5. Relational Contracts and Career Concerns

Transcription

1 5. Relational Contracts and Career Concerns Klaus M. Schmidt LMU Munich Contract Theory, Summer 2010 Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

2 Basic Readings Basic Readings Textbooks: Bolton and Dewatripont(2005), Chapters 10.4 and 10.5 Schmidt (1995), Chapter 8.3 Papers: MacLeod and Malcomson (1989) Levin (2003) Holmström (1999) Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

3 Introduction Introduction So far we assumed that all contracts are enforced by an outside third party: the courts. In this section we look at contracts and incentive mechanisms that do not rely on enforcement by a third party but are self-enforcing. A contract is self-enforcing, if it is in the best interest of all involved parties to stick to the terms of the agreement in every contingency at any point in time. Thus, a self-enforcing contract is an equilibrium of the game played by the involved parties. Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

4 Introduction Relational contracts: infinitely repeated relationship between two or more parties stationary environment infinitely repeated game has many (subgame perfect, perfect Bayesian) equilibria parties agree ex ante which equilibrium they want to play Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

5 Introduction Career concerns: agent s ability is unknown the firm and the market observe the agent s output over time output is observable by the firm and the market but not verifiable to the courts competition forces the firm to pay the agent his expected marginal product upfront in every period worker has an incentive to work hard in order to affect the firm s (and the market s) perception of his ability the firm understands this and cannot be fooled in equilibrium this game typically has only one equilibrium in which the moral hazard problem is partially solved These models are often called signal jamming or rat race models. Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

6 Relational Contracts: The Set Up Relational Contracts: The Set Up Principal and agent are both risk neutral Infinite time horizon, t = 0, 1, 2,.... At the beginning of date t the principal offers a fixed salary w t and a contingent bonus payment b t : Φ R, where Φ is the set of observed performance outcomes. The agent decides whether to accept or reject the offer: d t {0, 1} If the agent rejects, the principal and the agent receives their outside option utilities (π, u), with s = π + u. If the agent accepts, he observes a cost parameter θ t Θ = [θ,θ], with CDF P(θ). θ t is distributed independently across periods. Then the agent chooses an effort e t [0, e], and incurs a cost of c(e t,θ t ) with c(e t,θ t ) 0 and c(0,θ t ) = 0 for all θ t. Then output y t [y, y] is drawn from the cdf F(y e). Finally the principal decides on whether to pay the bonus b t. Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

7 Relational Contracts: The Set Up Remarks: The fixed wage w t can be enforced by the courts The bonus payment b t is voluntary. Thus, in equilibrium the principal must have an incentive to pay b t. Note that b t may be negative in which case the agent has to pay the principal. The agent observes all the relevant information: {e t,θ t, y t } The principal observes ϕ t {e t,θ t, y t }. The set of all possible realizations of ϕ t is denoted by Φ. This is a very rich framework allowing for the following cases: all information is observable but not verifiable (MacLeod-Malcomson 1989): ϕ t = {e t,θ t, y t } hidden action (Levin 2003): ϕ t = {θ t, y t } hidden information (Levin 2003): ϕ t = {e t, y t }. Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

8 Relational Contracts: The Set Up Payoffs: The principal s payoff is given by [ ] π t = (1 δ)e δ τ {d τ (y τ W τ )+(1 d τ )π}, τ=t where W τ is the total payment of the principal to the agent in period τ. (W τ = w τ + b τ if the promise is kept and W τ = w τ if no bonus is paid.) The agent s payoff is [ ] u t = (1 δ)e δ τ {d τ (W τ c(e τ,θ τ ))+(1 d τ )u} τ=t The expected surplus is given by s t = π t + u t Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

