agency costs, bank specialness and renegotiation

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Agency Costs, Bank Specialness and Renegotiation

Sreedhar T. Bharath

New York University

This Draft - January, 2002

First Draft - April, 2001

Job Market Paper - Comments Welcome

Please do not quote or distribute

I am indebted to my advisors Yakov Amihud and Anthony Saunders for constant advice and encouragement.

I wish to thank my other committee members Kose John, Anthony Lynch and Rangarajan Sundaram and seminar

participants at Board of Governors of the Federal Reserve System, Federal Reserve Bank of New York, New York

University for helpful comments and suggestions that have greatly improved the paper. I also thank Viral Acharya,

Linda Allen, Jennifer Conrad, Florian Heider, Eli Ofek, Matthew Richardson and David Yermack for their comments.

All errors are my responsibility. Contact: Sreedhar T. Bharath, Department of Finance, Stern School of Business,

New York University, 44 West 4th St., Suite 9-153, NY, NY 10012. Tel: 2129980376 Fax: 2129954233 email:

[email protected]

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Agency Costs, Bank Specialness and Renegotiation ............................................ 2

Agency Costs, Bank Specialness and Renegotiation

Abstract

This paper proposes the yield spread between public bonds and bank loans of the same firm

(the Bond-Bank spread) as a measure of compensation for agency costs that cannot be mitigated by

bondholders but can be mitigated by banks due to their ability to monitor the firm and renegotiate

the loan. In a model of debt pricing and choice, the tradeoff between firm moral hazard and bank

opportunism, leads to co existence of relationship debt (bank loans) and uninformed debt (bonds)

in its capital structure. Contrary to common concerns, bank oversight actually increases in the

presence of bonds.

Using a large and unique data set of bond and bank yields, for the same firm at the same point

in time, matched by Credit Rating, Seniority, Maturity and adjusted for collateral differences, it is

shown that the Bond - Bank Spread is negative for high credit quality firms and positive for low

credit quality firms, consistent with the theoretical model. Applying a new econometric methodol-

ogy on matching developed by Heckman et al(1998), the results of the sample are confirmed. The

Bond - Bank Spread is about -76 basis points for A borrowers, 75 and 53 basis points for BBB

and BB borrowers, increasing to 173 and 335 basis points for the B and CCC rated borrowers

respectively. Thus agency costs or the specialness of banks seem to be important for BBB and

below investment grade firms across the credit spectrum.


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Contents

1 Introduction 5

1.1 Main Results: A Synopsis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2 Literature Review 10

3 The Model 14

3.1 The Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.2 Lenders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.3 Information and Contracting Environment . . . . . . . . . . . . . . . . . . . . . . . . 15

4 Firms Choice of Financing 16

4.1 Borrowing from the Bond Market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4.2 Borrowing from Banks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4.2.1 Definition of Equilibrium at t = 1 and specification of cases . . . . . . . . . . 18

4.3 Borrowing from both Banks and Bond markets . . . . . . . . . . . . . . . . . . . . . 26

4.4 Endogenizing Bargaining Power k . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.5 Borrowing from Multiple Banks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

5 Empirical implications 34

6 Sample Selection and Data 34

6.1 Computation of Bond Bank Spread . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

7 Methodology and Empirical Results 36

7.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

7.1.1 Alternative Matching Estimators . . . . . . . . . . . . . . . . . . . . . . . . . 38

7.2 Adjustment for Collateral Differences between Bank Loans and Bonds . . . . . . . . 39

7.3 Mean and Median Spread Differences, Collateral Adjustment . . . . . . . . . . . . . 40

7.4 Possibility of mispricing by banks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

8 Conclusion 42


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9 Appendix 44


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1 Introduction

What is the magnitude of agency costs between stockholders and debtholders? What is the worth

of a banking relationship to a firm? How important is the ability to renegotiate contracts between

parties as information evolves and contingencies arise in the future? The main purpose of this paper

is to build a tractable model of firms debt financing choice and its pricing to answer these questions

and then empirically assess the magnitude using market determined yields of debt securities. The

model attempts to knit together in one tractable framework, specific elements of 3 distinct litera-

tures namely, (1) Agency Costs of Debt (2) Monitoring by Banks and (3) Renegotiation between

the firm and the bank, as more information is revealed in the relationship. The empirical work

constructs a unique and large data set of over 15,000 observations of market yields by carefullymatching bank loans and bonds of the same firm on multiple dimensions to offer empirical evidence

on the magnitude of agency costs, the value of bank specialness and the importance of renegotia-

tion. The empirical work also confirms the results by employing a new econometric methodology

on matching developed by Heckman et al(1998).

Debt financing by a corporation gives rise to conflicts of interest between creditors and stock-

holders that can reduce the value of the firm. Such conflicts are limited more effectively in private

loans extended by banks and other institutions than in publicly traded bonds. However, finance

literature is largely silent on the magnitude of this effect.1 Due to the limited evidence available on

the magnitude of agency costs of debt, no consensus has been reached on their overall importance2.

Much of the recent literature in corporate finance discusses agency issues in different settings. The

importance of these ideas finally rely on the magnitude of the shareholder-debtholder conflict.

Financial intermediation literature (both theoretical and empirical) beginning with Diamond

(1984) and Ramakrishnan and Thakor (1984) has emphasized the specialness of banks which arise

as delegated monitors in order to solve information gathering problems. This view suggests that

banks have a comparative advantage in preventing opportunistic behavior by borrowers during

the realization of the project and punishing a borrower who fails to meet contractual obligations.

However, the empirical evidence on the benefits of banking relationships is less direct and concerns

positive and negative stock price reactions of the borrower to loan renewals and loan sales respec-

tively. It is desirable to provide direct evidence on the specialness of banks.3 Gilson and Warner

(1999), however find that firms that want to maintain their ability to grow rapidly, replace bank

loans by junk bonds.

A third strand of literature is the financial contracting literature that takes its starting point

1Early discussions of these concepts include Fama and Miller (1972), Jensen and Meckling (1976) and Myers (1977)2The available evidence is also indirect, and relies on numerical simulations. Chief papers in this vein are Parrino

and Weisbach (1999) and Titman, Tompaidis and Tsyplakov (1999)3See James (1987),Lummer and McConnell (1989) and Dahiya, Puri and Saunders(2001)


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the idea that a relationship between a firm and its investors is dynamic rather than static. As

the relationship develops over time, eventualities arise that could not easily have been foreseen or

planned for in an initial contract between the parties. Beginning with Aghion and Bolton (1992),

the literature has focused on the allocation of control rights, cash flow rights and private benefits

once the relationship is underway.4 In such an incomplete contracting environment, the ability

to renegotiate leads to more efficient outcomes in some states of the world. However the value of

renegotiation, which is central to many of the papers in this literature is a matter of conjecture.

The setting that is used to study the issues of Agency costs of debt, Specialness of banks and

Renegotiation, is corporate debt in firm capital structures, of which public bonds and bank loans

are an important component. As can be seen from Figure 1 (top panel) , Corporate New Issues in

the US totalled 2.157 trillion dollars in 1997. Bank loans and Bonds accounted for 77% or 1.661trillion dollars of the total issuance. In contrast, equity issuance was at 0.194 trillion dollars (9%

of total), thus about an order of magnitude smaller. Figure 1 (bottom panel) provides evidence on

the composition of the capital stock of equity (in market value terms), bonds and bank loans of

US corporations in the 1990s. Even accounting for the high equity values in the decade, it can be

seen that as of 1999, equity and debt accounted for 48% and 52% of the total capital stock of US

corporations compared to a share of 27% and 73% respectively in 1990. Thus in terms of capital

stock, debt markets are comparable to equity markets, while in terms of flow they are an order of

magnitude bigger. This paper attempts to develop a theory and provide evidence on the magnitude

of the issues discussed above, in this economically important setting.The main object of interest in this paper is the yield spread between public bonds and bank

loans of the same firm (also referred to as the Bond-Bank spread in the paper). A bank can write

tighter and tailor made covenants for its loan. By being able to monitor the firm, it can also act to

enforce these covenants and ensure its welfare, whenever there is a conflict of interest. It can also

use the new information uncovered in monitoring to conduct renegotiation of the loan contracts

with the firm. On the other hand, bond holders are diffuse and suffer from a coordination problem

to monitor the firm and safeguard their interests. Thus one important adjustment that should be

taken into account is the compensation that is asked by the bond holders. As they can later be

victimized by the firm, they insist on a yield that is high enough to outweigh this danger. Thus

the yield spread between public bonds and bank loans of the same firm (after explicitly controlling

for the dimensions on which Bank Loan and Bond contracts differ) should be a direct measure of

the agency costs of debt of the firm. Alternatively, it can be interpreted as a measure of bank

specialness where the bank performs the role of a delegated monitor. A third interpretation of the

spread, is that, it is premium paid by the bank for the option to renegotiate.

