The Value of Information in Relationship Lending

Transcription

1 The Value of Information in Relationship Lending Nicola Pavanini, Fabiano Schivardi March 2016 Preliminary and incomplete. Please do not quote. Abstract In this paper we investigate whether relationship lending mitigates any informational asymmetries between borrowers and lenders, and quantify the value of information that a relationship generates. We develop a structural bayesian learning model of lenders and apply it to the Italian market for small business lines of credit. Using detailed data on loan contracts between Italian firms and banks over time, this framework allows us to estimate imperfect information, measured as variation in banks estimates of borrowers creditworthiness, as well as the speed and accuracy of the banks learning process, measured as the variance of the signals the lenders receive during the relationship. We find reduced form evidence consistent with theoretical predictions of banks learning, as interest rates increase over the course of a relationship, mostly for risky borrowers, and become more dispersed. Simulating data from our structural model we can reproduce the same reduced form findings with a high degree of uncertainty and high learning accuracy. We plan to recover the value of information in the relationship looking at how interest rates would change in a counterfactual scenario where lenders have complete information about their borrowers and no learning occurs. These results have important policy implications for banking regulation in terms of information sharing and competition policy. We thank Greg Crawford, Jeff Campbell and seminar participants at University of Zürich, Tilburg University. University of Zürich, nicola.pavanini@econ.uzh.ch Bocconi, EIEF and CEPR, fabiano.schivardi@unibocconi.it 1

2 1 Introduction Since the seminal work of Akerlof (1970), Rothschild & Stiglitz (1976), and Stiglitz & Weiss (1981), a large theoretical literature has showed how asymmetric information can be a source of inefficiencies in financial markets. In order to design regulatory policies that limit these inefficiencies, it is crucial to understand the causes and effects of asymmetric information, as well as whether and how financial intermediaries can reduce information asymmetries with their borrowers. The theoretical banking literature, since Sharpe (1990), von Thadden (2004), and Rajan (1992), has assumed that firm-bank relationships and banks monitoring mitigate informational asymmetries. According to these models banks learn about their borrowers creditworthiness through lending and acquire an informational advantage over rival banks that allows them to capture rents on older good customers, which cannot credibly signal their creditworthiness to other banks. This generates another source of inefficiency, commonly defined as the hold-up problem, as the information asymmetry between banks causes sound borrowers to be charged higher interest rates than their actual risk would suggest. There have been various empirical attempts at testing whether firm-bank relationships and banks monitoring mitigate informational asymmetries, with mixed results. Petersen & Rajan (1994), using U.S. data, find that the availability of financing increases over the course of the relationship, but prices don t vary. Using similar data but just focusing on lines of credit, Berger & Udell (1995) show that as a relationship evolves borrowers are charged lower prices and are less likely to pledge collateral. On the other hand, Degryse & Van Cayseele (2000) find that loan rates increase over the course of the relationship for Belgian firms, but also find that rates decrease when the firm purchases other information-sensitive bank products, which increase the scope of the firm-bank relationship. There is however no clear empirical evidence about the extent of the reduction in information asymmetries that relationship banking and monitoring can actually lead to, even though quantifying the relevance of these aspects is of crucial importance to the design of regulatory policies in lending markets. We address this question with this paper, where we investigate whether relationship banking mitigates any informational asymmetries between borrowers and lenders, and quantify the value of information that a relationship generates. We develop a structural bayesian learning model of lenders and apply it to the Italian credit market. Using detailed data on loan contracts over time, this framework allows us to estimate imperfect information, measured as variation in banks estimates of borrowers creditworthiness, as well as the speed and accuracy of the banks learning process, measured as the variance of the signals the lenders receive during the relationship. We recover the value of information in the relationship looking at how interest rates would change in a counterfactual scenario where lenders have complete information about their borrowers and no learning occurs. In this paper we first summarize the key features of a widely used theoretical framework, developed by Sharpe (1990) and later updated by von Thadden (2004). This model provides a basic structure for our problem, assuming that borrowers need credit from lenders and have private information about their own risk, but lenders can learn about this through lending to them. Moreover, the model allows for asymmetric learning, as banks become more informed about their borrowers compared to rival banks and exploit this information advantage locking in good borrowers. The testable prediction of this model are the following. First, on average interest rates charged will rise over the course of the relationship, and this will be mostly driven by increases to bad borrowers. Second, the dispersion of interest rates will also rise as banks learn about their borrowers over the course of the relationships. 2

