An alternative measure of financial service provided by branches – an application to thestrategy of Shinkin banks –†Hideto Azegami (Department of Economics, Kyoto Gakuen University)
1.

Introduction

Brick-and-mortar branches were decreasing in Japan since the 1990s because of bankruptcy of somefinancial institutions, consolidation based on the management strategy and decrease in population in rural
regions. Thereafter, several regional banks which succeeded to improve their business performance began
establishing new branches in the territories of the others. The number of branches became more different
between regions.
Horiuchi and Sasaki (1982) defined the measure of branch services in a region as the product of thenumber of branches per household in a region and the population density. However, the values of themeasure calculated with the municipal data at October 1, 2008 completely correlated with the number ofbranches per habitable land size for all the categories of financial institutions. The values of mostmunicipalities are zero or extremely small because the measure of Horiuchi and Sasaki (1982) does notinclude the factor of population or the number of establishments in a region. Therefore, an alternative
measure will be calculated that includes both the factors of the number of branches per unit size of habitableland and the population per the number of branches.
The answers to the question why the branch services should be measured are based on the two sides of thefinancial services market.
One side is consumers. In the United States, the way to improve consumers’ accessibility to banking
services is introducing a new bank under the branching restrictions. But it is not efficient on the basis of costbecause economies of scale exist in the financial service industry. Evanoff (1988) tests the impact ofbranching on the accessibility of banking services. He measures the accessibility as the number of branching
offices per square mile. Singh (2008) analyzes the response of customers in the small scale industries about
the quality of service provided through branches by the public sector banks in India. The location of branch iscounted as one of the factors to determine the level of customer service and satisfaction. Liu and Wu (2009)
also point out that locational convenience is considered significantly important in traditional banking
products. Ioannou et al. (2002) and Gri goroudis et al. (2002) investigate the optimization of the branch
network for consumers and customer satisfaction in the banking services market, respectively.
The other side is producers. Evanoff (1988), Al-Tami and Lootah (2007), and many other studies deal withissues on the cost efficiency or the profitability of financial institutions. After the Internet came into wide use,the cost efficiency of PC banking or online banking is included among the objects of research. Byers andLederer (2001) theoretically compare the traditional banking and the PC banking strategy.
One of the other issues is the branching restrictions and their removals, as seen in Calem and Nakamura(1998) and Avery et al. (1999).
Papias and Ganesan (2010) point out that the accessibility to financial services is notably different
between urban and rural areas especially in the developing countries. Although Japan Post Bank, privatized† This work was supported by JSPS KAKENHI Grant Number 90306241.

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postal bank, and the agricultural cooperatives are the principal providers of financial services in rural areasin Japan, the accessibility to services of commercial banks is lower than in urban areas as yet.
The paper is organized in the following manner. Section 2 and Section 3 review the original measure offinancial services provided through branches and the distribution of branches in Japan, respectively. Section
4 presents the empirical results and Section 5 suggests the alternative measures of financial services. The
final section contains a brief conclusion.
2.

Measure of branch services

Horiuchi and Sasaki (1982) defined their original measure of financial services provided by branches offinancial institutions as Eq. (1).

OMBS = N*B/H(1)

where OMBS, N, B, and H denote the measure of financial services, population density, the number ofbranches, and the number of households in a region, respectively1. This measure of branch services iscontroversial because of the reason as follows. When P and A denote the population and the size of a region,
Eq. (1) can be represented by Eq. (2).
OMBS = P*B/(A*H)(2)

If the number of family members is the same for all households in the region and it is  , then OMBS iscompletely proportional to the number of branches per square mile. That is, the Eq. (3) holds.