In order to get theoretical guidance on the yield spread between public bonds and bank loans,

this paper attempts to knit together in one tractable framework, specific elements of the aforesaid

4Related papers include Diamond (1991), Hart and Moore (1988)


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literatures namely, (1) Agency Costs of Debt (2) Monitoring by Banks and (3) Renegotiation

between the firm and the bank, as more information is revealed in the relationship. While one or

simultaneous interplay of two of these issues, has been studied in the literature, the model in this

paper attempts to unify all the three elements in one setting. The paper proceeds by constructing

a model of bank loans (private debt) and public bonds (public debt) in firm capital structures.

Co-existence of bank loans and bonds in equilibrium enables the computation of promised yields

on bank loans and bonds and hence the Bond-Bank spread.

In order to empirically assess the magnitude of Agency Costs or Bank Specialness or the value of

renegotiation, it is necessary to match the public bonds and bank loans of the same firm at the same

point in time and obtain their market determined yields. The matching problem is compounded

by the fact that bank loans and bonds are contractually very different on multiple dimensions suchas seniority, maturity, and collateral. Further bond spreads are measured relative to treasury rates

whereas loan spreads are relative to LIBOR, and the two must be put on a common basis before the

Bond-Bank spread can be computed. This paper undertakes the task of constructing such a unique

and large data set of over 15,000 observations of market yields by carefully matching bank loans

and bonds of the same firm on multiple dimensions to offer empirical evidence on the magnitude

of agency costs, the value of bank specialness and the importance of renegotiation.

To ensure that the results obtained are not driven by the matching procedure used, the pa-

per also employs a new econometric methodology developed by Heckman et al(1998), that views

matching of Bonds and Bank loans as an econometric evaluation estimator. Using seven differentmatching methods, the results of the matched sample are then confirmed by this methodology.

Alternative explanations for the spread such as mispricing by banks are also considered, but do not

find support.

Subsection 1.1 outlines the main theoretical and empirical results of the paper.

1.1 Main Results: A Synopsis

This paper proposes a model of debt pricing and choice with firm moral hazard and bank holdup.

It emphasizes that a firms desire for financial flexibility leads to co existence of relationship debt(bank loans) and uninformed debt (bonds) in its capital structure. Banks are useful because

they are able to monitor and check value reducing, risky, asset substitution activities of the firm.

Bonds alone are unable to perform this function and thus not contractible. However, by virtue of

information gained during the course of the lending relationship, banks behave opportunistically

and hold up the firm ex-post, to extract rents after projects are in place in return to providing

continuation financing. Uninformed lenders such as the bond markets can then be used by the

firm in conjunction with bank loans. Bonds are now contractible, free riding on the monitoring

performed by banks. The presence of bonds serves to limit the rent extraction aspect of bank


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financing , while the firm continues to enjoy the relationship benefits of bank financing. Optimal

trade off of the benefits and costs of bank financing results in coexistence of bank loans and bonds.

The paper provides detailed analytical characterization of the bank lending patterns for different

types of firms (proxied by the degree of bargaining power of the firm vis-a-vis the bank) highlighting

the costs and benefits of bank financing. It also explicitly derives closed form solutions for the case

of coexistence of banks and bonds. The model endogenizes the banks decision to engage in costly

and imperfect monitoring unlike the extant literature where monitoring is costless, perfect and

exogenous, while explicitly considering the benefits and costs of banks and incorporating the role

of public bonds. 5

Contrary to common concerns, the paper finds that bank oversight (monitoring) increases in the

presence of bonds. As bond markets develop in an economy, there is some concern expressed thatit reduces bank monitoring efforts and oversight thereby increasing value dissipating activities of

the firm. This model shows however that such concerns are misplaced. The presence of uninformed

bond holders increases the risk shifting incentives of the firm compared to a firm that has been

fully financed by the bank. This incentivizes the bank to monitor more intensely as the bank is

able to detect and liquidate value reducing projects (generated by the risk shifting activities of the

firm) only by the process of monitoring. The offsetting effect is the reduced ability of the bank to

hold up the firm and extract rents due to the presence of bonds in the capital structure. However

the firm chooses the optimal amount of bank debt to obtain efficient continuation benefits and yet

circumscribe the power of the bank to hold it up.It is also shown that multiple banking relationships are not as effective as bond markets in

satisfying the firms need for financial flexibility and as a possible solution to the hold up problem.

The reason is that, while monitoring enhances the chances of hold up, symmetrically informed banks

have the incentive to compete in order to improve their payoffs individually, rather than collectively

hold up the firm. While this reduces the extent of the hold up, the problem still persists when the

banks are asymmetrically informed. The informed bank continues to hold up in that case.

The object of testable empirical interest from the model is the Bond-Bank spread. The spread

is computed for two cases : (i) Bank loans senior to bonds and (ii) Banks and Bonds have equal

seniority.In the case when bank loans are senior to bonds, the Bond-Bank spread is shown to be positive

despite offsetting costs of bank finance, namely costly monitoring.6 The benefit of seniority to the

bank is sufficient to overcome the monitoring costs, thus enabling the bank to seek a lower promised

5Park(2000) and Rajan and Winton (1995) are notable exceptions. However they are concerned with showing

how features of bank contracts emerge endogenously and are not concerned with bonds. This paper builds on their

results and assumes bank contracts as given and incorporates bonds in the analysis6In the absence of offsetting costs, it is trivial to note that seniority of bank loans with respect to bonds implies

a positive Bond-Bank spread


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yield. However as a practical matter, seniority of bank loans implies higher recovery rates at the

time of default and advantages in the reorganization process during bankruptcy, which could affect

the Bond-Bank spread in ways other than what is identified in this paper. Thus the Bond-Bank

spread is also computed theoretically for the case when both types of debt are equally senior.

With equal seniority, the paper shows that for High Quality Firms, above a certain threshold

(proxied for in the model by how often the good project outcome is likely to be realized), the Bond-

Bank spread is negative. The only difference between bank loans and bonds with equal seniority

is the expected hold up benefits enjoyed by the bank and the monitoring costs incurred by it.

Monitoring costs increase the yield on bank loans while an increase in ex-post hold up benefits

for the bank serves to decrease the ex-ante yield. For a bank lending to a high quality firm,

monitoring costs outweigh the ex-post hold up benefits thus causing the bond-bank spread to turnnegative. For firms below this threshold or Low Quality Firms, the opposite is true, causing the

spread to be positive. For certain parameter restrictions of the model, ex-post hold up benefits

enjoyed by the bank always dominates the monitoring costs, thus causing the Bond-Bank spread

to remain positive for all firms. These are the implications that are tested empirically, with credit

rating used as the proxy for firm quality.

The empirical study uses matching which is a widely-used method of evaluation. The method-

ology is similar to that used in medicine and statistics. It is based on the intuitively attractive idea

of contrasting the outcomes (yields) for a bank loan to that of a bond. Differences in the yields

can then be attributed to the ability of banks to monitor and renegotiate and thus mitigate agencycosts. Sample selection criteria is thus used as a principal method for achieving comparability and

appropriateness.

