Efficiency and Productivity Growth (Modelling in the Financial Services Industry) || A dynamic network DEA model with an application to Japanese Shinkin banks

Efficiency and Productivity Growth: Modelling in the Financial Services Industry, First Edition. Edited by Fotios Pasiouras.

© 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd.

9

A dynamic network DEA model with an application to Japanese Shinkin banks

Hirofumi Fukuyama1 and William L. Weber2

1Department of Business Management, Faculty of Commerce, Fukuoka University, Japan2Department of Economics and Finance, Southeast Missouri State University, USA

9.1 Introduction

Bank managers face a dynamic network problem in their attempts to generate and transform

deposits into a portfolio of interest-bearing assets. Past successes or failures will enhance or

constrain their choices today, which in turn, will affect future production possibilities.

Moreover, various departments within the bank might have conflicting goals and the success-

ful manager will have to coordinate production to ensure that each department contributes to

the common goal. One type of network production model allows an intermediate output to be

produced at one stage or by one division of a firm and then subsequently used as an input at a

second stage to generate final outputs, which consist of desirable outputs and undesirable by-

products. Managers of stage one might seek to maximize production of the intermediate out-

put while the managers of stage two might seek to minimize its use. For instance, we consider

banks that use labor, physical capital, and equity capital in a first stage to produce the inter-

mediate output of deposits. In the second stage, those deposits are used to produce a portfolio

of desirable interest-bearing assets and other fee-generating activities. However, the presence

of risk and uncertainty usually means that an undesirable output is also produced: some loans

becoming nonperforming. In a dynamic framework, the choices made and the efficiency with

which resources are used in either stage will tend to impact future production. Nonperforming

loans generated in stage 2 will tend to negatively affect the ability of stage 1 managers to

194 EFFICIENCY AND PRODUCTIVITY GROWTH

generate deposits in a subsequent period. In addition, regional or macroeconomic upturns and

downturns will sometimes mean that the managers of stage 2 might more profitably forego

current production and ‘save’ deposits in an effort to minimize nonperforming loans in the

current period and subsequently increase future desirable outputs.

The purposes of this chapter are, first, to develop a dynamic network production model

that accounts for the scenario in the first paragraph and can be estimated using data envelop-

ment analysis (DEA) and, second, to apply the theoretical production model to analyze the

performance of Japanese Shinkin banks during fiscal years 2002–2009. Shinkin banks are

cooperative institutions which collect deposits from members and then use those deposits to

finance regional economic activities. We consider a three-year bank production horizon so

that bank performance depends not just on production within a single period, but instead

allows bank managers to account for regional/macroeconomic conditions and optimize

across periods. The dynamic portion of our model builds on the models of Shephard and Färe

(1980) and Färe and Grosskopf (1996) and Färe and Grosskopf (2000) and is related to

research by Bogetoft et al. (2009) and Tone and Tsutsui (2009). Following Fukuyama and

Weber (2010) and Fukuyama and Weber (2012), we control for undesirable outputs in a net-

work production model. In addition, we extend the research of Akther, Fukuyama, and Weber

(2013) by allowing the undesirable outputs generated in the second stage of production to

have a negative effect on stage 1 production in a subsequent period. In the next section, we

provide some background on Japanese Shinkin banks and briefly discuss the limited litera-

ture that has examined Shinkin bank performance. Then, in Sections 9.3 and 9.4, we develop

and integrate the dynamic two-stage network production model allowing for undesirable out-

puts to be by-products of final desirable output production. In Section 9.5, we discuss the data

and estimates of Shinkin bank performance. Section 9.6 summarizes and concludes.

9.2 Literature review of productivity analysis in credit banks in Japan

Shinkin banks are cooperative financial institutions organized under the Credit Associations

Law of 1951. These banks accept deposits from the general public, but limit their lending to

members: mortgage and personal loans are made to household members and commercial

loans within a prefecture are made to small and medium-sized business members. The

Financial Services Agency regulates Shinkin banks and the Shinkin Central Bank (formerly

Zenshiren) provides member banks with deposit and lending services and helps facilitate

foreign exchange transfers. From March 1998 to March 2011 the number of Shinkin bank

head offices declined from 401 to 271 as the number of members grew from 8.6 to 9.3 million.

During the same period, the total number of employees shrunk from 152 000 to 116000 and

total deposits grew from 98 to 120 trillion yen. In 1998, time and savings deposits were 79%

of total deposits and demand deposits were 20% of total deposits. By 2011, time and savings

deposits declined to 66% of total deposits and demand deposits grew to 33% of total deposits.

In 1998, Japanese individuals accounted for 74% of total deposits and corporations held 20%

of total deposits, with foreigners and the public holding the remainder. By 2011, individuals

held 81% of total deposits and corporations held 16%. From 1998 to 2011, total loans and

bills discounted by Shinkin banks shrunk from 70.4 to 63.4 trillion yen while investment

securities grew from 16.3 to 34.4 trillion yen. Corporations received 70% of total Shinkin

bank loans in 1998 and 65% in 2011. Of the corporate loans made in 1998, 23% were to

A DYNAMIC NETWORK DEA MODEL 195

manufacturing, 17% were to construction, 19% to wholesale and retail trade, 10.4% to real

estate, and the remainder to corporations in the service industry. By 2011, those shares were

17% to manufacturing, 13% to construction, 15% to wholesale and retail trade, and 19.2% to

real estate. Loans to individuals shrunk from 19.8 trillion yen in 1998 to 18.1 trillion yen in

2011 with the share of individual loans for housing increasing from 56% to 82%.1

Nishikawa (1973) estimated a simple log-linear cost function for Shinkin banks in 10

Japanese regions in 1968 and found that Shinkin banks operated in the range of constant

returns to scale, except in the Tokai region where Shinkin banks had increasing returns to

scale. Miyamura (1992) used data on 456 Shinkin banks in 1985 and 451 Shinkin banks in

1990 and estimated a translog cost function for six different outputs including interest income,

dividends from trust accounts, noninterest income, other fees and commissions, and loans per

branch office. He found that city banks and rural banks faced different production/cost tech-

nologies. In 1985, both city and rural banks operated in the range of constant returns to scale

for their respective technologies. By 1990, banks in both areas operated in the range of

increasing returns to scale and city banks exhibited greater scale economies than rural

banks. Miyakoshi (1993) used data from 1989 to 1998 for 114 Shinkin banks in the Kanto

area including Tokyo and 123 Shinkin banks in other areas including Hokkaido, Tohoku,

Koshinetsu, and Hokuriku. Using a translog cost function with two outputs – loans and

securities – he found scope economies for banks in the Kanto area and significant scale

economies for banks in both the Kanto area and other areas of Japan. Hirota and Tsutui

(1992) also used a translog cost function to test for scope economies in production loans,

securities, and deposits. For 452 banks operating in 1987, they found no scope economies

between any of the three pairs of outputs, although significant scale economies were found.

