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Important Coefficients in the Input-Output Models for Poland

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A C T A U N I V E R S I T A T I S L O D Z I E N S I S

______________ POLIA OECONOMICA 5 4 . 1 9 8 6 ______________1

C zesław L i p i ń s k i * , Ł u c ja T o m aszew io z* *

IMPORTANT COEFFICIENTS IN THE INPUT-OUTPUT MODELS FOR POLAND

• 1 . C r i t e r i a f o r t h e E v a l u a t io n o f I m p o r ta n c e o f I n p u t - O u t £ u t =£ o e f f i c i e n t s C o n s id e r t h e m odeli J t ■ С1 - (1 ’ w herei yt • [ y ^ ] i a a v e c t o r o t f i n a l o u t p u t , X^ - [ Xi t ] lB a ▼ eotor o f t o t a l o u t p u t , A^ ■ [ a ^ ^ ] I s a m a t r i x o f i n p u t - o u t p u t C o e f f i c i e n t s ( 1 ■ 1 , 2 , . . . » n j J ■ 1 , 2 , • • > , n ) .

A p r a c t i c a l a p p l i c a t i o n o f suoh a m odel i n s o l v i n g num erous P roblem s c o n n e c te d w ith t h e f o r m a tio n o f p r o p e r econom lo m acro - P r o p o r t l o n s and eoonomio e q u i l i b r i u m , i . e . among o t h e r s w ith

- t h e d e te r m i n a ti o n o f demand f o r t h e o u tp u t o f p a r t i c u l a r b r a n c h e s , - t h e d i s t r i b u t i o n o f o u tp u t among i n t e r m e d i a t e and f i n a l u s e r s , - t h e u t i l i z a t i o n o f p r o d u o tio n c a p a c i t i e s o f t h e b r a n c h . I s c o n n e c te d f i r s t o f a l l w ith t h e a n a l y s i s o f t h e b e h a v io u r o f I n p u t- o u tp u t c o e f f i c i e n t s i n t h e i n v e s t i g a t e d p e r i o d . A s i m p l i f y i n g a s s u m p tio n a b o u t t h e s t a b i l i t y o f t h e s e c o e f -f i c i e n t s i n t h e i n p u t - o u t p u t s y s te m s -f r e q u e n t l y u n d e r ta k e n ,c a n n o t

a p p li e d w ith o u t l i m i t a t i o n s due t o a t l e a s t t h e f o llo w in g r e a s o n s i 1) c h an g e o f t h e s t r u c t u r e o f p o s s i b l e i n p u t s i n b r a n c h e s ^ S e n i o r A s s i s t a n t , I n s t , o f E c o n o m e tric s and S t a t i s t i c s , U aiVer s i t y o f Ł ó d ź. _ -^ L e c t u r e r , I n s t , o f E c o n o m e tric s and S t a t i s t i c s , U n i v e r s i t y ° f Ł ódź.

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in d u c e d by ohan g es o f r e l a t i v e p r i o e s ( o a u s ln g s u b s t i t u t i o n among i n p u t s ) , by a v a i l a b i l i t y o f I n p u t s , p r o d u o tio n s c a l e e t c . , 2 ) change o f a s s o r tm e n t s t r u c t u r e o f p r o d u o tio n r e s u l t i n g m a in ly from d e te rm in e d m ark e t t e n d e n c i e s , 3) t e c h n o l o g i c a l in n o v a t io n s and i n t r o d u c t i o n o f new p ro d u o ts , 4) p o s s i b l e d i f f e r e n c e s i n t h e m ethods o f o o n s t r u o t l n g i n p u t - - o u t p u t b a la n c e s o o n o e rn in g m a in ly a d i f f e r e n t p r l o e b a s l o and c h a n g e s i n s e c t o r a l o l a s s l f i o a t i o n o f e o o n o m lo .s u b je c ts and p r o -duced goods and s e r v l o e s .

How ever, i t i s n o t a lw a y s p o s s i b l e , and som etim es even u n n e o e s a r y ,to o o n s id e r a l l t h e e le m e n ts o f m a t r ix A^. F o r p r a c t i -c a l r e a s o n s I t i s enough t o o o n o e n tr a te on t h e I m p o r ta n t c o e f -f i c i e n t s o n l y , e . g . by c o n s u l t i n g e x p e r t s on e x p e o te d o h an g es o r by c o n s t r u c t i n g a p p r o p r i a t e m odels o f o h a n g e s e t o .

O th e r c o e f f i c i e n t s w hich a r e l e s s im p o r ta n t oan b e d e te rm in e d u s in g t h e w ell-know n m ethods« b i p r o p o r t i o n a l R A S-type m ethods ( B a c h a r a o h 1970), I n p u t- O u tp u t R e l a t i o n s h i p s . . . o r m athe-m a t ic a l prograathe-m athe-m ing athe-m ethods ( o f . L e o o athe-m b e r 1971)*

We h a v e assum ed t h r e e b a s io o r l t e r l a o f o o e f f l o l e n t s im-p o r ta n c e : 1 . The l a r g e v a lu e s o f l n p u t - o u t p u t o o e f f l o l e n t s a ^ ^ o r r e l a t e d v a l u e s . I n t h i s c a s e even s m a ll in a o o u r a o y i n d e te r m in -i n g t h e v a lu e s o f t h e s e o o e f f l o l e n t s c a n i n f l u e n o e , t o a g r e a t e x t e n t , t h e c o r r e c t n e s s o f m odel s o l u t i o n ( 1 ) . 2 . S i g n i f i c a n t c h a n g e a b i l i t y o f o o e f f l o i e n t se q u en o e i n t im e .

