The Moral Hazard Problem Stefan P. Schleicher University of Graz Economics of Information Incentives and Contracts Chapter 3 The Moral Hazard Problem Stefan P. Schleicher University of Graz

1. Introduction (1) Asymmetric information creates incentive to use information advantage Moral hazard problem Agent has information advantage since his effort is not observable

A supplies non-verifiable effort N determines state of the world 1. Introduction (2) P designs the contract A accepts (or rejects) A supplies non-verifiable effort N determines state of the world Outcome and pay-offs Agent’s action is not verifiable or agent receives private information after the relationship has been initiated Informational asymmetry after the contract has been signed Examples Labor market, research project Automobile insurance

1. Introduction (3) Under a fixed wage contract the agent will always choose the smallest possible effort. Therefore the principal will choose a wage which exactly compensates the agent for this effort.

2. The Moral Hazard Problem (1) Asymmetric information with respect to effort Effort is not verifiable Solution concept Subgame perfect equilibrium

2. The Moral Hazard Problem (2) Stage 3: Agent chooses his effort Incentive restriction or Incentive compatibility constraint

2. The Moral Hazard Problem (3) Stage 2: Agent decides about acceptance of the contract proposed by the principal Participation constraint or Individual rationality condition

2. The Moral Hazard Problem (4) Stage 1: Principal designs the contract, anticipating the agent’s behaviour [P3.1]

3. Agent chooses between two effort levels (1) Risk-averse agent can choose between only two effort levels, H high L low Efforts and disutilities

3. Agent chooses between two effort levels (2) Ordered set of results Probability of outcome i under high or low effort pH first order stochastically dominates pL (bad results are more likely under lower effort)

3. Agent chooses between two effort levels (3) (1) Principal demands low effort eL Wage that guarantees reservation utility sufficient No true moral hazard problem exists. Symmetric information contract continues to be optimal.

3. Agent chooses between two effort levels (4) (2) Principal demands high effort eH Wage needs to depend on outcome Expected utility gain for agent must be greater than the implied increase in disutility.

3. Agent chooses between two effort levels (5) Principal solves

3. Agent chooses between two effort levels (6) Lagrangean

3. Agent chooses between two effort levels (7) First-order conditions

3. Agent chooses between two effort levels (8) Shadow price of participation restriction Shadow price of incentive restriction Wage will be larger the smaller the likelihood ratio and this will induce larger effort

3. Agent chooses between two effort levels (9) Wage will be larger the smaller the likelihood ratio and this will induce larger effort

4. Solution using the first-order approach (1) Attempt to handle effort as a continuous variable replaced by first-order condition

4. Solution using the first-order approach (2) Modified optimization problem of the principal [P3.2]

4. Solution using the first-order approach (3) First-order conditions w.r.t. w(xi)

4. Solution using the first-order approach (4) Wages increiase with increasing likelihood quotient (with high probability a good effort was exerted)

5. A simple case with continuous effort Probability function of the agent’s effort Condition of linearity of the distribution function Can be solved by the first-order approach

6. Moral Hazard with hidden information After contract is agreed upon the agent obtains information on the environment that will determine which effort level is the most adequate. This information is not observable or not verifiable by the principal. P designs the contract A accepts (or rejects) N determines state of the world which is only observed by A A supplies effort Outcome and pay-offs

7. Some comments on simple Moral Hazard models (1) 7.1 The value of information Loss of informtion about the agent’s effort implies a cost to the principal-agent relationship. Principal is interested in any signals that reveal information on the agent’s effort. Therefore, the contract can contain many contingencies, e.g. state of nature. The sufficient statistic result.

7. Some comments on simple Moral Hazard models (2) The sufficient statistic result. A contract should exploit all available information in order to filter out risk optimally. Principal may want to pay for control activities.

7. Some comments on simple Moral Hazard models (3) 7.2 Mechanisms based on severe punishments For results that are a perfect signal that the demanded effort was not excerted. The threat should be sufficient. Should lower the costs of controls.

7. Some comments on simple Moral Hazard models (4) 7.3 The stratigic effects of contracts Relevant, if contract effects third parties. Then the contract is not only an incentive device but also an instrument to influence the behavior of third parties.

7. Some comments on simple Moral Hazard models (5) 7.4 What happens when it is the agent who offers the contract If the agent designs the contract, he must take into account the fact that the pricipal will only accept believable contracts. The only difference – the pricipal instead of the agent – is put at her reservation utility level.

B.1 Incentives for managers (1) Objective of the shareholdes is to maximize profits, and this depends on the effort of the managers. Shareholders hire managers. The shareholders cannot control the effort of the managers.

B.1 Incentives for managers (2) Manager’s utility Shareholder’s profits Density distribution of sales

B.1 Incentives for managers (3) (1) Symmetric information Shareholder problem

B.1 Incentives for managers (4) First-order conditionj w.r.t. w(x) w(x) is constant

B.1 Incentives for managers (5) Rewritten shareholder problem First-order conditionj w.r.t. e

B.1 Incentives for managers (6) (2) Asymmetric information Shareholder problem

B.1 Incentives for managers (7) First-order condition w.r.t. w(x) Managers’ wages w(x) increase with sales x and the likelihood quotient (indicator for agent’s efforts).