On the Sequencing of Projects, Reputation Building, and Relationship Finance

Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 718 January 2002 ON THE SEQUENCING OF PROJECTS, REPUTATION BUILDING, AND RELATIONSHIP FINANCE Dominik Egli, Steven Ongena, and David C. Smith NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors. Recent IFDPs are available on the Web at www.federalreserve.gov/pubs/ifdp/.

On the Sequencing of Projects, Reputation Building, and Relationship Finance ∗∗∗∗ Dominik Egli, Steven Ongena, and David C. Smith Abstract We study the decision an entrepreneur faces in financing multiple projects and show that relationship financing will arise endogenously in an environment where strategic defaults are likely, even when firms have access to arm's-length financing. Relationship financing allows an entrepreneur to build a private reputation for repayment that reduces the cost of financing. However, in an environment where the risk of strategic default is low, the benefits from reputation building are outweighed by holdup rents extractable by the incumbent lender. Entrepreneurs then choose to finance projects from single or multiple, arm's-length lenders. Keywords: relationship financing, reputation building, staged financing, contract enforcement, judicial efficiency ∗ The authors are from the Swiss Ministry of Finance and University of Bern (dominik.egli@intergga.ch), Tilburg University (steven.ongena@kub.nl), and Board of Governors of the Federal Reserve System (david.c.smith@frb.gov), respectively. The views in this paper are solely the responsibility of the authors and should not be interpreted as reflecting the views of the Swiss Ministry of Finance, Board of Governors of the Federal Reserve System or of any other person associated with the Federal Reserve System. We thank Hans Degryse, Mariassunta Giannetti, Ralf Elsas, Jan Pieter Krahnen, Rafael Repullo, Joao Santos, Bas Werker, and seminar participants at the 2001 European (Barcelona) and German (Vienna) Finance Association Meetings, 2001 SSSE Meetings (Geneva), 2000 Tor Vergata Conference (Rome), the Swiss National Bank, and Tilburg University for providing helpful comments. Egli thanks the Department of Economics at UC Santa Cruz for their hospitality and the Swiss Science Foundation for their financial support. Ongena received partial support from the Netherlands Organization for Scientific Research (NWO).

1. Introduction Previous theory teaches us that close relationship-based (cid:222)nancing, such as that provided by banks and venture capitalists, is most important to so-called (cid:147)informationally-opaque(cid:148) borrowers. These borrowers (cid:151) typically small, young (cid:222)rms with no public track record (cid:151) value relationship lending because they are unable to credibly communicate their repayment ability to a wider set of (cid:147)arm(cid:146)s-length(cid:148) lenders. In reality, many informationally-transparent (cid:222)rms also rely on some form of relationship-based (cid:222)nancing. For instance, (cid:222)rms in Europe and Asia rely heavily on bank (cid:222)nancing, even when well-functioning capital markets exist within the countries they operate (Allen and Gale, 2000). In the U.S., Houston and James (2001) report that relatively large, publicly-traded (cid:222)rms obtain an average of 67% of their debt from banks and only 16% from public issues. In this paper, we provide a rationale for why all types of (cid:222)rms may at times prefer relationship-based (cid:222)nancing to arm(cid:146)s-length (cid:222)nancing. In particular, we study the decision (cid:222)rms face in (cid:222)nancing multiple independent investment projects. Inourmodel, anentrepreneurdeterminesthesequencingforinvestmentintwoprojects according to the availability and cost of funds. The entrepreneur can either try to (cid:222)nance both projects up front or sequence the (cid:222)nancing and investment over two periods, and can choose to (cid:222)nance the projects through one or multiple lenders. A lender bases its (cid:222)nancing decision on the perceived likelihood that an entrepreneur will strategically default on a loan, and on its ability to extract (cid:147)holdup(cid:148) rents. We assume that some entrepreneurs are good, 1

in that they never default on a loan, while others are bad in the sense that they will always default when it pays to do so. Lenders cannot observe an entrepreneur(cid:146)s default type, but knowthe unconditional likelihood of facing abad borrower. We showthat (cid:222)rms operating in an environment where strategic defaults are likely choose to have their projects sequentially (cid:222)nanced by the same lender. We term this behavior (cid:147)relationship (cid:222)nancing(cid:148). The intuition forthisresultisstraightforward. Therelationshiplenderobservesindividualloanrepayments in the (cid:222)rst period, which increases the ex-ante likelihood of repayment in both periods. The resulting decrease in the interest rate charged to the entrepreneur seeking to (cid:222)nance the sequenced projects more than offsets holdup rents accruing to the incumbent lender. Our model illustrates that even in cases where banks gain all of the bargaining power, relationship (cid:222)nancing may still be preferable to arm(cid:146)s-length (cid:222)nancing if the assessed likelihood of repayment is sufficiently low. However, relationship (cid:222)nancing is not always optimal. If the ex-ante risk of strategic default in the economy is low, then the bene(cid:222)ts of building a reputation are outweighed by the rents extractable by the relationship lender. In this environment, (cid:222)rms choose to (cid:222)nance both projects up front either from a single lender or from multiple lenders. We term this, as well as the opportunity to sequence projects using multiple lenders, (cid:147)arm(cid:146)s-length (cid:222)nancing(cid:148). The main contributions of our paper are three-fold. First, we demonstrate that relationship (cid:222)nancing can arise endogenously, even when (cid:222)rms have equal access to arm(cid:146)s-length (cid:222)nancing and banks are able to extract holdup rents. In our model, all entrepreneurs start 2

withtheopportunityfor(cid:222)nancingtheirprojectswitharm(cid:146)s-lengthsecuritiesandthenchoose whether or not to invest in a relationship. Second, our model provides a rationale for why entrepreneurs may optimally choose to delay the (cid:222)nancing of a project even when there is no uncertainty about project payoffs or discount rates (Dixit and Pindyk, 1994; Berk, 1999), nor a need to monitor progress through stages of (cid:222)nancing (Gompers, 1995). Firms delay projects to gain a good repayment reputation, which reduces future lending costs. Because a reputation for repayment can only be gained by borrowing from the same lender, when (cid:222)rms choose to sequence projects, they do so through relationship (cid:222)nancing. Third, by assigning more meaning to our strategic default parameter, we gain insight into cross-country differences in (cid:222)nancing behavior. For instance, if a country(cid:146)s legal system can reduce the incentive for (cid:222)rms to strategically default, then our model suggests that relationship (cid:222)nancing will be more prevalent in countries with weaker contract enforcement and less efficient judicial systems. The rest of the paper is organized as follows. We discuss associations with the related literature in Section 2. Section 3 introduces the model. In Section 4, we explore the characteristics of arm(cid:146)s-length (cid:222)nancing, while in Section 5 we focus on relationship (cid:222)nancing. Section 6 derives the set of equilibria that exist when entrepreneurs can choose between relationship and arm(cid:146)s-length (cid:222)nancing. In Section 7, we consider applications of our model and discuss robustness to weakening the model(cid:146)s assumptions. Section 8 concludes. 3