3. " S tr o n g " c o n n e c tio n s b e tw e e n c o e f f i c i e n t a ^ ^ and t h e w hole econom ic s y s te m . The ch an g e o f one su o h e le m e n t oan c a u s e s i g n i -f i c a n t c h a n g e s i n t h e p r o c e s s e s o -f p r o d u o tio n and d i s t r i b u t i o n i n t h e w hole econom ic s y s te m . I t I s w o rth n o t i n g t h a t e a c h o f t h e s e c r i t e r i a when o o n s ld e r e d s e p a r a t e l y , w i l l o r d e r t h e im p o r ta n c e o f t h e s e o o e f f l o l e n t s i n a d i f f e r e n t w ay. I t i s r e l a t i v e l y e a s y t o p o i n t o u t " l a r g e " , f a i r l y s t a b l e i n tim e v a lu e s o f t h e c o e f f i c i e n t s , m ost f r e q u e n t l y l i n k i n g t h e raw m a t e r i a l s e c t o r s w ith m a n u f a c tu r in g on es ( e . g . a g r i c u l t u r e w ith fo o d i n d u s t r y , m in in g w ith f u e l and pow er i n -d u s t r y an-d m e t a l l u r g y ) w hich a r e n o t a lw a y s s t r o n g l y o o n n e o te d w ith o t h e r econom ic s e c t o r s . I t i s a l s o e a s y t o p o i n t o u t r e l a t i

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-v e ly s m a ll a lth o u g h n o t s t a b l e I n tim e c o e f f i c i e n t s o r t h e s e s t r o n g l y c o n n e c te d w ith o t h e r b r a n c h e s ( e .g . c o n n e c tio n s o f t r a n s -p o r t a t i o n w ith o t h e r -p r o d u c t i v e b r a n o h e s ) . W ith r e l a t i o n t o t h i s i t seem s t h a t t h e s ta te m e n t t h a t o n ly - jo in t c o n s i d e r a t i o n o f t h e above o r l t e r l a w i l l a llo w t o e v a l u a t e p r o p e r l y t h e im p o rta n c e o f t h e c o n s id e r e d c o e f f i c i e n t , i s t r u e .

H ow ever, I t s h o u ld b e s t r e s s e d t h a t t h e t e s t i n g o f i t s im-p o r ta n c e m ust b e im-p e rfo rm e d i n t h e c o n te x t o f m odel (1 ) and on t h e b a s i s o f a d e te r m in e d i n p u t - o u t p u t b a la n o e o r t h e i r s e q u e n o e . I f n o d e l ( 1 ) was a p a r t o f a g e n e r a l m odel c o n s t r u c t e d n o t o n ly t o o b t a i n c o n s i s t e n t p r o d u c tio n p l a n s , th e n I t p r o b a b ly would n o t be n e c e s s a r y t o u s e a l l o f t h e s e t h r e e c r i t e r i a f o r e v a l u a t i n g t h e c o e f f i c i e n t s I m p o rta n c e . On t h e o t h e r h a n d , i t o a n n o t be e x c lu d e d t h a t q u i t e d i f f e r e n t m e a su re s m ight p ro v e u s e f u l , e . g . I n t h e o p t i m i z a t i o n model t h e m easu re w i l l be t h e d e g re e o f s e n s i t i v i t y o f t h e o p tim a l s o l u t i o n t o t h e ch an g e o f one o f them 1 .

T a k in g i n t o a c c o u n t t h e above f o r m u la te d c r i t e r i a f o r t h e e v a l u a t i o n o f im p o rta n c e o f i n p u t - o u t p u t c o e f f i c i e n t s , t h e m ethods f o r t h e i r d e te r m i n a ti o n oan be d i v id e d i n t o : 1 ) d i r e c t o n e s , i n w hich t h e b a s i s o f e v a l u a t i o n a r e t h e V a lu e s o f p a r t i c u l a r c o e f f i c i e n t s o r t h e i r s e q u e n c e s , and a c -c o r d in g t o t h e p u rp o s e o f t h e s tu d y , -c o n n e -c te d w ith t h e a p p l i c a -t i o n o f -th e i n p u -t - o u -t p u -t r e l a t i o n s - t h e i r r e l a t e d v a lu e s suoh a e , f o r I n s t a n c e , t h e v a lu e o f i n p u t - o u t p u t flo w r e l a t e d t o t h e ®um o f p r o d u c tio n demand o r , t h e s o - o a l l e d d i s t r i b u t i o n s t r u c t u r e c o e f f i c i e n t . The g ro u p o f d i r e c t m e a su re s i n c l u d e s a l s o t h e m ea su res b a se d on t h e I n v e s t i g a t i o n o f c o e f f i c i e n t c h a n g e a b i l i t y ! 2 ) I n d i r e c t o n es - i n w hich t h e b a s i s f o r e v a l u a t i o n o f im-p o r ta n c e i s t h e m easu re o f t h e I n f l u e n o e o f an i d e n t i c a l ( i n p e r o e n t) ch an g e o f v a lu e s o f e a c h o f p a r t i c u l a r c o e f f i c i e n t s on a ) t h e volum e o f f i n a l o u tp u t o f t h e b r a n o h ,u n d e r t h e assum p-t i o n p-t h a p-t p-t h e volum e o f g r o s s o u p-tp u p-t by b ra n c h e s i s u n c h a n g e d ,

, b ) t h e v a lu e o f g r o s s o u tp u t -of b r a n c h e s w ith u nchanged f i n a l o u t p u t .

