casualty loss reserve seminar september 9-11, 2007 san diego, ca copyright 2007 national council on...

Copyright 2007 National Council on Compensation Insurance, Inc. All Rights Reserved.

Casualty Loss Reserve SeminarSeptember 9-11, 2007

San Diego, CA

Analyzing Workers Compensation Reform Impacts on Loss Development Patterns in

NCCI Rate-Making

Frank SchmidDirector and Senior Economist

of 39 Copyright 2007 National Council on Compensation Insurance, Inc. All Rights Reserved.

Outline

• The Objective

• The Statistical Framework

• The Example of an Unidentified State

• Conclusion


The Objective

• Regulatory reforms may affect the pattern with which losses develop, starting with the initial (first) payment

– Loss development patterns matter in ratemaking and reserving

Changing run-off patterns bear on the tail factor

• The impact of reforms on the tail factor is difficult to gauge (because both numerator and denominator are affected)


The Statistical Framework

• Loss development can be modeled as a time series problem

• Once loss development is cast into a time series framework, the statistical technique of state-space modeling can be applied

• State-space models are flexible (by allowing fortime-variation of parameters) and accommodating(to regulatory details)



• There are three dimensions of time in a loss triangle

Exposure time (exposure growth across accident or policy years)

Calendar time (calendar year effect)

Development time (run-off, that is, decline in incremental payments, net of the calendar year effect)



• The model is written in terms of (logarithmic) growth rates of incremental payments—these growth rates are allowed to be time-varying



• The model is Bayesian

– A (posterior) parameter estimate is the result of a prior that is taken to the data

All prior distributions are conjugate, that is, they are from the same family as the posterior distribution

Expert priors are used for the calendar year effect—to be discussed below



• The model is estimated using the Metropolis-Hastings algorithm

– The technique is also known as MCMC (Markov-chain Monte-Carlo simulation)

– We use WinBUGS 1.4.2 and OpenBUGS 2.2.0 (the latter within the R package BRUGS)



• The model fits to the logarithm of incremental payments

– Negative incremental payments are coded as missing values

In Bayesian models, missing values are treated as parameters that need to be estimated



• There is a stochastic add-up constraint in the model

– This constraint ensures that for every development year, the sum of estimated incremental payments lines up with the observed cumulative payments

This technique, which is known as the cusum (cumulative sum) chart technique, is critical for interpolation when there are negative incremental payments



• The rate of exposure growth (eta)

– eta normalizes to the level of exposure the incremental payments within a given accident/policy year

eta is modeled as a random walk

eta has no bearing on the tail factor



• The calendar year effect (kappa)

– An expert prior is used for the calendar year effect

Rate of CPI Medical Care inflation (“M-CPI”) for medical claims

Average weekly wage (QCEW), CPI, or fixed rate for escalating indemnity claims, depending the regulatory stipulation

Zero for non-escalating indemnity claims



• The calendar year effect (kappa), cont’d.

– The fraction of the incremental payment that goes to escalating indemnity claims is allowed to vary across development years

The model can handle up to two non-zero inflation rates (as demonstrated below)

The calendar year effect varies along the diagonal (as opposed to being constant on a given diagonal)




– The inflation rate pertinent to workers compensation (WC) claims is known up to a constant

WC Infl. Rate = kappa + constant + error term

– For instance, if the WC-pertinent rate of medical inflation differs systematically to M-CPI inflation, then this difference (the “constant”) feeds into the run-off rate (delta)




– Because any systematic difference between theWC-pertinent rate of inflation and the official rate of inflation feeds into the run-off rate (delta), it is this official rate of inflation (e.g., the M-CPI) that is relevant when projecting payments into the future

– It is known that rates of inflation are close to random walks, which implies that the best forecast for any future rate of inflation is the current rate



• The run-off rate (delta)

– We assume a stationary rate of run-off for the unobserved development years

– The projected rate of run-off merges with the rate of mortality (www.ssa.gov) in development year 60, unless the run-off is faster

No dynamic mortality model is used

• According to a special report in the New England Journal of Medicine 352(11), pp.1138-1145, there is little ground for assuming continued gains in life expectancy


The Example of an Unidentified State

• Regulatory reforms

– 1982

– 1986 (minor; effect is modeled but not broken out)

– 1990

– 1992



• The object is to model the effect of the 1990/92 reform cluster on the loss development pattern

– Pre-reform: Policy years 1983 through 1989

– Post-reform: Policy years 1993-2004



• Major reform items

– Introduction of escalation of indemnity benefits at the rate of the CPI (regardless of the date of injury) for PTD claims, effective May 1991

Indemnity benefits for Fatal claims had been escalating at a fixed rate of 4 percent since June 1986

• The model accounts for the escalation of Fatal claims, but the effect of this reform is not broken out in the following analysis (as mentioned)



• Major reform items, cont’d.

