Adverse selection and moral hazard, and what an insurer does about them

CB2 · Business Economics · 12 min read

1One cause, two failures

Insurance is a contract between two parties who do not know the same things. The buyer knows their own health, their own driving, their own intentions. The insurer knows the statistics of a population. That gap produces two distinct failures, and the first thing to get right is which is which.

Adverse selection happens before the contract. The buyer's private knowledge decides whether they buy. At any single premium, the people for whom it is good value are the bad risks, so the pool that actually forms is worse than the population the premium was calculated from.

Moral hazard happens after the contract. Having transferred the cost of a loss to somebody else, the insured has less reason to prevent it. Their behaviour changes, and the claims that follow are worse than the behaviour the premium assumed.

The test that separates them in one line: did the information problem change who was in the pool, or what the people in the pool did? Selection is about entry. Hazard is about conduct.

2The adverse selection mechanism: why a pool unravels

This is the part worth being able to construct rather than recite, because it runs as a loop and each turn of the loop makes it worse.

Start with one premium for everybody, set at the average expected claim cost of the whole population. Buyers each know their own risk, so each can judge whether the premium is good value for them.

1. The premium is above the expected cost of the best risks. For them the cover is poor value, so some of them do not buy.
2. Those are the cheapest people in the pool. With them gone, the average claim cost of the remaining pool is higher than it was.
3. The premium was set for the old average, so the insurer is now losing money and must raise it.
4. The higher premium is now above the expected cost of the next-best group, so they leave. Go to step 2.

Each round strips out the best remaining risks and pushes the premium up, which strips out the next layer. The loop stops only when the people left are so bad that the premium, high as it is, is still worth paying to them. In the worst case it stops with only the worst risk class insured, at a premium close to that class's own expected cost — and everybody else uninsured, including people who would gladly have paid a fair price for their own risk.

That last clause is the whole reason this counts as a market failure rather than just an unpleasant outcome. The trades that fail to happen are trades both sides wanted.

3The four things that stop the unravelling

Each one attacks a different step of the loop, which is the useful way to hold them in mind.

Risk classification. Charge different premiums to groups you can tell apart using something observable that correlates with risk. This attacks step 1: if each group's premium matches its own expected cost, nobody is being asked to subsidise anybody, so nobody has a reason to walk out. This is what underwriting is, and it is why an insurer asks questions it could otherwise do without.

Compulsion. Require the cover by law, as third-party motor cover is required. This attacks step 1 from the other side by removing the choice to leave. It is blunt, and it is the only remedy that works when the risk is genuinely unobservable.

Screening by contract design. Offer a menu — low cover with a large deductible, or full cover at a high price — and let buyers sort themselves. A good risk, expecting few claims, will take the cheap high-deductible contract; a bad risk will pay for full cover. The buyer's choice reveals what the insurer could not observe.

Group schemes. Cover everybody in an employer or an association, for a reason unrelated to insurance. Because membership was not chosen with the cover in mind, the pool is not self-selected, and step 1 never gets started.

4The moral hazard mechanism, and why the cure is sharing the loss

Care costs something — money, time, inconvenience. An uninsured person takes care up to the point where the cost of more care exceeds the loss it prevents. Fully insure them and the loss it prevents is no longer theirs, so the calculation changes and the care stops. Claims rise, not because anybody was dishonest, but because the incentive was removed.

The cure follows directly from the diagnosis: leave the insured holding enough of the loss that care is still worth taking. Every standard device does this.

A deductible or excess keeps the first slice of each loss with the insured. A co-payment keeps a percentage of every loss. A no-claims discount keeps the cost in the future instead of the present, by making next year's premium depend on this year's claims — which also does a little classification work, because a long claim-free record is evidence about the risk as well as an incentive. Policy conditions — fit the approved lock, service the boiler, report the theft within a day — make specified care a term of the contract.

The result is the surprising part, and the worked example prices it. Because restored care means fewer real losses, there is genuinely less money being lost. In a competitive market the insurer breaks even either way, so the whole of that saving goes to the policyholder, who ends up with a lower total expected outlay than under full cover despite carrying part of each loss. The deductible is not the insurer winning an argument; it is both sides buying back something insurance had destroyed.

5Why insurance is regulated, which is the same problem running backwards

The information gap does not only run from buyer to insurer. A policyholder paying now for a promise to be kept years later cannot assess whether the promise is good: they cannot read a solvency position, and by the time the answer matters the money is gone. So the buyer faces an information problem about the insurer that they have no realistic way of solving on their own.

That is the economic case for prudential regulation — capital requirements, reserving rules, a regulator inspecting what a customer cannot. It is the same market failure as adverse selection, with the ignorant party on the other side of the table, and it is why insurance is regulated more heavily than most of what gets sold.

A worked example

An invented market, built for this page. A motor insurer covers a city with 30,000 drivers, in three equal classes of 10,000 that the insurer cannot tell apart. Every claim costs ₹50,000. Annual claim probabilities, which each driver knows about themselves, are

Each driver will buy if the premium is no more than 1.25 times their own expected cost — they will pay something for the certainty, but not without limit. All figures are illustrative and chosen for clean arithmetic.

