When setting or modifying insurance rates on the basis of observed data, adjustments should be made for inflation between the average claim date of the observation period and the average claim date covered by policies to which the new rates will apply. In automobile insurance ratemaking in the United States, the adjustment is made as follows:
where Lα = trended losses and loss adjustment expenses incurred,
L0 = observed losses and loss adjustment expenses incurred during the experience period,
= the predicted rate of inflation per quarter, and
k = the number of quarters for which losses are being trended.
The inflation coefficient, β, is an exponential growth factor that is estimated using the following equation:
where = average paid claim costs for the year ending in quarter t,
t = time, in quarters, t = 1, 2, …, 12, and
εt = a random disturbance term.
The estimation period for the equation is the twelve quarters immediately preceding the first forecast period, and the estimation is conducted utilizing ordinary least squares. Annual averages of claim costs are used as the dependent variable to smooth random and seasonal fluctuations.