NCCI’ 2007 H dG NCCI’s 2007 Hazard Group Mapping Presented by John Robertson, FCAS, MAAA Casualty Actuarial Society Meeting November 16, 2009 Boston MA Boston, MA © Copyright 2009 National Council on Compensation Insurance, Inc. All Rights Reserved.
NCCI’ 2007 H d GNCCI’s 2007 Hazard Group Mappingpp g
Presented byyJohn Robertson, FCAS, MAAA
Casualty Actuarial Society MeetingNovember 16, 2009
Boston MABoston, MA
© Copyright 2009 National Council on Compensation Insurance, Inc. All Rights Reserved.
IntroductionIntroduction• In 2007, NCCI implemented a new 7-hazard-group system,
replacing the previous 4-hazard-group systemreplacing the previous 4 hazard group system
• The new 7 Hazard Groups have been approved for use in the 35 jurisdictions for which NCCI provides ratemakingthe 35 jurisdictions for which NCCI provides ratemaking services and several independent bureau states; discussion here is for the 35 NCCI jurisdictions
• The new 7-hazard-group system is not a subdivision of the old 4-hazard-group system; it is a completely new
i t f l t h dassignment of classes to hazard groups
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BackgroundBackground
• In the US Workers Compensation (WC) insuranceIn the US, Workers Compensation (WC) insurance pays medical costs and lost wages to workers injured on the job
• NCCI uses about 900 WC classifications, which are groupings of risks in similar occupations
• WC classifications are often used in determining premiums for WC policies, and for other purposes
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Excess Loss FactorsExcess Loss Factors• An excess loss factor (ELF) is the ratio of expected
losses excess of some threshold to total expectedlosses excess of some threshold to total expected losses
• Mathematically:• Mathematically:
( )[ ] ( ) dttfLtLXELELFLt
)(10,max1)( ∫∞
=−=−=
µµwhere L is the threshold, X is the distribution of losses by size with density function f(t), and
µµ
[ ] dttftXEt
)(0∫
∞
===µ
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Hazard GroupsHazard Groups
• A hazard group is a collection of WCA hazard group is a collection of WC classifications with similar ELFs over a broad range of thresholds
• NCCI periodically publishes tables of ELFs by hazard group for certain states
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Injury TypesInjury Types• NCCI often distinguishes claims by the type of benefit
paidpaidFatal—Death claimsPermanent Total—Claimant expected to never be able to return workPermanent Partial—Claimant expected to return to work but with some permanent impairment orwork, but with some permanent impairment or disfigurementTemporary Total—Claimant expected to recover fullyMedical Only—No benefits for lost wages are expected to be paid
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NCCI Computes ELFs FromI j T CInjury Type Curves
The ELF for Hazard Group j and threshold L is
( ) ( )jii ijij LSwLELF ,, / µ∑=h S ( ) i th li d ELF f I j T i t t ti
∫∞
−=⎥⎤
⎢⎡
⎟⎠
⎞⎜⎜⎝
⎛−= i
ii dttgrtrXErS )()(0,max)(
where Si(r) is the normalized ELF for Injury Type i at entry ratio r
∫⎥⎦
⎢⎣ ⎠
⎜⎝ r i
ii g )()()(
µ
wi,j is the proportion of losses for Injury Type i in Hazard Group jµ is the average size of loss for Injury Type i in Hazard Group jµi,j is the average size of loss for Injury Type i in Hazard Group jXi is the random variable of sizes of loss for Injury Type i, with
normalized density gi
i th i f l f I j T i
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µi is the average size of loss for Injury Type i
The Previous 4 Hazard Group MappingThe Previous 4 Hazard Group Mapping
N b f Cl P t f P i3886
Number of Classes0.9%
45.6%51.1%
2.5%
Percent of Premium
