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Returns to scale and efficiency of credit associations in Japan: A nonparametric frontier approach
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Japan and the World Economy 8 11996) 259 277
Returns to scale and efficiency of credit associations in Japan: A nonparametric frontier approach Hirofumi Fukuyama* Faculty of Commerce, Fukuoka University, Nanakuma, .lonan-ku, Fukuoka 814-01, Japan Received April 1994: accepted April 1995
Abstract
We investigate the nature and extent of technical as well as scale efficiency by applying a nonparametric frontier approach to Japanese credit association (shinkin bank) data for fiscal year 1992. The main motivation of this study is the fact that there have been few significant frontier studies on the credit association industry, particularly in the aftermath of the collapse of the bubble economy in 1990. This study uncovers, among other things, the major causes of overall technical inefficiency and the relationships between size and various types of efficiency in terms of returns to scale regions.
Keywords: Nonparametric frontier approach; Technical efficiency; Returns to scale: Japanese credit associations J E L class![ication: D2; G21
1. Introduction
The e c o n o m i c landscape surrounding the Japanese banking industry dramatically changed in the aftermath of the collapse of the so-called bubble economy. The e c o n o m y enjoyed a b o o m during the last half of the 1980s
*Tel.: +81-92-863-5233 (ext. 4402): fax: +81-92-864-2938: e-mail: fukuyama/ajsat.fukuokau.ac.jp. 1234-5678/96/'$15.00 Copyright SSDI 0 9 2 2 - 1 4 2 5 ( 9 6 ) 0 0 0 4 1 - 0
1996 Elsevier Science B.V. All rights reserved
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fostered by easy financial policies on the part of the monetary authorities (e.g., the Bank of Japan maintained the official interest rate as low as 2.5% from the beginning of 1987 until the middle of 1989). After experiencing this vigorous boom, the economy underwent a sudden financial bust in 1990-land and stock prices plunged. Also as a consequence, financial institutions have been suffering from a substantial increase in nonperforming loans due to borrowers' inability to pay interest on loans. The dramatic economic change, along with accelerating financial innovations and rapidly improving communications, might have had considerable effects on the productive (scale and technical) efficiency structure of credit associations (shinkin banks) and these potential effects need to be examined. Being structured on a membership basis, credit associations are small financial institutions, of which not only operations are restricted in principle to a certain geographical area, but also financing is focused on small and mediumsized firms. Commercial banks are stock financial institutions with a national focus and in general a majority of them are much larger than credit associations. The membership basis, the focus on regional finance and the finance of small- and medium-sized local firms are the features which distinguish credit associations from commercial banks. The purpose of this paper is to offer empirical evidence on productive efficiency of Japanese credit associations within a nonparametric frontier framework. To model behavior of banks, a frontier approach allowing for productive inefficiency has been often employed in non Japanese banking studies such as Rangan et al. (1987), Elyasiani and Mehdian (1990), Berg et al. (1991), Drake and Weyman-Jones (1992) and Fried et al. (1993), all of which showed significant productive efficiency variations across banks. In the frontier literature there are mainly three commonly used approaches. The first is an econometric frontier approach and the second is a deterministic frontier approach, both of which utilize parametric production and/or cost functions. The last is a nonparametric frontier approach which has gained popularity in banking analyses. The present study employs the last approach, since it has some advantages over the first two frontier approaches. First, it does not require a priori functional specification on unknown technology. Secondly, it provides meaningful firm-level efficiency scores within a multiple output framework without reference to input prices and costs, in contrast to the parametric cost function estimation. Lastly, it can easily estimate scale inefficiency quantitatively and provide the source of the scale inefficiency. Nonetheless, it is not without drawbacks, the most important of which is that statistical noise or measurement error is assumed to be negligible. In Japanese banking, there are commercial banking studies such as Tsutsui (1986), Kasuya (1989) and Fukuyama (1993) within a frontier framework but there are few significant frontier studies on credit associations. Regarding estimation methodologies, the first two employed econometric techniques with
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a single output, while the last used a nonparametric frontier technique. As to credit association studies, there are nonfrontier analyses examining scale and scope economies 1 (see Nishikawa, 1973; Hirota and Tsutsui, 1992; Miyamura, 1992; Miyakoshi, 1993, which used parametric functions). These studies are based on data for years before 1990, except for Miyamura who employed both the 1985 and 1990 samples. Their scale estimates indicated mixed results: whereas the sample results of Hirota and Tsutsui (1987) and Miyamura (1985) showed significant scale economies, Nishikawa's (1968) and Miyakoshi's (19851 samples did not show scale economies. Among the studies mentioned the most recent data set used is Miyakoshi's (!990) sample, but 1990 was the year when the sudden collapse of the bubble economy occurred and the significant change due to prolonged economic slowdown have occurred since then. In view of the fact that data sets before 1991 may not represent the current economic c o n d i t i o n s - t h e years 1991 and 1992 suffered further economic slowdown or recession and the fact that the previous studies on this industry did not allow for technical inefficiency, they are not a very useful guide to understand the current credit association industry in the period of the economic slowdown. Since, employing the 1990 sample, the commercial banking study of Fukuyama (1993) focused on the determination of overall (input) technical inefficiency (which is decomposed into scale efficiency and pure (inputt technical efficiency) and the nature of returns to scale as well as the relationship between size and efficiency, the present paper proceeds by comparing our result with Fukuyama's for the purpose of facilitating the comparisons between credit associations and commercial banks. Overall technical inefficiency is the result of the operations off the isoquant constructed relative to the constant returns to scale technology, while pure technical inefficiency stems from the operations off the isoquant constructed relative to the variable returns to scale technology. Scale inefficiency occurs when there is either increasing or decreasing returns to scale and the operation at constant returns to scale corresponds to scale efficiency. The notion of scale efficiency implies that the output level with constant returns to scale represents the optimal output level from society's perspective since constant returns to scale is related to zero profit long-run competitive equilibrium. Yet, the operation at increasing or decreasing returns to scale may be optimal on the part of firm managers (i.e., in the private sense). In other words, overall technical efficiency refers to the efficiency associated with socially desired situations, whereas pure technical efficiency refers to the efficiency related to a credit association's private optimization behavior. The relationship among the three 1Scale and scope economies of thrifts in North America are studied by Murray and White (1983), Goldstein et al. (1987), Mester (1987), and Cebenoyan et ~d. (19931, whereas technical efficiency was investigated by Fried et al. (1993).
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types of efficiencies can be established as the overall technical efficiency decomposition into scale and pure technical efficiency and the decomposition can be used to identify major causes of overall technical inefficiency. In case of the commercial banking study of Fukuyama (1993), scale inefficiency was dominated by pure technical inefficiency. In the past, the credit association industry has witnessed quite a few merger activities which led to the steady reduction in number of firms (from 520 in May 1968 to 455 in March 1989 and 435 in March 1993). The mergers can be carried out with the intention of enhancing pure technical efficiency on the part of credit association managers. If so, large credit associations should be more pure(ly) technically efficient. According to Fukuyama's (1993) commercial banking evidence with respect to Spearman's rank correlation analysis, this is not the case. Both pure and overall technical efficiency were not significantly associated with asset size but scale efficiency was. In commercial banking, asset size does not explain pure and overall technical efficiency variations, but in contrast a positive asset size association with scale efficiency was evident from the result of the vast majority showing increasing returns to scale. It is of great interest to know whether or not similar evidence can be found in the case of credit associations. The remainder of the paper is organized as follows. Section 2 provides some information on credit associations, while Section 3 presents both input-based and output-based measures of efficiency. We examine both input and output sides of efficiency measurement because they may provide different implications output-based efficiency and input-based efficiency are fundamentally different concepts. In addition to the general estimation framework, we provide a methodology classifying the observations into six groups based on returns to scale, since predictions regarding returns to scale can be contradictory (though nothing wrong theoretically) once the operations off the frontier are allowed. This section also explains how to determine the nature of returns to scale. The data source and the input/output specifications are reported in Section 4 and empirical findings are provided in Section 5. A summary and conclusions are given in Section 6.