2. Related Literature Ourpaperis closely relatedto the literature exploringthe value of bank relationships. These papers are predicatedonthe ideathat banks, as insidelenders, canobserve andmonitorborrowersinawaythatallowsthemto(cid:222)nance(cid:222)rmsthatareotherwiseunabletoobtainvaluable (cid:222)nancing. Banks, it is argued, enjoy scale and scope economies in (cid:222)nancing informationallyopaque borrowers, and can therefore improve borrower welfare.1 However, banks(cid:146) ability to privately observe information could give them the ability to extract rents by threatening to (cid:147)hold up(cid:148) (cid:222)nancing to customers captured by the banks(cid:146) information monopoly.2 We differ from this literature along several dimensions. First, although information asymmetriesexistbetweenlendersandborrowersinourmodel,theasymmetryitselfdoesnot in(cid:223)uence the choice between relationship and arm(cid:146)s-length (cid:222)nancing. Therefore, our model moves away from relating the value of bank (cid:222)nancing to a (cid:222)rm(cid:146)s information problems. Instead, we relate the need for relationship (cid:222)nancing to the ability for entrepreneurs to strategically default. Second, rather than assume that (cid:222)rms require repeated (cid:222)nancing through time, we allow (cid:222)rms the choice between repeated lending and one-shot (cid:222)nancing, and derive conditions under which repeated (cid:222)nancing with one bank is optimal. Third, by assuming that entrepreneurs have multiple projects to (cid:222)nance, we are able to relate the 1See Diamond (1984), Fama (1985), Ramakrishnan and Thakor (1984), and Allen and Gale (1999). For formal reviews of this literature, see Boot (2000) and Ongena and Smith (2000a). 2The holdup problem is explored by Fischer (1990), Greenbaum, Kanatas, and Venezia (1989), Rajan (1992), Sharpe (1990), and von Thadden (2001). 4

timing and sequencing of projects to (cid:222)nancing choice. This provides a novel approach to thinking about some common capital budgeting issues. Becausewefocusonthein(cid:223)uenceofborrowerreputationon(cid:222)nancingchoice, ourpaper shares similarities with Diamond (1991), where (cid:222)rms decide whether to borrow repeatedly from banks to build a track record that is publicly observable. In his model, only high-rated borrowers with a good reputation receive arm(cid:146)s-length (cid:222)nancing. In our framework, an entrepreneur builds a reputation to lessen the cost of relationship (cid:222)nancing (the repayment history is private information and cannot be reported credibly by an incumbent bank). When the cost of reputation-building is too high relative to its bene(cid:222)ts, borrowers resort to arm(cid:146)s-length markets or do not borrow at all. Like our paper, Boot and Thakor (1994) model repeated borrowing. They show that even without learning or risk aversion, bank-borrower relationships are welfare enhancing and bene(cid:222)t the borrower. Borrowers in their model commit to a long-term contract that requires paying an above-market borrowing rate and committing collateral until a good project outcome is realized, then paying an in(cid:222)nite stream of below market rates with no collateral requirements after the realization. Hence, in their model durable relationships are valuable because they allow banks and (cid:222)rms to subsidize (cid:222)nancing intertemporally, which reduces the use of costly collateral. In contrast, in our model durable relationships enhance efficiency by enabling (cid:222)nancing of sequenced projects in cases where (cid:222)nancing of all projects at once cannot take place. 5

Our modeling is also related to the papers exploring the choice between relationship andarm(cid:146)s-lengthlending. Rajan(1992)arguesthatrelationshiplendingisbene(cid:222)cial because abank(cid:146)sthreattoholduprepeated(cid:222)nancingcaninduce(cid:222)rmmanagerstoacceptpositivenet present value projects. Boot and Thakor (2000) allow banks to determine the allocation of their lending capacity across relationship and arm(cid:146)s-length (cid:147)transaction(cid:148) lending, and study the impact of bank competition on relationship lending. In contrast to Rajan (1992) and Boot and Thakor (2000), we allow relationship (cid:222)nancing to arise endogenously and show that relationship (cid:222)nancing can expand (cid:222)nancing opportunities for entrepreneurs and will, in some cases, be preferable to arm(cid:146)s-length (cid:222)nancing. Because we link project timing to (cid:222)nancing method, our setup is also related to work focusing on the option value of waiting to invest and optimal contracting under uncertainty. For example, entrepreneurs may optimally choose to delay (cid:222)nancing a project when there is uncertaintyaboutinvestmentreturnsordiscountrates(DixitandPindyk, 1994; Berk, 1999). Moreover, (cid:147)staging(cid:148) (cid:151) or breaking into multiple rounds (cid:151) the (cid:222)nancing of an entrepreneurial venture may be optimal if there is a need to monitor its progress (Sahlman, 1990; Gompers, 1995; Admati and P(cid:223)eiderer, 1994; Bergemann and Hege, 1998; Neher, 1999; Cornelli and Yosha, 2001; and Kaplan and Stromberg, 2001). Complementing these papers, our model considers multiple projects and provides an additional rationale for why entrepreneurs may optimally choose to delay (cid:222)nancing a project or stage (cid:222)nancing. Entrepreneurs sequence projects when reputational gains from paying off early projects reduce future lending costs. 6

3. The Model An entrepreneur has access to two independent projects A and B. Both projects require an initial investmentk andyieldcertainpayoffsπ andπ , whichexceedk. Subjectto(cid:222)nancial A B constraints, the entrepreneur can choose to either invest in both projects jointly or delay one project and pursue the projects sequentially. Without loss of generality, assume that π > A π , and de(cid:222)ne ∆ 2k/(π +π ) and ∆ k/π , j = A,B, to be the inverse pro(cid:222)tability B B B j j ≡ ≡ measures for the joint and sequential projects, respectively. Note that by de(cid:222)nition ∆ < A ∆ < ∆ . B We assume that the entrepreneur has no initial wealth and that projects are nondivisible. Therefore, the entrepreneur must borrow the entire amount for each project from one lender. The entrepreneur has no mechanism for storing excess cash from period to period, so if she chooses to sequence the projects, she must also sequence her (cid:222)nancing. Moreover, the entrepreneur consumes all surplus earnings from aproject at the end of period 1, sothat any period-2 project must be completely (cid:222)nanced using outside sources. As will be discussed later, neither the non-divisibility nor the consumption-of-surplus assumption is restrictive. As part of the (cid:222)nancing decision, the entrepreneur must also choose whether to borrow from one lender or two. We label the (cid:222)nancing of sequential projects by one lender as (cid:147)relationship (cid:222)nancing(cid:148) because the lender can learn from the entrepreneur(cid:146)s (cid:222)rst-period behavior. We label as (cid:147)arm(cid:146)s-length (cid:222)nancing(cid:148) the funding of sequential projects by two different lenders, or the one-shot (cid:222)nancing of joint projects by either one or two lenders. 7

