Tables 2 through 4 show the regression results. In Table 2 Panel A, we show four columns based on the specification in equation (1) – one with firm size dummies only, one with technology dummies only, one with both sets of dummies, and one complete specification with all the dummies and the interaction terms. Tables 3 and 4 Panels A also show four columns, but replace lending technologies with relationship strength, as specified in equation (2). All estimations include the control variables for banking market characteristics and firm industry.
The control variable for firm profitability is included as an additional firm characteristic in all estimations that include the firm size dummies. For the complete specifications in column (4), we also show the predicted probabilities for each firm size when combined with either a lending technology or relationship-strength indicator, as explained below.
Instead of presenting the logit coefficients, we report odds ratios which are obtained by exponentiating the original coefficients. When a variable has an odds ratio that is greater than (is
less than) 1, a higher level of the variable is associated with higher (lower) odds of the loan being from a large bank. We also report the absolute value of robust z-statistics based on the Huber-White sandwich method to correct for heteroskedasticity.
We first turn to Table 2 Panel A, which shows the results of testing the five fixed-asset technologies. We exclude the small-firm dummy and the LEASE dummy as the base case and conduct most of our tests on the comparative advantage differences of large and small banks for the four collateral-based fixed-asset technologies versus leasing. As discussed above, we hypothesize that large banks have the strongest comparative advantage for LEASE because of the almost “perfect” collateral lien against the leased assets. This characteristic of leasing makes it the purest hard information technology with the least requirement for secondary sources of soft information for which small banks may have the advantage.
Column (1) of Table 2 Panel A shows the logit regression with firm size and control variables only. This version of the model is the most similar to prior empirical research, which focuses on the effects of firm size without identifying or separating out the effects of the different technologies. One key difference here is that we include three firm size classes and allow for a nonmonotonic relationship between firm size and bank size, rather than using a continuous measure of firm size that forces a monotonic relationship. Our goal is to allow for the possibility that large banks may tailor specific fixed-asset technologies to reach different firm sizes.
Under the current paradigm employed in much of the small business finance literature, the odds ratios on the firm size class dummies are expected to be greater than 1 and increasing.
Larger firms tend to be more informationally transparent, and therefore better served by large
banks with comparative advantages in hard technologies.15 When some of the most restrictive assumptions of the paradigm are relaxed, the comparative advantages of large banks in hard technologies may differ across firm sizes in various ways. The relationship between firm size and bank size may be increasing, decreasing, or nonmonotonic, depending on the sizes of firms for which large banks may best use their advantages in the different technologies.
The results in column (1) show a nonmonotonic effect of firm size on the probability of borrowing from a large bank, conditional on the control variables. The odds ratio on the medium firm dummy is significantly less than 1 and the odds ratio on the large firm dummy is statistically insignificant, which suggests that, all else held equal, small firms and large firms are more likely to borrow from large banks and medium firms are more likely to borrow from small banks.16 These findings are not consistent with the current paradigm, which predicts that the comparative advantage of large banks in hard technologies should be increasing in the size of the firm. Importantly, our findings suggest that large banks may use different lending technologies to serve the different firm sizes, which are not broken out in column (1). To evaluate the economic significance of these results, we note that the odds ratio for medium firm is 0.691.
This suggests that the odds of a medium firm borrowing from a large bank are about 69% as high as for a small firm.
Column (2) shows the regression with the dummies for fixed-asset technologies and control variables only. Under the current paradigm, large banks are predicted to have the same comparative advantage in all fixed-asset technologies, yielding an odds ratio of 1 on the lending technology variables. In contrast, we predict an odds ratio less than 1 on the included fixed-asset
15 This monotonically increasing effect may also be accentuated by legal lending limits or problems of diversification of small banks in lending to large firms, giving an additional advantage to large banks in lending to larger firms that is unrelated to the lending technologies.
16 When the firm size dummies are replaced with loan size dummies, we find similar results. Therefore, the nonmonotonicity results for firm size may be partly due to the effects of loan size.
technologies, based on our hypothesis that large banks have the strongest comparative advantage in the hardest technology, which is the excluded category of leasing. The statistically significant odds ratios of less than 1 are consistent with our prediction; therefore, column (2) confirms expectations of a comparative advantage for large banks in leasing relative to all of the other fixed-asset technologies. Given that the size classes are excluded from this specification, the results reflect an average effect of technology type across the firm size classes.
Column (3) shows the regression with both firm size and lending technologies, but without the interactions. The hypotheses are essentially the same and the odds ratios are similar to columns (1) and (2). The slight difference is that the medium firm odds ratio is no longer significant at the 10 percent level.
Column (4) shows the complete specification with firm size, lending technologies, and the interactions. Under the current paradigm, large banks are predicted to have the same comparative advantages in all fixed-asset technologies and these advantages should apply with monotonically increasing magnitude as firm size increases. In column (4), we relax some of the assumptions of the paradigm and allow the magnitude of the large banks’ comparative advantages in each fixed-asset technology to vary in any pattern with firm size.
