The Tuscany Interregional Input-Output Model (TIM): Mathematical Structure and Preliminary Results

NOT FOR QUOTATION WITHOUT PERMISSION OF THE AUTHOR

THE TUSCANY INTERREGIONAL INPUT- OUTPUT MODEL (TIM) : MATHEMATICAL STRUCTURE AND PRELIMINARY RESULTS

Dino Martellato

*

June 1982 CP-02-30

*

Faculty of Economics and Commerce University of Venice

Venice, Italy

C o Z Z a b o r a t i v e 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 organi- zations 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 f o r e m o s t 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 c o n c o m i t a n t 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 p r e - v a i l i n g c o m p a r a t i v e a d v a n t a g e s . Even l a r g e , and s t r o n g , econo- m 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 econ- omy. 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 i n d u s t r y .

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 c o m p a r a t i v e 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 o f s t r o n g l y s p e c i a l i z e d r e g i o n s i n i n d u s t r i a l i z e d c o u n t r i e s .

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 s y s t e m s 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 u n d e r t a k e n 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 s y s t e m 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 b e i n g 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 d e p e n d e n c i e s 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 c o m p u t e r i z e d model s y s t e m 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 i n p u t - o u t p u t 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 o f 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 o f 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 o f t h e world where e x p o r t s a r e exogenously determined. F o r e i g n 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. Com- p 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 o f i m p o r t s 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 B o r i s I s s a e v

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 s y s t e m 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 o f t h e e x p o r t s e c t o r s o f t h e d i f f e r e n t I t a l i a n r e g i o n s .

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 c a n b e 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 w i t h t h e s e phenomena. I n s u c h 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 p r o d u c t s .

*

* 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 o f t h e m o b i l i t y o f p r o d u c t s r a t h e r t h a n o f t h e produc- t 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 o f 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 proba- b 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 .

F u r t h e r m o r e , 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 , e v e n i f t h e r e a r e no problems f o r a b a l a n c e o f 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 o f 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 - of-view. 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 , 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 s y s t e m 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 c a n 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 c h a n n e l e d 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 f o r m e r ;

--

t h e s t r o n g e r t h e r e g i o n a l c o n n e c t i v i t y , t h e h i g h e r 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 o f 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 a n d / o r n o n - s p a t i a l n e u t r a l i t y o f f i s c a l and monetary p o l i c i e s .

The main f o c u s o f 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 o f 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. Under- l y i n g t h i s a p p r o a c h 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 d e p e n d e n t 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 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 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 ex- p 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 o n 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 a v a i l a b l e i n s u f f i c i e n t d e t a i l , p a r t i c u l a r l y f o r t r a d e w i t h 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 n e c e s s a r y b a s i c s t a t i s t i c s w i t h i t s d i r e c t i n n u t - o u t p u t 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 ( T I M ) i s i n t e n d e d a s 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 u s e d by t h e c u r r e n t s y s t e m o f n a t i o n a l a c c o u n t s . I t s h o u l d a l s o

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 h a v e 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 h a v e 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 s y s t e m a c c u r a t e l y , b u t a l s o on t h e s e e m i n g l y 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 c a n accom- modate a l l t h e i m p o r t s i n a row a t t h e bottom o f t h e i n p u t - o u t p u t 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 i m p a c t 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 draw- b a c k s : insomuch a s p a r t o f 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 ,

*

I R P E T 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 l o c a t e d i n F l o r e n c e , 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 c o n s i d e r a l l t h e i n t e r m e d i a t e f l o w s , d i s r e g a r d i n g 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 .

I n t h i s p u r e l y c o m p e t i t i v e h y p o t h e s i s , however, w e h a v e t o s u b t r a c t from t h e exogenous v e c t o r o f 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 e x o g e n o u s l y t h e l e v e l o f 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 o f 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 a n 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 a r g u m e n t s can b e p u t forward f o r p r o d u c t i o n

* .

^When

w e r e f e r t o a s i n g l e v e c t o r , i t s e f f e c t i v e p r o d u c t i o n ( x ) i s 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 b y - p r o d u c t s 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 o f p r o d u c t i o n between s e c t o r s s i m p l y 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 c o m p u t a t i o n o f Leon- t 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 consump- t 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 o b v i o u s s o l u t i o n . I n t h i s c a s e , t h e v e c t o r o f 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 o f

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 o v e r t h e e f f e c t i v e p r o d u c t i o n , b u t t h e e q u i l i b r i u m i d e n t i t y i s s t i l l d e f i n e d f o r d i s t r i b u t e d p r o d u c t i o n . 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 ) :

-

¹

x = ( I - A ) ( f - z )

.

