A theory of banking structure

Journal of Banking & Finance 23 (1999) 863±895 www.elsevier.com/locate/econbase

A theory of banking structure Sanjiv R. Das *, Ashish Nanda Harvard Business School, Soldiers Field, 361 Morgan Hall, Boston, MA 02163, USA Received 27 September 1997; accepted 11 August 1998

Abstract This paper proposes a theory to analyze the specialization of banking activities based upon the di€erent functions that banks perform when rendering a variety of ®nancial services. The functional di€erence in the services performed by banks is based upon two dimensions: the degree of information asymmetry involved in providing the service, and the degree of veri®ability of the value of the service rendered. This has implications for the length of banking relationships and also determines whether banks develop the right degree of skill specialization and resource intensity for the existing task mix. Costly overspecialization occurs in certain deal type transactions and underspecialization occurs in relationship type transactions. The paper examines how bank-client relationships are structured and proposes an explanation for phenomena such as bank syndication. First-mover advantages and monopoly skills are also shown to be natural outcomes of the model. The analysis has implications for banking regulation, such as for the Glass± Steagall Act, in the sense that it analyzes the e€ects of this specialization, ®rst enacted within the spirit of the Act. Ó 1999 Elsevier Science B.V. All rights reserved. JEL classi®cation: L20; G21; G24; M21 Keywords: Specialization; Spatial equilibrium

*

Corresponding author. Tel.: +1 617 495 6080; fax: 1 617 496 6592; e-mail: [email protected]

0378-4266/99/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 4 2 6 6 ( 9 8 ) 0 0 1 2 3 - X

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1. Introduction 1.1. Outline This paper proposes a model of the banking industry based on the functional di€erences between the various services provided by ®nancial ®rms (Merton, 1993). We categorize ®nancial services on the basis of two criteria: (a) the degree of relationship speci®c information between client and bank required to render the service, and (b) the degree to which the exact value of the service provided is veri®able by a third party. Employing these criteria, we focus on two categories of bank functions: (i) relationship banking, where the degree of relationship speci®city of information is high, and the value of throughput of the relationship is easily veri®able, and (ii) deal/transaction banking, where the degree of relationship speci®city of information is lower, and the value of the deal to the client is less readily measurable. The paper develops a modelling framework to analyze the structure of the banking industry in each of these two categories. Speci®cally, the paper examines how the functional service o€ered by a bank drives its specialization in equilibrium, and whether this equilibrium specialization is an ecient one. We draw two sets of implications: (i) in equilibrium some banking tasks are performed via a long-term relationship (relationship speci®c transactions), whereas others are performed through one-o€ transaction type relationship (deal speci®c transactions), and (ii) if engaged in relationship speci®c transactions, banks underspecialize in the skills they develop, whereas, if engaged in deal speci®c transactions, they overspecialize, relative to what their clients desire. After developing these primary results, we present other implications of our model which explain widely observed phenomena such as bank syndication, boutique services, megabanks, and excessive ®rst-mover growth. Whereas most work on banking structure has focussed on the relevance and impact of the legal separation between commercial and investment banks as mandated by the Glass±Steagall Act, this paper examines theoretically the impact of the implicit functional di€erentiation on the structure of the banking system. We argue that, regardless of the legal mandate, the functional di€erence between the various ®nancial services constitute a structural characteristic of the US banking system. This separation of banking services into di€erent types of functions, requiring the development of di€erent types of resources, has costly equilibrium e€ects: it has caused banks to underspecialize when engaged in relationship speci®c banking and to overspecialize when engaged in deal speci®c banking. Our model also analyzes approaches to alleviating these ineciencies. Certain features of banking practice such as syndication, where banks work in teams, have social bene®ts, since syndication reduces the degree of over and

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underspecialization which would occur otherwise. We demonstrate that the incentive among investment banks to create a skill monopoly results in the observed development of boutique ®nancial service ®rms (e.g. M&A ®rms such as Wasserstein-Perella). Our model supports two types of bank growth patterns: one set of banks (e.g. Banc One in the 1980s) build businesses by investing intensively in focussed skills; another set of banks grow by expanding their sphere of activity rather than by investing in deepening their skill in a given activity (e.g. Chase Manhattan). The model also suggests that when new markets open up, the ®rst mover incentive leads to racing behavior, where banks invest in the skill too early and too fast compared to the optimal. This leads to the observed headcount expansions and subsequent contractions so prevalent in banking ®rms. Thus, the simple assumption of functional dichotomy provides a model which explains several features of the banking industry. While the literature on banking has so far broadly examined ®nancial intermediation, our attempt is to take a closer look at the structure of speci®c types of intermediaries. 1.2. Relationship to the literature In this Section, we discuss the context of the paper and its relationship to the other literature on ®nancial institutions. This paper is sharply focussed on the structure and welfare implications of ®nancial intermediation in a bilateral banking relationship. In contrast, related literature on ®nancial intermediation deals with the broader issues of institutions versus markets, and within institutions, the demarcation between bilateral and multilateral intermediation relationships. Also, there is a substantial literature on universal banking, which is linked to our model. Several papers deal with the architecture of ®nancial systems. Merton (1995) emphasizes that ®nancial innovation leads to changes in markets and ®nancial institutions, resulting in competition between them. For instance, corporations raising ®nancing have a choice of accessing funds from either banks or the capital markets. Boot and Thakor (1997a) analyze the optimality of each alternative. Whereas banking relationships alleviate moral hazard through monitoring, they generate less public information. Funding via the capital markets provides reduced monitoring, but more public information. In a simple separating equilibrium, good credits prefer accessing the markets, and weak credits access banks. As average credit quality in the economy improves, capital markets play a bigger role. Dewatripont and Maskin (1995) also highlight that borrowers with longer time horizon prefer bank to investor ®nancing. Other papers dealing with ®nancial system architecture, more speci®c than Merton (1995), are Boot and Thakor (1997a), Bhattacharya and Chiesa (1995), von Thadden (1995), and Yosha (1995). Yosha (1995), Bhattacharya and

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Chiesa (1995), Sabani (1992), and Titman and Subrahmanyam (1996) look at the impact of proprietary information on banking relationships. These papers examine the equilibrium choice of lending structure versus the information e€ect once the structure is chosen. Proprietary information may drive the choice between bilateral and multilateral lending relationships. Bilateral relationships preserve proprietary information, and hence may be more attractive to better quality ®rms, whereas poorer quality ®rms may prefer multilateral lending as the lower costs of ®nancing compensates for the cost of information revelation. These papers argue that, in the presence of proprietary information, a result opposite to that of Rajan (1992) is obtained. Rajan develops an equilibrium model where better credits go to the capital markets, and weaker credits borrow from banks. Another strand of literature focuses on the question of whether universal banking improves welfare and innovation in the ®nancial system. Boot and Thakor (1997b) develop a model in which they demonstrate that when commercial banks and investment banks are separate (i.e. no universal banking), each has incentives to innovate in order to retain business. The commercial bank improves its monitoring systems, and the investment bank works towards better capital markets solutions for its clients. When these two businesses are commingled into a single universal bank, the institution as a whole prefers not to innovate, because the bene®ts in one division eat away those of the other. Other papers in the literature that deal with the eciency of universal banking are Berlin et al. (1994), Kanatas and Qi (1994), Puri (1994, 1996), Kroszner and Rajan (1994a,b), and Rajan (1993). The crucial debate that arises in most of these papers is whether there is a con¯ict of interest when banks that have made loans to ®rms also act as underwriters for new debt and equity issues. The cited papers present empirical work using data prior to the Glass± Steagall Act of 1933 to examine whether there is evidence of con¯icts of interest. By and large, they ®nd none and argue that there is little reason for the regulation. One of the by-products of our model is a theoretical argument in support of these empirical results. As a prelude to discussing the linkages of our paper with the literature, we summarize it here. We show that the functional di€erences among various banking activities have an impact on the degree of specialization and structural form of banking ®rms and examine the welfare implications of each form separately. Our model provides a framework to understand how banks choose an optimal position on the relationship/transaction dimension. We show that this choice is a consequence of the functional nature of the various banking transactions undertaken. Commercial banking activities lead to longer-term relationships with ex-post payo€s and low levels of specialization. Investment banking activities lead to short-term relationships with ex-ante payments and more than required levels of specialization. Our paper then uses the framework