3 To test these predictions and to estimate our structural model we will make use of the data previously used in Panetta, Schivardi & Shum (2009) and Crawford, Pavanini & Schivardi (2015). The dataset consists of small business lines of credit in Italy, and it is based on three main sources. Interest rate data and data on outstanding loans are from the Italian Centrale dei Rischi, or Central Credit Register. Firm-level balance sheet data are from the Centrale dei Bilanci database. Banks balancesheet and income-statement data are from the Banking Supervision Register at the Bank of Italy. By combining these data, we obtain a matched panel dataset of borrowers and lenders extending over an eleven-year period, between 1988 and We also collected data on bank branches at the local level since We test the theory predictions using a reduced form approach first. We run a series of OLS regressions of interest rates on various controls, with the most accurate model including firm-bank fixed effects and dummies for the age of the relationship. We find that on average interest rates almost monotonically increase over the course of the firm-bank relationship, and that this increase is mostly driven by riskier borrowers. As predicted by the theory, we also find that the dispersion in interest rates rises with the age of the relationship. Based on these findings, we develop a structural bayesian learning model of lenders to quantify the value of information that a firm-bank relationship generates. This framework follows the literature of bayesian models of consumer learning (Erdem & Keane (1996), Ackerberg (2003), and Crawford & Shum (2005)) and firm learning (Hitsch (2006)). We allow borrowers to choose one of the banks in their market every year, or choose not to borrow. Conditional on borrowing, firms might default on their loans. In line with Crawford et al. (2015) we allow demand and default unobservables to be jointly normally distributed, and interpret a positive correlation between them as evidence of adverse selection, as it implies that riskier firms are more likely to take credit. On the supply side, we define as inside banks the lenders chosen by the borrowers and outside lenders the ones not chosen. Every period banks offer to each potential borrower the interest rate that maximizes their firmbank-specific expected profit. However, the bank s profit depends on the imperfect information it has about each borrower. To overcome this uncertainty, every period both inside and outside lenders receive a signal about the creditworthiness of each firm, and we allow the variance of these signals to be different between inside and outside banks. Based on the signals they receive, banks update their belief about the firm s creditworthiness, which in turn changes the expected profits and the equilibrium interest rate. Our model allows for four important features. First, banks can learn about their borrowers creditworthiness. Second, lenders learn asymmetrically, as we allow inside banks to have a different variance of the signal compared to outside banks. Third, borrowers can also incur a switching cost from choosing a different bank than the inside lender. Last, we allow for adverse selection and estimate it s magnitude. We make an important assumption on banks behavior for both tractability and institutional reasons, that is modeling banks as myopic and not forward looking agents. We differ with this assumption from most the structural literature on consumer learning, but the tractability in our model is also substantially different from the usual setup. In the standard IO literature on this topic the optimal decision, which depends on the information set at every period and on the present discounted value of future utilities/profits, is usually a binary choice between buying or not a product, or using or not a specific drug. In our model instead the optimal decision is a continuous variable, the interest rate on a loan contract, and allowing for forward looking banks would make the identification of the learning parameters, though the banks profit s first order condition, almost intractable. If on one hand the assumption of myopic banks prevents us from investigating dynamic aspects of the strategic interest rates decisions, on the other hand it still allows us to have both asymmetric learning across banks and to let inside banks exploiting their informational advantage when competing with 3

4 outside lenders, which still leads to the hold up problem. Last, we believe that the myopic banks assumption is more reasonable for the specific type of loan contracts we consider, that is yearly un-collateralized credit lines of small size, whereas could be more problematic for long term loans of larger amounts. Compared to the reduced form literature in empirical banking (Petersen & Rajan (1994), Berger & Udell (1995), Degryse & Van Cayseele (2000)), which showed mixed qualitative results consistent with the theory papers, we are able to provide quantitative results, measuring the degree of uncertainty that banks have, their speed and accuracy at learning, and the value of information in relationship lending. This allows us to investigate some important policy implications of banks learning. First, banking regulation in the past decades as been encouraging information sharing across lenders to reduce information asymmetries. This might however affect banks incentives to learn, as described in Pagano & Jappelli (1993), because sharing information implies that banks are less able to exploit the informational advantage they gain through learning. Second, there has been a push in recent years for more competition in the banking sector for efficiency reasons, but learning can actually lead to more concentration, as Besanko, Doraszelski, Kryukov & Satterthwaite (2010) show, because incumbent banks in a local market gain an informational advantage that makes it less profitable for new banks to enter. Understanding the extent of learning is therefore crucial when designing regulatory policies to reduce agency costs and encourage competition. Before estimating the structural model on the dataset, we do a comparative statics exercise simulating data from our structural model, and then comparing the same reduced form results between actual and simulated data, varying some key parameters of the learning process in the simulation. Similarly to the reduced form evidence described earlier, we investigate how interest rates vary over the course of a firm-bank relationship, and how their dispersion evolves. We are interested in how this variation in interest rates depends on banks initial uncertainty, measured as the variance of the prior distribution of borrowers creditworthiness, and on the informational advantage of inside lenders, measured as the difference between the variances of the outside and inside banks signals. We also check how the variation in interest rates changes depending on the number of banks, to capture the effect of an increase in competition. We find that the interest rates increase over the course of the relationship is stronger the higher is the initial uncertainty, and the larger is the informational advantage of inside banks. We also find that average interest rates decrease as the number of banks increases, but they are still significantly increasing over the course of the relationship. This might suggest that the informational lock-in is weaker as competition increases. An important strand of the structural literature that this paper contributes to is on bayesian models of consumer learning (Erdem & Keane (1996), Ackerberg (2003), and Crawford & Shum (2005)) and firm learning (Hitsch (2006)), as well as to the literature on learning by doing (Benkard (2000) and Benkard (2004)). Following this literature, in a standard consumer learning setting agents are uncertain about some product s attribute, but can learn about it through experience (i.e. buying the product) and advertisement. This implies that their optimal purchasing pattern changes as they update their belief about the product s quality. Differently from this set up, but in line with the theoretical banking literature described above, we assume that the supplier (bank) is uncertain about a consumer s attribute (borrower s creditworthiness), and learns about it through lending. This can give rise to asymmetric learning between banks, because if a borrower chooses one bank, that bank is likely to learn more about the borrower than rival banks. This bank can then exploit its informational advantage and extract rents from good borrowers, who cannot credibly signal their creditworthiness to rival banks. A key feature of this market is that a bank can price discriminate at the borrower level, so as learning progresses over the course of the relationship the bank updates its belief and changes its equilibrium interest rate. 4