⁽²

T h i s i s c e r t a i n l y more s t a b l e t h a n t h e p r e c e d i n g r e l a t i o n because t h e m a t r i x (I-A) i s a t r u e L e o n t i e f i n v e r s e . Never- 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 f o l l o w i n g

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 i t s h i s t o r i c a l l e v e l .

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 e n c o u n t e r e d 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 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. I t i s t h e 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 o f 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 pro- d 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 o f 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, o n l y an a c c o u n t i n g t r i c k , w h i c h does n o t h e l p t h e modeler because he h a s 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 m a t r i x , 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 i n d e e d 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 ( 1 9 7 5 ) in t h e 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 - p a n c y ( w h i c h i s a l w a y s n e g a t i v e a n d i n m o s t 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 b y 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 , e q u a l t o t h e b i a s a n d k e p t c o n s t a n t a l o n g r o w s . 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 f r o m b i a s e d i n t e r - i n d u s t r y f l o w s .

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 f r o m 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 i s t o b u i l d ( f i r s t l y f o r 1 9 7 5 , a n d i n t h e f u t u r e f o r 1 9 7 8 ) 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 T u s c a n y and t h e rest o f I t a l y .

B e f o r e d e f i n i n q f u l l ( o r l i m i t e d ) i n f o r m a t i o n t a b l e s , i t 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 a n d 1978 a top-down a p p r o a c h w i l l b e u s e d , t h e d i f f e r e n c e b e i n g 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 7 5 ) b y 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 o n 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

r e g i o n a l l e v e l ( M a r l i a n i 1 9 8 1 ) . 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 r e s t 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 y e a r w i l l t h e r e f o r e b e i m w o s s i b l e . The 1977 t a b l e w i l l , how- e v e r , 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

ITALY TABLE

-

Model for interre- gional

(

trade (MITI

I

1975

v

Statistical information at regional TABLE ITALY level MIT 75

v

TUSCANY TABLE MIT 77

ITALY 1974 TABLE Full Information bi- regional system of 1/0 tables

-

TIM 75

Limited Information biregional system of 1/0 tables for

\

Figure 1. The derivation of TIM 1975.

implemented f o r 1975. I t i s now c l e a r why t h e a n a l y s i s r e s t s on a top-down approach f o r 1975: b o t h 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 T a b l e 1 )

.

1 31 32 62 63 64 65 66 67 68 69 70 n 72 73 Tt 75

Table 1 . A F u l l I n f o r m a t i o n i n p u t / o u t p u t t a b l e . INTERNAL

INTERMEDIATE FLOWS TUSCANY

INTERMEDIATE

IMPORTS TO

TUSCANY FROM

REST OF

ITALY

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 .

I n an F I b i r e g i o n a l s y s t e m , on t h e o t h e r hand, t h e same

. -

1

INTERMEDIATE P;

W P I

.

EXPORTS FROM ^{W W} CI Eil

z

PI

z xt n ^{0 W}

TUSCANY TO m m o z ^Z

REST OF

ITALY

a z o z w 4 z z a u a H u > . w E

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 r e s t 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 a b r o a d , i m p o r t s from a b r o a d , and a v a i l a b l e r e s o u r c e s .

INTERNAL INTERMEDIATE

FLOWS

REST OF

ITALY

0

& 8,

g 2 S & ~ Z

H D O O

2

0 Z 9 & 4 4 d U c 3 g H 2,; OH

C?

2

W F E W

m H

n

$3

*

⁴

W D G

e

U

*

E k r n

H

m a m W H o w m

p$' .

W C Q Vl 14

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 r e g i o n s . C o n s i d e r i n g , f u r t h e r m o r e , t h a t a p a r t o f r e g i o n a l t r a d e i s a c t u a l l y a k i n d o f i n d i r e c t f o r e i g n t r a d e , w e 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 r e s t s 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 s i m p l y 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

o f 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 Sec- t 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 o f 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 b a s e d 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. F i r s t , 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 h a v e t o choose between a f i x e d trade p a t t e r n c o u p l e d 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 c o u p l e d w i t h a f i x e d p r o - d u c t i o n p a t t e r n . 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 o f interaction w= w i s h t o d e v e l o p i n t h e model a t t h e present t i m e . 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 o f 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 o f 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 ap- p 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

( M a r t e l l a t o 1981 )

.

