J. Finan. Intermediation

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1 J. Finan. Intermediation 18 (2009) Contents lists available at ScienceDirect J. Finan. Intermediation Lending relationships in the interbank market João F. Cocco a, Francisco J. Gomes a,,nunoc.martins b a London Business School, Regent s Park, London NW1 4SA, UK, and CEPR b Universidade Nova de Lisboa and Banco de Portugal, Av. Almirante Reis, 71, Lisboa, Portugal article info abstract Article history: Received 4 March 2007 Availableonline14August2008 JEL classification: G21 Keywords: Banking Liquidity Bank reserves Monitoring Insurance We use a unique dataset to show that relationships are an important determinant of banks ability to access interbank market liquidity. More precisely, we find that: (i) banks with a larger reserve imbalance are more likely to borrow funds from banks with whom they have a relationship, and to pay a lower interest rate than otherwise; (ii) smaller banks and banks with more nonperforming loans tend to have limited access to international markets, and rely more on relationships; (iii) relationships are established between banks with less correlated liquidity shocks. These results suggest that relationships allow banks to insure liquidity risk in the presence of market frictions such as transaction and information costs. Our analysis explicitly controls for the endogeneity of bank relationships Elsevier Inc. All rights reserved. 1. Introduction Many interactions between economic agents are of a frequent and repeated nature. In such a setting agents may establish relationships, and equilibrium outcomes may be different from those that arise in an anonymous market. In a recent paper, Carlin et al. (2007) solve a dynamic model of trading based on liquidity needs. They show that cooperation is an equilibrium outcome of the repeated-game model. Cooperation involves refraining from predation and allows the trader who has suffered a liquidity shock (the distressed trader) to transact at more favorable prices. Their model predicts that the level of cooperation is an important determinant of traders ability to access funds, and of the amount of liquidity available in the market. Our paper studies the role (if any) of relationships in the process of liquidity provision in the interbank market. The importance of interbank markets as distributors of liquidity is well recognized in * Corresponding author. addresses: jcocco@london.edu (J.F. Cocco), fgomes@london.edu (F.J. Gomes), nmartins@bportugal.pt (N.C. Martins) /$ see front matter 2008 Elsevier Inc. All rights reserved. doi: /j.jfi

2 J.F. Cocco et al. / J. Finan. Intermediation 18 (2009) the literature. Ho and Saunders (1985) examine a model in which banks reserve positions are affected by stochastic customers deposits and withdrawals; interbank trading allows them to meet their reserve requirements. In Bhattacharya and Gale (1987) interbank market trading also provides insurance against inter-temporal liquidity shocks. Similarly, in Allen and Gale (2000) liquidity shocks arise from uncertainty in the timing of depositors consumption, whereas in Freixas et al. (2000) liquidity risk arises from consumers uncertainty about where to consume. A common feature to these models is that a well functioning interbank market is important for banks ability to access liquidity, and as a result, it is important for firms and consumers ability to access bank financing, and ultimately for the efficiency of the financial system. The interbank market is a natural setting to study the question of whether relationships play a role in the process of liquidity provision. The interbank market is fragmented in nature. For direct loans, which account for most of the market volume, the loan s terms are agreed on a one-to-one basis between borrower and lender. Other banks do not have access to the same terms. When quotes are posted on screens, they are merely indicative. In addition, there are frequent and repeated interactions between the same banks. This market structure allows relationships to play an important role. 1 In order to study this question we use a unique dataset that contains information on all direct loans that took place in the Portuguese interbank market between January 1997 and August The Portuguese market is smaller than the Fed Funds and most Euro area interbank markets, but its market structure is similar to that of these larger markets. Our dataset contains comprehensive information on each loan (date, amount, interest rate, maturity, and identity of lender and borrower). These data allow us to track loans between each and every pair of banks over time, information that we use to construct dynamic measures of relationships, based on the intensity of pair-wise lending activity. Our data also include daily information on banks reserve deposits, and quarterly information on balance sheet variables such as total assets and non-performing loans. Finally, we also observe all financial flows between banks, other than interbank market loans, which we use to construct a measure of other interactions that take place between them. Our results support the prediction that bank relationships are an important determinant of their ability to access funds, and of the amount of liquidity available in the market. First, we find that banks with a larger imbalance in their reserve deposits are more likely to borrow funds from banks with whom they have a relationship, and to pay a lower interest rate on these loans than they would otherwise. This result supports the prediction of Carlin et al. s (2007) model that under repeated interaction, cooperation among banks is an equilibrium outcome that involves refraining from predation, and that allows those with a larger reserve imbalance to transact at more favorable prices. Second, we find that small banks and banks with a higher proportion of non-performing loans tend to have limited access to international markets, and that they tend to rely more on relationships when borrowing funds in the domestic interbank market. This result is consistent with relationships allowing banks to access liquidity in the presence of market frictions, such as transaction and information costs. It provides support for the assumption of Freixas and Holthausen s (2005) model that information on foreign banks is coarser that on domestic peers, with whom inter-bank market relationships may have developed over a longer time period. We find evidence that these relationships are likely to extend beyond the interbank market. More precisely, we show that the relationship measure constructed using interbank market data is positively correlated with a measure of other relationships constructed using data on other financial flows. Third, we use the information on each bank s reserve deposits to construct a measure of liquidity shocks which is equal to the daily change in these deposits. We find that banks with more volatile liquidity shocks are more likely to rely on relationships, and they tend to do so with banks which face less volatile liquidity shocks. Furthermore, we find that banks establish relationships with those banks with whom they have a lower correlation of liquidity shocks, which may further enhance the liquidity of the overall market. This is an important finding since Allen and Gale s (2000) model predicts that 1 The issue of price formation and the properties of prices in centralized versus fragmented markets has been the subject of much research (see for example Wolinsky, 1990 or Biais, 1993).

