Managerial Reputation, Risk-Taking, and Imperfect Capital Markets

2.1 Description

The model has three periods, t=0,1,2 and a single good. There are two types of agents: a manager and a continuum of investors. The manager receives nothing at t=0 and non-verifiable capital A>0 at the beginning of t=1. All investors receive one unit of the good at t=0 and K units of the good at t=1. All agents are risk-neutral with the following utility function over consumption streams: c0+c1+c2. All agents have access to storage technology with a return of one.

The manager’s ability denoted by i takes two values: high (H) and low (L). This ability denotes the manager’s skill level in generating good performance with a high probability and is unknown to both investors and the manager, as in Holmstrom (1999). A manager’s reputation is defined as a belief concerning the probability of being type H. All agents share the prior beliefs π=Pr(i=H).

The manager has two opportunities at t=0,1 to invest. The following three strategies are options at t=0: investment in a risky asset (Gambling, G-strategy, or G), investment in the most value-enhancing asset (Middle, M-strategy, or M), or investment in storage technology (Safety, S-strategy, or S). To focus on a pure strategy equilibrium, the manager chooses the investment strategy x∈{G,M,S}. The G-strategy and the M-strategy either succeed or fail. The G-strategy selected by a manager of type i whose investment level is I0 yields good returns RGI0 with probability pi, whereas the M-strategy yields RMI0 (where RG>RM>0) with probability qi. In the case of failure, the returns from the investment are 0, regardless of whether the G-strategy or the M-strategy is selected. The S-strategy involves storage technology that yields a payoff of one regardless of the manager’s ability and the amount of investment. Our analysis introduces the notation R(x) that represents the return per unit of investment when the date-0 investment strategy x succeeds; that is, R(G)=RG,R(M)=RM, and R(S)=1.

At t=1, the manager has access to a new investment opportunity. ^[6] The investment technology is linear in investment level I1 but requires a minimum investment size Iˆ with Iˆ∈[A,K+A]. ^[7] If I1≥Iˆ, the investment managed by the manager of type i generates the return RNI1 with probability δi with 1>δH>δL>0 and nothing with probability 1−δi; otherwise, it also produces nothing. Most previous papers on reputation concerns with project choices (e. g., Hirshleifer and Thakor (1992) and Guerrieri and Kondor (2012))represent indivisibilities in investments (or start-up costs) as fixed size investments, but our model represents it in the form of a minimum investment requirement as in Acemoglu and Zilibotti (1997).Our approach has an advantage over the assumption of fixed size investment because we can clarify different implications of fixed investments and variable investments for project choices. Managerial incentives to behave con servatively are based on indivisibilities in investments, whereas the incentive to take risks is based on variable investments.

We make three assumptions concerning investments.

This implies that the project managed by an H-type manager succeeds with a higher probability than a project managed by an L-type manager (qH>qL and pH>pL). This reflects the intuition that a manager’s skill is associated with productivity. Additionally, under an H-type manager, the risky investment is more likely to succeed than the relatively safe investment (pH>qH), while under an L-type manager, the risky investment is less likely to succeed (qL>pL). This assumption captures the idea that outcomes of riskier investments depend more heavily on managerial skill. A manager with a high level of ability can more effectively manage riskier assets while a manager with a low level of ability cannot effectively manage risky assets, as in Hirshleifer and Thakor (1992).

where q‾=πqH+(1−π)qL and p‾=πpH+(1−π)pL.

This means that among the three strategies at t=0, the M-strategy yields the highest expected return and the G-strategy yields the second highest expected return. This assumption implies q‾>p‾, which makes the G-strategy more risky than the M-strategy.

This means that even if an L-type manager makes the new investment at t=1, it has a positive NPV. This assumption ensures that the date-1 investment is efficient regardless of reputation.

A manager confronts financial constraints because of a moral hazard problem where, after date-1 investment, the manager chooses to behave without receiving private benefits or to misbehave and take private benefits, as in Holmström and Tirole (1998, 2011). ^[8] If the manager behaves without receiving private benefits, the investment will continue as described above. If the manager misbehaves, the probability of success decreases by Δπ∈(0,δL), where we assume that Δπ is independent of managerial ability. Instead, the manager enjoys benefits BI1 that are inalienable to investors.

