Moral Hazard Economics 302 - Microeconomic Theory II: Strategic Behavior Shih En Lu Simon Fraser University (with thanks to Anke Kessler) ECON 302 (SFU) Moral Hazard 1 / 18
Most Important Things to Learn 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. ECON 302 (SFU) Moral Hazard 2 / 18
Moral Hazard Increased risk ("hazard") of bad ("immoral") behaviour due to hidden (unobserved and/or unverifiable) action. 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. Other example: moral hazard in insurance - take ineffi cient risks because you re insured. ECON 302 (SFU) Moral Hazard 3 / 18
Moral Hazard in Agency Parties sign a contract/agreement, but their interests diverge and some actions are not contractible. 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) Moral Hazard 4 / 18
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) Moral Hazard 5 / 18
Socially Optimal Outcome (I) If we didn t have an information problem, what outcome(s), among those where A and P get at least their outside option payoff, is/are Pareto effi cient? 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) Moral Hazard 6 / 18
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 suffi ciently valuable and likely to succeed, any effi cient outcome must involve A working for P and exerting effort. What if pv < 1? ECON 302 (SFU) Moral Hazard 7 / 18
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]. Again: when a risk-neutral and a risk-averse agent share risk, the risk-neutral agent should bear all of it, absent other considerations. ECON 302 (SFU) Moral Hazard 8 / 18
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? 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) Moral Hazard 9 / 18
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. We will use "first best", "social optimum" and "socially effi cient outcome" interchangeably for describing the optimal level of effort. However, "first best" refers specifically to the case where P pays A as little as possible, while effi ciency does not pin down how the surplus should be divided. ECON 302 (SFU) Moral Hazard 10 / 18
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) Moral Hazard 11 / 18
The Second Best We want to find the best that the firm can do with the information problem. This is called the second best. The second best cannot be better for the firm than the first best: if the firm has full information, it can always ignore the information and pretend that it is hidden. But when is the second best as good as the first best? When the second best is worse than the first best, how much worse is it? ECON 302 (SFU) Moral Hazard 12 / 18
Second-Best Maximization 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. Need to maximize subject to the above. ECON 302 (SFU) Moral Hazard 13 / 18
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) Moral Hazard 14 / 18
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 w 0 slightly, and both IR and IC would still hold. But reducing w 0 increases P s profit, which contradicts (w 0, w 1 ) being an optimum. So IR must actually bind. Similarly, if IC doesn t bind, P could decrease w 1 slightly, and increase w 0 slightly so that A s expected utility does not change, which implies that IR will still be satisfied. This would increase P s profit: by reducing the amount of risk borne by A, P can maintain A s expected utility while paying A less on average. Thus IC must actually bind. ECON 302 (SFU) Moral Hazard 15 / 18
Second-Best Outcome (II) Since both constraints are binding, we have u(w 0 ) = w 0 = 0 and therefore pu(w 1 ) = p w 1 = 1 = w 1 = 1 p 2. P s 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 instead to let workers slack off even though the first-best involves effort. ECON 302 (SFU) Moral Hazard 16 / 18
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) Moral Hazard 17 / 18
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 because varying the wage lowers A s certainty equivalent. So P has to compensate by paying more on average. 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) Moral Hazard 18 / 18