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 F O L IA O E C O N O M IC A 1 9 8 ,2 0 0 6
Jaku b B oratyń ski
IN DIR ECT TA X ES AND PRICE F O R M A T IO N -
A M O D E L FOR THE POLISH E C O N O M Y
I. I N T R O D U C T I O N
T h e aim o f th is s tu d y is e x te n d in g th e e le m e n ta ry in p u t- o u tp u t p ric e m o d e l to r e p r e s e n t th e ro le o f in d ire c t ta x e s ( fo r m u la tio n o f th e in p u t- o u tp u t p ric e m o d e l c a n b e fo u n d e.g . in R. E. M ille r & P. D. B la ir 1 9 8 5 ). T h e p r o p o s e d e x te n s io n is m a in ly b a s e d on th e s o lu tio n s p re s e n te d b y R. B a rd a z z i
& M . G ra s s in i
( 1 9 9 1 ) a n d M . G ra s s in i ( 1 9 9 7 ). T h e fin al fo rm u la tio n m e e ts th e p ro b le m o f u n a v a ila b ility o f d e ta ile d d a ta o n tax c o m p o n e n ts in in d iv id u a l c e lls o f in p u t-o u tp u t ta b le s , w h ic h is lik e ly n o t o n ly th e P o lis h -s p e c ific d if fic u lty .B u ild in g su c h a m o d e l w a s d ic ta te d m a in ly b y s o m e c a s u a l n e e d s , i.e. e x a m in in g e f f e c ts o f p o s s ib le im p o rt ta x in tro d u c tio n a n d e ff e c ts o f a d a p tin g V A T r a te s to th e E U s ta n d a rd s . H o w e v e r, m o d e l c a n a lso f u n c tio n a s a b lo c k o f th e IM P E C m o d e l o f th e P o lish e c o n o m y . II. I N D I R E C T T A X E S A N D P R I C E F O R M A T I O N - E X T E N S I O N O F T H E E L E M E N T A R Y I N P U T - O U T P U T P R I C E M O D E L A n im p o r ta n t f e a tu re o f th e p re s e n te d e x te n s io n in c lu d e s in th a t it is b a s e d o n th e s tr u c tu re o f th e a c tu a lly a v a ila b le in p u t- o u tp u t d a ta , w h ic h - in th e c a s e o f P o la n d - c o n fo r m w ith p r in c ip le s o f th e S y ste m o f N a tio n a l A c c o u n ts (S N A ). T h u s , fo r tr a n s p a r e n c y o f fu rth e r c o n s id e r a tio n s it is n e c e s s a ry a t th is p la c e to
fo c u s o n se le c te d d a ta is s u e s a n d p ric e c o n c e p ts .
In th e S N A , th e tw o m a in c a te g o rie s o f p ric e s a re u se d , i.e. b a s ic p ric e s and final p ric e s (se e
The System o f National Accounts vol. II (1 9 9 7 )). B a sic p ric e s a re
d e fin e d as a m o u n ts o f m o n e y re c e iv e d by p ro d u c e rs fo r th e ir p ro d u c ts , n o t c o u n t in g a n y ta x e s a n d s u b s id ie s , as w ell as tra d e an d tra n sp o rt m a rg in s. F in al p ric e s are a m o u n ts as se e n fro m c o n s u m e rs ' p o in t o f v ie w , i.e. th e y a re in c lu s iv e o f all ta x e s an d m a rg in s . T h e re la tio n b e tw e e n b a s ic a n d final p ric e s c a n b e p re s e n te d a s fo l lo w s (se e Z ie n k o w s k i 2 0 0 2 ):' Chair o f Theory and A nalyses o f Economic Systems, University o f Łódź. [ I l l ]
b a s ic p r ic e + c u s to m s d u tie s a n d o th e r im p o rt c h a r g e s + e x c is e a n d ta x e s o n se le c te d s e rv ic e s (g a m b lin g , lo tte r y e tc .) s u b s id ie s + V A T + tr a d e m a rg in + tr a n s p o r t m a rg in
= fin al p r ic e ( p u rc h a s e r ’s p ric e , m a rk e t p ric e ).
A c c o rd in g to p r in c ip le s o f th e S N A , in te r m e d ia te a n d fin a l c o n s u m p tio n are e v a lu a te d in fin al p ric e s , w h e r e a s g lo b a l o u tp u t, im p o rts a n d e x p o r ts - in b a s ic p ric e s.
R e fe rrin g to th e a b o v e d e fin itio n s , g lo b a l o u tp u t o f a g iv e n b ra n c h in b a s ic p ric e s is o b ta in e d b y a d d in g u p m a te ria l c o s ts - e v a lu a te d in fin al p r ic e s - and v a lu e a d d e d o f th a t b ra n c h . A s a c o n s e q u e n c e , b a s ic p ric e o f a g iv e n p ro d u c t is a m o n g o th e r th in g s , a fu n c tio n o f all in d ire c t ta x e s p a id o n p ro d u c ts a n d s e rv ic e s u se d in th e p r o d u c tio n p ro c e s s .
A m o n g in d ir e c t ta x e s , th e ro le o f V A T in p ric e f o rm a tio n r e q u ir e s a c lo s e r c o n s id e r a tio n . “ T h e p r o d u c e r ’s tax lia b ility is g iv e n b y th e d if fe r e n c e b e tw e e n th e tax c h a r g e d o n h is s a le s a n d th a t p a id o n h is p u r c h a s e s o f in te r m e d ia te g o o d s a n d s e r v ic e s ” ( s e e R. B a rd a z z i a n d M . G ra s s in i 1991). In su c h c a s e , V A T on in te r m e d ia te p r o d u c ts a n d s e rv ic e s m a k e s in fa c t no c o s t to th e p r o d u c e r, w h ile it c a n b e fu lly d e d u c te d fro m h is tax lia b ility . In te rm s o f p r ic e s , V A T d o e s not a ffe c t b a s ic p r ic e b u t r a th e r th e fin al p ric e a n d , th e re fo re , c a n b e tr e a te d as a tax o n fin al c o n s u m p tio n . H o w e v e r, o fte n th e re a re e x e m p tio n s fro m su c h a “ p u re ” V A T s y s te m , i.e. th e re a re ru le s lim itin g d e d u c tio n o f ta x p a id o n p r o d u c e r ’s in p u ts . R. B a rd a z z i an d M . G ra s s in i (1 9 9 1 ) m e n tio n th re e ty p ic a l r e a s o n s fo r w h ic h d e d u c tio n o f V A T is re s tr a in e d in m o s t o f th e EU c o u n trie s . F irs tly , s e c to rs s e llin g p r o d u c ts o r s e rv ic e s w h ic h a re e x e m p te d f ro m V A T (in P o la n d : e d u c a tio n , h e a lth c a re , p u b lic a d m in is tra tio n s e rv ic e s , fin a n c ia l s e r v ic e s e tc .) h a v e n o rig h t to d e d u c t th e ta x . A lso , sm a ll firm s, w h ic h d o n o t e x c e e d a c e r ta in lim it o f tu r n o v e r , c a n b e n e f it fro m V A T e x e m p tio n , re g a rd le s s o f p r o d u c t o r s e rv ic e th e y o ffe r. S e c o n d ly , th e g e n e ra l ru le is th a t V A T c a n b e d e d u c te d o n ly fo r th o se p r o d u c ts a n d s e rv ic e s w h ic h a re s tric tly c o n n e c te d w ith th e o u tp u t o f a g iv e n s e c to r. S in c e s u c h c la s s ific a tio n o f in te rm e d ia te g o o d s is o fte n d iffic u lt, e s p e c ia lly fo r u n in c o rp o r a te d fa m ily firm s, s p e c ia l ru le s a re u s u a lly a p p lie d , fo r e x a m p le th e ru le s lim itin g d e d u c tio n o f V A T p a id o n p a r tic u la r g o o d s (e .g . fu e ls). F in a lly , fo r sm a ll b u s in e s s th e re u s u a lly e x is t s im p lifie d a n d s ta n d a r d iz e d m e th o d s o f ta x se ttle m e n t. In su c h c a s e s th e d e d u c tib le V A T is e s ta b lis h e d b a s in g o n s o m e fix e d e c o n o m ic p a r a m e te rs ra th e r th a n th e a c tu a l v a lu e o f in te r m e d ia te g o o d s a n d s e rv ic e s u se d in p ro d u c tio n (e.g . fo r fa rm e rs ). In all o f th o se
e a s e s , n o n - d e d u c tib le V A T ta k e s p a rt in th e fo rm a tio n o f b a s ic p ric e s a n d , as w ell as o th e r in d ire c t ta x e s , s h o u ld b e p r e s e n t in th e e x te n d e d p r ic e e q u a tio n .
