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Insider rates versus outsider rates in lending
Finance Research Letters 8 (2011) 180–187
Contents lists available at SciVerse ScienceDirect
Finance Research Letters journal homepage: www.elsevier.com/locate/frl
Insider rates versus outsider rates in lending Lamont K. Black ⇑ Board of Governors of the Federal Reserve System, 20th and C Streets NW, Washington, DC 20551, United States
a r t i c l e
i n f o
Article history: Received 13 December 2010 Accepted 15 August 2011 Available online 22 August 2011 JEL classification: G21 C72 D44 D82
a b s t r a c t When information asymmetries exist between lenders, an uninformed outside bank that competes with an informed inside bank faces a winner’s curse. This paper examines a benchmark model’s prediction for interest rates. Although the outside bank wins more bad firms, the inside bank extracts rents from good firms and the outside bank underbids for bad firms. An analytical solution reveals the surprising result that the average interest rate paid to the inside bank following bidding outcomes can be higher than the average interest rate paid to the outside bank. Published by Elsevier Inc.
Keywords: Banking relationships Competition under asymmetric information Informational lock-in Auctions
1. Introduction In information-based theories of financial intermediation, banks are often modeled as acquiring information about firms through the process of lending (Rajan, 1992). The acquisition of private information implies that lenders will have different degrees of information about a firm when competing for a loan, which will affect observed interest rates. This paper examines how interest rates differ at inside and outside banks in a benchmark model of insider versus outsider lending. The issue is important for understanding the predicted outcome of competition between the informed bidding of inside banks and the uninformed bidding of outside banks. Although intuition may suggest that observed interest rates should be higher at an outside lender due to the winner’s curse, the results show that this apparent intuition is not always correct. The theoretical framework used in this paper is the Sharpe (1990) model of inside versus outside lending. Once a bank makes a loan, the bank becomes the ‘‘inside’’ bank with an information ⇑ Fax: +1 202 452 5295. E-mail address: [email protected] 1544-6123/$ - see front matter Published by Elsevier Inc. doi:10.1016/j.frl.2011.08.002
L.K. Black / Finance Research Letters 8 (2011) 180–187
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advantage in subsequent bidding on a new loan for the firm, whereas all other lenders are ‘‘outside’’ banks. The framework fits a number of competitive environments, such as a relationship lender with private information competing as an inside bank against other transaction-based lenders with public information (Petersen and Rajan, 1994; Boot and Thakor, 2000). Other papers have used similar models to analyze the effect of adverse selection in the loan market on the average creditworthiness of borrowers (Broecker, 1990) and the loan portfolio of the informed lender (Dell’Ariccia and Marquez, 2004). The winner’s curse in the model implies that a less informed bank will win more low quality firms relative to an informed bank, but the implications for interest rates are not as clear. Previous theoretical papers have examined the marginal effect of information asymmetries between lenders on interest rates. For example, Hauswald and Marquez (2006) show that the interest rates paid by both highand low-quality borrowers increase in the informativeness of the inside bank’s signal. The contribution of this paper is to establish the theoretical implication of the winner’s curse for the relative level of inside and outside rates. Surprisingly, the analysis shows that the inside bank’s information advantage can result in the interest rate paid by borrowers at the inside bank exceeding the rate paid by borrowers at the outside bank. The winner’s curse would seem to imply that the ‘‘accepted interest rate’’ at the outside bank is always higher.1 If the outside bank wins more bad firms than the inside bank and bad firms are required to pay a higher interest rate than good firms, the comparison of insider versus outsider rates seems clear. However, the following analysis shows that the model does not have a universal prediction. In fact, over a large part of the parameter space, the model predicts that the accepted interest rate at the inside bank is higher. The results in this paper are important for clarifying the empirical predictions of the model. Previous empirical findings generally indicate that observed outside rates are higher on average than observed inside rates (D’Auria et al., 1999; Degryse and Ongena, 2005), which is sometimes interpreted as support for the model’s predictions (Degryse and Van Cayseele, 2000). These papers analyze loan interest rates paid to inside and outside banks after controlling for publicly-available information about the borrower, such as firm size and profitability. The tests compare rates without observing private information about borrower type; therefore, the key theoretical prediction needed for such empirical work is a comparison of the average interest rate accepted by borrowers at inside and outside banks without conditioning on borrower type. von Thadden (2004) states that a higher accepted interest rate at the outsider is consistent with the prediction of the Sharpe model.2 Yet this paper shows that empirical findings of the opposite result would also be consistent with the model. Among some pools of borrowers, the model predicts that observed inside rates should be higher than observed outside rates. As further empirical work is done in this area, it is important to establish the theoretical predictions of the model. The implication of the winner’s curse for the pricing of loans to good and bad firms is fairly straightforward. For good firms, the inside bank is able to extract rents due to its information advantage. This causes good firms that borrow from an inside bank to pay a higher rate than good firms that borrow from an outside bank. For bad firms, the outside bank sometimes bids too low because it is trying to win good firms (the bank offers a rate below the break even rate for bad firms). This causes bad firms that borrow from an outside bank to pay less than bad firms that borrow from an inside bank. These two effects imply that, conditional on firm type, firms pay lower interest rates at an outside bank. The total effect of the winner’s curse on observed interest rates depends on (a) the proportion of good and bad firms that switch lenders and (b) the interest rates paid by good and bad firms conditional on switching lenders. The usual intuition for the winner’s curse only incorporates the increased probability of the outsider winning bad firms. However, when this is combined with the lower interest rates for good and bad firms at the outside bank, a surprising result follows. This paper shows
1 As explained in the next section, ‘‘accepted interest rate’’ refers to the interest rate paid by a borrower once it has accepted the lower of the interest rates offered by the inside and outside bank. 2 Von Thadden states that ‘‘Consistent with the prediction of the present analysis, Degryse and Van Cayseele (2000) conclude that ‘some firms occasionally switch to an outside bank (MAIN = 0), and the outside bank charges a higher interest rate, because it takes into account a winner’s curse effect’’’ (p. 12).