5 The structure of the paper is the following. In Section 1 we will outline the basic theory of relationship lending of Sharpe (1990) and von Thadden (2004). In Section 2 we will describe the dataset and the institutional details. Section 3 will present the reduced form evidence. We will introduce a structural model of relationship lending in Section 4, and its estimation strategy in Section 5. In Section 6 we will show some preliminary Monte Carlo results. In Section 7 we will conclude. 2 Basic Theory of Relationship Lending We develop in this section a simple framework based on Sharpe (1990) and von Thadden (2004), to give an insight of the existing theoretical features and predictions of the literature that we incorporate in our structural model. Take a 2 periods model with a continuum of risk neutral borrowers who need funds to finance a risky project every period, and a continuum of risk neutral lenders. Every period lenders offer one-period loans to borrowers and compete between each other on interest rates. Borrowers can be of low or high quality q = {L, H}, which implies different probabilities of a successful project p L < p H, and in turn different repayment probabilities, as unsuccessful borrowers are unable to repay. Lenders don t know the borrowers quality ex-ante, but the proportion of high quality borrowers θ (0, 1) is common knowledge. Lenders learn the quality of the borrowers who took their loans, as they observe the success (S) or failure (F ) of their project γ = {F, S}. We call these lenders inside banks, whereas the other lenders, defined as outside banks, only get a noisy signal of each borrower s quality γ. The timing of the game is the following. Every period each bank announces an interest rate for each borrower, as a function of its own and its rivals information sets, then borrowers choose their preferred alternative, and eventually repay or not. von Thadden (2004) shows that in the second period the bidding game between lenders has no Bayesian Nash equilibrium in pure strategies. The intuition for this result is given by a standard winner s curse example. If a borrower in period 2 switches to an outside bank it is both because the outside lender s offer is attractive and the inside lender didn t bid aggressively enough, hence the outside lender should take this information into account. Typically in this setting pure strategy equilibria don t exist. von Thadden (2004) shows instead that this game has a unique mixed-strategy equilibrium. According to this inside banks offer a high rate r F to unsuccessful borrowers and randomize the offer to successful ones in the interval [r p, r F ], with r S < r p < r F and r p being the rate offered in the first period when all lenders are uninformed. Outside banks will instead offer r F with probability 1 p(s), where p(s) is success probability in period 1, and randomize the rest of their offers in the interval [r p, r F ). This result implies that borrowers can switch banks in equilibrium, full competition is only effective for bad borrowers, and inside banks make positive expected profits on the good borrowers. What is also consistent with this finding is an average increase in interest rates over the course of the relationship. A bad borrower that is offered r F by the outside bank will remain with the inside bank and accept an interest rate increase from r p in period 1 to r F in period 2. By the same token, the inside bank will never offer a price decrease to a good borrower in the second period, so unless it switches it will accept a second period price greater or equal to the first period price. Another natural consequence of this finding is an increase in the dispersion of prices between the first period, when good and bad borrowers are charged r p, and the second period. 5

6 3 Data and Institutional Details In this paper we will make use of the data previously used in Panetta et al. (2009) and Crawford et al. (2015). 1 The dataset consists of small business lines of credit in Italy, and it is based on three main sources. Interest rate data and data on outstanding loans are from the Italian Centrale dei Rischi, or Central Credit Register. Firm-level balance sheet data are from the Centrale dei Bilanci database. Banks balance-sheet and income-statement data are from the Banking Supervision Register at the Bank of Italy. By combining these data, we obtain a matched panel dataset of borrowers and lenders extending over an eleven-year period, between 1988 and We also collected data on bank branches at the local level since The Central Credit Register (hereafter CR) is a database that contains detailed information on individual bank loans extended by Italian banks. Banks must report data at the individual borrower level on the amount granted and effectively utilized for all loans exceeding a given threshold, 3 with a breakdown by type of the loan (credit lines, financial and commercial paper, collateralized loans, medium and long-term loans and personal guarantees). Banks also report if they classify a loan as bad, meaning that they attach a low probability to the event that the firm will be able to repay the loan in full. In addition, a subgroup of around 90 banks (accounting for more than 80 percent of total bank lending) have agreed to file detailed information on the interest rates they charge to individual borrowers on each type of loan. We restrict our attention to short-term credit lines, which have ideal features for our analysis. First, the bank can change the interest rate every year, while the borrower can close the credit line without notice. This means that differences between the interest rates on loans are not influenced by differences in the maturity of the loan. This also implies that variations in interest rates over the course of firm-bank relationships, conditional on changes in firms observable characteristics, can be driven by banks acquisition of soft information on firms creditworthiness. Second, the loan contracts included in the CR are homogeneous products, so that they can be meaningfully compared across banks and firms. Third, they are not collateralized, a key feature for our analysis, as adverse selection issues become less relevant for collateralized borrowing. Fourth, short term bank loans are the main source of borrowing of Italian firms. For example, in 1994 they represented 53 percent of the total debts according to the Flow of Funds data. We define the interest rate as the ratio of the payment made in each year by the firm to the bank to the average amount of the loan. The interest payment includes the fixed expenses charged by the bank to the firm (e.g. which encompass the cost of opening the credit line or the cost of mailing the loan statement). The Centrale dei Bilanci (hereafter CB) collects yearly data on the balance sheets and income statements of a sample of about 35,000 Italian non-financial and non-agricultural firms. This information is collected and standardized by the CB, that sells these data to banks for their lending decisions. The unique feature of the CB data set is that, unlike other widely used data sets on individual companies (such as the Compustat database of US companies), it has wide coverage of small and medium enterprises; moreover, almost all the companies in the CB sample are unlisted. The coverage of these small firms makes the data set particularly well suited for our analysis, because informational asymmetries are potentially strongest for these firms. Initially, data were collected by banks themselves and transmitted to the CB. In time, the CB has increased the sample size drawing from balance sheets deposited with the chambers of commerce (limited liability companies are obliged to file their balance sheets to the chambers of commerce, that make them available to 1 Both of these papers present extended descriptive statistics of the data. 2 Detailed descriptives on the branch data are in Ciari & Pavanini (2014). 3 The threshold was 41,000 euros (U.S. $42,000) until December 1995 and 75,000 euros thereafter. 6

