Consolidation in the banking industry and the viability of small commercial banks: x-efficiency and bank size.

Rogers, Kevin E.

INTRODUCTION

The advent of the Riegle-Neal Interstate Banking and Branching Efficiency Act has relaxed historical geographic restrictions on banks, contributing to the trend of consolidation in the U. S. commercial banking industry. The prospect for such extensive change has led researchers to speculate about the future composition of the banking industry. Forecasts predict that a small number of large banks will control most financial assets in the industry, but many small banks will still survive (Berger, Kashyap & Scalise, 1995; Moore, 1995). The asset size composition of the industry has received much attention recently due to the concern that small business lending might decline if banks consolidate (Berger et al., 1998; Peek & Rosengren, 1998; Strahan & Weston, 1998). In fact, these studies have found that small business lending may not decline. They find evidence against the hypothesis that small business lending will decline as banks become larger. If small banks' presence in credit markets is reduced, then there may be an impact on the availability of credit to small borrowers. Petersen and Rajan (1994) find that the availability of credit is increased when a firm has close ties with its lender. If consolidation results in the disappearance of these lenders, then some loans may cease to have positive net present values and not be made.

One area of research that is relevant to the viability of small banks in a consolidating industry is that of efficiency. When new geographic markets are opened to allow more competition, inefficient banks will be forced to improve or be driven out of the industry by relatively more efficient, larger banks. Previously protected small banks could also be acquired by expanding banks, especially if de novo branching is not permitted. Hence, comparisons of X-efficiency in different bank size classes should reveal some information on the ability of small banks to compete with larger banks. Given standard approaches of X-efficiency estimation used with banks, such a comparison is not that meaningful. As noted by Berger (1993), because of the preponderance of small banks in any nationwide data sample of banks, the estimated frontier tends to fit small banks better, resulting in higher efficiency scores compared to larger banks. For this reason, comparing small banks with larger institutions is problematic. As a result of consolidation, small, medium, and large banks will in some cases share the same market even though they do not share the same technology. Hence, to provide a useful comparison between small banks and their future competitors, X-efficiency needs to be measured relative to efficient banks in larger size classes. Under this framework, more meaningful comparisons can be made between small banks and their potential competitors as the banking industry consolidates.

This paper attempts to make such comparisons. Following the procedure introduced in Mester (1997), frontiers for different size classes are estimated separately. Using the distribution free approach of Berger (1993), cost and profit X-efficiency of small banks are compared to medium and large banks. The results suggest that even after adjusting the frontiers for size classes, small banks still tend to be more cost efficient than large banks, but less profit efficient than some medium-sized banks. This suggests that while many small banks will be able to compete with larger banks in terms of costs, they may not be as profitable as the industry consolidates.

THE CONSOLIDATION OF THE BANKING INDUSTRY

Historically, states have placed geographic restrictions on the branching activities of commercial banks in the U. S. (For a more detailed summary of geographic restrictions on commercial banking, see Kaufman (1995, pp 373-377)). As noted by Kane (1996), these restrictions were implemented and have persisted to protect local markets from outside competition. Branching restrictions varied among states, with the most stringent limiting banks to only one office. The restrictions also applied to banks with national charters. The National Bank Act of 1864 did not address the ability of national banks to branch. They were effectively limited to only one office. National banks could not branch unless they had previously operated as a state chartered bank with branches and then converted to a national charter. The McFadden Act of 1927 permitted national banks to open branches within the same city, as long as branching was allowed in the state. It was not until the Banking Act of 1933 that national banks were given the same rights to branch within a state as state chartered banks.

Multibank holding companies evolved to circumvent geographic restrictions on banking. A bank could operate in different markets through multiple subsidiaries all owned by the same parent holding company. However, in 1956, the Douglas Amendment to the Bank Holding Company Act made it illegal for a holding company to open a bank or purchase an existing bank in a state which did not permit it. States effectively prohibited interstate banking by holding companies until 1978, when Maine started allowing out-of-state holding companies to operate banks in their state. Since then, interstate banking through multibank holding companies has spread as various reciprocity agreements and regional compacts have been enacted.

The removal of geographic restrictions took a major step forward with the Riegle-Neal Interstate Banking and Branching Efficiency Act of 1994 (IBBEA). IBBEA permits banks to acquire banks in other states, consolidate subsidiaries of the holding company into one bank, and open de novo branches across state lines (States can elect to "opt out" of the consolidation provision and have to "opt in" to allow de novo branching in their state. Kane (1996) constructs a rent-seeking model to examine the selection of regulatory regime in this application.). IBBEA would effectively permit a single bank to branch nationwide without having to work through a holding company.