1 C f . o u r re m a rk s on t h e s u b j e c t i n L l p l ú s k 1 ,T o m a - 8 z e w i c z 1981.

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158 Cz e s ł a w L l p l ň a k i , Łucja Tomaszewlcs_____________________ 2 . D ir e c t Mothoda f o r E v a lu a tin g th e C o e f f i c ie n t s Importanoe

The s im p l e s t m easure i n t h e g ro u p o f d i r e c t m easu res i s t h e

c o e f f i c i e n t v a lu e , i . e . d (1) H

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w here i s a v a lu e o f in p u t flo w o f t h e 1—th b ra n c h t o t h e J - t h b ra n c h and - t h e v a lu e o f g r o s s o u tp u t o f t h e J - t h b ra n o h . The h i g h e r t h e o o e f f i o i e n t v a l u e , t h e g r e a t e r im p o rta n o e la a t t r i b u t e d t o i t . S i m i l a r r e s u l t s a r e o b ta in e d u s i n g , a s a m e a s u re , t h e s h a r e o f in p u t o r i g i n a t i n g i n t h e i - t h b ra n o h i n t h e t o t a l m a t e r i a l c o s t s o f t h e j - t h u s e r , i . e . t h e m easu re i n t h e form» a U ) . f y --- f j _ . ( 3 , i j r-l i j О Ĺ jTÍ Í Ĺ jX i j i i . t ". B o th t h e s e m e a su re s s u p p ly d i r e c t i n f o r m a t io n a b o u t t h e in p u t

im portance ( i n p u t - o u t p u t c o e f f i c i e n t ) from t h e p o i n t o f view o f

p a r t ic u l a r u s e r s . T h is im p o rta n o e i s t h e h i g h e r , t h e g r e a t e r t h e v a lu e o f S i m i l a r l y , th e im p o rta n c e o f i n p u t i n t h e p r o c e s s o f p ro d u o -t i o n d i s -t r i b u -t i o n c a n be d e -te r m in e d from t h e p o i n t o f v iew o f p a r t ic u l a r p r o d u c e r s .'The s i m p l e s t m ea su re o f t h i s k in d i s » (•» ■) I t i s e a s y t o n o te th a t th e m easure d v ' i s th e s o - o a l l e d d i s t r i b u t i o n s t r u c t u r e o o e f f i o i e n t hi j • x F ( 5 ) I t i s n o t d i f f i c u l t t o s e e th a t th e m easures d and d g iv e a s im i la r h ie r a r c h y o f im portance o f th e c o e f f i c i e n t s , i f t h e sh a re o f v a lu e -a d d ed i n g r o s s output o f th e branch i s n o t to o much d i f f e r e n t i a t e d i n p a r t ic u l a r b r a n c h e s.

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._________ I a p o r t a n t C o e f f l c l e n t a l n tho Inp u t - Ou t p u t H o d e l g . . . ____________ ■; gg The m ea su re c o n s t r u c t e d i n t h e c o n c e p tio n a s d ^ J and b a s e d on t h e c o e f f i c i e n t h ^ h a s t h e form»

’ ai J T T “ - , (6 )

Some g e n e r a l i s a t i o n o f t h e s e m ea su res w hich e n a b le s to e v a lu a -t e -t h e s i g n i f i c a n c e o f a g iv e n ' o o e f f i o i e n -t b o -th from -t h e p o i n -t o f view o f t h e s u p p l i e r and t h e u s e r ( o f t h e i - t h and j - t h b r a n o h e s ) , would c o n s i s t i n a ssu m in g t h e f o llo w in g m e a s u re s :

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4 5 ' - . ев)

H ence, we o b t a i n t h e i n f o r m a t io n ab o u t t h e im p o rta n c e o f t h e c o e f f i c i e n t o n ly from t h e p o i n t o f view o f a g iv e n s u p p l i e r and u e e r . And s t i l l we l a c k t h e e v a l u a t i o n o f t h e c o e f f i c i e n t s im p o r-ta n c e from t h e p o i n t o f view o f t h e i r i n f l u e n c e on t h e b e h a v io u r o f a b a la n c e d econom ic sy ste m a s a whole"*.

