estimating the workers compensation tail richard sherman & gordon diss
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Estimating the Estimating the Workers Workers
Compensation Compensation TailTailRichard Sherman Richard Sherman
& &
Gordon Diss Gordon Diss
SAIF Corp. (Oregon State SAIF Corp. (Oregon State Fund)Fund)
Extensive data for 160,000 Extensive data for 160,000 permanent disability claims.permanent disability claims.
Accident years 1926-2002.Accident years 1926-2002. 77 years of development experience. 77 years of development experience. Medical & indemnity payments Medical & indemnity payments
separated.separated. Separate data by injury type.Separate data by injury type.
Workers Workers Compensation Compensation
Medical Permanent Medical Permanent Disability (MPD)Disability (MPD)
Paid Loss Development Paid Loss Development Factors Factors
Age to Age MPD Paid LDFs
Years of Development
2 3 4 5 6 7 8 9 10 11 12 13 14 15
6.624 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? ______
Age to Age MPD Paid LDFs
Years 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? ______
Age to Age MPD Paid LDFs
Years 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? ______
Comparison of Your Guesses Comparison of Your Guesses to SAIF’s Indicated Paid Tail Factorsto SAIF’s Indicated Paid Tail Factors
MaturityMaturity YourYour SAIF’s MPD SAIF’s MPD (Years)(Years) Guess Guess Tail Factor Tail Factor
15 15 ______________ ______ ______
25 25 ______________ ______ ______
INVESTIGATING THE CIAINVESTIGATING THE CIA
CCOMMONOMMON
IINTUITIVENTUITIVE
AASSUMPTIONSSUMPTION
CIA-1CIA-1MPD TAIL FACTORSMPD TAIL FACTORS
BEHAVE LIKE TAIL FACTORSBEHAVE LIKE TAIL FACTORS
IN OTHER CASUALTY LINES.IN OTHER CASUALTY LINES.
COMMON TAIL METHODSCOMMON TAIL METHODS
ARE APPLICABLE.ARE APPLICABLE.
COMMON TAIL METHODSCOMMON TAIL METHODS
REPEAT THE LAST FACTORREPEAT THE LAST FACTOR
LINEAR DECAYLINEAR DECAY
EXPONENTIAL DECAYEXPONENTIAL DECAY
INVERSE POWER CURVEINVERSE POWER CURVE
LATEST INCURRED TO PAID RATIOLATEST INCURRED TO PAID RATIO
CIA-2CIA-2Since there are relatively few MPD Since there are relatively few MPD
claimsclaims
andand
since they represent a small portion of since they represent a small portion of
current calendar year payments,current calendar year payments,
MPD reserves should be relatively smallMPD reserves should be relatively small
SAIF’s Indicated Paid Tail FactorsSAIF’s Indicated Paid Tail Factors
MaturityMaturity
(Years)(Years) MPDMPD Other WC Other WC Total WC Total WC
1010 2.4692.469 1.263 1.263 1.671 1.671
15 15 2.3282.328 1.234 1.234 1.613 1.613
25 25 2.0542.054 1.129 1.129 1.457 1.457
35 35 1.6801.680 1.052 1.052 1.294 1.294
CIA-3CIA-3
Medical Permanent Disability Medical Permanent Disability
Paid Loss Development FactorsPaid Loss Development Factors
DecreaseDecrease
MonotonicallyMonotonically
Model v. Actual SAIF PLDFs Less 1.0
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Year of Development
PL
DF
Les
s 1.
