Description
Banks are required to hold an adequate amount of liquid assets, such as cash, to manage any potential bank runs by clients.
Lending Relationships in the Interbank Market?
João F. Cocco† Francisco J Gomes‡ Nuno C. Martins§ July 2005
?
We would like to thank Viral Acharya, Andrea Buraschi, Jennifer Conrad, Francesca Cornelli, Denis
Gromb, Michel Habib, Philipp Hartmann, Narayan Naik, Jose Peydro-Alcayde, Mitchell Petersen, Maximiano Pinheiro, Raghuram Rajan, Rafael Repullo, Henri Servaes and seminar participants at the Bank of England, Banco de Portugal, Cass Business School, European Central Bank, London Business School, London School of Economics, the 2002 European Winter Meetings of the Econometric Society, the 2004 American Finance Association meetings, and the 2005 Conference on Competition, Stability, and Integration in European Banking for helpful comments and suggestions. We are especially grateful to an anonymous referee for detailed and constructive comments. The analysis, opinions and ?ndings of this paper represent the views of the authors, they are not necessarily those of the Banco de Portugal. † London Business School, Regent’s Park, London NW1 4SA, UK, and CEPR. Email [email protected]. ‡ London Business School, Regent’s Park, London NW1 4SA, UK, and CEPR. Email [email protected] § Universidade Nova de Lisboa and Banco de Portugal, Av. Almirante Reis, 71, 1150-012 Lisboa, Portugal. E-mail [email protected]
1
Abstract
We use a unique dataset to study lending relationships in the interbank market. We explicitly control for the endogeneity of lending relationships, and ?nd that borrowers pay a lower interest rate on loans from banks with whom they have a stronger relationship. Moreoever, we ?nd that smaller banks, banks with lower return on assets, banks with a higher proportion of non-performing loans, and banks subject to more volatile liquidity shocks rely more on lending relationships. Finally, we ?nd evidence that smaller banks with limited access to international markets tend to rely on lending relationships when borrowing in the domestic interbank market. This provides evidence that banks rely on lending relationships to overcome monitoring and default risk problems, and for insurance purposes.
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 very di?erent from those that arise in a spot market. One important setting in which there are frequent and repeated interactions between agents is the interbank market. Our paper studies the role of lending relationships in this market. Understanding lending behavior and price formation in the interbank market is important for banks who use it to engage in unsecured borrowing and lending of funds. It is also important for monetary authorities, since the interbank market lies at the heart of monetary policy. Moreover, it is in this market that the overnight rate is determined, which is the shortest-term market interest rate, and as such it has a crucial role in term structure models. The interbank market is fragmented in nature. For direct loans, which account for most of the lending volume, the loan’s amount and interest rate are agreed on a one-to-one basis between borrower and lender. Other banks do not have access to the same terms, and do not even know that the loan took place. When quotes are posted on screens, they are merely indicative. This market structure allows banks to establish lending relationships.1 But which economic purpose do lending relationships in interbank markets serve? The literature has focused on the function of these markets has distributors of liquidity. In the model of Ho and Saunders (1985), the reserve position of each bank is a?ected by stochastic deposits and withdrawals by customers. As a result banks trade in order to meet their reserve requirements. Similarly, in the model of Bhattacharya and Gale (1987) banks borrow and lend funds in order to insure against intertemporal liquidity shocks. In the model of Allen and Gale (2000) liquidity shocks arise from uncertainty in the timing of depositors’ consumption. Banks hold deposits with banks in other regions to insure against liquidity shocks in their own region. Finally, in the model of Freixas, Parigi and Rochet (2000) the uncertainty and
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, Biais, 1993, and O’Hara, 1995).
1
interbank lending arise from consumers’ uncertainty about where to consume. A common feature to these (and other) models of the interbank market are liquidity shocks, that give rise to borrowing and lending. Lending relationships may provide insurance against liquidity shocks. Another important strand of the literature focuses on the role of peer monitoring in interbank markets (see the models of Rochet and Tirole, 1996, Freixas and Holthausen, 2005, and the empirical analysis in Fur?ne, 2001). Peer monitoring is important because of the large and unsecured nature of the loans. Thus, lending relationships may help overcome agency problems. In addition to focusing on lending relationships in the interbank market, the main novelty of our analysis is that we recognize that the decision of whether to rely on lending relationships is an endogenous choice, and our econometric approach treats it as such. For this reason we are able to provide new insights into the determinants of lending relationships. 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 2001. The Portuguese interbank market is in many respects typical and, although smaller, it is organized similarly to the US Fed Funds market. Our dataset identi?es the date, interest rate, amount, maturity, lender and borrower of each loan. Thus, we can track loans between each and every pair of banks, and with other banks over time. Using this information, we construct dynamic measures of relationships based on the intensity of pair-wise lending activity. Our dataset also includes daily information on each bank’s reserve deposits, and quarterly information on banks’ balance sheet variables including total assets, return on assets and proportion of non-performing loans. We ?rst investigate the link between the loan interest rate and relationship measures. To address the endogeneity issue we estimate instrumental variables regressions, in which we explore the time-series dimension of our dataset by using 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. Importantly, we ?nd that 2
borrowers pay a lower interest rate on loans from banks with whom they have a stronger lending relationship. We also ?nd that once we control for the endogeneity of lending relationships, several other explanatory variables are no longer important for explaining the loan interest rate. The instrumental variables regressions allow us to identify the causal link between relationship measures and the loan interest rate, but they do not explain the determinants of lending relationships. To do so we estimate a seemingly unrelated regressions system of equations, with the amount lent, the interest rate, and the relationship measures for lender and borrower as dependent variables. This allows us to simultaneously study the determinants of loan pricing, loan amount, and of lending relationships. Our main ?ndings are as follows. First, we ?nd that borrowers with lower return on assets and with a higher proportion of non-performing loans are more likely to rely on lending relationships. These results provide empirical support for an explanation of these relationships based on default risk and monitoring. 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 ?nd that borrowers with more volatile liquidity shocks are more likely to rely on lending relationships. They tend to do so with lenders who have less volatile liquidity shocks, and also with whom they have less correlated shocks. In addition, borrowers are more likely to rely on lending relationships when they experience a larger imbalance in their reserve deposits. This provides evidence that banks rely on lending relationships for insurance. We ?nd that small borrowers are more likely to establish relationships and that they tend to choose larger banks as their preferred lenders. Furthermore, large banks tend to be net borrowers, while small banks tend to be net lenders in the market. Interestingly, this pattern of trade is also a distinctive feature of the US Fed Funds market (Fur?ne, 1999, Ho and Saunders, 1985). Finally, we investigate how banks’ ability to access international markets a?ect the nature of lending relationships in the domestic interbank market. We ?nd that small banks and banks 3
with a higher proportion of non-performing loans tend to have limited access to international markets, and that they tend concentrate their borrowing when borrowing funds in the domestic interbank market. This result may be due to peer monitoring across borders being less e?cient than at the domestic level, as in the model of Freixas and Holthausen (2005). Our results for the pricing or interbank loans are consistent with those of Fur?ne (2001) for the Fed Funds market. We ?nd that, controlling for the degree of lending relationship and holding the size of the counterparty ?xed, larger banks borrow and lend at more favorable terms. Banks with higher return on assets lend at higher interest rates. This is consistent with these banks having a higher opportunity cost of lending funds in the interbank market, and requiring a higher interest rate to do so. Borrowers with a higher proportion of nonperforming loans tend to pay higher interest rates. Again controlling for the degree of lending relationship, we ?nd that more pro?table banks lend less, and banks with a higher proportion of non-performing loans lend more and borrow less. Thus banks that have better investment opportunities tend to be net borrowers. There is a large literature on lending relationships that focuses on bank-?rm relationships. It has found evidence that lending relationships help overcome constraints that arise from monitoring and default risk between borrower and lender of funds,2 and allow banks to provide insurance to ?rms in the form of interest-rate smoothing.3 Thus this literature focuses on longterm relationships between banks and ?rms, by which banks acquire inside knowledge about ?rm characteristics or the project that is being ?nanced. Although somewhat related, it is important to note that these relationships are of a di?erent nature than the ones that we study in our paper, which are transaction based. The paper proceeds as follows. Section 2 describes the data, our relationship metrics and reports some summary statistics. Section 3 studies the pricing of interbank loans. Section 4
2
See Berger and Udell (1995), Lummer and McConnell (1989), Petersen and Rajan (1994), Slovin, Sushka,
and Poloncheck (1993). 3 See Berger and Udell (1992), Berlin and Mester (1999), Petersen and Rajan (1995), or Ongena and Smith (2000) for a survey of the literature on bank lending relationships.
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investigates the determinants of lending relationships. Section 5 presents additional evidence on the determinants of lending relationships, that allows us to be more precise with respect to their nature. Section 6 reports some robustness checks. Section 7 concludes.
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2.1
The Data
Description
We combine information from three di?erent datasets, which we have obtained from the Portuguese Central Bank. The ?rst dataset has information on all direct loans in the Portuguese interbank market from January 1997 to August 2001. The Portuguese interbank market is a typical interbank market, and although of a smaller size, it functions in a similar way 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, identi?es 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 di?erent quotes for di?erent banks that approach them, and it is common practice for banks 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 our sample period there were 44, 768 overnight loans accounting for
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over 75 percent of the total amount lent (casual evidence suggests that this is a common feature in most interbank markets). Even though credit risk for loans of overnight maturity may be small, it is important to note that these are large and uncollaterized loans, with an average loan amount of roughly twelve million euros. Therefore we expect that even small di?erences across banks in credit risk are re?ected on the loan interest rate. The second dataset provides daily information on the balance in banks’ reserve accounts. It allows us to study how banks’ reserve position a?ects their behavior in the interbank market. The third dataset contains quarterly information on bank characteristics, including total assets, ?nancial and pro?tability ratios and credit risk variables. This dataset also allows us to determine whether the bank belongs to a banking group, de?ned 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.
2.2
Measuring Lending Relationships
We measure lending relationships by the intensity of lending activity between banks. We use two alternative measures. Our ?rst measure is based on how concentrated the banks’ lending and borrowing activity is. More precisely, for every given lender (L) and every borrower (B ), we compute a lender preference index (LP I ), 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.4 Let Fij ??k denote the amount lent by bank j to bank k on loan i then:
% LP IL,B,q =
X
i?q
FiL??B /
X
i?q
FiL??all
(1)
where q denotes year/quarter. This ratio is more likely to be high if L relies on B more than on other banks to lend funds in the market.
4
We discuss our choice of time period in detail below.
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Similarly, we compute a borrower preference index (BP I ) as the ratio of total funds that B has borrowed from L in a given year/quarter, as a fraction of the total amount of funds that B has borrowed in the market in that same year/quarter:
% BP IL,B,q =
X
i?q
FiL??B /
X
i?q
Fiany??B .
(2)
Our second measure of lending relationships is simply the (absolute) number of di?erent banks to which bank L lent funds during year/quarter q, and similarly the number of di?erent banks from which bank B borrowed funds during year/quarter q :
# LP IL,q = Number of banks to which bank L lent funds in year/quarter q # = Number of banks from which bank B borrowed funds in year/quarter q BP IB,q
(3) (4)
Thus our ?rst measure of lending relationships is a relative measure, while our second measure is an absolute one. Elsas, Heinemann, and Tyrell (2004) solve a model in which for some borrowers it is optimal to rely on multiple but asymmetric ?nancing, i.e. borrowing a large amount from a single bank, and the remaining amount from several other banks. This asymmetry in ?nancing can not be captured by the absolute number of di?erent lenders. For this reason we have decided to use both an absolute and a relative measure of lending relationships. As one might expect, the correlation between these measures is negative. The correlation between the BP I % and BP I # indices is equal to ?0.46, while the correlation Figure 1 plots, for a given quarter and for a given borrower, its BP I % indices with di?erent
between the LP I % and LP I # indices is equal to ?0.42
lenders. The most important lender for this borrower during this quarter is the bank labeled as lender one, from which it borrowed roughly a quarter of the total funds that it borrowed during the quarter. This ?gure illustrates that in our data there are asymmetries in ?nancing, with some lenders being much more important than others. As an illustrative example of the time-series dimension of our relationship measures, Figure 2 plots the evolution of the LP I % and BP I % indices for a pair of banks in our sample, L and 7
B. This time-series dimension of our data is important because it will allow us to deal with the issue of the endogeneity of lending relationships. More precisely, since there is a timeseries dimension in our data we will be able to use lagged relationship measures as (exogenous) instruments. Figure 2 also illustrates that there is time variation in our relationship measures. In our regressions the explanatory power comes both from cross-sectional di?erences 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, pro?tability and credit risk. In section 6 we show that the results are robust to alternative ways of measuring relationships.
2.3
Pro?tability and Credit Risk Variables
One possible motive for lending relationships is that they may help overcome agency problems that arise from asymmetric information between borrowers and lenders of funds. Rochet and Tirole (1996) solve a model of the interbank market in which monitoring plays an important role.5 For this reason we include as explanatory variables total assets, the quarterly return on assets (ROA), and the proportion of non-performing loans (NPL). The latter is de?ned as loans that are past-due for a period exceeding 90 days, over total outstanding credit granted by the bank. Obviously, the latter includes loans granted to individuals and ?rms, and not only to other banks.
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.
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2.4
Insurance variables
A second possible reason for banks to establish lending relationships is to obtain insurance against idiosyncratic liquidity shocks, arising from withdrawals by retail depositors. A bank may borrow the funds needed to meet unexpectedly large withdrawals from other banks in the interbank market (see the models of Ho and Saunders, 1985, Bhattacharya and Gale, 1987, and Freixas, Parigi and Rochet, 2000). If lending relationships are important for insurance purposes, we might expect banks subject to more volatile liquidity shocks to rely more on them. To investigate this hypothesis we construct a measure of volatility of liquidity shocks, equal to the standard deviation of the daily change in the bank’s reserve deposits that is not due to loans in the interbank market. We compute this measure for each bank and quarter, and normalize it by the bank’s average quarterly reserves. One may expect that lending relationships are more valuable for both borrowing and lending banks when their liquidity shocks are less correlated. That is, when borrowing banks need funds lending banks are more likely to have a surplus of funds. For each quarter, we measure the correlation between each two banks’ daily change in reserve deposits that is not due to loans in the interbank market.6 Banks may borrow funds to satisfy 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).7 It is therefore natural to expect that banks’ reserve position, when they borrow or lend funds in the interbank market, a?ect the interest rate on the loans, and with whom they interact. To investigate these e?ects we construct a proxy for each bank’s reserve requirements, equal to the average of the daily
6
Note that the argument that lending relationships are more valuable when banks have less correlated
shocks does not require that the correlation be negative. 7 Campbell (1987), Hamilton (1996), Hartmann et al. (2001), and Spindt and Ho?meister (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.
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deposits in the bank’s reserve account over the reserve maintenance period. We then measure surplus deposits for bank i on day t (SDit ) 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: ? SDit = ? X Depositis ? /nt ? ?
s?{m(t):s6 t}
? ?
s?m(t)
X
(5)
where m(t) refers to the days in the same reserve maintenance period as day t, and nt and n are the up to t and the total number of days in the maintenance period, respectively. In words, this variable measures the average deposits in the bank’s reserve account up to day t of the current reserve maintenance period, relative to the average deposits in the account during the same reserve maintenance period. It captures the extent to which a bank’s requirements imply a need for or an excess of funds. As before we compute the average value of this variable over each quarter, for those days in which the bank intervened in the interbank market.
Depositis ? /n
2.5
Summary statistics
Table 1 reports summary statistics. The ?rst panel shows information on the Portuguese interbank market. The average total amount lent in each quarter is 27,123 million euros, with an average 2,217 loans. Thus, the average loan amount is roughly twelve million euros. The average number of di?erent borrowers (lenders) in each quarter is 37 (39). The next two panels of Table 1 report summary statistics for borrowing and lending banks, respectively, on total assets (Assets), quarterly return on assets (ROA), and proportion of non-performing loans (NPL). Table 1 reports that 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. 10
Table 1 also reports information on total amount and number of loans made and received by each bank in the interbank market during the quarter. On average each borrower 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 BP I % is 7.94 percent, and the average LP I % is 8.39 percent. These averages are signi?cantly 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. This is why it is important to consider these measures of relationships, in addition to simply the number of di?erent borrowers and lenders, whose summary statistics are shown in the next two rows of Table 1. Table 1’s last row reports summary statistics for the correlation of shocks (as de?ned in section 2.4). As one would expect, these correlations tend to be positive, with an average value of 12 percent. There is also signi?cant cross-section dispersion, with the 25th percentile equal to 1.6 percent and the 75th percentile equal to 23.6 percent. Table 2 shows the correlation matrix between several variables for borrowers and lenders. The largest correlations are between total assets, total amount lent/borrowed in the interbank market, and number of loans. Banks with more assets tend to be more active in the interbank market both in terms of total amount borrowed/lent and number of loans. For both borrowers and lenders of funds the LP I % and BP I % indices are negatively correlated with size, measured by total assets, amount and number of loans. As expected, larger banks also lend and borrow funds from a larger number of di?erent banks: the correlations between the LP I # and BP I # indices and total assets, amount, and number of loans are large and positive.
8
The average amount and number of loans for borrowing and lending banks are not exactly equal because
there is a di?erent number of borrowing and lending banks in the market.
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3
Pricing of Interbank Loans
This section investigates the determinants of the interest rate on interbank market loans. In most interbank markets the central bank sets a target rate. For this reason we focus on explaining the di?erence between the interest rate on a given loan and the average interest rate on overnight loans. Some numbers are helpful for understanding the daily variability in interest rates 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 proceed as follows. First for a loan from bank L to bank B on day t, we calculate the di?erence between the interest rate (iL,B,t ) and the average (market-wide) overnight interest rate on the same day (it ), divided by the standard deviation of overnight interest rates for that day (? i t ). This is to account for the well-documented GARCH e?ects in interbank market interest rates (Hamilton, 1996). Since our unit of observation is year/quarter, we then obtain the average interest rate di?erence for all loans from bank L to bank B during year/quarter q , with q = 1, ..., 19, as: iq L,B = 1 X (iL,B,t ? it )/? i t Tq t?q
(6)
where Tq denotes the number of trading days in period q.9
We ?rst study how interest rates so de?ned depend on size, pro?tability and relationship measures in a univariate framework. We then turn our attention to multivariate analysis that
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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 di?erent loans between the same pair of banks on a given day, the exact formula is: iq B,L = 1 X 1 X (iL,B,t,j ? it )/? i t Tq t?q JL,B,t j
where JL,B,t denotes the number of loans from L to B on day t.
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include these and other explanatory variables. Finally, in section 3.3, we recognize that our relationship measures are endogenous, and estimate instrumental variables (IV) regressions to address the endogeneity issue. These IV regressions also allow us to identify the causal link between relationship measures and the loan interest rate.
3.1
Univariate analysis
Table 3 reports the average interest rate (iq L,B ) as a function of di?erent characteristics of both borrowing and lending banks. In the ?rst panel we focus on Total Assets. There is evidence that in the Fed Funds market larger banks tend to obtain more favorable interest rates when borrowing or lending (Allen and Saunders, 1986, Stigum, 1990, Fur?ne, 2001). Table 3’s ?rst panel reports the interest rate di?erential on loans between banks in the di?erent quartiles of the total assets distribution (quartile 1 regroups the smallest banks). Each column regroups lenders, while each row regroups borrowers. The ?rst panel of Table 3 shows that in our data larger banks tend to obtain more favorable rates. The patterns are remarkably clear. Holding the quartile of the borrowing bank ?xed, the interest rate increases with the size of the lender. Similarly, holding the size of the lending bank ?xed, the interest rate decreases with an increase in the size of the borrower.10 Table 3’s second panel reports interest rate di?erentials as a function of the quartiles of the ROA distribution (Quartile 1 includes the banks with the lowest ROA). Although the interest rate patterns are not as clear as for total assets, more pro?table borrowing banks seem to pay a lower interest rate than less pro?table ones. Similarly, more pro?table lending banks tend to receive a higher interest rate, at least when we compare quartiles 1 and 4. Table 3’s last two panels report interest rate di?erentials, but now as a function of the relationship measures. The third panel reports the interest rate di?erentials as a function of BP I % and LP I % .11 The results appear to suggest that borrowers (lenders) tend to pay
10
The results are similar when we use other measures of size, such as total amount lent/borrowed in the
interbank market or number of loans. 11 Note that in the previous two panels all loans for a given lender in a given quarter would appear in the
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(receive) higher (lower) interest rates on loans with banks with whom they have a more intense lending relationship. As the next section shows, 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 a?ect the interest rate on the loan. The last panel of Table 4 reports interest rate di?erentials as a function of BP I # and LP I # . The patterns, although not always monotonic across quartiles, are symmetric to those in the previous panel, as one might have expected from the negative correlation between the two measures.
3.2
Multivariate Analysis
We ?rst estimate the unconditional correlation between the relationship metrics and the loan interest rate:
%,q %,q q q q iq L,B = ? + ?BP IL,B + ?LP IL,B + ? D + uL,B
(7)
where q indexes year/quarter, Dq are time (year/quarter) dummies, the subscripts L and B refer to lending and borrowing bank, respectively, and uq L,B is the residual. Column (i) of Table 4 shows the estimation results. The results con?rm the ones previously obtained in the univariate analysis (third panel of Table 3) and the coe?cients are statistically signi?cant in both cases. Next we include size, ROA and NPL as additional independent variables. The regression that we estimate is: iq L,B = ? + X £ ¤ q q %,q %,q q q q ? 1j Si zeq j + ? 2j ROAj + ? 3j NP Lj + ?BP IL,B + ?LP IL,B + ? D + uL,B (8)
j =L,B
As a size measure we use the logarithm of total assets. Finally, we include as independent variables those related to insurance motives. These include the net reserve position of borrowers and lenders when they borrow or lend funds in the interbank market (surplus deposits, or
same column, depending on its total assets or ROA. In the third panel, a given lender may have a LPI with a borrower that is in top quartile of the distribution of LPI indices, and a LPI with another borrower that is in the bottom quartile. The interest rate di?erential for loans with the former shows up in Table 3 under column Q4, whereas for the loans with the latter shows up under column Q1.
