An Empirical Analysis of Insider Rates vs. Outsider Rates in Bank Lending

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1 An Empirical Analysis of Insider Rates vs. Outsider Rates in Bank Lending Lamont Black* Indiana University Federal Reserve Board of Governors November 2006 ABSTRACT: This paper analyzes empirically the expected interest rates for insider (informed) vs. outsider (uninformed) lending. The analysis is based on a cross-section of small businesses that either borrow from an existing lender or borrow from a new lender. Existing lender rates proxy for insider rates and new lender rates proxy for outsider rates. The empirical results indicate that new lender rates are generally higher than existing lender rates in the total sample, which implies that outside rates are higher than inside rates. This finding is consistent with a benchmark theory of inside and outside rates, conditional on the borrower pool being of relatively high credit quality. The summary statistics indicate that the prediction is consistent with the data, given that the average firm in the data has a relatively high imputed probability of repayment. To further analyze the consistency of the theory and the data, the existing lender and new lender rates are compared across subsamples. According to the benchmark theory, the magnitude of the difference between the outside and inside rate is greatest for borrower pools in which the probability of success for a good firm is significantly higher than the probability of success for the average firm. The empirical results are consistent with this prediction. Lastly, two robustness checks are explored: the role of relationships and lending technologies. For the full sample, the results indicate that firms with an existing relationship at a new lender still pay a higher rate at the new lender relative to the existing lender rate. The new lender rate is also higher when controlling for similar lending technologies at the existing lender and most recent lender. However, the mitigating effect of an existing relationship does appear to be significant when controlling for lending technologies. * Ph.D. Candidate, Finance Department, Kelley School of Business, Indiana University, 1309 East Tenth Street, Bloomington, IN Tel: (812) , fax: (812) , The opinions expressed do not necessarily reflect those of the Federal Reserve Board or its staff. I would like to thank Greg Udell, Eric Leeper, Rich Rosen, Kim Huynh, Allen Berger, and Robert Marquez for helpful comments and discussions. I am also indebted to John Wolken for guidance with the data. All remaining errors are my own.

2 1. Introduction Some firms that borrow from financial intermediaries have an inside lender with private information about the firm. When a firm with an inside lender applies for a new loan, the firm may also consider bids from uninformed outside lenders. This situation creates an interesting problem of asymmetric information between two potential underwriters of a loan. The question arises as to how the information asymmetry between the two lenders should affect the relative interest rates observed for firms that borrow from an insider vs. firms that borrow from an outsider. Among a group of firms, some of which borrow from an inside lender and some of which borrow from an outside lender, where should we expect the interest rates to be higher? This paper empirically tests the theory of insider vs. outsider lending by analyzing the difference between interest rates at an existing lender vs. a new lender. The results indicate that outsider rates tend to be the same as or higher than insider rates. A benchmark theory suggests that the prediction for interest rates depends on the characteristics of the borrower pool. An analysis of subsamples within the data shows that the difference in rates is greatest for small, young firms. In a robustness check, the inclusion of relationships in the empirical model shows that firms with an existing relationship at a new lender still pay a higher rate than firms that borrow from an existing lender. The combination of these results supports the theoretical predictions for inside vs. outside lending. The framework for this empirical analysis is the Sharpe (1990) theory of insider vs. outsider lending, which is a benchmark model for analyzing competition between an informed and uninformed lender. The Sharpe theory begins with the assumption that a lender learns private information about a firm through the process of making a loan. The information gathering process then creates an information asymmetry between the existing lender and other potential lenders. Von Thadden (2004) shows that the asymmetry leads to a winner s curse for the outsider, who wins a higher proportion of bad firms. Despite the winner s curse, Black (2006) shows that the empirical implication of the model for observed interest rates differs across the parameter space. The expected interest rate for firms that borrow from the inside lender may be higher or lower than the expected interest rate for firms that borrow from an outside lender. The theoretical prediction depends on the characteristics of the borrower pool. This paper empirically analyzes the predictions of the Sharpe model for observed interest rates using data drawn from the Survey of Small Business Finance (SSBF). The data are ideal for analyzing the theory, because the SSBF includes information about all of a firm s loans and the source

