The Tuscany Interregional InputOutput Model (TIM):
Mathematical Structure and
Preliminary Results
Martellato, D.
IIASA Collaborative Paper
June 1982
Martellato, D. (1982) The Tuscany Interregional Input-Output Model (TIM): Mathematical Structure and
Preliminary Results. IIASA Collaborative Paper. IIASA, Laxenburg, Austria, CP-82-030 Copyright © June 1982 by
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THE TUSCANY INTERREGIONAL INPUTOUTPUT MODEL (TIM): MATHEMATICAL
STRUCTURE AND PRELIMINARY RESULTS
*
Dino Martellato
June 1982
CP-02-30
* Faculty
of Economics and Commerce
University of Venice
Venice, Italy
CoZZaborative Papers report work which has not been
performed solely at the International Institute for
Applied Systems Analysis and which has received only
limited review. Views or opinions expressed herein
do not necessarily represent those of the Institute,
its National Member Organizations, or other organizations supporting the work.
INTERNATIONAL INSTITUTE FOR APPLIED SYSTEMS ANALYSIS
A-2361 Laxenburg, Austria
PREFACE
S p e c i a l i z a t i o n i s one o f t h e foremost t r a i t s o f modern
i n d u s t r i a l development. T e c h n i c a l and commercial f a c t o r s have
i n t e r a c t e d t o make l a r g e - s c a l e p r o d u c t i o n more p r o f i t a b l e t h a n
e a r l i e r . T h i s p r o c e s s h a s been concomitant w i t h a r e g i o n a l
c o n c e n t r a t i o n o f p r o d u c t i o n a c t i v i t i e s a c c o r d i n g t o t h e prev a i l i n g comparative a d v a n t a g e s . Even l a r g e , and s t r o n g , econom i c r e g i o n s t e n d t o have an i n s u f f i c i e n t l y d i f f e r e n t i a t e d economy. I n Tuscany, I t a l y , it i s t h e l e a t h e r , f o o t w e a r , and t e x t i l e
i n d u s t r i e s t h a t c o n s t i t u t e t h e economic backbone o f t h e r e g i o n .
They a r e complemented by, and c o m p e t i t i v e w i t h , t h e t r a d i t i o n a l
t o u r i s t industry.
T e c h n i c a l p r o g r e s s and t h e development o f f a c t o r c o s t s have
e n t a i l e d a s h i f t i n i n t e r n a t i o n a l and i n t e r r e g i o n a l comparative
a d v a n t a g e s . Those i n d u s t r i e s demanding o n l y l o w - s k i l l e d l a b o r
have expanded i n low c o s t c o u n t r i e s o r r e g i o n s . How t h e s e f a c t o r s w i l l a f f e c t t h e long-term development i s a g e n e r a l problem
of strongly s p e c i a l i z e d regions i n i n d u s t r i a l i z e d countries.
Such q u e s t i o n s a r e a l s o a t t h e c o r e of t h e c a s e s t u d y o f
systems a n a l y s i s f o r r e g i o n a l i n d u s t r i a l development undertaken
by t h e Regional Development Group, I I A S A , i n c o l l a b o r a t i o n w i t h
t h e Regional I n s t i t u t e f o r Economic P l a n n i n g o f Tuscany ( I R P E T ) .
A t h i r d p a r t y i n t h i s c o l l a b o r a t i o n i s t h e I n s t i t u t e f o r Applied
Systems A n a l y s i s ( I A S I ) o f t h e N a t i o n a l Research C o u n c i l , Rome.
I n t h e c a s e study, a system o f economic f o r e c a s t i n g and p o l i c y
e v a l u a t i o n models t h a t a d d r e s s t h e above-mentioned development
i s s u e s a r e being b u i l t .
The models have a s t r o n g e r emphasis on
i n t e r r e g i o n a l and i n t e r n a t i o n a l dependencies t h a n e a r l i e r r e g i o n a l
s t u d i e s . kbreover, t h e r o l e o f t h e r e g i o n a l a u t h o r i t i e s i n p o l i c y
g e n e r a t i o n and e v a l u a t i o n i s more c l e a r l y d e s i g n e d h e r e t h a n
e l s e w h e r e . The aim of t h e work i s t o d e v e l o p a computerized model
system f o r more o r less permanent u s e , w i t h a d i r e c t a p p l i c a b i l i t y
t o o t h e r u r b a n i z e d r e g i o n s of t h e Tuscany t y p e .
The Tuscany i n t e r r e g i o n a l input-output model (TIM) d e s c r i b e d
i n t h i s paper forms t h e c o r e of t h e economic f o r e c a s t i n g and
p o l i c y - e v a l u a t i o n model system. TIM i s a l i n e a r s t a t i c r e c u r s i v e system of e q u a t i o n s of s m a l l dimensions t h a t i s i n t e n d e d
a s a t o o l f o r a n a l y z i n g t h e t r a d e r e l a t i o n s of Tuscany. Tuscany
and t h e R e s t - o f - I t a l y a r e c o n s i d e r e d a s two r e g i o n s i n TIM.
Each one i s l i n k e d t o t h e r e s t of t h e world where e x p o r t s a r e
exogenously determined.
Foreign t r a d e i s t a k e n i n t o account by
d i s t i n g u i s h i n g between n a t i o n a l and i n t e r n a t i o n a l flows. Comp l e m e n t a r i t y and c o m p e t i t i v e n e s s of imports a r e c o n s i d e r e d i n
t h i s model.
Laxenburg, June 1 9 82
Boris Issaev
Leader
Regional Development
Group
I IASA
THE TUSCANY INTERREGIONAL INPUT-OUTPUT
MODEL (TIM) : MATHEMATICAL STRUCTURE
AND PRELIMINARY RESULTS
Dino M a r t e l l a t o
1.
THE SCOPE O F THE INTERREGIONAL INPUT-OUTPUT
MODEL OF TUSCANY (TIM)
The d e c i s i o n t o c a r r y o u t an i n - d e p t h s t u d y o f t h e l i n k a g e s
o f Tuscany w i t h t h e r e s t o f I t a l y and t h e w o r l d , w i t h s p e c i a l
r e f e r e n c e t o t r a d e r e l a t i o n s , i s b a s e d on two f a c t o r s . The
f i r s t i s t h a t t r a d e i s e x t r e m e l y i m p o r t a n t f o r Tuscany. I t
d o e s n o t make s e n s e to s..tudy--however a c c u r a t e l y - - i t s economic
system i n i s o l a t i o n . The second i s t h a t a number of r e g i o n a l
growth d i s p a r i t i e s c a n b e e x p l a i n e d s i m p l y by t h e c o m p e t i t i v e
p o s i t i o n of t h e export s e c t o r s of t h e d i f f e r e n t I t a l i a n regions.
The i n c r e a s i n g p o p u l a r i t y o f i n t e r r e g i o n a l i n p u t - o u t p u t
a n a l y s i s can be a t t r i b u t e d t o i t s c a p a c i t y t o d e a l with t h e s e
phenomena.
I n such a n a n a l y s i s t h e emphasis i s d i v e r t e d from
*
t h e movement o f p r o d u c t i o n f a c t o r s t o t h e movement o f products.
* 1 t c o n c e n t r a t e s on t h e e q u i l i b r a t o r y ( o r d i s e q u i l i b r a t o r y )
e f f e c t s of t h e m o b i l i t y of p r o d u c t s r a t h e r t h a n o f t h e product i o n f a c t o r s . A s u r p l u s r e g i o n o f t e n h a s a more r a p i d growth
i n o u t p u t . The growth i n p r o d u c t i v i t y and t h e i n t r o d u c t i o n of
i n n o v a t i o n s w i l l , a c c o r d i n g l y , be more s u s t a i n e d . These f a c t o r s
w i l l enhance t h e c o m p a r a t i v e a d v a n t a g e o f t h e r e g i o n and probab l y p o l a r i z e t h e m o b i l i t y o f l a b o r and c a p i t a l .
Furthermore, it i s quite i m p o r t a n t t o pay a t t e n t i o n t o
t h e b a l a n c e o f t r a d e a t t h e r e g i o n a l l e v e l , even i f t h e r e a r e no
problems f o r a b a l a n c e of paymentsin f o r e i g n exchange. The
r e g i o n a l b a l a n c e of t r a d e may b e s i g n i f i c a n t from a n o t h e r p o i n t I t may b e a s s e r t e d t h a t t h e t i g h t e r t h e t r a d e l i n k a g e s ,
of-view.
t h e s t r o n g e r w i l l b e t h e i n s t a b i l i t y o f a system o f r e g i o n s .
Because o f t h e l a c k o f a f o r e i g n exchange c o n s t r a i n t and
t h e h i g h r e g i o n a l m o b i l i t y o f c a p i t a l , a r e q i o n can become
s t e a d i l y i n d e f i c i t . T h i s w i l l n o t n e c e s s a r i l y b e an a d v a n t a g e
b e c a u s e i t s d e f i c i t h a s t o b e m t e r b a l a n c e d by income and c a p i t a l
t r a n s f e r s . The income t r a n s f e r s a r e , however, u s u a l l y channeled
t h r o u g h t h e p u b l i c s e c t o r and t h e c a p i t a l t r a n s f e r s t h r o u q h t h e
c r e d i t and p u b l i c s e c t o r . T h i s means t h a t t h e c e n t r a l ( t i g h t )
f i s c a l and monetary p o l i c i e s w i l l n o t b e s p a t i a l l y n e u t r a l . To
summarize:
--
i t i s u s e f u l t o c o n c e n t r a t e on t r a d e r a t h e r t h a n
on f a c t o r m o b i l i t y b e c a u s e t h e l a t t e r may s i m p l y b e
--
a r e s u l t o f t h e former;
t h e stronger t h e regional connectivity, t h e higher
--
t h e i n s t a b i l i t y o f t h e s y s t e m of r e g i o n s ;
r e g i o n a l t r a d e may b e p e r m a n e n t l y i m b a l a n c e d and
t h i s means c u m u l a t i v e growth i n t h e s u r p l u s r e g i o n s
and/or n o n - s p a t i a l n e u t r a l i t y of f i s c a l and monetary
policies.