– Limitation of TTD claims to 52 weeks

– Tightening of standards for continued eligibility of indemnity benefits

– For injuries past age 55, there is an immediate retirement offset; otherwise, there is a retirement offset starting five years prior to the official retirement age



• Expected effects

– Faster run-off due to faster closing of claims

Spill-over into medical, as these claims may now close faster as well

– Escalation contributes to an increase of the tail, all else being equal

– Retirement offset will (in part) be picked up by the run-off rate; in addition, we reduce the benefits for development years 36 and later by 50 percent



• Pre-reform and post-reform “triangles”



• The pre-reform triangle consists of pre-1990 policy years only

– At the same time, this triangle includes elements from diagonals through calendar year 2004

– To the degree that the 1990/92 reform cluster affected existing claims (for instance by accelerating their closure), the model may underestimate the reform impact



• The post-reform triangle consists of post-1992 diagonals only

– Yet, only in the first column are all observations from the post-reform period

As development time progresses, the post-reform triangle phases in observations from the previous regulatory setting



• Indemnity: delta (“9”: pre-reform; “8”: post-reform)-0

.4-0

.3-0

.2-0

.10

.0

Ra

te o

f C

ha

ng

e (

0.1

Eq

ua

ls 1

0 P

erc

en

t)

10 20 30 40 50 60 70Development Year

(For Policy Years, the First Development Year Comprises 24 Months of Experience)

Run-off Rate(Delta.9)


Delta(Projected)



• Medical: delta (“9”: pre-reform; “8”: post-reform)-0

.6-0

.4-0

.20

.0

Ra

te o

f C

ha

ng

e (

0.1

Eq

ua

ls 1

0 P

erc

en

t)

10 20 30 40 50 60 70Development Year

(For Policy Years, the First Development Year Comprises 24 Months of Experience)



Delta(Projected)



• Indemnity: Change in Ultimate Loss (per $1 of Initial Payment)

-1.8 -1.7 -1.6 -1.5 -1.4

01

23

45

67

N = 20000 Bandwidth = 0.007089

De

nsi

ty



• Medical: Change in Ultimate Loss (per $1 of Initial Payment)

-0.40 -0.35 -0.30 -0.25 -0.20

05

10

15

N = 20000 Bandwidth = 0.003074

De

nsi

ty



• Indemnity: Tail Factors by Regulatory Regime1

.02

1.0

31

.04

1.0

5

Exposure Period

Ta

il F

act

or

1985 1990 1995 2000 2005

Tail Factors Based on b Tail Factor Based on y.hat



• Medical: Tail Factors by Regulatory Regime1

.02

1.0

41

.06

1.0

81

.10

Exposure Period

Ta

il F

act

or

1985 1990 1995 2000 2005

Tail Factors Based on b Tail Factor Based on y.hat



• Indemnity: Calendar Year Effect in First Column-0

.00

4-0

.00

20

.00

00

.00

20

.00

40

.00

6

Exposure Period

Ca

len

da

r Y

ea

r E

ffe

ct (

0.1

Eq

ua

ls 1

0 P

erc

en

t)

1985 1990 1995 2000 2005

Prior Posterior (EstimatedRate of Benefits Inflation)

Posterior (Forecast)



• Medical: Calendar Year Effect in First Column0

.06

0.0

80

.10

0.1

20

.14

Exposure Period

Ca

len

da

r Y

ea

r E

ffe

ct (

0.1

Eq

ua

ls 1

0 P

erc

en

t)

1985 1990 1995 2000 2005

Prior Posterior (EstimatedRate of Benefits Inflation)

Posterior (Forecast)



• Indemnity: Calendar Year Effect on Final Diagonal0

.00

00

.00

50

.01

00

.01

50

.02

00

.02

50

.03

0

Ca

len

da

r Y

ea

r E

ffe

ct (

0.1

Eq

ua

ls 1

0 P

erc

en

t)

Development Year(For Policy Years, the First Development Year Comprises 24 Months of Experience)

5 10 15 20

Prior (Medical CareInflation)

Posterior (Estimated Rateof Benefits Inflation)



• Medical: Calendar Year Effect on Final Diagonal0

.04

00

.04

50

.05

00

.05

50

.06

00

.06

5

Ca

len

da

r Y

ea

r E

ffe

ct (

0.1

Eq

ua

ls 1

0 P

erc

en

t)

Development Year(For Policy Years, the First Development Year Comprises 24 Months of Experience)

5 10 15 20

Prior (Medical CareInflation)

Posterior (Estimated Rateof Benefits Inflation)



• Indemnity: Diagnostic, Pre-Reform Triangle-0

.4-0

.20

.00

.20

.40

.6

Development Year

Diff

ere

nce

be

twe

en

b a

nd

y

5 10 15 20

1 2 3 45 6 7 8 9



• Indemnity: Diagnostic, Post-Reform Triangle-0

.50

.00

.51

.0

Development Year

Diff

ere

nce

be

twe

en

b a

nd

y

5 10 15 20

1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 17 18 19 20 21 22 23



• Medical: Diagnostic, Pre-Reform Triangle-1

.0-0

.50

.00

.51

.0

Development Year

Diff

ere

nce

be

twe

en

b a

nd

y

5 10 15 20

1 2 3 45 6 7 8 9



• Medical: Diagnostic, Post-Reform Triangle-1

01

2

Development Year

Diff

ere

nce

be

twe

en

b a

nd

y

5 10 15 20

1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 17 18 19 20 21 22 23


Conclusion

• NCCI has devised a loss development model that is capable of incorporating detailed statutory provisions

• The model allows the estimation of tail factors according to the applicable regulatory setting

• The model is capable of quantifying the impact of regulatory reforms on the ultimate loss and, hence, the tail factor

casualty loss reserve seminar september 9-11, 2007 san diego, ca copyright 2007 national council on...

Documents

statistical technique

calendar year effectto

dimensions of time

time series framework

development yearsthe

inflation rates

level of exposure

appliedstatespace models