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SD), the coe?cient of variation of their liquidity shocks (CVB and CVL ), and the correlation of liquidity shocks between lender and borrower (?L,B ): iq L,B = ? + X £ q q q q¤ ? 1j Si zeq j + ? 2j ROAj + ? 3j NP Lj + ? 4j SDj + ? 5j CVj
j =L,B
%,q %,q +? 6 ?L,B + ?BP IL,B + ?LP IL,B + ? q Dq + uq L,B
(9)
Including the relationship metrics as exogenous variables may seem surprising, given our previous discussion on the endogeneity of lending relationships. However, these equations are typically estimated in the lending relationships literature. Later on we will explicitly recognize the endogeneity problem, both with IV regressions and with SUR estimation. Comparing these results with those obtained when controlling for endogeneity allows us to investigate the potential biases introduced by treating the lending relationship measures as independent variables in the interest rate equation. Columns (ii) and (iii) of Table 4 show the estimation results. Interestingly, once we include the logarithm of total assets, ROA, and NPL as independent variables the estimated coe?cients on the relationship variables revert sign (column (ii)). Thus lenders receive a higher interest rates on loans to borrowers with whom they have a lending relationship, and borrowers pay a lower interest rate on loans from banks with whom they have a lending relationship. This result is the opposite of the unconditional results, and shows how crucial it is to control for bank characteristics in the pricing of interbank loans. The signs of the estimated coe?cients of the size variables, positive for lenders and negative for borrowers, con?rm that in the market larger banks receive better interest rates, whichever side of the market they are in. The estimated positive coe?cient on the ROA of borrowers is intuitive. Borrowers with a higher ROA have a more pro?table application for the funds, and are willing to pay a higher interest rate for the funds they borrow. Similarly, the estimated coe?cient on the ROA of lenders is positive, although not statistically signi?cant. A higher ROA means that lenders have a higher opportunity cost of lending in the interbank market, and require a higher interest rate to do so. 15
The e?ects of credit risk are captured by the proportion of non-performing loans (NPL) variable. We ?nd that borrowers with a higher proportion of NPL tend to pay higher interest rates on loans in the interbank market, a result which is statistically signi?cant at the one percent level. We also estimate a positive coe?cient on NPL of lenders, but it is not statistically signi?cant when we include the insurance variables (column (iii)). The results in column (iii) of Table 4 show that borrowers with a lower surplus deposit pay on average a higher interest rate on their loans. The magnitude of the coe?cient is also economically signi?cant: a 1% shortage of funds leads to an interest rate premium of 0.12
q standard deviations. The coe?cient on SDL is not statistically signi?cant. What seems to
matter for lenders is the volatility of liquidity shocks: the more volatile they are the lower is the interest rate that lenders receive on interbank market loans. Finally, the estimated coe?cient on ?L,B is not signi?cantly di?erent 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 reason may be the bilateral nature of the market. In a market with pairwise meetings such as the interbank market, the relative bargaining power of borrower and lender of funds will a?ect the interest rate on the loan. If size is correlated with bargaining power, then larger lenders (and larger borrowers) will receive better interest rates on their loans.12 In order to investigate this, and for each lender (and borrower) in our sample, we have calculated their respective market shares. That is: the total amount that the lender has lent (the borrower has borrowed) in the interbank market, over the total amount lent/borrowed by all banks in the market. Market shares thus calculated are positively correlated with bank size, as measured by the logarithm of total assets, with coe?cients of correlation equal to 0.59 (0.74) for lenders (borrowers). In columns (iv) and (v) of Table 4 we report the estimation
12
See Osborne and Rubinstein (1990) for a textbook treatment of models of bilateral markets that predict
this result.
16
results when we include market shares as explanatory variables for the interest rate on the loans. We ?nd 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 ?nd that the explanatory power of both variables is diminished, re?ecting the fact that they are co-linear. The last column of Table 4 reports the estimation results when we use BP I # and LP I # as relationship measures. The e?ects of the size, pro?tability, credit risk, and insurance variables on the interest rate are similar to those reported in column (iii) and therefore we refrain from commenting on them. Interestingly, the estimated coe?cient on BP I # is not statistically signi?cant, while the estimated coe?cients on BP I % was signi?cant. Thus it seems that for borrowers of funds it is important to use as a measure of the strength of the relationship a variable that re?ects the (possible) asymmetric nature of the ?nancing, such as borrowing a large amount from a single bank, and the remaining amount from several other banks. Obviously this asymmetry in ?nancing can not captured by the number of di?erent lenders (the BP I # variable).
3.3
Instrumental Variables Regressions
In order to address the issue of the endogeneity of the relationship measures we estimate instrumental variables (IV) regressions. These regressions allow 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 the relationship measures. The validity of the IV approach depends crucially on the quality of the instruments used in the ?rst stage regression. Good instruments include those which are simultaneously predetermined 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
17
in the existing literature on lending relationships. The quality of these instruments can be measured by the R-squared of the ?rst-stage regressions: for the BP I % (LP I % ) measure it is equal to 67% (78%), and for the BP I # (LP I # ) measure it is equal to 49% (52%).13 The estimation results for the second stage regressions are shown in Table 5. The tstatistics (reported below the estimated coe?cients) have been adjusted for ?rst-stage estimation error. When we compare the results in Table 5 to those in Table 4 we can draw the following conclusions. First, the coe?cients on total assets and non-performing loans remain essentially unchanged. Larger banks tend to receive higher interest rates when they lend, and pay lower interest rates when they borrow. Borrowers with more default risk pay on average a higher interest rates on their loans, while the lender’s default risk is now clearly non-signi?cant in both regressions. Second, the estimated coe?cient on the surplus deposit of borrowers is no longer signi?cant, and the estimated coe?cient on the coe?cient of variation of lenders is only signi?cant in (ii). Thus the level of signi?cance of the insurance variables is reduced once we control for the endogeneity of lending relationships. This suggests that relationships are important because they allow banks to obtain insurance in the interbank market. In the next section we will study the determinants of lending relationships. Third, the estimated coe?cients on the relationship variables are signi?cant throughout, and have the same signs as in Table 4. Moreover, the magnitude of the estimated coe?cients is either unchanged or even slightly increased (in absolute value). This result implies that, at least in our dataset, the endogeneity problem does not a?ect 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 coe?cients on the relationship metrics are robust to an IV approach, the inference on the coe?cients of some of the insurance
13
We have also estimated the IV regressions using the ?rst lag of all the explanatory variables in equation
(9) as instruments in the ?rst-state regression. The ?rst stage R2 was almost una?ected and the second stage results were the same and are therefore not reported.
18
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 coe?cients, then controlling for endogeneity is important.
4
The Determinants of Lending Relationships
The instrumental variables regressions that we have estimated in the previous section allow us to estimate the e?ects of lending relationships on the interest rate on the loan, 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 the loan amount and interest rate to be correlated with the identity of the borrowing and lending banks or on whether they have a lending relationship. More precisely, we now estimate a seemingly unrelated regressions (SUR) system of equations, with the amount lent, interest rate, and the relationship measures between lender and borrower (LP I and BP I ) as endogenous dependent variables. Thus, we estimate simultaneously the following system of equations:
1 iq L,B = ? +
j =L,B
%,q BP IL,B
%,q LP IL,B
(12) X £ ¤ q q q q q q q 4 4 4 4 4 q4 q4 Ln(VL,B ?4 ) = ?4 + 1j Sizej + ? 2j ROAj + ? 3j NP Lj + ? 4j SDj + ? 5j CVj +? 6 ? B,L +? D +vL,B
j =L,B
(11) X £ ¤ q q q q q q 3 3 3 3 3 q3 q3 = ?3 + ?3 1j Sizej + ? 2j ROAj + ? 3j NP Lj + ? 4j SDj + ? 5j CVj +? 6 ? B,L +? D +? L,B
j =L,B
(10) X £ ¤ q q q q q q 2 2 2 2 2 q2 q2 = ?2 + ?2 1j Sizej + ? 2j ROAj + ? 3j NP Lj + ? 4j SDj + ? 5j CVj +? 6 ? B,L +? D +?L,B
j =L,B
X £ q q q q q¤ q 1 1 1 1 1 q1 q1 ?1 1j Sizej + ? 2j ROAj + ? 3j NP Lj + ? 4j SDj + ? 5j CVj +? 6 ? B,L +? D +uL,B
(13)
q where VL,B is the total amount of funds lent by bank L to bank B during quarter q , and Ln
denotes logarithm. In this section we focus our attention on the LP I % and BP I % indices.
19
The results for the LP I # and BP I # are similar and reported in section 6. We estimate a reduced form system, and therefore allow for contemporaneous correlation across the di?erent innovations (u, ?, ? and v ). As before, we include time dummies in all equations.
4.1
BPI and LPI equations
Table 6 shows the estimation results for BP I % and LP I % indices. The results for the BP I % equation are shown in the second column. In this equation we try to determine which borrower and lender characteristics explain the variation in BP I % indices. In other words, who are the borrowers’ who have higher relationship indices, and who are the lenders with whom they have higher indices. The negative coe?cient on the logarithm of total assets of borrowers means that small borrowers rely more on lending relationships. The estimated coe?cient on the total assets of lender in the BP I % equation is positive and statistically signi?cant, meaning that small borrowers tend to have large banks as their preferred lenders. These results suggest a dichothomy between large and small banks in the market, an issue that we explore further in section 5.1. Interestingly, we ?nd that borrowers with higher default risk are more likely to rely on lending relationships: the estimated coe?cient on NPL of borrowers is positive and signi?cant. In addition, borrowers with a large proportion of NPL pay higher interest rates on their loans (the estimated coe?cient on NPL in the interest rate equation is 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 4 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 we do not ?nd 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 rates (Table 3, and column (i) in Table 4). It is only when controlling for default risk
20
that the estimated coe?cient on the BPI index is negative (Table 4 column (ii)), but even so it is an order of magnitude smaller than the coe?cient on the default risk variable. That is: borrowers with a high proportion of NPL pay on average higher interest rates. However, the interest rate premium is smaller if they borrow funds from a lender with whom they have a high BPI. Some calculations help to clarify this important point. Consider an increase in the proportion of NPL from the 25th to the 75th percentile, while everything else remains the same. Using the estimated coe?cients in the third column of table 4 we see that the interest rate on the loan increases by 2 basis points.14 However, if the increase in the proportion of NPL is accompanied by an increase in the BPI index from the 25th to the 75th percentile, the increase in interest rate is only 0.6 basis points. If instead we consider an increase in the proportion of NPL from the 10th to the 90th percentile the increase in interest rate is 20 basis points when the BPI index is unchanged, and 5 basis points when the BPI index also increases from the 10th to the 90th percentile.15 Several of the insurance variables are also signi?cant. The estimated negative coe?cient on the surplus deposit of borrowers implies that they are more likely to borrow funds from lenders with whom they have large relationship indices when they have a larger shortage of funds. Borrowers with more volatile liquidity shocks tend to rely more on lending relationships
q (the coe?cient on CVB is positive), and they tend to do so with lenders that have less volatile q liquidity shocks (the estimated coe?cient on CVL in the BP I % equation is negative and
statistically signi?cant). This supports the idea that lending relationships are important for insurance purposes. Finally, the correlation variable is also signi?cant and it has a negative coe?cient, which is consistent with the mutual insurance hypothesis. Borrowers are more likely to have lending relationships with lenders when their liquidity shocks are less correlated. In
14
Due to our scaling of the dependent variable we need to multiply the increase by the standard deviation
of the interest rate. 15 The e?ect of NPL on the interest rate may be larger because default risk is likely to be correlated with bank size, for which we are also controlling in Table 4.
21
such case the insurance bene?ts of the relationship are likely to be larger. The third column of Table 6 reports the results for the LP I % equation. Similarly to the borrowers, we ?nd that small lenders are more likely to have higher relationships indices, and that they tend to do so higher indices with large borrowers (the estimated coe?cient on total assets of lenders is negative and on the total assets of borrowers is positive). The estimated coe?cient on the credit risk of lenders is not statistical signi?cant. This is consistent with the results for the interest rate regression reported in Table 4. It is natural to expect that what matters in a loan is the credit risk of the borrower, and not that of the lender. In the LP I % equation, the estimated coe?cient on the reserve imbalance of borrowers is negative and statistically signi?cant. This means that banks that borrow funds at times when their reserve imbalance is larger tend to borrow funds from lenders which have high relationship indices with them (recall that the reserve imbalance variable for borrowers is de?ned in such a way that a lower value means a higher imbalance). Thus loans that take place when reserves imbalances are larger tend to be associated with higher relationship indices. This result comes from the time-series dimension of our panel. In addition, lenders with more volatile liquidity shocks tend to have higher relationship indices with borrowers that face less volatile liquidity shocks, although the estimated coe?cient for borrowers is not signi?cantly di?erent from zero. As in the BP I % equation, the estimated coe?cient on the correlation variable is negative, consistent with the mutual insurance motive for establishing relationships. As a whole, columns two and three of Table 6 show that it is mostly borrower characteristics that explain variation in the BP I % and LP I % indices. Among the lender characteristics the only two that seem to be important are the logarithm of total assets and liquidity risk. One might have an a priori expectation that for non-secure loans such as interbank market loans, borrowers’ characteristics are more important for explaining the terms of the loan than lenders’ characteristics. Table 6 suggests that this reasoning carries through when explaining lending relationships.
22
4.2
Interest rate and loan volume equations
The fourth column of Table 6 shows the results for the interest rate equation. This equation is similar to that estimated in speci?cation (iii) of Table 4, except that now we do not include the LPI and BPI indices as independent variables, but instead treat them as endogenous when estimating the system of equations. The main noticeable di?erence relative to the results in Table 4 is that the estimated coe?cient for the borrower’s ROA is now non-signi?cant. Given that several papers on lending relationships rely on regressions of the price of the loan on relationship measures and other control variables, it is re-assuring to ?nd out that in our data the results for this regression are robust to an approach that treats the relationship measures as endogenous variables. In the last column of Table 6 we report the results for loan volume (the fourth equation in the SUR system). We ?nd that larger banks borrow larger amounts. Interestingly, we ?nd that more pro?table banks lend less (the estimated coe?cients on ROAq L is negative). In addition, we ?nd that banks with a higher proportion of non-performing loans lend more
q and borrow less (the estimated coe?cients on NP Lq L and NP LB are positive and negative,
respectively). The estimated coe?cients for ROA and NPL are consistent with banks that have better investment opportunities borrowing more and lending less. Finally, the estimated coe?cients on surplus deposit show that banks which have smaller imbalances tend to rely on larger loans with any particular bank.
4.3
Correlation of residuals
At the bottom of Table 6 we show the estimated correlation matrix of residuals in the SUR system of equations. This allows us to study the correlation between the di?erent endogenous variables. However, we should point out that since our SUR system is a reduced form estimation, these correlations are not partial derivatives, i.e. when we look at the correlation between the residuals in two di?erent equations we are not holding the other endogenous variables constant. 23
Larger residuals for the BP I equation are associated with lower interest rates, and larger residuals for the LP I equation are associated with higher interest rates. Thus, borrowers pay lower interest rates when they borrow funds from banks with whom they have a lending relationship, and lenders receive a higher interest rate when they lend funds to banks with whom they have a lending relationship. Although the signs of the correlations between the LPI and BPI and interest rate are intuitive, the magnitude of the correlation is fairly small. From Table 6 we see that the largest correlations are of amount lent with LPI and BPI, which are equal to 0.44 and 0.31, respectively. This ?nding supports the idea that relationships have the greatest e?ect on the provision of credit, and not on the price at which banks are able to borrow or lend.
5
Further Evidence on the Determinants of Lending Relationships
In this section we provide further evidence on the determinants of lending relationships, that allows us to be more precise as to their exact nature.16
5.1
Small versus Large Banks
The estimation results in the previous sections show that bank size is an important determinant of interbank market interest rates, and of lending relationships. In this section we explore further the role of bank size in the market structure. In order to do so, and for each quarter in our sample, we classify banks into large and small, based on the quarterly distribution of bank assets. Large (small) banks are those whose assets are larger (smaller) than percentile 66 (33) of this distribution. We then compare several variables for small and large banks. The ?rst two rows of Table 7, Panel A report the average amount borrowed/lent per bank
16
We would like to thank an anonymous referee for suggestions that have led us to investigate the questions
in this section.
24
and quarter over the whole sample period. The third row reports the net amount borrowed, which is simply the di?erence between the ?rst two. The second column shows the results for all banks, i.e. not conditional on bank size, while columns three and four show the results for small and large banks, respectively. On average, and per quarter, each bank in our sample has lent/borrowed 596.5 million euros. There are signi?cant di?erences between small and large banks: large banks tend to be net borrowers, with an average net amount borrowed roughly equal to 400 million euros, while small banks tend to be net lenders, with an average net amount lent equal to 363 million euros. Interestingly, this pattern of trade, in which large banks tend to be net buyers of liquidity and small banks tend to be net sellers, is also a distinctive feature of the US Fed Funds market (see for example Fur?ne, 1999, or Ho and Saunders, 1985).17 It can be rationalized by the model of Ho and Saunders (1985). If large banks are better able to diversify their risk exposure than small banks, then larger banks will be more rate sensitive than small banks, and the slopes of the demand functions for interbank funds of large banks will be more price-elastic than those of small banks. An important policy implication is that open market operations by the central bank will be more e?ective when targeted at large rather than small institutions. Table 7, Panel A also reports information on the number of loans and average loan amount. Large (small) banks tend to transact mostly as borrowers (lenders), re?ecting the fact that they tend to be net borrowers (lenders) in the market. Unsurprisingly, average loan amount for small banks is signi?cantly lower than average loan amount for large banks. The last three rows of Table 7, Panel A report the proportion of non-performing loans, and relationship indices. Small banks tend to have a signi?cantly higher proportion of nonpreforming loans than large banks. Furthermore, they tend to have signi?cantly higher BPI indices than large banks when borrowing funds. This suggests that small banks when borrowing funds ?nd it optimal to concentrate their borrowing. Interestingly, the same is not
17
See also Stigum’s (1990) description of the Fed Funds market: “To cultivate correspondents that will sell
funds to them, large banks stand ready to buy whatever sums these banks o?er, whether they need all these funds or not."
25
true when lending funds, since there are no statistically signi?cant di?erences in LPI indices between small and large banks. We have also investigate the likelihood that banks appear on both sides of the market, i.e. as lenders and borrowers over a given time period. Panel B of Table 7 reports that 66.1% (50.2%) of all banks have been on average active market participants on both sides of the market at least once a month (week). Panel B of Table 7 also reports summary statistics for bank assets and proportion of nonperforming loans as a function of how often banks appear on both sides of the market. It shows that large banks are more likely to appear on both sides of the market, and in this way act as intermediaries. In addition, banks that reverse their positions more frequently tend to have a signi?cantly lower proportion of non-performing loans. Naturally, banks with lower credit risk are better-suited to act as intermediaries. Finally, we have investigated whether the volatility of liquidity shocks di?ers depending on the frequency with which banks appear on both sides of the market, but found no statistically signi?cant di?erences. Smaller banks are less likely to act as intermediaries, and are more likely to act as lenders. But is it the case that when they need to borrow funds they do so from banks to whom they usually lend funds? In order to investigate this we have estimated the probability that small banks borrow funds from a bank to whom they usually lend funds, where the latter means a bank in top ?fty percent (one third) of the distribution of LPI indices for that small bank. This probability is as high as 66.88% (54.58% for the one-third cuto? ). The corresponding probabilities for all banks, i.e. not conditional on bank size, are smaller and equal to 59.28% (48.43%). Thus small banks, when reversing roles, tend to rely more on banks with whom they usually interact on the other side of the market than the average bank in our sample.
5.2
International Linkages
Unfortunately our main dataset only includes information on loans in the domestic interbank market. However, and in order to explore international linkages between domestic and foreign
26
banks, we have obtained data from a di?erent dataset, namely from the Trans-European Automated Real-time Gross settlement Express Transfer system (TARGET). This is the realtime gross settlement system for the euro o?ered by the Eurosystem. It is mainly used for the settlement of large-value euro interbank transfers. This dataset contains information on the identity of both the sender and receiver of funds, and on the amount transferred. It has some shortcomings. First, transfers of funds between a pair of banks may be due to a variety of reasons, other than interbank loans. For example, if a large individual client of a foreign bank decides to transfer funds to a domestic bank, this transfer of funds will show up in the dataset, and cannot be distinguished from an interbank loan. Second, this dataset is only available from 1999 onwards, or roughly the second half of the sample period. We use this dataset to investigate how international linkages relate to the nature of lending relationships in the domestic interbank market. This is particularly interesting because the Euro area seems to be characterized by a two-tier structure, in which only large banks are usually able to access foreign interbank markets for liquidity, and in which small banks tend to do their interbank business through large domestic banks (European Central Bank, 2000). With this in mind, we ?rst construct a measure of access to international markets, by calculating the total amount of funds that each domestic bank has received from plus sent abroad during each quarter. We then scale this variable by bank size, as measured by total bank assets.18 We think that this variable is a better measure of access to international markets, than simply the di?erence between funds received from abroad and funds sent abroad scaled by bank assets. This is because a domestic bank may ?nd it easy to access international interbank markets, but during a given time period it may neither be net borrower nor net lender in these
18
We have calculated alternative measures of access to international markets equal to the total amount of
funds that each domestic bank has received from abroad during the quarter scaled by bank assets, and equal to the total amount of funds that each domestic bank has sent abroad during the quarter scaled by bank assets. The correlation coe?cient between these two variables is 0.97, and the correlation coe?cients between them and the total amount of funds sent plus received from abroad scaled by bank assets are over 0.99.
27
markets. In this case the latter variable would be zero. We classify banks into low and high access to international markets, according to this measure. Banks with high (low) access are those in the top (bottom) one third of the distribution of this variable. Table 8 shows the results for the mean of several variables for each of these two groups. The last column shows the p-value for a t-test of equality of means. The ?rst row con?rms the result that banks with better access to international markets tend to be larger: the di?erence in total bank assets between the two groups is almost ?vefold. Interestingly, we ?nd that banks with low access to international markets tend to have a much higher proportion of non-performing loans. Furthermore, these banks, when borrowing funds in the domestic interbank market, ?nd it optimal to concentrate their loans: their BPI indices are much higher than those with high access to international market. This result is consistent with peer monitoring across borders being less e?cient than at the domestic level, as in the model of Freixas and Holthausen (2005). It suggests that in international unsecured credit markets such as interbank markets, peer monitoring plays an important role in that it allows liquidity to ?ow across borders. However, an alternative explanation is that large banks are perceived by international markets as being too-big-too-fail, and for this reason they can borrow internationally at low rates. In either case, our results suggest that domestic regulators should direct their policies towards an improvement of the cross-border information available, particularly so on small banks, so as to enhance cross-border market integration. Finally, we ?nd that banks with high access to international markets tend to have a lower coe?cient of variation of liquidity shocks, but the di?erence relative to banks with low access to international markets is not statistically signi?cant.