Entrepreneurs have full bargaining power in the (cid:222)rst period of a relationship, but bargaining power transfers to lenders in the second period when (cid:222)nancing is repeated, allowing the relationship lender to accrue all information-related rents.3 Defaults are only observed by the incumbent lender and the entrepreneur cannot credibly communicate her repayment history to a new lender.4 We assume that a certain set of entrepreneurs will default on a loan even when they have the funds to repay. With probability 1 p , p (0,1], the lender faces a (cid:147)bad(cid:148) 0 0 − ∈ entrepreneur who will strategically default on her contracted payment, r (t = 1,2), if it t pays her to do so. With probability p , the borrower is a (cid:147)good(cid:148) entrepreneur who always 0 makeshercontractedinterestpayment. Eachentrepreneurknowshertype,whilelendersonly know p . In case projects are sequenced, the incumbent lender that (cid:222)nances the (cid:222)rst-period 0 project also knows whether the entrepreneur pays the contracted amount, r . Let β [0,1] 1 ∈ be the (endogenously determined) probability that a bad entrepreneur pays r . Given β, the 1 lender can deduce the total probability of receiving payment r , q = p +β(1 p ). Given 1 0 0 − that r is paid, the incumbent lender updates its prior belief, p , that the entrepreneur is 1 0 3Competitionfrompartiallyinformedoutsidebanksmaylimitsuch(cid:147)holdup(cid:148)rents. VonThadden(2001), for example, shows that an inside lender can earn positive pro(cid:222)ts on good risks by pricing slightly above the pooling interest rate most of the time, but charging occasionnally up to the break-even rate for loans to unsuccessful (cid:222)rms. Reputational concerns about future lending, market driven information leaks, or moral hazardproblemsassociatedwithassetsubstitutionmayfurtherconstrainthelender(cid:146)sabilitytoextractrents. 4Similarly, Fisher (1990), Rajan (1992), Sharpe (1990), and von Thadden (2001) assume that outside lendersobserveonly anoisysignal of project outcomeand loan repayment. While in some countries lenders share repayment information through (cid:145)black(cid:146) credit registers, such registers donot exist in many developing countries, do not cover cross-border transactions, and do not guarantee accurate and complete reporting (Jappelli and Pagano, 1999). 8

good using Bayes(cid:146) rule, p = p /q. 1 0 In (cid:222)xing p , we presume that an entrepreneur(cid:146)s temptation to default on a loan will 0 depend on exogenous factors that in(cid:223)uence debtor costs of bankruptcy. Such factors could include a country(cid:146)s choice of bankruptcy procedures, the degree of protection given to creditors, theefficiencyofthejudicialsystem, thelegaltraditionofthecountry, andothercultural traditions. For simplicity, we assume that lenders cannot recuperate any positive payment when a bad entrepreneur decides to default and a bad entrepreneur cannot precommit to a positive level of repayment. Both the entrepreneur and the lenders are risk neutral and maximize the expected present value of their payoffs. The parameter ρ is the entrepreneur(cid:146)s subjective discount factor. In order to facilitate the formal exposition, we assume that ρ > √∆ . This assumption B requires either that project B be quite pro(cid:222)table or that the entrepreneur not discount the future by very much. This completes the description of the game setup. We proceed as follows. We (cid:222)rst derive equilibrium contracts assuming that entrepreneurs have access to arm(cid:146)s-length or relationship (cid:222)nancing, but not both. We then analyze the optimal contracts assuming that entrepreneurs have access to both types of (cid:222)nancing. 9

4. Arm(cid:146)s-Length Financing To derive conditions under which projects are (cid:222)nanced with arm(cid:146)s-length contracts, we start with joint projects. The entrepreneur seeking to (cid:222)nance joint projects proposes a contract specifying the investment amount 2k and the repayment level r. A bad entrepreneur never repays r as sheis always betteroffrepudiating. Thegoodentrepreneur pays min r,π +π A B { } by assumption. The risk of repudiation in(cid:223)uences negotiations at the beginning of the game. A lender anticipates a breach of contract with probability 1 p . Hence the lender is only 0 − willing to sign a contract when its expected repayment p r at least covers investment 2k, i.e. 0 r 2k/p . On the other hand, any repayment r that exceeds π +π is impossible since the 0 A B ≥ entrepreneur has no initial wealth, i.e. r π +π . These two constraints are compatible A B ≤ if and only if p 2k/(π + π ) = ∆. When this condition holds, the good entrepreneur 0 A B ≥ can offer a repayment r = 2k/p which makes the lender indifferent between signing and 0 rejecting and maximizes the entrepreneur(cid:146)s pro(cid:222)t π +π r. To conceal her intentions, a A B − bad entrepreneur imitates the behavior of a good entrepreneur. Let γ [0,1] be the probability that a lender accepts the proposed repayment r.5 In ∗ ∈ 5Existenceofasequentialequilibriuminthetwo-periodcasemayrequirethatthesecond-periodcontract be randomly assigned. In general, it is possible for the entrepreneur to randomize in equilibrium between proposing a contract promising zero expected pro(cid:222)ts and one that leads to certain rejection. Alternatively, whenindifferentbetweenacceptingandrejecting,abankmayrandomizeinequilibrium. Weassumeinthese cases that the entrepreneur proposes a contract with certainty. 10

equilibrium: = 0 if r < 2k/p , 0  γ ∗  ∈ [0,1] if r = 2k/p 0 and p 0 = ∆, (4.1) = 1 if r 2k/p and p > ∆.  ≥ 0 0 The lender rejects with certainty an offer of r < 2k/p and accepts with certainty an offer 0 of r 2k/p when p > ∆.6 For r = 2k/p and p = ∆, any γ [0,1] represents a best 0 0 0 0 ∗ ≥ ∈ response for the lender because the only acceptable repayment leading to nonnegative value for the entrepreneur is r = 2k/p . 0 The arm(cid:146)s-length contract for (cid:222)nancing sequential projects is similar to the jointprojects contract. In particular, in the second period, the outside lenders cannot learn from the fact that an entrepreneur is seeking (cid:222)nancing from them, i.e., the second-period lenders are not exposed to a Winner(cid:146)s Curse problem. The reason for this is that lenders are able to compute a good entrepreneur(cid:146)s optimal choice of (cid:222)nancing scheme. A bad entrepreneur pursuing a different strategy than a good entrepreneur is immediately revealed. Therefore, a bad entrepreneur only chooses to switch after period 1 when it is also in the interest of a good entrepreneur to do so. Because the second-period lenders do not know the repayment history of the entrepreneur, they expect a good entrepreneur with probability p , 0 i.e., β = 0. Therefore, the two periods are structurally identical, and we can directly apply 6For r 2k/p and p > ∆, there is no equilibrium pro(cid:222)le under which the lender rejects with positive 0 0 ≥ probability because the entrepreneur would then propose a repayment r slightly above 2k/p , so that no 0 best response for the lender exists. 11

the analysis derived above. The results are summarized in Proposition 1. Proposition 1. Arm’s-Length Financing (ALF): (i) Joint projects: If p ∆, the entrepreneur, either good or bad, proposes a repayment 0 ≥ r = 2k/p in exchange for an investment 2k in equilibrium, and the lender accepts. ∗ 0 The bad entrepreneur defaults on r with certainty. If p < ∆, no contract is signed. 0 (ii) Sequentialprojects: Ifp ∆ ,j = A,B,theentrepreneur,eithergoodorbad,proposes 0 j ≥ repayment r = k/p in exchange for investment k, and the lender accepts. A bad ∗ 0 entrepreneur defaults with certainty. If p < ∆ , no contract is signed. 0 j The entrepreneur is able to (cid:222)nance both projects sequentially if and only if p ∆ . 0 B ≥ For ∆ p < ∆ , she can only (cid:222)nance the more pro(cid:222)table project A. The pro(cid:222)ts to a A 0 B ≤ good entrepreneur from arm(cid:146)s-length (cid:222)nancing are: (i) As joint projects: π +π 2k/p if p ∆ A B 0 0 ΠALF =  − ≥  0 if p < ∆ 0 (ii) As se quential projects: π k/p +ρ(π k/p ) if p ∆ A 0 B 0 0 B  − − ≥ ΠALF =  π A − k/p 0 if ∆ B > p 0 ≥ ∆ A 0 if p < ∆  0 A 12