Fukuyama (1996) used DEA to estimate technical efficiency for 435 Shinkin banks in

1992. He found that larger banks were more efficient than smaller banks, but the enhanced

efficiency was primarily due to better managerial oversight in minimizing input use rather

than efficiency gains due to larger banks operating in the range of constant returns to scale.

Harimaya (2004) showed similar results using DEA and a stochastic frontier cost function

and also found that bank efficiency declined as bank’s ratio of cost to deposits increased.

The market structure hypothesis posits that banks in concentrated markets can charge higher

rates on loans and pay lower rates on deposits due to their market power, thus increasing their

profits. In contrast, the efficient structure hypothesis posits that efficient banks obtain lower costs

and higher profits because of their efficiency, leading to a concentrated market. A stochastic

frontier analysis by Satake and Tsutsui (2002) found evidence supporting the efficient structure

hypothesis only up until the 1980s for Shinkin banks in Kyoto prefecture. Like Harimaya (2004),

Satake and Tsutsui (2002) also reported a negative relation between Shinkin bank inefficiency

and the ratio of costs to deposits. Fukuyama and Weber (2009) estimated slacks-based ineffi-

ciency for between 289 and 298 Shinkin banks in 2002–2005 and found that banks with a higher

ratio of equity capital to total assets were less inefficient, suggesting that owners with more

money at stake were able to exert more pressure on bank managers to be technically efficient.

Several papers investigated the actual or potential consequences of merger and acquisi-

tion activities among Shinkin banks. During the 1990–2002 period, Hosono, Sakai, and Tsuru

(2007) compared the five-year period before and after a merger by constructing pro formabalance sheets of target and acquired Shinkin banks for 97 mergers and acquisitions. Larger

1 Shinkin Central Bank Research Institute http://www.scbri.jp/e_statistics.htm


Shinkin banks were more likely to acquire smaller and slower growing banks. However, their

findings did not support the efficient structure hypothesis, but instead suggested that mergers

occurred as banks tried to be designated as ‘too big to fail’. In contrast to the work of Hosono,

Sakai, and Tsuru (2007), Färe, Fukuyama, and Weber (2010) allowed the potential gains from

mergers and acquisitions to be estimated ex ante, rather than be inferred from an ex postexamination of balance sheet and income statement data. For Shinkin banks on Kyushu Island

in Japan, the largest potential gain in final outputs for infra-prefecture mergers was for banks

in Nagasaki and the smallest potential gain in final outputs occurred for infra-prefecture

mergers in Fukuoka and Saga. For inter-prefecture mergers, banks in Miyazaki and Nagasaki

had the largest ex ante gains, while potential mergers between banks located in Fukuoka and

the other six prefectures on Kyushu Island had the smallest potential gains in final loan out-

puts. Barros, Managi, and Matousek (2009) and Assaf, Barros, and Matousek (2011) used

DEA to estimate a Malmquist productivity index. They found that Shinkin banks experienced

small average declines in annual productivity attributable to negative technical change during

the 2000–2006 period which they attributed to slow growth in Japanese economic activity.

The studies mentioned earlier did not account for the undesirable output of nonperforming

loans when measuring bank performance. To provide a more complete representation of

the bank technology, Fukuyama and Weber (2008) estimated a parametric directional dis-

tance function accounting for nonperforming loans and desirable bank outputs of loans and

securities investments. During 2001–2004, they found that regional banks which focused on

profits were more efficient, had faster technological progress, and a higher shadow cost of

reducing nonperforming loans than cooperative Shinkin banks.

9.3 Dynamic network production

9.3.1 The two-stage technology

In this section, we present a network production technology for banks that use inputs, t Nx +∈ℜ ,

in one stage to produce the intermediate output of deposits, zt ∈R+, which are then used in a sub-

sequent stage to produce a portfolio of final desirable outputs, t Mfy R+∈ , and undesirable outputs

of nonperforming loans, bt ∈R+. We assume there are j=1,…,J banks and production takes place

in periods t=0, …, T. Nonperforming loans produced in stage 2 during period t−1(bt−1) act as an

undesirable input to stage 1 production in period t. Undesirable inputs shrink the bank’s produc-

tion possibilities set and require greater use of desirable inputs to offset their effects. For instance,

banks that generate nonperforming loans are usually constrained in their ability to raise deposits

unless they offset those nonperforming loans with an injection of equity capital.

To allow a dynamic aspect to our model, we allow a bank to use deposits in the current

period to produce final outputs, or, the bank can save deposits for use in a subsequent period.

We denote carryover assets as ct. Bank managers might want to carryover some assets to a

future period when they expect a recession or other events to cause too many loans to become

nonperforming, or when expected increases in interest rates would reduce the market value

of securities investments. In such an environment, managers might find it more efficient to

forego purchasing securities or making loans in period t so that nonperforming loans are

also reduced and future production possibilities are expanded. Therefore, total output in the

second stage of production is

= + ,t t ty fy c (9.1)


where total output consists of the sum of final outputs and carryover outputs.

The stage 1 production possibility set in year t is denoted by

( ) ( ){ }1 11 , , such that , can producet t t t t t tP b z x b x z− −= (9.2)

and the stage 2 production possibility set in the same year is given by

( ) ( ) ( ){ }− −= + +1 12 , , , such that , can produce ,t t t t t t t t t t tP c z b fy c c z b fy c (9.3)

In stage 1, banks combine desirable inputs (xt) with undesirable inputs from the previous

period (bt−1) to produce the intermediate output (zt). In stage 2, the bank combines the inter-

mediate output from the first stage (zt) and carryover assets from the previous period (ct−1) to

produce total outputs (yt) which equal the sum of final outputs (fyt) and carryover assets (ct).