2. Banking system and credit associations The Japanese private banking system has developed along the lines of segmentation and specialization and thus there are various financial institutional forms. They may be divided into four categories: (1) commercial banks, (2) long-term financial institutions, (3) financial institutions for agriculture, etc. and (4) financial institutions for small businesses. Usually, commercial banks focusing on short-term finance are subdivided into three forms: city, regional
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and former sogo banks. 2 The second type of financial institutions focusing on long-term finance are long-term credit banks and trust banks. The third type of financial institutions are members of the Norinchukin bank, which is the central institution for cooperatives serving the agricultural, forestry and fishery industries. The last type of financial institutions, to which credit associations belong, include labor credit associations, 3 credit cooperatives and the Shokochukin bank. As stated in Section 1, credit associations, organized on a membership basis, are not stock companies. Regarding the origin of the credit associations, they were previously credit cooperatives created in the last century and were allowed to gain the present status under the Law for Small Business Cooperatives of 1949 and these credit cooperatives became the present credit associations by the Credit Associations Law of 1951. This conversion was necessitated by two conflicting characteristics. 4 The first characteristic is that the credit cooperatives were expected to mainly provide services to medium and small local firms and the general public in the region. The second characteristic is the cooperative nature of credit cooperatives, that is, serving members only. Zenshinren (which remodeled the National Federation of Credit Cooperatives) was established under the Credit Association Law as the central bank for the credit associations. Zenshinren not only accepts savings from member credit associations and provides loans to member associations, but also engages in foreign exchange operations for the member credit associations. In addition, it accepts deposits from the government, municipalities, public corporations, and nonprofit organizations. The establishment of Zenshinren has led to the smoothing of regional and seasonal funds, efficient investment of funds, concentrated settlement of foreign exchange, payment intermediation and mutual aid systems. Thus Zenshinren provides a safety mechanism and effective financing for credit associations. 5 Data of Table 1 indicate that total loans and assets of credit associations are greater than not only those of long-term financial institutions but also former sogo banks. In addition, credit associations are much more important financial intermediaries than credit cooperatives, while the total loans and assets of the credit associations are over twice as large as those of regional banks and roughly 30% of those of city banks. This fact, along with the status as the regional financial institutions for small and medium firms, means that credit associations play a very important role in the economy. 2Sogo banks were previously mutual banks but were converted int,~ ordinary banks. Therefore, we treat them as commercial banks. 3The central organization for credit cooperatives are the National Federation of Credit Cooperatives. The function of the Federation is similar to that of Zenshinren. '*See Shinyo Kinko Yon-jusshunen Shi (40 }~,ar History of Credit As,sociations} (p.105) written by the Federation of Credit Associations. SF'or more details, see Suzuki (1987) and Tatewaki [19911.
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Table 1 Relative size of financial institutions No.
City banks 11 Regional banks 64 Former sogo banks 68 Trust banks 7 Long-term credit banks 3 Credit associations 435 Credit cooperatives 393
Loans and discounts outstanding (banking accouns)
Savings
Assets (banking accounts)
2236217 1 255 804 508 878 245 275 472 030 650 478 183 108
1840529 1 550 577 583 532 88 072 53 369 882 085 229 195
3388113 1 873 150 701 437 530 549 786 381 1027 763 na
Note: (100 millions of yen; fiscal 1992). na: not available. Source: Economic Statistics Monthly published by Bank of Japan.
3. Input-based and output-based efficiency This paper utilizes nonparametric frontier (linear programming) models which originate from Farrell (1957) and have been extended and popularized by Charnes et al. (1978) and Ffire et al. (1985). To initiate the analysis, let y be a column vector of G outputs and let x be a column vector of N inputs. Regarding observations, let Y be the (G × J) matrix of outputs for each of J firms and let X be the (N x J) matrix of inputs for each of J firms. Now define a set J
~(z)= {Ix, y): V.z>.y,X.z<~x, y~ zj-- 1 , z ~ + } ,
tl)
j=l
where z with the restriction (ZJ=lz ~ = 1) is a vector of variables forming convex hulls of observations and the set is referred to as the variable returns to scale (VRS) reference technology. Relative to ~(z), the production possibility set (PPS) satisfying VRS can be denoted as PPS = {(x,y): 3z~[~s+ such that
(x,y)~(z)},
(2)
which is a convex set. By dropping the restriction (Zs= l zj--= 1), the following set referred to as the CRS reference technology
~*(z) = {(x, y): v- z/> y, x . z -<. x~ ze ~ }
(3)
is a cone and thus (3) satisfies constant returns to scale (CRS). Similar to PPS in (2), the production possibility set satisfying CRS can be obtained as P P S * = {(x,y): 3ze[~J+ such that
(x, y)e (*(z) }.
(4)
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Relative to the VRS reference technology (1), the pure (VRS) input technical efficiency measure can be obtained as ITE = minimize {2: (2x, y) ~ if(z)},
(5)
which computes the input saving while keeping the output level fixed. Similarly, the overall (CRS) input technical efficiency measure can be computed as ITE* = minimize {2: (2x, y)~ ~*(z)},
(6t
which computes the degree of the input saving when a benchmark is the CRS technology (3). The significance of CRS is that operations at a scale of constant returns is associated with the long-run competitive equilibrium, being the optimal level of operations from a societal point of view. Therefore, deviations from the long-run competitive equilibrium are thought of as scale inefficiency. Using two technical efficiency measures (ITE and ITE*), input scale efficiency can be computed as the ratio of the linear programming problems with and without CRS imposed ISE = ITE*/ITE,
(7)
which is called the input scale efficiency measure. If each of the input-based efficiency measures (ITE, ITE* and ISE) is less than one, then a firm is inefficient; the firm is efficient if it is unity. Owing to (7), overall input technical efficiency can be written as a multiplicative composite of input scale efficiency and pure input technical efficiency ITE* = ISE. ITE.
(8)
Similar to input-based efficiency, there are efficiency measures on the output side. They are the pure (VRS) output technical efficiency measure OTE = maximize {0: (x, Oy) e ~(z) },
(9)
O.z
and the overall (CRS) output technical efficiency measure OTE* = maximize {0: (x, 0y)~ ~'*(z)}.
(10)
O,z
Using (9) and (10), the output scale efficiency measure can be computed as OSE = OTE*/OTE.
(11)
In contrast to input-based efficiency, output-based efficiency indicates a firm's inefficiency if the value is greater than one. If the value is one, then the firm is efficient. To determine causes of overall output technical inefficiency, we write (11) as OTE* = OSE" OTE,
(12)
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which states that the overall output technical efficiency measure is a multiplicative composite of two efficiency measures (output scale efficiency and pure output technical efficiency). To illustrate each efficiency measure, consider Fig. 1, which is a simple one input one output situation. Here, A1-A 4 are observed firms and the VRS and the CRS frontier are AIAzA 3 and the ray 0D, respectively. For firm A4, pure input technical efficiency and overall input technical efficiency are EG/EA 4 and EB/EA 4, respectively, since input-based efficiency is defined as the proportional reduction in input quantities. Thus input scale efficiency is computed by the ratio EB/EG. On the output side, pure output technical efficiency and overall output technical efficiency are calculated by HI/HA 4 and HC/HA 4, respectively, since output-based efficiency computes the degree of output loss
C/
CRS
VRS
A2
E
............
+
A4
!~AI J i I I
6
0
F
H
Fig. 1. Input-based efficiency and output-based efficiency.
x
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due to underproduction. Thus, o u t p u t scale efficiency is calculated by the ratio HC/HI. To examine the existence of scale economies, we partition the set of all observations into six regions. 6 We do so because input-based and outputbased measures m a y possibly give different predictions concerning returns to scale. To understand this, consider Fig. 2 where the line segment BIB 2 is the IRS frontier and the line segment B3B * is the D R S frontier. Consider first the I D region where I D represents IRS for input-based efficiency and D R S for
, B4
DD
231 (53.1%)
r
CD
CC
0 (0%)
IC 0 (0%)
ID 45 (10.3%)
B2
0
x Fig. 2. Regions regarding returns to scale.
6This kind of partition is presented in F~ire et al. (1994, p. 122) without empirical applications.
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output-based efficiency. Here, input-based measures predict IRS since inputbased efficiency is calculated horizontally, whereas DRS is predicted by output-based efficiency measures since it computes vertical distances. Clearly the two types of measures provide inconsistent information on returns to scale. Similarly, we observe inconsistent implications in the IC region associated with IRS for input-based measures and CRS for output-based measures and the CD region related to CRS for input-based measures and DRS for outputbased measures. In contrast, the remaining three regions (the II, DD, CC regions) give consistent results in that input-based efficiency and output-based efficiency predict the same conclusion about returns to scale. This observation indicates that both input-based efficiency and output-based efficiency are fundamentally different, although they are a valid representation of returns to scale. Taking this fact into account, we have categorized all the observations into the six regions and present empirical results. Here it should be noted that this categorization can be generalized to a multiple input-multiple output case. To determine the nature of returns to scale, replace the restriction EJ= ~zj = 1 in (1) with E j= J ~zj ~< 1 and define the nonincreasing returns to scale (NIRS) reference technology as J
~A(z)= {ix, y): Y.z >~y,X.z<.x, ~ zj~ 1, z ~ + } . j=l
~13)
Similar to PPS and PPS*, the production possibility set satisfying NIRS can be obtained as PPS A = {(x,y): 3z~ ~s+ such that (x,y)e (A(z)}.
(14)
Therefore, the corresponding input-based and output-based technical efficiency measures are denoted as ITE A = minimize {2: (2x, y) e pPSA},
(15)
2,z
OTE A = maximize {0: (x, Oy)~ pPSA}.