5.3
Time-series probabilities of repeated interactions
In order to better understand the time-series dimension of the relationship between borrowers and lenders we estimate the probability of repeated interactions. More precisely, we estimate the probability that a given lender (L) will lend funds to a given borrower (B ) in the next k
28
days, that is from t + 1 to t + k, conditional on L having lent funds to B at t, and conditional on both L and B lending and borrowing funds in the market in the next k days. Thus, we are trying to answer the following question: given that B has borrowed from L at t, and given that B needs funds again sometime within the next k trading days, how likely is it that it will borrow from L again? Before we turn to the estimation results let us ?rst calculate what we should expect to observe if the matching mechanism was completely random. The average number of loans on a given day is 43.31, and the average daily number of active lenders in the market is 23.1. This corresponds to an average of 1.87 loans per lender each day. Since the average daily number of active borrowers is 17.95, if the matching was completely random the probability of a lender lending to the same borrower at t + 1, conditional on having done so at t and on both lender and borrower being active in the market at t + 1, is 10.2%.19 This probability is roughly one ?fth of the value that we have estimated in the data, and equal to 51% (Table 9, Panel A). This probability increases to 64% if we consider k equal to ?ve, and if we take a 30-day window the probability is as high as 87%. These probabilities are much larger than those we would obtain with a random matching mechanism, which are 18% and 51% for a ?ve and a thirty-day window, respectively. The di?erences are statistically signi?cant at the 1% signi?cance level. Thus, in the interbank market, lenders frequently use previous borrowers and vice-versa, and much more frequently than one would obtain if the matching mechanism was random. With our previous analysis of bank size in mind, in Panel B of Table 9 we take this analysis in that direction. In particular we estimate and ?nd that the probability of repeated interaction is higher if one of the banks is small (asset size below percentile 33) and the other one is large (asset size above percentile 66). When both the borrower and the lender are large the probability of repeated interaction is lower, and it is lowest when both lender and
19
With probability 1/17.95 the bank lends to the same borrower in its ?rst loan, plus with probability
(1 ? 1/17.95) it does not lend to the same borrower in the ?rst loan, but it does so with probability 0.87/17.95 in the 0.87 remaining loan, so that the probability is 1/17.95 + (1 ? 1/17.95) × 0.87/17.95.
29
borrower are small. These estimated probabilities suggest that lending relationship are most important when between small and large banks in the domestic market. In panel B of Table 9, below the estimated probabilities, we report whether these probabilities are statistically di?erent from one another. It is important to note that for k equal to one we do not ?nd that the probability of SS is signi?cantly di?erent than LL or LS because there are very few observations for SS and k = 1.
6
Robustness checks
In Tables 10 through 11 we present several di?erent robustness checks, in which we estimate the SUR system using alternative measures of lending relationships. Table 10 reports the estimation results for the previously constructed BP I # and LP I # indices. In interpreting the results in this table one should recall that a higher index means that banks rely less on lending relationships. That is the interpretation is symmetric to that of the BP I % and LP I % indices. The results in Table 10 are similar to those in Table 6, except for the fact that in the third column the NPL of lenders is positive and statistically signi?cant. Thus lenders with a higher NPL tend to rely more on lending relationships. This is the opposite of what one might have a priori expected. However, this result is not robust to other relationship measures (Tables 6 and 11). We have constructed the LP I % as being equal to the total amount that bank L has lent to bank B as a fraction of the total amount that bank L has lent in the interbank market during the quarter. However, during the same quarter bank L may borrow funds from bank B . We now investigate the robustness of the results to measures that take into account a two-sided relationship factor. More precisely, the relationship measures are: BP I 2L,B,q = LP I 2L,B,q = X¡ ¢ X ¡ all??B ¢ + FiB??all FiL??B + FiB??L / Fi X¡ ¢ X ¡ L??all ¢ + Fiall??L FiL??B + FiB??L / Fi
i?q i?q i?q i?q
(14)
(15)
30
Thus the borrower preference index is now de?ned as the total amount bank B borrowed from plus lent to bank L divided by the total amount of funds that B has borrowed plus lent in the market during quarter q . The estimation results for these alternative relationship measures are reported in Table 11. Although there are some di?erences in magnitude and statistical signi?cance of some of the estimated coe?cients, the results are similar to those we obtained before. Finally, we have constructed lender and borrower preference indices similar to LP I % and BP I % but using number of loans instead of loan amounts. That is the lender preference index was constructed as the number of times that L has lent funds to B during quarter q , as a fraction of the total number of times that bank L has lent funds in the interbank market during the same quarter. The results were similar and are not reported.
7
Conclusion and Policy Implications
Interbank markets play an important role in distributing liquidity across the ?nancial system. It is in this market that banks borrow and lend funds among themselves, allowing for the transfer of liquidity from banks that have excess funds to those that are short. However, since interbank market loans are unsecured, they also increase the exposure of lenders to borrowers. In this paper we have studied lending relationships in a typical interbank market. There are at least two sets of reasons why banks may bene?t from lending relationships. First, in the models of Ho and Saunders (1985), Bhattacharya and Gale (1987), and Freixas, Parigi and Rochet (2000) banks borrow and lend funds in the interbank market to insure against idiosyncratic liquidity shocks that arise from the behavior of retail depositors. Thus, banks may form lending relationships for insurance purposes. Second, Rochet and Tirole (1996) present a model of the interbank market in which asymmetric information and monitoring play an important role. Thus, banks may rely on lending relationships to overcome problems that arise from asymmetric information on credit worthiness. We have provided evidence that supports both of these motives for the existence of lending 31
relationships. Importantly, we have done so by explicitly recognizing that these relationships are endogenous, and addressing the issue by estimating instrumental variables regressions and a system of seemingly unrelated regressions. We have found that smaller banks, with lower return on assets, banks with a higher proportion of non-performing loans and banks that are subject to more volatile liquidity shocks rely more on lending relationships, and that they tend to form relationships with large banks, and banks that are subject to less volatile liquidity shocks. In order to be more precise as to the exact nature of lending relationships, we have investigated the role of bank size in the market structure. Interestingly, we have found that large banks tend to be net buyers of liquidity and small banks tend to be net sellers. This pattern of trade is also a distinctive feature of the US Fed Funds market (see for example Fur?ne, 1999, or Ho and Saunders, 1985). It can be rationalized by the model of Ho and Saunders (1985). If large banks are better able to diversify their risk exposure than small banks, then large banks will be more rate sensitive than small banks, and the slopes of the demand functions for interbank funds of large banks will be more price-elastic than those of small banks. One important policy implication is that open market operations by the central bank will be more e?ective when targeted at large rather than small institutions. We have also investigated how access to international markets a?ects the nature of lending relationships in the domestic market. We have found that large domestic banks tend to have better access to international markets. Interestingly, we have found that banks with low access to international markets tend to have a much higher proportion of non-performing loans. Furthermore, these banks, when borrowing in the domestic interbank market, ?nd it optimal to concentrate their loans. This result is consistent with peer monitoring across borders being less e?cient than at the domestic level, as in the model of Freixas and Holthausen (2005). It suggests that in international unsecured credit markets such as interbank markets, peer monitoring plays an important role in that it allows liquidity to ?ow across borders. However, an alternative explanation is that large banks are perceived by international markets as being too-big-too-fail, and for this reason they can borrow internationally. In either case, our results 32
suggest that domestic regulators should direct their policies towards an improvement of the cross-border information available, particularly so on small banks, so as to enhance crossborder market integration.
33
8
References
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Ongena, Steven and David C. Smith, 2001, “The duration of bank relationships,” Journal of Financial Economics, 61, pp. 449-475. Petersen, Mitchell, and Raghuram Rajan, 1995, “The E?ect of Credit Market Competition on Lending Relationships,” Quarterly Journal of Economics, 110, 407-443. Petersen, Mitchell and Raghuram Rajan, 1994, “The Bene?ts of Lending Relationships: Evidence from Small Business Data,” Journal of Finance, 49, 3-37. Rochet, Jean-Charles and Jean Tirole, 1996, “Interbank Lending and Systemic Risk,” Journal of Money Credit and Banking, 28, 733-762. Slovin, Myron B., Marie E. Sushka, and John A. Poloncheck, 1993, “The Value of Bank Durability: Borrowers versus Bank Stakeholders,” Journal of Finance, 48, pp. 298-302. Spindt, Paul A., and Ronald Ho?meister, 1988, “The Micromechanics of the Federal Funds Market: Implications for Day of the Week E?ects in Funds Rate Variability,” Journal of Financial and Quantitive Analysis, 23, 401-416. Stigum, Marcia, 1990, The Money Market, Dow-Jones Irwin. Upper, Christian, 2004, “Survey of The Literature on Interbank Lending,” manuscript, Deutsche Bundesbank. Wolinsky, Asher, 1990, “Information Revelation in a Market with Pairwise Meetings,” Econometrica, 58, 1-25.
36
Borrower Preference Indices for a Given Bank at a Speci?c Quarter.
0.3
0.25 BPI - Borrower Preference Index
0.2
0.15
0.1
0.05
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Lenders
Figure 1:
Note to Figure 1: This ?gure plots, on a given quarter q, the BP I % indices for a given bank B and all its lenders. The BP I % 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 BP I % is zero were omitted from the ?gure.
Borrower’s Preference Index and Lender’s Preference Index for a Pair of Banks.
0.4
0.35
0.3
0.25 LPI 0.2
0.15 BPI 0.1
0.05
0 1997 Q1 1997 Q2 1997 Q3 1997 Q4 1998 Q1 1998 Q2 1998 Q3 1998 Q4 1999 Q1 1999 Q2 1999 Q3 1999 Q4 2000 Q1 2000 Q2 2000 Q3 2000 Q4
Figure 2:
Note to Figure 2: This ?gure plots the evolution over time of the BP I % and LP I % indices for a pair of banks in our sample, B and L. For each quarter, the BP I % 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, BP I % 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.
Table 1: Summary Statistics.
Mean Stdev Median 25th perc. 75th perc. Interbank Market Amount (million Euros) 27,123 8,545 27,888 24,250 29,444 Number of loans (million Euros) 2,217 994 2,478 1,412 3,032 Number of borrowers 37.19 4.75 39 34 41 Number of lenders 39.31 4.48 40 35 43 Borrower Characteristics Assets (million Euros) 5,736 9,372 1,850 695 6,150 ROA (percent) 17.4 154.3 21.4 5.1 43.7 Non-performing loans (percent) 4.63 8.21 2.68 1.35 5.01 Amount (million Euros) 751 1,080 331 44 984 Number of loans 61 71 32 8 95 Surplus deposits 1.00 0.18 1.00 0.93 1.07 Coef. variation shocks 0.77 0.96 0.35 0.11 1.01 Lenders Characteristics Assets (million Euros) 5,168 8,864 1,334 619 4,967 ROA (percent) 13.6 163.2 22.0 5.1 45.4 Non-performing loans (percent) 5.47 11.71 2.62 1.16 5.05 Amount (million Euros) 712 1,048 419 166 817 Number of loans 58 57 46 20 76 Surplus deposits 1.04 0.17 1.03 0.97 1.10 Coef. variation shocks 0.34 0.43 0.15 0.04 0.41 Borrower/Lender Characteristics Borrower preference index: BPI% (percent) 7.94 14.50 3.07 1.25 7.79 % Lender preference index: LPI (percent) 8.39 13.30 4.09 1.54 9.71 Borrower preference index: BPI# (number) 20.95 9.68 22 14 29 # 16.72 6.75 17 12 21 Lender preference index: LPI (number) Correlation of shocks (percent) 11.98 17.31 12.36 1.62 23.6
Variable
Note to Table 1: 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 2001. Amount is the total volume of overnight loans during a quarter (corrected for double counting) in millions of Euros and number of loans the total number of overnight loans during a quarter. Number of borrowers (lenders) is the number of di?erent borrowing (lending) banks during the quarter. Assets is the value of total assets of the bank at the beginning of each quarter in millions of Euros; ROA is the ratio between the annualized quarterly returns and the bank’s total assets expressed in percentage terms; Non-performing loans is the percentage of past due loans (loans that are overdue for more than 90 days) on the total value of outstanding loans granted by the bank. Amount is the total amount of overnight loans during the quarter, in millions of Euros. Number of loans is the number of overnight loans for lenders (borrowers) during a quarter. Surplus deposits is the quarterly average of the ratio between the current level of deposits in the reserve account (average since the start of the current reserve requirement period until day i) and the reserve requirements of the period. Correlation of shocks is the correlation between the daily changes in the daily central bank deposits (not including the interbank market operations) of the lender and the borrower. Coe?cient of variation of shocks of borrower (lender) is the standard deviation of the daily changes in the bank’s reserve deposits not due to interbank market loans scaled by bank’s % % quarterly reserves. The Borrower (Lender) preference index BPI (LPI ) is equal to the ratio of total funds that the bank has borrowed (lent) from a speci?c lender (borrower) as a fraction of the total amount of funds that # # he has borrowed (lent) in the market during a quarter. The Borrower (Lender) preference index BPI (LPI ) is de?ned as the total number of banks from (to) which the bank has borrowed (lent) funds during the quarter.
Table 2: Correlation Matrix for Borrowers and Lenders.
Borrowers Assets ROA NPL Amt. NLoans RMet(%) RMet(#) SDep Total Assets 1.00 ROA 0.10 1.00 Non-performing loans -0.10 -0.20 1.00 Amount 0.51 0.08 -0.14 1.00 Number of loans 0.23 0.06 -0.10 0.82 1.00 Relationship metric (%) -0.10 -0.06 0.04 -0.25 -0.32 1.00 Relationship metric (#) 0.27 0.08 -0.05 0.67 0.80 -0.46 1.00 Surplus deposits 0.02 -0.01 -0.03 -0.03 -0.09 0.09 -0.13 Coef. variation 0.00 0.00 0.02 -0.05 -0.07 0.19 -0.09 -0.02 Lenders Assets ROA NPL Amt. NLoans RMet(%) RMet(#) SDep Total Assets 1.00 ROA 0.08 1.00 Non-performing loans -0.10 -0.10 1.00 Amount 0.42 0.08 -0.07 1.00 Number of loans 0.21 -0.08 0.12 0.78 1.00 Relationship metric (%) -0.02 -0.02 -0.02 -0.16 -0.22 1.00 Relationship metric (#) 0.32 0.00 -0.01 0.51 0.68 -0.42 1.00 Surplus deposits 0.02 0.00 0.01 -0.04 -0.10 0.01 -0.06 Coef. variation 0.06 0.01 -0.02 -0.05 -0.07 0.20 -0.10 0.01
Note to Table 2: This table reports the correlation matrix for the borrowers and the lenders. Total Assets is the value of assets of the bank at the beginning of each quarter; ROA is the annualized quarterly returns divided by the bank’s total assets expressed in percentage terms; Non-performing loans is the percentage of past due loans (loans that are overdue for more than 90 days) on the total value of outstanding loans granted by the bank. Amount is the total value of overnight loans during the quarter in millions of Euros. Number of loans is the number of overnight loans for lenders (borrowers) during a quarter. Relationship metric represents the values of the borrower and lender preference indices. The Borrower (Lender) preference index (%) is equal to the ratio of total funds that the bank has borrowed (lent) from a speci?c lender (borrower) as a fraction of the total amount of funds that he has borrowed (lent) in the market during a quarter. The Borrower (Lender) preference index (#) is de?ned as the total number of banks from (to) which the bank has borrowed (lent) funds during the quarter. Surplus deposits is the quarterly average of the ratio between the current level of deposits in the reserve account (average since the start of the current reserve requirement period until day i) and the reserve requirements of the period. Coe?cient of variation of shocks of the borrower (lender) is a measure of volatility of the shocks de?ned as the standard deviation of the daily changes in the bank’s reserve deposits not due to interbank market loans scaled by bank’s quarterly reserves. The sample period is January 1997 to August 2001.
Table 3: Average Interest Rate for Borrowers and Lenders. Lenders Borrowers Q1 Q2 Q3 Total assets Q1 0.140 0.345 0.484 Q2 -0.120 0.039 0.223 Q3 -0.343 -0.107 0.052 Q4 -0.738 -0.270 -0.095 Return on assets Q1 0.066 0.215 0.273 Q2 -0.064 0.143 0.114 Q3 -0.039 0.075 0.100 Q4 -0.144 0.022 0.091 Relationship metric (%) Q1 0.009 -0.101 -0.068 Q2 0.219 0.085 0.013 Q3 0.305 0.124 0.037 Q4 0.484 0.307 0.182 Relationship metric (#) Q1 0.239 0.150 0.306 Q2 -0.016 0.011 0.089 Q3 -0.042 0.006 0.069 Q4 -0.288 -0.125 -0.058
Q4 0.635 0.416 0.280 0.173 0.194 -0.007 0.146 0.111 -0.135 -0.021 0.070 0.002 0.474 0.209 0.221 -0.008
Note to Table 3: This table reports average interest rate as a function of the following variables: total assets, return on assets and relationship metrics, for lenders and borrowers. Interest rate is de?ned for every pair of lender and borrower, as the quarterly average of the di?erence between the interest rates on the loans between those two banks and the overnight interest rate on the same days, scaled by the standard deviation of overnight interest rates for each day. Total Assets is value of assets of the bank at the beginning of each quarter. Return on assets is the annualized quarterly returns divided by the bank’s total assets expressed in percentage terms. Relationship metric represents the values of the borrower and lender preference indices. The Borrower (Lender) preference index (%) is equal to the ratio of total funds that the bank has borrowed (lent) from a speci?c lender (borrower) as a fraction of the total amount of funds that he has borrowed (lent) in the market during a quarter. The Borrower (Lender) preference index (#) is de?ned as the total number of banks from (to) which the bank has borrowed (lent) funds during the quarter. The sample period is January 1997 to August 2001.
Table 4: Multivariate Model for Interest Rate.
Independent variables Assets Market share ROA Non-performing loans Surplus deposits Coef. variation
(i) (ii) (iii) Borrower Characteristics -0.098*** -0.103*** (13.43) (12.98)
(iv)
(v)
(vi)
0.090*** 0.091*** (13.02) (14.14) Market share 1.666*** -0.129 (8.29) (0.56) ROA 0.150 0.1333 1.184*** 0.146 0.057 (0.54) (0.44) (3.69) (0.47) (0.19) Non-performing loans 0.066* 0.089 -0.076 0.089 0.099 (1.66) (1.45) (1..19) (1.44) (1.61) Surplus deposits 0.063 0.052 0.059 0.049 (1.18) 0.95 (1.11) (0.91) Coef. variation -0.017*** -0.012*** -0.018*** -0.014*** (10.53) (3.89) (9.61) (7.93) Borrower/Lender Characteristics Correlation of shocks -0.003 -0.003 -0.004 -0.011 (0.06) (0.05) (0.09) (0.23) Borrower pref. index (%) 0.240*** -0.155*** -0.184*** -0.142*** -0.196*** (4.18) (2.71) (2.85) (2.00) (2.83) Lender pref. index (%) -0.180*** 0.218*** 0.347*** 0.445*** 0.404*** (3.15) (3.44) (4.78) (5.25) (4.97) Borrower pref. index (#) 0.001 (0.93) Lender pref. index (#) -0.005** (2.59) Number obs. 7724 7046 6410 6410 6410 6410 2 R 0.01 0.08 0.08 0.05 0.08 0.08
Assets
1.245* (1.85) 0.548*** (2.72) -0.117** (2.21) 0.000 (0.26) Lender Characteristics 0.083*** 0.087*** (15.25) (14.98)
1.194* (1.84) 0.512*** (2.67)
-0.086*** -0.097*** (8.72) (9.80) -2.141*** -0.603*** (9.80) (2.25) -0.318 1.116* 1.250* (0.48) (1.65) (1.86) 0.616*** 0.539*** 0.531*** (3.12) (2.70) (2.54) -0.100* -0.111** -0.105* (1.85) (2.09) (1.90) 0.000 0.000 -0.001 (0.30) (0.04) (0.83)
Note to Table 4: We estimate the following multivariate models:
%,q %,q q q q (i) iq L,B = ? + ?BP IL,B + ?LP IL,B + ? D + uL,B q q q %,q %,q q q q (ii) iq L,B = ? + ?j =L,B [? 1j Si zej + ? 2j ROAj + ? 3j N P Lj ] + ?BP IL,B + ?LP IL,B + ? D + uL,B q q q q q K,q (iii) to (vi) iq L,B = ? + ?j =L,B [? 1j Si zej + ? 2j ROAj + ? 3j N P Lj + ? 4j SDj + ? 5j CVj ] + ? 6 ? l,B + ?BP IL,B + K,q q q q ?LP IL,B + ? D + uL,B
where k = %, # represent the two relationship metrics. The dependent variable, interest rate, is de?ned for every pair of lender and borrower, as the quarterly average of the di?erence between the interest rates on the loans between those two banks and the overnight interest rate on the same days scaled by the standard deviation % % of overnight interest rates for each day. The variable BP I (LP I ) is the borrower (lender) preference index and is equal to the ratio of total funds that the bank has borrowed (lent) from a speci?c lender (borrower) as a fraction of the total amount of funds that he has borrowed (lent) in the market during a quarter. The Borrower (Lender) preference index BP I (LP I ) is de?ned as the total number of banks from (to) which the bank has borrowed (lent) funds during the quarter. Assets is the logarithm of the value of assets of the bank at the beginning of each quarter; Market Share is the total amount that the lender has lent (borrower has borrowed) in the interbank marketduring the quarter over the total amount lent/borrowed by all banks in the market; ROA are the annualized quarterly returns divided by the bank’s total assets expressed in percentage terms; Non-performing loans (NP L) is the percentage of past due loans (loans that are overdue for more than 90 days) on the total value of outstanding loans granted by the bank. Surplus deposits (SD) is the quarterly average of the ratio between the current level of deposits in the reserve account (average since the start of the current reserve requirement period until day i) and the reserve requirements of the period. Coe?cient of variation (CV ) of shocks of the borrower (lender) is a measure of volatility of the shocks de?ned as the standard deviation of the daily changes in the bank’s reserve deposits not due to interbank market loans scaled by bank’s quarterly reserves. Correlation of shocks measures the correlation between the daily changes in the daily central bank deposits (not including the interbank market operations) of lender and borrower. The variables D are dummy variables denoting quarter ?xed e?ects. Robust t-statistics are shown in parenthesis. The sample period is January 1997 to August 2001. ***, **, and * denotes signi?cance at the 1%, 5%, and 10% percent level respectively.
