AN INPUT-OUTPUT FORECASTING MODEL
OF THE JAPANESE ECONOMY
by
Young Sun Lee
T h e s is s u b m itte d t o th e F a c u lty o f th e G ra d u a te ,S c h o o l
o f th e U n iv e r s it y o f M a ry la n d i n p a r t i a l f u l f i l l m e n t
o f th e re q u ire m e n ts f o r th e d eg re e o f
D o c to r o f P h ilo s o p h y
1976
i
ABSTRACT
T itle
o f T h e s is :
An In p u t- O u tp u t F o re c a s tin g M odel o f th e Japanese
Economy
Young Sun L e e ,
D o c to r o f P h ilo s o p h y , 1976
T h e s is d ir e c t e d b y :
P r o fe s s o r C lo p p e r A lm on, D e p a rtm e n t o f E conom ics,
U n iv e r s it y o f M a ry la n d
The p u rp o se o f t h i s
s tu d y i s
to b u i l d an a n n u a l medium te rm in p u t -
o u tp u t f o r e c a s t in g model f o r th e Japanese economy w it h s u f f i c i e n t com­
m o d ity d e t a i l .
The m odel f o r e c a s ts y e a r - b y - y e a r f o r te n y e a rs ahead,
in d u s t r y o u t p u t , em ploym ent, in v e s tm e n t, in v e n t o r y change, e x p o r ts ,
im p o r t s , wage r a t e s , p r ic e s , and p r o d u c t i v i t y w i t h i n
an in p u t - o u t p u t t a b le .
model in
The model i s
th e fra m e w o rk o f
d e s ig n e d as a p r o to ty p e c o u n try
th e I n t e r n a t i o n a l I/O F o re c a s tin g System a t th e U n iv e r s it y
o f M a ry la n d .
The m ain c h a r a c t e r is t ic s o f th e I/O c o m p u ta tio n is c o n s is te n c y .
I n t h i s s tu d y , th e c o n s is te n c y i s
u s u a l in
p u rs u e d in th r e e w ays.
I/O m o d e ls , c o n s is te n t o u tp u t i s
in t e r m e d ia t e demand and f i n a l demand.
c a lc u la t e d
as
in th e sense o f
S e c o n d ly , c o n s is te n t p r ic e is
c a lc u la t e d a ssum ing o p tim a l p r i c i n g b e h a v io r o f f ir m s .
c o n s is te n t r e l a t i o n betw een o u tp u t and p r ic e i s
o u tp u t
F ir s tly ,
T h ir d ly ,
th e
p u rsu e d by m a kin g th e
a f u n c t io n o f p r ic e s and by m a kin g th e p r ic e _as a f u n c t io n
o f o u tp u t.
The t e c h n ic a l and b e h a v io r a l e q u a tio n s a re fo r m u la te d f o r a l l th e
econom ic v a r ia b le s
to be f o r e c a s te d .
The m a in e f f o r t s
a re made to
e s tim a te wage r a t e e q u a tio n s , la b o r re q u ire m e n t e q u a tio n s , c o n su m p tio n
r
e q u a tio n s , p r ic e e q u a tio n s , and in v e s tm e n t e q u a tio n s .
s t r u c t u r e o f th e m odel i s
A f t e r th e
d e s c r ib e d , each c h a p te r w i l l e x p la in th e
t h e o r e t i c a l b a s is , th e m a th e m a tic a l f o r m u la t io n , and th e e m p ir ic a l
r e s u l t s o f each e q u a tio n .
o f th e m odel i s
In th e l a s t c h a p te r , p r e d ic t iv e p e rfo rm a n c e
t e s te d b y s im u la t io n .
m odel and some p o s s i b i l i t i e s
c h a p te r .
A ls o , th e l i m i t a t i o n s
o f th e
f o r im provem ent a re d is c u s s e d in th e l a s t
Acknow ledgem ents
I
w o u ld l i k e
t o th a n k P r o fe s s o r C lo p p e r A lm on, my d i s s e r t a t io n
s u p e r v is o r , who in tr o d u c e d me to th e in p u t - o u t p u t e co n o m ics.
th e d e b t I owe h im t h i s
s tu d y w o u ld n e v e r have been p o s s ib le .
W ith o u t
I w is h
to e x p re s s my g r a t i t u d e t o Ms. M a rg a re t B u c k le r , D r. D ouglas N yh u s, and
M r. D a v id B e lz e r f o r t h e i r h e l p f u l a d v ic e .
to M r. N o b u yu ki Yamamura, i n
a c t u a lly jo in e d t h i s
S p e c ia l th a n k s a re a ls o due
th e Long-Term C r e d it Bank o f Ja pa n , who
s tu d y by p r o v id in g me w it h
th e n e c e s s a ry d a ta .
A ls o , my s p e c ia l th a n k s go to M rs . D a is y F o s te r f o r h e r c o n s c ie n tio u s
t y p in g o f th e m a n u s c rip t and to M rs.
Susan Sims f o r h e r c o r r e c t in g my
E n g lis h .
s tu d y was s u p p o rte d by th e Com puter
The co m p ute r tim e f o r t h i s
S c ie n ce C e n te r o f th e U n iv e r s it y o f M a ry la n d .
My w i f e , Kay, d e s e rv e s many th a n k s f o r u n d e rs ta n d in g and e n co u ra g e ­
ment th ro u g h f o u r y e a rs o f o u r g ra d u a te c a r e e r .
s u p p o rt o f my p a re n ts in K o re a .
I a ls o a p p r e c ia te th e
iv
TABLE OF CONTENTS
C h a p te r
Page
ACKNOWLEDGEMENTS......................................................................................................
iii
PART I
I.
INTRODUCTION .............................................................................................
1
II.
STRUCTURE OF THE JAPANESE M O D E L ...............................................
6
PART I I
III.
WAGE RATE EQUATION...............................................................................
23
IV .
LABOR REQUIREMENT EQUATION.............................................................
42
V.
MANHOURS E Q U A T IO N ...............................................................................
56
V I.
PRICE EQUATION........................................................................................
60
PART I I I
V II.
PERSONAL CONSUMPTION EXPENDITURES
..........................................
86
V III.
INVESTMENT............................ .....................................................................
109
IX .
TRADE E Q U A T IO N S ....................................................................................
133
X.
OTHER FINAL DEMAND COMPONENTS...................................................
153
X I.
COEFFICIENT CHANGE ...............................................................................
158
PART IV
X II.
SIMULATION TEST OF THE COMPLETE M O D E L .................................
168
APPENDIX A
DATA SO U R C E S ...............................................................................
193
APPENDIX B
THE FORECASTS...............................................................................
197
BIBLIOGRAPHY ................................................................................................................
246
V
L IS T OF TABLES
T a b le
Page
III- l.
Employment S h a r e ................................................... .... ...........................
25
III-2 .
R e la t iv e Wages
32
III-3 .
Wage Rate E q u a tio n R e g r e s s i o n ................................ ....
36
III-4 .
S im u la tio n o f Wage R ate L e v e l ...................................................
41
R e g re s s io n R e s u lts o f L a b o r R e q u ire m e n t E q u a tio n s
. .
52
R e g re s s io n R e s u lts o f Manhours P er Employee
...................
58
V I-1 .
R e g re s s io n R e s u lts o f M arkup R a tio E q u s tio n
...................
72
V I-2 .
P r ic e E q u a tio n R e g re s s io n
............................................................
79
V II- 1 .
Commodity Group C l a s s i f i c a t i o n and P r ic e E l a s t i c i t i e s .
96
V II-2 .
R e g re s s io n R e s u lts o f C onsum ption F u n c tio n
IV - 1 .
V - l.
V III-1 .
...................................................................................
In v e s tm e n t E q u a tio n R e g re s s io n R e s u lts
.......................
100
............................
116
IX - 1 .
R e g re s s io n R e s u lts o f Im p o rt E q u a tio n
.................................
139
IX -2 .
R e g re s s io n R e s u lts o f E x p o rt E q u a tio n
. . . . . . . .
146
X I-1 .
A cro ss-T h e -R o w C o e f f ic i e n t Change R e g re s s io n
. . . .
162
X II- 1 .
S im u la tio n T e s t o f th e F in a l Demand Components . . . .
170
X II-2 .
S im u la tio n E r r o r o f O u tp u t and P r ic e
.................................
176
X II-3 .
S im u la tio n T e s t o f In v e s tm e n t and L a b o r M a rke t
V a r i a b l e s ................................................... ..............................................
177
The W eighted A verage A b s o lu te P e rc e n ta g e E r r o r s o f th e
S im u la tio n
.............................................................................................
179
X II-5 .
S e n s i t i v i t y A n a ly s is w it h D is p o s a b le Income
...................
182
X II- 6 .
E r r o r s o f M a jo r Macro V a r ia b le F o re c a s ts
.......................
184
X II- 7 .
C om parison o f C o m p o s itio n s o f Two D if f e r e n t G row th
R a tes i n Y e a r 1985
..........................................................................
186
S e n s i t i v i t y A n a ly s is w it h I n t e r e s t R ates
188
X II- 4 .
X II-8 .
.......................
>
vi
T a b le
Page
B- 1
G .N .P . S u m m a ry ..............................................................................................
199
B- 2
F o re c a s t o f E x p o r t s ......................... .... ..................................................
200
B- 3
F o re c a s t o f C onsum ption
.......................................................................
208
B- 4
F o re c a s t o f I m p o r t s .................................................................................
216
B- 5
F o re c a s t o f I n v e s t m e n t .............................................................. ....
224
B- 6
F o re c a s t o f Employment ............................................................................
226
B- 7
F o re c a s t o f O u t p u t ................................................ .... ................................
22 7
B- 8
F o re c a s t o f N o m in a l H o u rly W a g e .....................................................
235
B- 9
F o re c a s t o f P r o d u c t i v i t y .......................................................................
238
B -1 0
F o re c a s t o f P r i c e .....................................................................................
237
B - ll
F o re c a s t o f M o n th ly M anhours Per Employee
245
. .........................
v ii
L IS T OF FIGURES
F ig u re s
Page
I I- l.
F low s o f th e P r o d u c t s .....................................................................
7
II-2 .
S t r u c t u r e o f th e M o d e l .................................................................
8
IV - 1 .
C om parison o f P r o d u c t iv it y F o re c a s t
V II- 1 .
C om parison o f C P I's
.....................................
55
..........................................................................
106
V III-1 .
Two D im e n s io n a l S e a rc h in g P ro ce d u re
.................................
114
V III-2 .
D e p r e c ia tio n R ate S chedule
........................................................
126
1
CHAPTER I
I n t r o d u c t io n
T h is s tu d y p re s e n ts an a n n u a l n a t io n a l e c o n o m e tric m odel f o r
i n t e r i n d u s t r y f o r e c a s t in g o f th e Japanese economy.
th e p u rp o s e o f medium— o r lo n g - te r m a n a ly s is .
It
is b u ilt fo r
C u r r e n t ly ,
th e i n t e r -
d u s t r y f o r e c a s t in g g ro u p a t th e U n iv e r s it y o f M a ry la n d i s w o rk in g on
a d ynam ic w o rld in p u t - o u t p u t f o r e c a s t in g system i n w h ic h e le v e n c o u n tr y
m odels and one c e n t r a l t r a d e m odel a re in c lu d e d .
T h is d is s e r t a t io n
d e s ig n e d t o make a p r o to ty p e c o u n tr y m odel f o r th e s y s te m .
The
C om puter F o r e c a s tin g Program , c a lle d
, FORPf ^ , w h ic h was d e v e lo p e d by
th is
1h o u s e k e e p in g 1 p ro gram
s tu d y , w i l l be used as a b a s ic
c o u n tr y f o r e c a s t in g m odels i n th e s y s te m .
T h is m odel i s
is
fo r a ll
d e s ig n e d as
t h e f i r s t o f a s e r ie s o f INFORUM m odels f o r c o u n t r ie s o th e r th a n th e
U .S .
A n o th e r p u rp o se o f th e s tu d y i s
to show a p o s s i b i l i t y o f m o d i­
f i c a t i o n o f INFORUM ty p e in p u t - o u t p u t f o r e c a s t in g m o d e ls .
b o o k , 1985:
S in c e th e
I n t e r i n d u s t r y F o re c a s ts o f th e A m e ric a n Economy was
p u b lis h e d , t h e r e has been c r i t i c i s m
as w e l l as a p p r e c ia t io n .
o
The
■^FORP was o r i g i n a l l y w r i t t e n by C lo p p e r Almon and was debugged,
ch an g ed , and expanded b y th e a u t h o r .
2
A lm o n , C. e t a l .
1 98 5 :
I n t e r i n d u s t r y F o re c a s ts o f th e A m e rica n
Economy.
R eview ed by W ig le y , K . J . i n th e Econom ic J o u r n a l, 1 97 5 , Ju n e ,
b y Anne C a r t e r , JE L, 1 9 7 5 ; and by S t i g l i t z , J .E . in The B ro o k in g s M o d e l:
P e r s p e c tiv e and R e ce nt D e v e lo p m e n ts ,
ed. b y Fromm, G and L .R . K le in .
N o r th - H o lla n d P u b lis h in g Co. 1975.
2
m a in c r i t i c i s m s
T h is s tu d y t r i e s
fo c u s on s t a t i s t i c a l method and on t h e o r e t i c a l s t r u c t u r e .
to re sp o n d to th o s e c r i t i c i s m s .
T h is m odel i s based on th e U .S . INFORUM ( I n t e r i n d u s t r y F o re c a s tin g
P r o je c t a t th e U n iv e r s it y o f M a ry la n d ) m o d e l.
m o d e l, th e b a s ic id e a i s
As i n th e U .S . INFORUM
t o f o r e c a s t , y e a r - b y - y e a r f o r te n y e a rs ahead,
in d u s t r y o u t p u t , em ploym ent, in v e s tm e n t, p r ic e s , and p r o d u c t i v i t y w it h in
th e fra m e w o rk o f an in p u t - o u t p u t t a b le .
v ia t e s
H ow ever, th e p re s e n t m odel de­
fro m th e U .S . INFORUM m odel i n s e v e r a l p o in t s .
re s p o n d c r e a t i v e l y to some o f th e v a l i d
It
a tte m p ts to
c r i t i c i s m s o f th e U .S . INFORUM
m o d e l.
I n th e i n t e r n a t i o n a l s yste m , c o u n try m odels w i l l be lin k e d to th e
c e n t r a l t r a d e m o d el^ th ro u g h th e p r ic e m echanism .
T h e r e fo r e , th e model
s h o u ld in c lu d e p r ic e m odel as w e ll as r e a l m odel w h ic h f o r e c a s t s o u t p u t .
The o ld v e r s io n o f th e INFORUM m odel f o r e c a s t r e l a t i v e p r ic e s w it h tim e
t r e n d , and th e new v e r s io n fo r e c a s t s m o n th ly w h o le s a le p r ic e s w it h
la g g e d r a t e s o f la b o r c o s ts , c o s ts o f m a t e r ia ls , and o u t p u t .
N e ith e r
o f th e s e m ethods c o u ld be a p p lie d to t h i s m o d e l, because we s h o u ld
f o r e c a s t a b s o lu te p r ic e s in s t e a d o f r e l a t i v e p r ic e s , and because we
do n o t e x p e c t to f i n d
enough in f o r m a t io n t o e s tim a te th e la g s t r u c t u r e
w it h m o n th ly d a ta i n Japan o r o th e r c o u n t r ie s .
A c c o r d in g ly , th e o p tim a l
p r ic in g
em ployed to f o r e c a s t
th e o r y w i t h i n
a n n u a l p r ic e s .
in p u t - o u t p u t fra m e w o rk i s
L a b o r m a rk e t c o n d it io n s ,
demand p re s s u r e s , and m a t e r ia l
c o s ts a re c o n s id e re d i n th e p r ic e fo r m a tio n e q u a tio n .
C o n s id e rin g th e
■^Nyhus, D .E .
"T he T ra d e M odel o f a Dynamic W o rld In p u t- O u tp u t
F o r e c a s tin g S ystem " INFORUM R e se arch R e p o rt No. 1 4 .
3
lin k a g e o f th e c o u n tr y m odels t o th e tr a d e m o d e l, th e fe e d -b a c k e f f e c t
o f w o r ld p r ic e change to d o m e s tic p r ic e i s
m o d e l.
in
in c o r p o r a te d i n
th e p r ic e
Openness o f th e economy i s much g r e a t e r i n o th e r c o u n t r ie s th a n
th e U .S .A .
The p r ic e m odel i n
INFORUM i s
s e p a ra te d fro m th e r e a l m o d e l.
P r ic e and o u t p u t a re n o t s o lv e d s im u lta n e o u s ly y e a r b y y e a r , b u t
ra th e r i t e r a t i v e ly .
Because o f th e expense o f th e i t e r a t i v e
s o lu tio n ,
p r i c e and o u tp u t a re s o lv e d each y e a r in t h i s m o d e l.
A s p e c ia l e f f o r t was made t o s p e c if y th e la b o r m a rk e t e q u a tio n s .
The la b o r m a rk e t v a r ia b le s
such as wage r a t e ,
em p loym en t, m a n -h ou rs
p e r e m p lo ye e , and p r o d u c t i v i t y have t h r e e im p o r ta n t r o le s i n t h i s
m o d e l.
These a re th e d e t e r m in a t io n o f wage i n f l a t i o n ,
fo r c a p ita l,
th e s u b s t i t u t i o n
and th e d e te r m in a t io n o f p o t e n t i a l o u t p u t .
c o u n t r ie s , wage i n f l a t i o n
d o m in a te s p r ic e i n f l a t i o n .
I n many
H ow ever, i t
is
n o t g e n e r a lly a c c e p te d t h a t th e Japanese p r ic e i n f l a t i o n was o f c o s t p ush t y p e . ^
The p r ic e s d id n o t grow up as f a s t as th e wage r a t e s
because p r o d u c t i v i t y grew so f a s t .
On th e o t h e r h and, th e n o m in a l
wage r a t e s grew f a s t o w in g t o th e r a p id g ro w th o f p r o d u c t i v i t i e s .
T h e r e fo r e , an e q u ili b r iu m wage r a t e e q u a tio n was fo r m u la te d u s in g
t h e m a r g in a l p r o d u c t i v i t y p r i n c i p l e .
The f a c t t h a t th e Japanese
economy had e n jo y e d a f u l l em ploym ent u n t i l 1973 and th e s u p p ly o f
la b o r had been th e m a jo r c o n s t r a in t on th e econom ic g ro w th makes th e
^ A c k le y , G and H. I s h i , " F i s c a l , M o n e ta ry , and R e la te d P o l i c i e s "
i n A s ia 's New G ia n t e d . b y H. P a t r i c k and H. R a so nsky.
The B ro o k in g s
I n s t i t u t i o n , 1976.
4
P h illip s
c u rv e ty p e wage s tu d y i n v a l i d
f o r th e Japanese economy.
One
o f th e c r i t i c i s m s on INFORUM m odel i n th e l i t e r a t u r e was t h a t th e
in v e s tm e n t e q u a tio n and th e la b o r re q u ire m e n t e q u a tio n w ere n o t based
on th e same p r o d u c tio n f u n c t io n .
la b o r and c a p i t a l ,
it
is
I f we a llo w s u b s t i t u t i o n betw een
c o n s is te n t to use th e same e l a s t i c i t y o f
s u b s t i t u t i o n t o c a lc u la t e in v e s tm e n t and la b o r a c c o r d in g to th e p r ic e
change.
I n t h i s m o d e l, th e la b o r re q u ire m e n t e q u a tio n i s
d e r iv e d fro m
a C .E .S . p r o d u c t io n f u n c t io n on w h ic h th e in v e s tm e n t e q u a tio n i s
based.
a ls o
The la b o r re q u ire m e n t d e r iv e d fro m th e p r o d u c tio n f u n c t io n
depends on th e r e a l wage.
s titu tio n
There i s
a s i g n i f i c a n t e v id e n c e o f th e sub­
o f c a p i t a l f o r la b o r as th e r e a l wage in c re a s e d o v e r tim e in
Japan.
The p o t e n t i a l o u tp u t g ro w th o f an economy can be a p p ro x im a te d
by i t s
p r o d u c t i v i t y g ro w th and i t s
em ploym ent g ro w th .
a v o id th e s im p le p r o je c t io n o f th e p r o d u c t i v i t y i n t o
In o r d e r to
th e f u t u r e fro m
th e h i s t o r i c a l p r o d u c t i v i t y g ro w th , w h ic h m ig h t o v e r p r e d ic t th e
p r o d u c t i v i t y o w in g to th e Japanese e x p e rie n c e o f r a p id g ro w th i n
th e
p a s t , we em ploy a Gom pertz f u n c t io n w h ic h c o u ld a llo w th e p r o d u c t i v i t y
to s lo w down i n
f u n c t io n .
th e f u t u r e
as a la b o r a u g m e n tin g f a c t o r i n p r o d u c tio n
The e x p o n e n tia l f u n c t io n w h ic h i s
f u n c t io n te n d s t o o v e r p r e d ic t p r o d u c t i v i t y i n
h o u rs p e r em ployee e q u a tio n i s
fo r m u la te d to
tr e n d o f w o rk in g h o u rs in a week i n
used i n u s u a l p r o d u c tio n
th e f u t u r e .
The man-
in c o r p o r a t e th e downward
d e te r m in in g th e p o t e n t i a l o u t p u t .
I n r e a l s id e o f th e m o d e l, v a r io u s e c o n o m e tric fo r m u la tio n s and
te c h n iq u e s a re t r i e d
i n o r d e r t o g e t a re a s o n a b le m odel w it h r e l a t i v e l y
5
poor e x is tin g
d a ta .
I n a la r g e m odel l i k e
e s t im a t io n a p p ro a c h i s
a lm o s t im p o s s ib le .
e s t im a t io n m ethod may be i n e v i t a b l e .
t r ie s
INFORUM, a 'l o v i n g
The so c a lle d
H ow ever, i n
c a re ’
'f ir m - h a n d e d '
t h i s m odel th e a u th o r
t o re d u c e th e a r b i t r a r y a s s u m p tio n s as much as p o s s ib le , and to
use some 'l o v i n g c a r e '.
The use o f a l t e r n a t i v e
in v e s tm e n t f u n c t io n i s an e xam ple .
f o r m u la t io n o f th e
The c o n s u m p tio n f u n c t io n i s
so
fo r m u la te d t h a t c o m p le m e n ta rity c o u ld a f f e c t c o n s u m p tio n p r o je c t io n s .
The t r a d i t i o n a l com m odity demand e q u a tio n w h ic h has o n ly i t s
r e la tiv e
own
p r ic e t o th e o v e r a l l consum er p r ic e as p r ic e v a r ia b l e f a i l s
t o c a tc h up th e c r o s s - p r ic e e f f e c t in
com m odity demand.
The b ia s
fro m n e g le c t in g th e c o m p le m e n ta lity i s n o t n e g l i g i b l e .
T h is r e p o r t c o n s is ts o f f o u r p a r t s .
The f i r s t
p a r t lo o k s o v e r
th e s t r u c t u r e o f th e m odel and th e s o lu t i o n p ro c e d u re .
th e e q u a tio n s i n
In p a r t tw o ,
th e p r ic e b lo c k o f th e syste m w i l l be p re s e n te d .
A ll
th e f i n a l demand e q u a tio n s and t r a d e e q u a tio n s w i l l be d is c u s s e d i n
p a rt th re e .
In p a r t fo u r ,
s im u la t io n w it h th e m odel w i l l be r e p o r te d .
P o s s ib le im p ro ve m e n t and e x te n s io n s o f th e m odel w i l l a ls o be su g g e s te d
in p a r t fo u r .
6
CHAPTER I I
S t r u c t u r e o f th e Japanese M odel
T h is model c o n s is ts o f o v e r e ig h t h u n d re d r e g r e s s io n e q u a tio n s ,
an in p u t - o u t p u t c o e f f i c i e n t m a t r ix
m a t r ix
( A ) , a c a p i t a l f lo w c o e f f i c i e n t
( B ) , and a governm ent demand d i s t r i b u t i o n m a t r ix
(G ).
The r e ­
g re s s io n e q u a tio n s e x p la in consumer demand, in v e s tm e n t a c t i v i t i e s ,
e x p o rts and im p o r ts , la b o r re q u ir e m e n ts , w ages, manhours p e r em ployee,
p r ic e s ,
and in p u t - o u tp u t c o e f f i c i e n t ch anges.
F o llo w in g th e Japanese 1970 I/O t a b le , com m odity p r o d u c tio n is
c la s s ifie d
in t o 156 s e c to r s .
P r iv a t e
in v e s tm e n t a c t i v i t i e s , la b o r
re q u ir e m e n ts , and wages a re c l a s s i f i e d
in to
tw e n ty in d u s t r y g ro u p s .
C o n s tr u c tio n a c t i v i t i e s
in to
e ig h t g ro u p s .
a re c l a s s i f i e d
form ed f o r th e 156 s e c to r s .
The d i s t r i b u t i o n
P r ic e s a re
o f th e 156 p ro d u c ts is
e x p la in e d in F ig u re I I - l .
I n th e f i r s t
a re r e la t e d .
s e c tio n o f t h i s
The p ro c e d u re used t o s o lv e th e syste m w i l l be e x p la in e d
in th e second s e c t io n .
e q u a tio n s i s
c h a p te r , we w i l l see how th e e q u a tio n s
I n th e t h i r d
s e c t io n , th e f o r m u la tio n o f th e
d e s c r ib e d .
I n t e r r e l a t i o n s o f th e E q u a tio n s
As we can see in F ig u re I I - 2 ,
th e w h o le syste m i s
d iv id e d in t o
tw o b ig b lo c k s , nam ely th e p r ic e d e te r m in a tio n b lo c k on th e l e f t and
th e o u tp u t d e te r m in a tio n b lo c k on th e r i g h t .
The p r ic e b lo c k in c lu d e s
wage e q u a tio n s , la b o r re q u ire m e n t e q u a tio n s , and p r ic e e q u a tio n s .
The
F ig u re I I - l .
Flows o f th e P ro d u c ts
28
C a p it a l E quipm ent
Government
O th e r F in a l
and C o n s tr u c tio n
C a te g o rie s
Demand
C a te g o rie s
Purchased
I
B - M a tr ix
and S o ld
G M a t r ix
S a le s to C a p it a l
S a le s to
Equipm ent
G o ve rn tie n t
In v e s tm e n t and
C o n s tr u c tio n
In v e s tm e n t
j
u
o
a
£
u
u
0
1
0)
3( 3
«—
(U ►J
<U
00
C
cd
£i
CJ
(0
d
o
o
cd
c
o
(0
u
<u
04
Figure II-2, St
ire of the Model
9
o u tp u t b lo c k in c lu d e s c o n s u m p tio n , in v e s tm e n t, in v e n t o r y ch an g e, im p o rt
and e x p o r t , and some o th e r f i n a l demand com ponents.
A lth o u g h th e tw o b lo c k s seem t o be s e p a ra te d , th e y a re r e la t e d
th r o u g h v a r io u s f u n c t io n a l r e l a t i o n s .
F ir s t o f a l l ,
to
g e t c o n s is te n t
o u tp u t and p r ic e , th e same A m a t r ix i s used in b o th b lo c k s .
c o e f f i c i e n t f o r e c a s t i s made by l o g i s t i c
c u rv e s a n d /o r by p r ic e in d u c e d
s u b s t i t u t i o n , w h ic h w i l l be d is c u s s e d l a t e r ,
c u la te d w it h t h a t A m a t r ix .
o u tp u ts and p r ic e s .
A f t e r th e
p r ic e and o u tp u t a re c a l­
T h e r e fo r e , c o e f f i c i e n t changes a f f e c t b o th
The e f f e c t o f p r ic e s on o u tp u ts i s o b v io u s .
The
p r ic e s fo r e c a s te d in th e p r ic e b lo c k w i l l be tra n s fo rm e d to be used in
v a r io u s f i n a l demand e q u a tio n s .
F o r th e co n su m p tio n e q u a tio n , th e
o u tp u t p r ic e w i l l be tra n s fo rm e d t o th e r e l a t i v e
p r i a t e l y w e ig h te d consum er p r ic e in d e x .
th e B m a t r ix i s
p r ic e w it h th e a p p ro ­
F o r th e in v e s tm e n t e q u a tio n ,
used to g e t th e PDE d e f l a t o r fro m o u tp u t p r ic e , and th e
e x p e c te d i n f l a t i o n
ra te is
c a lc u la t e d w it h a d i s t r i b u t e d
la g syste m .
A ls o , th e d o m e s tic o u tp u t p r ic e goes to th e im p o rt and e x p o rt e q u a tio n s
w h e re i t
i s used r e l a t i v e
presumed to
t o f o r e ig n p r ic e .
Labor p r o d u c t iv it y is
d e te rm in e th e p o t e n t i a l l e v e l o f d is p o s a b le in co m e, w h ic h
d e te rm in e s consumer demands and some o th e r f i n a l demands.
T h e re a ls o
e x is t s th e e f f e c t fro m o u tp u t t o p r ic e .
fro m th e I /O c o m p u ta tio n s h o u ld be in t e r p r e t e d
r e fle c tin g
as an e q u ilib r iu m
in f lu e n c e s o f b o th demand and s u p p ly .
ca n n o t e n te r th e p r ic e
The o u tp u t
T h e r e fo r e , t h a t v a lu e
e q u a tio n d i r e c t l y as a demand m easure because we
c a n n o t i d e n t i f y o u tp u t as demand e f f e c t o r as s u p p ly e f f e c t .
in t h i s
o u tp u t
s tu d y th e o u tp u t a f f e c t s
However,
p r ic e s th r o u g h c a p a c it y u t i l i z a t i o n
v a r ia b l e o r th ro u g h a p ro x y f o r demand m e a sure.
The d e s ir e d o u tp u t
10
c a p ita l r a t io
and th e e xp e cte d change o f o u tp u t a re used to d e te rm in e
th e lo n g te rm tre n d o f th e m arkup r a t i o
in
th e p r ic e
th e o u tp u t a f f e c t s p r ic e s th ro u g h wage e q u a tio n .
e q u a tio n .
In o r d e r to
A ls o ,
in c re a s e
o u t p u t , more la b o r s h o u ld be e m p loye d , w h ic h in c re a s e s demand in
la b o r m a rk e t.
In s te a d o f u s in g a b s o lu te em ploym ent change in
e q u a tio n , th e change in em ploym ent s h a re o f a c e r t a in in d u s t r y
th e
th e wage
is
used
to see th e r e a l la b o r m a rk e t demand p re s s u re in th e sense o f c o m p e titio n
w it h o th e r i n d u s t r ie s .
The e q u a tio n s in th e p r ic e b lo c k a re i n t e r r e l a t e d .
F ir s t,
th e wage
r a t e i s a f f e c t e d by th e p re v io u s y e a r s ’ p r o d u c t i v i t y fro m th e la b o r r e ­
q u ire m e n t e q u a tio n , and b y th e p re v io u s y e a r ’ s consumer p r ic e
o u tp u t p r ic e fro m th e p r ic e
th e r e a l wage r a t e .
e q u a tio n s .
in d e x and
L a b o r re q u ire m e n t is a f f e c t e d b y
Wage r a t e s , la b o r re q u ir e m e n ts , m arkup r a t i o ,
th e A m a t r ix d e te rm in e th e o u tp u t p r ic e s .
A ls o , th e r e is
e f f e c t fro m p r ic e to in p u t - o u t p u t c o e f f i c i e n t s w h ic h i s
r e l a t i v e p r ic e s ch an g e.
H ow ever, t h i s
and
a fe e d b a c k
changed when th e
s tu d y does n o t c o v e r th e p r ic e -
i n d u c e d - c o e f f ic ie n t change.
The s t r u c t u r e o f th e o u tp u t b lo c k i s
r a t h e r s im p le .
The demands
a re e x p la in e d by dem og ra p hic v a r ia b l e s , r e a l in co m e, s to c k s , and p r ic e
v a r ia b le s .
in
Each e q u a tio n w i l l be d is c u s s e d in th e f o llo w in g c h a p te rs
g re a t d e t a il.
S o lu t io n P ro c e d u re
As th e m odel c o n s is ts o f two b ig b lo c k s ,
b lo c k - r e c u r s iv e ty p e m e thod.
c u r s iv e system i f
lik e
it
can be s o lv e d by a
As W ald s a y s , an economy i s
th e tim e p e r io d i s v e r y s h o r t .
a la r g e r e ­
In an a n n u a l model
t h i s , h o w e ve r, th e a p p l i c a b i l i t y o f th e p u re r e c u r s iv e system i s
11
q u e s tio n a b le .
S im u lta n e o u s d e te r m in a tio n o f th e v a r ia b le s i n
b lo c k s o f t h e m odel i s
in e v i t a b l e .
m odel a re c lu s t e r e d i n t o
some
T h e r e fo r e , th e v a r ia b le s i n th e
a fe w b lo c k s .
The v a r ia b le s w i t h i n
each
b lo c k a re s o lv e d s im u lta n e o u s ly and th e d i f f e r e n t b lo c k s a re s o lv e d
r e c u r s iv e ly .
The s im u lta n e o u s s o lu t i o n o f th e v a r ia b le s w i t h i n
each
b lo c k s h o u ld be g o tte n by th e way i n w h ic h th e economy s o lv e s , n o t by
t h e m a th e m a tic a l s o lu t i o n .
The economy can u se o n ly i t e r a t i v e m e th o d s .
U n f o r t u n a t e ly , th e c o s t o f th e i t e r a t i v e
and o u tp u t i s
q u i t e la r g e .
s o lu t io n betw een p r ic e
I f we can b re a k t h e s im u lt a n e it y betw een
o u tp u t and p r ic e w it h o u t g r e a t lo s s o f in f o r m a t io n ,
The s im p le way o u t o f th e s im u lt a n e it y p ro b le m i s
one p e r io d la g .
s lu g g is h .
a re
If
o n ly
It
is
it
i s w o r th t r y i n g .
th ro u g h t h e u se o f a
g e n e r a lly b e lie v e d t h a t wage a d ju s tm e n ts a re
a l l th e e x p la n a to r y v a r ia b le s in t h e wage r a t e e q u a tio n
la g g e d v a r ia b le s o f th e system and o th e r exogenous
v a lu e s , th e s im u lt a n e it y b etw een p r ic e and o u tp u t i s b ro k e n .
As w i l l
b e seen in t h e wage r a t e e q u a tio n c h a p te r , t h e Japanese wage r a t e
e q u a tio n s w o rk w e ll w it h la g g e d e x p la n a to r y v a r ia b l e s .
H is to r ic a lly ,
t h e i r f a s t g ro w in g wage r a t e s w e re a lw a y s b e h in d t h e f a s t e r g ro w in g
p r o d u c t i v i t y in c r e a s e s .
T h e r e fo r e , we can s t a r t t o s o lv e t h e wage
r a t e e q a u a tio n s w it h o n ly t h e p re d e te rm in e d v a r i b l e s .
The s o lu t i o n p ro c e d u re c o n s is t s o f th e f o l lo w in g f i v e b lo c k s :
1 . w 88 fj_ ( z ° )
2.
wage r a t e b lo c k
*= f 2 ( w , p , z ° )
“ -
p r ic e b lo c k
f 3 (z °)
p = f 4 ( w , £ ,a
a = f 5 (p ,z ° )
, a , z°)
12
3. c = f 6 ( p , z ° )
c o n su m p tio n and e x p o rt b lo c k
x = f 7 (p ,z ° )
4. i = f g (p ,q ,z ° )
O u tp u t b lo c k
m = f 9 (p ,q ,z ° )
v = f io
q = fn
( i,m ,v ,c ,x ,z ° )
5. t = f 12
employment b lo c k
e = f 13 (q> A , t , z ° ;
A l l th e p re d e te rm in e d o r exogenous v a r ia b le s a re re p re s e n te d by
z°.
The sym bols a re :
w = wage
£
= la b o r re q u ire m e n t
p = p r ic e
a = markup
c = c o n s u m p tio n
x = e x p o rt
i = in v e s tm e n t
m = im p o rt
v = in v e n t o r y
q = o u tp u t
a = in p u t - o u t p u t c o e f f i c i e n t
t = m o n th ly m anhours p e r em ployee
e = employment
The s o lu t i o n p ro c e d u re s t a r t s
fro m th e wage b lo c k .
The wage
r a t e w h ic h i s
c a lc u la t e d in th e wage r a t e b lo c k w i l l be g iv e n t o th e
p r i c e b lo c k .
The la b o r re q u ire m e n t and th e p r ic e s o f o u tp u t a re
d e te rm in e d in th e p r ic e b lo c k .
c o n s u m p tio n and e x p o r t .
Once p r ic e i s
g iv e n , we can c a lc u la t e
In th e o u tp u t b lo c k , o u t p u t ,
t o r y ch a n g e , and in v e s tm e n t a re th e n d e te rm in e d .
o u tp u t,
em ploym ent i s
im p o r t,
in v e n ­
U s in g th e c a lc u la t e d
c a lc u la t e d in th e em ploym ent b lo c k .
The v a r ia b le s d e te rm in e d in th e p re v io u s b lo c k s w i l l be g iv e n
as exogenous t o th e c u r r e n t b lo c k .
s h o u ld be s o lv e d s im u lta n e o u s ly .
The e q u a tio n s o f each b lo c k
The m ain s im u lt a n e it y p ro b le m s
o c c u r in th e p r ic e b lo c k and th e o u tp u t b lo c k .
B e s id e s th e s im u lta n e o u s
d e te r m in a tio n o f th e o u tp u t p r ic e s , w h ic h can be s o lv e d by th e S e id e l
p ro c e d u re ,
w it h in
th e r e i s
s im u lt a n e it y betw een p r ic e and la b o r re q u ire m e n ts
th e p r ic e b lo c k .
The la b o r re q u ire m e n t i s a f u n c t io n o f th e
r e a l wage w h ic h i s n o m in a l wage d iv id e d b y c u r r e n t p r ic e .
an i t e r a t i v e m ethod i s n e c e s s a ry t o s o lv e t h i s
p ro b le m .
T h e r e fo r e ,
On th e f i r s t
i t e r a t i o n , we s t a r t by e x t r a p o la t in g th e p r e v io u s y e a r ’ s p r ic e change
t o be used in
s titu tio n
th e la b o r re q u ire m e n t e q u a tio n .
If
p r ic e - in d u c e d sub­
i s a llo w e d in th e c o e f f i c i e n t change f o r e c a s t , a n o th e r b ig
s im u lt a n e it y o c c u rs betw een p r ic e and th e in p u t - o u t p u t c o e f f i c i e n t s .
In t h i s c a s e , la b o r r e q u ir e m e n t, p r ic e ,
be d e te rm in e d s im u lta n e o u s ly ; t h i s
and in p u t c o e f f i c i e n t s
s h o u ld
s im u lta n e o u s d e t e r m in a t io n can be
a c h ie v e d o n ly b y th e la r g e i t e r a t i v e m e th o d , w h ic h i s
q u i t e e x p e n s iv e
c o m p u t a t io n a lly .
A m ore c o m p lic a te d s im u lt a n e it y p ro b le m o c c u rs i n th e o u tp u t
b lo c k .
In v e s tm e n t,
im p o r t , and in v e n t o r y depend upon th e c u r r e n t
o u tp u t.
INFORUM.
o u tp u t.
A s o lu t io n p ro c e d u re f o r t h i s
F ir s t,
in v e s tm e n t i s
k in d o f p ro b le m i s fo u n d in
c a lc u la t e d b y e x t r a p o la t in g th e p re v io u s
W ith th e f i n a l demands w h ic h w ere c a lc u la t e d
in th e p re v io u s
b lo c k s and w it h th e in v e s tm e n t, we s o lv e f o r th e o u tp u t by th e S e id e l
i t e r a t i v e p ro c e s s .
ite r a tio n
Im p o rt and in v e n t o r y a re d e te rm in e d in
u s in g th e new v a lu e o f o u t p u t .
The new o u tp u t i s
w it h th e p re v io u s o u tp u t and th e p ro c e s s i s
o u tp u t co n ve rg e s to th e p re v io u s o u t p u t .
e v e ry
compared
re p e a te d u n t i l th e new
Once th e new o u tp u ts o f a l l
s e c to r s a re g o tte n by th e i t e r a t i v e m ethod, we go b ack to th e in v e s t ­
ment c a lc u la t io n .
o u tp u t.
The new in v e s tm e n t i s
c a lc u la t e d u s in g th e c u r r e n t
Once a g a in , th e c u r r e n t in v e s tm e n t i s used to c a lc u la t e th e
f i n a l o u tp u t.
v e rg e n c e .
T r i a n g u li z a t io n o f th e A m a t r ix can speed up th e con­
T r i a n g u li z a t io n
can be done b y e n t e r in g th e s e c to r s in
d e c re a s in g o r d e r o f th e f i n a l demand r a t i o
to o u tp u t.
A ls o , th e
e x t r a p o la t io n o f th e p re v io u s y e a r 's o u tp u t in th e f i r s t
ite r a tio n
speeds up th e c o n v e rg e n c e .
The f i n a l b lo c k o f th e s o lu t io n p ro c e d u re i s
m in a tio n .
U s in g th e o u tp u t and th e la b o r re q u ire m e n ts w h ic h w ere
c a lc u la t e d in
th e p re v io u s b lo c k s , th e n e c e s s a ry employm ent i s
u s in g th e manhour e q u a tio n .
d e s ig n e d i n
employm ent d e t e r ­
th is
fo u n d
The incom e s id e o f th e m odel i s n o t
d is s e r ta tio n .
A c c o r d in g ly , th e em ploym ent s h o u ld
p la y a r o l e to d e te rm in e w h e th e r th e exogenous a s s u m p tio n a b o u t th e
d is p o s a b le incom e i s
re a s o n a b le o r n o t , b ecause employm ent can r e p r e ­
s e n t p o t e n t i a l incom e l e v e l .
I f we have an u n re a s o n a b le employment
p r o je c t io n , t h e a s s u m p tio n s h o u ld be r e v is e d and a l l th e p ro c e d u re
s h o u ld be re p e a te d .
15
F u n c tio n a l Forms o f th e E q u a tio n s
1 . Wage R ate
A (Wt ) =
H e re
a
+ a4A
s ta n d s f o r th e p e rc e n ta g e change.
(C P I)
W d e n o te s n o m in a l wage
r a t e , L th e em ploym ent o f an in d u s t r y , L th e t o t a l em ploym ent o f
th e economy.
and CPI i s
W is
th e a ve ra g e n o m in a l wage r a t e o f th e economy
th e consum er p r ic e in d e x .
o f a v e ra g e p r o d u c t.
VAP s ta n d s f o r th e v a lu e
The wage r a t e e q u a tio n t e s t s th e th r e e
h y p o th e s e s , th e e q u ilib r iu m
h y p o th e s is ,
th e d is e q u ili b r i u m
h y p o th e s is , and th e b a r g a in in g power h y p o th e s is .
The e q u ili b r iu m h y p o th e s is i s
th e d is e q u ili b r i u m h y p o th e s is i s
te s t e d b y th e v a r ia b l e , VAP,
te s t e d by th e v a r ia b l e ,
em ploy­
m ent s h a re ( " '') , and th e b a r g a in in g power h y p o th e s is b y th e Con-
L
y
sum er P r ic e In d e x ( C P I) , and th e r e l a t i v e wage r a t e ( - ) .
W
The
v a lu e o f a v e ra g e p ro d u c t i s assumed to a f f e c t th e wage r a t e
th ro u g h th e d i s t r i b u t e d la g scheme.
la g i s
K o yck.
The i n f i n i t e
The fo rm o f th e d i s t r i b u t e d
la g t a i l p ro b le m i s
t r e a t e d by a
s p e c ia l m ethod w h ic h w i l l be d is c u s s e d in C h a p te r I I I .
2 . L a b o r R e q u ire m e n t
The la b o r re q u ire m e n t e q u a tio n i s
p r o d u c t io n f u n c t io n .
d e r iv e d fro m a C .E .S
The C .E .S . p r o d u c tio n f u n c t io n em ployed
16
h e re i s
s u b je c t to c o n s ta n t r e t u r n s to s c a le and i t
a u g m e n tin g t e c h n o lo g ic a l change.
e x p o n e n tia l c u rv e w h ic h i s
used to f i t
has la b o r
G om pertz c u rv e , in s te a d o f
g ro w in g w it h o u t bound o v e r tim e ,
th e la b o r a u g m e n tin g t e c h n o lo g ic a l change.
is
W ith
th e p a r t i a l a d ju s tm e n t m echanism , th e r e g r e s s io n e q u a tio n tu rn e d
o u t to be
+ o ALN
H e re , E d e n o te s m anhours, ~ r e f e r s
o f s u b s titu tio n
to r e a l wage,
a is
e la s tic ity
e s tim a te d in in v e s tm e n t e q u a tio n , and V is
r a t e o f a d ju s tm e n t.
P is
th e
e s tim a te d by i t e r a t i v e m ethod.
3. P r ic e
e
w h e re
156
j
= 1 .................156
T h e re a re t h r e e d i f f e r e n t n o t a t io n s f o r p r ic e s .
Pe s ta n d s
17
f o r th e d o m e s tic e q u ilib r iu m
I/ O c o m p u ta tio n .
p r ic e w h ic h i s
c a lc u la t e d b y th e
The n o rm a l u n i t la b o r c o s t (U L C ^ ), and th e
m a t e r ia l c o s ts a re used t o g e t th e d o m e s tic e q u ili b r iu m
The m arkup r a t i o
/ Qe
{
t
\
is
r e la t e d t o th e d e s ir e d o u tp u t c a p i t a l r a t i o
] and t o th e e x p e c te d r a t e o f o u tp u t change
(A Q )•
U t- ij
-
v a r ia b l e s a r e e x p la in e d i n th e P r ic e C h a p te r.
w o r ld p r i c e .
S in c e t h e l a r g e p o r t io n s o f th e m a t e r ia ls a r e im ­
p r ic e c a lc u l a t i o n .
p r ic e is
These
c
Pw s ta n d s f o r th e
p o r t e d , im p o rte d m a t e r ia l c o s ts a re c o n s id e re d i n
u se (m)
p r ic e s .
e q u ilib r iu m
The r a t i o o f amount o f im p o r ts t o t o t a l d o m e s tic
i s used as a w e ig h t .
A f t e r th e d o m e s tic e q u ili b r iu m
c a lc u la t e d , th e a c t u a l o u tp u t p r ic e i s
th e b e h a v io r a l r e l a t i o n .
g o tte n th r o u g h
I n t h e b e h a v io r a l r e l a t i o n ,
th e a c t u a l
p r ic e s a r e r e la t e d t o t h e e q u ili b r iu m p r ic e s th ro u g h d i s t r i b u t e d
la g s y s te m .
K o yck la g scheme i s
used b eca u se we b e lie v e t h a t
t h e e q u ili b r iu m p r i c e o f th e c u r r e n t p e r io d has th e s t r o n g e s t
e f f e c t on th e a c t u a l c u r r e n t p r ic e .
4 . P e rs o n a l C o n sum p tio n E x p e n d itu r e
Ci t
H e re C^t s ta n d s f o r t h e p e r c a p it a p e r s o n a l c o n s u m p tio n e x p e n d i­
t u r e f o r c o m n o d ity i
in co m e .
i n y e a r t and Yfc i s
A l l c o m m o d itie s a r e c l a s s i f i e d
p e r s o n a l d is p o s a b le
i n t o s e v e r a l g ro u p s .
r e f e r s t o t h e p r i c e o f t h e g ro u p t o w h ic h i ^
b e lo n g s .
R e la t iv e p r i c e i s
com m odity
decomposed i n t o tw o p r i c e v a r ia b l e s ;
18
it s
own p r ic e r e l a t i v e to th e g ro u p p r ic e , a n d g ro u p p r ic e r e l a ­
t i v e 'to th e t o t a l consum er p r ic e in d e x (F t ) • The d e c o m p o s itio n
o f th e r e l a t i v e p r ic e i s
t a r ity
d e s ig n e d t o c o n s id e r t h e complemen­
i n th e consum er demand w it h i n
g ro u p s .
The demand s y ste m m u st s a t i s f y th e b u d g e t c o n s t r a in t .
In
f o r e c a s t in g , th e t o t a l co n s u m p tio n p lu s s a v in g s m ust add up to
d is p o s a b le in co m e.
I n o r d e r t o s o lv e th e a d d in g up p ro b le m , we
d e f in e Pt such t h a t
I
Ci t
( f t ) + St
-
Yt
w h e re
St - 8 l + s 2 Yt + s 3 Yt + 8 4 Rt
St i s
P
T
p e r c a p it a s a v in g s and Y t d e n o te s perm anent Inco m e , Y
r e f e r s t o t r a n s i t o r y in co m e, and
is
r e a l in t e r e s t r a te .
5 . In v e s tm e n t
The in v e s tm e n t e q u a tio n i s
p r o d u c t io n f u n c t io n .
a d ju s tm e n t fo rm .
d e r iv e d fro m th e s ta n d a rd C .E .S .
The e q u a tio n has th e n e o - c la s s ic a l s to c k
The o p t im a l c a p i t a l s t o c k , K * , w h ic h i s
de­
r iv e d b y e q u a tin g t h e r e n t a l r a t e and th e m a r g in a l p ro d u c t o f
th e c a p it a l, is
assumed t o a f f e c t th e n e t in v e s tm e n t th ro u g h a
d i s t r i b u t e d la g .
*
19
w h e re
K* - c R "a Q
The la g w e ig h t s , w f s , a re g e o m e t r ic a lly d e c l in i n g b y th e f a c t o r X ,
a f t e r th e
year t ,
f i r s t tw o p e r io d s ,
ij
d e n o te s th e n e t in v e s tm e n t in
and Qt s ta n d s f o r th e o u tp u t i n y e a r t , w h ile Rt , a , Kt ,
and c r e f e r t o th e c a p i t a l c o s t , t h e e l a s t i c i t y o f s u b s t i t u t i o n ,
t h e c a p i t a l s t o c k , and a c o n s ta n t, r e s p e c t iv e ly .
As we can see
in t h e e q u a tio n , th e m a in b u rd e n o f t h e e s tim a tio n i s
w e ig h t s .
t iv e ly
in t o
S in c e we have i n f i n i t e
th e la g
t a i l o f la g w e ig h ts and r e l a ­
s m a ll num ber o f o b s e r v a t io n s , t h e e q u a tio n i s
tra n s fo rm e d
an a p p r o p r ia t e fo rm f o r th e e s tim a tio n p u rp o s e s .
6 . Im p o r t and E x p o rt
M,. -
(e x + e2 Ut ) * P 3
Xt -
( f i + f 2 Ft ) * p [ 3
H e re ^
and
d e n o te m e rc h a n d is e im p o r ts and e x p o r ts a t y e a r t .
Ut s ta n d s f o r th e d o m e s tic u se o f a good a t y e a r t , w h ic h i s
d e fin e d b y o u tp u t p lu s im p o r ts le s s e x p o r ts .
Ft
is
th e f o r e ig n
demand in d e x w h ic h i s a v a i la b le fro m t h e W o rld T ra d e M o d e l.
l a s t te rm o f each e q u a tio n i s
The
t h e r e l a t i v e p r i c e l e v e l ( f o r e ig n
p r i c e t o d o m e s tic p r ic e f o r im p o r t s , and d o m e s tic p r i c e t o
fo r e ig n p r ic e f o r e x p o rts ).
p r ic e e l a s t i c i t i e s .