3 of the firm s most recent loan. This data can therefore be used to identify firms with an existing lender and whether a firm s most recent loan was from an existing lender or a new lender. The difference between an existing and new lender uniquely matches Sharpe s modeling of an inside and outside lender. The data also records the interest rate on the most recent loan. Therefore, the data is used to show whether interest rates are empirically predicted to be higher at an existing lender or higher at a new lender. Additionally, the analysis identifies whether the characteristics of the borrower pool in the data are consistent with the predictions of the theory. The empirical results of this paper appear to support the predictions of the Sharpe model for inside vs. outside interest rates. The regression results show that the interest rate at a new lender is empirically predicted to be higher than the interest rate at an existing lender. This result in itself is not necessarily consistent with the Sharpe theoretical predictions for insider vs. outsider rates, because the theory only predicts this result for a borrower pool of relatively high credit quality. However, the imputed probability of repayment of the average firm in the data appears to satisfy this condition. To further analyze the consistency of the theory and the data, the difference between new lender and existing lender rates are compared across different borrower groups. The summary statistics for subsamples of the borrowers show that the difference between new lender rates and existing lender rates is greatest for small, young firms. This is consistent with the theoretical predictions, under the assumption that small, young firms are a borrower pool in which good firms are of significantly higher credit quality relative to the average firm in the pool. The summary statistics are verified by interacting a small firm dummy with the ew lender dummy in the empirical model. The results indicate that the difference between new lender rates and existing lender rates is insignificant for large firms and significant for small firms, which is consistent with the theory. Finally, as a robustness check, the role of relationships and lending technologies are both considered. The length of a relationship and the existence of a relationship are analyzed at the source of the firm s most recent loan to examine any difference across existing lenders and new lenders. The results show that rates are lower for firms with a longer relationship when length is considered apart from the new lender status, but neither the new lender difference nor length of relationship is significant when these are considered together. This may be due to the correlation of these two variables. As a discrete measure of relationships, the existence of a relationship at a new lender is shown to be insufficient to eliminate the wedge between inside and outside rates. This implies that having a non-lending relationship with an outsider does not fully eliminate the private information

4 advantage of an existing lender. To test robustness to different lending technologies, the final specification defines an existing lender as a lender only if the institution is currently making a loan to the firm of the same type (line of credit, mortgage, etc.) as the most recent loan. Under this tighter specification, the new lender rates are still significantly higher than the existing lender rates. However, in this specification, an existing relationship at a new lender appears to fully mitigate the underlying information asymmetry between the lenders. The remainder of the paper is organized as follows: Section 2 reviews the theoretical framework as well as previous empirical results and clarifies the empirical implications of the theory. Section 3 describes the data and provides summary statistics. Section 4 explains the empirical methodology. Section 5 provides the results along with an analysis of borrower subsamples. Sections 6 and 7 analyze two robustness checks: the role of relationships and lending technologies. Section 8 concludes. 2. Literature Review and Theoretical Predictions The Sharpe (1990) model of inside vs. outside lending is based on the idea that a lender learns private information about a firm through the process of lending to a firm. The basic model involves two periods. In the first period, all lenders compete for a loan using public information about the borrower pool. One lender wins the bid and becomes the inside lender. This lender then observes the payment or default of the firm on its first loan, which is private information. If the firm successfully repaid the loan, then it is a good firm, whereas, if the firm defaulted on the loan, it is a bad firm. In the second period, the competition is between the informed inside lender and an uninformed outside lender. The inside lender can condition its offer on the firm type, but the outside lender does not know the firm type. Von Thadden (2004) proves that there is a unique, mixed-strategy equilibrium for the secondperiod bidding game. The outside lender knows that it faces a winner s curse, because it will win a higher proportion of the bad firms. The inside lender will bid high for the bad firms and low for the good firms, therefore the outside lender will be the low bidder more often for the bad firms. To win some of the good firms, the outside lender randomizes its bidding strategy. The inside lender also randomizes so as to earn a higher rate on each bid that is won. The empirical implication for interest rates based on the Sharpe model (with the von Thadden correction) would seem to be clear. In a previous empirical paper, Degryse and van Cayseele (2000)

5 claim to test the prediction of the model. The authors regress the interest rates for loans made by a Belgian bank on a set of variables including a main bank variable, which is a dummy variable indicating that the bank provides the firm with a significant amount of financial services. 1 The main bank variable, as a measure of the scope of the bank-firm relationship, may be considered a proxy for an inside lender. Based on this proxy, the negative coefficient on the variable is interpreted as follows: This empirical evidence supports the predictions of the mixed-strategy equilibrium in von Thadden (1998) 2. In equilibrium, some firms occasionally switch to an outside bank (MAIN=0), and the outside bank charges a higher interest rate, because it takes into account a winner s curse effect. In the introduction to his paper, von Thadden also refers to the Degryse and van Cayseele result as being consistent with the model s predictions. There are two main contributions of the current paper which extend the existing test of the Sharpe model prediction for interest rates. First, there are some important differences in the identification of an inside lender. This study contrasts two lenders, an existing lender vs. a new lender, rather than using a scope measure as the proxy for an inside lender. This approach more closely matches the framework of the Sharpe model. 3 Secondly, Black (2006) has shown that the theoretical prediction of the Sharpe model for the inside and outside rates is not universal for all groups of borrowers. This paper goes beyond the empirical test of the interest rate to analyze whether the result is consistent with the parameter space in which this prediction would hold. The borrower characteristics in the data are linked to the parameter space of the model and the magnitude of the difference between inside and outside rates is analyzed across different groups of borrowers. Theoretical Predictions Black (2006) shows that the Sharpe model prediction for insider rates vs. outsider rates depends on borrower characteristics. The winner s curse might seem to imply that the outside interest rate is always higher, because the outsider lends to more bad firms. However, the interest rates for each firm type, i.e. the expected interest rates conditional on firm type, are both higher at the inside lender. The inside lender extracts more rents from the good firms and the outside lender sometimes offers a low 1 The definition used by the bank to determine whether it is the main bank is having a monthly turnover on the current account of at least 100,000 BEF (U.S. $3,000), and buying at least two other products from the bank. Thus MAIN captures the scope of the relationship p97 2 An earlier version of von Thadden (2004). 3 The studies also differ in their data source. This study is based on a cross-section of US firms borrowing from multiple banks, whereas Degryse and van Cayseele analyze a cross-section of Belgian firms borrowing from a single bank.