HG IHG IIHG III
428318
HG IV
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OutlineOutline
• General ConsiderationsGeneral Considerations
• Credibility
• Cluster Analysis
• Underwriting ReviewUnderwriting Review
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General ConsiderationsGeneral Considerations
• New hazard groups are based only on ELFs
• Previous hazard group mapping used other criteria, such as the serious1 to total claim frequency ratio
• No crossoverCrossover is when at a high threshold the ELF for a high hazard group is lower than the ELF for a low hazard groupBased on our a priori expectations regarding size of loss distributions we had a guiding principle that there would bedistributions, we had a guiding principle that there would be no crossover
1 A serious claim is one for which at least one of the following benefits for lost wages is paid or is expected to be paid:•Fatal (death)
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•Fatal (death)•Permanent Total (injured worker not expected to ever be able to work)•Permanent Partial (able to work after recovery period, but with a permanent injury, such as loss of a limb) and benefits for lost wages exceed certain thresholds that vary by state and year
ELFs by ClassELFs by Class
• We computed ELFs for each class at several h h ldthresholds:
$100K, $250K, $500K, $1M, $5M
• Similar to computation of ELFs for a hazard group, but used
C t id b i j tCountrywide curves by injury typeWeights and average severities by class
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CredibilityCredibility• Some classes have only a small number of reported claims
• Several credibility formulas were tested
• We decided to retain the credibility formula used in the previous review,
⎟⎠⎞
⎜⎝⎛ ×
+= 1,5.1min
knnz
where z is the credibility, n is the number of claims for the class, k is the average number of claims per class
⎠⎝ + kn
• The complement of the credibility is applied to the vector of ELFs for the mean of the prior Hazard Group
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Classes by CredibilityClasses by Credibility
N b f % fCredibility Range Claims per Year
Number of Classes
% of Premiums
% % %0% ≤ z < 10% 0–237 355 1.2%10% ≤ z < 50% 238–1662 252 8.1%50% ≤ z < 100% 1663–6649 162 18.8%
z = 100% 6650 + 101 71.8%
Total 870 100 0%Total 870 100.0%
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Cluster AnalysisCluster Analysis
• Given a vector of five ELFs for each class theGiven a vector of five ELFs for each class, the question is how to group them so that classes with similar ELFs are in the same group
• Related questions that we addressed wereIf you knew you wanted to have m groups, how would you determine which classes are assigned to each group?How do you determine that one grouping is betterHow do you determine that one grouping is better than another?How many groups should there be?
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Cluster AnalysisCluster Analysis
• We tested divisions of the classes into m HazardWe tested divisions of the classes into m Hazard Groups where 4 ≤ m ≤ 9
• We used weighted k-means clustering for each m• We used weighted k-means clustering for each m, through the FASTCLUS routine in SAS®*
• We used the Calinski and Harabasz and the Cubic• We used the Calinski and Harabasz and the Cubic Clustering tests to determine the optimal number of hazard groups
* Version 8.2 of the SAS System for a SunOS 5.8 platform. Copyright © 1999-2001 SAS Institute Inc. SAS and all other SAS Institute
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Inc. product or service names are registered trademarks or trademarks of SAS Institute Inc., Cary, NC, USA.