# #
Table 5: Model for Interest Rate using Instrumental Variables
Independent variables (i) Borrower Characteristics Assets -0.103*** (10.16) ROA 1.166 (0.95) Non-performing loans 0.421** (2.12) Surplus deposits -0.075 (0.98) Coef. variation -0.011 (0.70) Lender Characteristics Assets 0.085*** (11.89) ROA -0.032 (0.05) Non-performing loans 0.095 (0.86) Surplus deposits -0.041 (0.54) Coef. variation -0.013 (0.32) Borrower/Lender Characteristics Correlation of shocks -0.016 (0.25) Borrower preference index (%) -0.208* (1.77) Lender preference index (%) 0.515*** (2.72) Borrower preference index (#) Borrower preference index (#) Number obs. R2 4358 0.073 (ii) -0.112*** (10.71) 1.489 (1.40) 0.502*** (2.74) -0.096 (1.34) -0.000 (0.01) 0.094*** (13.01) 0.014 (0.02) 0.094 (0.88) 0.068 (0.99) -0.015*** (2.64) -0.033 (0.56)
0.004** (2.19) -0.006** (2.02) 5846 0.071
Note to Table 5: We estimate the following model:
q q q q q k,q k,q iq L,B = ? + ?j =L,B [? 1j Si zej + ? 2j ROAj + ? 3j N P Lj + ? 4j SDj + ? 5j CVj ] + ? 6 ? l,B + ?BP IL,B + ?LP IL,B + q q ? D + uL,B q k,t?1 k,t?1 k,t using the variables BP IL,B and LP IL,B as instruments for BP IL,B and LP I L,B , respectively, and where k = %,# are the two relationship metrics. The dependent variable, interest rate, is de?ned for every pair of lender and borrower, as the quarterly average of the di?erence between the interest rates on the loans between those two banks and the overnight interest rate on the same days scaled by the standard deviation of overnight interest rates for each day. The variable BP I % (LP I % ) is the borrower (lender) preference index and is equal to the ratio of total funds that the bank has borrowed (lent) from a speci?c lender (borrower) as a fraction of the total amount of funds that he has borrowed (lent) in the market during a quarter. The Borrower (Lender) preference # # index BPI (LPI ) is de?ned as the total number of banks from (to) which the bank has borrowed (lent) funds during the quarter. Assets is the logarithm of the value of assets of the bank at the beginning of each quarter; ROA are the annualized quarterly returns divided by the bank’s total assets expressed in percentage terms; Non-performing loans (N P L) is the percentage of past due loans (loans that are overdue for more than 90 days) on the total value of outstanding loans granted by the bank. Surplus deposits (SD) is the quarterly average of the ratio between the current level of deposits in the reserve account (average since the start of the current reserve requirement period until day i) and the reserve requirements of the period. Coe?cient of variation (CV ) of shocks of the borrower (lender) is a measure of volatility of the shocks de?ned as the standard deviation of the daily changes in the bank’s reserve deposits not due to interbank market loans scaled by bank’s quarterly reserves. Correlation of shocks measures the correlation between the daily changes in the daily central bank deposits (not including the interbank market operations) of lender and borrower. The variables D are dummy variables denoting quarter ?xed e?ects. Robust t-statistics are shown in parenthesis and are corrected for ?rststage estimation error. The sample period is January 1997 to August 2001. ***, **, and * denotes signi?cance at the 1%, 5%, and 10% percent level respectively.
k,t
Table 6: SUR Model using BPI% and LPI%.
Independent variables Assets ROA Non-performing loans Surplus deposit Coef. Variation BPI% LPI% Borrower -0.025*** 0.024*** (20.67) (23.14) 0.088 -0.064 (0.49) (0.42) 0.152*** -0.009 (5.47) (0.36) -0.044*** -0.051*** (3.71) (5.05) 0.011*** -0.000 (16.03) (0.40) Lender 0.011*** -0.001 (10.33) (1.43) -0.025 -0.064 (0.23) (0.69) 0.003 -0.003 (0.19) (0.18) -0.009 -0.001 (0.77) (0.14) -0.002** 0.015*** (2.20) (18.45) Borrower/Lender -0.062*** -0.049*** (6.37) (5.85) 6410 6410 0.17 0.19 Int. Rate -0.090*** (13.40) 1.207 (1.22) 0.517*** (3.32) -0.143** (2.17) -0.002 (0.47) 0.084*** (14.37) 0.116 (0.19) 0.087 (0.89) 0.064 (0.98) -0.012** (2.26) -0.008 (0.16) 6410 0.08 Amount 6.313*** (7.33) -178.190 (1.41) -34.552* (1.74) 23.017*** (2.75) -0.776 (1.63) -5.442*** (7.27) -337.062*** (4.40) 44.831*** (3.55) -24.495*** (2.92) -1.423** (2.14) -64.583*** (9.31) 6410 0.05
Assets ROA Non-performing loans Surplus deposit Coef. Variation
Correlation of shocks Number obs. R2
BPI% LPI% Interest rate Amount
Correlation of residuals BPI% LPI% Int. Rate 1.000 0.128 1.000 -0.026 0.049 1.000 0.312 0.438 0.008
Amount
1.000
Note to Table 6: We estimate the following equations using a SUR system: £ 1 q q q q q¤ 1 1 1 1 1 q1 q1 1 iq + uq L;B = ? + ?j =L,B ? 1j Si zej + ? 2j ROAj + ? 3j N P Lj + ? 4j SDj + ? 5j CVj + ? 6 ? B,L + ? D L,B
£ 2 %q q q q q q¤ q 2 2 2 2 2 q2 q2 2 BP IL ;B = ? + ?j =L,B ? 1j Si zej + ? 2j ROAj + ? 3j N P Lj + ? 4j SDj + ? 5j CVj + ? 6 ? B,L + ? D + ?L,B £ 3 %q q q q q q¤ q 3 3 3 3 3 q3 q3 3 LP IL ;B = ? + ?j =L,B ? 1j Si zej + ? 2j ROAj + ? 3j N P Lj + ? 4j SDj + ? 5j CVj + ? 6 ? B,L + ? D + ? L,B £ 4 q q q q q q¤ q 4 4 4 4 4 q4 q4 4 Ln(VL ;B ) = ? + ?j =L,B ? 1j Si zej + ? 2j ROAj + ? 3j N P Lj + ? 4j SDj + ? 5j CVj + ? 6 ? B,L + ? D + ? L,B
The dependent variables are: the interest rate i, de?ned for every pair of lender and borrower, as the quarterly average of the di?erence between the interest rates on the loans between those two banks and the overnight interest rate on the same days scaled by the standard deviation of overnight interest rates for each day; BP I % (LP I % ) is the borrower (lender) preference index and is equal to the ratio of total funds that the bank has borrowed (lent) from a speci?c lender (borrower) as a fraction of the total amount of funds that he has borrowed (lent) in the market during a quarter; ln(V ) is the logarithm of the total volume of overnight loans during the quarter (corrected for double counting) in millions of Euros. The independent variables are: Assets is the logarithm of the value of assets of the bank at the beginning of each quarter; ROA are the annualized quarterly returns divided by the bank’s total assets expressed in percentage terms; Non-performing loans (NP L) is the percentage of past due loans (loans that are overdue for more than 90 days) on the total value of outstanding loans granted by the bank. Surplus deposits (SD) is the quarterly average of the ratio between the current level of deposits in the reserve account (average since the start of the current reserve requirement period until day i) and the reserve requirements of the period. Coe?cient of variation (CV ) of shocks of the borrower (lender) is a measure of volatility of the shocks de?ned as the standard deviation of the daily changes in the bank’s reserve deposits not due to interbank market loans scaled by bank’s quarterly reserves. Correlation of shocks measures the correlation between the daily changes in the daily central bank deposits (not including the interbank market operations) of the lender and the borrower. The variables D are dummy variables denoting quarter ?xed e?ects. Robust t-statistics are shown in parenthesis. The sample period is January 1997 to August 2001.
Table 7, Panel A: Small versus Large Banks. Variable All Small (S) Large (L) p-value S = L Total amount borrowed (million Euros) 596.50 124.18 923.87 0.000 Total amount lent (million Euros) 596.50 487.44 524.18 0.643 Net amount borrowed (million Euros) 0.00 -363.26 399.69 0.000 # Loans as borrower 48.77 21.02 62.59 0.000 # Loans as lender 48.77 66.91 35.24 0.000 # Loans as borrower - # Loans as lender 0.00 -45.89 27.35 0.000 Average loan size as borrower 12.23 5.91 14.76 0.000 Average loan size as lender 12.23 7.29 14.87 0.000 Non-performing loans (percent) 5.33 8.74 3.72 0.000 Borrower Preference Index (BP I % ) 9.13 15.22 6.85 0.000 % Lender Preference Index (LP I ) 9.65 10.13 12.06 0.148
Note to Table 7, Panel A: Large (small) banks are those in the top (bottom) one third of the total assets distribution. Total amount borrowed (lent) is the average total amount borrowed (lent) by each bank during the quarter. Net amount borrowed is the di?erence between total amount borrowed and total amount lent. # Loans as borrower (lender) is the average number of loans in which each bank has been a borrower (lender) during the quarter. Average loan size as borrower (lender) is the average amount borrowed (lent) in each loan. Non-performing loans is the percentage of past due loans (loans that are overdue for more than 90 days) on the % % total value of outstanding loans granted by the bank. The Borrower (Lender) preference index BPI (LPI ) is equal to the ratio of total funds that the bank has borrowed (lent) from a speci?c lender (borrower) as a fraction of the total amount of funds that he has borrowed (lent) in the market during a quarter. The table shows averages across all quarters in the sample. The division between large and small banks is made on a quarterly basis, using the respective total assets quarterly distribution. The last column shows the p-value of a t-test of equality of the values for small and large banks.
Table 7, Panel B: Frequency of Borrowing and Lending Positions. Frequency on both Proportion Bank Assets Non-Performing sides of the market of banks (million of euros) Loans At least once a month 66.1% 6,058 5.53% At least once every two weeks 61.3% 6,395 4.72% At least once a week 50.2% 7,271 4.42% At least twice a week 38.7% 8,420 4.20%
Note to Table 7, Panel B: This table shows the proportion of banks that appear on both sides of the market, i.e. as lenders and borrowers, over a given time period. The last two columns report the average bank assets and the proportion of non-performing loans for banks that on average appear on both sides of the market over the corresponding time period.
Table 8: International linkages. Banks with Banks with p-value of test low access high access eq. means Total assets (million Euros) 1940.74 9645.24 0.000 Non-performing loans (percent) 8.22 2.50 0.003 Coef. variation shocks 0.555 0.493 0.802 Borrower Preference Index (BP I % ) 18.41 9.25 0.000 % Lender Preference Index (LP I ) 13.60 12.64 0.644 Total amount borrowed (million Euros) 115.35 925.15 0.000 Total amount lent (million Euros) 592.52 538.36 0.711 # Loans as borrower 13.99 51.67 0.000 # Loans as lender 52.36 23.46 0.000
Note to table 8: This table shows several variables for banks with low and high access to international markets. We ?rst construct a measure of access to international markets equal to the funds that the bank has sent abroad plus received from abroad during each quarter, scaled by the bank’s assets. Banks with low (high) access to international markets are those in the bottom (top) one third of the distribution for this variable. The table reports means for these two groups. Assets is the value of total assets of the bank at the beginning of each quarter in millions of Euros. Non-performing loans is the percentage of past due loans (loans that are overdue for more than 90 days) on the total value of outstanding loans granted by the bank. The Borrower (Lender) preference % % index BPI (LPI ) is equal to the ratio of total funds that the bank has borrowed (lent) from a speci?c lender (borrower) as a fraction of the total amount of funds that he has borrowed (lent) in the market during a quarter. Total amount borrowed (lent) is the average total amount borrowed (lent) in the domestic interbank market by each bank during the quarter. # Loans as borrower (lender) is the average number of loans in which each bank has been a borrower (lender) in the domestic interbank market during the quarter. The table shows averages across all quarters from 1999 onwards, the sample period for which we have international data. The last column shows the p-value of a t-test of equality of the values for banks with low and high access.
Table 9: Probability of repeated interactions assuming random matching and in the data Number of 1 3 5 10 30 Number of 1 3 5 10 30 Panel A: Random Matching and in the Data for all banks Days Random Matching Data p-value: Random = Data 0.102 0.511 0.000 0.140 0.585 0.000 0.179 0.643 0.000 0.269 0.732 0.000 0.513 0.865 0.000 Panel B: In the data by bank size Days Large-Large (LL) Large-Small (LS) Small-Small (SS) 0.526 0.547 0.333 LS ?? LL?? 0.591 0.590 0.355 ?? ?? SS SS LL?? , LS ?? 0.653 0.671 0.429 ?? ??? ?? ??? ??? LS , SS LL , SS LL , LS ??? 0.741 0.779 0.447 LS ??? , SS ??? LL??? , SS ??? LL??? , LS ??? 0.875 0.904 0.581 LS ??? , SS ??? LL??? , SS ??? LL??? , LS ???
Note to table 9: This table shows the probability that a given lender (L) will lend funds to a given borrower (B ) in the next k days, that is from t + 1 to t + k , conditional on L having lent funds to B at t, and conditional on both L and B lending and borrowing funds in the market in the next k trading days. The table shows the results for k = 1, 3, 5, 10, 30. Panel A shows the calculated probability assuming random matching of lenders and borrowers, and the estimated probabilities in the data. The last column of table A shows the p-value of a test of the equality of the randome matching probailities and the estimated probabilities in the data. Table B shows the estimated probabilities in the data by bank size. Large (Small) banks are those in the top (bottom) one third of the distribution of total assets. Below the estimated coe?cients we report whether the estimated probabilities are statistically signi?cant across banks of di?erent sizes. ***, **, and * denotes signi?cance at the 1%, 5%, and 10% percent level respectively.
Table 10: Robustness Check: SUR Model using BPI# and LPI#. Independent variables Assets ROA Non-performing loans Surplus deposit Coef. Variation LPI# Borrower 3.987*** -0.409*** (64.88) (8.62) -9.949 5.901 (1.10) (0.85) -14.132*** -0.207 (9.98) (0.46) -1.292** 6.912*** (2.16) (14.96) -0.275*** 0.022 (8.10) (0.84) Lender -0.144*** 1.310*** (2.69) (31.76) 1.910 -11.005*** (0.35) (2.61) -0.911 2.101*** (1.01) (3.02) 0.396 -2.862*** (0.66) (6.20) 0.052 -0.375*** (1.10) (10.25) Borrower/Lender -0.383 -0.680* (0.77) (1.78) 6410 6410 0.54 0.43 BPI# Int. Rate -0.090*** (13.40) 1.207 (1.22) 0.517*** (3.32) -0.143** (2.17) -0.002 (0.47) 0.084*** (14.37) 0.116 (0.19) 0.087 (0.89) 0.064 (0.98) -0.012** (2.26) -0.008 (0.16) 6410 0.08 Amount 6.313*** (7.33) -178.190 (1.41) -34.552* )1.74) 23.017*** (2.75) -0.776 (1.63) -5.442*** (7.27) -337.062*** (4.40) 44831*** (3.55) -24.495*** (2.92) -1.423** (2.14) -64.583*** (9.31) 6410 0.05
Assets ROA Non-performing loans Surplus deposit Coef. Variation
Correlation of shocks Number obs. R2
Note to Table 10: We estimate the following equations using a SUR system: £ 1 q q q q q¤ 1 1 1 1 1 q1 q1 1 + uq iq L;B = ? + ?j =L,B ? 1j Si zej + ? 2j ROAj + ? 3j N P Lj + ? 4j SDj + ? 5j CVj + ? 6 ? B,L + ? D L,B
£ 2 #q q q q q q¤ q 2 2 2 2 2 q2 q2 2 BP IL ;B = ? + ?j =L,B ? 1j Si zej + ? 2j ROAj + ? 3j N P Lj + ? 4j SDj + ? 5j CVj + ? 6 ? B,L + ? D + ?L,B £ 3 #q q q q q q¤ q 3 3 3 3 3 q3 q3 3 LP IL ;B = ? + ?j =L,B ? 1j Si zej + ? 2j ROAj + ? 3j N P Lj + ? 4j SDj + ? 5j CVj + ? 6 ? B,L + ? D + ? L,B £ 4 q q q q q q¤ q 4 4 4 4 4 q4 q4 4 Ln(VL ;B ) = ? + ?j =L,B ? 1j Si zej + ? 2j ROAj + ? 3j N P Lj + ? 4j SDj + ? 5j CVj + ? 6 ? B,L + ? D + ? L,B
The dependent variables are: the interest rate i, de?ned for every pair of lender and borrower, as the quarterly average of the di?erence between the interest rates on the loans between those two banks and the overnight interest rate on the same days scaled by the standard deviation of overnight interest rates for each day; the # # variable BP I (LP I ) is the borrower (lender) preference index and is de?ned as the total number of banks from (to) which the bank has borrowed (lent) funds during the quarter; ln(V ) is the logarithm of the total volume of overnight loans during the quarter (corrected for double counting) in millions of Euros. The independent variables are: Assets is the logarithm of the value of assets of the bank at the beginning of each quarter; ROA are the annualized quarterly returns divided by the bank’s total assets expressed in percentage terms; Non-performing loans (NP L) is the percentage of past due loans (loans that are overdue for more than 90 days) on the total value of outstanding loans granted by the bank. Surplus deposits (SD) is the quarterly average of the ratio between the current level of deposits in the reserve account (average since the start of the current reserve requirement period until day i) and the reserve requirements of the period. Coe?cient of variation (CV ) of shocks of the borrower (lender) is a measure of volatility of the shocks de?ned as the standard deviation of the daily changes in the bank’s reserve deposits not due to interbank market loans scaled by bank’s quarterly reserves. Correlation of shocks measures the correlation between the daily changes in the daily central bank deposits (not including the interbank market operations) of the lender and the borrower. The variables D are dummy variables denoting quarter ?xed e?ects. Robust t-statistics are shown in parenthesis. The sample period is January 1997 to August 2001.
Table 11: Robustness Check: Using a Two Side Relationship Metric. Two sided relationship indices BPI2 LPI2 Int. Rate Amount Borrower Assets -0.007*** 0.013*** -0.090*** 6.313*** (9.58) (17.61) (13.40) (7.33) ROA 0.292** -0.076 1.207 -178.190 (2.57) (0.71) (1.22) (1.41) Non-performing loans 0.035** 0.013 0.517*** -34.552* (1.96) (0.75) (3.32) (1.74) Surplus deposits 0.013* -0.030*** -0.143** 23.017*** (1.70) (4.28) (2.17) (2.75) Coef. Variation 0.003*** -0.001 -0.002 -0.776 (7.02) (1.63) (0.47) (1.63) Lender Assets 0.011*** -0.007*** 0.084*** -5.442*** (16.88) (10.63) (14.37) (7.27) ROA -0.050 -0.045 0.116 -337.062*** (0.73) (0.70) (0.19) (4.40) Non-performing loans 0.003 0.009 0.087 44.831*** (0.29) (0.88) (0.89) (3.55) Surplus deposits 0.006 0.002 0.064 -24.495*** (0.82) (0.31) (0.98) (2.92) Coef. Variation -0.001* 0.003*** -0.012** -1.423** (1.76) (5.10) (2.26) (2.14) Borrower/Lender Correlation of shocks -0.067 -0.076*** -0.008 -64.583*** (10.80) (12.99) (0.16) (9.31) Number obs. 6410 6410 6410 6410 2 R 0.12 0.14 0.08 0.05 Independent variables
Note to Table 11: We estimate the following equations using a SUR system: £ 1 q q q q q¤ 1 1 1 1 1 q1 q1 1 + uq iq L;B = ? + ?j =L,B ? 1j Si zej + ? 2j ROAj + ? 3j N P Lj + ? 4j SDj + ? 5j CVj + ? 6 ? B,L + ? D L,B
£ 2 q q q q q¤ q 2 2 2 2 2 q2 q2 2 BP I 2q L;B = ? + ?j =L,B ? 1j Si zej + ? 2j ROAj + ? 3j N P Lj + ? 4j SDj + ? 5j CVj + ? 6 ? B,L + ? D + ?L,B £ 3 q q q q q¤ q 3 3 3 3 3 q3 q3 3 LP I 2q L;B = ? + ?j =L,B ? 1j Si zej + ? 2j ROAj + ? 3j N P Lj + ? 4j SDj + ? 5j CVj + ? 6 ? B,L + ? D + ? L,B £ 4 q q q q q q¤ q 4 4 4 4 4 q4 q4 4 Ln(VL ;B ) = ? + ?j =L,B ? 1j Si zej + ? 2j ROAj + ? 3j N P Lj + ? 4j SDj + ? 5j CVj + ? 6 ? B,L + ? D + ? L,B
The dependent variables are: the interest rate i,de?ned for every pair of lender and borrower, as the quarterly average of the di?erence between the interest rates on the loans between those two banks and the overnight interest rate on the same days scaled by the standard deviation of overnight interest rates for each day; BP I 2 (LP I 2) is the borrower (lender) preference index and is equal to the ratio of total funds that the bank has borrowed and lent from a speci?c lender (borrower) as a fraction of the total amount of funds that he has borrowed and lent in the market during a quarter; ln(V ) is the logarithm of the total volume of overnight loans during the quarter (corrected for double counting) in millions of Euros. The independent variables are: Assets is the logarithm of the value of assets of the bank at the end of each quarter; ROA are the annualized quarterly returns divided by the bank’s total assets expressed in percentage terms; Non-performing loans (NP L) is the percentage of past due loans (loans that are overdue for more than 90 days) on the total value of outstanding loans granted by the bank. Surplus deposits (SD) is the quarterly average of the ratio between the current level of deposits in the reserve account (average since the start of the current reserve requirement period until day i) and the reserve requirements of the period. Coe?cient of variation (CV ) of shocks of the borrower (lender) is a measure of volatility of the shocks de?ned as the standard deviation of the daily changes in the bank’s reserve deposits not due to interbank market loans scaled by bank’s quarterly reserves. Correlation of shocks measures the correlation between the daily changes in the daily central bank deposits (not including the interbank market operations) of the lender and the borrower. The variables D are dummy variables denoting quarter ?xed e?ects. Robust t-statistics are shown in parenthesis. The sample period is January 1997 to August 2001.
doc_451213750.pdf
Banks are required to hold an adequate amount of liquid assets, such as cash, to manage any potential bank runs by clients.
Lending Relationships in the Interbank Market?
João F. Cocco† Francisco J Gomes‡ Nuno C. Martins§ July 2005
?