The main f o c u s of t h e a n a l y s i s c a r r i e d o u t w i t h t h e i n t e r r e g i o n a l i n p u t - o u t p u t model w i l l t h e n b e on t h e t r a d e l i n k a g e s o f
Tuscany. T h i s means t h a t from t h e o u t s e t o f t h e a n a l y s i s c o n s i s t e n c y between p r o d u c t i o n and t r a d e w i l l b e embedded i n t h e model.*
I n t h e f o l l o w i n g s t a g e of t h e a n a l y s i s , more a t t e n t i m w i l l b e g i v e n
t o c o n s i s t e n c y between p r o d u c t i o n and f i n a l i n t e r n a l demand. Underl y i n g t h i s approach i s t h e assumption t h a t t h e i n t e r n a l l e v e l o f
economic a c t i v i t y i s strongly connected w i t h t r a d e , w h i l e consumption
and i n v e s t m e n t show weaker l i n k a g e s w i t h t h e l e v e l o f p r o d u c t i o n .
I n t e r n a l consumption i s i n d e e d dependent a l s o on income t r a n s f e r s ,
and i n v e s t m e n t may c e r t a i n l y be p u l l e d by t h e l e v e l o f c u r r e n t
*The
model w i l l have a s i m u l t a n e o u s s o l u t i o n o n l y f o r
p r o d u c t i o n and t r a d e , w i t h a g i v e n exogenous demand.
p r o d u c t i o n , b u t would t e n d t o have a h i g h i m p o r t c o n t e n t .
Thus, t h e b u i l d i n g of an i n t e r r e g i o n a l i n p u t - o u t p u t model w i t h
a s t r o n g o r i e n t a t i o n t o t h e a n a l y s i s o f t r a d e r e l a t i o n s i s exp e c t e d t o r e q u i r e a c o n s i d e r a b l e amount o f i n f o r m a t i o n on t h e
t r a d e r e l a t i o n s of t h e r e g i o n ( C a v a l ' i e r i 1980)
.
A t t h e p r e s e n t t i m e , however, t h i s i n f o r m a t i o n i s n o t
available i n s u f f i c i e n t detail, p a r t i c u l a r l y f o r t r a d e with
*
t h e rest of I t a l v . I R P E T w i l l , i n any c a s e , produce t h e
necessary b a s i c s t a t i s t i c s with i t s d i r e c t innut-output t a b l e
f o r 1978. A s r e g a r d s f o r e i g n t r a d e , c o n s i d e r a b l e improvements
w i t h r e s p e c t t o t h e 1975 t a b l e have a l r e a d y been o b t a i n e d w i t h
t h e i n d i r e c t 1977 i n p u t - o u t p u t t a b l e , w h i l e f u r t h e r i n s i g h t s
w i l l a l s o be p r o v i d e d by t h e c u r r e n t r e s e a r c h done by I R P E T .
Because t h e i n t e r r e g i o n a l i n p u t - o u t p u t model f o r Tuscany
(TIM) i s i n t e n d e d as a t o o l f o r b o t h a c c o u n t i n g and p o l i c y
a n a l y s i s , i t h a s t o a c c e p t t h e s t a t i s t i c a l c o n v e n t i o n s used by
It should a l s o
t h e c u r r e n t system of n a t i o n a l accounts.
p r e s e n t i t s r e s u l t s i n a way t h a t i s c l e a r t o t h e p o l i c y maker.
T h i s means t h a t t h e t r e a t m e n t of i m p o r t s and p r o d u c t i o n a t
a r e g i o n a l l e v e l d e s e r v e s much a t t e n t i o n , b e c a u s e w e have t o
choose between a number o f a c c o u n t i n g p r o c e d u r e s t h a t have d i f f e r e n t e f f e c t s on t h e m u l t i p l i e r s .
The u s e f u l n e s s o f t h e model
f o r p o l i c y a n a l y s i s rests n o t o n l y on i t s a b i l i t y t o r e p r e s e n t
t h e a c t u a l working o f t h e system a c c u r a t e l y , b u t a l s o on t h e
seemingly minor a c c o u n t i n g c h a r a c t e r i s t i c s g i v e n t o t h e model.
For i m p o r t f l o w s , f o r i n s t a n c e , w e have a r a n g e o f s o l u t i o n s .
I f , from t h e o u t s e t , w e a r e a b l e t o make a d i s t i n c t i o n between
what i s produced i n t e r n a l l y and what i s i m p o r t e d , w e can accommodate a l l t h e i m p o r t s i n a row a t t h e bottom of t h e i n p u t output t a b l e .
I n t h i s c a s e , w e can make a p u r e cmolementarity
h y p o t h e s i s , which e n a b l e s t h e a c t u a l i n t e r n a l impact o f t h e l e v e l
o f p r o d u c t i o n t o be measured. This solution has, however, two drawbacks:
insomuch a s p a r t of t h e i m p o r t s a r e c o m p e t i t i v e i n n a t u r e ,
* IRPET
i s t h e acronym f o r I s t i t u t o R e g i o n a l e p e r l a
Programmazione Economica d e l l a Toscana. The i n s t i t u t e i s
located i n Florence, I t a l y .
t h e computed column c o e f f i c i e n t s w i l l b e u n s t a b l e ; f u r t h e r m o r e ,
i t s s t a t i s t i c a l r e q u i r e m e n t s a r e q u i t e demanding. C o n v e r s e l y ,
i f w e consider a l l t h e intermediate flows, disregarding
t h e i r g e o g r a p h i c a l o r i g i n , t h e computed c o e f f i c i e n t s a r e more
s t a b l e and t h e s t a t i s t i c a l r e q u i r e m e n t s a r e r e d u c e d .
In
this
purely
c o m p e t i t i v e h y p o t h e s i s , however, w e have
t o s u b t r a c t from t h e exogenous v e c t o r of f i n a l demand t h e v e c t o r
o f t o t a l i m p o r t s . The i m p l i c a t i o n i n t h i s c a s e i s c l e a r : w e have
t o f o r e c a s t exogenously t h e l e v e l of i m p o r t s by s e c t o r , which i s
t h e s o l u t i o n t h a t i s e x p e c t e d from t h e model. The b a s i c i d e a of
t h e i n t e r r e g i o n a l i n p u t - o u t p u t model i s e x a c t l y t h i s : t o s p e c i f y
a p p r o p r i a t e s i d e c o n d i t i o n s i n o r d e r t o make i n t e r r e g i o n a l i m p o r t s
and f o r e i g n i m p o r t s endogenous. The model h a s a l s o t o make an
u n b i a s e d s p l i t o f t o t a l i m p o r t s i n t o r e g i o n a l and f o r e i g n i m p o r t s
i f t h e a v a i l a b l e d a t a d o e s n o t d i s t i n g u i s h between i n t e r r e g i o n a l
and i n t e r n a t i o n a l t r a d e , a s o c c u r s o f t e n .
*.
S i m i l a r arguments can b e p u t forward f o r p r o d u c t i o n
When
we r e f e r t o a s i n g l e vector, i t s e f f e c t i v e production (x) is d i f f e r e n t from i t s d i s t r i b u t e d p r o d u c t i o n (9) by an amount (2) e q u a l
t o t h e v a l u e o f i t s by-products and j o i n t - p r o d u c t s :
F o r t h e r e g i o n a s a whole, t h e r e i s no d i f f e r e n c e b e c a u s e
t h e t r a n s f e r s of p r o d u c t i o n between s e c t o r s simply sum t o
z e r o . The d i s t i n c t i o n i s r e l e v a n t f o r t h e computation o f Leont i e f c o e f f i c i e n t s f o r t h e d i f f e r e n t s e c t o r s . I f w e compute t h e s e
c o e f f i c i e n t s o v e r d i s t r i b u t e d p r o d u c t i o n , t h e i n t e r m e d i a t e consumpt i o n i s Ep, and t h e e q u i l i b r i u m r e l a t i o n f o r d i s p o s a b l e r e s o u r c e s
h a s an obvious s o l u t i o n .
I n t h i s c a s e , t h e vector of t r a n s f e r s
o f p r o d u c t i o n d o e s n o t a p p e a r i n t h e model, b u t we c a n n o t c a l l
t h e e l e m e n t s of A t e c h n i c a l c o e f f i c i e n t s .
*W e
d i s r e g a r d i m p o r t s f o r t h e monent.
We can compute
such c o e f f i c i e n t s o n l y over t h e e f f e c t i v e
production, but t h e equilibrium i d e n t i t y is s t i l l defined f o r
d i s t r i b u t e d production.
The system of e q u a t i o n s
can be s o l v e d o n l y i f we i n s e r t d e f i n i t i o n ( 1 ) :
x = (I-A)
-1(f-z) .
(2
This i s c e r t a i n l y more s t a b l e than t h e p r e c e d i n g r e l a t i o n
i s a t r u e L e o n t i e f i n v e r s e . Neverbecause t h e m a t r i x (I-A)
t h e l e s s , it can be used f o r f o r e c a s t i n g purposes o n l y i f one
h a s a f o r e c a s t f o r f and f o r z.
A r a t h e r c r u d e assumption of homogeneity w i l l be made i n
t h e following
which a l l o w s us t o circumvent t h e d i f f i c u l t y i n o b t a i n i n g a f o r e c a s t f o r x , because t h e d i a g o n a l m a t r i x Z i s simply k e p t f i x e d
a t its historical level.