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to understand the existence of several structural phenomena in the banking world, such as boutique shops and syndication transactions. Our paper is linked to the other literature on ®nancial institution structure in four ways. First, our paper is narrower in focus than the papers of Allen (1992), Allen and Gale (1995), Merton (1995) and Boot and Thakor (1997a). Whereas they examine the competing roles and information generation of markets versus banking intermediaries, we examine contracting and skill development within di€erent types of ®nancial intermediaries. Second, our paper is linked to the papers by Yosha (1995) and Bhattacharya and Chiesa (1995) in the sense that both examine the structure of the banking relationship. Whereas their papers look at the role of proprietary information in determining the choice of bilateral versus multilateral lending, our paper looks at the role of relationship speci®city and consequence veri®ability on the duration of the banking relationship and degree of bank specialization. Third, our work is connected to the work of Boot and Thakor (1997b) on the degree of innovation in universal banks as opposed to segregated commercial and investment banks. Whereas their paper argues that universal banking may lead to lower levels of innovation, our paper suggests that this e€ect may be mitigated on account of the distinct functional di€erences in commercial and investment banking activities. Fourth, the papers on con¯icts of interest ®nd little empirical evidence for retaining the Glass±Steagall Act. We argue that the functional dichotomies modeled in our paper provide a parallel theoretical justi®cation. Our model explores the narrow question of banking structure without addressing the issues of markets versus institutions. Whereas other works focus on the borrower and his decisions in the presence of proprietary information, our paper looks at equilibrium welfare e€ects given the institutional structure. We hope that this additional perspective will enhance the existing literature along interesting dimensions. 1.3. Model overview In this paper we focus on two criteria that are relevant to determining the structure and eciency of banking activities: (i) relationship speci®city and (ii) consequence veri®ability. These criteria are used to understand the nature of two types of banking relationships: (a) relationship banking (commercial banking), and (b) deal-oriented banking (investment banking). In order to ®x ideas, we focus on a lending transaction as an example of commercial banking, and a merger and acquisition (M&A) deal as an example of investment banking. We describe these in some detail below in order to provide a sharper context for the model. 1. Commercial lending is performed through long-term relationships with clients, with the bank's compensation being pegged to the delivery of the

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service. Assume that the loan in question is a revolving credit facility for a ®rm with seasonal working capital needs. At the beginning of the relationship, the bank invests in structuring the deal and does a credit analysis, and the client usually agrees to a long term relationship by paying a commitment fee on the size of the credit line for the period of the loan. Without the loan commitment, the client would have an incentive to terminate the revolver at any time and take the structure to another bank, which can piggy-back on the e€orts of the ®rst bank, since it has the bene®ts of a trained client, more credit history, and a signal of prior due diligence e€orts by another reputable bank. In exchange for the commitment fee, the commercial bank carries out an analysis of the client's needs and structures the best level of revolving commitment it should make. Overestimation of the size of the revolver is costly for both the bank and the client, as the bank must stand ready to put out funds which may never get utilized, and the client also pays commitment fees on a larger than necessary amount. Underestimation of the size of the loan hurts the client since it then needs to look for additional funds, and also reduces the volume of the business the bank does. Therefore, a bank is in e€ect compensated ex-post for its performance: a bad job of structuring the deal may lead to poor results for both bank and client, and vice versa. 2. The M&A transaction is performed via a short-term contract with a component of the compensation being negotiated ex-ante as ®xed fees. While performing its duties, the investment bank carries out a detailed analysis of the best deal structure, and learns deal-making skills, obtains insights into industry dynamics, and builds a valuable reputation. Subsequent banking activity is renegotiated; for example, a new merger or underwriting of an issue by the same client may be undertaken by a completely di€erent bank. Our ®rst criterion, relationship speci®city, de®nes the extent to which the bank's skills are part of the relationship. This criterion drives the length of the banking relationship. For transactions such as commercial lending, the bank makes a substantial investment up front in understanding the credit-worthiness of the borrower, thus resolving the high degree of information asymmetry that initially exists. The resources invested by the bank in building the relationship (e.g. personal contacts with the client CFO) are not fungible (i.e. are intrinsic to the relationship) and, in the absence of long-term commitment from the client, would be too costly to make. This investment is undertaken only because the bank obtains a long-term relationship with the client, who precommits to the relationship by paying a loan commitment fee. The existence of a `house' banker is attractive to the client as well, since it makes future transactions cheaper and easier. Another example of a high degree of relationship speci®city leading to a long-term relationship is that between venture capitalist and start-up ®rm. On the other hand, activities such as M&A advisory and the underwriting of IPOs are short-term, based on a high degree of public information. The payo€s

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from a successful deal are sucient to cover the costs to the bank in a one-shot transaction. Moreover, the skills developed by the banker (e.g. M&A valuation methodology) are fungible (i.e. are extrinsic to the relationship). Future transactions of similar nature may be performed by di€erent banks even when for the same client. The second criterion, consequence veri®ability, relates to the degree to which the outcomes of the relationship can be evaluated. In a lending relationship (e.g. a revolving working capital facility) the amount of loan usage each year is clearly quanti®able and contractible. In the case of the underwriting of an IPO, the amount of the security sold provides an observable measure of the service rendered. On the other hand, the value brought to the relationship in an M&A deal and the value of a venture capitalist are not easily veri®able by the client. Our model demonstrates the impact of these two criteria on the type of relationship that develops in equilibrium. First, relationship speci®city determines the length of the relationship. It is quite intuitive that when a bank's builds skills speci®c to the client, it will only be interested in doing so if assured a long term relationship. Hence, commercial lending transactions are longer term than M&A deals. Second, consequence veri®ability determines how the providers of ®nancial services are rewarded for their services. In M&A deals, since the output level is not easy to quantify, payment is based not on realized but on expected contribution to the deals. Since the throughput of a commercial lending transaction is easy to measure, commercial banks are paid for their throughput. The model demonstrates that these two conditions, length of relationship and nature of compensation, together determine the extent of specialization that the banks will develop. M&A ®rms, engaged in short-term transactions and paid on the basis of their reputation, tend to overspecialize in the skills they o€er the clients, compared to the ®rst-best; conversely, commercial lending involves long-term relationships and compensation based on throughput, leading commercial banks to underspecialize. By exploring the drivers of this conjoint under and over-specialization, our framework enables making recommendations towards alleviating these problems. Clearly, our model simpli®es reality by assuming that commercial banking and investment banking are polar situations. In reality the functional dichotomy is less stark. The choice of polar alternatives has been deliberately made to stress the point that functional di€erences can result in sharply di€erent structural outcomes in the banking industry. Without loss of generality, the model abstracts away from reputation e€ects and multiperiod gaming. The dichotomy of banking functions highlights how both the classic problems of hold-up and opportunism come into play in o€ering banking services. When relationship speci®city is high, and transactions are ex-post veri®able, as in commercial banking, there are incentives for the client to be opportunistic