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analytically that the accepted interest rate at the inside bank can be higher than the accepted interest rate at the outside bank. In this case, firms that borrow from an inside lender pay higher interest rates on average than firms that borrow from an outside lender. By analyzing bidding outcomes, the paper provides empirical predictions for observed interest rates in markets with asymmetric information. The analysis contributes most directly to the empirical literature on ‘‘switching,’’ which has studied firms switching from an existing lender to a new lender (Farinha and Santos, 2002; Gopalan et al., 2011). In a paper which examines data on banks’ private credit information, Ioannidou and Ongena (2010) confirm empirically that outside banks suffer from adverse selection, even with some public credit information available, and find that individual firms initially pay a lower interest rate when they switch. The analysis in this paper contributes to the literature by clarifying the predictions for average observed interest rates among switching and non-switching firms without conditioning on private information. More generally, the paper contributes to the literature on auctions with asymmetric information about the value of an asset (Engelbrecht-Wiggans et al., 1983; Hendricks and Porter, 1988) by analyzing the predictions for observed price outcomes of winning bids for informed and uninformed bidders.
2. Results and discussion In the model, there are firms of high (H) and low (L) quality, with probabilities of project success pH > pL. The proportion of high quality firms is h. For the entire pool of borrowers, the probability of success is p = hpH + (1 h)pL, such that pH > p > pL. In the first period, a bank makes a loan to each firm and becomes the ‘‘inside’’ bank. This inside bank receives a private signal c equal to S if the firm succeeds in repaying the first loan and F if the firm fails to repay, which allows the inside bank to distinguish between ‘‘good’’ firms (S) and ‘‘bad’’ firms (F). All other banks are ‘‘outside’’ banks. The probability of success in the second period conditional on success in the first period is p(S) = pHprob(H|S) + pL(1 prob(H|S)), where prob(H|S) = hpH/p. Likewise, conditional on failure in the first period, the probability of success in the second period is p(F). These conditional probabilities of success follow the order of p(S) > p > p(F). With a gross cost of funds per unit loaned of 1 þ r, this 1þr results in the corresponding break-even interest rate ordering of rS < rp < rF, where 1 þ r S ¼ pðSÞ , 1þr 1þr 3 1 þ rp ¼ p , and 1 þ r F ¼ pðFÞ. In the second stage of the model, the bidding is between the inside bank, which conditions its bid on its private signal, and an outside bank.4 The bidding is modeled as a simultaneous offer model of price competition, where the firm is assumed to take the lowest offer. As in Sharpe (1990), the inside bank is assumed to make the loan in the event of a tie bid. von Thadden (2004) establishes the unique equilibrium mixed-strategy bidding functions of both banks: ‘‘The inside bank’s equilibrium strategy is to offer r(F) = rF with certainty and is an atomless distribution on [rp, rF] for c = S, with density S
hi ðrÞ ¼
pðSÞð1 þ r p Þ ð1 þ r Þ ðpðSÞð1 þ rÞ ð1 þ r ÞÞ2
:
The outside bank’s equilibrium strategy has a point mass of 1 p(S) at r = rF and an atomless disS tribution on [rp, rF) with density ho ðrÞ ¼ pðSÞhi ðrÞ.’’ where i and o indicate inside and outside bank respectively. The inside bank offers the zero-profit rF to S F firms and, for S firms, it bids from hi , a distribution of rates which include rent-extraction above rS.5 S Because it does not know the firm type, the outside bank mitigates the winner’s curse by bidding from hi with probability p(S) and rF otherwise. This implies that the average offered rate of the inside bank, 3
It is assumed that second-period lending is profitable even if the firm is known to be bad. Black (2010) explores the case where the outsider receives a weaker version of the insider’s signal. 5 If lending to bad firms were not profitable, the bidding functions of the inside and outside bank would be somewhat different. The implications of this assumption are discussed later in the paper. 4
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relative to the outside bank, is lower for good firms and higher for bad firms. The expected proportion of good firms is p (the probability of succeeding in the first period), so it follows that the outside bank bids S from hi with greater probability than the inside bank. Therefore, unconditional on firm type, the average offered rate of the inside bank is higher than the outside bank. The contribution of this paper is to analyze the outcome of these bidding strategies for the inside and outside bank in terms of the probabilities of winning and the interest rates paid by borrowers. The probability of each bank winning can be calculated by combining the proportion of each firm type with the probability of winning that firm type:
Probi ðwinÞ ¼ p½pðSÞð1=2Þ þ ð1 pðSÞÞ þ ð1 pÞ½1 pðSÞ;
ð1Þ
Probo ðwinÞ ¼ p½pðSÞð1=2Þ þ ð1 pÞ½pðSÞ:
ð2Þ
The proportion of good and bad firms are p and 1 p, respectively, because a firm is the S type (succeeds in the first period) with probability p and an F type (fails in the first period) with probability 1 p. The terms in brackets are the probabilities of each bank winning conditional on firm type. For each S firm, the outside bank makes an offer from hi with probability p(S) or an offer of rF with probability S 1 p(S). For S firms, the inside bank makes an offer from hi . When the outside bank makes an offer S from hi , the inside and outside bank have both made an offer from the same distribution and each bank will win with probability ½, whereas the inside bank always wins when the outside bank offers rF. Therefore, the probability of winning an S firm is p(S)(1/2) + (1 p(S)) for the inside bank and p(S)(1/2) for the outside bank. For F firms, the inside bank offers rF. When the outside bank makes S an offer from hi , the outside bank wins the auction, but when the outside bank offers rF, the banks will have made identical bids, so the inside bank makes the loan. Therefore, the probability of winning an F firm is 1 p(S) for the inside bank and p(S) for the outside bank. The discussion below considers alternative assumptions about tie bids. The banks’ probabilities of winning differ due to the outside bank sometimes ‘‘guessing wrong.’’ The inside bank wins good firms which the outside bank guesses to be bad (occurring with probability p(1 p(S))) and the outside bank wins bad firms which it guesses to be good (occurring with probability (1 p)p(S)). The probability of the outside bank winning a good firm is lower than that of the inside bank, which is an implication of the winner’s curse. The interest rate paid by a borrower is determined by the three possible combinations for the numS S S ber of banks bidding from hi : both banks bid from hi , one bank bids from hi , or neither bank bids from S hi . The term ‘‘accepted interest rate’’ is used here to mean the interest rate paid by a borrower conditional on the strategies of each of the players, which include the bidding strategies of the inside and outside bank and the rule that the firm accepts the lowest rate offered. Therefore, it is not the offered rates, but rather the outcome rates following strategic bidding. S If both banks bid from hi , the accepted interest rate based on the minimum of two draws from the distribution is the ‘‘low accepted rate,’’ denoted as rL6:
rL ¼ Eðr j two biddersÞ ¼
Z
rF
rp
S
r½2ð1 HSi ðrÞÞhi ðrÞ dr;
ðLow Accepted RateÞ
S
S
where HSi is the cumulative distribution function of hi . The insider bids from hi for all S firms, so this is S the accepted rate for an S firm if the outsider also bids from hi . S If only one bank bids from hi , the accepted interest rate is the ‘‘medium accepted rate,’’ denoted as rM:
rM ¼ Eðr j one bidderÞ ¼
Z
rF
rp
S
rhi ðrÞ dr:
ðMedium Accepted RateÞ S
This is the accepted rate for an S firm if the insider bids from hi and the outsider bids rF or the S accepted rate for an F firm if the insider bids rF and the outsider bids from hi . 6
This is the general equation for the expected value of the minimum of two draws from a single distribution.