A t h i r d , and more d i f f i c u l t , p r o b l e m i s encountered when
c o n s t r u c t i n g an i n p u t - o u t p u t model from an i n p u t - o u t p u t t a b l e
It is the
b u i l t a c c o r d i n g t o t h e s o - c a l l e d EEC methodology.
t r e a t m e n t of t h e s e c t o r a l i n p u t of credit services. T h e i r amount,
which i s c o n s i d e r a b l e , i s n o t d i s t r i b u t e d among t h e rows, b u t
i s k e p t i n a dummy column a s i n t e r m e d i a t e consumption. The
dummy i n d u s t r y t h e n h a s a n e g a t i v e v a l u e added and a z e r o prod u c t i o n . I n t h i s way t h e n a t i o n a l v a l u e i s c o r r e c t e d f o r i t s
p o s i t i v e b i a s due t o t h e f a c t t h a t t h e i n t e r m e d i a t e consumption
of t h e n-1 s e c t o r s i s n e g a t i v e l y b i a s e d . This i s , however, only
an accounting t r i c k , w h i c h does n o t h e l p t h e modeler because he
has t o choose between two i l l - p o s e d a l t e r n a t i v e s : i n v e r t a
r e c t a n g u l a r [n
( n + l ) ] m a t r i x , o r a f t e r c o n s o l i d a t i o n of t h e
c r e d i t column w i t h t h e dummy column, i n v e r t a s q u a r e matrix,
which i s no l o n g e r a L e o n t i e f m a t r i x . The c o e f f i c i e n t s of t h e
c r e d i t column indeed add up t o a number g r e a t e r t h a n one, t h e
i n v e r s e i s no l o n g e r non-negative everywhere and t h e s o l u t i o n
v e c t o r may b e n e g a t i v e i n some o f i t s e l e m e n t s .
W e choose t o k e e p
t h e v a l u e o f t h e dummy column o u t o f t h e i n v e r t i b l e matrix.
Then
w e s o l v e t h e model f o r t h e r e f e r e n c e y e a r (1975) in the usual way and
c h e c k t h e p r o d u c t i o n o b t a i n e d w i t h t h e known v e c t o r .
The d i s c r e -
pancy (which i s a l w a y s n e g a t i v e and i n most c a s e s n e g l i g i b l e )
gives a c l e a r m e a s u r e o f t h e b i a s o f t h e computed m u l t i p l i e r s .
They are t h e n c o r r e c t e d by a c o e f f i c i e n t , g r e a t e r t h a n u n i t y ,
equal t o t h e b i a s
and k e p t c o n s t a n t a l o n g rows.
I n t h i s way,
u n b i a s e d L e o n t i e f m u l t i p l i e r s c a n b e o b t a i n e d from b i a s e d i n t e r i n d u s t r y flows.
2.
FROM THE LIMITED INFORMATION TABLE TO THE FULL INFORMATION
TABLE WITH A TOP-DOWN APPROACH
The p u r p o s e o f TIM from a p u r e a c c o u n t a n c y p o i n t - o f - v i e w
t o b u i l d ( f i r s t l y f o r 1975, and i n t h e f u t u r e f o r 1978) a f u l l
i n f o r m a t i o n (FI) s y s t e m o f i n p u t - o u t p u t t a b l e s f o r Tuscany and
t h e rest o f I t a l y .
Before d e f i n i n q
f u l l (or limited) information tables,
it i s u s e f u l t o n o t e t h a t b o t h f o r 1975 and 1978 a top-down
approach w i l l b e used, t h e d i f f e r e n c e being t h a t i n t h e
l a t t e r c a s e t h e amount o f f r e s h d a t a g a t h e r e d a t t h e r e g i o n a l
l e v e l i s much g r e a t e r .
F o r 1975, IRPET h a s d e v e l o p e d a l i m i t e d i n f o r m a t i o n ( L I )
t a b l e (MIT 75) by r e g i o n a l i z i n g a c o r r e s p o n d i n g n a t i o n a l t a b l e
f o r 1974 on t h e b a s i s o f some i n d i r e c t i n f o r m a t i o n a t t h e
regional l e v e l (Marliani 1981).
W e t h e n computed r e s i d u a l l y
t h e t a b l e f o r t h e rest o f t h e c o u n t r y ( F i g u r e 1 ) .
IRPET t h e n e s t i m a t e d t h e t a b l e f o r 1977 (see F i g u r e 1 ) .
U n f o r t u n a t e l y , t h e n a t i o n a l t a b l e f o r 1977 w i l l n o t become
a v a i l a b l e ; t h e c o n s t r u c t i o n o f a n LI b i r e g i o n a l t a b l e f o r t h e
year w i l l t h e r e f o r e be imwossible.
The 1977 t a b l e w i l l , how-
ever, b e u s e d f o r a s e n s i t i v i t y a n a l y s i s o f t h e model (TIM 7 5 )
b u i l t upon t h e 1975 d a t a b a s e .
IRPET i s c u r r e n t l y b u i l d i n g a d i r e c t t a b l e f o r t h e y e a r
1978.
When t h e c o r r e s p o n d i n g o f f i c i a l n a t i o n a l t a b l e becomes
a v a i l a b l e , t h e L I t a b l e and t h e c o r r e s p o n d i n g model (TIM 78)
w i l l i m m e d i a t e l y b e o b t a i n e d s i m p l y by u s i n g t h e p r o c e d u r e s
is
-
ITALY
1974
TABLE
Limited Information
b i r e g i o n a l system
o f 1/0 t a b l e s f o r \
1975
v
Statistical
information
a t regional
ITALY
TABLE
MIT 7 5
level
ITALY
v
TUSCANY
TABLE
MIT 77
(
Model f o r
interregional
t r a d e (MITI
I
F i g u r e 1.
The d e r i v a t i o n o f TIM 1975.
F u l l Information bir e g i o n a l system of
1/0 t a b l e s - TIM 75
TABLE
implemented f o r 1975.
I t i s now c l e a r why
rests on a top-down approach f o r 1975:
the
analysis
both r e g i o n a l t a b l e s
a r e o b t a i n e d from a break-down o f t h e n a t i o n a l t a b l e .
W e w i l l now c l a r i f y t h e t e r m s l i m i t e d i n f o r m a t i o n ( L I )
and f u l l i n f o r m a t i o n ( F I ) t a b l e s (see Table 1 )
.
. -
INTERNAL
1
INTERMEDIATE
P;
INTERMEDIATE EXPORTS FROM
W
W P I
CI
Eil
W
z
xt
TUSCANY TO
FLOWS
REST
TUSCANY
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n
m m zo
.
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ITALY
a z o z w 4
zzauaHu>.wE
00 Z 9 & 4 4 d U c 3 m a m W H o w m
8,
INTERMEDIATE
INTERNAL
IMPORTS TO
INTERMEDIATE
TUSCANY FROM
FLOWS
REST
REST
OF
31 32
Table 1 .
62 63 64 65
66
67
Ekrn
H
m
H
n
68 69
70
.
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72 73 Tt
75
A F u l l Information input/output t a b l e .
I n an L I b i r e g i o n a l system o f t a b l e s , p r o d u c t i o n i n e v e r v
s e c t o r o f e v e r y r e g i o n i s e a u a l t o t o t a l i n t e r m e d i a t e and f i n a l
demand i n t h e r e g i o n ( d i s r e g a r d i n g a e o g r a p h i c a l o r i g i n ) p l u s
e x p o r t s t o t h e o t h e r r e g i o n and p l u s e x p o r t s a b r o a d .
In
an F I b i r e g i o n a l system, on t h e o t h e r hand, t h e same
l e v e l of p r o d u c t i o n i s decomposed i n t o i n t e r m e d i a t e demand s a t i s f i e d i n Tuscany, i n t e r m e d i a t e demand s a t i s f i e d i n t h e rest of
I t a l y , f i n a l demand i n Tuscany, f i n a l demand i n t h e rest o f I t a l y ,
e x p o r t s abroad, i m p o r t s from abroad, and a v a i l a b l e r e s o u r c e s .
I t i s now c l e a r why an FI t a b l e g i v e s much more i n f o r m a t i o n on
t h e i n t e r n a l p r o d u c t i o n s t r u c t u r e and on t r a d e f l o w s between
regions.
Considering, furthermore, t h a t a p a r t of r e g i o n a l
t r a d e i s a c t u a l l y a kind of i n d i r e c t foreign t r a d e , we w i l l
a l s o t r y t o d i s e n t a n g l e t h i s component i n t h e F I t a b l e . The
r e s u l t i s a break-down f o r one y e a r between t h e two r e g i o n s o f
a l l t h e c o n s i d e r e d economic a g g r e g a t e s .
The p o s s i b i l i t y o f t r a n s f o r m i n g t h e L I t a b l e i n t o a n F I
t a b l e rests b a s i c a l l y on t h e a v a i l a b i l i t y o f t h e i n t e r r e g i o n a l
t r a d e f l o w s . The e s t i m a t i o n o f t h e s e f l o w s i s n o t p o s s i b l e ,
however, i f i n t e r r e g i o n a l s h i p m e n t s a r e n o t s t a t i s t i c a l l y
o b s e r v e d . T h i s i s why IRPET h a s d e r i v e d a v e c t o r o f n e t
r e g i o n a l t r a d e b a l a n c e s o n l y . The v e c t o r h a s been o b t a i n e d
simply as a r e s i d u a l , t a k i n g as a c o n s t r a i n t o f f i c i a l r e g i o n a l
economic a c c o u n t s and d a t a on f o r e i g n t r a d e , which means t h a t
t h e r e s i d u a l i s g r o s s o f i n v e n t o r y change and i n d i r e c t t a x e s
On f o r e i g n i m p o r t s ( M a r l i a n i 1 9 8 1 ) . I R P E T h a s an estimate
of t h e g r o s s a b s o l u t e v a l u e o f i n t e r r e g i o n a l e x p o r t s and i m p o r t s
t h a t w i l l b e u s e d i n t h e f i r s t i m p l e m e n t a t i o n o f TIM. The
methodology u s e d i n t h i s e s t i m a t i o n w i l l b e c o n s i d e r e d i n Sect i o n 5 i n c o n n e c t i o n w i t h a n i l l u s t r a t i o n of t h e p o s s i b i l i t i e s
f o r improving t h e estimate o f t r a d e c o e f f i c i e n t s .
3.
THE CHOICE OF MODEL
W e c a n now p r e s e n t t h e s t r u c t u r e o f t h e i n t e r r e g i o n a l model
based on t h e s t a t i s t i c a l i n f o r m a t i o n d i s c u s s e d above.
First,
w e have t o d e c i d e what s h o u l d b e c o n s i d e r e d a s exogenous and
what s h o u l d b e endogenous i n t h e model. Then, w e have t o choose
between a f i x e d trade p a t t e r n coupled w i t h a f l e x i b l e p r o d u c t i o n
p a t t e r n and a f l e x i b l e t r a d e p a t t e r n coupled w i t h a f i x e d production pattern.