6 rate to bad firms and lends at a loss. Therefore, there is not one universal prediction for expected interest rates. The difference between inside and outside rates can be negative, positive, or insignificant in different parts of the parameter space. The parameters of the model are the characteristics of the borrower pool, so the different predictions are associated with different borrower characteristics. This implies that an empirical test of inside vs. outside rates must be analyzed in association with the characteristics of the borrowers in the data. 4 In the Sharpe model, there are two types of firms: firms with a high probability of repayment ( p H ) and firms with a low probability of repayment ( p L ). The main idea of the model is that the inside lender receives a private signal about the firm type. This private information allows the insider to offer bids specific to the firm type, whereas the outside lender offers a single distribution of rates to all firms. The expected interest rate for a given firm depends both on the quality of the firm (the signal of the insider) as well as the number of competitive bidders (whether the insider and outsider bid low). The inside lender always bids low for a good firm and high for a bad firm. On the other hand, the outside lender may bid low or high for either firm type, because it is uninformed. The firm chooses the lowest of the two bids, so the expected rate is lowest when there are two competitive bidders and highest when there are no competitive bidders. Firms with only one low-bidder have an expected interest rate in the middle. The prediction for inside and outside rates changes with the proportion of low, medium, and high interest rate contracts won by each lender. The low rate contracts are good firms that receive a competitive bid from both banks. The interest rate is low in expectation, because the firm takes the lower offer of two bids. The medium interest rate contracts can be either good firms or bad firms. The medium rate contract at an inside lender is a good firm that did not get a competitive bid from the outsider. This rate is above the low rate, because the insider is able to extract rents from the good firm. The medium rate contract at an outside lender is a bad firm that received a below market offer from the outside bank. The outside bank does not know the firm type ex ante, so it sometimes underbids for bad firms. Finally, the high rate contracts are bad firms that did not receive a below market offer from the outsider. 4 The prediction of the Sharpe model for inside vs. outside rates may also depend on an assumption about which lender wins in the event of a tie bid; however, this paper proceeds under the assumption that the two lenders split the firms in a tie bid. This assumption seems to be the least controversial. It also has a minimal effect on the model s predictions for the part of the parameter space which appears to be consistent with the data. For a discussion of how alternative assumptions affect the theoretical predictions, see Black (2006).

7 The proportion of low, medium, and high rate contracts at the two lenders alters the weighted average of rates which comprise the inside and outside rates. The two lenders win the same number of low rate and high rate contracts in expectation. This is the probability space in which the outside bank bids correctly for the firm type. The difference between the two lenders is in the number of medium rate contracts. The outside bank always wins a greater proportion of these contracts than the inside bank, because the outside bank wins more bad firms at a loss than the inside bank wins good firms at a large profit. When the medium rate contracts raise the expected interest rate at a bank, the outside rate is higher than the inside rate. When the medium rate contracts lower the expected interest rate at a bank, the inside rate is higher than the outside rate. The parameters of the model, which describe the characteristics of the borrower pool, determine whether the difference between the inside and outside rate is predicted to be positive, negative, or insignificant. The primary borrower characteristics are the probabilities of success for good firms ( p H ) and bad firms ( p L ). The inside rate is higher than the outside rate when the quality of the borrower pool is relatively low. This occurs because most of the contracts are high rate contracts to bad firms. Although the inside bank wins some good firms at the medium rate, the outside bank underbids for a larger number of bad firms, reducing the average outside rate below the inside rate. The inside rate and outside rate are statistically the same if the good firms and bad firms have a similar probability of success. In this case, private information does not add much value beyond the public information about a firm, so the information asymmetry between lenders is not significant. The outside rate is higher than the inside rate when the quality of the borrower pool is relatively high. In this case, most of the contracts are low rate contracts to good firms. The inside bank lends to some good firms at the medium rate, but the outside bank bids aggressively, leading to a larger number of bad firms at the outsider at the medium rate, raising the average outside rate above the inside rate. It is also important to consider the magnitude of the difference between inside and outside rates when approaching the problem econometrically. Black (2006) analyzes the theoretical predictions for this measure over the areas of the parameter space where the outside rate is higher than the inside rate. The largest predicted difference between the two rates is the area of this parameter space where high and L p H is p is low. This large differential can be explained by the magnifying effect of p( S) p, which is the difference in the probability of success for a good firm and the probability of success for the average firm in the borrower pool. When this difference is large, the magnitude of the difference between the inside and outside rates is predicted to be large.