We can interpret the reduction in B as the manifestation of an improvement in investor protection or corporate governance, as argued in Tirole (2006, 359), Antràs, Desai, and Fritz Foley (2009), and Holmström and Tirole (2011, 86).The idea behind this interpretation is that a better regulatory system that protects investors is likely to prevent managers from taking private benefits or limit their ability to divert funds from the firm for personal use. For example, regulatory changes to improve the firm’s reporting and increase transparency can limit opportunities for insiders to tunnel resources out of the firm and increase investor protection.

2.2 Financial Contracts and Sequence of Events

A manager can make a take-it-or-leave-it offer to investors with the storage technology as an outside option. Both agents are protected by limited liability. The investment strategy selection x, its returns R(x)I0, and the date-1 return RNI1 are publicly observable and verifiable. For simplicity, R(x)I0 cannot be used for subsequent investments; therefore, capital accumulation is removed from the model. We assume that the contract structure is as follows.

1. The manager has access only to short-term contracts, that is, the manager offers the contract at t=0,1 because investors do not have the ability to commit to future financing. We discuss the lack of commitment in Section 4.1.

2. At t=0, the investors contribute their funds I0, and the manager invests them in an investment strategy x. When the strategy succeeds, the investors will receive d0, and the manager will receive R(x)I0−d0. When the investment fails, both parties receive nothing. Because the contract is contingent on the investment strategy x, the contract specifies the tuple (I0(x),d0(x)).

3. At t=1, the investors contribute their funds I1−A and the manager contributes personal capital A. When the project in which I1 has been invested succeeds, the investors will receive d1, and the manager will receive RNI1−d1. When the project fails, both parties receive nothing. Thus, the contract specifies the tuple (I1,d1).

We outline the timeline structure (see Figure 1). At the beginning of t=0, a manager offers the contract that specifies (I0(x),d0(x)), and the investors who receive the offer decide whether to accept. If the investors reject the offer, the manager is terminated, and investors must use storage technology. If the investors accept the offer, the manager borrows and chooses the investment strategy x with investment level I0(x) and the repayment d0(x). At t=1, all the agents observe the subsequent outcome sx∈{0,1} where 0 indicates failure and 1 indicates success. Both parties infer the manager’s true ability based on sx and update managerial reputation from π to π′ according to Bayes’ rule. Then, the manager offers the new contract that specifies (I1,d1). After receiving the new contract, investors decide whether to roll over their funds. At t=2, the manager decides whether to behave. Then, all the agents observe the outcomes of the investment made at t=1 and are paid as contracted.

Figure 1:

Timeline structure.

2.3 The Incentive Compatibility Condition and Parametric Assumptions

We will describe the incentive compatibility condition and some assumptions concerning the moral hazard problem.

First, we assume that the investment is worthless without effort:

This condition means that the project managed by even the H-type manager has negative NPV even if the private benefit is included, if the manager misbehaves. Under Assumption 4, the manager with any posterior reputation π′ cannot raise any funds if misbehaving and, thus, behaves if raising funds on the equilibrium. To behave, the manager has to obtain certain rents that satisfy the following incentive compatibility condition:

where δ‾(π′)=π′δH+(1−π′)δL. The left-hand side is the manager’s expected gross utility in the case of behavior at t=1: when the investment succeeds with probability δ‾(π′), the manager is paid RNI1−d1. The right-hand side is the manager’s expected gross utility in the case of misbehaving at t=1, that is, the sum of the expected amount the manager is paid (δ‾(π′)−Δπ)(RNI1−d1) and the private benefits BI1. The condition can be rewritten as

implying that δ‾(π′)B/Δπ is the minimum expected rent for the manager per unit of investment necessary to ensure that the manager behaves. Therefore, at most, δ‾(π′)(RN−B/Δπ)I1 are expected to be paid to investors without inducing the manager to misbehave; thus, we call it expected pledgeable income, as in Tirole (2006). It is decreasing in B/Δπ, that is, it is easier for managers to pledge more income in countries with better investor protection.

We make two other parametric assumptions regarding the moral hazard problem. First, the following assumption guarantees that the equilibrium investment at t=1 is finite:

This means that the expected pledgeable income per unit of investment for the H-type manager (the left-hand side) is lower than the unit cost of investment (the right-hand side). If this assumption is violated, a manager can promise to pay to investors without down payments A and collect funds without limits. This condition assures that even the H-type manager faces the financial constraint problem, implying that the manager with any reputation π′ also faces financial constraints. Assumption 4 and Assumption 5 are similar to the assumptions made in Holmström and Tirole (1998, 2011).