We would like to thank Viral Acharya, Andrea Buraschi, Jennifer Conrad, Francesca Cornelli, Denis
Gromb, Michel Habib, Philipp Hartmann, Narayan Naik, Jose Peydro-Alcayde, Mitchell Petersen, Maximiano Pinheiro, Raghuram Rajan, Rafael Repullo, Henri Servaes and seminar participants at the Bank of England, Banco de Portugal, Cass Business School, European Central Bank, London Business School, London School of Economics, the 2002 European Winter Meetings of the Econometric Society, the 2004 American Finance Association meetings, and the 2005 Conference on Competition, Stability, and Integration in European Banking for helpful comments and suggestions. We are especially grateful to an anonymous referee for detailed and constructive comments. The analysis, opinions and ?ndings of this paper represent the views of the authors, they are not necessarily those of the Banco de Portugal. † London Business School, Regent’s Park, London NW1 4SA, UK, and CEPR. Email [email protected]. ‡ London Business School, Regent’s Park, London NW1 4SA, UK, and CEPR. Email [email protected] § Universidade Nova de Lisboa and Banco de Portugal, Av. Almirante Reis, 71, 1150-012 Lisboa, Portugal. E-mail [email protected]
1
Abstract
We use a unique dataset to study lending relationships in the interbank market. We explicitly control for the endogeneity of lending relationships, and ?nd that borrowers pay a lower interest rate on loans from banks with whom they have a stronger relationship. Moreoever, we ?nd that smaller banks, banks with lower return on assets, banks with a higher proportion of non-performing loans, and banks subject to more volatile liquidity shocks rely more on lending relationships. Finally, we ?nd evidence that smaller banks with limited access to international markets tend to rely on lending relationships when borrowing in the domestic interbank market. This provides evidence that banks rely on lending relationships to overcome monitoring and default risk problems, and for insurance purposes.
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 very di?erent from those that arise in a spot market. One important setting in which there are frequent and repeated interactions between agents is the interbank market. Our paper studies the role of lending relationships in this market. Understanding lending behavior and price formation in the interbank market is important for banks who use it to engage in unsecured borrowing and lending of funds. It is also important for monetary authorities, since the interbank market lies at the heart of monetary policy. Moreover, it is in this market that the overnight rate is determined, which is the shortest-term market interest rate, and as such it has a crucial role in term structure models. The interbank market is fragmented in nature. For direct loans, which account for most of the lending volume, the loan’s amount and interest rate are agreed on a one-to-one basis between borrower and lender. Other banks do not have access to the same terms, and do not even know that the loan took place. When quotes are posted on screens, they are merely indicative. This market structure allows banks to establish lending relationships.1 But which economic purpose do lending relationships in interbank markets serve? The literature has focused on the function of these markets has distributors of liquidity. In the model of Ho and Saunders (1985), the reserve position of each bank is a?ected by stochastic deposits and withdrawals by customers. As a result banks trade in order to meet their reserve requirements. Similarly, in the model of Bhattacharya and Gale (1987) banks borrow and lend funds in order to insure against intertemporal liquidity shocks. In the model of Allen and Gale (2000) liquidity shocks arise from uncertainty in the timing of depositors’ consumption. Banks hold deposits with banks in other regions to insure against liquidity shocks in their own region. Finally, in the model of Freixas, Parigi and Rochet (2000) the uncertainty and
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, Biais, 1993, and O’Hara, 1995).
1
interbank lending arise from consumers’ uncertainty about where to consume. A common feature to these (and other) models of the interbank market are liquidity shocks, that give rise to borrowing and lending. Lending relationships may provide insurance against liquidity shocks. Another important strand of the literature focuses on the role of peer monitoring in interbank markets (see the models of Rochet and Tirole, 1996, Freixas and Holthausen, 2005, and the empirical analysis in Fur?ne, 2001). Peer monitoring is important because of the large and unsecured nature of the loans. Thus, lending relationships may help overcome agency problems. In addition to focusing on lending relationships in the interbank market, the main novelty of our analysis is that we recognize that the decision of whether to rely on lending relationships is an endogenous choice, and our econometric approach treats it as such. For this reason we are able to provide new insights into the determinants of lending relationships. 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 2001. The Portuguese interbank market is in many respects typical and, although smaller, it is organized similarly to the US Fed Funds market. Our dataset identi?es the date, interest rate, amount, maturity, lender and borrower of each loan. Thus, we can track loans between each and every pair of banks, and with other banks over time. Using this information, we construct dynamic measures of relationships based on the intensity of pair-wise lending activity. Our dataset also includes daily information on each bank’s reserve deposits, and quarterly information on banks’ balance sheet variables including total assets, return on assets and proportion of non-performing loans. We ?rst investigate the link between the loan interest rate and relationship measures. To address the endogeneity issue we estimate instrumental variables regressions, in which we explore the time-series dimension of our dataset by using 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. Importantly, we ?nd that 2
borrowers pay a lower interest rate on loans from banks with whom they have a stronger lending relationship. We also ?nd that once we control for the endogeneity of lending relationships, several other explanatory variables are no longer important for explaining the loan interest rate. The instrumental variables regressions allow us to identify the causal link between relationship measures and the loan interest rate, but they do not explain the determinants of lending relationships. To do so we estimate a seemingly unrelated regressions system of equations, with the amount lent, the interest rate, and the relationship measures for lender and borrower as dependent variables. This allows us to simultaneously study the determinants of loan pricing, loan amount, and of lending relationships. Our main ?ndings are as follows. First, we ?nd that borrowers with lower return on assets and with a higher proportion of non-performing loans are more likely to rely on lending relationships. These results provide empirical support for an explanation of these relationships based on default risk and monitoring. 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 ?nd that borrowers with more volatile liquidity shocks are more likely to rely on lending relationships. They tend to do so with lenders who have less volatile liquidity shocks, and also with whom they have less correlated shocks. In addition, borrowers are more likely to rely on lending relationships when they experience a larger imbalance in their reserve deposits. This provides evidence that banks rely on lending relationships for insurance. We ?nd that small borrowers are more likely to establish relationships and that they tend to choose larger banks as their preferred lenders. Furthermore, large banks tend to be net borrowers, while small banks tend to be net lenders in the market. Interestingly, this pattern of trade is also a distinctive feature of the US Fed Funds market (Fur?ne, 1999, Ho and Saunders, 1985). Finally, we investigate how banks’ ability to access international markets a?ect the nature of lending relationships in the domestic interbank market. We ?nd that small banks and banks 3
with a higher proportion of non-performing loans tend to have limited access to international markets, and that they tend concentrate their borrowing when borrowing funds in the domestic interbank market. This result may be due to peer monitoring across borders being less e?cient than at the domestic level, as in the model of Freixas and Holthausen (2005). Our results for the pricing or interbank loans are consistent with those of Fur?ne (2001) for the Fed Funds market. We ?nd that, controlling for the degree of lending relationship and holding the size of the counterparty ?xed, larger banks borrow and lend at more favorable terms. Banks with higher return on assets lend at higher interest rates. This is consistent with these banks having a higher opportunity cost of lending funds in the interbank market, and requiring a higher interest rate to do so. Borrowers with a higher proportion of nonperforming loans tend to pay higher interest rates. Again controlling for the degree of lending relationship, we ?nd that more pro?table banks lend less, and banks with a higher proportion of non-performing loans lend more and borrow less. Thus banks that have better investment opportunities tend to be net borrowers. There is a large literature on lending relationships that focuses on bank-?rm relationships. It has found evidence that lending relationships help overcome constraints that arise from monitoring and default risk between borrower and lender of funds,2 and allow banks to provide insurance to ?rms in the form of interest-rate smoothing.3 Thus this literature focuses on longterm relationships between banks and ?rms, by which banks acquire inside knowledge about ?rm characteristics or the project that is being ?nanced. Although somewhat related, it is important to note that these relationships are of a di?erent nature than the ones that we study in our paper, which are transaction based. The paper proceeds as follows. Section 2 describes the data, our relationship metrics and reports some summary statistics. Section 3 studies the pricing of interbank loans. Section 4
2
See Berger and Udell (1995), Lummer and McConnell (1989), Petersen and Rajan (1994), Slovin, Sushka,
and Poloncheck (1993). 3 See Berger and Udell (1992), Berlin and Mester (1999), Petersen and Rajan (1995), or Ongena and Smith (2000) for a survey of the literature on bank lending relationships.
4
investigates the determinants of lending relationships. Section 5 presents additional evidence on the determinants of lending relationships, that allows us to be more precise with respect to their nature. Section 6 reports some robustness checks. Section 7 concludes.
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2.1
The Data
Description
We combine information from three di?erent datasets, which we have obtained from the Portuguese Central Bank. The ?rst dataset has information on all direct loans in the Portuguese interbank market from January 1997 to August 2001. The Portuguese interbank market is a typical interbank market, and although of a smaller size, it functions in a similar way 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, identi?es 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 di?erent quotes for di?erent banks that approach them, and it is common practice for banks 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 our sample period there were 44, 768 overnight loans accounting for
5
over 75 percent of the total amount lent (casual evidence suggests that this is a common feature in most interbank markets). Even though credit risk for loans of overnight maturity may be small, it is important to note that these are large and uncollaterized loans, with an average loan amount of roughly twelve million euros. Therefore we expect that even small di?erences across banks in credit risk are re?ected on the loan interest rate. The second dataset provides daily information on the balance in banks’ reserve accounts. It allows us to study how banks’ reserve position a?ects their behavior in the interbank market. The third dataset contains quarterly information on bank characteristics, including total assets, ?nancial and pro?tability ratios and credit risk variables. This dataset also allows us to determine whether the bank belongs to a banking group, de?ned 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.
2.2
Measuring Lending Relationships
We measure lending relationships by the intensity of lending activity between banks. We use two alternative measures. Our ?rst measure is based on how concentrated the banks’ lending and borrowing activity is. More precisely, for every given lender (L) and every borrower (B ), we compute a lender preference index (LP I ), 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.4 Let Fij ??k denote the amount lent by bank j to bank k on loan i then:
% LP IL,B,q =
X
i?q
FiL??B /
X
i?q
FiL??all
(1)
where q denotes year/quarter. This ratio is more likely to be high if L relies on B more than on other banks to lend funds in the market.
4
We discuss our choice of time period in detail below.
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Similarly, we compute a borrower preference index (BP I ) as the ratio of total funds that B has borrowed from L in a given year/quarter, as a fraction of the total amount of funds that B has borrowed in the market in that same year/quarter:
% BP IL,B,q =
X
i?q
FiL??B /
X
i?q
Fiany??B .
(2)
Our second measure of lending relationships is simply the (absolute) number of di?erent banks to which bank L lent funds during year/quarter q, and similarly the number of di?erent banks from which bank B borrowed funds during year/quarter q :
# LP IL,q = Number of banks to which bank L lent funds in year/quarter q # = Number of banks from which bank B borrowed funds in year/quarter q BP IB,q
(3) (4)
Thus our ?rst measure of lending relationships is a relative measure, while our second measure is an absolute one. Elsas, Heinemann, and Tyrell (2004) solve a model in which for some borrowers it is optimal to rely on multiple but asymmetric ?nancing, i.e. borrowing a large amount from a single bank, and the remaining amount from several other banks. This asymmetry in ?nancing can not be captured by the absolute number of di?erent lenders. For this reason we have decided to use both an absolute and a relative measure of lending relationships. As one might expect, the correlation between these measures is negative. The correlation between the BP I % and BP I # indices is equal to ?0.46, while the correlation Figure 1 plots, for a given quarter and for a given borrower, its BP I % indices with di?erent
between the LP I % and LP I # indices is equal to ?0.42
lenders. The most important lender for this borrower during this quarter is the bank labeled as lender one, from which it borrowed roughly a quarter of the total funds that it borrowed during the quarter. This ?gure illustrates that in our data there are asymmetries in ?nancing, with some lenders being much more important than others. As an illustrative example of the time-series dimension of our relationship measures, Figure 2 plots the evolution of the LP I % and BP I % indices for a pair of banks in our sample, L and 7
B. This time-series dimension of our data is important because it will allow us to deal with the issue of the endogeneity of lending relationships. More precisely, since there is a timeseries dimension in our data we will be able to use lagged relationship measures as (exogenous) instruments. Figure 2 also illustrates that there is time variation in our relationship measures. In our regressions the explanatory power comes both from cross-sectional di?erences 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, pro?tability and credit risk. In section 6 we show that the results are robust to alternative ways of measuring relationships.
2.3
Pro?tability and Credit Risk Variables
One possible motive for lending relationships is that they may help overcome agency problems that arise from asymmetric information between borrowers and lenders of funds. Rochet and Tirole (1996) solve a model of the interbank market in which monitoring plays an important role.5 For this reason we include as explanatory variables total assets, the quarterly return on assets (ROA), and the proportion of non-performing loans (NPL). The latter is de?ned as loans that are past-due for a period exceeding 90 days, over total outstanding credit granted by the bank. Obviously, the latter includes loans granted to individuals and ?rms, and not only to other banks.
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.
8
2.4
Insurance variables
A second possible reason for banks to establish lending relationships is to obtain insurance against idiosyncratic liquidity shocks, arising from withdrawals by retail depositors. A bank may borrow the funds needed to meet unexpectedly large withdrawals from other banks in the interbank market (see the models of Ho and Saunders, 1985, Bhattacharya and Gale, 1987, and Freixas, Parigi and Rochet, 2000). If lending relationships are important for insurance purposes, we might expect banks subject to more volatile liquidity shocks to rely more on them. To investigate this hypothesis we construct a measure of volatility of liquidity shocks, equal to the standard deviation of the daily change in the bank’s reserve deposits that is not due to loans in the interbank market. We compute this measure for each bank and quarter, and normalize it by the bank’s average quarterly reserves. One may expect that lending relationships are more valuable for both borrowing and lending banks when their liquidity shocks are less correlated. That is, when borrowing banks need funds lending banks are more likely to have a surplus of funds. For each quarter, we measure the correlation between each two banks’ daily change in reserve deposits that is not due to loans in the interbank market.6 Banks may borrow funds to satisfy 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).7 It is therefore natural to expect that banks’ reserve position, when they borrow or lend funds in the interbank market, a?ect the interest rate on the loans, and with whom they interact. To investigate these e?ects we construct a proxy for each bank’s reserve requirements, equal to the average of the daily
6
Note that the argument that lending relationships are more valuable when banks have less correlated
shocks does not require that the correlation be negative. 7 Campbell (1987), Hamilton (1996), Hartmann et al. (2001), and Spindt and Ho?meister (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.
9
deposits in the bank’s reserve account over the reserve maintenance period. We then measure surplus deposits for bank i on day t (SDit ) 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: ? SDit = ? X Depositis ? /nt ? ?
s?{m(t):s6 t}
? ?
s?m(t)
X
(5)
where m(t) refers to the days in the same reserve maintenance period as day t, and nt and n are the up to t and the total number of days in the maintenance period, respectively. In words, this variable measures the average deposits in the bank’s reserve account up to day t of the current reserve maintenance period, relative to the average deposits in the account during the same reserve maintenance period. It captures the extent to which a bank’s requirements imply a need for or an excess of funds. As before we compute the average value of this variable over each quarter, for those days in which the bank intervened in the interbank market.
Depositis ? /n
2.5
Summary statistics
Table 1 reports summary statistics. The ?rst panel shows information on the Portuguese interbank market. The average total amount lent in each quarter is 27,123 million euros, with an average 2,217 loans. Thus, the average loan amount is roughly twelve million euros. The average number of di?erent borrowers (lenders) in each quarter is 37 (39). The next two panels of Table 1 report summary statistics for borrowing and lending banks, respectively, on total assets (Assets), quarterly return on assets (ROA), and proportion of non-performing loans (NPL). Table 1 reports that 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. 10
Table 1 also reports information on total amount and number of loans made and received by each bank in the interbank market during the quarter. On average each borrower 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 BP I % is 7.94 percent, and the average LP I % is 8.39 percent. These averages are signi?cantly 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. This is why it is important to consider these measures of relationships, in addition to simply the number of di?erent borrowers and lenders, whose summary statistics are shown in the next two rows of Table 1. Table 1’s last row reports summary statistics for the correlation of shocks (as de?ned in section 2.4). As one would expect, these correlations tend to be positive, with an average value of 12 percent. There is also signi?cant cross-section dispersion, with the 25th percentile equal to 1.6 percent and the 75th percentile equal to 23.6 percent. Table 2 shows the correlation matrix between several variables for borrowers and lenders. The largest correlations are between total assets, total amount lent/borrowed in the interbank market, and number of loans. Banks with more assets tend to be more active in the interbank market both in terms of total amount borrowed/lent and number of loans. For both borrowers and lenders of funds the LP I % and BP I % indices are negatively correlated with size, measured by total assets, amount and number of loans. As expected, larger banks also lend and borrow funds from a larger number of di?erent banks: the correlations between the LP I # and BP I # indices and total assets, amount, and number of loans are large and positive.
8
The average amount and number of loans for borrowing and lending banks are not exactly equal because
there is a di?erent number of borrowing and lending banks in the market.
11
3
Pricing of Interbank Loans
This section investigates the determinants of the interest rate on interbank market loans. In most interbank markets the central bank sets a target rate. For this reason we focus on explaining the di?erence between the interest rate on a given loan and the average interest rate on overnight loans. Some numbers are helpful for understanding the daily variability in interest rates 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 proceed as follows. First for a loan from bank L to bank B on day t, we calculate the di?erence between the interest rate (iL,B,t ) and the average (market-wide) overnight interest rate on the same day (it ), divided by the standard deviation of overnight interest rates for that day (? i t ). This is to account for the well-documented GARCH e?ects in interbank market interest rates (Hamilton, 1996). Since our unit of observation is year/quarter, we then obtain the average interest rate di?erence for all loans from bank L to bank B during year/quarter q , with q = 1, ..., 19, as: iq L,B = 1 X (iL,B,t ? it )/? i t Tq t?q
(6)
where Tq denotes the number of trading days in period q.9
We ?rst study how interest rates so de?ned depend on size, pro?tability and relationship measures in a univariate framework. We then turn our attention to multivariate analysis that
9
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 di?erent loans between the same pair of banks on a given day, the exact formula is: iq B,L = 1 X 1 X (iL,B,t,j ? it )/? i t Tq t?q JL,B,t j
where JL,B,t denotes the number of loans from L to B on day t.
12
include these and other explanatory variables. Finally, in section 3.3, we recognize that our relationship measures are endogenous, and estimate instrumental variables (IV) regressions to address the endogeneity issue. These IV regressions also allow us to identify the causal link between relationship measures and the loan interest rate.
3.1
Univariate analysis
Table 3 reports the average interest rate (iq L,B ) as a function of di?erent characteristics of both borrowing and lending banks. In the ?rst panel we focus on Total Assets. There is evidence that in the Fed Funds market larger banks tend to obtain more favorable interest rates when borrowing or lending (Allen and Saunders, 1986, Stigum, 1990, Fur?ne, 2001). Table 3’s ?rst panel reports the interest rate di?erential on loans between banks in the di?erent quartiles of the total assets distribution (quartile 1 regroups the smallest banks). Each column regroups lenders, while each row regroups borrowers. The ?rst panel of Table 3 shows that in our data larger banks tend to obtain more favorable rates. The patterns are remarkably clear. Holding the quartile of the borrowing bank ?xed, the interest rate increases with the size of the lender. Similarly, holding the size of the lending bank ?xed, the interest rate decreases with an increase in the size of the borrower.10 Table 3’s second panel reports interest rate di?erentials as a function of the quartiles of the ROA distribution (Quartile 1 includes the banks with the lowest ROA). Although the interest rate patterns are not as clear as for total assets, more pro?table borrowing banks seem to pay a lower interest rate than less pro?table ones. Similarly, more pro?table lending banks tend to receive a higher interest rate, at least when we compare quartiles 1 and 4. Table 3’s last two panels report interest rate di?erentials, but now as a function of the relationship measures. The third panel reports the interest rate di?erentials as a function of BP I % and LP I % .11 The results appear to suggest that borrowers (lenders) tend to pay
10
The results are similar when we use other measures of size, such as total amount lent/borrowed in the
interbank market or number of loans. 11 Note that in the previous two panels all loans for a given lender in a given quarter would appear in the
13
(receive) higher (lower) interest rates on loans with banks with whom they have a more intense lending relationship. As the next section shows, 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 a?ect the interest rate on the loan. The last panel of Table 4 reports interest rate di?erentials as a function of BP I # and LP I # . The patterns, although not always monotonic across quartiles, are symmetric to those in the previous panel, as one might have expected from the negative correlation between the two measures.
3.2
Multivariate Analysis
We ?rst estimate the unconditional correlation between the relationship metrics and the loan interest rate:
%,q %,q q q q iq L,B = ? + ?BP IL,B + ?LP IL,B + ? D + uL,B
(7)
where q indexes year/quarter, Dq are time (year/quarter) dummies, the subscripts L and B refer to lending and borrowing bank, respectively, and uq L,B is the residual. Column (i) of Table 4 shows the estimation results. The results con?rm the ones previously obtained in the univariate analysis (third panel of Table 3) and the coe?cients are statistically signi?cant in both cases. Next we include size, ROA and NPL as additional independent variables. The regression that we estimate is: iq L,B = ? + X £ ¤ q q %,q %,q q q q ? 1j Si zeq j + ? 2j ROAj + ? 3j NP Lj + ?BP IL,B + ?LP IL,B + ? D + uL,B (8)
j =L,B
As a size measure we use the logarithm of total assets. Finally, we include as independent variables those related to insurance motives. These include the net reserve position of borrowers and lenders when they borrow or lend funds in the interbank market (surplus deposits, or
same column, depending on its total assets or ROA. In the third panel, a given lender may have a LPI with a borrower that is in top quartile of the distribution of LPI indices, and a LPI with another borrower that is in the bottom quartile. The interest rate di?erential for loans with the former shows up in Table 3 under column Q4, whereas for the loans with the latter shows up under column Q1.
