the performance of the BTS is compared to the 5-point, 8-point, and 15-point ET, using the random walk as a benchmark. Finally, for the purpose of illustration, the BTS is implemented for an unidentified state.

A major strength of the BTS is its robustness. Although the BTS underperforms the 15-point ET on recent ratemaking data sets, the BTS performs well in an environment where the nature of the data-generating process is changing. Because there is always a degree of uncertainty surrounding the process that generates the growth rates of the loss ratios, the BTS emerges as a robust decision rule.