The next assumption insures that a manager with reputation π is expected to collect funds up to the minimum investment level Iˆ at t=1:

Given that the investment level is Iˆ, the left-hand side is the expected pledgeable income with an ex ante reputation, whereas the right-hand side represents the funds supplied by investors. The condition assures that when the managerial reputation does not change, investors contribute their funds to such a manager. This assumption captures the idea that investors believe that the manager to whom they lend their funds has the ability to produce enough returns in the future. Therefore, maintaining a reputation is valuable for the manager. Unless the manager’s reputation is damaged, the opportunity to continue to manage should persist.

2.4 Equilibrium Concept

In our paper as a whole, the appropriate equilibrium concept is the perfect Bayesian equilibrium.

3.1 Reputation Updates

Observing the investment strategy x and the subsequent outcome sx, all parties update managerial reputation from π to π′ along the equilibrium path. Managers who implement the S-strategy can conceal information about their ability and maintain their reputation π because the return structure of this strategy is independent of the manager’s ability. The reputation π′ along the equilibrium path of the G-strategy conditional on 0 and 1 successes, denoted by πG,0 and πG,1, respectively, are as follows:

For the M-strategy, the reputation π′ conditional on 0 and 1 successes, denoted by πM,0 and πM,1, respectively, are as follows:

From Assumption 1, we obtain the following relationship between the reputation π′:

All the agents perceive the manager to possess a high ability after a success and to possess low ability after a failure (πx,0<π<πx,1). The difference between the G-strategy and the M-strategy is the quantum of information: the former reveals more information about managerial ability. The G-strategy selected by an H-type (L-type) manager is more (less) likely to succeed than the M-strategy. Consequently, both parties consider the manager who succeeds using the G-strategy more capable than the manager who succeeds using the M-strategy (πM,1<πG,1), whereas both parties consider the manager who fails using the G-strategy less capable than the manager who fails using the M-strategy (πG,0<πM,0).

The investment strategies in our model feature the relationship between returns and reputation; that is, the G-strategy is more volatile concerning both returns and reputation than the M-strategy. The observation that investment risks and reputational risks are positively correlated is central to our results.

3.2 Benchmark Model

As a benchmark, suppose that a manager can commit to future effort although both agents do not know managerial ability. We solve the equilibrium by using backward induction. At t=1, because the manager offers the contract that specifies a tuple (I1,d1) after observing the date-0 investment outcome sx, the optimal contract depends on reputation π′. The optimal contract problem at t=1 is characterized as follows:

subject to

The objective function [5] is the manager’s net expected payoff at t=1. The constraint [6] is the participation constraint for investors at t=1. The left-hand side represents the expected payoff to investors, whereas the right-hand side represents the lending amount given so that the storage technology that produces zero profit is the outside option. The constraint [7] is the resource constraint at t=1 in which all resources are split into the manager’s capital A and the investors’ capital K. The constraint [8] is the minimum investment requirement.

Because any manager produces positive expected profits from Assumption 3, the manager increases the investment level I1 and decreases the payment d1 as much as possible. This means that [6] and [7] are binding, and [8] is not binding. A manager invests all resources regardless of her reputation π′. The value function of this optimal contract problem is given by

where the manager receives the entire social surplus because the investors have zero profit.

Given the result, we characterize the date-0 optimal contract that chooses (x,I0(x),d0(x)) in two steps. First, given the investment strategy x, the manager chooses (I0(x),d0(x)) to solve the following problem:

subject to

The objective function [10] is the manager’s net expected payoff at t=0, where the first term is the manager’s payoff in the case of success and the second term is the manager’s payoff in the case of failure. The constraint [11] is the participation constraint for investors at t=0 given that the storage technology is the outside option. The constraint [12] is the resource constraint at t=0. As with the date-1 contract problem. Assumption 2 implies that the manager decreases the payments d0 and increases the investment level I0 as much as possible, making [11] and [12] binding. Thus, the manager’s value function at t=0 with the investment strategy x is given by

where V(π′) is given by [9].