3 26 J.F. Cocco et al. / J. Finan. Intermediation 18 (2009) the financial system is less fragile when the correlation of liquidity shocks between banks that are related is lower. Overall, our results support the prediction that relationships play an important role in the process of liquidity provision in the interbank market. The potential for these relationships to develop is an important advantage of bilateral markets relative to anonymous ones. This may help to explain why the interbank market seems to function well, even in periods of financial crisis (Furfine, 2002). In addition, our results provide support for the notion that it is important to take into account offbalance sheet variables (in our case, relationships), when evaluating the ability of banks to cope with liquidity risk. Our analysis of the interbank market also uncovers a variety of patterns of trade that is consistent with evidence for the Fed Funds market. We find that large banks tend to be net borrowers, while small banks tend to be net lenders in the market (see Furfine, 1999; Ho and Saunders, 1985, for evidence on the Fed Funds market). We find that, controlling for the degree of lending relationship and holding the size of the counterparty fixed, larger banks trade at more favorable rates. In addition, borrowers with a higher proportion of non-performing loans tend to pay higher interest rates (Furfine, 2001). On the methodological side, our analysis recognizes that the decision of whether to rely on relationships is an endogenous choice. We estimate instrumental variables regressions, in which we explore the time-series dimension of the panel by using lagged relationship measures as instruments, and a seemingly unrelated regressions system of equations, with the loan characteristics and the relationship measures as dependent variables. This allows us to simultaneously study the determinants of the terms of the loan and of relationships. Our paper is related to the previously cited literature on the interbank market. There is also a literature on lending relationships that focuses on bank firm relationships. 2 This literature focuses on long-term relationships between banks and firms, by which banks acquire inside knowledge about firm characteristics or the project that is being financed. Although somewhat related, it is important to note that these relationships are of a different nature than the ones that we study in our paper, which are transaction based. Our paper is also related to the papers which show that more regular customers tend to receive better allocations or prices when buying shares, both in primary markets (Cornelli and Goldreich, 2005) and secondary markets (Bernhardt et al., 2004). Although related, our paper differs from these in that it emphasizes the role of relationships in the process of liquidity provision. In this respect, our paper is closer to Battalio et al. (2005). The paper proceeds as follows. Section 2 describes the data, our relationship metrics and reports summary statistics. Section 3 studies the pricing of interbank loans. Section 4 investigates the determinants of relationships. Section 5 presents additional evidence on these determinants, that allows us to be more precise with respect to their nature. Section 6 concludes. 2. The data 2.1. Description We combine information from three different datasets, which we have obtained from the Portuguese Central Bank. The first dataset has information on all direct loans in the Portuguese interbank market from January 1997 to August This market has a similar structure to other interbank markets in the Euro area, and to the Fed Funds market. Each loan may be either borrower or lender initiated. When a bank wishes to borrow or lend funds, it approaches another bank, identifies itself, and asks for prices, i.e. interest rates, for borrowing and lending funds at a given maturity. It is very rare that banks asking for quotes are turned down, or simply refused funds. But banks do provide 2 This literature has found evidence that relationships help overcome constraints that arise from monitoring and default risk (Berger and Udell, 1995; Petersen and Rajan, 1995; Slovin et al., 1993), and they allow banks to provide insurance to firms in the form of interest-rate smoothing (Ongena and Smith, 2000; Berlin and Mester, 1999; Petersen and Rajan, 1995; Berger and Udell, 1992).