Hence e^ and f ^ a r e t h e r e s p e c t iv e
The fo rm o f th e s e e q u a tio n s a r e b o rro w e d
fro m t h e INFORUM m o d e ls .
20
7 . H o u s in g C o n s tr u c tio n
t
+
0
-r hu2
t-1
(l-fi)1
I
z i= o
T h is i s a p a r t i a l s to c k a d ju s tm e n t e q u a tio n .
s t r u c t i o n e x p e n d itu r e p e r h o u s e h o ld ( I / H )
The H o u sin g Con­
i s assumed t o be some
f r a c t i o n o f th e gap betw een th e d e s ir e d s t o c k and th e a c t u a l
s to c k .
The d e s ir e d s to c k i s assumed t o be a f u n c t io n o f t h e d is ­
p o s a b le incom e p e r h o u s e h o ld , Y /H .
The a c t u a l s to c k i s
c a lc u la t e d
b y th e one b u c k e t r e s e r v o ir s y s te m , w h ic h w i l l be d e s c r ib e d in
C h a p te r V I I I .
The h o u s in g e x p e n d itu r e p e r h o u s e h o ld i s
in v e s t i­
g a te d b ecause th e d e c is io n u n i t f o r h o u s in g e x p e n d itu re i s
th e
h o u s e h o ld .
8 . I n v e n t o r y change
Vt = 5 (g Qt - vst )
The A c c e le r a t o r p r i n c i p l e i s
e q u a tio n .
em ployed i n t h e in v e n t o r y change
d e n o te s th e in v e n t o r y change a t y e a r t ,
t h e in v e n t o r y s t o c k .
6 is
and VS^
th e c o n s ta n t speed o f c lo s in g th e
gap b etw een th e d e s ir e d s t o c k and th e a c t u a l s t o c k .
s t o c k i s assumed to be p r o p o r t io n a l t o o u t p u t (g Qt ) .
9 . Manhours p e r Em ployee
MHt - h x + h 2 A Qt + h 3 T
D e s ire d
21
The M anhours p e r em ployee (MH) a re r e la t e d t o th e p e rc e n ta g e
change i n o u tp u t and to th e tim e tr e n d
(T ).
The S o c io -e c o n o m ic
f a c t o r s , c a p tu re d b y th e tim e t r e n d , have a g r e a t in f lu e n c e on
t h e m anhours p e r e m p lo ye e .
1 0 . C o e f f ic i e n t Change
a
w here
i = 1
156
The e q u a tio n i s
th e INFORUM m ethod o f f o r e c a s t in g th e A c r o s s - t h e -
ro w c o e f f i c i e n t change i n w h ic h C
ro w i n y e a r t ,
A is
a
is
i s th e c o e f f i c i e n t o f th e i
th e a s y m p to te o f th e l o g i s t i c
th e c o n s ta n t o f in t e g r a t i o n and b i s
g ro w th c u rv e ,
th e c o n s ta n t r a t e o f
th e p e rc e n ta g e change o f th e gap betw een C i t and a .
t h e - r o w c o e f f i c i e n t change m ethod i s
The a c r o s s -
d e s ig n e d t o in v e s t i g a t e th e
c o e f f i c i e n t change due t o t e c h n ic a l change and t o p r o d u c t m ix
change o v e r t im e .
1 1 . O u tp u t D e te r m in a tio n
w h e re
th
A l l th e f i n a l demand com ponents, nam ely p e rs o n a l co n su m p tio n
e x p e n d itu re
c o n s t r u c t io n
e x p o rts
(C ) , in v e s tm e n t ( I ) ,
governm ent e x p e n d itu re
( H ) , in v e n t o r y change ( V ) , im p o rts (M ), and
( X ) , a re combined to c a lc u la t e o u t p u t .
(G ),
23
CHAPTER I I I
Wage R a te E q u a tio n
Theory
There have been three approaches to w
a
g
e rate adjustm
ent.
T
hese
are:
1. Disequilibrium study, w
hich Is com
nonly presented by the
Phillip’ s curve,
2. Equilibrium study, which is based o
n the m
arginal productivity
principle, and
3. Bargaining pow
er hypotheses.
All of these hypotheses are em
ployed in the formulation of the Japanese
Industry w
ag
e rate equation.
In usual disequilibrium study, the rate of unem
ploym
ent or the
change in the unem
ploym
ent rate is considered as am
easure of dis­
equilibrium.
E
xcess d
e
m
a
n
d in the labor m
arket is m
easured by the un-
eaploym
ent rate, whether it is an aggregate m
acro m
odel or a
n industry
level m
odel.
Certainly there is no objection to use of the unem
ploy­
m
ent rate as a m
easure of excess d
e
m
a
n
d in an aggregate m
acro study.
Its use Is questionable, how
ever, in disaggregated m
odels.
T
h
e extent
of disequilibrium of the w
hole e
co
n
o
m
y does not necessarily indicate
Its extent in a certain industry.
Furtherm
ore, the Japanese statistics
of the unem
ploym
ent rate sh
o
wnot m
u
ch variation for the past 1
5 years,
although the industrial structure has changed very m
uch.
Therefore, the unem
ploym
ent rate is not expected to be significant
24
in the Industry level w
a
g
e rate determination.
N
o
w
, the problemis
to find an appropriate proxy for the m
easure of disequilibrium for
each Industry*
T
h
em
easure of disequilibrium in an industry should
cover not only the flow of labor betw
een the em
ployed and the un­
em
ployed, but also the flow of the em
ployed laborers betw
een indus­
tries.
W
h
e
n unem
ploym
ent is not very great, job competition betw
een
the em
ployed and the unem
ployed is w
eak.
M
o
n
e
yw
a
g
e rate will b
e
only weakly affected by the em
ploym
ent level.
Furtherm
ore, if there
exists excess d
e
m
a
n
d for labor so that labor b
e
co
m
e
s a constraint o
n
growth, the actual situation in Japan recently, the en$>loyers should
com
pete to get the laborers w
h
o are already em
ployed.
Therefore,
unem
ploym
ent rate could not be a significant variable in the w
a
g
e
equation.
T
h
e change in the em
ploym
ent share of each industry over the
total em
ploym
ent of the e
co
n
o
m
y is chosen a
s the proxy for the m
easure
of d
e
m
a
n
d pressure inthe labor m
arket.
There has heen a big change in
em
ploym
ent shares of Agrlwfifctuie, O
ther services, Hetal, and M
achinery in*,
duatries. T
hose changes are presum
ed to have been possible only
through shifts of labor a
m
o
n
g industries.
Table III- l com
pares the
em
ploym
ent shares in 1958 and in 1972.
In a
n equilibrium situation, the marginal productivity principle
says that the nom
inal w
age is equal to the value of marginal product.
This productivity approach to empirical w
age equations w
a
s suggested
25
TABLE I I I - l .
EMPLOYMENT SHARE*
1958
1
9
7
2
33.15
14.78
ining
2. M
1.06
.31
oods a
nd T
obacco
3. F
2.19
2.07
4. Textile
4.74
4.39
5. Pulp and paper
0.70
0.74
6. C
hem
ical Products
1.14
1.21
ary M
etals
7. Prim
1.17
1.52
etal Products
8. M
1.35
2.66
achinery
9. Non-electrical M
1.33
2.22
achinery
10. Electrical M
1.25
2.66
11. Transportation E
quipm
ent
1.16
2.06
12. M
iscellaneous M
anufacturing
6.12
7.50
13. Construction
5.25
8.45
.52
.57
16.91
20.53
eal Estate
16. R
0.17
0.64
nd C
om
m
unication
17. Transport a
4.61
6.37
.
0
0
H
Industry N
a
m
e
1.68
2.28
15.51
19.06
1. Agriculture, Forestry and Fishery
14. Electricty, G
a
s and W
ater Supply
15. W
holesale and Retail Trade
Finance and Insurance
19. O
ther Services
E
♦
E
m
p
lo
ym
e
n
t share is
— * 100.
T
E
and T
Eis total em
ploym
ent.
W
h
e
re E
. is i*k industry em
ploym
ent
1
26
b y Kuh^ as a c r i t i c i s m
P h illip 's
o f th e d is e q u ilib r iu m
th e o ry r e l y i n g on th e
c u rv e .
Based on K a ld o r 's
r o le o f p r o f it s
2
s u g g e s tio n , v a r io u s s t u d ie s
i n wage d e te r m in a tio n .
tr ie d
to f i n d
th e
K a ld o r argued t h a t th e P h i l l i p ' s
e m p ir ic a l r e s u lt s a ro s e fro m a s p u r io u s c o r r e la t io n betw een unem ploy­
ment r a te s and p r o f i t s .
N e v e rth e le s s , th e r o le o f p r o f i t s
d ir e c tly ju s t if ia b le
i n wage d e te r m in a tio n i s
fro m n e o c la s s ic a l th e o r y .
H ie re i s
th e o ry no re a o s n why e m p lo y e rs in c r e a s e wages as p r o f i t s
not
i n n e o c la s s ic a l
go u p.
T h is
t h e o r e t ic a l gap b etw e e n p r o f i t and wage was b r id g e d by K u h 's p ro d u c ­
tiv ity
a p p ro a c h .
As Kuh s t a t e s , " p r o f i t m ig h t be a p ro x y f o r a more
fu n d a m e n ta l d e te rm in a n t o f w ages, th e m a r g in a l v a lu e p r o d u c t i v i t y o f
la b o r , a c c o rd in g to n e o c la s s ic a l p r ic e t h e o r y .
w r itte n
h o u rs ).
as MU =
PX
(w here PX i s
WM
ttz
P r o f i t markup can be
v a lu e added. W th e wage r a t e , K man-
PX
The a verag e v a lu e p r o d u c t i v i t y o f la b o r i s — , and may
M
r e a d il y be c o n c e iv e d t o be s y s t e m a t ic a lly c o r r e la t e d w it h
v a lu e p r o d u c t i v i t y o f la b o r , w h ic h i s
th e m a rg in a l
th e d e te rm in a n t o f la b o r demand
i n n e o c la s s ic a l t h e o r y . "
The v a lu e o f m a r g in a l p r o d u c t i s
decomposed i n t o
p r ic e o f o u tp u t and th e m a rg in a l p r o d u c t .
tw o p a r t s ,
the
Because th e m a rg in a l
^K u h , E . , "A P r o d u c t iv it y Theory o f Wage L e v e ls ; an A lt e r n a t iv e
t o th e P h i l l i p ' s C u rv e ." The Review o f E conom ic S t u d ie s . V o l. XXXIV
( 4 ) , No. 100 ( O c t . , 1 9 6 7 ).
2
K a ld o r , N . , "E co n o m ic G rcw th and th e P ro b le m o f I n f l a t i o n , "
P a rt I I .
E conom ica.
V o l. 26 (1 9 5 9 ). p p . 2 8 7 -2 9 8 .
p r o d u c tiv ity
is n o t d ir e c t ly
o b s e r v a b le , we need one m ore s te p t o g e t
a p p r o p r ia t e d a ta f o r t h a t v a r i a b l e .
T here a re tw o a lt e r n a t i v e ways
to d e a l w ith
fro m th e p r o d u c t io n f u n c t io n w h ic h
t h i s p ro b le m .
i s e s tim a te d u s in g v a r io u s
p r o d u c tiv ity o f la b o r .^
F ir s tly ,
a s s u m p tio n s , we can c a lc u la t e
th e m a rg in a l
S e c o n d ly , r a t h e r th a n r e s o r t t o a tw o -s ta g e
e s t im a t io n p ro c e d u re b y f i r s t e s t im a t in g a p r o d u c t io n f u n c t io n and
th e n a wage r a t e e q u a tio n w it h m a r g in a l p r o d u c t i v i t y ,
t iv ity
a ve ra g e p ro d u c ­
c o u ld in s t e a d s e rv e as a p r o x y , s in c e th e tw o a re l i k e l y
t o be
s y s t e m a t ic a lly r e la t e d o v e r o b s e rv e d ra n ge s o f v a r i a t i o n . ^
If
th e p o s t u la te d p r o d u c t io n r e l a t i o n i s
C obb-D ouglas w it h
n e u t r a l t e c h n ic a l ch a n g e , m a r g in a l and a ve ra g e p r o d u c t i v i t y
o n ly b y a m u l t i p l i c a t i v e
f u n c t io n i s
u tiliz e d
in
c o n s ta n t.
th is
d iffe r
H ow ever, a C .E .S . p r o d u c t io n
s tu d y .
As we can see i n
th e la b o r r e ­
q u ire m e n t e q u a tio n d e r iv a t io n , th e m a r g in a l p r o d u c t i v i t y o f la b o r i s
some f u n c t io n o f th e a v e ra g e p r o d u c t i v i t y
o n ly t h in g we s h o u ld assume i s
s p e c t t o la b o r i s
o f la b o r .
t h a t th e e l a s t i c i t y
c o n s ta n t w i t h i n
In t h is
c a s e , th e
o f o u tp u t w it h
re ­
c e r t a i n ra n ge s o f t h a t p r o d u c tio n
f u n c t io n s o t h a t th e s y s t e m a t ic a l r e l a t i o n b etw e e n a ve ra g e p r o d u c t i v i t y
^■In la b o r re q u ire m e n t e q u a tio n e s t im a t io n , we e s tim a te d some
p a ra m e te rs o f p r o d u c t io n w h ic h make i t p o s s ib le t o c a lc u la t e m a r g in a l
p r o d u c t i v i t y , even th o u g h we d id n o t e s tim a te th e p r o d u c t io n f u n c t io n
it s e lf .
^K uh, E . , "A P r o d u c t i v i t y T h e o ry o f Wage L e v e ls - An A lt e r n a t iv e
t o th e P h i l l i p * s C u r v e ." The R eview o f E conom ic S t u d ie s . V o l. XXXIV
( 4 ) , No. 100 ( O c t . , 1 9 6 7 ).
28
and marginal productivity can be approxim
ated by a linear relation.*
T
h
e assum
ption involved in using average productivity is, therefore,
not m
o
re critical than those used in estimating production functions.
T
h
e price of output a
nd the proxy for marginal productivity
could both enter the w
a
g
e equation a
s independent variables.
But
with the small ntm
ber of observations, in order to save degrees of
freedomw
e generate the proxy for the value of marginal product by
multiplying the price of output by the average productivity.
S
o,
actually, the formulation implies that the nom
inal w
a
g
e is a linear
function of the value of average product.
At this point, the price variable in the w
a
g
e rate equation
needs s
o
m
e further explanation.
In a multisector m
odel a distinction
m
ust be m
a
d
ebetw
een the consum
er price index and the price of output.
T
h
e consum
er price index a
s a cost of living index has been cosm
only
used in w
a
g
e studies.
But the implication of these tw
o prices in the
w
ag
e equation is quite different.
T
h
e consum
er price index is used
to get real w
ages free fromm
o
n
e
y illusion; It relates to the supply
^Elasticity of output in a C.E.S. production function with
constant returns to scale Is
3
L
Q
gP
(see page 45 in this dissertation).
S
o, if w
ea
ssu
m
e output varies proportionally to em
ploym
ent within a
certain observable range of the production function, the elasticity
of output is constant.
1S I • £
3L
Q
■
.
k
so ^
3L
“
k
* L
4.
29
side of the labor product* T
h
e price of output is the relevant
m
easure for value of labor productivity, which relates to the d
e
m
a
n
d
side.
H
ow
ever, there is a statistical problemin disentangling the
effects of those prices in the w
a
g
e equation because the consum
er
price Index is related to the price of output through an i d e n t i t y
relation.
S
o far, w
e presum
e that the m
ost important com
ponent of steady
state w
age is labor productivity.
T
h
em
ost reasonable interpretation
of the labor productivity theory implies a long run w
age elasticity
with respect to labor productivity of unity.
Labor productivity in­
creases in the long run for various reasons, Including technical
change a
n
d education.
T
h
em
o
n
e
yw
age adjusts to it , but with a lag.
Therefore, there is a tim
e delay in w
ag
e adjustm
ent to the equili­
brium level.
T
h
e specific lag structure will be described later in
the formal w
age equation.
T
h
e bargaining hypothesis co
m
m
o
n
ly attributes w
age increases
to consum
er price increases.
In this study, both the relative w
a
g
e
rate a
nd the consum
er price index are used for the bargaining basis.
O
nly one of themw ill be used in an industry w
a
g
e rate equation.
If
w
e have the fast growing consum
er price index and the value of average
product as the Independent variables, the forecasts of w
ag
e rates of
different industries nay diverge very such.
T
he Japanese w
age differ­
entials betw
een industries have been quite stable, although there has
been a slight tendency to narrow interindustry differentials, a
s
30
B lu e m e n th a l^ p o in te d o u t .
e n t ia ls
T a b le I I I - 2
shows th e tr e n d o f wage d i f f e r ­
o v e r tim e ; th e s ta n d a r d d e v ia t io n d e c lin e s s l i g h t l y .
T h e r e fo r e ,
i n o rd e r t o a v o id th e d iv e rg e n c e i n wage r a t e i n f o r e c a s t in g , r e l a t i v e
wage r a t e change is p r e f e r r e d t o th e consumer p r ic e
f o r b a r g a in in g .
in d e x as th e b a s is
The n e g a tiv e s ig n on th e c o e f f i c i e n t o f th e r e l a t i v e
wage r a t e w i l l make th e wage l e v e l o f an in d u s t r y la ? i f
th e r e l a t i v e
wage l e v e l o f th e l a s t y e a r was h ig h .
Wage d i f f e r e n t i a l s
in
th e m a n u fa c tu rin g s e c to r o f an economy a t
a g iv e n tim e may be a t t r i b u t e d t o some c o m b in a tio n o f th e f o l lo w in g
fa c to rs :
a g e , s e x , e d u c a tio n and t r a i n i n g , in d u s t r y , o c c u p a tio n , w o rk
s t a t u s , r e g io n , d eg re e o f u n io n iz a t io n and s c a le o f f i r m .
Wage d i f f e r ­
e n tia ls
a re d e te rm in e d b y s o c i a l v a r ia b le s
as w e l l as e con o m ic v a r i ­
a b le s .
As tim e goes o n , we c o u ld presum e t h a t wage d i f f e r e n t i a l s
move
to w a rd s a s t a b le e q u ili b r iu m w h ic h depends o n ly on th e lo n g te rm c o s t
o f e d u c a tio n and t r a i n i n g f o r s p e c i f i c in d u s t r ie s
s t a b le i n s t i t u t i o n a l f a c t o r s .
la b o r e r s
a re more s e n s i t i v e
and some o th e r
T h e r e fo r e , we can h y p o th e s iz e t h a t
t o changes o f t h e i r r e l a t i v e wage p o s i t i o n
th a n t o s im p le wage d i f f e r e n t i a l s betw een i n d u s t r i e s .
s t r u c t u r e changed i n
p r ic e in d e x i s
th e wage
th e p re v io u s y e a r so t h a t th e r e l a t i v e wage in
a c e r t a i n in d u s t r y d e c re a s e d , i t s
more s t r o n g ly .
If
tr a d e u n io n i s
C o st o f l i v i n g , w h ic h i s
assumed t o b a r g a in
re p re s e n te d b y th e consum er
a ls o c o n s id e re d f o r t h i s h y p o t h e s is , b u t i t w i l l be
^ B lu e m e n th a l, T , "The E f f e c t o f S o c io -e c o n o m ic F a c to rs on Wage
D i f f e r e n t i a l s i n Japanese M a n u fa c tu rin g I n d u s t r i e s . "
E conom ic S tu d ie s
Q u a r t e r ly . V o l. X V I I , No. 1 ( S e p t . , 1 9 6 6 ).
31
em ployed o n ly i f
th e r e l a t i v e wage does n o t w o rk v e r y w e l l .
T h is i s
b e ca u se o f th e s t a t i s t i c a l d i f f i c u l t y w h ic h was m e n tio n e d a bove.
S u m m a rizin g a l l th r e e h y p o th e s e s and c o n s id e r in g th e o n e -p e rio d
la g o f wage a d ju s tm e n t w h ic h was d e s c r ib e d in
C h a p te r I I , we have th e
fo r m a l wage e q u a tio n s f o l lo w in g :
00
(1) A
= a0 +
A
_
+a
2—
^W
t-1 + a
3 ± -0
— ^^tvl“i
+ ut
(2) AW = a0 + aj A
_LS,.^ + a2 A
. CPI,.^
+ “3
il 0
* VAPt - l - i + U t
w here
A
s ta n d s f o r p e rc e n ta g e change
= n o m in a l wage l e v e l o f an
in d u s t r y a t tim e t .
LS = em ploym ent s h a re o f an in d u s t r y o v e r t o t a l em ploym ent
(LS « — w h e re L i s
L
RW
= r e l a t i v e wage o f an in d u s t r y
(RW*. ■ sart
wt
t
-
w here W i s
VAP. = P „ * AP
t
th e t o t a l em ploym ent o f th e economy \
a verag e wage o f th e n o n -fa rm in d u s t r ie s
1
)
t
Pt « o u tp u t p r ic e
in d e x
A g r i c u l t u r a l wage and wage o f O th e r s e r v ic e s a re e x c lu d e d i n
c a lc u la t in g r e l a t i v e wages beca u se o f th e d if f e r e n c e s i n th e n a tu re
o f la b o r b e tw e e n m a n u fa c tu rin g in d u s t r ie s and a g r i c u l t u r e .
32
TABLE I I I - 2 - RELATIVE WAGES *
Year
I n d u s t r y Name
1960
•
1965
1970
19 72
1 . M in in g
1 .0 5 4
1 .019
1 .0 1 8
0 .9 9 2
2 . Foods and to b a c c o
0 .7 8 2
0 .8 3 8
0 .8 4 9
0 .8 3 0
3 . T e x t ile
0 .5 5 8
0 .6 0 5
0 .6 5 1
0 .6 4 8
4 . P u lp and p a p e r
0 .9 3 3
0 .9 6 0
0 .9 4 7
0 .9 5 4
5 . C h e m ica l p ro d u c ts
1 .2 7 3
1 .1 8 2
1 .2 1 4
1 .2 0 1
6 . P rim a ry M e ta ls
1 .3 2 3
1 .1 9 2
1 .2 4 4
1 .1 9 4
7. M e ta l p ro d u c ts
0 .7 9 7
0 .8 6 3
0 .9 1 5
0 .9 0 5
8 . N o n - e l e c t r i c a l m a c h in e ry
0 .9 7 7
0 .9 5 3
1 .0 3 7
1 .0 3 4
9 . E l e c t r i c a l m a c h in e ry
0 .8 9 6
0 .8 3 4
0 .8 7 8
0 .9 0 2
1 0 . T r a n s p o r t a t io n e q u ip m e n t
1 .2 2 1
1 .0 8 2
1 .0 6 6
1 .0 4 1
1 1 . M is c e lla n e o u s m a n u fa c tu rin g
0 .7 7 8
0 .8 2 7
0 .8 4 7
0 .8 4 6
1 2 . C o n s tr u c tio n
0 .7 9 1
0 .8 2 7
0 .8 4 7
0 .8 4 6
1 3 . E l e c t r i c i t y , g a s , w a te r
1 .5 6 8
1 .6 1 8
1 .5 0 2
1 .4 5 6
1 4. W h o le s a le & r e t a i l tra d e
0 .9 2 6
0 .9 2 1
0 .9 1 7
0 .9 2 9
15. R e a l e s ta g e
1 .8 0 6
1 .2 2 3
1 .3 5 1
1 .332
16. T r a n s p o r t & co m m u n ic a tio n
1 .1 1 2
1 .1 3 8
1 .0 9 8
1.109
17. F in a n c e and in s u ra n c e
1 .4 6 6
1 .4 0 4
1 .2 6 8
1 .3 0 8
0 .3 2 8
0 .3 1 0
0 .2 1 4
0 .2 0 6
S ta n d a rd d e v ia t io n
*The r e l a t i v e wage i s d e fin e d b y th e n o m in a l wage d iv id e d b y th e a verag e
wage o f th e economy.
33
APt = a verag e p r o d u c t i v i t y
w ( i)
* w e ig h ts o f la g schem e, w i t h
u fc *= s t o c h a s t ic d is tu r b a n c e
te rm .
The r a t e o f wage a d ju s tm e n t i s
o f th e n o m in a l wage l e v e l .
and (2 ) i s
£ w ( i) * 1
m easured b y th e p e rc e n ta g e change
The o n ly d if f e r e n c e betw een e q u a tio n
th e b a r g a in in g v a r ia b l e .
The p r o d u c t i v i t y v a r ia b le w it h
la g s y s te m can b e c o n s id e re d as th e s ta n d a r d p r o d u c t i v i t y
w h ic h i s
change tr e n d
c a lc u la t e d fro m a w e ig h te d a verag e o f p a s t p r o d u c t i v i t y
c h an g es.
p o s itiv e
(1 )
The e x p e c te d s ig n s a re p o s i t i v e
f o r C P I, and p o s i t i v e
f o r L S , n e g a tiv e f o r RW,
f o r VAP.
E m p ir ic a l R e s u lts
I n o r d e r to e s tim a te
th e wage a d ju s tm e n t e q u a tio n , we p o s i t
t h a t th e la g w e ig h t s t r u c t u r e w ( i )
U s in g t h i s
is
la g scheme we can r e w r i t e
g e o m e t r ic a lly d e c lin in g i n
th e wage r a t e e q u a tio n s i n
i.
th e
s p e c ia l fo r m ^ :
(1) i W
t - o
.0 + a
x AL
S
+o
c
2a wt_! + “3
L V
A
P
t- l- i
+ ut
(2 ) A Wt - o0 + ox A L S ^
+ a 2 A CPI
00
+ a , (1 -A )
Z
J
i= o
X1 A VAP
+ u
~
t- l“ i
t
^■In g e n e ra l K o yck la g s t r u c t u r e , we do n o t see th e (1 -A ) f a c t o r
w h ic h a p p e a rs i n th e e q u a tio n a bove.
I f we do n o t m u l t i p l y by (1 -X ) ,
th e sum o f th e s e w e ig h ts i s n o t e q u a l t o u n i t y .
I n o r d e r t o see th e
t o t a l e f f e c t o f a one u n i t change o f th e e x p la n a to r y v a r ia b l e o v e r th e
w h o le tim e p e r io d , we have t o make th e sum o f th e w e ig h ts u n i t y .
34
w h e re
A is
th e g e o m e t r ic a lly d e c lin in g r a t e
o f th e la g syste m i n
a
s e c to r.
F o r th e e s t im a t io n o f e q u a tio n s l i k e
p ro b le m s have t o be fa c e d .
F ir s t,
sum w h ile we have o n ly a f i n i t e
is n o n lin e a r i n
th e p a ra m e te rs
th e s e , two e c o n o m e tric
th e l a s t v a r ia b le
amount o f d a ta .
cx^ and A .
is
S econd, th e e q u a tio n
The f i r s t p ro b le m was
s o lv e d b y th e f o l lo w in g p ro c e d u re w h ic h was o r i g i n a l l y
K lein-*- and
an i n f i n i t e
s u g g e s te d b y
d e v e lo p e d by S a r g e n t.2
The suiranation i n
th e l a s t te rm o f th e e q u a tio n can be w r i t t e n
as f o l lo w s :
t-1
.1
1=0
X1 A VAP
—
. - + .1
t- i- 1
i= t
S u b s t it u t i n g i ■ k + t i n
A1 A VAP
t- i- 1
—
th e second te rm g iv e s f o r t h a t te rm
w here
k= o
T h is
o -k -1
can be c o n s id e re d as th e i n i t i a l c o n d it io n o f th e d if f e r e n c e
e q u a tio n .
V o l.
^ • K le in , L . R . , f,The E s tim a tio n o f D is t r i b u t e d L a g s ."
2 5.
( O c t . , 1 9 5 8 ).
Econome t r i c a .
^ S a rg e n t, T . , "Some E v id e n c e on th e S m a ll Sample P r o p e r t ie s o f
D is t r i b u t e d Lag E s tim a tio n s i n th e P re sen ce o f A u t o c o r r e la te d D is t u r ­
b a n c e s ." Review o f E conom ics and S t a t i s t i c s . V o l. X IX .
( F e b ., 1 9 6 8 ).
35
S u b s t it u t i n g i n t o
( I 1) AWt = aQ +
( l 1) and ( 2 * )
A LS
+ a2 A R W ^
t-1
+ ou (1 -A ) .1
3
l- o
( 2 * ) AW
— L
= a
O
g iv e s
A
A VAP .
—
t- i- 1
+ a , A LS*. , + cto A CPI
J- —
L-L
+ ct (1 -A )
3
A* n
o
^
t-1
+ a3 (1 -A ) ± l 0 A* A VAPt _ i _ 1 + a3 (1 -A )
C o n s id e rin g (1 - A ) A t as a v a r ia b le we can e s tim a te n
n e o u s ly w it h
At n
s im u lt a ­
th e o t h e r p a ra m e te rs o f th e e q u a tio n , so t h a t we can
a v o id th e p ro b le m a s s o c ia te d w it h
th e i n f i n i t e
t a i l o f th e l a g . *
The secon d p ro b le m can be s o lv e d e a s i l y b y e m p lo y in g s e a rc h
p ro c e d u re s s u g g e s te d b y H i l d r e t h
s e a rc h e s o v e r
r e s id u a ls .
and
n
and L u .
o
The H ild r e t h - L u scheme
A f o r t h a t v a lu e w h ic h m in im iz e s th e sum o f sq u a re d
S o, th e s e le c te d v a lu e o f A , th e p a ra m te rs ctQ, a ^ ,
can be d e te rm in e d .
The r e g r e s s io n r e s u lt s
a re shewn i n
T a b le I I I - 3 .
T h is k in d o f e q u a tio n has an a d va n ta g e i n c o m p u ta tio n o f f o r e ­
c a s t and a ls o i n r e g r e s s io n . We do n o t need t o keep th e memory o f a l l
p a s t h i s t o r y o f VAP. U s in g th e r e l a t i o n
____
____
___
t-1
- VAPt+ i = A(AVAPt + A VAPt +i^ where AVAPt = ± ii
a1 (£ vAPt
)
we o n ly h a ve t o remember th e p r e v io u s y e a r ’ s ^ VAP.
^ H i ld r e t h , C. and J . Y . L u . , "Demand R e la t io n s W ith A u t o c o r r e la te d
D is t u r b a n c e s . "
T e c h n ic a l B u l l e t i n . V o l. 276. M ic h ig a n S ta te U n i­
v e r s i t y , A g r i c u l t u r a l S t a t io n (E a s t L a n s in g , M ic h . , 1 9 6 0 ).
TABLE I I I - 3
I n d u s t r y Name
C o n s ta n t
- WAGE RATE EQUATION REGRESSION
AliW
A_ CPI
ALS
A_VAP
n
o
X
R
D.W.
.10 7
( .1 6 8 )
- .2 7 4
(- 1 .1 4 1 )
.4 0
.347
1 .6 5 9
.1 4 0
(1 .0 4 5 )
.28 5
(1 .6 1 3 )
-.4 2 3
( - 1 .7 8 6 )
.4 5
.52 4
1 .0 6 1
.12 6
(1 .3 7 0 )
.63 5
(1 .1 3 6 )
.2 8 1
( .3 0 2 )
-.5 9 0
(1 .2 7 2 )
.7 0
.539
1 .2 0 1
4 . T e x t ile
.13 1
(7 .0 8 1 )
.539
(1 .5 4 4 )
.19 7
(1 .3 0 7 )
-.5 5 8
( - 3 .5 5 4 )
.3 5
.5 5 0
.8 3 8
5 . P u lp and pap e r
.0 6 4
(4 .5 3 3 )
- .1 4 4
( - .4 2 3 )
.68 6
(3 .7 0 6 )
.6 6 1
(6 .4 6 6 )
-.4 9 0
(- 6 .4 0 4 )
.6 5
.91 4
2 .5 0 8
.099
( .5 3 8 )
- .1 5 9
( - .9 2 0 )
1 .3 6 4
( .9 2 9 )
-.7 5 1
( - .1 9 3 )
.9 5
.7 8 0
1 .8 1 5
.5 2 6
(1 .0 0 4 )
.0 6 7
(.1 9 5 )
- .6 9 6
( - 1 .7 7 9 )
.75
.32 2
1 .2 1 4
.4 7 8
(1 .3 8 6 )
.1 7 3
(.9 2 5 )
-.9 1 1
( - 6 .1 4 8 )
.5 0
.79 2
1 .7 6 0
.1 7 4
(2 .2 3 4 )
- .7 0 0
( - 3 .0 0 4 )
.2 0
.5 7 4
1 .6 0 0
.6 4 1
(1 .0 2 5 )
-8 .4 8 9
( - 3 .2 1 0 )
.9 5 0
.91 0
1 .6 7 2
1 . A g r ic u lt u r e , f o r e s t r y , f is h e r y
- .0 0 3
( - .0 2 9 )
2 . M in in g
.09 2
(3 .1 3 9 )
3. Foods and to b a cco
6 . C hem ical p ro d u c ts
7. P rim a ry m e ta ls
.12 8
(2 .8 5 9 )
8. M e ta l p ro d u c ts
.1 1 3
(3 .6 0 6 )
9 . N o n - e le c t r ic a l m a ch in e ry
.087
(3 .4 3 3 )
1 0 . E l e c t r i c a l m a c h in e ry
.349
(2 .8 3 0 )
2 .3 5 9
(1 .8 6 8 )
- .1 6 9
( - .4 7 6 )
.5 3 6
(1 .1 6 6 )
1 .0 2 1
( - 1 .7 6 2 )
.0 3 3
( .6 9 0 )
TABLE I I 1-3
I n d u s t r y Name
C o n s ta n t
ARW
(CONTINUED)
A CPI
A_ LS
VAP
%
A
R2
D.W.
.78 2
(1 .4 2 1 )
.1 1 2
(.5 7 5 )
-.6 3 2
( - 2 .7 0 5 )
.5 5
.26 6
.91 3
.68 9
(1 .7 8 1 )
.5 0 1
(2 .4 4 0 )
-.5 7 7
( - 3 .2 1 2 )
.3 5
.695
1 .1 3 8
- .2 4 9
( - .6 3 4 )
.629
(2 .7 4 7 )
-.0 7 9
(- .4 0 0 )
.4 0
.52 8
1 .7 4 0
.030
(.7 6 1 )
- .6 8 3
(- 1 .8 7 1 )
.65 5
(2 .5 7 1 )
-.0 7 7
(- .5 0 2 )
.6 0
.6 8 0
2 .6 0 0
1 5. W h o le s a le & r e t a i l tra d e
.084
(1 .8 8 0 )
-.1 9 9
( - .3 6 2 )
.299
(1 .3 4 1 )
-.2 7 1
(-1 .2 7 1 )
.5 0
.44 2
1 .1 8 9
1 6 . R e a l e s ta t e
.047
(1 .2 4 5 )
- .5 7 3
( - 2 .1 9 4 )
.8 3 0
(2 .3 3 4 )
- 4 4 3 .6
(2 .3 3 0 )
.3 0
.2 5 1
1 .6 8 6
1 7 . T r a n s p o rt and co m m u n ica tio n
.070
(3 .5 1 1 )
- .3 8 8
( - .6 6 3 )
.0 7 2
( .1 8 4 )
.53 1
(4 .2 9 5 )
-.2 4 6
( - 2 .1 2 4 )
.3 0
.7 9 8
2 .6 5 1
1 8 . F in a n c e and in s u ra n c e
.105
(4 .2 8 7 )
-.4 1 2
( - .5 8 6 )
.22 6
( .4 5 0 )
.0 4 1
(.6 1 9 )
-.4 6 3
( - 2 .0 4 5 )
.3 0
.23 7
1 .2 0 1
1 9. O th e r s e r v ic e s
.107
(3 .4 5 4 )
-.0 5 8
1 .5 4 9
1 1. T r a n s p o r t a t io n equipm ent
.069
(1 .6 5 3 )
1 2 . M is c e lla n e o u s m a n u fa c tu rin g
.068
(2 .1 5 9 )
- .7 8 2
( - .9 7 4 )
1 3. C o n s tr u c tio n
.061
(1 .9 5 7 )
14. E le c t r ic it y ,
g a s , and w a te r
.332
( .5 8 2 )
38
As e x p e c te d , d i f f e r e n t in d u s t r ie s have d i f f e r e n t k in d s o f wage
r a t e e q u a tio n s .
The b a r g a in in g p ro c e d u re p la y s a s i g n i f i c a n t r o le in
E l e c t r i c a l m a c h in e ry and i n E l e c t r i c i t y ,
each o f w h ic h the tra d e u n io n i s
g a s , and w a te r s u p p ly , in
presumed t o be q u it e w e l l o rg a n iz e d .
As m e n tio n e d a bo ve , th e r e l a t i v e wage change is p r e f e r r e d t o th e con­
sumer p r ic e in d e x change as th e b a r g a in in g v a r ia b le so t h a t th e wage
f o r e c a s t s i n th e f u t u r e w i l l n o t d iv e rg e v e ry much betw een in d u s t r ie s .
The consumer p r ic e in d e x change i s s u b s t it u t e d when an u n e xp e cte d
s ig n i s
e n c o u n te re d i n
th e r e l a t i v e wage c o e f f i c i e n t .
D ie e q u ili b r iu m h y p o th e s is w o rks b e t t e r th a n th e d is e q u ilib r iu m .
T h is can be e x p la in e d b y th e f a c t t h a t t h i s
th e lo n g p e r io d , l i k e
a ve ra g e d o u t .
v a r ia b le i n
is
an a n n u a l m o d el.
a y e a r , some d is e q u ilib r iu m phenomena m ig h t be
O nly one s e c to r
o u t o f 19 s e c to r s
th e e q u a tio n , a lth o u g h in some s e c to r s
n o t s ig n if ic a n t ly
In
d i f f e r e n t fro m z e ro .
t h a t v a r ia b le
is
M ost o f th e s e c to r s have a
c o e f f i c i e n t o f VAP w h ic h i s n o t c lo s e to 1.
t h a t th e h y p o th e s is o f u n i t e l a s t i c i t y
do n o t have th e VAP
A c c o r d in g ly , we can say
o f wage r a t e w it h
r e s p e c t to
th e v a lu e o f a ve ra g e p r o d u c t is n o t a c c e p te d f o r th e Japanese economy.
The g e o m e t r ic a lly d e c lin in g r a te s
th e mean la g is
le s s
c o n c e n tra te a ro u n d 0 .6 .
T h e r e fo r e ,
th a n two y e a r s , w h ic h i s q u i t e u n d e rs ta n d a b le .
A lm o s t a l l o f th e D. W. s t a t i s t i c s
r e g io n o r th e in d e c is iv e r e g io n .
a v e r y im p o r ta n t p ro b le m h e r e .
e n t e r th e n o n - a u to c o r r e la te d
A c c o r d in g ly , a u t o c o r r e la t io n is n o t
F o r f o r e c a s t in g , th e s in p le RHO ad­
ju s tm e n t p ro c e d u re * w i l l be e m ployed f o r a b e t t e r f o r e c a s t .
* G o ld b e rg e r, A .S . " B lu e - G e n e r a liz e d L e a s t S quares R e g re s s io n
M o d e l." J o u r n a l o f th e A m e rica n S t a t i s t i c a l A s s o c ia t io n .
V o l. 5 7 ,
No. 2 , (J u n e , 1 9 6 2 ).
39
C o n s id e rin g th e bad p e rfo rm a n c e o f wage e q u a tio n s i n
m o d e ls th e
goodness o f f i t
_2
v e ry le w R s .
In th is
is
n o t d is c o u r a g in g .
I n o r d e r t o keep t h i s wage tr e n d
th o s e o f th e o th e r s e c t o r s , wage r a te s i n
a re s im p ly re g re s s e d on th e consum er p r ic e in d e x .
- 2
have R s b etw e e n 0 .5 and 0 .7 5 , w h ic h i s
bad
th is
s e c to r
O th e r in d u s t r ie s
n o t u s u a lly
c o n s id e re d a
f i t when we have p e rc e n ta g e change as th e dependent v a r ia b l e .
As we can see i n
le v e l,
O th e r S e rv ic e s has
s e c t o r , a l l v a r ia b le s shews th e "w ro n g s ig n o r
has v e r y i n s i g n i f i c a n t t - s t a t i s t i c s .
c o n s is t e n t w i t h
o th e r b ig
th e ta b le
o f s im u la t io n o f th e wage r a te
th e a c t u a l l e v e l o f th e wage r a te
re p ro d u c e d b y s im u la t io n .
2
can be a lm o s t e x a c t ly
The a ve ra g e p e rc e n ta g e e r r o r
3
and th e
^Fromm, G. and P . Taubman.
" P o lic y S im u la t io n W ith an E c o n o m e tric
M o d e l."
The B ro o k in g s I n s t i t u t i o n .
1968. p p . 11.
They s a id , "wages
and p r ic e s s e c t o r i s one o f th e l a r g e r c o n t r ib u t o r s o f e r r o r s i n th e
a g g re g a te r e s u l t s . "
^ Ih e s im u la te d wage l e v e l was c a lc u la t e d as f o l lo w s .
I n th e
i n i t i a l y e a r , we s t a r t w it h th e a c t u a l wage l e v e l .
The v a lu e o f th e
p e rc e n ta g e o f wage p r e d ic t e d b y th e r e g r e s s io n e s tim a te s i s used to
c a lc u la t e wage l e v e l i n th e c o n s e c u tiv e y e a r s .
The R2 o f th e s im u la ­
t i o n was c a lc u la t e d as i f th e s im u la te d v a lu e s w e re th e p r e d ic t e d v a lu e s
o f th e r e g r e s s io n .
So th e R^ i s th e r a t i o o f th e e x p la in e d v a r i a t i o n
o f th e wage l e v e l o v e r th e t o t a l v a r i a t i o n o f th e a c t u a l wage l e v e l .
^A ve rag e p e rc e n ta g e e r r o r i s
d e fin e d b y
T
APW = 100 *
*
v i t ~ vj t
^ T
wj t
and r o o t mean s q u a re d p e rc e n ta g e e r r o r I s
T
T
RMSPE = 100 *
a
w h e re w t i s
1
// «*
wi t -
i
\
w«.
th e s im u la te d wage l e v e l
2
2
d e fin e d b y
, \\ *5
*5
/ T]
»
40
r o o t mean sq u a re d p e rc e n ta g e e r r o r a re le s s th a n 10% f o r n e a r ly a l l
in d u s t r i e s .
2
R
i s v e r y c lo s e to 1 .
Even bad f i t
e q u a tio n s , l i k e
2
O th e r s e r v ic e s and R e a l e s t a t e , have a q u it e h ig h R above 0 .9 5 .
41
TABLE I I I - 4 - SIMULATION OF WAGE RATE LEVEL
R oot Mean Squared
P e rc e n ta g e E r r o r
R2
2 .5 7 7
3 .6 0 2
.9 9 5 4
2. M in in g
5 .0 9 7
6 .7 6 8
.9823
3 . Foods & to b a c c o m a n u fa c tu rin g
3 .6 4 1
4 .8 1 5
.99 2 3
4. T e x tile
5 .5 6 5
7 .6 6 1
.9809
.781
1 .0 5 8
.9996
6. C h e m ica l p ro d u c ts
1 .1 4 6
1 .4 5 8
.9990
7. P rim a ry m e ta ls
4 .8 1 1
5 .9 1 9
.9890
2 .7 5 2
3.3 9 6
.99 5 2
5 .1 7 7
6 .4 7 2
.9886
10. E l e c t r i c a l m a c h in e ry
1 .1 4 2
1 .5 5 4
.9989
1 1. T r a n s p o r t a t io n e q u ip m e n t
8 .9 9 7
10.7 44
.9591
1 2. M is c e lla n e o u s m a n u fa c t.p r o d .
3 .4 5 3
4 .629
.9911
1 3 . C o n s tr u c t io n
2 .8 9 8
3 .4 0 0
.99 4 9
1 4. E l e c t r i c i t y , gas & w a te r s u p p ly
1 .7 2 0
2 .0 1 4
.9 9 8 0
15. W h o le s a le & r e t a i l tr a d e
5 .2 1 0
6 .9 1 0
.97 9 3
16. R e a l e s t a t e
9 .8 8 4
1 3 .5 4 3
.96 1 7
17. T ra n s p o rt & co m m u n ic a tio n
1 .5 4 3
1 .9 5 7
.9 9 8 6
1 8. F in a n c e and in s u ra n c e
6 .9 6 8
7 .999
.9634
1 9. O th e r s e r v ic e s
3 .0 4 1
3 .4 6 7
.9945
I n d u s t r y Name
1
. A g r ic u ltu r e ,
A verag e A b s o lu te
P e rc e n ta g e E r r o r
F o r e s t r y , F is h in g
5 . P u lp and p a p e r
8
. M e ta l
p r o d u c ts
9 . n o n - e l e c t r i c a l m a c h in e ry
42
CHAPTER IV
L a b o r R e q u ire m e n t E q u a tio n
T h e o ry
The la b o r re q u ire m e n t e q u a tio n i s needed f o r th e employm ent p ro ­
je c tio n
in to
and f o r th e u n i t la b o r c o s t c a lc u la t io n , w h ic h , in t u r n ,
p r ic e d e te r m in a tio n in t h i s m o d e l.
e n te rs
The c h r o n ic s c a r c i t y o f la b o r
i n Japan has been a b in d in g c o n s t r a in t on o u tp u t g ro w th , and th e wage
r a t e in c re a s e s caused by th e excess demand f o r la b o r have been th e
le a d in g f a c t o r in th e p r ic e in c r e a s e s .
The la b o r re q u ire m e n t i s
th e la b o r r e q u ir e d p e r u n i t o f o u t p u t ,
i n o th e r w o rd s , th e r e c ip r o c a l o f th e a v e ra g e p r o d u c t i v i t y o f la b o r .
The re a s o n we d e a l w it h la b o r re q u ire m e n t r a t h e r th a n w it h p r o d u c t i v i t y
is
s im p ly t h a t i t
is
c o n v e n ie n t to h ave c u rv e s w h ic h a re bounded b e lo w
by z e ro r a t h e r th a n c u rv e s w h ic h grow
upw ard w it h o u t bound.
The la b o r re q u ire m e n t in a c e r t a i n in d u s t r y , EOQ^, ( s ta n d in g f o r
f E o v e r Q1) i s
d e fin e d by
(1 ) E0Q j > t = 1 2 .L j ) t .H j ( t /Q j > t
w here
L j t ® em ploym ent i n
H-
J >^
= w o rk in g h o u rs p e r m onth i n j
Qj r = a n n u a l o u t p u t o f j
EOQ i s
in d u s t r y a t tim e t
i-Vi
t"v»
in d u s t r y a t tim e t
in d u s t r y a t tim e t .
s im p ly th e m anhours r e q u ir e d t o p ro d u ce one u n i t o f o u t p u t .
43
The la b o r re q u ire m e n t e q u a tio n i s
f u n c t io n .
d e r iv e d fro m th e p r o d u c tio n
F o r th e c o n s is te n c y o f th e w h o le m o d e l, we em ploy th e
C .E .S . p r o d u c t io n f u n c t io n w h ic h i s
a ls o used in th e in v e s tm e n t
e q u a tio n d e r iv a t io n .
The C .E .S . p r o d u c t io n f u n c t io n w it h
c o n s ta n t r e t u r n s
to s c a le
and w it h la b o r a u g m e n tin g t e c h n o lo g ic a l change i s , ^
_0
(2 ) Qj > t = 6 la 1 ( g ( t )
- EJ t >
+ a2
+ a 3 (Mj ( t )
_ 1
] p
w h e re
E . . = 1 2 *L .
3 ,t
j,t
*H.
j,t*
manhours
K. ^ = r e a l c a p i t a l s to c k
J »t
M.
= in t e r m e d ia t e in p u t s
J »t
g (t)
p
= la b o r a u g m e n tin g f a c t o r
*
1 - a
a
- ± -----------
a =* e l a s t i c i t y
o f s u b s titu tio n
a *s = d i s t r i b u t i o n
p a ra m e te rs
3 = c o n s ta n t.
U s u a l m acro p r o d u c t io n f u n c t io n s in c lu d e o n ly c a p i t a l and la b o r
as in p u t s .
Even some d is a g g re g a te d s t u d ie s
in c lu d e o n ly p r im a r y
^ T h e re i s no re a s o n why m a t e r ia ls e n te r th e p r o d u c tio n f u n c t io n
i n th e same fo rm as la b o r and c a p i t a l .
B u t th e way m a t e r ia ls e n te r
e q u a tio n (2 )
does n o t a f f e c t o u r la b o r re q u ire m e n t e q u a tio n .
So,
we j u s t le a v e i t as above t o g u a ra n te e th e l i n e a r h o m o g e n e ity .
44
fa c to rs
i n th e p r o d u c tio n f u n c t io n because s u b s t i t u t a b i l i t y betw een
m a t e r ia ls
is
d o u b t f u l.
I f we d o n ’ t
in c lu d e th e m a t e r ia ls as in p u t ,
Qt s h o u ld be i n v a lu e added te rm , and th e d e f l a t o r s h o u ld be f o r
v a lu e added.
U n f o r t u n a t e ly ,
th e e f f o r t to c a lc u la t e th e v a lu e added
and v a lu e added d e f l a t o r w it h Japanese d a ta was n o t s u c c e s s fu l.
o f th e v a lu e added p r ic e s
tu r n e d o u t t o be n e g a tiv e when c a lc u la t e d u s in g
c o n s ta n t in p u t - o u t p u t c o e f f i c i e n t s .
in c lu d e s m a t e r ia ls
in
it
Some
H ow ever, a p r o d u c tio n f u n c t io n w h ic h
may be j u s t i f i e d .
I n a m easure o f economy-
w id e p r o d u c tio n such as GNP, th e in t e r m e d ia t e in p u t s have been n e tte d
o u t , so t h a t th e p r o d u c tio n f u n c t io n needs o n ly p rim a ry in p u t s .
But
f o r a s e c t o r a l p r o d u c tio n f u n c t io n , w it h s e c t o r a l g ro s s o u t p u t ,
in te r ­
m e d ia te in p u t s b e lo n g i n th e f u n c t io n .
T h is p o in t was j u s t i f i e d b y
K e n d ric k ,^ " who s a id :
" F o r p r o d u c tio n a n a ly s is i t may be u s e f u l in some cases to use
t o t a l g ro s s o u tp u t e s tim a te s and r e l a t e them to f a c t o r in p u t s ,
p lu s in te r m e d ia t e in p u t s p u rch a se d o u t s id e th e in d u s t r y .
The
re a s o n i s t h a t i n p r o d u c tio n d e c is io n s management has to w e ig h
a l t e r n a t i v e c o m b in a tio n o f a l l in p u t s i n th e l i g h t o f t h e i r
r e l a t i v e p r ic e s so t h a t th e le a s t c o s t c o m b in a tio n may be
s e le c t e d . "
The in c lu s io n o f in t e r m e d ia t e in p u t s i n a C .E .S . p r o d u c tio n f u n c t io n
was u t i l i z e d b y N ordhaus
9
and b y T h e il and T ilh a n u s .
3
^ •K e n d ric k , J .W ., P o s tw a r P r o d u c t i v i t y T re n d s in th e U .S . 1 9 4 8 -1 9 6 9 .
New Y o rk . NBER. 1 973. pg 1 7.
^N o rd h a u s, W .D ., "R e c e n t D e ve lop m e n ts i n P r ic e D y n a m ic s ," in The
E c o n o m e tric s o f P r ic e D e te r m in a tio n , C o n fe re n c e sp o n so re d b y B oard o f
G o ve rn o rs o f th e F e d e ra l R e se rve System and S o c ia l S c ie n c e R esearch
C o u n c il. , e d . b y O tto E c k s t e in .