Comparing pro(cid:222)ts in (i) with (ii), our setup implies that the entrepreneur will always choose to (cid:222)nance joint projects when possible. This result is summarized in the following corollary. Corollary 1.1. Under arm(cid:146)s-length (cid:222)nancing, projects are (cid:222)nanced jointly when p 0 ≥ ∆. For ∆ > p ∆ , only project A is chosen in the (cid:222)rst period, and there is no additional 0 A ≥ (cid:222)nancing provided in the second period. For p < ∆ , no (cid:222)nancing takes place. 0 A 5. Relationship Financing Wenowconsiderthe (cid:222)nancingof sequential projects throughrelationship (cid:222)nancingbyallowing the repayment behavior of the bad entrepreneur to play an important role in the setting of equilibrium contracts. We demonstrate that there are four possible equilibria associated with relationship (cid:222)nancing: a reputational equilibrium, de(cid:222)ned to be a sequential equilibriuminwhichthebadentrepreneurpays r withprobabilityβ (0,1), apoolingequilibrium 1 ∈ where the bad entrepreneur never defaults (β = 1), a separating equilibrium where the bad entrepreneur always defaults (β = 0), and a no-investment equilibrium in which no projects are (cid:222)nanced. The existence of a particular equilibrium will depend on the proportion of bad entrepreneurs in the lending pool, the absolute and relative magnitude of the payoffs, and how the entrepreneur chooses to sequence projects. We solve the relationship (cid:222)nancing problem by backwards induction, starting at the beginning of the second period. The intuition from Proposition 1 can be used to obtain the 13

second-period equilibrium conditions. However, we assume that the relationship lender has all of the bargaining power in the second period. Corollary 1.2. Suppose project i has been carried out in the (cid:222)rst period. If r has 1 been repaid and p ∆ , the lender proposes with probability γ a contract with repayment 1 j ∗ ≥ r = π and investment k, where γ is: 2∗ j ∗ [0,1] if r = k/p and p = ∆ , 2 1 1 j γ  ∈ ∗  = 1 if r k/p and p > ∆ . 2 1 1 j ≥  The bad entrepreneur defaults on r with certainty. If repayment r has not been paid or 2∗ 1 p < ∆ , no second-period contract is signed. 1 j We now step back to the end of period 1. Suppose project i has been (cid:222)nanced and realized, and repayment r is due. Anticipating the outcome of the second period, a bad 1 entrepreneur knows that she collects the payoff of project j with present value ρπ if she j pays r with probability β such that p ∆ . Obviously, she is better off defaulting when 1 1 j ≥ the cost r of (cid:147)reputation building(cid:148) exceeds the potential gain ρπ of having the reputation, 1 j i.e. in equilibrium, β = 0 if and only if r > ρπ . ∗ 1 j Forr ρπ ,abadentrepreneurwillchooseβ tomaximizetheprobabilityofcollecting 1 j ≤ the reputational rent ρπ r . For p ∆ , she can choose β = 1 to guarantee a secondj 1 0 j − ≥ 14

period contract. For p < ∆ , she needs to choose a β such that p = ∆ , 0 j ∗ 1 j p 1 ∆ 0 j β ∗ = β = − < 1. (5.1) 1 p ∆ 0 j − β = β successfully induces a second-period contract with probability γ [0,1]. For ∗ ∗ ∈ β = β to be an equilibrium, the bad entrepreneur must be indifferent between β and any ∗ ∗ other β that increases her reputational rent based on initial beliefs β .7 In other words, ∗ in equilibrium, the expected reputational rent γ ρπ r must equal zero, implying γ = ∗ j 1 ∗ − r /(ρπ ). 1 j Given β , the probability q = p +(1 p )β of repayment in the (cid:222)rst period is: ∗ ∗ 0 0 ∗ − 1 if r ρπ and p ∆ , 1 j 0 j  ≤ ≥ q ∗ =  p 0 /∆ j if r 1 ≤ ρπ j and p 0 < ∆ j , (5.2) p if r > ρπ ,  0 1 j and the updated equilibrium belief of the incumbent lender about the likelihood that the borrowing entrepreneur is good, given payment of r is: 1 p if r ρπ and p ∆ , 0 1 j 0 j  ≤ ≥ p ∗1 = p q ∗ 0 =  ∆ j if r 1 ≤ ρπ j and p 0 < ∆ j , (5.3) 1 if r > ρπ .  1 j 7Given small non-transferable private bene(cid:222)ts of running projects she will choose β =β. ∗ 15

Notethatp ,theupdatedlikelihoodoflendingtoagoodentrepreneur,isneverlessthan ∗1 ∆ . Let us now turn to the contracting problem at the beginning of period 1. Anticipating j q , the lender expects a repayment of q r . To cover its investment k, it only accepts a ∗ ∗ 1 contracted repayment equal to: r k/q . (5.4) 1 ∗ ≥ On the other hand, it also knows that any repayment promise r exceeding π is im- 1 i possible as entrepreneurs have no initial wealth, hence: r π . (5.5) 1 i ≤ We now derive conditions for a reputational equilibrium, i.e. an equilibrium in which β (0,1). A positive repayment probability less than 1 implies β = β and is only possible ∗ ∗ ∈ if the reputational rent is nonnegative, hence: r ρπ , (5.6) 1 j ≤ and if the choice of β matters, p < ∆ . Taking (5.2) into account, inequalities (5.4), ∗ 0 j (5.5) and (5.6) are compatible if and only if: k min π ,ρπ r ∆ , (5.7) i j 1 j { } ≥ ≥ p 0 16

which implies, ∆2 p max ∆ ∆ , j . 0 A B ≥ ( ρ ) Combined with p < ∆ , the former condition implies k < ρπ . 0 j j Suppose all conditions stated thus far are ful(cid:222)lled. Then, if the good entrepreneur chooses a contract promising a repayment r satisfying (5.7), she will choose r as low as 1 1 possible. We show in the appendix that proposing: k r = ∆ . 1∗ p j 0 maximizes the good entrepreneur(cid:146)s pro(cid:222)ts. Hence, we arrive at the following lemma. Lemma 1. Reputational Equilibrium: For ∆ > p max ∆ ∆ ,∆2/ρ , which j 0 A B j ≥ { } implies k < ρπ , there exists a unique reputational equilibrium in which the entrepreneur, j whether good or bad, proposes a contract promising repayment r = k∆ /p in exchange for 1∗ j 0 investment k in the (cid:222)rst period, and the lender accepts. At the end of period 1, the bad entrepreneur repays with probability β = β (0,1). ∗ ∈ We next turn to the conditions required for a pooling equilibrium (β = 1). A re- ∗ payment probability β = 1 is only possible if the reputational rent is nonnegative, i.e. ∗ r ρπ , and if the choice of β does not in(cid:223)uence the characteristics of the equilibrium 1 j ∗ ≤ contract. Proposition 1 implies that the latter occurs when p ∆ . Recalling inequalities 0 j ≥ (5.4)-(5.6), and taking (5.2) into account, we arrive at min π ,ρπ r k, which is only i j 1 { } ≥ ≥ 17