0
Model
SAIF
S
OPPOSITE INFLUENCESOPPOSITE INFLUENCES
FORCE OF MORTALITYFORCE OF MORTALITY
VERSUSVERSUS
FORCE OF MEDICAL COST FORCE OF MEDICAL COST ESCALATION ESCALATION
A) Incremental Paid Losses ($000’s)A) Incremental Paid Losses ($000’s)
AY 12 24 36 48 60 72AY 12 24 36 48 60 72 1997 2,823 15,936 9,182 4,282 2,064 1,4111997 2,823 15,936 9,182 4,282 2,064 1,4111998 2,638 14,250 9,096 2,936 3,2141998 2,638 14,250 9,096 2,936 3,2141999 3,331 15,806 9,735 4,3091999 3,331 15,806 9,735 4,3092000 3,170 18,602 12,4622000 3,170 18,602 12,4622001 3,143 20,3062001 3,143 20,306 2002 4,2632002 4,263
B) Open Counts
AY 12 24 36 48 60 72 1997 362 1,112 793 490 375 3241998 338 888 628 431 3521999 343 840 664 492 2000 268 867 7312001 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 3,7641998 42,159 10,244 4,675 7,4591999 46,021 11,589 6,489 2000 69,411 14,3742001 73,572 2002
CIA-4CIA-4
Historical incremental paid lossesHistorical incremental paid losses
prior to the development triangle prior to the development triangle
are useless.are useless.
Incremental data prior to the triangle
AY 1966
C
I
AY 1926
AY 2002
Development Years (DY) 10 20 30 40 50 60 70
MUELLER INCREMENTAL TAIL METHODMUELLER INCREMENTAL TAIL METHOD
Calculate future incremental payments as a percent Calculate future incremental payments as a percent of the incremental payment in a given anchor year.of the incremental payment in a given anchor year.
Cumulate and smooth these future payments as a % Cumulate and smooth these future payments as a % of payments in the anchor year.of payments in the anchor year.
Convert to a tail factor by applying the result above Convert to a tail factor by applying the result above to an age to age development factor from the main to an age to age development factor from the main triangle. triangle.
See paper for details.See paper for details.
CIA-5CIA-5
For a given development period, For a given development period,
Worker’s Compensation tail factorsWorker’s Compensation tail factors
should be constantshould be constant
for all accident years for all accident years
Testing CIA-5 with an Illustrative Testing CIA-5 with an Illustrative ModelModel
35 successive AYs that are identical 35 successive AYs that are identical except:except:
Applicable mortality table varies by CY.Applicable mortality table varies by CY. Used projected Social Security mortality Used projected Social Security mortality
table for future mortality rates.table for future mortality rates. Each AY starts with 5,000 permanent Each AY starts with 5,000 permanent
disability cases. All assumptions fit disability cases. All assumptions fit SAIF’s historical patterns.SAIF’s historical patterns.
Indicated WC MPD Tail FactorsIndicated WC MPD Tail Factors
End of Development YearEnd of Development Year
AY 10 20 30 40 50 60 70 AY 10 20 30 40 50 60 70 8080
1970 1970 2.570 2.570 2.1772.177 1.773 1.438 1.210 1.075 1.015 1.773 1.438 1.210 1.075 1.015 1.00121.0012
1975 1975 2.628 2.628 2.2232.223 1.805 1.456 1.220 1.080 1.016 1.0013 1.805 1.456 1.220 1.080 1.016 1.0013
1980 1980 2.701 2.701 2.2792.279 1.842 1.477 1.231 1.085 1.018 1.0014 1.842 1.477 1.231 1.085 1.018 1.0014
1985 1985 2.774 2.774 2.3362.336 1.879 1.499 1.242 1.090 1.020 1.0016 1.879 1.499 1.242 1.090 1.020 1.0016
1990 1990 2.848 2.848 2.3932.393 1.918 1.521 1.253 1.095 1.021 1.0017 1.918 1.521 1.253 1.095 1.021 1.0017
1995 1995 2.921 2.921 2.4512.451 1.957 1.543 1.265 1.101 1.023 1.0019 1.957 1.543 1.265 1.101 1.023 1.0019
2000 2000 2.990 2.990 2.505 2.505 1.993 1.563 1.275 1.105 1.023 1.993 1.563 1.275 1.105 1.023 1.00211.0021
Life Expectancies at Different Ages—MaleLife Expectancies at Different Ages—Male
Based on Social Security Administration Mortality TablesBased on Social Security Administration Mortality Tables
CurrentCurrent
Age 1960 1980 2000 Age 1960 1980 2000 2020 2040 2020 2040 2060 2080 2060 2080
20 20 49.7 51.7 54.7 49.7 51.7 54.7 56.8 58.7 60.3 56.8 58.7 60.3 61.8 61.8