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If neither bank bids from hi , the accepted interest rate is the ‘‘high accepted rate,’’ denoted as rH:
r H ¼ Eðr j no bidderÞ ¼ r F :
ðHigh Accepted RateÞ
This is the accepted rate for F firms if the insider bids rF and the outsider bids rF. The accepted interest rates can be ranked as rS < rL < rM < rH = rF. The preliminary setup regarding probability of winning and accepted rates yields an interesting result regarding insider and outsider interest rates. Proposition 1. For both good and bad firms, the accepted interest rate is higher when borrowing from the inside bank. This proposition is based on the interest rate of a bank’s loans conditional on the firm being of a certain type and the bank winning the bid. For good firms, the accepted rate at the inside bank is a combination of loans with a low rate and a medium rate, whereas the accepted rate at the outside bank is only the low rate. The inside bank wins loans to good firms at the medium accepted rate when S the outside bank does not bid from hi . Given that rM > rL, it follows that Ei(r|S) > Eo(r|S). For bad firms, the accepted rate at the inside bank is only the high rate whereas the accepted rate at the outside bank is a combination of loans with a medium rate and a high rate. The outside bank wins loans to bad firms S at the medium accepted rate when it bids from hi . Given that rH > rM, it follows that Ei(r|F) > Eo(r|F). When the inside bank wins good firms at the rate rM, the difference rM rL can be considered ‘‘overpricing’’ and, when the outside bank wins bad firms at the rate rM, the difference rH rM can be considered ‘‘underpricing.’’ The inside bank’s overpricing reflects its ability to extract rents from good firms and the outside bank’s underpricing implies that these bad firms receive loan rates below the bank’s break-even rate. These differences are another implication of the winner’s curse, which does not just affect the probability of winning each firm type but also the accepted interest rate. Proposition 1 complicates the apparent intuition of the model for observed interest rates, because it indicates a positive effect of the winner’s curse on the inside rate relative to the outside rate. It is clear that the implication of the winner’s curse for observed interest rates depends on which bank wins and at what rate. To calculate the accepted interest rate at the inside and outside bank, the probabilities of winning can be combined with the corresponding accepted interest rate for each bidding outcome. In other words, the accepted interest rates at each bank can be written as probability weightings of each of the three interest rates. The accepted interest rates at the inside and outside bank are:
p½pðSÞð1=2Þr L þ ð1 pðSÞÞr M þ ð1 pÞ½ð1 pðSÞÞrH ½1 pðSÞ þ ð1=2Þðp pðSÞÞ p½pðSÞð1=2Þr L þ ð1 pÞ½pðSÞr M Eo ðrÞ ¼ : ½pðSÞ ð1=2Þðp pðSÞÞ
Ei ðrÞ ¼
ð3Þ ð4Þ
Both banks win the same number of loans with a low accepted rate in expectation, because both S banks are bidding from hi . The loans with a high accepted rate are only realized with a tie bid, in which case the inside bank wins. Notably, the outside bank wins more loans with a medium accepted rate than the inside bank due to the outside bank ‘‘guessing wrong.’’ The probability of the inside bank winning a loan with the medium accepted rate is p(1 p(S)), which is the joint probability of a firm being good and the outside S bank not making an offer from hi , and the probability of winning for the outside bank is (1 p)p(S), S which is the joint probability of a firm being bad and the outside bank making an offer from hi . The important comparison for this analysis is the difference between the inside and outside accepted rates. As stated in the introduction, intuition might suggest that the outsider’s accepted rate is always greater than the insider’s accepted rate. However, the following proposition provides analytical proof that the apparent intuition of the winner’s curse for predicted interest rates does not always hold. Proposition 2. The accepted interest rate at the inside bank is higher than the accepted rate at the outside bank if the inside bank makes at least as many loans as the outside bank. This condition is satisfied if
L.K. Black / Finance Research Letters 8 (2011) 180–187
½hpH þ ð1 hÞpL ½pH ð2 hpH Þ þ pL ð2 ð1 hÞpL Þ 1 6 1: 2pH pL
185
ð5Þ
The proposition follows from the proportions of low, medium, and high accepted rate loans which the inside and outside banks are expected to win. Because the inside and outside bank have the same probability of winning loans at the low accepted rate, the difference in their accepted interest rates is in the probability of winning loans at the medium and high accepted rates. The inside bank has a positive probability of winning loans with a medium and high accepted rate, whereas the outside bank is only expected to make loans at the medium accepted rate. Therefore, if the inside bank makes at least as many loans as the outside bank, the accepted rate at the inside bank is higher than the accepted rate at the outside bank. Proposition 2 identifies a region of the parameter space where Ei(r) > Eo(r). In this region, the primitive parameters satisfy the sufficient condition that the probability of the inside bank winning the loan is at least as great as that of the outside bank. The condition as expressed in Eq. (5) is therefore derived from algebraic manipulation of Eqs. (1) and (2), which specify the respective probabilities of the inside and outside bank winning the loan. The full region of the parameter space in which Ei(r) > Eo(r) is larger than the region bounded by Eq. (5), but Proposition 2 offers a sufficient condition to illustrate where the model generates this counterintuitive result. Fig. 1 illustrates Proposition 2 in the parameter space (pH, pL, h). The curved surface marks the nonlinear boundary condition in Eq. (5). In the region to the right of this surface, the inside bank makes at least as many loans as the outside bank. Therefore, as stated in Proposition 2, the accepted interest rate at the inside bank is greater than the accepted rate at the outside bank (Ei(r) > Eo(r)) in this region of the parameter space to the right of the surface. The gray triangle at the base of the figure represents the parameter space in (pH, pL), which is triangular because pH > pL by definition. Based on this figure, it
Fig. 1. A region in the (pH, pL, h) parameter space where the accepted interest rate at the inside bank is greater than the accepted rate at the outside bank. The parameters pH and pL are the probability of success of high (H) and low (L) quality firms and h is the proportion of high quality firms. The nonlinear surface illustrates the condition of Eq. (5) in Proposition 2. The region to the right of the surface is where the inside bank makes at least as many loans as the outside bank. Therefore, as stated in Proposition 2, the accepted interest rate at the inside bank is greater than the outside bank (Ei(r) > Eo(r)) in this region of the parameter space to the right of the surface. The gray triangle at the base of the figure represents the parameter space in (pH, pL), which is triangular because pH > pL by definition.