14
SD), the coe?cient of variation of their liquidity shocks (CVB and CVL ), and the correlation of liquidity shocks between lender and borrower (?L,B ): iq L,B = ? + X £ q q q q¤ ? 1j Si zeq j + ? 2j ROAj + ? 3j NP Lj + ? 4j SDj + ? 5j CVj
j =L,B
%,q %,q +? 6 ?L,B + ?BP IL,B + ?LP IL,B + ? q Dq + uq L,B
(9)
Including the relationship metrics as exogenous variables may seem surprising, given our previous discussion on the endogeneity of lending relationships. However, these equations are typically estimated in the lending relationships literature. Later on we will explicitly recognize the endogeneity problem, both with IV regressions and with SUR estimation. Comparing these results with those obtained when controlling for endogeneity allows us to investigate the potential biases introduced by treating the lending relationship measures as independent variables in the interest rate equation. Columns (ii) and (iii) of Table 4 show the estimation results. Interestingly, once we include the logarithm of total assets, ROA, and NPL as independent variables the estimated coe?cients on the relationship variables revert sign (column (ii)). Thus lenders receive a higher interest rates on loans to borrowers with whom they have a lending relationship, and borrowers pay a lower interest rate on loans from banks with whom they have a lending relationship. This result is the opposite of the unconditional results, and shows how crucial it is to control for bank characteristics in the pricing of interbank loans. The signs of the estimated coe?cients of the size variables, positive for lenders and negative for borrowers, con?rm that in the market larger banks receive better interest rates, whichever side of the market they are in. The estimated positive coe?cient on the ROA of borrowers is intuitive. Borrowers with a higher ROA have a more pro?table application for the funds, and are willing to pay a higher interest rate for the funds they borrow. Similarly, the estimated coe?cient on the ROA of lenders is positive, although not statistically signi?cant. A higher ROA means that lenders have a higher opportunity cost of lending in the interbank market, and require a higher interest rate to do so. 15
The e?ects of credit risk are captured by the proportion of non-performing loans (NPL) variable. We ?nd that borrowers with a higher proportion of NPL tend to pay higher interest rates on loans in the interbank market, a result which is statistically signi?cant at the one percent level. We also estimate a positive coe?cient on NPL of lenders, but it is not statistically signi?cant when we include the insurance variables (column (iii)). The results in column (iii) of Table 4 show that borrowers with a lower surplus deposit pay on average a higher interest rate on their loans. The magnitude of the coe?cient is also economically signi?cant: a 1% shortage of funds leads to an interest rate premium of 0.12
q standard deviations. The coe?cient on SDL is not statistically signi?cant. What seems to
matter for lenders is the volatility of liquidity shocks: the more volatile they are the lower is the interest rate that lenders receive on interbank market loans. Finally, the estimated coe?cient on ?L,B is not signi?cantly di?erent 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 reason may be the bilateral nature of the market. In a market with pairwise meetings such as the interbank market, the relative bargaining power of borrower and lender of funds will a?ect the interest rate on the loan. If size is correlated with bargaining power, then larger lenders (and larger borrowers) will receive better interest rates on their loans.12 In order to investigate this, and for each lender (and borrower) in our sample, we have calculated their respective market shares. That is: the total amount that the lender has lent (the borrower has borrowed) in the interbank market, over the total amount lent/borrowed by all banks in the market. Market shares thus calculated are positively correlated with bank size, as measured by the logarithm of total assets, with coe?cients of correlation equal to 0.59 (0.74) for lenders (borrowers). In columns (iv) and (v) of Table 4 we report the estimation
12
See Osborne and Rubinstein (1990) for a textbook treatment of models of bilateral markets that predict
this result.
16
results when we include market shares as explanatory variables for the interest rate on the loans. We ?nd 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 ?nd that the explanatory power of both variables is diminished, re?ecting the fact that they are co-linear. The last column of Table 4 reports the estimation results when we use BP I # and LP I # as relationship measures. The e?ects of the size, pro?tability, credit risk, and insurance variables on the interest rate are similar to those reported in column (iii) and therefore we refrain from commenting on them. Interestingly, the estimated coe?cient on BP I # is not statistically signi?cant, while the estimated coe?cients on BP I % was signi?cant. Thus it seems that for borrowers of funds it is important to use as a measure of the strength of the relationship a variable that re?ects the (possible) asymmetric nature of the ?nancing, such as borrowing a large amount from a single bank, and the remaining amount from several other banks. Obviously this asymmetry in ?nancing can not captured by the number of di?erent lenders (the BP I # variable).
3.3
Instrumental Variables Regressions
In order to address the issue of the endogeneity of the relationship measures we estimate instrumental variables (IV) regressions. These regressions allow 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 the relationship measures. The validity of the IV approach depends crucially on the quality of the instruments used in the ?rst stage regression. Good instruments include those which are simultaneously predetermined 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
17
in the existing literature on lending relationships. The quality of these instruments can be measured by the R-squared of the ?rst-stage regressions: for the BP I % (LP I % ) measure it is equal to 67% (78%), and for the BP I # (LP I # ) measure it is equal to 49% (52%).13 The estimation results for the second stage regressions are shown in Table 5. The tstatistics (reported below the estimated coe?cients) have been adjusted for ?rst-stage estimation error. When we compare the results in Table 5 to those in Table 4 we can draw the following conclusions. First, the coe?cients on total assets and non-performing loans remain essentially unchanged. Larger banks tend to receive higher interest rates when they lend, and pay lower interest rates when they borrow. Borrowers with more default risk pay on average a higher interest rates on their loans, while the lender’s default risk is now clearly non-signi?cant in both regressions. Second, the estimated coe?cient on the surplus deposit of borrowers is no longer signi?cant, and the estimated coe?cient on the coe?cient of variation of lenders is only signi?cant in (ii). Thus the level of signi?cance of the insurance variables is reduced once we control for the endogeneity of lending relationships. This suggests that relationships are important because they allow banks to obtain insurance in the interbank market. In the next section we will study the determinants of lending relationships. Third, the estimated coe?cients on the relationship variables are signi?cant throughout, and have the same signs as in Table 4. Moreover, the magnitude of the estimated coe?cients is either unchanged or even slightly increased (in absolute value). This result implies that, at least in our dataset, the endogeneity problem does not a?ect 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 coe?cients on the relationship metrics are robust to an IV approach, the inference on the coe?cients of some of the insurance
13
We have also estimated the IV regressions using the ?rst lag of all the explanatory variables in equation
(9) as instruments in the ?rst-state regression. The ?rst stage R2 was almost una?ected and the second stage results were the same and are therefore not reported.
18
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 coe?cients, then controlling for endogeneity is important.
4
The Determinants of Lending Relationships
The instrumental variables regressions that we have estimated in the previous section allow us to estimate the e?ects of lending relationships on the interest rate on the loan, 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 the loan amount and interest rate to be correlated with the identity of the borrowing and lending banks or on whether they have a lending relationship. More precisely, we now estimate a seemingly unrelated regressions (SUR) system of equations, with the amount lent, interest rate, and the relationship measures between lender and borrower (LP I and BP I ) as endogenous dependent variables. Thus, we estimate simultaneously the following system of equations:
1 iq L,B = ? +
j =L,B
%,q BP IL,B
%,q LP IL,B
(12) X £ ¤ q q q q q q q 4 4 4 4 4 q4 q4 Ln(VL,B ?4 ) = ?4 + 1j Sizej + ? 2j ROAj + ? 3j NP Lj + ? 4j SDj + ? 5j CVj +? 6 ? B,L +? D +vL,B
j =L,B
(11) X £ ¤ q q q q q q 3 3 3 3 3 q3 q3 = ?3 + ?3 1j Sizej + ? 2j ROAj + ? 3j NP Lj + ? 4j SDj + ? 5j CVj +? 6 ? B,L +? D +? L,B
j =L,B
(10) X £ ¤ q q q q q q 2 2 2 2 2 q2 q2 = ?2 + ?2 1j Sizej + ? 2j ROAj + ? 3j NP Lj + ? 4j SDj + ? 5j CVj +? 6 ? B,L +? D +?L,B
j =L,B
X £ q q q q q¤ q 1 1 1 1 1 q1 q1 ?1 1j Sizej + ? 2j ROAj + ? 3j NP Lj + ? 4j SDj + ? 5j CVj +? 6 ? B,L +? D +uL,B
(13)
q where VL,B is the total amount of funds lent by bank L to bank B during quarter q , and Ln
denotes logarithm. In this section we focus our attention on the LP I % and BP I % indices.
19
The results for the LP I # and BP I # are similar and reported in section 6. We estimate a reduced form system, and therefore allow for contemporaneous correlation across the di?erent innovations (u, ?, ? and v ). As before, we include time dummies in all equations.
4.1
BPI and LPI equations
Table 6 shows the estimation results for BP I % and LP I % indices. The results for the BP I % equation are shown in the second column. In this equation we try to determine which borrower and lender characteristics explain the variation in BP I % indices. In other words, who are the borrowers’ who have higher relationship indices, and who are the lenders with whom they have higher indices. The negative coe?cient on the logarithm of total assets of borrowers means that small borrowers rely more on lending relationships. The estimated coe?cient on the total assets of lender in the BP I % equation is positive and statistically signi?cant, meaning that small borrowers tend to have large banks as their preferred lenders. These results suggest a dichothomy between large and small banks in the market, an issue that we explore further in section 5.1. Interestingly, we ?nd that borrowers with higher default risk are more likely to rely on lending relationships: the estimated coe?cient on NPL of borrowers is positive and signi?cant. In addition, borrowers with a large proportion of NPL pay higher interest rates on their loans (the estimated coe?cient on NPL in the interest rate equation is 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 4 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 we do not ?nd 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 rates (Table 3, and column (i) in Table 4). It is only when controlling for default risk
20
that the estimated coe?cient on the BPI index is negative (Table 4 column (ii)), but even so it is an order of magnitude smaller than the coe?cient on the default risk variable. That is: borrowers with a high proportion of NPL pay on average higher interest rates. However, the interest rate premium is smaller if they borrow funds from a lender with whom they have a high BPI. Some calculations help to clarify this important point. Consider an increase in the proportion of NPL from the 25th to the 75th percentile, while everything else remains the same. Using the estimated coe?cients in the third column of table 4 we see that the interest rate on the loan increases by 2 basis points.14 However, if the increase in the proportion of NPL is accompanied by an increase in the BPI index from the 25th to the 75th percentile, the increase in interest rate is only 0.6 basis points. If instead we consider an increase in the proportion of NPL from the 10th to the 90th percentile the increase in interest rate is 20 basis points when the BPI index is unchanged, and 5 basis points when the BPI index also increases from the 10th to the 90th percentile.15 Several of the insurance variables are also signi?cant. The estimated negative coe?cient on the surplus deposit of borrowers implies that they are more likely to borrow funds from lenders with whom they have large relationship indices when they have a larger shortage of funds. Borrowers with more volatile liquidity shocks tend to rely more on lending relationships
q (the coe?cient on CVB is positive), and they tend to do so with lenders that have less volatile q liquidity shocks (the estimated coe?cient on CVL in the BP I % equation is negative and
statistically signi?cant). This supports the idea that lending relationships are important for insurance purposes. Finally, the correlation variable is also signi?cant and it has a negative coe?cient, which is consistent with the mutual insurance hypothesis. Borrowers are more likely to have lending relationships with lenders when their liquidity shocks are less correlated. In
14
Due to our scaling of the dependent variable we need to multiply the increase by the standard deviation
of the interest rate. 15 The e?ect of NPL on the interest rate may be larger because default risk is likely to be correlated with bank size, for which we are also controlling in Table 4.
21
such case the insurance bene?ts of the relationship are likely to be larger. The third column of Table 6 reports the results for the LP I % equation. Similarly to the borrowers, we ?nd that small lenders are more likely to have higher relationships indices, and that they tend to do so higher indices with large borrowers (the estimated coe?cient on total assets of lenders is negative and on the total assets of borrowers is positive). The estimated coe?cient on the credit risk of lenders is not statistical signi?cant. This is consistent with the results for the interest rate regression reported in Table 4. It is natural to expect that what matters in a loan is the credit risk of the borrower, and not that of the lender. In the LP I % equation, the estimated coe?cient on the reserve imbalance of borrowers is negative and statistically signi?cant. This means that banks that borrow funds at times when their reserve imbalance is larger tend to borrow funds from lenders which have high relationship indices with them (recall that the reserve imbalance variable for borrowers is de?ned in such a way that a lower value means a higher imbalance). Thus loans that take place when reserves imbalances are larger tend to be associated with higher relationship indices. This result comes from the time-series dimension of our panel. In addition, lenders with more volatile liquidity shocks tend to have higher relationship indices with borrowers that face less volatile liquidity shocks, although the estimated coe?cient for borrowers is not signi?cantly di?erent from zero. As in the BP I % equation, the estimated coe?cient on the correlation variable is negative, consistent with the mutual insurance motive for establishing relationships. As a whole, columns two and three of Table 6 show that it is mostly borrower characteristics that explain variation in the BP I % and LP I % indices. Among the lender characteristics the only two that seem to be important are the logarithm of total assets and liquidity risk. One might have an a priori expectation that for non-secure loans such as interbank market loans, borrowers’ characteristics are more important for explaining the terms of the loan than lenders’ characteristics. Table 6 suggests that this reasoning carries through when explaining lending relationships.
22
4.2
Interest rate and loan volume equations
The fourth column of Table 6 shows the results for the interest rate equation. This equation is similar to that estimated in speci?cation (iii) of Table 4, except that now we do not include the LPI and BPI indices as independent variables, but instead treat them as endogenous when estimating the system of equations. The main noticeable di?erence relative to the results in Table 4 is that the estimated coe?cient for the borrower’s ROA is now non-signi?cant. Given that several papers on lending relationships rely on regressions of the price of the loan on relationship measures and other control variables, it is re-assuring to ?nd out that in our data the results for this regression are robust to an approach that treats the relationship measures as endogenous variables. In the last column of Table 6 we report the results for loan volume (the fourth equation in the SUR system). We ?nd that larger banks borrow larger amounts. Interestingly, we ?nd that more pro?table banks lend less (the estimated coe?cients on ROAq L is negative). In addition, we ?nd that banks with a higher proportion of non-performing loans lend more
q and borrow less (the estimated coe?cients on NP Lq L and NP LB are positive and negative,
respectively). The estimated coe?cients for ROA and NPL are consistent with banks that have better investment opportunities borrowing more and lending less. Finally, the estimated coe?cients on surplus deposit show that banks which have smaller imbalances tend to rely on larger loans with any particular bank.
4.3
Correlation of residuals
At the bottom of Table 6 we show the estimated correlation matrix of residuals in the SUR system of equations. This allows us to study the correlation between the di?erent endogenous variables. However, we should point out that since our SUR system is a reduced form estimation, these correlations are not partial derivatives, i.e. when we look at the correlation between the residuals in two di?erent equations we are not holding the other endogenous variables constant. 23
Larger residuals for the BP I equation are associated with lower interest rates, and larger residuals for the LP I equation are associated with higher interest rates. Thus, borrowers pay lower interest rates when they borrow funds from banks with whom they have a lending relationship, and lenders receive a higher interest rate when they lend funds to banks with whom they have a lending relationship. Although the signs of the correlations between the LPI and BPI and interest rate are intuitive, the magnitude of the correlation is fairly small. From Table 6 we see that the largest correlations are of amount lent with LPI and BPI, which are equal to 0.44 and 0.31, respectively. This ?nding supports the idea that relationships have the greatest e?ect on the provision of credit, and not on the price at which banks are able to borrow or lend.
5
Further Evidence on the Determinants of Lending Relationships
In this section we provide further evidence on the determinants of lending relationships, that allows us to be more precise as to their exact nature.16
5.1
Small versus Large Banks
The estimation results in the previous sections show that bank size is an important determinant of interbank market interest rates, and of lending relationships. In this section we explore further the role of bank size in the market structure. In order to do so, and for each quarter in our sample, we classify banks into large and small, based on the quarterly distribution of bank assets. Large (small) banks are those whose assets are larger (smaller) than percentile 66 (33) of this distribution. We then compare several variables for small and large banks. The ?rst two rows of Table 7, Panel A report the average amount borrowed/lent per bank
16
We would like to thank an anonymous referee for suggestions that have led us to investigate the questions
in this section.
24
and quarter over the whole sample period. The third row reports the net amount borrowed, which is simply the di?erence between the ?rst two. The second column shows the results for all banks, i.e. not conditional on bank size, while columns three and four show the results for small and large banks, respectively. On average, and per quarter, each bank in our sample has lent/borrowed 596.5 million euros. There are signi?cant di?erences between small and large banks: large banks tend to be net borrowers, with an average net amount borrowed roughly equal to 400 million euros, while small banks tend to be net lenders, with an average net amount lent equal to 363 million euros. Interestingly, this pattern of trade, in which large banks tend to be net buyers of liquidity and small banks tend to be net sellers, is also a distinctive feature of the US Fed Funds market (see for example Fur?ne, 1999, or Ho and Saunders, 1985).17 It can be rationalized by the model of Ho and Saunders (1985). If large banks are better able to diversify their risk exposure than small banks, then larger banks will be more rate sensitive than small banks, and the slopes of the demand functions for interbank funds of large banks will be more price-elastic than those of small banks. An important policy implication is that open market operations by the central bank will be more e?ective when targeted at large rather than small institutions. Table 7, Panel A also reports information on the number of loans and average loan amount. Large (small) banks tend to transact mostly as borrowers (lenders), re?ecting the fact that they tend to be net borrowers (lenders) in the market. Unsurprisingly, average loan amount for small banks is signi?cantly lower than average loan amount for large banks. The last three rows of Table 7, Panel A report the proportion of non-performing loans, and relationship indices. Small banks tend to have a signi?cantly higher proportion of nonpreforming loans than large banks. Furthermore, they tend to have signi?cantly higher BPI indices than large banks when borrowing funds. This suggests that small banks when borrowing funds ?nd it optimal to concentrate their borrowing. Interestingly, the same is not
17
See also Stigum’s (1990) description of the Fed Funds market: “To cultivate correspondents that will sell
funds to them, large banks stand ready to buy whatever sums these banks o?er, whether they need all these funds or not."
25
true when lending funds, since there are no statistically signi?cant di?erences in LPI indices between small and large banks. We have also investigate the likelihood that banks appear on both sides of the market, i.e. as lenders and borrowers over a given time period. Panel B of Table 7 reports that 66.1% (50.2%) of all banks have been on average active market participants on both sides of the market at least once a month (week). Panel B of Table 7 also reports summary statistics for bank assets and proportion of nonperforming loans as a function of how often banks appear on both sides of the market. It shows that large banks are more likely to appear on both sides of the market, and in this way act as intermediaries. In addition, banks that reverse their positions more frequently tend to have a signi?cantly lower proportion of non-performing loans. Naturally, banks with lower credit risk are better-suited to act as intermediaries. Finally, we have investigated whether the volatility of liquidity shocks di?ers depending on the frequency with which banks appear on both sides of the market, but found no statistically signi?cant di?erences. Smaller banks are less likely to act as intermediaries, and are more likely to act as lenders. But is it the case that when they need to borrow funds they do so from banks to whom they usually lend funds? In order to investigate this we have estimated the probability that small banks borrow funds from a bank to whom they usually lend funds, where the latter means a bank in top ?fty percent (one third) of the distribution of LPI indices for that small bank. This probability is as high as 66.88% (54.58% for the one-third cuto? ). The corresponding probabilities for all banks, i.e. not conditional on bank size, are smaller and equal to 59.28% (48.43%). Thus small banks, when reversing roles, tend to rely more on banks with whom they usually interact on the other side of the market than the average bank in our sample.
5.2
International Linkages
Unfortunately our main dataset only includes information on loans in the domestic interbank market. However, and in order to explore international linkages between domestic and foreign
26
banks, we have obtained data from a di?erent dataset, namely from the Trans-European Automated Real-time Gross settlement Express Transfer system (TARGET). This is the realtime gross settlement system for the euro o?ered by the Eurosystem. It is mainly used for the settlement of large-value euro interbank transfers. This dataset contains information on the identity of both the sender and receiver of funds, and on the amount transferred. It has some shortcomings. First, transfers of funds between a pair of banks may be due to a variety of reasons, other than interbank loans. For example, if a large individual client of a foreign bank decides to transfer funds to a domestic bank, this transfer of funds will show up in the dataset, and cannot be distinguished from an interbank loan. Second, this dataset is only available from 1999 onwards, or roughly the second half of the sample period. We use this dataset to investigate how international linkages relate to the nature of lending relationships in the domestic interbank market. This is particularly interesting because the Euro area seems to be characterized by a two-tier structure, in which only large banks are usually able to access foreign interbank markets for liquidity, and in which small banks tend to do their interbank business through large domestic banks (European Central Bank, 2000). With this in mind, we ?rst construct a measure of access to international markets, by calculating the total amount of funds that each domestic bank has received from plus sent abroad during each quarter. We then scale this variable by bank size, as measured by total bank assets.18 We think that this variable is a better measure of access to international markets, than simply the di?erence between funds received from abroad and funds sent abroad scaled by bank assets. This is because a domestic bank may ?nd it easy to access international interbank markets, but during a given time period it may neither be net borrower nor net lender in these
18
We have calculated alternative measures of access to international markets equal to the total amount of
funds that each domestic bank has received from abroad during the quarter scaled by bank assets, and equal to the total amount of funds that each domestic bank has sent abroad during the quarter scaled by bank assets. The correlation coe?cient between these two variables is 0.97, and the correlation coe?cients between them and the total amount of funds sent plus received from abroad scaled by bank assets are over 0.99.
27
markets. In this case the latter variable would be zero. We classify banks into low and high access to international markets, according to this measure. Banks with high (low) access are those in the top (bottom) one third of the distribution of this variable. Table 8 shows the results for the mean of several variables for each of these two groups. The last column shows the p-value for a t-test of equality of means. The ?rst row con?rms the result that banks with better access to international markets tend to be larger: the di?erence in total bank assets between the two groups is almost ?vefold. Interestingly, we ?nd that banks with low access to international markets tend to have a much higher proportion of non-performing loans. Furthermore, these banks, when borrowing funds in the domestic interbank market, ?nd it optimal to concentrate their loans: their BPI indices are much higher than those with high access to international market. This result is consistent with peer monitoring across borders being less e?cient than at the domestic level, as in the model of Freixas and Holthausen (2005). It suggests that in international unsecured credit markets such as interbank markets, peer monitoring plays an important role in that it allows liquidity to ?ow across borders. However, an alternative explanation is that large banks are perceived by international markets as being too-big-too-fail, and for this reason they can borrow internationally at low rates. In either case, our results suggest that domestic regulators should direct their policies towards an improvement of the cross-border information available, particularly so on small banks, so as to enhance cross-border market integration. Finally, we ?nd that banks with high access to international markets tend to have a lower coe?cient of variation of liquidity shocks, but the di?erence relative to banks with low access to international markets is not statistically signi?cant.