In order to substantially reduce bias in non experimental estimates, the literature on matching

suggests that (1) Controls and participants have the same distribution of observed personal char-

acteristics (2) Outcomes and characteristics are measured in the same way for both groups and (3)

Participants and controls are placed in the same economic environment. In the application con-

sidered, Bonds can be thought of as the participants and Bank Loans as the control group. In the

current case conditions (2) and (3) are met rather well, as market determined yields for both bank

loans and bonds are compared at the same point in time. Further the matching method attemptsmatches on personal characteristics (Seniority,maturity, credit ratings and collateral in this case)

as closely as possible between loans and bonds in order to meet condition (1). Thus the method of

collecting the sample and matching each loan and bond can produce a simple estimate of the yield

difference between bonds and bank loans which is the focus of this paper.

The paper uses a large and unique, carefully constructed data set from multiple data sources

of Bond and Bank yields for the same firm at the same point in time, matched by Credit Rating,

Seniority, Maturity and adjusted for collateral differences. It is then shown that the Bond Bank


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Agency Costs, Bank Specialness and Renegotiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Spread is negative for high credit quality firms and positive for low credit quality firms, consistent

with the theoretical model. Applying a new econometric methodology developed by Heckman et

al(1998), that views matching of Bonds and Bank loans as an econometric evaluation estimator,

the results of the sample are confirmed rigorously.

The Bond - Bank Spread is about -6 basis points for AAA,AA rated borrowers, -76 basis points

for A borrowers, 75 and 53 basis points for BBB and BB borrowers, increasing to 173 and 335 basis

points for the B and CCC rated borrowers respectively. Thus agency costs or value addition by

banks seem to be important for BBB and below investment grade firms across the credit spectrum.

The paper is organized as follows. Section 2 provides a literature review. Section 3 describes

the model set-up. Section 4 characterizes the firms choice of financing. Section 5 considers the

empirical implications of the model. Section 6 describes the data and sample selection. Section

7 describes the methodology for empirical analysis and describes the results. Section 8 concludes.

Proofs of theoretical results are relegated to the Appendix.

2 Literature Review

A number of factors have been advanced to explain the advantages of relationship debt held by

a bank relative to uninformed debt held by bond holders. However, firms that might find these

advantages from a bank, not relevant to their activities look towards financing from alternative

sources such as bonds. Most of the existing work, that has focused on this choice faced by firms

between bank loans and bonds, generates rationales based on the characteristics of firms, that find

it worthwhile to go to banks and markets. They deliver the implication that certain types of firms

borrow exclusively from banks and certain others from markets. Models that study the choice

of debt in this vein include Diamond (1991,1993), Bolton and Friexas (2000), Chemmanur and

Fulghieri (1994), Repullo and Suarez (1998), Hoshi, Kashyap, and Scharfstein (1993), and, Boot

and Thakor (1997a) among others. These models generate the simultaneous existence of both bank

loans and bonds at the economy wide level in equilibrium and are concerned with explaining inter

temporal change in demand for these types of financing, security design, and the architecture of

the financial system. Crucially, an individual firm in these models holds either bank debt or bondsonly, at a point in time.

A casual look at capital structure data at the firm level suggests that the very big firms such as

GE borrow almost exclusively from the bond markets. The very small firms which are covered by

the National Business Survey of Small Firms , are too small to access the bond markets and have

bank borrowing as the main source of debt. However for the vast majority of firms in between, both

bank loans and bonds are the source of financing. Indeed, in a random sample of 250 firms taken

from COMPUSTAT, Houston and James (1996) find that the average firm has 63 percent of its


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debt as bank debt and 16 percent as bonds with systematic cross sectional variation across firms.

The model in this paper proposes an explanation for this coexistence of bank loans and bonds in

firm capital structures.

This paper is related to the literature which considers the co existence of bank loans and

bonds at the firm level. Chief papers that examine this issue include Green and Juster (1995),

Holmstrom and Tirole (1997), Carey and Rosen (2001) and Besanko and Kanatas (1993). In

Green and Juster, firms choice of debt is intended as a signal of their quality based on their

expectation of renegotiation in financial distress. In contrast no signalling equilibrium is possible

in the model presented in this paper. Holmstrom and Tirole concern themselves with a model of

financial intermediation where firms and intermediaries are capital constrained and seek to explain

lending patterns observed during financial crises. This paper assumes no financial constraints andfollows the traditional literature. Carey and Rosen (2001) present a model of bank loans and

bonds based on incomplete contracting but no asymmetric information where public debt acts as a

punching bag for ex post renegotiations between the firm and the bank. This paper concerns itself

with renegotiation of incomplete contacts under asymmetric information. More importantly, this

paper assumes that monitoring by banks is costly, imperfect and endogenous driven by its

own incentives in contrast with the traditional assumption of costless, perfect and exogenous

monitoring employed in all these papers.

Besanko and Kanatas consider the moral hazard of the bank in not being able to contractually

commit to its monitoring activities and this limits the usage of bank debt. This paper follows theview of Diamond (1984) of banks as delegated monitors and assumes that gains from monitoring

exceed its costs and abstract from such considerations. Further while they demonstrate coexistence,

they do not explicitly solve for the mix of two types of debt and their prices in the model.

Seward (1990) is the first paper that demonstrates the complementarity between capital markets

and financial institutions by examining the optimal structure of financial contracts in an economy

subject to moral hazard. This paper builds on these results by assuming the contracts as given and

study the optimal mix and prices of the two types of debt at the firm level.

There is a growing literature on the design of appropriate bank loan contracts to enhance

efficiency taking into account the special nature of financial intermediation and its attendant costs.Gorton and Kahn (2000), Park (2000), Rajan and Winton (1995) study this problem in detail

and demonstrate how unique contract features of bank loans emerge endogenously. The latter two

papers explicitly consider endogenous monitoring incentives. This paper appeals to their results

and takes the contract features of bank loans as given and adds bonds to the analysis and sets out

to derive the optimal share of each in the firm capital structure. Further it also computes the prices

of bank loans and bonds and thus the Bond-Bank spread. The model structure employed in this

paper follows Park (2000) but adds bonds, the hold up problem leading to bargaining between the


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liquidation versus continuation decisions. It is not possible for the bond markets in the model

to combat the asset substitution problem and thus financing through bonds cannot exclusively

occur in equilibrium. However, this benefit of banks comes with the attendant cost of hold up as

discussed above. Firms do not wish to have their project profitability eroded due to the monopoly

rent extraction activities of the bank. In order to optimally circumscribe the power of the bank, the

firm brings in the uninformed lender in the form of bonds in its capital structure. Increased bank

monitoring which could be used for rent extraction activities of the bank also acts as a certification

device for the bond holders to participate in the lending activity. This positive externality enables

contracting of bonds which can then serve to circumscribe the rent seeking behavior of banks.

It is also seen that bank loans availability to firms and pricing varies in a non monotonic way

across the borrower spectrum. The very low bargaining power firms and the very high bargainingpower firms are not affected by the hold up problem of bank financing. It is too costly for the

bank to hold up the former and too difficult to hold up the latter. It is the intermediate firms that

are affected most by the dark side of relationship banking and thus stand to benefit most by the

introduction of bond holders.

The model also generates a set of testable empirical implications. Firstly, loan pricing is non

linear in the bargaining power the firm. The rate charged by the bank is decreasing in the bargaining

power of the firm. Secondly, firms with very high and very low bargaining power follow similar

asset substitution policies. Asset substitution is checked more efficiently in the case of the firms

with intermediate bargaining power. Thirdly, as costs of monitoring increases in the economy, thebanks portfolio of loans undergo a change in mix. If bargaining power is considered synonymous

with the quality of the firm, the average firm in the bank portfolio is of a lower quality as costs

of monitoring increase. Fourthly, the share of bank debt in the firms capital structure should be

lower as the firms bargaining power increases. This yields a cross sectional prediction. Also the

bank bond spread defined as yield of bond - yield of bank loan is positive, when banks are senior

to bonds. Further, it declines in periods when costs of monitoring increase and increases with the

value of collateral (a proxy for Liquidation value in the model). With equal seniority of bank loans

and bonds, the paper shows that for High Quality Firms, above a certain threshold (proxied for

in the model by how often the good project outcome is likely to be realized), the Bond-Bank spread

is negative. For firms below this threshold or Low Quality Firms, the opposite is true, (i.e.) the

spread is positive. Finally, in financial systems where the arms length bond markets are not well

developed, firms on average should have greater number of bank relationships.

