Dynamic Network Performance with an Application to Japanese Cooperative Shinkin Banks
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Transcript of Dynamic Network Performance with an Application to Japanese Cooperative Shinkin Banks
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Dynamic Network Performancewith an Application to Japanese
Cooperative Shinkin Banks
Hirofumi Fukuyama1* and William L. Weber2
1. Faculty of Commerce, Fukuoka University, Japan2. Department of Economics and Finance, Southeast Missouri State University, U.S.A.
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• Efficiency Measures-Distance Functions
• Farrell (JRSS-1957), Shephard (1970)
• Data Envelopment Analysis-Charnes, Cooper, Rhodes (EJOR-1978)
• Färe, Grosskopf, and Lovell (Production Frontiers-1994)
• Directional Distance Functions-Chambers, Chung, and Färe (JET-1996, JOTA-1998), Färe and Grosskopf (2004)
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Production With Undesirable Outputs
• Färe, Grosskopf, and Weber (Ecol. Ec.-2006)-Agriculture
• Färe, Grosskopf, Noh, and Weber (J.Econometrics-2005)- Färe, Grosskopf, Pasurka, and Weber (App. Ec- 2011)-Electric Utilities
• Fukuyama and Weber (2008, 2009, 2010, 2011)-Financial Institutions
• Rogers and Weber (2011)-Transportation
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Standard Black Box Model
x=(x1,…xN) inputs
P(x)=the output possibility set={(y,b): x can produce (y,b)}
y=(y1,…,yM) desirable outputs
b=(b1,…,bJ) undesirable outputs
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Directional Distance Function
( , , ; ) max{ : ( , ) ( )}y bD x y b g y g b g P x
y
b
(b,y)
y+βgy
b-βgb
gy
gb
P(x)
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y1
y2
P(xd, xu)
0
P(xd’,xu’)
1 1
desirable inputs undesirable inputs
( ,..., ) ( ,..., )d d u d Nx x x x x x
' , 'd d u ux x x x
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y
b
P(xd,xu)
0
P(xd’,xu’)
' , 'd d u ux x x x
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DEA (CRS) Production Technology
1
1
1
( , , ) : , 1,..., ,
, 1,..., ,
, 1,..., ,
0, 1,...,
Jt t t
nj j nj
Jt tmj j m
j
Jt tlj j l
j
tj
T x y b x x n N
y y m M
b b l L
j J
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1
1
1
( , , ; ) max{ : , 1,..., ,
, 1,..., ,
, 1,..., ,
0, 1,..., }
Jt t
o o o nj j no xj
Jt tmj j mo y
j
Jt tlj j lo b
j
tj
D x y b g x x g n N
y y g m M
b b g l L
j J
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y=loans, securities investments
xd=desirable inputs=labor, physical capital, net assets (equity capital) b=non-performing (bad) loans
xu=undesirable input=bt-1
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Are deposits an input (x) or an output (y)? Both?
Sealey and Lindley (J. of Finance -1977)-intermediation approach
Hancock (JPE-1985)-User cost approachCore deposits=inputTransaction deposits=output
Berger and Humphrey (NBER-1992, EJOR-1997)
Barnett and Hahm (J. Bus. Ec. Stat.-1994)-Banks produce the money supply
Fukuyama and Weber (2010)-Deposits are an input to one stage of production and an output at another stage of production.
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Network Production Models
• Färe and Grosskopf (Ec.Letters-1996, SEPS-2000)
• Färe and Whitaker (1996) (Dynamic and Network)
• Kao and Hwang (EJOR-2008)
• Tone and Tsutsui (EJOR-2009)
• Fukuyama and Weber (Omega-2010)
• Färe, Fukuyama, and Weber (IJISSC-2011)
• Akther, Fukuyama, and Weber (Omega-2012))
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A Two Stage Network Model
Stage 1P1(x,b)={z that can be produced by (x,b)}
Stage 2P2(z)={(y,b) that can be produced by z}
xt =(xt1,…xt
N), bt-1=(bt-11,…bt-1
J)
y t=(yt1,…,yt
M) bt =(bt1,…,bt
J)
zt =intermediate output=deposits
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1
1
{ , , , , such that
, , 1 and , , 2 }.