The passage of IBBEA has resulted in much speculation on the potential impact of the removal of geographic restrictions on the composition of the U. S. banking system. In a study of banking in the 1980's, Rose and Wolken (1990) find that affiliation with a geographically diversified bank holding company does not provide a long-term comparative advantage over small, independent banks. This result suggests that many small banks will survive the consolidation process. Berger, Kashyap, and Scalise (1995) conduct a simulation to assess the effect of nationwide banking on the distribution of banking assets and the number of banks. Their model predicts that within five years after nationwide banking is implemented, the share of banking held by banks with less than $100 million in assets will be cut in half, and there will be about 4,000 fewer banks. Per-capita, these numbers are comparable to California that has always permitted unlimited branching to its state banks.

Analysis of consolidation has addressed the impact on efficiency. Hughes et al. (1996) examine bank holding companies involved in interstate banking. They find that geographic expansion moves inefficient banks closer to the efficient frontier in both risk and return dimensions. The wave of bank mergers in recent years has resulted in a number of studies that look for changes in efficiency after mergers. In an investigation of megamergers, Berger and Humphrey (1992) found that of the megamergers of the 1980's, 55 to 72 percent of the acquiring banks were more efficient than the acquired banks. However, despite these potential efficiency gains from mergers, the scale diseconomies actually reduce overall efficiency. On average, they find no significant cost efficiency benefits resulting from megamergers. The result changes as profit efficiency is considered. Akhavein, Berger, and Humphrey (1997) find that although there was no significant increase in cost efficiency, profit efficiency did improve on average from megamergers. While costs may not improve, the merged banks were able to shift their output into more profitable areas.

These two studies on megamergers point to the usefulness of estimating both cost and profit efficiency. The benefits to consolidation may not be restricted just to cost savings. Revenues may also be enhanced as merged banks can shift resources into more profitable areas. Akhavein, Berger, and Humphrey (1997) suggest that there may be benefits due to diversification. As a bank grows in size through mergers, its potential customer base also expands. This diversification may result from the larger geographic base for the same products or the new types of products now profitable because of increased size. By estimating profit in addition to cost efficiency the full impact of consolidation can be measured.

The following is an attempt to apply cost and profit efficiency to small versus larger banks and examine the viability of small banks in a consolidating market. In the empirical analysis that follows, small banks refer to those with total assets less than $100 million. These banks are compared to different classes of medium and large banks with minimum size of at least $100 million. If small banks are inefficient relative to larger banks, then consolidation should result in a significant drop in the number of small banks. Conversely, if small banks tend to be more efficient, then many should survive and compete with their larger competitors.

A MODEL OF COST AND PROFIT EFFICIENCY

The distribution free approach is used to estimate cost and profit efficiency. Separate cost and profit frontiers are estimated for a panel of banks assuming that X-efficiency is constant over the sample period. Each bank is assigned an efficiency score ranging over [0,1], with the most efficient firm receiving a score of 1.

The cost frontier is structured to allow the comparison of the actual cost of producing a particular bundle of outputs to the minimum cost necessary to produce that same bundle. Here X-efficiency is the deviation from minimum cost. The cost frontier is given by the following:

C = C(y,w, [u.sub.C], [v.sub.C]) Formula (1)

where:

C = costs

y = vector of output quantities

w = vector of input prices

[u.sub.C] = cost inefficiency

[v.sub.C] = random error

The cost inefficiency component, [u.sub.C], raises costs above minimum costs. Each bank in the sample can be assigned an efficiency score, CostEFF, which is equal to the ratio of minimum predicted costs to actual predicted costs.

The profit frontier is constructed according to the alternative or nonstandard approach used by Berger and Mester (1997) and Humphrey and Pulley (1997). While the standard profit frontier treats output prices as exogenous, expressing profits as a function of the prices of inputs and outputs, the alternative specification takes output quantities as exogenous:

Pr = Pr(y,w, [u.sub.C], [v.sub.C]) Formula (2)

where:

Pr = profit [u.sub.Pr] = profit inefficiency [v.sub.Pr] = random error

In this case, [u.sub.Pr] represents how much profits could be augmented by efficient production. Given the estimation of Eq. (2), each bank can be given an efficiency score, ProfitEFF, which is equal to the ratio of actual predicted profits to maximum predicted profits. In practice, Eqs. (1) and (2) have identical explanatory variables with costs and profits as dependent variables, respectively.

