《金融经济学》（英文版） Chapter 5 Dynamic Contracting

Chapter 5 Dynamic Contracting 5.1 Incomplete contracts In our earlier treatment of contracting problems, we assumed that the in- centive problem was generated by asymmetric information, either a problem of moral hazard(hidden actions)or adverse selection(hidden information) The incomplete contracts approach eschews asymmetric information because of its intractability and instead focuses on environments in which informa- tion is observable but not verifiable. Observable "means the information is common knowledge among the contracting parties. Non-verifiable"means that the information cannot be confirmed by an outside agency such as a court and hence cannot be made an explicit part of any written contract A crucial aspect of the incomplete markets approach is that it allows for renegotiation, that is, agents can replace the pre-existing contract with a new contract at any point if it is mutually beneficial. Renegotiation under ncomplete information is analytically intractable, so this is another reason for avoiding informational asymmetries 5.1.1 The holdup problem This example comes from Hart(1995). There are two firms, MI and M2 Firm M2 produces a widget that is needed by firm Ml at a cost of C*. There is no alternative supplier or purchaser The gross return from the widget is R(i) if MI makes a prior investment

Chapter 5 Dynamic Contracting 5.1 Incomplete contracts In our earlier treatment of contracting problems, we assumed that the in￾centive problem was generated by asymmetric information, either a problem of moral hazard (hidden actions) or adverse selection (hidden information). The incomplete contracts approach eschews asymmetric information because of its intractability and instead focuses on environments in which informa￾tion is observable but not verifiable. “Observable” means the information is common knowledge among the contracting parties. “Non-verifiable” means that the information cannot be confirmed by an outside agency such as a court and hence cannot be made an explicit part of any written contract. A crucial aspect of the incomplete markets approach is that it allows for renegotiation, that is, agents can replace the pre-existing contract with a new contract at any point if it is mutually beneficial. Renegotiation under incomplete information is analytically intractable, so this is another reason for avoiding informational asymmetries. 5.1.1 The holdup problem This example comes from Hart (1995). There are two firms, M1 and M2. Firm M2 produces a widget that is needed by firm M1 at a cost of C∗. There is no alternative supplier or purchaser. The gross return from the widget is R(i) if M1 makes a prior investment 1

CHAPTER 5. DYNAMIC CONTRACTING of i>0. Assume that R(0)>C,R(0)>2,limR()<1,R(i)>0,R"(t)<0,v Both parties are risk neutral and the interest rate is zero. Ignore issues of ownership The first best maximizes total surplus Earg max(r(i)-i-C*)3), where x=0.1 If surplus is divided using symmetric Nash bargaining solution, invest nent is sub-optimal(Grout, 1984) (2)∈ arg max{(R(i) Contractual solutions If the type of widget produced can be specified in the contract, the first best can be achieved If the level of investment can be specified in the contract, the first best can be achieved The large, finite number of S. A widget of type is needed in state s, that is, a widget of type s produces a return of R(i) state s and nothing in other states. The cost of production is C* for every type and state. The cost of writing a complete contract with a large number of states would be very high. The first best might be achieved as follows: Ml specifies the type of widget she wants at date 1; if M2 supplies that type, she receives P1: if she fails to deliver, she receives Po.(Note the type of widget must be verifiable). To implement the first best, put po >0 and P1 >Po +C*. Since MI gets the full marginal returns, investment will be optimal Renegotiation causes problems with this setup. For example, suppose that M2 has the opportunity to make a take-it-or-leave-it counter offer. Then M2 gets the surplus and again we have the holdup problem In any case, when there is renegotiation, the outcome is independent of the contract