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after the bank has invested in the relationship. This leads to long-term relationships in commercial banking and underspecialization by the bank, since it wishes to minimize the costs of ex-post opportunism. Conversely, when relationship speci®city is low, and the deal is not easily quanti®ed ex-post, as in investment banking, the investment bank can hold up performance after obtaining the deal. This leads to short term contracts, and over-specialization by the bank. In the following sections, we provide a model of the structure of the banking industry and use it to propose a stylized rationale for several observed facts. We develop a common framework in which relationship banking and transaction-based banking equilibria are separately developed in a spatial model. Eciency of the equilibrium is analyzed, and then the model is employed to discuss speci®c features of the banking system. In conclusion, further extensions of the model are proposed. 2. The model In this section, we develop a spatial model of banking activity. The model is an applied version of the Nanda (1994) model of specialization. We introduce the notation for the model and the assumptions we will be working with. These assumptions are of two types: (i) assumptions describing the source and nature of the income and expense functions used in the model and (ii) assumptions related to the nature of the relationship between banks and clients, which lead to particular contractual outcomes. The model framework applies to two banking equilibria (one for relationship banks and the other for deal banks). We solve the model to obtain the separate relationship and deal banking equilibria. We develop the theoretical model, referring when appropriate to the examples introduced in the previous section. 2.1. Technology assumptions The modelling technology is general and applies to both banking situations, for each of which we derive separate equilibria. In each category consider a relationship between a client ®rm P and two identical banks A1 and A2 which service the ®rm's ®nancial needs. 1 The banks prefer more income to less, and

1

We assume that clients are of a minimum size relative to the banks, such that they access more than one bank for their needs. Hence, this model is more applicable to large US companies and multinational corporations. Although the intuition of the argument is general, the analytical model is restricted to a situation in which the client has chosen to employ two banks. As is observed in practice, corporations engage in relationships with a limited number of banks.

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are risk-neutral. The banks' pro®t U equals the di€erence between income I and the cost G(H) of building resource H. 2 G(H) is an increasing and convex function of the asset level H. For example, H may represent the quality and quantity of manpower required for a particular banking service. U …I; H † ˆ I ÿ G…H †; G…0† ˆ 0; G0 …H † P 0; G00 …H † > 0: Each bank has a reservation pro®t of U0 over the duration of the game. The client, like the banks, prefers more pro®ts to less, and is also risk-neutral. The client's payo€ V is equal to the net value generated from the banking relationship, i.e. V ˆ …x ÿ I1 ÿ I2 †, where x is the gross pro®t, and Ii ; i ˆ 1; 2, is the compensation paid to each bank. 3 The client±bank relationship is modelled as a two period game with no discounting.

In period 1, both banks invest in developing resources, and in period 2, they use these resources to perform tasks for the client. For example, in the case of the relationship bank, the client approaches the bank for long-term funding of its working capital needs, upon which the bank invests in client-speci®c activities such as credit analysis, due diligence and loan structuring (®rst period), followed by the bank providing the client with the revolving facility (second period). In the case of transaction banks doing an M&A deal, they structure the deal and make a proposal (®rst period) for which they receive a fee, and then undertake other merger related activities (second period). The length of the second period tends to be longer for the lending situation than for the M&A case. In building assets, each bank chooses the pair (a, H). The element a represents ``asset location'', whereas H represents the ``asset level''. Pursuing our example of a lending relationship, asset location for a relationship bank would be the kind of lending activity (local currency lending, interest rate swaps, structured notes, ¯oating rate instruments, etc.) it structures, and asset level would be the number of personnel dedicated to each particular task. For

2

We use the terms ``resources'' and ``assets'' and ``skills'' interchangeably to refer to the intangible and durable entities such as ``goodwill'' and ``merger and acquisition skills'' that the banks develop. We assume that one bank develops only one client-speci®c asset, and that the pro®t function is additively separable in income and cost. 3 The model assumes that supervision of banks is costless.

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transaction banks o€ering M&A services, the asset location would be the specialized deal type (LBO, MBO, issuance of junk bonds), and asset level would once again be the number of skilled personnel dedicated to this activity. Therefore, asset location identi®es the degree of resource specialization in the model, and asset level indicates the intensity of investment in that resource. Each bank simultaneously chooses the extent of specialization and the level of investment in the skill. Asset location a can take any value between 0 and 1, described by a horizontal line segment of unit length. 4 A task is best performed by a bank which has developed a particular ``type'' of asset. We model this phenomenon as a task ``arriving'' at a particular location on the line segment. If a task were to arrive exactly at the same point on the line segment where the resource is located, the gross pro®t to the client (transaction value including the bank's compensation) generated by the bank's employing the resource to perform the task would be x ˆ f …H †, an increasing ‰ f …H † > 0Š and (weakly) concave ‰f …H † 6 0Š function of asset level H. If no resource is applied, no gross pro®t is generated [f …0† ˆ 0]. The model assumes that adjustment costs and delays in changing asset location or building new assets are too prohibitive to allow the banks to modify the assets during the game, once they have been established. A bank cannot change the location (a) and level of its resource (H) during the game. In Fig. 1, bank A has developed a resource at location a to level H. The bank can generate gross pro®t f(H) for the client by performing a task that arrives at location a. The gross pro®t is depicted by the vertical height at the point at which it is generated, and serves as a measure of the bank's resource level. If a task arrives at a location (say b) di€erent from where the resource resides (a), then the resource is not exactly appropriate for the task. The task is ``transported'' from where it arrives to where the resource is located at a cost of t per unit distance. Thus, if a resource is separated from a task by distance z (z ˆ b ÿ a in this example), there is a cost tz of applying the resource to the task, and consequently, performance of the task yields a gross pro®t of f …H † ÿ tz. EABCD in Fig. 1 charts the pro®le of gross pro®ts that would be generated if bank A (whose resource is located at a) were to perform tasks arriving at different points on the segment [0, 1]. Tasks arrive randomly, and their arrival pattern on the line segment [0, 1] follows a uniform probability distribution. Let d be the distance from the point where the resource is located to the point where the gross pro®t generated by it becomes zero i.e. d ˆ f …H †=t. We term d (which is a function of resource level H) as the bank's resource span. 5

4

The notion of distance on the [0, 1] line is not meant to convey a sense of value; rather it is used to depict the closeness of task characteristics adopted by each bank. 5 Note that d is a one-sided rather than a two-sided span.

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Fig. 1.