Empirically, to the best of my knowledge, the only other paper that looks at yield spreads

between bonds and bank loans is Carey (1995). Careys focus is on the efficiency of the bank

loan pricing market and assumes that the bond markets are efficient and uses the spread between

bonds and bank loans to conclude that bank loan markets are efficient as well. Carey compares

loan spreads with spread index values of bonds with similar ratings (He also uses a smaller sample


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where loans and bonds are matched by firm) and also adjusts for collateral, maturity and seniority

differences. In contrast, this paper uses micro data at the firm level and explicitly matches the

loans and bonds on all these dimensions and more importantly differs in its focus, on the issues

of agency costs, bank specialness and renegotiation. This paper also employs a new econometric

methodology on matching developed by Heckman et al (1998) in order to estimate the magnitude

of the Bond-Bank spread.

3 The Model

3.1 The Project

Consider a world where all agents are risk neutral and the riskless interest rate is zero. The economy

has a single owner-managed firm (henceforth the firm). The firm contacts investors at the initial

date 0 to finance its project. Investment in the project requires a fixed amount of I dollars at date

0. The assets purchased at date 0 can be liquidated at date 1 for value L where L


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competitive.

Banks/Informed/Relationship lenders enter the market at date 0 and date 1 to acquire infor-

mation and make loans. A bank which makes a loan to a firm at date 0 can obtain information

about it by monitoring its activities (more on this below). Much of the information obtained

is not verifiable or cannot be credibly communicated to a third party (e.g.) a court.

Bond Market/Uninformed/Arms length investors lend at date 0 and return at date 2 for

their promised payments. I assume that these investors do not monitor the firm, by invoking

the standard argument that dispersion of security holders generates either free rider problems

or a wasteful multiplication of monitoring costs as in Diamond (1984).

3.3 Information and Contracting Environment

The firm makes an investment I at date 0 and chooses its -policy, which is its private information

on this date. The bank does not know the borrowers choice of and in turn chooses its monitoring

intensity (also termed as the -policy). The intensity of the banks monitoring activities is denoted

by [0, 1]. Then, at date 1, it will learn the true project type realized by the firm with probability

; with probability 1- it will obtain no more than the publicly available information. Monitoring

intensity of costs c dollars where c > 0 is the unit monitoring cost.8 The firms -policy becomes

public information at date 1 (i.e.) the choice of by the firm is known to the market.

9

This structureenables lenders to write covenants against .

I assume that it is not possible to write state contingent contracts on the type of project

investment, or state realized. Further, I allow only debt contracts, an assumption justified by

appealing to the costly state verification technology in Gale and Hellwig (1985). Since any debt

contract can be expressed as a linear combination of pure discount debt contracts, I consider only

the latter, in this model, to keep matters simple. The discount debt contract involves a borrowing

Xi at date i and a single repayment Dij at date j. The following subscripts are used : b denotes

bank and m bond market. Thus D02b represents the repayment at date 2 for an amount borrowed

from the bank at date 0. The bank debt contract is denoted by a pair (c, Dijb) where lenders have

the right but not the obligation to to liquidate the project if and only if the observed is less than

c. Thus c is the covenant restriction imposed by the contract. The bond contract is denoted

8This is a simple monitoring technology to bring forth the issues as clearly as possible. Alternatively one might

assume that the total monitoring cost is convex in ; to obtain finer information is increasingly expensive. Further,

one might reasonably expect that the unit monitoring cost is concave in the amount of loan, reflecting economies of

scale. In short, total monitoring cost = f()g(loan) where f is convex and g is concave. All results obtained in this

paper with the simpler cost structure survive this alternative specification.9This is reasonable, since markets do learn about investment decisions and investment outcomes of firms, albeit

with a lag.


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as (Dijm) with no covenant restrictions. This structure is intended to capture the fact that bank

loans have far more restrictive covenants compared to bonds, as noted in Smith and Warner (1979)

and Kahan and Tuckman (1996). In summary, the time line of events and information structure is

depicted in figure 2.

The contract design problem arises in this debt only environment because of moral hazard.

While the NPV of the bad project is negative, a borrower is inclined to shift risk to the lenders. I

assume

Assumption 2 (G I) < (B I)

Assumption 2 states that that the borrower prefers the bad project to the good one, if financed by

outside investors.

4 Firms Choice of Financing

Having defined the contracts in the previous section, I begin the analysis of the firms choice of

financing by outlining the main tradeoffs in the two types of financing.

Under bond financing there are no monitoring costs. However, the lack of oversight by the fi-

nanciers might encourage the firm to aggressively pursue risky investment strategies/manufacturing

policies.

Under a bank loan, a firms actions are actively monitored. The bank, endowed with superior

information and with a greater ability to renegotiate and restructure its loans, will liquidate

any realized projects that are negative NPV. However, if the project realized by the firm has a

positive NPV, the date 0 contract between the firm and the bank does not oblige the bank to

continue to lend at date 1.10 It can use this discretion to hold up the firm and demand a share

of the surplus in return for the funds needed to continue the project. The main drawback of

bank lending is the ex-post holdup cost that must be borne by the firm.

4.1 Borrowing from the Bond Market

Since the bond markets lend at date 0 and return to collect repayments at date 2, it is sufficient

to consider the two period debt contract.11 The firm borrows an amount I at date 0 and promises

10I assume that bank loans are short term, 1 period contracts which need to be rolled over at the interim date. In

contrast bonds are long term, 2 period contracts. later on the model allows for issuance of 1 period bonds. This is

consistent with empirical evidence in Tufano (1993) which shows that the average maturity of bank loans is about 5

years while that of bonds is about 10 years.11Since the bond markets neither monitor to receive information at date 1 nor act upon the publicly available

information, a 1 period debt is equivalent to the 2 period debt contract.


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to repay (D02m) at date 2. Since there is no monitoring from the bond market, the firm continues

the project realized at date 1 regardless of its type. The firm chooses the optimum m by solving

max m, D02m m(GD02m) + (1 m)((B D02m) + (1 ).0) (1)

Let m be the optimum value for the above problem. The market conjectures the choice of chosen by by the firm to be conjm , and lends I, if it is individually rational,

conjm D02m + (1

conjm )(D02m + (1 ).0) = I (2)

Equation (2) is met with equality due to the assumption of a competitive credit market, and

rational expectations equilibrium demands that that the markets conjecture is correct which implies

conjm = m.

Substituting this and equation (2) in the firm pay off yields,

max m, D02m mG + (1 m)(B) I

which implies m = 1 and D02m = I.

However this is not a sustainable equilibrium, as the firm has an incentive to deviate from m= 1 after the loan has been advanced by the bond market. Since (G I) < (B I) (due to

the presence of firm moral hazard) and the firm cannot be constrained in its activities, it choosesm = 0, ex-post. This choice of m violates lender rationality as the required face value becomesD02m =

I

at which point the firm surplus = (B I

) = B I < 0, unravelling the equilibrium.

In short, the inability of the firm to commit to choosing the good project ex-post after obtaining

the funds, in the absence of oversight by the market, causes the exclusive lending from the markets

an infeasible proposition in this set up.12 The above discussion is summarized in the following

Lemma.

Lemma 1 It is not possible for the firm to borrow exclusively from the market. No equilibrium

exists, which simultaneously meets the lender rationality constraint and allows the firm to pursueits optimal investment policy.

Proof : See Appendix

12In practice, reputation considerations and the need to access markets in the future, might prevent firms from

following such a strategy. However b oth these aspects are outside the scope of this model. See Diamond (1991) for

a model which explicitly builds in reputation considerations


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4.2 Borrowing from Banks

I consider the case of a single bank lender. I assume that it is economical for the bank to monitor

over the relevant range of picked by the firm at the time of investment. The bank issues a single

contract (c, D01b) specifying the covenant restriction and the debt repayment due at date 1, which

may be rolled over based on the negotiations between the bank and the firm. If negotiations break

down and the firm is in violation of its covenants, the loan contract confers contingent control rights

of liquidation to the bank.13

4.2.1 Definition of Equilibrium at t = 1 and specification of cases

For any given contract (c, D01b) the firm chooses a and the bank chooses a to maximize

their payoffs. Thus the strategy space is S =

. An equilibrium at date t=1 for a given

contract is

1. the strategy s S (, ) that maximizes the payoffs of the bank and the firm

2. such that the beliefs of the bank and the firm are consistent with strategy set S and are sub

game perfect and sequentially rational

The optimal contract chosen by the firm, maximizes its payoff while ensuring that the individual

rationality condition is met for the lender.