Combining Equations (9.2) and (9.3), the network production possibility set2 is

( ){( ) ( ) }

1 1

1 1

, , , , , such that

, , 1 and , , , 2 .

t t t t t t t t

t t t t t t t t t t

N b x z c b fy c

b x z P c z b fy c P

− −

− −

= +

∈ + ∈(9.4)

The directional distance function was introduced by Chambers, Chung, and Färe (1996) and

Chambers, Chung, and Färe (1998), and Färe and Grosskopf (2004) provided further theory

and applications. This distance function gives the maximum contraction in inputs and

undesirable outputs and simultaneous expansion in desirable outputs given a production tech-

nology. The directional distance function has been used in numerous empirical applications

and has recently been used to measure performance for firms that face a network technology

(Akther, Fukuyama, and Weber 2013). Let ( ) 1, , N Mx b yg g g R + +

+= ∈g be a directional vector

used to scale inputs and outputs to the production frontier. For the network technology given

by Equation (9.4), the directional distance function takes the form

{ }β β β β− −

−+

= − − + + ∈

1 1

1

( , , , , )

max subject to ( , , , , .ˆ )

t t t t t t t

t t t t t t tx b y

D x b b c fy cx g b b g z fy g c N

(9.5)

Here we note that the intermediate outputs of the first stage (zt) which become an input to the

second stage are not a parameter of ( )·D , but are instead optimally chosen to maximize the

size of the network technology. The optimal values are represented by ˆ tz and these optimal

values provide the link between stage 1 and stage 2 production. The network technology

represented by Equation (9.4) is illustrated in Figure 9.1.

Instead of measuring network performance for a single period, we want to allow bank

managers to optimize production over several periods by choosing not only the intermediate

output of deposits, but also the amount of assets to carryover from one period to the next.

In the empirical section of the chapter, we consider a three-year dynamic planning horizon

for production, although longer horizons can be used. To streamline notation, let

b=(bt−1,bt,bt+1,bt+2), x=(xt,xt+ 1,xt+ 2), z=(zt,zt + 1,zt+ 2), y=(yt,yt+1,yt+2), fy=(fyt, fyt +1, fyt +2), and

2 The standard two-stage network model without either bad outputs or carryover variables is presented by Kao

and Hwang (2008) and studied further by Chen, Cook, and Zhu (2010).


c=(ct−1,ct,ct +1,ct+ 2). The three-year dynamic technology (DN) is illustrated in Figure 9.2 and

is denoted by the dynamic network production possibility set

( ) ( ){( )( ) }

1 1

1 1 1 1 1 1

1 2 2 1 2 2 2 2

DN , , , , such that , , , , , ,

, , , , , , and

, , , , , .

t t t t t t t t

t t t t t t t t

t t t t t t t t

b x z c fy b x z c b fy c N

b x z c b fy c N

b x z c b fy c N

− −

+ + + + + +

+ + + + + + + +

= + ∈

+ ∈

+ ∈

(9.6)

We measure bank performance relative to Equation (9.6) by a three-year dynamic network

directional distance function:

1 2 1 2

1 1

1 1 1

1

1 1 1 1 1

1 1

, , , , ; max subject to :

, , , ,,

,

, , , ,

ˆ

ˆ

ˆ

ˆ ,

ˆ

t t t t t

t t t t tx t

t t t t ty b

t t t t t tb x t

t t t t ty b

t t

D b x c c fy g

b x g z cN

fy g c b g

b g x g z cN

fy g c b g

b g 2 2 2 1

2

2 2 2 2 2

ˆ, , ,ˆ,.

,

t t t tb x t

t t t t ty b

x g z cN

fy g c b g

(9.7)

Figure 9.1 Static two-stage network production for a bank. P1t is the stage 1 production

possibility set and P2t is the stage 2 production possibility set.


In Equation (9.7), banks choose intermediate outputs (deposits) ˆ ,tz 1ˆ ,tz + and

2ˆ tz + to maximize

each period’s production possibility set. The choice of these intermediate outputs provides

the network link between stage 1 and stage 2 in period t, t+1, and t+2. The dynamic link

between the three periods occurs because banks also choose the amount of assets to carryover

from period t to ( )ˆ1 tt c+ and the amount of assets to carryover from period t+1 to ( )1ˆ2 tt c ++ .

These carryover assets are chosen to maximize the size of the dynamic production possibility

set. The carryover assets from period t − 1 and from the final period t +2(ct −1 and ct+2) are

taken as given to satisfy tranversality conditions.

9.3.2 Three-year dynamic DEA

In this section, we show how data envelopment analysis (DEA) of Charnes, Cooper, and

Rhodes (1978) and Farrell (1957) can be used to represent the best-practice dynamic network

technology. In each period, we observe the inputs and outputs for j=1,…,J banks. The

method of DEA forms linear combinations of the observed inputs and outputs for the J banks

to generate a best-practice technology. The directional distance function is estimated using

linear programming methods given the best-practice frontier. An advantage of DEA over

stochastic methods of measuring performance is that it does not require the researcher to

specify an ad hoc functional form such as Cobb–Douglas, translog, or quadratic, and it does

not require the researcher to specify a form for the error structure. However, a limitation of

DEA is that all deviation of a firm’s outputs and inputs from the frontier is attributed to inef-

ficiency on the part of the bank’s managers, even though some of the deviation might be due

to luck or measurement error.

We define the intensity variables for stage 1 as ( )1 , ,t t t JJλ λ λ += … ∈ℜ and the intensity

variables for stage 2 as ( )1, ,t t t JJ +Λ = Λ … Λ ∈ℜ . The intensity variables form linear combina-

tions of all banks’ observed inputs and outputs for the two stages. Extending the network

model of Akther, Fukuyama, and Weber (2013) to allow for carryover assets, we define the

year t network technology as

Figure 9.2 Three-period dynamic network production.