This alternative specification for the profit frontier is preferred when banks have some degree of market power. The issue of market power can be important in considering small banks. Many small banks may operate in markets protected from competition previous to consolidation. In addition the quality of output may vary across banks allowing some to charge higher prices. In this situation, a specification that allows endogenous prices for bank output seems appropriate. The price of bank output is also difficult to measure accurately. For these reasons, the alternative profit frontier is used in this paper.

For the purposes of analyzing efficiency and bank size, Eqs. (1) and (2) are estimated using a nationwide sample of banks and various subsets of the entire sample. This approach has also been used in Mester (1997) for the estimation of frontiers in different Federal Reserve districts. The National model consisting of all 12 districts combined into one sample was rejected in favor of the District model that allows the efficient frontier to vary across each district. When the full sample of banks is used, small banks tend to dominate the sample, forcing the frontier to reflect the attributes of efficient, small banks. Herein, the frontiers are estimated separately for subsets of medium and large banks as well. Efficiency scores are then assigned to small banks according to the frontiers of medium and large banks. This provides for a more suitable comparison of efficiency between banks of different sizes. By constructing estimates of efficiency in this manner, small banks can be more accurately compared to their efficient counterparts and future competitors as branching restrictions are removed.

EMPIRICAL ESTIMATION

For the estimation of the frontiers in Eqs. (1) and (2) above, the familiar translog specification was selected using five outputs and four inputs. The only difference in the two frontiers is the dependent variable.

Given the translog specification, estimates of cost and profit efficiency are constructed for bank i according to the following:

Cost[EFF.sub.i] = [u.sub.C.sup.min] / [u.sub.C.sup.i] Formula (3) Profit[EFF.sub.i] = [u.sub.Pr.sup.i] / [u.sub.Pr.sup.max] Formula (4)

where:

[u.sub.C.sup.min] = minimum cost inefficiency factor

[u.sub.C.sup.i] = cost inefficiency for bank i

[u.sub.Pr.sup.max] = maximum profit inefficiency factor

[u.sub.Pr.sup.i] = profit inefficiency for bank i

Measuring relative efficiency using the minimum cost or maximum profit inefficiency factor may distort estimates due to outliers. Following Berger (1993), truncated versions of the u's are constructed to reduce the impact of outliers. For this study, the top 5 percent of banks are considered fully efficient.

The data used in the estimation are taken from the Reports of Income and Condition, also known as "Call Reports." A panel was constructed of annual data from 1991-1996. The six year time series has been found to be appropriate for estimating efficiency with the distribution free approach. DeYoung (1997) finds that a six-year time series is long enough to allow random error to balance out, but still short enough to assume that inefficiency is unchanging over time. A balanced panel of 8,386 banks was constructed of banks with nonmissing observations over the entire time series. The use of a balanced panel is associated with some costs. Although an acquiring bank in a merger would be included in the sample, an acquired bank would be left out due to a lack of nonmissing data after the merger, leading to a survivorship bias. However, it would also be difficult to interpret estimates from these banks if they were included since the random error would have had less time to cancel out of the residual term used in the distribution free approach. Outputs and inputs were selected according to the intermediation approach. Outputs consist of demand deposits, time and savings deposits, real estate loans, and all other loans. Inputs used were labor, physical capital, deposits, and purchased funds. For each of the inputs, prices were computed as the ratio of total expenditure on that input to the quantity of that input.

As discussed above, cost and profit frontiers are estimated with different subsamples of the data set according to size. First, for comparability, a frontier is estimated for the entire sample. As in Mester (1997), this specification is called the National model. Then, frontiers are estimated separately for five subsets comprised of banks with total assets of less than $100 million, $100 million to $300 million, $300 million to $500 million, $500 million to $1 billion, and over $1 billion. Collectively, these frontiers are called the Size model (The National model is a restricted version of the Size model which does not allow the frontier to vary across the five different size classifications.).

Following the distribution free approach, after estimating each frontier an average residual is computed for all banks, including those omitted from the frontier estimation. The average residual is the difference between actual cost (profit) and the efficient level of cost (profit) predicted by the frontier. Once the average residuals are computed, efficiency scores can then be calculated as in Eqs. (3) and (4). The resulting efficiency scores can be used to compare efficiency across different size classes.

