Frank Cowell: Microeconomics Moral Hazard MICROECONOMICS Principles and Analysis Frank Cowell Almost essential Risk Almost essential Risk Prerequisites June 2004

Frank Cowell: Microeconomics The moral hazard problem A key aspect of hidden information A key aspect of hidden information Information relates to actions. Information relates to actions. Hidden action by one party affects probability of favourable/unfavourable outcomes. Hidden action by one party affects probability of favourable/unfavourable outcomes.  Hidden information about personal characteristics is dealt with... ... under “adverse selection.” ... under “signalling.” However similar issues arise in setting up the economic problem. However similar issues arise in setting up the economic problem. Set-up based on model of trade under uncertainty. Set-up based on model of trade under uncertainty. Jump to “Adverse selection” Jump to “Signalling”

Frank Cowell: Microeconomics Overview... The basics A simplified model The general model Moral Hazard Information: hidden-actions model

Frank Cowell: Microeconomics Key concepts Contract: Contract:  An agreement to provide specified service…  …in exchange for specified payment  Type of contract will depend on information available. Wage schedule: Wage schedule:  Set-up involving a menu of contracts  The Principal draws up the menu  Allows selection by the Agent  Again the type of wage schedule will depend on information available Events: Events:  Assume that events consist of single states-of-the-world  Distribution of these is common knowledge  But distribution may be conditional on the Agent’s effort

Frank Cowell: Microeconomics Strategic foundation A version of a Bayesian game. A version of a Bayesian game. Two main players Two main players  Alf is the Agent.  Bill is the Boss (the Principal) An additional player An additional player  Nature is “player 0”  Chooses a state of the world Bill does not observe what this is... Bill does not observe what this is...

Frank Cowell: Microeconomics Principal-and-Agent: extensive- form game 0 [RED][BLUE]  Bill Alf [NO] [OFFER] [high] [NO] [OFFER] Alf [low][high][low]   "Nature" chooses a state of the world   Probabilities are common knowledge   Principal may offer a contract, not knowing the type   Agent chooses whether to accept contract

Frank Cowell: Microeconomics Extension of trading model Start with trading model under uncertainty Start with trading model under uncertainty  There are two states-of-the world  So exactly two possible events  Probabilities of the two events are common knowledge Assume: Assume:  A single physical good…  …so consumption in each state-of-the world is a distinct “contingent good”.  Two traders Alf, Bill CE in Edgeworth box determined as usual: CE in Edgeworth box determined as usual:  Draw a common tangent through the endowment point.  Gives equilibrium prices and allocation But what happens in noncompetitive world? But what happens in noncompetitive world?  Suppose Bill can completely exploit Alf

Frank Cowell: Microeconomics Trade:  common knowledge OaOa ObOb x RED a b x BLUE b a   Certainty line for Alf   Alf's indifference curves   Certainty line for Bill   Bill's indifference curves   Endowment point   CE prices + allocation  RED – ____  BLUE  RED – ____  BLUE  RED – ____  BLUE  RED – ____  BLUE   Alf's reservation utility   If Bill can exploit Alf...

Frank Cowell: Microeconomics Outcomes of trading model CE solution as usual potentially yields gains to both parties CE solution as usual potentially yields gains to both parties Exploitative solution puts Alf on reservation indifference curve Exploitative solution puts Alf on reservation indifference curve Under CE or full-exploitation there is risk sharing Under CE or full-exploitation there is risk sharing  Exact share depends on risk aversion of the two parties. What would happen if Bill, say, were risk neutral? What would happen if Bill, say, were risk neutral?  Retain assumption that  is common knowledge  We just need to alter the b-indifference curves The special case

Frank Cowell: Microeconomics Trade: Bill is risk neutral OaOa ObOb x RED a b x BLUE b a   Certainty line for Alf   Alf's indifference curves   Certainty line for Bill   Bill's indifference curves   Endowment point   CE prices + allocation  RED – ____  BLUE  RED – ____  BLUE   Alf's reservation utility   If Bill can exploit Alf...