A p a r t fro m tax e le m e n ts , th e e x te n d e d m o d e l m u s t a ls o ta k e in to a c c o u n t th e e x is te n c e o f im p o r ts in in te rm e d ia te u se o f p ro d u c ts a n d s e rv ic e s . O b v io u s ly , c h a n g e s in c o s ts o f d o m e s tic p ro d u c tio n s h o u ld n o t a ffe c t im p o r t p r ic e s in th e m o d e l (u n le s s e x c h a n g e ra te s a re c o n s id e r e d ) , o th e r w is e p r ic e e f f e c ts o f th e c o s t- p u sh in f la tio n a r y s p ira l c o u ld b e o v e r e s tim a te d in s im u la tio n s . T h e r e f o r e , in th e p r o p o s e d m o d e l, u se o f im p o r te d p r o d u c ts a n d s e rv ic e s is d is tin g u is h e d fro m th a t o f d o m e s tic o n e s . T h e a b o v e r e m a rk s lead to fo rm u la tin g th e in p u t- o u tp u t p r ic e m o d e l e x te n d e d w ith in d ire c t ta x e s a n d m a rg in s . A s s u m e th a t an e c o n o m y ’s o u tp u t c a n b e d iv id e d in to
n g r o u p s o f h o m o g e n e o u s p r o d u c ts a n d s e rv ic e s . D e n o te b y
хч
(/', / = I . ...,n
) th e v a lu e o f o u tla y s o n in te rm e d ia te p r o d u c ts a n d s e rv ic e s o f ty p ei u se d in p ro d u c tio n o f g o o d s o f ty p e
j (x,, are , th u s, e le m e n ts o f th e first p a rt o f
a p r o d u c t- to - p r o d u c t in p u t o u tp u t ta b le ). D e n o te f u rth e r b yX , { j = 1 ,..., « ) th e
g lo b a l p r o d u c tio n o f g o o d s o r s e rv ic e s o f ty p e j . G lo b a l o u tp u t o f a g iv e n ty p e is e q u a l to m a te ria l c o s ts a u g m e n te d b y c o s ts o f p rim a ry p r o d u c tio n fa c to rs (v a lu e a d d e d ), i.e.:x j = Ź xJ + v j
(>) (=i w h e re :VJ
s ta n d s fo r v a lu e a d d e d a s s o c ia te d w ith g o o d s a n d s e rv ic e s o f ty p ej.
A c c o rd in g to th e S N A ru le s o f e v a lu a tin g tr a n s a c tio n s , a s w e ll a s s o m e s im p lif y in g a s s u m p tio n s c o n c e r n in g ta x e s a n d m a rg in s , g lo b a l o u tp u t a n d in te r m e d ia te u se a re g iv e n a s fo llo w s:X r Q j P T
(2 ) and:+</,))(!+*,,0
P)
w h e re :Q] s ta n d s fo r g lo b a l o u tp u t in q u a n tity te rm s,,
qjjCl) a n d
q\'j ") re p re s e n t
q u a n titie s o f g o o d s o f ty p e / u s e d a s in te r m e d ia te in p u ts in p r o d u c tio n o f b ra n c hj ,
d o m e s tic a n d im p o rte d , re s p e c tiv e ly ,p (‘l] - b a s ic p ric e s o f d o m e s tic g o o d s ,
all in d ire c t ta x e s e x c e p t V A T (n e t - tax m in u s s u b s id y r a le s ) p a id o n d o m e s tic g o o d s o f ty p e / (i.e . e x c is e tax an d sp e c ia l ta x e s o n s e le c te d s e rv ic e s ),
s]m) -
a v e r a g e ra te o f all in d ir e c t ta x e s e x c e p t V A T (n e t) p a id o n im p o rte d g o o d s o f ty p e / (i.e . d u tie s a n d o th e r im p o rt c h a rg e s a s w e ll as e x c is e ta x , m in u s s u b s i d ie s ),dj = b, + с, , w h e re
b, is an a v e r a g e ra te o f tr a d e m a rg in , c, - a v e ra g e
ra te o f tr a n s p o r t m a rg in . S y m b o lt, s ta n d s fo r a v e ra g e n o m in a l V A T ra te fo r
p r o d u c ts o r s e rv ic e s o f ty p ei (th e s a m e for d o m e s tic a n d im p o r te d g o o d s ), /?,,
a c o e f fic ie n t s h o w in g w h a t p a rt o f an in d iv id u a l in te r m e d ia te p u r c h a s e (in te rm s o f v a lu e in c lu d in g all in d ire c t ta x e s e x c e p t V A T ) is s u b je c t to n o n - d e d u c tib le V A T . In o th e r w o rd s ,h^t, s h o w r a te s w h ic h c a n b e n a m e d a s “ e f f e c tiv e " V A T
ra te s fo r in d iv id u a l in p u ts o f in te r m e d ia te p r o d u c ts a n d s e rv ic e s .A s c a n b e s e e n fro m e q u a tio n (3 ), all in d ire c t ta x e s a r e a s s u m e d to b e
ad
valorem ta x e s w ith fix e d ra te s. S im ila rly , tra d e a n d tr a n s p o rt m a rg in s a re c o n
s id e re d fix e d in p r o p o rtio n to v a lu e o f p ro d u c ts a n d s e rv ic e s (in b a s ic p ric e s) b e lo n g in g to a g iv e n g ro u p . S u c h tre a tm e n t o f ta x e s is p e r h a p s n o t fu lly a d e q u a te , as it d o e s n o t re p r e s e n t th e a c tu a lly e x is te n t n o n - lin e a r itie s in c a lc u la tio n o f ta x e s. T h is re s tr ic tio n c a n b e , th o u g h , ju s tifie d b y th e fac t th a t m o s t o f th e c o n s id e r e d in d ir e c t ta x e s a r e a d valorem ta x e s. R a te s a re n a m e d “ a v e r a g e ” , s in c e in d iv id u a l g r o u p s o f p ro d u c ts o r se rv ic e s in m a n y c a s e s a re n o t h o m o g e n e o u s a n d , th u s , w ith in a g iv e n g ro u p th e re m a y c o e x is t p r o d u c ts o r s e rv ic e s ta x e d at d if fe r e n t n o m in a l ra te s. A c tu a lly , th e s im p lif y in g a s s u m p tio n s - e x p lic it in th e fo rm u la tio n o f th e m o d e l - a r e s tric tly c o n n e c te d w ith th e s tr u c tu re o f th e u s u a lly a v a ila b le in p u t- o u tp u t d a ta .R e g a rd in g (2 ) a n d (3 ), c o s t e q u a tio n (1 ) c a n b e w ritte n as:
i=i D iv id in g b y
Q , y ie ld s :
~(<0- I
MMl)
+ ‘0 + ^ - i r ( i + r - ч ) ( i + v . ) + 7 r
(5)
У.!
J У / D e n o tin g :an d :
(7)
~ VJ
Vi =
qJ
e q u a tio n (5 ) c a n b e th e n w ritte n as:p
T
- + r f , ) 0 + л , л ) + ? ! " ’Й ' " ( '+*■" + < 0 & + v - Ж P ) /»Iw h e re : « (yrf) a n d я,'"1 a re te c h n ic a l c o e ffic ie n ts s h o w in g in p h y s ic a l te rm s -th e a m o u n t o f p r o d u c ts o r s e rv ic e s o f ty p e / - d o m e s tic a n d im p o r te d , r e s p e c tiv e ly - n e c e s s a r y to s u p p ly a u n it o f p ro d u c ts o r s e rv ic e s o f ty p e j . F in a lly , i f “ ° ” s ta n d s fo r e l e m e n t- b y - e le m e n t m u ltip lic a tio n , e q u a tio n (9 ) c a n b e w ritte n in th e m a trix fo rm : P,/ = f o
°(J
+ H ' T)Xl
+s„
+ D ) p (/ + (a;„ ° ( j + H'
T)Xi
+s w
+ D )p m
+ v (10
) w h ic h a f te r s o lv in g y ie ld s : p,/ = (i -( к
° ( j + H' T ) X i + s „ + d) Y ■
((a;„ ° ( j + H' t ) X i + s„, + d)p„, + v ) o1
) w h e re : p ,7 = [p,(</)], p„, = [ д (,,,)], Ä ,, = A w = [ ^ m)] , H = [/г,у ] , S d is a d ia g o n a l m a tr ix o f e le m e n ts , S„, - d ia g o n a l m a trix o f e le m e n tssjm) , T -
d ia g o n a l m a trix o f e le m e n tst, , D - d ia g o n a l m a trix o f e le m e n ts
d, , I is a u n i
ta ry m a trix , J - m a trix w ith all e le m e n ts e q u a l 1 (/, j = 1...« ) .It is o b v io u s , h o w e v e r, th a t in p u t-o u tp u t ta b le s in p h y s ic a l te rm s a re p r a c ti c a lly u n a v a ila b le a n d , th u s , te c h n ic a l c o e f fic ie n ts c a n n o t b e o b ta in e d . In ste a d , v a lu e - b a s e d c o e f f ic ie n ts c a n b e u s e d in p ric e e q u a tio n , w h ic h is in fa c t e q u iv a le n t to a s s u m in g th a t in itia lly all p ric e s e q u a l 1. U n d e r su c h a s s u m p tio n , s o lv in g p r ic e fo rm u la le a d s to o b ta in in g p r ic e in d ic e s /?, r a th e r th a n le v e ls
p , (s e e R.