Table 1 presents the estimates of mean cost and profit efficiency. The results reported in Tables 1 and 3 were computed with a 5 percent truncation of the residuals. Here, the best 5 percent of the sample are considered fully efficient (Standard errors of the estimates of cost and profit efficiency were computed using bootstrapping techniques as outlined by Simar 1992). In all cases, as shown in tables 1 and 3, mean efficiencies were significantly less than one). The estimates in columns 1 and 3 are computed using the entire data sample for estimation of the frontier (the National model). Mean efficiency across all banks is reported as well as the mean efficiency across each of the five subsamples. At small banks, mean cost efficiency is 74.4 percent while mean profit efficiency is 77.5 percent. For the other four subsamples, mean efficiency ranges from 70.8 to 72.3 percent for costs and from 68.9 to 76.3 percent for profits. As expected, small banks are on average more efficient than medium and large banks. In columns 2 and 4, estimates of mean efficiency are reported for each of the subsamples (the Size model). For these estimates, five separate frontiers were estimated, one for each subsample, and then mean efficiency was computed for each group. Inspection of the estimates yields the same conclusion as before. Small banks have higher mean cost and profit efficiency, 76.3 and 77.6 percent respectively, than their larger counterparts with cost efficiency ranging from 49.5 to 65.9 percent and profit efficiency ranging from 69.4 to 76.4 percent. A series of specification tests were conducted to compare the National model to the Size model. For each year, an F-statistic was computed to test the null hypothesis that the frontier is the same across all size classes. The results given in Table 2 suggest that for both cost and profit frontiers, the null hypothesis can be rejected, implying that the Size model is more appropriate.

In an attempt to compare small banks to their potential competitors, small banks were also evaluated using the efficient frontiers of medium and large banks. The results from this procedure are reported in Table 3 for cost and profit efficiency. Five different frontier models were estimated including the National model and the four size classes with total assets above $100 million. Columns 1 and 3 report mean efficiency at small banks when evaluated at the respective frontiers. For example, when small banks are measured relative to the efficient banks in the $100 to $300 million size class, mean cost efficiency at small banks is 65.2 percent. The mean efficiency of the banks comprising the frontier sample is given in columns 2 and 4.

The results for cost efficiency imply that even when compared to the efficient frontier of larger banks, small banks are more cost efficient on average. Although mean efficiency at small banks declines relative to mean efficiency for the small bank size class (76.3 percent, from Table 1), mean efficiency is significantly higher than mean efficiency of each of the larger size classes. The results differ for profit efficiency. Using the same procedure for comparison, small banks are found to be more profit efficient, on average, than banks with $100 to $300 million and over $1 billion in total assets. This finding is reversed when small banks are compared to banks with total assets between $300 million and $1 billion; small banks are less efficient than these banks on average.

The results comparing small banks to banks with $300 million to $1 billion in total assets suggest that when the efficiency of small banks is estimated relative to the frontier of medium- sized banks, small banks are more cost efficient but less profit efficient. The advantages to operating at a small scale appear to be reflected in costs, not revenues. At the same time, the benefits to large scale production seem to be evidenced in higher revenues rather than reduced costs. At least some of the advantages to these medium sized banks must be through greater diversification of earnings. Since these banks have a broader customer base, they face a more diverse set of revenue sources and can hence shift resources into more profitable areas. Small banks, in contrast, are less likely to be able to take advantage of these opportunities. However, small banks can be more cost efficient, especially in local markets due to low cost information resulting from ongoing customer relationships. Although this study does not consider specific mergers, these results appear to correspond with the two studies on mergers mentioned above (Berger & Humphrey, 1992; Akhavein, Berger & Humphrey, 1997). These studies found that increasing bank size through mergers provided benefits through enhanced profit efficiency, not cost efficiency.

