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

ESTIMATING THE WORKERS COMPENSATION TAIL 593TABLE 1.3A Comparison of SAIF’s Empirical Tail Factor withExtrapolated Tail Factors at 15 Years(Based on a Fit to Historical PLDFS for DYs 10—15)Indicated Tail Extrapolated Reserve as aFactor atPortion of the ReserveExtrapolation Method 15 Years Indicated by SAIF’s HistoryLinear Decay 1.046 3.5%Exponential Decay 1.175 13.4%Inverse Power Curve 1.234 17.9%SAIF’s Historical Factors 2.309 100.0%As high as SAIF’s paid tail factor at 15 years is (2.309), itis understated because it implicitly assumes that past mortalityrates will continue indefinitely into the future. As noted in Section4, mortality rates have been declining steadily for at least thepast four decades, and the Social Security Administration (SSA)reasonably expects such declines to continue throughout the nextcentury.A second reserving model that explicitly accounts for thecompounding effects of downward trends in future mortality ratesand persistently high rates of future medical cost escalation willbe referred to as the trended mortality model. It will be describedin Section 5.The indications of the trended mortality model for MPD aresignificant and troubling:² Paid tail factors at the end of any selected year of developmentshould be expected to increase slowly but steadily oversuccessive accident years.² Incremental PLDFs for any selected year of developmentwill also trend upward slowly but inexorably for successiveAYs.