2 CHAPTER 5. DYNAMIC CONTRACTING of i ≥ 0. Assume that R(0) > C∗ , R0 (0) > 2, lim i→∞ R0 (i) < 1, R0 (i) > 0, R00(i) < 0, ∀i. Both parties are risk neutral and the interest rate is zero. Ignore issues of ownership. The first best maximizes total surplus: (i ∗ , x∗ ) ∈ arg max {(R(i) − i − C∗ ) x} , where x = 0, 1. If surplus is divided using symmetric Nash bargaining solution, invest￾ment is sub-optimal (Grout, 1984). (ˆı, xˆ) ∈ arg max ½1 2 (R(i) − i − C∗ ) x ¾ . Contractual solutions: • If the type of widget produced can be specified in the contract, the first best can be achieved. • If the level of investment can be specified in the contract, the first best can be achieved. There is a large, finite number of states s = 1, ..., S. A widget of type s is needed in state s, that is, a widget of type s produces a return of R(i) in state s and nothing in other states. The cost of production is C∗ for every type and state. The cost of writing a complete contract with a large number of states would be very high. The first best might be achieved as follows: M1 specifies the type of widget she wants at date 1; if M2 supplies that type, she receives p1; if she fails to deliver, she receives p0. (Note the type of widget must be verifiable). To implement the first best, put p0 ≥ 0 and p1 ≥ p0 + C∗. Since M1 gets the full marginal returns, investment will be optimal. Renegotiation causes problems with this setup. For example, suppose that M2 has the opportunity to make a take-it-or-leave-it counter offer. Then M2 gets the surplus and again we have the holdup problem. In any case, when there is renegotiation, the outcome is independent of the contract

5.1. INCOMPLETE CONTRACTS 5.1.2 Hart and Moore(1994) Another example of incomplete contracting is the Hart and Moore(1994) theory of debt. The returns to the asset are observable but not verifiable Managers can run away with the cash but not the assets themselves. The only option open to the bondholders is to rest control of the asset from the manager Suppose there are three dates t= 1, 2, 3 and at the initial date the in- vestors purchase an asset(a machine)which they put in the control of a manager. The machine produces a random return yt at dates t=2, 3 and can be liquidated for a fixed amount L in period t=2 ( it has no scrap value at the last date). All uncertainty is resolved at date t=2 in the sense that (y2, y3)become known for sure At the first date, the investors and the manager write a contract which specifies, among other things, the payments to be made by the manager in each period. The contract cannot be made conditional on the earnings of the firm, as these are unverifiable; in fact, the only thing that can be verified is whether the manager has made a specified payment or not. If he has not then the investors have the right to seize the asset and prevent the manager rom using it Let D be the minimum payment required at the second date. If the manager makes a payment of at least D at t=2, there is nothing the investors can do to stop him using the rest of the firms income for his own purposes after this. At the last date the manager will simply consume y3 There is nothing the investors can do to stop him. At the second to last date the manager may lose control of the firm if he does not pay d to the investors but he may get away with less. Clearly, he will never pay them more than D If he only pays them L it will not be worthwhile seizing the asset. The exact division of the surplus is determined by a bargaining problem, but assuming the manager gets to make a take-it-or-leave-it offer, he will clearly pay the minimum of D and L if he can. If y2 min(D, L then the investors will seize the asset. even though this is inefficient if L<y2 If y2> min(D, L the manager will retain control, and his rents equal 92+93-minD, L This story offers several lessons. First, the investors' power is restricted to the threat of taking away control of the asset. Secondly, this threat is credible

