NOT FOR QUOTATION WITHOUT PERMISSION OF THE AUTHOR
AN ECONOMETRIC INPUT-OUTPUT MODEL OF THE WEST GERMAN ECONOMY
Douglas E. Nyhus
May 1982 WP-82-41
Presented at Input-Output Modeling Task Force Meeting held at the
International Institute for Applied Systems Analysis, Laxenburg, on September 24-26, 1981.
Working Papers are interim reports on work of the International Institute for Applied Systems Analysis and have received only limited review. Views or opinions expressed herein do not necessarily repre- sent those of the Institute or of its National Member Organizations.
INTERNATIONAL INSTITUTE FOR APPLIED SYSTEMS ANALYSIS
A-2361 Laxenburg, Austria
ABSTRACT
T h i s p a p e r d e s c r i b e s an econometric i n p u t - o u t p u t model o f t h e economy o f t h e F e d e r a l Republic o f Germany having 51 s e c t o r s , t o g e t h e r w i t h a f o r e c a s t made u s i n g t h e m o d e l . M o s t o f t h e d a t a f o r t h e m o d e l comes f r o m t h e R h e i n i s c h e - W e s t f a l i s c h e I n s t i t u t f u r W i r t s c h a f t s f o r s c h u n g i n Essen. The model presented h e r e i s now p a r t o f t h e INFORLIM s y s t e m o f d y n a m i c i n p u t - o u t p u t models.
E q u a t i o n s h a v e b e e n e s t i m a t e d t o e x p l a i n 46 c a t e g o r i e s o f consumer e x p e n d i t u r e , i n v e s t m e n t demands ( p l a n t and e q u i p m e n t s e p a r a t e d ) f o r 3 4
i n d u s t r i e s , e x p o r t s f o r 51 i n d u s t r i e s , i m p o r t s and i n v e n t o r y change f o r 51 i n d u s t r i e s . E q u a t i o n s t o f o r e c a s t i n p u t - o u t p u t c o e f f i c i e n t s h a v e b e e n e s t i m a t e d . F o r e c a s t s o f p r i c e s and incomes have n o t been made and a r e now
l e f t as f u t u r e work.
INTRODUCTION
T h i s i s a r e p o r t o n t h e c o n s t r u c t i o n o f a d y n a m i c e c o n o m e t r i c i n t e r i n d u s t r y m o d e l o f t h e West German economy. 'The b a s i c purpose o f t h e model i s t o make p r o j e c t i o n s f o r t h e West German economy, y e a r - b y - y e a r f o r a p p r o x i m a t e l y t e n y e a r s ahead, o f i n d u s t r i a l output, employment, investment, and o t h e r components o f f i n a l demand w i t h i n t h e s t r u c t u r e o f an e v e r c h a n g i n g i n p u t - o u t p u t t a b l e . S t r u c t u r a l change o v e r t h e p a s t 15 y e a r s h a s b e e n c a r e f u l l y examined i n t h e c o n s t r u c t i o n o f t h e model. A t p r e s e n t , t h e m o d e l l a c k s a p r i c e and income side; t h i s i s a r e s e a r c h t o p i c f o r t h e f u t u r e .
T h i s m o d e l , w h i c h i s now p a r t o f t h e INFORUM s y s t e m o f d y n a m i c i n p u t - o u t p u t f o r e c a s t i n g models, has been s u c c e s s f u l l y li n k e d w i t h t h o s e o f t h e U.S.A., Canada, France and Belgium (see Almon and Nyhus (1981) and INFORUM (1981)).
S e c t i o n I d e s c r i b e s t h e g e n e r a l s t r u c t u r e o f t h e model and t h e r e s u l t s t h a t a r e a v a i l a b l e . S e c t i o n 11 d e s c r i b e s t h e d a t a a n d i t s p r e p a r a t i o n . S e c t i o n 111 s h o w s t h e m o d e l ' s e q u a t i o n s f o r e a c h o f t h e f i n a l demand components, l a b o r p r o d u c t i v i t y and i n p u t - o u t p u t c o e f f i c i e n t change. S e c t i o n I V e x p l a i n s t h e s p e c i f i c assumptions used i n t h e model and t h e r e s u l t s o f t h e f o r e c a s t .
