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Using Non-Insurance Information in Ratemaking (cont.)
Consider Chart 17. The illustrated relationship between the natural logarithm of the loss ratio and the natural logarithm of yield has been fit to the straight line:
where x is the yield and y is the loss ratio. The best fitting curve has parameter values a=34.0 and b=-6.3. In economic terms, this formula describes the elasticity of the loss costs relative to the yields. The interpretation is that a 1% increase in the average yield for Iowa Corn results in a -6.3% change in the loss ratio. As a result, even a small change in yields has a highly leveraged impact on losses.
The volatility of the loss ratios implied by the elasticity coefficient highlights one of the difficulties in MPCI ratemaking. When losses vary widely between years, as for MPCI, the uncertainty in the estimate of the mean pure premium will be large. However, the additional information provided by the relationship between losses (pure premiums) and yields can improve the analysis in the following manner.
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