As stated above, the results differ when small banks are compared to the largest banks (over $1 billion in assets). On average, small banks are more cost and profit efficient when evaluated relative to the most efficient large banks. Interpreting these results is quite difficult, however, since large banks derive a greater share of income from various fee generating activities. The output from these activities is not measured in the frontier specification used to compute the estimates in Table 3. As shown by Rogers (1998), cost and profit efficiency tends to be understated when these activities are not included as part of bank output. This problem would tend to be more serious for large banks, implying that the differences between the two groups (4.2 and 3.1 percent for cost and profit efficiency, respectively) are understated, and possibly even negative. The frontiers could be re-estimated allowing for output from fee generating activities. However, such a specification would not be very helpful either. Small banks cannot realistically produce large quantities of this output, and large banks are not likely to expand these activities greatly by moving into markets with small banks. For this reason, comparing small banks to large banks would still be problematic. Neither approach adequately compares small banks to the largest banks. It must be noted that heterogeneity in the cost and profit function may be due to more than just differences in size. Differences in product mix, geographic markets, and organizational form, to name a few, might also account for differences in X-efficiency. Nevertheless, it does appear that size may proxy for some of these factors.

Overall, the results indicate that when compared according to relative X-efficiency, many small banks are viable competitors in the banking industry. Although small banks may not be as profitable, they are more efficient with respect to costs. Banks should be able to continue to compete with larger competitors as geographic restrictions are relaxed. This outcome supports the predictions mentioned above on the number of banks after consolidation. While the number of banks will decline, we will still observe a significant quantity of small banks after consolidation.

CONCLUSIONS

In the above analysis, cost and profit frontiers were constructed to provide estimates of efficiency for banks for five different size classes. Three methods were used to compute these estimates. First, the National model that uses all banks to construct the frontier was estimated, resulting in an efficiency score for each bank. Mean efficiency was then computed for each of the five size classes. Next, using the Size model, a separate frontier was estimated for each size class, allowing for the computation of mean efficiency in each size class from the efficiency score assigned in each individual frontier. In a specification test, the National model was rejected in favor of the Size model. Lastly, using the frontiers estimated in the Size model, efficiency scores were assigned to small banks based on the efficient frontiers of each of the other four size classes. Under this procedure, small banks do not dominate the data sample, allowing for a comparison of small banks to their efficient competitors in larger size classes. The results of the National and Size model both suggest that small banks are more cost and profit efficient, on average, than medium and large banks. When small banks are evaluated using the efficient frontiers of medium and large banks, small banks are still found more cost efficient, but are less profit efficient, on average, than medium sized banks. Overall these results imply that small banks may be more cost efficient, but not necessarily more profit efficient. This supports predictions about the post-consolidation composition of the banking industry that forecast a reduced but still significant presence of small banks. Many small banks that are relatively more efficient should still survive.

REFERENCES

Akhavein, J. D., A. N. Berger & D. B. Humphrey (1997). The effects of megamergers on efficiency and prices: Evidence from the profit function. Review of Industrial Organization, 12, 95-130.

Berger, A. N. (1993). 'Distribution-free' estimates of efficiency in the U. S. banking industry and tests of the standard distributional assumptions. Journal of Productivity Analysis, 4, 261-92.

Berger, A. N. & D. B. Humphrey (1992). Megamergers in banking and the use of cost efficiency as an antitrust defense. Antitrust Bulletin, 33, 541-600.

Berger, A. N., A. K. Kashyap & J. M. Scalise (1995). The transformation of the US banking industry: What a long strange trip its been. Brookings Papers on Economic Activity 2, 55-218.

Berger, A. N. & L. J. Mester (1997). Inside the black box: What explains differences in the efficiencies of financial institutions? Journal of Banking and Finance, 21, 895-948.

Berger, A. N., A. Saunders, J. M. Scalise & G. F. Udell (1998). The effects of bank mergers and acquisitions on small business lending. Journal of Financial Economics, 50, 187-229.

DeYoung, R. (1997). A diagnostic test for the distribution-free efficiency estimator: An example using U. S. commercial bank data. European Journal of Operational Research, 98, 243-249.

Hughes, J. P., W. Lang, L. J. Mester & C. Moon (1996). Efficient banking under interstate branching. Journal of Money, Credit, and Banking, 28, 1045-1071.

Humphrey, D. B. & L. B. Pulley (1997). Banks' responses to deregulation: Profits, technology, and efficiency. Journal of Money, Credit, and Banking, 29, 73-93.

Kane, E. J. (1996). De jure interstate banking: Why only now? Journal of Money, Credit, and Banking, 28, 141-161.

Kaufman, G. G. (1995). The U. S. financial systems: Money, markets, and institutions. Englewood Cliffs, NJ: Prentice Hall.

Mester, L. J. (1997). Measuring efficiency at U. S. banks: Accounting for heterogeneity is important. European Journal of Operations Research, 98, 230-242.

