The Impact of Bank Health on Coordination among Creditors

We investigate how the health of a relationship bank impacts upon coordination among creditors and how it affects the firm’s behavior. We show that if the relationship bank is healthy, creditors coordinate each other and the firm takes an efficient action but if it becomes financially distressed, a coordination problem arises ex post and the inefficient liquidation of the firm’s projects may occur. This coordination failure, in turn, increases the interest payments ex ante so that the firm is more likely to choose an inefficient action.


Introduction
This paper investigates how the health of a firm's relationship bank affects the actions of firms and the coordination of creditors.In line with Modigliani and Miller's [1] seminal contribution, not only the financial structure of the firm but also the firm's sources of capital are irrelevant in terms of firm valuation.However, in practice, because of asymmetric information between agents, transaction costs, and the presence of social or traditional institutions, it is costly for the firm to switch creditors, especially away from its existing relationship bank.
The pros and cons of relationship banking have been discussed in many studies (Petersen and Rajan [2], Boot [3], Boot and Thakor [4], and Berger and Udell [5]) 1 .Within these studies, it is argued that the close ties between the relationship bank and the firm potentially provide improvements in information production and monitoring, assist in the renegotiation of contracts, and thus increase the availability of loans to the firm.However, this also grants monopoly power to the relationship bank, and thus the firm may face an ex post hold-up problem.
Moreover, these relations can be adversely affected when the relationship bank becomes financially distressed.For example, Gibson [6,7] concluded that pub-licly listed Japanese firms with ties to lower-rated relationship banks typically spent less on investment in the early 1990s than firms associated with higher-rated banks 2 .Similarly, Bae et al. [8] found that when relationship banks failed during the 1997-1998 Korean banking crisis, the stock returns of the borrowing firms generally fell 3 .
However, in practice, many firms, particularly in Europe and Asia, borrow from several banks.For instance, Ongena and Smith [9] showed that large European firms usually borrow from eight or more banks, while Miyakawa [10] found that the typical Japanese firm obtained funds from 9.8 banks in 1999.Detragiache et al. [11] showed that the benefit of establishing multiple banking relationships is to mitigate the liquidity risk in spite of higher transaction costs 4 .
In the multiple banking relationships, one bank acts as a relationship bank and other banks act as "arm's length" lenders (Bannier [12]).Unfortunately, the overriding prevalence of heterogeneous multiple bank financing has received scant attention in the theoretical literature.This is partly because of a technical difficulty faced in this sort of analysis.That is, when incorporating the coordination problem between a relationship bank and other arm's-length banks, we face the problem of multiple equilibria.With multiple equilibria, because it is impossible to determine which equilibrium is achieved, we cannot generally determine how the coordination problem affects the firm manager's incentives and the nature of the ex ante financial contract.However, recent progress in the literature on equilibrium selection, especially the notion of the global game, enables us to better analyze these issues.This is because when we introduce incomplete information and strategic complementarities among players into the model, we can obtain a unique equilibrium solution.
There has been much recent research on how coordination failure among creditors affects the financial contract based on the concept of the global game (Morris and Shin [20], Hubert and Schafer [21]).Recently, the coordination problem arising from heterogeneous multiple bank financing has also been the subject of some attention by Bannier [12].Bannier [12] extended the model in Corsetti et al. [22] using the asymmetric global game and derived a unique equilibrium, showing that in some circumstances because of the information advantages of the relationship bank, heterogeneous multiple bank financing urges the coordination between the relationship bank and the other arm's-length creditors and thereby leads to fewer inefficient credit decisions than either monopoly relationship lending or homogeneous multiple bank financing.
This paper, by incorporating the health of the relationship bank into the model, investigates how the relationship bank's health affects the coordination between itself and the firm's other creditors and how this expost coordination problem affects the ex ante efficiency of the firm's actions.Our main findings are as follows.First, as the relationship bank becomes financially distressed interest payments by the firm to both the relationship bank and its other creditors increase because of coordination failure.This is because as the relationship bank becomes distressed, it desires the firm to undertake riskier actions whereas the other creditors want the firm to undertake safer actions.Thus, a coordination problem arises in the interim period and the other creditors are then more likely to withdraw their loans from the firm.Therefore, the poor health of the relationship bank induces the inefficient liquidation of the firm's projects and this reduces the economy's ex post efficiency.Second, this increased ex post inefficiency also reduces the ex ante efficiency of the firm's actions.This is because the higher interest payments made to the relationship bank and other creditors encourage the firm to select inefficient and riskier projects.Overall, as the financial health of the relationship bank deteriorates, the efficiency of the economy also declines from both an ex ante and expost point of view through the increased coordination failure found among creditors.
The remainder of the paper is structured as follows.Section 2 describes the model to be used.In Section 3, we consider project choice by the firm.In Section 4, we derive the creditor's decision and derive the equilibrium strategies of the relationship bank and the firm's other creditors.In Section 5, we determine the interest payments by the firm to both the relationship bank and its other creditors.In Section 6, we investigate the comparative statics and derive how the health of the relationship bank affects the coordination among creditors and the firm's choice of project.Section 7 concludes the paper.