t t t t t t
t t t t t t t t
N b x z b y
b x z P z b y P
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1
11
1 11
1
11
21
21
21
( , , , , ) :
Stage 1:
, 1,..., ,
, 1,..., ,
, 1,..., ,
Stage 2:
, 1,..., ,
, 1,..., ,
t t t t t t
Jt t tn nj j
j
Jt t tl lj j
j
Jt tq qj j
j
Jt tq qj j
j
Jt t tm mj j
j
Jt tl lj j
j
T x b z y b
x x n N
b b l L
z z q Q
z z q Q
y y m M
b b
1 2
, 1,..., ,
0, 0, 1,..., ,
t
t tj j
l L
j J
The Network Technology
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11
, 1,..., ,J
t tq qj j
j
z z q Q
21
, 1,..., ,J
t tq qj j
j
z z q Q
1 21
0, 1,..., ,J
t t tqj j j
j
z q Q
The two constraints
First Stage
Second Stage
Can be rewritten as
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• Dynamic Models
• Färe and Grosskopf (1996, 1997)
• Bogetoft, Färe, Grosskopf, Hayes, and Taylor (JORSJ-2009)
• Färe, Grosskopf, Margaritis, and Weber (JPA-2011)
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Dynamic ModelProduction in period t-1 affects the technology in period t
Intermediate output produced in the second stage of production= ct
ct affects stage 2 production in period t+1
ct = carryover assets= Assets – Required Reserves – physical capital – loans - securities
Bad loans produced in period t-1, bt-1, become an undesirable inputin stage 1 production in period t
Total output consists of final outputs and carryover assets
t t tm m my fy c
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Dynamic Network Model (y=fy+c)
P1(xt,bt-1) P1(xt+1,bt) P1(xt+2,bt+1)
P2(zt P2(zt+1, ct) P2(zt+2, ct+1)
xt,bt-1 xt+1 xt+2,
ztzt+1 zt+2
(yt, bt) (yt+1,bt+1) (yt+2,bt+2)
bt
ctct+1
ct-1
bt+1
, ct-1)
bt+2
ct+2
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Dynamic Network DEA Technology
1 1 1 1 1 11 2
1 1
0 0 11
at 1,
Stage 1 Stage 2
, 1,..., , 1,..., J J
n nj j q qj jj j
l lj j
DN
t
x x n N z z q Q
b b
1 1 12
1 1
1 1 1 1 1 1 11 2
1 1
11
, 1,..., , 1,...,
, 1,..., , 1,..., ,
0, 1,...,
J J
l lj jj j
J J
q qj j m m mj jj j
j
l L b b l L
z z q Q fy c y m M
j J
0 0 12
1
12
, 1,...,
0, 1,...,
J
m mj jj
j
c c m M
j J
1 1
1 1 1 1 1 1
1 1
{ , , , , 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
DN 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
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1 21 1
1 11
1
Stage 1 Stage 2
, 1,..., , 1,...,
, 1,...,
J Jt t t t t tn nj j q qj j
j j
Jt t tl lj j
j
x x n N z z q Q
b b l L
21
1 21 1
1
, 1,...,
, 1,..., , 1,...,
0, 1,..., , 2,..., 1
Jt t tl lj j
j
J Jt t t t t t tq qj j m m mj j
j j
tj
b b l L
z z q Q fy c y m M
j J t T
1 12
1
2
, 1,...,
0, 1,..., , 2,..., 1
Jt t tm mj j
j
tj
c c m M
j J t T
In the intermediate periods, t=2,…,T-1
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1 21 1
1 11
1
Stage 1 Stage 2
, 1,..., , 1,..., J J
T T T T T Tn nj j q qj j
j j
T T Tl lj j
j
x x n N z z q Q
b b
21
1 21 1
1
, 1,..., , 1,...,
, 1,..., , 1,..., ,
0, 1,...,
J JT T Tl lj j
j
J JT T T T T T Tq qj j m m mj j
j j
Tj
l L b b l L
z z q Q fy c y m M
j J
1 12
1
2
, 1,...,
0, 1,...,
JT T Tm mj j
j
Tj
c c m M
j J
And in the final period, T,
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1 2