9 Relational Contracts: The Set Up Relational Contracts A relational contract is a complete contingent plan for the relationship. Let h t = (w 0, d 0,ϕ 0, W 0,..., w t 1, d t 1,ϕ t 1, W t 1 ) denote the history of play up to (but not including) date t and let H t denote the set of all possible histories up to date t. A relation contract describes for any period t and any history h t H t the compensation the principal should offer: w t, b t whether the agent should accept or reject this offer: d t the action the agent takes as a function of the realized cost parameter: e t (θ t ) Moreover, the relational contract describes a Perfect Public Equilibrium (PPE) of the repeated game. A PPE is a Perfect Bayesian Equilibrium in which strategies are contingent on public histories only. Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

10 Free Transfers Free Transfers Proposition 5.1 (Free Transfers) If there is a self-enforcing contract that generates expected surplus s > s, then there are self-enforcing contracts that give as expected payoffs any pair (u,π) satisfying u u, π π and u +π = s. Proof: Changing the fixed compensation in the initial period of the contract does not affect incentives in later play. Thus the parties can always transfer wealth between them at will. Q.E.D. Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

11 Stationary Contracts Stationary Contracts Definition 1 (Stationary Contract) A contract is stationary if on the equilibrium path W t = w + b(ϕ t ) and e t = e(θ t ) at every date t. Proposition 5.2 (Stationary Contracts) If an optimal contract exists, then there are stationary contracts that are optimal. Intuition for the Proof: Suppose that there are only two outcomes (High and Low). To induce the agent to exert effort the principal has to reward the High outcome. He can either pay a reward in this period or switch to a continuation equilibrium that gives a higher payment to the agent in the future. Given risk neutrality both parties are indifferent between both methods of pay. Thus, without loss of generality we can restrict attention to stationary contracts where the principal rewards the agent in the current period. Q.E.D. Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

12 Payoffs under a Stationary Relational Contract Payoffs under a Stationary Relational Contract Suppose a stationary contract calls for fixed wage w, bonus b(ϕ), and effort e(θ) in each period. Define W(ϕ) = w + b(ϕ). The expected per period payoffs offered by a stationary contract are given by: π = E θ,y [y W(ϕ) e = e(θ)] u = E θ,y [W(ϕ) c(e) e = e(θ)] s = E θ,y [y c(e) e = e(θ)] Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

13 Conditions for a Relational Contract Conditions for a Relational Contract A self-enforcing contract must satisfy the following conditions: 1. The contract must be individually rational, i.e. each party must get at least its outside option utility: u u; π π; 2. The contract must be incentive compatible, i.e. it must be optimal for the agent to choose e(θ): e(θ) arg max e E y [W(ϕ e)] c(e,θ); Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

14 Conditions for a Relational Contract 3. The dynamic enforcement constraint requires that at the end of each period no party has an incentive to renege on its payment obligations, i.e. δ (π π) sup b(ϕ) 1 δ ϕ δ (u u) inf 1 δ b(ϕ) ϕ 4. The dynamic enforcement constraint implies that δ (s s) sup b(ϕ) inf b(ϕ) = sup W(ϕ) inf 1 δ W(ϕ) ϕ ϕ ϕ ϕ Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

15 Conditions for a Relational Contract Proposition 5.3 (Implementable Relational Contracts) An effort schedule e(θ) that generates expected surplus s can be implemented with a stationary relational contract if and only if there is a payment schedule W : Φ R such that for all θ Θ and e(θ) arg max e {E y [W(ϕ) e] c(e,θ)]} (IC) δ (s s) sup W(ϕ) inf 1 δ W(ϕ) ϕ ϕ (DE) Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

16 Conditions for a Relational Contract Proof: We have shown already that these conditions are necessary for a relational contract to be implementable. To see that they are also sufficient consider a payment schedule W(ϕ) and an effort profile e(θ) that satisfies (IC) and (DE). Let b(ϕ) = W(ϕ) inf ϕ W(ϕ) w = u E[b(ϕ) c e(θ)]. Consider a stationary contract with w, b(ϕ) and e(θ) that threatens that the agent chooses d = 0 if the principal does not pay b(ϕ). This contract induces the agent to choose e(θ) (by assumption) and the principal to pay b(ϕ) (by construction). Furthermore, it gives the agent his reservation utility u and the principal the net social surplus s u > π. Q.E.D. Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