I. MODEL STRUCTURE
The m a j o r p a r t s o f t h e model a r e shown i n F i g u r e 1. A l s o shown a r e t h e p r i n c i p a l f u n c t i o n a l c o n n e c t i o n s i n t h e model. The c e n t e r b l o c k i s t h e i n p u t - o u t p u t t a b l e where some f i f t y - o n e i n d u s t r i e s a r e d i s t i n g u i s h e d . T h i s c e n t e r b l o c k shows t h e s a l e s o f each s e c t o r t o each o f t h e o t h e r s .
On t h e r i g h t - h a n d s i d e i s t h e f i n a l demand b l o c k , w h i c h shows t h e p r o j e c t i o n o f 46 t y p e s o f consumer e x p e n d i t u r e , e q u i p m e n t i n v e s t m e n t f o r
F I G U R E 1. T h e M o d e l
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I N F O R E I G N CURRENCY
3 4 - i n d u s t r i e s ( a g g r e g a t e s o f t h e 511, t h e c o n s t r u c t i o n i n v e s t m e n t f o r t h e s e same 3 4 i n d u s t r i e s p l u s r e s i d e n t i a l c o n s t r u c t i o n . I n v e n t o r y investment, e x p o r t s and imports, and government purchases f o r each o f t h e 51 s e c t o r s a r e a l s o e s t i m a t e d .
To t h e l e f t o f t h e c e n t e r b l o c k a r e t h e s e c t o r o u t p u t s . The outputs, o f course, a r e t h e sum o f a l l s a l e s i n c l u d i n g t h e n e g a t i v e s a l e s i m p o r t s ; h e n c e p r o d u c t i o n h e r e i s d o m e s t i c o u t p u t . P r o d u c t i v i t y a n d e m p l o y m e n t f o r 3 8 d i f f e r e n t i n d u s t r i e s a r e d i s t i n g u i s h e d h e r e ( a g a i n a g g r e g a t e s o f t h e 51 s e c t o r s ) .
E s t i m a t e s o f t h e l a b o r f o r c e , p e r c a p i t a d i s p o s a b l e income, t o t a l government spending, f o r e i g n demand f o r German goods, t h e p r i c e o f f o r e i g n c u r r e n c y ( e x c h a n g e r a t e ) and r e l a t i v e p r i c e trends, a r e a l l exogenous i n t h e model a t t h i s time. I n Secton IV, w h e r e a f o r e c a s t r e s u l t i s shown, t h e r e w i l l be more d i s c u s s i o n o f t h e exogenous assumptions.
P e r h a p s t h e m o s t i m p o r t a n t element i n t h e s t r u c t u r e o f t h e model i s n o t v i s i b l e i n F i g u r e 1, e.g. t h e numerous ways i n u h i c h i t i s p o s s i b l e f o r t h e u s e r t o i n t e r v e n e i n i t s w o r k i n g s . I t i s e a s y t o m o d i f y o r o v e r r i d e t h e o u t p u t o f any b e h a v o r i a l e q u a t i o n i n t h e m o d e l : one c a n a d d t o w h a t t h e e q u a t i o n p r o d u c e s ; m u l t i p l y b y what i t p r o d u c e s , o r s i m p l y r e p l a c e t h e e q u a t i o n a l t o g e t h e r . Thus, t h e model i s n o t j u s t a f o r e c a s t i n g model, b u t i s designed f r o m t h e s t a r t t o make p o l i c y a n a l y s i s easy.
The Model i n M o t i o n
The b e s t way t o u n d e r s t a n d t h e i n t e r w o r k i n g s o f t h e model i s t o f o l l o w i t t h r o u g h t h e f o r e c a s t i n g o f one year.