OMBS  B / A(3)

Since we can regard B/A as “branch density” of the region, the original definition is criticized for not including
the effects of population. However, Horiuchi and Sasaki (1982) estimate by using the data of population
density for densely inhabited districts as well as ordinary one in order to control the effects of population.
They show that the amounts outstanding of deposits in a prefecture positively relate to the branch services
provided by financial institutions with the cross-sectional data model including their measure of branchservices.
This research attempts to find the alternative measure of financial services provided through thebranches of institutions in a region. The next section observes the distribution of branches for financial
institutions including the city banks, the regional banks, the regional banks II, the Shinkin banks, the credit
cooperatives, the labor banks and Japan Post Bank.
3.

Distribution of branches

Figure 1 shows the relationship between the number of branches and population in 1,934 municipals on
October 1, 2008. While the positive relationship depicted in the figure is consistent to the results of existingstudies, the dots far above the mass indicate the regions in which more branches exist than those with muchthe same population. Figure 2 depicts the number of branches plotted in descending order with respect toregional population. (Figure 1, 2)
If the number of branches is completely proportion to population in a region, then every top of the bar
forms the straight line downward to the right in the graph. In Figure 2, however, some cities in which a large
1 The notation is not the same as that in their original paper.

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number of branches exist are outstanding compared to those with the same population in the range fromforty thousand to one hundred thousand. They are several small wards in Tokyo where there are a large
number of establishments.
4.

Estimation

Several existing researches estimate the data by prefecture to cover the nation and the others analyze more
minutely with the data by municipality but their researches are limited in a few prefectures. Our data are bymunicipality but cover the all prefectures. The descriptive statistics for the number of branches by business
operator category are listed in Table 1.
The city banks are Mizuho Bank, The Bank of Tokyo-Mitsubishi UFJ, Sumitomo Mitsui Banking
Corporation, Resona Bank, and Saitama Resona Bank. Amounts outstanding of their deposits are so large
but the branches are located in only major cities such as prefectural capitals. They are unevenly distributedin 22 % of municipalities and the skewness is 6.82, the largest between seven categories. Contrarily, Japan
Post Bank has the branches in all municipalities. It is a subsidiary of Japan Post Holdings (Japan Post
Group), which was founded by the privatizing of Japan Post on October 1, 2007. Japan Post was agovernment-owned corporation which offered postal, banking, and life insurance services. Since all theestablishments are continuously used as the branches of Japan Post Bank, any residents can find them intheir place of residence. The coefficient of variation is the smallest between the seven categories, whereas theskewness is larger than that of the labor banks because there are several cities in which quite a few ofbranches exist. (Table 1)
The city banks, the regional banks, and the regional banks II are commercial banks, so they arecorporation organizations. On the other hand, although the Shinkin banks and the labor banks include aword “bank” in their name, they are not commercial banks but cooperative financial institutions as well as
the credit cooperatives. The total number of branches of the cooperatives is 10,148 and it is not so smaller
than that of bank branches, excluding the branches of Japan Post Bank as seen in Table 2. In spite of thestrict regulations on business area, the branch distribution of the cooperative financial institutions is similar
to the commercial banks. The cooperative institutions have founded the branches in the densely inhabited
districts and the cities around them because the economic depression since the1990s does not come to an end
in the local areas. Accordingly, the difference of the branch distribution between commercial banks andcooperatives disappeared. (Table 2)
Since several municipalities have no branches for any of the business categories except for Japan Post
Bank, a researcher must pay attention to estimation. If the number of branches is selected as the dependent
variable, the values are divided into zero and non-zero.
Similar to the related studies, the set of the explanatory variables is composed by the habitable land size,
the day population, the share of older persons in the total population, and the number of establishments. The
value of the habitable land size of municipalities is in 2005, extracted from the TOYOKEIZAI DATABASE(CD-ROM series) edited by TOYO KEIZAI INC. The day population is extracted from the results of thenational census taken in 2005 and the share of older persons in the total population is calculated from them.
An older person is defined as a person age sixty-five and over. The number of establishments is extracted
from the results of the establishment and enterprise census in 2006.
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The results of the OLS estimation are listed in Table 3. To test the statistical significance, White’s standard
errors are used because there exists heteroscedasticity. Although it was doubted that the day population wascorrelated to the number of establishments, every variance inflation factor is less than five.
While the dependent variables significantly correlate with the number of establishments for all thecategories of institutions, the regression coefficient of the day population is significant for the regional banks
II, the Shinkin banks, and Japan Post Bank. The fact that the effects of population are not so strong isdifferent from the conclusions of the existing studies. However, this is because the estimation disregard thatthe data of the dependent variables are truncated.
The coefficients of the habitable land size are significantly positive except for the city banks. Since thebranches of the city banks concentrate in major cities as mentioned above, the number of branches
negatively correlate to the land size for the city banks. These results are consistent to those of the existingstudies.
The data of the dependent variable are truncated from below at one for Japan Post Bank and at zero forthe other categories of institutions. Thus, the same data set are estimated with the Tobit regression modeland the results are listed in Table 4.
While the coefficients of the day population are not significant for the city banks and the regional bankswith the OLS regression, they become significant with this model. For the credit cooperatives and the laborbanks, however, the coefficients of the day population are not significant.
The striking difference between the results of the OLS and the Tobit regression models is recognized forthe effects of the share of older persons in the total population. Although the coefficients of it are significantly
positive for the Shinkin banks and Japan Post Bank in the results of the OLS regression model, they are
significantly negative except for Japan Post Bank. As the population has been rapidly aging especially inrural area, the post offices are an important channel to provide the financial services to the older persons insmall towns and villages. (Table 4)
The number of branches positively correlates with the habitable land size, the day population, and thenumber of establishments for all the categories of institutions except for the effects of the habitable land sizefor the city banks. Nevertheless, the number of branches is not linearly proportional to these independent
variables. We would like to know the elasticity of the dependent variable. Since the regression coefficients are
not the same as the marginal effects in the Tobit regression model, they will be computed with the meanvalues. The values of the marginal effects in the Tobit regression model are listed in Table 5. Although thevalues of the day population are negative for the credit cooperatives and the labor banks, the regression
coefficients are not significant as seen in Table 4. (Table 5)
If the number of branches; B is determined by a function of the habitable land size; A, the day population;P, and the number of establishments; E, then the relationship is illustrated by Eq. (4).
B  f ( A, P, E )(4)