8 To accurately match the theoretical predictions with the empirical results, the parameter space of borrower types must also be matched with the characteristics of the borrowers in the data. This paper first analyzes the empirical prediction for existing lender rates vs. new lender rates, which proxies as a measure of insider rates vs. outsider rates. The result is evaluated in the context of the imputed borrower characteristics of the data. Next, the differences in new lender and existing lender rates are analyzed across subsamples of the borrowers. This approach is used to confirm whether the regression results are consistent with the predicted magnitude of the insider vs. outsider rate differential across borrower pools. 3. Data and Summary Statistics The data used for the analysis is the 1998 Survey of Small Business Finance (SSBF). This survey, collected by the Federal Reserve, covers over 3000 businesses with 500 employees or less. The data includes information about all of a firm s creditors at the time of the interview, including more specific information about the firm s most recent loan acceptance and/or denial. The data on creditors includes information such as institution type, financial services provided, length of relationship, type of loan, collateral, etc. The data on most recent loan includes the timing of the loan, the source of the loan and numerous contract features including the interest rate. The types of lenders include commercial banks, thrifts, finance companies, as well as non-financial institutions. This paper analyzes a sub-sample of the SSBF firms. The sample is first reduced to those firms which had a loan accepted in the last three years (the most recent loan data). This group includes 794 firms. 5 The sample size is relatively small, but it is the only data in the SSBF for which the interest rate on the loan is recorded. This group of firms is narrowed to the 621 firms which had an existing loan at the time when their most recent loan was accepted. 6 This step is important, because it aligns the sample specifically with the situation in which a firm has an existing lender, which is the proxy for an inside lender. Lastly, the sample is reduced by 30 observations which appear to have inconsistencies in the survey. For these 30 loans, the firm s most recent loan is from an existing lender, but the firm reports a length of relationship of zero with the lender. This results in a final 5 Loans from an individual or government institution are excluded, as well as two loans for which the SIC industry code is not reported. 6 To be in the sample, a firm must have an existing loan from a financial institution, a non-financial institution or a business and its most recent loan must also be from one of these institution types. Appendix A describes the procedure for dating the most recent loan relative to the balance sheet.

9 sample size of 591 firms. An alternative specification, in which only commercial banks are included, covers 386 firms. It is important to exclude firms without an existing loan, because firms receiving their first loan are also borrowing from a new lender. This would measure a different effect than firms with an existing lender choosing to borrow from an outside lender. The approach taken in this paper provides a new and more accurate analysis of the Sharpe theory. 7 Definitions for the variables are given in Table 1. The independent variables include firm characteristics, lender characteristics, market characteristics, and contract characteristics. Firm characteristics include the firm s size, age, return on assets, leverage, organization type, and recent denials. The primary factor in the cost of credit is usually firm size. Firm size is often a good proxy for default risk and the information transparency of a firm. For small firms, the information asymmetry between borrower and lender can produce a large premium on external finance. As firms grow in size, there is more public information available or hard information, such as audited financial statements; therefore, financial institutions are more willing to lend at lower rates. Size is measured as the natural log of a firm s total assets. Firm age, measured as the natural log of a firm s age in months, is another proxy for risk and public information. As firms survive the start-up years, their probability of failure decreases and the information publicly available about them increases. The profitability of a firm can be measured as its return on assets (ROA). A firm s leverage controls for the amount of a firm s liabilities relative to assets and the risk associated with that leverage. I also control for whether the firm is a corporation (versus a proprietorship or partnership). The final firm characteristic is Recent Denial, a dummy variable indicating that the firm recently had at least one loan application rejected. This variable proxies for poor quality firms that may have been marginally approved for their most recent loan. Of the 634 firms with a recent loan acceptance and an existing loan at the time of acceptance, 11% also had a loan application denied over the same period of time. The main variable of interest in this paper is the lender characteristic indicating whether the lender is an existing lender or a new lender. New Lender is a dummy variable equal to 1 if the loan is at a new lender (no existing loan with the lending institution at the time of the most recent loan) and 7 Degryse and van Cayseele (2000) do not have information on loans from other banks. A non-main borrower could be a new borrower that has not yet established a relationship with any bank

10 0 if the loan is at an existing lender. This variable is a proxy for Inside Lender (existing lender) vs. Outside Lender (new lender). It is the primary lender characteristic for the purpose of analyzing the Sharpe theory. The other lender characteristics include the number of the firm s existing lenders and whether the most recent lender is a bank. Using the number of a firm s lenders as a measure of relationship lending has been done in a number of previous papers (Petersen and Rajan (1994), Harhoff and Korting (1998), D Auria et al. (1999); Shikimi (2005)). The hypothesis is generally that the presence of multiple lenders weakens monitoring incentives, which increases interest rates. However, these papers have not identified whether the measure includes the number of lenders prior to the most recent loan or after the most recent loan. I measure the number of existing lenders as the number of lenders prior to the most recent loan. The variable Bank Lender also identifies whether the most recent lender is a bank. This controls for the possibility that bank lending rates differ from non-bank rates. The next set of lender characteristics are the lender characteristics based solely on commercial banks. These three measures repeat the previous lender characteristics, but the measures exclude all non-bank financial institutions. Only 411 of the firms have an existing bank lender and also took their most recent loan from a commercial bank. For this sample, the new bank lender dummy indicates a firm that borrowed from a new bank lender rather than an existing bank lender. Likewise, the variables for the number of lenders apply solely to the number of bank lenders. The final lender characteristics include the relationship variables which identify the length of relationship between the firm and the lender. These variables are included in the specifications in Section 6, which focus on the role of relationships. The log of the length of relationship has been used extensively in the relationship lending literature as a measure of the amount of private information which a lender has about a firm. This can be compared across existing lenders and new lenders, because it is possible for a firm to have a relationship with a new lender through non-lending financial services. The average length of relationship at an existing lender is 8.8 years whereas the average length at a new lender is 3.3 years. Because many of the firms that borrow from a new lender have no relationship with that lender (over 44%), the relationship variable is also considered in discrete form, for whether the firm has an existing relationship with the lender. These relationship measures can potentially affect the information asymmetry between an inside lender and an outside lender.