^ T h e il, B . , and C .B . T ila n u s . "T h e Demand f o r P ro d u c tio n F a c to rs
and th e P r ic e S e n s i t i v i t y o f I n p u t- O u tp u t P r e d ic t io n s , " I . E . R . v o l . 5 ,
No. 3 . , S ep te m be r, 1964.
45
T h is p r o d u c tio n f u n c t io n assumes s u b s t i t u t a b i l i t y betw een f a c t o r
in p u t s and in te r m e d ia te m a t e r ia ls .
The s u b s t i t u t i o n b etw e e n f a c t o r
in p u t s and in t e r m e d ia t e m a t e r ia ls i s
e xa m p le , i f
fir m
th e p r ic e o f m a t e r ia ls
u n d e rs ta n d a b le b e ca u se , f o r
in c re a s e s r e l a t i v e t o w ages, a
can em ploy la b o r t o p ro d u ce t h a t m a t e r ia l in s te a d o f b u y in g th e
e x p e n s iv e m a t e r ia l.
The la b o r re q u ire m e n t can be d e r iv e d fro m th e m a rg in a l p ro d u c ­
t iv ity
c o n d it io n .
The m a rg in a l p r o d u c t i v i t y c o n d it io n f o r p r o f i t
m a x im iz a tio n w i t h r e s p e c t t o manhour in p u t i s
3Q
. / Q. f \ p+1
(3) JJlt
(g( t ) W J l I
3Ej t
^
1
[ h
W.„
=31
pj t
t j
w here
W.
= r e a l wage r a t e o f j th in d u s t r y a t tim e t .
pj t
T h is c o n d it io n im p lie s p e r f e c t c o m p e titio n i n
it
th e m a rk e t.
But
a ls o can be a p p lie d t o d i f f e r e n t d e g re e s o f c o m p e titio n w it h s im p le
m o d if ic a t io n . *
E q u a tio n
(3 ) h o ld s o n ly i n
e q u ili b r iu m
s it u a t io n .
o r d e r t o d is t i n g u i s h th e e q u ili b r iu m v a lu e o f
Q.
J*
fro m th e a c t u a l
v a lu e , we e x p re s s th e e q u ili b r iu m v a lu e as
E jt
/ Q.
jt
*
\ V
;
In
* B la c k , S .W ., and H .H . K e le jia n . "A M acro M odel o f th e U .S . L a b o r
M a r k e t ." E c o n o m e tric a . V o l. 3 8, No. 5 (S e p te m b e r, 1970) p g. 7 2 1 -7 4 1 .
They e q u a te 3Q jt
to some f r a c t i o n o f r e a l wage,
R . w h e r e y s ta n d s
3E]7
Pj t
f o r th e d e g re e o f c o m p e t it io n .
B u t i n t h i s s tu d y , t h i s k in d o f m odi­
f i c a t i o n i s n o t n e c e s s a ry , beca u se i n r e g r e s s io n a n a ly s is th e p a ra m e te r
y i n e f f e c t w i l l be in c lu d e d i n t h e c o n s ta n t te rm , w h ic h i s a m ix t u r e o f
1 a and y .
T h e r e fo r e , we c a n n o t d is e n ta n g le y fro m th e c o n s ta n t te rm .
y
does n o t a f f e c t th e o t h e r c o e f f i c i e n t s a t a l l .
46
One im p o r ta n t f e a t u r e o f th e p r o d u c tio n f u n c t io n
a u g m e n tin g f a c t o r .
is
th e la b o r
U s u a l p r o d u c tio n f u n c t io n s have an e x p o n e n tia l
a u g m e n tin g f a c t o r b ecause th e e x p o n e n tia l f u n c t io n i s
easy to h a n d le .
T h e re i s no re a s o n why some o th e r f u n c t io n a l fo rm c a n n o t be u s e d .
A ls o ,
i f we assumed t h a t la b o r i s augm ented e x p o n e n t ia lly , we w o u ld
have i m p l i c i t l y
answ ered th e c r i t i c a l q u e s tio n o f th e s u s t a i n a b i l i t y
o f lo n g te rm g ro w th .
The e x p o n e n tia l la b o r a u g m e n ta tio n s im p ly means
t h a t th e la b o r p r o d u c t i v i t y w i l l grow b y th e same p r o p o r t io n i n th e
fu tu re .
T h is a s s u m p tio n i s n o t re a s o n a b le in th e Japanese economy.
I n Ja p a n , la b o r p r o d u c t i v i t y in c re a s e d b y a lm o s t te n p e rc e n t a y e a r
fro m 1958 to 1 972.
I f we f i t
th is
d a ta t o
th e e x p o n e n tia l c u rv e ,
i t w i l l p r e d ic t th e same h ig h g ro w th r a t e i n
may s lo w down i n
th e f u t u r e .
P r o d u c t iv it y
The h ig h g ro w th r a t e o f th e p a s t y e a rs
may have come fro m t r a n s i t i o n a l f a c t o r s . ^
comer to econom ic d e v e lo p m e n t, i t
f a s t e r th a n o t h e r c o u n t r ie s .
th e f u t u r e .
Because Japan was a l a t e
c o u ld a c c e le r a t e i t s
econom ic g ro w th
A f t e r th e t r a n s i t i o n a l f a c t o r s a re e x­
h a u s te d , o n ly th e s u s ta in a b le f a c t o r s w i l l c o n t r ib u t e t o th e g ro w th
r a t e , w h ic h w i l l th e n s lo w down.
I n o r d e r to p r e d ic t s lo w in g -d o w n p r o d u c t i v i t y g ro w th , la b o r is
augm ented b y th e G om pertz c u r v e .
( 4 ) d l o & g O ll
d t
w h e re a i s
The G om pertz c u rv e has th e p r o p e r t y ,
= b (a - lo g g ( t ) )
an a s s y m to tic l i n e ,
and b i s
^ - P a tr ic k , H. and H. R o so vsky.
In s titu tio n ,
pp 1 3 9 -1 4 1 .
1975.
th e r a t e b y w h ic h th e gap
A s ia ’ s New G ia n t .
The B ro o k in g s
47
betw een th e a s s y m p to tic l i n e and th e c u r r e n t v a lu e o f Log g ( t )
c lo s in g each p e r io d .
is
T h is f u n c t io n a l fo rm g u a ra n te e s t h a t th e p ro ­
d u c t i v i t y w i l l n e v e r go up beyond a c e r t a i n , p e rha p s v e r y h ig h , l e v e l
and t h a t ,
as tim e goes o n , th e g ro w th r a t e slo w s down.
(3) » and s o lv in g f o r
By t a k in g lo g a r ith m s o f b o th s id e s o f
E *
lo g O q ) > we g e t th e f o l lo w in g e q u a tio n w it h o u t s u b s c r ip t s .
(5) lo g (5 )
= C -
4
w h e re C i s
JU -
lo g
(g (t)) - 1
p
lo g
r + i
(&
P
c o n s ta n t.
R e ce n t re s e a rc h has u n co ve re d c o n s id e r a b le e v id e n c e f o r a la g g e d
r e l a t i o n s h i p b etw e e n o u tp u t and e m ploym ent.
As Kuh^ p o in te d o u t ,
d u r in g a s h a rp d e c lin e i n o u t p u t , o u tp u t p e r manhour w i l l d e c lin e
a b r u p t ly b e ca u se th e o v e rh e a d la b o r component i s n o t re d u c e d p ro ­
p o r tio n a lly ,
in
even th o u g h th e r e m ig h t be a p r o p o r t io n a t e r e d u c t io n
th e p r o d u c t io n l i n e w o rk f o r c e s .
T h is p r o p o s it io n s u g g e s ts t h a t
t h e r e c o u ld be a d i s t r i b u t e d la g i n th e re s p o n s e o f em ploym ent to
o u tp u t v a r i a t i o n .
The same p r o p o s it io n can be a c c e p te d i n o u r la b o r
r e q u ir e m e n t d e t e r m in a t io n .
As th e r e a l wage v a r ie s ,
a d ju s t th e em ploym ent o v e r o u t p u t r a t i o
as r a p i d l y .
We t h e r e f o r e assume t h a t a c t u a l ( ^ )
rj
( if )
*
f ir m s w o u ld n o t
is
a d ju s te d t o e q u ili b r iu m
th ro u g h a k o y c k ty p e d i s t r i b u t e d l a g , w h ic h we s t a t e i n p r o p o r t io n a l
■4cuh, E . , " C y c l i c a l and S e a so n a l L a b o r P r o d u c t iv it y i n U .S .
M a n u fa c t u r in g . ”
R eview o f Econom ics and S t a t i s t i c s .
F e b ru a ry , 1965.
48
o r in lo g a r it h m ic
(6 )
w h e re 0
fo rm t o m atch th e fo rm o f th e p r o d u c tio n f u n c t io n ;
lo g
< y <
(£ ) = v
( | ) * + (1 - y ) lo g
1
T h u s, o n ly th e f r a c t i o n
and l a s t y e a r s 1 0^) i s
S u b s t it u t i n g
<7> 1 o *
lo g
$
y o f th e d if f e r e n c e b etw een e q u ili b r iu m
x
e lim in a t e d i n th e c u r r e n t p e r io d .
(5 ) i n t o
-
r
( i)
( 6 ) , we g e t
p+T C ”
+ (1 -
T a k in g th e f i r s t
p ^T 108
(8 (t))
-
108
(f >
y) lo g
d if f e r e n c e o f th e b o th s id e s w it h re s p e s t to
tim e , we g e t
<8 >
m
.
$
- - &
<J
+ (1 - y
M > 2)> - £
)
*
<?>
A lo g
U s in g th e c h a r a c t e r i s t i c o f th e G om pertz c u rv e ( 4 ) , we can r e w r it e
e q u a tio n
(8 ).
( 8 ?) A lo g ( ^ ) = -
(b (a - lo g
+ (1 -
(g (t)))-
A lo g
(|)
y) A lo g
Now, we s o lv e (7 ) f o r lo g
(g (t)),
and s u b s t it u t e i n t o
( 8 1) .
Then
we g e t th e r e g r e s s io n e q u a tio n b y a r r a n g in g te rm s as f o l lo w s :
(9 )
A lo g (-|) +
A lo g
( j)
-
(1 - y ) A lo g
(^ ) 1
c ' - b ( lo g ( I ) + p-J j- lo g (£ ) - (1 - y ) lo g ( i ) ^ )
49
w h e re
c ' “ ' p+T a • b " p
If
(“ T
P
1 0 8
th e speed o f a d ju s tm e n t,
“i )
y , is
te rm w i l l d is a p p e a r i n b o th s id e s .
e q u a l to 1 , th e la g g e d EOQ
W ith o u t c o n s id e r in g th e r e a l wage
te r m , th e e q u a tio n says t h a t th e p e rc e n ta g e change o f EOQ i s
e q u a l to
some c o n s ta n t, w h ic h c o u ld be in t e r p r e t e d as a tim e t r e n d , m inus
lo g a r ith m o f th e l e v e l o f c u r r e n t EOQ m u l t i p l i e d b y th e r a t e o f
c lo s in g gap betw een th e a s s y m p to tic l i n e
fo re ,
and th e c u r r e n t EOQ.
T h e re ­
th e EOQ w i l l d e c re a s e f a s t e r when th e l e v e l o f EOQ i s h ig h th a n
when EOQ i s
p o n e n t ia lly .
lo w .
I f b is
e q u a l o f z e ro , th e EOQ w i l l grow up ex­
T h is fo rm o f th e e q u a tio n in c lu d e s e x p o n e n tia l g ro w th
o f th e EOQ as a s p e c ia l c a s e .
The r e a l wage te rm a ls o a f f e c t s
change o f EOQ th r o u g h th e e l a s t i c i t y o f s u b s t i t u t i o n .
th e
U n f o r t u n a t e ly ,
we c a n n o t t e s t th e s t a t i s t i c a l s ig n if ic a n c e o f r e a l wage i n th e EOQ
d e t e r m in a t io n w it h e q u a tio n
(9 ).
The a u th o r te s t e d th e s ig n if ic a n c e
o f th e r e a l wage w i t h th e e x p o n e n tia l f u n c t io n fo rm w h ic h w i l l be
shown l a t e r .
in
M ost o f th e wage v a r ia b l e show
s t a t i s t i c a l s ig n if ic a n c e
th e EOQ e q u a tio n .
S in c e we a re u s in g th e same p r o d u c t io n f u n c t io n
i n th e in v e s tm e n t
e q u a tio n e s t im a t io n , we can b o rro w th e in f o r m a t io n o f th e e l a s t i c i t y
o f s u b s t it u t io n
fro m th e in v e s tm e n t e q u a tio n .
s t i l l we h ave t o know y t o
is
Even i f we know p ,
e s tim a te e q u a tio n ( 9 ) .
We a re s u re t h a t
y
g r e a t e r th a n z e ro and le s s th a n o r e q u a l t o u n i t y , so we can e s tim a te
(9 ) w i t h d i f f e r e n t v a lu e o f y .
A l l v a lu e s fro m z e ro to one b y
i n t e r n a l 0 .0 5 w e re p lu g g e d i n b o th s id e s o f th e e q u a tio n and th e v a lu e
w h ic h g iv e s th e b e s t R
is
chosen as
y .
50
E s tim a tio n
The r e g r e s s io n r e s u lt s
a re shown in T a b le I V - 1 .
shows, th e s ig n o f b s h o u ld be p o s i t i v e .
p o s itiv e b.
As e q u a tio n
(4 )
A l l s e c to r s e x c e p t two have
The two s e c to r s a re Food and to b a c c o and R e a l e s ta t e .
F o r th o s e two s e c to r s , we use a d i f f e r e n t ty p e o f e q u a tio n w h ic h w i l l
be d e s c r ib e d l a t e r in t h i s s e c tio n .
Many s e c to r s have y c lo s e d to u n i t y .
u n ity .
Some o f th e s e a re j u s t
The h ig h r a t e o f a d ju s tm e n t i s u n d e rs ta n d a b le because t h i s
m odel i s
a n n u a l.
F o r th o s e s e c to r s , we c o u ld t h i n k ,
th e s h o r t ru n
v a r i a t i o n was washed o u t , and th e a c t u a l p r o d u c t i v i t y s e r ie s r e f l e c t
th e lo n g ru n p r o d u c t i v i t y movement.
B e s id e s th e p a r t i a l a d ju s tm e n t
m echanism , th e u s u a l way t o in v e s t ig a t e th e d is e q u ili b r i u m
to in c lu d e some d is e q u ili b r i u m v a r ia b l e i n th e e q u a tio n .
e f f e c t is
The change
o f o u tp u t w o u ld be th e m ost c o n v e n ie n t d is e q u ili b r i u m v a r ia b le i n t h i s
case.
t io n ,
When th e change o f o u tp u t was in c lu d e d i n th e r e g r e s s io n equa­
th e s ig n o f b tu r n e d o u t t o be n e g a tiv e i n many s e c to r s .
Be­
cause we w a n t s lo w in g down p r o d u c t i v i t y w h ic h can be form ed b y th e
Gom pertz c u rv e w it h p o s i t i v e b , we g iv e up th e d is e q u ili b r i u m v a r ia b l e .
R ! s have been c a lc u la t e d to com pare th e a c t u a l la b o r r e q u ir e ­
m ent s e r ie s and th e p r e d ic t e d la b o r re q u ire m e n t s e r ie s .
we have some lo w t
s ta tis tic s
Even th o u g h
on th e e s tim a te s o f p a ra m e te rs , th e
p r e d ic t e d v a lu e o f th e l e v e l o f la b o r re q u ire m e n t is v e r y c lo s e to
th e a c t u a l one.
The lo w t
A l l s e c to r s e x c e p t one have R
s ta tis tic s
d i f f e r e n t fro m z e ro .
p r o d u c t iv it y , i t
is
on b im p lie s
g r e a t e r th a n 0 .9 .
t h a t th e b i s n o t s i g n i f i c a n t l y
H ow ever, f o l lo w in g o u r ju d g m e n t o f s lo w in g down
d e c id e d t o s ta y w it h
th e b even i f
its
t s t a tis tic s
51
i s lo w .
The lo w t s t a t i s t i c s m ig h t be caused by th e lo w b i t s e l f
in s t e a d o f b y b ig s ta n d a rd e r r o r o f b .
gave w rong s ig n , a l o g i s t i c
s lo w in g down p r o d u c t i v i t y ,
£
F o r th e two s e c to r s w h ic h
c u rv e m e th o d ,^ w h ic h a ls o g u a ra n te e s
is
u se d .
The r e g r e s s io n e q u a tio n i s :
E
A l o g - = a 1 + a 2 ( ^ ) _ x + &3 A lo g Q t
The r e g r e s s io n r e s u l t s a r e :
3 . Foods and Tobacco
A lo g ( I ) ^
= - 0 .0 5 5
+
(-1 .9 3 )
1 6 6 .9 5 C q ) ^
( 2 .2 1 )
- 1 .1 1 A lo g Qt
( - 1 5 .4 6 )
R2 = 0 .9 4 8 0
D.W. = 1 .6 5 5
1 6. R e a l E s ta te
A lo g ( £ )
= 0 .8 4 4
Q t
( 3 .6 5 )
-
5 8 8 7 .7 ( I )
, - 2 .1 1 A lo g Qf
Q t-1
6 c
(-3 .0 1 )
(-5 .3 8 )
R2 = 0 .7 6 9
D.W. = 2 .2 3
^LAlmon.C. e t . a l .
1 985:
I n t e r i n d u s t r y F o re c a s ts o f th e A m e ric a n
Economy. L e x in g to n B o o ks, p p . 1 7 4 .
TABLE IV - 1 .
CN|
LT|
I n d u s t r y Name
R e g re s s io n R e s u lts o f L a b o r R e q uirem en t E q u a tio n s
C o e f f ic ie n t s
C o n s ta n t
-b
R ate o f
A d ju s tm e n t
E la s tic ity o f
S u b s t it u t io n
1 .0
^
R
RHO
.1 5 5
.9 6 5 5
.0444
.3 4 6
.9 6 5 6
.1897
- .6 2 3
( - .8 7 6 )
-.0 5 8
( - .7 9 9 )
- .6 2 9
( - 1 .7 3 1 )
- .1 0 2
( - 1 .3 3 4 )
4 . T e x t ile s
- 1 .0 2 8
( - .8 7 9 )
- .2 1 7
( - .8 5 1 )
1 .0
.4 5 0
.9429
.3779
5. P u lp and Paper
- .5 4 4
( - .9 2 8 )
- .0 8 7
( - .8 2 7 )
1 .0
.4 5 1
.94 8 7
- .1 6 3 3
6. C h e m ica l p ro d u c ts
- .6 4 7
( - 2 .8 6 6 )
-.0 8 5
( - 2 .3 8 4 )
.8 0
.0 0 6
.97 0 1
- .4 6 7 4
7. P rim a ry M e ta ls
-.7 6 5
( - 1 .5 1 3 )
- .1 1 9
( - 1 .3 7 4 )
.9 0
.32 9
.9 4 9 5
- .0 9 0 1
8. M e ta l P ro d u c ts
-3 .2 8
( - .5 3 1 )
- .0 9 1
( - .4 8 4 )
.75
.4 5 0
.9 5 2 5
-.1 7 7 7
9 . Non E l e c t r i c a l M a ch in e ry
-.3 1 5
( - .5 3 6 )
-.0 4 6
( - .4 2 1 )
.3 7 9
.9 3 6 1
.1765
- .5 5 9
( - .7 0 2 )
- .0 7 8
(-5 .9 5 )
.95
.1 9 5
.8 1 6 3
.2463
1 1 . T r a n s p o r ta tio n Equipm ent
- 1 .3 4 5
( - 2 .9 7 2 )
-.2 1 4
( - 2 .7 7 4 )
.9 5
.2 7 6
.9 6 8 6
.1653
1 2. M is c e lla n e o u s M a n u fa c tu rin g
- .2 4 9
( - 1 .1 7 6 )
- .0 5 9
( - .9 7 7 )
.7 5
.4 2 0
.9 9 2 0
- .2 5 1 7
1 . A g r ic u lt u r e , F o r e s tr y ,
and F is h e ry
2 . M in in g
1 0. E l e c t r i c a l M a ch in e ry
.9 5
1 .0
TABLE I V - 1 . C o n tin u e d
p">
in
In d u s t r y Name
C o e f f ic ie n t s
C o n s ta n t
-b
R ate o f
A d ju s tm e n t
E la s tic ity o f
S u b s t it u t i o n
_
R
RHO
1 3 . C o n s tr u c t io n
-.8 0 4
(- 2 .3 6 0 )
- .1 2 1
( - 2 .1 7 2 )
.9 5
.1 0 0
.98 1 9
-.0 9 7 9
1 4 . E l e c t r i c i t y , Gas, and W ater
- .4 3 3
( - 1 .5 8 3 )
- .0 6 9
( - 1 .3 6 5 )
.9 5
.3 8 4
.9800
.1814
1 5 . W h o le s a le and R e t a il T ra d e
- .2 8 5
( - 1 .9 1 2 )
- .0 3 9
( - 1 .3 3 8 )
.9 5
.1 2 0
.9 2 1 1
-.3 8 1 2
17. T r a n s p o rt and C om m unication
-.2 6 6
( - .9 8 7 )
- .0 3 4
( - .7 5 0 )
.9 5
.0 5 1
.9854
-.0 9 9 2
1 8 . F in a n c e and In s u ra n c e
-.2 8 0
( - .6 2 3 )
- .0 4 2
( - .5 2 5 )
.9 5
.2 6 4
.9391
- .1 2 1 7
1 9 . O th e r S e rv ic e s
-.2 6 6
( - .7 1 1 )
- .1 0 1
( - .6 3 7 )
.9 5
.3 1 1
.9878
.0819
54
C om parison o f th e F o re c a s ts
I f we have th e e x p o n e n t ia lly a u g m e n tin g t e c h n o lo g ic a l change o f
la b o r in
th e same C .E .S . p r o d u c tio n f u n c t io n , we can d e r iv e th e la b o r
re q u ire m e n t e q u a tio n as f o l l o w s :
lo g ( &
= C X t
yo l o g ( ^ )
+ y ( a -1 ) A
t + (1 - y) l o g (£ )
^ t —1
w here
A = r a t e o f t e c h n o lo g ic a l change o f la b o r
y = speed o f a d ju s tm e n t
o
In f a c t ,
= e l a s t i c i t y o f s u b s t it u t io n
th e e s tim a tio n o f t h i s
fo rm o f e q u a tio n i s
easy to h a n d le ,
and th e e s t im a t io n r e s u lt s a re n o t much w o rse th a n th e C om pertz
c u rv e fo rm .
B u t w it h
th e e x p o n e n tia l c u rv e fo rm , we a re im p o s in g
to o s t r i c t c o n s t r a in t because th e e x p o n e n tia l c u rv e fo rm i s a s p e c ia l
case o f e q u a tio n
(9 ).
The p r o d u c t i v i t y p r o je c t io n s made b y th e ex­
p o n e n t ia l c u rv e and b y th e U om pertz c u rv e a re compared in F ig u re I V - 1 .
The p r o d u c t i v i t i e s
shown i n
th e f i g u r e i s
th e a g g re g a te p r o d u c t i v i t i e s
o f th e ,e c o n o m y , w h ic h come fro m th e s im u la t io n o f th e w h o le m o d e l.
55
F ig u r e I V - 1 .
V a lu e o f a v e ra g e p ro d u c t
p e r manhour ( i n 1970 ye n )
---------------- e x p o n e n tia l c u rv e
------------- -Gompertz c u rv e
C om parison o f P r o d u c t iv it y F o re c a s t
56
CHAPTER V
Manhours E q u a tio n
The la b o r re q u ire m e n t e q u a tio n p r e d ic t s
manhours
th e EOQ, w h ic h i s
r e q u ir e d f o r p r o d u c tio n o f one u n i t o f o u t p u t .
th e
A c c o r d in g ly ,
we ca n n o t f o r e c a s t th e number o f th e em ployed d i r e c t l y fro m th e la b o r
r e q u ir e m e n t, even i f
we know th e o u t p u t , u n le s s we know th e m o n th ly
m anhours p e r em ployee.
The v a r ia b l e Et s h o u ld be decomposed i n t o
and manhours p e r em ployee.
th e number em ployed
In th e s h o r t ru n , th e d i v i s i o n between
employm ent and m anhours has a v e r y im p o r ta n t econom ic m e a ning.
In b a s ic econom ic th e o r y , we d is t in g u is h f ix e d c o s t and v a r ia b l e
c o s t.
T h e re a re f ix e d
h ir in g
and t r a i n i n g
ment c o m p e n s a tio n .
c o s ts in v o lv e d in h i r i n g a new p e rs o n , such as
c o s ts , f r i n g e b e n e f i t s , and l i a b i l i t y
The b u rd e n o f th o s e f ix e d
t o th e d u r a t io n o f t h e new w o r k e r ’ s jo b .
c o s ts i s
f o r unem ploy­
in v e r s e ly r e la t e d
On th e o th e r h an d , in c r e a s in g
w o rk in g h o u rs b r in g s a b o u t lo w e r e f f i c i e n c y and h ig h e r c o s ts , because
it
is
assumed t h a t w o rk e rs a re le s s
in c re a s e d .
h ir in g
T h e r e fo r e ,
th e re is
e f f i c i e n t as w o rk in g h o u rs a re
a t r a d e - o f f in th e s h o r t ru n between
a new p e rso n and in c r e a s in g w o rk in g h o u rs .
I n th e lo n g r u n , t h e s ig n if ic a n c e o f th e d i v i s i o n betw een number
em ployed and m anhours p e r em ployee d e c re a s e s .
As th e tim e p e r io d is
le n g th e n e d , f ix e d c o s t p e r em ployee co n ve rg e s to a c e r t a i n lo w e r bound.
I n Ja p a n , manhours p e r em ployee p e r m onth i n
d e cre a se d each y e a r by a s m a ll am ount.
each in d u s t r y have
T h e re i s n o t much v a r i a t i o n
in
57
th e d a ta .
The tr e n d i s much m ore in flu e n c e d b y s o c ia l r a t h e r th a n
econom ic f a c t o r s .
H ow ever, we can assume t h a t as o u tp u t in c re a s e s th e
manhours p e r em ployee go up beca u se in d u s t r y does n o t a d ju s t em ploym ent
as f a s t as o u t p u t ,
t h e r e f o r e , m anhours p e r em ployee a re r e la t e d
p e rc e n ta g e change in o u tp u t and t o
“V
= ao + ai
AQj t
to th e
tim e t r e n d .
+ a2 1
w here
MH = man h o u rs p e r em ployee
t = tim e tr e n d
A = p e rc e n ta g e change
We e x p e c t a p o s i t i v e
s ig n on th e c o e f f i c i e n t o f th e p e rc e n ta g e
change o f o u tp u t and a n e g a tiv e one on th e tim e tr e n d c o e f f i c i e n t .
e x p e c te d ,
each e q u a tio n has a n e g a tiv e s ig n on th e tim e t r e n d .
s e c to r s f a i l e d
As
T h re e
to show a p o s i t i v e s ig n on o u tp u t change; t h a t v a r ia b l e
was th e n d e le te d in th o s e s e c to r s .
As we can see in T a b le V - l ,
th e f i t
is
c lo s e .
B u t f o r some
s e c to r s we have v e r y s e r io u s a u t o c o r r e la t io n p ro b le m s .
T h is m ig h t
s u g g e s t m is s p e c if ic a t i o n o f th e e q u a tio n f o r th o s e s e c t o r s ; t h e r e
c o u ld be some o m itte d v a r ia b l e s .
e q u a tio n s i n t h i s m odel i s
w h ic h i s
H ow ever, th e o n ly r o l e o f th e m anhour
t o c o n v e rt th e EOQ to
em ploym ent b y u s in g Q,
a lr e a d y c a lc u la t e d w it h o u t th e h e lp o f th e manhour e q u a tio n s .
T h e r e fo r e ,
it
h a r d ly seemed w o r th w h ile to
b e t t e r m anhour e q u a tio n s f o r th o s e s e c to r s .
s e a rc h f o r t h e o r e t i c a l l y
TABLE V - l
R e g re s s io n R e s u lts o f Manhours p e r Employee
qq
In d u s try
C o e f f ic i e n t s
C o n s ta n t
Tim e
188 .04 8
(7 9 .4 4 8 )
-1 .4 6 5
( - 7 .0 5 0 )
3. Foods & Tobacco M a n u fa c tu rin g
184 .98 9
(1 6 6 .1 3 5 )
-1 .9 2 1
( - 1 1 .7 6 4 )
4. T e x tile
1 8 4 .65 7
(2 0 0 .4 2 9 )
-1 .6 1 9
(- 1 1 .6 3 3 )
5. P u lp & Paper
1 89 .52 2
(2 0 1 .6 4 8 )
6. C h e m ica l P ro d u c ts
Name
%A Q
R
D.W.
.7 8 8
.9 3 7
.914
1 .1 2 8
1 4 .7 0 5
(2 .2 2 5 )
.93 2
1 .5 0 3
-1 .7 0 9
(- 1 1 ./6 5 )
1 7 .8 3 5
(2 .0 5 3 )
.9 5 8
1 .8 3 3
1 73 .01 1
(1 5 5 .4 8 8 )
-1 .3 9 5
( - 8 .3 2 8 )
1 1 .0 5 5
(1 .6 6 9 )
.9 1 6
1 .0 9 8
7. P rim a ry M e ta ls
1 87 .51 8
(1 4 8 .3 8 7 )
-1 .2 4 5
( - 5 .8 3 2 )
1 9 .9 0 5
(2 .9 4 9 )
.8 7 3
1 .4 2 0
8. M e ta l P ro d u c ts
1 88 .87 7
(2 2 4 .8 5 1 )
-1 .5 5 4
(- 1 6 .9 3 7 )
2 2 .3 3 2
(4 .5 2 4 )
.9 6 8
1 .6 6 6
9. N o n - e le c t r ic a l M a ch in e ry
188.272
(2 7 2 .5 6 4 )
-1 .2 2 2
( - 1 1 .9 5 6 )
2 0 .4 2 3
(6 .9 9 5 )
.961
1 .2 2 8
1 0. E l e c t r i c a l M a ch in e ry
1 77 .57 3
(1 3 1 .6 9 3 )
-1 .4 9 2
( - 9 .4 1 7 )
1 3 .0 1 9
( 1 .9 4 4 )
.90 1
2 .5 5 6
11. T r a n s p o r ta tio n Equipm ent
1 8 8 .6 8 0
(1 8 4 .0 8 9 )
- 1 .3 9 0
( - 9 .8 4 8 )
1 4 .5 4 8
(3 .1 3 6 )
.922
1 .0 3 5
12. M is c e lla n e o u s M a n u fa c tu rin g P ro d u c ts
1 8 3 .7 6 6
(1 2 2 .3 3 8 )
-1 .5 7 6
(- 1 1 .8 2 3 )
1 5 .5 3 0
( 1 .3 5 7 )
.9 3 3
1 .1 8 9
2. M in in g
1 5 .0 7 4
(0 .8 0 7 )
TABLE V - l (CONTINUED)
CTv
tn
In d u s try
C o e f f ic ie n t s
%A Q
Rz
D.W.
2 3 .0 8 3
(1 .3 5 6 )
.8 5 1
.7 2 6
.7 5 6
.85 4
1 2 .4 6 5
(1 .7 1 9 )
.9 3 7
1 .2 2 5
-2 .0 7 1
( - 7 .0 7 5 )
9 .0 5 3
( .2 9 5 )
.86 9
1 .9 7 9
184.382
(8 6 .7 8 1 )
-1 .6 5 1
(- 1 1 .4 6 5 )
5 1.4 09
(2 .4 3 4 )
.9 3 9
1 .2 6 6
1 64.770
(1 4 0 .1 2 7 )
-1 .6 3 5
( - 9 .4 8 4 )
.87 2
.948
C o n sta n t
Tim e
194.972
(9 0 .3 6 4 )
-1 .5 4 2
(- 7 .0 3 3 )
1 4 . E l e c t r i c i t y , Gas, & W ater S up p ly
174 .33 5
(1 2 5 .5 2 8 )
-1 .3 0 9
( - 6 .4 2 5 )
1 5 . W h o le s a le & tr a d e
182 .51 0
(1 5 6 .7 4 0 )
- 1 .6 6 8
(- 1 1 .6 4 6 )
172.897
(5 9 .3 8 9 )
Name
1 3 . C o n s tr u c tio n
lb .
ile a l E s ta te
1 7 . T ra n s p o r t & C om m unication
1 8 . F in a n c e & In s u ra n c e
60
CHAPTER V I
P r ic e E q u a tio n
T h e o ry
The s tu d y o f p r ic e fo r m a tio n is
e c o n o m e tric s tu d y .
th e m ost u n d e ve lo p e d a re a in
R e c e n tly some s tu d ie s on th e a g g re g a te GNP de­
f l a t o r and on d is a g g re g a te d in d u s t r y p r ic e s have appeared in th e
econom ic l i t e r a t u r e .
T h e re i s
E a r l^ g iv e s a good summary o f th e s e s t u d ie s .
some consensus in th e s e s t u d ie s .
M ost t r y
to r e f l e c t
th e lo n g ru n c o s ts and s h o r t ru n c o s ts a n d , i n some w a y, excess
demand.
U n it la b o r c o s t and u n i t m a t e r ia l c o s t a re com bined w it h
v a r io u s p r o x ie s f o r e xce ss demand.
F o r lo n g ru n f o r e c a s t in g ,
th e c o s t h y p o th e s is i s a p p r o p r ia t e .
V a rio u s m odels o f lo n g r u n , o r e q u ili b r iu m , p r i c i n g w ere d e r iv e d by
N ordhaus
u s in g v a r io u s fo rm s o f th e p r o d u c tio n f u n c t io n .
r i v a t i o n o f th e p r ic e
e q u a tio n i s
s tr ic tly
c o n d it io n w h ic h he used t o g e t e q u ili b r iu m
re ve nu e e q u a ls m a rg in a l c o s t.
m iz a t io n o f p r o f i t s
n e o c la s s ic a l b ecause th e
p r ic e i s
t h a t m a rg in a l
The d e r iv a t io n p ro c e d u re i s m a x i­
g iv e n a c e r t a i n p r o d u c tio n f u n c t io n and a demand
^ E a r l, P . , I n f l a t i o n
L e x in g to n B oo ks.
1 97 3 .
2
H is de­
and th e S t r u c t u r e o f I n d u s t r i a l P r ic e s ,
N o rd h a u s, W .D ., "R e c e n t D evelopm ent in P r ic e D y n a m ic s ," in th e
E c o n o m e tric s o f P r ic e D e te r m in a tio n . C o n fe re n c e , O c to b e r 3 0 -3 1 , 1970.
W a s h in g to n , D .C ., S ponsored b y B oard o f G o ve rn o rs o f th e F e d e ra l R eserve
System and S o c ia l R e se arch C o u n c il.
f u n c t io n .
f u n c t io n ,
If
c o n s ta n t r e t u r n s to s c a le a re assumed in
th e p r ic e o f a p r o d u c t i s
a f u n c t io n o f i t s
As m e n tio n e d b e f o r e , N ordhaus has la b o r ,
in p u t s .
th e p r o d u c tio n
in p u t p r ic e s .
c a p i t a l , and m a t e r ia ls as
I n a d d it io n to th e s e c o s t v a r ia b l e s , some m easures o f excess
demand e n te r p r ic e e q u a tio n s .
o f excess demand m easure i s
I n u s u a l e m p ir ic a l s t u d ie s , ^ - th e r o l e
to d e te rm in e th e m a rk -u p o f p r ic e o v e r
u n i t la b o r c o s t.
The b a s ic id e a o f th e p r ic e f o r m u la t io n o f t h i s
based on o p tim a l p r i c i n g
w it h in
d is s e r ta tio n
is
t h e o r y , and t h a t th e o r y w i l l be d e ve lo p e d
th e in p u t - o u t p u t fra m e w o rk .
The p r ic e e q u a tio n f o r m u la t io n
c o n s is ts o f f o u r s ta g e s :
1 . The n o rm a l u n i t la b o r c o s t i s c a lc u la t e d u s in g th e wage r a t e
and th e s t e a d y - s t a t e p r o d u c t i v i t y .
2 . The m a rk -u p on th e n o rm a l u n i t la b o r c o s t (fro m S tep 1) i s
d e te rm in e d b y th e e s tim a te d b e h a v io r a l e q u a tio n in w h ic h th e
m a rk -u p r a t i o
is
r e la t e d to some demand, o r c a p a c ity u t i l i ­
z a t io n m easure.
3. The e q u ili b r iu m
p r ic e i s
n o rm a l u n i t la b o r c o s ts
c a lc u la t e d u s in g th e m a rke d -u p
(fro m S te p s 1 and 2) and th e i n p u t -
o u tp u t t a b le .
^■See th e O .B .E . m o d e l.
H ir s c h , A .A .
" P r ic e S im u la tio n s W ith
th e O .B .E . E c o n o m e tric M o d e l," i n th e E c o n o m e tric s o f P r ic e D e te r­
m in a t io n .
e d. b y 0 . E c k s te in .
62
4 . The a c t u a l p r ic e i s
c a lc u la t e d by a b e h a v io r a l e q u a tio n in
w h ic h th e e q u ilib r iu m p r ic e
(fro m S te p 3 ) ,
th e la g g e d p r ic e ,
and th e f o r e ig n p r ic e a re e x p la n a to r y v a r ia b le s .
Now th e p r ic e d e te r m in a tio n p ro c e d u re w i l l be d e s c r ib e d s te p
b y s te p .
S tep 1 .
N orm al U n it L a b o r C o sts
The f i r s t
s ta g e s t a r t s b y d e f in in g th e u n i t la b o r c o s t as
f o llo w s :
W. • E.
J !------- 1
(1 ) ULC. =
w here
ULC
« la b o r c o s t p e r u n i t o f o u tp u t o f th e j t h in d u s t r y
j
Wj = n o m in a l wage p e r h o u r o f th e j t h
Qj = o u tp u t i n
c o n s ta n t p r ic e s o f th e
E j = manhours i n
As we can see i n
th e
in d u s t r y .
in d u s t r y .
in d u s t r y .
( 1 ) , th e u n i t la b o r c o s t can be decomposed in t o
two
f a c t o r s , th e wage p e r h o u r and th e r e c i p i c a l o f th e a v e ra g e la b o r
p r o d u c t i v i t y , w h ic h i s
th e la b o r re q u ire m e n t p e r u n i t o u t p u t .
N orm al u n i t la b o r c o s t i s
la b o r c o s t , f o r i t
u tiliz e d
in s te a d o f a c t u a l u n i t
has been fo u n d t h a t th e p e rm a n e n t, n o t t r a n s i t o r y
'
63
p r o d u c t i v i t y movement, i s
im p o r ta n t in p r ic e d e te rm in a tio n .^ "
re a s o n to use th e n o rm a l u n i t la b o r c o s t i s
The
t h a t f ir m s s e t p r ic e s
p r i m a r i l y b y fo c u s in g on s t e a d y - s t a te o r e q u ilib r iu m u n i t la b o r
c o s ts r a t h e r th a n on a c t u a l u n i t la b o r c o s ts because th e c o s ts o f
c h a n g in g p r ic e s
to o h ig h .
i n re s p o n s e t o t r a n s i t o r y s h i f t s
F irm s do n o t h i r e o r f i r e
e v e r demand r is e s o r f a l l s .
la b o r e r s
i n la b o r c o s t a re
in s ta n ta n e o u s ly when­
T h e r e fo r e , we have t o
d is t in g u is h betw een
th e a c t u a l p r o d u c t i v i t y and th e n o rm a l o r e q u ili b r iu m p r o d u c t i v i t y .
T h is d i s t i n c t i o n was a lr e a d y made i n
It
is
th e la b o r re q u ire m e n t c h a p te r .
assumed t h a t changes i n wages a re c o n s id e re d by p ro d u c e rs to
be p e rm a n e n t, and th e s e e n te r im m e d ia te ly i n t o n o rm a l u n i t la b o r
c o s t.
We d e f in e th e n o rm a l u n i t la b o r c o s t ,
(2 ) ULC?
= W.
3
3
w here
/ E. ;
( ~ i
Is
s im p ly th e e q u ili b r iu m v a lu e o f la b o r re q u ire m e n t
j
w h ic h was d e r iv e d fro m th e C .E .S . p r o d u c tio n f u n c t io n i n C h a p te r IV .
^ S c h u lt z e , C .L . and J . L . T y ro n .
" P r ic e and W a g e s," i n J . S.
D u e s e n b e rry , G .4Fromm, L .R . K le in , and E. Kuh. e d s ., The B ro o k in g s
Q u a r t e r ly E c o n o m e tric M odel o f th e U n ite d S t a t e s . A m sterdam , l i o r t h H o lla n d , 1 9 6 5 ; and K uh, E . , and R .L . S chm alensee, "A n I n t r o d u c t i o n
t o A p p lie d M a cro e co n o m ics. A m sterdam , N o r t h - H o lla n d , 1 9 7 3 . pp. 1 3 7 -1 5 1 .
U s in g t h i s
e q u ilib r iu m la b o r r e q u ir e m e n t, we can e x c lu d e s h o r t ru n
v a r ia t io n s
i n u n i t la b o r c o s t due t o th e f a i l u r e o f em ploym ent to
a d ju s t t o v a r io u s changes in m a rk e t c o n d it io n s .
M o vin g a ve ra g e s
o f p a s t v a lu e s o f a c tu a l u n i t la b o r c o s t have been used i n o th e r
s t u d ie s as a p ro x y f o r th e n o rm a l u n i t la b o r c o s t.
B u t Kuh fo u n d
t h a t th e m oving a ve ra g e o f th e a c t u a l u n i t la b o r c o s t was i n f e r i o r
to th e n o rm a l u n i t la b o r c o s t o b ta in e d by u s in g s te a d y s t a t e la b o r
re q u ire m e n t.^ -
As Kuh d id , we can c a lc u la t e th e h i s t o r i c a l e q u ilib r iu m
la b o r r e q u ir e m e n t.
N o t ic in g t h a t e q u a tio n
(9 ) i n C h a p te r IV has th e
c u r r e n t v a lu e o f la b o r r e q u ir m e n t and th e la g g e d v a lu e o f t h i s v a r i ­
a b le , we can s o lv e f o r th e s te a d y s t a t e la b o r re q u ire m e n t as a f u n c t io n
o f th e o th e r v a r ia b le s .
F o r c o n v e n ie n c e , we re p e a t e q u a tio n
(S) i n
C h a p te r IV .
a lo g ( ^ ) + J jij.
a io g (~ ) -
= C ’ - b ( lo g
(|) +
( l - y ) a lo g
lo g
($ ) -
(^ )_ 1
(1 - y ) lo g
S tep 2 . M a rk-u p s on N orm al L a b o r C ost
The second s te p i s
to d e te rm in e th e u n i t v a lu e added in d e x
u s in g th e n o rm a l u n i t la b o r c o s t and th e m a rk -u p r a t i o s .
I f we
have a C obb-D ouglas p r o d u c tio n f u n c t io n , wage and p r o f i t s h a re s i n
^K uh, E . , and S chm alensee, R . L . , An I n t r o d u c t io n t o A p p lie d
M a cro e co n o m ics. Am sterdam , N o r th - H o lla n d , 1 97 J .
p p . 1 3 7 -1 5 1 .
65
v a lu e added a re c o n s ta n t o v e r tim e .
m a rk-u p r a t i o
I n t h a t ca se , s im p le c o n s ta n t
can be a p p lie d o v e r tim e .
H ow ever, th e h i s t o r i c a l
e v id e n c e does n o t s u p p o rt th e lo n g ru n c o n s ta n c y o f wage and p r o f i t
s h a r e .^
r a tio s ,
F o r th e e m p ir ic a l t e s t s o f th e c o n s ta n c y o f th e m a rk-u p
th e h i s t o r i c a l m a rk -u p s e r ie s w ere c a lc u la t e d .
The h i s t o r i c a l
m a rk-u p r a t i o s a re th e r a t i o s o f th e u n i t v a lu e added w h ic h w ere
o b ta in e d u s in g h i s t o r i c a l v a lu e o f o u tp u t and I/O c o e f f i c i e n t s
th e la b o r c o m p e n s a tio n p e r o u t p u t .
to
M ost o f th e s e c to r s r e j e c t th e
c o n s ta n c y o f th e m a rk-u p r a t i o .
I n th e s t u d ie s o f th e GNP d e f l a t o r d e t e r m in a t io n , demand
m easures a re in c lu d e d i n th e e q u a tio n w it h o t h e r c o s t v a r ia b l e s .
is
g e n e r a lly assumed t h a t th e m a rk-u p o v e r c o s t i s
r a t io
in
It
in f lu e n c e d by th e
o f o u t p u t t o c a p a c it y , a r e l a t i o n w h ic h shows demand p re s s u re
th e m a rk e t.
T h e r e fo r e , we fo r m u la te th e e q u a tio n o f th e u n i t
v a lu e added as f o l lo w s :
(4 ) UVA
(5 )
a * • ULCN
u
t
t
a t
=
ac + a .
Qt
* t-l
w h e re
UVAt = u n i t v a lu e added i n c u r r e n t p r ic e s
^"The e v id e n c e s a re fo u n d i n 1 9 6 0 -1 9 6 5 —1970 I n p u t- O u tp u t T a b le s ,
p u b lis h e d b y th e G overnm ent o f Ja p a n , 1 975.
= c a p i t a l s to c k ,
t = tim e t r e n d .
a t = m a rk-u p r a t i o
£
o v e r u n i t la b o r c o s t.
= e x p e c te d p e rc e n ta g e change o f o u tp u t w h ic h i s
d e fin e d by
a w e ig h te d a v e ra g e o f th e p r e v io u s y e a r s ’ o u tp u t changes.
More f o r m a lly ,
00
AQ
? = (1 -X )
1
Z
i_ i
X
1 &O
A_ s ta n d s f o r p e rc e n ta g e change.
c lin in g
The w e ig h ts a re de­
g e o m e t r ic a lly o v e r tim e .
= e xp e cte d o u tp u t a t tim e t w h ic h i s
The r a t i o
e q u a l to Qt ^
o f th e e x p e c te d o u tp u t t o th e c a p i t a l s to c k o f th e
p re v io u s y e a r i s used as a m easure o f c a p a c it y u t i l i z a t i o n ,
demand p re s s u r e .
+ 1)
A ls o ,
or of
th e e x p e c te d p e rc e n ta g e g ro w th r a t e o f o u tp u t
i s a ls o in c lu d e d as a p ro x y f o r th e demand p re s s u re o f th e m a rk e t.
The c u r r e n t o u t p u t - c a p it a l r a t i o ,
o r th e p e rc e n ta g e change o f c u r r e n t
o u tp u t c o u ld be b e t t e r demand m e a su re s, because th e y can re p re s e n t
s h o r t ru n v a r ia t io n s
i n th e p r ic e e q u a tio n .
The s im u lt a n e it y p ro b le m
betw een p r ic e and o u tp u t i n th e m odel p re v e n ts us fro m u s in g th e s e .
H ow ever, th e m o d ifie d o u t p u t - c a p it a l r a t i o
change c o u ld s e rv e i n
and th e e x p e c te d o u tp u t
t h i s m odel because t h i s m odel i s
d e s ig n e d to
e x p la in lo n g - te r m o r m e d iu m -te rm econom ic v a r i a t i o n s .
A ls o th e r e i s
a d iffic u lty
p r ic e e q u a tio n because i t
as a s u p p ly e f f e c t ,
i n u s in g th e c u r r e n t o u tp u t i n th e
c a n n o t be i d e n t i f i e d
e s p e c ia lly i n
as a demand e f f e c t o r
an a n n u a l m o d e l.
I t m ig h t be
67
b e t t e r to p r o je c t th e demand based on th e p re v io u s y e a r ’ s o u tp u t
r a t h e r th a n to use th e c u r r e n t o u tp u t as a demand m e a sure.
We e x p e c t t h a t
Ap® c o u ld p ic k up th e lo n g ru n demand tr e n d
and t h a t Q ^/& t ^ c o u ld r e p r e s e n t th e d e s ir e d c a p a c ity u t i l i z a t i o n
r a t e , o r d e s ir e d o u t p u t - c a p i t a l r a t i o .
C e r t a in l y , th e s e m o d ifie d
v a r ia b le s ca n n o t e x p la in th e e f f e c t o f th e s h o r t ru n demand p re s s u r e ,
b u t we hope t h a t th e y can e x p la in th e lo n g ru n v a r ia t io n s
m a rk -u p r a t i o s .
The tim e tr e n d i s
o f th e
in c lu d e d t o p ic k up th e s y s te m a tic
p r o d u c t i v i t y change o r p ro d u c t m ix change.
We e x p e c t p o s i t i v e
s ig n s
on th e c o e f f i c i e n t s o f th e e x p e c te d o u tp u t and th e e xp e cte d change
o f o u tp u t.
S tep 3.
The s ig n on th e tim e tr e n d can be p o s i t i v e o r n e g a tiv e .
The E q u ilib r iu m
P r ic e s .
So f a r , we have th e u n i t v a lu e added.
th is
I/O
add e d.
The p r ic e s we need in
f o r e c a s t in g m odel a re th e p r ic e s o f o u t p u t , n o t o f v a lu e
The v a lu e added p r ic e
u s in g in p u t - o u t p u t r e l a t i o n s .
can be c o n v e rte d i n t o
o u tp u t p r ic e
O u tp u t p r ic e i s n o t h in g b u t u n i t
v a lu e added p lu s in p u t m a t e r ia l c o s ts .
The in p u t p r ic e s w h ic h f ir m s
pay f o r th e m a t e r ia ls a re th e a c t u a l p r ic e p r e v a i l i n g i n
th e m a rk e t.
A ls o , a la r g e p a r t o f th e m a t e r ia ls used i n Japan a re im p o rte d .
T h e r e fo r e , th e e q u ili b r iu m p r i c e o f o u tp u t i s
(6 )
P®=
J
I
i
a
i
j
(m , P ? +
J
J
(1 - a , )
J
w here
P? = c a lc u la t e d e q u ili b r iu m
p r ic e
P *)
J
d e fin e d as f o l lo w s :
+ ai
j
• ULc”
J
68
PY = w o rld p r ic e
3
P j = a c t u a l d o m e s tic p r ic e
mj = im p o r t- u s e l e v e l r a t i o
The in p u t p r ic e s in s e r t e d i n
e q u a tio n (6 ) i s
th e a c t u a l p r ic e s and th e w o rld p r ic e s .
im p o rt r a t i o
a w e ig h te d a ve ra g e o f
As th e w e ig h t we use th e
to d o m e s tic u se.
The p r ic e v e c t o r we g e t fro m (6 ) i s
v e c to r because i t
is
th e e q u ilib r iu m
th e d u a l o f th e I/O s o lu t i o n , and i t
p r ic e
is
d e r iv e d
fro m th e n o rm a l u n i t la b o r c o s t.
fu lly
By r e l a t i o n
(6 ),
s a tis fie d .
The e q u ilib r iu m
in p u t p r ic e s .