Assume that the spans are suciently broad such that, no matter how the banks choose to locate their resources, they cannot prevent overlap of their resource pro®les (which is equivalent to the assumption that resource span d P 14). 6 An indi€erence point …a† exists in the interval ‰a1 ; a2 Š, such that the gross pro®ts generated by the two banks performing a task arriving at the indi€erence point are equal (see Fig. 2). f …H1 † ÿ t…a ÿ a1 † ˆ f …H2 † ÿ t…a2 ÿ a† ) a ˆ

a1 ‡ a2 f …H1 † ÿ f …H2 † ‡ : 2 2t

The client can observe the banks' resource levels and locations, but cannot verify them to a third party. 7 Hence, the client cannot write a contract with the banks that enjoins them to develop their skills at speci®c locations and up to speci®c levels. However, because the client can observe the banks' resources, it allocates an arriving task to the more ``e€ective'' bank, i.e. the bank that is

6 If the banks' assets are too narrow to cover the entire skill range, the situation is trivial: there is no moral hazard problem. The client and the banks want as much territory covered as possible, and hence, have the same motivation of avoiding asset overlap between banks. As a result, the banks' asset level and specialization choices are the same as what the client desires. 7 We do assume, however, that the client can roughly identify the region the bank's resource is located in: the client can verify which half of the line segment the bank's resource is located on. The observability assumption is made to simplify exposition of the discussion. However, it is not critical to the model ± it can be shown that the results still go through if we relax the assumption.

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Fig. 2.

capable of generating greater gross pro®t by performing the task. 8 Hence, bank A1 performs all the tasks that arrive in the interval ‰0; a†, whereas bank A2 performs all the tasks that arrive in the interval …a; 1Š. The expected gross pro®ts generated by banks A1 and A2 in period 2 are given by: Z a i th 2 Ex1 ˆ ‰ f …H1 † ÿ tja1 ÿ bjp…b† dbŠ ˆ f …H1 †a ÿ a21 ‡ …a ÿ a1 † ; …1† 2 0 h i t 2 2 …2† Ex2 ˆ f …H2 †…1 ÿ a† ÿ …1 ÿ a2 † ‡ …a2 ÿ a† : 2 The ®rst terms in these expressions would be the expected gross pro®ts if there were no transportation costs. These ®gures have to be reduced by expected transportation costs to arrive at the expected pro®ts. 2.2. Contracting assumptions Banks invest in developing resources, whereas pro®t accrues to the client. Contracts have to be built around the process, so that the banks have an incentive to build the resources and perform tasks. The timing of these contracts is as follows.

8 Another reason besides allocation of incoming tasks by the client could be that the bank with greater resource level is more sensitive to the arriving task, and hence, picks it up.

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The sequence of contracting events is as follows. In equilibrium, there is an optimal contract which the client o€ers to the banks. (We discuss the nature of this equilibrium contract in detail later.) Based on this optimal contract, each of the two banks locates in the skill space (a) and builds appropriate resource level (H), accounting for the optimal choices by the other bank (Nash Equilibrium). Then, a banking task arrives which the client allocates to the bank better positioned to service it. After provision of the service, the game terminates. Separate equilibria are derived for the relationship banking and transaction banking cases. For relationship banking, the sequence of events commences with the client o€ering long-term contracts, which are optimal in equilibrium. The two banks decide on their skill locations and levels. A relationship banking task arrives and is performed by the more suitable bank, with its compensation determined by the quantity and quality of service being put through the relationship. For transaction banking, the optimal contract which is o€ered is a one-shot arrangement, negotiated with each of the two transaction banks based on their relative specialized skills. The two banks determine their optimal skill locations and resource levels. A deal banking task arrives, is serviced by the more suitable bank for a ¯at fee. The nature of the contract that the client o€ers to the banks in equilibrium depends on the type of transaction: · Relationship banking tasks generate sharply identi®able instruments such as loans and credit terms to the client. For example, in the case of a ¯oating rate note or loan, the realized cost of funding is easily ascertainable. Proper structuring of the loan results in greater payo€s to both the bank and the client. The pro®t generated by these instruments is veri®able and the bank's compensation is determined by this throughput of the banking relationship. On the other hand, the deal banking service is typically in the form of advice during the deal-making process. It is not possible to verify the value of such service to the client. For example, the value of an M&A proposal is hard to estimate at the conclusion of the deal. · Deal type transactions lead banks to develop assets that are intrinsic to the bank: when the bank walks away from the client who it has been advising, it

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takes the M&A skill and knowledge of the industry away with it. On the other hand, the assets that relationship banks develop are typically resident in the relationship with the client. Once these assets have been developed, the relationship banks that have built these assets cannot take them away from the client, even if they were to walk away from the client. For example, once a bank invests in credit analysis of the client, it cannot take this analysis with it, if it terminates the relationship. Obviously, these are conceptual extremes occupying the corners of a twodimensional matrix (see Fig. 3). Reality does not lie simply on these sharp polarities. Relationship banking activities, for example, also lead banks to develop skills intrinsic to themselves (such as structuring derivatives-linked loans), whereas deal banking activities can lead to the development of relationship-speci®c skills (for example, the goodwill and contact the investment banker enjoys with the client's CFO). However, one can usually assess whether some tasks are more in the nature of `deal banking' or `relationship banking' compared to others. Because a relationship bank's asset is client-speci®c, the client can engage in ex-post opportunism with the bank (Williamson, 1975). Once a bank has invested in the resource in the ®rst stage, the client can replace it by another bank, pay the new bank reservation compensation to perform tasks in the second stage, and in the process, expropriate all the gains from resource development in the ®rst stage. For example, in the lending situation, unless loan commitment fees are imposed up front, a client has an incentive to shift midway through the relationship in favor of another bank that o€ers more attractive terms ex-post.

Fig. 3.

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The bank foresees that the client has an incentive to terminate the relationship, once it has developed the resource. Hence, the bank does not develop the resource in the ®rst stage. To overcome this problem, the client has to commit credibly that it will not terminate a relationship with a bank upon its developing the relationship speci®c asset. The only way that it can o€er a credible commitment at time 0 is by committing to a long term contract. Since the client cannot verify the bank's resource, it cannot o€er it a compensation contract that is based on the nature of the resource the bank has developed. However, since consequences are veri®able in relationship banking, the bank's compensation can be a function of service throughput. Thus, the client can o€er the bank a long-term compensation contract that is a function of its service throughput. 9 Since a deal bank develops a resource that is fungible beyond the particular transaction, the client has to bargain with the bank at the end of stage 1 as to how the gross pro®ts generated in stage 2 will be shared between the client and the bank. 10 For example, in the M&A situation, at the end of the ®rst stage, the bank has produced a proposal for the merger. The client has to negotiate anew with the bank for the second-stage (actual merger, ®nancing conditions), else the bank will simply walk away from the deal. Since the client cannot verify deal based banking service output, it cannot tie the bank's compensation to performance, and so, must base compensation on an estimate of the skill the bank brings to bear on the transaction. Therefore, the client o€ers a one-stage contract to the bank at time 0, followed by bargaining at the end of stage 1. The client cannot make the stage 1 contract contingent on the bank developing particular resources, since it cannot verify the resources. The one-stage contract is in the nature of a ¯at payment or fee. Hence, transaction banks are o€ered short term contracts ± a ¯at compensation initially, while they develop the proposal, and subsequently, compensation derived after bargaining between the client and the bank. 11 In

9 In this model, a one period contract which o€ers compensation based on future service output is essentially identical to a two period contract. 10 A long term contract o€ering ®xed compensation can be ruled out ± a bank that is o€ered such a contract does not invest in any resource at all. 11 Why can not a client mimic for the relationship bank the contract that it is o€ering the deal bank? If the relationship bank demands a rent-share from the client by threatening hold-up, all a client needs to do is replace it. Can the client credibly o€er a single-period contract to the relationship bank along with the promise of bargaining at the end of period 1? Underlying the promise to bargain at the end of period 1 is a commitment that the bank will not be replaced, if ®red. If a relationship bank cannot verify after being ®red that it has not been replaced, the client cannot credibly commit not to replace the bank, if ®red. Thus, there is no bargaining between a client and relationship banks at the start of period 2. Since the relationship banks are risk-neutral, renegotiation can also be ruled out.