11 Table 2 shows the sample means and standard deviations for the total sample of firms, as well as the subsamples of firms that borrow from an existing lender and firms that borrow from a new lender. The average interest rate for the whole sample is 9.01%. An important fact to note is that the average interest rate for firms that borrow from an existing lender is 8.71%, whereas the average interest rate for firms that borrow from a new lender is 9.44%. This evidence from the descriptive statistics already shows that the average interest rate paid by firms at a new lender is higher than the average interest rate paid by firms at an existing lender. With a new lender proxying for the outside lender and an existing lender proxying for the inside lender, this suggests that the expected outside rate is higher than the expected inside rate. The empirical methodology will test this difference in a multivariate framework. The firm characteristics appear to be similar in most respects. The table also shows the mean and standard deviation for lender characteristics, market characteristics, etc. 4. Empirical Methodology The empirical model analyzes the prediction of the Sharpe model using the SSBF data. The goal of this paper is to see whether the theoretical framework is consistent with the data. The first part of the analysis is an interest rate regression in a multivariate framework, focused primarily on whether a firm borrows from an existing lender or a new lender. This approach measures the independent correlation of borrowing from a new lender with the interest rate paid by the firm. The results of the theoretical model also depend on the characteristics of the borrower pool, so the second part of the analysis validates whether the results from the regression are consistent with the parameter space in the model. The Sharpe model can yield opposite theoretical predictions depending on the model s parameters. In some parts of the parameter space, the inside rate is higher and, in other parts of the parameter space, the outside rate is higher. Therefore, the model can not provide a universal hypothesis for whether the interest rate at the existing lender should be higher or lower than the interest rate at the new lender. Therefore, the regression analysis can identify the sign of the coefficient on new lender, but it cannot fully test the theory. To show whether or not this coefficient is consistent with the model, we must also identify some characteristics of the parameter space. If these characteristics are consistent with the finding in the regression, then the results are consistent with the theory.

12 The empirical model focuses on the source of the most recent loan. Because all the firms in the sample have an existing loan, the source of the most recent loan identifies whether the firm borrowed from an existing lender or a new lender. I will use existing lender and new lender as a proxy for inside lender and outside lender. 8 This empirical distinction between existing and new lender closely fits Sharpe s theoretical distinction between inside and outside lender. It reflects the assumption that an existing lender has learned private information about the firm by having already made a loan to the firm and it closely matches the bidding game in the second stage of the Sharpe model, where one of the lenders has already made a loan to the firm in the first stage. The goal of the empirical model is to identify whether the inside or outside interest rate is higher. This analysis compares the empirically predicted interest rate for firms that borrow from an existing lender with the empirically predicted interest rate for firms that borrow from a new lender. If the coefficient on new lender is negative, then the interest rate at the existing lender is higher. If the coefficient on new lender is positive, then the interest rate at the new lender is higher. Therefore, with the loan source proxying for the inside and outside lender, the sign on the new lender coefficient serves as an empirical identifier for the comparison of the inside and outside interest rates. The empirical model is the following: interest rate = f { firm characteristics, new lender, original number of lenders, i i i i bank lender, market characteristics, contract characteristics } i i i The dependent variable is the interest rate charged on the firm s most recent loan. The explanatory variables include firm characteristics, lender characteristics (new lender, original number of lenders, and bank lender), market characteristics, and contract characteristics. This model is estimated using OLS, with controls for the firm industry. The data in the base model include loans from all financial institutions, including thrifts, finance companies, etc. The main regressions are also repeated with only firms that have an existing bank lender and received their most recent loan from a bank. This model extends beyond the existing literature by differentiating the new lender effect from the number of lenders effect at the time of the most recent loan. Prior to the loan in the regression, the firm may have borrowed from one institution or multiple institutions. This is measured as the number of existing lenders. A measure of the ex-post number of lenders may conflate these two 8 Alternatively, Degryse and Van Cayseele (2000) use a scope measure to proxy for whether a bank is an inside lender.

