A6. Using multi-dimensional credibility to estimate class frequency vectors in work comp

Question 1

Couret & Venter main ideas

Answer 1

• Objective: estimate expected frequency by injury type in a given class
• Insight: physical circumstances underlying different injury types are correlated* in a given class*
• Solution: take advantage of that extra** information on frequency **of other injury types in the same class to derive the credibility weighted expected frequency instead of simply relying on the hazard group average

**ex: if higher frequencies of major/TT and minor/TT for a given class, then makes sense to expect a higher frequency of fatal/TT and PT/TT for that class

NCCI estimates excess ratios for each injury type separately, and does not use information about correlations between injury types ( no crebibility use )

Question 2

3 methods for estimating injury type ratios on a holdout sample

Answer 2

1. hazard group injury type ratios
2. raw training sample * injury type ratios**
3. multi-dimensional credibility weighted injury type ratios

the multi-dimensional credibility weighted method performed the best

Question 3

Reasons the multi-dimensional credibility showed almost no improvement using the individual class SSE test

Answer 3

Individual class SSE:

• class data is very volatile from year to year => estimators are credibility weighted to be best on average only
• relative ratios are impacted by unknown covariate with level varying between odd/even years => estimators derived from even years are designed to fit even years only*

Quintiles test:
-removed/smoothed out the random noise/volatility in the testing. Do so by grouping classes into quintile based on credibility procedure

Question 4

Reasons the multi-dimensional credibility showed no improvement for hazard group A, even when using the quintiles test

Answer 4

-the classes in hazard group A are very homogeneous so injury type ratios didn’t vary much within that hazard group. not much value added to using credibility for any specific class relative to the others

Question 5

why ELFs published by NCCI are difficult to estimate

Answer 5

because losses are driven by small # of very large claims

Question 6

Quintile test

Answer 6

1. Sort injury type relativities from the credibility procedure for all classes in the HG in increasing order
2. Group classes into quintiles based on the sorted relativities. Ech quintile should have about the same num of TT claims
3. Calculate the weighted average injury type relativity accross all classes within each quintile and within the hazard group. Do this step for each of the 3 methods and for the holdout sample using their respective relativites
4. Calculate SSe for each method
5. Method with lowest see is deemed best fot that particular injyri type and all classes in that hazard group