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becomes clear that over the majority of the parameter space the accepted interest rate at the inside bank is greater than the accepted interest rate at the outside bank. This is also where the probability of the inside bank winning the loan is at least as great as that of the outside bank, which is consistent with empirical studies finding that lenders retain the majority of their borrowers (e.g., Black, 2010). Fig. 1 also emphasizes the degree to which the difference between the inside and outside accepted rates depends on h. This is especially true where pH is high and pL is low, because this is where the difference between the high and low quality firms is the greatest and private information matters the most. A significantly high or low h weights the distribution of firms toward the high or low quality firms, so the outside lender is not at too severe of an informational disadvantage. However, a value of h around 0.5 implies that the outside bank faces a severe winner’s curse and has a high probability of winning firms with a very low probability of repayment. Loosening the assumption that the inside bank wins all of the tie bids with the high accepted rate would increase the size of the region where the outside accepted rate is greater than the inside accepted rate. The assumption about how tie bids are allocated does not affect the equilibrium solution to the model given in Proposition 2, because it has no effect on the banks’ expected payoffs. Tie bids all occur at the high accepted rate, so a reallocation of these loans to the outside bank would increase the outside accepted rate and decrease the inside accepted rate.7 It is also important to consider the assumption about the profitability of lending to bad firms. If lending to bad firms were unprofitable, the inside bank would not lend to bad firms and the banks’ bidding functions would change due to the more severe ‘‘curse’’ for winning bad firms. The outside bank would have to bid less aggressively, which would likely increase the outside accepted rate relative to the inside rate. 3. Conclusion This paper analyzes the predictions of a benchmark model for insider versus outsider interest rates. The Sharpe (1990) model (with the von Thadden (2004) correction) is a standard framework for analyzing the role of private information in the competition between lenders. The results of this paper show that the model provides a surprising prediction for inside and outside interest rates. Due to the winner’s curse, the outside bank wins more bad firms and less good firms than the inside bank, which might suggest that the average interest rate paid to the outside bank is always higher than the average rate paid to the inside bank. The reasoning would be that outside banks win more bad firms, bad firms borrow at a higher rate, and, hence, the outside rate is higher. The interesting result of this paper is that the apparent intuition does not necessarily follow. Although the outside bank wins more bad firms than the inside bank, good and bad firms pay a lower rate at the outside bank because the inside bank extracts rents from good firms and the outside bank bids too low for bad firms. Combining this result with the effect of the winner’s curse on winning bids reveals that the model does not have a universal prediction for observed interest rates at an insider versus outsider. When the inside bank makes at least as many loans as the outside bank, the average interest rate paid to the inside bank is higher than the average interest rate paid to the outside bank. This is an important step forward in clarifying the predictions of a benchmark model for observed interest rates when firms borrow from inside versus outside lenders. The analysis contributes to a growing literature on competition between informed and uninformed lenders, such as relationship lending versus transaction-based lending and the switching of borrowers between lenders. More generally, the results shown here should help refine future work on observed price outcomes in markets with information asymmetries. Acknowledgments The views expressed do not necessarily reflect those of the Federal Reserve Board or its staff. I would like to thank Allen Berger, Ken Brevoort, Rochelle Edge, Eric Leeper, Robert Marquez, Richard 7 See Black (2008) for a solution of the model under the assumption that the inside and outside bank split the tie bids. The results under the split-tie assumption are illustrated in Fig. 1, which shows that the insider rate is still higher than the outsider rate in most of the parameter space.
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Rosen, Greg Udell, and Ernst-Ludwig von Thadden for helpful comments and discussions. All remaining errors are my own. References Black, L., 2008. Insider Rates vs. Outsider Rates in Lending. FEDS Working Paper 36. Board of Governors of the Federal Reserve System, pp. 1–23. Black, L., 2010. Firm Transparency and Outside Lending. Unpublished Working Paper. Board of Governors of the Federal Reserve System. Boot, A., Thakor, A., 2000. Can relationship banking survive competition? Journal of Finance 55, 679–713. Broecker, T., 1990. Credit-worthiness tests and interbank competition. Econometrica 58, 429–452. D’Auria, C., Foglia, A., Reedtz, P., 1999. Bank interest rates and credit relationships in Italy. Journal of Banking and Finance 23, 1067–1093. Degryse, H., Ongena, S., 2005. Distance, lending relationships, and competition. Journal of Finance 60, 231–266. Degryse, H., Van Cayseele, P., 2000. Relationship lending within a bank-based system: evidence from European small business data. Journal of Financial Intermediation 9, 90–109. Dell’Ariccia, G., Marquez, R., 2004. Information and bank credit allocation. Journal of Financial Economics 72, 185–214. Engelbrecht-Wiggans, R., Milgrom, P., Weber, R., 1983. Competitive bidding and proprietary information. Journal of Mathematical Economics 11, 161–169. Farinha, L., Santos, J., 2002. Switching from single to multiple bank lending relationships: determinants and implications. Journal of Financial Intermediation 11, 124–151. Gopalan, R., Udell, G., Yerramilli, V., 2011. Why do firms form new banking relationships? Journal of Financial and Quantitative Analysis 46, forthcoming. Hauswald, R., Marquez, R., 2006. Competition and strategic information acquisition in credit markets. Review of Financial Studies 19, 967–1000. Hendricks, K., Porter, R., 1988. An empirical study of an auction with asymmetric information. American Economic Review 78, 865–883. Ioannidou, V., Ongena, S., 2010. ‘‘Time for a change’’: loan conditions and bank behavior when firms switch banks. Journal of Finance 65, 1847–1877. Petersen, M., Rajan, R., 1994. The benefits of lending relationships. Journal of Finance 49, 3–37. Rajan, R., 1992. Insiders and outsiders: the choice between informed and arm’s-length debt. Journal of Finance 47, 1367–1400. Sharpe, S., 1990. Asymmetric information, bank lending and implicit contracts: a stylized model of customer relationships. Journal of Finance 45, 1069–1087. von Thadden, E.-L., 2004. Asymmetric information, bank lending and implicit contracts: the winner’s curse. Finance Research Letters 1, 11–23.