E. M ille r a n d P. D. B la ir (1 9 8 5 )). D e fin e :a n d : w h e re : an d : _(»<) (1 3 )
V,
1
(l4)
У ' -
чГ
рГ
(1 5 ) w h e rez]'1'
a n dz)"')
r e p r e s e n t in te r m e d ia te c o n s u m p tio n e v a lu a te d in b a s ic p ric e s (w h ic h c a n b e c o n s id e r e d o b s e rv a b le at a c e rta in s ta g e o f e m p ir ic a l a n a ly sis - fo r d e ta ils s e e th e n e x t s e c tio n ),a]jl] a n d
ajj"' r e p r e s e n t v a lu e - b a s e d in p u t-
o u tp u t c o e f fic ie n ts , v ; - v a lu e a d d e d p e r u n it o f o u tp u t e v a lu a te d in b a s ic p ric e s. T h e fin a l, a p p lic a b le v e rs io n o f th e e x te n d e d p ric e m o d e l c a n b e , th u s , w ritte n as: p , = (I - ( A ' ° ( J + H T )X l + S rf + D ))-‘( (A m ° ( J + H ' T ) ) ( l + S (/ + D )p w + v ) (1 7 ) w h e re : p , = [/>ť(rf)], p„, = [/J,,'")], A (, = [ a £ ° ] , A HI = [я,уИ)], v = [v( ] ( / , / = 1 ,...,n). V e c to rs p (/ a n d p„, c o n ta in p ric e in d ic e s fo r d o m e s tic a n d im
p o rte d g o o d s , r e s p e c tiv e ly . M o d e l r e p r e s e n te d b y e q u a tio n (1 7 ) p r o v id e s a w id e r a n g e o f p o s s ib le a p p li c a tio n s . A p a rt fro m a n a ly s e s o f p r ic e re a c tio n to c h a n g e s in u n ita r y v a lu e a d d e d , it e n a b le s e x a m in in g th e e f fe c ts o f c h a n g e s in tax ra te s ( S (/, S,„ a n d T ) , a s w ell a s e ffe c ts o f f lu c tu a tio n s o f im p o r t p ric e s ( p,„) a n d c h a n g e s o f tr a d e a n d tra n s p o rt m a rg in r a te s ( В , С ). H o w e v e r, a p ro b le m a ris e s o f h o w to o b ta in th e r e q u ire d p a r a m e te r s o f m o d e l (1 7 ) u s in g th e a v a ila b le in p u t- o u tp u t d a ta . T h e n e x t se c tio n is d e d ic a te d to a s o lu tio n o f th is p ro b le m , w h ic h in v o lv e s p r o c e d ú r e o f in p u t- o u tp u t ta b le d e c o m p o s itio n .III. D E C O M P O S I T I O N O F T H E I N P U T - O U T P U T T A B L E
T h e m a jo r p r o b le m in p ra c tic a l a p p lic a tio n o f th e m o d e l g iv e n b y e q u a tio n (1 7 ) is th a t th e n e c e s s a r y p a r a m e te r m a tric e s ( A f/, A w. S (/, S ,„, D. T. II ) a re n o t im m e d ia te ly d e r iv e d fro m in p u t-o u tp u t ta b le s . G e n e ra lly , c a lc u la tio n o f th e s e p a r a m e te r s r e q u ir e s in f o rm a tio n o n tax c o m p o n e n ts in in d iv id u a l tr a n s a c tio n s o f final a n d in te r m e d ia te u se. S u c h d e ta ile d d a ta a r e u s u a lly u n a v a ila b le . T h e r e f o r e , in th e P o lis h c a s e , a s p e rh a p s fo r m o st E u ro p e a n c o u n trie s , a p p lic a tio n o f th e p ro p o s e d p r ic e m o d e l re lie s o n d e c o m p o s itio n o f in p u t- o u tp u t ta b le , b a s e d o n in c o m p le te d a ta a n d s im p lif y in g a s s u m p tio n s .
T h e iss u e o f th e g r e a te s t c o n c e r n is to d e te r m in e /;r/- c o e f f ic ie n ts , s h o w in g c o n te n ts o f n o n - d e d u c tib le V A T in in d iv id u a l in te r m e d ia te c o n s u m p tio n tr a n s a c tio n s . S o lu tio n o f th is p r o b le m s is fa irly a m b ig u o u s a n d , c o n s e q u e n tly , a n y s p e c ific a s s u m p tio n s a re n o t e m b o d ie d in th e f o rm u la tio n o f m o d e l ( 1 7 ). T h u s , th e m o d e l in th a t fo rm is in d e p e n d e n t o f th e a c tu a lly c h o s e n d e c o m p o s itio n m e th o d . It m u s t b e e m p h a s is e d th a t th e m e th o d o f d e c o m p o s itio n in tr o d u c e d b e lo w is n o t th e o n ly p o s s ib le o n e . It s h o u ld r a th e r b e c o n s id e re d as p r e s e n ta tio n o f a c e rta in g e n e r a l a p p r o a c h , w h ic h c a n b e a s u b je c t o f f u rth e r d is c u s s io n a n d d e v e lo p m e n t.
D e c o m p o s itio n p r o c e d u re s tric tly re lie s o n th e s tr u c tu r e o f th e in p u t-o u tp u t ta b le , w h ic h - f o r th e P o lish c a s e - is p re s e n te d in ta b le I (a ll c a lc u la tio n s p re s e n te d in th is p a p e r a re b a s e d u p o n th e p r o d u c t- to - p ro d u c t in p u t- o u tp u t ta b le for th e y e a r 2 0 0 0 w a s e la b o r a te d b y th e a u th o r b a s in g o n s u p p ly a n d u se ta b le s , p r o v id e d b y th e C e n tra l S ta tis tic a l O ffic e , u n p u b lis h e d ). F o r c o n v e n ie n c e o f th e a n a ly s is , w h ic h is a n y w a y fo c u s e d o n th e tax e ffe c t o n p r ic e s , th e v a lu e a d d e d is a g g r e g a te d in to o n e ro w , i.e. its c o m p o n e n ts a re n o t d is tin g u is h e d in th e p r e s e n te d T a b le 1. In th e in p u t- o u tp u t ta b le 2 0 0 0 , “ tr a n s p o rt, s to r a g e a n d c o m m u n ic a tio n ” s e r v ic e s a c c o u n t w a s d iv id e d in to tw o p a rts - o n e c o n c e r n in g tr a n s p o r t s e rv ic e s c o n n e c te d w ith tr a d e m a rg in s ( n a m e it " t r a n s p o rt- a s - m a r g in ” ), th e o th e r - in c lu d in g tr a n s p o r t s e rv ic e s tre a te d a s in te rm e d ia te u se o f o th e r s e c to rs , a s w e ll as s to ra g e a n d c o m m u n ic a tio n se rv ic e s . A s a re su lt, g lo b a l o u tp u t o f th e “ tr a n s p o r t- a s - m a r g in ” s e rv ic e s e q u a ls to ta l o f th e tr a n s p o r t m a rg in s p a id o n all p r o d u c ts in th e e c o n o m y . S im ila r ly , “ tra d e a n d re p a ir” w e re d iv id e d in to “ tr a d e ” a n d “ re p a ir” , h o w e v e r in th e c a s e o f tra d e , its o u tp u t e q u a ls th e to ta l o f tr a d e m a rg in s a c ro s s all tr a n s a c tio n s b y d e fin itio n . S u c h s e p a ra tio n o f tr a d e a n d tr a n s p o r t is n e c e s s a r y fo r th e m o d e l as w ell a s th e d e c o m p o s itio n p r o c e d u re to w o rk p r o p erly . It is w o rth n o tic in g th a t s in c e m a rg in s a re r e c o rd e d in e x p e n d itu r e s o n o th e r p ro d u c ts a n d s e rv ic e s , to ta l s u p p ly o f tra d e a n d “ tr a n s p o r t- a s - m a rg in ” , e q u a ls z e ro , a s d o all v a lu e s in th e c o r r e s p o n d in g ro w s o f th e in p u t- o u tp u t ta b le .