possible if k ρπ . j ≤ Given k ρπ and p ∆ , a good entrepreneur chooses r as low as possible in order j 0 j 1 ≤ ≥ to maximize her pro(cid:222)ts. Hence she proposes r = k. Again, a bad entrepreneur is forced to 1∗ mimic the good type to prevent detection. Based on this intuition, the appendix contains a formal proof of the following lemma. Lemma 2. Pooling Equilibrium: Suppose k ρπ and p ∆ . There exists j 0 j ≤ ≥ a unique pooling equilibrium in which the entrepreneur, whether good or bad, proposes a contract promising repayment r = k in exchange for investment k in the (cid:222)rst period, and 1∗ the lender accepts. At the end of period 1, the bad entrepreneur repays with certainty. A separating equilibrium (β = 0) is only possible if the reputational rent is negative ∗ (r > ρπ ). Recalling inequalities (5.4) and (5.5), and taking (5.2) into account, r must also 1 j 1 satisfy π r k/p , implying p ∆ . To analyze this con(cid:222)guration, we must consider i 1 0 0 i ≥ ≥ ≥ two cases: k > ρπ and k ρπ . Suppose p ∆ and k > ρπ . A bad entrepreneur j j 0 i j ≤ ≥ will never repay r since r k/q k > ρπ . The good entrepreneur chooses a contract 1 1 ∗ j ≥ ≥ with r as low as possible, i.e., r = k/p , and the bad entrepreneur mimics. Now suppose 1 1∗ 0 p ∆ and k ρπ . From Lemmata 1 and 2 we know that the good entrepreneur prefers 0 i j ≥ ≤ to propose a repayment r = kmax ∆ /p ,1 as long as p max ∆ ∆ ,∆2/ρ . Hence 1∗ { j 0 } 0 ≥ { A B j } a separating equilibrium only exists if max ∆ ∆ ,∆2/ρ > p ∆ . This is possible for { A B j } 0 ≥ i ∆2/ρ > p ∆ . Over this interval, the good entrepreneur once again proposes r = k/p j 0 ≥ i 1∗ 0 and the bad entrepreneur mimics. 18

The appendix demonstrates that proposing r = k/p maximizes the good entrepre- 1∗ 0 neur(cid:146)s pro(cid:222)ts in both cases. Lemma 3 follows from the proof. Lemma 3. Separating Equilibrium: Suppose (i) k > ρπ and p ∆ , or (ii) j 0 j ≥ k ρπ and ∆2/ρ > p ∆ . Then there exists a unique separating equilibrium in which ≤ j j 0 ≥ i the entrepreneur, whether good or bad, proposes a contract promising repayment r = k/p 1∗ 0 in exchange for investment k in the (cid:222)rst period, and the lender accepts. At the end of period 1, the bad entrepreneur defaults with certainty. To complete the analysis, we need to state the conditions under which a equilibrium with no investment exists. This is done by summarizing the logical counter-arguments of Lemmata 1, 2, and 3. Lemma 4. No-Investment Equilibrium: Suppose either k > ρπ and p < ∆ , j 0 i or k ρπ and p < min max ∆ ∆ ,∆2/ρ ,∆ . Then no contract is signed in the (cid:222)rst j 0 A B j i ≤ { { } } period. Figure 1 summarizes the in(cid:223)uence of the model parameters on the various equilibria, by varying p and π while holding π constant. The dotted lines plot critical values for 0 A B determining the equilibria, while the solid lines trace out the equilibrium regions. The top panel assumes that the entreprenuer chooses to sequence project A (cid:222)rst, while the bottom panel assumes that B is chosen (cid:222)rst. Several interesting features of the equilibria emerge from the (cid:222)gure. First, an intuitive ordering exists across the equilibria. For low enough values of p (i.e., high proportion of 0 19

bad entrepreneurs), no contract is signed. As p increases, (cid:222)rst-period equilibrium interest 0 rates begin to fall enough to induce bad entrepreneurs to repay; for high values of p all 0 entrepreneurs (cid:151) good and bad (cid:151) make their (cid:222)rst-period payment. Second, comparing the top and bottom panels, contracts can be written for lower values of p when projects are 0 sequenced such that the higher payoff project comes later (sequence B,A ). For a given { } value of r , bad entrepreneurs have more incentive to make the (cid:222)rst-period repayment and 1 get re(cid:222)nanced when they know the second period payoff will be relatively high. Third, when the high-valued project is chosen (cid:222)rst (sequence A,B ), the value of the project can be { } high enough to get a separating equilibrium whereby good entrepreneurs are (cid:222)nanced over the two periods and all bad entrepreneurs default on the (cid:222)rst-period contract. The two panels of Figure 1 imply that the good entrepreneur will choose project sequence B,A , whenever p is too low to allow for sequence A,B to be (cid:222)nanced. This 0 { } { } result is interesting by itself because it suggests that the (cid:222)nancing environment can in(cid:223)uence preferences on how projects with differing payoffs might be staged. As it turns out, sequencing preferences can be de(cid:222)ned over the entire interval of p by comparing the good 0 entrepreneur(cid:146)s pro(cid:222)ts from each sequencing permutation. For project sequence i,j , the { } pro(cid:222)ts from relationship (cid:222)nancing (RF) are given by k∆ ΠRF(RE, i,j ) = π j (5.8) i { } − p 0 ΠRF(PE, i,j ) = π k i { } − 20

k ΠRF(SE, i,j ) = π . i { } − p 0 Letκ = k/(π π +k)). Comparingthepayoffsfor A,B and B,A , andcombining A B − { } { } Lemmata 1-4, allows us to fully describe the relationship (cid:222)nancing equilibria. Proposition 2. Relationship Financing (RF) π > ρπ2 /k : There is a no-investment equilibrium for p < ∆ ∆ ; there is a rep- (cid:149) A B 0 A B utational equilibrium with project sequence B,A for ∆ ∆ p < ∆ ; there is a A B 0 A { } ≤ pooling equilibrium with project sequence B,A for ∆ p < κ; there is a separating A 0 { } ≤ equilibrium with project sequence A,B for κ p < ∆2 /ρ; there is a reputational 0 B { } ≤ equilibrium with project sequence A,B for ∆2/ρ < p < ∆ ; and there is a pooling { } B 0 B equilibrium with project sequence A,B for p ∆ . 0 B { } ≥ ρπ2 /k π > π /ρ : There is a no-investment equilibrium for p < ∆ ∆ ; there is a (cid:149) B ≥ A B 0 A B reputational equilibrium with project sequence B,A for ∆ ∆ p < ∆2 /ρ; there A B 0 B { } ≤ is a reputational equilibrium with project sequence A,B for ∆2 /ρ p < ∆ ; and B 0 B { } ≤ there is a pooling equilibrium with project sequence A,B for p ∆ . 0 B { } ≥ π /ρ π > π : There is a no(cid:151)investment equilibrium for p < ∆2/ρ; there is (cid:149) B ≥ A B 0 A reputational equilibrium with project sequence B,A for ∆2/ρ p < ∆2 /ρ; there A 0 B { } ≤ is a reputational equilibrium with project sequence A,B for ∆2 /ρ p < ∆ ; and B 0 B { } ≤ there is a pooling equilibrium with project sequence A,B for p ∆ . 0 B { } ≥ 21