A marginal effect is the partial derivative of the function of each variable. The elasticity of the number ofbranches;  is defined as below.
k 

f / k , k  A, P, E
f /k

(5)

Substituting a marginal effect value in Table 5 into f / k , the elasticity of the number of branches with4

respect to the independent variable is calculated. Figure 3, 4, and 5 illustrate the values of the elasticity
corresponding to the values of the independent variable in ascending order. (Figure 3-5)
The area elasticity measures the responsiveness of the number of branches to a change in the habitableland size of the municipality. Figure 3 shows that it is highly elastic in the municipalities with the larger
habitable land size except for the city banks. Especially, Japan Post Bank and the regional banks locate morebranches in a larger area. This is because the Act on Japan Post Holdings Co., Ltd provides that the
distribution of post offices must be uniform in the nation.
If the day population is above forty thousand, then its elasticity becomes more than one for the Shinkinbanks as seen in Figure 4. For the other categories of institutions, it is less than one on the whole. Since thebusiness area and the customers of a Shinkin bank are regulated, it likely founds a branch in a region withthe large population. On the other hand, the regional banks and the regional banks II can lend to any firms
regardless of the amount of the stated capital or the number of employees. The establishment elasticity isalso larger for them than for the others as seen in Figure 5. The reason why the establishment elasticity forJapan Post Bank is lower than the others might be that it does not lend the funds on its own but purchases
government bonds.
Since the population elasticity is smaller than the area elasticity, the regional population can be different
between two regions that have the same number of branches per square mile. It should be estimated that
more financial services are provided through the branches in the region with more population to the extent
of no congestion. An alternative measure of financial service provided by branches will be suggested in thenext section.
5.