5.1. INCOMPLETE CONTRACTS 3 5.1.2 Hart and Moore (1994) Another example of incomplete contracting is the Hart and Moore (1994) theory of debt. The returns to the asset are observable but not verifiable. Managers can run away with the cash but not the assets themselves. The only option open to the bondholders is to rest control of the asset from the manager. Suppose there are three dates t = 1, 2, 3 and at the initial date the in￾vestors purchase an asset (a machine) which they put in the control of a manager. The machine produces a random return yt at dates t = 2, 3 and can be liquidated for a fixed amount L in period t = 2 (it has no scrap value at the last date). All uncertainty is resolved at date t = 2 in the sense that (y2, y3) become known for sure. At the first date, the investors and the manager write a contract which specifies, among other things, the payments to be made by the manager in each period. The contract cannot be made conditional on the earnings of the firm, as these are unverifiable; in fact, the only thing that can be verified is whether the manager has made a specified payment or not. If he has not, then the investors have the right to seize the asset and prevent the manager from using it. Let D be the minimum payment required at the second date. If the manager makes a payment of at least D at t = 2, there is nothing the investors can do to stop him using the rest of the firm’s income for his own purposes after this. At the last date the manager will simply consume y3. There is nothing the investors can do to stop him. At the second to last date, the manager may lose control of the firm if he does not pay D to the investors, but he may get away with less. Clearly, he will never pay them more than D. If he only pays them L it will not be worthwhile seizing the asset. The exact division of the surplus is determined by a bargaining problem, but assuming the manager gets to make a take-it-or-leave-it offer, he will clearly pay the minimum of D and L if he can. If y2 < min{D, L} then the investors will seize the asset, even though this is inefficient if L<y2 + y3. If y2 ≥ min{D, L} the manager will retain control, and his rents equal y2 + y3 − min{D, L}. This story offers several lessons. First, the investors’ power is restricted to the threat of taking away control of the asset. Secondly, this threat is credible

CHAPTER 5. DYNAMIC CONTRACTING only if the manager cannot pay the investors as much as they would get by taking away his control of the asset.(Different bargaining stories would lead to somewhat different conclusions here). Thirdly, because the manager cannot commit to pay the investors in the future, the transfer of control may be inefficient 5.1.3 Aghion and Bolton(1992) Another example of incomplete contracts is provided by Aghion and Bolton (1992). Following Jensen(1986), Aghion and Bolton conclude that managers may use free cash How to overinvest in order to capture private benefits. Debt financing is a method that can be used to restrain managers(the need to pay interest restricts cash flow) and to transfer control of the firm in certain states of nature. The essential assumption is that in states where cash Hlow is low so that the manager cannot service the debt, it is optimal to restrain the manager(transfer control), whereas in states where cash How is high and the manager can service the debt, it is optimal to leave control in the hands of the manager 5.2 Renegotiation Renegotiation is typically regarded as a limitation on the ability of parties to write an efficient contract 5.2.1 Stiglitz and Weiss(1983) Credit markets are characterized by incomplete information, which gives rise to problems of adverse selection and moral hazard. Stiglitz and Weiss(1983) have argued that these problems are mitigated if lenders can threaten bor rowers with punishment in the event of default or poor performance. For example, a firm that defaults on a bank loan may be refused credit in the ture. We noted above that the threat of termination may improve incentives for making an effort In analyzing the optimal use of threats, it is assumed that the lender can commit itself to a particular se of action in advance. Without commit- ment, past default should be regarded as a sunk cost

4 CHAPTER 5. DYNAMIC CONTRACTING only if the manager cannot pay the investors as much as they would get by taking away his control of the asset. (Different bargaining stories would lead to somewhat different conclusions here). Thirdly, because the manager cannot commit to pay the investors in the future, the transfer of control may be inefficient. 5.1.3 Aghion and Bolton (1992) Another example of incomplete contracts is provided by Aghion and Bolton (1992). Following Jensen (1986), Aghion and Bolton conclude that managers may use free cash flow to overinvest in order to capture private benefits. Debt financing is a method that can be used to restrain managers (the need to pay interest restricts cash flow) and to transfer control of the firm in certain states of nature. The essential assumption is that in states where cash flow is low, so that the manager cannot service the debt, it is optimal to restrain the manager (transfer control), whereas in states where cash flow is high and the manager can service the debt, it is optimal to leave control in the hands of the manager. 5.2 Renegotiation Renegotiation is typically regarded as a limitation on the ability of parties to write an efficient contract. 5.2.1 Stiglitz and Weiss (1983) Credit markets are characterized by incomplete information, which gives rise to problems of adverse selection and moral hazard. Stiglitz and Weiss (1983) have argued that these problems are mitigated if lenders can threaten bor￾rowers with punishment in the event of default or poor performance. For example, a firm that defaults on a bank loan may be refused credit in the fu￾ture. We noted above that the threat of termination may improve incentives for making an effort. In analyzing the optimal use of threats, it is assumed that the lender can commit itself to a particular course of action in advance. Without commit￾ment, past default should be regarded as a sunk cost