{( )

}

1 1

1 1

1 1 1

1 1

1 1 1 1

, , , , , such that

, , , 0, 1, ,

, , , , 0, 1, , .

t t t t t t t t

J J Jt t t t t t t t t t

j j j j j j jj j j

J J J Jt t t t t t t t t t t t t t

j j j j j j j j jj j j j

N b x z c b fy c

b b x x z z j J

z z b b fy c y c c j J

λ λ λ λ

− −

− −

= = =

− −

= = = =

= +

= ≥ ≤ ≥ = …

≥ Λ = Λ + ≤ Λ ≥ Λ Λ ≥ = …

∑ ∑ ∑

∑ ∑ ∑ ∑

(9.8)

The right-hand side of each constraint equals a linear combination of the observed values of

inputs and outputs with the intensity variables for the j=1,…,J banks and the left-hand side

variables bt−1,xt, zt,bt, fyt +ct, and ct− 1 consist of the set of inputs and outputs that satisfy the

constraints. The equality constraint 1 1

1

Jt t t

j jj

b b λ− −

=

= ∑ is associated with stage 1 of production

and corresponds with the assumption that nonperforming loans produced in period t − 1 are

an undesirable input to stage 1 of the subsequent period. The equality models the notion of

weak disposability of inputs. Weak disposability of inputs means that if more undesirable

input is used, more desirable inputs must also be used to offset their negative effect if the

intermediate output is to remain constant. In stage 2, the equality constraint 1

Jt t t

j jj

b b=

= Λ∑models the notion of weak disposability of outputs. Weak disposability of outputs means that

if undesirable outputs (nonperforming loans) are to be reduced, some desirable outputs

(loans) must also be foregone.3 The remaining inequality constraints allow the standard

assumption of strong (free) disposability of inputs and outputs. Carryover assets from the

previous period (ct− 1) expand the stage 2 production possibility set. This effect is seen in the

constraints 1 1

1

Jt t t

j jj

c c− −

=

≥ Λ∑ , since increases in carryover assets (ct−1) relax the constraint and

allow the right-hand side technology to become larger. Finally, the link between stage 1 and

stage 2 is seen in the two constraints 1

Jt t t

j jj

z z λ=

≤ ∑ and 1

Jt t t

j jj

z z=

≥ Λ∑ . These two constraints

can be combined to yield ( )1

0J

t t tj j j

j

zλ=

− Λ ≥∑ . Thus, the intensity variables for stage 1 ( )tjλ

and stage 2 ( )tjΛ are chosen to satisfy the constraint and this constraint provides the network

link between the two stages of production.

Using the DEA network technology (9.8), the network directional distance function for

bank k is estimated as

λ λ λ

λ

1 1

1 1

1 1 1 1

1 1

1 1

( , , , , ) max subject to:

, , 0, ,

, , 0, 0, 1, , .

t t t t t t tk k k k k k

J J J Jt t t t t t t t t t t tk j j k x j j j j j k b j j

j j j j

J Jt t t t t t t t tk y k j j k j j j j

j j

D b x b c fy c

b b x g x z b g b

fy g c y c c j J

(9.9)

3 Formally, weak disposability of inputs in stage 1 means that if (bt −1, xt, zt)∈P1t then (qbt− 1,qxt, zt)∈P1t, for

q≥1. Weak disposability of undesirable outputs in stage 2 means that if (ct− 1,bt, zt, fyt +ct)∈P2t then (ct −1,fbt, zt,

f(fyt +ct))∈P2t for 0≤f≤1.


We extend the DEA network technology to a dynamic framework by allowing production to

take place in three periods: t, t+1, and t+2. The dynamic network production technology

given by Equation (9.6) is defined using DEA as

( )

( )1 1

1 1 1

1 1

1 1 1

DN , , , , such that in period

, , 0, 0, 1, , ,

, , , 0, 1, , ,


j j j j j j j jj j jJ J J

t t t t t t t t t t tj j j j j j j

j j j

b x z c y t

b b x x z j J

b b fy c y c c j J

λ λ λ λ− −

= = =

− −

= = =

⎧= ⎨⎩

= ≥ − Λ ≥ ≥ = …

= Λ + ≤ Λ ≥ Λ Λ ≥ = …

∑ ∑ ∑

∑ ∑ ∑(9.10)

in period t+1

(9.11)

and in period t+2

( )1 1 2 2 2 2 2 2 2 2

1 1 1

2 2 2 2 2 2 2 1 1 2 2

1 1 1

, , 0, 0, 1, , ,

, , , 0, 1, , .


j j j j j j j jj j j

J J Jt t t t t t t t t t t

j j j j j j jj j j

b b x x z j J

b b fy c y c c j J

λ λ λ λ+ + + + + + + + + +

= = =

+ + + + + + + + + + +

= = =

= ≥ − Λ ≥ ≥ = …

⎫= Λ + ≤ Λ ≥ Λ Λ ≥ = … ⎬⎭

∑ ∑ ∑

∑ ∑ ∑(9.12)

The network links between stage 1 and stage 2 are provided by the constraints

( )1

0J

t t tj j j

j

zλ=

− Λ ≥∑ in period t, ( )1 1 1

1

0J

t t tj j j

j

zλ + + +

=

− Λ ≥∑ in period t+1, and

( )2 2 2

1

0J

t t tj j j

j

zλ + + +

=

− Λ ≥∑ in period t +2. The dynamic links between period t and t+1 are pro-

vided by two sets of constraints. First, the undesirable outputs produced in period t at stage 2

become inputs in stage 1 during period t+1. This link means that the intensity variables

, 1, ,tj j JΛ = … in period t and 1, 1, ,t

j j Jλ + = … period t +1 must be chosen to satisfy both

1

Jt t t

j jj

b b=

= Λ∑ and 1

1

Jt t t

j jj

b b λ +

=

= ∑ . Second, carryover assets (ct) in period t become an input in

period t+1, so the intensity variables , 1, ,tj j JΛ = … and 1, 1, ,t

j j J+Λ = … and the choice of ct

must satisfy 1

Jt t t t

j jj

fy c y=

+ ≤ Λ∑ and 1

1

Jt t t

j jj

c c +

=

≥ Λ∑ . The dynamic links between period t+1

and t+2 are similar. For the undesirable outputs, the intensity variables 1, 1, ,tj j J+Λ = … and

2 , 1, ,tj j Jλ + = … must satisfy both 1 1 1

1

Jt t t

j jj

b b+ + +

=

= Λ∑ and 1 1 2

1

Jt t t

j jj

b b λ+ + +

=

= ∑ . For carryover assets,

( )1 1 1 1 1 1 1 1

1 1 1

1 1 1 1 1 1 1 1 1

1 1 1

, , 0, 0, 1, , ,

, , , 0, 1, , ,


j j j j j j j jj j jJ J J

t t t t t t t t t t tj j j j j j j

j j j

b b x x z j J

b b fy c y c c j J

λ λ λ λ+ + + + + + + +

= = =

+ + + + + + + + +

= = =

= ≥ − Λ ≥ ≥ = …

= Λ + ≤ Λ ≥ Λ Λ ≥ = …

∑ ∑ ∑

∑ ∑ ∑


the intensity variables 1, 1, ,tj j J+Λ = … and 2 , 1, ,t

j j J+Λ = … and the choice of ct +1 must satisfy

and 1 1 2

1

Jt t t

j jj

c c+ + +

=

≥ Λ∑ .