The f i r s t p o i n t o b v i o u s l y depends upon t h e
d e g r e e of interaction w= wish t o d e v e l o p i n t h e model a t t h e present
time.
I t s h o u l d b e mentioned t h a t t h i s d e g r e e w i l l , f o r t h e
moment, be w e l l below t h a t of t h e c o n s i s t e n c y w e d e s i r e f o r t h e
f o r e c a s t s . The r e a s o n b e i n g t h a t t h i s d e g r e e o f c o n s i s t e n c y
r e q u i r e s t h e s o l u t i o n o f a c o n s i s t e n t s e t o f models, which
*
a r e c u r r e n t l y b e i n g developed.
The second problem h a s s t r o n g c o n n e c t i o n s w i t h t h e s p e c i f i c
economic c o n t e x t w i t h which w e have t o d e a l . I f w e have t o f a c e
a s i t u a t i o n of f u l l u t i l i z a t i o n o f c a p a c i t y , it seems more app r o p r i a t e t o have a f i x e d - o u t p u t f l e x i b l e - t r a d i n g p a t t e r n i n t h e
model. But i f t h e economy i s r u n n i n g below i t s p o t e n t i a l , w e
must r e s o r t t o a f l e x i b l e - o u t p u t w i t h a f i x e d - t r a d i n g p a t t e r n
In t h i s case, the fixed-trading pattern i s
( M a r t e l l a t o 1981 )
simply t h e o b s e r v e d ( a l m o s t i n d i r e c t l y ) p a t t e r n o f r e g i o n a l t r a d e .
.
A t t h e p r e s e n t s t a g e of t h e study, w e a r e o n l y prepared t o
make p r o d u c t i o n , r e g i o n a l t r a d e , f o r e i g n i m p o r t s and employment,
which a r e t h e s t a n d a r d f e a t u r e s o f an i n t e r r e g i o n a l i n p u t - o u t p u t
model, endogenous. However, a s mentioned p r e v i o u s l y , t h e ongoing r e s e a r c h on t h e Tuscany c a s e s t u d y should a l l o w u s t o
d e v e l o p a system o f models f o r f o r e c a s t i n g e x p o r t s a b r o a d ,
consumption, and t h e s u p p l y o f l a b o r .
I n t h e c o n t e x t o f t h e s p e c i f i c submodel p r e s e n t e d i n t h i s
p a p e r , more a t t e n t i o n w i l l b e g i v e n i n t h e f u t u r e t o t h e endo.genous t r e a t m e n t o f p r i v a t e i n v e s t m e n t and t o t h e r e l a t i o n o f
t h e s t a b i l i t y assumption of t r a d e c o e f f i c i e n t s .
Thus, w e w i l l s t a r t w i t h a f l e x i b l e - o u t p u t and f i x e d - t r a d e
p a t t e r n model o f t h e Chenery-Moses f a m i l y . E s s e n t i a l l y , w e have
a s e t o f s u p p l y e q u a t i o n s , a set o f demand e q u a t i o n s , and a s e t
of r e g i o n a l t r a d e b a l a n c e s .
W e use t h e following notation f o r vectors (small letters)
and m a t r i c e s ( c a p i t a l l e t t e r s ) :
x
f
m
g
= e f f e c t i v e production;
= i n t e r n a l f i n a l demand p l u s e x p o r t s a b r o a d ;
= foreign imports;
= f - m ;
*we r e f e r t o models f o r t h e l a b o r market, f o r f o r e i g n
e x p o r t s , f o r consumption and f o r i n v e s t m e n t , which s h o u l d be
appended t o t h e i n t e r r e g i o n a l model.
d = t o t a l demand ( n e t o f r e g i o n a l e x p o r t s ) ;
A =
a
technical coefficients i n region s;
'ij s
B = {ibts)
z
regional trade coefficients:
= { z ) correction coefficients for efficient
i s
production i n region s;
S , t Ir = r e g i o n s ;
i I j = sectors.
The s u p p l y e q u a t i o n s f o r Tuscany ( t ) a n d f o r t h e r e s t o f
I t a l y ( r ) are:
The demand e q u a t i o n s are:
while t h e v e c t o r of t r a d e balances is:
A t t h i s stage, we note t h a t foreign trade has received
o n l y s c a n t a t t e n t i o n and, p a r t i c u l a r l y , t h a t a l l f o r e i g n imp o r t s are exogenous a s i f t h e y w e r e a l l c o m p e t i t i v e . C l e a r l y ,
t h e model s h o u l d be more s o p h i s t i c a t e d from t h i s p o i n t - o f - v i e w
t o a l l o w a s e n s i b l e a n a l y s i s o f a r e g i o n s u c h a s Tuscany. Sect i o n 4 w i l l b e d e v o t e d t o a n improved t r e a t m e n t o f f o r e i g n t r a d e .
I n t e r r e g i o n a l t r a d e w i l l a l s o b e a n a l y z e d below i n more d e t a i l .
I n t h e p r e s e n t f o r m u l a t i o n o f t h e model, w e u t i l i z e a s i m p l i f i e d t r e a t m e n t o f s h i p m e n t s between r e g i o n s . T h i s i s b e c a u s e
o f t h e s e v e r e l i m i t a t i o n on s t a t i s t i c a l i n f o r m a t i o n a v a i l a b l e .
Two b a s i c a s s u m p t i o n a r e made. The: s h i ~ m e n t so f goods f o r consumpt i o n ( b o t h f i n a l and i n t e r m e d i a t e ) and f o r i n v e s t m e n t a r e assumed
t o show a common p a t t e r n .
The s u p p l y p a t t e r n o f r e g i o n t t o
r e g i o n r i s t h e same f o r e a c h p r o d u c t i o n s e c t o r .
The r e s u l t i n g m a t r i x B i s t h e n formed by d i a g o n a l b l o c k s .
T h i s i m p l i e s t h a t f o r e v e r y s e c t o r i w e have a s h a r e s u b m a t r i x
o f f o u r c o e f f i c i e n t s w i t h u n i t y column sums.
I t would be i n t e r e s t i n g t o check t h e r o b u s t n e s s of t h e
r e s u l t s w i t h r e g a r d s t o t h i s s p e c i f i c a t i o n of t h e t r a d i n g p a t t e r n ,
i f t h e r e s u l t s o f t h e survey f o r t h e d i r e c t t a b l e w e r e already
a v a i l a b l e . Although s i m p l e , t h i s t r e a t m e n t of r e g i o n a l t r a d e h a s
some i n t e r e s t i n g p r o p e r t i e s .
By combining t h e demand and s u p p l y e q u a t i o n s :
one c a n o b s e r v e t h a t t h e l a s t term of b o t h e q u a t i o n s i m p l i e s (by
t h e d e f i n i t i o n o f f t and f r ) t h a t a f o r e i g n e x p o r t o f one r e g i o n
can b e s u s t a i n e d simply by a n import from t h e o t h e r .
T h i s i s t h e c a s e f o r i m p o r t s from abroad.
I f we c o n s i d e r ,
f o r i n s t a n c e , t h e t e r m b t rmr i n t h e f i r s t e q u a t i o n , w e c a n o b s e r v e
t h a t i f p r o d u c t i o n i n r e g i o n t i s d i s c o n t i n u e d (bv an assumpt i o n o f comparative a d v a n t a g e s ) , t h e demand o f r e g i o n t can s t i l l
be s u s t a i n e d by i m p o r t s from r e g i o n r i f btr i s n o t z e r o . T h i s
p o s s i b i l i t y c o u l d be v e r y i m p o r t a n t i f t h e model w e r e implemented
w i t h d a t a o b t a i n e d from r e g i o n a l t r a d e s t a t i s t i c s . But t h i s i s
n o t t h e c a s e f o r t h e p r e s e n t v e r s i o n of t h e model. B e s i d e s , i t i s
i m p o r t a n t t o n o t e t h a t a b i a s a r i s e s i n t h e arrangement o f customs
s t a t i s t i c s , i n which it c a n n o t be a s c e r t a i n e d whether a flow observed i n region t i s a c t u a l l y p e r t i n e n t t o another region r.
Furthermore, t h e r e i s room f o r some improvements, t o be
used i n S e c t i o n 4 , i n a t l e a s t two a s p e c t s . The h y p o t h e s i s of
p u r e c o m p e t i t i v e n e s s o f f o r e i g n i m p o r t s , f o r i n s t a n c e , can b e
removed w i t h a p p r o p r i a t e f u n c t i o n s . There i s , i n e q u a t i o n (8) the
p o s s i b i l i t y o f a s h o r t c i r c u i t on f o r e i g n t r a d e :
t h e flow of
i m p o r t s bttmt + btrmr c a n produce e x p o r t s abroad,which a r e i n c l u d e d , by d e f i n i t i o n , i n d t and f t .
T h i s i s however a minor
problem.
The c a u s a l s t r u c t u r e of t h e model i s shown i n F i g u r e 2 .
F i g u r e 2.
C a u s a l s t r u c t u r e of t h e s i m p l e s t v e r s i o n of TIM 75
( t = Tuscany, r = t h e rest of I t a l y ) .
From F i g u r e 2, it i s now c l e a r t h a t f o r a g i v e n exogenous
f i n a l demand and f o r e i g n t r a d e v e c t o r and f o r a g i v e n o r f i x e d
t r a d i n g p a t t e r n B , t h e model g i v e s c o n s i s t e n c y between p r o d u c t i o n
and i n t e r r e g i o n a l s h i p m e n t s .
4.
