PROCEEDINGS May 15, 16, 17, 18, 2005 - Casualty Actuarial Society

ESTIMATING THE WORKERS COMPENSATION TAIL 645possible to calculate a five-year average, shorter termcentered averages were used.The weighted average is similar but uses correspondingpaid losses as weights. The geometric mean providesanother level of smoothing. It is also a five-year centeredaverage, but it is the fifth root of the product of the fiveweighted average factors.2. Anchored decay factors. After selecting the geometricmean incremental age-to-age factors, they are then anchoredto a base year. Table A.5 shows the anchoreddecay factors using five different anchor years. The anchoreddecay factors represent incremental paymentsmade in year n + r relative to payments made in the anchoryear. These anchored decay factors are calculated asthe cumulative product starting with the anchor year andmoving up the last column on Table A.4. For example,as shown in Table A.5, payments made in developmentyear 50 are 88.0% greater than the payments made inyear 37. The main reason that payments rise over time isbecause the force of medical cost escalation exceeds theforce of mortality until most of the claimants are fairlyadvanced in age, when the force of mortality becomesstronger than the force of medical cost escalation.By summing the decay factors from 38 to 65, we get thepayments made in age 38 to 65 relative to the payments madein the selected anchor year. The sums of the decay factors aresimilar to tail factors, but instead of being relative to cumulativepayments they are relative to the incremental payments made ina given anchor year.The cumulative decay factors can be interpreted as follows:Payments made in ages 38 to 65 are 30.071 times the paymentsmade in age 37. Similarly, payments made in ages 38 to 65 are26.961 times the payments made in age 33.