adverse selection

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?

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.

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.

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.

Static adverse selection

Asymmetric information

Hidden values (moral hazard was hidden actions)

Information asymmetry is key

The client knows his risk.

The insurer doesn’t know the client’s risk, but it knows the situation.

Story of a house

It’s worth $1000.

Probability of loss is between 0 and .002.

Fair premium is between zero and two dollars.

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

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.

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

Probabilitydensity

.5

0 2

1= E(x)

f(x)=.5

Expected loss

1+.25P = E(x|P)

f(x|P)=1/(2-.5P)

.5P

Insurers response

E(x|P)>P Exit or raise price. E(x|P)<P Enter or lower price.

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.

Solutions

To capture profit and eliminate market failure...

Underwrite carefully. Use separating contracts.

George Akerlof

Writing about financial markets in less developed countries.

Why there are none (circa 1971). Illustrating with used cars.

Market for lemons.

A lemon is a car that is prodigiously prone to needing repair.

Used cars.

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.

Keys to adverse selection

The seller knows the quality. The buyer doesn’t. That is asymmetric information or

hidden value.

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

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

Probabilitydensity

.5

0 2

1=expectation

f(x)=.5

P

f(x|P)=1/P

P/2=conditionalexpectation

Quality of car

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.

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.

Nonexistence theory

Unfamiliar. Important.

Markets that do exist

Solve adverse selection through careful underwriting …

or separating contracts.

Solutions

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

removed.