THE TREATMENT OF FOREIGN TRADE W I T H I N THE INTERREGIONAL
INPUT-OUTPUT MODEL
I f a l l foreign imports a r e i n f a c t competitive, we a r e a l lowed t o keep t h e c o r r e s p o n d i n g v a l u e exogenous, and t h e s o l u t i o n
f o r e f f e c t i v e p r o d u c t i o n i s simply:
Here we c a n o b s e r v e t h a t w h i l e t h e n e g a t i v e d i r e c t e f f e c t on
t h e p r o d u c t i o n o f r e g i o n t of a c e r t a i n amount of c o m p e t i t i v e
i m p o r t s i s g i v e n by ( bttmt +bt r mr ), i t s t o t a l n e g a t i v e e f f e c t i s
htt(bttmt+btrmr)h t r ( brtmn t +br rm r )1 where htt
i s t h e upper l e f t
+
b l o c k of the partitioned inverse H = [I-(BA-Z) I-'
and htr i s t h e upp e r r i g h t b l o c k . T h i s k i n d of model c a n be used f o r f o r e c a s t i n g
p u r p o s e s o n l y i f i t i s p o s s i b l e t o know i n advance t h e v e c t o r m ,
which i s a p a r t of t h e s o l u t i o n . T h i s c o u l d be a problem i f one
does n o t have a v a i l a b l e a submodel w i t h which t o o b t a i n a f o r e c a s t f o r m, f o r a g i v e n p a t h of t h e t e r m s o f t r a d e , and f o r a
g i v e n p a t h of p r o d u c t i v e c a p a c i t y .
*
Because ( 9 ) i s t h e f i r s t s o l u t i o n o f t h e model, it i s necess a r y t o c o n s i d e r t h e e f f e c t s of h y p o t h e s i s ( 3 ) on t h e e x i s t e n c e
of t h e i n v e r s e H.
Normally, t h e d i a g o n a l m a t r i x Z s h o u l d have
s m a l l f i g u r e s i n r e l a t i o n t o t h o s e of t h e t e c h n i c a l m a t r i x A and,
consequently, t h e r e s h o u l d n o t b e a v i o l a t i o n o f m a t h e m a t i c a l cond i t i o n s f o r t h e e x i s t e n c e of an i n v e r s e H w i t h non-negative
elements only.
For t h e s e c t o r s where t h e r e a r e s i g n i f i c a n t s e c o n d a r y prod u c t s ( z i i s n e g a t i v e ) , t h e r e s u l t i n g d i a g o n a l e l e m e n t may be
s m a l l when compared w i t h t h e c o r r e s p o n d i n g row e l e m e n t s .
I n t h i s c a s e , t h e i n v e r t i b l e m a t r i x t e n d s t o have a less
dominant p o s i t i v e p r i n c i p a l d i a g o n a l a n d , t h u s , t o have a less
r a p i d convergence r a t e i n t h e i t e r a t i v e s o l u t i o n , b u t s h o u l d
always have a n i n v e r s e w i t h non-negative e l e m e n t s . W e n o t e t h a t
t h e L e o n t i e f m a t r i x o b t a i n e d from t h e Tuscany and r e s t - o f - I t a l y
t a b l e s i s r e d u c i b l e . T h i s i m p l i e s t h a t some e l e m e n t s of t h e
L e o n t i e f i n v e r s e are z e r o .
The p u r e c o m p e t i t i o n h y p o t h e s i s i s n o t v e r y r e a l i s t i c b e c a u s e
s e v e r a l r e s o u r c e s a r e produced n e i t h e r i n t h e r e g i o n c o n s i d e r e d
n o r i n t h e o t h e r r e g i o n s and, t h e r e f o r e , have t o be i m ~ o r t e d .
The model w i t h f o r e i g n complementary i m p o r t s o n l y i s :
( I + Z ) x = B(Ax+f)
-
MBAx
-
NBq
,
(10)
where M and N are d i a g o n a l m a t r i c e s o f c o e f f i c i e n t s and q i s t h e
f i n a l demand f n e t of e x p o r t s abroad e.
*when demand i s h i g h e r t h a n c a p a c i t y , t h e r e w i l l be more
i m p o r t s from abroad.
The s o l u t i o n i s :
x = [I+z-(I-M)BA]-I
.
[ ( I - N ) Bf+NBe]
(11)
T h i s model shows a h i g h e r d e g r e e o f e n d o g e n e i t y e v e n i f t h e
m u l t i p l i e r s of t h e new i n v e r s e are smaller t h a n t h o s e computed
i n ( 9 ) . F o r a g i v e n v e c t o r x h e r e w e h a v e a c t u a l l y smaller m u l t i pliers w i t h a h i g h e r f i n a l demand. A more r e a l i s t i c s o l u t i o n i s
t h e mixed o n e where b o t h c o m p e t i t i v e and complementary i m p o r t s
a r e p r e s e n t . Thus, t h e s y s t e m o f e q u a t i o n s :
(I+Z)x
+
MBAx
+
NBq
+
B m = BAx
+ Bf
,
has t h e solution:
x = [I+z- (I-M) BA]-'
[ ( I - N ) Bf+NBe-Bm]
.
(12 )
The d e g r e e o f e n d o g e n e i t y i s t h e same, b u t t h e f i n a l demand
v e c t o r i s r e d u c e d by t h e exogenous amount Bm which h a s t o b e
f o r e c a s t e d by a s i d e model.
I t i s u s e f u l t o w r i t e t h e same model i n a n e x t e n d e d way.
Some i n s i g h t s a r e g a t h e r e d on t h e i n d i r e c t l i n k a g e s o f Tuscany
w i t h t h e rest o f t h e world:
+
t t rA rx r + NtBtrqr
M B
=
Btt( At x t +qt
I n t h i s f o r m u l a t i o n , w e f i n d w i t h t h e l a s t two t e r m s b e f o r e
t h e e q u a l s i g n , t h e p o s s i b i l i t y t h a t a good i m p o r t e d by Tuscany
from a b r o a d i s s i m p l y s e n t t o t h e r e s t o f I t a l y . The l a s t t e r m
of t h e e q u a t i o n i m p l i e s i n s t e a d t h a t a good e x p o r t e d a b r o a d from
It is
t h e rest o f I t a l y i s s u s t a i n e d by T u s c a n y ' s p r o d u c t i o n .
obvious t h a t s i m i l a r flows a r e p r e s e n t i n t h e e a u a t i o n f o r t h e
rest o f I t a l y .
Furthermore, t h e same decompostion shows t h e absence o f any
s h o r t c i r c u i t i n f o r e i g n t r a d e , which seems t o be p r e s e n t i n t h e
reduced form ( 1 2 ) . The v e c t o r [(I-N)Bf + NBe - Bm] i s indeed
e q u a l t o (Bf - NBq - Bm] by t h e d e f i n i t i o n of q a s a v e c t o r of
f i n a l demand n e t of f o r e i g n e x p o r t s and a l s o e q u a l t o [ (I-N)Bq
+ B(e-m) 1. T h i s means t h a t t h e f i n a l demand component can be
d e f i n e d i n t h r e e d i f f e r e n t ways.
5.
TREATMENT OF REGIONAL TRADE
A l s o f o r t h e s h i p m e n t s between the two r e g i o n s one must
d e c i d e i f it i s b e t t e r t o c o n s i d e r them as c o m p e t i t i v e o r a s
complementary.
I f w e c o n s i d e r t h e low d e g r e e o f s e l f - s u f f i c i e n c y
of t h e r e g i o n a l economic system,we s h o u l d c o n c l u d e t h a t i m p o r t s
from t h e o t h e r r e g i o n a r e more complementary t h a n c o m p e t i t i v e .
I t does n o t make s e n s e t o p o s t u l a t e a r e a l p r i c e c o m p e t i t i v e n e s s
between regions, because t h e s h a r e of t h e r e g i o n a l market i s s o
l i m i t e d f o r t h e s e c t o r in which there is regional t r a d e t h a t a f i r m
c a n n o t f a c e an i n d e f i n i t e p r i c e c o m p e t i t i o n from o t h e r
r e g i o n s . W e a r e t h e n i n c l i n e d t o assume complementarity i n
regional trade.
I f f u l l c a p a c i t y i s r e a c h e d and demand i s r i g i d ,
t h e most p r o b a b l e outcome w i l l be--by a s i m i l a r argument--an i n crease i n i m p o r t s ( c o m p e t i t i v e i n t h i s c a s e ) from f o r e i g n coun-
tries.
I f w e are u n a b l e t o d i s t i n g u i s h t h e i m p o r t c o n t e n t of i n t e r m e d i a t e consumption and of f i n a l demand and i f w e assume complementarity, w e c a n r e l a t e r e g i o n a l i m p o r t s s i m p l y t o t h e l e v e l o f
With t h i s
p r o d u c t i o n u s i n g a d i a g o n a l m a t r i x of c o e f f i c i e n t s V.
and by chanffing some d e f i n i t i o n s :
V = Irvi}
r e g i o n a l t r a d e c o e f f i c i e n t s (complementary);
f = t o t a l f i n a l demand ( i n t e r n a l demand p l u s e x p o r t s
a b r o a d and p l u s r e g i o n a l e x p o r t s ) ;
q = f - e ;
d = Ax + f t o t a l demand;
w e o b t a i n t h e model:
x = [I
+
Z
+
V
-
(I-M)A]-'
[(I-N)q
+
(e-m)]
.
(13)
The c a u s a l s t r u c t u r e o f t h e model i s shown i n F i g u r e 3 .
I t h i g h l i g h t s n o t o n l y t h e t i g h t i n t e r d e p e n d e n c e s between t h e
two r e g i o n s , b u t a l s o t h e e x i s t e n c e of i n d i r e c t l i n k a g e s between
a r e g i o n and t h e rest of t h e world.
L e t u s , f o r example, c o n s i d e r Tuscany:
i t s foreign exports
a r e l i n k e d t o i t s r e g i o n a l imports, whereas a p a r t o f i t s f o r e i g n
imports a r e linked t o i t s regional exports.
If w e admit a c e r t a i n d e g r e e o f s u b s t i t u t a b i l i t y between
i n t e r n a l and e x t e r n a l p r o d u c t i o n , i t i s p r e f e r a b l e t o f o l l o w t h e
h y p o t h e s i s a l r e a d y made i n t h e p r e c e d i n g p a r a g r a p h s .
In t h i s
case, i n t e r r e g i o n a l t r a d e flows a r e dependent on t o t a l demand
( d i n t h i s c a s e i s n e t , o f r e g i o n a l e x p o r t s ) and t h e s o l u t i o n i s
g i v e n by ( 1 2 ) . The c o n c l u s i o n i s t h a t f o r e i g n and r e g i o n a l t r a d e
are t r e a t e d w i t h a k i n d of assymmetryj which s h o u l d be c l e a r from
T a b l e 2 (where q and d imply a d i f f e r e n t d e f i n i t i o n of f) .
