1. Loss Coverage Why Insurance Works Better with Some Adverse Selection

2. Orthodox view (adverse selection spiral)
Restrictions on risk classification (e.g. anti-discrimination laws) lead to the sequence known as an adverse selection spiral:-
(1) (The few) high-risk people are more likely to buy
(2) (The many) low-risk people are less likely to buy
(3) so the break-even price of insurance rises
(4) and the total number of people who buy insurance falls
(hand-waving stage…the sequence is arbitrarily assumed to be non-convergent)
(5) return to (1) and repeat….
Public policy implication:
Limit adverse selection. More risk classification is always good.
Orthodox view something like this. If policymakers restrict risk classification, we get the sequence known as an adverse selection spiral. You all know that story.
I think there is hand-waving stage in that story, where it is said that the sequence is non-convergent and it always repeats until the market spirals away to nothing.
But anyway, that is the usual story. And the public policy implication is that policymakers should limit adverse selection, and more risk classification by insurers is always good.

3. Loss coverage view
Models with plausible demand elasticities suggests that markets don’t spiral to nothing, they stabilise
A modest degree of adverse selection can be a good thing….
…because it increases the expected population losses compensated by insurance (the “loss coverage”).
This happens despite higher average price and smaller number of people insured
Public policy implication:
Target an optimal degree of adverse selection. Some restrictions on risk classification (and hence some induced adverse selection) may help.

4. Examples
Let’ me illustrate this for you with some toy examples. I’d like you to think of life insurance for context. That’s not necessary, but it helps to get us all on the same page. I’m going to assume all losses and insurance cover are for unit amounts. That simplifies, it’s not necessary.
The Scenario 1 on this slide of no adverse selection is the first of 3 scenarios I’m going to show you. The other scenarios will have some adverse selection, and severe adverse selection.
Think of a population of 10 people. 8 across the top row are lower risks with prob of loss 0.01, and 2 across the bottom row are higher risks with prob of loss That preponderance of lower risks is what we see in most insurance markets.
So in this Scenario 1, risk classification is unregulated. So insurers charge risk-differentiated premiums, actuarially fair premiums. I’m going assume that under those conditions, the take-up of insurance is 50% - that is exactly half the members of each risk-group buy insurance. That’s shown by the shaded over 1/2 risks. The figure of 50% very roughly corresponds to life insurance in practice – about 1/2 population has some life insurance. But doesn’t depend on it being 1/2, doesn’t depend on same for each risk-group – the 50% is purely illustrative.
OK, under those conditions, the weighted average of the premiums paid is The weights are just the numbers of people paying each premium. And because the high and low risks are covered in the same proportions as they exist in the population, we have no adverse selection. And because exactly half of each risk-group is covered, the expected losses compensated by insurance are half the population losses. I call that a loss coverage of 50%.
High and low risks covered in same proportions as in population => No adverse selection.

5. Examples (cont.)
Now on to Scenario 2 of some adverse selection. Let’s suppose a regulator bans risk classification, so insurers have to charge a single pooled premium to all risks. The pooled premium will be expensive for lower risks, so they will buy less insurance. It will be cheap for higher risks, so they will buy more insurance. That’s adverse selection.
In this Scenario 2, only one lower risk buys insurance, compared with 4 previously. And 2 higher risks buy insurance, compared with 1 previously. The pooled premium which gives zero profits for insurers, which balances the system, is then That’s higher than the previous weighted average premium of And the number of risks insured is lower – we have 3 risk insured, compared with 5 previously. So that’s adverse selection, and it is usually said to be bad.
But if we look at the loss coverage, the expected losses compensated by insurance are now higher.. 56% of the population’s losses are compensated by insurance, compared with 50% before. The shift in coverage towards higher risks has more than offset the fall in numbers insured. In that scenario, I argue that the adverse selection is good.
Higher weighted average premium, lower numbers insured
Moderate adverse selection. (Bad?)
But shift in coverage towards higher risks more than offsets lower numbers insured => higher loss coverage. Good!

6. Examples (cont.) Only one individual (higher risk) remains insured
Now in to Scenario 3 of severe adverse selection. In this scenario, risk classification is again banned, and adverse selection has progressed to the point where all of the lower risks have left the market, and only 1 higher risk buys insurance. The pooled premium which balances the system is then just the higher risk premium of And the loss coverage is only 25%, that’s lower than both the previous scenarios. So in that Scenario 3, I agree that adverse selection is bad.
Only one individual (higher risk) remains insured
Shift in coverage towards higher risks does not offset lower numbers insured => lower loss coverage. Bad!

7. Examples (summary)
Loss coverage is increased by the “right amount” of adverse selection….
…but reduced by “too much” adverse selection.

8. More: www.guythomas.org.uk
This talk is based on my book, which I hope you have received in the conference pack

9. APPENDIX

10. Probabilistic goods versus reassurance goods
APPENDIX
Probabilistic goods versus reassurance goods .
Probabilistic good:
Insurance pays out in certain future states of world
risk-weighting of coverage appropriately reflects the heterogeneity in the good provided to different individuals.
Reassurance good:
insurance provides reassurance (freedom from worry) in the present state
Less clear that risk-weighting appropriately reflects individual heterogeneity. (OK if 4x the risk = 4x the worry...but subjective.)
Most quantitative analysis views insurance as a probabilistic good => loss coverage is appropriate metric (linear in probability of loss)
But if insurance viewed as a reassurance good, then arguable that quantum of good is not necessarily linear in probability of loss. (Could be, but that value judgment isn’t obvious.)