The results in column (4) suggest that the comparative advantage of large banks in leasing relative to the other fixed-asset technologies is greater for larger firms. The odds ratios on the technologies with small-firm interactions are all statistically insignificant, consistent with no significant comparative advantage differences for large banks between leasing and the other fixed-asset technologies for small firms. The interactions with the medium- and large-firm dummies have odds ratios that are smaller in all cases and statistically significant in all cases except one, suggesting stronger comparative advantages in leasing for these firm sizes. That is,
the effect of non-leasing fixed-asset technologies is found to be strongest for medium and large firms as loans made to medium and large firms using a non-leasing fixed-asset technology are much less likely to be from large banks than leases.
These results clarify the findings in column (2) by showing that the difference between leasing and the other fixed-asset technologies is unique to medium and large firms. The implication is that the soft-information component in the other fixed-asset technologies is important for larger firms, but not for small firms. As noted above, the advantages in a given technology may differ by firm size because the relative importance of the hard and soft information components may differ by the size of the borrowing firm. The results in column (4) suggest that the benefit of assessing the soft-information component related to information other than the appraised value of the fixed asset may only be cost effective for larger firms.
Finally, we turn to the control variables in Panel A of Table 2 for firm profitability and banking market conditions. The odds ratio on ROE is always significantly greater than 1, consistent with the expectation that hard information about high ROE increases the probability of a firm borrowing from a large bank. The odds ratio on large-bank branch market share is greater than 1 and statistically significant, consistent with the convenience argument. Firms are more likely to borrow from a large bank if the branch offices of large banks are more convenient than those of small banks, and large-bank branch market share is a proxy for this relative convenience. The odds ratios on the Herfindahl index and MSA dummy are not significant, indicating that the competitive environment does not appear to be an important factor in determining the use of large versus small banks for fixed-asset lending.
Panel B of Table 2 converts the effects from the nonlinear logit model into predicted probabilities. That is, we illustrate the effects of firm size and technology on the probability that
a firm’s loan will be from a large bank using predicted values from the complete specification in column (4) of Panel A, where we assign the control variables to their means in all cases. The top four rows of Panel B show that for small firms, none of the predicted probabilities of the loan being made by a large bank change in a statistically significant fashion as the lending shifts from LEASE to another fixed-asset technology. The second set of rows shows that for medium firms, the predicted probability of a large bank decreases in a statistically and economically significant manner when technology shifts from LEASE to any of the other fixed-asset technologies except residential real estate. For example, the predicted probability of a loan being made by a large bank decreases from 80.4% to 36.6% – a statistically significant decline of 43.8% – as the lending shifts from leasing to commercial real-estate lending. For large firms, the findings are similar to those for medium firms. Thus, the use of other fixed-asset technologies decreases the probability of loan being from a large bank for both medium and large firms.
Next, we turn to Panel A of Table 3, which has the results of testing for the effect of strong relationships among non-fixed-asset lines of credit. As in Table 2, the results in column (1) show a nonmonotonic effect of firm size on the probability of borrowing from a large bank, conditional on the control variables. This similarity in results between columns (1) in Tables 2 and 3 is interesting, because it is the same empirical specification applied to two totally separate samples. This suggests that our finding – a nonmonotonic comparative advantage of large banks in lending to different sized firms – is identical across both fixed-asset loans and lines of credit excluding fixed asset collateral. In both samples, there is little difference in large banks’
comparative advantage in lending to small and large firms, but medium firms are less likely to borrow from large banks.
Columns (2) and (3) include the role of relationship strength in determining the
likelihood of a firm borrowing from a large bank. As in Table 2, column (2) excludes firm size whereas column (3) includes it. Under the current paradigm, small banks are predicted to have a comparative advantage in relationship lending. Although we cannot identify relationship lending directly, we use the strength of the bank-firm relationship as a proxy for the likelihood that the loan was underwritten using information from the relationship. The prediction of the current paradigm implies an odds ratio less than 1 on the relationship strength variable. Here, in Table 3, we measure relationship strength by “Strong Relationship,” which is a dummy variable based on relationship length, breadth, and exclusivity. In both columns, the odds ratio on strong relationship is less than 1 and significant at the 1% level, suggesting a comparative advantage for small banks in relationship lending. Therefore, the results of these two columns are consistent with the current paradigm. In terms of economic significance, the odds ratio for strong relationship is 0.570, which suggests that the odds of a firm with a strong relationship borrowing from a large bank are 57% as high as for a firm without a strong relationship.