13 effects. To show this, several specifications of the empirical model include regressions with the new number of lenders. The theory can also be analyzed to identify whether the gap between existing lender and new lender rates differs across borrower groups. The theory predicts that the gap changes with the characteristics of the borrower pool. When firms in a group have very similar probabilities of repayment, the gap between existing lender and new lender rates should be small. When firms in a group have very diverse probabilities of repayment, the gap between existing lender and new lender rates should be large. This can be analyzed empirically by analyzing the interaction between new lender and borrower type. The empirical model for this analysis is as follows: interest rate = f { firm characteristics, new lender, new lender i firm characteristic, i i i i i original number of lenders, bank lender, market characteristics, contract characteristics } i i i i The firm characteristic interacted with new lender defines a certain borrower pool based on observable characteristics. In the Sharpe theory, both banks know the characteristics of the borrower pool. The private information is the information about which type of borrower within the pool is applying for a loan. The interaction of an observable firm characteristic with new lender will indicate the relative difference between existing lender and new lender rates across borrower pools. This paper analyzes two different groupings according to firm size and firm age. There are many other possible distinctions, but these two groupings are straightforward. The argument is that large and mature firms are similar in their probabilities of repayment. The difference between a good firm and bad firm is small. On the other hand, small and young firms are diverse in their probabilities of repayment, so the difference between a good firm and bad firm is large. 5. Results for Interest Rates and Borrower Characteristics The regression results are shown in Table 3. Column 1 shows the results for the regression using the total sample and including both the identifier of a new lender and the number of existing lenders. The coefficients on the firm characteristics have the expected signs, though not all of them are significant. The interest rate on a loan decreases with the firm size and the firm s return on assets. These firm characteristics indicate that firms of publicly verifiable higher quality tend to pay a lower

14 rate. The coefficient with the strongest significance is the indicator variable for firms recently denied for a loan. Firms recently denied for a loan are predicted to pay a full percentage point higher interest rate on their most recent loan. The main variable for comparison with the Sharpe model is the indicator of the new lender. The results in Column 1 show that the coefficient on new lender is positive and significant. This implies that the model predicts a higher interest rate when a firm borrows from a new lender. In the language of the Sharpe model, the outside interest rate is predicted to be higher than the inside interest rate. The coefficient for a new lender is 0.521, significant at the 1% level. Specifically, firms with existing loans pay 52 basis points more on a loan when they borrow from a new lender rather than an existing lender. 9 Based on the findings of Black (2006), the empirical methodology must also identify whether this empirical result is consistent with the prediction of the Sharpe model. This result supports the case in the Sharpe model where the expected interest rate at the outside bank is higher than the expected interest rate at the inside bank. The Sharpe model does not predict that the outside rate is always higher; therefore, this finding is not a universal test of the Sharpe model. The result indicates an empirical outcome, which must still be shown below to be consistent with the underlying Sharpe parameter space. Among the other empirical results, the coefficient on the original number of lenders is positive, but not significant. This does not support earlier findings that the cost of credit is greater for firms with a greater number of existing institutions. Likewise, Column 2 is the regression with the number of existing lenders after the most recent loan. The coefficient on the new number of lenders is again positive and insignificant. Columns 3 and 4 repeat the regressions with only firms who have an existing loan at a bank and whose most recent loan was from a bank. The findings are consistent with the findings for the total sample and the coefficient on a new bank lender is similar. The coefficient for a new bank lender is 0.492, significant at the 5% level. Specifically, firms with existing loans pay 49 basis points more on loans that originate from a new bank lender. Column 4 replicates Column 2 for firms borrowing from banks. This regression focuses on the new number of bank lenders, which is the number of bank lenders after the most recent loan. The 9 [[The empirical prediction of the average interest rate on an inside bank loan is about 8.85%. Therefore, the difference between the outside and inside rate is only 4.4 percent of the outside rate.]]- These numbers need to be updated.

15 results indicate that firms with more lenders pay a higher interest rate on average. However, this measure is simply an addition of the existing number of bank lenders and the new number of bank lenders. The results in Column 3 indicate that the main factor in the higher interest rate is whether the firm is adding a bank lender. This finding shows that previous empirical work may have conflated the effect of borrowing from a new lender with the effect of having multiple existing lenders. Borrower Characteristics and the Parameter Space The second part of the analysis is to determine whether the empirical result is consistent with the Sharpe theory. The result from the empirical model is that the interest rate for firms that borrow from a new lender is predicted to be higher than the interest rate for firms that borrow from an existing lender. The next step is to decide whether this result fits the right part of the parameter space. As shown by Black (2006), the outside rate is higher than the inside rate when the quality of the borrower pool is relatively high. This condition can be evaluated by doing a rough imputation of probabilities of 1+ r repayment using observed interest rates. In the Sharpe model, 1+ rp =, where r is the cost of p capital for the lender and p is the probability of success for the average firm. The observed r p in the data is 0.09, which is the average interest rate for the full sample, shown in Table 2. If r is assumed to be zero 10, this value of r p corresponds to p = 0.92, which is a high average probability of success relative to the entire parameter space of the model. Therefore, the borrower characteristics in the data appear to be consistent with the area of the parameter space where the Sharpe predicts that outside rates are higher than inside rates. The theoretical prediction for the magnitude of the difference between the inside and outside rate can also be analyzed across subsamples of the borrower pool. This is done as a way to identify groups of firms which may be more likely to match the parameter space of the empirical finding. As noted, the difference between the outside and inside rate is largest when This difference can also be stated as the difference p( S) p H is high and p L is low. p, which is the difference in the probability of success for a good firm and the probability of success for the average firm in the borrower pool. Therefore, the difference should be greatest for subsamples of borrowers in which good firms are of significantly higher quality than the average firm in the subsample. 10 A positive value of r increases p, which strengthens the implied result.