The Model
We assume there are three periods, and three types of agents, a firm, a relationship bank, and a continuum of other creditors.The firm has a fixed scale technology that requires one unit of capital at 0,1, 2, t  t 0  .The firm also has no wealth and borrows units from the relationship bank and We assume i is i.i.d.across the other creditors and  B  and i are independent of each other and   .We also assume that    such that the relationship bank has the ability to acquire relatively more precise information about the firm.
Given the signals concerning the firm's project, the creditors decide whether to continue or withdraw their loans from the firm.If the relationship bank withdraws its loans, it receive a liquidation value and the other creditors' liquidation value is .Let L  be the amount of loans that are continued at 1 t  and be the proportion of creditors that continue their loans.At l 1 t  , knowing  , the firm's manager decides whether to implement the safe project or the risky project.At 2 t  , the firm's final output is realized.Then the relationship bank demands repayment of B r and each other creditor demands a repayment of I r , both of which are determined at 0 t  .If the project generates suffi-cient cash to meet the repayment demands of the firm's creditors, the firm then receives the residual output.
The payoff of the project thus depends on the decisions of both the manager and the creditors; that is, whether the manager chooses the safe project or the risky project and how many creditors continue their loans.Consider if project quality  is realized at 1 t  and the amount  of loans are continued at t  hen the firm chooses the safe project, the firm's output at 2 t is, the firm's output increases when more creditors continue at 1 t .That  egic complementarity).Alternatively, when the firm chooses the risky project, the firm's output is    bility of with a proba 1 2 and 0 wit probability of h a 1 2 where 0   .That is, it is assumed that choosing the safe project is always efficient for every value of  .
If the final outp does not meet the total repayments of creditors, the firm goes bankrupt at 2 t  and the crediivide the output in proportion to the size of their loans to the firm.We assume that the liquidation value of the asset is 0 at 2 t  .ut tors d

Project Choice by the Firm
In this section, we consider the firm's incentives.The condition for the safe project to be chosen depends on the number of creditors willing to continue their loans until .Let 2 t  i  and be the amount of creditors and the total amount of repayment when the relationship bank continues (withdraws) at .Then, When the firm chooses the safe project, the final output at Next, consider the case in which the firm chooses the risky project.In this case, given the project quality is realized with probability 1 2 and 0 with probability 1 2 .Then, as in the previous case, let R M be the firm's expected payoff at when the firm chooses the risky project.Then, The firm chooses the safe project if . That is, the firm chooses the safe project at when the following inequality is satisfied.
Obviously, this condition is affected by whether the relationship bank continues its loan.We further investigate this condition in the next section.

The Creditors' Decision
In this section, we investigate the choice of the creditors in whether to continue or withdraw their loans at 1 t  .Under the settings of this model, we can characterize this as a switching strategy whereby the relationship bank withdraws (continues) the loan if it observes the signals below (above) B x  and the other creditors withdraw (continue) their loans if they observe the signals below (above) I x  5 .In this section, we first derive the equilibrium switching strategies for both types of creditors.We then consider how the health of the relationship bank affects the coordination of creditors and the risk-taking of the firm.

The Other Creditors' Choice
In this subsection, we derive the equilibrium switching strategies of the other creditors (not the relationship bank).The payoffs for the other creditors depend on three factors: that is, how many creditors continue their loans at 1 t  , whether the relationship bank continues its loan, and the project the firm chooses.First, the proportion of other creditors continuing their loans at 1, t l  , is given by those that receive private information higher than I x  .Note that 1 , denote the threshold above which the firm chooses the safe project when the relationship bank continues (withdraws) its loan.Then, we can derive the following lemma.
Lemma 1.When and R  are small and the degree of strategic complementarity is small, the firm is more likely to choose the safe project.
(Proof) See Appendix 1. Lemma 1 indicates that when is large, or R  is small, the firm is more likely to choose the risky project.Moreover, given the same number of creditors who continue their loan, the payoff of the firm becomes smaller as the degree of the strategic complementarity becomes larger.Thus, the firm can obtain more when it chooses the risky project than when it chooses the safe project.
Next, we calculate the expected payoff for the other creditors at .As their payoffs are affected by whether the relationship bank continues its loan and which project the firm chooses, we can categorize their payoffs into four cases.