Column (4) shows the complete specification with firm size, relationship strength, and the interactions. Under the current paradigm, the comparative advantage of small banks in relationship lending should be greatest for lending to the smallest firms. However, in the complete specification results, the interaction of strong relationship with small firm size is insignificant. This result does not support the prediction of the current paradigm, because it does not appear that small banks have a comparative advantage in using relationship lending to lend to the smallest firms. The interactions of strong relationship with medium and large firm size have an odds ratio of less than 1 and are statistically significant at the 5% level. These results indicate that small banks have a comparative advantage in relationship lending primarily when it is applied to medium and large firms. This suggests that the collection of soft information through
relationships has less value for the smallest firms, which might appear to be a counterintuitive result. However, it appears to be consistent with our findings in column (1) that small banks are more likely to lend to medium firms than to small firms. It is also consistent with our results in Table 2 which suggest that the collection of soft information has greater value for larger firms.
The control variables in Panel A of Table 3 show that firm profitability is not a relevant factor in the likelihood of a line of credit without fixed-asset collateral being issued by a large bank, but that the banking market conditions are relevant. Unlike in the fixed-asset regressions, the odds ratios on ROE are not significant, perhaps because hard information like ROE is less important than other types of soft information for non-fixed-asset lines of credit. The odds ratio on large-bank branch market share is significantly greater than 1, again supporting the convenience argument. The odds ratios on the Herfindahl index and MSA dummies are greater than 1 and statistically significant in the non-fixed-asset line of credit sample, whereas they were not significant in the fixed-asset loan sample. This suggests that the competitiveness of the local banking market may be more important for determining the comparative advantage of banks of different sizes when lending is based on soft-information. The odds ratio greater than 1 on the Herfindahl index, the measure of local market banking concentration, suggests that firms in more concentrated bank markets are more likely to have their non-fixed-asset line of credit at a large bank. The odds ratio greater than 1 on the MSA dummy suggests that firms in metropolitan markets are also more likely to have their non-fixed-asset line of credit at a large bank.
Panel B of Table 3 shows the predicted probabilities of borrowing from a large bank for the three firm size classes and the statistical significance of these differences. For medium and large firms, the predicted probability of borrowing from a large bank is 13.1 and 11.3 percentage points lower, respectively, with a strong relationship. The effect on medium firms’ predicted
probability of borrowing from a large bank is almost double the effect for small firms. Thus, the presence of a strong relationship appears to have an economically significant role in increasing the likelihood of a medium firm having their non-fixed-asset line of credit at a small bank.
Table 4 Panel A also shows the results for the sample of lines of credit without fixed-asset collateral, but here we use the separate components of strong relationship to measure relationship strength. The purpose of Table 4 is to see which elements of a strong relationship – length, breadth, or exclusivity – are most important to the comparative advantage of small banks in relationship lending. Column (1) is identical to column (1) of Table 3 Panel A, because it is the same sample and we only include firm size. Column (2) only includes the individual components of relationship strength and column (3) includes these components along with firm size. As discussed for Table 3, the current paradigm predicts that small banks have a comparative advantage in relationship lending, which implies that the odds ratios on the relationship characteristics in column (2) should be less than 1. The results show that the institution which issued the non-fixed-asset line of credit is more likely to be a small bank when the firm has a longer relationship and a checking account with the institution. This adds support to the prediction of the current paradigm that small banks have a greater comparative advantage in relationship lending relative to the other types of lending in the sample. However, there does not appear to be a significant effect of exclusivity on this comparative advantage.
Column (4) includes the interactions between firm size and the components of relationship strength. The current paradigm predicts that the comparative advantage of small banks in relationship lending should be the greatest for small firms. However, our results for relationship length do not confirm this prediction. The odds ratio on log of relationship length is significantly less than 1 only when interacted with the large firm dummy. As in our previous
results in Table 3, our results suggest that the advantage of small banks in relationship lending is primarily among larger firms. Only checking accounts appear to contribute significantly to a comparative advantage of small banks in relationship lending to small firms. The exclusive lender results appear to go the opposite direction as predicted. Large banks have a comparative advantage in lending to large firms when they are the exclusive lender. When looking across the three components of strong relationship, it appears that the comparative advantage of small banks in using strong relationships to lend to large firms is driven primarily by the length of the relationship. This confirms our prior finding that the comparative advantage of small banks in relationship lending is greater for large firms and also shows that the result is primarily driven by length of relationship.
Table 4 Panel B shows the effects of the strong relationship components on the predicted probability of borrowing from a large bank. For large firms, a one standard deviation increase in the log of relationship length leads to a reduction in the probability of borrowing from a large bank of 7.3 percentage points. In contrast, large firms with an exclusive lender are 11.6 percentage points more likely to borrow from a large bank than large firms without an exclusive lender. Among small firms, those firms with a checking account at their lender are 14 percentage points less likely to borrow from a large bank.
Table 4 Panel B shows the effects of the strong relationship components on the predicted probability of borrowing from a large bank. For large firms, a one standard deviation increase in the log of relationship length leads to a reduction in the probability of borrowing from a large bank of 7.3 percentage points. In contrast, large firms with an exclusive lender are 11.6 percentage points more likely to borrow from a large bank than large firms without an exclusive lender. Among small firms, those firms with a checking account at their lender are 14 percentage points less likely to borrow from a large bank.