17 Perfect Information Perfect Information Suppose that the cost parameter θ t, the agent s action e t and the outcome y t are observable by the principal and the agent, but cannot be verified to the courts. For simplicity we will also assume that θ t is a constant. This is the case considered by MacLeod and Malcomson (1989). In this case we have: Proposition 5.4 (Perfect Information) Suppose that θ t = θ and that the action e t is observable by the principal. The stationary action e that gives rise to expected social surplus s can be implemented with a stationary relational contract if and only if δ (s s) c(e) 1 δ (DE) Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

18 Perfect Information Proof: With perfect information a stationary contract is incentive compatible if w + b c(e) w which is equivalent to b c(e). Thus, necessity follows from the dynamic enforcement constraint and the arguments we have given for Proposition 5.3. To see that this condition is also sufficient consider the following stationary relational contract. The agent gets the fixed wage w = u at the beginning of each period. If he chooses action e the principal pays an additional bonus b = c(e). If he chooses any other action ẽ e the principal pays no bonus and the agent chooses d = 0 in all future periods. If the agent took action e and the principal did not pay b c(e) the agent chooses d = 0 in all future periods. This is a subgame perfect equilibrium. The agent is just indifferent between choosing e and choosing ẽ = 0 (his most profitable deviation), and he just gets his reservation utility u. Note that the principal gets all the net social surplus. If the agent did choose e the principal prefers to pay b = c(e) and get s s in all future periods rather than getting c(e) in this period and π thereafter. Q.E.D. Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

19 Perfect Information Remarks: 1. By Proposition 4.1 the surplus that is generated can be allocated in any proportion (α, 1 α) between the two players. 2. The closer the discount factor to 1 the larger is the set of implementable actions. 3. The larger the social surplus, the easier it is to implement a given action. 4. The higher the cost of an action, the more difficult it is to implement this action. 5. The effort cost shows up twice in condition (DE). Note that s = E(y e) c(e). Thus, we have δ δ (E(y e) s) c(e)+ 1 δ 1 δ c(e) = 1 1 δ c(e) which is equivalent to δ(e(y e) s) c(e) Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

20 Moral Hazard Moral Hazard Assume that the cost parameter θ t is observable but the agent s action e t is not. Let effort be a continuous variable with c (e) > 0 and c (e) > 0. Finally assume that F(y e) satisfies the monotone likelihood ratio property, i.e. f e(y e) f(y e) is monotonically increasing in y. A stationary contract specifies W(θ, y) = w + b(θ, y). The next proposition shows that the optimal contract has has a very simple structure: Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

21 Moral Hazard Proposition 5.5 (Moral Hazard) The optimal contract implements an effort schedule e(θ) e FB (θ). For each θ the payments W(θ, y) are one-step: W(θ, y) = W for all y < ŷ(θ) and W(θ, y) = W = W + δ 1 δ (s s) for all y ŷ(θ), where the threshold ŷ(θ) is the point at which the likelihood ratio f e(y e) f(y e) switches from negative to positive. Intuition for the Proof: Since both parties are risk neutral, insurance is not an issue. Therefore, it is optimal to give the strongest possible incentives by paying the lowest possible wage for low outcome and the highest possible wage for high outcomes. The difference in the two wage payments is restricted by the dynamic enforcement constraint, however. Compare this to the limited liability contracts of Innes (1990). Note that the payments do not depend on θ but the cutoff ŷ(θ) does. Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

22 Hidden Information Hidden Information Assume that the principal can observe the agent s effort level e t, but he does not observe the cost parameter θ t. Proposition 5.6 (Hidden Information) With hidden information, an effort schedule e(θ) that generates expected surplus s can be implemented by a stationary contract if and only if (i) (ii) e(θ) is nonincreasing and δ 1 δ (s s) c(e(θ),θ)+ θ θ c(e(θ),θ) θ dθ. Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