B e fo re we p a s s t o t h e i n d i r e c t m e a s u re s , w hich a llo w t o c a r r y o u t s u c h an e v a l u a t i o n , we s h a l l d e v o te some a t t e n t i o n t o th e m ea su res w hich we c o n s i d e r a s d i r e c t and w hich a r e b a s e d on t h e ° h a n g e a b i l i t y o f t h e c o e f f i c i e n t s i n t im e . I f su c h an e v a l u a t i o n i e made on t h e b a s i s o f two i n p u t - o u t p u t b a la n c e s d e s c r i b i n g th e same econom ic sy ste m ( i n t h e i d e n t i c a l b r a n c h c l a s s i f i c a t i o n )

3

N o te t h a t a l l d i r e c t m ethode r e q u i r e a r b i t r a r y d e te r m in a -t i o n o f -t h e v a l u e above w hich -t h e g iv e n c o e f f i c i e n -t i s c o n s id e r e d

im p o r t a n t . I n a s im p le p r o c e d u r e o f c o e f f ic iv . t im p o rta n c e ? £ ® iy a tio n b ^ s e d on a d i r e c t m ethod a p p l i e d by Еь.С ( J i 1 e к i t was assum ed, f o r i n s t a n c e , t h a t t h e m ost im p o r ta n t e l e -m ents a r e t h e s e w hich I n t h e d e c r e a s i n g l y o r d e r e d row s o r colu-m ns 4i*e a t t h e b e g in n in g and c o n s t i t u t e 90% o f t h e sum o f rows o r °o lu m n s.

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i n moment» t Q and t , f t h e n t h e moet f r e q u e n t l y u s e d m eaeuree a r e r e l a t i v e d i f f e r e n c e s . , 4 J ) . * 4 1 , - ‘ 4 ° . ( 9 ) a i j O o r i , o 4

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The h i g h e r t h e a b s o l u t e v a lu e s o f t h e s e m e a s u r e s , t h e more a t t e n t i o n s h o u ld be p a id t o r e s p e o t i v e e le m e n te , u s in g t h e l n p u t - o u t p u t c o e f f i c i e n t s t o f o r e o a s t t h e b ra n o h s t r u o t u r e o f p ro d u c -t i o n and d i s -t r i b u -t i o n . A n o th e r way t o i n v e s t i g a t e c h a n g e a b i l i t y o f t h e c o e f f i c i e n t s i n tim e i s t o e s t i m a t e t h e r e g r e s s i o n f u n o ti o n o f t h e fo rm t a . . - f ( t ) , (1 1 ) 13 e i j

(w h ere t i s a tim e v a r i a b l e ) and t o assum e a s a c r i t e r i o n o f im p o r ta n c e , t h e d e r i v a t i v e o f t h i s f u n o ti o n a t some p o i n t t « T, g e n e r a l l y , a t t h e moment f o r w hioh t h e f o r e o a s t o f t h e o o e f f i o i e n t i s e v a l u a t e d . H ence, d f ( t ) d , , » _____ У ___ ( t ■ T ) . (12) d t T h is way r e q u i r e s , h o w e v e r, a s u f f i c i e n t l y lo n g s e r i e s on th e b a s i s o f w hich t h e c l a s s o f f u n o ti o n s f_ oan be c h o s e n and t h e i r p a r a m e te r s e s t i m a t e d . S in c e i n t h i s c a s e

we

u s e , i n f a c t , n o t a d e r i v a t i v e b u t i t s e s t i m a t e , o b t a i n e d on t h e b a s i s o f t h e s a m p le , we s h o u ld a l s o t a k e i n t o a o c o u n t mean e r r o r s o f t h e o b ta in e d r e s u l t s . H ence, i t seem s p o s s i b l e t o c o n s i d e r n o t one b u t t h r e e c r i t e r i a : 1 ) t h e a l r e a d y m e n tio n e d e v a l u a t i o n o f t h e d e r i v a t i v e a t t h e moment t « T , 2 ) lo w e r bound o f c o n f id e n c e i n t e r v a l a ssu m in g t h a t t h e c o e f f i c i e n t i s im p o r ta n t i f , a t h ig h p r o b a b i l i t y , i t c h a n g e s s i g n i f i -c a n t l y i n t im e , and

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3 ) u p p e r bound o f t h l e i n t e r v a l ,a s s u m i n g t h a t t h e c o e f f i c i e n t I s im p o r ta n t i f I t i s p o s s i b l e ( e . g . 5% p r o b a b i l i t y ) t h a t i t ohanges a i g n i f i o a n t l y . The c h o io e o f t h e s e o r i t e r l a w i l l c e r t a i n l y depend on a d d i - * t i o n a l i n f o r m a t io n o o n o e rn in g t h e c o e f f i c i e n t , w hich r e s u l t s from t h e a p p l i c a t i o n o f o t h e r m e a s u re s o f im p o r ta n c e . 3 . I n d l r e c t Me th o d s f o r t h e E v a l u a t io n c f C o e f f i c i e n t Im p o rta n c e I n d i r e c t m ethods o f e v a l u a t i n g t h e im p o rta n c e o f i n p u t - o u t p u t c o e f f i c i e n t s g e n e r a l l y d e n o te t h e d e t e r m i n a t i o n , th ro u g h t h e ohange o f t h e v a lu e o f a g iv e n c o e f f i c i e n t , o f t h e ch an g e i n f ix e d r e l a t i o n s b etw e en t h e o u tp u t o f a g iv e n b ra n o h and t h e in p u t f o r t h i s o u t p u t . A ch an g e o f ohe c o e f f i c i e n t b e in g a p rim a ry im p u ls e , c a n l e a d , i n many c a s e s , t o s i g n i f i c a n t c h a n g e s i n t h e s t r u c t u r e o f p r o d u o tio n and d i s t r i b u t i o n th r o u g h many s e c o n d a r y i m p u ls e s .

