Estimating the Workers Compensation Tail Richard Sherman & Gordon Diss

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

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

Age to Age MPD Paid LDFs Years of Development Your guess of a tail factor at 15 years? ______

Age to Age MPD Paid LDFs Years of Development Your guess of a tail factor at 25 years? ______

Age to Age MPD Paid LDFs Years of Development Your guess of a tail factor at 35 years? ______

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

INVESTIGATING THE CIA C OMMON I NTUITIVE A SSUMPTION

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

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

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

SAIF’s Indicated Paid Tail Factors SAIF’s Indicated Paid Tail FactorsMaturity (Years)MPDOther WC Total WC (Years)MPDOther WC Total WC

CIA-3 Medical Permanent Disability Paid Loss Development Factors DecreaseMonotonically

OPPOSITE INFLUENCES FORCE OF MORTALITY VERSUS FORCE OF MEDICAL COST ESCALATION

A) Incremental Paid Losses ($000’s) A) Incremental Paid Losses ($000’s) AY AY ,823 15,936 9,182 4,282 2,064 1, ,638 14,250 9,096 2,936 3, ,331 15,806 9,735 4, ,170 18,602 12, ,143 20, ,263 B) Open Counts AY , C) Incremental Paid per Prior Open AY ,022 8,257 5,399 4,212 3, ,159 10,244 4,675 7, ,021 11,589 6, ,411 14, ,

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

Incremental data prior to the triangle

MUELLER INCREMENTAL TAIL METHOD Calculate future incremental payments as a percent of the incremental payment in a given anchor year. 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. 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. 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. See paper for details.

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

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

Indicated WC MPD Tail Factors End of Development Year AY AY

Life Expectancies at Different Ages—Male Based on Social Security Administration Mortality Tables Current Current Age Age

Number of Open Claims for Representative Accident Years at Five Year Intervals of Development End of Development Year AY AY

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

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 AY 15/10 20/15 25/20 30/25 35/30 40/35 45/40 50/45 55/

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

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 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 “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. Standard mortality rates fit SAIF’s historical experience well.

CIA-8 CIA-8 As permanently disabled claimants age, neitherutilization nor norseveritychanges.

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

Calculating a Realistic Expected Case Reserve Age 35, $5,000 current annual medical costs, 9% future medical inflation. 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. 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. Expected total payout over scenarios of all possible years of death: $2.88 million, or 70% more.

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

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. 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. Better to model year-by- year payments for individual claimants using a Markov chain approach. Calendar Year of Payment Claim

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