16 The sample is split by firm size and firm age as a way of separating different borrower pools with different characteristics (see Appendix B for alternative groupings of the data). Small firms likely fit the characteristics in which the difference between the inside and outside rate is large, because high quality small firms likely have a high probability of repayment relative to the average small firm. The small firms that are good may be small growth firms with high future earnings prospects. Large firms, on the other hand, are more likely to have a smaller variance in probability of repayment. Because large firms tend to have a higher probability of repayment on average, the good firms among large firms are likely less distinct from the average quality large firm. Like firm size, the age of firms may also function as a distinguishing borrower characteristic. Loans to young firms are likely to have a greater variance in probability of repayment than loans to mature firms. If these assumptions about the different borrower pools are accurate, a comparison between the pools can help identify whether the regression results are consistent with the Sharpe model. Table 4 shows the split sample summary statistics on interest rates for small vs. large firms and young vs. old firms. Firms are first split by firm size, with the split above and below $1M in total assets. Firms are then split by firm age, with the split above and below 10 years of age. The final analysis compares small, young firms with large, mature firms. The statistics in Table 4 are similar to those shown in Table 2, but only the interest rates are shown. For each sample, the mean interest rate, the standard deviation of the interest rate, and the number of observations are reported. Standard errors are reported for differences in sample means. The first column is the total number of loans for each subsample, which is then broken into firms that borrow from an existing lender and firms that borrow from a new lender. The fourth column shows the difference between the new lender and existing lender rates. The first part of Table 4 analyzes the difference between small and large firms. The first column shows that small firms pay an average interest rate of 9.5%, whereas large firms pay an average interest rate of 8.2%. The second and third columns then split the small and large firm samples by existing lender and new lender. Column 4 shows the difference between the average new lender rate and the average existing lender rate for both small firms and large firms. Interestingly, the difference between new lender and existing lender rates for small firms is positive and significant, while the difference for large firms is not statistically significant. The final statistic for firm size in Column 4 compares the differences across the two groups. This difference is 77 basis points, which is statistically significant at the 5% level.

17 The second part of Table 4 analyzes the difference between young and old firms. Young firms pay an average interest rate of 9.3%, whereas mature firms pay an average interest rate of 8.6%. Similarly to the firm size comparison, Column 4 shows the difference between the average new lender rate and the average existing lender rate for both young firms and old firms. The difference between the new lender rate and existing lender rate for young firms is 110 basis points. The difference between the new lender rate and existing lender rate for old firms is 51 basis points. The final statistic for firm ages in Column 4 compares the two differences and finds that they are statistically the same. The third part of Table 4 analyzes the difference between small, young firms and large, mature firms. Small, young firms are firms that have total assets $1M and are no more than 10 years old, whereas large, mature firms have total assets > $1M and are more than 10 years old. As discussed above, the new lender difference is greater for small firms than large firms, but not significant. Likewise, for firm age, the new lender difference is greater for young firms than mature firms, but not significant. This third part combines these two effects by comparing firms that are both small and young with firms that are both large and mature. Column 4 shows that the new lender difference for small, young firms is 102 basis points and the new lender difference for large, mature firms is -8 basis points. In this case, the difference between existing lender and new lender rates for the two groups is 110 basis points, which is significant at the 5% level. As expected, the new lender difference for small, young firms is significantly greater than for large, mature firms. This indicates that size and age have a compounding effect in differentiating the two groups. The summary statistics from the subsamples of borrower groups support the predictions of the Sharpe model. Compared to large firms, small firms are more likely to be characterized as a borrower group in which p H is high and p L is low. Therefore, the Sharpe model is more likely to predict a significant positive difference between the outside rate and inside rate for these firms. For large firms, a borrower pool in which the probabilities of repayment are closer for good and bad types, there is likely a smaller difference between the outside and inside rate. The subsample statistics show that the existing and new lender rates are not statistically different for large firms. Likewise, the difference between new lender and existing lender rates is greater for young firms. This implies that the difference between the outside and inside rate should be greater for small, young firms than large,

