Estimating the relationship between collateral and interest rate: A comparison of methods

This paper uses a variety of estimation methods to explore the empirical relationship between interest rate and collateral requirements in bank loan contracts. Methods that do not allow for endogenous contract terms detect a positive reciprocal association between interest rate and collateral. Methods that allow for endogenous contract terms point to a strong positive effect of interest rate on collateral but the effect of collateral on interest rate is weaker. This highlights the importance of incorporating the endogenous nature of contract terms in empirical work.


Introduction
Extant theoretical work in the area of loan contracting usually models interest rate and collateral as interrelated components of the same contract.Despite theoretical postulates, early empirical research on the relationship between collateral requirements and interest rate estimates single-equation models that either treat one of the contract terms (usually collateral) as exogenous or predetermined, or impose implicit constraints on the estimated models (e.g., Berger and Udell, 1990;Degryse and Van Cayseele, 2000;Harhoff and Körting, 1998).Building upon this reduced-form method, some studies approach the analysis by endogenizing the probability of collateral being pledged and including it as an explanatory variable in models of interest rate (e.g., Dennis et al., 2000;Bharath et al., 2011;Calcagnini et al., 2014), or by testing for exogeneity of the interest rate (e.g., Ono and Uesugi, 2009).
In this paper, we adopt a comprehensive approach and explore several methods for estimation of the empirical relationship between interest rate and collateral in bank loan contracts.Ultimately, we specify a system of equations without imposing any directional constraints on the relationship between the contract terms.Our approach is similar to the one followed by Brick and Palia (2007) but we improve the analysis along two key dimensions.First, our analysis, conducted at the loan contract level, is based on a proprietary dataset of credit lines extended to a large number of small and medium-sized enterprises (SMEs) that includes specific information on interest rate and collateral requirements.This overcomes limitations stemming from the use of survey data with self-reported information and allows us to unambiguously match collateral and interest rate within specific credit lines.Second, we consider the amount We are grateful for comments and suggestions from Samuel Vigne (the Editor) and from an anonymous referee.Disclaimer: The opinions expressed are those of the author(s) only and should not be considered as representative of the European Commission's official position.
Contents lists available at ScienceDirect of collateral pledged by a borrowerdegree of collateralization or collateral intensityand its joint determination with interest rate, which is in line with theory that also models degree or magnitude of collateral use.

Empirical models and data
We estimate several alternative econometric models of the following general set of equations: (1) where i denotes borrower and t time period.Each contract term depends on the other term, as well as a vector of control variables, W for interest rate and Z for collateral.Coefficients with a subscript R (C) refer to the interest rate (collateral) equation, respectively.We begin our analysis by using ordinary least squares (OLS) regressions.Then, we estimate a model of seemingly unrelated regressions (SUR) to allow the errors to be cross-correlated across equations.We next proceed by allowing for endogenous loan contract terms.We first implement equation-by-equation instrumental variable (IV) analysis by estimating 2-stage least squares (2-SLS) models.Last, we model the simultaneity present in the determination of the contract terms by jointly estimating the system of equations ( 1) and (2) using 3-SLS method (Zellner and Theil, 1962).

Data and outcome variables
We estimate the models of collateral and interest rate using a dataset of a large number of credit lines extended to Italian SMEs by a major Italian bank.Our dataset contains an extensive cross-section of borrowers and provides a wide array of borrower characteristics and information on contract terms.In terms of the time dimension, we observe the credit lines at two points in time as of September 2004 and September 2006.Thus, we effectively have a very short, unbalanced panel because a number of borrowers appear only in the 2006 extract of the data as they start doing business with the bank post-September 2004. 1e focus on two outcome variables.Rate is the annualized interest rate charged by the bank and measured in percentage terms.Collateral is the amount of collateral pledged by the borrower, expressed as a percentage of the limit on the credit line. 2 Table 1 reports summary statistics for the variables and Appendix A provides descriptions and construction.