T a b l e 1 Structure o f the input-output table’2000 for Poland
[1] [2] [3] Row totals [1] tty «*/1 W I нх/ f ô ] «Xi f o b [2] V L / J /»»x« - - -Subtotals ( [1], [2]) k , ] i * „ - -[3] M j. i x" - - -[4] H L > J| x n - - -[5] о (m) j J l x « - - -[6] V j \ \T - - -[7] к ] , хя - - -[8] . j J 1 ХЛ - - -C o l u m n t o ta ls - -
-w h e re :
y ik
r e p r e s e n t fin al d e m a n d , / b e in g th e n u m b e r o f th e d is tin g u is h e d fin al d e m a n d c a te g o r ie s ( n o t c o u n tin g e x p o rts , w h ic h is tre a te d s e p a r a te ly ) ,G, -
g lo b a l s u p p ly o f p r o d u c ts o r s e rv ic e s o f ty p e /,E, -
e x p o r ts o f p ro d u c ts o r s e r v ic e s o f ty p e /,M j - im p o rts o f p ro d u c ts o r s e rv ic e s o f ty p e j , S ' f
- to ta l a m o u n t o f in d ir e c t ta x e s , o th e r th a n V A T , p a id o n d o m e s tic p r o d u c ts o r s e rv ic e s o f ty p e j , S 1"1' - to ta l a m o u n t o f in d ire c t ta x e s, o th e r th a n V A T , p a id o n im p o rte d p r o d u c ts o r s e rv ic e s o f ty p e j , Г, - to ta l a m o u n t o f n o n - d e d u c tib le V A T p a id o n b o th d o m e s tic a n d im p o rte d p r o d u c ts a n d s e rv ic e s o f ty p e /',В
, - to ta l a m o u n t o f tr a d e m a rg in p a id o n p ro d u c ts a n d s e rv ic e s o f ty p e /', C , - total a m o u n t o f tr a n s p o r t m a rg in p a id o n p r o d u c ts a n d s e rv ic e s o f ty p e j .3 .1 . E x t r a c t i n g V A T f r o m t h e i n p u t - o u t p u t t a b le
A t th e first s ta g e , V A T is e x tra c te d fro m in p u t-o u tp u t ta b le . A t th e s a m e tim e , V A T r a te s /, a n d c o e ffic ie n ts
hy - s h o w in g c o n te n ts o f n o n - d e d u c tib le
V A T in in te r m e d ia te flo w s - a re d e te rm in e d . T h e p r o c e d u r e is b a s e d o n th e f o l lo w in g re la tio n ( s e e a ls o J. C . C o lla d o & F. S a n c h o (2 0 0 2 ) fo r m e th o d o f r e c o v e rin g h id d e n tax r a te s in in p u t-o u tp u t ta b le s in w h ic h all tr a n s a c tio n s c o n ta in full a m o u n t o f d e d u c tib le ta x ):In (1 8 ) w e h a v e n e q u a tio n s w ith >i(« + l ) v a ria b le s (r, a n d
hy ). T h u s , to o b
tain th o s e p a r a m e te r s ,a priori k n o w le d g e a n d /o r s im p lif y in g a s s u m p tio n s m u st
b e a p p lie d . F o r e x a m p le , c o n s id e r th e s e c to rs w h o s e p ro d u c ts a n d s e r v ic e s a re fu lly e x e m p te d fro m V A T . In th e c a s e o f P o la n d th e s e are : f is h e r y , fin a n c ia l s e rv ic e s , p u b lic a d m in is tra tio n a n d d e fe n c e , e d u c a tio n , h e a lth c a r e a n d so c ia l s e c u r ity s e rv ic e s . A s th e y d o n o t h a v e r ig h t to V A T d e d u c tio n , it is d e f in ite th a t all in te rm e d ia te in p u ts in th e s e s e c to rs in c lu d e full a m o u n ts o f V A T . T h u s , c o e f fic ie n ts in th e c o r r e s p o n d in g c o lu m n s o f th e H m a trix a re all e q u a l 1.E q u a tio n (1 8 ) a s s u m e s th a t all final p u rc h a s e s a r e in c lu s iv e o f fu ll V A T a m o u n t. H o w e v e r, th is n e e d n o t b e tru e fo r in v e s tm e n t. S im p lif y in g , it c a n b e a s s u m e d th a t e n te r p r is e s fu lly e x e m p te d fro m V A T p a y th e ta x o n in v e s tm e n t g o o d s , o th e r d o n o t (it is d e d u c te d ). A m o n g in s titu tio n a l s e c to r s o f th e P o lish e c o n o m y , th e n o n - p ro f it in s titu tio n s , g o v e r n m e n t a n d f in a n c ia l e n te r p ris e s c a n b e tre a te d a s th e p e r f o rm e r s o f m o s t a c tiv itie s e x e m p te d fro m V A T . C o n s e q u e n tly , it w a s a s s u m e d th a t in v e s tm e n t o u tla y s o f th e m e n tio n e d in s titu tio n a l s e c to rs in c lu d e full V A T a m o u n ts , w h ile n o n -fin a n c ia l e n te r p ris e s a n d h o u s e h o ld s (h o u s e h o ld firm s ) d e d u c t th e w h o le tax. T h e o n ly e x c e p tio n is th a t fo r p riv a te e x p e n d itu r e s o n b u ild in g s , w h ic h are a lso re c o rd e d a s h o u s e h o ld in v e s t m e n t, b u t V A T c a n n o t b e d e d u c te d . T h u s , fo r c la rity o f th e s o lu tio n p re s e n te d b e lo w , in v e s tm e n t in b u ild in g s w e re m o v e d to h o u s e h o ld c o n s u m p tio n .
F o llo w in g th e a b o v e r e m a rk s , e q u a tio n (1 8 ) s h o u ld b e s u b s titu te d w ith : ( 1 8 )
(1 9 )
w h e re : Í2, = { /,1 ' , / V >....,y'i)l ) } is a c la s s o f s u b s e q u e n t n u m b e rs o f g r o u p s o f c o m m o d itie s w h ic h a re n o t e x e m p te d fro m V A T ,
со b e in g th e to ta l n u m b e r o f
su c h p r o d u c ts a n d s e rv ic e s , £?2 = {/i<2>. ^ 2>... Уя- L / ~ a d a s s o f s u b s e q u e n t n u m b e rs o f g r o u p s o f c o m m o d itie s w h ic h a re fu lly e x e m p te d fro m V A T ,
Г = \kl ,k2...ky\ -
a c la s s o f s u b s e q u e n t n u m b e rs o f fin a l e x p e n d itu r e c a te g o rie s fu lly in c lu s iv e o f V A T ,у b e in g th e to ta l n u m b e r o f s u c h c a te g o r ie s . S till, h o w
e v e r it is im p o s s ib le to s o lv e (1 9 ) fo rt, a n d
hy w ith o u t f u rth e r s im p lific a tio n .
In o r d e r to illu s tr a te th e a p p r o a c h b e tte r, a s s u m e fo r a w h ile th a t V A T is p r e s e n t o n ly in fin a l d e m a n d ( e x c e p t in v e s tm e n t o f h o u s e h o ld s a n d n o n -fin a n c ia l e n te r p ris e s ) a n d in in te r m e d ia te e x p e n d itu re s o f b r a n c h e s fu lly e x e m p te d fro m V A T . In te rm s o f
hy c o e f f ic ie n ts it m e a n s th a t
hy = 0 fo r
j
e . T h u s , w e get:71 = Z Т+Г*''+ ^ т + г л
(20)
y e O ,A + */ * e r 1 + »r S o lv in g ( 2 0 ) fo r /, y ie ld s:t, = T,
\
-i + Z ^~ T>
уjeSh
(2 1
) R e s u lts o f th is e x p e r im e n t f o r th e in p u t-o u tp u t ta b le ’2 0 0 0 a re p r e s e n te d in T a b le 2. T h e f irs t c o lu m n c o n ta in s r a te s c a lc u la te d a c c o r d in g to e q u a tio n (2 1 ). M a n y o f th o s e r a te s p r o v e to b e h ig h e r th a n th e h ig h e s t n o m in a l V A T ra te a c tu a lly u se d in P o la n d (2 2 % ). T h e o n ly e x p la n a tio n o f su c h re s u lts (a p a rt fro m in a c c u ra c y o f d a ta ) is th a t th e d e n o m in a to r in fo rm u la (2 1 ) is to sm a ll fo r c e r ta in ty p e s o f g o o d s a n d , c o n s e q u e n tly , it s h o u ld b e a u g m e n te d b y a p a rt o f th o s e in te r m e d i a te c o s ts , w h ic h w e re a s s u m e d V A T -fre e . T h u s , it g iv e s an in d ire c t e v id e n c e fo r w h a t is n o t e x p lic it in th e in p u t-o u tp u t ta b le , th a t is fo r th e e x is te n c e o f n o n d e d u c tib le n o t o n ly in c o s ts o f th e s e c to rs fu lly e x e m p te d .VAT rates (in %) and /?, coefficients
/ Products and services Results o f
(21)
Reference rates
Destination
rates hi
1 Agriculture and forestry 0.8 3.0 0.8 0.000
2 Fishery 0.0 0.0 0.0 0.000 3 Mining 27.2 7.1 7.1 0.226 4 Food 6.6 6.0 6.0 0.216 5 Tobacco 10.8 22.0 10.8 0.000 6 Fabrics 18.8 22.0 18.8 0.000 7 Textile 16.8 22.0 16.8 0.000 8 Leather 11.6 22.0 11.6 0.000 9 Wood 16.0 17.7 16.0 0.000 10 Paper 39.6 22.0 22.0 0.093