1 1 11 1
1
( , , ; ) max{ ... ... ) :
1,
Stage 1 Stage 2
, 1,...,
k k k t T
Jx
nk n nj jj
D x y b g
t
x g x n N z
1 1 12
1
0 0 1 1 1 11 1 2
1 1
1 1 1 11 1
1
, 1,...,
, 1,..., , 1,...,
, 1,...,
J
q qj jj
J J
lk lj j lk b lj jj j
J
q qj j mk yj
z q Q
b b l L b g b l L
z z q Q fy g
1 1 12
1
0 0 12
1
, 1,..., ,
, 1,...,
J
m mj jj
J
mk mj jj
c y m M
c c m M
1 1 11 2 1
Choice variables in t=1 are
and , 1,..., , , 1,..., ,j j mj J c m M
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2 1 21 1
1 11 1
Stage 1 Stage 2
, 1,..., , 1,...,J J
t t t t t tnk x nj j q qj j
j j
t t tlk t b lj j
j
x g x n N z z q Q
b g b
21 1
1 21 1
, 1,..., , 1,...,
, 1,..., , 1,...,
J Jt t tlk t b lj j
j
J Jt t t t t t tq qj j mk t y m mj j
j j
l L b g b l L
z z q Q fy g c y m M
1 12
1
, 1,..., J
t t tm mj j
j
c c m M
In the intermediate periods, t=2,…,T-1
1 2
Choice variables in t=2,...,T-1 are
and , 1,..., , , 1,..., ,t t tj j m tj J c m M
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1 21 1
11
Stage 1 Stage 2
, 1,..., , 1,...,J J
T T T T T Tnk T x nj j q qj j
j j
Tlk T b
x g x n N z z q Q
b g
11 2
1 1
1 21
, 1,..., , 1,...,
, 1,..., , 1
J JT T T T Tlj j lk T b lj j
j j
JT T T T T T Tq qj j mk T y mk mj j
j
b l L b g b l L
z z q Q fy g c y m
1
1 12
1
,..., ,
, 1,..., .
J
j
JT T Tm mj j
j
M
c c m M
And in the final period, T,
1 2
Choice variables in t=T are
and , 1,..., ,T Tj j Tj J
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• Network Links:
• in t,
• In t+1,
• In t+2,
• Etc.
1 21
0, 1,...,J
t t tqj j j
j
z q Q
1 1 11 2
1
0, 1,...,J
t t tqj j j
j
z q Q
2 2 21 2
1
0, 1,...,J
t t tqj j j
j
z q Q
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• Dynamic links:
• Between t and t+1, Undesirable output at stage 2 in t becomes and input to stage 1 in t+1
Carryover assets from period t become an input to stage 2 in period t+1
• Similar dynamic links between t+1 and t=2, etc.
12 1
1 1
J J
t t t t t tj j j j
j j
b b b b
12 2
1 1
and J J
t t t t t t tj j j j
j j
fy c y c c
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269 Japanese Shinkin Banks, 2002-2009
• Shinkin Banks are cooperative
• Accept deposits from members, make loans (real estate and commercial) to member firms within a given prefecture.
• Decline in Shinkin banks from 401 to 271 during 1998-2011 and shrank in size relative to for profit Regional Banks and City Banks
• Research by Nishikawa (1973) , Miyamura (1992) , Miyakoshi (1993) , and Hirota and Tsutsui (1992) has generally found some scale economies, not many scope economies.
• Fukuyama (1996) - large banks more technically efficient than small banks: better managerial oversight dominates any scale economies.
• Färe, Fukuyama, and Weber (2010)-ex ante merger gains: for infra-prefecture mergers biggest gains in Fukuoka and Saga, for inter-prefecture mergers, biggest gains between banks in Miyazaki and Nagasaki.
• Fukuyama and Weber (2008)-For profit regional banks were more efficient, had greater technical progress, but a higher shadow cost of reducing bad loans than cooperative Shinkin banks.