Moore, R. R. (1995). Does geographic liberalization really hurt small banks? Federal Reserve Bank of Dallas, Financial Industry Studies, December, 1-12.

Peek, J. & E. S. Rosengren (1998). Bank consolidation and small business lending: It's not just bank size that matters. Journal of Banking and Finance, 22, 799-819.

Petersen, M. A. & R. G. Rajan (1994). The benefits of lending relationships: Evidence from small business data. Journal of Finance, 49, 3-37.

Rogers, K. E. (1998). Nontraditional activities and the efficiency of U. S. commercial banks. Journal of Banking and Finance, 22, 467-482.

Rose, J. T. & J. D. Wolken (1990). Geographic diversification in banking, market share changes, and the viability of small independent banks. Journal of Financial Services Research, 4, 5-20.

Simar, L. (1992). Estimating efficiencies from frontier models with panel data: A comparison of parametric, non-parametric and semi-parametric methods with bootstrapping. Journal of Productivity Analysis, 3, 167-203.

Strahan, P. E. & J. P. Weston (1998). Small business lending and the changing structure of the banking industry. Journal of Banking and Finance, 22, 821-845.

Kevin E. Rogers, Mississippi State University

Table 1

 Mean Efficiency Cost
 (percent)

 (1) (2)

 Data Sample National Model Size Model
 (total assets)

All Banks 73.45 (a) *****
 (0.303) *****

0 - $100 m 74.35 (a) 76.33 (a)
 (0.309) (0.392)

$100 m - $300 m 72.11 (a) 62.62 (a)
 (0.323) (0.686)

$300 m - $500 m 71.67 (a) 65.90 (a)
 (0.515) (1.31)

$500 m - $1 b 72.26 (a) 49.50 (a)
 (0.645) (1.96)

over $1 b 70.77 (a) 59.65 (a)
 (0.516) (0.948)

 Mean Efficiency Profit
 (percent)

 (3) (4)

 Data Sample Model National Size Model
 (total assets)

All Banks 76.64 (a) *****
 (0.0984) *****

0 - $100 m 77.49 (a) 77.55 (a)
 (0.100) (0.179)

$100 m - $300 m 76.17 (a) 75.72 (a)
 (0.085) (0.445)

$300 m - $500 m 76.34 (a) 76.40 (a)
 (0.125) (2.23)

$500 m - $1 b 74.98 (a) 69.40 (a)
 (0.143) (3.28)

over $1 b 68.88 (a) 72.43 (a)
 (0.124) (2.56)

(a) Significantly different from 100 percent at the 5
percent level, two tailed test.

Table 2: National Model vs. Size Model
Null Hypothesis: The frontier does not vary across size classes.

 Year Cost Profit

 1991 63.22 33.44
 1992 66.54 31.19
 1993 88.19 20.64
 1994 74.63 22.63
 1995 45.48 25.53
 1996 17.94 31.85

Note: critical value for F36,8206 .1.62, at a 99 percent
significance level

Table 3

Mean Efficiency Cost
(percent)

 (1) (2)

 Frontier Sample Small Banks (b) Frontier Banks

All banks 74.35 (a) 73.45 (a)
 (0.309) (0.303)

$100 m - $300 m 65.20 (a) 62.62 (a)
 (0.683) (0.685)

$ 300 m - $ 500 m 68.78 (a) 65.90 (a)
 (0.958) (1.31)

$ 500 m - $1 b 52.66 (a) 49.50 (a)
 (1.04) (1.96)

over $1 b 63.84 (a) 59.65 (a)
 (0.838) (0.948)

Mean Efficiency Profit
(percent)

 (3) (4)

 Frontier Sample Small Banks (c) Frontier Banks

All banks 77.49 (a) 76.64 (a)
 (0.100) (0.0984)

$100 m - $300 m 77.38 (a) 75.72 (a)
 (0.460) (0.445)

$ 300 m - $ 500 m 74.30 (a) 76.40 (a)
 (2.26) (2.23)

$ 500 m - $1 b 65.69 (a) 69.40 (a)
 (3.29) (3.28)

over $1 b 75.60 (a) 72.43 (a)
 (2.63) (2.56)

(a) Significantly different from 100 percent at the 5 percent
level, two tailed test.

(b) For each frontier sample, mean cost efficiency for small
banks is significantly different from mean cost efficiency for
the frontier banks.

(c) For each frontier sample, mean profit efficiency for small
banks is significantly different from mean profit efficiency for
the frontier banks.