Unnatural Selection -Chapter 20 & Sept 2019 Paper A Q8(iv)

[Bill SD]

Hi,
I am repeatedly confused by what 'selection' and 'selective effect' actually mean in CP1. Chapter 20 of the CMP notes (page 14) says:
"..we talk about ‘selection’ in the context of ‘anti-selection’. In actuarial practice, however, it has become customary to refer to the source of heterogeneity itself as ‘selection’. Alternatively, it can refer to the subdivision of heterogeneous data into homogeneous classes (so that all risks within a particular group have similar characteristics and can therefore be modelled together)."

Page 19 says: "Those getting married usually experience lighter mortality and morbidity than those of the same age who do not get married. Marriage is said to have a selective effect in respect of mortality and morbidity."

Thanks in advance for any answers to this barrage of questions:

1. Is 'selection' a process which an insurer performs by identifying (proxy) rating factors to split its policies into homogeneous groups so it can better price/project/monitor them?

2. How does this definition apply to temporary initial selection - this means, for example, that an insurer treats life assurance policyholders differently than general population by assuming they have lighter mortality (even though the initial health check becomes increasingly irrelevant in the subsequent months/years)

3. Spurious selection - Page 17 of notes and the Examiners Report for Sept 2019 Paper A Q8(iv) give the example of postcodes/regions in Wales & England as spurious selection. But surely geography is an example of class selection! (page 11 of notes: a postcode with a local, high-performing hospital should have lighter mortality)

4. Time selection -I understand this to mean that an insurer should classify data separately based on its calendar year - if mortality for all ages was better/worse that year. So for example, time selection refers to treating the number of deaths in 2020 different to 1990s (due to medical advances) and separate from 2022 (since less covid-related deaths)

Sept 2019 Paper A Q8(iv) asks: "Suggest possible reasons for the selection occurring in these policies" (influencing a higher number of deaths in recent years) -Why isn't time selection included in the solution: ie. mortality experience in last 3 years may have worsened due to calendar year-specific events like a pandemic?

5. Does 'selective effect' mean that a policyholder moves into a different homogeneous group (since a rating factor has changed) -so an actuary switching career to a stunt performer is considered a 'selective effect' on their mortality?

6. CP1 only mentions selection in context of mortality. Is it equally relevant for banks dividing mortgage borrowers or that an insurer offering cyber insurance should price differently for companies with poor IT security, previous cyber incidents, etc. to avoid anti-selection.

 

[Lindsay Smitherman]

Hi - thanks for all the interesting questions!

I agree that the definition of 'selection' is not straightforward, and there are lots of different ways in which that term can be used - as indicated in the course notes.

It might be easiest to think about it as the division of 'lives' into groups that exhibit differences in key risk characteristics, such as mortality & morbidity.

 

[Lindsay Smitherman]

1. Is 'selection' a process which an insurer performs by identifying (proxy) rating factors to split its policies into homogeneous groups so it can better price/project/monitor them?

The rating factors that the insurer chooses will relate to class selection. Class selection means that the differences in risk characteristic (eg mortality) arise due to something that permanently impacts experience. For example, for a term assurance contract, one rating factor would be age, because you would always expect mortality to vary by age. So the insurer will consider class selection effects when choosing appropriate rating factors. The insurer may also use underwriting to gain more information about the individual in order to assess their risk level - this would be an example of temporary initial selection (see next question).

 

[Lindsay Smitherman]

2. How does this definition apply to temporary initial selection - this means, for example, that an insurer treats life assurance policyholders differently than general population by assuming they have lighter mortality (even though the initial health check becomes increasingly irrelevant in the subsequent months/years)

Temporary initial selection means that the differences in risk characteristic reflect the amount of time that has passed since an event. A good example of such an event would be underwriting. An individual who was underwritten six months ago would be expected to have a lighter mortality / morbidity than an identical individual who was underwritten three years ago.