(16)
O,z
Regarding the relationship among the efficiency measures, we have 1 ~>ITE >t ITE A >~ ITE*, 1 ~
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4. Production of credit associations and data sources T h e m o d e l follows b a n k i n g studies r e g a r d i n g the choice of inputs a n d outputs, since a credit a s s o c i a t i o n b e h a v e s like an o r d i n a r y b a n k as m o r e a n d m o r e d e p o s i t s c o m e from n o n m e m b e r s . In the b a n k i n g literature, there are m a i n l y two a p p r o a c h e s called the i n t e r m e d i a t i o n a p p r o a c h a n d the p r o d u c t i o n a p p r o a c h . T h e first a p p r o a c h r e g a r d s a b a n k as an i n t e r m e d i a r y of financial services a n d the latter considers it as a p r o d u c e r of l o a n a n d d e p o s i t a c c o u n t services. D u e to d a t a availability as well as the c o n s i d e r a t i o n of recent e m p i r ical studies in J a p a n e s e b a n k i n g , 7 we e m p l o y a version of the first a p p r o a c h , i.e., we c o n s i d e r a credit a s s o c i a t i o n as a financial i n t e r m e d i a r y that e m p l o y s l a b o r (X1) , capital (X2) a n d d e p o s i t s (x3) to p r o d u c e l o a n (Yl) a n d securities (Y2) outputs. Here, o u t p u t s are m e a s u r e d in values in billions of yen at the end of fiscal y e a r 1992. Thus, the o u t p u t specification in this s t u d y is b a s e d on stock measures. 8 W e d o so by following H u m p h r e y (1992) s h o w i n g the stock m e a s u r e s to be r o b u s t a n d their use c a p t u r e s the a m o u n t of business activities a credit a s s o c i a t i o n carries from p e r i o d to period. x 1 is the n u m b e r of full-time employees a n d x 2 is the balance sheet capital items p u r c h a s e d by the b a n k or acquired by means of a capital lease; i.e., x 2 is premises a n d real estate, x 3 is the reserve funds which comprise the vast m a j o r ity of liabilities, including current a n d o r d i n a r y deposits, time deposits, instalment savings and others. The reason that we identify two o u t p u t s (Yl and Y2) is that a credit association is viewed as a firm to p r o d u c e two o u t p u t s (the loan o u t p u t a n d the security investment output) from the three inputs, yl, Y2, x2 and x 3 also represent b o o k values in billions of yen at the end 9 of fiscal year 1992. T h e d a t a sources 1° are the Analysis of Financial Statements of All Credit Associations d o c u m e n t e d b y K i n - y u t o s h o K o n s a r u t a n t o ( F i n a n c i a l L i b r a r y C o n s u l t a n t ) for the 1992 fiscal y e a r e n d i n g 31 M a y 1993, as well as the 1993
Yearbook of Credit Associations. T a b l e 2 d i s p l a y s the s u m m a r y statistics of the s a m p l e including the means, s t a n d a r d d e v i a t i o n s (SD) a n d e x t r e m e values on inputs, o u t p u t s a n d the asset
7When a bank is regarded as the firm producing a single output within a framework adopting the intermediation approach, deposits may be treated as an intermediate product and loans may be used as the final output (Noma and Tsutsui, 1987). However, quite often a bank has been modeled as a multiple output intermediary in recent banking efficiency literature. 8When an econometric nonfrontier approach uses the average loan and securities data of both the beginning and the end of periods, outputs are thought of as flows. 9japan's fiscal (accounting) year starts from 1 April and ends on 31 March. 1°The data used in this study are not the official documents which are prepared by the Federation of Credit Associations in Japan and are sent to the Ministry of Finance. Yet, the official data are not publicly available and Kin-yutosho Consultant reports the balances and the change of the figures every year and thus we may be able to correct possible typos to some extent. Thus, the use of this data set may not be unreasonable.
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Table 2 Descriptive statistics of input and output variables Variable
No.
Mean
SD
Min
Max
xI x2 x3 Yl Y2
435 435 435 435 435 435
364.526 3.566 201.041 148.633 28.412 233.373
387.758 5.130 276.399 211.476 35.640 314.402
20.000 0.090 5.355 4.561 0.590 6.806
2990.000 40.110 2546.217 1608.612 301.859 2780.861
Asset
Note: (billions of yen). Our sample comprises all active credit associations operating in 1992.
size variable. Our sample consists of all 435 active credit associations operating in Japan.
5. Empirical results Table 3 provides descriptive statistics for various technical and scale efficiency scores based both on the VRS and the CRS technology. For the purpose of making direct comparisons of input-based and output-based efficiency measures, we report the inverses of output-based efficiency measures since output-based efficiency scores are greater than or equal to one while inputbased efficiency scores are no greater than one and, as have been noted earlier, the overall output technical efficiency measure can be computed as the reciprocal of the overall input technical efficiency measure. Thus we will use ,the term "overall technical efficiency" to signify both overall input technical efficiency and overall output technical efficiency. In addition, we refer to the simultaneity of pure input and pure output technical efficiency simply as "pure technical efficiency". It should be noted that the pure input technical efficiency measure is generally not equal to the reciprocal of the pure output technical efficiency measure unlike the case of overall technical efficiency.
Table 3 Summary statistics of efficiency scores Variable
No.
Mean
SD
Min
Max
I T E * = 1/OTE* 1TE ISE 1/OTE 1/OSE
435 435 435 435 435
0.82203 0.83921 0.98053 0.83927 0.98043
0.09130 0.09531 0.03645 0.09623 0.03194
0.55305 0.56192 0.70348 0.56764 0.76086
1.00000 1.00000 1.00000 1.00000 1.00000
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To proceed we turn to the identification of sources of overall technical inefficiency. With respect to input and output orientation, Table 3 shows that scale inefficiency is much less significant than pure technical inefficiency according to minimum values and arithmetic means. Table 4 also indicates that overall input technical inefficiency is primarily due to pure input technical inefficiency and pure output technical inefficiency is predominantly the source of overall output technical inefficiency. Here, we identified major sources by comparing the values of pure technical efficiency and scale efficiency for each credit association. In Fukuyama (1993), pure input technical inefficiency was reported to be the major source of overall technical inefficiency. In this respect, credit associations and commercial banks have similar productive efficiency structure-overall technical inefficiency is primarily due to mismanagement of resource usage (error on the part of management). Now we turn to Table 5 to examine the nature of returns to scale. According to input-based measures, the majority of credit associations (53.1%) exhibit DRS, while credit associations with IRS are 191 (43.9%). With respect to output-based measures, as much as 63.4% shows DRS. This may appear to indicate that over a half of credit associations exhibit DRS but it may be too hasty to conclude that the whole industry is primarily associated with DRS input-based measures and output-based measures may give different predictions on returns to scale, as explained at the end of Section 3. Therefore, we investigate returns to scale more closely by categorizing the observations into six classes (the II, DD, CC, ID, IC and CD regions).
Table 4 Sources of overall technical inefficiency with respect to the whole sample Major source of overall input technical inefficiency
Major source of overall output technical inefficiency
No.
Scale Inef.
Tech. lnef.
Scale Inef.
Tech. lnef.
435
40(9.5%)
382(90.5%)
40(9.5%1
382(90.5%)
Note: Tech.: Technical. Inef.: Inefficiency.
Table 5 Returns to scale with respect to input-based and output-based measures
IRS DRS CRS Pooled
Input-based
Output-based
191 (43.9%) 231 (53.1%) 13 (3.0%) 435
146(33.6%) 276 (63.4% } 13 (3./)%) 435
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Evidence of Table 6 as well as Fig. 2 indicate that 10.3% belongs to the inconsistent regions consisting of the ID, IC and C D regions (though there are no credit associations falling in the IC and C D regions). Yet, as much as 90% belongs to the consistent regions comprising the II, D D and CC regions. Therefore, the result on consistent regions seems to explain well the efficiency structure of credit associations in Japan. 53.1% of credit associations (231 out of 435) exhibits DRS (see the D D region in Table 6). This is somewhat consistent with the result of Nishikawa's (1973) pioneering paper indicating DRS on the average within a single output framework. With more recent data sets, the econometric nonfrontier results obtained by M i y a m u r a (1992) and Miyakoshi (1993) contrast well with ours. By splitting the credit associations into two on the basis of the location (urban vs. rural) of the headquarters, Miyamura indicated IRS at the credit association level for the 1990 sample but not for the 1985 sample. Miyakoshi's study, on average, indicates IRS for the 1990 sample of 123 credit associations locating at eastern Japan. Reasons why our results differ from theirs are probably that our estimation technique is quite different and, more importantly, that ours m a y be influenced by the collapse of the bubble economy. The commercial banking result of F u k u y a m a 11 (1993) is more dramatically different-his finding was that the vast majority (stock commercial banks are much larger in size than credit associations and have much more branches) exhibited IRS. Along with this evidence and the existence of large city banks having exhausting scale economies and now operating at constant returns to
Table 6 Sources of overall technical inefficiencywith respect to regions of returns to scale Major source of overall input technical inefficiency
Major source of overall output technical inefficiency
Scale Inef.
Pure Tech. Inef.
Scale lnef.
Pure Tech. Inef.
337 135(92.5%) 202(87.5%)
40 8(5.5%) 32(13.8%)
337 138(94.5%) 199(87.5%)
45 45(100%) 0(0.0%)
0 0(0.0%)
45 45(100%)
Regions
No.
