Moral Hazard in Insurance Markets

1
Moral Hazard in Insurance Markets

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

2
Plan

• Information Problem
• How does hidden action enter insurance markets?
• Requirements for Moral Hazard
• Possible Remedies
• Legal Doctrines
• Contract Provisions
• Example
• Movie and Discussion

3
Introduction

• Moral hazard (Hidden Action )
• The situation where an insurance policy affects
  an insureds incentive to reduce insurable
  losses.
• Examples
• Franchises
• Partnerships
• Students

4
Requirements

• Action must affect the distribution of indemnity
• Example Health Insurance
• Action must be costly or impossible to observe
• Example Workers Comp. and Loss Control

5
Types of Moral Hazard

• Ex-ante moral hazard
• refers to incentive for insureds to reduce
  activity that affects the likelihood of insurance
  claims
• Ex-post moral hazard
• refers to the incentive for insureds to choose
  actions that affect the size of an insurance
  claim, given that the loss has already occurred.

6
Remedies Legal Doctrine

• Indemnity Principle
• Limits indemnity to amount of financial loss
• Valued Contracts
• Fix indemnity amount ex ante
• Insurable Interest
• P-holder must suffer financial consequences

7
Remedies Contract Provisions

• Policy Exclusions
• Indemnity Structure
• Partial insurance contract to align incentives
• Deductible
• Coinsurance
• Upper Limit

8
Example

• 2 Players
• One Monopolist Insurer - Maximizes Profits
• One Insured - Max Expected Utility U(W) 2W .5
• Parameters
• Loss Distribution under Control of Insured
• Insured can Spend 0 or 50,000 on Loss Control
• Initial Wealth 1M
• Assumptions The loss control spending of the
  insured is not observable by the insurance
  company.

9
Example (Continued)

• Moral Hazard Example Set-Up
• Low-Spending
  High-Spending
• Initial Wealth 1,000,000
  1,000,000
• Loss Control Costs 0
  50,000
• Potential Loss Amt 500,000
  500,000
• Probability of Loss 50
  20

10
Example (Continued)

• Benchmark Full Information
• Assume loss control spending is specified in the
  insurance contract
• Full Insurance
• Premium is Maximum Willingness to Pay

11
Example (Continued)

• Low Effort and No Insurance
• State Prob InitialW Loss
  Control FinalW U(W)
• No Loss .50 1M 0
  0 1M 2,000.0
• Loss .50 1M .5M
  0 .5M 1,414.2
• Expected .25M
  1,701.1
• High Effort and No Insurance
• State Prob InitialW Loss
  Control FinalW U(W)
• No Loss .80 1M 0
  50K .95M 1,949.4
• Loss .20 1M .5M
  50K .45M 1,341.6
• Expected .10M
  1,827.8

12
Example (Continued)

• Low effort
• Yielding
• High risks
• Yielding

13
Example (Continued)

• Perfect Information Policy Offerings
• Low Effort High
  Effort
• Premium Amt 164,773
  114,773
• Indemnity for 500k Loss 500,000
  500,000
• Prob of Paying Indemnity 50
  20
• Expected Indemnity 250,000
  100,000
• Expected Profit -85,227
  14,773
• Maximum Expected Profit 14,773

14
Example (Continued)

• Moral Hazard and Full Insurance
• Full Insurance Policy
• Premium Amount 164,773
• Indemnity for 500,000 Loss 500,000
• Loss Control Chosen LOW
• Prob of Paying Indemnity 50
• Expected Indemnity 250,000
• Expected Profit - 85,227

15
Example (Continued)

• The Coinsurance Alternative
• Insurer only offers a partial insurance contract.
• Policy coinsurance of 40 and premium of 70,000
• Indemnity for 500,000 loss is 300,000.

16
Example (Continued)

• Low Level of Loss Control and Coinsurance
• State Prob InitialW Loss Control
  FinalW U(W)
• No Loss .50 1M 0 0
  .93M 1,928.7
• Loss .50 1M .5M 0
  .73M 1,708.8
• Expected
  1,818.8
• High Level of Loss Control and Coinsurance
• State Prob InitialW Loss Control
  FinalW U(W)
• No Loss .80 1M 0 50K
  .88M 1,876.2
• Loss .20 1M .5M 50K
  .68M 1,649.2
• Expected
  1,830.8

17
Example (Continued)

• Moral Hazard and Coinsurance
• Premium Amount
  70,000
• Indemnity for 500k Loss 300,000
• Loss Control Chosen HIGH
• Probability of Paying Indemnity 20
• Expected Indemnity
  60,000
• Expected Profit
  10,000

18
Example (Continued)

• Optimal Policy is Partial Insurance
• Insured can be induced to spend on loss control.
• Reduction in premium to reflect loss control.
• Less profits than full information case (10,000 lt
  14,773)
• Both the insurer and the insured benefit from
  moving to partial insurance

19
Example (Continued)

• Costly Monitoring
• Spend C to perfectly observe loss control
• Monopolist offers full insurance at the maximum
  premium that the insured will pay.
• The insurer demands 50,000 loss control at a
  premium of 114,773.

20
Example (Continued)

• Moral Hazard and Costly Monitoring
• Premium Amount
  114,773
• Indemnity for 500k Loss
  500,000
• Loss Control Chosen
  HIGH
• Probability of Paying Indemnity
  20
• Expected Indemnity
  100,000
• Monitoring Cost
  C
• Expected Profit
  14,773-C

21
Conclusions

• Moral Hazard and Adverse Selection
• Contractual Provisions
• Bulk pack Readings
• Akerloff
• Rothschild and Stiglitz