L e t u s c o n s i d e r two e x tre m e c a s e s w hich c a n r e s u l t from a ch an g e o f some c o e f f i c i e n t a ^ j t 1 . At unch an g ed l e v e l o f g r o s s o u tp u t i n p a r t i c u l a r b r a n c h e s . 2 . At unch an g ed l e v e l o f f i n a l p r o d u o ti o n . I n t h e f i r s t c a s e e x a c t l y one e le m e n t o f v e c t o r у i s changed I n f a c t . T h is i s t h e e le m en t y ^ . The ch an g e i s H • - т Ь л л * (1 3 ) wheres p - p e r c e n t o f th e ohange o f c o e f f i c i e n t a ^ .

T h is v a lu e c o u ld c o n s t i t u t e some m easu re o f im p o rta n c e o f t h e c o e f f i c i e n t b e in g c h a n g e d . H ow ever, t h i s e v a l u a t i o n o f im p o rta n c e i s e q u a l l y o n e - s id e d a s t h e above p r e s e n t e d d i r e c t m e a s u re s . I t h a s b e e n in c l u d e d i n t o t h e g ro u p o f i n d i r e c t m e a su re s o n ly b e c a u s e we c o n s i d e r h e r e d i r e c t l y n o t t h e c o e f f i c i e n t s , b u t i n d i r e c t l y t h e i r im p o r ta n c e , th ro u g h c h a n g e s i n t h e f i n a l p ro d u c -- t i o n . I n t h e o t h e r c a s e , due t o t h e n e c e s s i t y o f m a i n ta i n in g th o r e l a t i o n X* - ( i - A*)“ 1y , (1 4 )

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w h e re : A* - m a t r ix o f l n p u t - o u t p u t c o e f f i c i e n t s w ith e le m e n t a ^ r e p la o e d by a j j , X* - a r e s p e c t i v e l y changed v e o t o r o f g r o s s o u tp u t, t h e s u b s t i t u t i o n o f a ^ by some e le m e n t a * j can ln d u o e a change I n t h e g r o s s o u tp u t l e v e l o f e a c h b r a n c h , s i n c e tn e n t h e r e a r e c h a n g e s i n a l l e le m e n ts o f t h e m a t r ix o f f u l l m a t e r i a l - i n p u t o o e f f l o l e n t s ( i - A )” 1 ,

The m ost f r e q u e n t l y u s e d m easu re o f s e n s i t i v i t y o f g r o s s o u tp u t t o a c h an g e o f one o f t h e l n p u t - o u t p u t c o e f f i c i e n t s i s t h e e s o - c a l l e d c o e f f i c i e n t o f t o l e r a b l e l i m i t s . d ^ > . ---—--- L ---— --- • U 5 )

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w here b ^ , bk l a r e t h e e le m e n ts o f m a t r ix ( I - A )- 1 . The v a lu e s assum ed by t h i s m ea su re a r e i n t e r p r e t e d a s a p e r o e n t c h an g e o f t h e v a lu e o f o o e f f l o i e n t a j j • whioh o a u s e s a ch an g e i n t h e o u tp u t l e v e l o f t h e i - t h b ra n o h by 1 % .It l e e v id e n t t h a t t h e lo w e r t h e v a lu e o f t h e o o e f f l o i e n t o f t o r e l a b l e l i m i t s , t h e more im p o r ta n t - i s a g iv e n e le m e n t o f t h e m a t r ix A f o r t h e econom ic sy ste m a s a w h o le . Even s l i g h t o h a n g e s o f I t s v a lu e s oan c a u s e s i g n i f i c a n t c h a n g es I n t h e l e v e l o f g r o s s o u tp u t o f p a r t i -c u l a r b r a n -c h e s .

^ j& n J ltte ra £ it__at_jJo^itJE5valua^

o f C o e f f i c i e n t s &j* on t h e B a s i s o f V a rio u s C r i t e r i a

I n o r d e r t o com pare s im u lta n e o u s ly t h e im p o rta n c e o f i n p u t - o u t p u t c o e f f i c i e n t s w ith r e s p e o t t o v a r i o u s c r i t e r i a , t h e f o llo w -i n g p ro c e d u r e f o r r a n k -in g o f t h e Im p o rta n c e m e a s u re s c a n be p r o -p o s e d . P a r t i c u l a r e le m e n ts a i ; j a r e o r d e r e d w i t h in e a c h c r i t e r i o n i n d e c r e a s in g im p o rta n c e o r d e r by g i v in g them t h e r a n k s R1U ) - 1 , R^k) - 2 ...R<k ) - m, w h e re : к * 1 , 2 , . . . , к - s u c c e s s i v e c r i t e r i a , m » n x ra - t h e num ber o f e le m e n ts o f m a t r ix A.

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I f t h e v a lu e s o f s e le m e n ts , s t a r t i n g w ith th o e le m e n t h + 1, a r e i d e n t i c a l , we g iv e them a medium r a n k .

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h+2 ... h+s в

---■ h + ® j 1 . (1 6 )

The aura o f r a n k s o b ta in e d . by a g iv e n e le m en t w ith r e s p e c t to •11 c r i t e r i a , i . e . ' К R^ ■ / ' R^ ( 1 * 1 , 2 , . . . ( m ), k-1 o r a mean o f ra n k s К Äi ■ К Z / Ri*

d e te r m in e s th e n a m easure o f Im p o rta n c e o f a g iv e n e le m e n t. The Im p o rta n c e i s t h e g r e a t e r t h e lo w e r t h e r a n k .