1. 1Round 1: one premium for everybody

   The insurer prices on the population average:

   premium = (2,000 + 5,000 + 8,000) ÷ 3 = ₹5,000

   Who buys? Careful drivers will pay at most ₹2,500, and ₹5,000 is more than that, so they do not buy. Average drivers will pay up to ₹6,250, so they buy. Risky drivers will pay up to ₹10,000, so they buy.

   The insurer now holds 20,000 policies at ₹5,000 and faces the claims of the average and risky classes only:

   premium income = 20,000 × 5,000 = ₹10,00,00,000 (₹10 crore)
   expected claims = 10,000 × 5,000 + 10,000 × 8,000 = ₹13,00,00,000 (₹13 crore)
   expected loss = ₹3 crore

   Check per policy: the pool's average cost is (5,000 + 8,000)/2 = ₹6,500 against a premium of ₹5,000, so ₹1,500 is lost on each of 20,000 policies — 20,000 × 1,500 = ₹3 crore. The same figure.

2. 2Round 2: re-price for the pool that actually formed

   premium = (5,000 + 8,000) ÷ 2 = ₹6,500

   Average drivers will pay at most ₹6,250. ₹6,500 is more than that, so they now leave too. Only risky drivers remain, paying ₹6,500 against an expected cost of ₹8,000 — a loss of ₹1,500 on each of 10,000 policies, ₹1.5 crore.

3. 3Round 3: where it stops

   premium = ₹8,000

   Risky drivers will pay up to ₹10,000, so they stay. The insurer breaks even. The loop has stopped.

   And look at what is left. Two classes out of three — 20,000 of the 30,000 drivers — are uninsured. Both would have bought cover priced at their own risk: careful drivers would pay up to ₹2,500 for cover costing ₹2,000, and average drivers up to ₹6,250 for cover costing ₹5,000. Every one of those trades was wanted by both sides and none of them happened. Nobody lied, and nothing was mispriced on the information available. The market still collapsed to a third of its proper size.

4. 4The remedy: give the insurer something it can observe

   Suppose the insurer finds a factor it can verify — years of licence held, vehicle age, a telematics record — that separates the three classes. It prices each at its own expected cost:

   Class	Premium	Most they will pay	Buys?
   Careful	₹2,000	₹2,500	yes
   Average	₹5,000	₹6,250	yes
   Risky	₹8,000	₹10,000	yes

   premium income = 10,000 × (2,000 + 5,000 + 8,000) = ₹15 crore
   expected claims = the same ₹15 crore — the insurer breaks even on each class

   All 30,000 drivers are insured, and the insurer is no better off than before: it broke even at round 3 and it breaks even now. The entire gain goes to the 20,000 people who can now buy cover. The market was restored by information, not by price, and that is the mechanism the whole topic turns on.

5. 5Now moral hazard, on the risky class

   Take those 10,000 risky drivers, correctly priced at ₹8,000 for full cover. Under full cover a claim costs them nothing, so there is no reason to take care, and the claim probability stays at 16%.

   The insurer introduces a ₹10,000 deductible: the driver pays the first ₹10,000 of any claim, the insurer the remaining ₹40,000. Now a claim does cost the driver something, care becomes worth taking, and suppose the claim probability falls from 16% to 12%.

   The insurer's side.

   expected cost = 0.12 × (50,000 − 10,000) = 0.12 × 40,000 = ₹4,800

   So the competitive premium for the deductible policy is ₹4,800, down from ₹8,000.

   The driver's side. They pay the premium, and they pay the deductible whenever they claim.

   premium ₹4,800 + expected deductible 0.12 × 10,000 = 4,800 + 1,200 = ₹6,000

   ₹6,000 against ₹8,000 under full cover. The driver is ₹2,000 a year better off while carrying part of every loss, and the insurer breaks even in both cases.

6. 6Where the ₹2,000 came from

   This is the check that makes the result believable rather than a trick of the arithmetic. Count the real losses, ignoring who pays for them:

   under full cover: 0.16 × 50,000 = ₹8,000 of expected loss per driver
   under the deductible: 0.12 × 50,000 = ₹6,000 of expected loss per driver

   ₹2,000 of accidents stopped happening — exactly the saving. The money was not moved from the insurer to the driver; it was never spent, because the deductible bought back the care that full cover had removed. Across 10,000 drivers that is ₹2 crore of real losses avoided in a year.

   Two closing observations. The driver now bears risk again, which has a cost not in these figures: someone very averse to a ₹10,000 shock may rationally prefer full cover at ₹8,000, and the right deductible balances the two. And the same ₹2,000 could be delivered as a no-claims discount instead — the incentive arrives next year rather than at the moment of the claim, which is easier to bear and does some risk-classification work besides, since a long clean record is evidence as well as encouragement.

Where this fits in CB2

This page explains one idea from CB2 Business Economics. The full CB2 syllabus, with what each part is examined on, sits on the course page, and past-paper style mock exams with full solutions are where you find out whether the idea has stuck under time pressure.

Other CB2 topics explained

• Price elasticity of demand, and what it decides about a price rise
• Income and substitution effects: splitting one price change in two
• Profit maximisation and the shutdown decision, from one cost table
• Cournot and Bertrand: why the same two firms give two different answers
• National income and the multiplier: where the rest of the spending comes from
• The IS-LM model and crowding out, solved with numbers
• How monetary policy reaches the economy: the transmission mechanism

Stuck on a term rather than the idea? The actuarial glossary defines the notation used above. If something here is wrong or unclear, tell us — these pages get corrected.