adverse selection
DESCRIPTION
Adverse Selection. The good risks drop out.. 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. What’s wrong with that story?. - PowerPoint PPT PresentationTRANSCRIPT
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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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Probabilitydensity
.5
0 2
1= E(x)
f(x)=.5
Expected loss
1+.25P = E(x|P)
f(x|P)=1/(2-.5P)
.5P
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Insurers response
E(x|P)>P Exit or raise price. E(x|P)<P Enter or lower price.
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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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Probabilitydensity
.5
0 2
1=expectation
f(x)=.5
P
f(x|P)=1/P
P/2=conditionalexpectation
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<x<P are offered. Expected quality is P/2. The buyers will pay 1.5 times P/2. Or 3/4 times P. Therefore P cannot be the market price. And that is true for any P.
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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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