N o rd h a u s1 o p tim a l p r i c i n g c o n d it io n s can be
A ls o , t h i s
p r ic e i s j u s t a f u n c t io n o f a l l
f o r m u la t io n i s c o n s is t e n t w it h th e p r ic e
f o r m u la t io n o f E c k s te in and W yss,^ who in c lu d e la b o r , m a t e r ia l, and
c a p i t a l c o s ts i n
t h e i r e q u a tio n and e x p e c t t h a t th e c o e f f i c i e n t s
a re c lo s e t o th e in p u t - o u t p u t c o e f f i c i e n t s f o r th o s e in p u t s .
S tep 4 .
A c tu a l P r ic e A d ju s te d t o E q u ilib r iu m P r ic e
The l a s t s ta g e o f th e p r ic e f o r m u la t io n i s
a c tu a l p r ic e s e r ie s fro m th e e q u ili b r iu m
t o p r e d ic t th e
p r ic e th ro u g h a b e h a v io r a l
^ E c k s t e in , 0 . and D. W yss.
I n d u s t r y P r ic e E q u a tio n s i n
Econo­
m e t r ic s o f P r ic e D e te r m in a tio n . « pp 1 3 3 -1 6 5 .
C o n fe re n c e .
O c to b e r 3 0 -3 1 ,
1 9 7 0 . W a s h in g to n , D .C ., S ponsored b y B oard o f G o ve rn o rs o f th e F e d e ra l
R eserve System and th e S o c ia l S c ie n c e R e se arch C o u n c il.
69
e q u a tio n .
p r ic e s .
The o u tp u t p r ic e s w h ic h e x is t as d a ta a re n o t th e e q u ilib r iu m
Due to v a r io u s re a s o n s , su ch as m o n o p o lis t ic p o w e r, and c o s t
o f a d ju s tm e n ts , a c tu a l p r ic e s a d ju s t to e q u ilib r iu m
p r ic e s lo w ly .
In
o r d e r t o c o n s id e r th e a d ju s tm e n t p ro c e d u re , we fo r m u la te a b e h a v io r a l
r e l a t i o n betw een th e a c t u a l and th e e q u ilib r iu m
p r ic e s .
Owing to th e
s m a ll number o f o b s e r v a t io n s , we use th e K oyck ty p e la g scheme.
la g system i s
a c c e p ta b le because i t
c u r r e n t e q u ilib r iu m
T h is
i s g e n e r a lly b e lie v e d t h a t th e
p r ic e has th e la r g e s t im p a c t on th e a c tu a l p r ic e
and t h a t th e la g w e ig h ts o f p a s t y e a rs s h o u ld be g o in g down.
The
a c t u a l p r ic e a d ju s tm e n t e q u a tio n i s :
(7 ) Pa
jt
= C +
o
V If
jt
+ (1 - V ) P® „ .
J t-1
w here
y = speed o f a d ju s tm e n t
E q u a tio n
(7 ) in v e s t ig a t e s how th e a c tu a l p r ic e i s
e q u ili b r iu m
r e la t e d
to th e
p r ic e and th e la g g e d p r i c e . *
The p r ic e m odel i s n o t c o m p le te d w it h e q u a tin o n s ( 5 ) ,
(7 ),
(6 ),
and
f o r th e s e e q u a tio n s do n o t e x p la in w e ll th e p r ic e o f c o m m o d itie s ,
a la r g e p r o p o r t io n o f w h ic h i s
im p o rte d , such as p e tro le u m and ir o n
*A s i m i l a r ty p e o f r e g r e s s io n was done i n th e B ro o k in g s m odel
and FED-MIT-PENN m o d e l.
See F is h e r , F .M ., L .R . K le in , and Y. S h in k a i.
" P r ic e and O u tp u t A g g re g a tio n i n th e B ro o k in g s E c o n o m e tric M o d e l,"
i n E c o n o m e tric M odel o f th e U .S . e d s . , b y D u e s e n b e rry , J . D . , G. Fromn,
L .R . K le in , and E. Kuh. A m sterdam , N o r th - H o lla n d .
1965
A ls o , see Hymans, S . H . , " P r ic e and P r ic e B e h a v io r in T h re e U .S .
E c o n o m e tric M o d e l’ s , i n E c o n o m e tric s o f P r ic e D e te r m in a tio n , pp 3 0 9 -3 2 4 .
70
o re .
I n th e s e e q u a tio n s th e im p o rt p r ic e s o f th e s e goods can a f f e c t
th e p r ic e s o f th e o th e r co m m o d itie s b u t n o t i t s
own d o m e s tic p r ic e s .
F o r e xam ple , a lth o u g h Japan p ro d u ce s o n ly one p e rc e n t o f i t s
p e tro le u m
c o n s u m p tio n th e e q u a tio n s p r o v id e no way f o r th e f o r e ig n p r ic e o f th e
p e tro le u m t o d i r e c t l y
in f lu e n c e th e d o m e s tic p r ic e .
A c tu a lly , o f
c o u rs e , th e p r ic e o f th e p e tro le u m in th e d o m e s tic m a rk e t f o llo w s
th e im p o rte d p r ic e s .
I n o r d e r to c o n s id e r t h i s
w o r ld p r ic e as an e x p la n a to r y v a r ia b l e i n
p o i n t , we in c lu d e
e q u a tio n (7 ) f o r th e com­
m o d it ie s w h ic h have r e l a t i v e l y la r g e im p o rt s h a re .
S um m arizing th e s e s te p s , we have th e p r ic e m o d e l,
(8 )
= I a ..
(9 ) o
= ^
(m j P " t + (1 - y
Qe
+ C2 XJ t
Jt
Kj
do) p; t = cQ +
Vl
+ C3 AQJt
+ C4 t
t-1
P* t + y2 P*e +
I n e q u a tio n ( 1 0 ) , we im pose r e s t r i c t i o n s
and t h a t th e sum o f
Pja t ) + «J t D L C ^
y 's a re u n i t y .
?• t -1
t h a t a l l y *s a re p o s i t i v e
These r e s t r i c t i o n s
th e a c tu a l p r ic e goes up one p e rc e n t i f
th e e q u ilib r iu m
im p ly t h a t
p r ic e and
th e w o r ld p r ic e go up one p e r c e n t.
T h is p r ic e m odel s h o u ld be s o lv e d s im u lta n e o u s ly .
s titu te
e q u a tio n (1 0 ) i n t o
li b r i u m
p r ic e o f
o th e r g oo d s.
e q u a tio n ( 8 ) , we can f i n d t h a t th e e q u i­
good depends on th e e q u ilib r iu m
T h e r e fo r e , th e S e id e l p ro c e d u re i s
th e e q u ilib r iu m
p r ic e s .
I f we sub­
p r ic e s o f a l l
em ployed t o s o lv e
A l l o th e r v a r ia b le s in t h i s
p r ic e m odel a re
p re d e te rm in e d e x c e p t th e e q u ilib r iu m and a c t u a l p r ic e s .
I n th e f i r s t
i t e r a t i o n , we p lu g th e p re v io u s a c t u a l p r ic e s
speed up th e c o n v e rg e n c e .
fir s t
The e q u ilib r iu m
i t e r a t i o n w i l l be used in
e q u a tio n (8 ) to
p r ic e s o b ta in e d in th e
e q u a tio n CIO) to g e t th e new a c tu a l
p r ic e s .
I n th e second i t e r a t i o n ,
s titu te d
in to
e q u a tio n ( 8 ) .
in t o
th e new a c t u a l p r ic e s a re sub­
The same p ro c e d u re s a re re p e a te d u n t i l
th e n e w ly c a lc u la t e d e q u ilib r iu m p r ic e s co n v e rg e t o
p re v io u s i t e r a t i o n .
.001 i s
th o s e o f th e
used as th e t o le r a n c e l e v e l .
E m p ir ic a l R e s u lts
I n th e p r ic e s y s te m , e q u a tio n s
b y r e g r e s s io n a n a ly s is .
In o rd e r to
(9 ) and (1 0 ) a re to be e s tim a te d
e s tim a te e q u a tio n ( 9 ) , we need
t o have th e h i s t o r i c a l s e r ie s o f m a rk -u p r a t i o s .
Because we have th e
wage r a t e d a ta and th e la b o r re q u ire m e n t d a ta o n ly by tw e n ty s e c t o r s ,
it
was d e c id e d to have th e a g g re g a te d m a rk -u p r a t i o
tw e n ty s e c to r o r d e r .
e q u a tio n s by
A g g re g a te d v a lu e added r a t e s p e r u n i t o u tp u t by
20 s e c to r s a re c a lc u la t e d w it h th e c o n s ta n t in p u t - o u t p u t t a b le .
The
h i s t o r i c a l m a rk -u p r a t i o s a re made f o r t h e tw e n ty s e c to r s by d i v id in g
th e v a lu e added r a t e s p e r u n i t o f o u tp u t by th e u n i t la b o r c o m p e n s a tio n
r a t e s w h ic h a re o b ta in e d fro m th e wage d a ta and th e la b o r re q u ire m e n t
d a ta .
The r e g r e s s io n r e s u lt s
The r e g r e s s io n was f i r s t
f o r e q u a tio n (9 ) a re shown in T a b le V I - 1 .
done w it h a l l f o u r in d e p e n d e n t v a r ia b l e s .
U n f o r t u n a t e ly , th e r e s u l t s w e re n o t good a t a l l .
e ff ic ie n t s
th e f i r s t
Some o f th e co­
had w rong s ig n s and many o f them w ere i n s i g n i f i c a n t .
r e g r e s s io n r e s u l t s ,
c o l l i n e a r i t y p ro b le m .
it
From
was r e a liz e d t h a t t h e r e was a s e r io u s
TABLE V I-1
CM
^
R e g re s s io n R e s u lts o f M arkup R a tio E q u a tio n
C o e f f ic ie n t s w it h t S t a t i s t i c s
In d u s t r y Name
C o n s ta n t
Qe/ K ( - 1 )
1 .1 8 2
(1 .4 7 7 )
A_ Qe
3 .529
(7 .4 8 4 )
2 . M in in g
2 .5 4 0
(8 .7 1 1 )
2 .3 7 1
( .8 2 0 )
3 .2 3 9
(3 3 .5 1 5 )
1 .0 0 0
(1 .0 3 2 )
4 . T e x t ile
5 . P u lp and Paper
.6 2 5
(2 .8 6 3 )
.2 9 3
(3 .4 1 2 )
R2
D.W,
.6 8 4
2 .6 6
.079
(3 .9 6 2 )
.74 2
1 .3 8
- .0 8 1
(7 .3 0 1 )
.8 6 1
1 .2 1
- .0 6 5
(9 .1 7 2 )
.88 4
1 .2 2
- .0 1 1
.7 5 0
.9 7
8 .6 5 6
(1 .6 9 1 )
1 . A g r ic u lt u r e , F o r e s tr y , F is h e ry
3. Foods and Tobacco
Tim e
3.7 0 3
(2 3 .4 0 4 )
6 .1 7 6
(4 .4 6 2 )
(.8 2 7 )
6. C hem ical P ro d u c ts
2 .0 1 2
(6 .9 0 1 )
5 .0 8 4
(2 .8 5 5 )
- .0 3 2
(2 .6 9 7 )
.5 5 2
1 .6 6
7. P rim a ry M e ta ls
2 .2 6 1
(4 .2 1 3 )
.0 5 5
( .2 0 2 )
-.0 5 6
(3 .7 8 0 )
.5 6 5
1 .7 0
8 . M e ta l P ro d u c ts
.949
(2 .4 1 3 )
.11 1
( .9 5 3 )
- .0 6 9
(2 .0 1 3 )
.822
1 .5 3
9. N o n e le c t r ic a l M a ch in e ry
1 .2 0 2
(4 .3 9 3 )
.2 0 8
(3 .8 2 2 )
- .0 1 6
(1 .3 5 7 )
.6 0 7
1 .2 4
-.0 2 7
(1 .2 7 0 )
.13 9
1 .6 9
1 0.
E l e c t r i c a l M a c h in e ry
2 .0 9 6
(1 9 .9 0 2 )
TABLE V i-1 (C o n tin u e d )
CO
in
C o e f f ic ie n t s w it h t S t a t i s t i c s
In d u s t r y Name
11.
T r a n s p o r t a t io n Equipm ent
C o n s ta n t
Qe/ K ( - 1 )
A_ Qe
2 .3 0 2
(2 .2 6 5 )
2 .1 4 7
(1 0 .6 1 4 )
Tim e
R2
D.W.
-.0 0 9
(.7 3 7 )
.3 9 3
2 .0 9
.0 0 3
( .6 9 6 )
.2 8 0
2 .4 9
.4 0 1
1 .6 3
1 .2 0 2
(6 .0 1 5 )
.198
(2 .0 7 0 )
1 .4 5 7
(1 5 .7 9 7 )
.0 2 0
(2 .6 8 2 )
2.5 2 0
(2 .5 0 6 )
5 .2 7 8
(1 .8 3 3 )
-.0 3 4
(1 .5 0 0 )
.24 1
1 .4 6
-.7 2 6
(.6 5 2 )
1 .1 8 0
(1 .7 4 3 )
-.0 5 4
(.9 3 1 )
.6 4 0
.7 5
16. R eal E s ta te
12.5 02
(8 .3 7 0 )
.69 3
(1 .3 5 0 )
-.0 3 3
( .0 9 9 )
.72 2
2.10
1 7. T ra n s p o rt and C om m unication
.6 5 5
(1 .7 4 3 )
.7 0 3
(2 .1 9 7 )
- .0 0 7
(1 .4 4 3 )
.5 3 1
1 .7 0
1 2. M is c e lla n e o u s M a n u fa c tu rin g
1 3 . C o n s tr u c tio n
1 4. E l e c t r i c i t y , Gas, and W ater
15. W h o le s a le and R e t a il tr a d e
.0 8 0
(.1 5 0 )
1 8 . F in a n c e and In s u ra n c e
3 .1 9 0
(5 1 .8 4 3 )
-.0 1 1
( .8 4 0 )
.0 6 6
2 .3 6
1 9. O th e r S e rv ic e s
1 .6 3 3
(7 1 .4 0 5 )
-.0 0 5
(1 .3 1 0 )
.1 3 5
1 .1 8
74
T h e r e fo r e , s te p w is e r e g r e s s io n s w ere done to choose th e b e s t
c o m b in a tio n o f th e in d e p e n d e n t v a r ia b le s f o r each s e c t o r .
th e c o e f f i c i e n t , R2 , and t s t a t i s t i c s
th e b e s t e q u a tio n .
a re th e c r i t e r i a
used t o choose
G e n e r a lly , th e d e s ir e d o u t p u t - c a p it a l r a t i o s
more s i g n i f i c a n t th a n th e e x p e c te d o u tp u t change.
t h a t , in
S ig n o f
is
T h is m ig h t s u g g e s t
t h i s lo n g ru n m o d e l, th e o u tp u t change m ig h t n o t be a good
m easure f o r demand p re s s u r e .
The s i g n i f i c a n t c o e f f i c i e n t s on th e
o u t p u t - c a p it a l r a t i o make more sense fro m th e m ic ro e c o n o m ic p o in t
o f v ie w .
As th e o u t p u t - c a p it a l r a t i o
A ls o , when u t i l i z a t i o n
in c r e a s e s , m a rg in a l c o s t r is e s .
r a te s a re h ig h ,
in c re a s e s in
to s u p p ly b o t t le n e c k s , th u s r a i s i n g p r ic e s .
demand can le a d
The tim e tr e n d i s an
im p o r ta n t v a r ia b l e in some s e c to r s , a f a c t w h ic h m ig h t s u g g e s t th e
e x is te n c e o f t e c h n o lo g ic a l change and p r o d u c t- m ix change.
E le c tr ic a l
m a c h in e ry , F in a n c e and in s u ra n c e , and O th e r s e r v ic e s show bad r e s u lt s
o f r e g r e s s io n .
The o u t p u t - c a p it a l r a t i o
had w rong s ig n s .
in
th e r e g r e s s io n .
F o r th e s e s e c to r s , o n ly th e tim e t r e n d i s
The f i t s
f o r th e t h r e e s e c to r s .
s e r io u s p ro b le m .
and r a t e o f o u tp u t change
in c lu d e d
o f th e r e g r e s s io n w e re n o t bad e x c e p t
F o r a fe w s e c to r s , a u t o c o r r e la t io n i s
The R H O -a d ju stm en t m ethod i s
a
em ployed in f o r e c a s t in g .
B e fo re we e s tim a te e q u a tio n ( 1 0 ) , we m ust have an e q u ilib r iu m
p r ic e s e r ie s .
I n o r d e r to c a lc u la t e th e e q u ilib r iu m
p r ic e s , we need
t o know th e m a t e r ia l c o s ts , and th e n o rm a l u n i t la b o r c o s ts .
The
n o rm a l u n i t la b o r c o s t can be fo u n d by u s in g th e wage r a t e p e r manhour
and th e e q u ilib r iu m
la b o r re q u ire m e n t p e r u n i t o f o u tp u t.^ "
As i s
m e n tio n e d a b o ve , th e wage r a t e d a ta and la b o r re q u ir m e n t d a ta a re
a v a i la b le o n ly by tw e n ty s e c to r s .
To c a lc u la t e th e e q u ilib r iu m
p r ic e s f o r 156 s e c t o r s , we assume t h a t each in d u s t r y w i t h i n
th e tw e n ty s e c to r s has th e same v a r i a t i o n
in wage r a t e and p r o d u c t i v i t y
o v e r tim e b u t th e l e v e l o f th o s e can be d i f f e r e n t .
e q u ili b r iu m
each o f
I f we m u l t i p l y
la b o r re q u ire m e n t (EOQ*) b y th e wage r a t e we g e t th e la b o r
c o m p e n s a tio n r a t e p e r u n i t o u t p u t .
A ls o , i f
we m u l t i p l y th e c a lc u la t e d
u n i t la b o r co m p e n s a tio n r a t e b y th e m a rk -u p r a t i o s
r a t e o f v a lu e added p e r u n i t o f o u t p u t .
we w i l l g e t th e
N o t ic in g t h a t we a re u s in g
th e I/O t a b le w h ic h i s based on 1970 p r ic e s , we can e x p e c t t h a t th e
v a lu e added p e r u n i t o f o u tp u t in 1 970, w i l l be s im p ly 1 m inus th e
colum n sum o f th e I/O m a t r ix .
tiv ity
w ith in
If
th e a s s u m p tio n o f th e same p ro d u c ­
each in d u s t r y c a te g o r y i s
s h o u ld be c lo s e t o 1 - I a
i
ij
.
r ig h t,
th e v a lu e added r a t e
As e x p e c te d , some s e c t o r s , by th e 156
c l a s s i f i c a t i o n , w h ic h a re v e r y homogenous w i t h i n an in d u s t r y c a te g o ry
b y th e tw e n ty s e c to r c l a s s i f i c a t i o n have v e r y s i m i l a r v a lu e added r a t e s .
I n an a lg e b r a ic fo rm , we can g e t th e n o rm a l u n i t la b o r c o s t s e r ie s
as f o l lo w s :
F o r th e a g r i c u l t u r a l s e c to r and o t h e r s e r v ic e s we have wage
r a t e p e r m o n th . We do n o t have th e in f o r m a t io n a b o u t m anhours f o r
th e s e s e c to r s .
B u t i f we u se th e m an-m onth re q u ire m e n t p e r u n i t o f
o u t p u t , we g e t th e same u n i t la b o r c o s t.
w here
j
= 1 .....................
156.
j d = 20 o r d e r s e c to r in w h ic h s e c to r j
is
a p a r t.
V .^ = n o rm a l u n i t la b o r c o s t o f s e c to r i b y 156 c l a s s i f i c a t i o n
Jt
J J
a t tim e t .
id
L“
= e q u ilib r iu m la b o r re q u ire m e n t
w n ic h s e c to r j
is
o f th e 20 o rd e r s e c to r in
a p a r t.
= wage o f th e 20 o r d e r s e c to r i n w h ic h s e c to r j
is a p a r t.
t
When we c a lc u la t e th e u n i t v a lu e added, we a ls o assume t h a t th e m ark­
up r a t i o s
o f th e in d u s t r ie s o f 156 s e c to r o r d e r w h ic h b e lo n g to th e
same in d u s t r y o f tw e n ty s e c to r o r d e r have th e same v a r ia t io n s o v e r
tim e .
The m a t e r ia l c o s ts a re g o tte n u s in g th e a c t u a l p r ic e s e r ie s ,
th e w o r ld p r ic e s , and th e in p u t - o u t p u t t a b le .
The w o r ld p r ic e s e r ie s
a re a v a i la b le fro m th e I n t e r n a t i o n a l T ra d e M o d e l.
Because o n ly one
A m a t r ix o f th e base y e a r i s a v a i la b le , we use th e c o n s ta n t in p u t o u tp u t t a b le i n
a lm o s t c e r t a i n
t im e .
e q u ili b r iu m p r ic e c a lc u la t io n .
H ow ever, we a re
t h a t th e in p u t - o u t p u t c o e f f i c i e n t s a re c h a n g in g o v e r
The b ia s caused by a ssum ing c o n s ta n t in p u t - o u t p u t c o e f f i c i e n t s
c o u ld be c o n s id e re d i n
The e q u ilib r iu m
s e c to r s .
th e b e h a v io r a l e q u a tio n .
p r ic e s e r ie s show much v a r i a t i o n
in d iffe r e n t
F o r e xam ple , d e s p it e th e e x p e c ta tio n o f a r i s i n g
p r ic e t r e n d ,
77
some m in in g s e c to r s have a downward t r e n d .
The downward tr e n d in
m in in g s e c to r p r ic e s a c t u a l l y happened because o f th e r a p id f a l l
th e la b o r re q u ire m e n t r a t e ,
in
even th o u g h th e n o m in a l wage r a t e had
in c r e a s e d .
The e q u ilib r iu m
p r ic e s e r ie s i s
e x p e c te d to be c lo s e r t o
a c t u a l p r ic e s e r ie s f o r th e m ore c o m p e t it iv e i n d u s t r ie s .
m ost c o m p e t it iv e
in d u s t r ie s th e e q u ilib r iu m
th e
In th e
p r ic e s h o u ld d o m in a te
th e a c t u a l p r ic e a d ju s tm e n t, s in c e th e in d u s t r y s h o u ld n o t be a b le
t o move away fro m th e e q u ilib r iu m
o f tim e .
As th e in d u s t r y becomes le s s c o m p e t it iv e , th e im p o rta n c e
o f e q u ili b r iu m
p r ic e s h o u ld d e cre a se and a d ju s tm e n t becomes s lo w e r
and m ore u n c e r t a in .
T h is
beca u se th e e q u ili b r iu m
and in
p r ic e f o r any s u b s t a n t ia l p e r io d
e x p e c ta tio n tu r n e d o u t t o be c o r r e c t ,
p r ic e s e r ie s in th e a g r i c u l t u r a l s e c to r s
some o t h e r c o m p e t it iv e in d u s t r ie s a re v e r y c lo s e to th e
a c t u a l p r ic e s e r ie s .
The e s tim a tio n o f e q u a tio n
th e e q u ili b r iu m
p r ic e .
(1 0 ) was c a r r ie d o u t a f t e r we g o t
The id e a b e h in d t h i s
th e e m p ir ic a l r e l a t i o n s h i p
r e g r e s s io n i s
to f i n d
t h a t was supposed t o e x is t betw een th e
o b s e rv e d p r ic e s on th e one hand and th e com puted p r ic e s and th e
la g g e d v a lu e s o f
b ia s i n
th e o b s e rv e d p r ic e s on th e o t h e r .
th e e q u ilib r iu m
We hope t h a t th e
p r ic e c a lc u la t io n due t o th e u se o f c o n s ta n t
in p u t - o u t p u t c o e f f i c i e n t can be c o r r e c t e d th ro u g h th e r e g r e s s io n
e q u a tio n .
If
th e r e e x i s t a s t r u c t u r a l change o v e r tim e o f th e in p u t -
o u tp u t c o e f f ic ie n t s ,
it
c o u ld be p ic k e d up by th e r e l a t i o n betw een
73
th e o b s e rv e d p r ic e s and th e computed p ric e s .^ "
In e q u a tio n
( 1 0 ) , th e sum o f th e c o e f f i c i e n t s ,
c o n s ta n t te rm , i s
u n ity .
be n o n - n e g a tiv e .
In o r d e r to s a t i s f y th e c o n s t r a in t t h a t th e sum
o f th e c o e f f i c i e n t s
is
A ls o ,
e x c e p t th e
a l l o f th o s e c o e f f i c i e n t s
u n i t y , we use r e s t r i c t e d l i n e a r r e g r e s s io n .
A c o n s ta n t te rm i s
in c lu d e d in e q u a tio n
(1 0 ) because i t
p re v e n t th e p r e d ic t e d p r ic e fro m b e in g u n d e re s tim a te d .
te n d s to be r i s i n g
s h o u ld
o v e r tim e .
th e c o e f f i c i e n t t o u n i t y ,
T h e r e fo r e , i f
c o u ld
The p r ic e
we c o n s t r a in th e sum o f
th e p r e d ic t e d p r ic e , w h ic h i s a c t u a l l y a
w e ig h te d a ve ra g e o f th e e q u ilib r iu m
p r ic e and th e la g g e d a c t u a l p r ic e ,
can be a lw a y s u n d e re s tim a te d because th e la g g e d p r ic e i s u s u a lly lo w e r
th a n th e c u r r e n t p r ic e .
H ow ever, we e x p e c t th e c o n s ta n t te rm to be
s m a ll.
The r e g r e s s io n r e s u lt s o f th e e q u a tio n
T a b le V I - 2 .
(1 0 ) i s
shown in
As e x p e c te d , th e c o n s ta n t te rm s a re s m a ll and g e n e r a lly
in s ig n ific a n t.
The c o e f f i c i e n t s on th e e q u ilib r iu m p r ic e and th e
la g g e d p r ic e a re p o s i t i v e e x c e p t a few s e c to r s .
If
th e s ig n o f th e
c o e f f i c i e n t on th e la g g e d p r ic e i s n e g a tiv e , we assume t h a t th e p r ic e
o f th e s e c to r a d ju s t s r a p i d l y so t h a t th e a c tu a l p r ic e s h o u ld be e q u a l to
th e e q u ili b r iu m
p r ic e .
Tne n e g a tiv e c o e f f i c i e n t o f th e e q u ilib r iu m
p r ic e ,
The same p r ic e a u to r e g r e s s io n i s done in th e B ro o k in g s m odel
f o r th e same re a s o n .
F is h e r , F .M ., L .R . K le in , and Y. S h in k a i.
" P r ic e
and O u tp u r A g g r e g a t io n ," i n E c o n o m e tric M odel o f th e U n ite d S t a t e s , eds.
b y J .S . D u e s e n b e rry , e t a l .
A m sterdam , N o r th - H o lla n d ,
1965.
2
J o h n s to n , J . E c o n o m e tric M e th o d , Second e d i t i o n .
New Y o rk .
1972. pp 1 55 .
McGraw
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w h ic h was a c t u a l l y shown up in few s e c to r s , i s n o t t h e o r e t i c a l l y
in t e r p r e t a b l e .
H ow ever, we assume t h a t th o s e s e c to r s have v e r y s lo w
speed o f a d ju s tm e n t o f a c tu a l p r ic e to e q u ilib r iu m
tr a r ily
p r ic e .
We a r b i ­
a s s ig n 0 .1 as th e speed o f a d ju s tm e n t to th o s e s e c to r s .
As we e x p e c te d , th e e q u ilib r iu m
p r ic e has la r g e r w e ig h t in
d e te r m in in g th e a c tu a l p r ic e th a n th e la g g e d p r ic e f o r c o m p e t it iv e
in d u s t r i e s .
Food in d u s t r ie s and some t e x t i l e
and l i g h t m a c h in e ry
in d u s t r ie s a d ju s t r a p i d l y ; some h eavy m a c h in e ry in d u s t r ie s and p u b lic
u tility
s lo w ly .
i n d u s t r i e s , w h ic h a re more o r le s s m o n o p o lis t ic , a d ju s t v e r y
B u t th e t h e o r e t i c a l e x p e c ta tio n d id n o t t u r n o u t to be r i g h t
f o r a l l s e c to r s .
N am ely, some fo o d in d u s t r ie s l i k e
and B everages a d ju s t v e r y s lo w ly .
B a ke ry p ro d u c ts
The w o r ld p r ic e was in c lu d e d in
th e r e g r e s s io n as an in d e p e n d e n t v a r ia b l e f o r th e s e c to r s whose
im p o r t- u s e r a t i o
is
good.
is
g r e a t e r th a n 0 .2 .
G e n e r a lly , th e f i t
o f r e g r e s s io n
A few s e c to r s have v e r y lo w R , b u t th e a b s o lu te p e rc e n ta g e
e r r o r s o f th o s e s e c to r s a re n o t v e r y la r g e .
o f e q u ili b r iu m
c o r r e la tio n
p r ic e s a re s t a t i s t i c a l l y
p ro b le m i s n o t s e r io u s .
p ro c e d u re w i l l be em ployed in
G e n e r a lly , th e c o e f f i c i e n t s
s ig n ific a n t.
The a u to ­
H ow ever, th e RHO a d ju s tm e n t
f o r e c a s t in g .
86
CHAPTER V I I
P e rs o n a l C onsum ption E x p e n d itu re
I n t r o d u c t io n
The m ain component o f f i n a l demand f o r o u tp u t i s
s u m p tio n e x p e n d itu re (PCE) w h ic h i s
p e rs o n a l con­
5 0 .4 p e rc e n t o f th e GNP in 1970.
T h e r e fo r e , c o n s u m p tio n e x p e n d itu re s h o u ld be h ig h ly im p o rta n t b a s is
i n lo n g te rm in t e r i n d u s t r y o u tp u t f o r e c a s t in g .
i s n o t much c y c l i c a l v a r i a t i o n
o th e r
F o r t u n a t e ly ,
th e r e
in c o n su m p tio n e x p e n d itu re compared to
f i n a l demand com ponents such as in v e s tm e n t and in v e n t o r y s to c k .
N in e t y - s ix c o m m o d itie s o u t o f 156 I/O s e c to r s a re s o ld f o r p e rs o n a l
c o n s u m p tio n .
The PCE e q u a tio n s a re e s tim a te d f o r a l l o f th o s e s e c to r s
e x c e p t f o r a few s e c to r s w h ic h w i l l be t r e a t e d as exogenous.
I n th e second s e c t io n ,
th e th e o r y o f th e PCE e q u a tio n w i l l be
d is c u s s e d and th e j u s t i f i c a t i o n
e x p la in e d .
s e c t io n .
s e c t io n .
o f th e fo rm o f th e e q u a tio n w i l l be
The e m p ir ic a l r e s u lt s w i l l be p re s e n te d in th e t h i r d
The s a v in g s e q u a tio n w i l l be p re s e n te d in th e f o u r t h
By d e f i n i t i o n ,
sum o f co n s u m p tio n e x p e n d itu re o f each
s e c to r and s a v in g s s h o u ld be e q u a l t o d is p o s a b le incom e.
B u t th e PCE
f o r e c a s t s w it h th e e s tim a te d e q u a tio n do n o t a u t o m a t ic a lly g u a ra n te e
t h a t c o n d it io n .
T h is i s
so c a lle d "a d d in g up p r o b le m ," w h ic h w i l l
be d e a lt h w i t h in th e f i f t h
s e c t io n .
T h e o ry o f th e E q u a tio n
E c o n o m e tric m odels c o u ld be c l a s s i f i e d
in t o
two b ro a d c a te g o r ie s
a c c o r d in g t o th e ty p e o f co n s u m p tio n f u n c t io n u sed .
One g ro u p uses
87
a g g re g a te c o n s u m p tio n f u n c t io n s ;
th e W h a rton m odel i s an exam ple .
The
a g g re g a te c o n s u m p tio n f u n c t io n p r e d ic t s t o t a l p e rs o n a l c o n su m p tio n ex­
p e n d it u r e , and t o t a l e x p e n d itu re i s
a llo c a t e d to th e I/O s e c to r s by
c o n s ta n t p r o p o r t io n s o v e r tim e .
The o th e r g ro u p uses a system o f demand f u n c t io n s , one f o r each
s e c to r.
C e r t a in l y ,
th e l a t t e r i s
d e s ir a b le i n an in p u t - o u t p u t m o d e l,
beca u se th e a g g re g a te f u n c t io n lo s e s a
i n d i v i d u a l c o m m o d itie s , l i k e
lo t
o f in f o r m a t io n a b o u t
incom e and p r ic e e l a s t i c i t i e s .
S tu d ie s o f demand system s c o u ld a ls o be c l a s s i f i e d
c a t e g o r ie s .
One i s
th e demand syste m w h ic h i s
f u n c t io n ; th e syste m o f S to n e ,
a re i n t h i s
c a te g o r y .
1
in t o
two
d e r iv e d fro m a u t i l i t y
P o lia k and W a le s,
2
Brown and K e r in
3
T h e ir r e c e n t s t u d ie s have made s i g n i f i c a n t
c o n t r i b u t io n s t o c o n s u m p tio n s t u d ie s based on m ic ro -e c o n o m ic t h e o r y .
They use a p r e s p e c if ie d a g g re g a te u t i l i t y
f u n c t io n w it h a b u d g e t con­
s t r a i n t to d e te rm in e b o th th e f u n c t io n a l fo rm o f th e demand e q u a tio n
and th e in t e r e q u a t io n r e s t r i c t i o n s .
The o t h e r g ro u p , w h ic h w i l l be
c a lle d th e p r a c t i c a l fo rm , c o n s is ts o f th o s e s t u d ie s w it h a s in g le
e q u a tio n f o r each co m m o d ity, in w h ic h in co m e , r e l a t i v e
o t h e r v a r ia b le s a re e x p la n a to r y v a r ia b l e s .
p r ic e and some
T h is ty p e o f s tu d y does
^ S to n e , R . , " L in e a r E x p e n d itu re System s and Demand A n a ly s is . "
The Economic J o u r n a l, 1 9 5 4 .
^ P o lia k , R . , and W a le s, T . " E s t im a t io n s o f th e L in e a r E x p e n d itu re
S y s te m s ," E c o n o m e tric a , 1 96 9 .
^B ro w n , H . , and H e r in , D . , "T he S B ra n ch U t i l i t y T re e ; a G e n e ra l­
i z a t i o n o f th e L in e a r E x p e n d itu re S y s te m ," E c o n o m e tric a , 1 973.
88
n o t use a u t i l i t y
f u n c t io n i m p l i c i t l y
o r e x p lic itly ,
in v e s t ig a t e c ro s s p r ic e e l a s t i c i t i e s .
INFORUM
had t h i s
H o u th a k k e r and T a ylo r^" and
k in d o f demand e q u a tio n syste m .
The demand system w it h u t i l i t y
B u t th e r e i s a q u e s tio n a b o u t i t s
e x is te n c e o f th e s t a b le u t i l i t y
re a s o n s ;^
f u n c t io n i s
t h e o r e t i c a l l y n ic e .
e m p ir ic a l a p p l i c a b i l i t y .
f u n c t io n
is
th o s e re a s o n s a re in d i v i d u a l d if f e r e n c e s
tre a tm e n t o f d u ra b le goods in a u t i l i t y
i n c o n s u m p tio n .
Even i f
The
d o u b tf u l f o r s e v e r a l
in t a s t e s , th e
s p o r a d ic a pp e a re n ce o f new c o m m o d itie s , d i f f i c u l t i e s
a c tiv itie s
and does n o t
in s t a t i s t i c a l
f u n c t io n , and nonm arket
th e r e e x is t s a s t a b le u t i l i t y
f u n c t io n f o r each i n d i v i d u a l , we may n o t d e r iv e an a g g re g a te demand
e q u a tio n .
The S lu t z k y 's
demand e q u a tio n .
e q u a tio n may n o t h o ld w it h an a g g re g a te
The S lu t z k y 's e q u a tio n shows th e s u b s t i t u t i o n e f f e c t
and th e incom e e f f e c t .
The a ve ra g e o f th e a g g re g a te d s u b s t i t u t i o n
e f f e c t can be e q u a l to t h a t o f a r e p r e s e n t a t iv e p e rs o n .
incom e e f f e c t w h ic h s t a t e s
a
B u t th e
co n su m e r’ s r e a c t io n w it h re s p e c t to
p u rc h a se s o f a com m odity to changes i n h is
incom e c a n 't be a g g re g a te d
to g e t th e a v e ra g e incom e e f f e c t o f a r e p r e s e n t a t iv e p e rso n because
h o u t h a k k e r , H .S ., and L .D . T a y lo r .
Consumer Demand in th e U n ite d
S t a t e s , 1 9 2 9 -1 9 7 0 .
H a rv a rd U n iv e r s it y P re s s .
1966.
2A lm o n , C. e t a l .
1 985: I n t e r i n d u s t r y F o re c a s ts o f th e A m e rica n
Economy. L e x in g to n B oo ks. L e x in g to n , M a s s a c h u s e tts .
1974.
■^Taubman, P ."C o n s u m p tio n F u n c tio n s f o r S h o rt Rim M o d e ls .” in th e
B ro o k in g s M o d e l: P e r s p e c tiv e and R ecent D e v e lo p m e n ts ,
e ds. by Fromm, C
and L . K le in .
N o r th - H o lla n d P u b lis h in g Co.
1975.
89
o f th e d i f f e r e n t incom e and th e d i f f e r e n t u t i l i t y
f u n c t io n o f each
in d iv id u a l
B e s id e s t h a t ,
it
i s n o t p r a c t i c a l to a p p ly u t i l i t y
a p p ro a ch to th e demand system w it h so many s e c to r s .
m ain a d va n ta g e o f u t i l i t y
f u n c t io n a p p ro a ch i s
f u n c t io n
H ow ever, th e
th a t i t
in v e s t ig a t e s
s im p le fo rm o f th e S lu t z k y ’ s e q u a tio n o f an i n d i v i d u a l , n ,
•»;
i " A
‘
J
u = c o n s ta n t
p = c o n s ta n t
Now suppose t h a t th e S lu t z k y ’ s e q u a tio n o f r e p r e s e n t a t iv e p e rs o n , T ,
is
Then,
aqn
—i
n
aPj
-
I q?
n
n
1
1
dq?
3qT
_ i
* N • _ i
.
«
ayn
'N n
8q!
- H q?
1
w here
N is
n
i
th e number o f i n d i v i d u a l s , because
4r, n
oy
i* " q 1
—
i
^ T
o y
1
3y
is
90
♦J
th e c ro s s p r ic e e f f e c t .
s u m p tio n f u n c t io n s f a i l
c o m m o d itie s .
U su a l p r a c t i c a l ways o f f o r m u la t in g con­
t o c a p tu re th e c o m p le m e n ta lity between
The " p r a c t i c a l fo rm " c o n s id e rs a com m odity a g a in s t
a l l o th e r c o m m o d itie s .
The e x p e c ta tio n o f a n e g a tiv e s ig n f o r th e
r e l a t i v e p r ic e c o e f f i c i e n t im p lie s t h a t a com m odity i s more o r le s s
a s u b s t it u t e f o r a l l o th e r c o m m o d itie s .
I f we have a d e t a ile d d is ­
a g g re g a te d demand s y s te m , t h i s a s s u m p tio n i s n o t re a s o n a b le .
in s t a n c e , i f
th e p r ic e o f c o ffe e r i s e s ,
th is
For
co n su m p tio n f u n c t io n
p r e d ic t s t h a t th e demand f o r s u g a r w i l l r i s e because th e r e l a t i v e
p r ic e o f s u g a r goes down
in d e x .
T h is i s
ow in g to
c o n t r a r y to b a s ic p r ic e th e o r y s in c e c o ffe e and
s u g a r a re co m plem ents.
Even th e s u b s t i t u t i o n e f f e c t i s n o t w e ll
c a p tu re d by th e " p r a c t i c a l f o r m . "
in to
th e in c re a s e o f consum er p r ic e
s e v e r a l c a te g o r ie s ,
I f we c l a s s i f y a l l c o m m o d itie s
f o r some c o m m o d itie s i t
th a t s u b s titu tio n w i l l o c c u r w it h in ,
H e re , we t r y
i s more l i k e l y
r a t h e r th a n among, c a te g o r ie s .
to r e f o r m u la t e th e " p r a c t i c a l fo rm " o f th e co n su m p tio n
e q u a tio n ^ - to e x p la in c o m p le m e n ta lity and s u b s t i t u t i o n betw een and
among c a t e g o r ie s .
The fo r m a l r e g r e s s io n e q u a tio n i s
i
= 1
156
^A lm o n , C.
"T he INFORUM M odels 1 9 7 6 ,"
No. 1 5 , June 1976.
INFORUM R esearch R e p o rt
w here
= per capita consum
er expenditure o
n the i
th
com
m
odity, in
1
970 constant prices.
= per capita disposable incom
e in 1
9
7
0 constant prices.
t = tim
e trend
P
= price of the i t ^1 com
m
odity at time t.
P
^ = average price of the category to w
hich the i 1"*1 com
m
odity
it
belongs.
P
t = overall consum
er price index.
S
t = per capita savings.
Equation (1) is the d
e
m
a
n
d equation for a com
m
odity a
n
d equation
(2) is the budget constraint.
add u
p to total incom
e.
to be estim
ated.
Total consum
ption plus savings should
Equation (1) is not linear in the param
eters
T
h
e usual types of the d
e
m
a
n
d equation are linear
form in all variables or double log form
.
rejected because of problem
s with them
.
T
hese usual form
sw
ere
T
h
e double log form equation
is rejected because it gives a serious adding u
p problem
.
T
h
e linear
form is also rejected because it doe
s not allow interaction betw
een
prices a
n
d incom
e.
W
ithout the interaction w
em
a
y get unreasonable
consum
ption forecast.
Let suppose that the per capita disposable
incom
e at year 1 is $
1 ,000 , and that a consum
er spends $10 o
n peas.
S
uppose further that prices d
o not change in year 2, but that incom
e
92
h
a
s doubled a
n
d that h
e spends $
2
0o
n peas.
N
o
w
, suppose that the
price at year 1 is higher so that he spends only $8 o
n peas.
w
e suppose this different price rem
ains the s
a
m
e in year 2.
Also,
T
h
e
n
the linear formof equation will predict a $
1
6 expenditure o
n that
com
m
odity while the multiplicative formof equation will predict $16.
In other w
ords, the m
agnitude of the price effect in the linear form
is independent of the a
m
o
u
n
t spent o
n the com
m
odity, a
n unlikely state
of affairs.
It se
e
m
s reasonable to expect that changes of d
e
m
a
n
dd
u
e
to price change over tim
e are proportional to the size of the incom
e
over tim
e.
Therefore, equation (1) has a linear form in incom
e vari­
ables a
n
d mulitplicative form in price variables.
T
h
e efforts to deal with com
plem
entality is sh
o
w
n by the tw
o
relative price variables.
T
h
eo
w
n relative price in the usual
"practical form
s" of consum
ption function is d
e
co
m
p
o
se
d into tw
o
parts; the o
w
n price relative to the category price, a
n
d the category
price relative to the overall average price.
W
e expect a negative
sign on jS
^ if there is substitution within categories, and w
e expect
a negative sign o
n ^ ^ there is substitution a
m
o
n
g categories.
w
e can say that com
plem
entarity prevails w
here the 3^
Also,
greater than
3^ w
h
e
n all price indices are 100 .
Em
pirical Results
In the regression analysis tw
o item
s of a
^priori information
93
are used.
First, the cross-section incom
e elasticities^ are used to
calculate the coefficient of the incom
e variable.
Since the disposable
incom
ea
n
d the tim
e trend are highly correlated, it is very hard to
disentangle the incom
e effect if w
e use both of these variables in
the regression.
E
ve
n though the concept of cross-section incom
e
elasticity is not exactly the s
a
m
ea
s that of tim
e series incom
e
elasticity, it is not unusual to use cross-section information in
that case.
R
eim
bold sh
o
w
s that, in the U
.S.A. case, the incom
e coefficient
borrow
ed from cross-section data gives better forecasts than the
incom
e coefficient estim
ated directly from tim
e series data.
2
T
h
e other information available before the estim
ation is the
group price elasticities.
using tim
e series data.
3
Saito estim
ated com
m
odity d
e
m
a
n
d equations
Following Saito’s classification, all con­
sum
ption goods are grouped into 2
1 categories, so that Saito’s
^T
he cross-section elasticities are gotten from ’A
nnual R
eport
on the Fam
ily Incom
ea
n
d Expenditure S
urvey^
. Japanese G
overnm
ent. 1970.
This report sh
o
w
s the cross section incom
e elasticities at 1967. U
sing
this information w
e calculate incom
e coefficient a
s follows:
r
a. = n
.67
w
here n
,--. is the a priori incom
e elasticities.
2
6
7 “T"
6/
6
7
2
R
eim
bold, T., "Sim
ulation W
ith a D
yna
m
ic Input-Output Fore­
casting M
odel." U
npublished P
h.D
. dissertation. University of
M
aryland. 1974.
3
Saito, M
. "A G
eneral Equilibrium Price a
n
dO
utputs in Japan.
1953-1965." In the W
orkings of E
conom
etric M
odels, ed. by M
. M
orishiisa.
C
am
bridge. 1972.
94
estim
ates of price elasticities can b
e used in this study.
H
ow
ever,
the Saito’s elasticities are not sim
ply plugged into the consum
ption
equations.
B
ecause the data Saito used covers only up to 1965, there
could be a
n inconsistency betw
een the _
a priori information a
n
d the
data w
e use right n
o
w
.
W
eallow the group price elasticity to vary within a certain
range w
hich is given by the subjective judgm
ents.
Aw
ide range is
given if the m
agnitude of the _
a priori price elasticity of a certain
g
o
o
d is large a
n
d if the com
m
odities in the group are heterogeneous.
T
h
e rule of th
u
m
b is that, in norm
al case, w
e allow the group price
elasticity to vary within 50% of the_
§ priori elasticity in either
side.
If com
m
odities within the group are h
om
ogeneous, w
e allow less
than 50% a
nd m
ore than 50/c for heterogeneous case.
In Table VII-1,
the a priori price elasticities a
n
d the given ranges are sh
o
w
n with
the Saito’s com
m
odity group classification.
T
h
e reason w
h
yw
e use the a priori information on the group price
is that it m
a
y prove advantageous to com
pel ^ to be the s
a
m
e for all
item
s within a group.
If all prices within a group increase pro­
portionally, the com
position of expenditures o
n the group dep
e
nd
s
only
Therefore, different
within a group will predict different
com
position of expenditure within a group even if all the relative
prices in the group rem
ain the sa
m
e
, w
hich is not theoretically con­
sistent.
W
h
e
n all prices within a group change proportionately, incom
e
effect m
ignt cause a change in the percentage com
position of expendi­
ture within the group.
B
ut this incom
e effect should b
e captured by
the incom
e term in the equation.
95
This strict uniformity of ^ within group m
a
yb
e theoretically
consistent only if the group classification is perfect, so that there
exists independence betw
een com
m
odity groups.
If the com
m
odity groups
are not com
pletely separable or not com
pletely independent, the equi —
proportionate price rise of all com
m
odities within the group ca
n
cause different com
position of expenditure within the group because
the change of the overall consum
er price index ow
ing to the equi—
proportionate price rise ca
n affect the consum
ption in other com
m
odity
group w
hich will affect the consum
ption of the com
m
odity group in
w
hich the price rise w
a
s originated.
If there exists independence,
the feedback effect does not change the com
position of expenditure
in that group because the feedback effect affects the com
position only
I pG \ B2
through
]
w
hich is s
a
m
e for all com
m
odity in the group.
If
independence does not exist, the feedback effect affects the co
m
/p
G\ $2
position not only through I—
but also through cross elasticities
\ p /
betw
een com
m
odities.
B
ecause w
e are certain that the group classifi­
cation in this study cannot be perfect, w
e allow
to vary from the
a priori information; strict uniformity on the estim
ates of ^ ^
s
a
m
e group is not im
posed.
H
ow
ever, the estim
ates of group price
elasticities of the com
m
odities within a s
a
m
e group did not differ
very m
uch.
In m
ost cases, the group price elasticities of the
com
m
odities within a group
range.
approach the s
a
m
e limit of the allow
ed
vO
CT\
T
A
B
L
EVII-1.
G
ro
u
p ite
m
e
C
O
M
M
O
D
IT
YG
R
O
U
P C
L
A
S
S
IF
IC
A
T
IO
N
SA
N
DP
R
IC
EE
LA
S
T
IC
IT
IE
S
G
ro
up Price
Elasticity
A
llow
ed
R
a
n
g
e +/-
1/0 Sectors
-.35
.10
2 , 4, 3
1
2. V
egetables
-.77
.35
29, 3
3. M
eat, Fish a
n
d Dairy
-.77
.35
6 , 14, 15, 16, 26, 27, 28, 3
0
4. O
ther F
o
o
d
-.70
.35
32, 33, 3
4
5. B
everages
-1.80
.50
36, 3
7
6. R
estaurant
-.97
.40
1
5
4
1.
C
ereals
7. Fabric*
-1.11
.50
39, 40, 41, 45, 46, 47, 48, 51,
8. G
a
rm
e
n
t
-1.11
.50
54, 55, 5
6
9. R
ubber a
n
d Leather
-1.11
.50
65, 66
-.96
.50
11, 17, 22, 81, 128, 1
2
9
-1.17
.50
1
30
10. Fuel
11. W
ater
12. Furniture
58, 59, 100, 1
0
1
13. M
edical care
-2.53
14. A
utom
otive
-1.40
1.0 0
.70
78, 79, 1
5
0
80, 114, 115, 1
1
6
* Fabric, G
arm
ent, a
n
dR
ubber a
n
d Leather w
ere not separated in Saito's classification.
r-»
CTv
TABLE V I I - 1 . COi f f li-ftJKD
C
roup N
a
m
e
16. Transportation
G
ro
u
p Price
Elasticity
-1.40
A
llow
ed
R
a
n
g
e +/.70
. Tobacco
-.47
.20
19. Education
-3.82
1.00
20
21
137, 138, 139, 140, 141, 142, 143, 144,
145, 1
4
6
61, 62, 6
3
aper
17. P
16
1 /0 S e c to rs
3
8
1
4
9
. Machinery
104, 106, 107, 110, 111, 119, 120, 121,
. Services
9, 131, 132, 133, 134, 135, 151, 152, 1
5
5
22.
N
o group
122
,
10, 13, 85, 87, 136, 153, 1
5
6
98
T
h
e efforts to find com
plem
entarity in consum
er d
e
m
a
n
d is
successful in s
o
m
e cases.
F
or instance, w
e could find the im
portant
com
plem
entarity in autom
otive group.
T
h
e price elasticities of the
com
m
odities in the group are:
6i
62
P
etroleum refinery product
-1.67
-1.93
P
assenger cars
-1.41
-2.10
R
epair of passenger cars
0
-2.10
M
otorcycles a
n
d bicycles
-1.78
-2.10
6, of the three com
m
odities in this group hit the s
a
m
e limit of the
given range of
-1.4.
Originally a priori group price elasticity w
a
s
Judging by the m
agnitude of
this group sh
o
wcom
plem
entarity.
a
n
dB2 *
com
m
odities in
G
asoline a
n
d Hotor cars are surely
com
plem
ents, a
n
d our statistical fitting bears out this expectation.
B
ecause the 6
for R
epair of passenger cars is zero, the hypothesis
that consum
ers repair a
n old car if the price of n
e
w car is high w
a
s
rejected.
T
h
e result says that there is n
o substitute for the R
epair
of passenger cars.
T
h
e fuel group sh
o
w
s substitutability within a group.