We b e g i n w i t h a s s u m p t i o n s f o r t h e p o p u l a t i o n a n d r e a l p e r c a p i t a d i s p o s a b l e income. The p e r s o n a l c o n s u m p t i o n e x p e n d i t u r e e q u a t i o n s u s e t h e
above assumptions, t o g e t h e r w i t h r e l a t i v e p r i c e trends, t o p r e d i c t e x p e n d i t u r e b y consumer c a t e g o r y . A b r i d g e m a t r i x w i 11 l a t e r t r a n s f e r these demands by consumer category, i.e. b u t t e r , i n t o demands f o r t h e p r o d u c t s , i .e. d a i r y p r o d u c t s , i n t h e i n p u t - o u t p u t t a b l e . Next, government demands by p r o d u c t a r e c a l c u l a t e d . A c o n s t a n t s t r u c t u r e o f government spending i s assumed.
Next we use p r o j e c t f o r e i g n demands (some d e r i v e d from o t h e r models, e.g.
France, U.S.A., Belgium and Canada; some by assumpt i on, e.g. N e t h e r lands, I t a l y and U.K.) and p r o j e c t e d t r e n d s i n domestic t o f o r e i g n p r i c e r a t i o s by product, i n o r d e r t o c a l c u l a t e t h e demand f o r e x p o r t s by i n p u t - o u t p u t s e c t o r . F o r e i g n demands and r e l a t i v e G e r m a n - t o - f o r e i g n p r i c e t r e n d s a r e u s e d t o produce e x p o r t s by i n p u t - o u t p u t category.
Investment f u n c t i o n s g e n e r a t e equipment and c o n s t r u c t i o n i n v e s t m e n t o n t h e b a s i s o f p a s t and p r e s e n t changes i n output. There a r e e q u a t i o n s r e l a t i n g i m p o r t s t o d o m e s t i c demand and r e l a t i v e foreign-to-domestic p r i c e s . Other e q u a t i o n s e x i s t t o c a l c u l a t e i n v e n t o r y change b y p r o d u c t e m p l o y i ng d o m e s t i c use and s t o c k s o f i n v e n t o r y o f t h e products.
The f i n a l demand p r o j e c t i o n s a r e of g r e a t i n t e r e s t , p a r t i c u l a r l y s i n c e t h e y have a g r e a t e f f e c t on i n d u s t r i a l s t r u c t u r e .
When t h e f i n a l demands a r e ready, we t h e n u s e t h e p r o j e c t e d d i r e c t 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 i n p u t s o f each p r o d u c t r e q u i r e d t o produce one u n i t o f output. When t h e s e a r e ready, we b e g i n t h e s o l u t i o n p r o c e d u r e known a s t h e S e i d e l Loop. Here, consumer demand f o r autos i s c o n v e r t e d i n t o demand f o r steel, s t e e l i n t o m i n i n g , and m i n i n g i n t o g a s o l i n e , e t c . T h i s c o n t i n u e s u n t i 1 a1 l demands f o r a t l products, d i r e c t l y o r i n d i r e c t l y r e q u i r e d t o make t h e f i n a l goods, have been accounted f o r . Note t h a t t h i s process doesn o t c a l l f o r m a t r i c i n v e r s i o n . _At no ti_m_e.-_d_o-_w_e_j_n_v_ey_t-_a-_m_a_trI_x-i_n-J_h_e- s o l u t i o n erocedure. I t i s a l s o t o be noted t h a t t h e whole process needs t o be
--- ---
repeated due t o t h e dependence o f i n v e s t m e n t and c o n s t r u c t i o n s p e n d i n g on c u r r e n t o u t p u t . The e x t e n t o f t h i s dependence i s r e l a t i v e l y s m a l l and t h e r e f o r e we o n l y need t o r e p e a t t h e p r o c e s s t w i c e . A t h i r d c y c l e was performed b u t found t o be unnecessary and i s no l o n g e r performed
P r o d u c t o u t p u t s a r e now r e a d y a n d we a r e p r e p a r e d t o c a l c u l a t e employment. Labor requirements p e r u n i t o f o u t p u t a r e c a l c u l a t e d on t h e b a s i s o f t h e l e v e l o f output, i t s change and trends. We t h e n m u l t i p l y by o u t p u t t o g e t e m p l o y m e n t . I n d u s t r y employment i s t h e n c a l c u l a t e d and t h e r e s u l t
compared w i t h t h a t o f t h e l a b o r f o r c e . The d i f f e r e n c e b e t w e e n t h e two, unemployment, i s t h e n s c r u t i n i z e d . I f t h i s f i g u r e i s u n r e a l i s t i c a l l y low, t h e n p e r c a p i t a d i s p o s a b l e income, g o v e r n m e n t s p e n d i ng, and t h e p r i c e o f f o r e i g n c u r r e n c y a r e e x a m i n e d and r e v i s e d , i n o r d e r t o p r o d u c e a l a r g e r economy, t h u s c r e a t i n g more employment.