Contents lists available at SciVerse ScienceDirect
Finance Research Letters journal homepage: www.elsevier.com/locate/frl
Insider rates versus outsider rates in lending Lamont K. Black ⇑ Board of Governors of the Federal Reserve System, 20th and C Streets NW, Washington, DC 20551, United States
a r t i c l e
i n f o
Article history: Received 13 December 2010 Accepted 15 August 2011 Available online 22 August 2011 JEL classification: G21 C72 D44 D82
a b s t r a c t When information asymmetries exist between lenders, an uninformed outside bank that competes with an informed inside bank faces a winner’s curse. This paper examines a benchmark model’s prediction for interest rates. Although the outside bank wins more bad firms, the inside bank extracts rents from good firms and the outside bank underbids for bad firms. An analytical solution reveals the surprising result that the average interest rate paid to the inside bank following bidding outcomes can be higher than the average interest rate paid to the outside bank. Published by Elsevier Inc.
Keywords: Banking relationships Competition under asymmetric information Informational lock-in Auctions
1. Introduction In information-based theories of financial intermediation, banks are often modeled as acquiring information about firms through the process of lending (Rajan, 1992). The acquisition of private information implies that lenders will have different degrees of information about a firm when competing for a loan, which will affect observed interest rates. This paper examines how interest rates differ at inside and outside banks in a benchmark model of insider versus outsider lending. The issue is important for understanding the predicted outcome of competition between the informed bidding of inside banks and the uninformed bidding of outside banks. Although intuition may suggest that observed interest rates should be higher at an outside lender due to the winner’s curse, the results show that this apparent intuition is not always correct. The theoretical framework used in this paper is the Sharpe (1990) model of inside versus outside lending. Once a bank makes a loan, the bank becomes the ‘‘inside’’ bank with an information ⇑ Fax: +1 202 452 5295. E-mail address: [email protected] 1544-6123/$ - see front matter Published by Elsevier Inc. doi:10.1016/j.frl.2011.08.002
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advantage in subsequent bidding on a new loan for the firm, whereas all other lenders are ‘‘outside’’ banks. The framework fits a number of competitive environments, such as a relationship lender with private information competing as an inside bank against other transaction-based lenders with public information (Petersen and Rajan, 1994; Boot and Thakor, 2000). Other papers have used similar models to analyze the effect of adverse selection in the loan market on the average creditworthiness of borrowers (Broecker, 1990) and the loan portfolio of the informed lender (Dell’Ariccia and Marquez, 2004). The winner’s curse in the model implies that a less informed bank will win more low quality firms relative to an informed bank, but the implications for interest rates are not as clear. Previous theoretical papers have examined the marginal effect of information asymmetries between lenders on interest rates. For example, Hauswald and Marquez (2006) show that the interest rates paid by both highand low-quality borrowers increase in the informativeness of the inside bank’s signal. The contribution of this paper is to establish the theoretical implication of the winner’s curse for the relative level of inside and outside rates. Surprisingly, the analysis shows that the inside bank’s information advantage can result in the interest rate paid by borrowers at the inside bank exceeding the rate paid by borrowers at the outside bank. The winner’s curse would seem to imply that the ‘‘accepted interest rate’’ at the outside bank is always higher.1 If the outside bank wins more bad firms than the inside bank and bad firms are required to pay a higher interest rate than good firms, the comparison of insider versus outsider rates seems clear. However, the following analysis shows that the model does not have a universal prediction. In fact, over a large part of the parameter space, the model predicts that the accepted interest rate at the inside bank is higher. The results in this paper are important for clarifying the empirical predictions of the model. Previous empirical findings generally indicate that observed outside rates are higher on average than observed inside rates (D’Auria et al., 1999; Degryse and Ongena, 2005), which is sometimes interpreted as support for the model’s predictions (Degryse and Van Cayseele, 2000). These papers analyze loan interest rates paid to inside and outside banks after controlling for publicly-available information about the borrower, such as firm size and profitability. The tests compare rates without observing private information about borrower type; therefore, the key theoretical prediction needed for such empirical work is a comparison of the average interest rate accepted by borrowers at inside and outside banks without conditioning on borrower type. von Thadden (2004) states that a higher accepted interest rate at the outsider is consistent with the prediction of the Sharpe model.2 Yet this paper shows that empirical findings of the opposite result would also be consistent with the model. Among some pools of borrowers, the model predicts that observed inside rates should be higher than observed outside rates. As further empirical work is done in this area, it is important to establish the theoretical predictions of the model. The implication of the winner’s curse for the pricing of loans to good and bad firms is fairly straightforward. For good firms, the inside bank is able to extract rents due to its information advantage. This causes good firms that borrow from an inside bank to pay a higher rate than good firms that borrow from an outside bank. For bad firms, the outside bank sometimes bids too low because it is trying to win good firms (the bank offers a rate below the break even rate for bad firms). This causes bad firms that borrow from an outside bank to pay less than bad firms that borrow from an inside bank. These two effects imply that, conditional on firm type, firms pay lower interest rates at an outside bank. The total effect of the winner’s curse on observed interest rates depends on (a) the proportion of good and bad firms that switch lenders and (b) the interest rates paid by good and bad firms conditional on switching lenders. The usual intuition for the winner’s curse only incorporates the increased probability of the outsider winning bad firms. However, when this is combined with the lower interest rates for good and bad firms at the outside bank, a surprising result follows. This paper shows
1 As explained in the next section, ‘‘accepted interest rate’’ refers to the interest rate paid by a borrower once it has accepted the lower of the interest rates offered by the inside and outside bank. 2 Von Thadden states that ‘‘Consistent with the prediction of the present analysis, Degryse and Van Cayseele (2000) conclude that ‘some firms occasionally switch to an outside bank (MAIN = 0), and the outside bank charges a higher interest rate, because it takes into account a winner’s curse effect’’’ (p. 12).