11 Publishing and printing 8.5 5.1 5.1 0.793
12 Petrol 36.4 21.1 21.1 0.137
13 C hem icals 8.9 19.4 8.9 0.000
14 Rubber and plastic 58.1 22.0 22.0 0.093
15 O ther non-metallic 15.3 12.7 12.7 0.031
16 Metal 4 783.5 21.2 21.2 0.090
17 Metal products 38.3 15.5 15.5 0.117
18 Machines 16.1 19.6 16.1 0.000
19 O ffice machines and computers 22.4 22.0 22.0 0.021
20 Electric machines 72.4 22.0 22.0 0.170
21 Radio and TV devices 16.9 22.0 16.9 0.000
22 Medical and optical devices 11.4 17.3 11.4 0.000
23 M otor vehicles 19.7 22.0 19.7 0.000
24 O ther transport equipm ent 9.7 7.8 7.8 0.159
25 Furniture and other goods 7.0 22.0 7.0 0.000
26 Recycling -105.6 22.0 22.0 0.007
27 Electricity, gas, water 3.0 7.0 3.0 0.000
28 Construction 6.8 7.0 6.8 0.000
29 Hotels and restaurants 11.5 22.0 11.5 0.000
30 Financial services 0.1 0.1 0.1 0.000
31 Business and real estate services 11.6 22.0 11.6 0.000
32 Public administration and defence 0.0 0.0 0.0 0.000
33 Education 0.0 0.0 0.0 0.000
34 Health care and social security 0.0 0.0 0.0 0.000
35 O ther services 3.1 22.0 3.1 0.000
36 Repair 14.5 22.0 14.5 0.000
37 Transport, storage, communication 10.6 22.0 10.6 0.000
38 Trade 0.0 0.0 0.0 0.000
39 T ransport-as-margin 0.0 0.0 0.0 0.000
T h e a b o v e o b s e rv a tio n is th e b a s is fo r th e fu rth e r p r o c e d u re . T h e id ea a m o u n ts to s e a r c h in g fo r su c h /;); v a lu e s (fo r
j
e f í , ) w h ic h w o u ld b r in g d o w n th e r e s u ltin gti r a te s a t le a st to th e le v el o f 2 2 % , (th e h ig h e s t n o m in a l ra te ) th u s
a llo w in g to fin d V A T a m o u n ts w h ic h a re d e f in ite ly p r e s e n t in in te r m e d ia te flo w s. In fac t, in s te a d o f u s in g th e te rm in a l le v el o f 2 2 % , o n e c a n c a lc u la te “ r e f e r e n c e r a te s " , b a s in g on v a lid tax re g u la tio n s , w h ic h a s s ig n n o m in a l V A T ra te s to d if fe r e n t k in d s o f p r o d u c ts a n d se rv ic e s . T h is so rt o f c a lc u la tio n is fa irly a p p ro x im a te . I f w ith in a g r o u p o f p ro d u c ts th e re a re g o o d s c h a r g e d a t d iffe re n t V A T ra te s, th e y s h o u ld b e w e ig h te d b y s h a re s in g lo b a l s u p p ly o f th o s e g o o d s. H o w e v e r, r e f e r e n c e r a te s s h o u ld p e rh a p s b e tre a te d a s u p p e r b o u n d s fo r a c tu a l e f f e c tiv e r a te s r a th e r th a n a s a c tu a l e ff e c tiv e ra te s th e m s e lv e s . T h is r e s tric tio n re s u lts fro m th e fa c t th a t a g iv e n g o o d c a n b e u s u a lly s u p p lie d b y e ith e r a V A T - p a y in g p r o d u c e r o r b y a V A T - e x e m p te d o n e. In su c h a c a s e , th e e f f e c tiv e V A T ra te b e c o m e s lo w e r th a n th e n o m in a l ( re fe re n c e ) on e.A c c o rd in g to th e p ro p o s e d a p p ro a c h , th e so c a lle d “ d e s tin a tio n ra te s ” a re d e te rm in e d . D e s tin a tio n r a te s a re se t to th e r e fe re n c e r a te s fo r th o s e p r o d u c ts an d s e rv ic e s , fo r w h ic h ra te s re s u ltin g fro m e q u a tio n (2 1 ) p ro v e h ig h e r th a n th e r e f e re n c e o n e s . F o r th e r e m a in in g c o m m o d itie s , d e s tin a tio n ra te s a re s e t a t th e level d e te r m in e d b y a p p ly in g fo rm u la (2 1 ). D e s tin a tio n ra te s a c tu a lly c o m p o s e th e T m a trix ( s e e m o d e l (1 7 )).
G iv e n V A T d e s tin a tio n ra te s , it is p o s s ib le to c a lc u la te
hy c o e f fic ie n ts , p ro
v id e d th a t th e n u m b e r o f u n k n o w n v a ria b le s is r e d u c e d ton. T h is c a n b e o b
ta in e d b y a s s u m in g th a t th o s e c o e ffic ie n ts a re u n ifo rm a c ro s s r o w s o f th e in p u t- o u tp u t ta b le . It m e a n s th a t in all b r a n c h e s w h ic h a re n o t fu lly e x e m p te d fro m V A T , th e s a m e f ra c tio n o f v a lu e o f a p a r tic u la r m a te ria l is c h a rg e d w ith th e n o n d e d u c tib le ta x . R e g a r d in g th is a s s u m p tio n , e q u a tio n (1 9 ) c a n b e r e w ritte n as:Т , -
I yeO, 1 + / Л■Xtl + У J i - X + y J í
^ l + ,
4
yefl,Ун
(
2 2)
T h a t s im p lif ic a tio n e n a b le s s o lv in g (2 2 ) fo r e a c h
h, s e p a r a te ly . T h e s o lu tio n
y ie ld s:h, =
T + t
I
*/ Ч V \ \Ti - 1 л “ Z *
jeSJj
keľ
f I f + ‘r-)Y . x4 ~ T<
+ *2 Z y »+ Z -v-V'e°l \ \кеГ
jeQ-,
-I J J (2 3 )w h e re : /, a re V A T d e s tin a tio n ra te s, as sh o w n in ta b le 2. C o e f f ic ie n ts /?, a re se t to z e ro w h e n e v e r d iv is io n b y z e ro a ris e s in (2 3 ). F in a lly e le m e n ts o f T a n d H c a n b e s e t as: - . . . ( 2 4 > for
i = j
fori * j
fo r / е Ц forJ e ü 2
Л / / Ч ' (2 5 ) [ 1 fo rj
£ Qj It c a n b e se e n fro m ta b le 2 th a t th e h ig h e st c o n te n ts o f n o n d e d u c tib le V A T a re fo u n d in in te r m e d ia te p u r c h a s e s o f fo o d , le a th e r, p r o d u c ts o f p u b lis h in g , fu e ls a n d fa b ric s. T h e la st s te p in w h ic h V A T is in v o lv e d is p u r ify in g in p u t- o u tp u t ta b le o f th is ta x , in o r d e r to e n a b le c a lc u la tio n o f th e r e m a in in g p a ra m e te rs . D e n o tin g b yw:i
in te r m e d ia te flo w s p u r ifie d o f V A T an d b yf jk
- fin al d e m a n d p u rifie d o f V A T , o n e c a n f o rm u la te th e fo llo w in g p u rific a tio n ru les:" * - 77^
'
(26)
—■—У it
• f ° rк е Г
1 + / / (2 7 >Уik>
fo rk * r
It m u s t b e e m p h a s is e d th a t th e p ro p o s e d m e th o d o f d e t e r m in in g T a n d H p a r a m e te r m a tr ic e s is b a s e d o n r a th e r s tr o n g a s s u m p tio n s , w h ic h c a n le ad to s o m e u n d e s ira b le e f f e c ts in th e m o d e l. F irs tly , u n a q u a in ta n c e w ith th e a c tu a l e ff e c tiv e ra te s a n d u s in g r e f e r e n c e r a te s in s te a d , c a n le ad to u n d e r e s tim a tin g c o n te n ts o f n o n - d e d u c tib le V A T in in te r m e d ia te flo w s. T h u s , p r ic e r e s p o n s e s to V A T ra te c h a n g e s in th e m o d e l c a n b e in te rp re te d a s th e m in im a l o f w h ic h o n e c a n b e c e rta in , i.e. a c tu a l r e s p o n s e s a r e lik e ly to b e g re a te r. T h e o n ly re a s o n fo r su c h lim ita tio n in th e f u n c tio n a lity o f th e m o d e l is th e la ck o f d a ta o n n o n - d e d u c tib le V A T . S e c o n d ly , a r e s e a r c h e r m u s t still d e a l w ith th e n o tio n o f e f f e c tiv e r a th e r th a n p u r e n o m in a l r a te s w h ic h o fte n c a u s e s d if fic u ltie s in a d e q u a te fo rm u la tio n o f s im u la tio n s c e n a rio s . T h ir d ly , th e ru le s in th e m o d e l a r e r a th e r c o m p a tib le w ith ru le s lim itin g d e d u c tio n o f V A T o n p a r tic u la r g o o d s , w h ile p e r h a p s in th e P o lish c o n d itio n s a g r e a te r ro le s h o u ld b e a ttrib u te d to V A T e x e m p tio n fo r sm a ll e n te rp ris e s . M o d e llin g o f th e la tte r c a s e , h o w e v e r, c o m p lic a te s th e p r o c e d u re o f d e te r m in in g n o n - d e d u c tib le V A T in in p u t- o u tp u t ta b le . A s a re s u lt, th e p r o p o s e dm e th o d le a v e s a s u b s ta n tia l m a rg in fo r fu rth e r c o n s id e ra tio n a n d , p o s s ib ly , im p r o v e m e n t.