Individuals choosing to purchase insurance would be expected to have a different level of mortality / morbidity risk than the general population for many reasons, for example:

• might be more affluent than average, hence able to afford insurance - class selection
• might be more likely to be married and have dependants - class selection
• might undergo underwriting - temporary initial selection
• might be attempting to anti-select against the insurer - adverse selection

 

[Lindsay Smitherman]

3. Spurious selection - Page 17 of notes and the Examiners Report for Sept 2019 Paper A Q8(iv) give the example of postcodes/regions in Wales & England as spurious selection. But surely geography is an example of class selection! (page 11 of notes: a postcode with a local, high-performing hospital should have lighter mortality)

I think what this is getting at is that if we just say that regions X and Y have different levels of mortality, we aren't properly describing the underlying selection processes. Person X doesn't have a higher level of mortality just because they live in region X; moving between the regions wouldn't make any difference per se. What we are actually seeing is the impact of different mixes of occupation or housing quality etc between those regions, and that is what is driving the differences.

 

[Lindsay Smitherman]

4. Time selection -I understand this to mean that an insurer should classify data separately based on its calendar year - if mortality for all ages was better/worse that year. So for example, time selection refers to treating the number of deaths in 2020 different to 1990s (due to medical advances) and separate from 2022 (since less covid-related deaths)

Sept 2019 Paper A Q8(iv) asks: "Suggest possible reasons for the selection occurring in these policies" (influencing a higher number of deaths in recent years) -Why isn't time selection included in the solution: ie. mortality experience in last 3 years may have worsened due to calendar year-specific events like a pandemic?

Probably partly because in September 2019 we didn't have the same pandemic experience that we now have! Back then, time selection fundamentally referred to gradual mortality / morbidity improvements over calendar time due to things such as medical advances etc, as you mention - and that would not have been a concern for term assurance business.

There aren't many marks available for this question part, so we should focus on key relevant types of selection. Bear in mind that the line above that question part refers to the team raising 'concerns around selection', so we need to think about what might generate such concerns. The pandemic is not something that the insurer has any control over, so it would not necessarily generate the same level of internal 'concern' as other selective effects might. For example, it should be concerned if there is a high level of adverse selection from policyholders (perhaps indicating that its underwriting process is not good enough), or perhaps the temporary initial selection effect from underwriting is not in line with what it was expecting (similarly a need to review its underwriting process). Perhaps it isn't understanding the risk differences correctly (spurious selection), or perhaps it needs to reconsider its target market (class selection).

 

[Lindsay Smitherman]

5. Does 'selective effect' mean that a policyholder moves into a different homogeneous group (since a rating factor has changed) -so an actuary switching career to a stunt performer is considered a 'selective effect' on their mortality?

Yes - it is just something that acts to cause a difference in one of the risk characteristics.

 

[Lindsay Smitherman]

6. CP1 only mentions selection in context of mortality. Is it equally relevant for banks dividing mortgage borrowers or that an insurer offering cyber insurance should price differently for companies with poor IT security, previous cyber incidents, etc. to avoid anti-selection.

CP1 also covers morbidity selection, which is very similar to mortality. And yes, the concept can relate to other examples too, as you indicate.

 

[Bill SD]

I think what this is getting at is that if we just say that regions X and Y have different levels of mortality, we aren't properly describing the underlying selection processes. Person X doesn't have a higher level of mortality just because they live in region X; moving between the regions wouldn't make any difference per se. What we are actually seeing is the impact of different mixes of occupation or housing quality etc between those regions, and that is what is driving the differences.

Thanks very much for your helpful responses!

So i guess in your example of spurious selection, regions X and Y are equally close to hospitals, exposed to natural catastrophes, etc? Or is your point that even if region X has a hospital and Y doesn't, it's not strictly 'geography' causing a difference in mortality, it's 'closeness to a hospital'.

I just find the Core Reading confusing (quoted on page 7) that geographical location is a proxy factor but climate/geography "provide a direct causal explanation of the observed differences" in mortality.

From a quick google it seems that the term 'spurious selection' is related to the 19th century concept of 'spurious correlation' which seems to simply mean that: 'Correlation Is Not Causation' Spurious Correlation - an overview | ScienceDirect Topics and nicely 'correlates' with your answer. Anyway, now back to past papers

 

[Lindsay Smitherman]

Yes it is a bit messy isn't it!

It's reasonably easy to see that climate and other aspects of geography such as living on a tectonic plate faultline / at the base of an active volcano could have a direct causal impact on mortality rates.

Regions will have lots of other factors that differ between them which directly cause mortality / morbidity differences, such as the number of hospitals etc.

So I think what the Core Reading and the question that you reference are getting at is that it's rather lazy just to say 'region X has greater mortality than region X' and leave it at that. Identifying and analysing the causal factors that generate those differences would lead to a more accurate grasp of the actual selective processes.