T
h
e
estim
ated elasticities are:
C
ooking coal
*1
6 2
-2.95
-0.46
0
-0.46
C
oal products
-1.32
-0.46
Electricity
-1.90
-0.56
G
a
s
-0.44
-0.46
Natural g
a
s
99
C
oking coal, C
oal products, a
nd Electricity sh
o
wstrong substitut­
ability.
Natural g
a
s sh
o
w
s com
plem
entarity, but the consum
ption of
the natural gas in Japan is negligible.
(5
^a
n
d £ of g
a
s are very
close to each other.
A
s you can se
e in Table VII-2, the interpretation of
is not straightforward for s
o
m
e groups.
a
n
d
Especially the fabric
group a
n
d the m
achinery group sh
o
ws
o
m
e contradictory results.
W
e
suppose that those results are caused by the inappropriate aggre­
gation of groups.
T
h
em
ore aggregated groups w
e have, the m
o
re
difficult to interpret the results.
Since the equation is non-linear, w
e cannot estim
ate the para­
m
eters by the ordinary least square m
ethod.
T
h
e non-linear regression
algorithm developed by M
arquardt^ is em
ployed.
T
h
e regression results
sh
o
wthat the fit is g
o
o
de
n
o
u
g
h to produce reasonable forecasts.
T
h
e
incorporation of the tw
o a priori information does not distort the
fit very m
u
ch
.
M
ost of the sectors sh
o
whigh autocorrelation.
P
ost
regression R
H
Oadjustm
ent is used in forecast.
T
h
eS
avings Equation
T
h
e savings equation in this m
odel has a secondary role.
It
does not directly affect the determ
ination of final d
e
m
a
n
da
n
d the
output of industries.
B
ut it is required in solving the adaing-up
problem in consum
ption determ
ination.
^Kuester, J.L. a
n
d J.H. M
ize. Optimization Techniques with
Fortran. M
cG
raw
-H
ill C
o
m
p
a
n
y. N
e
wYork. 1973.
7ABLE VI1 -2 . REG
RESS Oh Rt SillS Of C
ONSUni'TION FUCNT1CN
1J J
SECTO
R
G10U
P)
PI/P fc
C(EF
THER C
RO
PS
2O
1 )
3 FRUITS
2 ) -2 .48
4 OTHtR CRO
PS FO
R 1KDUSTR1
1 )
6 LIVE STOCKS.POULTRY
9 AGRICULTURAL SERVICES
AL K FIREW
O
O
D
11 CHARCO
15 hUNTlNGS
14 FISHERIES
.00
-.22)
-.005373
. C056
.98
.81
.56
694.
-.3079 .005373
.0053 .00U031
.000247
-.0114
.93
.13
1.
.0037
228.
392.
)
.00
.00) -1 12
< -3.41)
-•CP72 .003633
.99
.71
-.55
-.22) -1 12
< -.15)
-.0074 .001049
-.000049
.0099
.80
.94
4.
-.000159
.0085
.95
34.
.002057
-.0330
-.0089 .000010
.0001)78
.0137
-.2345 .004843
-.004843
.0063
-.0037 .000208
-.000208
.0034
.0380 .000811
-.000811
-.60)
.002P .000031
.000331
.0014
.0071
< -.39)
-.0012 •00G009
-.000009
-.63)
-.4110 .006097
-.003591
< -.OS)
-.40)
-.CB44 .001577
-.2P90 .006051
-.001577
.0094
.82
.96
129.
.010225
.004 7
.99
.55
418.
21 )
10 )
21 J
.00
.00 ) - 42
< -1.08)
.0789 .000159
.O
C
.00) - 46
(
-.36)
.2653 .000106
.00
16 INLAND W
ATER FISHERIES
3 )
26 CARCASSES
27 M
EAT PRO
DUCT
(
R
H
O PCE70
2C )
3 )
.00
t 1 -.38
22 NATURAL G
AS
< -.71 )
T1W
E
RBARSQ
X 70PCE
-.002959
.0045
.96
.002340
15 KHALING
1/ COKING CO
AL
-2.09) - 42
.00 ) - 25
DELTA V
.00
10 ) -2.95
10 )
.00
j ) -1 .10
3 ) -1 .37
.00) - 46
(
.00) - 42
-.4«>
< -.33)
-2.b3) -1 12
.CO) - 42
1 -2.56)
< - .09)
-3.81 ) - 46
(
.00) - 46
0
•
1
10 FO
RESTRY
-CO
PLG/PbAR
CO
NSTAN YC
O
EF (ELAS)
CT)
(T)
CCtF
-.37)
.00) _ 25
t
-.0053 .009738
.20
.95
.93
.67
3.
.96
.87
344.
.99
.37
12.
.83
.94
.60
40.
.09
4.
.0100
.91
.88
1.
.0067
.97
.89
465.
11.
-1.50) - 42
t
(
(
-.87)
-.1920 .002305
-.002305
.0078
.98
.79
196.
-.46)
-.5797 .00b292
-.008292
.0070
.97
.92
641.
2 )
.00
~.2’ > - 42
-.46) - 42
.00) - 42
)
.00
.00) - 42
t
31 GRAIN WILL PRO
DUCTS
1 )
.00
.00) - 25
< -.56)
.8005 .015187
-.015187
.0071
.97
.83
1381.
O
UCTS
32 BAKERY PRO
33 REFINED SUG
AR
4 ) -1 .65
-1.10) - 35
C -.41)
-.3613 .001)131
-.008131
.0075
.99
.70
705.
4 )
.00
.00) - 35
C -.17)
.1204 .001097
.004088
.0008
.85
.85
78.
THER FO
O
D PREPARED
34 O
4 >
5 )
.00
i
-.45)
-.011346
C-2.47)
-.2170 .011346
-.1052 .007672
.0070
.0072
.98
1.00
.83
.49
937.
691.
(
-.91)
-.5410 .002190
-.002190
.0115
.96
.82
261.
.005466
.0122
.97
.69
743.
0.
O
UCT
20 DAIRY PRO
29 VEGETABLE ft FRUIT PRESER
O
D PRESERVED
iU SEA FO
)
-.36
.00
.CO) - 35
.00) -2 16
5 )
-.25
-.09) -2 30
17 )
.00
.OC) - 63
( -1.45)
-.2552 .001181
39 SILK REELING K W
ASTE S1L
4b CO
TTO
N SPINNING
7 ) -.39
7 ) -1 .56
-.37) -1 61
-1.08) -1 61
< -.43)
( -2.20)
.0046 .000013
1.
.000034
-.0278
.10
.91
.0065 •00ti052
1.
-.000030
-.0125
.97
.74
1.
41 W
O
O
LEN ft UCRS1ED YAR
N
45 SILK & RAYO
NW
EAVING
7 )
.00
1.
-.00C054
-.00*9
.96
.75
9.
.00
< -1.15)
( -.36)
.0278 .000285
7 )
.00) -1 38
.00) -1 48
.1296 .007281
1.
-.007281
-.0000
.95
.52
30b.
46 C0TION & SPUN RAYO
N FABR
7 )
.00
.00) -1 61
< -3.25)
1.
.000174
-.0154
.95
.77
89.
47 SYNTHETIC FIBERS W
O
VE
N
7 )
.OC
.00) -1 61
( -2.08)
.5*25 .002832
.5019 .003385
1.
-.003385
-.0080
.97
.66
120.
4a W
O
O
LEN FABRICS W
O
VEN & F
7 > -1 .49
.00
7 )
-1.36) -1 61
.00) -1•01
( -1.41)
1 -.98)
1.3186 .007250
1.4848 .014353
1.
.020117
-.0177
.92
.69
230.
1.
.004396
-.0102
.94
.85
460.
36 ALCOHOLIC BEVERAGES
37 SOFT DRINK
38 TO
BACCO
51 KNITTED FABRICS
-.002145
V
lA blt
V I I - ? ( COhT 1 KUE D ) • P E I M S S I O H
RESULTS
Cf
CONSUIs
T 1 Oh
ruNCTI ON
<
7 )
.00
<
CO
NSTAN YC
O
EF (ELAS)
PU
GyPb R
C
C
EF
<T)
-.19)
-.0968 .001446 1.
.00) -1 .61
b4 FO
O
TW
EAR EKCIPT RUBBER N <
* )
.00
(
.CO) -.61
bi W
EARING APPAREL
(
0 )
.00
c
.00) -.61
-.76)
-.1168 .0?L574
1.
b6
C
H)
.00
.00
(
(
.00) -.61
-.4’ )
-.0452 .002164
1.
.G
O) -.61
-.54)
-.0296 .000663
1.
.00
(
-.4ft)
-.1743 .0021*49
StClOR
bi OThtH FIBER PRO
DUCTS
textile garments
<G10UP)
P1/F-frt
CCl F
(T)
-.7^)
.1222 .002727
1.
R
BARSQ
TI H
E
X 70PCE
.94
• 002949 - • C006
DELTA
y
R
H
O PCE70
.43
67.
.86
105.
.99
.72
902.
.98
.60
94.
.0047
.66
.78
33.
002849
. 0060
.67
.80
178.
-.0027
.99
-.020574
.0005
-.002164
.0017
-.000663
-.002727
O
O
D
EN PRODUCTS
be W
< 12 )
b9 FURNITURE W
O
O
D
EN & M
ETAL
£1 PAPER
12 )
1 16 )
-.26
.00) -.61
< -1.09) -.61
-.4’ )
.2366 .OOC890
1.
.000633
-.0160
.87
.75
31.
F PAPER & PAPE
£2 ARUCLES O
(
16 )
-.27
< -.58) -.61
-.57)
.0001 .000520
1O
-.000520
.002 3
.97
.83
26.
.00
(
.00) -.61
.00) -1 .56
<
< -3.62) -1.12
-2.7!)
-2.15)
.0635 .009948
1.
-.009948
-.0033
1.00
.65
348.
.4801 .002347
1.
• 00*780
.95
.73
73.
-6.16)
.4412 .002910
1.
.003713
-.0199
-.0098
1.00
-.03
112.
(
-.26) -1 .53
.004024
.0033
.98
.68
288.
.CO) -1.53
-1.21)
-3.19)
•
(
-.1493 .004563
•
.000333
.0052
.002148
.0035
-.20
-.39
320.
1.
•
1.00
.99
-.000140
.0130
.85
.82
23.
.0039
.92
.90
51.
.0207
.91
.95
9.
.0085
.55
.91
143.
(
63 PRIMING & PUBLISHING
(
16 )
6b LEATHER PRODUCTS EX. F00
(
9 )
66 ARTICLES O
F RUEbER
*
70 BEDICIKE
< 13 > -.57
( 11 )
.00
7V O
THER CHEMICAL PRO
DUCTS
•oc
9 ) -2.35
.0266 .004379
DU i
to PETROLEUM REFINERY PRO
n
) -1.67
C-1.49) -1.93
-1.75)
-.2224 .034796
ei COAL PRODUCTS
f
10 ) -1.32
< -.86) -.46
-.33)
-.0050 .0C0140
Bb POTTERY
« 21 )
.CO) -.46
-2.05)
•
-.000934
-.000009
•
-.002562
07 0THIRNCN-METALL1C M
1NCRA
< 21 )
.OC
<
.00) -.71
-1.60)
-.0214 .000934
-.0401 .000009
ICO STRUCTURAL M
ETAL PRO
DUCT
< 12 )
.00
(
.00 ) -.46
-.13)
-.3231 .002562
.00
(
.00
•
.00) -.46
-.70)
-.0613 .002805
•
.000682
.0020
.96
.82
156.
< -.46) -.46
-.73)
•
.000060
.40
15.
-.99) -1 .46
-.6?)
•
-.nooooo
-.0093
.0246
.90
(
.0P52 .000358
-.C069 .O
O
G
O
O
O
.83
.72
1.
.00
(
.00) -.46
-.27)
-.0799 .002650
•
.004689
-.0005
.77
.59
123.
TNER M
ETAL PRO
DUCTS
1t1 O
< 1? )
1L4 INDUSTRIAL MACHINERY
1C6 O
FFICE M
ACHINERY
(
C 19 > -1.66
USEHOLD PACH1NERV
111/ HO
< 19 )
110
1 19 )
19 )
(
285.
-.20
.00
(
.00) -1.46
-.76)
-2.3058 .009605
•
-.009605
.0101
.92
.70
785.
THER W
EAK ELECTRICAL AP < 19 )
.00
111 O
AR
1U PASSENGER fORTCR C
( 14 ) -1.41
(
.CO) -1.46
C-1.63) -2.10
-.75)
•
1.
-.000213
.011064
.0104
-.0014
.92
-2.23)
-.0540 .000213
.0266 .004566
1.00
.70
.27
226.
11b REPAIR O
F PASSENGER M
O
TO (
(
household electrical mac
17.
.00) -2.10
-.50)
-.8726 .003731
1.
-.003731
.0098
.91
-.01
214.
116 M
OTORCYCLES 8 BICYCLES
< 14 ) -1.7*
< -.70) -2.10
-I.U4)
3.3940 .007564
1.
.066110
-.0967
-.08
.66
108.
1IV PR
CClS1O
N PACHINERY
C 1« ) -3.86
< -2.20) -2.10
-1 .43)
-.0234 .000272
1.
-.000272
.0071
.89
.71
23.
121) PHOTOGRAPHIC S OPTICAL I
< 19 )
.00
-.44)
-.126E .002341
1.
-.002341
.0043
.86
.93
112.
121 W
ATCHES fc CLO
CKS
C 19 )
n
)
.00
<
.00) -.70
-.53
C-1.35) -.70
-1.11)
.2062 .004274
1.
.002303
-.0089
.98
.27
135.
122 O
THER MANUFACTURING G
O
O
D < 19 ) -2.10
( -4.53) -1.95
-4.17)
.4266 .010906
1.
-.010906
-.0013
.99
.43
477.
120 ELECTRICITY
( -1.12) -.56
( -.09) -.46
-1 .V?»)
-.2192 .003876
•
-.003876
.0100
.99
.95
400.
-.h?)
.1952 .004535
1.
-.004509
-.0091
.93
.87
121.
129 G
AS
< 10 ) -1.90
10 } -.44
(
V
TA P I {
VI1-2(C0NT1NUID> .
Nt C t - f i S I O ^
KtiULTS
Cf
CONSUMPTI ON
FUNCT I ON
EC
TO
R
<b»oup)
3U UAl [fi-SUPPLT ,SEU£RAGE
(
11 )
.00
H
O
LESALE TR
AD
E
31 W
32 RETAIL TRADE
< 2i: )
-.50
(
2C )
.00
.00) -.67
-.56)
-2.3976 .076883
1.C
-.011631
.0018
2J FINANCIAL BUSINESS
(
2C. )
.00
.00) -1.67
-.2036 .013832
1.3
-.013U32
.0026
34 INSURANCE bUSlKESS
< 2C )
.00
.00) -1 .67
-.32)
-.34)
-.4295 .015725
1.3
-.015725
35 NEAL ESTATE AG
ENCY
36 KENT FO
N HO
USE
i
2C )
21 )
.00
.uo >-1.67
-.0775 .000001
.00
.00) -.67
-3.5667 .084610
.0
1.0
37 NATIONAL RAILROAD
< 15 >
.00
.00) -.70
.0388 .009907
3tt LOCAL RAILROAD
i
C 15 )
P1/P I
C(E1
-.oe
TIME
R
BARSO
C
O
N
STA
N rCOEF (ELAS) DELTA 1
PUG/Pb R
X 70PC
(T)
E
CCEF
.002649
.0074
1.00
-6.90)
.5
.00) -1.67
-.1260 .001651
• 00*9
.98
-.5?) -.67
-.21) -2.4760 .041357 1-0 -.041357
(I)
-.26) -.70
- . 3T)
-3.95)
- 2• 51)
-1.60)
.0296 .007483
R
H
O PCE70
2030
.99
.20
3778
.81
.79
799
.0027
.60
.80
902
-.000001
-.057957
.01P0
.0034
.91
.90
35
.96
.78
4546
1.2
.0037ei
-.0027
1.00
.13
398
1.2
.003991
-.0029
1.00
•03
301
.009679
-.0023
1.00
.11
938
3V R
O
AD PASSEK6ER TRANSPO
RT
< 15 )
.00
.00)
-1.78)
< 15 )
.00
.00 ) -.70
-.28)
-.1177 .023450
-.5726 .003891
1.2
O
AD FREIGHT TRANSPO
RT
*.U H
1.2
-.003891
.0088
.70
.96
206
41 fcO
AD TRANSPORTATION FAC1
< 15 )
.00)
0
•
1
152.
.78
0
•
1
.23
-.34)
-.1411 .000855
1.2
-.000855
.008 5
.85
.91
45
42 SEA TRANSPORT
< 15 ) -1 .29
-3.01) -1 .55
-2.03)
-.0008 .000020
1.2
.000038
.0009
.99
.25
1
43 INLAND W
ATER TRANSPORT
44 AIR TRANSPORT
1 15 )
-.1 '
-.42) -.70
-1.64)
.*7
75
-.30)
1.2
1.2
.99
-1.2E) -.70
-.001435
.00*598
-.0031
< 15 ) ~2 .87
.0766 .001945
.5456 .002114
-.0069
.96
.12
11*
45 O
THER TRANSPORT
46 STO
RAG
E
< 15 ) -1 .58
C 15 ) -1 .24
-11.91 )-1.55
-4.54)
1.2
-.00C040
.0038
1.00
.35
3
-1.87) -1 .50
-.0041 .000059
.0684 .001353
1.2
.000900
-.0057
.99
50
.00
-5.17) -.70
-2.67)
- •6’’ )
-.1084 .005230
1.4
-.001584
.0004
.97
.27
.37
.00
.00) -2.82
-2.23)
-.2241 .010031
1.C
.012958
-.0014
.97
.78
*2*
) -3.24
.00
2Q )
-2.78) - l .80
.00) -1.53
-3.?7)
- .8809 .039904
-2.34)
.0880 .009066
1.0
1.C
-.039904
.Q0C081
.0036
-.0007
1.00
.98
.40
.52
2103
392
-.14
-.2E) -1.53
-1.56)
-.0012 .000345
1.0
-.000093
.0004
1.00
.20
16
.00
.00) -1.53
-1.16)
-.5806 .019606
.7
-.019606
.0084
.78
.96
1306
.00
.00) -.57
.7
-.003301
.0069
.93
.89
1571
.00) -.57
-.55)
-.99)
-1.7331 .018229
.00
-1.4777 .072640
.7
-.019533
.0064
.98
.88
17*3
.00
.00) -.57
-1.03)
-.0039 .000098
1.0
-.000098
.0034
.96
.11
47 TELE
COliNUNICATIGN
(
4V EDUCATION
< IP )
*0 N
EDICAL.HEALTH SERVICE
SI O
THER PUBLIC SERVICES
C M
(
52 SERVICE FO
R eUSlNESS EN
T
< 2C )
53 AM
U
SEBENT
54 R
ESTAURANT
< 21 )
(
6 )
5b O
THER PERSONAL SERVICES
(
2C )
56 N
O
T CLASSIFIED
< 21 )
15 ) <3.84
2*1
S
103
Since the savings function is the counterpart of the m
a
cro
consum
ption function, m
acroeconom
ic considerations are appropriate
for it.
T
h
e perm
anent incom
e hypothesis has explained consum
ption
a
s a function of perm
anent incom
e, w
hich is m
easured a
s aw
eighted
average of past incom
e.
T
h
e determ
inant of savings in that hypothesis
is transitory incom
e, w
hich is the g
ap betw
een current incom
ea
n
d
perm
anent incom
e.
S
avings is not a decision variable; it is a
residual in that hypothesis.
That hypothesis can b
e valid only if by "consum
ption" w
e
accept its definition of consum
ption.
T
h
e definition includes only
consum
ption of services of consum
er goods.
It is not w
hat the
national accounts m
easure as consum
er expenditure.
This concept of
pure consum
ption is not observable a
n
d is im
possible to quantify.
C
onsum
ption in the m
odel presented here is not pure consum
ption of
services of consum
er goods, but consum
er expenditure.
T
h
e conceptual
discrepancy betw
een pure consum
ption a
n
d consum
er expenditures is
inventory adjustm
ent.*
Certainly, the inventory adjustm
ent com
ponent in consum
er ex­
penditure is related to transitory incom
e.
Therefore, if w
e use only
perm
anent incom
e in the consum
er expenditure equation, w
ewill get
biased estim
ates due to the om
itted variable.
*D
arby, M
.R
. "Postw
ar U
.S
. C
onsum
ption, C
o
n
su
m
e
r Expenditures,
a
n
d Saving." A.E.R
. M
a
y, 1975. p
p 217-222.
104
S
ince consum
er expenditure is a function of perm
anent a
n
d
transitory incom
e, the opposite side of consum
er expenditure, savings,
is also a function of perm
enent a
nd transitory incom
e.
It is n
o longer
just a residual w
hich is determ
ined only by transitory incom
e.
T
h
e form
al regression equation is a
s follows:
(i) S
t = aD+ a
xY
+a
2 Y
T t + a3 R
£
w
here
S
t = saving per capita.
Y
p = perm
anent incom
e per capita.
Yrj, = transitory incom
e per capita.
R
t = real interest rate.
F
or empirical purposes, perm
anent incom
e has been com
puted a
s
(2) Y
pt -BYt + (1 - 6 ) Y
p t-1
w
here 3is the adjustm
ent coefficient, a
n
d Y is current incom
e.
S
ince w
ed
o not have a
n infinite num
ber of observations, w
e need
an estim
ate of the initial value, Y .
7 p
o
fromthe incom
e trend regression.
Log Y
t * r
then
Y = e X1
p
o
+ r2t + ut
T
h
e initial value ca
n be taken
105
T
h
e adjustm
ent coefficient, 6 , is chosen by the scanning
m
ethod.
is calculated by substraction of the expected rate of
inflation, w
hich is a w
eighted s
u
mof past inflation using the s
a
m
e
weights as in the investm
ent equation^" from the nom
inal interest
rate.
Transitory incom
e is sim
ply current incom
em
inus perm
anent
incom
e.
T
h
e regression result is
S= -15.5261 + 0.1929
(-3.589)
P
+ 0.331 Y
m+ 0.701 R
T
(3.777)
(3.839)
(2.025)
R
2 = 0.992
D
.W
. = 1.548
3 = 0.15
T
h
e regression result sh
o
w
s a very stable savings-incom
e relation.
All independent variables are significantly different from zero.
B
oth perm
anent incom
ea
nd transitory incom
e have positive signs, a
s
w
e expected.
T
h
em
agnitude of the coefficients are quite reasonable.
T
h
e equation says that the Japanese save about 1
9
%of their perm
anent
incom
ea
n
d3
3
%of their transitory incom
e.
T
h
e bigger coefficient of
transitory incom
e than that of perm
anent incom
e corresponds to our
expectation.
A
s the perm
anent incom
e hypothesis states, saving is
m
ore influenced by transitory incom
e than perm
anent incom
e.
A
s the
real interest rate increases by one percentage point, saving increases
by seven hundred yen per person.
^S
ee p
a
g
e1
3
0 of this report.
106
Adding-up P
roblem
B
y definition, consum
ption plus savings is total disposable
incom
e in current prices.
(3 )
i pi t
c i t + ? t st E
• Yt
B
ut param
eters estim
ated without consideration of the constraint d
o
not necessarily satisfy the budget constraint in forecasting.
E
ve
n
in estimation, it is not u
n
c
o
m
m
o
n to get
i
pi t
c i t
+
p t
st
*
pt
\
a
w
here
is a predicted value of the estim
ated consum
ption equation,
This is because
pi t
ci t - pi t
• c i t + Ei t and
Ei t * 0
H
ow
ever, in estimation, w
em
inim
ize the s
u
mof squared residuals.
Therefore, w
em
a
y think that the budget constraint is m
ore or less
satisfied.
In forecasting, the adding-up problem could be serious.
According to the author1
s experience, the total consum
ption in 1
9
8
5
forecasted by double log form equation exceeds the disposable incom
e
in 1
9
8
5 by 3
0
%
. T
h
e double log formhas m
ore serious adding-up
problem
s than the formw
e are n
o
wusing.
N
onetheless, in order to
forecast consistent consum
ption expenditures, w
e need a
n adjustm
ent
procedure.
In order to forecast consum
ption, w
e have to kn
o
wall the
variables in right hand side of the equation*
and prices of each sector are know
n.
Incom
e, tim
e trend
B
ut the weights w
hich m
ust be
107
used in consum
er price index calculation a
n
d group price index cal­
culation are not know
n.
Therefore, assum
ing that com
position of
weights within group is constant, w
e ca
n define Psuch that P
guarantees the budget constraint.
(3) I P
. C (P ) + P
.
i it
it
t
t
M
o
re formally,
S= P Y
t
t t
In order to forecast consum
ption, the N
ew
ton’s algorithm is em
ployed.
W
e start to calculate consum
ption with an initial value of P
^.
O
n
ce
*
w
e get
for all com
m
odities, w
e calculate the necessary change of
P
t using the first derivation of total consum
ption with respect to
P
^.
T
h
e new
ly calculated P
^ is used in the next iteration to get n
e
w
consum
ption expenditures.
Three or four iterations are e
no
u
gh to
satisfy the budget constraint with .001 tolerance level.
Another reason to use a priori information on the group price
elasticities is that w
e solve the adding-up problem through the group
price elasticities.
W
h
e
nw
e estim
ate the consum
ption equation with­
out the group price information, s
o
m
e of
turned out to be zero.
If those are zero, the consum
ption forecast of those sectors are
not affected in the adding-up adjustm
ent procedure.
It is exam
ined w
hether the calculated P
t changes radically.
If
the calculated P
t jum
ps at the starting year of forecast, it m
a
y
indicate that there m
ust b
ea
n inconsistency betw
een the estim
ation
of consum
ption a
n
d the forecasts of consum
ption.
Fortunately, the
calculated P
t *s sh
o
wa sm
ooth curve, as it is sh
o
w
n in Figure VII-1.
T
he consum
er price index calculated with the constant weights using
1970 P
C
Eis also sh
o
w
n in Figure VII-1.
108
F ig u re V I I - 1
Com parison o f C P I’ s
C
P
I
0.1
1970 7
1
7
2
7
3
7
4 7
5
7
6
------------ constant w
eights
- ----- - variable weights
(p )
7
7 7
8 7
9
8
0
8
1 8
2 8
3
8
4
8
5
CHAPTER V I I I
IN
V
E
S
T
M
E
N
T
Introduction
T
h
e necessary concomitant of the rapid econom
ic grow
th in Japan
has been an investm
ent rate unusually high com
pared to other countries.
T
h
e ratio of investm
ent to total final d
e
m
a
n
dw
a
s3
4
%
, w
hich am
ounted
to 26,257 billion yen in 1970.
T
h
e investm
ent equation is im
portant
in the U
.S.A. m
odel because investm
ent is very volatile a
n
d it is very
sensitive to cyclical econom
ic m
ovem
ent.
B
ut in the Japanese m
odel,
investm
ent is im
portant not only because of its variation but also be­
cause of its m
agnitude.
T
h
e Japanese gross fixed capital form
ation consists of four m
ain
com
ponents:
1 . 20 sectors of private industry investm
ent
2. H
ousing construction
3. G
overnm
ent business type investm
ent
4. S
e
ve
n sectors of governm
ent social overhead capital form
ation.
Various theories and estimation results for (1) a
nd (2) will be dis­
cussed in the following sections.
T
w
o kinds of investm
ent equations
are form
ulated, a
n
d housing investm
ent will be treated differently
from other industry investm
ent.
All types of governm
ent capital
form
ation will be given exogenously.
110
The T h e o ry o f th e In v e s tm e n t E q u a tio n s o f th e P r iv a t e S e c to r
Investm
ent behavior has been investigated in tw
o steps:
deter­
m
ination of optim
al capital stock a
n
d sp
e
e
d of adjustm
ent of the g
a
p
betw
een actual capital stock a
n
d desired capital stock.
According to
neoclassical investm
ent theory, w
e can derive the optim
al capital stock
from the production function with the assum
ption of firms1 profit m
axi­
m
ization behavior.
Various distributed lag system
s have been developed
to investigate the speed of adjustm
ent.
AC
.E.S. production function is utilized for this m
odel with labor
augm
enting technological change.
Also, constant returns to scale are
a
ssu
m
e
d in the production function.
S
o
m
e other studies, such a
s
Saito’s,^ use the C
obb-D
ouglas production function a
n
d Hicksian neutral
technological change in a Japanese econom
etric m
odel.
T
h
e restriction
of unitary elasticity of substitution, how
ever, is not only unnecessary
but too restricted for disaggregated m
odels like this.
Hicksian neutral
technical change tells h
o
wthe production function shifts over tim
e.
A
s
it w
a
s described in the labor requirem
ent chapter, w
e are interested in
the labor productivity change over tim
e.
Therefore, w
ew
ould rather use
labor augm
enting technological change.
T
he production function w
a
s described in the labor requirem
ent
equation.
For convenience, w
e can rewrite the function without expla­
nation of the variables.
(1 )
Qt
= 6 [a x K "p
+ a2
( g O O D -*
+ a
M- 0
]
-
^
^Saito, M
. "A G
eneral Equilibrium Analysis of Prices a
nd O
utputs
in Japan." 1953-1965. in T
he W
orkings of Econom
etric M
odels, ed. by
M
. M
orishim
a. C
am
bridge, 1972. pp 147-242.
After solving the production function for K
, w
e can get the
optim
al capital stock by equating the m
arginal productivity of capital
to the rental rate.
T
h
e expression for the optim
al capital stock is:
(2) K
* = cR
~
°Q
w
here
c=
w
hich is constant
R= rental rate
Q* output
a * elasticity of substitution
T
h
e next step is to determ
ine the speed of adjustm
ent of the
actual capital stock to the optim
al stock.
theory into investm
ent theory.
This step converts capital
Investm
ent is a
ssu
m
e
d to be determ
ined
by a w
eighted distributed lag of change of optim
al capital stock a
n
d by
replacem
ent.
(3) 1° =
A
K
t*± + «t
w
here
n
I£ = gross investm
ent
6
■ depreciation rate
w
^ = weight of distributed lag
K
= actual capital stock at tim
e t.
T
h
e actual capital stock,depreciation rate and rental rate, will be
discussed in later sections.
investm
ent, w
e get,
Substracting replacem
ent from gross
112
(4>
w
here I
N
t
> ? ■
J o
Wl
A K t - i
= net investm
ent,
T
he K
oyck lag systemis em
ployed with tw
o assum
ptions:
1 . the su
mof the weights is unity.
2 . after the first tw
o periods all consecutive weights are d
e
­
clining geometrically, at the rate X .
M
ore formally, these assum
ptions can be expressed by
(5 ) 1^ = w
QA
k£
+ w^ X^
+ w
1 A Kt * x + w
2 X AKt * 2
AK^ ^
+ . . . . . . +
+ w
.^ X2 A Kt * 3
ut
w
here
W1A * w2
,2
wx X
_
* w^
w
, X
1*-1 = w
n
i l l
Wi
=
1
ut = disturbance term
.
Equation (5) has a
n infinite tail.
C
onsidering the tail, w
e can re­
write it without the disturbance term a
s follows:
N
*
i-1
*
»
(5') l “ = W
DA
K
t + w l£l X
AK^i + w
x i£t
i- i
X
*
AK^
113
The l a s t te rm o f th e e q u a tio n
( 5 T) can be re -e x p re s s e d as
Therefore, w
e could have the regression equation from (5*) a
s follows:
All param
eters, n , w
Q
, w
^, a
n
d A could be estim
ated by nonlinear
iterative m
ethod.
Unfortunately, the results of the regression o
n this equation
w
ere not good.
S
o
m
e of the coefficients o
n the first a
n
d second term
had a negative sign, w
hich is not reasonably interpretable.
delete the first termw
hich has negative sign.
W
e could
B
ut the second term
cannot be deleted because if it is deleted the last term is also
m
eaningless.
Therefore, the equation is reform
ulated as follows:
Let
and
i=o
t-i
I
i=o
t-i
=x*
i
*
A A
K
.
t-i
1 =X
t- 1
1
T
hen the equation (6 ) can be written a
s
(6 f)
1^ ■w
QX
t +
(w-^-WqA) x t - 1
+ X1 n0 + ut
T
he equation (6 f) allows negative sign o
n the coefficient of the second
term
.
T
h
e negative sign o
n the second coefficient sim
ply says that the
114
lag weight at period 1 declines m
o
re than by the geom
etric declining
factor.
For regression a
n
d forecast, the independent variable matrix
it
is easily generated by the relation, X
t *
=A
K
t
+ X ^t-i*
Therefore,
w
e can save the com
puter space by storing only the value of Xof the
previous year.
T
h
e regression equation (6 *) sh
o
w
s that X cannot be estim
ated by
the ordinary least square m
ethod.
O
n
ew
a
y out of this problem is to
use the m
a
xim
u
mlikelihood m
ethod, a non-linear iterative search pro­
cedure.
W
e can search for the value of X , lying betw
een zero a
n
d
unity w
hich gives the sm
allest s
u
mof squared residuals.
-c
*
If w
e substitute cK Qfor K
., w
e notice that there is another
non-linear param
eter to be estim
ated.
T
h
e estimation procedure is
seeking for a com
bination of X a
nda w
hich gives the m
a
xim
u
mlikeli­
hood over all possible com
binations.
Figure VIII-1.
T
w
oD
im
ensional Searching P
rocedure
115
T
h
e tw
o dim
ensional search procedure starts with s
o
m
e fixed
elasticity of substitution, for exam
ple, with fixed a
. = 0.5.
search for the X
W
e
w
hich gives the m
in
im
ums
u
mof squared residuals.
After w
e get a
n estim
ate of \ t w
e search for the a with fixed X.
This procedure is continued until Xa
n
d o converge to s
o
m
e value a
0
and a0.
Actually, those values converge very fast.
iterations are enough to find a stable Xa
n
do .
Three or four
In the search pro­
cedure, c is a
ssu
m
e
d to be bounded by zero a
n
d 2.
T
h
e results of the estim
ations are sh
o
w
n in Table VIII-1.
B
y
all of the standard criteria, the investm
ent hypothesis perform
s well
except for three sectors.
For these, a
n alternative investm
ent form
u­
lation w
hich will be described in the next section is tried.
G
o
o
d
n
e
ss of fit is high e
no
u
gh to produce a reasonable forecast.
Alm
ost all of the sectors have a
n R greater than 0.95.
have a
nR
^ around 0.8.
factory.
A few sectors
T
h
eD
urbin-W
atson statistics are all satis­
For so
m
e sectors, w
e delete the first term in the regression
equation (6 ).
In that case, the weight of the current year is zero,
and the lag weight begins in the (t-l)st period, declining geom
etric­
ally.
All of the lag weights can be calculated by using the coeffi­
cients of the regression equation a
n
d the constraint Zw
^ - 1.
of the distributed lag coefficients are positive.
All
Also, the pattern
of the lag se
e
m
s to be reasonable except for a few sectors w
hich have
a very slowly declining lag system
.
reasonably high x •
sectors.
For those sectors, w
e got un­
Therefore, w
e constrained Aby 0.9 for those
T
he estim
ates of the elasticity of substitution are generally
less than unity, w
hich corresponds to the general results of other
studies.
116
T
A
B
L
EVII1-1.
Industry N
a
m
e
IN
V
E
S
T
M
E
N
TE
Q
U
A
T
IO
NR
E
G
R
E
S
S
IO
NR
E
S
U
L
T
S
a
A
R
2
D
.W
.
C
oef 2
C
oef 3
0.594
22.799
19.063
0.324
0.115
0.927
0.9581
2.1863
0.334
2.017
159.027
5.811
0.650
0.900
0.9118
1.5745
1.111
4. Textile
0.291
2.797
0.059
0.538
-48.633
-1.632
0.450
0.936
0.8895
1.9657
5
. P
ulp a
n
dP
aper
0.255
3.296
0.382
4.684
103.201
3.421
0.451
0.612
0.9534
2.5390
7. P
rim
ary M
etals
0.277
4.151
0.461
6.464
390.068
2.424
0.329
0.605
0.9567
1.3444
8. M
etal P
roducts
0.293
2.851
0.360
3.264
70.031
3.014
0.450
0.681
0.9723
1.5223
0.218
10.743
0.082
3.875
101.785
5.320
0.379
0.718
0.9828
2.5785
10 . Electrical M
achinery
0.180
5.206
0.034
0.933
491.727
6.349
0.195
0.596
0.8784
1.4545
11 . Transportation E
quipm
ent
0.315
1.759
0.283
1.462
392.528
1.845
0.276
0.554
0.8691
1.5834
12 . M
iscellaneous M
anufacture
0.791
37.372
390.444
3.621
0.420
0.675
0.9697
1.3962
13. Construction
0.093
16.688
39.752
1.008
0.100
0.900
0.9333
0.8937
C
oef 1
1 . Agriculture, Forestry
a
n
d Fishery
3. F
o
o
d
sa
n
dT
obacco
9. Non-electrical M
achinery
0.164
117
TABLE V III- 1 .
Industry N
a
m
e
14* Electricity, G
a
sa
n
d
W
ater S
upply
C
oef 3
R
2
D
.W
.
0.845
0.9740
i.7892
0.138
0.900
0.9453
1.7199
C
oef 1
C
oef 2
1.025
3.441
0.457
1.324
368.079
8.874
0.384
0.237
19.577
35.424
1.214
16. R
eal Estate
t
CONTINUED
o
A
17. Transport &C
om
m
unication
0.415
3.988
-0.097
-0.866
53.196
1.096
0.051
0.845
0.9786
1.6377
18. Finance a
nd Insurance
0.003
0.069
0.150
2.608
120.756
9.775
0.264
0.896
0.9022
1.6158
19. O
ther Services
0.068
0.601
0.230
1.788
146.114
2.369
0.311
0.900
0.9680
1.4016
118
A lte r n a tiv e
In v e s tm e n t E q u a tio n F o rm u la tio n
T
h
e accuracy of capital stock information m
a
y affect the perfor­
m
a
n
ce of the investm
ent equation in the previous section.
T
h
e dependent
variable of that regression equation is net investm
ent, w
hich is derived
by subtracting replacem
ent from gross investm
ent.
If the capital stock
estim
ation or the depreciation rate estim
ation is not accurate, the de­
pendent variable can be affected very m
u
ch
,
because the dependent
variable is m
a
d
e by subtracting the calculated replacem
ent from the
gross investm
ent.
Fortunately, the formulation of the previous section perform
s
pretty well except in the following three sectors:
1. M
ining
2. C
hem
ical m
anufacturing, a
n
d
3. W
holesale a
n
d retail trade.
It can be believed that the capital stock information for those sectors
is not accurate.
T
he unreliability of capital stock information a
n
d
the continuous bad perform
ance of the chem
ical m
anufacturing industry
equation require another formulation of the investm
ent equation w
hich
does not need the capital stock information.
In the alternative formulation of the investm
ent equation, capital
stock is going to be estim
ated in the regression process, rather than
using the given historical data of capital stock.
T
h
e capital stock
estimation m
ethod, the tw
o bucket reservoir system
, will be described
in the next section.
T
h
e idea involved in this n
e
w formulation is
based o
n the tw
o bucket reservoir systemof capital stock.
119
Let us say that there w
a
s capital stock S
Qin the initial year
a
n
d the ratio of the first class capital stock to the total capital
stock in the initial year is a.
T
h
e
n the first class capital stock
in year t is,
(1) sl f t = a s0 a-sf + Hi I t . i ( l- a ) 1
w
here 6 = depreciation rate.
T
h
e first term stands for the rem
nants from the intital first class
capital stock at tim
e t.
T
h
e second term stands for the increase in
capital stock d
ue to the investm
ent It since the initial year, s
o
m
e
part of w
hich w
a
s depreciated by 6 each year.
T
he am
o
un
t of depre­
ciation in the first class capital stock will be added to the second
class capital stock.
T
h
e second class capital stock in year t can be expressed a
s
follows:
(2) S
2>t * b
S
0 (1-5)* + t a S
0 (l- 6 )t ” 1 $+6^
i (l-5) i ” 1
It_±
w
here b = 1 - a.
T
he first term is the rem
nant of the second class capital stock of the
initial year at tim
e t.
T
h
e second term is the rem
aining part of the
capital stock w
hich ca
m
e from the first term of the first class capital
stock equation (1).
Similarly, the third term is the rem
aining part of
120
the capital stock w
hich ca
m
e fromthe second term of the first capital
stock equation.^
N
o
wthe actual capital stock at year t is the s
u
mof these tw
o
bucket capital stocks.
t
*
S,
. +S
o
2 ,t
t-1
_•
=aS
Q( I - ® * + ±l Q It- i (1-fi)
i (1-5) 1 -1
+
r
+bSG(1- 6)
i
+ t a SQc { l -
It _ 1
R
earranging the equation,
t
(3) S « S
0 (1- 6)
t"1
+ 6±l
t-1
+t aS
c 6(1- 6)
+ I
i=o
I
. (1-6) 1
i-1
i (1- 6)
1 It-i
T
he formof the equation can be explained by the inductive
m
ethod. That is not a real equation but a
n identity following defi­
nitions in the tw
o bucket reservoir systemof capital.
T
he reason w
h
yw
e have the t factor in the second termm
a
y not be
clear at first glance. T
he capital stock w
hich has existed fromthe
initial year w
a
s continuously discounted by the factor, (i -<
$ ), w
hether
it is in the first class bucket or in the second bucket. Intuitively,
at tim
e t there have been flows of the initial capital stock from the
first class bucket to the second class bucket t tim
es. W
hether it c
a
m
e
earlier to the second class bucket or later does not affect the form of
S
Q(i - 6 ). B
ecause it is depreciated by (1 - 6 ) each year w
hether it
w
a
s in the first bucket or in the second class bucket. T
h
e factor i in
the third termcan be understood the s
a
m
ew
ay. T
he new
ly invested
capital stock at tim
e t - i has flowed over to the second class bucket
i tim
es a
nd it has depreciated by i - 1 tim
es w
hether it ca
m
e to the
second class bucket earlier or later.
121
T
h
e optim
al capital stock in this formulation has the s
a
m
e form
K
* = cR
~
°Q
.
T
h
en
e
w formulation a
ssu
m
e
s that gross investm
ent at tim
e
t is s
o
m
e fraction of the g
a
p betw
een the desired capital stock a
n
d the
actual capital stock.
J
(4) I®= 8(K
*- S
t)
Substituting (3) into (4), a
nd adding a constant term
, y , the alterna­
tive formulation looks like
t-1
(5) I? = >+ 8K
* - 6S (l-d)* -g S
. a t 6 (1-6)
t
o
°
(l- ® 1 I°_±
- 66 ^
i (1 - 6)1 -1 I^_i
After rearranging this equation, w
ee
n
du
p with the final re­
gression equation:
(6 )
I® -■ Y +
t
ecR^Q -
t
t
°
V , - 6 V
2
w
here
V
1 = (1- 6)11 + a t 6(1 - 6 )t " 1
v2 “
s i
a ~ 6 )i
zt - i - 6 ± s i 1 ( i * 5 ) 1 - 1 4 - i
This equation allows u
s to indentify y, 3 , c, a
n
dS
Q
, from the re­
gression coefficients, with the assum
ption of a
n appropriate value
122
for a.'*’
a is gotten by the iterative scanning m
ethod.
This form of
the equation has a
n advantage in com
puting the regression a
n
d in fore­
casting.
W
ed
o not have to store all the historical values of the
actual capital stock.
T
h
e information w
e have to store is current
investm
ent a
n
d the value of each term of the equation.
Therefore, w
e
ca
n save a lot of com
puter tim
ea
n
d space.
T
h
e regression results of the three sectors with the alternative
investm
ent formulation are very good.
W
h
e
nw
e apply equation (6 *) o
n
page 113 to the m
ining sector w
e get a very low R
^, 0.28.
B
ut with
2
the alternative formulation R is 0.874, despite tw
o insignificant t
statistics.
T
h
e R ’s in the other tw
o sectors are also high, a
n
d all
coefficients are significantly different from zero.
T
h
e signs of the
coefficients are all correct a
n
d the m
agnitude of the coefficients are
all reasonable.
M
ining has a slow adjustm
ent rate of desired to
actual capital stock, while
fast adjustm
ent rates.
C
hem
icals a
nd
Trade have relatively
Also, the autocorrelation problem
s are not
serious.
T
h
e regression results of these three sectors are:
M
ining
I®= 229.2 + 0.19 D
K- 203.1 V
x - 0.057 V
(2.68)
(0.33)
(-1.69)
(-0.24)
R
2 = 0.874
D
.W
. = 1.28
^T
he value of a will be explained in the capital stock section.
"a11 can also be estim
ated in this equation by regression, but it
causes loss of another degree of freedom
.
123
rate of adjustm
ent (£ ) = 0.0566
depreciation rate (6 ) = 0.21
o= 0.346
C
hem
ical Products
1^ = 622.9 + 0.334 D
K- 743.4
(1.71)
(4.20)
(-1.96)
- 0.39 V
2
(-3.49)
R
2 = 0.928
D
.W
. = 1.42
e= 0.39
0 = 0.13
o = 0.006
W
holesale a
n
d Retail Trade
I® = 551.6 + 0.283 D
K- 758.5
(1.81)
(3.04)
(-1.92)
- 0.311 V
^
(-1.64)
R
2 = 0.992
D
.W
. = 1.57
3 = 0.31
6
=
0.10
o « 0.120
w
here
D
K =R
~
aQ
.
vx = (1- 6 )* + b t 6 (1
^5)t-;L
V = t-l
i=o
(w )i rG _ { t-1 ±
1
jG
t” 1
124
Capital S
tock
E
ve
n though the historical capital stock data by tw
enty indus­
tries are available, they are re-estim
ated by the tw
o bucket reservoir
system
,^ because w
ew
ant the capital stock w
hich represents the pro­
ductive capacity rather than the book value of the stock.
Also, for
forecasting, w
e need the depreciation rate for the future, w
hich
m
ust be estim
ated by using the historical capital stock a
n
d the re­
placem
ent data.
O
n
ce w
e estim
ate the depreciation rate, w
hich has a
functional form
, the capital stock series a
n
d gross investm
ent a
n
d
net investm
ent data should be consistent with that depreciation rate.
Therefore, it is inevitable that w
em
ust recalculate the capital stock
data.
T
hose recalculated capital stock a
n
d the depreciation rate w
ere
used in the estimation of the investm
ent equations.
T
he tw
o classes of capital stock are
Ki , t ■
+ vt
-
*2.t ■ *2.t-l + 6
t
- £
t K
2 ,t- 1
w
here
V = gross investm
ent
6t * depreciation rate.
Total capital stock at tim
e t is
K
t
= K,
. + K
T-,t
2 ,t
^A
lm
on, C
. et al. 1985: Interindustry Forecasts of the A
m
erican
E
co
n
o
m
y. Lexington B
ooks, 1974. Lexington, p
p 67-71.
Notice that the information w
e need to calculate the capital
stock series is the capital stock of the initial year, the ratio of
the first class capital stock to the total capital stock in the
initial year, gross investm
ent series, a
n
d the depreciation rate.
this information, w
e rely o
n the existing capital stock data.
the capital stock value in 1
9
5
4 as the initial stock value.
For
W
e use
T
h
e error
in the initial year capital stock estim
ate is not very im
portant, be­
cause m
ost of the variation in the data series will be caused by the
investm
ent data, w
hich is actually used to generate the capital stock
series.
T
he various ratios of the first class capital stock to the total
capital stock in the initial year w
ere tried.
0 .6 is chosen as the
ratio because it gives the best fit for the depreciation equation w
hich
will be described later.
If the e
co
n
o
m
y is in equilibrium, the ratio
of first class capital stock to total capital stock is 0.5.
C
onsider­
ing that in 1
9
5
4 the Japanese e
co
n
o
m
yw
a
s not in a
n equilibrium
situation, the ratio, 0 .6 is probably appropriate.
T
h
e depreciation rate is calculated by using the historical
capital stock a
nd replacem
ent. G
ross investm
ent is net increase in
capital stock plus replacem
ent.
For forecasting purposes, w
ea
ssu
m
e
that the depreciation rate is so
m
e function of tim
e.
T
he following
figure sh
o
w
s an appropriate shape for the depreciation rate in alm
ost
all the industries.
R
eplacem
ent requirem
ents are determ
ined by losses in efficiency
of existing durable goods as well as actual physical disappearance or
retirement of capital goods.
126
6
Figure VIII-2
Depreciation R
ate S
chedule
T
h
e Japanese e
co
n
o
m
y has experienced rapid grow
th w
hich w
a
s
possible only through a rapid increase in the capital stock.
There­
fore, w
e postulate that as the e
co
n
o
m
y grow
s, the relative efficiency
of the old capital stock with its old technology goes d
o
w
n
.
H
ence,
the replacem
ent requirem
ent rate is grow
ing until the e
co
n
o
m
y reaches
the advanced situation.
After that, the depreciation rate rem
ains
constant.
For this kind of curve, w
e could use the following function:
w
here
t
= tim
e
127
<
$
t = depreciation rate at tim
et
c,v,w = constants.
A
s t increases, the depreciation rate approaches v asymptotically.
A
s
c appears in nonlinear form
, several iterative regressions w
ere d
o
n
e
to pick u
p the best c.
For simplicity 0.1 is chosen a
s c for all
industry depreciation functions.
industries
H
ow
ever, a different c for different
does not im
prove the regression very m
u
ch
.
va
n
d ware estim
ated by the ordinary least square m
ethod with
the kn
o
w
n value of c.
A
s expected, the sign of the coefficient turned
out to be negative for all sectors but one.
w
ater supply, wis negative.
In Electricity, gas, a
n
d
If -w is greater than zero, the
curve is d
o
w
n
w
a
rd sloping tow
ard a
n asym
ptotic line.
Rental R
ate
T
he rental rate is the s
a
m
e concept a
s Jorgenson’s* user cost
of capital, except that w
ea
ssu
m
e a no-tax-econom
y.
According to
Jorgenson’s basic theory, the firm’s object is to choose gross in­
vestm
ent at all points in tim
e so as to m
axim
ize the present dis­
counted value of its net cash inflow.
This ca
n be expressed a
s
(1) M
a
x J" (p
Q- w
L - ql - p
M
)e ^
dt
^Jorgenson, D
.W
. Capital Theory a
n
d Investm
ent Behavior.
53, 1963.
A
E
R
.
Jorgenson, D
.W
. Anticipations a
n
d Investm
ent Behavior. In J.S.
D
usenbery, G
, F
row
n, L.R. Klein, and E
. K
uh, eds. T
h
e Brookings
Quarterly E
conom
etric M
odel of the United States. A
m
sterdam
, NorthHolland.
128
w
here
I = Kj + K 2
w= w
a
g
e rate
p = price of output
q = price of capital g
o
o
d
s
r = interest rate
u = expected rate of increase of prices
<
$* depreciation rate.
M= materials
T
h
e necessary condition for a m
a
xim
u
mof (1) with respect to
capital is
(2)
iS =Si (6f r - u)
3
1
P
Therefore, the rental rate in this investm
ent study is defined by
equation (2 ) following the m
arginal productivity principle.
N
o
ww
e need a
n explanation of each com
ponent of the rental rate.
Price of output in investm
ent study is usually value added price.
A
s
m
entioned before, w
e use price of gross output rather than value a
d
d
e
d
price.
1
B
ecause w
e have 1
5
6 sector price series for output, w
e have to
aggregate to the tw
enty sector classification level.