Using Equation (9.12), we define the dynamic three-period network directional distance

function for bank k as

1 2 1 2

1 1

1 1 1

1 1

1 1

1

( , , , , ) max subject to:

, , 0,

ˆ, ,

, 0, 1, , ,

t t t t tk k k k k

J J Jt t t t t t t t t tk j j k x j j j j j

j j jJ J

t t t t t t t t tk b j j k y j j

j jJ

t t t t tj j j j

j

D b x c c fy

b b x g x z

b g b fy g c y

c c j J

1 1 1 1 1 1 1 1

1 1 1

1 1 1 1 1 1 1 1 1

1 1

1 1 1

1

0, 1, , ,

, , 0,

ˆ, ,

ˆ , 0, 1, , , 0, 1, ,

J J Jt t t t t t t t t t tk b j j k x j j j j j

j j jJ J

t t t t t t t t tk b j j k y j j

j jJ

t t t t tj j j j

j

j J

b g b x g x z

b g b fy g c y

c c j J j

1 1 1 2 2 2 2 2 2 2 2

1 1 1

2 2 2 2 2 2 2 2 2

1 1

1 1 2 2 2

1

, , 0,

, ,

ˆ , 0, 1, , , 0, 1, ,

J J Jt t t t t t t t t t tk b j j k x j j j j j

j j jJ J

t t t t t t t t tk b j j k y k j j

j jJ

t t t t tj j j j

j

J

b g b x g x z

b g b fy g c y

c c j J j .J(9.13)

The distance function given by Equation (9.13) is maximized by choosing the intensity

variables jτλ and j

τΛ for t= t, t+1, t+2 and j=1,…,J; carryover assets ˆ tc and 1ˆ tc + ; and the vari-

ables b t, b t +1, and b t+ 2 subject to the constraints.

9.4 Cooperative Shinkin banks: An empirical illustration

9.4.1 Defining bank inputs and outputs

We apply the dynamic network model to 269 cooperative Japanese Shinkin banks operating

during 2002–2009. There exists some disagreement on whether deposits should be treated as

an input or an output. Berger and Humphrey (1992) and Berger and Humphrey (1997)

reviewed various financial institution efficiency studies and the various methods used to

define inputs and outputs. Sealey and Lindley’s (1977) asset approach assumes deposits are

an input and loans and other interest-bearing assets are outputs. The value-added approach

defines outputs as any liability or asset that adds significant value to a bank with inputs equal

to labor and the value of fixed assets, including premises and physical capital. The user cost

approach of Hancock (1985) defines outputs as any asset or liability that contributes to

1 1 1 1

1

Jt t t t

j jj

fy c y+ + + +

=

+ ≤ Λ∑


revenues and inputs equal labor and any asset or liability that adds significantly to costs.

Berger, Hanweck, and Humphrey (1987) and Goddard, Molyneux, and Wilson (2001) pro-

vided further discussion about the treatment of deposits. Fukuyama and Weber (2009) used

the asset approach in measuring Shinkin bank performance and assumed that a bank uses

deposits, labor, and physical capital to produce a portfolio of assets, including loans and

securities investments. Fukuyama and Weber (2010) proposed a two-stage network model for

Japanese credit cooperative Shinkin banks where deposits are an intermediate output of the

first stage of production and an input to a second stage where they produce the portfolio of

assets. More recently, Akther, Fukuyama, and Weber (2013) extended their network model by

including nonperforming loans from a preceding year to estimate the technical inefficiency

of a bank in the current year. Wang, Gopal, and Zionts (1997) and Chen and Zhu (2004)

treated deposits as an intermediate product in a two-stage network problem. Their initial

inputs are fixed assets, employees, and information technology investments, and the final

outputs are profits, loans recovered, and marketability. Therefore, the Wang-Gopal-Zionts

and Chen-Zhu frameworks differ from Sealey and Lindley’s asset approach and the network

version of Fukuyama and Weber (2010). Given the disagreement on deposits, a feature of our

network model is that we treat deposits as an intermediate output of the first stage of produc-

tion and as an input to the second stage of production.

9.4.2 NPLs in the efficiency/productivity measurement

We assume that nonperforming loans from a previous period are an undesirable input to the

first stage of production in a subsequent period. As such, these nonperforming loans require

the use of other inputs to offset their negative effects, or else output will fall. Consider the

following example which examines a hypothetical bank balance sheet in period t and period

t+1. The balance sheet for period t is given in Table 9.1.

The leverage ratio (Equity/Assets) for the bank is (0.074 =8/108) and the bank is classi-

fied as ‘well-capitalized’ (see Saunders and Cornett, 2008, p. 595). Suppose that during the

period, 5 out of 60 loans become nonperforming or bad loans. The new balance sheet at the

start of period t+1 is given in Table 9.2.

In period t+1 the bank’s leverage ratio equals 0.029 (=3/103) and the bank is categorized

as ‘significantly undercapitalized’. One of two things (or some combination) must now occur:

the bank can shrink deposits and with it, loans and securities, until it meets the leverage ratio

requirement of 4% to be categorized as ‘adequately capitalized’ or, it must raise additional

equity capital. One possible way to reorganize the balance sheet and become ‘adequately

capitalized’ is given in Table 9.3.

Thus, the bad loans that occur in period t act as an undesirable input in period t+1, and

require additional inputs (equity) to offset their effect, or, constrain the amount of the inter-

mediate output (deposits) that can be produced, which in turn causes securities to shrink.

Table 9.1 Hypothetical bank’s balance sheet for period t.

Assets Liabilities+equity

Cash 10 Deposits 100

Total loans 60 Equity 8

Securities 38


9.4.3 Data

We employ a balanced panel data set consisting of 269 Japanese Shinkin banks during a span

of eight fiscal years from 2002 to 2009. The Japanese fiscal year begins on 1 April and ends

on 31 March of the subsequent year, thus our data is from the period beginning 1 April 2002

and ending 31 March 2010. During the last year there were 272 Shinkin banks operating, but

we use only 269 banks because some data was missing for three of the banks.4 The data

source is Nikkei’s Financial Quest (Table 9.4).

