Efficiency Wage. Economics of Information and Contracts Moral Hazard: Applications and Extensions. Financial Contracts. Financial Contracts

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1 Efficiency Wage Economics of Information and Contracts Moral Hazard: Applications and Extensions Levent Koçkesen Koç University A risk neutral agent working for a firm Assume two effort and output levels There is limited liability: w0,w1 0 We have already studied this problem If ((s1 s0 ψ Firm prefers to induce high effort and the solution is ψ w0 = 0, w1 = > 0 Positive wage is called efficiency wage because it induces the agent to exert high (efficient level of effort For further development of this idea see Shapiro and Stiglitz (1984 Levent Koçkesen (Koç University Moral Hazard: Applications 1 / 19 Levent Koçkesen (Koç University Moral Hazard: Applications / 19 A risk averse entrepreneur has a project that needs I dollars of investment Return on the project is s1 or s0 Entrepreneur s effort is either 0 or 1 pi= probability of s1 if effort is i = 0,1 A risk neutral lender offers a contract that specifies repayment levels conditional on return: (r0,r1 Assuming that lender prefers to induce high effort, her problem is r0,r1 p1r1 +(1 p1r0 I p1u(s1 r1+(1 p1u(s0 r0 ψ 0 p1u(s1 r1 +(1 p1u(s0 r0 ψ p0u(s1 r1 +(1 p0u(s0 r0 Let w0 = s0 r0 and w1 = s1 r1 The problem is identical to what we have studied before At the solution ( r1 = s1 h ψ +ψ 1 p1 < s1 ( r0 = s0 h ψ ψ p1 > s0 Levent Koçkesen (Koç University Moral Hazard: Applications 3 / 19 Levent Koçkesen (Koç University Moral Hazard: Applications 4 / 19

2 Lender s expected payoff is where p1s1 +(1 p1s0 C I ( ( C = p1h ψ +ψ 1 p1 +(1 p1h ψ ψ p1 is the cost (to the lender of moral hazard The project will be funded only if I I = p1s1 +(1 p1s0 C Under complete information project will be funded as long as If there is limited liability: ri si, i = 0,1 Solution has ( ψ r0 = s0 and r1 = s1 h This looks like a debt contract: In the bad state no money is left to borrower In the good state a positive amount is left I I = p1s1 +(1 p1s0 Moral hazard creates credit rationing for projects with investment requirement in [I,I] Levent Koçkesen (Koç University Moral Hazard: Applications 5 / 19 Levent Koçkesen (Koç University Moral Hazard: Applications 6 / 19 Commonly used model agent s preferences have constant absolute risk aversion (CARA outcome is normally distributed contracts are linear More precisely the agent s preferences can be represented by u(w,a = e η(w ca where η > 0 is the coefficient of absolute risk aversion (η = u /u. Outcome q is equal to effort a plus noise ε q = a+ε where ε is normally distributed with zero mean and variance σ Contracts are limited to be linear w = t+sq where t is the fixed and s is the performance related component of the payment Levent Koçkesen (Koç University Moral Hazard: Applications 7 / 19 Principal s problem is a,t,s E[q w] E[ e η(w ca ] u(w a arge[ e η(w câ ] â where E is the expectation operator and u(w is the reservation utility of the agent Note that w ca ca ca = t+sq = t+s(a+ε Levent Koçkesen (Koç University Moral Hazard: Applications 8 / 19

3 Therefore, agent s utility can be written as We can show that E[ e η(t+s(a+ε ca ] = e η(t+sa ca E[e ηsε ] E[e ηsε ] = η s σ / Levent Koçkesen (Koç University Moral Hazard: Applications 9 / 19 Density of N(µ,σ f(x = 1 σ π exp ( (x µ σ Therefore, for any γ E[exp(γε] = 1 σ exp(γxexp ( x π σ dx = 1 σ exp (γx x π σ dx = 1 σ exp ( (x γσ γ (σ π σ ( γ σ 1 = exp σ exp ( (x γσ π σ ( γ σ = exp dx dx Levent Koçkesen (Koç University Moral Hazard: Applications 10 / 19 Therefore, E[ e η(w ca ] = e η(t+sa ca / ηs σ / Agent s imization problem is ( t+sa ca / ηs σ / a with solution a = s/c Principal s problem becomes which is solved as s s (t+ t,s c c t+s /c ηs σ / = w 1 s = 1+ηcσ Levent Koçkesen (Koç University Moral Hazard: Applications 11 / 19 Levent Koçkesen (Koç University Moral Hazard: Applications 1 / 19

4 Properties of the Solution 1 a = s/c, s = 1+ηcσ As the agent becomes more risk-averse, performance sensitive component s decreases η s As risk increases, performance sensitive component and effort decrease s exposes the agent to risk σ s,a Principal has to compensate agent for increased risk Better to reduce s As cost of effort for the agent decreases, performance sensitive component and effort increases c s,a Inefficient Behavioral Responses to Incentive Contracts Performance sensitive contracts have the cost of exposing the agent to risk They may also have unintended consequences Agents may act in a way that hurts employers Many jobs are complex and have aspects that are difficult to specify in contracts Explicit contracts may induce the agent to focus on aspects included in the contract to the detriment of others Levent Koçkesen (Koç University Moral Hazard: Applications 13 / 19 Levent Koçkesen (Koç University Moral Hazard: Applications 14 / 19 Inefficient Behavioral Responses to Incentive Contracts Football quarterback Ken O Brien mid-80s Used to throw a lot of interceptions Received a contract that penalized every time he threw the ball to opposition It worked: He threw fewer interceptions But largely because he refused to throw the ball at all AT&T programmer contracts Rewarded on the number of lines of code Resulted in longer programs than was necessary Examples of multi-tasking Holmstrom and Milgrom (1991 Prendergast (1999 Survey with simple models and empirical evidence Levent Koçkesen (Koç University Moral Hazard: Applications 15 / 19 A Simple Model Agent is risk neutral u(w,a = w ca Outcome q is equal to effort a plus noise ε where ε N(0,σ Compensation is based on q = a+ε q = µa+ε Agent privately knows µ, principal believes µ N(1,σµ Models the divergence between the privately and socially optimal effort level σµ = 0 no divergence Example: If agent is rewarded on quantity produced, then she may work hard even if she knows there is no demand for it Levent Koçkesen (Koç University Moral Hazard: Applications 16 / 19

5 A Simple Model Contracts are limited to be linear w = t+s q A model with both hidden information and hidden action We assume that principal cannot design screening contracts See Baker (199 Agent s problem is to choose a to imize Solved as Principal s problem is t+s q ca ca = t+s(µa+ε t,s a = µs c E[q w] E[w ca ] w Substituting for a and using the fact that the constraint must hold as equality, problem becomes s s c s c (σ µ +1 Levent Koçkesen (Koç University Moral Hazard: Applications 17 / 19 Levent Koçkesen (Koç University Moral Hazard: Applications 18 / 19 This is solved as s = 1 σ µ +1 Optimal contract in the standard model with a risk-neutral agent is s = 1 Here, incentives are muted (s < 1 in order to constrain inefficient behavioral responses See Prendergast (1999 for empirical evidence Levent Koçkesen (Koç University Moral Hazard: Applications 19 / 19