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

614 ESTIMATING THE WORKERS COMPENSATION TAIL41 38.0 352.6 8.28 106.6 33.5 197.7 231.3 1.0136 1.19542 34.6 314.6 8.08 116.2 32.5 201.7 234.3 1.0131 1.18043 31.5 279.9 7.89 126.7 31.5 205.7 237.2 1.0125 1.16544 28.5 248.5 7.71 138.1 30.4 209.7 240.0 1.0119 1.15145 25.8 219.9 7.52 150.5 29.2 213.6 242.8 1.0114 1.13846 23.3 194.1 7.33 164.0 28.0 217.4 245.4 1.0108 1.12647 21.0 170.8 7.15 178.8 26.8 221.1 247.9 1.0103 1.11548 18.8 149.9 6.97 194.9 25.5 224.8 250.3 1.0097 1.10449 16.8 131.0 6.78 212.4 24.3 228.4 252.6 1.0092 1.09450 15.0 114.2 6.60 231.6 23.0 231.8 254.8 1.0086 1.085A review of this table reveals the following:² Although there are ILDFs less than 1.0 for the fifth, sixth,and 11th development years, subsequent factors become noticeablygreater than 1.0, even up through the 50th year ofdevelopment, and beyond.² Incurred loss development factors are expected to increase duringeach development year from the 12th through the 21styears.² The rate of decrease in ILDFs after the 21st development yearis surprisingly small, resulting in very large incurred tails fornearly all ages.This example raises major concerns about the practice of estimatingthe paid tail by taking the ratio of incurred (perhaps withsome modest upward adjustment) to paid at the most mature developmentyear. If case reserves do not include any provisionfor future medical inflation, then reported incurred at each givenDY should be multiplied by the corresponding incurred tail factorshown in the last column of Table 3.6 before the ratio ofincurredtopaidisappliedtopaidlossesforthemostmatureyears. At DY 10, the incurred tail factor is 2.022. Even at DY30, an incurred factor of 1.426 is needed. Obviously, to the extentthat case reserves include a realistic provision for escalationof future medical costs, the above indicated incurred tail factorswould be reduced.