T a b l e 2.
T h e t r e a t m e n t of f o r e i g n and r e g i o n a l t r a d e .
COMPLEMENTARY IMPORTS
COMPETITIVE IMPORTS
REGIONAL
TRADE
FOREIGN
MBAx
+
NBq
m
exogenous
TRADE
The f a c t i s t h a t c o m p e t i t i v e n e s s o f i m p o r t s means s u b s t i t u I n an
t i o n between t h e two p o s s i b l e l o c a t i o n s of p r o d u c t i o n .
i n t e r r e g i o n a l i n p u t - o u t p u t model, s u b s t i t u t i o n between r e g i o n s
i s p o s s i b l e u s i n g Bd ( s e e system (5)) , b u t s u b s t i t u t i o n between c o u n t r i e s i s n o t p o s s i b l e because o n l y one n a t i o n a l prod u c t i o n i s c o n s i d e r e d and t h i s i s why m i s exogenous.
W e now f o c u s a t t e n t i o n on t h e e s t i m a t i o n of t r a d e flows
between r e g i o n s . T h i s problem i s common t o a l l i n t e r r e g i o n a l
models. I n o u r c a s e , t h e r e a r e o n l y two r e g i o n s ; t h i s i s a
v e r y s p e c i a l s i t u a t i o n and s h o u l d t h e r e f o r e be s i m p l e r t o handle.
More p r e c i s e l y , t h e p u r p o s e o f o u r a n a l y s i s i s t o improve t h e
e s t i m a t e of f l o w s between t h e two r e g i o n s a l r e a d y obtained (Marliani
1981 ) and used i n t h e a p p l i c a t i o n of system ( 1 2)
This estimate
.
imports from abroad
\
regional imports
t
national*
competitive
imports from
abroad
\
total demand
\
consump tion
\
\
\
\
I
Figure 3 .
C a u s a l s t r u c t u r e of TIM when r e g i o n a l i m p o r t s a r e
complementary ( t = Tuscany, r = t h e rest o f I t a l y ) .
*
( F o r e i g n c o m p e t i t i v e i m p o r t s depend, i n t h i s c a s e , on
t h e e x c e s s i n demand o v e r c a p a c i t y . )
d o e s n o t a d m i t , by d e f i n i t i o n , c r o s s h a u l i n g e f f e c t s . B a s i c a l l y ,
i t h a s b e e n assumed t h a t e x p o r t s are e q u a l t o a s u r p l u s , e x p o r t s
and i m p o r t s e q u a l t o a d e f i c i t b a l a n c e .
Now, i f w e c o n s i d e r t h e b a s i c s y s t e m (51, w e c a n i m m e d i a t e l y
s a y t h a t f o r a given x and d t h i s assumption minimizes t h e i n t e r a c t i o n between t h e two r e g i o n s .
I n o r d e r t o g r a s p t h e problem
b e t t e r , l e t u s c o n s i d e r o n e s p e c i f i c s e c t o r , i. The s y s t e m
w i l l be
I f w e i g n o r e f o r a moment t h e estimate o f IRPET, t h e unknowns
a r e t h e t r a d e c o e f f i c i e n t s iB, w i t h ix and id a s g i v e n .
The f i r s t two e q u a t i o n s o f ( 1 4 ) a l l o w f o r a s u b s t i t u . t a b i l i t y
between Tuscany and t h e r e s t o f I t a l y t h a t c a n be u s e d t o d e f i n e
two t r a n s f o r m a t i o n f u n c t i o n s , w h i l e t h e t h i r d g i v e s t h e c o n s t r a i n t s
These e q u a t i o n s a r e r e p r e s e n t e d i n F i g u r e 4,.where t h e a t t a i n a b l e a r e a f o r t h e t r a d e p a r a m e t e r s i s d e l i m i t e d by ABCDEO.
The two t r a n s f o r m a t i o n s ( s t r a i g h t l i n e s ) are r e p r e s e n t e d
on t h e l a t e r a l p l a n e s .
Their location is clearly related t o
the r e l a t i v e v a l u e o f t h e two demands d r / d t
t i o n within n a t i o n a l production.
* The
f o u r t h c o n s t r a i n t btt
( 7 ) a r e redundant.
+ brt -
and t o t h e i r composi-
and t h e t r a d e b a l a n c e
I n t h e f o l l o w i n g w e o m i t t h e i.
.gure 4.
Parameter s p a c e f o r t r a d e c o e f f i c i e n t s of a Chei-ieryMoses model w i t h two r e g i o n s ( t = Tuscany, r = resf
of I t a l y ) .
There i s c l e a r l y a l a t i t u d e of c h o i c e and w i t h ,no informat i o n o t h e r t h a n t h a t on t h e t r a d e b a l a n c e , t h e p a r a m e t e r s f o r
e v e r y s e c t o r i cannot be determined.
I f w e a r e a b l e t o f i x t h e e x i s t i n g d e g r e e of freedom ( f o r
i n s t a n c e , by choosing the p o i n t F), t h e s o l u t i o n i s immediately
o b t a i n e d a l o n g t h e d o t t e d l i n e . But t h e r e a r e many p o s s i b i l i t i e s . IRPET h a s chosen one p a r t i c u l a r s o l u t i o n . I t i s c h a r a c t e r i z e d by t h e c o r n e r s o l u t i o n G I which i s below A i f Tuscany
h a s a d e f i c i t b a l a n c e and t o t h e r i g h t of A (between A and B )
i f Tuscany h a s a s u r p l u s . I f w e now r e p e a t e x a c t l y t h e same
procedure f o r a d i f f e r e n t y e a r , w e o b t a i n two d i f f e r e n t l i n e s
of t r a n s f o r m a t i o n .
I f t h e y i n t e r c e p t t h e former lines inside the
admissible area OABCDE, we can assume stability for the trade
parameters and solve the problem immediately,
If we reject this hypothesis or if the new lines do not
intercept the old lines in the feasible area, we have four different possible situations (Figure 5).
Figure 5.
Shifting trade coefficients of a Chenery-Moses model
with two regions,
A t p r e s e n t , however, w e c a n n o t a p p l y t h e p r o c e d u r e d e s c r i b e d
b e c a u s e o f t h e a b s e n c e o f t h e n a t i o n a l t a b l e ' s for 1977 and 1978.
W e c a n , however, a t t e m p t a s e n s i t i v i t y a n a l y s i s o f t h e r e s u l t s
of changing t h e t r a d e c o e f f i c i e n t s B along t h e transformation
l i n e s f o r 1975.
T h i s means t h a t s t a r t i n g from p o i n t G on F i g u r e
4 , w e go down t h e l i n e GF d e c r e a s i n g t h e v a l u e o f b t t ,
u s i n g ( 1 5)
f o r t h e computation o f t h e o t h e r c o e f f i c i e n t s .
6.
STRUCTURAL ANALYSIS AND FORECAST FOR TUSCANY
I n t h i s section, we discuss t h e preliminary r e s u l t s f o r t h e
r e f e r e n c e v e a r 1975 o b t a i n e d from t h e i m p l e m e n t a t i o n of TIM on
t h e b a s i s of s p e c i f i c a t i o n ( 1 1 ) .
sequence d e p i c t e d i n F i g u r e 6.
In doinq so, w e follow t h e
S t a r t i n g w i t h t h e t a b l e s f o r Tuscany and I t a l y f o r 1975, w e
b u i l d t h e L I b i r e g i o n a l t a b l e , which h a s t h e c h a r a c t e r i s t i c s
discussed i n Section 2.
We
then
compute
t h a t year--which
the
coefficients
of
the
system
are t h e t e c h n i c a l m a t r i x A , t h e i m p o r t
for
para-
meters M and B, the labor c o e f f i c i e n t s L, and t h e t r a n s f e r c o e f f i For t h e r e f e r e n c e y e a r , w e can immediately s o l v e t h e
c i e n t s 2.
model and check t h e c o n s i s t e n c y o f t h e s o l u t i o n (see S e c t i o n 1 ) .
The model h a s t h e s t r i c t l y r e c u r s i v e s t r u c t u r e shown i n T a b l e 3 .
Table 3 .
The s t r u c t u r e of t h e model.
I+Z
-MBA
Thanks t o t h i s p r o p e r t y , w e can s o l v e t h e model by i n v e r t i n g
t h e upper b l o c k and t h e n go down from t h e o t h e r unknowns:
labor
r e q u i r e m e n t s 1, r e g i o n a l i m p o r t s n , and f o r e i g n i m p o r t s m.
The t r e a t m e n t o f t r a n s f e r s o f p r o d u c t i o n and o f i n p u t c r e d i t
s e r v i c e s h a s been b a s e d on t h e a s s u m p t i o n s g i v e n i n S e c t i o n 1 ,
whereas foreign i m p o r t s are a l l t r e a t e d a s complementary w i t h a
common p a t t e r n M.
Read i n p u t f l o w s o f
t h e LIMITED INFORMATION 1 / 0 TABLE
reference year
I
Compute t h e
coefficients
o f t h e model
Chanqe
trading
pattern
-
SPLIT FOR TUSCANY
I
t h e forecasts given
NO
at national level (
by INFORUM
NO
YES
I
SOLUTION
f o r t h e f l o w s o f t h e FULL
INFORMATION 1 / 0 TABLE f o r
t h e two regions
f o r employment r e q u i r e m e n t s
by source demand
Compute i n d i c a t o r s
of regional
development
A
YES
NO
S T O P
Figure 6 .
Flow c h a r t o f t h e p r e l i m i n a r y a n a l y s i s c a r r i e d o u t
u s i n g TIM 7 5 .