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the following paragraphs, we summarize the relationship bank game and the deal bank game. 2.3. Game between client and relationship banks · At time 0, the client P makes a take it or leave it o€er to the banks A1 and A2 in the form of a long term contract through stage 2 and announces how the banks A1 and A2 are to be paid at the end of stage 2. We restrict attention to compensation schemes that are linear functions of a relationship bank's output: I ˆ a ‡ lx. 12 · A1 and A2 each decide whether P's o€er is reasonable enough for them to build resources. A bank accepts the client's o€er if it expects to receive at least its reservation pro®t upon signing the contract. The game ends if the banks reject the o€er. If the banks accept P's o€er, they commit that they will not quit till the end of stage 2. · If the banks have accepted the compensation scheme, they develop the resources during stage 1. The banks simultaneously and irrevocably choose resource locations ai and levels Hi …i ˆ 1; 2†. Without loss of generality, assume that A1 always locates its resource to the left of A2 (i.e. a1 < a2 ). · During stage 2, a task arrives and the bank with the greatest ``e€ective resource level'' performs the task. · At the end of stage 2, pro®t x is generated, and the banks are paid their compensations on the basis of the long term contract they had entered at time 0.

12 Holmstrom and Milgrom (1987) argue that a linear compensation scheme is particularly robust. Speci®cally, they show that if: (1) an agent has an exponential pro®t function over its consumption rate (our assumption of additive separability between income pro®t and e€ort cost is transformable into, and hence, equivalent to, such a pro®t function), and (2) the agent controls the drift rate of the Brownian motion that describes the agent's e€ort over time, then a linear compensation rule is optimal: it provides the agent with the same incentive, irrespective of past performance.

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2.4. Game between client and deal banks · At time 0, the client P makes a take it or leave it o€er in the form of a short term contract to the deal banks A1 and A2 . The contract o€ers an up-front fee to be paid upon acceptance of P's o€er. · A1 and A2 accept or reject P's o€er. If the deal banks reject the o€er, the game ends. If the deal banks accept P's o€er, they commit that they will not quit until time 1. · If the deal banks accept P's o€er, they are paid the compensation as per the terms of the contract. · During stage 1, the deal banks simultaneously and irrevocably decide how much resources to develop (H1 and H2 ), and where to locate them (a1 and a2 ). Assume that a1 6 a2 . · At the end of stage 1, P bargains with A1 and A2 on a contract for stage 2. We assume that an ecient bargain is struck.

Each deal bank is rewarded for the incremental pro®t (over the other deal bank's possible contribution) that it expects to bring to the ®rm. In particular, we assume that a deal bank earns a fraction b of the expected additional gross pro®t that it generates, relative to the gross pro®t that would have been generated were it not engaged by the ®rm (see Fig. 4). The parameter b is assumed to be exogenously determined during the bargaining at time 1. 13 · During stage 2, a task arrives and is performed by the deal bank with the greatest ``e€ective resource level''. · At the end of stage 2, pro®t x is generated, and the deal banks are paid the ®xed fees agreed to in the second stage contract.

13

In terms of payo€, the bargaining solution is equivalent to a bidding game of the following type: the task arrives; the client asks both banks to bid the pro®t they will generate from the task; the winning bidder is charged its bid price and the task is handed over to it along with a reward that is a fraction b of the di€erence between the two bids; the winning bidder performs the task and retains the gross pro®ts.

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Fig. 4.

3. Equilibrium choices In this section, we extend the intuitive description provided in Sections 1 and 2 by formally deriving the equilibria of the model, and then we analyze the eciency of banking structure. Proofs are relegated to the Appendix A. 3.1. The ®rst best We begin by solving the social planner's problem. The social planner attempts to realize the structure that yields the maximum total surplus. This provides the ®rst-best solution, devoid of e€ects of gaming interactions between the two banks. The optimization program for the social planner, max Ex1 ‡ Ex2 ÿ G…H1 † ÿ G…H2 †;

H1 ;H2 ;a1 ;a2

yields the following ®rst order conditions: f 0 …H1 †a ˆ G0 …H1 †; a ˆ 2a1 ;

14

14

f 0 …H2 †…1 ÿ a† ˆ G0 …H2 †;

a ˆ 2a2 ÿ 1:

Note that the expressions for Ex1 and Ex2 are de®ned in Eqs. (1) and (2).

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The ®rst two equations set the marginal bene®t of additional resource accumulation equal to its marginal cost, and the second set minimizes task transportation cost. Since the banks are symmetric, the ®rst order conditions yield the solution (superscript 0 denotes equilibrium values):    0 0 1 3 ; ; a1 ; a2 ˆ 4 4 f 0 …Hi0 † ˆ 2G0 …Hi0 †; i ˆ 1; 2: If the client could verify the banks' resources, then it would impose ®rst best resource level and location choices on the banks, and ensure that they secure their reservation compensation. 3.2. Game between the client and relationship banks We now analyze the relationship banking equilibrium. Competition for long-term contracts between the two banks results in a result that it socially suboptimal relative to the ®rst-best. Here, we o€er the following proposition. Proposition 1. Relationship banks underinvest and underspecialize, compared to the ®rst best, and compared to what the client desires ex-post. This proposition is embodied in the following Nash equilibrium (* denotes optimal values):   5 ÿ 2d  f 0 …H  † ˆ G0 …H  †; 9      1 d 5 d a1 ; a2 ˆ ; ‡ ; ÿ 6 3 6 3 5 ÿ 2d  ; l ˆ 3…1 ‡ 2d† where d ˆ f …H †=t is the resource span (de®ned before). The client's desired specialization (ex-post) is given by h i 1 3 ; : a^1 ; a^2 ˆ 4 4 Proof. The proof is given in Appendix A. In equilibrium, d  P 14, which implies that the incentive parameter l 2 …0; 1†, the Nash equilibrium resource level is sub-optimal ‰2G0 …H  † 6 f 0 …H  † ) H  6 H 0 Š, and the specialization level is less than the ®rstbest (a P 14). 

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Intuition for Proposition 1 When a client contemplates relocating a bank, it trades o€ the expected increase in pro®t over the territory in which the bank's resource pro®le has risen (marginal bene®t area in Fig. 5) against the expected decline in pro®t over the territory in which the bank's resource pro®le has declined (marginal loss area in Fig. 5). At the optimum, if a bank is marginally relocated, these two areas are equal. This trade-o€ is identical to the trade-o€ that a benevolent planner contemplates in maximizing gross pro®t. Hence, the client desires the ®rst-best specialization of its banks. When a bank contemplates relocating, it trades o€ the expected increase in pro®t attributed to it (marginal bene®t area in Fig. 6) against the expected decline attributed to it (marginal loss area in Fig. 6). Compared to the client's decision, there is an externality in the bank's specialization choice. A bank values snatching intermediate tasks away from the other bank, even though total pro®t to the client does not increase.