Second, the manager chooses the strategy x that produces the highest payoff to solve

The important point is that the investment strategy x does not affect the expected payoff at date 1, that is, EV(π′)|x=V(π). This means that the manager is concerned only with expected return Pr(sx=1)R(x), not reputation. Figure 2 explains the point intuitively. The horizontal line represents reputation π′, and the vertical line represents V(π′) given by [9]. Here, superior reputation does not affect the investment level but increases the probability of the success and the NPV, which generates a linear relationship between π′ and V(π). This implies that there is no distortion caused by the inflow of funds in response to the manager’s past performance and no bias concerning the risk preference. Thus, the manager adopts the M-strategy, which yields the highest expected returns from Assumption 2. ^[10]

Figure 2:

Benchmark case.

3.3 Model with Moral Hazard

This section introduces the moral hazard problem and shows how the investment decision is distorted depending on the level of investor protection. On the equilibrium, the manager must behave to obtain financing because investors do not lend to a manager who jeopardizes their funds from Assumption 4. Given a posterior reputation π′, the optimal contract problem at t=1 is characterized as follows: choosing (I1,d1) to solve the problem [5]–[8] plus the incentive compatibility condition [1]. As with the benchmark problem, the manager increases the investment level I1 and decreases the payment d1 as much as possible from Assumption 3, making [6] binding. Then, combining [1] and [6], we obtain

where the left-hand side represents expected pledgeable income. As long as it is greater than the lending amount, the manager can borrow money; that is, the manager raises funds up to the binding condition:

where

from Assumption 5, which represents the leverage per unit of personal capital. This implies that I1 is increasing in π′; that is, a manager with a superior reputation is perceived more likely to succeed in the investment and collects more funds. If K is sufficiently large, the condition [7] is not binding.

However, the manager obtains refinancing only when the amount she can invest satisfies the minimum investment level [8] or, equivalently, managerial reputation exceeds the threshold denoted by πˆ:

where πˆ<π from Assumption 6. If π′≥πˆ, the manager will obtain financing; otherwise, the manager will not obtain financing and will just invest personal capital in storage technology.

The relationship between reputation π′ and level of investment I1 is depicted in Figure 3 In contrast with the benchmark, there is a positive and non-linear flow-performance relationship, which leads to reputation concerns and bias about risk preference. The essential point is the effect of investor protection on the necessary reputation that assures management continuity. [15] implies that πˆ is increasing in B/Δπ, that is, the stronger the investor protection, the more tolerant investors are towards managers’ failures. Thus, when investor protection is strong, the manager is likely to continue to invest even after showing an investment failure and obtaining a poor reputation.

The value function of the date-1 optimal contract problem is given by

When π′≥πˆ, V(π′) represents the benefits of informativeness because V(π′) is convex in π′. A better reputation increases the probability of success and pledgeability, leading to the convexity. Given the function, the manager can take advantage of the information by managing funds. However, when π′<πˆ, V(π′) goes to 0, which represents the cost of informativeness. If the investment failure reveals the manager’s incompetence and the reputation becomes lower than the threshold, the manager must simply save the endowment A.

Given the result, we solve the date-0 optimal contract problem. First, we choose (I0(x),d0(x)) to solve the problem [10]–[12] given the strategy x. Because there is no moral hazard at t=0, the problem is the same as the benchmark model, except for the value function V(π′), which is given by [16] but not [9]. The manager decreases the repayments d0(x) and increases the investment level I0(x) as much as possible, making [11] and [12] binding. Thus, the manager’s value function at t=0 with the investment strategy x is given by

where V(π′) is given by [16]. In contrast with the benchmark given by [13], [17] implies that the investment strategy x affects the date-1 payoff EV(π′)|x. This is because the superior reputation increases both NPV and pledgeability as shown in Figure 3. The investors’ responses to reputation motivate managers to build their reputation through project risk.

Figure 3:

Investment level.

Then, consider the date-0 strategy x to solve the problem [14] as a function of the level of investor protection B/Δπ. First, we suppose the situation where the quality of investor protection is high (B/Δπ is small) such that πˆ≤πG,0, as depicted in Figure 4. Strong investor protection encourages tolerance among investors with respect to failures and leads them to roll over their funds regardless of the manager’s reputation. Thus, the manager is willing to reveal information about managerial competence to exploit an opportunity to adjust funds. Because the G-strategy is the most informative strategy in the sense of Blackwell and produces the highest benefit, as Figure 4 shows, the manager chooses the G-strategy if the difference of expected returns between the M-strategy and the G-strategy q‾RM−p‾RG is sufficiently small.