Then f o l l o w s a s t r u c t u r a l a n a l y s i s o f t h e d e g r e e o f i n t e r d e ~ e n d e n c eo f t h e two r e g i o n s . T h i s i s based unon i n d e x e s obtained
from t h e upper b l o c k sumrnina t h e m a t r i c e s a l o n q t h e rows ( n l a r t e l l a t o 1980) :
The r e s u l t s show t h a t t h e t o t a l i n d e x o f dependence o f
Tuscany on t h e o t h e r r e g i o n i s almost20 t i m e s t h a t of t h e r e s t
o f I t a l y on Tuscany (see T a b l e 4 ) .
T a b l e 4.
R e g i o n a l dependence by s e c t o r , 1975.
Sector
Tuscany upon
r e s t of I t a l y
Rest of I t a l y
upon Tuscany
2.694
0.139
Agriculture
Coal and o i l
Other energy forms and water
Minerals
Minerals, non-me tal
Chemicals
Metal products
Machinery f o r i n d u s t r y , agr.
Other machinery
E l e c t r i c a l equipment
Transport equipment
Meat
Milk
Other food products
Beverages
Tobacco
Textiles
Footwear
Wood and Furniture
Paper and paper products
Rubber and rubber products
Other manufactures
Construction
Commerce
Hotels
Transport
Communications
C r e d i t and insurance
Housing
Other marketable s e r v i c e s
Non-marketable s e r v i c e s
.
T O T A L
A t t h i s s t a g e , w h i l e m a i n t a i n i n g t h e c o e f f i c i e n t s con-
s t a n t , f o r e c a s t s a r e performed f o r q i v e n v a l u e s o f f ( t h a t i s ,
f o r consumption, i n v e s t m e n t , and f o r e i g n e x p o r t s )
.
Another e x e r c i s e i s t o keep e v e r y t h i n g c o n s t a n t a t t h e
l e v e l of 1975 e x c e p t f o r f i n a l demand i n Tuscany, which i s
o b t a i n e d from t h e t a b l e f o r 1977. I n t h i s way, it i s p o s s i b l e
t o a s s e s s - - f o r e v e r y component of t h e exoeenous v e c t o r - - i t s
e f f e c t on t h e l e v e l o f employment i n Tuscany and i n t h e rest
of I t a l y and, h e n c e , t h e r e g i o n a l s p i l l o v e r o f t h e g l o b a l
demand e f f e c t o f Tuscany, v a l u e d a t c u r r e n t p r i c e s .
L e t us c o n s i d e r t h e n a t i o n a l employment e f f e c t f i r s t .
For
a g i v e n 1 % i n c r e a s e i n p r i v a t e consumption, p u b l i c consumption,
investments and foreign.exports of Tuscany, w e g e t an i n c r e a s e i n
I t a l y o f 3 . 2 % , 3.51, U.8%, and 5 . 8 % , r e s p e c t i v e l y . On t h i s b a s i s ,
w e s h o u l d conclude t h a t t h e most e f f e c t i v e demand component i s
foreign exports.
L e t u s , however, c o n s i d e r t h e r e s u l t s i n t e r m s o f e l a s t i -
c i t y (Table 5 ) .
T a b l e 5.
E l a s t i c i t i e s of employment i n c r e a s e w i t h r e s p e c t t o
f o u r c a t e g o r i e s o f f i n a l demand i n Tuscany o n l y (1977).
F i n a l demand
Employment i n c r e a s e
P r i v a t e consumption
P u b l i c consumption
Investment
Foreign exports
We may n o t e t h a t t h e e l a s t i c i t y o f p u b l i c consumption i s
t h e h i g h e s t (which i s n o t s u r p r i s i n g ) , b u t a l s o t h a t t h e e l a s t i c i t y of f o r e i g n e x p o r t s i s t h e l o w e s t (which i s s u r p r i s i n g ) .
The e x p l a n a t i o n c o u l d be t h a t t h e l e a k a g e i s s t r o n g e r f o r
e x p o r t - o r i e n t e d s e c t o r s i n Tuscany. W e o b s e r v e t h a t t h e e l a s t i c i t i e s a r e below u n i t y , which means t h a t t h e p o s i t i v e e f f e c t
of t h e i n c r e a s e d p r o d u c t i o n i n the r e s t o f I t a l y i s n o t s u f f i c i e n t l y s t r o n g t o c o u n t e r b a l a n c e t h e s p i l l o v e r e f f e c t of Tuscany
i n favor of t h e rest of I t a l y .
Now l e t u s move t o a more t r a d i t i o n a l e x e r c i s e r e l a t e d
t o e v a l u a t i n g t h e i m p a c t o f an i n c r e a s e ( 1 9 7 8 ) on t h e f i n a l
demand i n b o t h r e g i o n s a t c o n s t a n t p r i c e s ( 1 9 7 5 )
.
The f i r s t outcome o f t h e c o n s t r u c t i o n o f t h e Tuscany
d i r e c t i n p u t - o u t p u t t a b l e f o r 1978 i s t h e a v a i l a b i l i t y o f f i n a l
demand.
Having o b t a i n e d comparable d a t a f o r I t a l y from n a t i o n a l
a c c o u n t i n g s t a t i s t i c s , and h a v i n g d e f l a t e d t h e f l o w s ,
w e com-
p u t e d t h e s e t o f e l a s t i c i t i e s shown i n T a b l e 6 .
Table 6.
E l a s t i c i t i e s o f e m ~ l o y m e n ti n c r e a s e w i t h r e s p e c t t o
f o u r c a t e g o r i e s o f f i n a l demand, 1 9 7 8 .
F i n a l demand
Employment i n c r e a s e
Tuscany
R e s t of I t a l y
P r i v a t e consumption
1.68
2.40
P u b l i c consumption
1 .OO
0.99
Investment
0.82
1.16
Foreign exports
0.95
1.09
With r e s p e c t t o t h e p r e c e d i n g s i m u l a t i o n , t h e i n c r e a s e i n
t h e f i n a l demand o f t h e rest o f I t a l y a l l o w s u s t o compute
t h e e l a s t i c i t i e s f o r t h i s r e g i o n and t o a d j u s t t h e e l a s t i c i t i e s
o f Tuscany. These e l a s t i c i t i e s depend i n t h i s c a s e b o t h on t h e
d i r e c t and t h e i n d i r e c t e f f e c k s .
The f i r s t i s t h a t produced
l o c a l l y by t h e i n c r e a s e i n l o c a l f i n a l demand, whereas t h e
second i s g e n e r a t e d by t h e feedback g i v e n by i n t e r r e g i o n a l
trade.
The d i f f e r e n c e between t h e two e l a s t i c i t i e s i s s t r o n g
o n l y i n two c a s e s : p r i v a t e consumption, and i n v e s t m e n t .
In
t h e r e m a i n i n g two c a s e s , t h e r e l a t i v e i n c r e a s e i n t h e l e v e l o f
employment i s v e r y c l o s e t o t h e r e l a t i v e i n c r e a s e i n t h e f i n a l
demand component.
For p r i v a t e consumption and i n v e s t m e n t , t h e demand e f f e c t s
seem t o f a v o r t h e r e s t o f I t a l y . T h i s i s c l e a r l y a r e s u l t o f t h e
lower s e l f - s u f f i c i e n c y
o f Tuscany, e s p e c i a l l y i n l i g h t
industry.
I n b o t h r e g i o n s , f i n a l l y , t h e employment e f f e c t o f
p r i v a t e consumption i s t w i c e t h a t o f investment, which i s t o
be e x p e c t e d .
7.
FUTURE DEVELOPMENT
OF TIM
I n t h e f i r s t s e c t i o n , t h e relevance of analyzing t h e t r a d e
r e l a t i o n s of a r e g i o n s u c h a s Tuscany, r a t h e r t h a n a n a l y z i n g t h e
f a c t o r m o b i l i t y of p r i c e r e l a t i o n s , h a s been s t r e s s e d . The hypot h e s i s h a s been t h a t t h e l e v e l o f i n t e r n a l economic a c t i v i t y i n
a v e r y open r e g i o n i s n e c e s s a r i l y s t r o n g l y i n f l u e n c e d by i t s
trade relations.
One may wonder w h e t h e r t h e r e s u l t s d i s c u s s e d i n t h e p r e c e d i n g s e c t i o n are s u f f i c i e n t l y c l e a r and c o n v i n c i n q t o v a l i d a t e our
hypothesis.
C e r t a i n l y , w e have t o t a k e a c c o u n t of t h i s , which
means t h a t w e h a v e t o b e p r e p a r e d t o r e j e c t t h e h y p o t h e s i s .
There i s a n o t h e r argument i n f a v o r o f an a n a l y s i s f o c u s e d on
trade relations.
I t i s t h a t t h e fundamental t a s k o f T I M and
o t h e r models d e v e l o p e d w i t h i n t h e Tuscany c a s e s t u d y i s t o a i d
i n a s u f f i c i e n t l y comprehensive a s s e s s m e n t o f t h e economic
It is
impact of n a t i o n a l pol'icies a t t h e r e g i o n a l l e v e l .
d o u b t f u l whether s u c h a s a s s e s s m e n t c o u l d i n d e e d b e made w i t h o u t c o n s i d e r i n g t h e i n t e r i n d u s t r i a l and i n t e r r e g i o n a l r e l a t i o n s
o f t h a t r e g i o n . Without t h e s e d i m e n s i o n s , a model c a n n o t g i v e a
c o r r e c t estimate o f t h e income o r employment m u l t i p l i e r s and
regional spillovers.
I t s h o u l d b e c l e a r t h a t TIM a l o n e c a n n o t comprehensively
evaluate the regional effects.
It constitutes the starting
p o i n t and can be c o n s i d e r e d as t h e c o r e o f a system o f models.
I n t h i s way, w e a r e i n d u c e d t o s t a t e some p o s s i b l e f u t u r e d e v e l opments o f t h e c u r r e n t v e r s i o n o f TIM h a v i n g a s a k e r n e l t h e
interregional trade pattern.
I n s o d o i n g , w e f i n d a t l e a s t t h r e e d i f f e r e n t avenues o f
f u t u r e r e s e a r c h . These f u t u r e developments w i l l imply s o l u t i o n
p r o c e d u r e s t h a t d i f f e r from t h o s e t h a t a r e c u r r e n t l y used.
A.