5.2. RENEGOTIATION Renegotiation thus creates a time-consistency problem. This is typical of contracting problems. However, when contracts are incomplete, renegotia- tion may fill a more beneficial role 5.2.2 Aghion, Dewatripont and Rey(1994) The inability t fy all contingencies and what happens in those contin- gencies does not necessarily prevent achievement of the first best. Even if the state is not verifiable, messages from agents may be. If agents know the state and the contract is contingent on their messages, the outcome can in principle be made contingent on the state through a communication game Here is an example from ADR in which the first best is achieved Consider a two-person risk sharing problem in which there is a finite number of states. Without loss of generality we can assume that the states are numbered s= 1,. S. Descriptions of the state may be more complicated but we can replace those with a simpler message space. Let ys denote the income to be shared in state s. The optimal allocation requires agent l and 2 to receive s and zs ys-Is in state s respectively. Notice that s and ys- s are increasIng in ys A contract c=(as, is) specifies the amount that should be received by each agent in state s. If state s occurs, both agents announce numbers σ,′=1,…,S. If they agree, agent 1 receives r and agent2 receives y-xa If they disagree, the agent who announces the state associated with the higher income becomes the residual claimant and the other agent receives the amount specified in the contract Truth-telling is a Nash equilibrium and implements the first best 523Gale(1991) Rer ay as the following example shows. The venture capitalist and the en- peated renegotiation can reduce the incompleteness of contracts enor oreneur share project revenue w. A complete contract is a pair of functions ) and y(w) that solve max Ela(a)+ Au(g) st.x+y≤ua.s. A simple calculation shows that 0 a(w)< l and 0< y(w)< 1 for all values of a

5.2. RENEGOTIATION 5 Renegotiation thus creates a time-consistency problem. This is typical of contracting problems. However, when contracts are incomplete, renegotia￾tion may fill a more beneficial role. 5.2.2 Aghion, Dewatripont and Rey (1994) The inability to specify all contingencies and what happens in those contin￾gencies does not necessarily prevent achievement of the first best. Even if the state is not verifiable, messages from agents may be. If agents know the state and the contract is contingent on their messages, the outcome can in principle be made contingent on the state through a communication game. Here is an example from ADR in which the first best is achieved. Consider a two-person risk sharing problem in which there is a finite number of states. Without loss of generality we can assume that the states are numbered s = 1, ..., S. Descriptions of the state may be more complicated but we can replace those with a simpler message space. Let ys denote the income to be shared in state s. The optimal allocation requires agent 1 and 2 to receive xs and zs = ys − xs in state s respectively. Notice that xs and ys − xs are increasing in ys. A contract c = {(xs, zs)} specifies the amount that should be received by each agent in state s. If state s occurs, both agents announce numbers σ, σ0 = 1, ..., S. If they agree, agent 1 receives xσ and agent 2 receives ys−xσ. If they disagree, the agent who announces the state associated with the higher income becomes the residual claimant and the other agent receives the amount specified in the contract Truth-telling is a Nash equilibrium and implements the first best. 5.2.3 Gale (1991) Repeated renegotiation can reduce the incompleteness of contracts enor￾mously as the following example shows. The venture capitalist and the en￾trepreneur share project revenue w. A complete contract is a pair of functions x(w) and y(w) that solve: max E[u(x) + λv(y)] s.t. x + y ≤ w a.s. A simple calculation shows that 0 < x0 (w) < 1 and 0 < y0 (w) < 1 for all values of w