Before I turn the discussion of the various cases that could arise due to a strategy s, I describe

the ex-post opportunistic behavior by the bank. At date 1, the project of the firm crystallizes as

good or bad and the bank probabilistically uncovers this information by the process of monitoring.

In the event, the bank knows that the project is good,it can threaten to not continue the financing

at date 1. This forces a renegotiation game between the bank and the firm to split anew the surplus

of the good project returns, which will be realized at date 2. As a result of this bargaining game,

the firm gets k(G-L) while the bank gets L+(1-k)(G-L) where the currently exogenous k[0, 1]

13In the corporate world where there is default, creditors obtain defacto veto power over any corporate action

(Amihud, Garbade and Kahan(1999)). In the model this is interpreted as liquidation of the project


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is the share of the unallocated surplus that the firm gets after bargaining.1415 Proper design of

the governing mechanism might ensure the commitment of the bank to re lend, by constraining

the bargaining process. However this paper does not focus on these contract design issues (see

Aghion,Dewatripont and Rey (1989) and Hart and Moore (1988) for details). Finally it may be

noted that it is common knowledge that the firm knows the banks informational status at date 1.

I now consider the various cases that arise on this date. The main considerations are (i) the type

of project that has crystallized (ii) whether the bank is informed or not and (iii) whether there

is a covenant violation or not. I repeatedly use the ideas (a) an informed bank can liquidate any

project if there is a covenant violation and (b) an uninformed bank does not liquidate the project

as long as the expected payoff exceeds L, even though the covenant might have been violated.

Project turns out to be good and the bank is informed

The bank holds up the firm and they split the surplus based on their bargaining power as

described above

Project turns out to be good and the bank is uninformed

Based on the publicly available information on , the bank calculates the probability of

repayment P() of the loan = ( + (1 )). If P()D01b L, letting the project continue

is more profitable than liquidation and vice versa. In the case of liquidation which is costless

in this set up, the bank captures the entire proceeds L16

Project turns out to be bad and the bank is informed

If there is a covenant violation, the bank acts efficiently, liquidating the project and capturing

the surplus L B, over the negative NPV project, and is thus value enhancing. The firm

cannot commit to liquidation at date 1 if the bad project were to be realized. If there is no

14The parameter k can be thought of as the result of this background bargaining game between the firm and the

bank. As the firm approaches the bank for continuation financing it can propose a sharing rule for the surplus as

the bank does not respond otherwise. If the firm is liquidated all payoffs accrue to the bank and thus the firm can

do strictly better by renegotiating. Further assume that a delay in obtaining continuation financing hurts the firm

more than the bank (i.e. the bank is more patient) and that the returns from the project decays if there is a delay in

its implementation. For example, competition from the product market could cause a decay in returns if the projectis delayed. In such a situation the bank can wait until the moment when the project value falls to the value of the

debt repayment and offer continuation financing. The firm can do no better than accept. If I know the discount

rates which is accepted as an exogenous primitive for the bank and the firm, I can determine the share of the surplus

obtained by the firm.15One can also think of this situation as a line of credit advanced by the bank to the firm, callable at the banks

discretion16It is not possible for a good project firm to credibly reveal its project at date 1 to the bank if the latter is

uninformed. This is because no signalling equilibrium exists in this set up and each type can always mimic the other

type. If there is a covenant violation, a bad project firm can always mimic the good and vice versa


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covenant violation, the firm and the bank bargain and split the surplus LB such that the

firm gets a payoff greater than (B D01b).

Project turns out to be bad and the bank is uninformed

This case is similar to to the second case.17 The bank liquidates the firm if P()D01b < L

and lets it continue otherwise, based on , the public information at date 1.

I enumerate two cutoffs min and max, such that P(min)G = L and P(max)D01b = L and

summarize the above discussion as the payoffs of the firm (X) and the bank (Y). Notice that the

bank will set a covenant c at least as stringent as max in its contract.

X(, ) =

(1 )(G + (1 )B P()D01b)+ [c, 1]

( k(G L) + (1 )((B D01b) + k(L B)))

(1 )(G + (1 )B P()D01b)+ [max, c)

( k(G L))

(1 )(G + (1 )B P()D01b)+ [min, max)

( k(G L))

( k(G L)) [0, min)

Note that an uninformed bank simply liquidates the firm if (0, min] as P()D01b < L in this

range. If falls in (min, max], the firm and the bank know that P()D01b < L. However the firm

can offer a new repayment D01b at date 2 such that P()D01b = L and D

01b L. The bank then

accepts this repayment schedule and lets the firm continue the project.

The payoff of the bank is summarized as under :

17In this case the good project firm mimics the bad project firm, trying to get a payoff X > (BD01b) > (GD01b).

Thus signalling by the bad project firm to get itself liquidated is not effective here.


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Y(, ) =

(1 )(P()D01b) c+ [c, 1]

( (L + (1 k)(G L)) + (1 )(D01b + (1 k)(L B)))

(1 )(P()D01b) c+ [max, c)

( (L + (1 k)(G L)) + (1 )L)

(1 )(P()D01b) c+ [min, max)

( (L + (1 k)(G L)) + (1 )L)

(1 )L c+ [0, min)

( (L + (1 k)(G L)) + (1 )L)

Having characterized the payoff of the bank and the firm, I turn to the solution which outlines

the strategy of the firm and the bank and the optimal contract offered in equilibrium. It is useful

to record the following result, while searching for the optimal policy of the firm.

Lemma 2 The firms optimal choice of lies in the closed interval [max, c]


Lemma 2 establishes the limits on the optimal manufacturing policy that can be followed by

the firm. Since c is the covenant set by the bank, it does not pay the firm to over comply with

the restriction (i.e.) pick a > c. This establishes the upper limit on . At the same time, the

firm does not want to get liquidated or offer a higher face value to avoid liquidation, if the bank is

not informed at date 1. Accomplishing these objectives improves the payoffs of the firm, and the

lowest that enables the firm to do so is max defined such that P(max)D01b = L. Lemma 2 states

that the optimal policy of the firm has to lie between these limits.

Using the payoff functions X and Y and Lemma 2 it is now possible to characterize the equi-

librium for the case of bank borrowing. Note that the individual rationality condition for the bank

implies P()D01b = I.

Proposition 1 (Bank Borrowing Equilibrium) There exists an unique optimal single bank

contract ((c), D01b). The manufacturing policy and the monitoring intensity of the firm

and the bank respectively, are also unique. They are given by

1. (c) = 1

2. D01b=I(1k)(GL)

(I+cL)(1)+(1k)(GL)

3. = I+cL)(1k)(GL)


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4. = 11+ k(G

L)A

(1)I(1k)(GL)(GB)A

where A = (I + c L) (1 ) + (1 k)(G L)


Proposition 1 assumes implicitly that the firm with the good project is being held up by the

informed bank at the time of loan renewal at date 1. The bank would hold up if the pay off from

this strategy L + (1 k)(G L) exceeds D01b, the payoff with no hold up.

Intuitively the proposition says the following

The bank wishes to obtain full control rights to liquidate the project if it turns out to be bad.This can be ensured only by setting the strictest possible covenant in this model (i.e.)( c) = 1.If the bank were to set a relaxed covenant, and the firm adhere to it, the former lacks the

control rights and cannot unilaterally liquidate the project, were the bad project to be realized.

The bank has to induce the firm to voluntarily liquidate the bad project by sharing some of

the liquidation surplus with it. Setting the strictest covenant obviates this possibility. It also

means that covenants are always breached in equilibrium. This is not necessarily a bad thing,

since decisions are driven completely by incentives and renegotiation in this set up. From

now on we set (c) = 1 in the model.