The decline in the number of operating banks from 326 in 2002 to 272 in 2009 reflects

consolidation in the Shinkin banking industry. We follow Fukuyama and Weber (2010) in

defining inputs and outputs. The first-stage inputs are labor (x1), fixed capital (x

2), and net

assets (x3). Labor (x

1) equals the unconsolidated total number of employees excluding directors

holding concurrent posts, temporary employees, and temporary retired workers. Fixed capital

equals the asset value of tangible and intangible fixed assets. Net assets for cooperative Shinkin

banks correspond to equity capital (assets minus liabilities) for joint stock commercial banks.

The intermediate output of the first stage is deposits (z), which equals the sum of current

deposits, ordinary deposits, savings deposits, deposits at notice, time deposits, and other

deposits. Deposits produced in the first stage are used as an input in the second stage to

Table 9.2 Hypothetical bank’s balance sheet for period t+1.


Cash 10 Deposits 100

Performing loans 55


Bad loans −5

Securities 38

Table 9.3 Hypothetical bank’s reorganized balance sheet for period t+1.


Cash 10 Deposits 72

Performing loans 55


Bad loans −5

Securities 10

Table 9.4 Number of existing and sample Shinkin banks.

No. of banks 2002 2003 2004 2005 2006 2007 2008 2009

Existing 326 306 298 292 287 281 279 272

Sample 269 269 269 269 269 269 269 269

4 We deleted Tsurugi Shinkin Bank, Himifushiki Shinkin Bank, and Hinase Shinkin Bank.


produce the final outputs of total loans (fy1) and securities (fy

2), carryover assets (c

1 and c

2),

and the undesirable output of nonperforming loans (b). Loans equal the sum of total loans and

bills discounted. Nonperforming loans (b) equal the unconsolidated bank account sum of

loans to customers in bankruptcy, nonaccrual delinquent loans, loans past due more than three

months, and restructured loans. The data does not allow us to distinguish between carryover

assets that come from loans (c1) and carryover assets that come from securities (c

2). However,

total carryover assets (c1+c

2) are derived as c

1+c

2=assets− (required reserves+x

2+

fy1+ fy

2). That is, total carryover assets equal the difference between total assets and the sum

of required reserves, fixed capital, loans, and securities investments. The required reserve

ratio for Shinkin banks depends on bank size and varies for time deposits and other deposits

(O’Brien, 2007). For banks with deposits between 50 and 500 billion yen, the required reserve

ratio for time deposits (other deposits) is 0.05% (0.1%). For banks with deposits between 500

billion yen and 1.2 trillion yen, the required reserve ratio for time deposits (other deposits) is

0.05% (0.8%). For banks with deposits between 1.2 and 2.5 trillion yen, the required reserve

ratio for time deposits (other deposits) is 0.9% (1.3%). For banks with deposits greater than

2.5 trillion yen, the required reserve ratio for time deposits (other deposits) is 1.2% (1.3%).

To estimate the model we arbitrarily assume that all carryover assets correspond with securi-

ties. Thus, we assume c1=0 and y

1= fy

1.

Table 9.5 presents descriptive statistics of the inputs and outputs. All financial data are in

billions of Japanese yen deflated by the Japanese GDP deflator. The average Shinkin bank uses

412 workers, approximately 7.2 billion yen in fixed capital, and 23.8 billion yen in net assets

(equity capital). These inputs are used to generate an average of 430.9 billion in deposits which

are then transformed into 246.2 billion in loans, 118.8 billion in securities, and 91 billion yen

in carryover assets. The average Shinkin bank had 19.5 billion yen in nonperforming loans.

9.5 Estimates

To estimate performance we must first choose a directional vector to scale outputs and inputs

for each bank to the frontier of the network technology. An infinite number of directional

vectors are possible and are dependent on the objective of the researcher, bank manager, and/or

Table 9.5 Descriptive statistics for the pooled sample (N=2152).

Mean Std. dev. Minimum Maximum

y1= loans 246.2 321.7 18.6 2409.3

y2= securities 118.8 139.7 2.0 1119.1

c1+c

2=carryover assets 90.9 111.2 5.4 1023.2

x1= labor 412 408 35 2651

x2=physical capital 7.2 9.7 0.2 69.3

x3=net assets (equity) 23.8 27.7 0.9 204.6

z=deposits 431.0 523.4 33.1 4263.6

b=nonperforming loans 19.5 24.5 0.8 211.9

Labor equals number of employees. Physical capital, net assets (equity), deposits, loans, nonperforming

loans, securities investments, and carryover assets are in billions of Japanese yen deflated by the

Japanese GDP deflator (base year=2000).


policy-maker. For instance, if policy-makers are interested in reducing bad loans holding

inputs and desirable outputs constant, an appropriate choice of directional vector might be

g=(0,gb,0). If instead, the decision-maker is interested in seeing how much desirable outputs

could be expanded holding inputs and nonperforming loans constant, then they might instead

choose g=(0,0,gy). Briec (1997) suggested using the firm’s observed values of inputs and

outputs as the directional vector. That is, for firm k, the directional vector would be g=(xk,b

k,y

k).

This directional vector means that the estimated directional distance function multiplied by

100% gives the percent expansion in desirable outputs and simultaneous percent contraction

in inputs and undesirable outputs making it easier to compare with Shephard (1970) distance

functions. As an alternative, Färe and Grosskopf (2004) showed that when all firms are evalu-

ated using a common directional vector, it is possible, under certain conditions, to aggregate

the individual firm’s directional distance functions to an industry directional distance func-

tion. Such an aggregation is not possible with the Briec (1997) specification. One possible

directional vector that would be common to all firms is g=(x,b,y) = (1,1,1). In this case, the

directional distance function gives the simultaneous unit contraction in inputs and undesira-

ble outputs and unit expansion in outputs. Another possibility would be to evaluate each firm

for the directional vector ( ) ( )= =, , , ,x b yg g g x b yg . This choice of directional vector implies

that the estimates of dynamic network inefficiency, ( )·D , multiplied by 100%, gives the simulta-

neous percentage contraction in inputs and undesirable outputs, and percentage expansion in

desirable outputs relative to the mean values that are feasible given the technology. We choose

this mean directional vector using the mean values of inputs and outputs reported in Table 9.5.

To estimate the three-period dynamic network directional distance function requires data

from four periods, since nonperforming loans and carryover assets from period t − 1 are part

of the network technology in period t. Our data corresponds with fiscal years 2002–2009.