Reconsidering the measure of branch services
Measuring the branch services provided in a municipality on October 1, 2008 with the method of Horiuchi

and Sasaki (1982), the correlation coefficients between the value and the number of branch per square
kilometer are listed in Table 6. (Table 6)
In the municipal data the OMBS can be substitute to the number of branches per square kilometer.
Moreover, only some big cities have the high value of OMBS and almost municipalities belong to the lower
classes when they are classified with respect to the value of this measure. While this is true for all thecategories of institutions, the histograms for Japan Post Bank and the Shinkin banks are illustrated as
Figure 6 and 7, respectively. (Figure 6,-7)
In many municipalities a value of the OMBS with respect to Japan Post Bank is smaller than the meanvalue of the OMBS, 0.50. Similarly, there is no branch of Shinkin bank in 478 municipalities and a value of
the OMBS is smaller than the mean value, 0.20 in most municipalities. If the data with which distribution ispositive skew are used in estimation, then heteroscedasticity may exist.
The branch density defined as the number of branches per unit area is an important factor of the measureof the branch services because it proxies the accessibility for residents to a branch if they are uniformly
distributed in a region. Another factor is the population in a region. It is recognized that a branch can haveopportunities to provide financial service if the population is larger. Therefore, the regional population perbranch will be considered.
An alternative measure of branch services BS0 is defined as Eq. (6).
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BS 0  f B / Ag ( P / B)

(6),

where f B / A and g P / B illustrate the factors of the branch density and the regional population perbranch, respectively. A logarithmic function is suggested as a functional form of f(・) and g(・) because of
tractability.
BS 0  f B / Ag ( P / B)  ln( B / A) ln( P / B)

(7)

Whether the measure of (7) rises up as increase in branch depends on the scale of the variable. That is, forsome A>0 and P>0, it is not guaranteed that BS0 is increasing to B. In practice, it is clear that the first
derivative of (7) with respect to B is positive when the scale of area is square kilometer and the scale of
population is the number of residents as seen in (8).
dBS 0 / dB  ln A  ln P  2 ln B  / B(8)When the municipal data are used, the more fundamental problem is that the number of branches B
becomes zero in some regions and the measure BS0 diverges. In such a case, the Box-Cox transformation, thegeneral form of logarithm, is sometimes used to remove the problem. Since the number of branches canbecome zero, the number of branches per resident is used in spite of P/B. Inserting the parameters λ1 andλ2 into the measure, the general form of (7) is represented by (9)2.





 





BS 1   1 / 1  B / A 1  1 / 1 / 2  B / P  2  1 , 1 , 2  0,1




(9)

Figure 8 and 9 show the values of the measure by setting 1  2  0.6 for Japan Post Bank and the Shinkinbanks, respectively. (Figure 8- 9)
An alternative measure BS1 generates the unimodal distribution for Japan Post Bank. The population
does not work as the weight in the original measure OMBS because it is proportional to the number ofbranches per unit area. Therefore, it becomes the same value between the regions with the same branchdensity even though the regional population is different between them. In contrast, an alternative measure
BS1 increases with regional population under the same branch density. Similarly, the effects of population
can be included into the measure and the distortion is corrected in the distribution.
6.

Conclusions

Even though more financial services have been provided by using the Internet, a brick-and-mortal branchplays an important role as the channel of financial service provision especially in rural areas in Japan. The
number of branches continues to decrease in most categories of institutions for nearly twenty years becauseof consolidation, economic depression, and depopulation in rural regions. Therefore, measuring the financial
services provided by branches of institutions in a region is meaningful.
Several researches deal with this issue but it is difficult to include the effects of population into themeasure. Moreover, in the case of using the municipal data set, so many towns and villages with no branch
is troublesome. This paper suggests two types of measure. A measure composed by logarithms of branchdensity and of the population per branch is tractable but it is not used when the data include zero values.
Although the general form is also tractable, the value computed by the measure depends on the parameters
selected.
※ Figures, tables, references, and, appendices are in the complete version of the document.
2 The minus sign of denominator is to make the first derivative of (9) with respect to B be positive.

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