# Borrower-lender distance and its impact on small business lenders during the financial crisis

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3 In this study, we focus on the relationship between borrower-lender distance, a bank s net interest income, loan size, bank size and the bank s ability to assess credit loss. We hypothesize that borrower-lender distance impacts the banks interest income. Concurrently, bank size and a bank s ability to assess credit loss determines the proximity of the lending relationship. As such, a simultaneous structural relationship is observed where net interest income and borrowerlender distance are endogenous. We analyze this relationship for the time period from 2006 to Methodology We propose a model that relates a bank s net interest income (lnii) to borrower-lender distance and gross loan approval amount (l and lappvgross). Simultaneously, borrower-lender distance depends on bank size as measured by total assets (lta) and provision for credit loss (lpcl). We use a natural log transformation of the variables in the regression analysis. The model is expressed as: lnii = l+ lappvgross l lta lpcl it 0it 1it 2it 1it it 3it 4it 5it 2it, (1). We will take equation (1) to be the full system. In this case, lnii and l are endogenous variables while lappvgross, lta and lpcl are exogenous instrumental variables. In this system, there are 6 structural parameters and 8 reduced form parameters. Hence, it is an over-identified system. For an over-identified system, Zellner and Theil (1962) recommend that a three stage least squares method of estimation (3SLS) of the parameters be used to analyze a simultaneous equation system to ensure that the estimation of the coefficients of the over-identified system is efficient. According to Greene (2003), a simultaneous system of equations can be formulated as follows: y1 Z y 2 0 Z (2) : : : : : : : ym ZMM M, where Z is a matrix of all instrumental variables used. The 3 stage least square estimator is given as: 1 ^ ^ ^ ^ SLS Z '( I) Z Z'( I) y, (3) where is the asymptotic variance-covariance matrix. The estimation is performed for each of the years from 2006 to Results Table 3 (See Appendix D) provides the results for the three stage least squares estimation. As both dependent and independent variables are in natural log form, the coefficients are interpreted as elasticity coefficients. We find that a 1% increase in borrower-lender distance results in 3.14% increase in net interest income in In 2007, this increase in net interest income drops to 2.5%. In 2008, the increase drops further to 2.162% during the height of the crisis. In 2009, we find that the impact of borrower-lender distance on net interest income regains strength and a 1% increase in distance raises net interest income by 2.643%. We find that net interest income increases as distance increases for the entire period. This implies the greater the borrowerlender distance, the more lucrative the loans. Two potential reasons for this are: when borrowers are further away, banks are unable to obtain soft information. It is likely that banks assess borrower creditworthiness by using more stringent procedures such as credit-scoring. Hence, the credit quality is likely to be better when the borrower is located further away. Alternatively, borrowers further away maybe charged higher interests due to lack of soft information and hence, increasing a bank s net interest income. We find that the parameter estimate on gross loan approval amount was not statistically significant for all the four years. This implies that the loan amount itself did not explain any changes in net interest income between 2006 and This could be due to the fact that informational opacity related to soft-information remains the same regardless of the amount borrowed. Hence, banks are likely to price the distance-related risk as opposed to loan-amount related risk. We also study how bank size impacts borrower-lender distance. As bank size increases, lenders are more likely to lend further away. In 2006, a 1% increase in bank size resulted in a 0.285% increase in borrowerlender distance. However, in 2007 and 2008, this number declined to 0.208% and 0.236%, respectively. In 2009 as banks received infusions of capital, the number rose to 0.371%. One possible explanation for this is: bigger banks have more resources to evaluate the creditworthiness of the borrowers. Smaller community and regional banks have less resources to devote to credit-scoring models to evaluate their lenders. Finally, we examine if provision for credit loss impacts the lending distance. We find that when banks expect a higher level of credit loss the following year, they were more likely to lend further away. This is related to the results found in Figure 4 (See Appendix E). The loans that were further away bring in more interest income. This suggests that a level of geographic diversification is taking place. From 2006 to 2008, the borrower lender distance increased as the provision for credit loss increased. We see that a 1% increase in 63

5 Table 1(cont.). Small business loans 7(a) loan program, : descriptive statistics Year Variable Mean St. Dev. Min Max (in 10,000's) 920,719 1,106, ,080,300 Approval gross 135, , ,450, (miles) ,726 Total assets (in 10,000's) 33,317,778 42,234, ,283,252 Provisional credit loss (in 10,000's) 1,898 28, ,068,600 Number of observations 80,342 (in 10,000's) 670,275 1,115, ,623,500 Approval gross 188, , ,000, (miles) ,230 Total assets (in 10,000's) 24,257,487 41,768,443 1, ,501,299 Provisional credit loss (in 10,000's) 6,901 84, ,083,200 Number of observations 45,002 (in 10,000's) 288, , ,013,400 Approval gross 217, ,580 1,000 2,050, (until October) (miles) ,845 Total assets (in 10,000's) 10,886,024 26,071, ,359,720 Provisional credit loss (in 10,000's) 5,601 79, ,353,859 Number of observations 26,311 Appendix B. (a) (in 10,000s) (b) Gross approved loan amount (1000s) (c) Borrower lender distance (in miles) (d) Total assets of lending bank (in 10,000s) (e) Provision for credit losses (in 10,000s) Fig. 1. Plot of variables based on descriptive statistics

6 Appendix C. (Percentage points) Note: Interest rate spreads over the prime rate for all commercial and industrial loans are for loans made by commercial banks in amounts between \$100,000 and \$999,999. *Source: Congressional Budget Office Report (2007) based on data from the Small Business Administration and the Board of Governors of the Federal Reserve System. This figure was also cited in Andrade and Lucas (2009). Appendix D. Fig. 2. Interest rate spreads over the prime rate for SBA 7(a) loans and for all commercial and industrial loans, by Cohort * Table 3. Results of 3 stage least for Independent variables (natural log) lappvgross l lta lpcl Dependent variables (natural log) 2006 lnii ** l 0.285** ** 2007 lnii ** l 0.208** 0.155** 2008 lnii ** l 0.236** 0.173** 2009 lnii ** l 0.371** Legend: Gross approval amount lappvgross Borrower-lender distance l Total assets lta Provision of credit losses lpcl Note: ** Indicates parameters are statistically significant at the 5% level of a 2-tailed test. 66

7 Appendix E. % Change net interest income in response to a 1% increase in distance % Change net interest income to a 1% increase in distance Fig. 4. Plot of elasticity parameter estimates showing the percentage in net interest income due to a 1% increase in distance. % Change in distance in response to a 1% increase in bank size % Change in distance to a 1% increase in bank size Fig. 5. Plot of elasticity parameter estimates showing the percentage in lending distance due to a 1% increase in bank size. % Change in distance in response to a 1% increase in loan loss provision % Change in distance to a 1% increase in loan loss provision Fig. 6. Plot of elasticity parameter estimates showing the percentage in lending distance due to a 1% increase in loan loss provision. 67

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