40 40 31.331.3 33.533.5 36.236.2 38.138.1 39.839.8 41.441.4 42.742.7
60 60 15.9 17.3 19.3 15.9 17.3 19.3 20.8 22.2 23.4 20.8 22.2 23.4 24.6 24.6
80 80 6.0 6.8 7.2 6.0 6.8 7.2 7.8 8.6 9.4 7.8 8.6 9.4 10.1 10.1
Number of Open Claims for Representative Number of Open Claims for Representative
Accident Years at Five Year Intervals of Accident Years at Five Year Intervals of DevelopmentDevelopment
End of Development YearEnd of Development Year
AY 10 20 30 40 50 60 70 AY 10 20 30 40 50 60 70 8080
1970 1970 196 196 119119 71 33 12 3.5 0.5 0.02 71 33 12 3.5 0.5 0.02
1975 1975 197 197 120120 73 34 13 3.7 0.6 0.03 73 34 13 3.7 0.6 0.03
1980 1980 200 200 123123 76 36 14 3.9 0.6 0.03 76 36 14 3.9 0.6 0.03
1985 1985 202 202 126126 79 38 14 4.2 0.7 0.04 79 38 14 4.2 0.7 0.04
1990 1990 204 204 128128 81 39 15 4.4 0.7 0.04 81 39 15 4.4 0.7 0.04
1995 1995 206 206 130130 83 41 16 4.7 0.8 0.05 83 41 16 4.7 0.8 0.05
2000 2000 207 207 132132 86 42 17 5.0 0.9 0.06 86 42 17 5.0 0.9 0.06
CIA-6CIA-6For a given development period, For a given development period,
Worker’s Compensation age-to-age Worker’s Compensation age-to-age
paid loss development factorspaid loss development factors
should be constantshould be constant
for all accident years for all accident years
Trends in Five Year Paid Loss Development FactorsTrends in Five Year Paid Loss Development Factors
Development YearsDevelopment Years
AY 15/10 20/15 25/20 30/25 35/30 40/35 45/40 50/45 AY 15/10 20/15 25/20 30/25 35/30 40/35 45/40 50/45 55/5055/50
1970 1970 1.082 1.091 1.082 1.091 1.1031.103 1.113 1.114 1.107 1.097 1.084 1.069 1.113 1.114 1.107 1.097 1.084 1.069
1975 1975 1.083 1.092 1.083 1.092 1.105 1.105 1.115 1.116 1.110 1.099 1.086 1.071 1.115 1.116 1.110 1.099 1.086 1.071
1980 1980 1.084 1.094 1.084 1.094 1.1071.107 1.118 1.119 1.114 1.103 1.089 1.073 1.118 1.119 1.114 1.103 1.089 1.073
1985 1985 1.084 1.095 1.084 1.095 1.1091.109 1.120 1.123 1.117 1.106 1.092 1.076 1.120 1.123 1.117 1.106 1.092 1.076
1990 1990 1.085 1.096 1.085 1.096 1.1111.111 1.123 1.126 1.120 1.109 1.094 1.078 1.123 1.126 1.120 1.109 1.094 1.078
1995 1995 1.086 1.097 1.086 1.097 1.1131.113 1.126 1.129 1.123 1.112 1.097 1.081 1.126 1.129 1.123 1.112 1.097 1.081
2000 2000 1.087 1.098 1.087 1.098 1.1141.114 1.128 1.132 1.126 1.115 1.100 1.083 1.128 1.132 1.126 1.115 1.100 1.083
CIA-7CIA-7
Mortality rates of the disabled Mortality rates of the disabled
are distinctly greater than are distinctly greater than
those for the general publicthose for the general public
Injured Worker Mortality RatesInjured Worker Mortality Rates For ages < 60, injured worker mortality rates somewhat For ages < 60, injured worker mortality rates somewhat
higher. “Between age 60 and 74, the injured worker higher. “Between age 60 and 74, the injured worker mortality rate does not differ appreciable from U.S. Life. mortality rate does not differ appreciable from U.S. Life. The differences in mortality, even if accepted, do not The differences in mortality, even if accepted, do not imply significant redundancy or inadequacy of tabular imply significant redundancy or inadequacy of tabular reserves.” Gillam, William R., “reserves.” Gillam, William R., “Injured Worker Injured Worker MortalityMortality”, CAS Forum, Winter 1991”, CAS Forum, Winter 1991
““Injured worker mortality after some years comes close Injured worker mortality after some years comes close to standard mortality, and after some age may actually be to standard mortality, and after some age may actually be lower.” Venter, Schill and Barnett, “lower.” Venter, Schill and Barnett, “Review of Report of Review of Report of Committee on Mortality for Disabled LivesCommittee on Mortality for Disabled Lives”, CAS Forum, ”, CAS Forum, Winter 1991Winter 1991
Standard mortality rates fit SAIF’s historical experience Standard mortality rates fit SAIF’s historical experience well. well.