Frank Cowell: Microeconomics Outcomes of trading model (2) Minor modification yields clear-cut results Minor modification yields clear-cut results Risk-neutral Bill bears all the risk Risk-neutral Bill bears all the risk  So Alf is on his certainty line Also if Bill has discriminatory monopoly power Also if Bill has discriminatory monopoly power  Bill provides Alf with full insurance  But gets all the gains from trade for himself This forms the basis for the elementary model of moral hazad. This forms the basis for the elementary model of moral hazad.

Frank Cowell: Microeconomics Overview... The basics A simplified model The general model Moral Hazard Lessons from the 2x2 case

Frank Cowell: Microeconomics Outline of the problem Bill employs Alf to do a job of work Bill employs Alf to do a job of work The outcome to Bill (the product) depends on The outcome to Bill (the product) depends on  A chance element  The effort put in by Alf Alf's effort affects probability of chance element. Alf's effort affects probability of chance element.  High effort – high probability of favourable outcome  Low effort – low probability of favourable outcome The issues are: The issues are:  Does Bill find it worth while to pay Alf for high effort?  Is it possible to monitor whether high effort is provided?  If not, how can Bill best construct the contract? Deal with the problem in stages Deal with the problem in stages

Frank Cowell: Microeconomics Simple version – the approach Start with simple case Start with simple case  Two unknown events  Two levels of effort Build on the trading model Build on the trading model  Principal and Agent are the two traders  But Principal (Bill) has all the power  Agent (Alf) has the option of accepting/rejecting the contract offered. Then move on to general model Then move on to general model  Continuum of unknown events.  Agent has general choice of effort level

Frank Cowell: Microeconomics Power: Principal and Agent Because Bill has power: Because Bill has power:  Can set the terms of the contract ...constrained by the Alf’s option to refuse  Can drive Alf down to reservation utility If the effort supplied is observable: If the effort supplied is observable:  Contract can be conditioned on effort: w(z)  Get all the insights from the trading model Otherwise: Otherwise:  Have to condition on output: w(q)

Frank Cowell: Microeconomics The 2  2 case: basics A single good A single good Amount of output q is a random variable Amount of output q is a random variable Two possible outcomes Two possible outcomes  Failure q – _  Success q Probability of success is common knowledge: Probability of success is common knowledge:  given by  (z)  z is the effort supplied by the agent The Agent chooses either The Agent chooses either  Low effort z _  High effort z

Frank Cowell: Microeconomics The 2  2 case: motivation The Agent's utility derives from The Agent's utility derives from  consumption of the single good x a (  )  the effort put in, z (  )  Given vNM preferences utility is E u a (x a, z). The Agent is risk averse The Agent is risk averse  u a (, ) is strictly concave in its first argument The Principal consumes all output not consumed by Agent The Principal consumes all output not consumed by Agent  x b = q – x a (In the simple model) Principal is risk neutral (In the simple model) Principal is risk neutral  Utility is E q – x a Can interpret this in the trading diagram Can interpret this in the trading diagram

Frank Cowell: Microeconomics Low effort OaOa ObOb x RED a b x BLUE b a  RED – ____  BLUE  RED – ____  BLUE ObOb   Certainty line for Alf (Agent)   Alf's indifference curves   Certainty line for Bill   Bill's indifference curves   Endowment point   Alf's reservation utility   If Bill exploits Alf then outcome is on reservation IC,  a   If Bill is risk- neutral and Alf risk averse then outcome is on Alf's certainty line. aa Switch to high effort

Frank Cowell: Microeconomics High effort OaOa ObOb x RED a b x BLUE b a ObOb ObOb   Certainty line and indifference curves for Alf   Certainty line and indifference curves for Bill   Endowment point   Alf's reservation utility  RED – ____  BLUE  RED – ____  BLUE   High effort tilts the ICs, shifts the equilibrium outcome.   Contrast with low effort Combine to get menu of contracts

Frank Cowell: Microeconomics Full information: max problem The Agent's consumption is determined by the wage paid. The Agent's consumption is determined by the wage paid. The Principal chooses a wage schedule... The Principal chooses a wage schedule...  w = w(z)...subject to the participation constraint:...subject to the participation constraint:  E u a (w,z)   a. So, problem is choose w() to maximise So, problem is choose w() to maximise  E q – w + [ E u a (w,z) –  a ] Equivalently Equivalently _  Find w(z) that maximise  (z) q + [1 –  (z)] q – w(z)... _ ... for the two cases z = z and z = z.  Choose the one that gives higher expected payoff to Principal