Monitoring benefits the bank in two ways : For a good project an informed bank extracts

rents by holding up the firm. In the case of a bad project, liquidation enables it to capture

the surplus L B. The bank chooses the level of monitoring which drives the marginal

return to risk shifting of the firm to zero while maximizing its benefits.

The firm faces the hold up cost of a good project and liquidation losses of the bad project,

if it is confronted by an informed bank (notice that these are the benefits of the bank listed

above). An uninformed lender enables it to enjoy benefits from the good project and returns

to risk shifting from the bad. The firm thus chooses the optimum level of risk shifting to

drive the banks value from monitoring to zero.

The optimal debt value, conditional on the firms - policy is then driven by the competitive

credit market rationality condition P()D01b = I

I now turn to the optimal policies of the firm and the bank, when the bank does not find it

worthwhile to hold up. This implies the payoff from hold up is less than the payoff from not

holding up, for the bank: L + (1 k)(GL) D01b which is equivalent to (GD01b) k(GL)

The inequality condition is satisfied for 2 combinations of k and D01b. The first is low k and

high D01b and the second is high k and low D01b. The first case corresponds to that of a firm with


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very low bargaining power. Low bargaining power does not provide sufficient incentives to pick the

good project (i.e the firm follows a low -policy) as most of the returns from it would be usurped by

the bank. This consequently raises the face value of debt demanded by the bank further reinforcing

the inequality.

The second case corresponds to that of a firm with very high bargaining power. Thus holdup

is not an issue with these firms. These firms can follow a high -policy leading to a low face value

of the debt, further reinforcing the inequality. What is the optimal policy of the firm and the bank

in the absence of hold up? Lemma 3 answers this question.

Lemma 3 The optimal policies of the firm and the bank in the absence of hold up is given by

1. = (LD

01bc)(LD01b)

2. =1- (GD

01b)

(BD01b)

3. D01b = min(a

a24IL2 ), such that I D

01b G where a = I + L c(1 )

Proof : Similar to Proposition 1 and hence omitted

Proposition 1 and Lemma 3 delineate the optimal policies of the bank and the firm in the

presence and absence of hold up respectively. It is intuitively clear from the discussion preceding

Lemma 3 that both high and low k firms are not affected by the banks information monopolyleading to a hold up problem. How high or low should k, the bargaining power be in order to

be not affected by the bank? I turn to Proposition 2 which states the borrowing patterns of the

continuum of firms, indexed by the parameter k, the bargaining power.

Proposition 2 (Patterns of Bank Borrowing) 1. For k [0, k) no lending and borrowing

occurs in equilibrium.

2. For k [k, kcrit) the bank does not hold up the firm and the equilibrium is given by Lemma

3.

3. For k [kcrit, k) the bank holds up the firm and the equilibrium follows proposition 1.

4. For k [k, k+) no lending and borrowing occurs in equilibrium.

5. For k [k+, 1] the bank does not hold up the firm and the equilibrium is per Lemma 3. The

expressions for the cutoff points are as under

(a) k = max[1 (I+cL)(1)G(GL)(IG) , 0]

(b) kcrit = kx wherex =

e(IL)c(1+)2(GL) ande = c

2(1)22c(1)(I+L)+(IL)2


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(c) k = (GIc)(G

L)

(d) k+ = (GI)(GL)


The reasoning behind this proposition is best explained by considering an example.

Example 1 Let L = 1.8, I = 2, G = 2.5, B = 3.5, = 0.4 and c = 0.2 satisfying assumptions 1

and 2. The critical cutoff points are given by k = 0.143, kcrit = 0.259, k = 0.429 and k+ = 0.714.

If the bargaining power of the firm is very low, it does not have sufficient incentives to undertake

the good project as most of the returns are garnered by the informed bank. The firm undertakes

the bad project (asset substitution) and forces the bank to demand a higher face value of debt to

break even. However, the face value of debt cannot exceed G, and this limits the set of firms that

are able to obtain financing. For k < 0.143, no firm is able to borrow from the bank.

For k between 0.143 and 0.259, the returns to the bank by holding up are lower than the

returns from not holding up. Thus the no hold up solution of Lemma 3 applies to all firms, in

this region. The optimal choice of the firm and the bank is shown in figure 3 (The two regions

are labelled A and B). As k increases further, holdup is profitable to the bank and the optimal

choices are characterized by proposition 1. For k [0.259, 0.429) the firms choice of increases as

its bargaining power increases and the banks monitoring intensity decreases as the good project

is more likely to materialize. approaches 1 at the upper limit of this interval (Region C). The

face value of the debt demanded by the bank falls towards I making the loan, virtually a risk-free

proposition. However at = 1 , the banks incentive to monitor disappears as it can save on the

monitoring cost and yet prevent the firm from engaging in asset substitution. This deviation causes

the firm to deviate from its choice of = 1, as it cannot be caught by the bank and liquidated, if

it were to undertake the bad project. This unravels the equilibrium and no feasible solution exists

in the interval [0.429,0.714) (Region D in figure 3). As the bargaining power of the firm increases

further beyond 0.714, hold up by the bank is no more an issue, and once again Lemma 3 applies.

This solution relates to region E in figure 3.Since P()D01b = I, the price of a bank loan contract in this set up can be represented as

rbank =1

P() 1, where P() = + (1 ). By inspection of in figure 2, it is immediately

clear that loan pricing is highly nonlinear in the bargaining power of the firm, a testable empirical

implication of the model.

Corollary 1 The price of bank loan for a dollar lent to the firm at date 0 is 1P() 1. Further

loan pricing is nonlinear in the bargaining power of the firm.


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I now turn to the issue of comparative statics on the optimal policies of the the firm and the

bank when hold up is an issue for the firm (i.e.) study behavior in the [kcrit, k) region. Further

what is the economy wide implication on how the type of firms that obtain bank loans, change

in this set up? Stated differently what is the effect of an increase in costs of monitoring c on the

various cut off points identified in proposition 2? Proposition 3 provides answers to these questions.

Proposition 3 (Comparative statics) Let k [kcrit, k) where kcrit, k and are given by proposi-

tion 2. Then

1. The firms optimal manufacturing policy is increasing in k

2. The banks optimal monitoring intensity is decreasing in k

3. The price of bank debt rbank and the face value of debt D01b are decreasing in k

Letk [0, 1]. An increase in bank monitoring costs c, causes the critical cut offs of proposition

2 to change. In particular

(a) k and k are decreasing in c

(b) kcrit is increasing in c

(c) k+ is independent of c


The reasoning behind the first part of the proposition is as follows. As the firm becomes more

powerful in the bargaining process vis-a-vis the bank, it can capture a larger share of the surplus.

This incentivizes the firm to choose the good project with a higher probability. Consequently the

banks intensity of monitoring falls as it can extract less by holding up in the good state. A higher

probability of choosing the good project, also causes a reduction in the price of bank debt and the

face value of debt demanded by the bank, as expected.

The second part of the proposition is illustrated in figure 4. Increases in monitoring costs causes

the intensity of monitoring to decline thus weakening the hold up problem. At the same time it

increases the incentive of the firm to engage in asset substitution. However the expected increase

in payoff to the firm due to the reduced hold up problem, if the good project is realized, outweighsthe expected increase in payoff by asset substitution. Consequently a firm on average with the

same bargaining power picks the good project more often. This shrinks the region of hold up and

increases the region of no hold up. Thus, more firms with very low bargaining power are granted

credit by the bank. The range of firms with high bargaining power which were not affected by the

hold up earlier remains unaffected as the threshold is independent of c (Region E). This along with

the fact that k (firms pick a higher on average) decreases causes an increase in the range of firms

in Region D where there is no lending by the bank. Thus an increase in monitoring costs causes a

decrease in lending in Region D.