Figure 2 summarizes the essential features of the proposition. For relatively low values of p , entrepreneurs choose to (cid:222)nance the low-payoff project B (cid:222)rst because lenders will not 0 sign contracts that start with project A. However, for higher values of p , lenders view the 0 risk of default to be low enough that high-valued projects can be (cid:222)nanced (cid:222)rst, before a reputation has been established. Because of the discount rate, the entrepreneur will always select to (cid:222)nance the high-valued project (cid:222)rst when it is feasible to do so. 6. Choice of Financing Method We now combine the results from the previous two sections to determine an entrepreneur(cid:146)s optimal choice of (cid:222)nancing method. With arm(cid:146)s-length (cid:222)nancing the entrepreneur retains full bargaining power in the second period, while under relationship (cid:222)nancing the lender obtains full bargaining power in the second period. To avoid the loss of bargaining power and associated rents, the entrepreneur will always switch lenders whenever an outside lender is willing to (cid:222)nance a pro(cid:222)tably second-period project. From Proposition 1, we know that an outside lender is willing to provide arm(cid:146)s-length (cid:222)nancing for one project when p ∆ and for both projects when p ∆. Moreover, 0 i 0 ≥ ≥ Corollary 1.1 tells us that entrepreneurs that can (cid:222)nance both projects with arm(cid:146)s-length (cid:222)nancing always (cid:222)nd it more pro(cid:222)table to (cid:222)nance the projects jointly, rather than sequentially. This limits the analysis to choosing between arm(cid:146)s-length (cid:222)nancing of joint projects and relationship (cid:222)nancing of sequential projects. 22

Because lenders are unwilling to (cid:222)nance joint projects at arm(cid:146)s length when p < ∆, 0 only Proposition 2 applies below that cutoff . On the other hand, no relationship-(cid:222)nancing contract will be written when p ∆ and arm(cid:146)s-length (cid:222)nancing is available. This is true 0 B ≥ because any relationship contract offered over the p ∆ interval (cid:151) including the most 0 B ≥ pro(cid:222)table that sequences A,B and leads to a pooling of borrowers (cid:151) can be dominated by { } a second-period offer from a new arm(cid:146)s length lender (see Proposition 1). For ∆ p < ∆ , we have to compare the entrepreneur(cid:146)s pro(cid:222)ts from relationship 0 B ≤ (cid:222)nancing to pro(cid:222)ts from arm(cid:146)s-length (cid:222)nancing with joint projects. It turns out that, over this interval, the entrepreneur always chooses relationship (cid:222)nancing. Lemma 5. For ∆ p < ∆ , the entrepreneur sequences projects with relationship 0 B ≤ (cid:222)nancing. Proof. 1. ΠRF(SE, A,B ) > ΠALF. Suppose not: π k/p π +π 2k/p p /∆ A 0 A B 0 0 B { } − ≤ − ⇐⇒ ≥ 1, a contradiction. 2. ΠRF(RE, A,B ) > ΠALF. Suppose not: π k∆ /p π + π 2k/p A B 0 A B 0 { } − ≤ − ⇐⇒ p ∆ (2 ∆ ). 0 B B ≥ − From Lemma 1, it follows that a Reputational Equilibrium only exists if p < ∆ . 0 B Combining the two inequalities leads to ∆ 1, a contradiction. B ≥ Proposition 3 summarizes the main result of the section. Proposition 3. For p ∆ , arm(cid:146)s-length (cid:222)nancing emerges and the projects are 0 B ≥ 23

jointly (cid:222)nanced in period 1. For max(∆ ∆ ,∆2/ρ) p < ∆ , relationship (cid:222)nancing A B A ≤ 0 B emerges. For p < max(∆ ∆ ,∆2/ρ), no (cid:222)nancing takes place. 0 A B A Theproposition,whichisillustratedinFigure3,providesaninterestingandstraightforwardpinnacletotheanalysis. Thepresenceoftoomanybadentrepreneursinamarket(i.e., low values of p ) implies that no (cid:222)nancial contracts are written, relationship or arm(cid:146)s-length. 0 However, relationship-lending does allow for (cid:222)nancing over intervals in which the proportion of bad entrepreneurs prevents arm(cid:146)s-length contracts. Moreover, when the proportion of bad entrepreneurs drops to a point where arm(cid:146)s-length contracts are feasible, entrepreneurs can still (cid:222)nd it optimal to choose relationship lending, even though this implies sequencing the projects and foregoing all bargaining power in the second period. The latter result stems from the fact that repayment r = 2k/p of the arm(cid:146)s length contract rises faster than the 0 present value of the repayment r +ρr = k∆ /p +ρπ under a reputational equilibrium, 1 2 B 0 B or r +ρr = k/p +ρπ under a separating equilibrium. For lower values of p , this effect is 1 2 0 B 0 strong and more than adequately compensates for the loss of the entire second period payoff. These results highlight the value of relationship lending. Our stylized model shows that if the lender assesses repayment to be unlikely, an entrepreneur will defer a project and borrow repeatedly from the same lender in order to build a reputation for repayment. Such relationship (cid:222)nancing occurs even though banks have the power to extract holdup rents from the borrowers. As the likelihood of repayment falls, the entrepreneur may even reverse project order, exacerbating holdup costs. 24

7. Applications and Robustness 7.1. Judicial Efficiency and Financial Development Recent empirical work documents a strong positive correspondence between judicial efficiency, development of (cid:222)nancial intermediation, and ultimately economic growth. For example, Levine (1999) and Levine, Loayza, and Beck (2000) show that cross-country differences increditorrights, thequalityofcontract enforcement, andaccountingstandardshelpexplain cross-countrydifferencesin(cid:222)nancialintermediarydevelopment.8 Thecomponentof(cid:222)nancial development determined by the legal and regulatory environment in turn helps account for cross-country differences in economic growth. In particular, these studies document a strong positive association between proxies for the quality of contract enforcement in a country and the overall size of the (cid:222)nancial intermediary sector. Our model illustrates this positive association. In our setup, bad entrepreneurs have the option not to repay. This proportion of bad entrepreneurs may in reality directly stem from the quality of the available contract enforcement mechanism, or be a general function of the judicial efficiency. Stringent contract enforcement leaves few entrepreneurs with the strategic option to default. Lax enforcement, on the other hand, creates opportunities for many entrepreneurs never to repay. For example, an entrepreneur may know the local judge or in general have enough legal skills and resources to elude, delay, and ultimately derail 8See also La Porta, de Silanes, Shleifer, and Vishny (1997, 1998, 2000). 25