23 Hidden Information Remarks: 1. The agent has to be induced to reveal his type truthfully. Thus, each type θ has to be deterred to mimick type θ and choose e( θ). 2. The principal has to pay an informational rent to the agent. This rent is limited by the future social surplus. If the principal would have to pay a higher information rent, he would prefer to pay nothing and quit. 3. If the future social surplus is small, no rents can be paid. In this case the optimal contract induces all types to choose the same effort. 4. If the future social surplus is sufficiently high the optimal contract induces the agent to choose e FB. 5. Recall that this is not an adverse selection but a hidden information model. The parties can always allocate the surplus at will among themselves by making sidepayments before the agent learns θ. Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

24 Interaction of Implicit and Explicit Contracts Interaction of Implicit and Explicit Contracts Schmidt and Schnitzer (1995) consider how the possibility to write explicit contracts affects the stability of implicit contracts. Consider the case of perfect information and assume that the parties can write an explicit contract on e at some cost k(e). In this case any e can be implemented with an explicit contract, but at k(e). Thus, in order to save this cost the parties may prefer to write an implicit contract. However, the possibility to write an explicit contract may render the implicit contract infeasible. The reason is that the threat to terminate the relationship is no longer credible. If one of the parties deviates, the parties may not trust each other any more. But they can now sign an explicit contract that does not require any trust! Therefore, they will renegotiate. Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

25 Interaction of Implicit and Explicit Contracts Proposition 5.7 (Costly Explicit Contracts) Consider the perfect information case and assume that the parties can contract on e at cost k(e). Let e = arg max[e(y e) c(e) k(e)]. Then there exists an implicit contract that induces the agent to take action e which generates surplus s if and only if c(e) δ 1 δ [s max{s, s(e ) (1 δ)k(e )}] Proof Sketch: Two cases have to be distinguished. Either writing the explicit contract is so costly, that no positive net surplus can be generated, then we are back to the case where only implicit contracts are feasible. Or a positive net surplus can be generated with an explicit contract. Then it becomes more difficult to punish deviations and the set of implementable actions shrinks. Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

26 Interaction of Implicit and Explicit Contracts Suppose now that the agent has to engage in two different actions e 1 and e 2. The first action can be contracted upon at no cost, while contracting on the second action is infinitely costly. Schmidt and Schnitzer (1995) show that the explicit contract on e 1 has two effects: 1. It makes deviations less attractive for the agent, because the agent can no longer deviate on e 1 but only on e It makes it more difficult to punish, because the worst punishment equilibrium is less severe if the parties can continue their relationship with an explicit contract on e 1. Each of these effects can dominate. It is easy to find examples where the possibility to write an explicit contract on e 1 makes both parties worse off. Example: cartels. Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

27 Interaction of Implicit and Explicit Contracts Baker, Gibbons and Murphy (1994, 1999, 2002) have a sequence of papers in which changes in the governance structure of the relationship (e.g. the allocation of property rights or decision rights) affects the punishment opportunities and thereby what can be implemented in a relational contract. Halonen (1999) finds that it may be optimal to have joint ownership on an asset (which is very inefficient in a one-shot relationship) in order to be able to credibly threaten to punish each other more severely in a relational contract. Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

28 Career Concerns Career Concerns Consider a risk neutral agent who offers his services on a perfectly competitive market several periods in a row. Because of competition the agent will be offered his marginal product. His output or productivity is observable not only by the firm he is working with, but also by all other potential employers. However, his output cannot be verified to the courts. Thus, in every period only a fixed wage can be offered. Fama (1980) argued, that the competition for the agent will induce the agent to work hard: By working hard the agent shows to the market that his productivity is high. The higher the output in this period the higher is the wage the worker will be offered in the next period. Competition for the agent solves the principal-agent problem at least partially. Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

29 Career Concerns As it stands, this argument is not convincing: In the last period before retirement that agent will not work any more Therefore his wage in the last period will always be zero, independent of how much the agent worked in the second to last period. Therefore the agent has no incentive to work in the second to last period... However, Holmström (1982, 1999) has a very nice model showing how career concerns can have an effect. However, in his model there is no reason why career concerns should give efficient incentives. To the contrary: Incentives may be too small or too large. Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