Figure 4:

The manager’s expected utility in the case of πˆ≤πG,0.

Next, we suppose the quality of investor protection is intermediate (B/Δπ is intermediate) such that πG,0<πˆ≤πM,0. This case is illustrated in Figure 5. The difference compared to the previous case is that a failure of the G-strategy results in bankruptcy, which is the cost of informativeness. If the cost is sufficiently large, the manager has strong disincentives to adopt the G-strategy to avoid disclosing information about managerial incompetence. Consequently, to mitigate reputational risk, an opaque strategy that is less informative becomes a more attractive option, leading the manager to engage in the M-strategy.

Figure 5:

The manager’s expected utility in the case of πG,0<πˆ<πM,0.

Finally, consider that the quality of investor protection is poor (B/Δπ is large) such that a failure by either strategy does not assure management continuity corresponding to the case where πM,0<πˆ≤π (see Figure 6). The decrease in the quality of investor protection reduces the benefits of the M-strategy because the failure leads to the cost of losing investment opportunity. The cost renders the manager reluctant to reveal information. If the value of investment opportunity at t=1 is sufficiently high, the manager adopts the S-strategy, although it is the least profitable, to conceal managerial ability and continue management. This entire discussion is summarized as a proposition.

Figure 6:

The manager’s expected utility in the case of πM,0<πˆ<π.

the date-0 equilibrium strategy is the M-strategy and the date-1 investment levels arek(πM,1)Aafter a success andk(πM,0)Aafter a failure.

1. Suppose πM,0<πˆ≤π. If

the date-0 equilibrium strategy is the S-strategy and the date-1 investment level isk(π)A.

Finally, we note the welfare implications. Given utilitarian social welfare and the zero-profit condition for the investors, the manager receives all of the social surplus. Thus, social welfare is equivalent to the manager’s value function W, which is given by

As the investor protection improves, the social welfare [20] increases through two channels. First, given that the equilibrium strategy x is constant, the manager can increase the investment level k(π′)A and the social surplus the investment produces. Second, since the cutoff reputation πˆ decreases from [15], the equilibrium strategy becomes more risky. The more informative investment increases the value of the option to invest and social welfare improves. (i. e., WG>WM>WS). Therefore, the volatility in our model is beneficial to the economy, as in Bartram, Brown, and Stulz (2012). Compared to the benchmark solution, in which social welfare is given by q‾RM−1+(δ‾(π)RN−1)(K+A), the above two channels decrease social welfare.

3.4 Comparative Statics

This section examines comparative statics to derive more empirical predictions and welfare implications from our model. To clarify the explanation, before conducting comparative statics, suppose πˆ≤πG,0 and the equilibrium strategy is the G-strategy, which leads to social welfare WG.

First, we study the comparative statics with respect to the minimum investment level Iˆ. [15] implies that an increase in Iˆ leads to an increase in the cut-off reputation πˆ. Because more funds must be invested, the manager who will borrow funds requires a higher reputation. Figure 7(a) shows the effect. When πˆ<πG,0, a marginal increase in Iˆ does not change the equilibrium strategy and social welfare. When πˆ=πG,0, a marginal increase in Iˆ, combined with Figures 4 and 5, implies that increased fear of missing an investment opportunity makes the G-strategy less attractive. Therefore, the manager chooses the M-strategy, which reduces the value of the option to invest and social welfare by WG−WM.

Figure 7:

Comparative statics. (a) On minimum investment level Iˆ. (b) On agency costs B/Δπ and a manager’s capital A. (c) On informativeness of the G-strategy pH and pL.

Next, we consider the effect of a decrease in the manager’s capital A (Figure 7(b)). A decrease in A affects the manager’s date-1 payoff V(π′) from [16], which is a similar prediction as the increase in agency costs B/Δπ. When πˆ<πG,0, a marginal decrease in A induces a fall in the investment level k(π′)A. This makes the expected date-1 payoff with the G-strategy EV(π′)|G smaller than the payoff with other strategies. If p‾RG is sufficiently close to q‾RM, the equilibrium strategy remains the G-strategy, but social welfare WG is lower. When πˆ=πG,0, a marginal decrease in A induces an increase in πˆ from [15], which leads to the inequality πˆ>πG,0. Thus, the manager is induced to invest in the M-strategy, which lowers social welfare by WG−WM. Therefore, our model predicts that capital-poor firms have a tendency to make less risky investments to control reputational risk.

