Moral Hazard. Economics Microeconomic Theory II: Strategic Behavior. Instructor: Songzi Du

Transcription

1 Moral Hazard Economics Microeconomic Theory II: Strategic Behavior Instructor: Songzi Du compiled by Shih En Lu (Chapter 25 in Watson (2013)) Simon Fraser University July 9, 2018 ECON 302 (SFU) Lecture 9 July 9, / 17

2 Objectives 1 Understand what moral hazard is. 2 Know how to find the first-best outcome. 3 Know how to set up the second-best problem, and how to solve it in simple cases. 4 Understand the economic intuition behind the above procedures. 5 Understand how moral hazard results in inefficiency ECON 302 (SFU) Lecture 9 July 9, / 17

3 Moral Hazard Increased risk ( hazard ) of bad ( immoral ) behaviour due to unobserved and/or unverifiable actions. Hidden action: what happens when one side of the market doesn t observe what the other side does. Hidden action can lead to moral hazard: informed side might engage in bad behaviour. Moral hazard in agency slack off because your boss doesn t observe your effort. If actions were observed and verifiable, the problem would go away: can condition pay on effort. ECON 302 (SFU) Lecture 9 July 9, / 17

4 Moral Hazard in Agency Parties sign a contract/agreement, but their interests diverge and some actions are not contractible (because those actions are not observable, or not verifiable). The agent will engage in opportunistic behaviour if what he/she does doesn t impact pay. Need to provide incentives by contracting on an observable and verifiable outcome that correlates with the hidden actions. This is part of why we have various forms of performance pay: commissions, piece rates, bonuses, stock options, penalties for bad performance, etc. ECON 302 (SFU) Lecture 9 July 9, / 17

5 Example Two parties: an agent/employee (A) and a principal/employer (P) P hires A to work on a project, which can be a success (s = 1) or a failure (s = 0) A can exert effort (e = 1) or slack off (e = 0) A has utility u(w) e = w e, where w is her wage, normalized so that her outside option gives utility 0. P is risk-neutral, and therefore has utility sv w, where V is the value of a successful project. P s outside option is cancel the project and get 0. When A exerts effort, the project succeeds with probability p > 0; otherwise, it fails. ECON 302 (SFU) Lecture 9 July 9, / 17

6 Socially Optimal Outcome (I) What outcome is best socially if we didn t have an information problem? If A and P take their outside options, they both get 0. If A works for P and slacks off, they get w and w respectively. Obviously, we need w = 0 for both parties to be willing, so we re back to 0 and 0. ECON 302 (SFU) Lecture 9 July 9, / 17

7 Socially Optimal Outcome (II) If A works for P and exerts effort, they get w 1 and pv w respectively. When pv > 1, we can set w (1, pv ) and make both P and A better off. In other words, if the project is sufficiently valuable and likely to succeed, any Pareto efficient outcome must involve A working for P and exerting effort. What if pv < 1? ECON 302 (SFU) Lecture 9 July 9, / 17

8 Optimal Risk-Sharing We assumed that conditional on effort, P pays A a fixed wage. Why is that socially optimal? Effective benefit of compensation scheme to A is its certainty equivalent CE. If the wage weren t fixed, then CE < E[w] because A is risk-averse. But P is risk-neutral, so the effective cost of the compensation scheme is E[w]. Therefore, can create Pareto improvement by moving to a fixed wage between CE and E[w]. In a nutshell: when a risk-neutral and a risk-averse agent share risk, the risk-neutral agent must bear all risk in any Pareto efficient outcome (absent other considerations). ECON 302 (SFU) Lecture 9 July 9, / 17

9 Principal s First-Best Outcome Let s keep our assumption that we don t have an information problem, so P can observe A s effort. What would P like to do (the first-best outcome for P)? By optimal risk-sharing, P should only condition wage on effort. P needs to pay A enough to make A as well off as her outside option. (Paying less means that A will not work for P; paying more is just throwing away money.) If P doesn t require effort, we need w 0, so w = 0. If P requires effort, she needs to make sure w 1 0, so she will choose w = 1 when effort is exerted, and w = 0 when it isn t. P will require effort when that gives her a higher profit: pv 1 > 0 pv > 1. ECON 302 (SFU) Lecture 9 July 9, / 17