4 J.F. Cocco et al. / J. Finan. Intermediation 18 (2009) different quotes for different banks that approach them, and it is common practice for them to shop around for the best rates. Our dataset is unique in that it comprises all direct loans, and contains information on the loan s date, amount, interest rate, and maturity, as well as the identity of the lender and the borrower. Being able to identify the lender and borrower for each loan, and to observe all loans over a long period of time, is crucial for our study of lending relationships. Even though interbank loans are privately negotiated, they must be reported to the central bank, who is responsible for their settlement, by debiting and crediting the reserve accounts of borrowers and lenders. We restrict our analysis to overnight loans, i.e. loans maturing on the next business day. We do so because the interbank market is mainly a market for short-term borrowing and lending of funds: during there sample period there were 44,768 overnight loans accounting for over 75 percent of the total amount lent. And the vast majority of the remaining loans are also short term in nature: over the sample period there were only 2145 (303) loans with maturity longer than one month (six months). If we were to include these loans in the analysis together with the overnight loans, and given that such loans are very infrequent, it would be very difficult to calculate a valid benchmark or market wide interest rate. This is why we have decided to exclude such transactions from the sample, and to focus the analysis on the overnight loans. One could question the appropriateness of measuring a long-term economic behavior relationships with something that is short-term in nature overnight loans. However, we would like to note that even though the focus of the analysis are overnight loans, over the sample period there are frequent and repeated loans between the same banks. One may expect that under such circumstances relationships may be formed. Furthermore, we will present evidence that relationships based on overnight loans are part of wider relationship between banks. Finally, even though credit risk for loans of overnight maturity may be small, it is important to note that these are large and uncollateralized loans, with the average loan amount of roughly twelve million euros. Therefore we expect that even small differences across banks in credit risk are reflected on the loan interest rate. The second dataset provides daily information on the balance in the banks reserve accounts. It allows us to study how the banks reserve position affects their behavior in the interbank market. The third dataset contains quarterly information on bank characteristics, including total assets, financial and profitability ratios, and credit risk variables. This dataset also allows us to determine whether the bank belongs to a banking group, defined in terms of control of the institution. We exclude loans between banks belonging to the same group, which leaves us with a total of 37,701 overnight loans Measuring lending relationships We measure lending relationships by the intensity of lending activity between banks. More precisely, for every lender (L) and every borrower (B), we compute a lender preference index (LPI), equal to the ratio of total funds that L has lent to B during a given year/quarter, over the total amount of funds that L has lent in the interbank market during that same year/quarter. Thus each time period, t, in our analysis is a year/quarter. Overall there are nineteen time periods during our sample period. 3 Let F j k denote the amount lent by bank j to bank k on loan i then: i LPI L,B,t = i t F L B i / F L all i i t (1) where t denotes time period. This ratio is more likely to be high if L relies on B more than on other banks to lend funds in the market. 3 We discuss our choice of time period in detail below. Since our data is from January 1997 until August 2001, there are 18 quarters and 2 months. We had the option of dropping the last two months or grouping them into one (smaller) quarter. We chose the second option so as to increase our sample size.

5 28 J.F. Cocco et al. / J. Finan. Intermediation 18 (2009) Note. This figure plots, on a given quarter q, the BPI% indices for a given bank B and all its lenders. The BPI% index for bank B and each borrower j is equal to the ratio of total funds that bank B has borrowed from bank j, as a fraction of the total amount of funds that he has borrowed in the market, during the quarter. Lenders for whom the BPI% is zero were omitted from the figure. Fig. 1. Borrower preference indices for a given bank at a specific quarter. Similarly, we compute a borrower preference index (BPI) as the ratio of total funds that B has borrowed from L in a given time period, as a fraction of the total amount of funds that B has borrowed in the market in that same period: BPI L,B,t = i t F L B i / F any B. (2) i i t Fig. 1 plots, for a given quarter, and for a given borrower, its BPI indices with different lenders. The most important lender for this borrower during this quarter is the bank labeled as lender one, from whom it borrowed roughly 25% of the total funds that it borrowed during the quarter. This figure illustrates that, in our data, there are asymmetries in financing, with some lenders being much more important than others. As an illustrative example of the time-series dimension of our relationship measures, Fig. 2 plots the evolution of the LPI and BPI indices for a pair of banks in our sample, L and B. This time-series dimension of our data is also important because it will allow us to deal with the issue of the endogeneity of lending relationships. More precisely, we will be able to use lagged relationship measures as (exogenous) instruments. Fig. 2 also illustrates that there is time variation in our relationship measures. In our regressions the explanatory power comes both from cross-sectional differences across banks, as well as changes over time in bank characteristics. We have chosen the calendar quarter to measure lending relationships. To some extent this choice is arbitrary. A lending relationship should be fairly stable over time, but not immutable through time. In addition, there is a practical reason to choose the calendar quarter as unit of analysis, since some of our bank data is quarterly, namely information about the banks assets, profitability and credit risk. In Section 5.5 we show that the results are robust to alternative ways of measuring relationships Interest rate measure In most interbank markets the central bank sets a target rate. For this reason we focus on explaining the difference between the interest rate on a given loan and the average interest rate on overnight loans. We proceed as follows. First for a loan from bank L to bank B on day d, wecalculatethedifference between the interest rate (i L,B,d ) and the average (market-wide) overnight interest rate on the

6 J.F. Cocco et al. / J. Finan. Intermediation 18 (2009) Note. This figure plots the evolution over time of the BPI and LPI indices for a pair of banks in our sample, B and L. Foreach quarter, the BPI index is equal to the ratio of total funds that bank B has borrowed from bank L, as a fraction of the total amount of funds that he has borrowed in the market during the quarter. Similarly, LPI index is equal to the ratio of total funds that bank L has lent to bank B, as a fraction of the total amount of funds that he has lent in the market, during the quarter. Fig. 2. Borrower s preference index and lender s preference index for a pair of banks. same day (i d ), divided by the standard deviation of overnight interest rates for that day (σ i ). This is to d account for the well-documented GARCH effects in interbank market interest rates (Hamilton, 1996). Since our unit of observation is year/quarter, we then obtain the average interest rate difference for all loans from bank L to bank B during time period t, witht = 1,...,19, as: i t L,B = 1 (i L,B,d i d )/σ i d (3) T t d t where T t denotes the number of trading days in period t. 4 It is important to note that the average market-wide interest rate shown in (3) is the endogenous result of the market-wide bank relationships that exist. Therefore, one can not interpret it as a measure of the market-wide interest rate that would prevail if there were no relationships. Our paper allows us to address the question of whether banks that use relationships to borrow (lend) do so at rates that are higher (lower) than the average market-wide interest rate, conditional on the average level of relationships that exist in the market. In other words, our analysis allows us to identify the value of using a relationship in a given loan, but conditional on the average level of relationships that exist in the market. If all loans in the market were carried out in the absence of relationships 4 The exact formula is slightly more complicated, since we must account for the possibility of more than one loan between the same pair of banks on a given day. If we let index j denote different loans between the same pair of banks on a given day, the exact formula is: i t B,L = 1 1 (i L,B,d, j i d )/σ i d T t J L,B,d d t j where J L,B,d denotes the number of loans from L to B on day d.