Finally, we perform comparative statics with respect to the informativeness of the investment strategy. In particular, we consider a marginal increase in the probability of success for the H-type manager, pH, affecting the manager’s payoff [20] through two channels. ^[11] First, the expected return of the G-strategy p‾RG increases. Second, the G-strategy becomes more informative in the sense of Blackwell, leading to a lower posterior reputation in the case of failure πG,0 from [2] and a higher posterior reputation in the case of success πG,1 from [3]. When πˆ<πG,0, the second effect makes the expected date-1 payoff with the G-strategy EV(π′)|G greater because the more informative investment renders the option to invest more valuable, thereby improving social welfare WG. However, when πˆ=πG,0, as Figure 7(c) shows, the second effect leads to the inequality πˆ>πG,0, and the manager with reputation πG,0 misses the investment opportunity. This reduces the expected value of the date-1 investment EV(π′)|G dramatically. Figure 5 implies that the risk created by increased informativeness leads the manager to prefer the M-strategy, which lowers social welfare. Thus, the welfare effect of the increase in pH is not monotonous.

4.1 Long-term Contracts

In this section, investors do not have a commitment problem, which allows a manager to offer long-term and state-contingent contracts. The manager offers contracts only at t=0 that specify (I0(x),I1(sx),d0(x),d1(sx)). We have to consider two optimal contract problems. The first contract is one from which the manager obtains refinancing regardless of the outcome sx, and the second contract is one from which the manager obtains refinancing in the case of success sx=1 but gives up refinancing and invests the capital A into storage technology in the case of failure sx=0. Comparing both contract problems, the manager chooses the contract that yields higher expected utility.

First, the optimal contract problem is set to assure financing necessarily. We characterize the optimal contract that chooses (x,I0(x),I1(sx),d0(x),d1(sx)) and solves the following problem:

subject to for each x [12],

The objective function [21] is the manager’s net expected payoff. The first term is the expected payoff at t=0, the second and the third terms are the expected payoff at t=1 in the case of success of the date-0 investment and in the case of failure of the date-0 investment, respectively. The fourth term is the self-investment. The constraint [22] is the participation constraint of the investors given their outside option that yields zero profit. The left-hand side is the expected payments for investors, and the right-hand side is the expected cost of the investment. The constraint [23] is the limited liability condition. ^[12] The constraints [24] and [25] are resource constraints at t=1 in which all resources are split into the manager’s capital A and the investors’ capital K. The constraints [26] and [27] are the minimum investment requirement. The constraints [28] and [29] are the incentive compatibility conditions, which mean that financing requires that the manager can promise investors, at most, income (RN−B/Δπ)I1(sx=1) and (RN−B/Δπ)I1(sx=0) without misbehavior in case of success and failure, respectively.

The second contract can be characterized to obtain refinancing only when sx=1. This optimal contract problem is to choose (x,I0(x),I1(sx=1),d0(x),d1(sx=1)), to solve

subject to for each x [12], [23], [24], [26], [28], and the participation constraint for investors

The equilibrium investment strategy is the G-strategy. If the inequality

is satisfied, the date-1 investment levels are k(πG,1)[A+RG−1/p‾−(1−p‾){Iˆ/k(πG,0)−A}/p‾] after a success and Iˆ after a failure. If [32] does not hold, the date-1 investment levels are k(πG,1)[A+RG−1/p‾] after a success and 0 after a failure.

The moral hazard problem that creates financial constraints restricts the investment level at t=1 and, thus, the manager cannot obtain full funding. It is optimal for the manager to offer a contract under which investment must be contingent on reputation; that is, a good reputation attracts more funds than a bad reputation. The important feature of such state-contingent contracts is that the manager can offer an insurance-like contract in which even when sx=0, the manager attracts funds up to the minimum investment level Iˆ. The option-like nature generates benefits to adjust funds based on the information the date-0 investment produces. The benefits of informativeness induce the manager to undertake the most informative strategy, the G-strategy.

When investor protection is weak (B/Δπ is large) such that the condition [32] is violated, it becomes costly to assure the minimum investment level Iˆ when the manager obtains a bad reputation. Thus, even though the insurance-like contract is available, the manager prefers aggressive investments: choosing to forsake the date-1 investment opportunity when sx=0 and selecting the G-strategy.