Weighted k-Means Clustering AlgorithmWeighted k Means Clustering Algorithm
• The number of clusters is specified in advanceThe number of clusters is specified in advance
• Make an initial assignment of classes to clusters
• Iterate these steps:Compute the weighted centroid of each clusterF h l fi d th l t t id dFor each class, find the closest centroid and assign the class to that clusterContinue the iterations until no class changesContinue the iterations until no class changes clusters
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Weighted k-Means Clustering AlgorithmWeighted k Means Clustering Algorithm
2k
∑ ∑Weighted k-means clustering minimizes:
2
21ic
i HGcc RRw
i
−∑ ∑= ∈
where
,∑∑ ∈= iHGc cc
i w
RwR
where
the weighted centroid for cluster i∑ ∈ iHGc cw
k is the number of clusters
HGi for 1 ≤ i ≤ k is the i-th cluster (hazard group) of classes cHGi for 1 ≤ i ≤ k is the i-th cluster (hazard group) of classes c
wc is the percentage of the total premium in class c
Rc is the vector of ELFs for class c
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|| *||2 is Euclidean distance
Tests Applied to ClusteringsTests Applied to Clusterings
• Calinski and Harabasz StatisticI ti ll th ti f th b t l tIs essentially the ratio of the between-cluster sum of squares to the within-cluster sum of squares, adjusted for the number of classes and number of clustersA higher value indicates better clusters
• Cubic Clustering CriterionCompares amount of variance explained by a set of clusters to that expected when clusters are formedclusters to that expected when clusters are formed at randomA higher value indicates better clustersg
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Calinski and Harabasz StatisticCalinski and Harabasz Statistic
35003500
3000
-H S
tatis
tic
2500C-
20004 5 6 7 8 9
Number of Hazard Groups
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Cubic Clustering CriterionCubic Clustering Criterion
130130c
105
CC
C S
tatis
ticC
804 5 6 7 8 9
Number of Hazard Groups
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Statistics for Classes withAt L t 50% C dibilitAt Least 50% Credibility
1200 70
800
1000
1200
c
50
60
70
ic
400
600
800
C-H
Sta
tistic
30
40
CC
C S
tatis
ti0
200
400C
0
10
20
C0
4 5 6 7 8 9
Number of Hazard Groups
50%+ Credibility Classes
04 5 6 7 8 9
Number of Hazard Groups
Fully Credible Classes
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y y
NCCI Selected 7 Hazard GroupsNCCI Selected 7 Hazard Groups
• Almost all of these tests indicated 7 hazard groups
• Milligan and Cooper found that the Calinski and Harabasztest performed better than the Cubic Clustering Criterion
• The CCC procedure does not perform as well when correlation is present, as when correlation is not present. There is significant correlation between ELFs at the five thresholds used
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NCCI Selected 7 Hazard GroupsNCCI Selected 7 Hazard Groups
• We have more confidence in the results for the large classes, where most of the experience is concentrated
• There is crossover in the 9-hazard-group mapping, and we had a guiding principle that there would not be crossover. We ascribed the observed crossover to random fluctuations and took this as a sign that 9 hazard groups is too fine aand took this as a sign that 9 hazard groups is too fine a split
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The New 7 Hazard Group MappingThe New 7 Hazard Group Mapping
N b f Cl P t f P i55
24157
88
Number of Classes9.3%
17 4%18.7%
4.8%
Percent of Premium
HG A241
224
17.4%HG BHG CHG DHG E
1604521.3%
10 1%
18.4%
HG EHG FHG G
45 10.1%
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The new 7 hazard group mapping is prior to underwriting review.
Hierarchical Mapping From 7 Hazard GroupsT N 4 H d GTo New 4 Hazard Groups
7 Hazard Groups New 4 Hazard GroupsA B 1A, B 1C, D 2E F 3E, F 3G 4
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The Previous 4 Hazard Group MappingThe Previous 4 Hazard Group Mapping
N b f Cl P t f P i3886
Number of Classes0.9%
45.6%51.1%
2.5%
Percent of Premium
318
HG IHG IIHG III
428HG IV
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The New 4 Hazard Group MappingThe New 4 Hazard Group Mapping
N b f Cl P t f P i
29688
Number of Classes
26.7%37.1%4.8%
Percent of Premium
281HG 1HG 2HG 3
205 31.4%
HG 4
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The new 4 hazard group mapping is prior to underwriting review
Old 4 Hazard GroupsE R ti t $100KExcess Ratios at $100K
All Classes
IV
All Classes
III
rd G
roup
I
II
Haz
ar
0.2 0.3 0.4 0.5 0.6 0.7
I
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Credibility-Weighted Class Excess Ratios at $100KThe vertical line within each bar represents the overall excess ratio for the hazard group
New 7 Hazard GroupsE R ti t $100KExcess Ratios at $100K
All Classes
F
G
All Classes
D
E
rd G
roup
B
CHaz
ar
0.2 0.3 0.4 0.5 0.6 0.7
A
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Credibility-Weighted Class Excess Ratios at $100KThe vertical line within each bar represents the overall excess ratio for the hazard group.The new 7 hazard group mapping is prior to underwriting review.