any weak attempts at judicial enforcement. Lenders may not know ex-ante whether or not an entrepreneur has access to such skills and resources. For countries with weak judicial systems, entrepreneurs may be better off delaying projects and seeking relationship-type (cid:222)nancing. Consequently, our stylized model not only links contract enforcement and judicial ef- (cid:222)ciency with decisions about project sequencing, but ultimately also with the development of the (cid:222)nancial intermediary sector and the level of investment. According to our model, when the judicial system is efficient, entrepreneurs will immediately undertake all accessible projects by borrowing from arm(cid:146)s-length lenders. An inefficient judicial system on the other hand impels entrepreneurs to delay projects to build a reputation for repayment. If such delays are costly, then inefficient judicial systems may hamper current investment and reduce contemporaneous demand for funding. In this sense, our setup complements recent papers by Fabbri (2000) and Iacovoni and Zazzaro (2000) that posit a positive link between the quality of contract enforcement and investment. Fabbri assumes that weak contract enforcement increases the cost of repossessing collateral in case of default, while Iacovoni and Zazzaro postulate that legal inefficiencies increase banks(cid:146) screening and monitoring costs. 7.2. Loan Commitments Our model also embodies characteristics of a revolving line of credit. Lines of credit are capped, forcing (cid:222)rms to repay their drawn credit before (cid:222)nancing new projects. A pattern 26

of drawdowns and repayments enables a (cid:222)rm to build a reputation for repayment with its bank. Given this interpretation, our model implies that (cid:222)rms should opt for lines of credit (cid:222)nancing with a low credit limit over a large term loan when operating in an environment where strategic default is likely. On the other hand, large term loans should be preferred in settings where strategic default is unlikely. Because of the similarity between relationship lending in our model and a bank line of credit, our paper is closely related to the literature analyzing the optimality of loan commitment lending. According to this literature, loan commitments can be used to optimally balance reputational and (cid:222)nancial capital, to forecast future loan demand, to lower regulatory taxes, or to exploit cost advantages in providing liquidity. Commitments can further mitigate investment distortions and suboptimal liquidation problems, enable borrowers to signal unobservable characteristics, and function as insurance contracts to risk-averse borrowers.9 Complementing this literature, our model aims to demonstrate why it may be optimal to have repeated borrowing instead of single-shot (cid:222)nancing. We do so by formally showing that an entrepreneur may opt for project delay to allow the lender to learn from observing drawdowns and repayments. The ensuing but voluntary exposure to the lender(cid:146)s scrutiny rendersbettercontracttermsfortheentrepreneur,eveninthepresenceofanticipatedholdup. 9For example, see Boot, Thakor and Udell (1987, 1991), Houston and Venkataraman (1994), Morgan (1994), and Shockley and Thakor (1997). 27

7.3. Robustness of the Model Our main results are robust to various alterations and extensions. For example, as shown in the appendix, we can introduce divisibility by allowing letting entrepreneurs decide how they want to split up a project across periods. Allowing for divisibility widens the reach of both arm(cid:146)s-length and relationship (cid:222)nancing versus the no-investment outcome. On the other hand, arm(cid:146)s-length (cid:222)nancing may become less prevalent if borrowers face credit limits that prevent them from (cid:222)nancing joint projects and if entrepreneurs incur a (cid:222)xed cost when approaching a second lender. Similarly, introducing a (cid:222)xed cost to sequencing projects, increasing the discount rate (i.e., decreasing the discount factor ρ), or introducing bank fragility may make relationship (cid:222)nancing less attractive. The main intuition of the model also remains intact in generalizations to multiple projects and/or multiple periods. As shown in the appendix, enabling the entrepreneur and the (cid:222)nanciers to write long-term contracts similarly does not alter the results. Allowing entrepreneurs to (cid:222)nance second-period projects using retained earnings from the (cid:222)rst period reduces the region over which a reputational equilibrium exists because the value of building a reputation decreases. However, if the initial proportion of good entrepreneurs is too low to establish a reputational equilibrium, the good entrepreneur could offer a contigent contract to a second-period lender at the beginning of the (cid:222)rst period. The contract would contain a condition that the project will proceed only in case the (cid:222)rst-period lender is repaid. The introduction of such a contract reestablishes the reputational equilibrium because the bad 28

entrepreneur is once again forced to imitate the good entrepreneur by proposing a similar contract. 8. Conclusion Our model suggests that repeated funding of sequential projects may arise as the dominant form of (cid:222)nancing when the aggregate risk of strategic default is high, as is likely in nations with poor contract enforcement and low judicial efficiency. To build a reputation, good entrepreneurs delay projects to seek repeated (cid:222)nancing from the same lender. Hence a low ex-ante likelihood of repayment goes hand-in-hand with delayed projects. While our stylized framework links judicial efficiency and the prevailing type of (cid:222)nancing, it remains silent on the precise linkage between judicial efficiency and the number of (cid:222)nancing relationships. For example, Detragiache, Garella, and Guiso (2000) and Ongena and Smith (2000b) document a negative correspondence between different proxies for judicial efficiency and the occurrence of multiple bank-(cid:222)rm relationships in samples containing Italian and large European (cid:222)rms respectively. Their results may suggest that in regions where judicial efficiency is poor, relationship (cid:222)nancing forces project delay, in effect reducing per period funding and worsening holdup. Multiple bank arrangements may then arise to increase per period access to funding and to abate holdup. On the other hand, in regions where judicial efficiency is high, (cid:222)rms can immediately (cid:222)nance all currently accessible projects possibly using a single lender. Such arm(cid:146)s-length (cid:222)nancing is further untainted by 29

holdup, even when (cid:222)rms would borrow repeatedly from the same bank. However, we leave investigating these conjectures for future research. 30

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Appendix Proof of Lemma 1 From Proposition 2 follows that for p ∆ , project sequence A,B results. It was 0 A ≥ { } showninthetext that given∆ > p max ∆ ∆ ,∆2 /ρ (implyingk < ρπ ), repayment B 0 ≥ { A B B } B r = k∆ /p satis(cid:222)es the relevant rationality constraints (5.4), (5.5) and (5.6). To complete 1∗ B 0 the proof, we show that promising repayment r maximizes the good entrepreneur(cid:146)s income. 1∗ Recalling Corollary 1.2, the good entrepreneur(cid:146)s income Π under r over both periods is ∗ 1∗ given by Π = π k∆ /p . ∗ A B 0 − Note that given the assumptions made on p , income Π is nonnegative. 0 ∗ Step 1: Consider any repayment ro an lender is not willing to sign. Then, a contract over 1 project A promising repayment r = k/p is signed in the second period if p ∆ . For p < 2∗ 0 0 ≥ A 0 ∆ , no contract is signed. Hence by promising ro in the (cid:222)rst period, the good entrepreneur A 1 achieves income Πo = max 0,π k/p in the second period. It is straightforward to show A 0 { − } that Πo Π . ∗ ≤ Step 2: Any repayment promise ro < k∆ /p violates the lender(cid:146)s rationality constraint 1 B 0 (5.4) since in that case qo = p /∆ . Hence the lender rejects, and we are back at Step 1. 0 B Step 3: Consider any repayment ro such that k∆ /p < ro( ) ρπ . If the lender 1 B 0 1 • ≤ B accepts, it follows from equation (5.3) that p = ∆ , and according to Corollary 1.2, a ∗1 B second-period contract with r = π is induced. The good entrepreneur(cid:146)s income is then 2 B given by Πo = π ro, which is less than Π A − 1 ∗ Step 4: Consider any repayment ro > ρπ . The lender only accepts if β = 0. According 1 B ∗ to (5.4), this is only rational for the lender if ro k/p . If that is the case, the good 1 ≥ 0 entrepreneurs(cid:146)s income is given by Πo = π ro+ρ(π k). This is at least as big as pro(cid:222)t A − 1 B − Π if ro k∆ /p + ρ(π k). But this is only compatible with the lender(cid:146)s constraint ∗ 1 ≤ B 0 B − ro k/p if p ∆ , leading to a contradiction with the assumptions made on p . 1 ≥ 0 0 ≥ B 0 SummarizingStep1to4,proposingtorepayr = k∆ /p maximizesthegoodentrepreneur(cid:146)s 1∗ B 0 income. Proof of Lemma 2 The proof is analogous to the proof of Lemma 1. We showed in the text that given k ρπ B ≤ and p ∆ , repayment r = k satis(cid:222)es the relevant rationality constraints. To complete 0 ≥ B 1∗ the proof, we show that promising repayment r = k maximizes the good entrepreneurs(cid:146)s 1∗ 34

