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

ESTIMATING THE WORKERS COMPENSATION TAIL 621TABLE 5.5Indicated Tail FactorsEnd of Development YearAY 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 801970 3.037 2.570 2.375 2.177 1.973 1.773 1.592 1.438 1.311 1.210 1.132 1.075 1.037 1.015 1.004 1.0011975 3.108 2.628 2.428 2.223 2.012 1.805 1.617 1.456 1.325 1.220 1.139 1.080 1.040 1.016 1.005 1.0011980 3.197 2.701 2.492 2.279 2.058 1.842 1.645 1.477 1.340 1.231 1.146 1.085 1.043 1.018 1.006 1.0011985 3.286 2.774 2.558 2.336 2.106 1.879 1.674 1.499 1.356 1.242 1.154 1.090 1.046 1.020 1.007 1.0021990 3.376 2.848 2.624 2.393 2.154 1.918 1.704 1.521 1.372 1.253 1.162 1.095 1.049 1.021 1.007 1.0021995 3.466 2.921 2.690 2.451 2.203 1.957 1.733 1.543 1.388 1.265 1.170 1.101 1.053 1.023 1.008 1.0022000 3.549 2.990 2.752 2.505 2.248 1.993 1.761 1.563 1.402 1.275 1.177 1.105 1.054 1.023 1.008 1.002TABLE 5.6Indicated Percentage Understatement in AY 2000 LossReserves (if Based on AY 1970 Tail Factors)End of Development Year5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 8025 27 27 28 28 28 28 29 29 31 34 39 47 59 85 102Table 5.6 displays the percentage understatement in AY 2000loss reserves at different development ages, if such reserves werebased on AY 1970 tail factors. It clearly indicates that the useof constant tail factors will result in material inadequacies in theindicated loss reserves.The trended mortality model also indicates that incrementalPLDFs at any given maturity will trend upward over time. InTable 5.7, five-year paid loss development factors, each of whichare the cumulative products of five successive one-year paid lossdevelopment factors, inch upward over time within any givendevelopment column.Table 5.7 rebuts the conjecture that the paid loss developmentfactors for earlier (as well as middle) development years willhold constant over successive accident years. However, it is alsoevident that the rate of increase in these paid development factors