CIA-8 CIA-8
As permanently disabled As permanently disabled
claimants age, claimants age,
neither neither
utilizationutilization
nor nor
severity severity
changes.changes.
Model v. Actual SAIF PLDFs Less 1.0
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Year of Development
PL
DF
Les
s 1.
0
Model
SAIF
S
CIA-9CIA-9Case reserves based on Case reserves based on
inflating payments until inflating payments until
the expected year of death the expected year of death
are at the are at the
expected levelexpected level
Calculating a Realistic Calculating a Realistic Expected Case ReserveExpected Case Reserve
Age 35, $5,000 current annual medical Age 35, $5,000 current annual medical costs, 9% future medical inflation.costs, 9% future medical inflation.
Total inflated payments through Total inflated payments through expected year of death (at age 75): expected year of death (at age 75): $1.69 million.$1.69 million.
Expected total payout over scenarios of Expected total payout over scenarios of all possible years of death: $2.88 all possible years of death: $2.88 million, or 70% more.million, or 70% more.
Deaths and Expected Payouts by Age
0.00
0.01
0.02
0.03
0.04
0.05
0.06
Age
Exp. Losses
Deaths
CIA-10CIA-10Monte Carlo simulation ofMonte Carlo simulation of
MPD lossesMPD losses
will reasonably estimatewill reasonably estimate
the variability of the variability of
MPD reservesMPD reserves
Markov Chain ModelMarkov Chain Model Typical Monte Carlo Typical Monte Carlo
simulation involves simulation involves utilization of size of loss utilization of size of loss distribution based on distribution based on incurred amounts, all of incurred amounts, all of which are well below their which are well below their expected value.expected value.
Better to model year-by-Better to model year-by-year payments for year payments for individual claimants using a individual claimants using a Markov chain approach.Markov chain approach.
Calendar Year of Calendar Year of PaymentPayment
ClaiClaimm
20020044 20052005 20062006 20072007
11 3.23.2 3.53.5 3.83.8 4.04.0
22 12.712.7 13.813.8 - -- - - -- -
33 8.18.1 8.88.8 9.69.6 - -- -
CONCLUSIONSCONCLUSIONS Data prior to traditional triangle can be used Data prior to traditional triangle can be used
effectively.effectively. All 10 CIAs do not apply to MPD payments and All 10 CIAs do not apply to MPD payments and
reserves.reserves. MPD PLDFs increase for many mature DYs.MPD PLDFs increase for many mature DYs. MPD paid tails and incremental PLDFs trend MPD paid tails and incremental PLDFs trend
upward as mortality rates decline.upward as mortality rates decline. Utilization and severity are higher than expected for Utilization and severity are higher than expected for
elderly permanently disabled claimants.elderly permanently disabled claimants. Common methods significantly underestimate the Common methods significantly underestimate the
expected value of MPD case reserves.expected value of MPD case reserves. Common methods understate MPD reserve Common methods understate MPD reserve
variability.variability.