Technological Change and
Accumulated Capital
:A Dynamic Decomposition of
Japan’s Growth
Masahiro KURODA , Keio University
Koji NOMURA , Keio University
Keio Data Base：Keio Economic Observatory
Japan , May 30, 2003
Contents
• Official Statistics and Our Database
– IO-Table, Capital Measurement
• Structural Change ｖｓ New Technology
– Aij(Input Coefficient), Bij (Capital Coefficient)
• TFP and Structural Change
– Total Factor Productivity:TFP
– TFP under Static Structure
: Static Unit TFP through Static Interdependency
– TFP under the Dynamic Structural Change
: Dynamic Unit TFP through Capital Accumulation
Official Statistics
• Input-Output Table
– Basic Table : every five years from 1955
• activity base - 519×403 (1995)
– Extended Table : every year from 1973
• Capital Measurement
– Capital Formation Matrix : every five years from 1970
– Capital Stock Matrix : National Wealth Survey in 1955,70
KEO Data Base (KDB)
Demography
Environment
Economy
Technology
KDB
• Input-Output Table
– every year during 1960-95
• Measurement of Capital
– every year during 1955-92
• Capital Formation Matrix : Iij
• Capital Stock Matrix : Sij
• Measurement of Labor
– every years during 1960-92
• Man, Hour and Wage
industry×age×sex×education×employment status
Input-Output Table
com.
commodity
industry
X
U
scrap input
ind.
V
non-competitive
import
scrap output
value
added
Output
va
Final Demand
domestic E M Output
fd
I-O Table: X Table
Time-Series X-table
[Intermediate Inputs]
commodity
com.
43 commodities
8 scraps
scrap input
[Non-competitive Imports]
raw oil, natural gas,
ind.
iron ore, others
non-competitive
[Year]
import
1960-95
scrap output
Final Demand
industry domestic E MOutput
X
value
added
Output
「Input-Output Table」
Management and Coordination Agency
in 1960,65,70,75,80,85,90
Private Investment
Private Fixed Capital Formation Matrix
Private
Investment
commodity P
Ii
;i
industry ; j
P
I ij
「Fixed Capital Formation Matrix」
Management and Coordination Agency
in 1970,75,80,85,90
Public Investment
Public Fixed Capital Formation Matrix
Public
Investment
commodity
G
;i
I i
industry ; j
G
I ij
infrastructure ; k
G
I ik
「Fixed Capital Formation Matrix」
Management and Coordination Agency
Estimation of
Capital
Formation Matrix
Estimation of
Capital
Stock Matrix
Capital Stock and Value Added
：Aggregated Level
1200
(trillion yen−1985 price)
Capital Stock
1960-70 : 7. 10%
1970-80 : 9. 17%
900
90
1980-90 : 4. 66%
600
Bij ↑
80
Real Value Added
300
1960-70 : 7. 20%
70
1970-80 : 4. 13%
1960
1980-90 : 4. 28%
0
0
100
200
300
400
500
Capital Coefficient -Bij
：Aggregated Level
3.0
2.5
Electric
Machinery
2.0
General
Machinery
1.5
1.0
Building &
Construction
0.5
0.0
1960
1970
1980
1990
Capital Coefficient -Bij
：Agriculture, Forestry and Fishery Industry
0.3
Transportation
Equipment
(Ships)
0.2
General
Machinery
for Agri.
0.1
Building &
Construction
(Land
Improve. ,etc)
Animal,
Plants
0.0
1960
1970
1980
1990
Capital Coefficient -Bij
：Road Transportation
0.2
Motor
Vehicle
0.1
Building &
Construction
0.0
1960
1970
1980
1990
Capital Coefficient -Bij
：Service except Commerce, Trans., Medical, etc
0.4
0.3
Motor
Vehicle
0.2
Electric
Machinery
0.1
0.0
Building &
Construction
1960
1970
1980
1990
Capital Coefficient -Bij
：General Machinery Manufacturing
0.3
Electric
Machinery
General
Machinery
0.2
0.1
Building &
Construction
0.0
1960
1970
1980
1990
Capital Coefficient -Bij
：Motor Vehicle Manufacturing
0.10
Electric
Machinery
General
Machinery
0.05
Building &
Construction
0.00
1960
1970
1980
1990
Capital Coefficient -Bij
：Electric Machinery Manufacturing
0.3
Electric
Machinery
General
Machinery
0.2
0.1
Building &
Construction
0.0
1960
1970
1980
1990
Structural Change
• Definition of Economic “Structure”
– Aij =Xij / Xj : Input Coefficient
– Bij =Sij / Xj : Capital Coefficient
Static
Structure
Dynamic
Structure
Aij
Bij
Ii
Industry-base TFP
I-O Table
j-Industry
Intermediate
Input
Aij Xj
TFP ; Tj
・ Industry-base
・ Structural Change
Aj , Bj , Lj
Capital
Input
Bij Xj
・ Production Function
Xj =f ( Kj, Lj, Xij, Tj )
Labor
Input
Lkj Xj
Output
Xj
The Rate of Traditional TFP Growth
in sector j
Xj :real gross output
Xij : intermediate input I
Llj : labor input of type l
Kkj:capital input of type k
pjt,plj,pkj:prices of output, labor and capital
inputs
L
K
&
&
&
&
Tj  Xj 
pi,t Xij,t Xij 
plj,tLlj,t Llj 
pkj,tKkj,t K&kj
  =  −∑
  −∑
  −∑
 