T
h
e output of
each industry by the 1
56 sector classification is used as the weight
^S
ee C
hapter IV.
Labor R
equirem
ent.
129
for that industry in determ
ining the price of the output by tw
enty
sector classification.
n 20 _
pi
-
„
1
5
6
' . z w«
pj
156
w
here
Q
7
w« ■
j Q |f
p2^ * price of the i**1output by 2
0 sector classification.
P^j^ " P
ri ce °f the j**1output by 1
56 sector classification.
^ ij * outP
ut
t^e
industry by 1
56 sector classification,
w
hich belongs to the i**1industry by 2
0 sector classifi­
cation.
n£ =set of industries belonging to the i ^
industry by 2
0 sector
classification.
T
h
e prices of capital goods are derived by using the Bmatrix.
1
3
6
1
5
6
b.. p
51
J1 j
q •= J
4i
For nom
inal interest rate, w
e use the loan rate of com
m
ercial
banks.^ T
he expected inflation rate is taken to be a sim
ple w
eighted
su
mof past inflation rates.
3
u = ± l0
wi
(Apt - i 1
S
e
eA
ppendix 1 for data description.
130
T
h
e weight systemem
ployed is
w
c = .4,
= .3, w
2 = .2, w
3 = .1
T
he physical depreciation rate is explained in the capital stock section.
H
ousing Construction
T
h
ea
m
o
u
n
t of spending o
n housing construction is quite high, a
n
d
the nature of investm
ent in housing is different fromother investm
ent,
so it is necessary to form
ulate a separate equation for this sector.
Like a usual investm
ent equation, housing investm
ent will be explained
by tw
o steps: (1) optim
al stock determ
ination and, (2) adjustm
ent of
optim
al stock to actual stock.
T
h
e desired housing stock has been ex­
plained by a
n incom
e variable, a relative price variable, and financial
m
arket conditions.
All of these three variables w
ere tried but only
disposable incom
eh
ad the right sign, a
n
d it dom
inated the regression.
Relative price a
n
d the interest rate sh
o
w
e
d the w
rong sign a
n
dw
ere
insignificant.
Therefore, w
e sim
ply a
ssu
m
e that the desired housing
stock is a function of disposable incom
e.
T
h
e actual stock is calculated by the IN
F
O
R
U
Mm
ethod:
(1) S, t
1=0
<1 - i ) 1 I t . i
+ S0 (1 -6 ) t
w
here
t = time, t
1.
5 = initial stock
o
6 = depreciation rate
It ■ n
e
whousing investm
ent at tim
e t.
131
For the adjustm
ent procedure, w
ea
ssu
m
e that the housing investm
ent
in year t + 1 is s
o
m
e fraction a of the g
a
p betw
een the desired a
n
d
the actual stock at the e
n
d of year t.
S
o, the equation is
(2) It + i - a[ PY
t+1 - S
t]
w
here
Y
t - disposable incom
e.
B
ecause the decision unit for housing investm
ent is the house­
hold, w
e divide all the variables by thenum
ber of households.
Finally,
our regression equation is
(3) (i)
-atP (|)
" (#
> 1
Ht+1
Ht+1
Ht
Substituting (1) into (3), w
e get
(*)(£)
=a[ g(| )
- ‘ I 1 (1-6 )i (I)
- ( f)
(1-5 )«
=
]
Ht+1
Ht+1
1
=
0
Ht-i
H0
B
ecause 6 is unknow
n, w
e should estim
ate this equation with a search
procedure over reasonable values of 6 .
T
he best regression result
is
<s>t =
’ -015 i (5.398)
w
here
6
=
0.02
R
2 = 0.993
D
.W
. « 1.164.
(.608)
(1_4
'
- 052 (1_6 } t
(3.092)
132
E
ve
n though it has a
n insignificant coefficient, all signs are
2
correct a
n
d the R is very high.
existence of autocorrelation.
T
he D
.W
. statistic indicates the
T
he R
H
Oadjustm
ent procedure will be
perform
ed for autocorrelation correction in forecasting.
P
er household housing investm
ent is converted to total housing
investm
ent.
2
D
u
e to the high R in the per household regression, the
total housing investm
ent sh
o
w
s very g
o
o
d fit.
133
CHAPTER IX
T ra d e E q u a tio n s
A
sm
entioned in the introduction, this m
odel is designed to b
e
linked to the W
orld Trade M
odel.
T
h
e connection betw
een the trade
m
odel a
n
d the national m
odels will b
e through the trade equations.*
A special formulation a
n
d estimation technique for the trade
equations have b
e
e
n developed by IN
F
O
R
U
M
, w
hich will b
e used here.
Therefore, the regression results will b
e presented without going
into the motivation back of the equation or into the estimation
technique.
2
T
h
e equations for com
m
odity trade are:
(1) Im
ports
Mt
-
(a + b
U
t) ( P " /
p j? ) n
w
here
M
t = im
ports of a com
m
odity in year t
U = dom
estic use of a good in year t.
D
om
estic use is defined
by use = output - export + import.
^Actually, the im
port equation is used to connect the trade m
odel
a
n
d the national m
odels. T
h
e export equation is not necessary for the
connection because exports are im
ports from the buyer’s point of view
.
For details, see N
yhus, D.E., "The Trade M
odel of a D
ynam
ic W
orld InputO
utput Forecasting S
ystem
" IN
F
O
R
U
MR
esearch R
eport N
o. 14. 1
9
7
5
2
For the theory a
nd estim
ation technique, see A
lm
on, C., et al.
C
hapter 6.
134
P
^
f =w
orld price of a g
o
o
da
s seen by Japan, a
s estim
ated in the
trade m
odel.^
P
^ = dom
estic price of a com
m
odity.
(2) Export
X
, = (a + bDj (pf / p
”)n
t
t
t
t
w
here
= exports of a com
m
odity in year t
D
t = world d
e
m
a
n
d
, w
hich is estim
ated in the trade m
odel in
year t.
9
P
^ = world export price of a good, a
s estim
ated in the trade
m
odel.
T
h
e regression results are in Tables IX-1 a
n
d IX-2.
In both of
^-In the trade m
odel, the world price of a g
o
o
da
s seen by Japan is
P
w =I M
. P.„
Jt
x it it
w
here
Pj
= world price of a g
o
o
da
s seen by Japan
M
it = share of Japanese im
port of a g
o
o
d from i 1
"*1country
= dom
estic price of good in i 1
"*1country.
2
In the trade m
odel, world d
e
m
a
n
d is estim
ated using production
index of each country. Production indices of each country is aggregated
to m
a
ke world d
e
m
a
n
d
.
135
im
port a
n
d export equations w
e expect positive sign o
nba
n
d negative
sign on n .
B
ecause of the nonlinearity of the equation, the IN
F
O
R
U
M
technique to estim
ate the trade equations require _
a priori information
about the price elasticity with w
hich the estim
ation procedure starts.
T
h
e basic idea of the estimation procedure is to choose the param
eters
2
w
hich m
axim
ize the utility function w
hich depends o
n the R a
n
d the
deviation of the price elasticity from the given information of the
price elasticity.
T
h
e information of the price elasticity are borrow
ed
from the U
.S.A. trade equation estimation.
In im
port equation estimation, the estim
ated price elasticities
are not very different from the _
a priori price elasticity except pro­
cessed foods, chem
ical products, industrial m
achinery, and transportation
equipm
ents.
Japan does not im
port those products very m
u
ch
.
B
ecause
the large proportion of these products are produced domestically with
protection,
the im
ported products are not really com
petitive with
the dom
estic products.
H
ence, the estim
ated price elasticities are
generally m
u
ch lower than the a priori elasticities.
Generally, esti­
m
ated export price elasticities are closer to the _
apriori price elas­
ticities than im
port price elasticities.
T
h
e aggregate relative price
elasticity of im
port w
eighted by 1
9
7
2 im
ports is -0.594 a
n
d that of
export is -2.839.
A
s is generally believed, the Japanese im
ports are
price inelastic since
the Japanese im
ports are m
ainly rawmaterials.
O
n the other hand, the Japanese exports are very price elastic.
B
e
­
cause the Japanese exports are usually m
anufactured goods, Japan should
com
pete with other countries for exports.
For sectors w
hose im
port
ratio to dom
estic u
se is greater than 0.9, such a
s Petroleum crude,
Iron ore, a
n
dN
on-m
etalic minerals, the im
port equations are not esti­
m
ated.
If these sectors are included in the aggregate price elasticity
calculation, the price elasticity of im
port w
ould b
em
u
ch lower.
F
or
those sectors, w
e calculate im
port requirem
ent to b
e used a
s im
puts a
n
d
final d
e
m
a
n
d
s.
since
W
e cannot use the regression equation for those sectors,
with the regression equation w
e sim
ply regress the im
ports o
n
the dom
estic use w
hich is alm
ost equal to the im
ports.
T
h
e price
elasticities for those sectors should b
e low because those are non­
com
petitive im
ports; the alternative to im
porting themis to not use
them
, not to produce themdomestically.
T
h
e coefficient o
n dom
estic use, b, should
im
port equations.
be positive in the
This expectation turned out to b
e right for m
ost
cases, and the coefficients are generally significant.
U
sing the
coefficient b, point d
e
m
a
n
d elasticities at 1
9
7
2w
ere calculated a
n
d
sh
o
w
n in the tables.
T
h
e aggregate d
e
m
a
n
d elasticity of export
w
eighted by 1
9
7
2 exports are 1.84 a
n
d the aggregate d
e
m
a
n
d elasticity
of im
port w
eighted by 1
9
7
2 im
ports is 1.44.
F
or the sectors w
hich
have w
rong sign o
n b, w
e use the tim
e trend equation:
p
w
log M * a + bt + c log
1
1
P
d
t
pd
_
log X
t = a + bt + c log _
w
here t is tim
e trend.
137
T
h
e regression results of the sectors w
hich have tim
e trend equations
w
ere sh
o
w
n at the e
n
d of the Tables IX-1 a
nd IX-2.
R
2 is g
o
o
d enough to produce reasonable forecasts.
2
Generally, R
is high for the sectors w
h
o
se im
ports or exports are large.
C
onversely,
it is hard to predict the im
ports or exports of the sectors w
hich have
sm
all a
m
o
u
n
t of im
ports a
n
d exports.
In the regression tables the stan­
dard errors of estim
ation (S
E
E
) are show
n.
In order to see h
o
wthe
standard errors could affect the forecast of output a
nd use level, w
e
calculate the percentage of the standard error of export over output a
n
d
the percentage of the standard error of im
port over use level.
O
nly five
sectors have standard error ratio greater than 5
%for im
port equations
a
n
d seven sectors for export equations.
Im
ports a
n
d exports of transportation a
n
d other services are re­
lated to the total a
m
o
u
n
t of im
ports and exports.
are:
a. Export of transportation
X= -67.64 + 0.19 T
X
(-5.198)
(54.980)
w
here
T
X= total a
m
o
u
n
t of exports
R
2 * 0.9531
D
.W
. = 1.1028
b. Exports of O
ther Services
X= 202.78 + 0.05 T
X
(6.566)
(9 .628)
T
h
e regression results
138
R
2 = 0.8843
D
.W
. = 0.5739
c. Im
ports of Transportation
M= -28.17 + 0.07 T
M
(-3.417)
(31.508)
w
here T
M= total a
m
o
u
n
t of im
ports
-2
R = 0.9793
D
.W
. = 1.2675
d. Im
ports of O
ther Services
M= -115.57 + 0.08 T
M
(-9.923)
R
2 = 0.9748
D
.W
. = 1.7447
(28.547)
TABLE
REGRESSION RESULTS Of
IK -1.
SECTOR,
IMPORT EQUATION
PHI CE EL AS 1 1C 1 T Y
ESTIMATE
A PRI ORI
CONST(A
HAND( B)
ELAS OF
DEHAND
RBARSQ
RHO
SEE/ USE
(X)
S EE
1972
IMPORTS
* .50
t
.50
14 5 . 7
1 .84)
.009
.25)
.105
.362
.264
29.059
1.495
184.
2 OTHER CROPS
- .2 7
-.27
-811.3
-6.75)
.795
10.98)
2.655
.903
.342
49.207
3.008
561.
J FRUI T S
-.27
-.27
-30.6
-3.25)
.202
10.01)
1.287
.884
.231
7.410
1.089
118.
4 OTHER CROPS FOR I N D U S T R I A L P
-.2?
-.22
-346.4
-3.67)
1.503
5.63)
3.007
.739
.576
30.196
8.743
180.
6 LIVE
-.27
-.27
-2.8
-1 .6 5 )
.009
4.84)
1.440
• 562
.366
1.167
• 114
12.
-.95
-.27
.054
1.57)
3.264
.595
•482
.459
•364
3.
-1 .05)
10 FORESTRY
-.50
-1.00
-5.8
-1.79)
.028
4.15)
1.560
. 468
.112
.845
.143
11.
1*
-.60
-1.65
-860.2
-6.75)
1.257
9.81)
2.707
.913
.494
34.523
3.181
634.
-1.00
-1.00
-56.4
-5.26)
.116
8.38)
1.945
.766
.309
6.459
.645
81.
.00
-1.00
-.4
-.42)
.088
2.69)
1.272
.384
.557
.539
2.452
2.
-1.00
-1.00
-2.9
-4.06)
.128
8.03)
1.749
.823
•398
.400
.763
6.
-1.00
-1.00
•r»
sTO
1.408
16.40)
1.992
.955
• 518
23.749
4.761
432.
20 ORES K CONCENTRATES OF NON' F
-.22
—. 22
-81.1
-7.59)
1.011
33.20)
1.189
.990
• 725
12.746
2.527
429*
a
-.22
- .22
-6.4
-8.70)
.574
15.29)
1.621
.953
•367
.765
2.627
15.
1.9
2.78)
.021
17.28)
.920
.964
•271
1.072
•103
25.
STOCKS,POULTRY
8 SERI CULTURE
LOGS
14 F I S H E R I E S
UHAL1N6
16
I NLAND WATER F I S H E R I E S
17 COKING COAL
NATURAL GAS
23 L I R E
STONE SAND GRAVEL
26 CARCASSES
27 HEAT PRODUCT
28
DAI RY
PRODUCT
29 VEGETABLE
S FRUI T
JO SEA FOOD PRESERVED
t
PRESERVED
-.22
11
1 GRAIN
-.70
—1 . 6 3
-14.4
-1 .1 0 )
.168
7.09)
1.114
.628
•352
14.486
1.725
204.
•00
—1 . 6 3
1.1
1 .67)
.004
.92)
.480
-.016
•402
.725
•300
3.
-2.10
—1 . 6 3
-4.1
-2.34)
.038
8.64)
1.230
.663
• 143
3.908
.680
36.
-.20
—1 . 6 3
18.2
5.49)
.045
2.82)
.429
.246
• 180
3.90S
1.281
39.
-.50
-1.63
-22.6
-2.79)
.121
9.75)
1.249
.875
•639
9.640
1.031
134.
TABLE
1X-1CCONTINUED).
REGRESSI ON
RESULTS O f
I MPORT
EQAT ION
I—
|
SECTOR,
Ffi l CE E L A S T I C I T Y
ESTIMATE
A P R I OR I
22 BAK ER V PRODUCTS
.GO
-1.63
33 REFI NED SUGAR
-.8 0
-1.63
34 OTHER FOOD PREPARED
-.10
-1.63
-1.63
-1.63
-.70
-1.63
-1,50
-1.63
-.VO
-1.65
35 PREPARED FEEDS FOR ANI MAL &
56 ALCOHOLIC BEVERAGES
37 SOFT DRINK
itt
TOBACCO
39 S I L K
REELI NG S WASTE S I L K
SP
4U COT ION SPI NNI NG
-1.65
-1.65
-1.65
-1.65
41 WOOLEN ft WORSTED YARN
-2.40
-1.65
42 LI NEN
-2.30
-1.65
FIBER YARN
.00
- 1 .65
K RAYON WEAVING
-1.65
- 1 .65
YARN
44
SYNTHETI C
4*
SILK
47 SYNTHETI C
48
FIBERS WOVEN
WOOLEN FABRI CS WOVEN ft FELTS
49 LI NEN
FABRI CS WOVEN
11 KNI TTED FABRI CS
-1.65
-1.65
-1.65
^1.65
-1.80
-1.65
-2.00
14
FOOTWEAR EXCEPT RUBBER HADE
-1.65
-1.65
WEARING APPAREL
—1 . 6 0
-1.65
ELAS OF
DEMAND
RBARSQ
RHO
SEE
SEE/ USE
(X)
19 72
IMPORTS
6.9
.95)
.011
1.08)
.5 7 9
.016
.404
2.672
.299
-3*.7
-2.42)
.367
8.76)
1.315
.724
.454
11.095
2.458
172
<
-e.e
-1.62)
.031
6.63)
1.208
.797
.697
5.072
.311
56
C
7.9
3.08)
.004
.58)
.217
-.082
•488
2.706
•454
10
(
-3.6
-1.05)
.012
3.94)
1.241
.622
• 278
2.343
• 149
<
20
-.2
-.47)
.007
3.30)
1.098
.131
•2 93
.658
.192
3
<
2.6
1.91)
.002
1.21)
.453
• 111
• 232
.776
.081
6
C
-65.2
-4.04)
.508
5.61)
2.047
.805
•635
10.395
4.140
91
<
-62 .7
-6.31)
.291
6.89)
4.414
.871
.251
1 .750
.628
20
<
«
-10 .8
-1.30)
.115
2.33)
2.100
.337
.605
3.855
2.146
27
(
-I$5>
.047
2.02)
2.472
.394
•498
.244
1.709
1
-.1
-1.64)
.002
6.09)
1.187
.783
.677
• 146
.038
(
1
-14.5
-7.57)
.082
13.77)
1.694
.972
• 137
1 .409
.325
27
(
-.3
-.56)
.007
4.98)
1.094
.732
• 150
•676
.121
5
C
-31 .8
-1.97)
.113
2.70)
2.803
• 42 2
• 420
3.198
.730
17
<
-3.9
-3.13)
.346
4.30)
4.792
• 688
• 575
.734
5.194
<
3
-33.8
-5.42)
.120
8.21)
1.798
C
• 83 9
•692
5.613
.888
48
(
-4.1
-4.51)
.043
9.80)
1.511
• 912
• 16 1
• 78 8
.276
12
C
-5 ? fii)
.033
8.53)
1.622
• 87 0
• 51 1
• 529
.300
6
<
3.S i >
.014
3.40)
.868
• 508
-.156
4.488
•300
24
-1.65
-2.00
0 H A N D ( B)
C
-1.65
13 OTHER FI BER PRODUCTS
IS
CONST( A)
21.
TABLE
1X-KCONTINUED).
REGRESSION
SECTOR,
OIF
IMPORT EQAT ION
FRICE ELASTI
ESTIMATE
56
TEXTILE
5/
WOOD M I L L I N G
6ARMENTS
59 FURNITURE
WOODEN ft METAL
6U PULP
61 PAPER
6 2 A R T I CL E S
OF PAPER ft PAPERBOA
63 P R I M I N G
ft PU B L I SH I NG
64 LEATHER MANUFACTURES ft FUR P
65 LEATHER PRODUCTS E X .
FOOTWEA
67 BASI C
I NORGANI C
60 BASI C
ORGANIC
SYNTHETI C
INDUSTRIAL C
I NDUSTRI AL
CHE
DVESTUFF
?U BL A STI NG POWDER
72 MATERI ALS
OF SYNTHETI C
FIBER
73 P L A S T I C
74 CHE HI CA L
FERTI R1ZER
75 MI SCELLANEOUS BAS I C
76 VEGETABLE
CHEMICAL
ft ANI MAL O I L
CONST ( A )
(i MAND(B)
ELAS OF
DEMAND
RBARSQ
RHO
SEE/ USE
(X)
SEE
1972
IMPORTS
• 042
8.01)
1.303
• 876
.132
1 .162
.419
12
2.00
.073
11.46)
1.398
.963
.046
6.040
.353
125
-2.77
.014
6.63)
1.622
• 801
.392
.658
.119
6
-.80
.003
4.07)
1.348
.658
.442
.756
.057
6
.00
.097
4.17)
.791
.621
.620
7.624
1.423
68
-1.65
.017
3.53)
1.496
.371
.019
3.336
.311
11
•00
.005
10.77)
1.120
.920
.631
.602
.038
10
-.80
.016
3.85)
1.334
.531
.748
S . 349
.276
27
-.80
.142
9.02)
1.556
.852
.194
.894
1.208
13
-5.00
.074
8.78)
1.506
.901
.091
.554
.517
7
5. 2 8 )
.014
1.277
.729
.686
1 .404
.200
13
-1.65
.007
16.05)
1.461
.944
.294
.101
.029
2
-.70
.024
12.60)
.679
.836
.134
2.753
.207
49
- .1 0
.214
4.82)
• 930
.682
-.341
2.114
3.631
21
-1.50
.165
5.75)
1.718
.684
.237
1 .181
3.041
5
.00
.008
5.74)
1.100
• 761
.579
.942
.164
6
-1.40
.033
9.09)
1.046
.817
.437
2.011
•343
22
.00
.067
2.31)
.710
• 303
• 716
3.015
1 *379
27
.0 0
.126
6.17)
1.147
• 788
•311
7.863
1.575
84
.00
.0 3 9
2.28)
.489
• 295
•688
9*246
1.303
56
.00
6 6 ART I CL E S OF RUBBER
IT*
I 0R 1
-1.65
-
58 WOODEN PRODUCTS
69
RESULTS
T ABL E
I X - 1 < CONTINUED).
REGRESSI ON
SECT OR,
il
RESULTS
Of
I MPORT
PRICE ELAST 1CITY
A P R I OR I
ESTIMATE
EQAT ION
CONST (A
HAND( B )
1 .37)
3 17
. 4 58
6
1.081
.950
.388
5.917
.529
104
.894
.840
-.324
13.719
1.419
162
.087
11 22
.964
.906
-.160
20.310
.6 8 6
306
.001
.403
-.083
.385
1.127
.169
0
.011
1.457
.140
.589
.096
.347
0
.0 1 0
1.189
.723
.608
.253
.118
3
?tt MEDI CI NE
-1.65
-1
65
-6.8
-1 . 3 5 )
.081
12.73)
-.2 0
-1
65
16.9
1 .39)
8.08)
81
COAL PRODUCTS
65
9.6
.65)
.00
-1
65
.8
1 . 0 7)
82 MI SCELLANEOUS ANT 1 SEPT 1 CI ZED
-1.65
83 CLAY PRODUCTS FOR B U I LD I N G U
.00
t4
GLASSWARE
85 POTTERY
tit
CEMENT
87 0THERN0N- METALL1C MINERAL PR
-1
1972
IMPORTS
1 .130
65
-1
SEE/ USE
(X)
SEE
-.208
-1
*1.65
RHO
.474
.00
uu PETROLEUM REFINERY PRODUCTS
RBARSQ
.766
COA 11NGS
7V OTHER CHEMICAL PRODUCTS
ELAS OF
DEMAND
.017
. )
.148
. )
• 48)
65
-.1
-.55)
1.44)
-3 77
-.3
-1.03)
5.21)
.00
-3 77
-.0
-.02)
.017
5.64 )
1 .0 0 2
.755
.016
1 .344
.265
10
-2.77
-3 77
-.6
-.74)
.015
1.241
.515
.543
.751
.393
4
2 88
1.321
.954
.605
.101
•022
2
.560
.397
.498
.833
.052
6
-.20
-3 77
-.20
-3 77
. )
-5.27)
.0 0 5
15.24)
2.4
3.33)
2.69)
.002
-2.00
-2
00
-3.6
-1 .9 0 )
.075
5.60)
1.372
.745
-.629
2.532
1.427
10
91
-2.20
-2
00
-1.0
-2.17)
001
1.532
.770
-.591
.405
.017
2
-2.00
-2
00
lih
.002
.532
-.107
.118
3.958
.230
6
-1.60
-2
00
.2
.63)
.003
3.26)
.865
.021
-.343
.445
.145
1
- e .o o
-6
00
.6
7.81)
-.113
.825
-.234
.087
.0 06
1
0
STEEL
INGOT
¥2 HOT-ROLLED PL A T ES*
93
STEEL
PI PE
& TUBE
V4 COLD-ROLLED I
95 CAST t
SHEETS
COATED STEEL P
FORGE IRON
9 6 NONFERROUS METAL INGOTS
-2.00
-2
00
#*•
VU FERROALLOYS
.43)
.90)
-.000
-.60)
.0
.38)
.000
.952
.748
-.086
.038
.003
5.77)
-.40
-1
65
9.5
.14)
.392
5.95)
.983
.744
.587
61 . 7 1 3
4.340
547
97 COPPER BRASS PROOUCTS
-1.20
-1
65
-2.9
-4.27)
.024
8.50)
1.809
.872
.511
.547
•207
3
98 ALUMINUM EXTRUDED PRODUCTS
-1.65
-1
65
.008
5 . 96)
.807
•472
.441
•490
.132
3
.7
2.82)
~t
TABLE
IX-1CC0NTINUED).
REGHES SION
RESULTS 0 1
P«1 CE ELA
ES11MATE
SECTOR,
V9 OTHER NONFERROUS METAL PRODU
-.30
-
IMPORT
11CI TV
PRIOR I
EG AT ION
CONST ( A )
MAND( B)
ELAS OF
DEMAND
RBARSQ
RHO
SEE
SEE/ USE
U )
19 7 2
IMPORTS
2.1
.015
5.63)
• 785
• 655
.290
1 .471
.215
13.
2.83)
.65
-
.77
2.6
2.15)
.004
4.00)
• 74 8
• 600
.413
1 .792
• 081
15.
-.20
-
.77
-1.3
-1 .07)
.012
10.76)
1.070
• 918
.008
1.399
.086
24.
-1.05
-
.05
1C.9
1 .45)
.022
1.87)
• 632
.130
•230
7.537
•868
30.
.00
-
.05
3S.0
.29)
.153
.81)
• 6 88
-.035
.897
99.220
17.642
52.
-.40
-
.42
4C.3
4.59)
.694
.867
.339
9.871
s?IS.
•325
152.
.00
-
• 42
V . ih
.033
5.82)
• 634
.767
.297
8.741
•646
84.
.00
-
.42
6.4
1 .95)
.078
2.54)
• 50 5
.353
.803
8.400
7.692
40.
-1.20
•
• 42
• 'O
0 •
• 053
7.01)
2.645
• 808
•2 53
.885
.273
8.
-.60
-
• 42
.024
15.80)
.935
.929
• 785
2.022
.159
2.04)
33.
•00
-
• 42
-1.0
-.34)
.0 2 3
7.78)
1.035
.856
•698
3.108
•234
32.
1 1 0 HOUSEHOLD EL E CTRI CAL MACHINE
.00
-
• 42
.6
.55)
.010
10.67)
• 96 8
.919
.481
1.898
.100
27.
111
OTHER
WEAK ELE CTRI CAL
• 00
-
• 42
1S.1
1 .61)
.050
11.66)
.91 7
• 931
• 165
16.257
•385
276.
112
SHI PS
1 BOATS
•00
-
• 77
17.2
1.93)
.004
.19)
.114
-.107
•016
10.968
2.109
31.
113
RAI LWAY VEHI CLES
-.80
-
• 77
.4
.40)
.002
.80)
• 656
-.086
.377
• 467
• 137
2.
11*
PASSEN6ER MOftTOR CAR
•00
-
• 77
3.1
1 .49)
.0 0 7
8.96)
• 902
.888
.447
3.068
.073
42.
1 1 6 MOTORCYCLES & BI CYCLES
.00
-
.77
.0
.22)
.000
.51)
• 658
-.080
.841
.089
.030
0.
1 1 ? AI RCRAFTS
.00
-
.77
-34.8
-4 .44)
.694
15.74)
1.238
• 961
.372
8.803
3.375
169.
-.40
-
• 77
-.7
-1.23)
.026
3.05)
1.334
.442
.029
.933
•799
2.
•00
-
• 77
.6
.17)
.113
7.88)
• 98 5
.859
>509
4.744
1.281
59.
1U1
OTHER
METAL
PRODUCTS
1(1? POWER GENERATING MACH1NARY &
It)
MACHINE
104
INDUSTRIAL
I CS
GENERAL
TOOLS METALWORKING H
MACHINERY
I NDUSTRI AL
MACHINERY
1 0 6 OFFI CE MACHINERY
10/
HOUStHOLD
lUtt
PARTS
1 uv
MACHINERY
OF MACHINERY
STRONG ELE CTRI C MACHINERY
1 1 8 OTHER
TRANSPORTATION
11V PR E C I S I ON
MACHINERY
APPLIA
1 1
.00
I CO STRUCTURAL METAL PRODUCTS
2.2
-r■j„
^
TABLE
1X-KC0NUNUED).
REGRESSION
W O PHOTOGRAPHIC
WATCHES I
IMPORT EQ AT ION
CONS!(A)
P M CE E L A S T I CI TY
A PRI ORI
ESTIMATE
SECTOR,
121
RESULTS OF
& OPTI CAL
1NSTR
CLOCKS
Mi OTHER MANUFACTURING GOODS
.00
-3.77
-.40
-3.77
•00
-3.77
DEMAND(B)
ELAS OF
DEMAND
RBARSQ
RHO
SEE
SEE/ USE
(X)
19 72
IMPORTS
-9.0
-1 .9 3 )
.813
.261
4.913
1 .379
SO.
(
.120
6.67)
1.267
<
-5.7
-1 .1 6 )
.186
6.61)
.796
-.179
5.050
2.212
47.
(
1.154
(
-19.7
-1.59)
.831
.525
21.072
•826
219.
(
1.138
(
TABLE
I X - 1 (C O N TIN U E D ).
REGRESSI ON
SECTOR
PRICE
11 CHARCOAL It FIREWOOD
HILL
41
GRAI N
43
SPAN RAYON YARN
PRODUCTS
4 6 C O H O N ft SPUN RAYON FABRI CS
»
71
ROPESS F I S H I N G NETS
SPUN RAYON
li b P1 6
IRON
RESULTS O f
I MPORT
ELASTICITIES
EQ AT ION
CONST A N T ( A)
-5.44
.00
RHO
SEE
SEE/ USE
(X>
1972
IMP
-.072
-.27)
.226
3.67)
.555
.152
1.8
13.7
3.
3 . 220
.32)
-.175
- f .02)
.427
.700
1.9
.1
6.
1
4.0?8
1 .U )
.159
1.52)
.150
.091
2.7
3.0
0.
(
2.726
33.20
.279
14.82)
.956
.289
1.2
.4
40.
(
2.677
2.4S)
-.043
-2.21)
.760
-.200
1.1
1.8
2.
(
1.104
.61)
.014
.17)
.316
-.031
2.0
1.9
0.
C
7.54 7
2.60)
.031
.44)
-.043
.626
1.8
.1
28.
(
-2.27
-3.74
RBARSQ
(
.00
*•68
1ME( B)
-3.03
TABLE
REGRESSION RLSULTS OF
SECTOR,
FRI CE E L A S T I C I T Y
EST IMATE
A P R I OR I
1 GRAI N
10 FORESTRY
12 LOGS
21
PETROLEUMS CRUDE
23 L I ME
EXPORT EUUAT10N
STONE SAND GRAVEL
CONST ( A
MAND(B)
ELAS OF
DEMAND
RBARSQ
RHO
SEE
SEE/OUT
(X)
1972
EXPORTS
-.50
-.50
-54.5
-1 .66)
.730
1.97)
3.255
.207
.300
15.268
•929
-.JO
-1.00
-3.6
-1 .16)
.093
2.69)
1.587
.194
•654
1.200
•242
7
-1.65
-1.65
.3
.55)
.004
.65)
.587
.091
.636
.283
.051
1
-.22
-.22
-a .5
.100
2.42)
5.559
.316
.251
1.129
20.968
5
-2.25)
-.22
-.22
-7.4
-3.29)
.090
3.83)
4.924
.593
• 120
.386
.048
2
-.50
-.22
2.0
.21)
.019
.19)
.490
.157
.537
1.986
8.633
5
27 MEAT PRODUCT
-2.20
-1.63
-.7
-2.90)
.014
5.46)
1.800
.586
-.255
• 171
•086
1
2tt DAIRY
-1.63
-1.63
-6*1
-4.61)
.096
6.43)
2.451
.852
•062
• 52 6
•089
4
-1.63
-1.63
-28.2
-2.97)
.392
3.66)
3.022
.559
.382
4.328
.221
11
-.50
-1.63
.-11.5
-3.63)
.175
S .06)
2.665
.593
.445
1.025
.117
7
33 REFI NED SUGAR
-1.63
-1.63
-.3
-.39)
.009
1.10)
1.421
.190
• 215
.350
.096
1
34 OTHER
-1.63
-1.63
-2C .4
-2.91)
.384
4.99)
1.996
.740
•433
2.34 5
•150
22
-.90
-1.63
-2.0
-3.07)
.040
5.62)
1.869
.722
-.102
• 248
• 043
2
36 ALCOHOLIC BEVERAGES
-1.63
-1.63
-1.7
-5.03)
.044
11.73)
1.549
.947
• 201
• 151
•010
3
37 SOFT DRINK
-1.63
-1.63
-2.3
-3.96)
.042
6.28)
2.097
.550
• 518
• 308
• 098
3
‘ -1.65
-1.65
-1.0
-3 .14)
.015
4.37)
2.540
• 584
•265
• 136
•015
1
-1.10
-1.65
-36.7
-4.41)
.633
7.04)
2.193
• 812
• 309
2.511
1.266
28
-1.65
-1.65
-.6
-6.89)
.009
8.69)
3.076
.630
•0 54
• 031
.1 7 1
0
-2.20
-1.65
-3.0
-3.33 )
.063
6.51)
1.770
• 944
-•234
• 318
•4 07
5
-1.65
-1.65
-145.1
-9.24)
1.826
10.72)
3.760
• 968
-.097
5.183
1.312
71
25 N0N- METAL1C MINERALS
PRODUCT
31 GRAIN M I L L PRODUCTS
J 2 BAKERV PRODUCTS
FOOD PREPARED
35 PREPARED FEEDS FOR ANI MAL
it
TOBACCO
41
WOOLEN ft WORSTED YARN
42 L I NEN
43
YARN
SPAN RAYON YARN
44 SYNTHETIC
FI BER YARN
ft
TABLE
I X-2.(CONTINUED).
REGRESSI ON
4? SYNTHETI C
53 OTHER
FI BERS UOVEN
-
PRODUCTS
CON S T ( A )
0 MAND(B)
El. A S OF
RBARSQ
RHO
SEE/OUT
(X)
SEE
DEMAND
-95 4.4
-10 .5 8)
-iU J )
•222.6
19 7 2
EXPORTS
4.191
.915
.424
29.142
3.254
32 8
1.829
.537
.405
.278
1.860
1
3.135
9.79)
2.732
.839
.387
15.403
2.338
139
-.6 0
2.8
.23)
.288
2.20)
.921
.002
.626
4.717
1.537
46
1.20
-5.7
-1 .6 1 )
.108
2.94)
2.093
.572
.445
•605
.378
5
2.059
. 688
.338
2.597
. 9 05
30
54 fOOTUEAR EXCEPT RUBBER MADE
-
56
-1.65
T E X T I L E GARMENTS
EQUATI ON
-7.65)
-1.65
FABRI CS
F I BER
1 .00
-2.20
FABRI CS UOVEN
51 KNI TT E D
E PORT
PRICE ELAS 1 1 I TT
ESTIMATE
I OR I
SECTOR,
4 9 LI NE N
RESULTS 01
-.40
8.7
2.76)
.082
2.43)
.539
.137
.533
1.706
.365
19
-.40
-18 .0
-3.97)
.282
5.81)
2.140
.684
.644
2.377
.191
20
6U PULP
-1.65
-3.4
-2.84)
.051
3.65)
2.550
.460
.617
.815
• 178
3
61 PAPER
-1.65
1 .644
.878
.642
4.286
.425
53
5ft WOODEN PRODUCTS
59 FURNITURE
WOODEN I
METAL
-19.4
-6.75)
.393
11.60)
1.832
.941
.737
1.695
.117
26
1 0 .1
.254
15.75)
1 .585
.969
.432
.888
.042
16
-7.07)
•1.60
-44.3
-2.64)
.526
2.93)
4.966
.450
.440
3.412
4.043
18
-.6 0
-11.4
-2.55)
.287
5.65)
1.611
.708
.746
2.206
1 .876
21
6 6 A R T I CL E S OF RUBBER
-2.60
-85.7
-5.37)
2.031
11.29)
1.621
.954
-.016
8.837
1.091
152
6 7 B ASI C
1N0R6 ANI C
-1.65
-9.4
-4.51)
.155
6.35)
2.275
.782
•709
1 .276
•428
10
6 8 BA SI C
ORGANIC I N D U S T R I A L
-1.65
-157.0
-5.74)
2.361
7.50)
2.531
.873
.705
15.611
1.198
132
-1.65
-16.6
-8 .64)
.265
11.85)
2.339
.936
.731
1.044
1.528
14
70 B L A S T I NG POUOER
-1.65
-1.5
-3.17)
.041
7.55)
1.499
.901
•392
.239
•525
3
71
-1.70
-13.1
-1.35)
.464
4.11)
1.354
.732
•462
S . 950
4.429
S3
62 A R T I CL E S OF PAPER *
65 PRINTING *
PAPERBOA
-1.60
PU B L I SH I NG
64 LEATHER MANUFACTURES ft FUR P
65 LEATHER PRODUCTS E X .
6 9 SYNTHETI C
SPUN RAYON
FOOTUEA
INDUSTRIAL C
DVESTUf f f
-3.77
CHE
-
.
^
s T ABL E
IX-^LlCONTlNUED).
REGRESSI ON
SE CTORv
RESULTS OT
PRI CE
E S T IM AT E
EXPORT
ELASTIC ITY
EQUATI ON
CONST(A>
MAND( B)
A PRIOR 1
EL AS
OF
RBARSQ
RHO
SEE/ OUT
(X)
SEE
DEMAND
1 9 72
EXPORTS
-1.65
-1
65
-203.6
-8.67)
3.387
12.29)
2.184
.959
.464
14.740
1 .739
205.
-1.65
-1
65
r*» I
l
r*l •
2.438
10.11)
2.295
.922
.732
13.406
1 .977
142.
F ERTI R1ZER
-1.65
-1
65
-28.8
-2.26)
.863
5.76)
1.442
.826
.398
8.342
3.436
87.
MI SCELLANEOUS BASI C CHEMICAL
-1.65
-1
65
-2S.5
-3.07)
.720
6.37)
1.607
.840
.592
6.431
1 .417
66.
-.80
-1
65
2.8
1 .05)
.009
.31)
.263
.099
• 63 S
1.219
.474
6.
?7 COATINGS
-1.65
-1
65
-7.9
-7.32)
10.61)
2.142
.934
.473
.665
.279
8.
78 MEDI CI NE
-1.65
-1
65
-16.0
-3.46)
.378
6.94)
1.630
.607
.724
3.065
.268
29.
79 OTHER CHEMICAL PRODUCTS
-1.65
-1
65
-121.3
-6.76)
2.193
10.40)
2.036
.945
.508
12.239
1 . 4 79
151.
ISO PETROLEUM REFINERY PRODUCTS
-1.65
-1
65
-45 .9
-5.30)
.983
9.66)
1.757
.912
.489
4.740
.165
69.
.00
-1
65
-3.5
-3.90)
.056
5.24)
2.384
.726
.729
.564
.075
4.
65
.0
.46)
.001
2.95)
.891
.086
.091
.017
.067
0.
2.233
.508
.716
1 .S11
.665
12.
u
MATERI ALS OF SYNTHETIC
FIBER
1 3 PL A ST I C
?4 CHEKI CAL
n
76 VEGETABLE
HI
8 ANI MAL O I L
COAL PRODUCTS
M2 MISCELLANEOUS ANT 1SE PTI CI ZED
-1.65
ttJ CLAY PROOUCTS FOR B U I LD I N G U
-1.80
-3
77
0 4 GLASSWARE
-2.77
-3
77
12.8
3.88)
.141
3.74)
.552
.991
.078
.902
.171
34.
ft*
-1.60
-3
77
-5.5
-.50)
.797
6.29)
1 .068
.282
.685
6.038
2.210
97.
87 OTHERNON-METALL1C MINERAL PR
-1.40
-3
77
-11.5
-5.41)
.198
8.14)
2.164
.845
.545
1.185
•08S
13.
88 P I G
-3.60
-2
00
-6.4
-1.56)
.088
1.89)
3.534
.476
.562
3.189
.211
10.
-2.00
-2
00
.046
.61)
.910
.249
.536
3.030
1.297
13.
.07)
-2
00
- T iiii
.03?
2.08)
2.598
.179
.106
.907
.050
1.
POTTERY
IRON
VO FERROALLOYS
91
STEEL
INGOT
92 HOT-ROLLED P L A T E S !
9 3 STEEL P I P E ft TUBE
-2.00
SHEETS
S!$6)
-2.00
-2
00
-823.8
-3.89)
13.347
5.55)
2.503
.775
.752
109.405
3.342
753.
-2.00
-2
00
-300.9
-3 .9 5 )
4.838
5.68)
2.548
.838
.622
30.132
5.533
248.
T ABL E
I X - ; - < CONTINUED).
REGRESSI ON
SECTOR*
¥4 COLO-ROLLED & COATED STEEL P
95
CAST & FORGE
IRON
96
NONFERROUS METAL
INGOTS
97 COPPER BRASS PRODUCTS
98
ALUMINUM EXTRUDED PRODUCTS
99 OTHER NONFERROUS METAL PRODU
RESULTS OF
EXPORT
EQUATI ON
FRI CE E L A S TI CI TY
A PRI ORI
ESTIMATE
CONST (A
H A N D ( B)
ELAS OF
DEMAND
RBARSQ
RHO
SEE/OUT
(X)
SEE
19 7 2
EXPORTS
6.662
Z.51)
2.104
.791
.763
59,762
3.607
4 5 j.
-14.6
-1 .8 7 )
.235
2.68)
2.546
.291
.721
3.349
.236
13.
65
-29.7
-2.57)
•75S
1.503
.865
-.172
9.792
1.180
92.
5.90)
65
-2 k.2
.433
5.49)
2.132
.818
-.451
3.587
1.509
25.
-3.52)
65
-13.4
-7.31)
.258
11.92)
1.918
.942
•408
1.186
.449
17.
-1
65
-6.7
-5 .78)
.171
13.22)
1.505
.989
• 319
• 702
.149
17.
-6.00
-6
00
-2.00
-2
00
-1.65
-1
-1.65
-1
-1.65
-1
-1.65
I CO
STRUCTURAL METAL PRODUCTS
-4.00
-3
77
-247.4
-7.40)
3.739
10.45)
2.504
.957
-.022
11.489
.505
222.
101
OTHER
-3.60
-3
77
-127.3
-6.27)
2.558
11.14)
1.816
• 906
• 231
13.011
.770
211.
1 0 2 POWER GENERATING MACH1NARV &
-1.05
-1
05
-112.5
-4.16)
2.057
6.19)
2.168
• 791
.530
17.916
1.811
144.
1 0 3 MACHINE
-2.10
-1
05
-30 .0
-1 .3 3 )
.989
3.58)
1.449
.783
• 506
26.513
3.065
90*
-1.20
-5
42
-232.9
-5.66)
5,125
10.25)
1.798
.913
• 180
26.517
.772
367.
-2.00
-5
42
-126.0
-3 .97)
2.505
6.45)
2.002
.871
•278
21.951
1 . 4 08
196.
1 0 6 O F F I CE MACHINERY
-3.20
-5
42
-96 .0
-4 .71)
1.881
7.28)
1*941
.973
•404
16.770
4.530
252.
1 0 7 HOUSEHOLD MACHINERY
-5.4 2
-5
42
-P5.5
-4.20)
1.520
6.27)
2.098
.780
•463
13.029
3.887
107.
10U PARTS OF MACHINERY
-5.42
-5
42
73.3
2.83)
.141
.45)
.164
.946
-.080
10.428
1.014
147.
* -1 .80
-5
42
-129.9
-5.38)
2.446
8.52)
1.987
• 870
.144
17.533
1.201
183.
11(1 HOUSEHOLD ELE'CTRl CAL MACHINE
-5.42
-5
42
-231.7
-2.57)
8.251
7.63)
1.340
.974
• 250
55.934
2.229
1125.
111
OTHER WEAK EL E CTRI CAL A P P L I A
-2.20
-5
42
-311.0
-6 .62)
5.370
9.95)
2.069
• 874
-.247
40.945
1*098
419.
112
SHI PS
-2.00
-3
77
-596.0
-4.24)
12.761
7.51)
1.726
• 768
•198
107.470
8.357
1027.
-3.77
- 3 .77
-1015.8
-5.05)
1 5 .▲9 2A3A %
2.160
• 887
.757
138.883
2.837
1328.
104
METAL PRODUCTS
I N D U S T R I A L MACHINERY
1 0 5 6ENE«AL
109
TOOLS METALU0RK1N6 M
I N D U S T R I A L MACHINERY
STR0N6 ELECTRI C MACHINERY
ft BOATS
1 1 4 PASSENGER MORTQR CAR
TABLE
1 X - C: ( C 0 N T 1 N U E D > .
REGRESSI ON
SECTOR*
RESULTS O f
PRICE
ESTIMATE
EXPORT
E L A S T I CI TY
A P R I OR I
EQUA TI ON
CONST( A)
OEMAND(B)
ELAS Of
DEMAND
RBARSQ
RHO
SEE/ OUT
(X)
SEE
19 7 2
EXPORTS
116 MOTORCYCLES S BICYCLES
-3.77
-
.77
-146.2
-3.26)
3.355
6.11)
1 .526
.824
.505
51.871
7.665
425.
(
117 AI RCRAFTS
-1.80
-
.77
-16 .3
-3.83)
.314
6.42)
2.112
.685
.138
3.950
3.244
13.
(
118 OTHER TRANSPORTATION
-*.40
-
.77
-1.2
-4.51)
.018
6.12)
2.814
.894
.404
.105
.099
1.
(
119 PRECI SI ON MACHINERY
-3.77
-
-63 .7
-4.23)
1.084
6.60)
2.204
.876
.690
6.451
1.572
76.
(
120 PHOTOGRAPHIC & OPTI CAL 1NSTR
-3.77
.77
-157.7
-9.45)
3.273
16.75)
1.731
• 930
• 297
14.803
2 .650
271.
(
121 MATCHES I
-2.60
.77
-84 .7
-5 .41)
’ >;«>
2.377
.829
•363
11.982
4.602
96.
«
CLOCKS
-
.77
l X - t‘ ( C O N T I N U E O > .
REGRESSI ON
RESULTS OF
ELASTICITIES
SECTOR
2 OTHER CROPS
-4.18
3 FRUI TS
- S . 26
4 OTHER CROPS FOR I N D U S T R I A L P
5 CROP FOR F I B E R
INDUSTRIAL
PR
6 LIVE
STOCKS,POULTRY
7 LIVE
STOCKS,POULTRY FOR F I 8 E
-.66
-4.31
.00
-2.95
FISHERIES
-2.02
WHALING
.00
-1.58
16 I NLAND UATER F I S H E R I E S
2 0 ORES ft CONCENTRATES OF NON-F
-.77
2 6 CARCASSES
-.26
PRESERVED
JO SEA FOOD PRESERVED
39 S I L K
SEE
.829
-.048
1
.012
1 .41 )
.927
.479
2.257
4.56)
.043
1.38)
.969
<
-.731
-.57)
.258
2.73)
(
4,590
3.43)
(
-1.574
-9.89)
<
1.902
1.46)
(
5.400
6.78)
<
1.314
29.10)
<
-.804
-1.51)
C
ME (B )
<
V . lh
s!S!>
<
3.585
16.04)
<
REELI NG ft WASTE S I L K
-2.16
SP
S I L K ft RAYON WEAVING
4 6 COTTON ft SPUN RAYON FABRI CS
4 8 WOOLEN FABRI CS WOVEN ft FELTS
-3.12
-.69
SEE/OUT
(X )
1 9 7 2 EXP
5.
1 1
.2
4.
.390
1 1
.5
5.
.612
.379
2 1
10.4
0.
• 754
-.141
1 2
.1
1.
.093
2.54)
.352
-.177
1 5
397.8
0.
.017
-.17)
.757
.010
1 5
1.1
0.
.675
-.019
1 1
.1
39.
.881
• 143
1 1
3.6
4.
.017
-.59)
.792
• 012
1 2
2.1
0.
-1.442
-.54)
.109
3.90)
.628
• 063
1 3
.9
0.
-.335
-.19)
.118
1.40)
• 248
-.367
2 0
2*7
1.
<
.170
.23)
.053
2.77)
.578
.213
1 2
.2
1.
C
4.729
10.09)
.010
-.93)
.725
.082
1
(
4.475
123.65)
.010
1.23)
.049
.133
1 1
.1
115.
(
4.719
3.88)
-.230
3.38)
.955
-.005
1 4
.8
(
1.
4.907
2.16)
.064
2.65)
.617
(
-•061
1 2
.5
7.
C
6.186
7.25)
.063
•1.60)
.983
-.004
1 1
.3
19.
C
5.334
5.43)
.098
•3.33)
•938
• 265
1 1
.3
103*
7.106
2.91)
-.026
> .63)
• 215
• 634
(
1 5
.4
10*
-4.19
-3.15
RBARSQ
*1
.00
4 0 COTTON SP1NN1N6
45
RHO
CONSTANT( A)
-.59
17 COKING COAL
ft FRUI T
EQUATI ON
-1.10
b SERI CULTURE
29 VEGETABLE
EXPORT
-4.20
\s*
T ABLE
• o
j
i
1
13.
r '
TABL E
I * - k (C0NTINU£0).
REGRESSI ON
SECTOR
RESULTS O f
PRICE
ELASTICITIES
52 ROPESS F I S H I N G NETS
-1.00
55 HEARING APPAREL
-1.67
57 WOOD M I L L I N G
-1.87
86 CEMENT
EXPORT E QUA T I ON
-.89
1 1 3 RAILWAY VEHI CLES
-1.73
1 2 2 OTHER MANUFACTURING GOODS
-1.61
T in t(o )
CONST A N T ( A )
RBARSQ
RHO
SEE
3.252
4.53)
.091
1• 1
<
-.022
-1.69)
.234
<
6.730
3.82>
C
-.055
-.92)
.497
.553
(
5.395
8.20)
1
-.034
-1.97)
.931
<
C
3.913
5.74)
(
.005
.18)
(
4,681
3.27)
(
(
7.163
85.01)
(
SEE/OUT
(X)
1972
EXP
1 4
10.
1
1
88.
-.179
1 #1
1
34.
• 490
.075
1• I
2
18.
.001
.02)
.100
.246
1•5
5
20.
.099
16.80)
•995
-.137
1.0
0
370.
153
C
H
A
P
T
E
RX
O
ther Final D
e
m
a
n
dC
o
m
p
o
n
e
n
ts
T
he four rem
aining final d
e
m
a
n
d com
ponents are inventory change,
governm
ent consum
ption expenditure, business consum
ption expenditure,
a
n
d special procurem
ent exports.
T
h
e total governm
ent purchases ex­
cluding governm
ent investm
ent expenditure w
hich w
a
s treated in the
investm
ent chapter am
ounts to 6,248 billion yen in 1970.
T
h
e proportion
of the Japanese governm
ent spending in total gross national product is
9
%
, w
hich is m
u
ch low
er than that of U.S.A..
