Adverse Selection in Insurance Markets

1
Adverse Selection in Insurance Markets

• INSR 205/Spring 2000
• Pierre Lemaire
• The Wharton School
• University of Pennsylvania

2
Plan

• Discuss Market for Chocolate Pot Pies
• How does hidden information enter insurance
  markets?
• Requirements for Adverse Selection
• Possible Remedies
• Classification
• Legal Doctrines
• Contract Provisions
• Big Example
• Public Policy Issue

3
Introduction

• Adverse selection (Hidden Action)
• The situation where the consumer possesses
  private information over the insurance company.
• Examples
• Employees of a firm
• Bond issuers
• A regulated monopoly

4
Requirements

• Private information must affect the distribution
  faced by the insurer
• Example Health Insurance
• Information must be costly or impossible for the
  insurer to observe
• Example Automobile Insurance

5
Remedies

• Classification
• Identification of loss distribution for each
  insured
• Premium accurately reflects expected losses
• Underwriting
• Risk classification
• Assess the expected claims costs for the insured
• Decide whether to offer insurance coverage
• Set premium for the coverage
• Premiums
• Based on the characteristics of the insured
• prior claims experience of the insured

6
Remedies

• Schedule rating
• Process of modifying premiums based on
  particular insured characteristics.
• Conditions of business premises and property
• Existence of safety programs
• Background of employees
• Experience rating
• Practice of basing premiums on claim history.

7
Remedies Legal Doctrine

• Law governing insurance transactions requires
  negotiation with utmost good faith.
• Misrepresentation
• Lying about a material fact
• Concealment
• Failure to offer information

8
Remedies Contract Provisions

• Policy Exclusions
• Provisions that exclude coverage for particular
  types of losses.
• Indemnity Function
• Menu of partial insurance contracts to induce
  insureds to voluntarily disclose their risk type.
  
• Deductible
• Coinsurance
• Upper Limit

9
Example

• Two Types of Insureds
• High-Risk
• Low-Risk
• 1/2 of Population is Low-Risk
• 1/2 is High-Risk U(W) 4W .25
• Loss Distribution Varies by Type
• Initial Wealth 1M
• Assumption The risk type is private information

10
Example (Continued)

• Adverse Selection Example Set-Up
• Low-Risks High-Risks
• Percentage of Pop. 50 50
• Initial Wealth 1,000,000 1,000,000
• Potential Loss Amt 750,000
  750,000
• Probability of Loss 10
  15

11
Example (Continued)

• Low-Risk and No Insurance
• State Prob InitialW Loss FinalW
  U(W)
• NoLoss .90 1M 0 1M
  126.5
• Loss .10 1M .75M .25M
  89.4
• Expected 122.8
• High-Risk and No Insurance
• State Prob InitialW Loss FinalW
  U(W)
• NoLoss .85 1M 0 1M
  126.5
• Loss .15 1M .75M .25M
  89.4
• Expected 120.9

12
Example (Continued)
Low-Risks
Yielding High-Risks Yielding
13
Example (Continued)

• Perfect Information Policy Offerings
• Low-Risk Policy
  High-Risk Policy
• Premium Amt 112,110
  164,490
• Indemnity for 750k Loss 750,000
  750,000
• Prob. of Paying Indemnity 10
  15
• Expected Indemnity 75,000
  112,500
• Expected Profit 37,110
  51,990
• Percentage of Pool 50
  50
• Total Expected Profit 44,550

14
Example (Continued)

• For low-risks, the insurer makes
• For high-risks, profit is
• Total expected profit is

15
Example (Continued)

• Asymmetric Info and Pooling Alternative
• Risk type is private information to the insured.
• Above contracts not equilibrium
• Pooling Policy
• Insurer offers full insurance and charges
  164,490
• This premium level is acceptable to only Highs
• Low-risks driven out (see BP Akerloff)

16
Example (Continued)

• Hidden Information and a Pooling Policy
• Low-Risk
  High-Risk
• Premium Amt 164,490
  164,490
• Indemnity for 750k Loss -
  750,000
• Prob. of Paying Indemnity 10
  15
• Expected Indemnity -
  112,500
• Expected Profit -
  25,995
• Percentage of Pool -
  100
• Total Expected Profit 25,995

17
Example (Continued)

• Asymmetric Info and Separating Alternative
• Two separate policies with different
  indemnities and premiums
• Policy 1 has a deductible of 500,000 and
  premium 50,000.
• Policy2 offers full insurance for a price of
  140,000.
• Self-Selection
• Insureds volunteer their private information
• Low-risk types prefer the deductible policy
• High-risk types prefer the full insurance policy

18
Example (Continued)

• Low Risk and Deductible Policy
• State Prob InitialW Loss FinalW
  U(W)
• NoLoss .9 1M 0 .95M
  124.9
• Loss .1 1M .75M .45M
  103.6
• Expected
  122.8
• Low Risk and Full Insurance Policy
• State Prob InitialW Loss FinalW
  U(W)
• NoLoss .9 1M 0 .86M
  121.8
• Loss .1 1M .75M .86M
  121.8
• Expected
  121.8

19
Example (Continued)

• High Risk and Deductible Policy
• State Prob InitialW Loss FinalW
  U(W)
• NoLoss .85 1M 0 .95M
  124.9
• Loss .15 1M .75M .45M
  103.6
• Expected
  121.7
• High Risk and Full Insurance Policy
• State Prob InitialW Loss FinalW
  U(W)
• NoLoss .85 1M 0 .86M
  121.8
• Loss .15 1M .75M .86M
  121.8
• Expected
  121.8

20
Example (Continued)

• Asymmetric Info and Separating Alternative
• Low-risks prefers the deductible policy to no
  insurance and the full insurance policy
• High-risks prefer the full insurance to no
  insurance and deductible policy.
• The insurance company induces Self-Selection.

21
Example (Continued)

• Hidden Information and Separating Policies
• Low-Risk
  High-Risk
• Premium Amt 50,000
  140,000
• Indemnity for 750k Loss 250,000
  750,000
• Prob. of Paying Indemnity 10
  15
• Expected Indemnity 25,000
  112,500
• Expected Profit 25,000
  27,500
• Percentage of Pool 50
  50
• Total Expected Profit 26,250

22
Example (Continued)

• Costly Monitoring
• Spend C to perfectly identify type
• Monopolist offers full insurance at the maximum
  premium that the insured will pay.
• These premium levels
• 112,110 for low-risks
• 164,490 for high-risks.

23
Example (Continued)

• Hidden Information and Costly Classification
• Low-Risk
  High-Risk
• Premium Amt 112,110
  164,490
• Indemnity for 750k Loss 750,000
  750,000
• Prob of Paying Indemnity 10
  15
• Expected Indemnity 75,000
  112,500
• Classification Cost C
  C
• Expected Profit 37,110-C
  51,990-C
• Percentage of Pool 50
  50
• Total Expected Profit 44,550 - C

24
Risk Classification

• Risk Classification
• Counter Arguments
• Mandatory Insurance
• Location
• Inherited Traits
• Subjective Criteria
• Consideration
• Income Redistribution
• Market Failure
• Transaction Costs
• Behavioral Effects

25
Conclusions

• Asymmetric Information in Insurance
• Separating Equilibrium
• Additional Readings
• Rothschild and Stiglitz