1) The case when the relationship bank continues and the firm chooses the safe project
In this case, when the creditors receive a signal I x , they consider that  is distributed according to 1 , the creditors consider that B x is distributed according to , Thus, creditors receiving the signal I x believe that the relationship bank will continue with probability In addition, the probability they assign to the firm choosing the safe project given that the relationship bank continues is6 In this case, the proportion of loans that a e continued becomes , the firm goes bankrupt and creditors receive the output in proportion to their stake in the firm.

2) The case when the relationship bank continues and the firm chooses the risky project
In this case, the probability that other creditors assign to the firm choosing the risky project given that the relationship bank continues is

3) The case when the relationship bank withdraws and the firm chooses the safe project
In this case, when creditors receive a signal I x , they consider that the relationship bank withdraws with probability In addition, the probability that they assign to the firm choosing the safe project given that the relationship bank withdraws is In this case,   . Let be the expected payoff of each other creditor.Then, be the expected payoff of each other creditor.Then,

4) The case when the relationship bank withdraws and the firm chooses the risky project
In this case, the probability that creditors assign to the firm choosing the risky project given that the relationship bank withdraws is In this case, as in the previous case, Denoting by   the expected payoff of creditors when they receive a signal I x , then, Then, the trigger value I x  is determined so that creditors are indifferent between withdrawing and continuing their loans: Then, we can derive the following proposition.Proposition 1.
x and thus I x  is uniquely determined.(Proof) See Appendix

The Relationship Bank's Choice
Next, consider the relationship bank's switching strategy.The payoff for the relationship bank when it continues its loan depends on how many of the other creditors continue their loans, the project the firm chooses, and the amount of outstanding debt, .First, when the firm chooses the safe project, the expected payoff for the relationship bank, d π S B , can be described as follows: Next, consider the case when the firm chooses the risky project.Let π R B be the expected payoff for the relationship bank.Then, Comparing π S B with π R B , we derive the following lemma.
Lemma 2 indicates firstly that the relationship bank wants the firm to undertake the safe project when the bank is prudent (i.e., is small), and secondly that when as the relationship bank becomes less prudent and  is small, it becomes better off if the firm undertakes the risky project.Therefore, from Lemma 2, when the relationship bank is less prudent, the relationship bank wants the firm to select the risky project, and this incentive lies contrary to that of the other creditors.
Next, consider the optimal switching strategy of the relationship bank.When the relationship bank receives a signal B x , it considers  to be distributed as . Then, if the relationship bank continues its loan, it considers that the firm will choose the safe project with Given that under the optimal switching strategy the relationship bank receives the same expected payoff for continuing and withdrawing, B x  is determined to satisfy the following equation. Copyright The first term on the RHS in (4) denotes the expected liquidation value at , while the second term is the expected payoff when both the relationship bank and the other creditors continue their loans and the firm chooses the safe project.
) Note that, in determining the level of B r , the firm is unconcerned about the amount of outstanding debt held by the relationship bank.In other words, the level of B r is determined regardless of the level of .Therefore, the second and third terms in (5) are included . In sum, the equilibrium of this model , , , , , , , is solved by (1), ( 2), ( 3), ( 4), (5).

Comparative Statics
In this section, we investigate how the prudence of the relationship bank affects the ex ante and ex post efficiency of the model economy.To prove this problem, we analyze the comparative statics of the model, especially by changing the size of .To derive this, we firstly consider the relation between x  and .Then, we can derive the following proposition 7 .
(Proof) See Appendix 5.This proposition indicates that when is small, such that x  and I x  .In terms of this, we can derive the following proposition.Proposition 4. When  is small or I L is small, 0

Concerning the relation between B
x  and I x  , the other creditors are affected by the relationship bank's decision in two ways.Suppose the relationship bank decreases B x  .First, because the relationship bank assigns a greater probability to continuing its loan, the decision informs the good state of the firm to the other creditors.This is because the relationship bank has an information advantage over the other creditors 8 .Given that there exists a strategic complementarity between the other creditors and the relationship bank about the return from the project (i.e., 0, ), this effect brings about a greater payoff for each of the creditors.Second, the decrease in B x  increases the probability of the firm choosing the risky project.In this case, creditors receive the payoff  .Thus, if the first positive effect outweighs the second negative effect, I x  also decreases (i.e., > 0 ).On the other hand, if the second effect outweighs the first effect, I x  increases (i.e., 0 