5.3
Time-series probabilities of repeated interactions
In order to better understand the time-series dimension of the relationship between borrowers and lenders we estimate the probability of repeated interactions. More precisely, we estimate the probability that a given lender (L) will lend funds to a given borrower (B ) in the next k
28
days, that is from t + 1 to t + k, conditional on L having lent funds to B at t, and conditional on both L and B lending and borrowing funds in the market in the next k days. Thus, we are trying to answer the following question: given that B has borrowed from L at t, and given that B needs funds again sometime within the next k trading days, how likely is it that it will borrow from L again? Before we turn to the estimation results let us ?rst calculate what we should expect to observe if the matching mechanism was completely random. The average number of loans on a given day is 43.31, and the average daily number of active lenders in the market is 23.1. This corresponds to an average of 1.87 loans per lender each day. Since the average daily number of active borrowers is 17.95, if the matching was completely random the probability of a lender lending to the same borrower at t + 1, conditional on having done so at t and on both lender and borrower being active in the market at t + 1, is 10.2%.19 This probability is roughly one ?fth of the value that we have estimated in the data, and equal to 51% (Table 9, Panel A). This probability increases to 64% if we consider k equal to ?ve, and if we take a 30-day window the probability is as high as 87%. These probabilities are much larger than those we would obtain with a random matching mechanism, which are 18% and 51% for a ?ve and a thirty-day window, respectively. The di?erences are statistically signi?cant at the 1% signi?cance level. Thus, in the interbank market, lenders frequently use previous borrowers and vice-versa, and much more frequently than one would obtain if the matching mechanism was random. With our previous analysis of bank size in mind, in Panel B of Table 9 we take this analysis in that direction. In particular we estimate and ?nd that the probability of repeated interaction is higher if one of the banks is small (asset size below percentile 33) and the other one is large (asset size above percentile 66). When both the borrower and the lender are large the probability of repeated interaction is lower, and it is lowest when both lender and
19
With probability 1/17.95 the bank lends to the same borrower in its ?rst loan, plus with probability
(1 ? 1/17.95) it does not lend to the same borrower in the ?rst loan, but it does so with probability 0.87/17.95 in the 0.87 remaining loan, so that the probability is 1/17.95 + (1 ? 1/17.95) × 0.87/17.95.
29
borrower are small. These estimated probabilities suggest that lending relationship are most important when between small and large banks in the domestic market. In panel B of Table 9, below the estimated probabilities, we report whether these probabilities are statistically di?erent from one another. It is important to note that for k equal to one we do not ?nd that the probability of SS is signi?cantly di?erent than LL or LS because there are very few observations for SS and k = 1.
6
Robustness checks
In Tables 10 through 11 we present several di?erent robustness checks, in which we estimate the SUR system using alternative measures of lending relationships. Table 10 reports the estimation results for the previously constructed BP I # and LP I # indices. In interpreting the results in this table one should recall that a higher index means that banks rely less on lending relationships. That is the interpretation is symmetric to that of the BP I % and LP I % indices. The results in Table 10 are similar to those in Table 6, except for the fact that in the third column the NPL of lenders is positive and statistically signi?cant. Thus lenders with a higher NPL tend to rely more on lending relationships. This is the opposite of what one might have a priori expected. However, this result is not robust to other relationship measures (Tables 6 and 11). We have constructed the LP I % as being equal to the total amount that bank L has lent to bank B as a fraction of the total amount that bank L has lent in the interbank market during the quarter. However, during the same quarter bank L may borrow funds from bank B . We now investigate the robustness of the results to measures that take into account a two-sided relationship factor. More precisely, the relationship measures are: BP I 2L,B,q = LP I 2L,B,q = X¡ ¢ X ¡ all??B ¢ + FiB??all FiL??B + FiB??L / Fi X¡ ¢ X ¡ L??all ¢ + Fiall??L FiL??B + FiB??L / Fi
i?q i?q i?q i?q
(14)
(15)
30
Thus the borrower preference index is now de?ned as the total amount bank B borrowed from plus lent to bank L divided by the total amount of funds that B has borrowed plus lent in the market during quarter q . The estimation results for these alternative relationship measures are reported in Table 11. Although there are some di?erences in magnitude and statistical signi?cance of some of the estimated coe?cients, the results are similar to those we obtained before. Finally, we have constructed lender and borrower preference indices similar to LP I % and BP I % but using number of loans instead of loan amounts. That is the lender preference index was constructed as the number of times that L has lent funds to B during quarter q , as a fraction of the total number of times that bank L has lent funds in the interbank market during the same quarter. The results were similar and are not reported.
7
Conclusion and Policy Implications
Interbank markets play an important role in distributing liquidity across the ?nancial system. It is in this market that banks borrow and lend funds among themselves, allowing for the transfer of liquidity from banks that have excess funds to those that are short. However, since interbank market loans are unsecured, they also increase the exposure of lenders to borrowers. In this paper we have studied lending relationships in a typical interbank market. There are at least two sets of reasons why banks may bene?t from lending relationships. First, in the models of Ho and Saunders (1985), Bhattacharya and Gale (1987), and Freixas, Parigi and Rochet (2000) banks borrow and lend funds in the interbank market to insure against idiosyncratic liquidity shocks that arise from the behavior of retail depositors. Thus, banks may form lending relationships for insurance purposes. Second, Rochet and Tirole (1996) present a model of the interbank market in which asymmetric information and monitoring play an important role. Thus, banks may rely on lending relationships to overcome problems that arise from asymmetric information on credit worthiness. We have provided evidence that supports both of these motives for the existence of lending 31
relationships. Importantly, we have done so by explicitly recognizing that these relationships are endogenous, and addressing the issue by estimating instrumental variables regressions and a system of seemingly unrelated regressions. We have found that smaller banks, with lower return on assets, banks with a higher proportion of non-performing loans and banks that are subject to more volatile liquidity shocks rely more on lending relationships, and that they tend to form relationships with large banks, and banks that are subject to less volatile liquidity shocks. In order to be more precise as to the exact nature of lending relationships, we have investigated the role of bank size in the market structure. Interestingly, we have found that large banks tend to be net buyers of liquidity and small banks tend to be net sellers. This pattern of trade is also a distinctive feature of the US Fed Funds market (see for example Fur?ne, 1999, or Ho and Saunders, 1985). It can be rationalized by the model of Ho and Saunders (1985). If large banks are better able to diversify their risk exposure than small banks, then large banks will be more rate sensitive than small banks, and the slopes of the demand functions for interbank funds of large banks will be more price-elastic than those of small banks. One important policy implication is that open market operations by the central bank will be more e?ective when targeted at large rather than small institutions. We have also investigated how access to international markets a?ects the nature of lending relationships in the domestic market. We have found that large domestic banks tend to have better access to international markets. Interestingly, we have found that banks with low access to international markets tend to have a much higher proportion of non-performing loans. Furthermore, these banks, when borrowing in the domestic interbank market, ?nd it optimal to concentrate their loans. This result is consistent with peer monitoring across borders being less e?cient than at the domestic level, as in the model of Freixas and Holthausen (2005). It suggests that in international unsecured credit markets such as interbank markets, peer monitoring plays an important role in that it allows liquidity to ?ow across borders. However, an alternative explanation is that large banks are perceived by international markets as being too-big-too-fail, and for this reason they can borrow internationally. In either case, our results 32
suggest that domestic regulators should direct their policies towards an improvement of the cross-border information available, particularly so on small banks, so as to enhance crossborder market integration.
33
8
References
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European Central Bank, 2000, “The Euro Area One Year After the Introduction of the Euro: Key Characteristics and Changes in The Financial Structure,” Monthly Bulletin, January, 35-49 Flannery, Mark J., 1996, “Financial Crisis, Payment System and Discount Window Lending," Journal of Money Credit and Banking, 28, pp. 804-824. Freixas, Xavier, and Cornelia Holthausen, 2005,“Interbank Market Integration under Asymmetric Information,” Review of Financial Studies, 18, 2, 458-490. Freixas, Xavier, Bruno Parigi and Jean-Charles Rochet, 2000, “Systemic Risk, Interbank Relations and Liquidity Provision by the Central Bank,” Journal of Money Credit and Banking, 32, pp. 611-638. Fur?ne, Craig, 1999, “The Microstructure of the Federal Funds Market,” Financial Markets, Institutions, and Instruments, 8, 24-44. Fur?ne, Craig, 2001, “Banks as Monitors of Other Banks: Evidence from the Overnight Federal Funds Market,” Journal of Business, 74, 33-57. Hamilton, James, 1996, “The Daily Market for Federal Funds,” Journal of Political Economy, 104, 26-56. Hartmann, Philipp, Michele Manna and Andrés Manzanares, “The microstructure of the euro money market,” October 2001, ECB Working Paper No. 80. Ho, Thomas and Anthony Saunders, 1985, “A Micro-Model of the Federal Funds Market,” Journal of Finance, 40, 977-990. O’Hara, Maureen, 1995, Market Microstructure Theory. Blackwell, Cambridge. Ongena, Steven and David C. Smith, 2000, “Bank relationships: a review.” in Zenios, S. A. and P. Harker (eds.), Performance of Financial Institutions, Cambridge University Press, pp. 221-258. 35
Ongena, Steven and David C. Smith, 2001, “The duration of bank relationships,” Journal of Financial Economics, 61, pp. 449-475. Petersen, Mitchell, and Raghuram Rajan, 1995, “The E?ect of Credit Market Competition on Lending Relationships,” Quarterly Journal of Economics, 110, 407-443. Petersen, Mitchell and Raghuram Rajan, 1994, “The Bene?ts of Lending Relationships: Evidence from Small Business Data,” Journal of Finance, 49, 3-37. Rochet, Jean-Charles and Jean Tirole, 1996, “Interbank Lending and Systemic Risk,” Journal of Money Credit and Banking, 28, 733-762. Slovin, Myron B., Marie E. Sushka, and John A. Poloncheck, 1993, “The Value of Bank Durability: Borrowers versus Bank Stakeholders,” Journal of Finance, 48, pp. 298-302. Spindt, Paul A., and Ronald Ho?meister, 1988, “The Micromechanics of the Federal Funds Market: Implications for Day of the Week E?ects in Funds Rate Variability,” Journal of Financial and Quantitive Analysis, 23, 401-416. Stigum, Marcia, 1990, The Money Market, Dow-Jones Irwin. Upper, Christian, 2004, “Survey of The Literature on Interbank Lending,” manuscript, Deutsche Bundesbank. Wolinsky, Asher, 1990, “Information Revelation in a Market with Pairwise Meetings,” Econometrica, 58, 1-25.
36
Borrower Preference Indices for a Given Bank at a Speci?c Quarter.
0.3
0.25 BPI - Borrower Preference Index
0.2
0.15
0.1
0.05
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Lenders
Figure 1:
Note to Figure 1: This ?gure plots, on a given quarter q, the BP I % indices for a given bank B and all its lenders. The BP I % 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 BP I % is zero were omitted from the ?gure.
Borrower’s Preference Index and Lender’s Preference Index for a Pair of Banks.
0.4
0.35
0.3
0.25 LPI 0.2
0.15 BPI 0.1
0.05
0 1997 Q1 1997 Q2 1997 Q3 1997 Q4 1998 Q1 1998 Q2 1998 Q3 1998 Q4 1999 Q1 1999 Q2 1999 Q3 1999 Q4 2000 Q1 2000 Q2 2000 Q3 2000 Q4
Figure 2:
Note to Figure 2: This ?gure plots the evolution over time of the BP I % and LP I % indices for a pair of banks in our sample, B and L. For each quarter, the BP I % 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, BP I % 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.
Table 1: Summary Statistics.
Mean Stdev Median 25th perc. 75th perc. Interbank Market Amount (million Euros) 27,123 8,545 27,888 24,250 29,444 Number of loans (million Euros) 2,217 994 2,478 1,412 3,032 Number of borrowers 37.19 4.75 39 34 41 Number of lenders 39.31 4.48 40 35 43 Borrower Characteristics Assets (million Euros) 5,736 9,372 1,850 695 6,150 ROA (percent) 17.4 154.3 21.4 5.1 43.7 Non-performing loans (percent) 4.63 8.21 2.68 1.35 5.01 Amount (million Euros) 751 1,080 331 44 984 Number of loans 61 71 32 8 95 Surplus deposits 1.00 0.18 1.00 0.93 1.07 Coef. variation shocks 0.77 0.96 0.35 0.11 1.01 Lenders Characteristics Assets (million Euros) 5,168 8,864 1,334 619 4,967 ROA (percent) 13.6 163.2 22.0 5.1 45.4 Non-performing loans (percent) 5.47 11.71 2.62 1.16 5.05 Amount (million Euros) 712 1,048 419 166 817 Number of loans 58 57 46 20 76 Surplus deposits 1.04 0.17 1.03 0.97 1.10 Coef. variation shocks 0.34 0.43 0.15 0.04 0.41 Borrower/Lender Characteristics Borrower preference index: BPI% (percent) 7.94 14.50 3.07 1.25 7.79 % Lender preference index: LPI (percent) 8.39 13.30 4.09 1.54 9.71 Borrower preference index: BPI# (number) 20.95 9.68 22 14 29 # 16.72 6.75 17 12 21 Lender preference index: LPI (number) Correlation of shocks (percent) 11.98 17.31 12.36 1.62 23.6
Variable
Note to Table 1: 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 2001. Amount is the total volume of overnight loans during a quarter (corrected for double counting) in millions of Euros and number of loans the total number of overnight loans during a quarter. Number of borrowers (lenders) is the number of di?erent borrowing (lending) banks during the quarter. Assets is the value of total assets of the bank at the beginning of each quarter in millions of Euros; ROA is the ratio between the annualized quarterly returns and the bank’s total assets expressed in percentage terms; Non-performing loans is the percentage of past due loans (loans that are overdue for more than 90 days) on the total value of outstanding loans granted by the bank. Amount is the total amount of overnight loans during the quarter, in millions of Euros. Number of loans is the number of overnight loans for lenders (borrowers) during a quarter. Surplus deposits is the quarterly average of the ratio between the current level of deposits in the reserve account (average since the start of the current reserve requirement period until day i) and the reserve requirements of the period. Correlation of shocks is the correlation between the daily changes in the daily central bank deposits (not including the interbank market operations) of the lender and the borrower. Coe?cient of variation of shocks of borrower (lender) is the standard deviation of the daily changes in the bank’s reserve deposits not due to interbank market loans scaled by bank’s % % quarterly reserves. The Borrower (Lender) preference index BPI (LPI ) is equal to the ratio of total funds that the bank has borrowed (lent) from a speci?c lender (borrower) as a fraction of the total amount of funds that # # he has borrowed (lent) in the market during a quarter. The Borrower (Lender) preference index BPI (LPI ) is de?ned as the total number of banks from (to) which the bank has borrowed (lent) funds during the quarter.
Table 2: Correlation Matrix for Borrowers and Lenders.
Borrowers Assets ROA NPL Amt. NLoans RMet(%) RMet(#) SDep Total Assets 1.00 ROA 0.10 1.00 Non-performing loans -0.10 -0.20 1.00 Amount 0.51 0.08 -0.14 1.00 Number of loans 0.23 0.06 -0.10 0.82 1.00 Relationship metric (%) -0.10 -0.06 0.04 -0.25 -0.32 1.00 Relationship metric (#) 0.27 0.08 -0.05 0.67 0.80 -0.46 1.00 Surplus deposits 0.02 -0.01 -0.03 -0.03 -0.09 0.09 -0.13 Coef. variation 0.00 0.00 0.02 -0.05 -0.07 0.19 -0.09 -0.02 Lenders Assets ROA NPL Amt. NLoans RMet(%) RMet(#) SDep Total Assets 1.00 ROA 0.08 1.00 Non-performing loans -0.10 -0.10 1.00 Amount 0.42 0.08 -0.07 1.00 Number of loans 0.21 -0.08 0.12 0.78 1.00 Relationship metric (%) -0.02 -0.02 -0.02 -0.16 -0.22 1.00 Relationship metric (#) 0.32 0.00 -0.01 0.51 0.68 -0.42 1.00 Surplus deposits 0.02 0.00 0.01 -0.04 -0.10 0.01 -0.06 Coef. variation 0.06 0.01 -0.02 -0.05 -0.07 0.20 -0.10 0.01
Note to Table 2: This table reports the correlation matrix for the borrowers and the lenders. Total Assets is the value of assets of the bank at the beginning of each quarter; ROA is the annualized quarterly returns divided by the bank’s total assets expressed in percentage terms; Non-performing loans is the percentage of past due loans (loans that are overdue for more than 90 days) on the total value of outstanding loans granted by the bank. Amount is the total value of overnight loans during the quarter in millions of Euros. Number of loans is the number of overnight loans for lenders (borrowers) during a quarter. Relationship metric represents the values of the borrower and lender preference indices. The Borrower (Lender) preference index (%) is equal to the ratio of total funds that the bank has borrowed (lent) from a speci?c lender (borrower) as a fraction of the total amount of funds that he has borrowed (lent) in the market during a quarter. The Borrower (Lender) preference index (#) is de?ned as the total number of banks from (to) which the bank has borrowed (lent) funds during the quarter. Surplus deposits is the quarterly average of the ratio between the current level of deposits in the reserve account (average since the start of the current reserve requirement period until day i) and the reserve requirements of the period. Coe?cient of variation of shocks of the borrower (lender) is a measure of volatility of the shocks de?ned as the standard deviation of the daily changes in the bank’s reserve deposits not due to interbank market loans scaled by bank’s quarterly reserves. The sample period is January 1997 to August 2001.
Table 3: Average Interest Rate for Borrowers and Lenders. Lenders Borrowers Q1 Q2 Q3 Total assets Q1 0.140 0.345 0.484 Q2 -0.120 0.039 0.223 Q3 -0.343 -0.107 0.052 Q4 -0.738 -0.270 -0.095 Return on assets Q1 0.066 0.215 0.273 Q2 -0.064 0.143 0.114 Q3 -0.039 0.075 0.100 Q4 -0.144 0.022 0.091 Relationship metric (%) Q1 0.009 -0.101 -0.068 Q2 0.219 0.085 0.013 Q3 0.305 0.124 0.037 Q4 0.484 0.307 0.182 Relationship metric (#) Q1 0.239 0.150 0.306 Q2 -0.016 0.011 0.089 Q3 -0.042 0.006 0.069 Q4 -0.288 -0.125 -0.058
Q4 0.635 0.416 0.280 0.173 0.194 -0.007 0.146 0.111 -0.135 -0.021 0.070 0.002 0.474 0.209 0.221 -0.008
Note to Table 3: This table reports average interest rate as a function of the following variables: total assets, return on assets and relationship metrics, for lenders and borrowers. Interest rate is de?ned for every pair of lender and borrower, as the quarterly average of the di?erence between the interest rates on the loans between those two banks and the overnight interest rate on the same days, scaled by the standard deviation of overnight interest rates for each day. Total Assets is value of assets of the bank at the beginning of each quarter. Return on assets is the annualized quarterly returns divided by the bank’s total assets expressed in percentage terms. Relationship metric represents the values of the borrower and lender preference indices. The Borrower (Lender) preference index (%) is equal to the ratio of total funds that the bank has borrowed (lent) from a speci?c lender (borrower) as a fraction of the total amount of funds that he has borrowed (lent) in the market during a quarter. The Borrower (Lender) preference index (#) is de?ned as the total number of banks from (to) which the bank has borrowed (lent) funds during the quarter. The sample period is January 1997 to August 2001.
Table 4: Multivariate Model for Interest Rate.
Independent variables Assets Market share ROA Non-performing loans Surplus deposits Coef. variation
(i) (ii) (iii) Borrower Characteristics -0.098*** -0.103*** (13.43) (12.98)
(iv)
(v)
(vi)
0.090*** 0.091*** (13.02) (14.14) Market share 1.666*** -0.129 (8.29) (0.56) ROA 0.150 0.1333 1.184*** 0.146 0.057 (0.54) (0.44) (3.69) (0.47) (0.19) Non-performing loans 0.066* 0.089 -0.076 0.089 0.099 (1.66) (1.45) (1..19) (1.44) (1.61) Surplus deposits 0.063 0.052 0.059 0.049 (1.18) 0.95 (1.11) (0.91) Coef. variation -0.017*** -0.012*** -0.018*** -0.014*** (10.53) (3.89) (9.61) (7.93) Borrower/Lender Characteristics Correlation of shocks -0.003 -0.003 -0.004 -0.011 (0.06) (0.05) (0.09) (0.23) Borrower pref. index (%) 0.240*** -0.155*** -0.184*** -0.142*** -0.196*** (4.18) (2.71) (2.85) (2.00) (2.83) Lender pref. index (%) -0.180*** 0.218*** 0.347*** 0.445*** 0.404*** (3.15) (3.44) (4.78) (5.25) (4.97) Borrower pref. index (#) 0.001 (0.93) Lender pref. index (#) -0.005** (2.59) Number obs. 7724 7046 6410 6410 6410 6410 2 R 0.01 0.08 0.08 0.05 0.08 0.08
Assets
1.245* (1.85) 0.548*** (2.72) -0.117** (2.21) 0.000 (0.26) Lender Characteristics 0.083*** 0.087*** (15.25) (14.98)
1.194* (1.84) 0.512*** (2.67)
-0.086*** -0.097*** (8.72) (9.80) -2.141*** -0.603*** (9.80) (2.25) -0.318 1.116* 1.250* (0.48) (1.65) (1.86) 0.616*** 0.539*** 0.531*** (3.12) (2.70) (2.54) -0.100* -0.111** -0.105* (1.85) (2.09) (1.90) 0.000 0.000 -0.001 (0.30) (0.04) (0.83)
Note to Table 4: We estimate the following multivariate models:
%,q %,q q q q (i) iq L,B = ? + ?BP IL,B + ?LP IL,B + ? D + uL,B q q q %,q %,q q q q (ii) iq L,B = ? + ?j =L,B [? 1j Si zej + ? 2j ROAj + ? 3j N P Lj ] + ?BP IL,B + ?LP IL,B + ? D + uL,B q q q q q K,q (iii) to (vi) iq L,B = ? + ?j =L,B [? 1j Si zej + ? 2j ROAj + ? 3j N P Lj + ? 4j SDj + ? 5j CVj ] + ? 6 ? l,B + ?BP IL,B + K,q q q q ?LP IL,B + ? D + uL,B
where k = %, # represent the two relationship metrics. The dependent variable, interest rate, is de?ned for every pair of lender and borrower, as the quarterly average of the di?erence between the interest rates on the loans between those two banks and the overnight interest rate on the same days scaled by the standard deviation % % of overnight interest rates for each day. The variable BP I (LP I ) is the borrower (lender) preference index and is equal to the ratio of total funds that the bank has borrowed (lent) from a speci?c lender (borrower) as a fraction of the total amount of funds that he has borrowed (lent) in the market during a quarter. The Borrower (Lender) preference index BP I (LP I ) is de?ned as the total number of banks from (to) which the bank has borrowed (lent) funds during the quarter. Assets is the logarithm of the value of assets of the bank at the beginning of each quarter; Market Share is the total amount that the lender has lent (borrower has borrowed) in the interbank marketduring the quarter over the total amount lent/borrowed by all banks in the market; ROA are the annualized quarterly returns divided by the bank’s total assets expressed in percentage terms; Non-performing loans (NP L) is the percentage of past due loans (loans that are overdue for more than 90 days) on the total value of outstanding loans granted by the bank. Surplus deposits (SD) is the quarterly average of the ratio between the current level of deposits in the reserve account (average since the start of the current reserve requirement period until day i) and the reserve requirements of the period. Coe?cient of variation (CV ) of shocks of the borrower (lender) is a measure of volatility of the shocks de?ned as the standard deviation of the daily changes in the bank’s reserve deposits not due to interbank market loans scaled by bank’s quarterly reserves. Correlation of shocks measures the correlation between the daily changes in the daily central bank deposits (not including the interbank market operations) of lender and borrower. The variables D are dummy variables denoting quarter ?xed e?ects. Robust t-statistics are shown in parenthesis. The sample period is January 1997 to August 2001. ***, **, and * denotes signi?cance at the 1%, 5%, and 10% percent level respectively.