I n t h i s c a s e , t h e f i x e d - t r a d i n g p a t t e r n i s s i m p l y 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 o f t h e s t u d y , w e a r e o n l y p r e p a r e d 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 on- g o i n g r e s e a r c h on t h e Tuscany c a s e s t u d y s h o u l d a l l o w u s t o d e v e l o p a s y s t e m 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 a s s u m p t i o n 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 s e t 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 u s e t h e f o l l o w i n g n o t a t i o n f o r v e c t o r s ( s m a l l l e t t e r s ) and m a t r i c e s ( c a p i t a l l e t t e r s ) :

x = e f f e c t i v e p r o d u c t i o n ;

f = 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 ; m = f o r e i g n i m p o r t s ;

g = f - m ;

*we r e f e r t o models f o r t h e l a b o r m a r k e t , 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 t e c h n i c a l c o e f f i c i e n t s i n r e g i o n s ;

' i j s

B = {ibts) 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 :

z

= { z ) c o r r e c t i o n c o e f f i c i e n t s f o r e f f i c i e n t i s

p r o d u c t i o n i n r e g i o n s ;

S , t I r = r e g i o n s ; i I j = s e c t o r s .

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:

w h i l e t h e v e c t o r o f t r a d e b a l a n c e s i s :

A t t h i s s t a g e , w e n o t e t h a t f o r e i g n t r a d e h a s r e c e i v e d o n l y s c a n t a t t e n t i o n a n d , 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 i m - p o r t s are e x o g e n o u s 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 b e 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 T u s c a n y . Sec- t 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 b e t w e e n 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 s o f g o o d s f o r consump- t 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 o f 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 s u r v e y f o r t h e d i r e c t t a b l e w e r e a l r e a d y 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 c a n b e s u s t a i n e d s i m p l y by a n i m p o r t 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 a b r o a d . 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 r m r 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 ( b v an assump-

t i o n o f c o m p a r a t i v e a d v a n t a g e s ) , t h e demand o f r e g i o n t c a n 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 ob- s e r v e d i n r e g i o n t i s a c t u a l l y p e r t i n e n t t o a n o t h e r r e g i o n r .

F u r t h e r m o r e , 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 a b r o a d , w h i c h 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 o f 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 o f t h e s i m p l e s t v e r s i o n o f TIM 7 5 ( t = Tuscany, r = t h e rest of I t a l y ) .

From F i g u r e 2, i t 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 f o r e i g n i m p o r t s a r e i n f a c t c o m p e t i t i v e , w e 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 o f a c e r t a i n amount o f 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 ( b m +b m t t t t r r ), i t s t o t a l n e g a t i v e e f f e c t i s

( b n +b m ⁾ where htt i s t h e upper l e f t htt ( b t t m t + b t r m r ) ⁺ h t r rtm t r r r ¹

b l o c k of the partitioned inverse H ₌ [I-(BA-Z)

I-'

and htr i s t h e up- p e r r i g h t b l o c k . T h i s k i n d o f model c a n b e 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 b e a problem i f one d o e s 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 o f 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 neces- s a r y t o c o n s i d e r t h e e f f e c t s o f h y p o t h e s i s ( 3 ) o n t h e e x i s t e n c e o f 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 o f t h e t e c h n i c a l m a t r i x A and, c o n s e q u e n t l y , 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 con- d i t i o n s f o r t h e e x i s t e n c e o f an i n v e r s e H w i t h n o n - n e g a t i v e

e l e m e n t s o n l y .

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 pro- d 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 c o n v e r g e n c e 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 h a v e a n i n v e r s e w i t h n o n - n e g a t i v e 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 o f 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 b e 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 a b r o a d 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 a b r o a d .

The s o l u t i o n i s :

x = [I+z-(I-M)BA]-I [ ( I - N ) Bf+NBe]

.

^{( 1 1 )}

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 o f 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 a n d 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

,

h a s t h e s o l u t i o n :

x = [I+z- (I-M) BA]-' [ ( I - N ) Bf+NBe-Bm]

.

^{( 1 2 )}

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 r e s t o f t h e w o r l d :

+

M B A x

+

NtBtrqr =

t t r r r Btt ^{( A} t x t t +q

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 o f 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 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 . I t i s o b v i o u s t h a t s i m i l a r f l o w s 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 r e s t o f I t a l y .

F u r t h e r m o r e , t h e same decompostion shows t h e a b s e n c e 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 ) B f

+

^NBe

-

Bm] i s i n d e e d e q u a l t o (Bf

-

NBq

-

Bm] by t h e d e f i n i t i o n o f q a s a v e c t o r of

f i n a l demand n e t o f 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 t h e two r e g i o n s one must d e c i d e i f i t 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 d o e s 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 r e g i o n s , b e c a u s e 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 a n 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 c o m p l e m e n t a r i t y i n

r e g i o n a l t r a d e . 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 o f f i n a l demand and i f w e assume comple- m e n t a r i t y , 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 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 o f c o e f f i c i e n t s V. With t h i s and by c h a n f f i n g 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 r e s t 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 f o r e i g n e x p o r t s 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 i m p o r t s a r e l i n k e d t o i t s r e g i o n a l e x p o r t s .