3.2 . P u r i f y i n g t h e i n p u t - o u t p u t t a b le o f in d i r e c t ta x e s o t h e r t h a n V A T
N e x t s ta g e s o f th e d e c o m p o s itio n p ro c e d u re a re p e rh a p s m o r e tr a n s p a r e n t th a n th e p r e v io u s o n e . T o d e te r m in e d ia g o n a l e le m e n ts o f S f/, S m, li a n d С m a tric e s , th e f o llo w in g f o rm u la s a re used:
S?>
X;
s f
= ~ r r (2 8 )С
(w )M,
'■ • Л' " u ( 3 0 )(3,)
T h e re s u ltin g ra te s a re p re s e n te d in T a b le 3. N e g a tiv e v a lu e s o f tax ra te s m e a n th a t s u b s id ie s e x c e e d ta x e s.
D is tin g u is h in g b e tw e e n d o m e s tic a n d im p o rte d p ro d u c tio n re lie s o n th e a s s u m p tio n th a t th e re is a fix e d s h a re o f im p o rts fo r p a r tic u la r c o m m o d ity , id e n ti ca l in all in d iv id u a l p u r c h a s e s o f th a t c o m m o d ity , i.e.:
4 Ш) = V’z i (3 2 ) w h e re :
z y r e p r e s e n t in te r m e d ia te flo w s e v a lu a te d a t b a s ic p r ic e s ( s e e (1 5 ) an d
(1 6 )): 7 = J 1' ) 4- <j ij + г Г ' (3 3 ) C o e ff ic ie n ts /<, c a n b e c a lc u la te d a c c o r d in g to th e f o llo w in g ru le:T a b i c 3 Rates o f indirect taxes excluding VAT (in %), margin rates
/' Products and services i ^ ’-lOO _Us о о O О
о
о
о
1 Agriculture and forestry -0.1 8.1 11.8 l.l
2 Fishery -0.8 0.6 41.8 10.6 3 Mining 0.0 0.1 5.5 9.8 4 Food 4.8 21.1 27.7 0.2 5 Tobacco 118.4 230.5 92.6 0.0 6 Fabrics 0.0 2.6 18.7 l.l 7 Textile 0.0 9.0 44.7 1.6 8 Leather 0.0 7.0 48.6 1.7 9 Wood 0.0 2.4 12.5 1.4 10 Paper 0.0 0.9 13.1 2.1
11 Publishing and printing -0.1 0.9 19.1 0.8
12 Petrol 30.0 120.5 56.0 3.5
13 Chemicals -0.1 1.6 26.8 0.6
14 Rubber and plastic 0.1 1.9 15.6 3.9
15 O ther non-metallic 0.0 1.5 14.0 7.5
16 Metal 0.0 2.4 5.9 0.5
17 Metal products 0.0 2.7 10.2 3.2
18 Machines 0.0 1.4 8.1 0.5
19 Office machines and computers 0.0 1.1 18.4 2.3
20 Electric machines 0.0 1.4 8.0 0.9
21 Radio and TV devices 0.0 2.2 16.6 1.0
22 Medical and optical devices 0.0 2.5 6.9 2.3
23 M otor vehicles 1.4 8.8 12.3 0.6
24 O ther transport equipm ent 0.0 1.7 7.3 0.5
25 Furniture and other goods 0.0 4.8 13.7 1.8
26 Recycling 0.0 0.0 0.0 1.5
27 Electricity, gas, water 0.0 2.3 0.5 0.0
28 Construction 0.0 0.0 0.0 0.0
29 Hotels and restaurants -0.1 0.0 0.0 0.0
30 Financial services 0.0 0.0 0.0 0.0
31 Business and real estate services -0.5 -0 .3 0.0 0.0
32 Public administration and defence 0.0 0.0 0.0 0.0
33 Education 0.0 0.0 0.0 0.0
34 Health care and social security 0.0 0.0 0.0 0.0
35 O ther services -1.1 -0.9 0.0 0.0
36 Repair 0.0 0.0 0.0 0.0
37 Transport, storage, comm unication -0 .9 -0 .9 0.0 0.0
38 T rade 0.0 0.0 -100.0 0.0
39 Transport-as-margin 0.0 0.0 0.0 -100.0
S o u r c e : Own calculations.
T h e a b o v e a s s u m p tio n m a k e s it p o s s ib le to p u rify tr a n s a c tio n s o f b o th in d i rec t ta x e s o n d o m e s tic g o o d s a n d th o s e o n im p o rte d o n e s , a s w e ll a s tr a d e an d tra n s p o r t m a rg in , at o n c e . T h e a p p r o p r ia te ru le is g iv e n by:
(3 5 )
H a v in g
z у a n d / / , , it is p o s s ib le to d e te r m in e e le m e n ts o f th e last tw o p a
r a m e te r m a tr ic e s , A ,/ a n d A,„:F in a lly , all o f th e a c q u ir e d p a r a m e te r m a tric e s s h o u ld b e d im in is h e d by r e m o v in g ro w s a n d c o lu m n s c o r r e s p o n d in g w ith tr a d e a n d “ tr a n s p o r t- a s -m a rg in ” . O th e r w is e th e m o d e l c o u ld n o t b e so lv e d a s all e le m e n ts o f A (/ a n d A ,H m a tri c e s in ro w s c o r r e s p o n d in g w ith tra d e a n d “ tr a n s p o r t- a s -m a rg in ” e q u a l z e ro (m a r g in s a re p r e s e n t e x p lic itly in th e p ric e e q u a tio n , so th e s o lu tio n re m a in s c o rre c t). T h e te st fo r c o r r e c tn e s s o f th e d e c o m p o s itio n p r o c e d u re is d o n e b y c a l c u la tin g p ric e s a c c o r d in g to fo rm u la ( 1 7 ), u s in g th e a c q u ire d p a r a m e te r m a tric e s - all o f th e re s u ltin g p ric e in d ic e s s h o u ld e q u a l o n e.
IV. F I N A L P R I C E S A N D A G G R E G A T E P R I C E I N D I C E S
A t th e last s ta g e o f th e a n a ly s is , final p ric e s , a s w e ll a s a g g r e g a te p ric e in d i c e s a r e d e te rm in e d . F in al p ric e fo r a p a r tic u la r g r o u p
i o f p ro d u c ts o r s e rv ic e s c a n b e c a lc u la te d
as: (3 6 ) (3 7 ) (3 8 )V a lu e s o f
>f'n sh o w th e re la tio n o f th e fin al to th e b a s ic p ric e . C h a n g e s o f
final p ric e s o f d o m e s tic g o o d s a re re p re s e n te d by th e fo llo w in g in d ic e s :w h e re : >(1|/) sta n d f o r in itia l v a lu e s o f , th a t is th e v a lu e s c a lc u la te d b a s in g o n o rig in a l p a r a m e te r s o f th e m o d e l ( n o t c h a n g e d d u e to s c e n a rio a s s u m p tio n s ).
A n a lo g o u s ly , fin al p r ic e s a s w e ll fin al p ric e in d ic e s fo r p a r tic u la r im p o rte d c o m m o d itie s c a n b e c a lc u la te d , i.e.: = (l + / , ) (l + sf"0 + d i )pl'n> (4 0 ) and: _(m) _ ri
П :
---(»I) ( I I I ) (4 1 )F o r in te rp re ta tio n p u rp o s e s , it is u s u a lly c o n v e n ie n t to u s e a w e ig h te d p ric e in d e x fo r s u b s e q u e n t g r o u p s o f p ro d u c ts a n d s e rv ic e s , in c lu d in g b o th d o m e s tic a n d im p o rte d o n e s :
(4 2 )
A g g re g a te p r ic e in d e x fo r c a te g o ry
к o f fin al e x p e n d itu r e s ( n o t e x e m p te d
fro m V A T - e .g . fin a l c o n s u m p tio n ) c a n b e c a lc u la te d a s fo llo w s :"
\f n
V 1 V. /=I У \ i=l / (4 3 ) w h e re :к e
Г .
V a lu e s o f y jk a re ta k e n d ir e c tly fo rm th e in p u t- o u tp u t ta b le (s e e T a b le 1). A g g re g a te p r ic e in d e x o f g lo b a l d o m e s tic o u tp u t is g iv e n by:km -
1 Л ■I
х .
\ /=1 \ - i / V <=i / (4 4 ) D e fin e a lso :« « Л * # ' * * ' ) # '
1 + + •</,.i (III) _ ( i+ Ą (,,,)+ ^ k
i + -i!"'1 + V/
п т an d 0 - / 0 l ( l + .ľ ' + d ] 1
p \ ‘ \+ / ' / 1[i + s ! * > + d j! p j - » ( 1 - / ' , ) ! [l + ^ ’ + Y/Jl+/i,.|(1 + 'S < ", , + ' d , ) (4 6 ) (4 7 )w h e re : ,
's)m>
a n d'd, a re in itia l v a lu e s o f in d ire c t tax ra te s ( e x c e p t V A T )
a n d m a rg in s - a s d e te r m in e d in th e d e c o m p o s itio n p r o c e d u re . V a lu e s o f ca n b e tre a te d as fin al p r ic e in d ic e s for c o m m o d itie s fo r w h ic h full d e d u c tio n o f V A T is a llo w e d . T h u s , it le a d s to fo rm u la tin g a g g r e g a te p r ic e in d ic e s fo r th o s e final d e m a n d c a te g o r ie s w h ic h a re fre e o f V A T b u rd e n (e .g . e x p o r ts a n d in v e s t m e n t o f n o n - fin a n c ia l e n te r p ris e s ) , a s w ell as to th e m ix e d a g g r e g a te d p r ic e in d e x fo r a w id e r ra n g e o f fin a l g o o d s , r e s p e c tiv e ly (e.g . G D P ):( »
v i=i J Vi*i 4S/ ) = ■ Ž - 1'« (4 8 ) w h e re :k e ( l,2 ... /} an d :
; M) = Z Х а д * + z z ^ * • Z Ż у* + Z Ż y>kkeU^ 1= I *eU2 i> l J l ' “ I keU-, i= l
(4 9 )
w h e re : ( / , с Г ,
U 2 a {
1 ,2 .../} .A c c o rd in g to a n a ly tic a l n e e d s , o th e r p ric e in d ic e s c a n b e d e fin e d .