Therefore, the first three-period problem we estimate corresponds to fiscal years 2003–2005.

We report estimates of the dynamic network directional distance function for each year in

Table 9.6. To illustrate, consider the estimates for the 2003–2005 period. The mean estimate

for ( ) 1 2 3· 0.137ˆ ˆ ˆD β β β= + + = , which indicates that each of the three inputs and nonper-

forming loans could be reduced by 13.7% of the mean values for those variables reported in

Table 9.5, while loans and securities could be increased by 13.7% of their mean values. For the

2003–2005 period, the year 2005 is the most inefficient year with 3 0 47ˆ .0β = which indicates

4.7% of the inefficiency occurred in that year. From 2003–2005 to 2006–2008, bank ineffi-

ciency rises from 13.7% to 15% and then declines slightly to 14.4% in the 2007–2009 period.

A bank is efficient in a particular year of a three-year period if either 1ˆ 0β = or 2ˆ 0β =or 3ˆ 0β = . A bank produces on the frontier of the dynamic network technology if

( ) 1 2 3ˆ ˆ· ˆ 0D β β β= + + = . Table 9.6 also reports the number of banks that are efficient in at

least one subperiod of each three-year period. For 2003–2005, 10 Shinkin banks were effi-

cient for the 2003 subperiod ( )1ˆ 0β = , nine banks were efficient for the 2004 subperiod

( )2ˆ 0β = , and nine banks were efficient for the 2005 subperiod ( )3ˆ 0β = , but only six banks

were efficient for all three subperiods ( )1 2 3ˆ ˆ ˆ 0β β β+ + = . Six banks were efficient during

2004–2006, five banks were efficient during 2005–2007, three banks were efficient during

2006–2008, and four banks were efficient during 2007–2009. Table 9.7 reports the names of

the efficient banks in each year. Kochi Shinkin Bank was efficient in each three-year period,

2003–2005 to 2007–2009 and Osaka Higashi Shinkin Bank was efficient in 2004–2006 to

2007–2009. Two banks, Kyoto and Himawari, were efficient in three out of the five periods


Table 9.6 Estimates of inefficiency ( ) β β β+ += + +1 2, , , t t tD x b c y .

Mean Std. dev. Minimum Maximum No. on frontier

2003–2005a 1β 0.045 0.039 0 0.238 102β 0.045 0.038 0 0.225 93β 0.047 0.042 0 0.257 9

1 2 3ˆ ˆ ˆβ β β+ + 0.137 0.115 0 0.674 6

2004–2006 1β 0.045 0.038 0 0.220 102β 0.048 0.043 0 0.260 103β 0.051 0.045 0 0.256 7

1 2 3ˆ ˆ ˆβ β β+ + 0.144 0.125 0 0.709 6

2005–2007 1β 0.047 0.043 0 0.257 112β 0.052 0.047 0 0.264 83β 0.051 0.046 0 0.264 6

1 2 3ˆ ˆ ˆβ β β+ + 0.150 0.134 0 0.756 5

2006–2008 1β 0.051 0.046 0 0.275 92β 0.053 0.048 0 0.268 53β 0.046 0.043 0 0.26 6

1 2 3ˆ ˆ ˆβ β β+ + 0.150 0.135 0 0.777 3

2007–2009 1β 0.051 0.047 0 0.262 82β 0.047 0.045 0 0.261 73β 0.046 0.043 0 0.245 7

1 2 3ˆ ˆ ˆβ β β+ + 0.144 0.132 0 0.765 4

a 269 Shinkin banks are used in each year.

Table 9.7 Efficient Shinkin banks.

2003–2005 2004–2006 2005–2007 2006–2008 2007–2009

Karatsu Shinkin Bank x

Kanonji Shinkin Bank x x

The Kyoto Shinkin Bank x x x

Yamanashi Shinkin Bank x

Sapporo Shinkin Bank x

Johnan Shinkin Bank x x

Choshi Shinkin Bank x

Sawayaka Shinkin Bank x

Osaka Higashi Shinkin Bank x x x x

Himawari Shinkin Bank x x x

Kochi Shinkin Bank x x x x x


and two banks, Kanonji and Johnan, were efficient in two out of the five periods. Five

other banks, Karatsu, Yamanashi, Sapporo, Choshi, and Sawaka, were efficient in one of the

three-year periods.

For comparison purposes, we also estimated the Shephard output distance function for

each year for two standard models that are found in the literature. In the first standard model,

we assumed that banks produce loans and securities investments using labor, physical capital,

and equity capital. In both 2003 and 2009, average output efficiency5 was 74% with 17 banks

operating on the frontier. Other years had similar levels of efficiency and frontier banks. In

the second standard model, we assumed that banks produce loans and securities investments

as desirable outputs and nonperforming loans as an undesirable output, using labor, physical

capital, equity capital, and deposits. Output efficiency averages 0.92 in 2003 and falls to 0.88

in 2009 with 43 banks operating on the frontier in both years. Since the network model that

we estimate allows a larger production possibility set, there are fewer banks producing on the

frontier in the dynamic network model than the standard single-period production model.

This finding indicates that bank managers and regulators who use single-period benchmarks

are potentially getting a misleading picture of bank performance.

As part of the solution to Equation (9.13), carryover assets are chosen for periods t and

( )11 anˆ ˆdt tt c c ++ , given carryover assets from period t−1(ct −1) and period t+2(ct+2). Recall

that although we were able to identify total carryover assets for loans and securities (c1+c

2),

we could not identify the specific amounts associated with loans (c1) and securities (c

2) and

thus assumed that all carryover assets would be put into securities. The optimal values for

carryover assets that could go into securities are compared with the actual values and are

reported in Table 9.8. As seen in the table, the actual values are always significantly greater

than the optimal values. The ratios of actual to optimal carryover assets (not reported), ˆ/t tc cand + +1 1ˆ/t tc c , average between 1.43 in 2004–2006 and 2.38 in 2007–2009 for ˆ/t tc c and

average between 1.40 in 2004–2006 and 2.24 in 2007–2009 for + +1 1ˆ/t tc c . These results indi-

cate that Shinkin banks could reduce inefficiency by reducing carryover assets and simulta-

neously expanding securities.

5 The Shephard output distance function measures output efficiency as the ratio of actual output to maximum

potential output.

Table 9.8 Average optimal and actual carryover assets (std. dev.).

