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Adverse Selection The good risks drop out.

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A common story. Insurer offers a new type of policy. Hoping to make money. It loses money. Reason given: too many bad risks bought the policy. That is, adverse selection.

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What’s wrong with that story? It’s naive: Of course the bad risks want in. That’s no surprise. What matters are the good risks who didn’t buy. The answer is, usually, tighter underwriting.

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Why do the good risks drop out? High premium Why is the premium high? Too many bad risks. More good risks drop out. Vicious circle.

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The result is lack of markets Some things that aren’t insured. Results of medical tests. Private health insurance gaps. Financial markets in less developed countries.

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Static adverse selection Asymmetric information Hidden values (moral hazard was hidden actions)

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Information asymmetry is key The client knows his risk. The insurer doesn’t know the client’s risk, but it knows the situation.

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Story of a house It’s worth $1000. Probability of loss is between 0 and.002. Fair premium is between zero and two dollars.

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Notation x is probability of loss, x on [0,2]. This x is in thousandths. P is the market price of insurance, between 0 and 2 thousandths. f(x) is the probability density function of risk. f(x)=.5 on [0,2] E(x) is expected probability of loss, =1

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Adverse selection: given market price P Assumed behavior: consumers with risks of.5P and above buy insurance. They will pay no more than twice the fair price. The good risks, x<.5P, drop out.

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Result: more notation f(x|P) is probability density function of risk, given market price P. f(x|P) = 1/(2-.5P). E(x|P) is expected risk given market price P. E(x|P) =.5(.5P)+.5(2) = 1+.25P

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Probability density.5 0 2 1 = E(x) f(x)=.5 Expected loss 1+.25P = E(x|P) f(x|P)=1/(2-.5P).5P

14 Insurers response E(x|P)>P Exit or raise price. E(x|P)

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P Exit or raise price. E(x|P)

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The market clears When E(x|P)=P. 1+.25P=P P=4/3. Risks from [0,2/3] (the good risks) are not insured. Lost profit opportunity. Market failure.

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Solutions To capture profit and eliminate market failure... Underwrite carefully. Use separating contracts.

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George Akerlof Writing about financial markets in less developed countries. Why there are none (circa 1971). Illustrating with used cars.

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Market for lemons. A lemon is a car that is prodigiously prone to needing repair. Used cars.

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Nightmare You are about to pay someone $10K for his used car. He knows the car, you don’t. He prefers the $10K. Shouldn’t you do likewise.

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Keys to adverse selection The seller knows the quality. The buyer doesn’t. That is asymmetric information or hidden value.

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Notation x is the quality of the car. On [0,2] P is the market price. f(x) is the probability density function of quality. f(x)=.5 on [0,2] E(x) is the expected quality. =1

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More notation f(x|P) is probability density function of quality, given market price P. f(x|P)=1/P. E(x|P) is expectation of quality given market price P. E(x|P)=P/2

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Probability density.5 0 2 1 =expectation f(x)=.5 P f(x|P)=1/P P/2 =conditional expectation Quality of car

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Buyers like cars more than sellers If quality is x, seller will accept x dollars. If expected quality is x, the buyer will pay 1.5x dollars.

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The market does not exist Suppose there is a market with price P (we’ll see that that can’t be). Cars of quality 0

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Nonexistence theory Unfamiliar. Important.

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Markets that do exist Solve adverse selection through careful underwriting … or separating contracts.

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Solutions Get an inspection. Get a warrantee. Either way, informational asymmetry is removed.

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