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.