7 30 J.F. Cocco et al. / J. Finan. Intermediation 18 (2009) the market-wide interest rate would change and our results are not informative about what would happen Other variables In this section we describe the variables that we use to explain the interest rate and lending relationships. The first set of variables that we include are bank size (measured by total assets), quarterly return on assets, and the proportion of non-performing loans (NPL). The latter is defined as loans that are past-due for a period exceeding 90 days, over the total outstanding credit granted by the bank. Several papers have shown that these variables matter for the pricing of Fed Fund loans (Allen and Saunders, 1986; Furfine, 2001, among others). These variables may also constitute important determinants of relationships. Several papers in the interbank market literature model agency problems that arise from asymmetric information between borrowers and lenders of funds, which monitoring may help to overcome (Rochet and Tirole, 1996). 5 The asymmetries of information may be larger, and monitoring may be more important when banks are smaller, profitability is lower, or credit risk (as measured by the proportion of non-performing loans) is higher. It is conceivable that this monitoring also takes place outside of the interbank market. After all, banks undertake many kinds of transactions with each other, of which interbank overnight loans are just one. In Section 5 we construct a measure of interactions between banks that take place outside of the interbank market, to explore this possibility further. Banks face liquidity risk that arises from the behavior of retail depositors (Ho and Saunders, 1985; Bhattacharya and Gale, 1987; and Freixas et al., 2000). Lending relationships may help banks to insure against such liquidity risk. For example, the model of Carlin et al. (2007) predicts that relationships allow traders who have suffered a liquidity shock (the distressed traders) to transact at more favorable prices. In order to test this prediction we need to obtain a measure of distress. A natural measure can be constructed from the fact that banks are required to satisfy minimum reserve requirements. Over a given reserve maintenance period (or settlement period) a given bank s average reserves must not fall below a given proportion of its short-term liabilities (mostly customer deposits). 6 If relationships allow banks which have suffered a liquidity shock to transact at more favorable prices, we would expect that, banks who have a higher shortage of funds in their reserve account, would borrow funds from banks with whom they have a relationship, and through this pay a lower interest rate than they would otherwise. To investigate this prediction we construct a proxy for each bank s reserve requirements, equal to the average of the daily deposits in the bank s reserve account over the reserve maintenance period. We then measure surplus deposits for bank i on day d (SD id ) as the ratio between the current average level of deposits in the reserve account (since the start of the current reserve requirement period) and our proxy for reserve requirements. 7 We calculate the average value of this variable over each time period, for those days in which the bank intervened in the interbank market. To investigate further the extent to which bank relationships provide insurance against liquidity risk, we construct a measure of such risk. First, we measure liquidity shocks by the daily change in the bank s reserve deposits, that is not due to interbank market loans. For each bank and year/quarter, liquidity risk is measured by the standard deviation of liquidity shocks, divided by the bank s average 5 Broecker (1990), Flannery (1996), and Freixas and Holthausen (2005) also solve models of the interbank market with asymmetric information and credit risk. Freixas and Holthausen (2005) solve such a model in an international setting, when cross-country information is noisy. 6 Campbell (1987), Hamilton (1996), Hartmann et al. (2001), andspindt and Hoffmeister (1988) have noticed how shortages of liquidity at the end of the maintenance period often lead to special behavior of overnight rates during those days. 7 The formula for surplus deposits is: SD id = s {m(d): s d} Deposit is/n d s m(d) Deposit is/n (4) where m(d) refers to the days in the same reserve maintenance period as day d, andn d and n are the up to d and the total number of days in the maintenance period, respectively.