T
h
e expenditure for the
national defense in the U
.S
.A
. m
a
ke
s the proportion twice a
s big a
s
that of Japan.
G
overnm
ent spending in m
a
n
y econom
etric m
odels is taken a
s exo­
genous, given from outside the m
odel.
T
he social and political change
could affect the governm
ent spending w
hich m
a
y not b
e explained by
econom
ic variables.
H
ow
ever, the exogenous gom
em
m
ent spending enables
m
odel builders to experim
ent with alternative policies to sh
o
w the
effect.
Following this state of art, governm
ent spending is a
ssu
m
e
d
to increase at a rate in the forecasts given in this study.
B
usiness consum
ption expenditures cover expenditures for social
relations, reception, etc. w
hich are similar to the consum
ption expendi­
ture of household.
In the Japanese input-output table, these expenses
are not treated as a kind of operating expenses necessary for production
or a
s intermediate inputs.^"
Although the a
m
o
u
n
t of business consum
ption
^
■
1
9
7
0 Input-Output Tables, Explanatory Report, G
overnm
ent of Japan,
M
arch, 1974.
expenditure is not negligible, about 4
%of G
N
P
, w
e could not form
ulate
a
n equation for this expenditure ow
ing to the lack of tim
e series.
Therefore, business consum
ption expenditure is also taken a
s exogenous.
T
h
ea
m
o
u
n
t of special procurem
ent export is very sm
all a
n
d also taken
a
s exogenous.
In order to distribute governm
ent expenditure, business consum
ption
expenditure, a
n
d special procurem
ent export over different input-output
sectors, Gmatrix is m
a
d
e
.
T
h
e data of the distribution of these ex­
penditures over the input-output sectors are available for 1970.
T
h
e
s
a
m
e distribution will be used in forecasting.
Inventory change is treated a
s endogenous, although it has a very
crude form
.
T
h
e inventory change equation will be discussed here.
Inventory C
h
a
n
g
e Investm
ent
In a long-run projection m
odel like IN
F
O
R
U
M
, the inventory
investm
ent equation is m
u
ch less im
portant than in a m
acro, cyclical
m
odel.
O
ver the long haul, the net d
e
m
a
n
d for output for the purpose
1
of inventory accum
ulation is a very sm
all proportion of total output.
Also, the sensitivity of inventory change to cyclical variation in the
short run does not play very m
u
ch role in the long run.
Therefore, the
following inventory equation, w
hich is rather sim
ple, will not a
dd very
m
u
ch error in the forecast of the w
hole m
odel.
Darling, P
.G
. a
nd M
. C
. Lovell. Factors Influencing Investm
ent
in Inventories in Econom
etric M
odels of the United States, ed. by
D
uesenberry, F
ro
m
m
, Klein, and K
uh. p
p 133.
155
T
h
e recent econom
etric studies* of inventory behavior em
ploy
flexible accelerator concepts.
This approach relies u
p
o
n the a
ssu
m
p
­
tion that the cost involved in changing the level of stocks leads to
only a partial adjustm
ent tow
ards the long run equilibrium.
This ca
n
b
e expressed a
s
A
V
t ■ vt - V i
■6
<
vt - V i 5
w
here
V= actual inventory stock
V
= desired level of stock
6= speed of adjustm
ent, w
hich is bounded by 0 a
n
d 1.
Since the desired inventory stock is not observable, w
e need
s
o
m
e proxy for it.
S
o
m
e studies use capacity utilization a
n
d un­
filled orders a
s proxy variables for desired stocks.
B
ut these cannot
b
e used here because they m
ust b
e calculated so
m
e
w
h
e
re else in the
m
odel in order to be used.
For simplicity, w
ea
ssu
m
e that the desired stock of inventory
is a portion of the dom
estic use of the product.
Following the
IN
F
O
R
U
Mm
odel, w
e define dom
estic use a
s
^Lovell, M
.C
. "Buffer Stock, S
ales Expenditures and Stability."
Econom
etrica, 1962.
E
dw
in, M
., "The Theory of Inventory Decisions."
Econom
etrica, 1957.1
156
D
U= Q- A
V+ IM
P
w here
D
U= dom
estic u
se
Q= output
IM
P= im
ports
F
ro
mthe assum
ptions, our equation is
A
V * 6
(a
D
U
t - V
t_1)
a
n
d
V
t = 6a
D
U
t - (1 - 6) V
t_1
U
sing this equation, w
e could determ
ine the desired ratio betw
een
inventory stock a
n
d dom
estic use, a
n
d the speed of adjustm
ent.
Unfortu­
nately, this equation cannot b
e estim
ated because w
e lack the appropriate
tim
e series of inventory stock.
T
h
e author is forced to fall back o
n
a priori estim
ates of a a
n
d 6
.
For forecasting w
ea
ssu
m
e that the 1970 inventory-sales ratio
w
a
s a desirable one a
n
d that 6
0
%of the g
ap betw
een this year's d
e
­
sired inventory a
n
d last year’s actual inventory stock will b
e closed
during this year.
M
o
re precisely, w
e set a = V (1970)/ D
U(1
9
7
C
T
), a
n
d
then set inventory change in year t equal to
V
t - V
t-1 = .6 (a
D
U
t - V
t_1)
T
h
e6
0
%factor c
a
m
e from exam
ination of the inventory equations in
several aggregate m
odels.
T
h
e inventory stock data for 1
9
7
0 are available by 2
0 sector
classification.
Therefore, the coefficient is gotten for these 2
0
157
sectors a
n
d is applied to the input-output sectors w
hich belong to the
2
0order sector.
M
ore formally,
.d
d
a, = I V
1 (1970)/I D
U
1 (1
9
7
0
)
1
d
id
i
w
here
i = 1..........................1
56
i d=2
0 sector order in w
hich sector i is a part.
158
C
H
A
P
T
E
RXI
Coefficient C
h
a
n
g
e
T
h
em
odel is incom
plete unless w
e ca
n forecast the input-output
coefficient change.
Coefficient change is still a
n open, im
portant,
a
n
d challenging question in input-output econom
ics.
T
o hope to advance
the state of the art, w
ew
ould need annual tim
e series o
n individual
coefficients.
Since w
e have n
o such series, but only series on outputs
a
n
d final d
e
m
a
n
d
s., w
e have to b
e content for the tim
e being to take
account of w
ide-spread, pervasive coefficient change in a fairly sim
ple
fashion.
nam
ely:
T
w
o reasons for coefficient change are usually m
entioned,
(1) price induced substitution, a
n
d (2) technical change a
n
d
changes in product m
ix.
In this w
ork, w
e limit ourselves to the second
source of changes a
n
dd
o not consider price-induced change explicitly.
T
h
e logistic grow
th curve, w
hich is specified by a starting point,
asym
ptote, a
n
d speed of adjustm
ent, will b
e used to predict the coeffi­
cient changes due to technical change and to changes in product m
ix.
T
h
e changes induced by relative price change should be considered
separately, because the logistic curve m
ethod is valid only if relative
price is stable over tim
e.
Logistic C
urve M
ethod
This m
ethod investigates the coefficient change over tim
ed
u
e
only to technological change and product m
ix change.
Therefore, the
technique implicitly a
ssu
m
e
s the constancy of relative prices.
T
h
e coefficient change over tim
e is expressed as,
159
<u c‘ ’ T T T ^ r
where
®coefficient at tim
et
a * value of the asym
ptote
b = the constant ratio of the percentage change in C
t to the
gap betw
een the asym
ptote a
n
d the current value of the
coefficient
t * tim
e trend
In order to apply the ordinary least squares m
ethod, equation (1)
should be rearranged as:
if 4 > 1
C
t
(3) log(1 - |
if 7
Ct
)
= log (-A) - bat
<!•
O
n
e of these tw
o equations is used for the actual regression,
depending on w
hether the coefficients are rising over time^^.
declining
<1^ .
Although the equation is well specified in the
linear form
, the dependent variable is not know
n.
are involved in the dependent variable.
series of C
^.
> 1^ or
T
w
o kinds of problem
First, w
ed
o not have the tim
e
B
ecause w
ew
ant to apply this equation to all coefficients
in a row of the Aand Bmatrices, the information of the total inter­
m
ediate use of com
m
odities a
n
d investm
ent use are enough to investi­
gate the variation of C
t across the row
.
following m
ethod:
C
t is calculated by the
Where
U
^t = the actual interm
ediate use a
n
d the investm
ent use of
com
m
odity i
X
^t = the output of com
m
odity i
F^t = all final d
e
m
a
n
d of com
m
odity i, less investm
ent
V
^t = the indicated use, the a
m
o
u
n
t w
hich w
ould have b
e
e
n used
if all coefficients rem
ained constant
Sjt = the investm
ent of industry j
C
^t = the indicated coefficient w
hich can b
e applied across
the i ^
row
.
B
ecause w
ed
o not have investm
ent data for the 1
5
6 sectors, w
e
include investm
ent in the intermediate use a
n
d calculate C
. w
hich has
it
investm
ent use in it.
T
h
e
nw
e ca
n apply
to the Aand Bm
atrices.
T
h
e second problemwith the dependent variable is the u
n
kn
o
w
n a,
the asym
ptote.
This problem can b
e solved by the iterative m
ethod.
T
h
e
regression routine starts with a
n arbitrary value of a, a
n
d it searches
for the a w
hich gives the best fit.
T
h
e empirical results are in Table X-l.
equation varies over the different sectors.
T
h
e perform
ance of the
M
a
n
y sectors sh
o
wsignifi­
cant coefficient change over tim
e, fromw
hich w
e ca
n conclude that the
intermediate dsnand forecast is as im
portant as final d
e
m
a
n
d in the I/O
forecasting m
odel.
“ 2
larger the R.
In general, the higher the adjustm
ent rate, b, the
T
h
e simulation with coefficient change will b
e discussed
in the simulation chapter.
162
TABLE
X 1-1 ACROSS
10 ft•
THE
ROW C O E F F I C I E N T
CMNGk
JSYMPTCTE
title
REGRESSI ON
ADJUSTMEU1
RJ
GROWTH RATE
CHANGE OF GR RATE
RBARSQ
1 GRAIN
.0077
,1)707
-•0628
.0037
2 OTHER CROPS
.0094
.0972
-.0953
.0084
.2385
3
.0092
.0061
-.0700
.0046
.2687
PRC
• 0U£9
.0730
-.0676
.0043
. 8 506
PROC
.010C
.0564
-.0642
.0039
.7560
.0087
.0105
-.0098
.0001
.2711
FRUITS
4 C1HER CROPS FOR I NDUSTRI AL
5 CROP FOR FIBER
I NDUSTRI AL
6 L I VE STOCKSfPOULTRV
7 L I VE
STOCKS ' POULTRY
FOR
.8691
.0096
.0505
-.0569
.0031
.5057
8 SERICULTURE
1 .4668
.0114
.0049
- .0 0 0 1
.0762
9 AGRICULTURAL SERVICES
2 .3626
.0728
.1 0 6 2
-.0080
.9015
2 .0C1C
.0126
.0143
-.0 0 0 2
.3832
CHARCOAL ft FIREWOOD
•008 5
.0830
-.0997
.0091
.6293
LOGS
.0093
.0*67
-.0443
.0019
.9113
2 .1 5 1 C
.0^78
.0294
-.0009
.7801
. 6 4 22
.1323
-.0428
.0050
.9644
.0075
.0688
-.0614
.0036
.9384
fiber
10 FORESTRY
HUNTINGS
F I SHERI ES
COKING COAL
LIGNITE
BRI QUETTES
AND L I G N I T E
.0055
.0949
-.0998
.0091
.6739
IRON ORE& CONCENTRATES
•ooee
.0083
-.0086
.0001
-.0031
ORES K CONCENTRATES OF N O K - F t ft
.0092
.0033
-.0034
.0000
-.0176
PETROLEUMS CRUDE
.0097
.0764
-.0825
.0063
.2989
NATURAL GAS
.0092
.0157
-.0147
.0002
.2886
2.3371
.04 I d
.0547
-.0025
.9243
LI ME STONE SAND GRAVEL
N0N-METAL1C MINERALS
.0082
• 0n06
-.0656
.0041
.0522
CARCASSES
.3688
• 0U89
-.0493
.0038
.8833
PEAT PRODUCT
.0026
.1307
-.0862
.0069
-.4475
1 .8244
.1757
.0595
-.0144
.7403
(RAIN MILL
PRODUCTS
TAfc'LE/i ((CONTINUED).
10
M
ACROSS
THE
TITLE
33
REFINED
34
OTHER FOOD PREPARED
35
PREPARED
36
ALCOHOLIC
ASYHPTCTE
SUGAR
FEEDS
FCW C O E F F I C I E N T
FOR ANIMAL
& PC
BEVERAGES
CHANGE
REGRESSI ON
ADJUSTMENT
RATE
.0044
.0JP5
1 .1067
.2097
1 .3194
• 1 5 *• 2
.0078
.0557
GROWTH RATE
CHANGE OF GR RATE
RBARSQ
.0002
.2371
.0324
-.0060
• 6797
.0306
-.0050
• 8603
-.0485
.0023
• 7232
-.0126
39
SI LK
1 .4492
.0199
.0090
-.0002
• 1472
40
COTTON S PI NNI NG
1 .3775
.1248
.0422
-.0054
• 9696
41
WOOLEN 8 WORSTED YARN
1 .9813
.0078
.0084
-.0001
.0900
42
LI NEN
.6524
. 2 6 ‘>7
-.0313
.0057
• 77 3 1
43
SPAN RAVON YARN
1 .305*
.1371
.0402
-.0054
• 800C
44
SYNTHETI C
1 .4007
.1090
.0500
-.0052
• 8056
46
COTTON K SPUN RAYON FABRI CS WC
.0875
.1097
-.0957
.0091
• 8503
4/
SYNTHETIC
1 .6495
.1297
.0873
-.0115
• 8949
48
WOOLEN FABRI CS
.0083
.0444
-.0778
•0057
• 7362
49
LI NEN
50
VARN K FABRIC
52
ROPES&
53
CTH ER FI BER PRODUCTS
56
T EXTI LE
57
REELI NG & WASTE SI LK
SPU
TARN
FI BER
VARN
FI BERS WOVEN
FABRI CS
WOVEN & FELTS
UOVEN
.7067
.1000
-.0337
.0049
•6212
DYEI NG S F I K I S H 1
.0079
.0275
-.0239
.0006
• 5719
1 .7756
.0190
• 0122
-.0003
• 1279
.0095
.0087
-.0093
.0001
.0715
1 .3531
.1957
.0301
-.0065
• 7960
WOOD M I L L I N G
.5179
.0356
-.0118
.0003
• 4266
58
WOODEN PRODUCTS
.0091
.0238
-.0215
.0005
.6272
59
FURNITURE WOODEN i
.9785
.1309
-.0136
.0018
• 7436
.0087
•0001
-.0001
•0000
• 0001
.1894
FISHING
NETS
6ARMENTS
METAL
60
PULP
61
PAPER
.0081
• 0129
-.0115
.0001
62
ARTI CLES OF PAPER & PAPEREOARD
.9188
.1508
.0129
-.0015
• 6194
63
P R I NT I NG 8 PU B L I SH I NG
•0083
.001)4
-.0080
.0001
-.0063
•
TAELE
10
Af-|<
CON F X N U tO ) .
A
ACROSS
THE
T IT L E
fiCw C O E F F I C I E N T
ASYMPTCTE
64
LEATHER MANUFACTURES & FU*
65
LEATHER PRODUCTS EX.
66
ARTI CLES
67
BASIC
IKORGANIC
68
BASIC
ORGANIC
69
SYNTHETIC
to
ELASTI NG
71
SPUN RAYON
PkC
FOOTWEAR
OF RUBBER
.0067
1 .2291
.393 1
I NDUSTRI AL
I NDUSTRI A L
REGRESSI ON
ADJUSTMENT
RATE
.0362
GROWTH RATE
CHANGE
OF GR RATE
RBARSQ
-.0269
.0007
.4045
.1713
.0334
-.0056
.4457
.0329
-.0187
.0006
.8281
CHE
.0091
.0267
-.0238
.0006
.9232
CHEN 1
1 .2712
.0383
.0250
-.0006
.9429
2.338C
.0685
.0889
-.0069
.9473
1 .6879
.0535
• 0514
-.0021
.7039
.0089
*0377
-.0362
.0013
.5730
.9626
.2946
.0321
-.0073
• 8811
.0065
.0078
-.0077
.0001
.0294
1 .8048
.0437
.0415
-.0016
• 9037
1 .0317
• C640
.0086
-.0005
.3290
1 .900C
.0111
DYESTUFF
POWDER
72 MATERIALS OF SYNTHETIC
CHANGE
F16ER
73
FLASTI C
74
CHEMICAL
75
MISCELLANEOUS BASI C
76
VEGETABLE ft ANIMAL
.0113
-.0001
.0863
77
COATINGS
1 .1769
.1 170
.0158
-.0018
.8833
78
MEDI CI NE
2.0975
.0710
.0831
-.0060
.9581
79
OTHER CHEMICAL PRODUCTS
2 .9301
.0249
.0439
-.0014
.4490
80
PETROLEUM REFINERY PRODUCTS
1 .0604
• 1 329
.0143
-.0018
.9185
81
COAL PROOUCTS
1 .0857
.1638
.0224
-.0033
.7616
82
MISCELLANEOUS ANTI SEPT 1 CI IE 0 9
. 2 6 28
.0748
-.0517
.0035
.9051
F ERT I RI Z ER
CHEMICALS
OIL
83
CLAY PRODUCTS FOR BU1LDI NC USE
.8409
.1795
-.0205
.0032
.8492
84
CLASSWARE
1 .6878
.0611
.0545
-.0028
.8757
85
POTTERY
1 .0651
•2388
.0325
-.0066
.8903
86
CEMENT
.8593
.1278
-.0133
.0015
.6353
87
OTHERNON-METALL1C MINERAL PROD
1 .5021
.0354
.0154
-.0006
.1694
8ft
FI G IRON
3.0358
•*0132
.0253
-.0004
•2691
165
TA ELE A M U O N T I N U E D ) .
10
*
90
FERROALLOYS
ACROSS THE
ASYMPTCTE
UTLE
VI
STEEL
92
HOI - ROLLE D
PL A T E S *
93
STEEL P I P E
8 TUBE
V4
COLD-ROLLED £ COATED STEEL PLA
INGOT
V5
CAST fc FORGE
V6
NONFERROUS METAL
SHEETS
IRON
INGOTS
97
COPPER GRASS PRODUCTS
98
ALUMINUM EXTRUDED PRODUCTS
99
OTHER NONFERROUS METAL
PRCDUCT
100
SIRUCTURAL
101
OTHER
102
FOWER GENERATING MACHINARV & 6
103
MACHINE TOOLS ME TALW0RK1NC MAC
104
I NDU ST R I A L
105
GENERAL
106
OFFI CE
107
HOUSEHOLD MACHINERY
108
PARTS OF PACHINERY
109
STRONG ELECTRI C MACHINERY
111
OTHER WEAK ELECTRI CAL APPL1ANC
112
SHI PS
11 3
RAILWAY VEHI CL ES
114
PASSENGER MORTOR CAR
115
REPAIR Of
4
METAL PRODUCTS
PETAL PRODUCTS
MACHINERY
I ND U S T R I A L
MACHINERY 1
MACHINERY
t
RCW CO t F f I C 1ENT CHANGE REGRESSION
BOATS
PASSENGER MOTOR CAR
ADJUSTMi NT
RATE
GROWTH RATE
CHANGE OF GR RATE
RBARSQ
2 .4325
•0240
.0355
-.0009
.5059
.0075
.0160
-.0145
.0002
.2111
-.0069
.0000
.1717
. OOf £
• C 07 5
. 9 2 7C
.0625
.0129
-.0006
• 3341
.0072
•C 1 37
-.0111
.0001
• 1398
2.1244
. C1 2 1
• 0138
-.0002
• 4601
.0074
.0358
-.0286
.0008
• 6161
. 01 0 C
.0449
-.0473
.0022
•6837
1 .5506
.0812
.0444
-.0037
• 8987
.0085
.0062
-.0062
.0000
-.0017
2.1344
.0389
.0467
-.0018
• 8466
.5745
.0411
-.0122
.0004
.3488
.6614
.0596
-.0158
.0008
• 5510
.6774
.2140
-.0318
• 0050
•8548
.9395
.0745
• 0084
-.0005
• 4306
1 .7428
.0549
.0484
-.0024
• 8602
2.0605
.0659
.0819
-.0049
.7 0 06
.8093
.2067
-.0280
.0049
•6792
1 .7617
.0299
.0285
-.0007
.6205
2.0965
.0007
.0007
.0000
•0005
1 .7426
.0048
.0044
•0000
• 1595
2 .2652
.1125
.0476
-•0093
•2455
.0076
.0396
-.0393
•0015
• 1798
1.0368
.1390
.0153
-.0019
. 7 5 22
.0087
• G2 4 5
-.0229
•0005
•6429
166
TAfcLE XI ( ( C O N T I N U E D ) .
10
116
A
ACROSS
THE
TITLE
ASVNPTC1E
MOTORCYCLES ft BI CYCLES
T 1 7 AIRCRAFTS
118
Cl HE R TRANSPORTATION
119
FfcECl SI CN MACHINERY
1<!0 PHOTOGRAPHIC & OPTI CAL
*CW C O E F F I C I E N T
IN STRUP
CHANCE
REGRESSI ON
ADJUSTMENT
RATE
GROWTH RATE
CHANGE OF GR RATE
RBARSQ
.C035
,1021
-.0535
.0027
.5369
.0059
.0446
-.0320
.0010
.2445
.7719
.2366
.0276
-.0041
.8731
1 .8444
.0050
.0042
.0000
.1281
1 .6656
.0017
.0014
.0000
.0022
122
Cl HER MANUFACTURING GOODS
1 .0453
.3349
.0499
-.0135
• 8918
123
HOUSING CONSTRUCTION
1 .2726
.0567
• 0084
-.0005
• 3226
124
CONSTRUCTION NOT FOR RE S I CE N T I
. 01CS
.0151
-•0178
.0003
.3700
125
BUI LDI NG
1 .0967
.1678
.0215
-.0033
.8613
12 7
OTHER CONSTRUCTION
.7982
.0117
-.0065
•0001
.1645
128
E L E CTRI CI T Y
1 .9987
• C0 6 7
.0068
.0000
.6178
12 9
GAS
REPAI RI NG
1 .2791
.0718
.0218
-.0015
• 2290
1 JO WATER-SUPPLY,SEWERAGE
1 .1036
.2795
• 0283
-•0071
•8370
131
WHOLESALE
1 .7894
•0059
• 0027
•0000
•0917
132
RETAI L
1 .2719
.1002
• 0149
-.0016
• 765C
133
F I NANCI AL
BUSINESS
.0093
.0318
-.0300
•0009
• 9402
134
INSURANCE BUSI NESS
.0065
.0975
-.0869
•0070
-•4198
135
REAL ESTATE AGENCY
.8721
.1252
-.0147
•0017
•8952
137
NATIONAL
.0089
.0859
-.0804
• 0060
• 8374
138
LOCAL RAILROAD
•009C
• 1014
-.0979
•0088
-.3407
13 9
ROAD PASSENGER TRANSPORT
.0081
.0768
-.0760
•0054
• 3397
140
ROAD FREIGHT
2.2677
.0647
• 0776
-.0058
•9775
141
ROAD TRANSPORTATION F A C I L I T I E S
1.9146
.0969
.0867
-.0091
.9869
14 3
INLAND WATER TRANSPORT
.4804
.0797
-.0388
•0028
•9872
144
AI R TRANSPORT
1 .8577
.0661
.0781
-.0039
.5556
TRADE
TRADE
RAILROAD
TRANSPORT
table
0
XHCCOMINUED).
fi
ACROSS THE
TITLE
5 Cl HER TRANSPORT
new CO EM IC1ENT
ASVMPT CTE
CHANGE REGNESS10N
A DJ U S T M l Nl
RATE
GROWTH RATE
1 .OV 7 k
• 2302
.0357
CHANGE Of
GR RATE
RBARSQ
-.0072
.9223
6
STORAGE
• 01 C2
.0111
-.0116
.0001
• 5695
7
l E L E C O f l P U K I CA T l O N
•009 V
.0250
-.0247
.0006
.9215
.0066
.0603
-.0545
.0028
.9450
.6687
.0472
-.0132
• 0006
.9438
.0096
•0234
-.0235
.0005
• 7010
1 OTHER P UBL I C
2
SERVICE
SERVI CES
FOR BUSI NESS ENTERPRIS
5 OTHER PERSONAL
SERVICES
168
C
H
A
P
T
E
RXII
Sim
ulation Test of the C
om
plete M
odel
This chapter evaluates the predictive perform
ance of the m
odel in
so far a
s is presently possible.
W
e have not estim
ated all equations
with the m
ost recent data, so that s
o
m
e observations w
ould b
e left for
this test.
In the base year
their actual value.
of the forecast, 1970, all variables have
T
h
e forecasts starts in 1971.
T
he simulation test
is done over 1971-1972 because w
e have the actual data only through
1972.
T
h
e forecast of the m
odel w
a
sm
a
d
e up to 1985.
In testing the
predictive perform
ance, a num
ber of assum
ptions are m
a
d
ew
hich will b
e
explained in the next section.
After the plans a
n
d the assum
ptions are
described, the sim
ulations will b
e sh
o
w
n
.
P
lans a
n
dA
ssum
ptions
T
h
e simulation test is planned to answ
er the following questions:
1. H
o
waccurate a
n
d reliable are the forecasts generated by all
the equations a
n
d by the im
put-output com
putations?
2. H
o
wdoe
s across-the-row coefficient change affect the per­
form
ance of the m
odel?
3. H
o
wsensitive is the forecast of the m
odel to the exogenous
assum
ptions?
For those questions, the simulation is carried out in tw
o steps.
1. T
h
em
odel is sim
ulated.
a. with constant input-output coefficients.
b. with variable input-output coefficients forecasted b
y
the across-the-row m
ethod.
169
2. T
h
e effects of the exogenous assum
ptions on long term grow
th
are investigated with the variable input-output coefficient
forecasted by the across-the-row m
ethod.
T
h
em
odel requires exogenous assum
ptions on:
1. disposable incom
e,
2. the interest rate,
3. all kinds of governm
ent expenditure,
4. the world prices of im
ported goods a
n
d exported goods,
5. the foreign d
e
m
a
n
d for Japanese goods,
6. the grow
th rate of population, a
n
d the grow
th rate of the
num
ber of households.
In order to evaluate the predictive perform
ance of the m
odel,
the simulation test is done with all of the actual values of the
exogenous variables in 1
9
7
1 and 1972.
T
h
e actual world prices are
available up to 1
97
2 fromthe world trade m
odel, a
n
d the foreign
d
e
m
a
n
d is also generated by the world trade m
odel.
Sim
ulation Test
T
h
e simulation errors are sh
o
w
n in three tables.
Table XII-1
sh
o
w
s the simulation errors of consum
ption, im
ports, a
n
d exports for
156 sectors.
For output and price, the simulation errors w
ere cal­
culated by 2
0 sector aggregation level a
nd sh
o
w
n in Table XII-2.
Table XII-3 sh
o
w
s the simulation errors of investm
ent, labor require­
m
ent, m
anhours per em
ployee, a
n
d em
ploym
ent by 1
9 sector classification.
It is unfortunate that w
e cannot test the m
odel by the simulation
of output a
nd price in the 156 sector classification.
T
h
e output data
w
hich w
e have at hand for the 156 sectors w
ere aggregated from census
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N
S
P
O
R
TA
N
DC
O
M
M
5.8F7
2.963
.29
8
.647
fc.7
7
R
?9 7
.7 0 4
9.181
1# F
IN
A
N
C
EA
N
D IN
S
U
R
A
.1 93
2.505
2.266
.9U
M M
.188
*.7 8 4
2 266
.9 1 4
1 .199
19 O
T
H
E
RS
E
R
V
IC
E
S
.2 ^4
1 .9 9 C
.161
.000
1.1 *>3
.2 6 9
1.967
160
.0 0 0
.779
A
V
E
R
A
G
E E
R
R
O
R
1 .3 <6
2.795
.586
.872
4.632
1.602
2.7 5 2
5
8
8
.8 1 4
4.00S
2.P
43
178
reports but are not consistent with the various final d
e
m
a
n
d data for
1
9
7
1a
n
d 1972.
T
hey are also inconsistent with the production indices
of agriculture, m
ining, a
nd m
anufacturing industries.
T
hese production
indices se
e
m
e
d in closer agreem
ent with the final d
e
m
a
n
d
s.
Until w
e
ca
n solve this data puzzle, therefore, w
e have aggregated the outputs
of the m
odel to a 2
0 sector level for com
parison with the indices of
industrial production published at that level.
T
h
e production index
is not available for non-m
anufacturing industries except Agriculture.
T
h
e tables of simulation errors sh
o
wthe simulation errors of
the forecasts with a
n
d without the across-the-row coefficient ch
a
n
g
e
m
ethod.
T
h
e predictive perform
ance is evaluated by com
paring the absolute
percentage error of output, price, a
n
d other variables.-*-
Also, the
w
eighted absolute average errors are calculated using the actual outputs in 1
9
7
1a
s weights.
2
^T
he form
ula for absolute percentage error is
i
1
9
7
2
A
P
E
i =
i
1
\± = 1
9
7
1
l \ - xi
x
i
5
6
i = 1............................1
A
w
here
is the predicted value a
n
dX
^ is the actual value.
2
W
eighted absolute percentage error is
W
A
P
E- 1f6
i=l
w
here
A
PE.-.q./T
1 *
is output of i ^ sector in 1971, a
n
d T^ is total output in 1
9
7
1
179
TABLE X I I - 4
x
T
h
eW
eighted A
verage Absolute P
ercentage Errors of the Sim
ulations
N
o Coefficient
C
h
a
n
g
e
Coefficient
C
h
a
n
g
e
a. O
utput
3.614
4.011
b. Price
4.251
4.222
c. C
onsum
ption
1.393
1.403
d. Im
ports
.626
.636
e. Exports
.995
.995
f. Investm
ent
1.366
1.602
g. W
a
g
eR
ate
2.795
2.752
h. Productivity
.586
.588
i. M
anhours per em
ployee
.832
.814
4.832
4.005
j. E
m
ploym
ent
For consum
ption, exports, and im
ports, error a
s a percentage of
output^- of e
ach sector
d
e
m
a
n
d of that sector
is calculated to see h
o
wthe error in the final
is im
portant in determ
ining the output error of
that sector.
T
h
ew
eighted average absolute percentage errors are sh
o
w
n in
Table XII-4.
T
h
e errors d
o not change very m
u
ch in these tw
o cases.
Unfortunately, the coefficient change m
ethod did not reduce the sim
u­
lation errors.
H
ow
ever, w
e could not judge the effectiveness of the
^•Error in percentage of output is
A
P
E
Q
±
1 ................................. 156
180
coefficient change m
ethod by this simulation test because this test
covers only tw
o years.
T
h
e functional form of the across-the-row
change m
ethod is a tim
e trend equation.
Therefore, within tw
o years,
w
ed
o not expect the coefficient change to play a significant role in
determ
ining the simulation errors.
Final d
e
m
a
n
d equations w
ork very well; the percentage errors are
all less than 2
%
. Labor m
arket equations also w
ork very well.
T
h
e
relatively high error of em
ploym
ent to other variables are ow
ing to
the errors of output forecast.
T
he errors caused through input-output
com
putation are not significant because the output error is not m
u
ch
bigger than the s
u
mof those of final d
e
m
a
n
d com
ponents.
S
o far, w
e have discussed the sectoral errors.
T
h
e aggregate
overall error is m
u
ch sm
aller than the w
eighted average sectoral error.
T
h
e aggregate overall output error is less than 3
%
. A
s can be se
en in
the simulation error tables, so
m
e sectors have very large errors.
B
ut
those sectors are not very im
portant in output share, a
nd d
o not in­
crease the w
eighted average error very m
u
ch
.
T
h
e sm
aller the output
of a sector, the m
ore difficult it is to predict it accurately.
Sensitivity of the M
odel to Different E
xog
e
no
u
sA
ssum
ptions
In this section, the forecasting results of the m
odel with
different exogenous assum
ptions are described.
T
h
e tw
om
ost im
portant
exogenous assum
ptions are chosen to test the sensitivity of the m
odel,
nam
ely, the rate of grow
th of disposable incom
ea
n
d the interest rate.
T
h
e across-the-row coefficient change m
ethod is utilized with the dis­
posable incom
ea
n
d interest rate experim
ents.
T
h
e rest of the exogenous
181
assum
ptions are fixed in each simulation.
In e
a
ch simulation, fore­
casts are m
a
d
e up to 1985; these forecasts will be com
pared with e
a
ch
other.
A
. Sim
ulation W
ith Different D
isposable Incom
es
Disposable incom
e in Japan grewby a
n average of 8
%a year until
1972.
After the oil shock in 1
973, the grow
th rate slow
ed d
o
w
na
little bit, but the trend is expected to stay around 6
%a year.
W
h
e
n
w
e ran the m
odel with 6
%grow
th rate of disposable incom
e, labor
supply w
a
s a binding constraint in the 1980's.
Accordingly, tw
o
grow
th rates are chosen, nam
ely, 4
%for low grow
th, a
n
d6
%for high
grow
th.
T
hese grow
th rates are applied from 1976 to 1985.
U
p through
1975, the actual grow
th rates for disposable incom
ew
ere used.
T
h
e changes of disposable incom
eaffect directly consum
ption w
hich
then brings about output changes.
em
ploym
ent also change.
A
s output changes, investm
ent and
S
ince em
ploym
ent could indicate potential
incom
e, w
em
a
y judge the plausibility of the exogenous assum
ptions
about incom
e by the em
ploym
ent forecast.
A
sw
e can see in Table XII-5,
the 6
%grow
th rate of disposable incom
e requires very m
u
ch higher e
m
­
ploym
ent in 1985 than the potential labor force.
T
h
e slowing d
o
w
n of
labor productivity and declining m
anhours per w
orker m
a
ke the grow
th
in the potential labor supply not fast enough to support a 6
%increase
in incom
e.
O
n the other hand, the 4
%annaul grow
th of incom
ew
ould
bring about large unem
ploym
ent^ in the late 1970's.
T
h
e simulation
^-U
n
e
m
p
lo
ym
e
n
t rate cannot b
e calculated because w
e lack the labor
force projection. U
sing constant labor force participation rate of 1970,
w
e only kn
o
wthe approxim
ate trend of unem
ploym
ent rate.
182
T
A
B
L
EXI1-5
Sensitivity Analysis W
ith D
isposable Incom
e
D
isposable
Incom
e
Y
ear
1
9
7
6
1
9
7
8
1
9
8
0
1
9
8
2
1
9
8
5
C
onsum
ption
Private
Investm
ent
E
m
plo
ym
e
n
t
in 1,000!s
G
.K
.P
.
(A
)
63,887
6
%
*
53,039
12,413
5
.9
%
4
.1
%
56,731
1
.2
%
98,751
6
.4
%
(B
)
62,682
4
%
52,176
12,185
4
.2
%
2
.2
%
50,252
.3
%
97,626
5
.2
%
(A
)
71,783
6
%
59,514
5
.9
%
19,374
2
5
.3
%
54,581
4
.1
%
115,692
8
.3
%
(B
)
67,797
4
%
56,595
4
.1
%
18,005
2
2
.3
%
52,719
2
.7
%
111,359
6
.9
%
(A
)
80,656
6
%
66,759
5
.9
%
26,839
1
5
.1
%
56,111
4
.0
%
133,868
7.3?
(B
)
73,329
4
%
61,302
4
.1
%
24,220
1
3
.7
%
55,741
2
.8
%
125,791
6
.0
%
(A
)
90,625
6
%
74,851
5
.9
%
29,890
2
.5
%
62,558
2
.5
%
148,741
4
.8
%
(B
)
79,312
4
%
66,308
4
.0
%
26,757
2
.4
%
57,825
1
.5
%
137,071
3
.9
%
(A
)
107,936
6
%
88,926
5
.9
%
34,342
1
0.1%
68,734
4.0?
172,742
5
.6
%
(B
)
89,216
4
%
74,566
4
.0
%
29,876
8
.2
%
61,474
2
.7
%
153,889
4
.2
%
^P
ercentages are grow
th rate from the previous year.
183
sh
o
w
s that the balanced grow
th rates are 6
%in the late 1970's a
n
d4
%
in 1980’s.
A
ppendix Bsh
o
w
s a standard forecast in w
hich the balanced
grow
th rates of disposable incom
e are used.
T
h
em
odel sh
o
w
s a serious depression in 1975.
been grow
ing by alm
ost 1
0
%a year u
p to 1972.
T
h
eG
.N
.P
. h
a
d
T
h
e relatively low grow
th
rate of 1971, 6
.8
%a
n
d the actual reduction of disposable incom
e in
1974, -0.6%
, caused the depression through 1975 w
hich dem
onstrates the
dynam
ic aspects of this m
odel.
In Table XII-6, the predictions of m
ajor m
acro variables w
hich
w
ere m
a
d
e by using the actual disposable incom
e through 1
97
5w
ere c
o
m
­
pared with the actual values.
T
h
e percentage errors are generally low
.
Relatively large errors occured in consum
ption of 1973 a
n
d 1974.
T
hrough
1972, the grow
th rate of consum
ption had been approxim
ately s
a
m
e to that
of disposable incom
e.
For exam
ple, in 1
9
7
2 consum
ption increased b
y
10.7%
, while disposable incom
e increased by 11.1%
.
B
ut in 1
973, in
spite of 1
1
%increase of disposable incom
e, consum
ption grew only 7
.5
%
.
Instead of consum
ing the increm
ental disposable incom
e the Japanese
people invested m
ore in 1973.
This kind of change in short-term be­
havioral pattern m
a
d
e the error in consum
ption relatively bigger than
the errors in other years.
T
h
e errors of em
ploym
ent in 1
9
7
2 and 1973 are large.
This is
ow
ing to the unexpected productivity grow
th in 1
9
7
2a
n
d in 1973.
T
h
e
rates of productivity grow
th w
ere greater than 1
0
%in these years.
grow
th rate of productivity in 1
97
1w
a
s only 4
.5
%
T
h
e
184
T
A
B
L
EXII-6
Errors of M
ajor M
a
cro Variable Forecasts
,N
.P
.
Actual
Predicted
Error
1
9
7
1
1
9
7
2
1
9
7
3
1
9
7
4
82,212
89,668
98,508
97,365
9S
,839
82,102
91,807
99,272
97,900
96,67
2
.1
%
2
.4
%
.8
%
.5%
1
97
5
2.2%
m
sum
ption
A
ctual
40,482
44,293
47,945
48,632
51,535
Predicted
40,512
44,684
49,619
50,152
52,538
Error
Investm
ent
Actual
Predicted
Error
E
m
ploym
ent
Actual
Predicted
Error
.1
%
.9
%
3
.5
%
3
.1
%
1
.9
%
27,059
29,663
33,912
30,530
29,529
27,478
31,042
33,365
31,574
28,049
1
.5
%
4
.6
%
1
.6
%
3
.4
%
5
.0
%
52,812
52,760
54,041
53,710
50,881
52,843
54,920
56,423
53,668
51,006
.0
%
4
.1
%
4
.4
%
.0
%
.5
%
There is a data inconsistency betw
een national accounts and the 1
9
7
0
Input-Output table. According to national account, G
.N
.P
. in 1
9
7
0 is
70,634 billion yen, and consum
ption expenditure is 36,258 billion yen.
B
ut the I/O table sh
o
w
s that G
.N
.P
. in 1
9
7
0 is 76,258 billion yen a
n
d con­
sum
ption expenditure is 37,733 billion yen. T
h
e actual n
um
be
r in the table
ca
m
e fromnational accounts. B
ecause this m
odel is based o
n1
9
7
0 1/0 m
odel,
the actual num
bers in the table are adjusted to b
e consistent to the 1/0
table. T
h
e actual num
bers are taken from 1
A
nnual R
eport on National Incom
e
Statistics, f published by E
conom
ic Planning A
gency, G
overnm
ent of Japan a
n
d
'M
ain E
conom
ic Indicators, * published by O
.E
.C
.E
.
185
Investm
ent is very sensitive to incom
e change.
After the de­
pression in 1975, investm
ent soars in 1978; private investm
ent in­
creases 2
5
.3
%for 6
%incom
e grow
th case a
n
d2
2
.3
%for 4
%incom
e grow
th
case.
T
he constant grow
th of incom
e causes stable grow
th of output,
w
hich causes steady grow
th of investm
ent.
of investm
ent are low in both cases.
In 1982, the grow
th rates
T
h
e high grow
th rate of invest­
m
ent in 1978 a
n
d the low grow
th rate of investm
ent in 1
9
8
2 can be ex­
plained by the dynam
ic aspect of the investm
ent equation.
T
h
e high
grow
th rate of output ow
ing to the high grow
th rate of disposable
incom
e in 1976 a
n
d1
9
7
7m
a
ke
s the desired capital stock high.
S
ince
the investm
ent has b
e
e
n low through 1976, the actual capital stock
is low in 1
97
7a
n
d in 1978.
Therefore, the m
odel predicts the high
grow
th rate of investm
ent in 1978.
Since the grow
th rate of output
declines after 1978, the desired capital stock doe
s not grow fast
enough to keep the grow
th rate of investm
ent high.
T
he m
odel predicts
that the grow
th rate of investm
ent in 1
9
8
2 is the lowest even though
the am
ount of investm
ent is grow
ing.
N
ot only on the aggregate m
acro variable, but also o
n com
position
of the sectoral com
ponents does this change of disposable incom
e have
an influence.
T
he different incom
e elasticities of consum
ption give
different product com
positions of consum
ption with the different
grow
th rates, a
n
d therefore, different output shares, w
hich, in turn,
determ
ine the com
position of em
ploym
ent a
nd investm
ent.
Table XII-7
sh
ow
s the com
parison of com
position of these variables in 1985 for 2
0
sectors.
A
sw
e expected, the low incom
e elasticity of Agricultural
product causes low consum
ption share, low em
ploym
ent share, and low
186
TABLE X I I - 7
C
om
parison of C
om
positions of
T
w
o Different G
row
th R
ates in Y
ear 1
9
S
5
Industry
1. Agriculture, forestry
a
n
d fishery
C
onsum
ption
4
%
6%
E
m
ploym
ent
4
%
6
%
O
utput
6
%
4/t
3.81
3.93
10.31
10.49
3.00
3.08
0
0
.46
.47
1.40
1.42
17.32
17.71
1.11
1.27
3.08
2.92
4. Textile
8.70
8.43
5.13
4.89
2.60
2.47
ulp a
n
dP
aper
5. P
1.27
1.23
.74
.73
1.97
1.95
.92
.92
2.20
2.21
4.98
4.99
7. Prim
ary M
etals
0
0
1.69
1.73
3.98
4.10
etal Products
8. M
.94
.95
2.35
2.33
2.66
Z .f”
achinery
9
. Non-Electrical M
.38
.35
2.58
2.61
5.68
5.7*
achinery
10. Electrical M
1.47
1.54
2.40
2.50
3.51
3.67
quipm
ent
11. Transportation E
1.48
1.12
3.18
3.23
3.78
3.86
12. M
iscellaneous M
anufact.
3.92
3.83
7.78
7.75
7.77
7.79
0
0
11.76
11.62
6.93
6.89
1.97
2.04
.60
.60
2.67
2.68
holesale &Retail Trade 20.62
15. W
21.00
16.93
16.52
2. M
ining
o
o
d
sa
n
dT
obacco
3. F
hem
ical Products
6. C
13. Construction
14. Electricity, G
a
s &W
ater
14.94 14.68
eal Estate
16. R
8.97
8.80
1.19
1.17
4.75
4.47
n
d
17. Transportation a
C
o
m
m
u
n
ica
tion
8.31
7.96
9.09
9.02
8.81
8.69
18. Finance &Insurance
6.02
6.15
2.24
2.21
4.59
4.53
ther Services
19. O
13.93
14.05
14.54
14.91
20. Non-Classified
.01
.01
3.71
3.75
(N
um
bers are in percentages)
10.84 11.27
2.06
2.0'"
187
output share if disposable incom
e grow
s fast.
O
n the other hand,
Textile gains larger share of em
ploym
ent a
n
d output with 6
%grow
th
of disposable incom
e.
B
. Sim
ulation W
ith Different Interest R
ates.
T
h
em
odel doe
s not consider the financial m
arket at all.
T
h
e
only connection to the financial m
arket in this m
odel is through the
interest rate, w
hich is given exogenously.
T
h
e interest rate affects
investm
ent and savings, through w
hich it affects total consum
ption
indirectly.
T
w
o simulations are done with different interest rates.
First,
a constant interest rate, the 1
9
7
2 level, w
a
s used up to 1985.
Secondly, the interest rates are chosen so that they have anticyclical
effects.
L
o
winterest rates are assigned in the depression period a
n
d
high interest rates are assigned in the 1980fs.
D
isposable incom
e is
a
ssu
m
e
d to increase 6
%per year in both cases.
E
ve
n though the elasticities of substitution in the investm
ent
equation are very low, investm
ents turned out to be sensitive to the
interest rates.
T
h
e low interest rate in 1975 increases investm
ent
by 5
0
4 billion yen, a
nd the high interest rate in 1985 low
ered invest­
m
ent by 8
9
6 billion yen.
ploym
ent a
n
d output.
T
h
e change of interest rate also affects e
m
­
In 1985, the chosen interest rates w
hich have
anticyclical effects reduced em
ploym
ent by 3
2
4 thousand persons, a
nd
reduced G
N
Pby 8
9
1 billion yens.
C
onsum
ption is also affected through
savings equation by interest rate change.
T
h
e difference of co
nsu
m
p
­
tion in these tw
o cases in 1985 is 1
0
8 billion yens.
*
188
T
A
B
L
EXII-8
Sensitivity Analysis W
ith Interest R
ates
Interest
R
ate
Y
ear
1
9
7
3
1
9
7
5
1
9
7
8
1
9
8
0
1
9
8
2
1985
C
onsum
ption
Private
Investm
ent
E
m
ploym
ent
in 1, O
O
P
's
G
.Is.P
(A
)
7
.0
%
47,240
6
.9
%
15,265
-7.9%
53,801
-.1%
91,627
4
.8
%
(B
)
6
.7
%
47,267
7
.0
%
15,402
-7.1%
53,874
.0
1
%
91,780
4
.8
%
(A
)
7
.0
%
50,072
4
.2
%
11,922
-14.5%
50,125
-3.4%
92,845
.8
%
(B
)
6
.7
%
50,100
4
.2
%
12,426
-13.8%
50,356
-3.4%
93,324
.7
%
(A
)
7
.0
%
59,514
5
.9
%
19,374
2
5
.3
%
54,581
4
.1
%
115,693
8
.3
%
(B
)
7
.6
%
59,467
5
.9
%
18,444
2
2
.0
%
54,208
3
.6
%
114,771
7
.8
%
(A
)
7
.9
%
66,759
5
.9
%
26,839
1
5.1%
59,111
4
.0
%
133,868
7
.3
%
(B
)
7
.9
%
66,686
5
.9
%
24,843
1
4.0%
58,336
3
.7
%
131,982
7
.0
%
(A
)
7
.0
%
74,851
5
.9
%
29,890
2
.5
%
62,558
2
.5
%
148,741
4
.8
%
(B
)
8
.1
%
74,763
5
.9
%
28,285
4
.4
%
61,926
2
.3
%
147,274
5
.2
%
(A
)
7
.0
%
88,926
5
.9
%
34,342
1
0
.1
%
68,734
4
.0
%
172,742
5
.6
%
(B
)
8
.3
%
88,818
5
.9
%
33,446
9
.0
%
68,410
3
.9
%
171,851
5
.4
%
189
V
P ro s p e c ts
F
ro
mthe simulation test a
n
d the various sensitivity analyses,
w
e could conclude that the m
odel behaves quite reasonably.
there is still m
u
ch ro
o
mfor im
provem
ents.
H
ow
ever,
H
ere the m
odel will be
review
ed critically a
n
d possible im
provem
ents will be proposed.
A
. E
xogenous A
ssum
ptions
A
sw
e can see in the sensitivity analyses, the exogenous a
ssu
m
p
­
tions are very critical in forecasting.
E
ve
n though this m
odel is not
designed to forecast short term cyclical m
o
ve
m
e
n
ts of the econom
ic
variables, the cyclical path of the e
co
n
o
m
y is im
portant in forecasting
long run outputs a
n
d prices in the future.
D
u
e to the dynam
ic features
of the m
odel, the forecasts will vary according to w
hether w
eh
a
da
recession before or not.
Therefore, the forecasting ability of the
m
odel could be im
proved by replacing the exogenous assum
ptions o
n
disposable incom
e, interest rate, a
n
d labor force, with endogenously
generated ones w
hich are very sensitive to short run variations.
In fact, incom
e of the 1
56 sector level can be determ
ined within
the m
odel, because w
e can calculate w
a
g
e com
pensation and profit from
the w
a
g
e equation a
n
d the m
arkup equation in the price system
.
H
ow
ever,
for that purpose, w
e need a lot of tim
ea
nd a wealth of data to reform
u­
late and test the equations.
At the m
o
m
e
n
t w
e only calculate w
a
g
ea
n
d
labor requirem
ent by 2
0 sectors.
O
ther incom
e com
ponents such as in­
co
m
e from assets, transfer incom
e, a
n
d taxes, could be treated with
m
acro equations.
Attaching a m
acro aggregate m
odel to this I/O m
odel could eliminate
the exogenous assum
ptions on incom
e, interest rate, and labor force.
B
y
190
doing so, w
em
a
y pursue consistency betw
een the aggregate m
acro m
odel
a
n
d the multisectoral input-output m
odel.
B
. T
h
e Behavioral Equations
T
h
e forecasts m
a
d
e by the behavioral equations in the m
odel d
e
­
p
e
n
do
n the assum
ptions of the functional form
s of the equations.
F
or
instance, in the labor requirem
ent equation, w
ea
ssu
m
e that labor is
agum
ented over tim
e by the G
om
pertz curve, w
hich forces the labor pro­
ductivity grow
th to slow d
o
w
n in the future.
T
h
e reason for the choice
of the G
om
pertz curve is the expectation that labor productivity in
Japan will slow d
o
w
n in the future.
using recent data.
This expectation should be tested
In the investm
ent equation, w
e em
ploy the K
oyck
lag sch
e
m
e because of the sm
all n
um
be
r of observations.
O
w
ing to the
infinite tail of the lag sch
e
m
e
, w
e found s
o
m
e unreasonably slow
adjustm
ents of actual capital stock to optim
al capital stock.
T
h
e
A
lm
on lag sch
e
m
em
ight w
ork better if w
e had e
n
o
u
g
hn
um
be
r of obser­
vations.
T
h
e functional form of the consum
ption equation is nonlinear.
This form allows the interaction betw
een the incom
e variable a
n
d the
price variables w
hich m
a
ke
sm
ore sense than linear form in w
hich n
o
interaction is allowed.
price forecasts.
B
ut this nonlinear form requires m
ore accurate
It has b
e
e
nc
o
m
m
o
n to rely m
ore heavily on incom
e
elasticity to forecast consum
ption because it is hard to kn
o
wthe price
in the future.
B
ut in this m
odel, price elasticities are equally im
­
portant in consum
ption forecasting.
Therefore, w
e should be m
ore care­
ful to get g
o
o
d price forecasts.