7 the public). The database is fairly representative of the Italian non-financial sector. The firms in the CB sample represent about 49.4% of the total sales reported in the national accounting data for the Italian non-financial, non-agricultural sector. In addition to collecting the data, the CB computes an indicator of the risk profile of each firm, which we refer to in the remainder of this paper as the SCORE. The SCORE represents our measure of a firm s observable default risk. It takes values from 1 to 9 and is computed annually using discriminant analysis based on a series of balance sheet indicators (assets, rate of return, debts etc.) according to the methodology described in Altman (1968) and Altman, Marco & Varetto (1994). In Table 1 we provide detailed descriptive statistics of our data. In Panel A we show the loan contracts characteristics. The average loan amount that is granted is around e500,000, and the amount used is roughly half of that. The mean of interest rates is 14%, and in 2% of the cases firms default on a credit line. In Panel B we list some main characteristics of banks in our sample. Last, in Panel C we present the main yearly balance sheet information about borrowing and non-borrowing firms in our sample. Borrowers and non-borrowers have similar characteristics, with the first ones being moderately larger in terms of assets and sales, slightly riskier and older. 4 Reduced Form Evidence We provide some reduced form evidence to document two important empirical regularities, consistent with the theory predictions outlined above, that could be explained with the presence of a banks learning pattern. First, interest rates significantly increase over the course of the firm-bank relationship, conditional on several observables. Second, the dispersion in interest rates raises the longer is the relationship between a firm and a bank. These findings are documented in Table 3 with several OLS regressions of the interest rate charged on a set of explanatory variables and fixed effects, focussing only on the relationships that started within our sample. Graphical illustrations of these results are showed in Figures 1 and 2. The main regression of interest is the following: P ijt = α + βx ijt + γz ijt + ω ij + τ jt + ε ijt, (1) where X ijt include loan specific variables, such as the amount of credit granted and used, whether the loan is with the main bank (the bank from which the firm borrows the most), whether the firm just switched its main bank, and distance between firm and bank. Depending on the specification used, in some cases X ijt also includes firm-year specific controls, including sector and score fixed effects, several balance sheet controls, and the total number of bank relationships a firm has. The year of relationship dummies are included in Z ijt, ω ij are firm-bank specific fixed effects, and τ jt are bank-year specific fixed effects. In one case we allow instead for firm-year specific fixed effects, with similar results. 4 We provide in Table 2 some descriptive statistics for our main variables of interest, namely how interest rates vary over the years of a relationship. Two interesting patterns emerge from this Table. First, the mean and the median of the interest rates are almost monotonically declining over the course of the relationships, where the mean effect is equivalent to regression 1 with only Z ijt as controls. Second, the variance of these rates is also declining over time. The decline in interest rates 4 We are not able to include both firm-bank and firm-year fixed effects at the same time as the number of parameters would exceed the number of observations. 7

8 Table 1: Summary Statistics Variable Obs Mean Std. Dev. Obs Mean Std. Dev. Panel A: Amount Granted 690, , Loan Level Amount Used 690, Interest Rate 690, Default 690, Panel B: Total Assets , ,965.6 Bank Level Employees 896 3, ,582.5 Bad Loans Number of Provinces Panel C: Borrowing Firms Non-Borrowing Firms Firm Level Fixed Assets 235,318 10, , ,494 8, ,118 Intangible/Tot Assets 235, , Net Worth 235,318 6, , ,494 5, ,176 Short Term Debit 235,318 5,791 45, ,494 2,162 74,077 Trade Debit 235,318 3,518 29, ,494 4,150 61,121 Sales 235,318 29, , ,494 11, ,202 Profits 235,318 2,586 54, ,494 1,160 52,512 Cash Flow 235,318 1,813 45, ,494 1,187 43,989 Score 235, , Firm s Age 235, , N. of Relationships 235, Branch distance (km) 690, Note: In Panel A an observation is a firm-bank-year loan contract. Amount Granted and Amount Used are in thousands of euros, Default is a dummy for a firm having any of its loans classified as bad (90 days past due). In Panel B an observation is a bank-year. Employees is the number of employees at the end of the year. Bad loans is a percentage of total loans. In Panel C an observation is a firm-year, and all the variables apart from Intangible/Tot Assets and the last four are in thousands of e. The SCORE is the indicator of the risk of the firm computed each year by the CB (higher values indicate riskier companies). Number of relationships is the number of banks from which the firm borrows through these credit lines. 8

