Estimating the Workers Compensation Tail

1. Estimating the Workers Compensation Tail Richard Sherman & Gordon Diss

2. SAIF Corp. (Oregon State Fund) • Extensive data for 160,000 permanent disability claims. • Accident years 1926-2002. • 77 years of development experience. • Medical & indemnity payments separated. • Separate data by injury type.

3. Workers Compensation Medical Permanent Disability (MPD) Paid Loss Development Factors

4. Age to Age MPD Paid LDFsYears of Development2 3 4 5 6 7 8 9 10 11 12 13 14 156.624 1.525 1.140 1.072 1.041 1.027 1.019 1.020 1.015 1.013 1.012 1.013 1.012 1.010 Your guess of a tail factor at 15 years? ______

5. Age to Age MPD Paid LDFsYears of Development 16 17 18 19 20 21 22 23 24 25 1.011 1.013 1.011 1.011 1.012 1.012 1.014 1.012 1.015 1.015 Your guess of a tail factor at 25 years? ______

6. Age to Age MPD Paid LDFsYears of Development 26 27 28 29 30 31 32 33 34 35 1.016 1.020 1.023 1.027 1.026 1.022 1.018 1.015 1.017 1.018 Your guess of a tail factor at 35 years? ______

7. Comparison of Your Guesses to SAIF’s Indicated Paid Tail FactorsMaturity Your SAIF’s MPD (Years) Guess Tail Factor 15 _______ ______ 25 _______ ______

8. COMMON INTUITIVE ASSUMPTION INVESTIGATING THE CIA

9. CIA-1 MPD TAIL FACTORS BEHAVE LIKE TAIL FACTORS IN OTHER CASUALTY LINES. COMMON TAIL METHODS ARE APPLICABLE.

10. COMMON TAIL METHODS • REPEAT THE LAST FACTOR • LINEAR DECAY • EXPONENTIAL DECAY • INVERSE POWER CURVE • LATEST INCURRED TO PAID RATIO

11. CIA-2 Since there are relatively few MPD claims and since they represent a small portion of current calendar year payments, MPD reserves should be relatively small

12. SAIF’s Indicated Paid Tail Factors Maturity (Years) MPD Other WC Total WC 10 2.469 1.263 1.671 15 2.328 1.234 1.613 25 2.054 1.129 1.457 35 1.680 1.052 1.294

13. CIA-3 Medical Permanent Disability Paid Loss Development Factors Decrease Monotonically

15. OPPOSITE INFLUENCES FORCE OF MORTALITY VERSUS FORCE OF MEDICAL COST ESCALATION

16. A) Incremental Paid Losses ($000’s) AY 12 24 36 48 60 72 1997 2,823 15,936 9,182 4,282 2,064 1,411 1998 2,638 14,250 9,096 2,936 3,214 1999 3,331 15,806 9,735 4,309 2000 3,170 18,602 12,462 2001 3,143 20,306 2002 4,263 B) Open Counts AY 12 24 36 48 60 72 1997 3621,112 793 490 375 324 1998 338 888 628 431 352 1999 343 840 664 492 2000 268 867 731 2001 276 897 2002 333 C) Incremental Paid per Prior Open AY 24 36 48 60 72 1997 44,022 8,257 5,399 4,212 3,764 1998 42,159 10,244 4,675 7,459 1999 46,021 11,589 6,489 2000 69,411 14,374 2001 73,572 2002

17. CIA-4 Historical incremental paid losses prior to the development triangle are useless.

18. Incremental data prior to the triangle

19. MUELLER INCREMENTAL TAIL METHOD • Calculate future incremental payments as a percent of the incremental payment in a given anchor year. • Cumulate and smooth these future payments as a % of payments in the anchor year. • Convert to a tail factor by applying the result above to an age to age development factor from the main triangle. • See paper for details.

20. CIA-5 For a given development period, Worker’s Compensation tail factors should be constant for all accident years

21. Testing CIA-5 with an Illustrative Model • 35 successive AYs that are identical except: • Applicable mortality table varies by CY. • Used projected Social Security mortality table for future mortality rates. • Each AY starts with 5,000 permanent disability cases. All assumptions fit SAIF’s historical patterns.