Consistent II DD CC
390 40 146(33.6%) 11(7.5%) 231(53.1%) 29(12.5%) 13(3.0%)
Inconsistent 45 0 ID 45(10.3%) 0(0.0%) If 0(0.0%) 0(0.0%) CD 0(0.0%) --
--
--
--
0(0.0%)
0(0.0%)
Note: Tech.: Technical. Inef.:Inefficiency.
11Recall that Fukuyama (1993) used only input-based measures to investigatescale economies.
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scale, most of the commercial banks (except for city banks lz) can gain scale merits through mergers. In contrast, a majority of credit associations may not be able to gain scale merits by doing so. As has been mentioned previously, scale efficiency is not the only thing needed to be considered. Our overall technical efficiency benchmark consists of scale efficiency and pure technical efficiency with respect to both input and output orientation, and our analysis indicates that pure technical efficiency has more dominant effects than scale efficiency in the credit association industry. To further analyze merger benefits, therefore, we apply Spearman's rank correlation coefficient between each efficiency measure and the asset size with respect to the pooled sample as well as the II and the DD region. We focus on results related to consistent regions, 13 since our conjecture is that credit associations operating at a scale of decreasing returns may behave differently from those with increasing returns. So, consider Table 7. Pairwise relationships among various types of efficiency and asset size are summarized by the triplets ( + , +, +), ( + , - , +), (+,0, - ) , etc., where the first entry, the second and the last are related to the II region, the DD region and the pooled sample, respectively. At the 5% level, the plus sign ( + ) and the minus sign ( - ) indicate a positive significant and a negative significant relationship, respectively. In addition, zero (0) indicates statistical insignificance. In any consistent region and for the pooled sample, pure input technical efficiency and pure output technical efficiency are positively significantly related, and so are two types of scale efficiencies-these results are indicated by Table 7 Results on Spearman's rank correlation coefficient
1TE* = I/OTE* ITE I/OTE ISE
1/OSE
ITE
I/OTE
(+,+,+)
{+,+, (+,+,
+) +)
ISE
1/OSE
Asset
+,-,+) IO,-,-)
(+0,0)
(0,-,-)
(0, + , +} (0, + , + ) (0, + , +) (+,-,0) (+, ,
(+.-,
)
(0,-,0) ( - , + , +)
)
Note:(+J positive and significant relationship; ( - ) negative and significant relationship: (0) statistical insignificance. The first entry in the bracket is for the 11 region; the second entry is for the DD region; the last entry is for the pooled sample. Statistical tests are conducted at the 5°/,, level of significance.
~21n case of city banks, we cannot provide the prediction of merger benefits due to a lack of comparable large sized banks. laThe CC region is not of particular interest here and thus we concentrate on the II region and the DD region.
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( + , +, +). Yet, the results on relationships between pure technical efficiency and scale efficiency are somewhat mixed. They are negatively associated in the DD region. By contrast, 1/OTE and 1SE are positively associated and, except for this, pure technical efficiency is not significantly related to any type of scale efficiency in the II region. Overall technical efficiency has a positive association with pure technical efficiency, irrespective of whether a credit association operates at the scale of increasing or decreasing returns. With scale efficiency, overall technical efficiency does not have a positive association except for the II region. The table also indicates that the asset size is positively associated with pure technical efficiency and overall technical efficiency in the DD region, while it is not significantly associated in the II region. Regarding the relationship of assets with (input and output) scale efficiency, we have somewhat an obvious result. The positive sign for ISE as well as 1/OSE and assets in the II region is that as a credit association operating at the scale of increasing returns becomes larger, it becomes closer to the minimum efficient scale operation. In case of the DD region, the negative sign indicates that the smaller a credit association becomes, the closer it will be to the minimum efficient scale operation. This result appears to imply that assets may be a good indicator of size of credit associations. What Spearman's rank correlation coefficient analysis above indicates is as follows: In the II region, asset size and scale efficiency has a positive relationship but the association between asset size and (pure and overall) technical efficiency is not significant, implying that greater pure technical inefficiency offsets scale merits through mergers. In the DD region, asset size and scale efficiency have a negative association but asset size and (pure and overall) technical efficiency have a positive association, implying that scale demerits through mergers are offset by an improvement in pure technical efficiency. This result is in sharp contrast with Japan's commercial banking evidence obtained by Fukuyama (1993). Spearman's correlation coefficient analysis of his showed that overall technical efficiency was essentially unaffected by asset size, implying mergers in commercial banking industry are not necessarily desired from the viewpoint of society, even though there existed some scale merits.
6. Summary and conclusions Using 1992 data, the present study has analyzed scale and technical efficiency to shed some light on the productive efficiency performance of credit associations in Japan. Empirical evidence with respect to the whole sample was that: (1) there were considerable efficiency variations across credit
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associations; (2) the major factor contributing to overall technical inefficiency is primarily pure technical inefficiency, not scale inefficiency; and (3) both pure and overall technical efficiency improves as asset size increases. To evaluate the productive efficiency performance further, we classified the sample credit associations into six groups (the II, DD. CC, ID, IC and CD regions) on the basis of the input-based and output-based predictions on returns to scale. The evidence indicates that input-based and output-based measures are predicted consistently: the credit association industry is mainly subject to decreasing returns to scale, though there were more than 30% of credit associations operated with increasing returns. Evidence of the II, DD, ID regions and the sample as a whole indicates that overall technical inefficiency was predominantly due to pure (input and output} technical inefficiency. According to Spearman's rank correlation coefficient analysis, improvements in overall technical efficiency was significantly associated with improvements in pure technical efficiency, irrespective of the regions on returns to scale. In addition, better performances in pure technical efficiency were associated with larger asset size in the DD region. It follows that merger activities of credit associations in the DD region were socially desired. But merger activities of credit associations in the II region cannot be explained by the pure and overall technical efficiency factors. Put in another way, from a societal perspective, mergers may be desirable for credit associations in the DD regions since they will reduce pure technical efficiency and hence overall technical inefficiency as the credit associations in the region become larger; yet, merger activities in the small size class (the II region) are not necessarily desired. The Ministry of Finance along with the Japanese government appears to have recently made use of administrative guidance to promote merger activities to improve the financial positions of financial institutions. Our empirical evidence indicated that mergers of large credit associations (those in the DD region) may be justified socially. However, horizontal (in-market) merger benefits are socially minimal for credit associations in the II region. Similarly, mergers between commercial banks appear to enhance scale efficiency but do not improve overall technical efficiency since resource utilization deteriorates as the size of a commercial bank increases (Fukuyama, 1993). Therefore, a policy implication is that the conversion of credit associations to commercial banks and/or mergers between a credit association and a commercial bank may be desired, if policy makers implement the incentive system in which larger commercial bank managers are able to further improve pure technical efficiency (efficiency on the part of management). However, it should be noted that this policy implication is given on the basis of productive efficiency computed from nonparametric frontier techniques and thus further research is needed to provide final policy recommendations.
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Acknowledgements I a m grateful to P r o f e s s o r R o l f F/ire for his v a l u a b l e c o m m e n t s . T h e a n o n y m ous referee c o m m e n t s h e l p e d s h a r p e n the focus of the paper. H o w e v e r , they b e a r n o r e s p o n s i b i l i t y for a n y r e m a i n i n g errors.
References Berg, S. A., F. R. Fersund and E. S. Jansen, 1992, Malmquist indices of productivity growth during the deregulation of Norwegian banking 1980-1989, The Scandinavian Journal of Economics 94 (Suppl.), 211 228. Cebenoyan, A. S., E. S. Cooperman and C. A. Register, 1993, The relative efficiency of stock versus mutual S&Ls: A stochastic cost frontier approach, Journal of Financial Services Research 7, 151-170. Charnes, A., W. W. Cooper and E. Rhodes, 1978, Measuring the efficiency of decision making units, European Journal of Operational Research 2, 429 444. Drake, L. and T. G. Weyman-Jones, 1992, Technical and scale efficiency in UK building societies, Applied Financial Economics 2, 1 9. Elyasiani, E. and S. M. Mehdian, 1990, Efficiency in the commercial banking industry: A production frontier approach, Applied Economics 22, 539 551. Fare, R., S. Grosskopf and C. A. K. Lovell, 1985, The measurement of efficiency of production (Kluwer Nijhoff, Boston). Fare, R., S. Grosskopf and C.A.K. Lovell, 1994, Production frontiers (Cambridge University Press, New York). Farrell, M.J., 1957, The measurement of productive efficiency, Journal of the Royal Statistical Society, Series A, General, 120, 253 281. Fried, H. O., C. A. K. Lovell and P.V. Eeckaut, 1993, Evaluating the performance of US credit unions, Journal of Banking and Finance 17, 251 265. Fukuyama, H., 1993, Technical and scale efficiency of Japanese commercial banks: A nonparametric approach, Applied Economics 25, 1101-1112. Goldstein, S., J. McNulty and J. Verbrugge, 1987, Scale economies in the savings and loan industry before diversification, Journal of Economics and Business 39, 199 207. Hirota, S. and Y. Tsutsui, 1991, Ginkogyo niokeru Han-i no Keizai (Scope economies in banking), in: Akiyoshi Horiuchi and Naoyuki Yoshino, eds., Structural analyses of the Japanese financial system (University of Tokyo Press, Tokyo) (in Japanese). Humphrey, D. B., 1992, Flow versus stock indicators of banking output: Effects on productivity and scale economy measurement, Journal of Financial Services Research 6, 115 135. Kasuya, M., 1989, Empirical analysis of cost structure in banking: Efficiency, technical change, factor substitution and organizational status, Kin-yu Kenkyu 8, 79 118. Mester, L.J., 1987, Efficient production of financial services: Scale and scope economies, Business Review of Federal Reserve Bank of Philadelphia 73, 15 23. Miyakoshi, T., 1993, Shinyokinko ni okeru Han-i no Keizai (Scope economies of credit associations), Keizai Kenkyu 44 (3), 233-242 (in Japanese). Miyamura, K., 1992, Shinyokinko no Hiyo to Kibo no Keizaisei (Costs and scope economies of Shinkin banks), Keiei Ronshu (Toyo University, Tokyo) 38, 63-83 (in Japanese). Murray, J. D. and R. W. White, 1983, Economies of scale and economies of scope in multiproduct financial institutions: A study of British Columbia credit unions, The Journal of Finance 38, 887 902.