The d e c i s i o n , r e g a r d in g w hich l e v e l o f R^ o r s t i l l c h a r a c -t e r i z e s -t h e im p o r -ta n -t i n p u -t - o u -t p u -t o o e f f i o i e n -t s , i s a r b i -t r a r y and depends e s p e c i a l l y on t h e " s c a t t e r " o f im p o rta n c e m easu res o b ta in e d w ith r e s p e c t to v a r io u s c r i t e r i a . I t c a n be t h e r e f o r e d i f f e r e n t f o r e a ch c a s e o f t h e i n p u t - o u t p u t b a la n c e .

5 . E m p irlo a l R e s u l ts

I n p u t- o u tp u t c o e f f i c i e n t s have b e e n a n a ly s e d f o r two i n p u t - - o u tp u t b a la n c e s p r e p a r e d f o r P o la n d f o r t h e y e a r s 1975 and 1980. These b a la n c e s have b e e n c h o s e n t o com pare t h e s t r u c t u r e o f ec o -nomy i n t h e p e r i o d o f r e l a t i v e l y s t a b l e d evelopm ent (1975) and i n th e p e r i o d when econom ic d e p r e s s io n b eg a n (1 9 8 0 ). The b a la n o e s a r e p r e s e n t e d a t c u r r e n t p r o d u c e r s ' p r i c e s i n 15 a g g re g a te d i n d u s t r i e s : 1) f u e l and pow er i n d u s t r y , 2 ) m e t a ll u r g y , R( k ) h+1

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6.Í Сй-зslAii b l p l ń a k l , Łucja Tomassawlcz 1 5 7 9 15 3) m e ta l and e l e c t r o - e n g i n e e r i n g i n d u s t r y , 4 ) c h e m ic a l i n d u s t r y , 5) b u i l d i n g m a t e r i a l s , g l a s s and p o t t e r y i n d u s t r y i 6 ) wood, and p a p e r i n d u s t r y , 7 ) l i g h t i n d u s t r y . I m p o r ta n t i n p u t - o u t p u t 1 2 3 4 5 6 9 5 6 91 3 5 1 2 5 6 1 2 3 4 5 6 9 1 2 3 4 5 6 9 1 2 3 4 5 6 9 1 2 3 5 6 9 4 5 6 91 2 3 1 2 3 4 5 6 9 1 2 3 4 5 6 9 1 I 3 9 2 3 4 5 6 9 i 1 2 3 4 5 6 9 9 3 9 4 6 I i •; i I 1 2 3 íLi.-L-ÍL_ i 1 4 4 4 4 4 f ___________I a p o r t a n t C o e f f i c i e n t s In t h e I n p ut - Ou t p u t M o d a l a . . . _________________ ^ g ę T a b l e 1 o o e f f l o l e n t s f o r t h e y e a r 1975 __8 9 10 11 12_______ 13 14 15 1 2 3 4 5 6 9 1 21 3 5 6 9 1 2 1 5 6 9 1 2 3 5 9 -1 3 4 5 6 9 1 5 6 9 3 49 .1 2 3 J J 6 9 1 2 4 5 6 3 9 1 2 3 5 6 9 5 6 93 4 1 2 3 5 6 9 4 5 2 6 .1 2 3 t ! _ 6 9 1 2 4 5 6 91 2 3 3 1 2 3 4 5 6 9 2 1 2 5 6 1 2 3 5 6 9 4 5 4 4 8 ) fo o d I n d u s t r y , 9 ) o t h e r i n d u s t r i a l b r a n c h e s , 10) c o n s t r u c t i o n i n d u s t r y , a g r i c u l t u r e , 12) f o r e s t r y ,

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I m p o r ta n t i n p u t - o u t p u t 1 2 3 4 5 6 7 1 1 2 3 4 5 63, 5 6 91 3 2 4 5 6 91 2 3 4 5 6 91 2 3 • 3 1 2 4 5 6 91 2 3 1 2 4 3 4 9 4 5 6 91 2 3 2 3 5 6 9 5 4 5 6 91 2 3 ' ď 6 3 9 4 5 6 91 2 3 7 4 5 6 91 2 3 8 9 10 4 11 # • 12 4 5 6 91 2 3 13 14 5 4 6 4 15 3 4 9 1 3 ) t r a n s p o r t a t i o n and co m m u n ic a tio n , 1 4 ) t r a d e , 15) o t h e r m a t e r i a l goods and s e r v i o e s . T h ese num bers a r e a l s o u s e d i n t h e t a b l e s *

T a b l e 2 c o e f f i c i e n t s f o r t h e y e a r 1980 8 9 10 11 12 13 14 15 1 2 3 4 6 9 3 5 9 » 1 1 2 5 6 9 1 2 5 6 9 1 2 3 9 • . 1 3 4 5 6 9 3 4 9 1 2 3 4 5 6 9 1 2 4 5 6 1 2 3 4 5 6 9 3 4 5 6. 9 2 3 5 6 9 4 6 1 2 3 4 5 6 9 1 2 5 6 1 2 3 4 5 6 9 1 2 3 4 5 6 9 3 4 5 6 91 2 3 1 2 5 6 91 2 3 4 5 6 91 2 3 4 4 4 5 6 .... F i r s t o f a l l t h e above p r e s e n t e d d i r e c t m e a s u re s d - d i and t h e c o e f f i c i e n t o f t o l e r a b l e l i m i t s d ^9) h av e b e e n t a k e n i n t o a c c o u n t. The s e r i e s o f t h e s e m e a su re s o r d e r e d from t h e p o i n t o f view o f d e c r e a s in g im p o rta n c e a s w e ll a s t h e one o b ta in e d from

