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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.

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Presentation on theme: "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."— Presentation transcript:

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2 Adverse Selection The good risks drop out.

3 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.

4 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.

5 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.

6 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.

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

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

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

10 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

11 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.

12 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

13 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)

{ "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/13/3842344/slides/slide_14.jpg", "name": "Insurers response  E(x|P)>P Exit or raise price.  E(x|P)

P Exit or raise price.  E(x|P)


15 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.

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

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

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

19 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.

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

21 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

22 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

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

24 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.

25 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 { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/13/3842344/slides/slide_25.jpg", "name": "The market does not exist  Suppose there is a market with price P (we’ll see that that can’t be).", "description": " Cars of quality 0

26 Nonexistence theory  Unfamiliar.  Important.

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

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

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