I f w e a d m i t 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 . I n 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 o f 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 o f 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 exogenous m

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 - 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 o f p r o d u c t i o n . I n a 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 s y s t e m (5) )

,

b u t s u b s t i t u t i o n be- tween c o u n t r i e s i s n o t p o s s i b l e b e c a u s e o n l y one n a t i o n a l pro- d 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 o f t r a d e f l o w s 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 o f s y s t e m ( 1 2)

.

T h i s e s t i m a t e

imports from abroad

\

national*

competitive regional imports imports from

t abroad

\

total demand ^\

\

\

\

\ I consump tion

F i g u r e 3 . C a u s a l s t r u c t u r e o f 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 r e s t 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 a r e e q u a l t o a s u r p l u s , e x p o r t s a n d 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 g i v e n x a n d d t h i s a s s u m p t i o n m i n i m i z e s 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 p r o b l e m 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 b e

I f w e i g n o r e f o r a moment t h e estimate o f I R P E T , 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,. w h e r e 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 . T h e i r l o c a t i o n i s c l e a r l y r e l a t e d 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 a n d t o t h e i r composi- t i o n w i t h i n n a t i o n a l p r o d u c t i o n .

*

The f o u r t h c o n s t r a i n t b t t

+

b r t

-

- and t h e t r a d e b a l a n c e ( 7 ) a r e r e d u n d a n t . I n t h e f o l l o w i n g w e o m i t t h e i.

. g u r e 4. P a r a m e t e r 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 o f a Chei-iery- Moses model w i t h two r e g i o n s ( t = Tuscany, r = resf o f 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 informa- t 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 c a n n o t be d e t e r m i n e d .

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 p r o c e d u r e 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 l i n e s 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 dif- ferent 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 o f c h a n g i n g t h e t r a d e c o e f f i c i e n t s B a l o n g t h e t r a n s f o r m a t i o n 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 c o m p u t a t i o n 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 s e c t i o n , w e d i s c u s s t h e p r e l i m i n a r y 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 o f TIM on t h e b a s i s o f s p e c i f i c a t i o n ( 1 1 ) . I n d o i n q s o , w e f o l l o w t h e s e q u e n c e d e p i c t e d i n F i g u r e 6 .

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 d i s c u s s e d i n S e c t i o n 2 .

We t h e n compute t h e c o e f f i c i e n t s o f t h e s y s t e m f o r t h a t year--which a r e 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 p a r a - 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 - c i e n t s 2. F o r t h e r e f e r e n c e y e a r , w e can i m m e d i a t e l y s o l v e t h e 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 .

T a b l e 3 . The s t r u c t u r e o f 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 u p p e r b l o c k and t h e n go down from t h e o t h e r unknowns: l a b o r 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 a r e 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 INFORMA-

TION 1 / 0 TABLE r e f e r e n c e y e a r

I

Compute t h e Chanqe

c o e f f i c i e n t s t r a d i n g o f t h e model

-

p a t t e r n

SPLIT FOR TUSCANY

t h e f o r e c a s t s g i v e n NO NO

a t n a t i o n a l l e v e l (

I by INFORUM

YES

I

Compute i n d i c a t o r s

SOLUTION o f r e g i o n a l

f o r t h e f l o w s o f t h e FULL d e v e l o p m e n t INFORMATION 1 / 0 TABLE f o r

t h e t w o r e g i o n s A

f o r employment r e q u i r e m e n t s Y E S

by source demand

NO

S T O P

F i g u r e 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 e o f t h e two r e g i o n s . T h i s i s b a s e d 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.

Tuscany upon Rest of I t a l y S e c t o r

r e s t of I t a l y upon Tuscany A g r i c u l t u r e

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 , a g r . Other machinery

E l e c t r i c a l equipment Transport equipment Meat

Milk

Other food products Beverages

Tobacco T e x t i l e s Footwear

Wood and F u r n i t u r e

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 2.694 0.139

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 o f 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 o f 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 o f I t a l y a n d , 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 u s 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, i n v e s t m e n t s and f o r e i g n . e x p o r t s 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

f o r e i g n e x p o r t s .

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 ( T a b l e 5 ) .

T a b l e 5. E l a s t i c i t i e s o f 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 ( 1 9 7 7 ) .

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 I n v e s t m e n t

F o r e i g n e x p o r t s

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 o f 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 b e 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 o f t h e i n c r e a s e d p r o d u c t i o n i n t h e 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 o f Tuscany i n f a v o r o f t h e r e s t o f I t a l y .