9 is also evident in the first column of Table 3, where we present various specifications of regression 1. Interestingly, as we add more controls and fixed effects, the pattern of interest rates reverses, becoming monotonically increasing in the most accurate specification of column (6). We interpret the initial negative trend as evidence of selection bias. Consider ω ij as borrower specific riskiness, observed by each bank with some noise, and ε ijt as idiosyncratic shocks. Selection bias affects the estimates of γ as follows. For short relationships, we will observe prices for both high and low risk firms, but for long relationships we will only observe prices for low risk firms, as high risk firms have exited the relationship (i.e. have been offered a very high price that they refused, or have been rejected). This implies that the γ coefficients will be downward biased, given the negative relationship between ω ij and Z ijt, and explains why we find that γ < 0 in the first column of Table 2 and γ > 0 in the last columns, when we control for firm-bank fixed effects. Table 2: Descriptive Statistics for Interest Rates over Relationships Sample Obs Mean Std. Dev. 5 th Pctile Median 95 th Pctile 1 st Year 228, nd Year 165, rd Year 107, th Year 74, th Year 49, th Year 30, th Year 17, th Year 9, th Year 4, th Year 1, Total 690, Note: An observation is a firm-bank-year. In all the specifications we consider, apart from column (1), we find that interest rates increase over the course of the relationship, in some cases even almost monotonically. Our most accurate model in column (6) shows that as the relationship progresses, interest rates increase up to 0.2 percentage points per period, with a monotonic increase until the 9 th year of the relationship. Using the residuals from the regression in column (6), we propose a graphical representation of this increase in interest rates for the first 5 years of relationship in Figure 1, as well as the rise in price dispersion as shown in Figure 2. Consistent with the theoretical predictions outlined above, we want to investigate whether this increase in prices and in their dispersion can be explained by banks information acquisition. Building up on these preliminary findings, we examine in Table 4 any potential heterogeneity in this price increase over borrowers risk categories. In von Thadden (2004) s model the main price increase is experienced by risky borrowers, and we test this result running separate regression of Table 3 s column (6) model across separate risk categories. We use two dimensions to determine risk categories. The first dimension we consider is the SCORE, a measure of credit rating computed by the Centrale dei Bilanci for every borrower every year, and provided to each bank. This indicator goes from 1 (safe) to 9 (very risky). The second dimension we use is ex-post risk, that 9

10 is whether a firm defaults. As shown in Table 4, we find that the price increase is mostly driven by risky borrowers, consistent with von Thadden (2004) s prediction. This last finding contradicts the hypothesis that switching costs may be driving the interest rate increase over the relationship, because if that was the case then also safe firms should face switching costs and experience a rise in interest rates. We also investigate alternative reasons that would explain a price variation over the course of the relationship. We show in Table 5 that amounts granted don t vary over the relationship, and that amounts used increase slightly up to the 5 th year. The latter result goes against a price increase, as the interest rate is calculated as a combination of initial fixed fees and actual amount used, and the unit price of a loan is decreasing in amount used. 10

11 Table 3: Reduced Form Pricing OLS regressions Variables (1) (2) (3) (4) (5) (6) Constant (0.192) (0.180) (0.260) (0.043) (0.324) (0.338) 2 nd Year (0.011) (0.012) (0.011) (0.017) (0.022) (0.022) 3 rd Year (0.015) (0.015) (0.015) (0.021) (0.038) (0.039) 4 th Year (0.018) (0.017) (0.018) (0.025) (0.055) (0.055) 5 th Year (0.022) (0.021) (0.022) (0.029) (0.072) (0.072) 6 th Year (0.028) (0.026) (0.028) (0.035) (0.089) (0.089) 7 th Year (0.035) (0.033) (0.034) (0.043) (0.106) (0.107) 8 th Year (0.044) (0.041) (0.043) (0.055) (0.125) (0.125) 9 th Year (0.062) (0.058) (0.058) (0.076) (0.147) (0.146) 10 th Year (0.096) (0.091) (0.087) (0.114) (0.178) (0.177) Loan Controls No Yes Yes Yes Yes Yes Firm Controls Yes Yes Yes No Yes Yes Sector FE Yes Yes Yes No Yes Yes Score FE Yes Yes Yes No Yes Yes Year FE No No Yes No Yes Yes Province FE No No No No No No Bank FE No No Yes Yes No No Bank-Year FE No No No No No Yes Bank-Year-Province FE Yes Yes No No No No Firm FE No No Yes No No No Firm-Year FE No No No Yes No No Firm-Bank FE No No No No Yes Yes R N obs. 690, , , , , ,167 Note: An observation is a firm-bank-year. This sample only includes relationships that start within our data period. Standard errors are clustered at the firm-bank level. Firm controls include total assets, tangible and intangible assets, fixed active, total active, net assets, short term debt, sales, profits, cashflow, leverage, long and short term bank debt, trade debit, return on assets, ratio of intangible assets, total number of relationships. 11