22. Indicated WC MPD Tail Factors End of Development Year AY 10 20 30 40 50 60 70 80 1970 2.570 2.177 1.773 1.438 1.210 1.075 1.015 1.0012 1975 2.628 2.223 1.805 1.456 1.220 1.080 1.016 1.0013 1980 2.701 2.279 1.842 1.477 1.231 1.085 1.018 1.0014 1985 2.774 2.336 1.879 1.499 1.242 1.090 1.020 1.0016 1990 2.848 2.393 1.918 1.521 1.253 1.095 1.021 1.0017 1995 2.921 2.451 1.957 1.543 1.265 1.101 1.023 1.0019 2000 2.990 2.505 1.993 1.563 1.275 1.105 1.023 1.0021

23. Life Expectancies at Different Ages—Male Based on Social Security Administration Mortality Tables Current Age 1960 1980 2000 2020 2040 2060 2080 20 49.7 51.7 54.7 56.8 58.7 60.3 61.8 40 31.333.536.238.139.841.442.7 60 15.9 17.3 19.3 20.8 22.2 23.4 24.6 80 6.0 6.8 7.2 7.8 8.6 9.4 10.1

24. Number of Open Claims for Representative Accident Years at Five Year Intervals of Development End of Development Year AY 10 20 30 40 50 60 70 80 1970 196 119 71 33 12 3.5 0.5 0.02 1975 197 120 73 34 13 3.7 0.6 0.03 1980 200 123 76 36 14 3.9 0.6 0.03 1985 202 126 79 38 14 4.2 0.7 0.04 1990 204 128 81 39 15 4.4 0.7 0.04 1995 206 130 83 41 16 4.7 0.8 0.05 2000 207 132 86 42 17 5.0 0.9 0.06

25. CIA-6 For a given development period, Worker’s Compensation age-to-age paid loss development factors should be constant for all accident years

26. Trends in Five Year Paid Loss Development Factors Development Years AY 15/10 20/15 25/20 30/25 35/30 40/35 45/40 50/45 55/50 1970 1.082 1.091 1.103 1.113 1.114 1.107 1.097 1.084 1.069 1975 1.083 1.092 1.105 1.115 1.116 1.110 1.099 1.086 1.071 1980 1.084 1.094 1.107 1.118 1.119 1.114 1.103 1.089 1.073 1985 1.084 1.095 1.109 1.120 1.123 1.117 1.106 1.092 1.076 1990 1.085 1.096 1.111 1.123 1.126 1.120 1.109 1.094 1.078 1995 1.086 1.097 1.113 1.126 1.129 1.123 1.112 1.097 1.081 2000 1.087 1.098 1.114 1.128 1.132 1.126 1.115 1.100 1.083

27. CIA-7 Mortality rates of the disabled are distinctly greater than those for the general public

28. Injured Worker Mortality Rates • For ages < 60, injured worker mortality rates somewhat higher. “Between age 60 and 74, the injured worker mortality rate does not differ appreciable from U.S. Life. The differences in mortality, even if accepted, do not imply significant redundancy or inadequacy of tabular reserves.” Gillam, William R., “Injured Worker Mortality”, CAS Forum, Winter 1991 • “Injured worker mortality after some years comes close to standard mortality, and after some age may actually be lower.” Venter, Schill and Barnett, “Review of Report of Committee on Mortality for Disabled Lives”, CAS Forum, Winter 1991 • Standard mortality rates fit SAIF’s historical experience well.

29. CIA-8 As permanently disabled claimants age, neither utilization nor severity changes.

31. CIA-9 Case reserves based on inflating payments until the expected year of death are at the expected level

32. Calculating a Realistic Expected Case Reserve • Age 35, $5,000 current annual medical costs, 9% future medical inflation. • Total inflated payments through expected year of death (at age 75): $1.69 million. • Expected total payout over scenarios of all possible years of death: $2.88 million, or 70% more.

34. CIA-10 Monte Carlo simulation of MPD losses will reasonably estimate the variability of MPD reserves

35. Markov Chain Model • Typical Monte Carlo simulation involves utilization of size of loss distribution based on incurred amounts, all of which are well below their expected value. • Better to model year-by-year payments for individual claimants using a Markov chain approach.

36. CONCLUSIONS • Data prior to traditional triangle can be used effectively. • All 10 CIAs do not apply to MPD payments and reserves. • MPD PLDFs increase for many mature DYs. • MPD paid tails and incremental PLDFs trend upward as mortality rates decline. • Utilization and severity are higher than expected for elderly permanently disabled claimants. • Common methods significantly underestimate the expected value of MPD case reserves. • Common methods understate MPD reserve variability.