Adverse Selection

Study guide: Exam 6C

Adverse Selection is the tendency for those who know they are worse-than-average risks to buy more insurance, and better-than-average risks to buy less, when the insurer cannot distinguish between them. It arises from information asymmetry — the buyer knows their own risk better than the seller — and it is the mechanism that unravels a voluntary insurance market priced at an average rate.

$\text{Price} = E[\text{Loss} \mid \text{purchase}] \; > \; E[\text{Loss} \mid \text{population}]$

The death spiral. Price at the population average; low risks find the price poor value and leave; the remaining pool is worse, so the price rises; more of the remaining low risks leave; repeat. The endpoint is a market serving only the worst risks at a price only they will pay.
Defences: risk classification (price to the risk, so nobody is overcharged), underwriting and medical or inspection requirements, waiting periods and pre-existing condition exclusions, compulsion (mandatory purchase removes the choice to leave), and pooling by group rather than individual.
Regulation can cause it. Every classification restriction reintroduces adverse selection by forcing a single price across risks the insurer knows differ — the cost quantified in Risk Classification Restrictions. This is the standard argument against banning a predictive variable.
Distinguish from Moral Hazard. Adverse selection is about who buys — a selection effect present before the contract. Moral hazard is about how the insured behaves after being insured. Confusing them is a common exam error.
Adverse selection is the principal justification for compulsory government programs: Employment Insurance, Health Care Insurance and Workers Compensation Insurance are all universal precisely because a voluntary version would attract only the high risks. It also explains why flood has historically been unwritable — only those in the floodplain want it.

Unravelling a Voluntary Pool A population of $10{,}000$ has two equal groups: low risks with expected loss $\$200$ and high risks with expected loss $\$1{,}000$ . The insurer cannot tell them apart and charges the average. Buyers purchase only if the premium is at most $1.3$ times their own expected loss.

Trace the market.

Answer Round 1. Average expected loss is

$\tfrac{1}{2}(\$200) + \tfrac{1}{2}(\$1{,}000) = \$600$

Low risks will pay at most $1.3(\$200) = \$260$ , so they do not buy. High risks will pay up to $1.3(\$1{,}000) = \$1{,}300$ , so they do.

Round 2. The pool is now entirely high risks, so the required premium is $\$1{,}000$ . High risks still buy at $\$1{,}000$ , so the market stabilises — but only as a market for high risks at a high price. Half the population is uninsured, and the pooling benefit of insurance has been destroyed.

What restores the market:

Classification. Charge $\$200$ and $\$1{,}000$ respectively; both groups buy; everyone is insured. This is the efficiency argument for risk-based pricing.

Compulsion. Require purchase at $\$600$ ; both groups buy; low risks subsidise high risks by $\$400$ each. Everyone is insured, but the cross-subsidy is real and should be stated as such.

Do nothing and accept that half the population is uninsured.

Every Canadian government insurance program in Section B is an instance of the second option, adopted because the first was politically or practically unavailable.