8 J.F. Cocco et al. / J. Finan. Intermediation 18 (2009) Table 1 Summary statistics Variable Mean Stdev Median 25th perc. 75th perc. Interbank market Market amount (million Euros) 27, ,888 24,250 29,444 Market number of loans (million Euros) Number of borrowers Number of lenders Borrower characteristics Assets (million Euros) ROA (percent) Non-performing loans (percent) Amount (million Euros) Number of loans Surplus deposits Coef. variation shocks Lender characteristics Assets (million Euros) ROA (percent) Non-performing loans (percent) Amount (million Euros) Number of loans Surplus deposits Coef. variation shocks Borrower/lender characteristics Borrower preference index: BPI (percent) Lender preference index: LPI (percent) Correlation of shocks (percent) Notes. This table reports summary statistics for overnight loans and main characteristics of borrowers and lenders in the Portuguese Interbank market. The sample period is January 1997 to August The variables are defined in Appendix A. reserves (we denote this variable by CV). We expect banks that face more liquidity risk to rely more on relationships. An important parameter in Allen and Gale s 2000 model is the correlation of liquidity shocks between banks that are related. When this correlation is lower, it implies that when borrowing banks need funds lending banks are more likely to have a surplus of funds. Allen and Gale (2000) show that the larger this correlation is, the more fragile is the financial system. Therefore, we calculate the correlation between each two banks liquidity shocks, and we use this variable to explain the determinants of relationships (we denote this variable θ L,B, where L and B identify the borrower and lender) Summary statistics Table 1 reports summary statistics. The first panel shows information on the Portuguese interbank market. The average total amount lent in each quarter is 27,123 million euros, with an average 2217 loans. Thus, the average loan amount is roughly twelve million euros. The average number of different borrowers (lenders) in each quarter is 37 (39). The next two panels of Table 1 report summary statistics for borrowing and lending banks. On average borrowing banks are larger (as measured by total assets), have a higher ROA, and a smaller proportion of NPL than lending banks. This is consistent with borrowing banks having better investment opportunities than lending banks, which explains why they show up as borrowers in the market. Table 1 also reports information on the total amount and the number of loans made and received by each bank in the interbank market during the quarter. On average each bor-

9 32 J.F. Cocco et al. / J. Finan. Intermediation 18 (2009) rower receives 751 million Euros in 61 loans, while each lender loans out 712 million Euros in 58 loans. 8 Table 1 s last panel shows summary statistics for the relationship metrics, and for the correlation of shocks. The average BPI is 7.94 percent, and the average LPI is 8.39 percent. These averages are significantly higher than the median values (3 and 4 percent respectively), a sign of a skewed distribution. That is, banks borrow/lend relatively little from most banks, but large amounts from a few of them. Our interest rate measure is the difference between the loan interest rate and the average overnight interest rate, so that on average it is zero. But some numbers are helpful for understanding interest rate cross-sectional variability in our sample. The standard deviation of interest rates on a given day is on average 8 basis points. Moreover, this is naturally a strongly skewed distribution. While the median standard deviation is 6 basis points, in ten percent of the days the standard deviation of interest rates is higher than 18 basis points. We have calculated several summary statistics that allow us to understand by how much the interest rate vary across lenders/borrowers. On average the interest rate is 43 basis points higher for small than for large borrowers, and it is 39 basis points higher for large than for small lenders (small (large) are those banks in the bottom (top) one-third of the total assets distribution). 9 Interestratesalsotendtovarywithreturnonassets:onaveragethe interest rate is 17 basis points higher for borrowers with a low return on assets (bottom one third) than with a high return on assets (top one third). 3. Pricing of interbank loans 3.1. Baseline regressions We investigate the determinants of the interest rate on interbank market loans. We do so using a regression analysis. An alternative approach would have been to use a matching methodology, in which we would matched banks according to size and other bank characteristics. The matching approach could offer some advantages relative to regression analysis, in that we might have a more appropriate choice for the benchmark interest rate. However, we have decided to use regression analysis since it has several advantages relative to the matching methodology. First, it allows us to simultaneously establish different benchmarks depending on multiple bank characteristics (e.g. bank size, percentage of non-performing loans, profitability), without significantly decreasing cell size, which would happen if we performed matches along several bank characteristics. Second, it allows us to estimate the impact of different bank characteristics (size, profitability, etc.) on the loan interest rate, within the context of a single regression. We first estimate the unconditional correlation between the relationship metrics and the loan interest rate defined in Section 2.3: i t L,B = α + γ BPIt L,B + κlpit L,B + βt D t + u t L,B (5) where t indexes time, D t are time dummies, the subscripts L and B refer to lending and borrowing bank, respectively, and u t L,B is the residual. Column (i) of Table 2 shows the estimation results. These results appear to suggest that borrowers (lenders) tend to pay (receive) higher (lower) interest rates on loans with banks with whom they have higher relationship indices. We will show that the reason for this result is that the decision of whether to rely on lending relationships is endogenous, and correlated with bank characteristics that also affect the interest rate on the loan. With this in mind we include size, ROA and NPL as additional independent variables. The regression that we estimate is then: i t L,B = α + [ β1 j Size t j + β 2 jroa t j + β 3 jnpl j] t + γ BPI t L,B + κlpit L,B + βt D t + u t L,B. (6) j=l,b 8 The average amount and number of loans for borrowing and lending banks are not exactly equal because there is a different number of borrowing and lending banks in the market. 9 ThesenumbersareverysimilartotheonesreportedbyFurfine (2001) for the FED Funds Market.