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Nishikawa, S., 1973, Ginko: Kyoso to sono Kisei (Banks: Competition and its Regulations). In: H. Kumagai, ed., Nihon no Sangyo Soshiki I (Japanese industrial organization 1), (Chuo-Koronsha, Tokyo) tin Japanese). Noma, T. and Y. Tsutsui, 1987, Economic Review 38, 251-262, Wagakuni Ginkogyo niokeru Kibono Keizaisei to sono Gensen (Economies of scale and its Causes in Japanese banking), (in Japanese). Rangan, N., R. Grabowski, H. Y. Aly and C. Pasurka, 1988, The technical efficiency of US banks, Economics Letters 28, 169-175. Suzuki, Y., 1987, The Japanese financial system (Oxford University Press, New York). Tatewaki, K., 1991, Banking and finance in Japan: An introduction to the Tokyo market (Routledge & Kegan Paul, London).
Japan and the World Economy 8 11996) 259 277
Returns to scale and efficiency of credit associations in Japan: A nonparametric frontier approach Hirofumi Fukuyama* Faculty of Commerce, Fukuoka University, Nanakuma, .lonan-ku, Fukuoka 814-01, Japan Received April 1994: accepted April 1995
Abstract
We investigate the nature and extent of technical as well as scale efficiency by applying a nonparametric frontier approach to Japanese credit association (shinkin bank) data for fiscal year 1992. The main motivation of this study is the fact that there have been few significant frontier studies on the credit association industry, particularly in the aftermath of the collapse of the bubble economy in 1990. This study uncovers, among other things, the major causes of overall technical inefficiency and the relationships between size and various types of efficiency in terms of returns to scale regions.
Keywords: Nonparametric frontier approach; Technical efficiency; Returns to scale: Japanese credit associations J E L class![ication: D2; G21
1. Introduction
The e c o n o m i c landscape surrounding the Japanese banking industry dramatically changed in the aftermath of the collapse of the so-called bubble economy. The e c o n o m y enjoyed a b o o m during the last half of the 1980s
*Tel.: +81-92-863-5233 (ext. 4402): fax: +81-92-864-2938: e-mail: fukuyama/ajsat.fukuokau.ac.jp. 1234-5678/96/'$15.00 Copyright SSDI 0 9 2 2 - 1 4 2 5 ( 9 6 ) 0 0 0 4 1 - 0
1996 Elsevier Science B.V. All rights reserved
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H. Fukuyama / Japan and the World Economy 8 (1996) 259-277
fostered by easy financial policies on the part of the monetary authorities (e.g., the Bank of Japan maintained the official interest rate as low as 2.5% from the beginning of 1987 until the middle of 1989). After experiencing this vigorous boom, the economy underwent a sudden financial bust in 1990-land and stock prices plunged. Also as a consequence, financial institutions have been suffering from a substantial increase in nonperforming loans due to borrowers' inability to pay interest on loans. The dramatic economic change, along with accelerating financial innovations and rapidly improving communications, might have had considerable effects on the productive (scale and technical) efficiency structure of credit associations (shinkin banks) and these potential effects need to be examined. Being structured on a membership basis, credit associations are small financial institutions, of which not only operations are restricted in principle to a certain geographical area, but also financing is focused on small and mediumsized firms. Commercial banks are stock financial institutions with a national focus and in general a majority of them are much larger than credit associations. The membership basis, the focus on regional finance and the finance of small- and medium-sized local firms are the features which distinguish credit associations from commercial banks. The purpose of this paper is to offer empirical evidence on productive efficiency of Japanese credit associations within a nonparametric frontier framework. To model behavior of banks, a frontier approach allowing for productive inefficiency has been often employed in non Japanese banking studies such as Rangan et al. (1987), Elyasiani and Mehdian (1990), Berg et al. (1991), Drake and Weyman-Jones (1992) and Fried et al. (1993), all of which showed significant productive efficiency variations across banks. In the frontier literature there are mainly three commonly used approaches. The first is an econometric frontier approach and the second is a deterministic frontier approach, both of which utilize parametric production and/or cost functions. The last is a nonparametric frontier approach which has gained popularity in banking analyses. The present study employs the last approach, since it has some advantages over the first two frontier approaches. First, it does not require a priori functional specification on unknown technology. Secondly, it provides meaningful firm-level efficiency scores within a multiple output framework without reference to input prices and costs, in contrast to the parametric cost function estimation. Lastly, it can easily estimate scale inefficiency quantitatively and provide the source of the scale inefficiency. Nonetheless, it is not without drawbacks, the most important of which is that statistical noise or measurement error is assumed to be negligible. In Japanese banking, there are commercial banking studies such as Tsutsui (1986), Kasuya (1989) and Fukuyama (1993) within a frontier framework but there are few significant frontier studies on credit associations. Regarding estimation methodologies, the first two employed econometric techniques with
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a single output, while the last used a nonparametric frontier technique. As to credit association studies, there are nonfrontier analyses examining scale and scope economies 1 (see Nishikawa, 1973; Hirota and Tsutsui, 1992; Miyamura, 1992; Miyakoshi, 1993, which used parametric functions). These studies are based on data for years before 1990, except for Miyamura who employed both the 1985 and 1990 samples. Their scale estimates indicated mixed results: whereas the sample results of Hirota and Tsutsui (1987) and Miyamura (1985) showed significant scale economies, Nishikawa's (1968) and Miyakoshi's (19851 samples did not show scale economies. Among the studies mentioned the most recent data set used is Miyakoshi's (!990) sample, but 1990 was the year when the sudden collapse of the bubble economy occurred and the significant change due to prolonged economic slowdown have occurred since then. In view of the fact that data sets before 1991 may not represent the current economic c o n d i t i o n s - t h e years 1991 and 1992 suffered further economic slowdown or recession and the fact that the previous studies on this industry did not allow for technical inefficiency, they are not a very useful guide to understand the current credit association industry in the period of the economic slowdown. Since, employing the 1990 sample, the commercial banking study of Fukuyama (1993) focused on the determination of overall (input) technical inefficiency (which is decomposed into scale efficiency and pure (inputt technical efficiency) and the nature of returns to scale as well as the relationship between size and efficiency, the present paper proceeds by comparing our result with Fukuyama's for the purpose of facilitating the comparisons between credit associations and commercial banks. Overall technical inefficiency is the result of the operations off the isoquant constructed relative to the constant returns to scale technology, while pure technical inefficiency stems from the operations off the isoquant constructed relative to the variable returns to scale technology. Scale inefficiency occurs when there is either increasing or decreasing returns to scale and the operation at constant returns to scale corresponds to scale efficiency. The notion of scale efficiency implies that the output level with constant returns to scale represents the optimal output level from society's perspective since constant returns to scale is related to zero profit long-run competitive equilibrium. Yet, the operation at increasing or decreasing returns to scale may be optimal on the part of firm managers (i.e., in the private sense). In other words, overall technical efficiency refers to the efficiency associated with socially desired situations, whereas pure technical efficiency refers to the efficiency related to a credit association's private optimization behavior. The relationship among the three 1Scale and scope economies of thrifts in North America are studied by Murray and White (1983), Goldstein et al. (1987), Mester (1987), and Cebenoyan et ~d. (19931, whereas technical efficiency was investigated by Fried et al. (1993).