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analytically that the accepted interest rate at the inside bank can be higher than the accepted interest rate at the outside bank. In this case, firms that borrow from an inside lender pay higher interest rates on average than firms that borrow from an outside lender. By analyzing bidding outcomes, the paper provides empirical predictions for observed interest rates in markets with asymmetric information. The analysis contributes most directly to the empirical literature on ‘‘switching,’’ which has studied firms switching from an existing lender to a new lender (Farinha and Santos, 2002; Gopalan et al., 2011). In a paper which examines data on banks’ private credit information, Ioannidou and Ongena (2010) confirm empirically that outside banks suffer from adverse selection, even with some public credit information available, and find that individual firms initially pay a lower interest rate when they switch. The analysis in this paper contributes to the literature by clarifying the predictions for average observed interest rates among switching and non-switching firms without conditioning on private information. More generally, the paper contributes to the literature on auctions with asymmetric information about the value of an asset (Engelbrecht-Wiggans et al., 1983; Hendricks and Porter, 1988) by analyzing the predictions for observed price outcomes of winning bids for informed and uninformed bidders.
2. Results and discussion In the model, there are firms of high (H) and low (L) quality, with probabilities of project success pH > pL. The proportion of high quality firms is h. For the entire pool of borrowers, the probability of success is p = hpH + (1 h)pL, such that pH > p > pL. In the first period, a bank makes a loan to each firm and becomes the ‘‘inside’’ bank. This inside bank receives a private signal c equal to S if the firm succeeds in repaying the first loan and F if the firm fails to repay, which allows the inside bank to distinguish between ‘‘good’’ firms (S) and ‘‘bad’’ firms (F). All other banks are ‘‘outside’’ banks. The probability of success in the second period conditional on success in the first period is p(S) = pHprob(H|S) + pL(1 prob(H|S)), where prob(H|S) = hpH/p. Likewise, conditional on failure in the first period, the probability of success in the second period is p(F). These conditional probabilities of success follow the order of p(S) > p > p(F). With a gross cost of funds per unit loaned of 1 þ r, this 1þr results in the corresponding break-even interest rate ordering of rS < rp < rF, where 1 þ r S ¼ pðSÞ , 1þr 1þr 3 1 þ rp ¼ p , and 1 þ r F ¼ pðFÞ. In the second stage of the model, the bidding is between the inside bank, which conditions its bid on its private signal, and an outside bank.4 The bidding is modeled as a simultaneous offer model of price competition, where the firm is assumed to take the lowest offer. As in Sharpe (1990), the inside bank is assumed to make the loan in the event of a tie bid. von Thadden (2004) establishes the unique equilibrium mixed-strategy bidding functions of both banks: ‘‘The inside bank’s equilibrium strategy is to offer r(F) = rF with certainty and is an atomless distribution on [rp, rF] for c = S, with density S
hi ðrÞ ¼
pðSÞð1 þ r p Þ ð1 þ r Þ ðpðSÞð1 þ rÞ ð1 þ r ÞÞ2
:
The outside bank’s equilibrium strategy has a point mass of 1 p(S) at r = rF and an atomless disS tribution on [rp, rF) with density ho ðrÞ ¼ pðSÞhi ðrÞ.’’ where i and o indicate inside and outside bank respectively. The inside bank offers the zero-profit rF to S F firms and, for S firms, it bids from hi , a distribution of rates which include rent-extraction above rS.5 S Because it does not know the firm type, the outside bank mitigates the winner’s curse by bidding from hi with probability p(S) and rF otherwise. This implies that the average offered rate of the inside bank, 3
It is assumed that second-period lending is profitable even if the firm is known to be bad. Black (2010) explores the case where the outsider receives a weaker version of the insider’s signal. 5 If lending to bad firms were not profitable, the bidding functions of the inside and outside bank would be somewhat different. The implications of this assumption are discussed later in the paper. 4
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relative to the outside bank, is lower for good firms and higher for bad firms. The expected proportion of good firms is p (the probability of succeeding in the first period), so it follows that the outside bank bids S from hi with greater probability than the inside bank. Therefore, unconditional on firm type, the average offered rate of the inside bank is higher than the outside bank. The contribution of this paper is to analyze the outcome of these bidding strategies for the inside and outside bank in terms of the probabilities of winning and the interest rates paid by borrowers. The probability of each bank winning can be calculated by combining the proportion of each firm type with the probability of winning that firm type:
Probi ðwinÞ ¼ p½pðSÞð1=2Þ þ ð1 pðSÞÞ þ ð1 pÞ½1 pðSÞ;
ð1Þ
Probo ðwinÞ ¼ p½pðSÞð1=2Þ þ ð1 pÞ½pðSÞ:
ð2Þ
The proportion of good and bad firms are p and 1 p, respectively, because a firm is the S type (succeeds in the first period) with probability p and an F type (fails in the first period) with probability 1 p. The terms in brackets are the probabilities of each bank winning conditional on firm type. For each S firm, the outside bank makes an offer from hi with probability p(S) or an offer of rF with probability S 1 p(S). For S firms, the inside bank makes an offer from hi . When the outside bank makes an offer S from hi , the inside and outside bank have both made an offer from the same distribution and each bank will win with probability ½, whereas the inside bank always wins when the outside bank offers rF. Therefore, the probability of winning an S firm is p(S)(1/2) + (1 p(S)) for the inside bank and p(S)(1/2) for the outside bank. For F firms, the inside bank offers rF. When the outside bank makes S an offer from hi , the outside bank wins the auction, but when the outside bank offers rF, the banks will have made identical bids, so the inside bank makes the loan. Therefore, the probability of winning an F firm is 1 p(S) for the inside bank and p(S) for the outside bank. The discussion below considers alternative assumptions about tie bids. The banks’ probabilities of winning differ due to the outside bank sometimes ‘‘guessing wrong.’’ The inside bank wins good firms which the outside bank guesses to be bad (occurring with probability p(1 p(S))) and the outside bank wins bad firms which it guesses to be good (occurring with probability (1 p)p(S)). The probability of the outside bank winning a good firm is lower than that of the inside bank, which is an implication of the winner’s curse. The interest rate paid by a borrower is determined by the three possible combinations for the numS S S ber of banks bidding from hi : both banks bid from hi , one bank bids from hi , or neither bank bids from S hi . The term ‘‘accepted interest rate’’ is used here to mean the interest rate paid by a borrower conditional on the strategies of each of the players, which include the bidding strategies of the inside and outside bank and the rule that the firm accepts the lowest rate offered. Therefore, it is not the offered rates, but rather the outcome rates following strategic bidding. S If both banks bid from hi , the accepted interest rate based on the minimum of two draws from the distribution is the ‘‘low accepted rate,’’ denoted as rL6:
rL ¼ Eðr j two biddersÞ ¼
Z
rF
rp
S
r½2ð1 HSi ðrÞÞhi ðrÞ dr;
ðLow Accepted RateÞ
S
S
where HSi is the cumulative distribution function of hi . The insider bids from hi for all S firms, so this is S the accepted rate for an S firm if the outsider also bids from hi . S If only one bank bids from hi , the accepted interest rate is the ‘‘medium accepted rate,’’ denoted as rM:
rM ¼ Eðr j one bidderÞ ¼
Z
rF
rp
S
rhi ðrÞ dr:
ðMedium Accepted RateÞ S
This is the accepted rate for an S firm if the insider bids from hi and the outsider bids rF or the S accepted rate for an F firm if the insider bids rF and the outsider bids from hi . 6
This is the general equation for the expected value of the minimum of two draws from a single distribution.