income. Recalling Corollary 2.1, the good entrepreneur(cid:146)s income Π under repayment r ∗ 1∗ over both periods is given by Π = π k +ρ(π k/p ). ∗ A B 0 − − Note that given the assumptions made on p , income Π is nonnegative. 0 ∗ Step 1: Consider any repayment ro the lenders are not willing to sign. Then, a contract 1 promising repayment r = k/p is signed in the second period if p ∆ . For p < ∆ , no 2∗ 0 0 A 0 A ≥ contract is signed. Hence by proposing ro in the (cid:222)rst period, the good entrepreneur achieves 1 income Πo = max 0,π k/p which is less than Π . A 0 ∗ { − } Step 2: Any repayment promise ro < k violates the lenders(cid:146) rationality constraints (5.4). 1 Hence the lenders reject, and we are back at Step 1. Step 3: Consider any repayment ro such that k < ro ρπ . the lender accepts ro, and from 1 1 B 1 ≤ equation (5.3) it follows that p = p . According to Corollary 1.2, a second-period contract ∗1 0 with r = k/p is induced. The good entrepreneur(cid:146)s income is then given by Πo = π 2∗ 0 A ro +ρ(π k/p ). Since ro > r = k, this is less than Π . 1 B 0 1 1∗ ∗ − − Step 4: Consider any repayment ro > ρπ . A lender only accepts if β = 0. According 1 B ∗ to (5.4), this is only rational for the lender if ro k/p . If that is the case, the good 1 0 ≥ entrepreneur(cid:146)s income is given by Πo = π ro+ρ(π k). This is at least as high as pro(cid:222)t A 1 B − − Π if ro k(1 ρ)+ρk/p . Since ro k/p , this implies p 1, leading to a contradiction. ∗ 1 0 1 0 0 ≤ − ≥ ≥ Steps 1 to 4 show that choosing r = k maximizes the income of the good entrepreneur. 1∗ Proof of Lemma 3 We showed in the text that given (i) k > ρπ and p ∆ , or (ii) k ρπ and B 0 A B ≥ ≤ ∆2 /ρ > p ∆ , repayment r = k/p satis(cid:222)es the relevant rationality constraints. Note B 0 ≥ A 1∗ 0 that in both cases (i) and (ii), k/p exceeds ρπ since (i) k/p > k > ρπ , and (ii) k/p > 0 B 0 B 0 ρπ /∆ > ρπ . This implies that in both cases only separating equilibria exist. Recalling B B B Corollary 2.1, the good entrepreneur(cid:146)s income Π under repayment r over both periods is ∗ 1∗ given by Π = π k/p +ρ(π k). ∗ A 0 B − − It remains to show that proposing r = k/p dominates the strategy to sign no contract in 1∗ 0 the (cid:222)rst period and a contract with repayment r = k/p in the second period. Following 2∗ 0 the latter strategy, the entrepreneur achieves an income with present value ρ(π k/p ), A 0 − which is less than income Π . ∗ Project Divisibility 35

Let π + π = C, a constant, and assume that the entrepreneur (cid:222)xes project size A B by determining the proportion α of C to be allocated to project A and the proportion (1 α) allocated to project B. We have to consider only the representative project sequence − B,A . For this project sequence, p max ∆ ∆ ,∆2/ρ is a necessary condition for a { } 0 ≥ { A B A } Reputational Equilibrium to exist. In case of endogenous project split the latter condition changes top max k2/(α(1 α)C2),k2/(ρα2C2). Obviously, k2/(α(1 α)C2) is minimized 0 ≥ { − − for α = 1/2, and increases in α for α > 1/2. However for π close to π , p k2/(ρα2C2) A B 0 ≥ is the relevant condition (see Figure 1), and k2/(ρα2C2) decreases in α. Hence by increasing α, that is by placing more weight on the second-period project, the entrepreneur is able to broaden the range of p for which (cid:222)nancing is feasible. The maximum she can attain is to 0 set α = α = 1/(1+ρ). Increasing α beyond α makes k2/(α(1 α)C2) the relevant condition, − which, as mentioned before, increases in α. To conclude, endogenous project split-up and an increase in total project payoffs (C) widens the reach of both arm(cid:146)s-length and relationship (cid:222)nancing versus the No Investment outcome. Long-Term Contracts We implicitly assumed that the entrepreneur is not able to credibly commit to stay with the incumbent (cid:222)nancier. The threat of switching in the second period disappears if she is able to commit. Hence it is possible that the entrepreneur prefers relationship (cid:222)nancing for p ∆ . In order to check for this possibility, we compare pro(cid:222)ts for a Pooling 0 B ≥ Equilibrium for A,B with the pro(cid:222)ts for arm(cid:146)s-length (cid:222)nancing of the joint projects. we { } can conclude that the writing of long-term contracts does not alter our results because ΠALF > ΠRF(PE, A,B ). Suppose not, then π + π 2k/p π k p A B 0 A 0 { } − ≤ − ⇐⇒ ≤ 2k/(π +k). Combined with p < 1 leads to π < k, a contradiction. B 0 B 36

Figure 1: Comparing relationship financing equilibria for project sequencing {A,B} versus {B,A} Sequence: {A,B} π A Separating ∆ A 2/ρ ∆ A ∆ B ∆ A κ ∆ B 2/ρ ∆ B π -k+ρπ 2/k B B No Investment Reputational Pooling ρπ 2/k B π /ρ B π B p o 0 1 Sequence: {B,A} π A ∆ A 2/ρ ∆ A ∆ B ∆ A κ ∆ B 2/ρ ∆ B π -k+ρπ 2/k B B Reputational Pooling ρπ 2/k B π /ρ B No Investment π B 0 1 p o 37

Figure 2: Summary of Proposition 8 (relationship financing) Pooling Separating {B,A} {A,B} π A ∆ A 2/ρ ∆ A ∆ B ∆ A κ ∆ B 2/ρ ∆ B Reputational Pooling No Investment {A,B} {A,B} π -k+ρπ 2/k B B Reputational {B,A} ρπ 2/k B π /ρ B π B 0 1 p o 38

Figure 3: Summary of Proposition 10 (choice between arm’s-length and relationship financing) Pooling Separating {B,A} {A,B} π A ∆ A 2/ρ ∆ A ∆ B ∆ A κ ∆ B 2/ρ ∆ B Reputational Arm’s-Length No Investment Reputational {A,B} Financing {B,A} π /ρ B π B 0 1 p o 39