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types of efficiencies can be established as the overall technical efficiency decomposition into scale and pure technical efficiency and the decomposition can be used to identify major causes of overall technical inefficiency. In case of the commercial banking study of Fukuyama (1993), scale inefficiency was dominated by pure technical inefficiency. In the past, the credit association industry has witnessed quite a few merger activities which led to the steady reduction in number of firms (from 520 in May 1968 to 455 in March 1989 and 435 in March 1993). The mergers can be carried out with the intention of enhancing pure technical efficiency on the part of credit association managers. If so, large credit associations should be more pure(ly) technically efficient. According to Fukuyama's (1993) commercial banking evidence with respect to Spearman's rank correlation analysis, this is not the case. Both pure and overall technical efficiency were not significantly associated with asset size but scale efficiency was. In commercial banking, asset size does not explain pure and overall technical efficiency variations, but in contrast a positive asset size association with scale efficiency was evident from the result of the vast majority showing increasing returns to scale. It is of great interest to know whether or not similar evidence can be found in the case of credit associations. The remainder of the paper is organized as follows. Section 2 provides some information on credit associations, while Section 3 presents both input-based and output-based measures of efficiency. We examine both input and output sides of efficiency measurement because they may provide different implications output-based efficiency and input-based efficiency are fundamentally different concepts. In addition to the general estimation framework, we provide a methodology classifying the observations into six groups based on returns to scale, since predictions regarding returns to scale can be contradictory (though nothing wrong theoretically) once the operations off the frontier are allowed. This section also explains how to determine the nature of returns to scale. The data source and the input/output specifications are reported in Section 4 and empirical findings are provided in Section 5. A summary and conclusions are given in Section 6.
2. Banking system and credit associations The Japanese private banking system has developed along the lines of segmentation and specialization and thus there are various financial institutional forms. They may be divided into four categories: (1) commercial banks, (2) long-term financial institutions, (3) financial institutions for agriculture, etc. and (4) financial institutions for small businesses. Usually, commercial banks focusing on short-term finance are subdivided into three forms: city, regional
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and former sogo banks. 2 The second type of financial institutions focusing on long-term finance are long-term credit banks and trust banks. The third type of financial institutions are members of the Norinchukin bank, which is the central institution for cooperatives serving the agricultural, forestry and fishery industries. The last type of financial institutions, to which credit associations belong, include labor credit associations, 3 credit cooperatives and the Shokochukin bank. As stated in Section 1, credit associations, organized on a membership basis, are not stock companies. Regarding the origin of the credit associations, they were previously credit cooperatives created in the last century and were allowed to gain the present status under the Law for Small Business Cooperatives of 1949 and these credit cooperatives became the present credit associations by the Credit Associations Law of 1951. This conversion was necessitated by two conflicting characteristics. 4 The first characteristic is that the credit cooperatives were expected to mainly provide services to medium and small local firms and the general public in the region. The second characteristic is the cooperative nature of credit cooperatives, that is, serving members only. Zenshinren (which remodeled the National Federation of Credit Cooperatives) was established under the Credit Association Law as the central bank for the credit associations. Zenshinren not only accepts savings from member credit associations and provides loans to member associations, but also engages in foreign exchange operations for the member credit associations. In addition, it accepts deposits from the government, municipalities, public corporations, and nonprofit organizations. The establishment of Zenshinren has led to the smoothing of regional and seasonal funds, efficient investment of funds, concentrated settlement of foreign exchange, payment intermediation and mutual aid systems. Thus Zenshinren provides a safety mechanism and effective financing for credit associations. 5 Data of Table 1 indicate that total loans and assets of credit associations are greater than not only those of long-term financial institutions but also former sogo banks. In addition, credit associations are much more important financial intermediaries than credit cooperatives, while the total loans and assets of the credit associations are over twice as large as those of regional banks and roughly 30% of those of city banks. This fact, along with the status as the regional financial institutions for small and medium firms, means that credit associations play a very important role in the economy. 2Sogo banks were previously mutual banks but were converted int,~ ordinary banks. Therefore, we treat them as commercial banks. 3The central organization for credit cooperatives are the National Federation of Credit Cooperatives. The function of the Federation is similar to that of Zenshinren. '*See Shinyo Kinko Yon-jusshunen Shi (40 }~,ar History of Credit As,sociations} (p.105) written by the Federation of Credit Associations. SF'or more details, see Suzuki (1987) and Tatewaki [19911.
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Table 1 Relative size of financial institutions No.
City banks 11 Regional banks 64 Former sogo banks 68 Trust banks 7 Long-term credit banks 3 Credit associations 435 Credit cooperatives 393
Loans and discounts outstanding (banking accouns)
Savings
Assets (banking accounts)
2236217 1 255 804 508 878 245 275 472 030 650 478 183 108
1840529 1 550 577 583 532 88 072 53 369 882 085 229 195
3388113 1 873 150 701 437 530 549 786 381 1027 763 na
Note: (100 millions of yen; fiscal 1992). na: not available. Source: Economic Statistics Monthly published by Bank of Japan.
3. Input-based and output-based efficiency This paper utilizes nonparametric frontier (linear programming) models which originate from Farrell (1957) and have been extended and popularized by Charnes et al. (1978) and Ffire et al. (1985). To initiate the analysis, let y be a column vector of G outputs and let x be a column vector of N inputs. Regarding observations, let Y be the (G × J) matrix of outputs for each of J firms and let X be the (N x J) matrix of inputs for each of J firms. Now define a set J
~(z)= {Ix, y): V.z>.y,X.z<~x, y~ zj-- 1 , z ~ + } ,
tl)
j=l
where z with the restriction (ZJ=lz ~ = 1) is a vector of variables forming convex hulls of observations and the set is referred to as the variable returns to scale (VRS) reference technology. Relative to ~(z), the production possibility set (PPS) satisfying VRS can be denoted as PPS = {(x,y): 3z~[~s+ such that
(x,y)~(z)},
(2)
which is a convex set. By dropping the restriction (Zs= l zj--= 1), the following set referred to as the CRS reference technology
~*(z) = {(x, y): v- z/> y, x . z -<. x~ ze ~ }
(3)
is a cone and thus (3) satisfies constant returns to scale (CRS). Similar to PPS in (2), the production possibility set satisfying CRS can be obtained as P P S * = {(x,y): 3ze[~J+ such that
(x, y)e (*(z) }.
(4)
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Relative to the VRS reference technology (1), the pure (VRS) input technical efficiency measure can be obtained as ITE = minimize {2: (2x, y) ~ if(z)},
(5)
which computes the input saving while keeping the output level fixed. Similarly, the overall (CRS) input technical efficiency measure can be computed as ITE* = minimize {2: (2x, y)~ ~*(z)},
(6t
which computes the degree of the input saving when a benchmark is the CRS technology (3). The significance of CRS is that operations at a scale of constant returns is associated with the long-run competitive equilibrium, being the optimal level of operations from a societal point of view. Therefore, deviations from the long-run competitive equilibrium are thought of as scale inefficiency. Using two technical efficiency measures (ITE and ITE*), input scale efficiency can be computed as the ratio of the linear programming problems with and without CRS imposed ISE = ITE*/ITE,
(7)
which is called the input scale efficiency measure. If each of the input-based efficiency measures (ITE, ITE* and ISE) is less than one, then a firm is inefficient; the firm is efficient if it is unity. Owing to (7), overall input technical efficiency can be written as a multiplicative composite of input scale efficiency and pure input technical efficiency ITE* = ISE. ITE.
(8)
Similar to input-based efficiency, there are efficiency measures on the output side. They are the pure (VRS) output technical efficiency measure OTE = maximize {0: (x, Oy) e ~(z) },
(9)
O.z
and the overall (CRS) output technical efficiency measure OTE* = maximize {0: (x, 0y)~ ~'*(z)}.
(10)
O,z
Using (9) and (10), the output scale efficiency measure can be computed as OSE = OTE*/OTE.
(11)
In contrast to input-based efficiency, output-based efficiency indicates a firm's inefficiency if the value is greater than one. If the value is one, then the firm is efficient. To determine causes of overall output technical inefficiency, we write (11) as OTE* = OSE" OTE,
(12)
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which states that the overall output technical efficiency measure is a multiplicative composite of two efficiency measures (output scale efficiency and pure output technical efficiency). To illustrate each efficiency measure, consider Fig. 1, which is a simple one input one output situation. Here, A1-A 4 are observed firms and the VRS and the CRS frontier are AIAzA 3 and the ray 0D, respectively. For firm A4, pure input technical efficiency and overall input technical efficiency are EG/EA 4 and EB/EA 4, respectively, since input-based efficiency is defined as the proportional reduction in input quantities. Thus input scale efficiency is computed by the ratio EB/EG. On the output side, pure output technical efficiency and overall output technical efficiency are calculated by HI/HA 4 and HC/HA 4, respectively, since output-based efficiency computes the degree of output loss
C/
CRS
VRS
A2
E
............
+
A4
!~AI J i I I
6
0
F
H
Fig. 1. Input-based efficiency and output-based efficiency.
x
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due to underproduction. Thus, o u t p u t scale efficiency is calculated by the ratio HC/HI. To examine the existence of scale economies, we partition the set of all observations into six regions. 6 We do so because input-based and outputbased measures m a y possibly give different predictions concerning returns to scale. To understand this, consider Fig. 2 where the line segment BIB 2 is the IRS frontier and the line segment B3B * is the D R S frontier. Consider first the I D region where I D represents IRS for input-based efficiency and D R S for
, B4
DD
231 (53.1%)
r
CD
CC
0 (0%)
IC 0 (0%)
ID 45 (10.3%)
B2
0
x Fig. 2. Regions regarding returns to scale.
6This kind of partition is presented in F~ire et al. (1994, p. 122) without empirical applications.