10 Relation between P s First-Best and Social Optimum The conditions for P s first-best to require effort and for the social optimum to require effort are the same. This is not a coincidence! P wants to maximize total surplus because she can get all of it by paying A just enough to make her as well off as the outside option. For the rest of this week, we will use first-best, social optimum and socially efficient outcome interchangeably. ECON 302 (SFU) Lecture 9 July 9, / 17

11 Moral Hazard in Example Now, let s look at the problem: P doesn t actually observe A s effort level, so can t condition wage on it. But if wage doesn t depend on e, A should just slack off! As a result, there is no way to get the first-best outcome when pv > 1. There is another way to induce effort: conditioning wage on the outcome. This won t give us the first-best outcome because the agent will bear some risk. But it is sometimes better than not inducing effort at all. ECON 302 (SFU) Lecture 9 July 9, / 17

12 Second-Best Problem Let w 0 be the wage in case of failure, and w 1 be the wage in case of success. To induce effort, P needs to make effort as attractive as slacking off (incentive compatibility - IC) pu(w 1 ) + (1 p)u(w 0 ) 1 u(w 0 ) P also still needs to offer no worse than the outside option (individual rationality - IR) pu(w 1 ) + (1 p)u(w 0 ) 1 0 P s payoff is p(v w 1 ) (1 p)w 0. P needs to maximize this subject to the above two constraints. This is P s second-best outcome. ECON 302 (SFU) Lecture 9 July 9, / 17

13 Binding Constraints Suppose you re doing a constrained optimization problem, and you have constraints that are inequalities, like IC and IR. We say that a constraint binds if it holds with equality at an optimum. Example: max x s.t. x 2 and x 0. x 2 is binding since the maximum occurs at x = 2. x 0 is not binding and can be ignored. ECON 302 (SFU) Lecture 9 July 9, / 17

14 Second-Best Outcome (I) Suppose IR doesn t bind in our problem, so that the optimum (w 0, w 1 ) satisfies pu(w 1 ) + (1 p)u(w 0 ) 1 > 0. Then P could reduce w0 slightly, and both IR and IC would still hold. But reducing w0 increases P s profit, which contradicts (w 0, w 1 ) being an optimum. So IR must actually bind: pu(w1 ) + (1 p)u(w 0 ) 1 = 0 at the the optimum (w0, w 1 ). Therefore, IC becomes: 0 u(w0 ). Thus, w 0 = 0 at the the optimum (w0, w 1 ). ECON 302 (SFU) Lecture 9 July 9, / 17

15 Second-Best Outcome (II) At the the optimum (w 0, w 1 ), we have u(w 0 ) = w 0 = 0 and therefore pu(w 1 ) = p w 1 = 1 = w 1 = 1 p 2. P s second-best payoff is then p(v w 1 ) (1 p)w 0 = p(v 1 p 2 ). This is better than allowing A to slack off and getting 0 when V > 1 p 2. Compare the above condition to the condition for the first-best to involve effort pv > 1 V > 1 p. So when 1 p < V < 1 p 2, the second-best is cancelling the project even though the first-best involves undertaking the project. ECON 302 (SFU) Lecture 9 July 9, / 17

16 Second-Best Outcome (III) We can also compare P s second-best (when V > 1 p 2 ) payoff to P s first-best payoff. Second-best payoff: p(v 1 p 2 ) = pv 1 p First-best payoff: pv 1 Which one is bigger? What s the intuition? ECON 302 (SFU) Lecture 9 July 9, / 17

17 Comments In the second-best when V > 1 p 2, P knows that A will exert high effort. But P still varies the wage because she has to provide incentives for effort. P makes a lower profit in the second best because varying the wage lowers A s certainty equivalent. So P has to compensate by paying more on average. Sometimes this lower profit causes the project to be cancelled, even though the project will be undertaken in the first best. Second best is not Pareto efficient. If the cost of monitoring effort is lower than the profit loss in the second-best, then P will instead monitor. Repeated interactions can also reduce the severity of moral hazard. ECON 302 (SFU) Lecture 9 July 9, / 17