Tj  Xj  i p X Xij  l p X Llj  k p X Kkj
j,t j,t  t
j,t j,t  t
j,t j,t 
 t  t
t
Static Unit TFP
Unit Structure
of i - commodity
Intermediate
Input
Capital
Input
Labor
Input
Output
Aij Xj
Static Unit TFP ; Ti
・ Unit Structure
・ Structural Change
Aij , Bij , Lkj
Bij Xj
・ Aggregation of
Industry-base TFP
Lkj Xj
・
Ti
Ti
Xj
・
PjXj Tj
= Σj
PvV Tj
・ Pecuniary Spillover Effects
through Static Technological
Relationship
Static Unit TFP of Commodity i
L =B
L
t
K =B
K
t
*
t
*
t
−1
(I − A t ) e ( i )
−1
(I − A t ) e ( i )
*
*
K *
L *
&
&
&
plj,t Llj,t  Llj 
pkj,t Kkj,t  Kkj 
Ti 
 *
 *  −∑∑
  = −∑∑




T
p
L
p
K
j l
j k
i,t
i,t  lj 
 i t
 kj 
U
t
t
Dynamic Inverse
Static IO Balance ; Aij Xj +Iij+ Ci= Xi
ｔ
t+1
ｔ
Capital Accumulation ; Kij = (1-δi) Kij+ Iij
ｔ
t+1 t+1
ｔ ｔ
ｔ
ｔ
Dynamic IO Balance ; Aij Xj + Bij Xj - (1-δi)Bij Xj+ Ci= Xi
t =0
Intermediate
Input
Aij Xj
Capital
Input
Bij Xj
Labor
Input
Lkj Xj
Output
Xj
ｔ
t = -1
t = -2
t = -5
t = -3
t = -4
t = -6
t = -7
・
・
・
・
Dynamic Unit TFP
Dynamic Unit Structure
of i - commodity
t =0
t = -1
t=-2
t=-3
t=-4
＊
Dynamic Unit TFP ; Ti
・ Decomposition by Dynamic Inverse
・ Structural Change
t
t
t
Aij , Bij , Lkj ,t=0,…,-∞
・ Aggregation of
Time-series Static Unit TFP
t=-5
t=-6
t=-7
・＊ ・ 0
Ti Ti
＊=
Ti Ti 0
00
・t
K r -∞ t Ti
+ 0 0Σ Φ
Ti t
PvV t=-1
・ Pecuniary Spillover Effects
through Capital Accumulation
and Structural Change
Dynamic Unit TFP
 T&