V . S I M U L A T I O N R E S U L T S
S im u la tio n a s s u m p tio n s w e r e in s p ire d m a in ly by th e tw o facts. F irs tly , it w a s th e d is c u s s io n a m o n g th e P o lis h p o litic s a n d e c o n o m is ts o n th e p o s s ib ility of in tr o d u c in g a 5 % im p o rt tax . A s th e im p o rt tax c o n n o t b e a c tu a lly im p o s e d a fte r th e EU a c c e s s io n , th e s im u la tio n c u rr e n tly h a s a c o u n te r fa c tu a l c h a ra c te r. S e c o n d ly , it w a s th e a d a p ta tio n o f V A T ra te s on c e rta in p r o d u c ts a n d s e rv ic e s to th e EU s ta n d a r d s . T h e r e f o r e , th e e m p ir ic a l p a rt o f th e s tu d y is d iv id e d in to tw o p a rts, a d e q u a te for th e a n a ly s e d issu e s.
5.1. S i m u l a t i o n 1 - im p o r t tax
A p p ly in g s c e n a rio fo r th e first s im u la tio n is fa irly s im p le . It a m o u n ts to a d d in g 0 .0 5 to e a c h ra te o f in d ire c t ta x e s o n im p o rte d g o o d s
sj"°. T h e re s u lts a re
p r e s e n te d in T a b le s 4 a n d 5.T a b l e 4 Results o f simulation 1. Rates o f growth o f prices, share o f imports in supply (in %) —
/ Products and services Basic prices
(domestic) Final prices (dom estic + imported) Actual share o f imports in total supply
1 Agriculture and forestry 1.0 1.3 10.0
2 Fishery 1.2 1.7 22.9 3 Mining 0.7 2.1 38.9 4 Food 0.9 l.l 8.0 5 Tobacco 0.6 0.7 2.5 6 Fabrics 1.5 2.6 42.4 7 Textile 0.8 1.2 16.7 8 Leather 1.1 1.6 26.1 9 Wood 1.0 1.3 9.9 10 Paper 1.7 2.8 40.6
11 Publishing and printing 0.9 l.l 7.9
12 Petrol 1.6 1.6 15.4
13 Chemicals 1.0 2.5 50.7
14 Rubber and plastic 1.5 2.4 34.6
15 O ther non-metallic 1.0 1.6 20.9
16 Metal 1.3 2.2 27.0
17 Metal products 1.2 2.0 25.1
18 Machines 1.3 2.9 50.4
19 O ffice m achines and computers 2.2 3.9 90.5
20 Electric machines 1.6 2.6 35.3
21 Radio and TV devices 1.5 3.1 60.6
22 Medical and optical devices 1.0 2.2 34.7
23 M otor vehicles 1.8 3.1 55.9
24 O ther transport equipment 1.6 1.9 9.7
25 Furniture and other goods 1.2 1.6 13.4
26 Recycling 1.5 1.5 0.0
27 Electricity, gas, water 1.0 1.0 0.3
28 Construction 0.9 1.0 2.5
29 Hotels and restaurants 0.6 0.6 0.0
30 Financial services 0.9 1.8 21.2
31 Business and real estate services 0.5 0.7 4.4
32 Public administration and defence 0.1 0.1 0.0
33 Education 0.2 0.2 0.0
34 Health care and social security 0.2 0.2 0.0
35 O ther services 0.5 0.5 1.2
36 Repair 0.6 0.6 0.8
T a b l e 5 Results oľ simulation 1. Rates o f growth o f aggregate prices (in %) Categories o ffin al expenditures + global output Price change
Private consumption 1.3
Government consumption 0.3
Investment 2.0
Export 1.9
Global domestic output (basic prices) 0.8
S o u r c e : Own calculations.
T h e r e la tiv e ly h ig h e s t g r o w th s o f fin al p ric e s c a n b e o b s e rv e d fo r o f fic e m a c h in e s , m o to r v e h ic le s a n d ra d io a n d T V d e v ic e s , m a in ly a s a r e s u lt o f h ig h im p o rt s h a re s fo r th e s e p ro d u c ts . H o w e v e r, fin al p ric e s a re a ls o d riv e n by s ig n ifi c a n t in c re a s e in m a te ria l c o s ts , w h ic h is v is ib le in b a s ic p ric e s ( fo r in d u s try ra te s o f g ro w th o f b a s ic p ric e s o s c illa te a ro u n d l% - 2 % ) . It is th e o f fic e - m a c h in e in d u s try w h ic h b e a r s th e h ig h e s t in d ire c t c o s ts o f in tr o d u c in g im p o rt tax . A m o n g c o m m o d itie s s h o w in g th e w e a k e s t re a c tio n , a s far as p ric e s a r e c o n c e r n e d , th e re a re e s s e n tia lly th o s e w h ic h a b s o rb little m a te ria l c o s ts. O n e s h o u ld m e n tio n h e re m a in ly e d u c a tio n , p u b lic a d m in is tra tio n an d d e fe n c e an d h e a lth c a r e s e rv ic e s .
T a b le 5 s h o w s c h a n g e s o f p ric e s fo r m a jo r c a te g o rie s o f fin a l d e m a n d , as w ell a s g lo b a l o u tp u t. D if fe re n c e s a m o n g th e ra te s o f g ro w th c a n b e e x p la in e d , f irs tly , by d if fe r e n c e s in e x p e n d itu r e s tru c tu re s a c r o s s c a te g o rie s . T h e se c o n d re a so n is, th a t to e v a lu a te g lo b a l o u tp u t b a sic p ric e s a re u s e d , w h ile fo r th e d e m a n d - fin al p ric e s. T h e h ig h e s t p ric e in c re a s e is fo r in v e s tm e n t, th e lo w e s t - fo r g o v e r n m e n t c o n s u m p tio n . In g e n e ra l, in tr o d u c in g im p o rt tax w o u ld r a th e r h a v e u n fa v o u r a b le im p a c t o n in v e s tm e n t c o n d itio n s , s in c e r e la tio n o f p ric e s o f in v e s tm e n t g o o d s to p ric e s o f c o n s u m p tio n w o u ld w o rs e n . T h e in c re a s e o f p ric e s is a lso c o m p a r a tiv e ly h ig h fo r e x p o rts . O n th e o th e r h a n d , h o w e v e r, im p o rt tax s e e m s an a ttr a c tiv e s o u r c e o f b u d g e t re v e n u e s . G o v e r n m e n t c o n s u m p tio n b e c o m e s re la tiv e ly c h e a p , m e a n in g th a t b e s id e s d ire c t o u tc o m e in a fo rm o f tax re v e n u e in c re a s e , a d d itio n a l r e d is trib u tio n e ffe c t a p p e a rs.
5.2. S i m u l a t i o n 2 - V A T a d a p t a t i o n to th e E U s t a n d a r d s
In th e s e c o n d e x p e rim e n t, e f fe c ts o f th e V A T ra te c h a n g e s a re a n a ly s e d . T h e p o in t o f c h a n g e s is lim itin g th e r a n g e o f re d u c e d a n d z e ro r a te s (e .g . in c o n s tru c tio n an d a g ric u ltu re ). T h e m a jo r c h a n g e s in V A T ra te s a re p o in te d o u t in T a b le 6.
T a b l e 6 M ajor forthcoming changes in VAT rates in Poland (rates in %).