I n i t s p r e s e n t s t a t e , TIM i s a l i n e a r s t a t i c r e c u r s i v e s y s tem o f e q u a t i o n s o f s m a l l dimensions. Because o f t h e l i m i t a t i o n s of t h e d a t a base, t h e treatment of t r a d e r e l a t i o n s
i s v e r y s i m p l e b o t h f o r r e g i o n a l and f o r e i g n r e l a t i o n s .
It
i s s o l v e d i n a way t h a t t r i e s t o t a k e a d v a n t a g e o f i t s
i n t r i n s i c r e c u r s i v e n e s s . F i r s t l y , t h e s o l u t i o n f o r product i o n i s o b t a i n e d by s t r a i g h t i n v e r s i o n , then the v e c t o r s o f
employment, regional Wrts, and f o r e i g n i m p o r t s a r e computed
f o r given p a r a m e t e r s and v e c t o r s o f exogenous demand.
B.
One way t o improve t h e f e a t u r e s o f t h e model c o u l d be a
more s o p h i s t i c a t e d t r e a t m e n t o f t r a d e : d i f f e r e n t i a t i o n o f
t r a d e p a t t e r n s f o r i n t e r m e d i a t e consumption and f i n a l u s e ,
and w i t h i n t h i s , f o r f i n a l consumption and i n v e s t m e n t . For
f o r e i g n t r a d e it would a l s o be u s e f u l t o s e p a r a t e c o m p e t i t i v e
i m p o r t s from complementary i m p o r t s . T h i s would imply a
r i c h e r d a t a base ( d i r e c t t a b l e f o r 1978), b u t t h e s o l u t i o n
procedure d e s c r i b e d under A would s t i l l remain v a l i d . These
improvements a r e i n t e r n a l improvements t o a model t h a t can
give only short-term f o r e c a s t s .
C.
A second way would be t o r e l a x t h e assumption o f parameter
s t a b i l i t y , i n order t o
make t h e model c a p a b l e
of giv-
i n g long-range p r o j e c t i o n s . Aside from t h e obvious p o s s i b i l i t v o f changing t h e t e c h n i c a l c o e f f i c i e n t s , p a r t i c u l a r
a t t e n t i o n should be given t o t h e s t a b i l i t y h y p o t h e s i s f o r t h e
r e g i o n a l t r a d e c o e f f i c i e n t s , because o f t h e i r h i g h d e g r e e o f
i n s t a b i l i t y and because o f t h e possibility of obtaining endogenously
a b e t t e r e s t i m a t e o f regional trade. Since the mthod of doing this
h a s been presented elsewhere ( M a r t e l l a t o 1981b1, w e need o n l y
mention h e r e t h a t c o n s i s t e n c y of e q u i l i b r i u m between t h e prod u c t i o n a l l o c a t i o n and t r a d e p a t t e r n s h a s t o be reached. The
model becomes n o n - l i n e a r because some o f i t s p a r a m e t e r s a r e
s i m u l t a n e o u s l y determined i n t h e c o u r s e o f t h e s o l u t i o n o f
t h e production l e v e l .
There a r e e s s e n t i a l l y f o u r p o s s i b i l i t i e s :
- t o b r e a k t h e s i m u l t a n e i t y by s p e c i f y i n g exogenously a
t r e n d f o r t h e t r a d e parameter u s i n g employment d a t a o r
lagged p r o d u c t i o n d a t a by s e c t o r and regbon;
t o assume o p t i m i z a t i o n b e h a v i o r f o r t h e economic a g e n t s
and t o minimize t o t a l t r a n s p o r t c o s t s ;
-
-
-
t o assume c o n s e r v a t i v e b e h a v i o r o f a g e n t s and t o minimize t h e i n f o r m a t i o n g i v e n by t h e new p a t t e r n o f prod u c t i o n and t r a d e i n r e l a t i o n t o t h e o l d p a t t e r n s f o r
a g i v e n exogenous demand;
t o u s e an i t e r a t i v e t e c h n i q u e o f power expansion o f t h e
i n v e r s e o f t h e c u r r e n t c o e f f i c i e n t m a t r i x o f t h e model.
D.
The t h i r d avenue f o r p o s s i b l e f u t u r e developments i s t h a t o f
i n c r e a s i n g t h e s c o p e o f t h e model i t s e l f . T h i s c a n imply a n
i n c r e a s e d c o n s i s t e n c y w i t h i n T I M a s it c u r r e n t l y s t a n d s .
T h i s can b e done by t r a n s f e r r i n g - - w h e r e possible--some
o f t h e c u r r e n t f i n a l demand components from t h e exogenous
vector t o t h e i n v e r t i b l e matrix:
consumption, i n v e s t m e n t ,
e x p o r t s abroad. A l t e r n a t i v e l y , it can r e q u i r e t h e implement a t i o n o f s a t e l l i t e -1s
t o be appended t o TIM. T h i s can b e
done f o r oonsmptian, investment, and f o r e i g n e x p o r t s , b u t a l s o
f o r t h e demographic-migration component, h o u s i n g i n v e s t m e n t ,
e n e r g y and e n v i r o n m e n t a l a s p e c t s , w a t e r demand, f i n a n c i a l
m a r k e t s , p u b l i c f i n a n c e . An a l t e r n a t i v e would b e t o b u i l d a
s a t e l l i t e model f o r i n v e s t m e n t ( t h e same a s for exports and consumption) aiming t o f i n d t h e s h a r e of Tuscany w i t h i n a f o r e c a s t e d
national total.
T h i s k i n d o f model h a s a l r e a d y been used f o r
some r e g i o n s i n I t a l y ( M a r t e l l a t o , 1 9 8 0 ) .
A l l t h e s e p o s s i b i l i t i e s imply t h a t t h e model w i l l become much
l a r g e r . A more a p p r o p r i a t e s o l u t i o n p r o c e d u r e i s t h e r e f o r e
i n o r d e r , b e c a u s e t h e model would s t a n d a s a l a r g e l i n e a r
model w i t h many e q u a t i o n s and a s p a r s e m a t r i x o f c o e f f i c i e n t s .
One s h o u l d t r y t o s o l v e i t by i n v e r s i o n u s i n g an approp r i a t e routine f o r sparse matrix inversion o r t r y t o
t a k e advantage of t h e c a u s a l s t r u c t u r e of t h e matrix.
Thus, one c o u l d s o l v e p a r t o f t h e model r e c u r s i v e l y and
t h e n u s e a Gauss-Seidel i t e r a t i o n f o r t h e s i m u l t a n e o u s
p a r t of i t .
A s p e c i a l c a s e o f p o i n t D o c c u r s when t h e i n v e s t m e n t i s made
endogenous w i t h i n t h e i n p u t - o u t p u t model v i a a m a t r i x
c a p i t a l c o e f f i c i e n t s ( f o l l o w i n g t h e work o f L e o n t i e f ) .
t h i s c a s e , t h e r e a r e two problems.
of
In
The f i r s t i s t h e e s t i m a -
t i o n of t h e s e c o e f f i c i e n t s , t h e second i s t h e s o l u t i o n procedure,which r e q u i r e s s p e c i a l a t t e n t i o n . The model becomes
dynamic and i t s s t r u c t u r a l m a t r i x i s no l o n g e r i n v e r t i b l e
because t h e c a p i t a l s t o c k c o e f f i c i e n t s matrix i s t y p i c a l l y
singular.
While t h e second problem can b e s o l v e d i n s e v e r a l ways, t h e
f i r s t i s a c h a l l e n g i n g one w i t h o u t a d i r e c t measure o f t h e
s t o c k o f c a p i t a l , and t h e p o t e n t i a l o u t p u t by s e c t o r . T h i s
problem, however, can b e t a c k l e d w i t h p r o c e d u r e s advanced,
f o r example, by Andersson and M a r t e l l a t o ( 1 9 8 0 )
Why s h o u l d
we challenge t h e d i f f i c u l t i e s o f t h e implementation o f a b i -
.
r e g i o n a l dynamic i n p u t - o u t p u t model? O r , i n o t h e r words,
why do w e c o n s i d e r a s t a t i c model t o b e u n s a t i s f a c t o r y and
t r y t o o b t a i n i t s dynamic c o u n t e r p a r t ?
The s t a t i c i n p u t - o u t p u t model c l e a r l y p r o v i d e s a p o w e r f u l and
f l e x i b l e a p p r o a c h more s u i t e d t o r e g i o n a l economic problems
t h a n a more a g g r e g a t e d t e c h n i q u e . However, t h e r e are a t l e a s t
t h r e e arguments i n f a v o r o f t h e dynamic i n p u t - o u t p u t model.
The f i r s t i s t h e f a c t t h a t t h e m u l t i p l i e r s o f a s t a t i c model
do n o t p r o v i d e any i n f o r m a t i o n a b o u t t h e t i m e p a t h o f t h e
economic s y s t e m , t h e y s i m p l y g i v e t h e i m p a c t o f t h e f i r s t
p e r i o d and d i s r e g a r d t h e l a g g e d r e s p o n s e o f t h e system.
The second argument i s r e l a t e d t o t h e s h o r t - t e r m c h a r a c t e r i s t i c s o f s t a t i c i n p u t - o u t p u t a n a l y s i s . Because
r e g i o n a l growth d i s p a r i t i e s a r e always s t r o n g and
o f t e n r e l a t e d t o b u s i n e s s c y c l e s , and b e c a u s e r e g i o n s
i n e v i t a b l y show d e e p i n t e r a c t i o n s , w e s h o u l d a l s o pay
a t t e n t i o n t o t h e r e g i o n a l growth l i n k a g e s . However,
a s t a t i c model c a n n o t t r a c e t h e dynamic ( o r l o n g - r u n )
feedbacks.
F i n a l l y , w i t h a s t a t i c model, w e a r e f o r c e d t o g i v e a
r e g i o n a l and s e c t o r a l breakdown o n l y o f t h e t r a d e f l o w s
g e n e r a t e d by i n t e r m e d i a t e consumption, d i s r e g a r d i n g
those linked t o c a p i t a l formation. I t follows t h a t
o n l y w i t h a dynamic i n p u t - o u t p u t model c a n w e o b t a i n
unbiased i n t e r r e g i o n a l m u l t i p l i e r s .
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