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output-based efficiency. Here, input-based measures predict IRS since inputbased efficiency is calculated horizontally, whereas DRS is predicted by output-based efficiency measures since it computes vertical distances. Clearly the two types of measures provide inconsistent information on returns to scale. Similarly, we observe inconsistent implications in the IC region associated with IRS for input-based measures and CRS for output-based measures and the CD region related to CRS for input-based measures and DRS for outputbased measures. In contrast, the remaining three regions (the II, DD, CC regions) give consistent results in that input-based efficiency and output-based efficiency predict the same conclusion about returns to scale. This observation indicates that both input-based efficiency and output-based efficiency are fundamentally different, although they are a valid representation of returns to scale. Taking this fact into account, we have categorized all the observations into the six regions and present empirical results. Here it should be noted that this categorization can be generalized to a multiple input-multiple output case. To determine the nature of returns to scale, replace the restriction EJ= ~zj = 1 in (1) with E j= J ~zj ~< 1 and define the nonincreasing returns to scale (NIRS) reference technology as J
~A(z)= {ix, y): Y.z >~y,X.z<.x, ~ zj~ 1, z ~ + } . j=l
~13)
Similar to PPS and PPS*, the production possibility set satisfying NIRS can be obtained as PPS A = {(x,y): 3z~ ~s+ such that (x,y)e (A(z)}.
(14)
Therefore, the corresponding input-based and output-based technical efficiency measures are denoted as ITE A = minimize {2: (2x, y) e pPSA},
(15)
2,z
OTE A = maximize {0: (x, Oy)~ pPSA}.
(16)
O,z
Regarding the relationship among the efficiency measures, we have 1 ~>ITE >t ITE A >~ ITE*, 1 ~
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4. Production of credit associations and data sources T h e m o d e l follows b a n k i n g studies r e g a r d i n g the choice of inputs a n d outputs, since a credit a s s o c i a t i o n b e h a v e s like an o r d i n a r y b a n k as m o r e a n d m o r e d e p o s i t s c o m e from n o n m e m b e r s . In the b a n k i n g literature, there are m a i n l y two a p p r o a c h e s called the i n t e r m e d i a t i o n a p p r o a c h a n d the p r o d u c t i o n a p p r o a c h . T h e first a p p r o a c h r e g a r d s a b a n k as an i n t e r m e d i a r y of financial services a n d the latter considers it as a p r o d u c e r of l o a n a n d d e p o s i t a c c o u n t services. D u e to d a t a availability as well as the c o n s i d e r a t i o n of recent e m p i r ical studies in J a p a n e s e b a n k i n g , 7 we e m p l o y a version of the first a p p r o a c h , i.e., we c o n s i d e r a credit a s s o c i a t i o n as a financial i n t e r m e d i a r y that e m p l o y s l a b o r (X1) , capital (X2) a n d d e p o s i t s (x3) to p r o d u c e l o a n (Yl) a n d securities (Y2) outputs. Here, o u t p u t s are m e a s u r e d in values in billions of yen at the end of fiscal y e a r 1992. Thus, the o u t p u t specification in this s t u d y is b a s e d on stock measures. 8 W e d o so by following H u m p h r e y (1992) s h o w i n g the stock m e a s u r e s to be r o b u s t a n d their use c a p t u r e s the a m o u n t of business activities a credit a s s o c i a t i o n carries from p e r i o d to period. x 1 is the n u m b e r of full-time employees a n d x 2 is the balance sheet capital items p u r c h a s e d by the b a n k or acquired by means of a capital lease; i.e., x 2 is premises a n d real estate, x 3 is the reserve funds which comprise the vast m a j o r ity of liabilities, including current a n d o r d i n a r y deposits, time deposits, instalment savings and others. The reason that we identify two o u t p u t s (Yl and Y2) is that a credit association is viewed as a firm to p r o d u c e two o u t p u t s (the loan o u t p u t a n d the security investment output) from the three inputs, yl, Y2, x2 and x 3 also represent b o o k values in billions of yen at the end 9 of fiscal year 1992. T h e d a t a sources 1° are the Analysis of Financial Statements of All Credit Associations d o c u m e n t e d b y K i n - y u t o s h o K o n s a r u t a n t o ( F i n a n c i a l L i b r a r y C o n s u l t a n t ) for the 1992 fiscal y e a r e n d i n g 31 M a y 1993, as well as the 1993
Yearbook of Credit Associations. T a b l e 2 d i s p l a y s the s u m m a r y statistics of the s a m p l e including the means, s t a n d a r d d e v i a t i o n s (SD) a n d e x t r e m e values on inputs, o u t p u t s a n d the asset
7When a bank is regarded as the firm producing a single output within a framework adopting the intermediation approach, deposits may be treated as an intermediate product and loans may be used as the final output (Noma and Tsutsui, 1987). However, quite often a bank has been modeled as a multiple output intermediary in recent banking efficiency literature. 8When an econometric nonfrontier approach uses the average loan and securities data of both the beginning and the end of periods, outputs are thought of as flows. 9japan's fiscal (accounting) year starts from 1 April and ends on 31 March. 1°The data used in this study are not the official documents which are prepared by the Federation of Credit Associations in Japan and are sent to the Ministry of Finance. Yet, the official data are not publicly available and Kin-yutosho Consultant reports the balances and the change of the figures every year and thus we may be able to correct possible typos to some extent. Thus, the use of this data set may not be unreasonable.
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Table 2 Descriptive statistics of input and output variables Variable
No.
Mean
SD
Min
Max
xI x2 x3 Yl Y2
435 435 435 435 435 435
364.526 3.566 201.041 148.633 28.412 233.373
387.758 5.130 276.399 211.476 35.640 314.402
20.000 0.090 5.355 4.561 0.590 6.806
2990.000 40.110 2546.217 1608.612 301.859 2780.861
Asset
Note: (billions of yen). Our sample comprises all active credit associations operating in 1992.
size variable. Our sample consists of all 435 active credit associations operating in Japan.
5. Empirical results Table 3 provides descriptive statistics for various technical and scale efficiency scores based both on the VRS and the CRS technology. For the purpose of making direct comparisons of input-based and output-based efficiency measures, we report the inverses of output-based efficiency measures since output-based efficiency scores are greater than or equal to one while inputbased efficiency scores are no greater than one and, as have been noted earlier, the overall output technical efficiency measure can be computed as the reciprocal of the overall input technical efficiency measure. Thus we will use ,the term "overall technical efficiency" to signify both overall input technical efficiency and overall output technical efficiency. In addition, we refer to the simultaneity of pure input and pure output technical efficiency simply as "pure technical efficiency". It should be noted that the pure input technical efficiency measure is generally not equal to the reciprocal of the pure output technical efficiency measure unlike the case of overall technical efficiency.
Table 3 Summary statistics of efficiency scores Variable
No.
Mean
SD
Min
Max
I T E * = 1/OTE* 1TE ISE 1/OTE 1/OSE
435 435 435 435 435
0.82203 0.83921 0.98053 0.83927 0.98043
0.09130 0.09531 0.03645 0.09623 0.03194
0.55305 0.56192 0.70348 0.56764 0.76086
1.00000 1.00000 1.00000 1.00000 1.00000
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To proceed we turn to the identification of sources of overall technical inefficiency. With respect to input and output orientation, Table 3 shows that scale inefficiency is much less significant than pure technical inefficiency according to minimum values and arithmetic means. Table 4 also indicates that overall input technical inefficiency is primarily due to pure input technical inefficiency and pure output technical inefficiency is predominantly the source of overall output technical inefficiency. Here, we identified major sources by comparing the values of pure technical efficiency and scale efficiency for each credit association. In Fukuyama (1993), pure input technical inefficiency was reported to be the major source of overall technical inefficiency. In this respect, credit associations and commercial banks have similar productive efficiency structure-overall technical inefficiency is primarily due to mismanagement of resource usage (error on the part of management). Now we turn to Table 5 to examine the nature of returns to scale. According to input-based measures, the majority of credit associations (53.1%) exhibit DRS, while credit associations with IRS are 191 (43.9%). With respect to output-based measures, as much as 63.4% shows DRS. This may appear to indicate that over a half of credit associations exhibit DRS but it may be too hasty to conclude that the whole industry is primarily associated with DRS input-based measures and output-based measures may give different predictions on returns to scale, as explained at the end of Section 3. Therefore, we investigate returns to scale more closely by categorizing the observations into six classes (the II, DD, CC, ID, IC and CD regions).
Table 4 Sources of overall technical inefficiency with respect to the whole sample Major source of overall input technical inefficiency
Major source of overall output technical inefficiency
No.
Scale Inef.
Tech. lnef.
Scale Inef.
Tech. lnef.
435
40(9.5%)
382(90.5%)
40(9.5%1
382(90.5%)
Note: Tech.: Technical. Inef.: Inefficiency.