18 mature firms. This is supported by the finding that the difference between the new lender rate and existing lender rates for these two groups is significant. 11 This finding shows that the regression results are consistent with the prediction of the Sharpe model. Small and young firms that are bad are more likely to have a low probability of success on a new loan than large and old firms. In the model, the outside rate is high relative to the inside rate when p H is high relative to p L. Therefore, the Sharpe model predicts that the difference between the outside and inside rate should be greater for small and young firms. As the probabilities of repayment diverge, the difference increases. The statistics for small, young firms show greater differences between new lender and existing lender rates than large, mature firms. This indicates that the regression results from the data are consistent with the predictions of the Sharpe model. The positive coefficient on the new lender indicator is consistent with the Sharpe model prediction for a borrower pool in which there is significant variance in the probabilities of repayment. Interaction of New Lender with Borrower Characteristics The gap between existing and new lender rates can be compared across borrower groups by using an interaction term within the empirical model. The summary statistics indicate that the gap may be larger for small firms and young firms relative to large and mature firms. This can be tested within the model by interacting these firm characteristics with the new lender dummy. Table 5 shows the results of the empirical model with an interaction between a firm characteristic and the new lender dummy. The first firm characteristic is a grouping of small and large firms, split at a threshold of $1 million in total assets. Column (1) shows the results with just the log of firm assets replaced by a small firm dummy. The positive and significant coefficient on small firm confirms that small firms pay a higher interest rate than large firms. Column (2) adds the interaction between small firm and new lender. The coefficient on the interaction is 0.779, which is both positive and significant, and the coefficient on new lender becomes insignificant. Small firms that borrow from an outsider are predicted to pay 78 basis points above the interest paid by small firms that borrow from an inside lender. The empirical results indicate that the new lender rate is significantly higher than the existing lender rate for small firms, but that the two rates are not statistically different for large firms. This result conforms to a Sharpe model prediction in which p H and θ are constant across the two 11 The proportionality of the difference with the underlying rates is consistent with differences in p L, as shown in Black (2006).

19 groups, but small firms have a lower p L than large firms. The connection between the data and the theory appears to be strongest at this point in the analysis. The third and fourth columns of Table 5 show the empirical results for firms in different age groups. Young and mature firms are split at a threshold of 10 years in age. Column (3) shows the results with just the log of firm age replaced by a young firm dummy. Like the small firm dummy, the young firm coefficient is positive and significant, confirming that small firms pay a higher interest rate on average. However, the interaction between young firm and new lender in Column (4) is insignificant. This suggests that the young firm vs mature firm grouping may not conform to a theoretical shift in borrower characteristics toward a lower p L. It is difficult to tell whether this indicates that firm age does not map to this part of the parameter space or whether the Sharpe prediction for relative rates is not supported by this aspect of the data. 6. The Role of Relationships In the Sharpe model, a financial institution learns private information about a firm through the process of lending. This premise is based on the more general idea that financial institutions learn private information about firms through ongoing interactions, which could be through other activities, such as financial services. This idea has been developed as the concept of relationship lending. Much of the empirical literature in this area has used length of relationship as the measure of private information known to the financial institution [Petersen and Rajan (1994); Berger and Udell (1995)]. Some of these papers reference the Sharpe model to formulate hypotheses about the predicted effect of the length of relationship [Harhoff and Korting (1998); Degryse and van Cayseele (2000); etc.]. The model predicts that interest rates rise with the length of the relationship. However, the implication is limited, because the Sharpe model does not explicitly model degrees of relationship strength through duration or scope. The model only has two stages, so the role of relationship can only be inferred as the change between period 1 and period 2 of the model. Therefore, relationship length was left out of the base regressions of this paper, because it is not explicitly present in the Sharpe model. To address the role of relationship lending, this section analyzes the role of relationship length specifically for observed inside vs. outside interest rates. Based on the previous literature on relationships, the exclusion of relationship length from the base specification has specific implications. The first consideration must be the correlation between relationship length and the new lender dummy. These variables are clearly correlated, because firms

20 tend to have a very short relationship with a new lender relative to the length of relationship with an existing lender. Table 2 shows that firms that borrow from an existing lender have an average log relationship length of 4.24, whereas firms that borrow from a new lender have an average log relationship length of This corresponds to an average of about 9 years at an existing lender and about 3.5 years at a new lender. More specifically, all firms that borrow from an existing lender also have an existing relationship with that lender, whereas firms that firms that borrow from a new lender may or may not have an existing relationship with that lender. Those firms that borrow from an outsider and have an existing relationship with the outsider may have formed the relationship through financial services. Table 2 shows that 45% of firms that borrow from a new lender do not have an existing relationship with that institution. This results in a negative correlation between the new lender dummy and the length of the relationship. The implication of this correlation is that the previous results for new lender may be due to omitted differences in relationship length. This section analyzes whether the new lender dummy and relationship length have an independent effect on interest rates. The general empirical specification for this section includes a relationship characteristic among the independent variables. This type of specification allows for a more complete separation of the effects of the new lender dummy and relationship length. The empirical model for this analysis is as follows: interest rate = f { firm characteristics, new lender, relationship, i i i i new lender i relationship, original number of lenders, i i i market characteristics, contract characteristics } i i The basic relationship characteristic used in the analysis is the log of the length of the firm-institution relationship in months. This measure is then interacted with the new lender dummy to identify the effects of relationship length at an inside bank vs. an outside bank. Due to the extreme left-censoring of relationship lengths at new lenders, the relationship characteristic is also analyzed as a dummy variable for an existing relationship (length of relationship > 0). The second part of the analysis repeats the same relationship specifications using the existing relationship dummy rather than the continuous relationship length. In the final specification, the model includes an interaction between the new lender dummy and the existing relationship dummy. This provides a test for whether existing

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