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If neither bank bids from hi , the accepted interest rate is the ‘‘high accepted rate,’’ denoted as rH:
r H ¼ Eðr j no bidderÞ ¼ r F :
ðHigh Accepted RateÞ
This is the accepted rate for F firms if the insider bids rF and the outsider bids rF. The accepted interest rates can be ranked as rS < rL < rM < rH = rF. The preliminary setup regarding probability of winning and accepted rates yields an interesting result regarding insider and outsider interest rates. Proposition 1. For both good and bad firms, the accepted interest rate is higher when borrowing from the inside bank. This proposition is based on the interest rate of a bank’s loans conditional on the firm being of a certain type and the bank winning the bid. For good firms, the accepted rate at the inside bank is a combination of loans with a low rate and a medium rate, whereas the accepted rate at the outside bank is only the low rate. The inside bank wins loans to good firms at the medium accepted rate when S the outside bank does not bid from hi . Given that rM > rL, it follows that Ei(r|S) > Eo(r|S). For bad firms, the accepted rate at the inside bank is only the high rate whereas the accepted rate at the outside bank is a combination of loans with a medium rate and a high rate. The outside bank wins loans to bad firms S at the medium accepted rate when it bids from hi . Given that rH > rM, it follows that Ei(r|F) > Eo(r|F). When the inside bank wins good firms at the rate rM, the difference rM rL can be considered ‘‘overpricing’’ and, when the outside bank wins bad firms at the rate rM, the difference rH rM can be considered ‘‘underpricing.’’ The inside bank’s overpricing reflects its ability to extract rents from good firms and the outside bank’s underpricing implies that these bad firms receive loan rates below the bank’s break-even rate. These differences are another implication of the winner’s curse, which does not just affect the probability of winning each firm type but also the accepted interest rate. Proposition 1 complicates the apparent intuition of the model for observed interest rates, because it indicates a positive effect of the winner’s curse on the inside rate relative to the outside rate. It is clear that the implication of the winner’s curse for observed interest rates depends on which bank wins and at what rate. To calculate the accepted interest rate at the inside and outside bank, the probabilities of winning can be combined with the corresponding accepted interest rate for each bidding outcome. In other words, the accepted interest rates at each bank can be written as probability weightings of each of the three interest rates. The accepted interest rates at the inside and outside bank are:
p½pðSÞð1=2Þr L þ ð1 pðSÞÞr M þ ð1 pÞ½ð1 pðSÞÞrH ½1 pðSÞ þ ð1=2Þðp pðSÞÞ p½pðSÞð1=2Þr L þ ð1 pÞ½pðSÞr M Eo ðrÞ ¼ : ½pðSÞ ð1=2Þðp pðSÞÞ
Ei ðrÞ ¼
ð3Þ ð4Þ
Both banks win the same number of loans with a low accepted rate in expectation, because both S banks are bidding from hi . The loans with a high accepted rate are only realized with a tie bid, in which case the inside bank wins. Notably, the outside bank wins more loans with a medium accepted rate than the inside bank due to the outside bank ‘‘guessing wrong.’’ The probability of the inside bank winning a loan with the medium accepted rate is p(1 p(S)), which is the joint probability of a firm being good and the outside S bank not making an offer from hi , and the probability of winning for the outside bank is (1 p)p(S), S which is the joint probability of a firm being bad and the outside bank making an offer from hi . The important comparison for this analysis is the difference between the inside and outside accepted rates. As stated in the introduction, intuition might suggest that the outsider’s accepted rate is always greater than the insider’s accepted rate. However, the following proposition provides analytical proof that the apparent intuition of the winner’s curse for predicted interest rates does not always hold. Proposition 2. The accepted interest rate at the inside bank is higher than the accepted rate at the outside bank if the inside bank makes at least as many loans as the outside bank. This condition is satisfied if
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½hpH þ ð1 hÞpL ½pH ð2 hpH Þ þ pL ð2 ð1 hÞpL Þ 1 6 1: 2pH pL
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ð5Þ
The proposition follows from the proportions of low, medium, and high accepted rate loans which the inside and outside banks are expected to win. Because the inside and outside bank have the same probability of winning loans at the low accepted rate, the difference in their accepted interest rates is in the probability of winning loans at the medium and high accepted rates. The inside bank has a positive probability of winning loans with a medium and high accepted rate, whereas the outside bank is only expected to make loans at the medium accepted rate. Therefore, if the inside bank makes at least as many loans as the outside bank, the accepted rate at the inside bank is higher than the accepted rate at the outside bank. Proposition 2 identifies a region of the parameter space where Ei(r) > Eo(r). In this region, the primitive parameters satisfy the sufficient condition that the probability of the inside bank winning the loan is at least as great as that of the outside bank. The condition as expressed in Eq. (5) is therefore derived from algebraic manipulation of Eqs. (1) and (2), which specify the respective probabilities of the inside and outside bank winning the loan. The full region of the parameter space in which Ei(r) > Eo(r) is larger than the region bounded by Eq. (5), but Proposition 2 offers a sufficient condition to illustrate where the model generates this counterintuitive result. Fig. 1 illustrates Proposition 2 in the parameter space (pH, pL, h). The curved surface marks the nonlinear boundary condition in Eq. (5). In the region to the right of this surface, the inside bank makes at least as many loans as the outside bank. Therefore, as stated in Proposition 2, the accepted interest rate at the inside bank is greater than the accepted rate at the outside bank (Ei(r) > Eo(r)) in this region of the parameter space to the right of the surface. The gray triangle at the base of the figure represents the parameter space in (pH, pL), which is triangular because pH > pL by definition. Based on this figure, it
Fig. 1. A region in the (pH, pL, h) parameter space where the accepted interest rate at the inside bank is greater than the accepted rate at the outside bank. The parameters pH and pL are the probability of success of high (H) and low (L) quality firms and h is the proportion of high quality firms. The nonlinear surface illustrates the condition of Eq. (5) in Proposition 2. The region to the right of the surface is where the inside bank makes at least as many loans as the outside bank. Therefore, as stated in Proposition 2, the accepted interest rate at the inside bank is greater than the outside bank (Ei(r) > Eo(r)) in this region of the parameter space to the right of the surface. The gray triangle at the base of the figure represents the parameter space in (pH, pL), which is triangular because pH > pL by definition.