Frank Cowell: Microeconomics Full-information contracts OaOa ObOb x RED a b x BLUE b a – w(z)w(z) q – – w(z)w(z) – w(z)w(z) – w(z)w(z) – q   Alf's low-effort ICs   Alf's high-effort ICs   Bills ICs   Low-effort contract   High-effort contract

Frank Cowell: Microeconomics Full-information contracts: summary Schedule of contracts for high and low effort Schedule of contracts for high and low effort  Effort is verifiable Contract specifies payment in each state-of-the-world Contract specifies payment in each state-of-the-world State-of-the-world is costlessly and accurately observable State-of-the-world is costlessly and accurately observable  Equivalent to effort being costlessly and accurately observable Alf (agent) is forced on to reservation utility level Alf (agent) is forced on to reservation utility level Efficient risk allocation Efficient risk allocation  Bill is risk neutral  Alf is risk averse  Bill bears all the risk

Frank Cowell: Microeconomics Second best: principles Utility functions Utility functions  As before Wage schedule Wage schedule  Because effort is unobservable… ...cannot condition wage on effort or on the state-of-the-world.  But resulting output is observable... ... so you can condition wage on output Participation constraint Participation constraint  Essentially as before  (but we'll have another look) New incentive-compatibility constraint New incentive-compatibility constraint  Cannot observe effort  Agent must get the utility level attainable under low effort Maths formulation

Frank Cowell: Microeconomics Participation constraint The Principal can condition the wage on the observed output: The Principal can condition the wage on the observed output: _ _ _ _  Pay wage w if output is q Agent will choose high or low effort. Agent will choose high or low effort.  This determines the probability of getting high output ...and so the probability of getting a high wage. Let's assume he would choose high effort Let's assume he would choose high effort  (check this out in next slide) To ensure that Agent doesn't reject the contract... To ensure that Agent doesn't reject the contract......must get the utility available elsewhere:...must get the utility available elsewhere: _ _ _ _ _ _ _ _ _ _   (z) u a (w, z) + [1 –  (z)] u a (w, z)   a

Frank Cowell: Microeconomics Incentive-compatibility constraint Assume that the Agent will actually participate Assume that the Agent will actually participate _ _ _ _  Pay wage w if output is q Agent will choose high or low effort. Agent will choose high or low effort. To ensure that high effort is chosen, set wages so the following holds: To ensure that high effort is chosen, set wages so the following holds: _ _ _ _ _ _ _ _ _ _   (z) u a (w, z) + [1 –  (z)] u a (w, z)  _ _ _ _  (z) u a (w, z) + [1 –  (z)] u a (w, z)  (z) u a (w, z) + [1 –  (z)] u a (w, z) This condition determines a set of w-pairs This condition determines a set of w-pairs  a set of contingent consumptions for Alf  must not reward Alf too highly if failure is observed

Frank Cowell: Microeconomics Second-best contracts OaOa ObOb w – – w x RED a b x BLUE b a   Alf's low-effort ICs   Bills ICs   Alf's high-effort ICs   Bills ICs   Full-information contracts   Participation constraint   Incentive-compatibility constraint aa   Second-best contract   Bill’s second-best feasible set   Contract maximises Bill’s utility over second-best feasible set

Frank Cowell: Microeconomics Simplified model: summary Participation constraint Participation constraint  Set of contingent consumptions giving Alf his reservation utility.  If effort is observable get one such constraint for each effort level Incentive compatibility constraint Incentive compatibility constraint  Relevant for second-best policy.  Set of contingent consumptions such that Alf prefers to provide high effort.  Implemented by making wage payment contingent on output Intersection of these two sets gives feasible set for Bill Intersection of these two sets gives feasible set for Bill Outcome depends on information regime Outcome depends on information regime  Observable effort: Bill bears all the risk  Moral hazard: Alf bears some risk