10 J.F. Cocco et al. / J. Finan. Intermediation 18 (2009) Table 2 Multivariate model for interest rate Independent variables (i) (ii) (iii) (iv) (v) (vi) Fixed effects Borrower characteristics Log assets *** *** *** *** (13.43) (12.98) (8.72) (3.96) Market share *** *** (9.80) (2.25) ROA * * (1.84) (1.85) (0.48) (1.65) (0.04) Non-performing loans *** *** *** *** (2.67) (2.72) (3.12) (2.70) (0.02) Surplus deposits ** * ** *** (2.21) (1.85) (2.09) (4.19) Coef. variation (0.26) (0.30) (0.04) (0.55) Lender characteristics Log assets *** *** *** *** (15.25) (14.98) (13.02) (4.89) Market share *** (8.29) (0.56) ROA *** (0.54) (0.44) (3.69) (0.47) (0.74) Non-performing loans * (1.66) (1.45) (1.19) (1.44) (0.78) Surplus deposits (1.18) 0.95 (1.11) (0.97) Coef. variation *** *** *** *** (10.53) (3.89) (9.61) (8.92) Borrower/lender characteristics Correlation of shocks (0.06) (0.05) (0.09) (0.26) Borrower pref. index *** *** *** *** *** *** (4.18) (2.71) (2.85) (2.00) (2.83) (3.60) Lender pref. index *** *** *** *** *** *** (3.15) (3.44) (4.78) (5.25) (4.97) (4.44) Number obs R Notes. The dependent variable is interest rate defined for every pair of lender and borrower as the quarterly average of the difference between the interest rate on the loans between those two banks and the market interest rate on the same days, divided by the standard deviation of interest rates for the day. The independent variables are defined in Appendix A, andthey include time fixed effects. Column (vi) shows the estimation results including bank fixed effects in addition to the time fixed effects. The sample period is January 1997 to August Robust t-statisticsareshowninparenthesis. * Significance at the 10% level. ** Idem, 5%. *** Idem, 1%. As a size measure we use the logarithm of total assets. Column (ii) of Table 2 shows the estimation results. Interestingly, when we include the logarithm of total assets, ROA, and NPL as independent variables, the estimated coefficients on the relationship variables revert sign. Thus lenders receive higher interest rates on loans to borrowers with whom they have a lending relationship, and borrowers pay lower interest rates on loans from banks with whom they have a lending relationship. This result is the opposite of the unconditional results. The estimated coefficients change signs since the relationship measures are correlated with these bank characteristics that also affect the loan interest rate. The signs of the estimated coefficients of the size variables, positive for lenders and negative for borrowers, show that in the market larger banks receive better interest rates, whichever side of the market they are in. This is consistent with the evidence for the Fed Funds market (Allen and Saunders,

11 34 J.F. Cocco et al. / J. Finan. Intermediation 18 (2009) ; Stigum, 1990; Furfine, 2001). The estimated positive coefficient on the ROA of borrowers is intuitive: borrowers with a higher ROA have a more profitable application for the funds, and thus are willing to pay a higher interest rate for borrowing them. As expected we find that borrowers with a higher proportion of NPL tend to pay higher interest rates on interbank market loans, a result which is statistically significant at the one percent level. The estimated coefficients on ROA and NPL of lenders are not statistically significant, at least when we include as independent variables those that capture liquidity risk (column (iii)). The equation that we estimate is now: i t L,B = α + [ β1 j Size t j + β 2 jroa t j + β 3 jnpl t j + β 4 jsd t j + β 5 jcv j] t j=l,b + β 6 θ L,B + γ BPI t L,B + κlpit L,B + βt D t + u t L,B (7) where SD denotes surplus deposits, or the net reserve position of borrowers and lenders when they borrow or lend funds in the market, CV denotes the coefficient of variation of liquidity shocks, and θ L,B denotes the correlation of liquidity shocks between lender and borrower of funds. The results in column (iii) of Table 2 show that borrowers with a lower surplus deposit pay on average a higher interest rate on their loans. The magnitude of the coefficient is economically significant: an increase in the shortage of funds from the 25th to the 75th percentile leads to a 13 basis point increase in the loan interest rate. However, if this change is accompanied by an increase in the BPI index from the 25th to the 75th percentile, then the increase in the interest rate is only 7 basis points. Thus relationships seem to allow borrowers with a larger reserve imbalance to transact at more favorable rates. The estimated coefficient on the surplus deposits of lenders is not statistically significant. What seems to matter for lenders is the volatility of liquidity shocks: the larger the volatility the lower is the interest rate that lenders receive on interbank market loans. The estimated coefficient on θ L,B is not significantly different from zero. In columns (iv) and (v) we investigate why larger banks receive better rates. The fact that borrowers size matters is intuitive and could be due to better information being available for larger banks, or to larger banks being too-big-to-fail. However, the reason why larger lenders receive better rates is less clear. A possible explanation may be that larger banks have more bargaining power (Osborne and Rubinstein, 1994). In order to investigate this explanation, we have calculated market shares for borrowers and lenders. Market shares are positively correlated with bank size, as measured by the logarithm of total assets, with coefficients of correlation equal to 0.59 (0.74) for lenders (borrowers). When we include market shares as explanatory variables for the loan interest rate we find that lenders/borrowers with larger market shares receive better rates (column (iv)). When in column (v) we include both market shares and the logarithm of total assets as independent variables we find that the explanatory power of both variables is diminished, reflecting the fact that they are co-linear. One may be concerned that our results on the impact of the relationship measures on interest rates are driven by unobserved bank heterogeneity. In order to address this concern, the last column of Table 2 shows the estimation results when we include bank fixed effects among