Fig. 5. Client's trade-o€ in relocating a resource

Fig. 6. A relationship bank's trade-o€ from resource relocation

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In order to control the banks' underspecialization, the client decreases incentive compensation so that the banks develop suboptimal resource levels, compared to the ®rst best. At the margin (in equilibrium), the loss averted by controlling underspecialization is equal to the loss incurred from inducing the banks to develop suboptimal resource levels. 3.3. Game between the client and deal banks We now consider the game between the client and its deal banks. In this case, competition for short-term rents leads to an equilibrium that is second best. Here, we o€er the following proposition. Proposition 2. Deal banks underinvest but specialize optimally, compared to the ®rst best. However, they overspecialize compared to what the client desires expost. This is embodied in the following statement:   1 3 0  0    ; : bf …H † ˆ 2G …H †; ‰a1 ; a2 Š ˆ 4 4 The client's desired specialization (ex-post) is given by h i 3ÿ4b 1 ÿ b ÿ 2b min d  ; 4…1ÿb† : a^2 ÿ a^1 ˆ 2 ÿ 3b Proof. The proof is given in Appendix B. Intuition for Proposition 2 The deal bank trades o€ the expected marginal increase in compensation from relocation against the expected marginal loss. For incremental relocation, the deal bank's trade-o€ is identical to the ®rst-best trade-o€. Hence, deal banks wish to specialize as much as the ®rst best. However, there is an element of dynamic inconsistency in the client's desires. Once the banks have developed their resources, the client wishes ex-post that the banks were less specialized than they are. The marginal loss from one bank relocating closer to the other bank (marginal loss area in Fig. 7) is the same as ex-ante marginal loss (marginal loss area in Fig. 5). The marginal bene®t from the relocated bank generating greater pro®t (marginal bene®t area in Fig. 7) is equivalent to the ex-ante marginal bene®t (marginal bene®t-1 area in Fig. 8). However, there is an additional marginal bene®t in ex-post relocation of the bank. The increased overlap of the banks' skills implies that the client has to compensate the other bank less (represented by marginal bene®t-2 area in Fig. 8). The client wishes, ex-post, that the banks underspecialize. It hopes the banks' appropriation of rents could be reduced by increasing overlap between their resource pro®les, thus intensifying their mutual competition for tasks.

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Fig. 7. Transaction bank's trade-o€ in relocating its resource

Fig. 8. Client's ex-post trade-o€ in relocating a transaction bank

3.4. Model summary The table below summarizes the discussion of over and underspecialization by relationship and deal banks. Versus ®rst-best Versus client's (ex-post) preference Specialization

Relationship banks Deal banks

Underspecialize Same

Skill-level

Relationship banks Deal banks

Underinvest Underinvest

Underspecialize Overspecialize

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Hence, relationship banks underspecialize, and deal banks overspecialize, compared to what their clients desire. The relationship banks underspecialize, compared to the ®rst best. The deal banks specialize to the ®rst best extent. However, due to dynamic inconsistency in their clients, their specialization level is more than what the clients desire, ex-post. Since, in neither case do the bank get the full bene®t from their investments, in both circumstances, the banks underinvest in their skills, compared to the ®rst best. This result is analogous to Holmstr om's result that agents who are paid less than their productive margin tend to underinvest in e€ort Holmstr om (1982). 3.5. Robustness of the model The model developed here is fairly robust. Several of the simplifying assumptions have been made for analytical tractability, but are not needed for the model results to hold true. For example, the assumption of a uniform distribution on the [0, 1] line segment of the arrival probabilities of banking tasks can be replaced by an assumption of any other form of distribution. So long as the arrival pro®le of tasks is symmetric around 12, the results of the model go through. We model the transportation cost to be a linear function of skill ``distance'' purely for expositional ease. We could model this cost as another type of function of distance. So long as it is a smooth and symmetric function (quadratic, for example), the results would still go through. The assumption that the banks' skill position and level are observable, but not veri®able, by the client can also be weakened. We could assume that the banks' skills are unobservable to the client. In such a case, a less optimally skilled bank could get hold of a task. So long as we allow exchange of tasks between the banks against side-payments for these exchanges, the model results would still hold. In our model, we are allowing one party (the client) to make a take-it or leave-it o€er to the others (the banks), hence imputing the entire bargaining power to the client. Obviously in real life, the situation is not so asymmetric. The relative bargaining powers of the two parties are determined by their outside options. However, the relative bargaining power does not a€ect the contracting equilibrium. It only in¯uences how the surplus is divided between the client and the banks. Our spatial model lives on a line segment. This implies that some resources are more ``central'' while others are more ``peripheral'' or specialized. We believe that this is more representative of banking activities than an alternate model in which specialization is depicted on a circle, where neighborhood is relative but there are no central or peripheral tasks. An example of a central relationship banking activity would be working capital lending, whereas that of an peripheral activity would be lending to emerging markets. Likewise, an

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example of a central activity in deal banking would be traditional M&A advisory, whereas more peripheral would be the structuring of credit derivatives for institutional investors. While we have operationalized the concept of neighborhood in one dimension for analytical tractability, the intuition carries over to more than one dimension. 4. Implications of the model The model developed here can be used to understand certain practices commonly observed in the banking industry. We extend our analysis to ®ve such cases: loan syndication, skill monopolies, span sizes, ®rst-mover issues and Glass±Steagall. Whereas detailed proofs have not been provided for these propositions, the intuition for them is provided. Proofs would be similar to those developed in Propositions 1 and 2 and are available from the authors on request. 4.1. Bank syndication We often observe that relationship banks transact with their clients as a team. Syndication results in the banks' compensation being pegged to their combined performance. This alleviates the problem of underspecialization that otherwise plagues the banks. Now each bank becomes sensitive to the externality it would impose on the other banks if it were to aggressively claim intermediate skills. However, one negative consequence of loan syndication is that banks tend to free-ride on each others' resources. This leads to resource underinvestment at a global level. Hence, in instances of bank syndication, relationship banks tend to specialize optimally but they do not invest in the relationship quite as much as they would if they were operating independently. 4.2. Boutique services Often, clients excessively value the unique skills of their deal banks. In other words, a client gives a higher fraction of pro®t to its deal bank when the bank has monopoly over some skill region than when the resource pro®les of the deal banks overlap. Such a compensation pattern exacerbates overspecialization, since each deal bank seeks to minimize its overlap with the other banks. This phenomenon is particularly evident in the M&A business, which is characterized by a large number of boutique ®rms carrying out very specialized kinds of deals. For example, ®rms such as Kohlberg, Kravis and Roberts and Wasserstein-Perella are rewarded for the highly specialized transactions they undertake, and their very renown leads these ®rms to overspecialize even more.

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4.3. Issues of bank scope The banking industry has seen the development of focussed banks such as Banc One and Nations bank on the one hand and megabanks such as ChaseChemical on the other. There is a natural trade-o€ between the bene®t of wide scope and the bene®t of heavy investment in resources. Banks can increase pro®ts in two di€erent ways. (1) A bank may choose to limit its scope of operations (limited span) but invest heavily in building its resources. (2) A bank may choose to develop a broad range of services (wide span) without investing intensively in any one speci®c skill. The model demonstrates that the more limited a relationship bank's scope is, the less it underspecializes. We observe relationship banks such as Banc One and Nationsbank which have been highly successful through following narrowly focussed lines of businesses. Since they have been focussed these banks have tended not to underspecialize. The services and skills they have o€ered have been relatively unique compared to other banks, allowing them to charge premium prices. Secondly, since they have had narrow spans they have invested intensely in developing their unique skills, achieving industry-wide recognition over time in these skills. In contrast, the model suggests that banks such as Chase-Chemical which have grown by widening their scope of operations but not investing heavily in any particular skills are especially prone to underspecializing, and hence, not creating a unique image in the minds of their clients. 4.4. Racing behavior/®rst mover bene®ts If all banks do not enter the market place simultaneously, the ®rst mover gains substantially more than subsequent entrants by aggressively underspecializing and overinvesting in resource development. Attracted by these prospective bene®ts, banks exhibit ``racing'' behavior whenever new opportunities open up. These aggressive rushes to be the ®rst in the market are characterized by ``wasteful'' behavior such as expending in¯uence costs, insucient due diligence, excess entry and early overinvestment in resources, followed thereafter by the inevitable shake-outs. This pattern is exempli®ed in Wall Street booms and busts, the overexpansion of Latin American debt, and the cyclical fortunes of the M&A business. 4.5. Glass±Steagall The discussion in this paper may help in addressing the debate around the Glass±Steagall Act. It appears that the divide between relationship and deal banks is functional and inherent in the nature of activities performed. This may be unlikely to change simply with the removal of the legal veil that Glass±