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Mean Std. dev. Min. Max.y1=loans 246.2 321.7 18.6 2409.3y2=securities 118.8 139.7 2.0 1119.1c1+c2=carryover assets 90.9 111.2 5.4 1023.2x1=labor 412 408 35 2651x2=physical capital 7.2 9.7 0.2 69.3x3=net assets (equity) 23.8 27.7 0.9 204.6z=deposits 431.0 523.4 33.1 4263.6b=non-performing loans 19.5 24.5 0.8 211.9
Except labor, all variables in billions of Japanese yen deflated by the Japanese GDP deflator
Descriptive Statistics (Pooled data 269 banks x 8 years, 2002-2009
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Directional Vector( , , ) ( , , )x y bg g g g x y b
Model uses a three period window: t, t+1, t+2Need 4 years of data, t-1, t, t+1, t+2
1
1
2
is fixed
and are endogenous
is fixed
tk
t t
tk
c
c c
c
100%t Is the percent of mean inputs and undesirable outputsthat can be contracted and percent of mean desirable outputsthat can be simultaneously expanded.
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mean Std. dev.
Min. Max. # on frontier
2003-20050.045 0.039 0 0.238 10
0.045 0.038 0 0.225 9
0.047 0.042 0 0.257 9
0.137 0.115 0 0.674 6
1̂2̂3̂
1 2 3ˆ ˆ ˆ
Estimates for 2003-2005
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Estimates of Dynamic Inefficiency
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2003-2005 2004-2006 2005-2007 2006-2008 2007-2009Karatsu Shinkin Bank xKanonji Shinkin Bank x xThe Kyoto Shinkin Bank x x xYamanashi Shinkin Bank xSapporo Shinkin Bank xJohnan Shinkin Bank x xChoshi Shinkin Bank xSawayaka Shinkin Bank xOsaka Higashi Shinkin Bank
x x x x
Himawari Shinkin Bank x x xKochi Shinkin Bank x x x x x
Frontier Banks
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Actual Optimalt-value
(prob>t)
Actual Optimalt-value
(prob>t)
2003-2005 83.4(104.7)
53.9(78.6)
10.81(.01)
87.8(107.9)
71.5(100.2)
6.82(.01)
2004-2006 87.8(107.9)
70.2(94.6)
7.28(.01)
86.7(108.7)
64.1(87.1)
8.54(.01)
2005-2007 86.7(108.7)
63.4(88.1)
8.5(.01)
89.8(106.0)
57.9(75.2)
9.93(.01)
2006-2008 89.8(106.0)
56.4(74.6)
10.53(.01)
97.5(117.8)
52.2(80.1)
11.33(.01)
2007-2009 97.5(117.8)
48.7(66.6)
11.67(.01)
97.2(119.4)
58.5(94.9)
10.43(.01)
tc ˆtc 1tc 1ˆtc
Optimal and Actual Values of Carryover Assets
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Calculating optimal deposits from the intensity variables two
max 11
min 21
ˆmaximum value:
ˆminimum value :
Jt t t
j jj
Jt t t
j jj
z z
z z
2 11 1
ˆ ˆJ J
t t t t tj j j j
j j
z z z
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Mean(s) Min. Max.
Mean(s) Min. Max.
Mean(s) Min. Max.
2003-2005 0.869(.097)
0.612
1.313
0.868(.095)
0.516
1.190
0.893(.082)
0.545
1.132
2004-2006 0.863(.100)
0.511
1.362
0.870(.095)
0.500
1.118
0.895(.080)
0.544
1.114
2005-2007 0.868(.099)
0.499
1.178
0.862(.097)
0.479
1.115
0.903(.077)
0.574
1.175
2006-2008 0.859(.106)
0.473
1.268
0.856(.097)
0.488
1.203
0.921(.072)
0.646
1.253
2008-2009 0.855(.099)
0.480
1.122
0.874(.097)
0.546
1.328
0.922(.070)
0.658
1.252
ˆt
t
z
z
1
1
ˆt
t
z
z
2
2
ˆt
t
z
z
Ratios of Optimal Deposits to Actual Deposits
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• Extension
• Dynamic Luenberger Productivity Growth
• Policy Implication-”Easy to fix” versus “Hard to Break”
1
1 1 1 1 1 1 1
1[ ( , , ; ) ( , , ; )
2
( , , ; ) ( , , ; )]
t t t t t t t t
t t t t t t t t
DL x y b g x y b g
x y b g x y b g