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becomes clear that over the majority of the parameter space the accepted interest rate at the inside bank is greater than the accepted interest rate at the outside bank. This is also where the probability of the inside bank winning the loan is at least as great as that of the outside bank, which is consistent with empirical studies finding that lenders retain the majority of their borrowers (e.g., Black, 2010). Fig. 1 also emphasizes the degree to which the difference between the inside and outside accepted rates depends on h. This is especially true where pH is high and pL is low, because this is where the difference between the high and low quality firms is the greatest and private information matters the most. A significantly high or low h weights the distribution of firms toward the high or low quality firms, so the outside lender is not at too severe of an informational disadvantage. However, a value of h around 0.5 implies that the outside bank faces a severe winner’s curse and has a high probability of winning firms with a very low probability of repayment. Loosening the assumption that the inside bank wins all of the tie bids with the high accepted rate would increase the size of the region where the outside accepted rate is greater than the inside accepted rate. The assumption about how tie bids are allocated does not affect the equilibrium solution to the model given in Proposition 2, because it has no effect on the banks’ expected payoffs. Tie bids all occur at the high accepted rate, so a reallocation of these loans to the outside bank would increase the outside accepted rate and decrease the inside accepted rate.7 It is also important to consider the assumption about the profitability of lending to bad firms. If lending to bad firms were unprofitable, the inside bank would not lend to bad firms and the banks’ bidding functions would change due to the more severe ‘‘curse’’ for winning bad firms. The outside bank would have to bid less aggressively, which would likely increase the outside accepted rate relative to the inside rate. 3. Conclusion This paper analyzes the predictions of a benchmark model for insider versus outsider interest rates. The Sharpe (1990) model (with the von Thadden (2004) correction) is a standard framework for analyzing the role of private information in the competition between lenders. The results of this paper show that the model provides a surprising prediction for inside and outside interest rates. Due to the winner’s curse, the outside bank wins more bad firms and less good firms than the inside bank, which might suggest that the average interest rate paid to the outside bank is always higher than the average rate paid to the inside bank. The reasoning would be that outside banks win more bad firms, bad firms borrow at a higher rate, and, hence, the outside rate is higher. The interesting result of this paper is that the apparent intuition does not necessarily follow. Although the outside bank wins more bad firms than the inside bank, good and bad firms pay a lower rate at the outside bank because the inside bank extracts rents from good firms and the outside bank bids too low for bad firms. Combining this result with the effect of the winner’s curse on winning bids reveals that the model does not have a universal prediction for observed interest rates at an insider versus outsider. When the inside bank makes at least as many loans as the outside bank, the average interest rate paid to the inside bank is higher than the average interest rate paid to the outside bank. This is an important step forward in clarifying the predictions of a benchmark model for observed interest rates when firms borrow from inside versus outside lenders. The analysis contributes to a growing literature on competition between informed and uninformed lenders, such as relationship lending versus transaction-based lending and the switching of borrowers between lenders. More generally, the results shown here should help refine future work on observed price outcomes in markets with information asymmetries. Acknowledgments The views expressed do not necessarily reflect those of the Federal Reserve Board or its staff. I would like to thank Allen Berger, Ken Brevoort, Rochelle Edge, Eric Leeper, Robert Marquez, Richard 7 See Black (2008) for a solution of the model under the assumption that the inside and outside bank split the tie bids. The results under the split-tie assumption are illustrated in Fig. 1, which shows that the insider rate is still higher than the outsider rate in most of the parameter space.
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Rosen, Greg Udell, and Ernst-Ludwig von Thadden for helpful comments and discussions. All remaining errors are my own. References Black, L., 2008. Insider Rates vs. Outsider Rates in Lending. FEDS Working Paper 36. Board of Governors of the Federal Reserve System, pp. 1–23. Black, L., 2010. Firm Transparency and Outside Lending. Unpublished Working Paper. Board of Governors of the Federal Reserve System. Boot, A., Thakor, A., 2000. Can relationship banking survive competition? Journal of Finance 55, 679–713. Broecker, T., 1990. Credit-worthiness tests and interbank competition. Econometrica 58, 429–452. D’Auria, C., Foglia, A., Reedtz, P., 1999. Bank interest rates and credit relationships in Italy. Journal of Banking and Finance 23, 1067–1093. Degryse, H., Ongena, S., 2005. Distance, lending relationships, and competition. Journal of Finance 60, 231–266. Degryse, H., Van Cayseele, P., 2000. Relationship lending within a bank-based system: evidence from European small business data. Journal of Financial Intermediation 9, 90–109. Dell’Ariccia, G., Marquez, R., 2004. Information and bank credit allocation. Journal of Financial Economics 72, 185–214. Engelbrecht-Wiggans, R., Milgrom, P., Weber, R., 1983. Competitive bidding and proprietary information. Journal of Mathematical Economics 11, 161–169. Farinha, L., Santos, J., 2002. Switching from single to multiple bank lending relationships: determinants and implications. Journal of Financial Intermediation 11, 124–151. Gopalan, R., Udell, G., Yerramilli, V., 2011. Why do firms form new banking relationships? Journal of Financial and Quantitative Analysis 46, forthcoming. Hauswald, R., Marquez, R., 2006. Competition and strategic information acquisition in credit markets. Review of Financial Studies 19, 967–1000. Hendricks, K., Porter, R., 1988. An empirical study of an auction with asymmetric information. American Economic Review 78, 865–883. Ioannidou, V., Ongena, S., 2010. ‘‘Time for a change’’: loan conditions and bank behavior when firms switch banks. Journal of Finance 65, 1847–1877. Petersen, M., Rajan, R., 1994. The benefits of lending relationships. Journal of Finance 49, 3–37. Rajan, R., 1992. Insiders and outsiders: the choice between informed and arm’s-length debt. Journal of Finance 47, 1367–1400. Sharpe, S., 1990. Asymmetric information, bank lending and implicit contracts: a stylized model of customer relationships. Journal of Finance 45, 1069–1087. von Thadden, E.-L., 2004. Asymmetric information, bank lending and implicit contracts: the winner’s curse. Finance Research Letters 1, 11–23.