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Steagall mandates. Thus, allowing the same bank to underwrite securities and make loans to the same corporation may not a€ect the degree of specialization and eciency characteristics of these two functions of the banking industry. 5. Conclusions We employ a spatial model of the banking industry to analyze the di€erent equilibria emanating from a functional classi®cation of ®nancial service activities. In particular, we examine relationship (commercial) banking versus deal-based (investment) banking. The model parsimoniously analyzes the equilibrium contracts and ineciencies this functional dichotomy implies, and explains several stylized features of the banking system. Fundamental di€erences in the nature of banking activities result in di€erent specialization strategies adopted by relationship and deal banks. It also causes disparate levels of investment in skills by each type of bank. The model shows that underspecialization by relationship banks and overspecialization by deal banks takes place, relative to the what the client desires. Short-term contracting by deal banks and long-term contracting by relationship banks is shown to be an equilibrium outcome. These functional di€erences are inherent in the nature of tasks performed by each type of bank. Hence the structure of the banking industry is unlikely to change with alterations in the legal framework that govern banking in the United States. Besides explaining the structure of the industry, our model also has additional implications. We show that the problems of underspecialization by relationship banks may be mitigated by syndication, where individual compensation is substituted for by team compensation, although it would exacerbate the problem of underinvestment in skills. The model shows that banks with a broad scope of activities tend to underspecialize more deleteriously than banks that choose to focus on a narrow range of activities. We demonstrate that clients particularly valuing the unique skills of deal banks leads to the creation of boutique out®ts in deal banking. The desire to be a ®rst mover leads banks to exhibit racing behavior, with structural booms and busts. Acknowledgements We would like to thank participants at seminars at the Western Finance Association Meetings, NBER, Harvard University Economics Dept., Hong Kong University of Science and Technology, Richard Caves, Dwight Crane, Scott Mason, Andre Perold, Manju Puri, Richard Ruback, Peter Tufano and especially Arnoud Boot and Michael Whinston for helpful discussions. The comments of an anonymous referee helped improve the paper substantially.

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Appendix A. Proof of Proposition 1 The relationship banks' resources are unveri®able. The client o€ers them a two stage output-based linear contract, I ˆ a ‡ lx. Each bank maximizes its own expected pro®t. Bank A1 's optimization program, for instance, is 15 n o  i th max a1 ‡ l1 f …H1 †a ÿ a21 ‡ …a ÿ a1 †2 ÿ G…H1 † : a1 ;H1 2 The ®rst order conditions of the optimization program with respect to resource-location A1 and resource-level H1 are: 16 f …H1 † ÿ t…3a1 ÿ a† ˆ 0;   f …H1 † a ‡ a1 0 ˆ G0 …H1 †: ‡ l1 f …H1 † 2 2t

…A:1† …A:2†

The ®rst order conditions for bank A2 are symmetric. The ®rst order conditions for resource location (Eq. A.1) for A1 and its symmetric equation for A2 ) imply that the banks' resource location choices are functions of their resource levels: 17 1 2 1 a1 ˆ ‡ d1 ÿ d2 ; 6 3 3

a2 ˆ

5 2 1 ÿ d2 ‡ d1 : 6 3 3

The banks' specialization choice is not directly a€ected by the compensation scheme o€ered to them, but it is in¯uenced by their resource levels. From the ®rst order condition for resource level, one can derive that, for a non-trivial solution (H1 ; H2 6ˆ 0), concavity of the pro®t function implies that

15 Given the other relationship bank's resource choices, the best response for a relationship bank would be to locate arbitrarily close to the other bank and build in®nitesimally greater resource, thereby dominating its resource pro®le. However, since the client can verify which half of the line segment the relationship banks are located on (footnote 7), and prefers the banks not to locate too close to each other, it imposes the condition that the banks locate in di€erent halves of the resource segment. Hence, an indi€erence point a always exists between the two banks. Instead of assuming partial veri®ability of resource location, one could assume complete unveri®ability along with one of the following assumptions, in order to ensure that the banks locate at a distance from each other: · The banks have asymmetric preferences over resource locations (e.g. bank A1 strongly prefers to locate in the left half of the resource segment, and A2 strongly prefers to locate in the right half). · Each bank has a very high cost of building resource in the other half of the resource segment. 16 Grossman and Hart (1983) pointed out that an agent's choice variable which satis®es the ®rst order conditions may not be globally optimal for the agent. If the optimizing function is concave in a and H, then the ®rst order condition identi®es a global maximum. A sucient condition to ensure concavity of the gross pro®t function, and hence of the optimizing function, is that f(H) is suciently concave: …9f 00 …H†=f 0 …H †† ‡ …8f 0 …H†=f …H†† 6 0. 17 Recall that bank Ai 's resource span di is a function of its resource-level Hi ; ‰di ˆ f …Hi †=t; i ˆ 1; 2Š.

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the banks invest more in their resources if the incentive contract is more high powered [dH1 =dl1 > 0]. Since the two banks are symmetric, and are o€ered symmetric compensation, we focus on the net expected pro®t generated by one of the two banks. The client maximizes net expected pro®t generated by A1 : max Ex1 ÿ a1 ÿ l1 Ex1 a1 ;l1

subject to the participation constraint a1 ‡ l1 Ex1 ÿ G…H1 † P U0 and the incentive compatibility constraints (A.1) and (A.2). The client tailors each bank's compensation to ensure that it develops the desired resource level, and adjusts the ®xed component of the compensation so that the banks' expected pro®t equals their reservation pro®t ± the participation constraint binds at the optimum. 18 The client's optimization program simpli®es to max Ex1 ÿ G…H1 † ÿ U0 : l1

The ®rst order condition of the above program is   dH1 oEx1 ÿ G0 …H1 † ˆ 0: dl1 oH1 Since a bank's incentive compensation determines its choice of resource deal, the client can get a relationship bank to choose any H it wants by choosing l appropriately. Hence, the client can be thought of as optimizing ®rm pro®ts over H. The ®rst order condition yields the following symmetric Nash Equilibrium in resource-level: 19 18 If the participation constraint is a strict inequality at the optimum, the client can lower ai , the ®xed component of the bank's salary by a small amount, and none of the constraints is violated while expected pro®t increases. This is not possible. 19 The ®rst order condition states a necessary condition for the equilibrium. It need not be sucient, however. A relationship bank may ®nd a non-local deviation preferable to the internal optimum. It may prefer to locate closer to the other bank and raise its resources suciently in order to completely dominate the other relationship bank's resource pro®le. The other bank reacts by changing its resource level and location so that it is no longer dominated. Hence, there is no Pure Strategy Nash Equilibrium in such a circumstance. The issue of non-local deviation becomes especially acute as the two banks come close together. One condition which ensures that a relationship bank does not prefer the non-local deviation is that the resource acquisition cost function and/or the gross pro®t function are highly elastic to changes in resource level i.e. G…H† is suciently convex and/or f …H† is suciently concave in resource level H. Based on these results, two things can be said about the model solution: (1) If a pure strategy Nash Equilibrium exists, it is characterized by the equations derived in the text. (2) The model is valid if G…H † is suciently convex and/or f …H† is suciently concave in resource H.