30 The Model The Model There is one agent who lives for T periods. In each period t, t {1,...,T} the agent s output is given by where y t = η + a t +ε t, η is the agent s ability in period t that is drawn in period 0 from the normal distribution N(m 0, 1/h 0 ) with mean m 0 and variance 1/h 0 (h 0 is called the precision ) a t 0 is the agent s effort in period t ε t is a noise term, ε t N(0, 1/h ε ) η and ε t are stochastically independent, and the noise is uncorrelated over time. Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

31 The Model The agent maximizes his utility that is given by U(w, a) = T β t 1 [w t c(a t )], t=1 where β < 1 is the agent s discount factor c(a t ) 0 is the agent s cost of effort with c 0, c (0) = 0, c > 0 Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

32 The Model Informational Assumptions Neither the agent nor the firm nor any potential employee know η. All parties start from the common prior that η N(m 0, 1/h 0 ). Only the worker observes a t (moral hazard). However, all other parties can infer which effort the agent will choose in equilibrium. All parties observe y t in each period and use this signal to update their beliefs about η. y t cannot be verified to the courts. Therefore only fixed wage contracts can be written in each period. Discussion: 1. From a technical point of view it is very convenient to assume that all parties are symmetrically informed (otherwise we get a signalling model). 2. But is it also an economically sensible assumption? What do you think? Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

33 Effort Choice Effort Choice In period t the agent chooses a t such that { T } a t arg max β τ t [E(w τ I τ ) c(a τ )] τ=t where I τ is the information the market received up to and including period τ. In the last period this reduces to a T arg max{w T c(a T )} Thus, the agent will clearly choose a T = 0. However, in all other periods the agent may have an incentive to work in order to affect the markets perception of his ability. Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

34 Bayesian Updating Bayesian Updating Suppose that the market observes output y t after period t. All market participants who want to bid for the agent s services in period t + 1 must update their beliefs about the agent s ability. Suppose that the market believes that the agent chose effort at in period t. Define z t = y t at = η +ε t Note that z t is a normally distributed signal with mean η and variance 1/h ε. Suppose that before observing this signal the market believed that the agent s ability was normally distributed with mean m t and variance 1/h t. Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

35 Bayesian Updating Thus, the updated belief about the agent s ability is m t+1 = E(η I t ) = α t m t +(1 α t )z t where α t = h t h t +h ε and h t = h η + t h ε, so α t = h η+t h ε h η +(t+1) h ε Remarks: 1. The updated probability distribution after observing a normally distributed signal is again a normal distribution. 2. The updated expected value of η is a convex combination of the prior m t and the signal z t. Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

36 Bayesian Updating 3. The weight of the signal z t depends on its precision relative to the precision of the prior. If the signal is very precise while the prior is rather imprecise, then the signal is very informative and gets a lot of weight. If the prior is already very precise while the signal is rather imprecise in comparison, then the signal gets little weight. 4. The more signals the market receives about the agent s ability, the higher the precision of the prior becomes and the smaller is the weight of each new signal. 5. As t, h t, alpha t 1 and E(η I t ) η. Thus, the market eventually learns the ability of the agent. Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

37 Wages Wages All firms have the same information and will form the same expectations. Therefore they will all offer Remarks: w t+1 = E(η I t )+a t+1 = α t m t +(1 α t )z t + a t+1 = α t m t +(1 α t )(y t a t )+a t+1 = α t m t +(1 α t )(η + a t +ε t ) (1 α t )a t + a t+1 1. w t+1 depends on a t+1 but is independent of a t+1, i.e., it depends on what the market believes what the agent will do in period t + 1, but it cannot depend on what the agent actually does, because this is only observed by the agent. Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

38 Wages 2. However, the action a t does affect w t+1! The market believes that the manager chooses at, but the market cannot observe a t. Thus, if the agent works a little more than at, his output will be a little higher, the market will believe that his ability is a little higher and the market will offer a somewhat higher wage in this and all future periods. This gives an incentive to the agent to work. 3. However, in equilibrium the market cannot be fooled. The market will correctly anticipate the action that the agent chooses. Nevertheless, the agent has an incentive to work. 4. Note that the incomplete information about the manager s ability is a good thing in this model. If ability was observable the manager would always choose a t = 0. Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

