Simpson's Paradox, Confounding Variables, and Insurance Ratemaking

The insurance process is complex, with numerous factors combining to produce both premiums and losses. When compiling rates, actuaries often aggregate data from more than one source, while at the same time stratifying the data to achieve homogeneity. Such exercises may lead to biased and sometimes even surprising results, called Simpson's paradox, because the variables involved in the aggregation process or the stratification process are confounded by the presence of other variables. In this paper, we will describe Simpson's paradox and confounding and the statistical underpinning associated with those phenomena. We will further discuss how such bias may exist in P&C actuarial rating applications and solutions that can resolve the bias.