# #
Table 5: Model for Interest Rate using Instrumental Variables
Independent variables (i) Borrower Characteristics Assets -0.103*** (10.16) ROA 1.166 (0.95) Non-performing loans 0.421** (2.12) Surplus deposits -0.075 (0.98) Coef. variation -0.011 (0.70) Lender Characteristics Assets 0.085*** (11.89) ROA -0.032 (0.05) Non-performing loans 0.095 (0.86) Surplus deposits -0.041 (0.54) Coef. variation -0.013 (0.32) Borrower/Lender Characteristics Correlation of shocks -0.016 (0.25) Borrower preference index (%) -0.208* (1.77) Lender preference index (%) 0.515*** (2.72) Borrower preference index (#) Borrower preference index (#) Number obs. R2 4358 0.073 (ii) -0.112*** (10.71) 1.489 (1.40) 0.502*** (2.74) -0.096 (1.34) -0.000 (0.01) 0.094*** (13.01) 0.014 (0.02) 0.094 (0.88) 0.068 (0.99) -0.015*** (2.64) -0.033 (0.56)
0.004** (2.19) -0.006** (2.02) 5846 0.071
Note to Table 5: We estimate the following model:
q q q q q k,q k,q iq L,B = ? + ?j =L,B [? 1j Si zej + ? 2j ROAj + ? 3j N P Lj + ? 4j SDj + ? 5j CVj ] + ? 6 ? l,B + ?BP IL,B + ?LP IL,B + q q ? D + uL,B q k,t?1 k,t?1 k,t using the variables BP IL,B and LP IL,B as instruments for BP IL,B and LP I L,B , respectively, and where k = %,# are the two relationship metrics. The dependent variable, interest rate, is de?ned for every pair of lender and borrower, as the quarterly average of the di?erence between the interest rates on the loans between those two banks and the overnight interest rate on the same days scaled by the standard deviation of overnight interest rates for each day. The variable BP I % (LP I % ) is the borrower (lender) preference index and is equal to the ratio of total funds that the bank has borrowed (lent) from a speci?c lender (borrower) as a fraction of the total amount of funds that he has borrowed (lent) in the market during a quarter. The Borrower (Lender) preference # # index BPI (LPI ) is de?ned as the total number of banks from (to) which the bank has borrowed (lent) funds during the quarter. Assets is the logarithm of the value of assets of the bank at the beginning of each quarter; ROA are the annualized quarterly returns divided by the bank’s total assets expressed in percentage terms; Non-performing loans (N P L) is the percentage of past due loans (loans that are overdue for more than 90 days) on the total value of outstanding loans granted by the bank. Surplus deposits (SD) is the quarterly average of the ratio between the current level of deposits in the reserve account (average since the start of the current reserve requirement period until day i) and the reserve requirements of the period. Coe?cient of variation (CV ) of shocks of the borrower (lender) is a measure of volatility of the shocks de?ned as the standard deviation of the daily changes in the bank’s reserve deposits not due to interbank market loans scaled by bank’s quarterly reserves. Correlation of shocks measures the correlation between the daily changes in the daily central bank deposits (not including the interbank market operations) of lender and borrower. The variables D are dummy variables denoting quarter ?xed e?ects. Robust t-statistics are shown in parenthesis and are corrected for ?rststage estimation error. The sample period is January 1997 to August 2001. ***, **, and * denotes signi?cance at the 1%, 5%, and 10% percent level respectively.
k,t
Table 6: SUR Model using BPI% and LPI%.
Independent variables Assets ROA Non-performing loans Surplus deposit Coef. Variation BPI% LPI% Borrower -0.025*** 0.024*** (20.67) (23.14) 0.088 -0.064 (0.49) (0.42) 0.152*** -0.009 (5.47) (0.36) -0.044*** -0.051*** (3.71) (5.05) 0.011*** -0.000 (16.03) (0.40) Lender 0.011*** -0.001 (10.33) (1.43) -0.025 -0.064 (0.23) (0.69) 0.003 -0.003 (0.19) (0.18) -0.009 -0.001 (0.77) (0.14) -0.002** 0.015*** (2.20) (18.45) Borrower/Lender -0.062*** -0.049*** (6.37) (5.85) 6410 6410 0.17 0.19 Int. Rate -0.090*** (13.40) 1.207 (1.22) 0.517*** (3.32) -0.143** (2.17) -0.002 (0.47) 0.084*** (14.37) 0.116 (0.19) 0.087 (0.89) 0.064 (0.98) -0.012** (2.26) -0.008 (0.16) 6410 0.08 Amount 6.313*** (7.33) -178.190 (1.41) -34.552* (1.74) 23.017*** (2.75) -0.776 (1.63) -5.442*** (7.27) -337.062*** (4.40) 44.831*** (3.55) -24.495*** (2.92) -1.423** (2.14) -64.583*** (9.31) 6410 0.05
Assets ROA Non-performing loans Surplus deposit Coef. Variation
Correlation of shocks Number obs. R2
BPI% LPI% Interest rate Amount
Correlation of residuals BPI% LPI% Int. Rate 1.000 0.128 1.000 -0.026 0.049 1.000 0.312 0.438 0.008
Amount
1.000
Note to Table 6: We estimate the following equations using a SUR system: £ 1 q q q q q¤ 1 1 1 1 1 q1 q1 1 iq + uq L;B = ? + ?j =L,B ? 1j Si zej + ? 2j ROAj + ? 3j N P Lj + ? 4j SDj + ? 5j CVj + ? 6 ? B,L + ? D L,B
£ 2 %q q q q q q¤ q 2 2 2 2 2 q2 q2 2 BP IL ;B = ? + ?j =L,B ? 1j Si zej + ? 2j ROAj + ? 3j N P Lj + ? 4j SDj + ? 5j CVj + ? 6 ? B,L + ? D + ?L,B £ 3 %q q q q q q¤ q 3 3 3 3 3 q3 q3 3 LP IL ;B = ? + ?j =L,B ? 1j Si zej + ? 2j ROAj + ? 3j N P Lj + ? 4j SDj + ? 5j CVj + ? 6 ? B,L + ? D + ? L,B £ 4 q q q q q q¤ q 4 4 4 4 4 q4 q4 4 Ln(VL ;B ) = ? + ?j =L,B ? 1j Si zej + ? 2j ROAj + ? 3j N P Lj + ? 4j SDj + ? 5j CVj + ? 6 ? B,L + ? D + ? L,B
The dependent variables are: the interest rate i, de?ned for every pair of lender and borrower, as the quarterly average of the di?erence between the interest rates on the loans between those two banks and the overnight interest rate on the same days scaled by the standard deviation of overnight interest rates for each day; BP I % (LP I % ) is the borrower (lender) preference index and is equal to the ratio of total funds that the bank has borrowed (lent) from a speci?c lender (borrower) as a fraction of the total amount of funds that he has borrowed (lent) in the market during a quarter; ln(V ) is the logarithm of the total volume of overnight loans during the quarter (corrected for double counting) in millions of Euros. The independent variables are: Assets is the logarithm of the value of assets of the bank at the beginning of each quarter; ROA are the annualized quarterly returns divided by the bank’s total assets expressed in percentage terms; Non-performing loans (NP L) is the percentage of past due loans (loans that are overdue for more than 90 days) on the total value of outstanding loans granted by the bank. Surplus deposits (SD) is the quarterly average of the ratio between the current level of deposits in the reserve account (average since the start of the current reserve requirement period until day i) and the reserve requirements of the period. Coe?cient of variation (CV ) of shocks of the borrower (lender) is a measure of volatility of the shocks de?ned as the standard deviation of the daily changes in the bank’s reserve deposits not due to interbank market loans scaled by bank’s quarterly reserves. Correlation of shocks measures the correlation between the daily changes in the daily central bank deposits (not including the interbank market operations) of the lender and the borrower. The variables D are dummy variables denoting quarter ?xed e?ects. Robust t-statistics are shown in parenthesis. The sample period is January 1997 to August 2001.
Table 7, Panel A: Small versus Large Banks. Variable All Small (S) Large (L) p-value S = L Total amount borrowed (million Euros) 596.50 124.18 923.87 0.000 Total amount lent (million Euros) 596.50 487.44 524.18 0.643 Net amount borrowed (million Euros) 0.00 -363.26 399.69 0.000 # Loans as borrower 48.77 21.02 62.59 0.000 # Loans as lender 48.77 66.91 35.24 0.000 # Loans as borrower - # Loans as lender 0.00 -45.89 27.35 0.000 Average loan size as borrower 12.23 5.91 14.76 0.000 Average loan size as lender 12.23 7.29 14.87 0.000 Non-performing loans (percent) 5.33 8.74 3.72 0.000 Borrower Preference Index (BP I % ) 9.13 15.22 6.85 0.000 % Lender Preference Index (LP I ) 9.65 10.13 12.06 0.148
Note to Table 7, Panel A: Large (small) banks are those in the top (bottom) one third of the total assets distribution. Total amount borrowed (lent) is the average total amount borrowed (lent) by each bank during the quarter. Net amount borrowed is the di?erence between total amount borrowed and total amount lent. # Loans as borrower (lender) is the average number of loans in which each bank has been a borrower (lender) during the quarter. Average loan size as borrower (lender) is the average amount borrowed (lent) in each loan. Non-performing loans is the percentage of past due loans (loans that are overdue for more than 90 days) on the % % total value of outstanding loans granted by the bank. The Borrower (Lender) preference index BPI (LPI ) is equal to the ratio of total funds that the bank has borrowed (lent) from a speci?c lender (borrower) as a fraction of the total amount of funds that he has borrowed (lent) in the market during a quarter. The table shows averages across all quarters in the sample. The division between large and small banks is made on a quarterly basis, using the respective total assets quarterly distribution. The last column shows the p-value of a t-test of equality of the values for small and large banks.
Table 7, Panel B: Frequency of Borrowing and Lending Positions. Frequency on both Proportion Bank Assets Non-Performing sides of the market of banks (million of euros) Loans At least once a month 66.1% 6,058 5.53% At least once every two weeks 61.3% 6,395 4.72% At least once a week 50.2% 7,271 4.42% At least twice a week 38.7% 8,420 4.20%
Note to Table 7, Panel B: This table shows the proportion of banks that appear on both sides of the market, i.e. as lenders and borrowers, over a given time period. The last two columns report the average bank assets and the proportion of non-performing loans for banks that on average appear on both sides of the market over the corresponding time period.
Table 8: International linkages. Banks with Banks with p-value of test low access high access eq. means Total assets (million Euros) 1940.74 9645.24 0.000 Non-performing loans (percent) 8.22 2.50 0.003 Coef. variation shocks 0.555 0.493 0.802 Borrower Preference Index (BP I % ) 18.41 9.25 0.000 % Lender Preference Index (LP I ) 13.60 12.64 0.644 Total amount borrowed (million Euros) 115.35 925.15 0.000 Total amount lent (million Euros) 592.52 538.36 0.711 # Loans as borrower 13.99 51.67 0.000 # Loans as lender 52.36 23.46 0.000
Note to table 8: This table shows several variables for banks with low and high access to international markets. We ?rst construct a measure of access to international markets equal to the funds that the bank has sent abroad plus received from abroad during each quarter, scaled by the bank’s assets. Banks with low (high) access to international markets are those in the bottom (top) one third of the distribution for this variable. The table reports means for these two groups. Assets is the value of total assets of the bank at the beginning of each quarter in millions of Euros. Non-performing loans is the percentage of past due loans (loans that are overdue for more than 90 days) on the total value of outstanding loans granted by the bank. The Borrower (Lender) preference % % index BPI (LPI ) is equal to the ratio of total funds that the bank has borrowed (lent) from a speci?c lender (borrower) as a fraction of the total amount of funds that he has borrowed (lent) in the market during a quarter. Total amount borrowed (lent) is the average total amount borrowed (lent) in the domestic interbank market by each bank during the quarter. # Loans as borrower (lender) is the average number of loans in which each bank has been a borrower (lender) in the domestic interbank market during the quarter. The table shows averages across all quarters from 1999 onwards, the sample period for which we have international data. The last column shows the p-value of a t-test of equality of the values for banks with low and high access.
Table 9: Probability of repeated interactions assuming random matching and in the data Number of 1 3 5 10 30 Number of 1 3 5 10 30 Panel A: Random Matching and in the Data for all banks Days Random Matching Data p-value: Random = Data 0.102 0.511 0.000 0.140 0.585 0.000 0.179 0.643 0.000 0.269 0.732 0.000 0.513 0.865 0.000 Panel B: In the data by bank size Days Large-Large (LL) Large-Small (LS) Small-Small (SS) 0.526 0.547 0.333 LS ?? LL?? 0.591 0.590 0.355 ?? ?? SS SS LL?? , LS ?? 0.653 0.671 0.429 ?? ??? ?? ??? ??? LS , SS LL , SS LL , LS ??? 0.741 0.779 0.447 LS ??? , SS ??? LL??? , SS ??? LL??? , LS ??? 0.875 0.904 0.581 LS ??? , SS ??? LL??? , SS ??? LL??? , LS ???
Note to table 9: This table shows the probability that a given lender (L) will lend funds to a given borrower (B ) in the next k days, that is from t + 1 to t + k , conditional on L having lent funds to B at t, and conditional on both L and B lending and borrowing funds in the market in the next k trading days. The table shows the results for k = 1, 3, 5, 10, 30. Panel A shows the calculated probability assuming random matching of lenders and borrowers, and the estimated probabilities in the data. The last column of table A shows the p-value of a test of the equality of the randome matching probailities and the estimated probabilities in the data. Table B shows the estimated probabilities in the data by bank size. Large (Small) banks are those in the top (bottom) one third of the distribution of total assets. Below the estimated coe?cients we report whether the estimated probabilities are statistically signi?cant across banks of di?erent sizes. ***, **, and * denotes signi?cance at the 1%, 5%, and 10% percent level respectively.
Table 10: Robustness Check: SUR Model using BPI# and LPI#. Independent variables Assets ROA Non-performing loans Surplus deposit Coef. Variation LPI# Borrower 3.987*** -0.409*** (64.88) (8.62) -9.949 5.901 (1.10) (0.85) -14.132*** -0.207 (9.98) (0.46) -1.292** 6.912*** (2.16) (14.96) -0.275*** 0.022 (8.10) (0.84) Lender -0.144*** 1.310*** (2.69) (31.76) 1.910 -11.005*** (0.35) (2.61) -0.911 2.101*** (1.01) (3.02) 0.396 -2.862*** (0.66) (6.20) 0.052 -0.375*** (1.10) (10.25) Borrower/Lender -0.383 -0.680* (0.77) (1.78) 6410 6410 0.54 0.43 BPI# Int. Rate -0.090*** (13.40) 1.207 (1.22) 0.517*** (3.32) -0.143** (2.17) -0.002 (0.47) 0.084*** (14.37) 0.116 (0.19) 0.087 (0.89) 0.064 (0.98) -0.012** (2.26) -0.008 (0.16) 6410 0.08 Amount 6.313*** (7.33) -178.190 (1.41) -34.552* )1.74) 23.017*** (2.75) -0.776 (1.63) -5.442*** (7.27) -337.062*** (4.40) 44831*** (3.55) -24.495*** (2.92) -1.423** (2.14) -64.583*** (9.31) 6410 0.05
Assets ROA Non-performing loans Surplus deposit Coef. Variation
Correlation of shocks Number obs. R2
Note to Table 10: We estimate the following equations using a SUR system: £ 1 q q q q q¤ 1 1 1 1 1 q1 q1 1 + uq iq L;B = ? + ?j =L,B ? 1j Si zej + ? 2j ROAj + ? 3j N P Lj + ? 4j SDj + ? 5j CVj + ? 6 ? B,L + ? D L,B
£ 2 #q q q q q q¤ q 2 2 2 2 2 q2 q2 2 BP IL ;B = ? + ?j =L,B ? 1j Si zej + ? 2j ROAj + ? 3j N P Lj + ? 4j SDj + ? 5j CVj + ? 6 ? B,L + ? D + ?L,B £ 3 #q q q q q q¤ q 3 3 3 3 3 q3 q3 3 LP IL ;B = ? + ?j =L,B ? 1j Si zej + ? 2j ROAj + ? 3j N P Lj + ? 4j SDj + ? 5j CVj + ? 6 ? B,L + ? D + ? L,B £ 4 q q q q q q¤ q 4 4 4 4 4 q4 q4 4 Ln(VL ;B ) = ? + ?j =L,B ? 1j Si zej + ? 2j ROAj + ? 3j N P Lj + ? 4j SDj + ? 5j CVj + ? 6 ? B,L + ? D + ? L,B
The dependent variables are: the interest rate i, de?ned for every pair of lender and borrower, as the quarterly average of the di?erence between the interest rates on the loans between those two banks and the overnight interest rate on the same days scaled by the standard deviation of overnight interest rates for each day; the # # variable BP I (LP I ) is the borrower (lender) preference index and is de?ned as the total number of banks from (to) which the bank has borrowed (lent) funds during the quarter; ln(V ) is the logarithm of the total volume of overnight loans during the quarter (corrected for double counting) in millions of Euros. The independent variables are: Assets is the logarithm of the value of assets of the bank at the beginning of each quarter; ROA are the annualized quarterly returns divided by the bank’s total assets expressed in percentage terms; Non-performing loans (NP L) is the percentage of past due loans (loans that are overdue for more than 90 days) on the total value of outstanding loans granted by the bank. Surplus deposits (SD) is the quarterly average of the ratio between the current level of deposits in the reserve account (average since the start of the current reserve requirement period until day i) and the reserve requirements of the period. Coe?cient of variation (CV ) of shocks of the borrower (lender) is a measure of volatility of the shocks de?ned as the standard deviation of the daily changes in the bank’s reserve deposits not due to interbank market loans scaled by bank’s quarterly reserves. Correlation of shocks measures the correlation between the daily changes in the daily central bank deposits (not including the interbank market operations) of the lender and the borrower. The variables D are dummy variables denoting quarter ?xed e?ects. Robust t-statistics are shown in parenthesis. The sample period is January 1997 to August 2001.
Table 11: Robustness Check: Using a Two Side Relationship Metric. Two sided relationship indices BPI2 LPI2 Int. Rate Amount Borrower Assets -0.007*** 0.013*** -0.090*** 6.313*** (9.58) (17.61) (13.40) (7.33) ROA 0.292** -0.076 1.207 -178.190 (2.57) (0.71) (1.22) (1.41) Non-performing loans 0.035** 0.013 0.517*** -34.552* (1.96) (0.75) (3.32) (1.74) Surplus deposits 0.013* -0.030*** -0.143** 23.017*** (1.70) (4.28) (2.17) (2.75) Coef. Variation 0.003*** -0.001 -0.002 -0.776 (7.02) (1.63) (0.47) (1.63) Lender Assets 0.011*** -0.007*** 0.084*** -5.442*** (16.88) (10.63) (14.37) (7.27) ROA -0.050 -0.045 0.116 -337.062*** (0.73) (0.70) (0.19) (4.40) Non-performing loans 0.003 0.009 0.087 44.831*** (0.29) (0.88) (0.89) (3.55) Surplus deposits 0.006 0.002 0.064 -24.495*** (0.82) (0.31) (0.98) (2.92) Coef. Variation -0.001* 0.003*** -0.012** -1.423** (1.76) (5.10) (2.26) (2.14) Borrower/Lender Correlation of shocks -0.067 -0.076*** -0.008 -64.583*** (10.80) (12.99) (0.16) (9.31) Number obs. 6410 6410 6410 6410 2 R 0.12 0.14 0.08 0.05 Independent variables
Note to Table 11: We estimate the following equations using a SUR system: £ 1 q q q q q¤ 1 1 1 1 1 q1 q1 1 + uq iq L;B = ? + ?j =L,B ? 1j Si zej + ? 2j ROAj + ? 3j N P Lj + ? 4j SDj + ? 5j CVj + ? 6 ? B,L + ? D L,B
£ 2 q q q q q¤ q 2 2 2 2 2 q2 q2 2 BP I 2q L;B = ? + ?j =L,B ? 1j Si zej + ? 2j ROAj + ? 3j N P Lj + ? 4j SDj + ? 5j CVj + ? 6 ? B,L + ? D + ?L,B £ 3 q q q q q¤ q 3 3 3 3 3 q3 q3 3 LP I 2q L;B = ? + ?j =L,B ? 1j Si zej + ? 2j ROAj + ? 3j N P Lj + ? 4j SDj + ? 5j CVj + ? 6 ? B,L + ? D + ? L,B £ 4 q q q q q q¤ q 4 4 4 4 4 q4 q4 4 Ln(VL ;B ) = ? + ?j =L,B ? 1j Si zej + ? 2j ROAj + ? 3j N P Lj + ? 4j SDj + ? 5j CVj + ? 6 ? B,L + ? D + ? L,B
The dependent variables are: the interest rate i,de?ned for every pair of lender and borrower, as the quarterly average of the di?erence between the interest rates on the loans between those two banks and the overnight interest rate on the same days scaled by the standard deviation of overnight interest rates for each day; BP I 2 (LP I 2) is the borrower (lender) preference index and is equal to the ratio of total funds that the bank has borrowed and lent from a speci?c lender (borrower) as a fraction of the total amount of funds that he has borrowed and lent in the market during a quarter; ln(V ) is the logarithm of the total volume of overnight loans during the quarter (corrected for double counting) in millions of Euros. The independent variables are: Assets is the logarithm of the value of assets of the bank at the end of each quarter; ROA are the annualized quarterly returns divided by the bank’s total assets expressed in percentage terms; Non-performing loans (NP L) is the percentage of past due loans (loans that are overdue for more than 90 days) on the total value of outstanding loans granted by the bank. Surplus deposits (SD) is the quarterly average of the ratio between the current level of deposits in the reserve account (average since the start of the current reserve requirement period until day i) and the reserve requirements of the period. Coe?cient of variation (CV ) of shocks of the borrower (lender) is a measure of volatility of the shocks de?ned as the standard deviation of the daily changes in the bank’s reserve deposits not due to interbank market loans scaled by bank’s quarterly reserves. Correlation of shocks measures the correlation between the daily changes in the daily central bank deposits (not including the interbank market operations) of the lender and the borrower. The variables D are dummy variables denoting quarter ?xed e?ects. Robust t-statistics are shown in parenthesis. The sample period is January 1997 to August 2001.
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