New 7 Hazard GroupsE R ti t $100KExcess Ratios at $100K
Classes with at Least 75% Credibility
F
G
Classes with at Least 75% Credibility
D
E
rd G
roup
B
CHaz
ar
0.2 0.3 0.4 0.5 0.6 0.7
A
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Credibility-Weighted Class Excess Ratios at $100KThe vertical line within each bar represents the overall excess ratio for the hazard group.The new 7 hazard group mapping is prior to underwriting review.
Percent of Premium MovedOld Mapping to New 4 Hazard GroupsOld Mapping to New 4 Hazard Groups
Before Underwriting Review 70%
552
50%
60%
miu
m
300
552
Number of Classes
20%
30%
40%
rcen
t of P
re
0%
10%
20%Per
153
0%No Movement Up 1 HG Down 1 HG Down 2 HG
Movement
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We Sought Input from UnderwritersWe Sought Input from Underwriters• Following the initial analytic assignment of classes to hazard
groups the draft hazard group assignments were sentgroups, the draft hazard group assignments were sent individually to NCCI’s Underwriting Advisory List (27 affiliates) and were also reviewed by NCCI staff underwriters
• Underwriters were asked to consider:Given that a claim occurs, the likelihood of it being serious, Similarity of operations between classes
• Underwriters provided written reasons for suggestions for changes to assignments that NCCI considered in its final selectionsselections
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Underwriting ReviewUnderwriting Review
• Underwriters also commented onExposure to motor vehicle accidentsExtent of use of heavy machineryExposure to dangerous substancesExposure to dangerous substances
• Considerations for NCCI’s final assignment of l t h d i l d dclasses to hazard groups included
Consistency of the underwriting inputCredibility of the classCredibility of the classPosition of the class relative to the two nearest cluster centroids
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Example of Reassignment of Classes B d U d it I tBased on Underwriter Input
• Class 0030 is for employees in the sugar cane plantation p y g pindustry
Has 12% credibility; applies in only a few statesWas in Hazard Group IIIWas assigned to Hazard Group E by the cluster analysis
• Class 2021 is for employees who work at sugar cane refining
Has 31% credibility; applies nationallyHas 31% credibility; applies nationallyWas in Hazard Group IIWas assigned to Hazard Group C by the cluster analysisWas assigned to Hazard Group C by the cluster analysis
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Example of Reassignment of Classes B d U d it I t (C t’d)Based on Underwriter Input (Cont’d)
• Considerations included:Insureds in either class can have both farming and refining operationsFarming and refining both involve use of heavy machineryPrior to credibility weighting, Class 2021 had ELFs close to those for the centroid of Hazard Group DAfter credibility weighting Class 2021 had ELFs between the centroids for Hazard Groups C and D
• NCCI assigned Class 2021 to Hazard Group D based on its ELFs prior to credibility weighting and its mix of
tioperations
• NCCI assigned Class 0030 to Hazard Group D to put it in th H d G Cl 2021the same Hazard Group as Class 2021
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Movement of Classes as a Result of Underwriting ReviewUnderwriting Review
90%100%
732
50%60%70%80%
%
Prem
ium
20%30%40%50%
Per
cent
of P
121
0%10%
NoM t
Up 1 HG Down 1 HG Up 2 HGs Up > 2 HGs
P
10 6 1
Number above bar represents the number of classes in each category Movement is number of classes that NCCI moved relative to
Movement
Movement
Number above bar represents the number of classes in each category. Movement is number of classes that NCCI moved relative to the new 4 hazard groups after considering input from the underwriting review.
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ConclusionConclusion
• In 2007 NCCI implemented a new 7 Hazard Group System
• Cluster analysis was used to make initial assignments of classes to hazard groups based on similarity of excess loss factorsloss factors
• Underwriting review provided input that helped NCCI refine the assignments
• The new 7-Hazard-Group system has been approved for use in all 35 NCCI jurisdictions and several independent b t tbureau states
• The full paper is available at ncci.com under Research & OutlookOutlook
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QUESTIONS?
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