12 Figure 1: Distribution of Pricing Residual over the Relationship x Year 2 Year 3 Year 4 Year 5 Note: Kernel densities of the residuals from the pricing regression in column (6) of Table 3, where zero is the average residual for the first year of the relationship, and the shift in mean every period is given by the Year coefficients. Figure 2: Standard Deviation of Pricing Residual over the Relationship Standard Deviation Pricing Residuals Years of Relationship Note: Standard deviation by year of relationship of the residuals from the pricing regression in column (6) of Table 3. 12

13 Table 4: Reduced Form Pricing OLS regressions by Risk Category Variables (Score 1-3) (Score 4-6) (Score 7-9) Defaulters Constant (1.374) (0.432) (0.558) (1.573) 2 nd Year (0.103) (0.034) (0.052) (0.278) 3 rd Year (0.173) (0.060) (0.096) (0.544) 4 th Year (0.238) (0.085) (0.140) (0.811) 5 th Year (0.301) (0.111) (0.185) (1.902) 6 th Year (0.369) (0.138) (0.231) (2.251) 7 th Year (0.440) (0.165) (0.277) (1.753) 8 th Year (0.533) (0.192) (0.326) 9 th Year (0.604) (0.223) (0.379) 10 th Year (0.795) (0.268) (0.447) Loan Controls Yes Yes Yes Yes Firm Controls Yes Yes Yes Yes Sector FE Yes Yes Yes Yes Score FE Yes Yes Yes Yes Year FE Yes Yes Yes Yes Province FE No No No No Bank FE No No No No Bank-Year-Province FE No No No No Firm-Bank FE Yes Yes Yes Yes R N obs. 62, , ,311 26,274 Note: An observation is a firm-bank-year. This sample only includes relationships that start within our data period. Standard errors are clustered at the firm-bank level. Firm controls include total assets, tangible and intangible assets, fixed active, total active, net assets, short term debt, sales, profits, cashflow, leverage, long and short term bank debt, trade debit, return on assets, ratio of intangible assets, total number of relationships. 13

14 Table 5: Reduced Form Amounts Granted and Used OLS regressions Variables (Granted) (Used) Constant ( ) (27.177) 2 nd Year (10.328) (1.628) 3 rd Year (19.381) (2.806) 4 th Year (30.811) (4.019) 5 th Year (40.762) (5.258) 6 th Year (50.578) (6.559) 7 th Year (59.566) (7.824) 8 th Year (74.022) (9.292) 9 th Year (87.164) (10.535) 10 th Year ( ) (13.477) Loan Controls Yes Yes Firm Controls Yes Yes Sector FE Yes Yes Score FE Yes Yes Bank-Year FE Yes Yes Firm-Bank FE Yes Yes R N obs. 690, ,167 Note: An observation is a firm-bank-year. This sample only includes relationships that start within our data period. Standard errors are clustered at the firm-bank level. Firm controls include total assets, tangible and intangible assets, fixed active, total active, net assets, short term debt, sales, profits, cashflow, leverage, long and short term bank debt, trade debit, return on assets, ratio of intangible assets, total number of relationships. 14

15 5 A Model of Relationship Lending Assume there are i = 1,.., I borrowers in a market m = 1,.., M who can choose to take a loan every t = 1,.., T periods from a bank j = 1,.., J mt paying a price P ijmt, or not to take a loan. Conditional on taking out a loan, borrowers may default or not. Borrowers choose to take up the loan based on the following utility: Uijmt D = α1i D αd 2 P ijmt + η D 1 ijmt 1 + X ijmt βd + ɛ ijmt, Ui0mt D = ɛ i0mt, (2) where Ui0mt D is the utility from not borrowing, ηd represents switching costs, X ijmt are other covariates, and ɛ ijmt, ɛ i0mt are distributed as type 1 extreme value. We allow for a random coefficient on the constant term α1i D = ᾱd 1 + σd ν 1i, with ν 1i N(0, 1). Conditional on borrowing, borrowers may default based on the following utility: U F ijmt = α F 1 + αf 2 P ijmt + η F 1 ijmt 1 + X ijmt βf + q ijmt, (3) where the residual q ijmt represent the creditworthiness of a firm, unobserved to both the econometrician and the bank, private information to the firm. We allow q ijmt to be jointly normally distributed with α1i D, such that: ( α D 1 q ) N ( ( ᾱd 1 0 ) ( σ D2 ρσ, D ρσ D 1 ) ). (4) We interpret a positive correlation between demand and default unobservables ρ > 0 as evidence of adverse selection, as it implies that riskier firms are more likely to demand. Banks are uncertain about the true creditworthiness q i of each borrower, but can learn about it through lending to them. At period t = 0 a bank s prior belief about a borrower s creditworthiness is q ijm0 α1i D N(µ 0 + σ 0 ρν 1i, σ0 2(1 ρ2 )). We define the bank chosen by a borrower as inside bank, and the other banks as outside banks. Every time a borrower takes up a loan with a bank and doesn t default, the inside bank receives a private information experience signal s I ijmt N(q i, τi 2 ) that it uses to update its belief about the borrower s creditworthiness. On the other hand, when a firm doesn t default each outside bank receives another experience signal s O ijmt N(q i, τo 2 ), also used to update their beliefs. This generates an asymmetric information between banks, as inside and outside banks receive different signals about borrowers creditworthiness. Each bank chooses the price P ijmt that maximizes its expected profit from the relationship, which depends on the information set I ijmt it has for each borrower: E(Π ijmt I ijmt ) = ( ) P ijmt E(MC ijmt I ijmt ) d ijmt where d ijmt is the probability that a borrower takes up the loan with bank j, based on the demand model described earlier, and E(MC ijmt I ijmt ) = f(e(q i I ijmt ), C ijmt ) are the bank s expected marginal costs for this loan, expressed as a function of expected borrower s creditworthiness and other costs C ijmt. The first order condition delivers the following equilibrium pricing equation: P ijmt = E(MC ijmt I ijmt ) d ijmt, d ijmt 15