Actual Optimal t-Value Actual Optimal t-Valuetc ˆ tc (prob> t) (prob> t)

2003–2005 83.4 53.9 10.81 87.8 71.5 6.82

(104.7) (78.6) (.01) (107.9) (100.2) (0.01)

2004–2006 87.8 70.2 7.28 86.7 64.1 8.54

(107.9) (94.6) (0.01) (108.7) (87.1) (0.01)

2005–2007 86.7 63.4 8.5 89.8 57.9 9.93

(108.7) (88.1) (0.01) (106.0) (75.2) (0.01)

2006–2008 89.8 56.4 10.53 97.5 52.2 11.33

(106.0) (74.6) (0.01) (117.8) (80.1) (0.01)

2007–2009 97.5 48.7 11.67 97.2 58.5 10.43

(117.8) (66.6) (0.01) (119.4) (94.9) (0.01)

1tc + 1ˆ tc +


Next, we compare actual deposits with optimal deposits by examining the network link

between deposits produced as an intermediate output of stage 1 and used as an input in stage

2. To calculate optimal deposits we combine the intensity variables for stages 1 and 2 with

actual deposits for the j=1,…,J Shinkin banks. In the dynamic problem, in period t, optimal

deposits in stage 1 must satisfy the constraint that 1

Jt t t

j jj

z zλ=

≤ ∑ , and in stage 2, optimal depos-

its must satisfy the constraint that 1

Jt t t

j jj

z z=

≥ Λ∑ . Let 1,ˆ , ,tj j Jλ = … and 1,ˆ , ,t

j j JΛ = …

represent the optimal period t intensity variables for the dynamic problem. Combining the

two constraints shows that the intensity variables must be chosen so that

1 1

ˆˆJ J

t t t t tj j j j

j j

z z zλ= =

Λ ≤ ≤∑ ∑ (9.14)

Let the minimum value of deposits that satisfies both constraints in Equation (9.14) equal

min

1

ˆˆJ

t t tj j

j

z z=

= Λ∑ and let the maximum value of deposits that satisfies both constraints in Equation

(9.14) equal max

1

ˆˆJ

t t tj j

j

z zλ=

= ∑ . Similar minimum and maximum values for optimal deposits can

be calculated for periods t+1 and t+2 in the three-period dynamic problem. If the two con-

straints in Equation (9.14) are binding, then min maxˆ ˆt tz z= . The two constraints were binding for

all but two or three banks in each year. Table 9.9 reports the average ratios of optimal to actual

deposits. On average, the ratios range from 0.855 to 0.922, but some Shinkin banks would use

only 48% of their actual deposits and other Shinkin banks would use as much as 136% of

actual deposits if they were to produce the optimal level of deposits consistent with the

dynamic network technology in a given three-year period. We used a t-test to test the null

hypothesis that the ratio of optimal to actual deposits equals 1. In every year the t-test rejected

the null. These results indicate that on average, Shinkin banks produce too many deposits in

stage 1 and then use too many deposits relative to the amount needed to efficiently produce

the portfolio of loans and securities in stage 2. We also examined the Pearson and Spearman

correlation coefficients and there was no significant correlation between the ratios of optimal

to actual deposits with total Shinkin bank assets in any of the years. Thus, bank size has no

systematic correlation with the tendency of bank managers to overuse or underuse deposits

relative to their optimal levels.

9.6 Summary and conclusions

Shinkin banks are small cooperative banks operating in regional markets in Japan. They

collect deposits from members and nonmembers and then use those deposits to purchase

securities and make loans within their prefecture. In this chapter, we used DEA to examine

the performance of Shinkin banks. Our method provided some structure to the production

technology that is not often found in bank efficiency/productivity studies. We allowed Shinkin

banks to have a network structure where deposits were produced as an intermediate output in

one stage of production and then used as an input to produce the portfolio of loans and securi-

ties investments in a subsequent stage. We also allowed a dynamic structure to the production

technology by allowing Shinkin banks to carryover some assets from one period to the next.

Tabl

e 9.

9R

atio

s of

opti

mal

dep

osi

ts t

o a

ctual

dep

osi

ts.

ˆt tz z

1 1

ˆt tz z

+ +

2 2

ˆt tz z

+ +

Mea

nM

inim

um

Max

imum

Mea

nM

inim

um

Max

imum

Mea

nM

inim

um

Max

imum

(s)

(s)

(s)

2003–2005

0.8

69

0.6

12

1.3

13

0.8

68

0.5

16

1.1

90

0.8

93

0.5

45

1.1

32

(0.0

97)

(0.0

95)

(0.0

82)

2004–2006

0.8

63

0.5

11

1.3

62

0.8

70

0.5

00

1.1

18

0.8

95

0.5

44

1.1

14

(0.1

00)

(0.0

95)

(0.0

80)

2005–2007

0.8

68

0.4

99

1.1

78

0.8

62

0.4

79

1.1

15

0.9

03

0.5

74

1.1

75

(0.0

99)

(0.0

97)

(0.0

77)

2006–2008

0.8

59

0.4

73

1.2

68

0.8

56

0.4

88

1.2

03

0.9

21

0.6

46

1.2

53

(0.1

06)

(0.0

97)

(0.0

72)

2008–2009

0.8

55

0.4

80

1.1

22

0.8

74

0.5

46

1.3

28

0.9

22

0.6

58

1.2

52

(0.0

99)

(0.0

97)

(0.0

70)

Opti

mal

dep

osi

ts a

re z

and a

ctual

dep

osi

ts a

re z

.


The effect of carryover assets was to allow bank managers to choose the period in which to

use deposits and equity capital to produce the portfolio of loans and securities. If poor eco-

nomic conditions in one period would cause many loans to become nonperforming, bank

managers could effectively carryover assets to a subsequent period when economic condi-

tions might have improved enough for them to make the same amount of loans, but with

fewer loans becoming nonperforming.

We estimated the dynamic network model giving bank managers three-year horizons

using data from 2002 to 2009. We found that if Shinkin banks were to become efficient and

produce on the frontier of the dynamic network technology, they could simultaneously reduce

inputs and nonperforming loans and expand performing loans and securities investments by

an average of 14.4–15.6% of average inputs and outputs. We also found that Shinkin banks

could improve performance by producing fewer deposits and by carrying over fewer assets

from one period to the next.

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Documents

Efficiency and Productivity Growth (Modelling in the Financial Services Industry) || A dynamic network DEA model with an application to Japanese Shinkin banks