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summing up o f r a n k s , g iv e n t o t h e i n p u t - o u t p u t c o e f f i c i e n t s , have been a n a ly s e d . Each o f t h e s e s e r i e s c o n s i s t s o f 30 e le m e n ts s i n c e i t was o b s e rv e d t h a t t h e e o a t t e r o f v a lu e s o f d i f f e r e n t im p o rta n c e c r i t e r i a f o r f u r t h e r e le m e n te i n t h e o r d e r e d e e r i e e i n c r e a s e d s i g n i f i c a n t l y . I n t h e r a n k in g p r o c e d u r e t h e c h a n g e a b i l i t y o f th e c o e f f i c i e n t s i n tim e h a s n o t b e e n ta k e n i n t o a c c o u n t. T h is c r i t e r i o n h a s b een c o n s id e r e d s e p a r a t e l y . T a b le s 1 and 2 p r e s e n t t h e e s t i m a t i o n o f i n p u t o u t p u t o o e f -f i o i e n t s im p o rta n c e -f o r t h e 1975 and 1980 b a l a n c e s . Baoh f i e l d c o r r e s p o n d s t o a p a r t i c u l a r o o e f f i o i e n t . The num bers p la o e d i n t h e s e f i e l d s In fo rm u s a b o u t t h e m ea su re w ith r e s p e c t t o w hioh t h e g iv e n e le m e n t h a s b e e n e s ti m a t e d a s t h e m ost i m p o r t a n t . The f i e l d s i n t h i c k fra m e s c o r r e s p o n d t o t h e e le m e n ts w hioh a r e m ost im p o r ta n t from t h e p o i n t o f view o f t h e t o t a l sum o f r a n k s .

On t h e b a s i s o f t h e a n a l y s i s o f t h e above t a b l e s i t oan be o o n c lu d e d t h a t t h e m ost im p o r ta n t i n p u t - o u t p u t c o e f f i c i e n t s a r e p la c e d f i r s t o f a l l on t h e m ain d ia g o n a l ( i t nay b e a r e s u l t o f som etim es s i g n i f i c a n t a g g r e g a ti o n o f b r a n o h e s ) .T h e c h a r a c t e r i s t i c c o n n e c tio n s b e tw e en s e o t o r s and b r a n c h e s o f r a w - m a te r ia l and ma-n u f a c t u r i ma-n g ty p e a r e a l s o assum ed a s i m p o r t a ma-n t . The i n p u t - o u t p u t c o e f f i c i e n t s f o r t h e f o llo w in g r e l a t i o n s c o rr e s p o n d t o them i

f u e l and pow er i n d u s t r y f o r t h e m e t a ll u r g y and t r a n s p o r t a -t i o n aDd c o m m u n ic a -tio n , - m e t a ll u r g y f o r m e ta l and e l e c t r o - e n g i n e e r i n g i n d u s t r y , - m e ta l and e l e c t r o - e n g i n e e r i n g i n d u s t r y f o r c o n s t r u c t i o n and t r a n s p o r t a t i o n and c o m m u n ic a tio n , - c h e m ic a l i n d u s t r y f o r l i g h t i n d u s t r y , - a g r i c u l t u r e f o r fo o d i n d u s t r y , - f o r e s t r y f o r wood and p a p e r i n d u s t r y , - t r a n s p o r t a t i o n f o r c o n s t r u c t i o n and t r a d e . The im p o rta n c e o f t h e s e c o e f f i c i e n t s i s a lm o s t i d e n t i c a l f o r b o th y e a r s from t h e p o i n t o f view o f t h e above m e n tio n e d m e a s u r e s . An a d d i t i o n a l e v id e n c e s u p p o r t i n g t h i s h y p o t h e s i s c a n be t h e r e s u l t s o b ta in e d on t h e b a s i s o f c h o o s in g 5 s u b s e q u e n t m ost im-p o r t a n t c o e f f i c i e n t e f o r e a c h m easu re and e a c h b a la n o e . I t a p -p e a re d t h a t i n m ost e a s e s t h e s e a r e t h e same c o e f f i c i e n t s . The below m e n tio n e d c o e f f i c i e n t s