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4.3 Borrowing from both Banks and Bond markets

Having outlined the cases of exclusive borrowing from the bond markets and banks, in the previous

sections, I now consider simultaneous borrowing from both sources of finance. First I consider

the case where bank loans are senior to bonds (The case when both bank loans and bonds have

equal seniority is analyzed later). Let s be the proportion total funds required (which is I) that

is borrowed from banks and the balance 1-s is borrowed from bond holders. The face value of 1

period bank debt and 2 period bonds is denoted by D01b and D02m respectively. Further, assume

D01b > L. If D01b L the bank can always demand liquidation and will be made whole,

destroying the incentives to monitor. In such a situation an outside financier cannot participate

in funding as illustrated in Lemma 1. An argument along the lines of Lemma 2 establishes the

firms optimal choice of in the interval [max, c]18. The payoff for the firm(X), bank(Y) and

bondholders(Z) is outlined as under :

X(, ) :=

(1 )(1 )(B D01b D02m) + ( k(G L) + (1 )(GD01b) D02m)

Y(, ) :=

(1 )(L + (1 )D01b) + ( (L + (1 k)(G L)) + (1 )D01b) c

Z(, ) :=(1 )(1 )D02m + D02m

The individual rationality conditions for the bank loan and bonds due to a competitive credit

market implies

P()D01b = sI

P()D02m = (1 s)I

An equilibrium solution provides the values of the five variables in the model (,,D01b, D02m, s).Proposition 4 characterizes this equilibrium.

Proposition 4 (Bank Bond Equilibrium) There exists an unique equilibrium in mixed financ-

ing of bank loans and bonds. The optimal values of the parameters are given by

1. = (I+cL)(GL)

2. () = 118I further set the covenant c = 1 for reasons discussed earlier


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3. s = 1 k k(cL)I

4. D02m=k(G L)

5. D01b=I(1k)(GL)

(I+cL)(1)+(1k)(GL)


Proposition 4 has interesting implications on the monitoring activities of the bank. The bank

advances only a share s of the total investment I compared to the total outlay of I in the single bank

case (in proposition 1). However, its monitoring intensity increases to 1 from in the single bankcase. Intuitively, the bank becomes the senior lender compared to bonds in the capital structure

of the firm. Thus its liquidation rents L remain unchanged compared to the single bank case but

is however contingent on detecting the bad project realization and liquidating it. The presence of

uninformed bond holders increases the risk shifting incentives of the firm compared to a firm that

has been fully financed by the bank. This can be seen by the lower value of compared to the

single bank case. This incentivizes the bank to monitor more intensely as the bank is able to detect

and liquidate value reducing projects (generated by the risk shifting activities of the firm) only by

the process of monitoring. The offsetting effect is the reduced ability of the bank to hold up the

firm and extract rents if a good project were to materialize, due to the presence of bonds in the

capital structure. However the firm chooses the optimal amount of bank debt to obtain efficient

liquidation benefits and yet circumscribe the power of the bank to hold it up. Proposition 4 saysthat the banks incentives are sufficient enough, to invest in full monitoring.

This result has important implications to the ongoing debate on the development of bond mar-

kets in Europe. There are concerns expressed that as the bond markets develop in bank dominated

financial systems such as Germany, banks might have less incentives to invest in the oversight of the

firms. Proposition 4 suggests that such concerns might be misplaced. Further comparing Lemma

1 and Proposition 4, it is clear that presence of bank debt in the firm capital structure facilitates

the contracting of bonds. While banks use their proprietary and soft information from monitoring

to hold up the firm, there is positive externality to monitoring. Bank monitoring provides the

necessary certification needed by the bond market to step in and participate in the financing. Thisin turn limits the rents that the bank can extract with the good project. The firm chooses the

optimal amount of bank debt such that marginal net benefit of choosing an extra dollar of bank

debt equals 0. The firm also chooses an optimum level of which is lower compared to the

in Proposition 1 (single bank case). This is because, the residual risk of asset substitution is now

borne by the bond holders and fairly priced.

It is now possible to compute the prices of bonds and bank loans in the model. Further based

on these prices the bond bank spread defined as the price of bond - price of bank loan can be

explicitly derived. Lemma 4 collects these results and also the comparative statics.


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Lemma 4 The bond bank spread is defined asD02m(1

s)I D01b

sI

= (GL)(GIc)(I+cL)((I+cL)(1)+(GL)) and is positive. F urtherc

< 0

and L

> 0


Banks in the model have the benefit of seniority while bonds do not. This effect outweighs the

fact that banks incur a cost of monitoring. Seniority drives down the price of bank loans compared

to bonds while the high cost of monitoring drives it up. Since bond holders do not have this net

benefit they require a higher compensation compared to the bank causing the bank bond spread to

be positive. As costs of monitoring increase, the price demanded by the bank begins to increase,

driving the spread down. As liquidation value increases, the bank by virtue of its seniority captures

the full benefits of liquidation. This causes the bank bond spread to widen.

The analysis of the bond bank equilibrium assumed the seniority of bank loans with respect to

bonds. However as a practical matter, seniority of bank loans implies higher recovery rates at the

time of default and advantages in the reorganization process during bankruptcy, which could affect

the Bond-Bank spread in ways other than what is identified in this paper. Thus the Bond-Bank

spread is characterized for the case when both bonds and bank loans are equally senior. The main

difference in the analysis is that at the hold up stage, the banks threat point is s.L the share it

can get by liquidation when it is pari passu with bonds compared to L in the senior case. Lemma

5 records the result.

Lemma 5 Consider the case when bank loans and bonds are equally senior. The bond bank spread

is defined asD02m(1s)I

D01bsI

=(1) 1

L

I

(+(1))( ), where = (1)(

IL 1)

Define s = I+cG

L(1) and k = I(1s

)cILs)

Then > s < s k > k

If k [kcrit, k) then1. If > , then , the Bond-Bank spread is < 02. If < , then , the Bond-Bank spread is > 0

If k [kcrit, k) then , the Bond-Bank spread is > 0

Proof : Follows along the lines of proposition 4 and lemma 4 and hence omitted.


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In order to develop intuition for this result, I rewrite the first order condition of the bank as

under

[sL + (1 k)(G sL) Db] expected expost holdup benef its f or the bank

cmonitoring costs

= (1)s(1)+(1) [

]

Thus the sign of the bond-bank spread depends on the relative importance of the expected

ex-post hold up benefit vis-a-vis the monitoring cost. Higher monitoring costs drive up the yield

on bank loans relative to bonds. Higher ex-post hold up benefits for the bank serve to lower the

ex-ante yield on the bank loan relative to bonds. The relative importance of these two effects

determine the sign of the Bond-Bank Spread. When the monitoring costs dominate the expected

ex-post hold up benefits, bank loans have a higher yield than bonds thus causing the bond-bank

spread to be negative. When the the expected ex-post hold up benefits dominate monitoring costs,bank loans have a lower yield than bonds thus causing the bond-bank spread to be negative.

in the model is the probability with which the good project outcome is likely to be realized.

> can thus be thought of as a good quality firm. > is a firm with a bargaining powerk which is at least k . Such a firm is affected less by the ex-post hold up problem because ofits high bargaining power. For the bank lending to such a firm, the ex-post hold up benefits are

outweighed by the cost of bank monitoring. Thus bank loan yields are higher than that of bonds,

causing the spread to become negative.

< can be thought of as a poor quality firm. < is a firm with a bargaining power k

which is at most k . Such a firm is affected more by the ex-post hold up problem because of itslow bargaining power. For the bank lending to such a firm, the ex-post hold up benefits are higher

than the cost of bank monitoring. Thus bank loan yields are lower than that of bonds, causing the

spread to become positive.

Recall from Proposition 2 that the ex-post hold up by the bank is an issue only for firms whose

bargaining power k [kcrit, k). The above analysis considered the case when the critical cutoff

k where the Bond-Bank spread changes its sign, lies in this interval. A second possibility is thatthe critical cutoff k enumerated above lies outside the upper limit of this interval. In such a casefor all values of k [kcrit, k), the ex-post hold up benefits of the bank are higher than the cost

of bank monitoring. Thus bank loan yields are lower than that of bonds, causing the spread tobecome positive for all values of . Both of these cases are depicted in figure 4b.

The above empirical implications are then tested in the data, with credit rating as a proxy for

the quality of the firm.

