Session # P2 & P3 November 14, 2006, 10:00 am Estimating the Workers Compensation Tail Richard E. Sherman, FCAS, MAAA Gordon F. Diss, ACAS, MAAA

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

Workers Compensation Medical Permanent Disability (MPD)

Dead on Arrival (DOA) Data Standard Triangle Diagonals Only Area (DOA)

Mueller Incremental Tail Method Using the incremental data, calculate decay factors. Incremental to incremental ratios. Use various smoothing techniques if data is volatile. Square the cumulative triangle. Increment the squared triangle. Apply decay factors.

WC: Two Different Worlds %-age Of Permanent Disability Claims All Other WC Claims Counts 10 %90 % AY Losses 86 %14 % Loss Reserves 96.5 %3.5 %

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

SAIF’s Actual PLDFs – 1.0

We assume a brontosaurus tail.

PLDFs – 1.0 Out to DY 58

Washington State Fund PLDFs – 1.0

MPD payments: Stegosaurus tail.

INVESTIGATING THE CIA C OMMON I NTUITIVE A SSUMPTIONS

CIA # 1 MPD paid loss development factors decrease monotonically

Mortality Model vs. SAIF’s Actual 9% rate of future medical cost escalation assumed. Mortality rates of general population assumed. Model fit well out to development year (DY) 40. Model noticeably underestimated actual development beyond DY 40.

OPPOSITE INFLUENCES FORCE OF MORTALITY VERSUS FORCE OF MEDICAL COST ESCALATION

The Need to Separate We must separately analyze: 1)The effects of mortality on the remaining number of open claims; and 2) The effects of medical cost escalation on claim severities. This cannot be done with the standard paid loss development method.

OPEN COUNTS PROJECTED USING MORTALITY FACTORS AVERAGE PAYMENTS PROJECTED USING MEDICAL ESCALATION RATES

A) Incremental Paid Losses ($000’s) 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, ,

Estimation of Incremental Payments by Static Mortality Model MPD Losses for Accident Year 2002

CIA # 2 As permanently disabled claimants age, neither utilization nor on-level severity changes.

CIA # 3 Future MPD paid severities should increase in line with historical changes in the medical component of the Consumer Price Index.

Comparison of SAIF’s Historical Rate of Medical Cost Escalation with Changes in the Medical Component of the Consumer Price Index

Comparison of SAIF’s Recent Rates of Medical Cost Escalation with Average Changes in the Medical Component of the Consumer Price Index

CIA # 4 After stabilization, mortality rates of the disabled are 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 appreciably 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

Is it appropriate to Use the Ratio of Incurred to Paid for Most Mature AY? AY Years of Development Triangle of Historical Development Data Development Factors Helpful Tail Region

CIA # 5 MPD case reserves based on inflating payments until the expected year of death should be adequate.

What Causes Expected Value to Exceed Simple Reserve Estimates? Inflation balloons the cost of scenarios where the claimant lives longer than their life expectancy. Expected Value Contemplates Possibility of “Worst Case” Situation Medical Cost Escalation.

CIA # 6 For a given development period, Worker’s Compensation tail factors should be constant for all accident years

Testing CIA # 6 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.

Indicated WC MPD Tail Factors End of Development Year AY

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

CIA # 7 For a given development period, WC age-to-age paid loss development factors 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/

CIA # 8 Paid tail factors will not change much when the retention changes.

CIA # 9 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. 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. All 9 CIAs do not apply to MPD paid and reserves. MPD PLDFs increase for many mature DYs. MPD paid tails and incremental PLDFs trend upward as mortality rates decline. Utilization and severity tend to increase as permanently disabled claimants become elderly. Common methods significantly underestimate the expected value of MPD case reserves. Common methods understate MPD reserve variability. Predictive model produces more realistic estimates.

Average On-Level Incremental Paid Avg AgeDYs at Injury ,9578,57916,0947, ,4956,707 5, ,6475,132 3,509 All4,6307,12611,749