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arj 7 ( l i g h t i n d u s t r y - l i g h t i n d u s t r y ) , a ^ 11 ( a g r i c u l t u r e - a g r i c u l t u r e ) , a ^ g ( a g r i c u l t u r e - fo o d I n d u s t r y ) , o o c u rr e d m ost f r e q u e n t l y ( i n 9 -1 2 o a s e s o u t o f 14)» Onoe a g a in t h e h y p o t h e s i s o f s i g n i f i c a n t im p o rta n c e o f d i r e c t t e c h n o l o g i c a l con-n e c t i o con-n s h a s b e e con-n p ro v e d . F o r t h e o o e f f l o l e n t s p r e s e n t e d i n T a b . 1 and 2 t h e i r r a t e s o f c h a n g e s ( d ^ p ) b e t w e e n 1975 and 1980 h av e b e e n e s t a b l i s h e d . The r a t e o f c h a n g e s o f more t h a n a h a l f o f th e o o e f f l o l e n t s ra n g e d from -15% t o +15%. A s i g n i f i c a n t i n c r e a s e ( o v e r 30%) o f u n i t i n n e r I n p u t s o f f u e l and pow er and i n p u t s o f f u e l and power f o r e l e c t r o - e n g i n e e r i n g i n d u s t r y h a s b e e n o b s e r v e d . U n it i n p u t s o f p r o d u o tio n o f o t h e r b r a n c h e s ( f o d d e r i n d u s t r y ) f o r a g r i c u l t u r e and e l e o t r o - e n g i n e e r i n g i n d u s t r y p r o d u o tio n f o r t r a n s p o r t a t i o n a l s o showed s i g n i f i c a n t i n o r e a s e . The i n n e r I n p u t s a l s o i n c r e a s e d i n f o r e s t r y . A d e c r e a s in g te n d e n c y o f u n i t I n p u ts ( o v e r 30%) was o b s e rv e d I n i n p u t s o f c o n s t r u c t i o n f o r t h e l i g h t i n d u s t r y , i n i n p u t s o f wood i n d u s t r y and f o r e s t r y f o r o t h e r b r a n c h e s , i n i n p u t s o f m e t a ll u r g y f o r c o n s t r u c t i o n and i n I n p u t s o f t r a n s p o r t a t i o n f o r f u e l and pow er i n d u s t r y . T h e r e f o r e , a t l e a s t h a l f o f t h e p r e s e n t e d im p o r ta n t c o e f f i c i e n t s changed s i g n i f i c a n t l y b e tw e e n t h e y e a r s 1975 and 1980. R e f e r e n c e s B a c h a r a c h M ., 1970, B i p r o p o r t i o n a l M a tr ic e s and I n - P u t-O u tp u t C hange, C am bridge U n i v e r s i t y P r e s s , C am bridge.

I n p u t- O u tp u t R e l a t i o n s h i p s 1 9 5 4 -1 9 6 6 . A Programme f o r G row th, D ep artm en t o f A p p lie d E co n o m ics, U n i v e r s i t y o f C am b rid g e. Chapman

and H a l l , London 1963.

J i 1 e k J . , 1971, The S e l e c t i o n o f Most I m p o r ta n t I n p u t C o e f f i c i e n t s , Econ^ B u l l , f o r E u ro p e , v o l . 2 3 . ,

L e c o m b e r R . , 1 9 7 1 ,A C r i t i q u e o f M ethods o f A d j u s t i n g , U p d a tin g and P r o j e c t i n g M a tr ic e s ( T o g e th e r w ith Some New P ro -p o s a l s ) . C o n fe re n c e " I n -p u t- O u t-p u t and T h r o u g h -p u t" , N o rw ic h , Sep-te m b e r.

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1JQ C z o slax L i p i ń s k i , Łucj a Toaaszawl ci _____________________ L i p i ń s k i C z ., T o m a s z e w i o z Ł . , 1981, O k re ś-l a n i e w spółczynników ważnych w t a b ś-l i c y przepływ ów m ś-le d z y g a łę z io - wych, GUS, mimeo, Ł ódź.

S h e r m a n J . , M o r r i s o n W. J .* . 1950, A d ju stm en t o f an I n v e r s e M a tr ix C o rre s p o n d in g t o a Change I n One E lem ent o f a G iven M a tr ix , Ann, M ath. S t a t i s t . , v o l . 2 1 .

C zesław L i p i ń s k i , Ł u c ja Tomaazewicz

WAŻNE WSPÓŁCZYNNIKI W TABLICACH PRZEPŁYWÓW MięDZYGAŁęZIOWYCH DLA POLSKI

Z a g a d n ie n ie p o s z u k iw a n ia ważnych w spółczynników ma I s t o t n e z n a c z e n ie d l a w ie lu p r a c p r a k ty c z n y c h zw iązanych z a n a l i z ą i n p u t - - o u t p u t , p r z e d e w szy stk im zná d l a p rze w id y w an ia zm ian w s p ó łc z y n n i-ków n akładów b e z p o ś r e d n ic h .

W a r t y k u l e przep ro w ad zo n o pewną s y e te m a ty z a o ję 1 a n a l i z ę me-t o d sto so w an y c h p r z y w yznaozaniu w ażnych w epółozynników . S f o r -mułowano z o s t a ł y t r z y z a a a d n io z e g ru p y k r y te r ió w w a ż n o śc i w sp ó ł-czynników*

1) przyjm ow anie duży ch w a r to ś c i p r z e z w s p ó łc z y n n ik i nakładów

b e z p o ś r e d n ic h p o chodne,

2 n i e s t a b i l n o ś ć o ią g u w spółczynników | а 1 ^ } " c *a e i e i 3) " s i l n e p o w ią z a n ie " w epółozynników ’ z oałym układem

Wyrazem p ra k ty c z n e g o z a s to s o w a n ia omawianych m etod b y ło zb a -d a n ie ważnych w spółczynników w b i la n s a c h i n p u t - o u t p u t d l a l a t 1975 i 1980 w u k ł a d z i e 15 g a ł ę z i .

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