Hitherto in the analysis k the bargaining power of the bank was considered exogenous. The

next section formally models the bargaining game between the bank and the firm and endogenizes

bargaining power


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4.4 Endogenizing Bargaining Power k

I model explicitly the bargaining game between the Bank (Player A) and the Firm (Player B)

at the intermediate date 1 when the bank holds up the firm for rents after the good project has

been realized and is common knowledge. The two players in the game bargain over a cake of size

= GD02a according to the following, alternating-offers procedure. Player A begins by making

an offer to Player B. An offer is a proposal of a partition of the cake. Player B can respond to

the offer by (i) accepting the offer, (ii) rejecting the offer and making a counter offer time units

later, and (iii) reject the offer and opt out, in which case negotiations terminate in disagreement.

Player B while bargaining continues to search for an outside option (in this case the possibility

of raising money from the bond market) and has to immediately accept or reject such an option

should it arise, in the model. This model is appropriate as Player B need not physically leave the

negotiations with Player A while conducting the search process. Player A can respond to the offer

from Player B by (i) accepting the offer, (ii) rejecting the offer and making a counter offer time

units later. The outside option for Player B in this case is the ability to successfully raise funds

from the bond market at date 1 in order to continue the project. The probability of success is

assumed to be p. Thus the negotiations between Player A and B break down with probability p,

the measure of Player Bs ability to raise finances in the bond market in any time period.

Let xA and xB be the shares of the cake (< ) from bargaining and A and B be the

discount factors (< 1) for Players A and B respectively. A sub game perfect equilibrium of the

bargaining process is such that (i) Whenever a player has to make an offer, her equilibrium offer

is accepted by the other player (no delay) and (ii)In equilibrium, a player makes the same offer

whenever she has to make an offer(stationarity). Let xA and xB denote the equilibrium offers.

Then,

xB = A xA

This equation states that Player A is indifferent between accepting and rejecting Player Bs equi-

librium offer. To see this consider an arbitrary point in time when player B has to make an offer

to player A. By the properties of no delay and stationarity it follows that player As equilibrium

payoff from rejecting any offer is A xA. This is because by stationarity, A offers x

A after rejecting

any offer which by the principle of no delay is accepted by Player B. Sub game perfection requires

that player A accept any offer xB such that xB > A xA, and reject any offer xB , such that

xB < A xA. Further more it follows from the property of no delay that x

B A x

A.

However, xB A xA ; otherwise player B could increase his payoff by instead offering x

B

such that xB > xB > A x

A ;

By a similar symmetric argument with the roles of A and B reversed and noting that B has

an outside option of value y


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xA = (1p) B xB + p y

In order to simplify further I assume A = B =

Solving these two equations simultaneously for a unique solution, I obtain, xA =py(1p)2

(1(1p)2)and

xB =py+(1)1(1p)2

y is the payoff to the firm if it successfully raises funds from the bond market and pays off the

bank at date 1. For simplicity I assume floatation costs are negligible. Let D12a be the repayment

to bond holders at date 2 for funds amounting to D01b raised at date 1. By lender rationality

( + (1 ))D12a = D01b. Then y = GD02a D12a .

Enumeration of firm payoffs (I now revert back to the original assumption of bank loans beingsenior to bonds)

The payoff to the firm X(, )

= [xB]+(1)[p (BD02aD12a)]+(1)[GD01bD02a]+(1)(1)[(BD01bD02a]

The payoff to the bank Y(, )

= [xA] + (1 )[ p D01b + (1p) L ] + (1 )[D01b] + (1 )(1 )[D01b] c

The payoff to the bondholders Z(, )

= D02a + (1 )D02aAs before let s be the share of bank loans and 1 s the share of bonds in firm capital structure.

Optimization of the individual payoffs and competitive credit markets supply the following equa-

tions.

xB + (1 )[GD01b D02a] p[B D02a D12a] (1 ) [B D02a D01b] = 0

xA D01b + (1 )[pD01b + (1 p)L] (1 ) D01b c = 0

( + (1 ))D02a = (1 s)I

Y = sI

XD01b

= 0 x

B

D01b= 0 ( + (1 ))(1 ) = 0

( + (1 ))D12a = D01b

I further simplify the calculations by assuming p =1. Proposition 5 characterizes the solution.


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Proposition 5 (Endogenous Bargaining Power) The optimal policies to the investment prob-

lem faced by the firm when faced with the bargaining game is given by the solution to the following

equations

1. = 1

2. D01b = f(s) =I2

[1 2

] +

[1 2

]2 + 4s[(2

)GB]

3. = g(s) = s(1)1

[1 2

]+q

[12

]2+4s[( 2

)GB]

= s(1) I2f(s)

4. D02a = f(s)(1s)

s

5. D12a =(f(s))2

sIand

6. sIf(s)

G(1 1

) + f(s)

I(1 s) G (1 1

) (f(s))2

sI+ (1s)

sf(s) +

f(s) sI(2 ) c(1 ) = 0

Solving for s from the last equation enables computation of all other variables in the model.

Proof : By Simultaneous solution of the equations listed above

So far I have considered the use of bond markets by the firm to optimally circumscribe the

power of the bank and achieve financial flexibility. Can multiple banking relationships achieve the

same effect? This question is addressed in the next section.

4.5 Borrowing from Multiple Banks

For simplicity I consider the case of 2 identical banks each lending I/2 to the firm at date 0. They

are also assumed to have the same unit monitoring cost c and undertake independent monitoring.

The key difference in the analysis arises when both banks are informed about the good project.

The incentive to collectively hold up the firm disappears in this case as one bank can gain by

unilaterally deviating from the hold up coalition with the other bank. Thus competition between

symmetrically informed banks eliminates the hold up problem. Since the banks are identical in all

respects, their choice of monitoring and face value of debt demanded will be identical. Monitoring is

independent,identical and non cooperative to rule out free rider problems. Let be the monitoring

intensity chosen and D01b2 the face value of debt. Further by the result of Lemma 1, I limit


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the analysis to the region [max, 1]. The payoff of the firm (X), Bank1(Y1) and Bank2(Y2) are

summarized as under19

X(, ) := (1 )(1 )2(B D01b)+

(2(1 ) k

G D01b2 L2

+ (2 + (1 )2)(GD01b))

Y1(, ) := (1 )

L2 (1 )

2 D01b2

(2(1 )

L2 + (1 k)

G D01b2

L2

+

2 + (1 )2) D01b2 ) c

Y2(, ) := Y1(, )

Proposition 6 characterizes the solution triplet (, , D01b) for the multiple bank lending case.

Proposition 6 (Multiple Banking Relationships) Let there be 2 banking relationships sus-

tained by the firm. The optimal policies to the investment problem faced by the firm is given by the

solution to the following set of simultaneous equations

1. = (1)(LD01b)2c

(1)((1)D01b(1k)(2GD01bL))

2. ()2(1 (BD

01b)

E) +

(GD01b)(BD01b)E

= 0 where E= 2(GD01b)(BD01b)

k(2GD01b L)

3. P()D01b = I where P() = + (1 )


It can be seen from Proposition 6 that = 1 is not a solution to this system of equations. Thusthe monitoring intensities in a multiple banking relationships are always lower than the single bank

case. Further it follows that if < 1 , there exists states of the world when one bank is informedand the other is not. The informed bank can then continue to hold up the borrower thus not fully

eliminating the hold up problem faced by the firm. In this sense, multiple banking relationships

are not as effective as bond markets in resolving the hold up problem. Thus firms with these two

alternatives to mitigate the hold up problem would favor the bond market alternative. Those firms

which do not have this access would resort to multiple banking relationships. This leads to the

testable empirical prediction that in financial systems where the arms length bond markets are

not well developed, firms on average should have greater number of bank relationships.

19Note that there are 4 cases to be considered. Both banks are either informed or uninformed, and case where one

is informed and the other is not as a result of their monitoring efforts


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5 Empirical implications

I summarize the main empirical implications of the model. In these implications, firm quality

indicated by credit rating might be considered as a reasonable proxy for the bargaining power of

the firm

Loan pricing is non linear in the bargaining power the firm. The rate charged by the bank is

decreasing in the bargaining power of the firm.

Firms with very high and very low bargaining power follow similar asset substitution poli-

cies. Asset substitution is checked more efficiently in the case of the firms with intermediate

bargaining power.

As costs of monitoring increases in the economy,

agency costs, bank specialness and renegotiation

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