T
D ( f t* )


t
 T&
= 
T
U ( f t* )


t
+σ
∗
K ,t
∞
Φ
∑
τ
=1
*
t −τ
 T&

T
U ( f t*− τ )


 t −τ
and
D(f t* )
 T& 
 
 T t
&*
 f& * 

L
=  *  − σ L∗ ,t  *
L
f 

 t
Φ*t −τ
&*
∞


L
 − σ K∗ ,t ∑ Φ *t −τ σ L∗ ,t −τ 
*


τ =1
L
t
*


(
)
S
1
δ
−
∗
*
*
t −τ +1
= st −τ st −τ +1 
+ σ K ,t −τ +1 
*
 I t −τ +1




 t −τ
Dynamic Inverse
：Required Output Induced by Motor Vehicle Demand in 1992
180
Motor Vehicle
t=0
160
140
120
100
Demand as
Capital Goods,
mainly
80
60
40
20
t=-10
Building &
Construction
t=-1
t=-2
t=-3
0
t=0
General
Machinery
t=-1
t=-2
Other
Service
t=0
t=-1
Wholesale
Electric & Retail
Machinery
t=0
Demand as
Intermediate
Goods,
mainly
Dynamic Inverse
：Required Output Induced by Motor Vehicle Demand in 1980
160
Motor Vehicle
t=0
140
120
100
80
60
40
20
t=-10
Demand as
Capital Goods,
mainly
Building &
Construction
t=-1
t=-2
t=-3
0
t=0
General
Machinery
t=-1
Iron& Steel
t=0
Other
Service
t=0
t=-1
Wholesale
Electric & Retail
Machinery
t=0
Demand as
Intermediate
Goods,
mainly
Comparison of TFP
3.5
：Electric Machinery
(1970=1.0)
3.0
2.5
2.0
1.5
1.0
Industry-base TFP
Static Unit TFP
Dynamic Unit TFP
0.5
0.0
1960
1970
1980
1990
Composition of Bij
Comparison of TFP
1.4
： Agriculture, Forestry and Fishery
1.2
1.0
(1970=1.0)
0.8
0.6
Industry-base TFP
Static Unit TFP
Dynamic Unit TFP
0.4
0.2
0.0
1960
1970
Composition of Bij
1980
1990
Comparison of TFP
2.5
： Motor Vehicle
(1970=1.0)
2.0
1.5
1.0
Industry-base TFP
Static Unit TFP
Dynamic Unit TFP
0.5
0.0
1960
1970
1980
1990
Composition of Bij
Comparison of TFP
2.0
： General Machinery
1.8
(1970=1.0)
1.6
1.4
1.2
1.0
0.8
0.6
Industry-base TFP
Static Unit TFP
Dynamic Unit TFP
0.4
0.2
0.0
1960
1970
Composition of Bij
1980
1990
Comparison of TFP
1.3
： Aggregated Level
1.2
(1970=1.0)
1.1
1.0
0.9
0.8
0.7
0.6
TFP (Industry-base TFP=
Static Unit TFP)
0.5
Dynamic Unit TFP
0.4
1960
1970
Composition of Bij
1980
1990
Contribution to Growth
： Aggregated Level
1.0
15%
TFP
TFP
(t= -1・・-∞)
0.8
30%
0.6
Labor
Input
0.4
55%
0.2
Capital
Input
23%
TFP
Labor
Input
(t= -1・・-∞)
72%
Labor
Input
0.0
Static
Contribution
Dynamic
Contribution
(Real GDP Growth =1.0 during 1975-90)
Contribution to Growth
:Aggregated Level
0.08
31%
L(t=-1,・・・,-∞)
L(t=0)
TFP(t=0)
TFP(t=-1,・・・,-∞)
0.06
4%
8%
0.04
86%
23%
52%
0.02
13%
21%
16%
40%
34%
42%
27%
30%
36%
17%
26%
0.00
13%
15%
-34%
-0.02
1970-75
1975-80
1980-85
1985-90
1975-90
Thank you for your attention.
If you need more information,
please take a contact to the
following address.
E-mail:kuroda@fbc.keio.ac.jp
nomura@sanken.keio.ac.jp