Comparing Proposition 1 with Proposition 2, we show that the limited commitment of investors prevents the manager from transferring funds across states and offering an insurance-like contract, which induces the manager to behave conservatively to avoid the possibility of missing investment opportunities. Figure 8 clarifies this point by comparing the equilibrium investment level in Proposition 1, which is depicted as the light (red) line, with the equilibrium investment level in Proposition 2 under condition [32], which is depicted as the dark (black) line, for each B/Δπ. ^[13]Figure 8 implies that the long-term contract using the transfer between states allows the manager to hedge the risks in which she loses the investment opportunities at t=1 regardless of the level of investor protection.

Figure 8:

The comparison of the investment level in the equilibrium between the model in Section 3.3 (depicted as the light (red) line) and the model in Section 4.1 under condition [32] (depicted as the dark (black) line).

In region [1] where πˆ≤πG,0, although the investment strategy is the G-strategy in both models, the investment level in Section 4.1 is more volatile than in Section 3.3. In Section 4.1, the manager transfers available funds from the state of failure (sG=0) to the state of success (sG=1). In Section 3.3, however, the limited commitment prevents such transfers across states and forces the manager to hedge against failure.

In region [2] where πG,0<πˆ≤πM,0, the manager with the G-strategy who faces the investors’ limited commitment (in Section 3.3) cannot assure the minimum investment level Iˆ when sG=0 (i. e., k(πG,0)A<Iˆ). ^[14] The only way to avoid the bankruptcy is to select a less risky investment strategy, the M-strategy, which results in less volatile investment levels than Section 4.1. In region [3] where πM,0<πˆ≤π, a lack of commitment prevents the manager with the M-strategy from assuring Iˆ when sM=0 (i. e., k(πM,0)A<Iˆ) and induces the manager to adopt the S-strategy to avoid the risk of bankruptcy.

4.2 Date-1 Risk Choice

Suppose at t=1 the manager chooses the investment strategy x′ among the three strategies, not new investment technology. Accordingly, we introduce the minimum investment requirement into the G-strategy and the M-strategy. If I1≥Iˆ, the G-strategy (the M-strategy) operated by a manager of type i yields RG(RM) with probability pi (qi) and nothing with probability 1−pi (1−qi); otherwise, it produces nothing. We make the following stronger assumption concerning the investment return than Assumption 2:

where q‾(π′)=π′qH+(1−π′)qL and p‾(π′)=π′pH+(1−π′)pL.

This condition implies that the investment made by any manager is always efficient and, for the manager with possible reputation on the equilibrium, the M-strategy yields higher expected return than the G-strategy. The condition assures that under a benchmark case in which there is no moral hazard problem, the M-strategy is the equilibrium investment strategy in both periods 0 and 1.

Then, we modify the moral hazard problem. When the manager chooses the S-strategy, the moral hazard is irrelevant because only storage technology is used. Choosing the G-strategy or the M-strategy, the manager faces the moral hazard problem. If the manager behaves without receiving private benefits, the probability of success for each investment strategy is not affected. If the manager misbehaves and enjoys private benefits BI1, the probability of success decreases by Δπ regardless of the type and the investment strategy. We modify three assumptions about the moral hazard problem (Assumptions 4–6) in the following way:

The only difference from Assumptions 4–6 is that the date-1 investment is not new investment technology. The first assumption implies that even the H-type manager with the G-strategy produces negative NPV if the manager misbehaves. The second assumption means that even the H-type manager with the G-strategy cannot offer sufficient expected pledgeable income and must face financial constraints. Under these assumptions, managers with any reputation and any date-1 investment strategy have to behave on the equilibrium and face financial constraints. The third assumption means that the manager whose reputation remains unchanged can collect funds up to Iˆ by choosing either the G-strategy or the M-strategy.

Consider the date-1 contract problem. The manager with reputation π′ can offer the contract that is contingent on the date-1 investment strategy x′. Under Assumption 1 and Assumptions 7–10, we solve the date-1 optimal contract problem by choosing (x′,I1(x′),d1(x′)) in two steps.

