Credibility for groups with multi-years of experience

[hopper]

How do you handle credibility for groups with multi-years of experience? Let's suppose that the experience of any groups with at least 600 employees in the most recent period is considered fully credible, then what level of credibility should one assign to a group with 200 employees and three years of experience? Are there any books/papers that address this issue?

[mr.c]

You could use total member (or ee) months over the entire three-year period for creidibility, but then put more emphasis on more recent experience for rate levels. That way, you can make the employer feel better about accounting for continued good experience but also have some assurance of placing more weight on recent trends. Sure, it's totally subjective, but what isn't subjective in credibility?

[oscar peterson]

On the course four syllabus, techniques are discussed which consolidate information across policy years such that you derive an estimate with a lower MSE than if you didn't use the method. There is a section in the Loss Models textbook dealing with nonparametric estimation/Buhlmann credibility model (see chapter five, pages 460ish).

A curiosity of my own: Is it common/customary to use several years of data in credibility analysis? Anyone ever used the aforementioned method from the syllabus?

[thing]

Offhand, I would think it's a bad idea to give them higher credibility based on a longer exposure period. You can, of course, include more than just the most recent period: if you want to use 3 years you could e.g. weight them 50%/30%/20% in calculating the experience portion. But 3 lucky years does not a credible group make.

Check out http://www.soa.org/library/record/2000-09/rsa02v28n242pd.pdf An excerpt:
To make money, do not give any credibility whatsoever to the good groups. Instead, just give them the same normal rate increase as for the block as a whole. This is because if you were to drop a client's rates because they are really good, then you'd get a big surprise at the end of the day.

[Dr T Non-Fan]

I thought basic credibility has to do with claim dollars or amounts, and not exposure.
Three lucky years might not provide enough claims to be credible. Consider the underlying trend, and it gets more messy. Consider the add-ons and cancels within group, changes to benefits, etc.

[twig93]

Offhand, I would think it's a bad idea to give them higher credibility based on a longer exposure period. You can, of course, include more than just the most recent period: if you want to use 3 years you could e.g. weight them 50%/30%/20% in calculating the experience portion. But 3 lucky years does not a credible group make.

I would disagree about giving higher credibility based on a longer exposure period. I think it's reasonable to look at past trends. When experience rating, my company does not discount past years (i.e. trust them less than the most recent year), but that's an interesting idea. We just go off of life-years. A 200 life group that's been with us for three years is just as credible as a 600 life group that's been with us for one year. But we don't assign as much credibility to good experience as we do to bad experience.

[Double High C]

I thought basic credibility has to do with claim dollars or amounts, and not exposure.
Three lucky years might not provide enough claims to be credible. Consider the underlying trend, and it gets more messy. Consider the add-ons and cancels within group, changes to benefits, etc.

Theoretically, in a direct sense, it should have more to do with exposure than claim amounts.

Having said that, the amount of exposures that is needed to meet a given credibility threshold is a function of the underlying probability distribution, which of course significantly affects the actual claim amounts experienced.

Having said that, prior expectations (null hypotheses) could cause one to place higher credibility on poor experience than what seems to be, FLOABW, flukily good experience.

Having said that, I have nothing more to say.

[Shop Girl]

In my opinion, three years of experience on a 200 life group does not have the same amount of credibility as one year of experience on a 600 life group due primarily to the impact of employee turnover.

Assuming a 10% employee turnover rate which occurs uniformly throughout the year, after one year, on average 95% of the experience for the 600 life group reflects that of employees who are still currently in force, those for who you are estimating claims for the following year.

Assuming the same 10% employee turnover rate on the 200 life group, after three years, only 85.7% (.95^3) of the experience for that three year period is for employees who are currently in the group.

The fact that for the 200 life group you would be using more experience from people who are no longer in the group to predict claims for those who are currently in the group reduces its credibility. Especiall since the average claim cost of the terminating employees and that of the persisting employees may be quite different. Even though the two may have the same number of "employee years" of data, there is more variance in the 200 life group, and variance is risk. The more risk assigned to something, the less credible it becomes. At the same time, I believe the prior year of experience for the 200 life group should be taken into account, placing more weight on the current period.

While longitudinal data adds to the credibilty of things such as predicting rainfall, estimating traffic accidents at a given interesection, or predicting accidental deaths among construction workers, the health and makeup of an employer group changes to a greater degree such that what happened 5 years ago has almost no bearing on what will happen next year for a majority of the group. There will always be that cronic conditions such as diabetes where the longitudinal data would help in estimating next year's claims.

In my days as an underwriter, two years of experience was the most used in large group experience rating as the make up of the group changed too much when looking back any further (employee turnover, births, deaths, newly diagnosed conditions, etc.). Current year experience was blended with the prior years experience to determine the experience portion of the rate, more weight being given to the current year. The experience portion was then blended with the manual claims, based upon the credibility assigned to the group, to produce to projected claims.

I think that some of these risk adjusters that are we are starting to see that use diagnosis, types of drugs used, etc will add more credibilty to your prediction of claims for the 200 life group than what happened three years ago.