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 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
Diagonals
Only Area
(DOA)
Standard
Triangle
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
SAIF PLDFs Le ss 1.0
0. 0700
0. 0600
PLDF Less 1.0
0. 0500
0. 0400
0. 0300
0. 0200
0. 0100
0. 0000
6
7
8
9
10
11
12
13
14
Ye a r of De ve lopme nt
We assume a brontosaurus tail.
PLDFs – 1.0 Out to DY 58
SAIF's Actual PLDFs - 1.0
0.07
0.05
0.04
0.03
0.02
0.01
Year of Development
58
54
50
46
42
38
34
30
26
22
18
14
10
0.00
6
PLDF Less 1.0
0.06
Washington State Fund PLDFs – 1.0
Washington State Fund
Medical Tail
0.6%
Incremental Payout
0.5%
0.4%
0.3%
0.2%
0.1%
0.0%
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
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
0.07
0.06
0.04
Model
SAIF
0.03
0.02
0.01
58
54
50
46
42
38
34
30
26
22
18
14
10
0.00
6
PLDF Less 1.0
0.05
Year of Development
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.
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
1997
1998
1999
2000
2001
2002
12
2,823
2,638
3,331
3,170
3,143
4,263
24
15,936
14,250
15,806
18,602
20,306
36
9,182
9,096
9,735
12,462
48
4,282
2,936
4,309
60
2,064
3,214
72
1,411
B) Open Counts
AY
1997
1998
1999
2000
2001
2002
12
362
338
343
268
276
333
24
1,112
888
840
867
897
36
793
628
664
731
48
490
431
492
60
375
352
72
324
C) Incremental Paid per Prior Open
AY
1997
1998
1999
2000
2001
2002
24
44,022
42,159
46,021
69,411
73,572
-
36
8,257
10,244
11,589
14,374
48
5,399
4,675
6,489
60
4,212
7,459
72
3,764
Estimation of Incremental Payments by Static Mortality Model
MPD Losses for Accident Year 2002
Development
Year
21
22
23
24
25
26
27
28
29
30
Paid/
Increm. Cumu# Prior Prior Open Paid
lative
Open
Open
Loss Paid Loss
133
19.0
2.5
125.5
128
20.7
2.7
128.2
124
22.6
2.8
130.9
119
24.6
2.9
133.9
114
26.9
3.1
136.9
109
29.3
3.2
140.1
104
31.9
3.3
143.4
98
34.8
3.4
146.8
93
37.9
3.5
150.4
88
41.3
3.6
154.0
PLDF
1.0205
1.0212
1.0218
1.0223
1.0228
1.0232
1.0236
1.0239
1.0241
1.0242
Death Rate v. Inflation by DY
20.0%
15.0%
Death
9% Infl
10.0%
5.0%
Development Year (DY)
70
66
62
58
54
50
46
42
38
34
30
26
0.0%
22
9% Inflation v . Death Rate
25.0%
Model v. Actual SAIF PLDFs Less 1.0
0.07
0.06
0.04
Model
SAIF
0.03
0.02
0.01
58
54
50
46
42
38
34
30
26
22
18
14
10
0.00
6
PLDF Less 1.0
0.05
Year of Development
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)
12,000
10,000
8,000
6,000
4,000
2,000
Development Year (DY)
55
52
49
46
43
40
37
34
31
28
25
22
19
16
13
0
10
Incremental Paid Severity
14,000
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
Accident
Years
Average Rate of
Medical Cost
Escalation for Time
Loss Claims
Average Rate of
Change in Medical
Component of the Average
CPI
Difference
1966-1973
1973-1983
1983-1993
1993-2003
10.5%
12.2%
7.2%
7.3%
5.7%
10.0%
7.2%
4.0%
4.8%
2.2%
0.0%
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
Average Rate of
Medical Cost
Change in Medical
Escalation for
Com ponent of the
Tim e Loss Claim s
CPI
Average
Difference
1998
1999
2000
2001
2002
2003
9.2%
5.3%
18.6%
13.6%
12.7%
9.1%
3.2%
3.5%
4.1%
4.6%
4.7%
4.0%
6.0%
1.8%
14.5%
9.0%
8.0%
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?
Years of Development
AY
Triangle of
Historical
Development
Data
Tail
Region
Development
Factors
Helpful
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
0.06
0.05
0.04
Exp. Losses
0.03
Deaths
0.02
0.01
Age
10
8
10
2
96
90
84
78
72
66
60
54
48
42
36
0.00
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
1970
2.570
1975
2.628
1980
2.701
1985
2.774
1990
2.848
1995
2.921
2000
2.990
20
2.177
2.223
2.279
2.336
2.393
2.451
2.505
30
40
50
60
70
80
1.773
1.438
1.210
1.075
1.015
1.0012
1.805
1.456
1.220
1.080
1.016
1.0013
1.842
1.477
1.231
1.085
1.018
1.0014
1.879
1.499
1.242
1.090
1.020
1.0016
1.918
1.521
1.253
1.095
1.021
1.0017
1.957
1.543
1.265
1.101
1.023
1.0019
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
AY
1970
1975
1980
1985
1990
1995
2000
10
196
197
200
202
204
206
207
End of Development Year
20 30 40 50 60 70
119 71 33 12 3.5 0.5
120 73 34 13 3.7 0.6
123 76 36 14 3.9 0.6
126 79 38 14 4.2 0.7
128 81 39 15 4.4 0.7
130 83 41 16 4.7 0.8
132 86 42 17 5.0 0.9
80
0.02
0.03
0.03
0.04
0.04
0.05
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-byyear 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