T
h
e forecasts of the behavioral equation depend also o
n the
191
a
^priori information used in the estim
ation procedure.
In the esti­
m
ation of the consum
ption equation param
eter, w
e em
ployed a_ priori
information about incom
e elasticity a
n
d group price elasticity.
A
c
o
m
m
o
n econom
etric m
ethod to incorporate existing information in para­
m
eter estim
ation is the m
ixed estim
ation technique with w
hich w
e can
test compatibility betw
een existing information and historical data
series.
B
ecause of the nonlinearity of the consum
ption equation, w
e
could not apply the m
ixed estim
ation technique.
c
o
m
e elasticities
T
h
e cross section in­
w
ere plugged in without any statistical test.
arbitrary limits w
ere assigned to the group price elasticities.
Also,
There­
fore, the next step to b
ed
o
n
e for the consum
ption equation is to test
this a
_priori information in m
ore statistically consistent w
ay.
T
h
e
IN
F
O
R
U
Mim
port a
n
d export equation estim
ation m
ethod w
a
s devised to
incorporate existing information with historical data.
T
h
e utility
O
function w
hich depends o
nR a
n
d the deviation of estim
ates from exist­
ing information is m
axim
ized in the technique.
T
h
es
a
m
e idea could b
e
used in the consum
ption equation estimation.
There is ro
o
mfor im
provem
ent in the inventory equation.
m
ain problem in the inventory equation w
a
s the lack of data.
T
he
N
o
n
­
m
erchandise im
ports and exports need m
ore sophisticated equations.
T
h
e price forecast could b
e im
proved by using appropriate d
e
m
a
n
d
m
easures w
hich could bring in short run effect in prices.
H
ow
ever,
these tasks require a large extension of the m
odel a
n
d a wealth of
data.
C.I/O Coefficient Forecasts
Unfortunately, the effectiveness of the across-the-row coefficient
192
change m
ethod w
a
s not really tested in the simulation because of the
short simulation period.
E
ve
n though the errors with constant input-
output coefficients w
ere not large, the coefficient change ow
ing to
the technological change or relative price change could produce large
errors in the future if not accounted for.
T
h
e projection of input-
output coefficients is still a
no
p
e
n question in input-output econom
ics.
T
h
e IN
F
O
R
U
Mm
ethod is designed to project the coefficient change ow
ing
to technological change a
n
d product m
ix change.
H
ow
ever, w
e are certain
that input-output coefficients change a
s relative prices change.
This m
odel sh
o
w
sa
n exam
ple for country m
odels in the IN
F
O
R
U
H
international I/O forecasting m
odel.
W
e expect that different
countries have different natures of data.
Therefore, w
h
e
nw
e build
other country m
odels, these problem
s could b
e dealth with a
n
d different
m
ethods of handling themcould be tried.
193
A
P
P
E
N
D
IXA
D
ata S
ources
T
o build this large forecasting m
odel w
e need awealth of data.
B
esides the input-output table and the capital flow matrix, w
e had to
collect various econom
ic data series.
M
a
n
y of these series w
ere not
readily available from published sources.
T
h
e difficulty in collecting
the data of Japan, w
here the author has never been, w
a
se
ased by the
joint efforts of our Japanese sponsor, the Long T
e
rmCredit B
ank in
Tokyo, a
nd the author.
Lots of data w
ere collected a
nd created from
unpublished sources by the research teamin the bank.
T
h
e following is a short description of w
hat is the sources of
the im
portant data a
nd h
o
wthose w
ere created if they w
ere not readily
available from published sources.
Input-Output Table a
n
d Capital F
low Matrix
T
he G
overnm
ent of Japan published 1
97
0 Input-Output Table w
hich
is used as the basic input-output table in this m
odel in M
arch, 1974.
Explanations of the input-output table are found in
Tables. Explanatory Report,
Tablesc
.
a
nd in
1970 Input-Output
1960-1965-1970 Link Input-Output
T
h
e sector classification of output and capital in this
m
odel follows the Input-Output Table of 1970 and the capital flow
matrix.
194
♦
Price, V
alue a
n
d Quantity of O
utput
Collecting data series of price, value a
n
d quantity of output is
am
ain burden of the data w
ork.
It w
a
s possible to get the value a
n
d
quantity series of output of six-digit S
IT
C code com
m
odity for the
m
anufacturing industries from 1
9
5
8 to 1
9
7
2 from the C
e
n
su
s of M
a
n
u
­
factures published in 1967, 1
97
0 and 1973.
T
h
e price series are
obtained by dividing the value by the quantity.
aggregated into 1
5
6 input-output sectors.
T
hese series w
ere
For tne non-m
anufacturing
industries, the data could be obtained from
Statistical Y
ear B
o
o
k
published by the B
ureau of Statistics, Office of the P
rim
e Minister.
T
he appropriate conversion w
a
s needed from the classification of the
book to the input-output sector classification.
C
onsum
ption Expenditures a
n
d Prices of C
o
n
su
m
e
rs G
o
o
d
s
"A
nnual R
eport o
n the Fam
ily Incom
ea
nd Expenditure Survey,"
published by the G
overnm
ent of Japan has the consum
ption expenditure
series a
n
d price series of consum
er goods.
T
h
e classification of the
consum
er goods in the report is not s
a
m
e to the input-output sector
classification.
code.
Therefore, the conversion w
a
sm
a
d
e by using the S
IT
C
T
h
e length of the consum
ption expenditure series is different
for different com
m
odities.
series from1947 to 1971.
enough data series to give
estimation.
M
a
n
y of the sectors have consum
ption data
B
ut a few of the sectors d
o not have long
appropriate degree of freedom in the
Also, there w
ere a few sectors for w
hich w
e could not
convert the consum
ption expenditure classification into the input-output
classification.
For the sectors in w
hich w
e could not get long e
no
u
gh
195
data series or w
e could not convert the sector classification, w
e use
the output series to get consum
ption expenditure series assum
ing that
the consum
ption-output ratio of the sector are constant over tim
e.
This arbitrary assum
ption is not expected to influence
very
m
u
ch our
consum
ption forecast because the am
ount of the total expenditure of
these sectors is not large.
T
hese sectors are input-output sector
num
ber 4, 9, 10, 13, 18, 22, 39, 65, 66, 69, 70, 77, 87, 106, 131, 132,
135, 140, 141, 143, 145, 146, and 147.
Investm
ent a
n
d Capital Stock
Investm
ent, Capital Stock a
n
d deflator of investm
ent g
oods by
the classification of the capital flow matrix are gotten from un­
published docum
ents.
T
h
e docum
ent w
a
s obtained from the E
conom
ic
Planning A
gency of the Japanese G
overnm
ent.
N
on-m
anufacturing industry
investm
ent data are available in " A
nnual R
eport o
n National Incom
e
Statistics" published by the E
conom
ic Planning A
gency of Japan.
T
h
e
investm
ent data of m
anufacturing Industries are not broken d
o
w
n into
the capital flow matrix classification sectors in the report.
T
he
G
overnm
ent investm
ent on the social overhead capital is also available
in the report.
All investm
ent and capital stock data w
ere available
from 1953 to 1972.
Im
ports and Exports
T
he data series of the Japanese im
ports and exports of 1
1
9
tradable com
m
odities are available in the IN
F
O
R
U
MInternational Trade
M
odel D
ata B
ank.
T
he data in the data bank are obtained fromU
Na
n
d
196
O
E
C
Dpublications.
T
he 1
1
9 sectors in the data bank w
ere converted
to the 1
56 input-output sectors.
T
h
e foreign prices a
n
d the foreign
d
e
m
a
n
d
s for the Japanese com
m
odities are also borrow
ed from the IN
F
O
R
U
M
International Trade M
odel.
T
h
e im
ports a
nd exports of non-com
m
odity,
such as transportations a
n
d services, are obtained from the "A
nnual
R
eport o
n National Incom
e Statistics” published by the E
conom
ic Planning
A
gency, G
overnm
ent of Japan.
M
iscellaneous D
ata
T
h
e sources of other data series are following:
a. G
overnm
ent expenditure:
Statistics.
A
nnual R
eport on National Incom
e
E
conom
ic Planning A
gency, G
overnm
ent of Japan.
b. Inventory Stocks:
Japanese Statistical Y
earbook, B
ureau of
Statistics, Office of the P
rim
e Minister.
c. W
a
g
e
s, m
anhours per worker, a
n
d em
ploym
ent:
Y
earbook of Labor
Statistics, Division of Labor, Statistics and R
esearch, Office
of Labor Minister.
d. Population, num
ber of households, a
n
d disposable incom
e:
Japan Statistical Y
earbook, B
ureau of Statistics, Office of
the P
rim
e Minister.
e. Interest rate (C
om
m
erical B
ank Loan Rate):
Annual, the B
ank of Japan.
E
conom
ic Statistics
197
A
P
P
E
N
D
IXB
T
h
e Forecasts
T
h
ew
hole output of the m
odel is sh
o
w
n in this appendix.
Table B-l
sh
o
w
s the G
.N
.P
. forecasts with various m
acro-variable forecasts.
Also,
the exogenous assum
ptions o
n disposable incom
e, population, a
n
d interest
rates are sh
o
w
n in Table B-l.
A
s you m
a
y realize, the forecast of out­
put price in 1
9
7
4 is m
u
ch low
er than the actual price level.
T
h
e high
inflation of Japan in 1
9
7
4w
a
sm
ainly caused by the foreign inflation,
for instance, the high oil price.
B
ecause the international system
s
are not com
pleted yet, the foreign price forecasts are not available.
T
h
e foreign price a
s se
e
n from Japan is a
ssu
m
e
d to increase 5
%per year.
Therefore, the actual inflation in 1
9
7
4w
a
s not sh
o
w
nu
p in the price
forecasts.
Also, in im
ports a
n
d exports forecast, w
ea
ssu
m
e constant
relative prices after 1
9
7
2 because only foreign price series are avail­
able up to 1
9
7
2 for the tim
e being.
In the tables, all forecasts are in
billions of 1
9
7
0 yen except w
a
g
e rate.
sh
o
w
n in tw
o lines:
T
h
e forecasts of each item are
the first line is the m
agnitude of the forecast
a
n
d the second is the annual grow
th rate of the forecast.
O
nly the
private investm
ent are sh
o
w
n in Table 5, the values of investm
ent in
1970 a
n
d in 1
9
7
1 are actual.
Actual values are inserted in 1
97
0 for
all variables.
T
he tables are:
Table B-l
G
.N
.P
. S
u
m
m
a
ry
Table B
-2
Forecast
of Exports
of C
onsum
ption
- 3
Table B
Forecast
- 4
Table B
ports
Forecast of Im
- 5
Table B
ent
Forecast of Investm
- 6
Table B
m
p
lo
ym
e
n
t
Forecast of E
- 7
Table B
utput
Forecast of O
- 8
Table B
a
g
e
Forecast of W
- 9
Table B
equirem
ent.
Forecast of Labor R
-1
0
Table B
Forecast of Price
-1
1
Table B
anhours P
er E
m
ployee
Forecast of M
I *N*F
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9.41
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6.47
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6.71
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5.63
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98(0.9
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5.62
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11769.8
9.27
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6.96
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2.61
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5.26
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860.3
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200
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1971
26.6
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1979
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201
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32 BAKERY PRCDLCTS
33 REFINED SL6AR
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prepared
FEEDS FO
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79.8
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5.7
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16.2
2.5
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2.6
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37 SO
1.7
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2.3
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1981
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1979
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1978
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.ci 1 0 . 2 8 1 1 , 2 3 1 C . 6 4 9 , 6 3 "I3
299.9
310.7
322,6
5J‘t! ’i'.tt
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3.60
3 . £9
Mlrt 5
.63
75 Ml SCELLANEOLS BASIC CH£M
453.1
76 VEtETAbLE i
25£.7
292 .«
11.15
321.5
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362.5
1 2 . o7
272.1
2.35
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5.29
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5,3 7
465.6
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514. 5
5.5E
562.3
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612.5
8.52
664.3
£.46
765.5
7.44
694,8
7,74
224. S
244 .2
S.6C
2(4.5
16.52
311. 7
5.56
202 .1
-3.C6
292.C
-3.24
316.5
t .37
357 , 7
13 ,C2
4C2. 2
12.44
445 . 5
1 0 . 6£
48£ . 8
9.61
523 ,1
7.C2
564.C
3.5 2
637.7
7.10
ISiS.J
6.1?
I62t.fi
5.82
1726.6
6.13
184C.2
6.45
1958.4
6.42
2076.4
6.12
2 2 C 4 . 4 243 £ , 7 2 6 8 5 . 4
4.94
4 .93
6.C6
«MKAL OIL
77 COAT1NGS
7b MEC1CINE
79 01FE R CHEF1CAL PRODUCTS
1L23.2
727.5
12C6.5 12 5 i .C 14 5 6,1
7.14
16. £1
15.H
9 7£. 5
12.19
557.7
- 2. 13
9b 5 . 6
<.51
1054.7
7.C2
1135,8
7,69
1229,2
8,22
1329,2
6.14
1433.5
7.85
1539.1
7.27
1 7 3 6 .5
6.15
1961.4
6.5 2
26C1 .1 3CC 6 .5 3351.8
5.44
11.47
l i .£C
3222.3
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335t,6
1.C9
3677,4
5.49
4119.8 4618,2
12,1C
1 2 , C3
5145.3
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5691.8
10.62
6211.5
5.1 3
7116.1
6*86
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6,96
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835.r
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949.0
13.11
1 1 20 .4 13C9.9
1 6 . C6
16.51
1706.7
1678.5
5.5 4
22.B
-13.£3
22.4
-1.63
24.3
8.6 e
6.6?
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3C3 . 8
1C. C3
T 30.0
14. C9
eO PETROLEUM REFINERY PRODU 2376.7
664 .5
4.16
621.0
692 . 6
11.54
8CS.7
1 £ . SC
MISCELLANEOUS ANTISEPTIC
27.2
27.4
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25.4
7.47
£3 CLAY PROOLCTS FOR GU1L0I
226.0
2 35.0
4 . CO
262.1
11.si
275.4
6.20
<62.5
-6.C2
243, a
-7.12
250.8
2.(4
276.1
1C. 1C
£4 GLASSWARE
475.5
513.0
?.ee
6C2.3
I f .4C
65C.0
12.62
706.5
2.3 9
731.4
3.52
815.2
11.46
536.7 1 0 7 6 .C 1227.3 1366.7
13.15
1 4 . CC
14 . tC
14.66
cl
COAL PROOLC1S
tz
9C4.2
11.o7
25. e
26. 4
1.33 -11 .26
328.6
8.14
346.6
6.17
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29.C
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357,5
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373.2
3.36
1547.7 1640.9
1 1 . 45
8.76
2256.2
11.36
360.6
3.36
?
JAPANtSk
lA b li
B -
7 ( CCKl l Nl ( D)
:
I OMI A S I
OF CUl Ful
1570
1971
*5 PG IT 11) V
2tt.2
27? .4
4.5P
kb
<*2.2
449.2
1.5?
I C-NO
2
3
1
HOUL
U U t
CEPENT
(IK 1 S
fcULJCK TEN)
1 S7J
1V,’ <
1V75
1576
1577
157®
1979
1980
1581
1962
1985
31 i . t
1C .48
325.7
1C.44
241. t
.tc
222 .1
-2.53
3T3.2
t .C4
285.7
10.23
42C.2
1C.42
471 .2
9 . 45
511.3
8.31
542 .C
6.4C
58 5.4
3.4!
647. 9
5. 70
4S< ,7
11. C2
5 2i .9
t . c4
-4^7
473.7
-0.26
* K i l
55C.4
10.41
« iiS
659. 5
8 . 66
’lh
?‘ ! l i
758.5
4 . 66
fc7 OltENNCN-PE 1ALL1C NINE NA W71. 6
13 29 .4 15 11 , 2 16 5£.9
5. * 7
5.?3
IJ.iC
fc8 P i t
1412 .4 1 71 < .4 1E5C.2 113 9.7 1 d t 5. 5
1C. JC
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1 5 . 7C 1C .12
1NON
1244.9
fc9 INCH K STEEL SCRAPS
50 FE fcROALL CIS
5t.6
29.S
-25.59
AUl
47.4
t.c9
( C5.7
1NGCT
2453.1
52 HOI-ROLLED FLATESt SHEET 3527.1
53 STEEL PIPE S TUBE
556.4
2 5 7 8 . t 2ES2.5
5.12
i;.*c
44. 9
36.2
>5.14 - 14. 56
207.6
- 1. 15
H itt
51 STktL
15 J c . 2
-5.C2 M i ! r t
31 ?
1847.1
1C.51
41.5
P-SC
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257C.C
- 4. 56 - W i ?
1
I f 35.3 2086.4 2229.2 2555.1
11.64
9. 70
13.26
12.43
27 26 . C 2865. 3 3169.0
6. 95
6.(5
1 .94
2148.8 2474.3 2800.7
13.15
15.15
1 c . 23
3118.3
11.34
3359.6 3584. 8 4043.8
6. 69
7.74
2 . 53
56. 6
9 . 31
6G.8
7.42
6!. 2
3.85
6 2. 5
-.83
6 4. 9
1.61
486. 8
13. b t
545.7
12.09
552. 5
8.65
646. 2
4 . 05
M ’. sS
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46. 6
12.52
ii.c e
369.9
16.76
427. 7
1!.63
2844.1 3199.1 3565.5 3913. 7
12 .48
1 1. 4}
9 . 75 " V . t l
7.73
4432. 7 4495, 2
.36 * ' ! ! « ?
4 . tC
3766.9 42c 2.5 46 7( .0 4142.5 4112.8 4486.1 5C56.3 5742.2 6378.2 6982. 0 7420.2 7759. 6 6471.4
1 .51
4. 68
9 . 47
1 3 . tC
6 . (8
5.C7
12.7!
6.5C
12.67
5.1S
-5.48
11.08
-2.E ?
5^4 .5
5.C6
6S5.1
12. L I
7 2C. 2
11.48
726.?
-.55
665.!
-7.84
752.8
12.48
861.4
14.43
571.1 1083.7 1194.9
1 1 . 6C 10.25
12.73
1284.3 1389.9 1534.0
3 .75
4.46
7.48
54 COLD-ROLLED K CCA1E0 STE 1785.5
189C.9 2114.8 i 2 7 5 . 5 2183.0 1990-0 2154.2 2426. 7 27C8.0 297 8. 5 3231.7
12.65
8 . 49
- a .u
e .25
11.55
5.67
1(1.OC
11. *4
7.78
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s!;?
3811.5
4. 28
55 CAST t
154F .7
5.75
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3865. 8 4463.4
1C.26
1 .15
F0R6E IRON
141C.6
56 NOMERROUS PE1AL 1K60TS
557.9
926. 9
-6.12
1 7 7c . 1 1542.5
5.67
14.43
l o t 2 .e
1* .68
417. 4
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427. 6
2.51
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18.77
596.6
18.14
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16.24
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14.44
881. 3
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26i 4. C <9 E2.5 2524.2 2745.1
-4.62
-1 .95
14 .22
12.38
30e3.7
5541 .6 6375.5 7430.3
3 .?5
9.41
8.72
152s;.5 1825.2
- 6. 2b
-5.28
1933.4 2 2 1 5 . 5 2428.7 2633. 5 2624.0
8.4!
7. 23
8.C8
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5.62
2959.4 3 0 5 5 . 5
4.75
1 .35
11J 6 .4
l.t, 2
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-5.58
10C9.6
f 12.8
14.54
945.9
1C.79
744.2
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- 4 V.51
319.9
-14.86
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3729.5 4115.7
1 1 . 3C
1C.46
4251.6
6.60
4174.7
-4.54
3475.8
-16.74
35C9.3
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15C2.0
18C6.8
2C.3C
<364.9
14.53
2 2 0 0 .B 1857.1
-2 .71 - 1 5 . 2 8
1925.4
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( 55. 4
2 £4 .1
11.25
24< . 8
21 . C5
352.2
445.6
499, 5
1T.C9
572,3
ICO STRUCTURAL PE1AL PRODUCT 21E3.8
2243.0
2.71
1C1 OHEI)
16C0.8
1699.1
6.14
19< S.4 ( 065. 4
1! .51
5.08
1C2 POkER GENERATING PACH1HA
663.9
10C2.5
12.42
1C72.9
7.1!
1C3 HA(HIKE
5Cc .7
742 .8
-15.26
1C5
INtUSTRlAL PACHINERV
1497.C
3.78
393. 7
7 . 91
56 ALLMNUP EXTRUDED PRODUC
1 04
1415.8 1410.8
-.44
3.45
264.8
5.53
3 t C.4
2.37
TCOL S PETALhORKl
1C68.4 1180.4 1280.8 1366.1
11.75
1C. 48
6.82
6 . 51
231.9
1C.61
34* .7
11.15
HETAL PRODUCTS
956.1
6.11
255. 5
4.21
311.6
4. SC
PETAL P
1733.2 2100.8 2547. 3 2991. 5 3417.5
14.22
6. 43
<1. ( 1
21. 25
17.45
247.1
- 1 2. 5 9
2<8.2
01UK NONFERRCUS
'-w .ii
501.1
1 1 i 7 . 9 1C26.1
-9.C3 - U . 1 8
4.17
57 COFPER bRASS FRODUIS
59
" . t t t
U .JS
2 0 6 ! .C
14.25
22J.5
*8.86
1 2 . 08
‘ ) ! i !
Hill
3 6 0 5 . C 42C0.5 4796. 6 5372.8
1 2 . Cl
16.25
14.15
1C.56
1 7 . C!
414. 2
-1 .98
426. 6
2. 26
ii.c s
1005.3
6 . !6 M H r t
* l! il
’ " i i t
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3321.2
4. 95
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1406.1
10.92
1542.6
9. 71
1630.6 1661.4 1799.1
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4. 97
5.70
886.8
45.35
1091.8
22.64
1213.3
11.12
1216.4
.<6
905.4
-16.22
4241.7
<0.87
5276.6 6 3 3 6 .C 7277.6
2 4 . 4C
2 0 . CC
14.86
7607.1
7.i7
7593. 6 6 3 3 8 . 2
-2.46
7.64
2624.4
2 5 . tC
3547.9
35.15
6 1 6 1 .C 6420.1
12.52
•43
M f t r i
4.26 ’ H ’ r f
595. C
85.59
4505.5
26.9f
5455.9
21 * 0 9
925. 0
10.30
r
JAPAMSt
TABLl
B -
?(CCMlNOEt>)
:
fOktCAST
Of
Cl l TPu T
(IN
1 S ?U t l l l H S
YEN)
1 WO
1971
1 Vt i.
1 S73
19 7 4
1 975
1C6 Of 11Cf MCHlKEkY
342.7
312.4
- 3.C2
71.’ .C
114.52
026. 4
1( . I E
tlC.J
.26
6 14.4
- 1 . S6
1L7 HOLSEHOLD MACHINERY
323.7
33" .1
4.44
3 t l .5
12.54
424. 9
1 1 .67
371.4
- 1 2 . iO
3 VC . 5
5.14
U14.1
11 V7 .7
16.11
1C-NO
in
P O lll
1I1U
ice PAHS Of PA Ck INE R*
tc« STfcON6 ELEClfilC MACHINED 1427.7
110 HOLSEHOLD ELECTRICAL MAC 2397.1
14 2 * .C 16J 1.1
n.cd
1 <.<e
1626 .9 1 f t * . t
1 4 . 4;
14. C9
2415. 9
.78
3164.9
27. ( 9
1 54 £ • 5 1 3 4 6 . 3
-3 .41 - 1 2 . S5
195S.8 1 i 3 5 . 4 U i . 5 . 4
5 .09 -11 .45 - I V . C 2
3266.5
5.e9
114 PASSENGER MCRTOR CAR
4430.0
115 RE fA IR Of PASSENGER M010 1OCd.9
116 MOTORCYCLES t
dlCYCLES
333.0
-1.65
339.8
2.(2
-!^c?
5067.9 59 ( C .1 65 14.6 610 2.7 5 7 5 V . 4 6 1 3 5 . 8
-5.*2
14. 65
17.14
S. 30
- 6. 32
(.54
6946.4
13.21
3£C .1
U .27
362 .7
.71
,2,-U f
,0ShJ ’ i t ! ) ! ’ M !r t
IV .tl
8 56.7
14.57
1999.4
1 2 .se
2514.7
12.45
3285.3
14.48
491.5
4.93
51 1 . 4
4 . £4
52e . 3
3.32
.(
?H!f« 2 26 0t 4. 4S
2 3 ' 7 . 2 2744.9
17.45
23.83
3136.4
16.90
3472.2
3626.9
1 .12
4327.2
12.72
3C93.5
12.70
3266 . 8 3 1 9 3 . 2
-2.J5
6 . <5
35S4.5
3877.3
4.87
4049.3
4*8.4
5.31
3697.2
5.25
4. 44
ie.*4
5
i!;<
564 . 3
1.35
9. 13
41V2.4 4 4 3 2 . 7 4 5 4 9 . 5
3.53
2.6 6
>.00
358.2
2.31
363.4
1 .45
7 8 6 5 . e 87B1 . 2
11.64
13.24
365.7
.64
3(5.3
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35 2 .1
-1 . 9 7
“ !c»
9718.410396 .810B20 .2 12000.6
10.67
6.9 6
1.4 1
6.73
1 8 6 5 ^ 1 2 0 09 ^
1716.3
,55
‘.?5
5.33
1158
lo n > i ’’Uii ’’iisg ’ ’ i ’. t S "\*A
137.C
3.51
142.0
3.63
146.6
156.C
3.£9
167.2
3.52
164.1
6.66
211.8
15.C8
247 . C
16.59
28 3 . 9
14.94
322.6
13.64
361.1
11.S3
433.5
9.12
547.0
13.32
443.1
7.12
522 . 5
1 7 . S2
6C4.6
15.71
677.S
12.12
742.9
9.59
783 . e
5.5C
79 5 . 8
.36
862.7
6.89
tiUi
652.5
7.67
7L6.1
8.21
756 . f i
7.16
806.
6.76
9C2.1
5 . [4
978.8
4.16
1037.2
1.48
329.6
7.29
359.6
37S.3
5.49
398.2
4.96
416.6
4.61
453.7
484.0
3.C8
501,4
.<9
1C3.5
130. 0
25.64
154.8
K. C S
1(1.4
4 .4.2
163.6
1 .38
16 V . 1
3.34
119 PRECISION MACHINERY
367.9
397 .9
2.56
4 * 1. 4
1 5 .se
5C5.0
S. 45
46U .3
- 7. 17
472.9
4 20.0
-11.16
5S! , 2
4 1.5c
6 4S . ?
S. C7
<39.6
-1 .45
3 C* .C
14.56
344. 2
12. i l
2.S3
9.10
1 its!
434.5
4.31
3.43
4. 42
3214.1 3 5 6 0 . 5 4C26.7 4 5 C 0 . 7 4992.6 5 5 0 6 . 6 6CC2.4 6914.1 813?.7
£.65
s. ce
7.12
10.30
4. 47
11.77
10.93
11 .4 C 12.46
8 6 7 5 . 2 90 91 . 2 9796. 810484, 9
7847.7
5137.9 46 84.9 55 S3.9 62* 3. 5 6274. 4 6 5 7 1 . 2 6 9 5 3 . 8
3. 49
3.46
( . C4 12I t s ?
4.6C
4.61
1 1.97
-6.62
4.73
.I E
IS ,4C
5 . 8 2 ?T . i !
122 OTEER MANUFACTURING 600D 2221.3
fOR RES 4335.7
125 BUILDING REFA1R1NG
1769.7
15.31
1 3 2 5 . S 1534.6
15.74
13.53
132.3
3.44
118 OTEER 1RANSFCR1AT1CN
12* CONSTRUCTION KOI
1985
127.9
3.60
116.0
- 1. 25
307.2
- 1 0. 7 6
1 9 83
123.4
2.40
1 17.4
-1.59
267.C
1C.45
” i!>?
’2!s! u l U i
l5! i !
1981
1979
7Wi8 *0!!sS
M
” i! 6H!at
2354.5 2553.4 2944. 6
20C6.1
"JhS 7 . C6 " t f i i 9 . 4 0 6 . 4 5 7 . 3 6
339 .3
-11 .15
344 .7
4.56
19 8C
1978
831C .3 9354.6
1 .43
7.46
1746.1
6.6 1
i n .3
3.29
123 NOISING CCNSTfcUCT ICN
14SU.C 1 6 6 7 . 3
U3D1
571.0
241.8
1761.3
<4.56
U23.1
-.2<
115 .5
- 3 . S7
121 WATCHES ft CLCCKS
1430.0
6.22
M'!fJ
12C.3
OPTICAL I
444.6
5 . SC
4487.4
9.14
117 AlfcCRAfTS
(
16.(7
3227 .8 314V .9 3 3 5 4 . 3
-1. 1S
-2.41
5.86
119.4
120 PHCT0GRAPH1C
22.91
3512.9
5.35
1CCG.9 1316,0 15 C* .9
24. £4
14.*1
329.6
lo c i .0 1167.8
26.(7
51CC.2 4* 7 4 . 5
-8.15
t u l
113 RAILWAY VEHICLES
1977
6.C2
111 OlrER NEAK ELECTRICAL AP 36C5.0 4125. 9 47SS.7
1* .33
S . 43
112 SHIPS ft BCA1S
1976
13( 8. 8
126 PUtLIC UTILITY CONSTRUCT 21*2. 7
<121. 7 26 5* .3 2976.5
-4.49
2 5 . 2C 12.13
3( 76 . 6
3.>9
42 t 2 . 0
-1.24
*9( ! i e
4129.3 36 q3.4
- 5. 34 - 1 i . 6 £
36C5.2 4 1 9 7 . C 49J5.C
-2.12
16.41
1?.5t
’ ?J!j 1
1S56.3 2 0 1 2 . 7
2.68
3. 42
2164.8
7.56
2355.3
a.ec
2557.7
6.59
3156.6
276 l , (
8. u< 2V . i I
6.42 > % ]
2843.1
3.8 9
2S78 . 4
4.7 6
3124.7
4.91
3289.2 3462.4
5.27
S.24
46 5 3 .9
£.(e
2312 .7 242 C.3 2561.7 2 * 8 7 . 3 2 7 3 6 . 6
4.C9
1.64
6. 54
*.c 7
4 .66
5t l ! ? 2
64 C1 .C 5 9 0 3 . 6
-5.30
3.(5
362 7 . 1
4.76
3905.0
3.62
O034.7
4.3 9
” s : «8
4221.0
4.13
r
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:
IO M IASI
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1 S7l
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198C
* i n . I 3* *6 .7
-9.? 7 -15.51
2*7c.5
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19.61
5 CC6 . 6
2C.3*
5/93.8
15.72
6*56.2
11.47
6811 . 2 6 5 0 * . *
5.47
-3.51
2 43. ' . 5 2 * 6 V . *
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2 6 5 b . 2 252( .3 3 2 18 . C 3 5 13 .2
9.17
5.97
7.65
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1977
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FRCCLCTS
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9 NO A E t E C H H A l
0 ELECTRI CAL
PACfl NERf
PACt l l NERI
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4 ELECTRICITY,
CAS AKD NAT
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9 OttER
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SERVI CES
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1 2 . 25
C o n s ta n t manhours per eaployee a re assumed to c a lc u la te no m inal wage f o r s e c to rs 1 and 19 because th e model doe* n o t fo r e c a s t manhours pe r
employee f o r th e s e s e c to rs . The c o n s ta n t manhours a re 100 f o r A g r ic u lt u r e and 170 f o r O th e r S e rv ic e s . Theee n ia b e rs e re fro m S t a t i s t i c a l
Y ear Book. 1972. p u b lis h e d by th e Japsnese Government.
r
1«N*F * C “ R*U»K
lA bLk
8
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JAPAMSE
9
:
f C h i CAST
H’O I E L
Of
PRODUCTIVITY
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ftK
K. AKhOUR)
19 70
1 V7 1
H i 2
19 73
1974
1975
1976
1977
197 e
1979
1980
1981
1963
1965
5( 7. 0
61. 1 .6
t . 11
6M .9
a .te
6 57.6
4.24
(64.3
4.ft
711 .4
3.96
737 .6
3.69
76 3.3
3.48
M W
814.7
3.25
64C.2
3.13
865 .4
2.55
91 4.3
2. 72
961 .4
2. 49
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:c i i . A
2 ' j c ' .a
~3.2<
24(1 .L <661.4
t.i9
22.77
313C.2
13.64
7.51
iSiUl 4659.5
4979.1
6. 86
5252.3 5895.5 6465.3
4. 54
5.31
6. 29
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9. 67
6.96
5. 62
5.11
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e.38
5.C4
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58 59 . 61186C. 514213.0
5.<2
9 . 31
V.57
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12C4.7
1315 .C 1414.2
.' .37
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1967.7 2C92.C 2195.7 2300.5
4.76
4 .V 5
5.25
6.22
24C7 . 4 2 6 3 7 . 9 2 8 6 8 . 6
4.64
4.67
4.CC
5 PULP ANO FAFtf.
5223.9 5546 .3
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1 AbfclCCLlUNt .
FORESTRY AN
6.17
e u i.2
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1524.8
7 .06
1633.t
7.15
375< .0 3676.3 4C04.7
9 .68
6.93
10.62
1744 .6
6.78
6 4 e e . o 6145.7 7 4 3 2 . 4
t.c 7
7.C5
5291 .5
t . i5
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1871.3
7.26
7 9 0 6 . 3 8335.3 872C. 1 9083.7 9436.3 9767. 310503. 511179. 0
6.38
5.43
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4. 17
3.50
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3. 56
2.95
7 3 2 1 . 9 77CG.5 8 0 6 6 . 7 8 4 1 9 . 6 8758.6 9393.2 9968.2
2. 69
3.41
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5.62
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6 CHEMICAL FRCOUC1S
<.573.3 4894.5
7.C2
7 PR IHAf)V PETALS
7172.4
7608.1 624S.1 £839.5
t .42
7.16
£ . C7
9921 . 3 1 C352. 11C505. 811513. 912104. 712675. 4132 2 e .714 23 5.115 21,5.7
5.51
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4.71
4.27
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8 HE1AL PRODUCTS
1224.1
1413 ,4 1542 .fc 16( 2. 5
9.1.6 " I ’M
15.46
9.15
”
3511 .5 396 2.3 4296.9 4 ( 6 7 . 6
15.46
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8. 63
1 i . 17
5C7C.8 54E4.C 583C.1 6111.6 6358.3 6624.9 6932.8 7676.3 8 3 7 0 . 3
3.99
5.31
4. 19
4.65
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2659.1
7. 76 2? r . c ?
3661 .7 3940, e 4203.6 4466.1
(.29
6. 67
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7.48
9 NOA ELECTRICAL MACHINERY 3*41.2
10 ELECTRICAL MACHINERY
2467.6
11 TR ANSPORT AT ICN EQUIPMENT 3446.1
12 M1SCELLALCUS PANUfACTURI
1597.2
13 CONSTRUCTION
1728.5
14 ELECTRICITY, tAS ANO MAT 4541.4
15 WHCLE SALE ANO RETAIL TR
16 REAL ESTATE
17 TRANSFQR1 AND COMPUN1CAT
16
FINANCE ANO INSURANCE
19 OTFER SERVICES
t36.5
6 5 3 2 . C e932.1
6. 12
6. (5
3172.4 3425.5
7. 98
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5
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2 1 2 l . ?2277.5 2416.9
17C5 .1
6.76 ie
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1956.3 198C.6 1997.8 2013.3
1862.2
1.14
7.74 1W3 !‘1 1. 60
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5U67.1
11.57
702 .6
1C.3A
54 2 ,3 5816.5
7.25
7.(7
761.6
t .te
83C.2
6.43
6 i r e . 5 65cl.2
6 . 22
t.li
197.2
P .CC
96t .8
7.97
2256.4
7.51
2577.6
6.56
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7.12
2574.1 2733.4
6.19
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“ i!sI ‘T.ji "¥.\i
2888.4 3041.8
"i!«? 5.61 5.31
2C28.4 2042.7 2055.9 2 0 6 7 . 9
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.74
.64
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29CC .5 327C.7 3692.7
6. 23
6. 22
6.11
5244 .Q 575 1 . e 6247. 6
4 .55
4. 0?
5.13
<M C,J «TOJ{E
32C1 .5 352 1 .9 3845.5
4. 42
4.8 3
5.25
2 0 7 9 . 0 2099.9 2119.3
• 14
6928.3
5.61
7301.1
76PC.C 8 0 5 5 . C 8428.5 88CC.J
4.64
5.15
4.6!
1044.2
7.79
1122.7
7.51
12T3.6 1287.4 1373.9
6.72
7.22
6.95
5 .5 e
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10284.9
3.73
1463.4 1653 .2 1BSe.9
5.$7
6.51
6.22
100C6.6 1 0 1 * 1 . 4 1 C4 4< . 31C65f . 31CE6C. 4l 1054. 311306. 611512. 811718. 711922. 412125. 412328. 112736. 813152. 6
1. 5
2. I C
2.1.3
2.Ct
1.(7
1.91
1.62
1.79
1 .74
1. 70
1.67
1 .<4
1.62
1
997.2
1054.3
5.72
111 ».1 11 E l . 3 1 24 7.1
1.74
5. 57
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«
2235.5 2268,8 2 4 ( 2 , 0
9CC. 6
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1023.8
4.4C
1061.4
4.C7
1315.C i 3 e 4 . a
1.45
5.25
25*2,6
4.C9
5.C1
1523.3
4.81
3.99
1199.7
3.91
1245.8
3.64
1593.5
4.63
1665.3
4.47
1 7 3 7 . 3 1883.5 2 0 3 1 . 6
3.79
4.C6
4.3 2
3120. 6 3 2 5 8 . 1
4.41
” V.li s>
iUi
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1293.2 1 3 4 2 . 2
3.7f
3 .£ t
1392.2 1443.2
3. 66
3. 73
1 4 9 4 . 9 1 5 9 9 . 7 1705,7
3 . AC
3.22
3.58
4.5 8
in c .3 1 1 5 4 . 5
4.21
1453.4
For s e c to rs 1 a n d 19, th e aane manhours pe r en p lo ye e a r e used a s tho se In h o u r ly wage c a lc u la t io n .
l« N *r *0N«U«R
TABL t b -
U
JAPANESE
HOCtL
: FORECAST OF PUCE
1978
1979
1980
1981
19£3
132.7
3.27
127.7
2.79
1 3. 7
.37
15C.8
4. 91
158. 9
5. 40
17 £. 8
6. 28
126.7
4. 72
123.C
4. 97
1 9 »*
147.4
5. 26
155. 5
5 . ?1
V . il
12C.8
3.58
134.3
4. 24
140.8
4.84
1 8. 5
.48
157.5
6.C7
167. 9
6.6C
193.4
7 . 56
1<t.9
4.28
124.0
2.94
139.1
3.64
144.4
2 . PC
1 9. 4
. 84
162 .2
4 .16
176.5
4. 41
127.9
5.95
127.8
-.ce
129.2
1.C5
134.6
4. 19
140.8
4.62
1 8.3
.32
155 .8
3.<3
156.9
5. 83
166. 8
6. 25
19C.4
7.C7
'lIs J
2.94
M
'.iS 124.5
'S ii
1 6. 4
.22
T .x i
146. 4
3. 70
158.7
4 .26
U iiJ
163.7
5.12
1
T i?
19C.2
5. 13
21C.2
5. 12
232.3
5. 13
141.4
6. 47
151.2
7. L5
175.8
8 . Cl
207, 6
8. 96
175.4
4. 83
i vn
IV l i
14 7.1
1974
1975
1CC. 0
1C4.7
4.6?
1U.C
? .C5
1 15 . 1
4.09
12 C. 9
5 .04
1CC. 0
se . 5
-1.49
1 C1 . 1
2 . 66
1C5.7
4.30
11 1 . 0
5 . Cl
1<5.C 126.5
3.4C
2.74
115. 9. ■121.0
4. 45
4.25
3 FRU IS
1CC. 0
1T2.4
i.n
1Ci.5
<.46
112.0
5.13
119.4
5.7 0
124.4
4. 14
4 Ol FER CROFS FCR 1NDUSTRI
1CC. 0
K 5.e
5 . fit
111.7
; . 59
1 17.5
5 .tC
123.5
5 . C5
5 C R CP FOR F1EER 1NDUSTR1A
1 C0. 0
1 C8 . 7
E.67
1 1C .C
i.n
1 i C. 7
4.J6
6 L J WE S10CKS ,FCOLTRV
I CO. O
1C5. 5
5.5!
V .iS
M k i
*7 . 6
-12.37
121.3
36.29
I11LE
1 GRAIN
2
3
7
1977
1w o
1C-NO
2 OTt ER
CfcOFS
7 L I WE STCCKS.PCULTRV FOR
e SE MCULTURE
1CC. 0
M M
U i.P
4.10
WS
’^ i?
115.1
2. 67
119.7
4.CC
125.5
4. 92
15 ! » ]
Y .;S
124.1
3.20
128.1
3. 25
122.4
!.!4
1 7.C
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142.0
3. 66
147. 5
2.£5
16C.1
4.3C
MM
’ iJ il
’ !!??
126.5
?.44
1
’iir i
148.7
4 .65
’iiil
175.0
6.C4
T«5
1i?iS
’ ?c.si
135.1
2.77
1
155. 5
5.28
174.5
6. 12
198.6
6. 93
imll
114.1
2.tc
117.6
2. 99
121.4
2.24
'. s i
1 5.6
.52
147.7
4. 81
130.5
3. 87
136. 0
4. 22
149.3
4.97
166.4
5.*7
169.6
7.58
180.6
6. 45
191.0
5. 77
2C1.C
5.27
2 0.9
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220. 7
4. 65
23C.6
4. 47
251. 0
4.3C
273.1
4. 35
131.4
3. 11
126.5
! . 91
1 2. 8
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150.2
5. 16
158. 6
5. 19
17E .5
6. 2 3
203.4
7. 04
’ * '. { ?
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1CC. 0
1C4.2
4.17
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2.t9
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1C4.5
4.46
11C.3
«.<1
115.8
4.96
1CC. 0
1C4.4
4.42
1Ci.2
2.61
112.0
4.4.6
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12 LOt S
1CC. 0
1C1 . 1
1.1!
H i . 9
1.76
1 C5.2
2.21
102.c
2.71
111.C
13 H U M I N6 S
1CC. 0
115.7
15.7 C
1 2 i.t
12.65
144.5
1C.63
157.7
9.1 5
14 F I <HEI>1ES
1CC. 0
1C5. C
4.97
15 WHAL1K6
ICC.3
1C3.1
2.fe
5.7
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5.54
’Sid ’!:j8 121.0
16 INLAND WATER FI SHERI ES
1CC. 0
ic?.e
*.8C
11i
125.2
6.79
17 COKING COAL
1CC. 0
1C2.1
. C6
1C4. C
1.69
18 L l t N I T E
u c.a
105.9
5.92
11 CHARCOAL I
FIREWOOD
6R1GLETI ES AND L
2
124.9
2.68
132.9
3.26
128.9
2.69
1
132.9
6.15
139.9
5.25
146.3
4. 57
158.4
2.92
176. 5
2. 59
189.3
3. 59
2C3.6
3.76
109.C
2.54
111.8
2.55
114.7
2.61
1 4.4
.75
1 7.C
.82
17U.4
3. 64
1C6.3
2.26
152.4
4. 20
118.2
3.C2
132.1
4.C6
137.8
4. 25
15C.2
4.47
164.7
4. 84
1U . 6
4. 4 C
115.5
4.41
1
146.3
3. 80
165.9
3.PC
179.3
133.7
5.13
'¥.\l
T.i*
2
1.1.1
ICO. O
ICE.2
6.16
1C4. 5
1.22
115.1
5.13
20 ORES I
I CO. O
1C4.3
4.29
1C* . 5
. 18
1C6. fi
2.18
nc.r.
3.0 3
113.5
3. 18
117.3
2.98
122.3
154.9
54.86
2C4. C
3 ‘ . 46
Mil!
252.0
J9 . 6 1
420.0
15.32
441. 5
I CO. O
ft!
129.7
2.87
19 1RCN ORES CONCENTRATES
21 PEI ROLEUHS CRUDE
.77
Y . ic
'itti ’iiii
’?:?5 'iUl
CONCENTRATES OF N
;?!
2.8
221. 0
8. 16
112.1
3. 23
46.S
i.ti
10 FOfcESTRV
155.7
5. 13
’ltd
226. 7
6. 54
10JJ.6
5.61
96.0
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SERVICES
148.1
5. 13
.Is
1985
1
1CC. 0
9 AGRICULTURAL
19 71
5.13
122.3
!.4£
“.'A
’liiS
1
W
\\ ’Hi! T.i?
f}«
134.9
5.2C
142.1
4.22
128.3
4. 91
464. 2
488.C
513 . C
S . 13
5.13
5.12
2C0.1
6. 47
4.04
T i !
165. 7
5.26
149. 6
S.2C
5.2!
104.2
5.56
539.3
S . 13
566 .9
5.1 3
62 6 . 6
5.13
692.5
5.1 3
1 *N • f • ( * fc • U * H
lA b L I
U
-
J / PAN I S t
1C U C M 1M II))
1C-NO
WOUL
;
lIlLt
(OHICAS1
Of
fR lC l
1WO
1W l
H it
1W i
1974
1975
1976
1977
1976
1 9 79
1960
1961
19t3
1965
HC.O
U 3 .5
1.51
11 * .9
C
1C5.8
i .tC
1(^ .1
3.16
113.2
1.69
117.6
124.7
132.6
6.46
1 4 1 .2
6.36
149 .9
6 . 16
16-7 . 6
5 .59
188.7
6.49
1CL.0
1C1 .1
1.14
1C 1.4
. 12
’ fc?
1C4.6
1.(2
111.3
i.C4
1 ii C. 4
1.75
IC t.3
1.76
111.1
2.65
115.1
2.6C
125.4
4.56
131 . 4
4.76
144.6
4 .91
160.1
5.41
1CC.0
1 L9 .6
9.£i
US ,4
*.32
T :i?
^1 3
Y.i!
133.6
5.13
1 4 C. 4
5.13
147.6
5.13
'tJii
171 . 5
5.13
189.6
5.13
209.5
5.13
25 NCk-ME1ALIC MINERALS
ICfl.O
90.1
-9.67
K .5
- 4.C3
S2.8
1U2
91..5
6. 19
104.5
6.C9
110.8
t . C7
117.9
6.3 4
125.4
6.3?
133.2
6.26
141 . 4
6*16
15 C. C
6.C9
16 6 . 6
5 .97
189.4
26 CAtCASSES
1CC.0
1L4 .4
4.3E
111.4
6.73
1 15.9
4.L5
121.0
3. 50
123 . 5
2.96
126.7
2.53
129.5
2.22
132.1
2.C4
134.7
1 .99
137.5
2.C3
140.4
2.15
147.3
2.53
156.0
3.06
27 HE/1 PRuOLC1
1CC.0
97 ,9
-2.12
1C1,3
2. ;3
10i l ?
’S:tJ
1C4. £
1.C0
105.C
u,. d
1C5. C
- .C 2
104.9
-.12
104.8
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105.1
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106.5
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1C9. 8
1.69
1C0.0
1C9.2
9.16
11(.3
t .5C
172.3
2.41
'Jiil
138.ii
2.16
141 . 5
1 .91
144.2
1.89
147,1
2.C2
'V.il ’its?
29 VE (EIAbLE & ffiUl T PRESER
1C0.0
99 .3
-.67
9S .3
-.C3
99.1
-.24
9£ . 5
-.61
ICO.7
1.17
101.3
.57
101.6
.37
102.1
.47
102.8
.69
103.6
.S5
106.7
1 .55
111.1
2.17
30 SEA rCOO PRESERVED
HC.O
1C3.9
2.69
1C< .7
i .75
le t.4
1.S8
109.4
.It
111.3
i.e c
113.1
1.61
114.3
1 .04
115.2
.76
116.2
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117.4
1.05
116.9
1.33
123.3
2 .CC
129.5
2.64
31 GRAIN MILL PRC00C1S
1C0.0
1C7.1
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106.9
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1U5. C
-i.e 3
102.0
-2.81
99.2
-2.74
96.9
-2.3C
-t’fi
94.1
-1.21
93,4
-.72
'ill
32 BAftERV PRCDLC1S
1CC.0
146.7
’lisS
35 REflNED SUGAR
34 01 KR
u
NAIUMAL GAS
21 L i f t
STOM m o
GRAVEL
24 SALT CRUDE
2f
OAIRT PROOUC1
T .il
’ SJsJ
Y :s S
1C0.0
1L5 .0
4. 95
1C0.0
35 PREPARED FEEDS fOR ANIhA
36 ALCOHOLIC BEVERAGES
37 SOfl
FOOD PREPARED
DRINK
se TOLACCO
40 CO11 Oh SPINMAG
135.2
1 .67
137.2
1.46
14C. 7
1.24
144.1
1.19
130.7
2. C 2
133.3
1.94
136.1
2.13
139.5
2.45
148.1
J a.t
159.9
4.04
105.6
.52
1C6. 2
.56
106.9
.69
107.8
.84
108.9
1.(4
11 2 .C
116.4
2.12
117.6
3.11
T.iS
124.0
2.48
126.6
2.11
128.9
1 .62
131.0
1.63
135.1
i • 54
139.5
1.65
112.7
2.C2
116.e
2. 6 C
12C. 5
3.17
123.7
2.62
126.4
2.22
128.9
2 . CO
131.4
1.94
137.1
144.4
2.76
115.1
3.42
1 2u • 1
4.33
123.6
2 .SC
125.4
1.41
125.6
.36
125.5
-.24
124.9
-.49
124.1
-.17
124.6
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3 . pH
119.6
<.96
148.6
4.52
163.8
5.14
1a2.9
S . 91
9t. .9
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96.5
-2.43
92.4
-1.54
121.1
2 .5C
120.9
’lijJ 1 32 .61. 59 1 53 1. 4. 37 1 33 .68. 45 1 44 .22. 12
-V.it iii! 5!ii '-U
S 9- .37. 68
121.1
.16
Mid ’filt nUi uut
AUi
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SU
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11L.9
1.2J
112.9
-5.C 4
111.1
-1.52
112.5
-1.20
107.3
-2.68
’i’ri 'iUi
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127.5
2.66
124.9
3 .04
126.2
2.62
1L4.5
.61
105.0
.53
11 1. C
2 .CC
114.1
2.? 5
1C7.7
2. ^7
109.4
1 .56
111. 0
i .12
111.3
-27
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4 .36
M if l
117. C
3 . Cl
1C7.9
7. 9 2
111.9
3.65
114. 3
2 .< 3
115 .8
1 .24
1 <!t. 3
3 .e 9
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i : i .5
1.46
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1C3.1
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103. 1
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1C0.0
1C3.1
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1C6.1
2 .93
ue.s
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1 C2 .6
2.63
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i .65
1CQ.0
1C4 . e
IC t.7
3 .77
1C4.J
4.3?
2.57
i ii.o
3.61
1CC.0
99.4
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41 WOCLEN ft fcORSICD VARN
1CC.0
1G4 .6
4.65
1 14.C
t - 72
42 LIAEN
1CC. 0
111 . 1
11.13
116.1
4.46
VAR*
2.6 8
133.C
1.94
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192.9
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-2.14
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.48
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19 7i
1974
1975
1976
1577
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246
B
IB
L
IO
G
R
A
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