39 Incentives Incentives The impact of a t on w t+1 is w t+1 a t = (1 α t ) Consider now w t+2 : w t+2 = E(η I t+1 )+a t+2 = α t+1 m t+1 +(1 α t+1 )z t+1 + a t+2 = α t+1 (α t m t +(1 α t )[(η + a t +ε t ) (1 α t )a t ]+(1 α t )z t+1 + a t+2 = α t m t +(1 α t )(η + a t +ε t ) (1 α t )a t + a t+1 Thus, the impact of a t on w t+2 is and so on. w t+2 a t = α t+1 (1 α t ) Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

40 Incentives A marginal increase of a t affects the agent s expected utility as follows: U a t = T t τ=1 β τ w t+τ a t } {{ } k t c (a t ) Remarks: 1. The agent chooses a t such that c (a t ) = k t. 2. Efficiency requires that c (a t ) = As t T, k t becomes smaller and smaller and the agent works less and less, until he chooses a T = 0 in the last period. 4. However, it is possible that k t > 1, so the agent may work inefficiently hard! 5. The agent works harder, the less the market knows about his ability (the smaller h η, the higher the precision of output as a signal about his ability (the larger h ε ) and the more patient he his (the larger β). Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

41 Incentives Discussion: 1. Why does the agent work so hard at the beginning of his career? 2. It may be optimal to reduce the exposure of the agent in the beginning of his career and in order to weaken his incentives. How could this be done? 3. Why are students shy when they make their first remarks in a seminar? 4. Why is this type of models sometimes called signalling jamming or rat race models? Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

42 Extensions Extensions Shocks to Ability: Holmström also considers an infinite horizon model in which the ability of the agent follows a Markov process, i.e., η t+1 = η t +δ t where δ t is again normally distributed with mean 0 and variance 1/h δ. In this model the market can never learn η. There is a stationary equilibrium in which the agent chooses a constant effort level a in all periods. The agent works harder the smaller h δ and the larger h ε. However, for β < 1 we have a < a FB. Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

43 Extensions Investment Choices: Homström and Ricard-i-Costa (1986) extend this model to a manager who has to choose an investment project (or a portfolio) in every period. Choosing a project/portfolio is costless to the manager. However, the market uses the performance of the project to update its beliefs about the manager s ability. In this model the manager may choose a project/portfolio that is too conservative (too little risk) in order to insure himself against the risk of future income variations. Chevalier and Ellison (1999) conducted an empirical study of mutual fund managers. They show that portfolio choices seem to be influenced by career concerns. Young fund managers are more likely to be terminated than older managers if their funds perform poorly as compared to the market. Young fund managers tend to select portfolios with less unsystematic risk and more conventional sector weights. Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

44 Extensions Interaction of Career Concerns and Explicit Incentives: Gibbons and Murphy (1992) consider a dynamic model with career concerns in which a risk averse agent can be given linear incentives: At the beginning of the career career concerns are very strong and the agent faces a lot of risk about his future income. Additional linear incentives expose the agent to additional risk. Therefore, the slope of the incentive scheme will be low. At the end of the career career concerns are very weak and the agent faces little risk about his future income. Therefore it is now optimal to give him strong additional incentives. This model is consistent with the observation that CEOs get much stronger incentives than younger employees on lower levels of the hierarchy. Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45

45 Extensions Meyer and Vickers (1997) show that having a more precise signal about the agent s effort need not improve welfare. On the one hand it allows for better explicit incentives. On the other hand it increases the incentives due to career concern. Even if explicit incentives are optimally chosen, it may be that efficiency is reduced if the performance signal becomes more precise. Klaus M. Schmidt (LMU Munich) 5. Relational Contracts and Career Concerns Contract Theory, Summer / 45