16 where d ijmt is the derivative of the demand probability with respect to price. Every period each bank may receive either an inside or an outside signal, depending on the firm s choice of bank. Once the bank receives the signal, it updates its beliefs according to Bayes rule. This gives the following posterior means and variances: µ ijmt+1 = µ ijmt σ ijmt 2 1 σ ijmt 2 µ ijmt σ ijmt 2 1 σ ijmt 2 + si ijmt τ 2 I + 1 τ 2 I + so ijmt τ 2 O + 1 τ 2 O if i buys from j otherwise σijmt+1 2 = 1 1 σ ijmt σ ijmt τ 2 I + 1 τ 2 O if i buys from j otherwise 6 Estimation We estimate the model described above in two steps. In the first step we recover the parameters of the demand and default probabilities Θ 1 = {ᾱ1 D, σd, α 2, η D, β D, α1 F, αf 2, ηf, β F, ρ}, following the simulated likelihood approach of Crawford et al. (2015). In the second step we estimate the parameters of the learning process and of the cost function Θ 2 = {γ, µ 0, σ0 2, τ I 2, τ O 2 }. We don t estimate these two steps jointly for tractability, as we need to use the estimated parameters from the demand model and ρ to construct the probabilities in the second step. The key parameters of this structural model are the variance of a bank s initial valuation of its borrowers creditworthiness σ0 2, which we interpret as a measure of lenders imperfect information, as well as the variance of the signals the lenders receive during the relationship τi 2 and τ O 2, which we interpret as the speed and accuracy of the banks learning process, and the informational advantage that inside banks acquire with respect to outside banks. Based on the model defined above, we can define the demand probability as follows: d ijmt = exp ( α D 1i αd 2 P ijmt + η D 1 ijmt 1 + X ijmt βd) 1 + l exp ( α D 1i αd 2 P ilmt + η D 1 ilmt 1 + X ilmt βd)f(αd 1i θ)dα D 1i, where f(α1i D θ) is the density of αd 1i, and θ are the parameters of its distribution that we want to estimate. The default probability will be defined as: f ijmt,f =1 D=1 = Φ qijmt α D 1i ( α F 1 + α2 F P ijmt + η F 1 ijmt 1 + X ijmt ) βf µ qijmt α D 1i f(α σ 1i θ)dα D 1i, D qijmt α D 1i where D ijmt are borrowers bank choices, F ijmt are borrowers defaults, µ qijmt α D = ρν 1i and 1i σ qijmt α D = (1 ρ 2 ). We use these demand and default probabilities to construct the following likelihood function for the first 1i step: log L 1 = { [ ( I 1 R T log R i=1 r=1 t=1 ( J mt j=1 )( ) )]} d D ijmt ijmtr f F ijmt ijmtr (1 f ijmtr) (1 F ijmt), 16

17 where we simulate the integrals in both probabilities using R simulation draws from a Halton sequence. In the second step of the estimation we recover the parameters of the learning process and of the cost function. First, we assume that marginal costs are linear in E(q i I ijmt ), C ijmt, such that: E(MC ijmt I ijmt ) = µ ijmt + γc ijmt + ω ijmt, where ω ijmt N(0, 1). Using the first order condition outlined above, we can re-express marginal costs as equal to prices minus the estimated markups: P ijmt + d ijmt d ijmt = µ ijmt + γc ijmt + ω ijmt, where P ijmt is data and d ijmt is estimated in the demand model. The experience signals that d ijmt determine µ ijmt are unobserved to the econometrician, therefore we follow Ackerberg (2003) and simulate them as: s k ijmtr = µ 0 + σ 0 ρν 1i + σ0 2(1 ρ2 )ν 2ir + τ k ν3ijmtr k where ν 2i N(0, 1) and ν3ijmt k N(0, 1), r is the simulation draw, k = {I, O}, and ρ was estimated in the first stage. Hence, the probability of having a marginal cost E(MC ijmt I ijmt ) will be: ( p ijmtr = φ P ijmt + d ijmt µ ijmtr γc ijmt ), d ijmt where φ is a standard normal pdf. In the second step we estimate the parameters of the learning process and of the cost function Θ 2 = {γ, µ 0, σ0 2, τ I 2, τ O 2 } using the following simulated maximum likelihood: log L 2 = { [ ( I J mt 1 R T log R i=1 j=1 r=1 t=1 ( p ijmtr ) )]}. 7 Monte Carlo Results Before estimating the structural model on the dataset, we do a comparative statics exercise simulating data from our structural model, and then comparing the same reduced form results between actual and simulated data, varying some key parameters of the learning process in the simulation. We run a Monte Carlo exercise simulating data using the structural model outlined above for 1,000 firms across 10 years, facing 2 to 4 banks. Similarly to the reduced form evidence presented earlier, we investigate how interest rates vary over the course of a firm-bank relationship, and how their dispersion evolves. We are particularly interested in how this variation in interest rates depends on 17