Determinants of contract terms
We control for firm size using indicator variables D(Sales i) for each of the seven classes in which the bank classifies its borrowers on the basis of their annual sales (where i = 1…7, from smaller to larger classes). 3Our regressions also include three characteristics of the lending relationship.Relationship Length reflects the time since the firm has first borrowed from the bank.Multiple Lending takes value of 1 if a firm borrows from multiple banks and 0 if it has exclusive relationship with the bank.Other Services takes value of 1 if a borrower uses additional services by the bank and 0 otherwise.We also control for borrower risk by using the internal credit rating assigned by the bank, which categorizes borrowers into 9 classes in order of increasing risk.We use a separate indicator D(Rating i) for each rating class i.As we do not have a rating for all borrowers, we adopt a modified zero order regression approach following Hollander and Verriest (2016).To this end, we re-code the rating as 0 for borrowers without a rating, create an indictor D(Rated) that takes value of 1 for rated borrowers, and interact it with D(Rating i).Last, Portfolio is an indicator that takes value of 1 if the bank considers a credit line as part of its corporate market and 0 if it is part of its small business market.All estimations include industry, branch, and year fixed effects.

Instruments
To instrument the interest rate (Rate), and identify the interest rate equation (1) in the system, we rely on the contractual nature of the credit lines, as well as the industrial organization of the local credit markets where the bank operates. 4Our first instrument is Overdraw, a variable that takes value of 0 if a borrower uses funds not exceeding the contractual limit of the credit line, and the logarithm of the actual amount of excess funds if the borrower exceeds the limit and overdraws.This is based on a contract clause that borrowers pay a fixed interest rate if they use funds within a pre-specified limit, but pay a penalty fee, increasing in the amount of withdrawn excess funds, if they exceed the limit.Hence, the interest rate depends on whether a borrower exceeds the credit limit and by how much.By contrast, the contract does not condition the collateral requirements on overdrawn funds.Our second instrument for interest rate is Branch HHI constructed as the branch-based Herfindahl-Hirschman Index (HHI) to capture market competition in the local credit market.In concentrated markets, banks can use explicit loan rates as a strategic tool to establish long-term relationships and secure rents on future business (e.g., Petersen and Rajan, 1995;Brick and Palia, 2007;Bellucci et al., 2013).
To instrument the collateral requirements (Collateral), and identify the collateral equation (2), we develop three instruments.The first, Real Estate Prices, is equal to the logarithm of the average price per square meter for industrial and commercial real estate during the period 2003-2004 in the local credit market of the borrower.The underlying rationale is that fluctuations in the values affect the liquidation values of properties in the market and can thus change the incentives of the bank to secure the loans granted to borrowers in this market.
Our second instrument for collateral is Bankruptcy Costs, measured as the average cost of bankruptcy procedures as of 2003 and 2005 for the judicial district of each borrower.The rationale is that collateral becomes relevant if a borrower cannot meet repayment obligations, but the actual realization of bankruptcy and seizure of collateral by the bank, vis-à-vis other outcomes such as out-of-court renegotiation, depends on the cost of the procedures: Higher bankruptcy costs could lead to higher probability of renegotiation and lower collateral relevance (Degryse et al., 2020).
The third instrument Individual Firm is an indicator that takes value of 1 if a borrower has sole proprietorship as organizational form and 0 otherwise.Sole proprietorships are not covered by limited liability and this could affect the asset base recoverable by banks in a bankruptcy, and thus the importance of collateral requirements.In addition, sole proprietorships are informationally less transparent and are expected to face differential collateral requirements (Berger and Udell, 1998).