I B
).Then, as Proposition 3 suggests, if the relationship bank is in the region where it wants the firm to undertake the risky project, the other creditors should set x  .Then, from Propositions 3 and 4, we can immediately derive the following proposition.
holds. 8Of course, this effect is strengthened if  increases.
Copyright © 2013 SciRes.TEL wise, 0 This proposition indicates that when the relationship bank becomes less prudent, creditors are more likely to withdraw their loans.This is because, as the previous arguments suggest, when becomes larger, the relationship bank wants the firm to choose the risky project, unlike the other creditors.In sum, if the relationship bank has outstanding debt at the starting period, it breaks the coordination between the relationship bank and the other creditors, and thus early liquidation of the project may take place.In Corsetti et al. [22] and Bannier [12], the existence of a single large stakeholder motivates the numerous other small creditors to coordinate their choices, as derived from the ability of a large stakeholder to acquire information about the firm more precisely.However, in this model, the existence of the relationship bank brings about both a positive and negative effect on the firm's other stakeholders (here, other creditors).This difference arises because in this analysis, the firm can choose a safe or a risky project, and, due to the existence of the outstanding debt of the relationship bank, the criteria on which the project choice is based differ between the relationship bank and other creditors.d Finally, we derive the following proposition.
This proposition indicates that when the relationship bank is not prudent, the firm is more likely to select a risky project.The intuition behind this is as follows.
Suppose  is small so that the other creditors have the large stakes of the firm.Then, as becomes larger, the coordination problem among creditors arises at d 1 t  and thus more other creditors withdraw at .This, in turn, affects the determination of r should be increased.As Lemma 1 denotes, the firm is more likely to choose the risky project as increases.Therefore, the increase in R I r shifts c  and w  higher.On the other hand, when  is large so that the relationship bank holds the large stakes of the firm, then as Proposition 3 denotes, it sets B x  lower when is large.This, in turn, urges the firm to undertake an inefficient risky project.Therefore, regardless the size of d  , the ex ante efficiency of this economy is deteriorated as the relationship bank becomes less prudent.
This proposition therefore sheds light on the dark side of relationship banking.Proposition 5 shows, when it is difficult for borrowers to switch their relationship bank, the availability of loans decreases because of the coordination failure between the relationship bank and the continuum of smaller creditors.In other words, the health nation between the relationship bank and smaller creditors, which in turn affects the ex ante financial condition of borrowers.Therefore, even if two firms have similar technology available to produce the same output and identical financial positions, one firm will be able to borrow more easily because its relationship bank is financially healthier than that of the other firm. of the relationship bank can affect the ex post coordi-

Conclusions
ated how the health of a relationship we assumed the liquidatio

REFERENCES
[1] F. Modigliani st of Capital, Cor-This paper investig bank affects the coordination between the relationship bank and other creditors and how the ex post coordination problem affects the ex ante efficiency of the firm's actions.Our main findings are as follows.First, as the relationship bank becomes more financially distressed, it desires the firm to take risky actions while other creditors require the firm to take safe actions, and thus a coordination problem arises in the interim period.Therefore, the poor health of the relationship bank induces the inefficient liquidation of the firm's project and thereby reduces the expost economic efficiency.Second, the presence of expost inefficiency also reduces the ex ante efficiency of the firm's actions because the higher interest payments to the relationship bank and other creditors encourage the firm to choose the inefficient and risky project.These conclusions shed light on the dark side of relationship banking and provide important implications about the efficiency of multiple yet asymmetric bank financing arrangements.
To simplify our arguments, n values for both types of creditors are given.However, it would be interesting to construct a framework in which the liquidation value is determined endogenously and is affected by the coordination of creditors.This is left for future research.

Appendix 1: Proof of Lemma 1
From (1), i  is determined so as to satisfy   holds.When the degree of strategic compley is large (i.e., 0 v  and 0 v  ), becomes small.Then, , , roposition 1 Appendix 3: Proof of P First, we define the three parameters.
Then, we can derive the following equation.

Appendix 6: Proof of Proposition 4
For the proof, we consider how B x  affects I x  because I x  is determined by the level of the case of B r .B r is determined so as to satisfy

Appendix 5 :
, by Corsetti et al. (2004), I x  is uniquely determined.(q.e.d.) Proof of Proposition 3 By totally differentiat ect to d , we can its loan becomes lower and thus the p ff ecom gher, the probability th e relationship ba k co ayo That is, as the higher Bx  decreases the range of  uch over which the firm choo he risky project, the second te et on the RHS of (2) becomes m smaller than the first term nverselyd is lar probability that the firm chooses the risky project and the relationship bank continues its loan becomes higher.this region of  , the relationship bank considers that the firm is more likely to choose the risky project ex ante and thus 0 

with probability one if the project quality  is realized at . Let
SM can be written as:

The Determination of r I and r B
© 2013 SciRes.TEL Then, we can derive the following proposition.Proposition 2. As the LHS of (3) is strictly increasing, B x  is uniquely determined.