the set of explanatory variables. Comparing these results with those in column (iii) of the same table, two conclusions can be drawn. First, some of the variables that we use to capture the effects of borrower characteristics on the loan interest rate are no longer significant. This tells us that these variables were previously significant due of cross sectional differences in bank characteristics, which are now captured by the fixed effects. Second, and importantly, we find that the effects of the relationship measures on the loan interest rate are robust to the introduction of bank fixed effects. More precisely, the estimated coefficients on the BPI and LPI indices are still negative and positive, respectively, and statistically significant. It is important to clarify that we do not find that small banks that lend funds in the interbank charge higher interest rates. In fact, we find exactly the opposite. The estimated positive coefficients on log assets for lender characteristics in the second panel of Table 2 shows that larger (smaller) banks receive a higher (lower) interest rate when lending funds in the market. These results hold across all specifications. Therefore we find that: (i) small banks are net lenders in the market but, within all lenders, small banks receive lower interest rates than large banks on the funds that they lend; (ii) large banks are net borrowers in the market but, within all borrowers, large banks pay lower

12 J.F. Cocco et al. / J. Finan. Intermediation 18 (2009) interest rates than small banks on the funds that they borrow. With respect to lending relationships, the results in Table 2 show that, both smaller and larger banks receive better terms both when borrowing and when lending (pay a lower interest rate when borrowing and receive a higher interest rate when lending) when they interact with banks with whom they have high relationship indices Instrumental variables In order to address the issue of the endogeneity of relationships we estimate Eq. (7) using instrumental variables (IV). This allows us to identify the causal link between the relationship measures and the loan interest rate. This is a departure from most of the existing literature on lending relationships, which does not address the endogeneity of those relationships. The validity of the IV approach depends crucially on the quality of the instruments used in the first stage regression. Good instruments include those which are simultaneously pre-determined and highly correlated with the relationship metrics. Therefore, we explore the time-series dimension of our data set, and use the lagged relationship measures as instruments. Obviously, such instruments are not available in cross sectional data, which is typically used in the existing literature on lending relationships. The quality of these instruments can be measured by the R-squared of the first-stage regressions: for the BPI (LPI) measure it is equal to 67% (78%). 10 The estimation results for the second stage regressions are shown in the column (i) of Table 3. The t-statistics (reported below the estimated coefficients) have been adjusted for first-stage estimation error. We compare the results in column (i) of Table 3 to those in column (iii) of Table 2, in which we did not use instruments for the relationship metrics. First, the coefficients on total assets and non-performing loans remain essentially unchanged. Second, the estimated coefficient on the surplus deposit of borrowers is no longer significant, and the estimated coefficient on the coefficient of variation of lenders is only significant in (ii). Thus the level of significance of the insurance variables is reduced once we control for the endogeneity of relationships. This suggests that relationships are important because they allow banks to obtain insurance in the interbank market. In the next section we will explicitly study the determinants of lending relationships. Third, the estimated coefficients on the relationship variables are significant throughout, and have the same signs. Moreover, the magnitude of the estimated coefficients is either unchanged or even slightly increased (in absolute value). This result implies that, at least in our dataset, the endogeneity problem does not affect the inference regarding the causal link between lending relationships and interest rates. Of course, one should be careful about generalizing this result to other applications, since we have only shown that it holds in our data. Furthermore, and even though the estimated coefficients on the relationship metrics are robust to an IV approach, the inference on the coefficients of some of the insurance variables changes. If these are only control variables, then this is not an issue. However, if one is interested in the economic interpretation of those coefficients, then controlling for endogeneity is important. In column (ii) of Table 3 we report the results of estimating Eq. (7) using instrumental variables, but including bank fixed effects among the set of explanatory variables. As it was the case in Table 2, we see that the effects of the relationship metrics on the loan interest rate are robust to the inclusion of bank fixed effects. The use of lagged relationship indices as instruments raises some concerns in the presence of measurement error. In that case, even though the true dependent variable and consequently the residual of a hypothetical true regression would only be measurable at time t, the observed value of dependent variable would have a component that is measurable at time t 1. This would create serial correlation in the regression residual and lead to inconsistent estimators. However, our data is unlikely to be affected by measurement error in any significant way: we observe the variables directly from central bank data, including the terms of the loan which must be reported separately by borrower and lender to the central bank, which in turn is responsible for the settlement of the loan. 10 We have also estimated the IV regressions using the first lag of all the explanatory variables in Eq. (7) as instruments in the first-state regression. The first stage R 2 was almost unaffected, and the second stage results were the same and are therefore not reported.