18 some key parameters of the banks learning process, that is the degree of banks initial uncertainty σ0 2, measured as the variance of the prior distribution of borrowers creditworthiness, and on the informational advantage of inside lenders τo 2 τ I 2, measured as the difference between the variances of the outside and inside banks signals. We also check how the variation in interest rates changes depending on the number of banks, to capture the effect of an increase in competition. We do this regressing equilibrium interest rates on firm-bank fixed effects and year of relationship dummies, and find that for some values of the key parameters of interest interest rates tend to significantly increase over the course of the relationship, which might be evidence of learning and hold-up due to the informational advantage of the inside banks. These results are presented in Table 6. We also look in Figure 3 at how the price dispersion varies over the relationship, and find that the standard deviation of prices is increasing over time, which might be evidence of learning, as inside banks are able to separate good and bad borrowers. We then check the sensitivity of these results to the key parameters of interest and the number of banks. We find that the interest rates increase over the course of the relationship is stronger the higher is the initial uncertainty (σ0 2 ), and the larger is the informational advantage of inside banks (τo 2 τ I 2 ). As expected, average interest rates decrease as the number of banks increases, but they are still significantly increasing over the course of the relationship, even though not as much as with 2 banks. This might suggest that the informational lock-in is weaker as competition increases. 18

19 Table 6: Monte Carlo Pricing OLS regressions Variables (1) (2) (3) (4) (5) (6) Constant (0.024) (0.024) (0.029) (0.037) (0.037) (0.025) 2 nd Year (0.034) (0.034) (0.041) (0.053) (0.052) (0.035) 3 rd Year (0.034) (0.034) (0.041) (0.053) (0.052) (0.035) 4 th Year (0.034) (0.034) (0.041) (0.053) (0.052) (0.035) 5 th Year (0.034) (0.034) (0.041) (0.053) (0.052) (0.035) 6 th Year (0.034) (0.034) (0.041) (0.053) (0.052) (0.035) 7 th Year (0.034) (0.034) (0.041) (0.053) (0.052) (0.035) 8 th Year (0.034) (0.034) (0.041) (0.053) (0.052) (0.035) 9 th Year (0.034) (0.034) (0.041) (0.053) (0.052) (0.035) 10 th Year (0.034) (0.034) (0.041) (0.053) (0.052) (0.035) Firm-Bank FE Yes Yes Yes Yes Yes Yes σ τi τo N of Banks N of Firms 1,000 1,000 1,000 1,000 1,000 1,000 Adjusted R N obs. 20,000 20,000 20,000 20,000 20,000 20,000 Note: An observation is a firm-bank-year. We set the other parameters as: µ 0 = 2, α 1 = 2, α 2 = 5, β = 0.5, γ = 0. 19

20 Figure 3: Standard Deviation of Monte Carlo Prices Standard Deviation Prices Years of Relationship Note: Standard deviation by year of relationship of the prices for the results in column 5 of Table 4. 20

21 8 Conclusion In this paper we developed a structural model of relationship lending for the Italian market of small business lines of credit. The purpose of this model is to determine the value of information that lenders generate in a firm-bank relationship, quantifying the degree of uncertainty that banks have at the beginning of a relationship, as well as the speed and accuracy of their learning process about borrowers creditworthiness. We reviewed the modeling assumptions and testable implications of the theoretical framework developed by Sharpe (1990) and von Thadden (2004), and based on these we provided reduced form evidence consistent with lenders learning, finding that interest rates increase over the course of a firm-bank relationship, mostly for risky borrowers, and become more dispersed. Based on the theoretical features for the model by Sharpe (1990) and von Thadden (2004), and on the reduced form findings, we developed a structural bayesian learning model of lenders in line with the literature on consumer learning (Erdem & Keane (1996), Ackerberg (2003), and Crawford & Shum (2005)) and firm learning (Hitsch (2006)). We simulate data using this structural model and investigate whether for some key parameter values we can reproduce the reduced form evidence. We find that the interest rates increase over the course of the relationship is stronger the higher is the initial uncertainty, and the larger is the informational advantage of inside banks. We also find that average interest rates decrease as the number of banks increases, but they are still significantly increasing over the course of the relationship. This might suggest that the informational lock-in is weaker as competition increases. Our results have important policy implications. In the recent years banking regulation has moved towards an increase in both information sharing between banks, to reduce agency costs, and higher level of competition, to reduce interest rates and improve access to credit. It is however important to reconsider the effects of these two policies in the presence of banks learning. If on one hand information sharing might reduce information asymmetries between borrowers and lenders, on the other hand it also affects banks incentive to learn, as it reduces the rents they can gain from an informational advantage. Making the banking sector more competitive also requires a greater understanding of the extent of banks learning, because banks informational advantage obtained through learning can serve as an entry barrier for new uninformed lenders, eventually leading to more concentration. 21