First, given the investment strategy x′∈{G,M} and the outcome of the date-0 investment sx, we choose (I1(x′),d1(x′)) to solve

subject to

The problem is almost the same as the date-1 optimal contract problem ([1] and [5]–[8]), except for the date-1 investment technology. The objective function [33] is the manager’s expected payoff at t=1, the constraint [34] is the participation constraint of the investors, the constraint [35] is resource constraints at t=1, the constraint [36] is the minimum investment requirement, and the constraint [37] is the incentive compatibility condition. Because we can apply the same analysis in Section 3.3 to the problem [33]–[37], we have the investment level and the value function with the strategy x′,

and

If the manager has a sufficiently good reputation, financing is secured for investment; otherwise, the manager cannot continue management.

Second, the manager chooses the investment strategy x′ to solve

where the S-strategy that produces zero payoff is not selected at t=1. This result is summarized in Figure 9. When B/Δπ is low (Figure 9(a)), any manager chooses x′=M (i. e., U1(G)<U1(M)) because Assumption 7 assures that the M-strategy is efficient. When the manager’s rents B/Δπ is high (Figure 9(b)), the manager with the M-strategy must receive much larger expected rents q‾(π′)B/Δπ to behave than the manager with the G-strategy p‾(π′)B/Δπ. This, in turn, leads to lower pledgeable income with the M-strategy q‾(π′)RM−B/Δπ than with the G-strategy p‾(π′)RG−B/Δπ. As reputation π′ increases, the difference in pledgeability also increases. Consequently, when B/Δπ and π′ are high, the G-strategy reduces the moral hazard problem and leads to larger investments than the M-strategy (i. e., I1(G)>I1(M)). The benefit of the additional inflow of funds induces the manager with high π′ to choose the G-strategy (i. e., U1(G)>U1(M)).

Figure 9:

The manager’s expected payoff and the investment at t=1. (a) Low B/Δπ. (b) High B/Δπ.

Based on Figure 9, we consider the date-0 investment strategy. In the case of Figure 9(a), where investor protection is strong, because the shape of the manager’s net expected payoff at t=1V(π′) changes minimally, we use the same logic in Section 3.3. The manager prefers risky investments, and the conclusion is not affected. In the case of Figure 9(b), where investor protection is weak, the option to select the G-strategy at t=1 increases the benefits of obtaining a good reputation. The additional reputation benefit can induce the manager to take risks. Thus, when the reward for a good reputation is small, the manager still has a fear of losing her reputation and behaves conservatively at t=0.

4.3 Date-0 Moral Hazard Problem

We incorporate the minimum size requirement and the moral hazard problem at t=0 into the model in Section 3.3. If I1≥Iˆ, the G-strategy (the M-strategy) operated by a manager of type i yields RG(RM) with probability pi (qi) and nothing with probability 1−pi (1−qi); otherwise, it produces nothing. The manager with the G-strategy or the M-strategy faces a moral hazard problem t=0 as well as t=1. When she behaves, the project will proceed as described above. When the manager misbehaves, the probability of success decreases by Δπ regardless of the type and the investment strategy. We assume that the date-0 investment in the case of misbehavior is inefficient regardless of the investment strategy:

This ensures that the manager does not misbehave on the equilibrium path. Also, we assume that Iˆ≤1 because there is only one unit of good in the economy at t=0.

Suppose that Assumptions 1–6 and Assumption 11 hold. Because the date-1 contract problem is the same as in Section 3.3, we consider the modified date-0 contract problem. In this phase, the manager chooses the contract (x,I0(x),d0(x)) to maximize [10] subject to the participation constraint for investors [11], the resource constraint [12], and the following incentive compatibility constraint,

The left-hand side represents the manager’s gross expected utility at t=0 in case of behaving, whereas the right-hand side represents the manager’s gross expected utility at t=0 in the case of misbehaving.

The incentive compatibility condition can be rewritten as

where the right-hand side is the minimum rent at t=0 necessary for the manager to make an effort. Compared to the date-1 incentive compatibility condition [1], the manager is more likely to behave at t=0 because of reputation benefits, which is represented as V(πx,1)−V(πx,0). The reward for success gives the manager the incentive to behave. This implies that the manager’s expected pledgeable income at t=0 is higher and financial constraints are less severe than the case at t=1. Consequently, when the reputation benefits are sufficiently large, the manager can collect all funds in the economy despite the presence of moral hazard, and Proposition 1 does not change. ^[15]