13 36 J.F. Cocco et al. / J. Finan. Intermediation 18 (2009) Table 3 Multivariate model for interest rate: instrumental variables Independent variables (i) IV (ii) IV fixed effects (iii) Arellano Bond Borrower characteristics Log assets *** *** (10.16) (3.89) (0.99) ROA (0.95) (0.76) (0.60) Non-performing loans ** (2.12) (0.27) (0.67) Surplus deposits *** (0.98) (3.13) (1.54) Coef. variation (0.70) (0.45) (0.49) Lender characteristics Log assets *** *** (11.89) (3.99) (0.12) ROA (0.05) (1.29) (1.20) Non-performing loans (0.86) (0.24) (0.04) Surplus deposits *** (0.54) (0.02) (2.78) Coef. variation (0.32) (0.80) (1.62) Borrower/lender characteristics Correlation of shocks (0.25) (0.24) (0.90) Borrower pref. index * *** * (1.77) (2.79) (1.90) Lender pref. index *** *** *** (2.72) (3.41) (2.94) Lagged bor. pref. index * (1.90) Lagged lend. pref. index *** (2.34) Lagged dependent variable *** (4.18) Number obs R Notes. The dependent variable is interest rate defined for every pair of lender and borrower as the quarterly average of the difference between the interest rate on the loans between those two banks and the market interest rate on the same days, divided by the standard deviation of interest rates for the day. The independent variables are defined in Appendix A, and they include time fixed effects. Column (i) shows the estimation results for instrumental variables regressions. We use BPI t 1 L,B and LPIt 1 L,B as instruments for BPI t L,B and LPIt L,B, respectively. Column (ii) shows the estimation results for instrumental variables regressions in which we include bank fixed effects among the set of explanatory variables. Column (iii) shows the estimation results using the Arellano Bond (1991) dynamic panel data estimator. The lagged borrower and lender preference indices are treated as predetermined variables. The sample period is January 1997 to August Robust t-statistics are shown in parenthesis. * Significance at the 10% level. ** Idem, 5%. *** Idem, 1%. In spite of the fact that our data is unlikely to be affected by measurement error, we use the Arellano and Bond (1991) dynamic panel data estimator to investigate the effects of the relationship variables on the loan interest rate. The estimation results are shown in column (iii) of Table 3. These results show that the effects of the relationship indices on the loan interest rate, negative for borrowers and positive for lenders, are robust to the use of the Arellano Bond estimator.

14 J.F. Cocco et al. / J. Finan. Intermediation 18 (2009) The determinants of lending relationships The instrumental variables regressions that we have estimated in the previous section allow us to estimate the effects of lending relationships on the loan interest rate, but they do not explain the determinants of lending relationships. In this section we investigate which bank characteristics explain the decision of whether or not to rely on lending relationships. We do so in a setting in which we allow both the loan amount and interest rate to be correlated with the identity of the borrowing and lending banks (i.e. on whether they have a lending relationship). More precisely, we estimate a seemingly unrelated regressions (SUR) system of equations, with the amount lent, interest rate, and the relationship measures between lender and borrower (LPI and BPI) as our endogenous dependent variables. Thus, we estimate simultaneously the following equations: i t L,B = α1 + [ β 1 1 j Sizet j + β1 2 j ROAt j + β1 3 j NPLt j + β1 4 j SDt j + ] β1 5 j CVt j j=l,b + β 1 6 θ B,L + β t1 D t1 + u t L,B, (8) BPI t L,B = α2 + [ β 2 1 j Sizet j + β2 2 j ROAt j + β2 3 j NPLt j + β2 4 j SDt j + ] β2 5 j CVt j j=l,b + β 2 6 θ B,L + β t2 D t2 + ε t L,B, (9) LPI t L,B = α3 + [ β 3 1 j Sizet j + β3 2 j ROAt j + β3 3 j NPLt j + β3 4 j SDt j + ] β3 5 j CVt j j=l,b + β 3 6 θ B,L + β t3 D t3 + ξ t L,B, (10) ( ) Ln V t L,B = α 4 + [ β 4 1 j Sizet j + β4 2 j ROAt j + β4 3 j NPLt j + β4 4 j SDt j + ] β4 5 j CVt j j=l,b + β 4 6 θ B,L + β t4 D t4 + v t L,B (11) where V t L,B is the total amount of funds lent by bank L to bank B during time period t, and Ln denotes logarithm. We estimate a reduced form system, and therefore allow for contemporaneous correlation across the four different innovations (u, ε, ξ and v). We include time dummies in all equations BPIandLPIequations Table 4 shows the estimation results. The results for the BPI equation are shown in the second column. In this equation we try to determine which borrower and lender characteristics explain the variation in BPI indices. In other words, who are the borrowers who have higher relationship indices, and who are the lenders with whom they have those higher indices. For instance, the negative estimated coefficient on the logarithm of total assets of borrowers shows that small borrowers rely more on lending relationships. On the other hand, the estimated positive coefficient on the total assets of lenders in the same equation, implies that small borrowers tend to have large banks as their preferred lenders. These results suggest a dichotomy between large and small banks in the market, an issue that we explore further in Section 5.1. Interestingly, we find that borrowers with higher default risk are more likely to rely on lending relationships (the estimated coefficient on NPL in the BPI equation is positive) and to pay higher interest rates (the estimated coefficient on NPL in the interest rate equation is also positive). From these two results one may reasonably expect that banks which borrow funds from banks with whom they have a lending relationship pay higher rates. This may seem inconsistent with the result in Table 2 that loan rates tend to be lower for banks borrowing from lenders with whom they have large relationship indices. The key to understanding this apparent inconsistency is to note that in Table 2 we did not find that unconditionally borrowers with a high default risk and large BPI indices pay lower interest rates. In fact the reverse is true: large values for BPI indices tend to be associated with higher interest