Table 5 Returns to scale with respect to input-based and output-based measures
IRS DRS CRS Pooled
Input-based
Output-based
191 (43.9%) 231 (53.1%) 13 (3.0%) 435
146(33.6%) 276 (63.4% } 13 (3./)%) 435
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Evidence of Table 6 as well as Fig. 2 indicate that 10.3% belongs to the inconsistent regions consisting of the ID, IC and C D regions (though there are no credit associations falling in the IC and C D regions). Yet, as much as 90% belongs to the consistent regions comprising the II, D D and CC regions. Therefore, the result on consistent regions seems to explain well the efficiency structure of credit associations in Japan. 53.1% of credit associations (231 out of 435) exhibits DRS (see the D D region in Table 6). This is somewhat consistent with the result of Nishikawa's (1973) pioneering paper indicating DRS on the average within a single output framework. With more recent data sets, the econometric nonfrontier results obtained by M i y a m u r a (1992) and Miyakoshi (1993) contrast well with ours. By splitting the credit associations into two on the basis of the location (urban vs. rural) of the headquarters, Miyamura indicated IRS at the credit association level for the 1990 sample but not for the 1985 sample. Miyakoshi's study, on average, indicates IRS for the 1990 sample of 123 credit associations locating at eastern Japan. Reasons why our results differ from theirs are probably that our estimation technique is quite different and, more importantly, that ours m a y be influenced by the collapse of the bubble economy. The commercial banking result of F u k u y a m a 11 (1993) is more dramatically different-his finding was that the vast majority (stock commercial banks are much larger in size than credit associations and have much more branches) exhibited IRS. Along with this evidence and the existence of large city banks having exhausting scale economies and now operating at constant returns to
Table 6 Sources of overall technical inefficiencywith respect to regions of returns to scale Major source of overall input technical inefficiency
Major source of overall output technical inefficiency
Scale Inef.
Pure Tech. Inef.
Scale lnef.
Pure Tech. Inef.
337 135(92.5%) 202(87.5%)
40 8(5.5%) 32(13.8%)
337 138(94.5%) 199(87.5%)
45 45(100%) 0(0.0%)
0 0(0.0%)
45 45(100%)
Regions
No.
Consistent II DD CC
390 40 146(33.6%) 11(7.5%) 231(53.1%) 29(12.5%) 13(3.0%)
Inconsistent 45 0 ID 45(10.3%) 0(0.0%) If 0(0.0%) 0(0.0%) CD 0(0.0%) --
--
--
--
0(0.0%)
0(0.0%)
Note: Tech.: Technical. Inef.:Inefficiency.
11Recall that Fukuyama (1993) used only input-based measures to investigatescale economies.
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scale, most of the commercial banks (except for city banks lz) can gain scale merits through mergers. In contrast, a majority of credit associations may not be able to gain scale merits by doing so. As has been mentioned previously, scale efficiency is not the only thing needed to be considered. Our overall technical efficiency benchmark consists of scale efficiency and pure technical efficiency with respect to both input and output orientation, and our analysis indicates that pure technical efficiency has more dominant effects than scale efficiency in the credit association industry. To further analyze merger benefits, therefore, we apply Spearman's rank correlation coefficient between each efficiency measure and the asset size with respect to the pooled sample as well as the II and the DD region. We focus on results related to consistent regions, 13 since our conjecture is that credit associations operating at a scale of decreasing returns may behave differently from those with increasing returns. So, consider Table 7. Pairwise relationships among various types of efficiency and asset size are summarized by the triplets ( + , +, +), ( + , - , +), (+,0, - ) , etc., where the first entry, the second and the last are related to the II region, the DD region and the pooled sample, respectively. At the 5% level, the plus sign ( + ) and the minus sign ( - ) indicate a positive significant and a negative significant relationship, respectively. In addition, zero (0) indicates statistical insignificance. In any consistent region and for the pooled sample, pure input technical efficiency and pure output technical efficiency are positively significantly related, and so are two types of scale efficiencies-these results are indicated by Table 7 Results on Spearman's rank correlation coefficient
1TE* = I/OTE* ITE I/OTE ISE
1/OSE
ITE
I/OTE
(+,+,+)
{+,+, (+,+,
+) +)
ISE
1/OSE
Asset
+,-,+) IO,-,-)
(+0,0)
(0,-,-)
(0, + , +} (0, + , + ) (0, + , +) (+,-,0) (+, ,
(+.-,
)
(0,-,0) ( - , + , +)
)
Note:(+J positive and significant relationship; ( - ) negative and significant relationship: (0) statistical insignificance. The first entry in the bracket is for the 11 region; the second entry is for the DD region; the last entry is for the pooled sample. Statistical tests are conducted at the 5°/,, level of significance.
~21n case of city banks, we cannot provide the prediction of merger benefits due to a lack of comparable large sized banks. laThe CC region is not of particular interest here and thus we concentrate on the II region and the DD region.
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( + , +, +). Yet, the results on relationships between pure technical efficiency and scale efficiency are somewhat mixed. They are negatively associated in the DD region. By contrast, 1/OTE and 1SE are positively associated and, except for this, pure technical efficiency is not significantly related to any type of scale efficiency in the II region. Overall technical efficiency has a positive association with pure technical efficiency, irrespective of whether a credit association operates at the scale of increasing or decreasing returns. With scale efficiency, overall technical efficiency does not have a positive association except for the II region. The table also indicates that the asset size is positively associated with pure technical efficiency and overall technical efficiency in the DD region, while it is not significantly associated in the II region. Regarding the relationship of assets with (input and output) scale efficiency, we have somewhat an obvious result. The positive sign for ISE as well as 1/OSE and assets in the II region is that as a credit association operating at the scale of increasing returns becomes larger, it becomes closer to the minimum efficient scale operation. In case of the DD region, the negative sign indicates that the smaller a credit association becomes, the closer it will be to the minimum efficient scale operation. This result appears to imply that assets may be a good indicator of size of credit associations. What Spearman's rank correlation coefficient analysis above indicates is as follows: In the II region, asset size and scale efficiency has a positive relationship but the association between asset size and (pure and overall) technical efficiency is not significant, implying that greater pure technical inefficiency offsets scale merits through mergers. In the DD region, asset size and scale efficiency have a negative association but asset size and (pure and overall) technical efficiency have a positive association, implying that scale demerits through mergers are offset by an improvement in pure technical efficiency. This result is in sharp contrast with Japan's commercial banking evidence obtained by Fukuyama (1993). Spearman's correlation coefficient analysis of his showed that overall technical efficiency was essentially unaffected by asset size, implying mergers in commercial banking industry are not necessarily desired from the viewpoint of society, even though there existed some scale merits.
6. Summary and conclusions Using 1992 data, the present study has analyzed scale and technical efficiency to shed some light on the productive efficiency performance of credit associations in Japan. Empirical evidence with respect to the whole sample was that: (1) there were considerable efficiency variations across credit
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associations; (2) the major factor contributing to overall technical inefficiency is primarily pure technical inefficiency, not scale inefficiency; and (3) both pure and overall technical efficiency improves as asset size increases. To evaluate the productive efficiency performance further, we classified the sample credit associations into six groups (the II, DD. CC, ID, IC and CD regions) on the basis of the input-based and output-based predictions on returns to scale. The evidence indicates that input-based and output-based measures are predicted consistently: the credit association industry is mainly subject to decreasing returns to scale, though there were more than 30% of credit associations operated with increasing returns. Evidence of the II, DD, ID regions and the sample as a whole indicates that overall technical inefficiency was predominantly due to pure (input and output} technical inefficiency. According to Spearman's rank correlation coefficient analysis, improvements in overall technical efficiency was significantly associated with improvements in pure technical efficiency, irrespective of the regions on returns to scale. In addition, better performances in pure technical efficiency were associated with larger asset size in the DD region. It follows that merger activities of credit associations in the DD region were socially desired. But merger activities of credit associations in the II region cannot be explained by the pure and overall technical efficiency factors. Put in another way, from a societal perspective, mergers may be desirable for credit associations in the DD regions since they will reduce pure technical efficiency and hence overall technical inefficiency as the credit associations in the region become larger; yet, merger activities in the small size class (the II region) are not necessarily desired. The Ministry of Finance along with the Japanese government appears to have recently made use of administrative guidance to promote merger activities to improve the financial positions of financial institutions. Our empirical evidence indicated that mergers of large credit associations (those in the DD region) may be justified socially. However, horizontal (in-market) merger benefits are socially minimal for credit associations in the II region. Similarly, mergers between commercial banks appear to enhance scale efficiency but do not improve overall technical efficiency since resource utilization deteriorates as the size of a commercial bank increases (Fukuyama, 1993). Therefore, a policy implication is that the conversion of credit associations to commercial banks and/or mergers between a credit association and a commercial bank may be desired, if policy makers implement the incentive system in which larger commercial bank managers are able to further improve pure technical efficiency (efficiency on the part of management). However, it should be noted that this policy implication is given on the basis of productive efficiency computed from nonparametric frontier techniques and thus further research is needed to provide final policy recommendations.
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Acknowledgements I a m grateful to P r o f e s s o r R o l f F/ire for his v a l u a b l e c o m m e n t s . T h e a n o n y m ous referee c o m m e n t s h e l p e d s h a r p e n the focus of the paper. H o w e v e r , they b e a r n o r e s p o n s i b i l i t y for a n y r e m a i n i n g errors.
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