Empirical results
We begin by estimating OLS models that do not allow for endogenous contract terms.In columns (1) and (3) of Table 2 we present baseline specifications that do not include control variables, while in columns (2) and (4) we augment the models by including an array of borrower-specific controls.The results show that the contract terms exhibit positive empirical association.The point estimate of the coefficient on Collateral (Rate) is positive and statistically significant at the 1% level in columns (1) and (3) (columns (2) and ( 4)) of the table.To provide some insights into the economic significance, we focus on the comprehensive models in the even-numbered columns.We estimate that an increase in Collateral of a standard deviation is associated with an increase in the interest rate of about 9 basis points (bps).Compared to unsecured loans, a fully collateralized loan has 27 bps higher interest rate.Similarly, an increase in Rate of a standard deviation is associated with an increase in degree of collateralization of about 1%.This represents a meaningful economic Notes: The sample size is 14,672.Appendix A provides a detailed description of each variable.
A. Bellucci et al. effect given that the mean value of Collateral is 19%. 5able 3 shows the SUR estimates.In columns ( 1) and ( 2) we use as explanatory variables the variables that are in the set of common controls as well as the contract terms.We augment the models by adding the instruments for each contract term in columns ( 3) and (4).Our insights about the positive empirical relationship between interest rate and collateral continue to hold.
We next focus on estimation procedures that account for the endogeneity of interest rate and collateral.We first adopt equation-byequation IV models based on 2-stage estimation process, where we predict each endogenous variable in the first stage using the relevant instruments and all other explanatory variables, and then use the predicted value as explanatory variable in the second stage, along with the controls.Columns (1) and (2) of Table 4 show the results of the first stages for the estimation of the endogenous Collateral and Rate, respectively.Columns (3) and (4) show the second stages of the estimation.The instruments are significant determinants of the contract terms.In column (1), we note that if real estate prices increase, degree of collateralization increases.If bankruptcy costs increase, making formal court procedures more expensive, and less likely, collateralization decreases.Last, the coefficient on Individual Firm is positive and statistically significant.This is consistent with the idea that individual firms, which are considered as less transparent, are more likely to be asked for collateral.In column (2), we observe that the amount of overdrawing by a borrower increases interest rates.The effect of Branch HHI is not statistically significant.
Both first stages produce sufficiently high significance at the 1% level) F-statistics of 29.43 for Collateral and 36.93 for Rate, respectively, thus reducing concerns about weak instruments.In the last row of the table, we report the results of a Sargan test for overidentifying restrictions.The p-values of the test show we cannot reject the null hypothesis that the instruments are uncorrelated with the error terms and correctly excluded.
The IV analysis of Rate in column (3) reveals that after endogenizing the loan contract terms, the effect of collateral on interest rate is weaker and not robust as indicated by the coefficient on the predicted value of collateral, Collateral (predicted), which is positive but not significant.By contrast, interest rate continues to have a robust effect on collateral as indicated by the positive and significant coefficient on the predicted value of interest rate, Rate (predicted) in column (4).
Last, we approach equations (1) and (2) as a system of simultaneous equations using 3-SLS estimation method.For identification purposes we rely on the instruments used in IV analysis.The results of our analysis, presented in columns ( 5) and (6) of Table 4, are consistent with our insights generated through the IV analysis that interest rate is a robust determinant of collateral, while the reverse does not hold.
Hence, we conclude that loan contract features such as interest rate and collateral requirements exhibit a largely positive empirical association even after we allow for endogenous contract terms.However, the link between the two contract terms is unidirectional: Firms that pay higher interest rates also pledge more collateral, but pledging more collateral is not associated with higher rates.This underscores the importance of using methods that endogenize contract terms, as predicted by theory, and suggests that the use of collateral might be driven by a variety of mechanisms related to its role as an enforcing, incentivizing, or screening device.

Conclusion
We use a variety of methods to explore the empirical relationship between collateral requirements and interest rates in bank loan contracts.Consistent with extant research, our estimations generally document a positive link between these two contract terms but the magnitude of the link depends on estimation method.In conclusion, our analysis highlights the importance of incorporating the endogenous nature of contract terms in empirical work.

Declaration of Competing Interest
None.

Supplementary materials
Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.frl.2021.101962.Notes: The table reports coefficient estimates with robust standard errors in parentheses of IV analysis of equations ( 1) and (2) using 2-SLS (columns 1 to 4) and 3-SLS (columns 5 and 6).Appendix A provides a detailed description of each variable.***, **, and * indicate statistical significance at the 1%, 5%, and 10% levels, respectively.

Table 1
Summary statistics.

Table 2
OLS estimation.The table reports coefficient estimates with robust standard errors in parentheses, of OLS analysis of equations (1) and (2).Appendix A provides a detailed description of each variable.***, **, and * indicate statistical significance at the 1%, 5%, and 10% levels, respectively.

Table 3
SUR estimation.The table reports coefficient estimates with standard errors in parentheses of SUR analysis of equations (1) and (2).Appendix A provides a detailed description of each variable.***, **, and * indicate statistical significance at the 1%, 5%, and 10% levels, respectively.