Session # P2 & P3November 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 1926-2005.

• 80 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

DiagonalsOnly 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 – 1.0SAIF PLDFs Less 1.0

0.0000

0.0100

0.0200

0.0300

0.0400

0.0500

0.0600

0.0700

6 7 8 9 10 11 12 13 14

Year of Development

PL

DF

L

ess

1.0

We assume a brontosaurus tail.

PLDFs – 1.0 Out to DY 58

SAIF's Actual PLDFs - 1.0

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Year of Development

PL

DF

Less 1.

0

Washington State Fund PLDFs – 1.0

0.0%

0.1%

0.2%

0.3%

0.4%

0.5%

0.6%

10.5 12.8 15 17.3 19.5 21.8 24 26.3 28.5 30.8 33 35.3 37.5 39.8 42 44.3 46.5 48.8 51 53.3 55.5 57.8 60

Washington State FundMedical Tail

Incr

emen

tal

Pay

ou

t

Maturity (Years)

MPD payments: Stegosaurus tail.

INVESTIGATING THE CIA

COMMON

INTUITIVE

ASSUMPTIONS

CIA # 1

MPD paid loss

development factors

decrease monotonically

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

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.

Payout Patterns--Lifetime v. Short Term MPD Payments for a Single Accident Year

0.00

5.00

10.00

15.00

20.00

25.00

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49

Development Year (DY)

$ M

illi

on

s

Lifetime

ShortTerm

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 PAYMENTSPROJECTED USING MEDICAL

ESCALATION RATES

A) Incremental Paid Losses ($000’s)

AY 12 24 36 48 60 72 1997 2,823 15,936 9,182 4,282 2,064 1,4111998 2,638 14,250 9,096 2,936 3,2141999 3,331 15,806 9,735 4,3092000 3,170 18,602 12,4622001 3,143 20,306 2002 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 -

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

Develop- Paid/ Increm. Cumu-ment # Prior Prior Open Paid lativeYear Open Open Loss Paid Loss PLDF

21 133 19.0 2.5 125.5 1.020522 128 20.7 2.7 128.2 1.021223 124 22.6 2.8 130.9 1.021824 119 24.6 2.9 133.9 1.022325 114 26.9 3.1 136.9 1.022826 109 29.3 3.2 140.1 1.023227 104 31.9 3.3 143.4 1.023628 98 34.8 3.4 146.8 1.023929 93 37.9 3.5 150.4 1.024130 88 41.3 3.6 154.0 1.0242

Death Rate v. Inflation by DY

0.0%

5.0%

10.0%

15.0%

20.0%

25.0%

22

26

30

34

38

42

46

50

54

58

62

66

70

Development Year (DY)

9%

Infl

ati

on

v.

De

ath

Ra

te

Death

9% Infl

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 # 2

As permanently disabled claimants age,

neither utilization nor on-level

severity changes.

Incremental Paid per Claim with Payment (at 2003 Cost Level)

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

Development Year (DY)

Incr

emen

tal

Pai

d S

ever

ity

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

IndexIndex

Accident Years

Average Rate of Medical Cost

Escalation for Time Loss Claims

Average Rate of Change in Medical Component of the

CPIAverage

Difference

1966-1973 10.5% 5.7% 4.8%1973-1983 12.2% 10.0% 2.2%1983-1993 7.2% 7.2% 0.0%1993-2003 7.3% 4.0% 3.3%

1966-2003 9.2% 6.8% 2.4%

Comparison of SAIF’s Recent Rates of Medical Cost Escalation with Average Changes in the Medical

Component of the Consumer Price Index

Accident Year

Average Rate of Medical Cost Escalation for

Time Loss Claims

Average Rate of Change in Medical Component of the

CPIAverage

Difference

1998 9.2% 3.2% 6.0%1999 5.3% 3.5% 1.8%2000 18.6% 4.1% 14.5%2001 13.6% 4.6% 9.0%2002 12.7% 4.7% 8.0%2003 9.1% 4.0% 5.0%

1998-2003 11.4% 4.0% 7.4%

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?

AYYears 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.

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 # 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 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

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

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 55/50 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

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 2004 2005 2006 2007

1 3.2 3.5 3.8 4.0

2 12.7 13.8 - - - -

3 8.1 8.8 9.6 - -

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 Age DYs DYs DYs DYs

at Injury 16-25 26-40 41+ 16+

15-35 5,957 8,579 16,094 7,482

36-45 5,495 6,707   5,952

46+ 2,647 5,132   3,509

All 4,630 7,126 11,749