Products and services Current rate New rate
Agriculture 3 7
Means o f agriculture production 3 7
Construction 7 22
Materials for construction 7 22
S o u r c e : Own calculations. T o s e t p r o p e r v a lu e s o f
t, f o r s im u la tio n , n e w r e fe r e n c e ra te s w e r e c a lc u
la ted ( s e e th e p r e v io u s s e c tio n ) ta k in g in to a c c o u n t th e p la n n e d c h a n g e s . C a lc u la tin g d if f e r e n c e s b e tw e e n th e s e ra te s a n d th e o ld r e f e r e n c e r a te s (s e e T a b le 2 ), le a d s to f in d in g th e n e c e s s a ry a d ju s tm e n ts o f /, in th e s im u la tio n . T h e a d ju s t m e n ts a re p r e s e n te d in T a b le 7. T a b le s 8 & 9 s h o w re s u lts o f s im u la tio n 2. In th e c a s e o f V A T in c re a s e , p ric e c h a n g e s a re p r e d o m in a te d b y d ir e c t e f fe c ts, v is ib le in fin al p ric e s. H o w e v e r, a slig h t re a c tio n o f b a s ic p r ic e s c a n a lso b e o b s e rv e d - g e n e r a lly b e in g a t th e le v el o f 0 .1 % - 0 .2 % . F o r p ro d u c ts an d s e rv ic e s fu lly e x e m p te d fro m V A T th is re a c tio n is r e a s o n a b ly s tr o n g e r. F o r e x a m p le , g r o w th s o f b a s ic p ric e s o f fis h e ry p ro d u c ts e x c e e d s 1% , w h ile fo r p u b lic a d m in is tra tio n a n d d e f e n c e , e d u c a tio n , a s w ell as p u b lis h in g a n d p r in tin g , th e se r a te s a re c lo s e to 0 .5 % . A s fa r a s a g g r e g a te c a te g o rie s a re c o n c e r n e d , it is c o n s u m p tio n th a t g o e s u p th e h ig h e s t, fo r o th e r c a te g o rie s , p r ic e r e a c tio n is v e ry slig h t. A g a in , a s in th e c a s e o f im p o rt ta x , th e s ta te b u d g e t a d d itio n a lly b e n e f its fro m r e la tiv e p r ic e c h a n g e s , b u t th e c o s t th is tim e is n o t tr a n s f e rre d n e ith e r to in v e s tm e n t n o r e x p o rts .T a b l e 7 C hanges o f VAT rates in simulation 2 (in percentage points)
/' Products and services Changes o f VAT rates
1 Agriculture and forestry 7.0
9 Wood 4.3
11 Publishing and printing 2.3
13 Chemicals 0.1
15 O ther non-metallic 9.3
16 Metal 0.8
17 Metal products 6.5
18 Machines 0.5
25 Furniture and other goods 0.3
Results oľsim ulation 2. Rates o f growth o f prices (in %)
i Products and services Basic prices
(domestic)
Final prices (domestic + imported)
1 Agriculture and forestry 0.0 7.0
2 Fishery 1.1 0.9 3 Mining 0.1 0.0 4 Food 0.1 0.1 5 Tobacco 0.1 0.1 6 Fabrics 0.0 0.0 7 Textile 0.0 0.0 8 Leather 0.1 0.0 9 Wood 0.1 3.8 10 Paper 0.0 0.0
1 1 Publishing and printing 0.5 2.7
12 Petrol 0.0 0.0
13 Chemicals 0.0 0.1
14 Rubber and plastic 0.0 0.0
15 Other non-metallic 0.1 8.3
16 Metal 0.1 0.7
17 Metal products 0.2 5.7
18 Machines 0.1 0.5
19 Office machines and computers 0.0 0.0
20 Electric machines 0.1 0.1
21 Radio and TV devices 0.0 0.0
22 Medical and optical devices 0.1 0.1
23 Motor vehicles 0.2 0.1
24 O ther transport equipment 0.1 0.1
25 Furniture and other goods 0.1 0.3
26 Recycling 0.1 0.1
27 Electricity, gas, water 0.0 0.0
28 Construction 0.1 14.2
29 Hotels and restaurants 0.0 0.0
30 Financial services 0.2 0.1
31 Business and real estate services 0.1 0.1
32 Public administration and defence 0.4 0.4
33 Education 0.4 0.4
34 Health care and social security 0.3 0.3
35 Other services 0.1 0.1
36 Repair 0.0 0.0
37 Transport, storage, communication 0.0 0.0
T a b l e 9 Results o f simulation 2. Rates o f growth o f aggregate prices (in %)
Categories o f final expenditures + global output Price change
Private consumption 1.7
Government consumption 0.3
Investment 0.1
Export 0.1
Global domestic output 0.1
S o u r c e : Own calculations.
It c a n b e s tr e s s e d th a t in th e c a s e o f in c re a s e o f th e c o n s id e r e d V A T ra te s (a g ric u ltu re p r o d u c ts , c o n s tru c tio n s e rv ic e s , m a te ria ls fo r a g r ic u ltu r e , m a te r ia ls fo r c o n s tru c tio n , p u b lis h in g a n d p r in tin g p ro d u c ts ), th e ro le o f in d ir e c t c o s t-p u s h e ff e c ts in p ric e fo rm a tio n p ro v e d r a th e r in s ig n ific a n t. It m e a n s th a t V A T on th e s e p a r tic u la r p r o d u c ts h a v e little s h a re in th e n o n - d e d u c tib le V A T in th e e c o n o m y a n d c a n b e m o s tly d e d u c te d b y p ro d u c e rs , b e in g r a th e r lu c k y c o in c i d e n c e as far a s in fla tio n in P o la n d is c o n c e rn e d . O n e s h o u ld h a v e in m in d , h o w e v e r, th a t th e c u r r e n tly p ro p o s e d p ro c e d u re o f p u r if y in g in p u t- o u tp u t ta b le o f V A T is im p e r fe c t a n d m a y lead to u n d e re s tim a tin g th e ro le o f n o n - d e d u c tib le V A T in f o rm a tio n o f b a s ic p ric e s. T h u s , th is is th e m a in in d ic a tio n th e m a in p o in t in f u rth e r d e v e lo p m e n t o f th e p r ic e m o d e l.
R E F E R E N C E S
B a r d a z z i R ., G r a s s i n i M . (1 9 9 1 ), V alu e-added Taxes a n d O th er In direct Taxes in
an E E C C o u n try M o d el: the Italian C a se , “ Economic System s Research”, vol. 3, no. 1 C o l l a d o .1. C., S a n c h o F. (2002), R eco verin g H idden In direct Tax R ates f o r Im
p r o v e d C a lib ra tio n in M u ltise c to ra l M o d ellin g , „E conom ic S ystem s R esearch” , Vol. 14. No. 1
G r a s s i n i M. (1997), The S tru ctu re o f th e M odern M u ltise c to ra l M odel. The Input-
O u tpu t M o d e l o f IN F O R U M S ystem , [in:] P ro ceed in g s o f the 3 r d W orld IN F O R U M
C o n feren ce, A bsolw ent, Lodz
M i l l e r R. E., B l a i r P. D. (1985), Input-O utput A n alysis: F ou n dation s a n d E xten
sio n s, Prentice-1 lall, inc., Englew ood Cliffs, N ew Jersey
S ystem R ach u n ków N a ro d o w y c h t. II (Tlie S ystem o f N a tio n a l A c c o u n ts vol. II), (1997), G U S (C entral Statistical O ffice), W arszawa
T o m a s z e w i c z L., B o r a t у ń s k i J. (2003), A n aliza cen ow ych efek tó w zm ian p o
d a tk ó w p o śr e d n ic h na p r z y k ła d z ie p o d a tk u im p o rto w e g o (P ric e E ffects o f In direct Tax C hanges. The C a se o f Im p o rt Tax), [in:] W zrost g o sp o d a r c zy , restru k tu ryza cja i
ryn ek p r a c y w P o lsc e . U jęcie te o r e ty c z n e i em p iryczn e, K atedra Ekonom ii UL, Ł ódź.
Jaku b B oratyń ski
RO LA P O D A T K Ó W P O Ś R E D N IC H W PROCESIE K S Z T A Ł T O W A N IA CEN - M O D E L DLA POLSKIE J G O S P O D A R K I
P o d sta w o w y m ce le m o p ra c o w a n ia je s t s fo rm u ło w a n ie w ie lo s e k to ro w e g o m o d elu o d z w ie rc ie d la ją c e g o w p ły w p o d a tk ó w p o śre d n ic h na cen y w p o ls k ie j g o sp o d a rc e . S ta now i on ro z s z e rz e n ie sta n d a rd o w e g o m o d elu cen typu input-output. M o d el ten p o k a z u je w z a je m n e z a le ż n o śc i cen p ro d u k tó w p o sz c z e g ó ln y c h gałęz i g o s p o d a rk i, w y n ik a ją c e z o d d z ia ły w a n ia n a k o sz ty p ro d u k c ji.
P o z a k o n s tru k c ją m o d e lu o m a w ia n y je s t p ro b le m u z y s k iw a n ia j e g o p a ra m e tró w w o p arciu o ta b lic e p rz e p ły w ó w m ię d z y g a łę z io w y c h . P ro p o n o w a n a j e s t m e to d a d e k o m p o z y c ji tej ta b lic y , p ro w a d z ą c a m .in . do u z y sk a n ia e fe k ty w n y c h sta w e k p o sz c z e g ó ln y c h p o d a tk ó w p o śre d n ic h . O m a w ia n a je s t m .in. p ro c e d u ra s z a c o w a n ia cz ę śc i p o d a tk u od to w a ró w i u s łu g (V A T ), k tó ra n ie p o d le g a o d lic z e n iu p rz e z p rz e d s ię b io rc ó w .
S k o n stru o w a n y m o d el w y k o rz y sty w a n y je s t d o a n a liz y sk u tk ó w e w e n tu a ln e g o w p ro w a d z e n ia 5 -p ro c e n to w e g o p o d atk u im p o rto w e g o , a ta k ż e d o o c e n y sk u tk ó w d o s to s o w a n ia sta w e k V A T d o w y m o g ó w U nii E u ro p ejsk iej.