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 5 ÿ 2d  f 0 …H  † ˆ G0 …H  †: 9

The banks accumulate positive resource levels [f …0† > 0; & G…0† ˆ 0 ) H  > 0] that are suboptimal, compared to the ®rst best [2G0 …H  † < f 0 …H  † ) H  < H 0 ]. In Nash Equilibrium, the resource level condition (A.2) is   1 ‡ 2d  f 0 …H  † ˆ G0 …H  †: l 3 Thus, the optimal incentive parameter l is l ˆ

5 ÿ 2d  : 3…1 ‡ 2d  †

The resource-level incentive compatibility condition implies l > 0. The model assumes that all points on the segment ‰0; 1Š generate positive gross pro®ts, i.e. d  P 14, which implies that l < 1. Hence, in equilibrium, the incentive parameter l 2 …0; 1†. The symmetric Nash Equilibrium in resourcelocations is   1 d 5 d   : ‡ ; ‡ ‰a1 ; a2 Š ˆ 6 3 6 3 d  P 14 implies that the Nash Equilibrium level of specialization is less than the ®rst best (a1 P 14). Comparative static analysis of the Nash Equilibrium indicates that …oa1 =ot† < 0 and …oH1 =ot† > 0. Now ask the hypothetical question: what location choices ai ; i ˆ 1; 2 would the client want for the relationship banks at time 1, holding Hi ; …i ˆ 1; 2† ®xed? The client wants to maximize net expected pro®ts in the second stage: max ‰ Ex1 ‡ Ex2 ÿ EI1 ÿ EI2 Š ˆ ‰…1 ÿ l†…Ex1 ‡ Ex2 † ÿ 2aŠ: a1 ;a2

The symmetric solution to the optimization program is h i 1 3 ; : a^1 ; a^2 ˆ 4 4

Appendix B. Proof for Proposition 2 If the client cannot verify the deal banks' resources, both deal banks locate in the ®rst stage so as to maximize their own pro®t functions. The deal banks' resource location choices can be one of two possible types, depending on their resource-spans.

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1. If resource-spans are narrow, only one of the two deal banks can perform tasks that appear within a particular range of resources. 2. If resource-spans are broad, both deal banks can generate positive gross pro®ts over the entire range of arriving tasks. B.1. Case 1. Deal bank monopoly over some resource range Deal bank A1 can expect to extract second stage compensation: Z a2 ÿd2 b‰ f …H1 † ÿ tjb ÿ a1 jŠp…b† db EI12 ˆ 0

Z ‡

a a2 ÿd2

b‰… f …H1 † ÿ tjb ÿ a1 j† ÿ … f …H2 † ÿ t…a2 ÿ b††Šp…b† db

ˆ b‰ f …H1 †a ÿ f …H2 †…a ÿ a2 ‡ d2 †Š i th 2 2 ‡ b d22 ÿ a21 ÿ …a2 ÿ a† ÿ …a ÿ a1 † : 2 Similarly, deal bank A2 's expected second stage compensation is: EI22 ˆ b‰ f …H2 †…1 ÿ a† ÿ f …H1 †…a1 ‡ d1 ÿ a†Š h i ‡b 2t d12 ÿ …1 ÿ a2 †2 ÿ …a2 ÿ a†2 ÿ …a ÿ a1 †2 : B.2. Case 2. Broad resource spans Deal bank A1 can expect to extract second stage compensation: Z a EI12 ˆ b‰… f …H1 † ÿ tjb ÿ a1 j† ÿ … f …H2 † ÿ t…a2 ÿ b††Šp…b† db 0 h i 2 ˆ b‰ f …H1 † ÿ f …H2 †Ša ‡ bt a…a2 ÿ a1 † ÿ …a ÿ a1 † : Similarly, A2 's expected second stage compensation is h i 2 EI22 ˆ b‰ f …H2 † ÿ f …H1 †Š…1 ÿ a† ‡ bt …1 ÿ a†…a2 ÿ a1 † ÿ …a2 ÿ a† : b 2 …0; 1† is exogenously determined: it should be suciently large so that the deal banks' expected second stage earnings are at least equal to U0 /2, their one stage reservation pro®t, else the deal banks will prefer to quit before the second stage begins. Since they bargain after having made their deals, the deal banks can credibly threaten hold-up. Hence, they extract second stage surplus beyond their reservation pro®t, i.e. their expected second stage earning is strictly greater than U0 /2.

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The deal banks' resource level and specialization choices do not depend on their ®rst stage compensations, since they are ¯at payments. The deal banks develop their resources during the ®rst stage in order to maximize their second stage expected compensation less the e€ort made to develop their resources. 8 b‰ f …H1 †a ÿ f …H2 †…a ÿ a2 ‡ d2 †Š; > > h i > > > < ‡ bt2 d22 ÿ a21 ÿ …a2 ÿ a†2 ÿ …a ÿ a1 †2 ÿ G…H1 †; Case 1; h i max EI 2 ˆ 2 a1 ;H1 > > b f …H ‰ † ÿ f …H † Ša ‡ bt a…a ÿ a † ÿ …a ÿ a † > 1 2 2 1 1 > > : ÿG…H1 †; Case 2: In both cases, the ®rst order conditions with respect to resource location and resource level are identical. The symmetric Nash Equilibrium is:      1 3 a 1 ; a2 ˆ bf 0 …H  † ˆ 2G0 …H  †; ; : 4 4 Thus, if resources are unveri®able, deal banks build suboptimal resource levels but specialize optimally, compared to the ®rst best. At time 0, the client and the deal banks know that a ®rst stage contract will be followed by a second stage bargain. 20 The deal banks participate in the contract if their pro®t over two periods is not less than their two stage reservation pro®t. 21 The client pays the minimum possible ®rst stage compensation to the deal banks, such that their two stage participation constraint binds. Compared to their reservation pro®t, the deal banks earn higher second stage pro®t, and hence, lower ®rst stage pro®t. The deal banks invest intensively in building their human capital in anticipation of earning positive surplus by using the human capital in future, to the extent that ®rst stage compensation may even be negative if second stage compensation is large enough. Consider how the client would desire its banks to specialize ex-post at time 1. The client wants to maximize expected second stage pro®ts: max Ex1 ‡ Ex2 ÿ EI12 ÿ EI22 : a1 ;a2

The deal banks' expected second stage earnings depend upon whether they have monopoly over some resource range or not.

20 Besides, the client knows that the deal banks also know (and the deal banks know that the client knows) at time 0 that a ®rst period contract will be followed by a second period bargain. This is possible because we are assuming that the client and the transaction banks always arrive at a pro®t during bargaining, such that they prefer to continue their relation with rather than separate from the ®rm. 21 The underlying assumption behind the deal banks being not concerned about per period reservation utilities is that they are able to freely borrow and lend. Hence, a lower pro®t in one period can be made up by higher pro®t in the other period.

894

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