11. DATA
The Economic Research I n s t i t u t e f o r R h i n e l a n d - W e s t f a l i a i n Essen, F.R.G., p r e p a r e d i n p u t - o u t p u t t a b l e s i n c u r r e n t and 1970 p r i c e s f o r t h e y e a r s 1962-1975 ( R W I , 1 9 7 9 ) . These d a t a were t h e p r i m a r y source o f most o f t h e c a l c u l a t i o n s . Employment and i n v e s t m e n t by i n d u s t r y d a t a came f rom d e t a i l e d n a t i o n a l accounts ( S t a t i s t i s c h e s Bundesamt, 1980). The investment m a t r i x was d r a w n f r o m a 1 9 7 2 m a t r i x p r e p a r e d b y t h e German I n s t i t u t e f o r E c o n o m i c R e s e a r c h i n B e r l i n (Baumgart, 1 9 7 6 ) . Only m o d i f i c a t i o n s t o t h e above d a t a base w i l l be d i s c u s s e d below.
Only minor changes t o t h e R W I t a b l e s were made:
(1) Most o f t h e government s a l e s were moved f r o m i n t e r m e d i a t e t o f i n a l demand s a l e s . O n l y g o v e r n m e n t p r o d u c t i o n necessary t o supply t h e government's s a l e s t o p r i v a t e c o n s u m p t i o n ( p r e s u m a b l y g o v e r n m e n t
p u b l i c a t i o n s such as maps, s t a t i s t i c a l yearbooks, etc.) were l e f t i n t h e i n t e r m e d i a t e column.
( 2 ) Row 5 1 c o n t a i n s i n v e s t m e n t s u b s i d i e s . I t h a s n o c o l u m n o r row i n t e r m e d i a t e e n t r i e s .
( 3 ) I m p o r t s were t r e a t e d as a f i n a l demand c o l u m n o f n e g a t i v e e n t r i e s . Thus, t h e row sums a r e now domestic p r o d u c t i o n .
( 4 ) The R W I row f o r secondary p r o d u c t i on (Kuppleprodukt i on) was a 1 lo c a t e d b a c k t o t h e p r i m a r y s e c t o r . A new sector, Row 50, c o n t a i n s domestic p r o d u c t i o n o f n a t u r a l gas, w h i c h i s a p r o d u c e d i n Germany a s a b y p r o d u c t o f o t h e r processes.
The sum o f t h e i n d u s t r y i n v e s t m e n t d i d n o t m a t c h t h e t o t a l equipment investment. The d i f f e r e n c e , a p p r o x i m a t e l y one percent, was due t o some s l i g h t s t a t i s t i c a l d e f i n i t i o n a l d i f f e r e n c e s and probably, l a t e r , t o r e v i s i o n s i n t h e n a t i o n a l a c c o u n t s data. The d i f f e r e n c e s , however, were small.
The i n v e s t m e n t m a t r i x , o n t h e o t h e r hand, had many, more s u b s t a n t i a l , d i f f e r e n c e s . The D I W m a t r i x c o n t a i n e d f l o w s f o r c o n s t r u c t i o n w h i l e o n l y f l o w s o f i n v e s t m e n t goods were d e s i r e d . Matches were made b e t w e e n t h e 57 b r a n c h e s o f t h e D I W and t h e i n p u t - o u t p u t rows o f t h e R W I t a b l e . Matches were a l s o made between t h e D I W m a t r i x and t h e d e t a i l e d n a t i o n a l a c c o u n t s s e r i e s o f i n v e s t m e n t b y p u r c h a s e r . S t a r t i n g w i t h t h e D I W matrix, we produced an i n v e s t m e n t m a t r i x which showed t h e n a t i o n a l account i n d u s t r i e s as columns and t h e R W I s e c t o r s as rows. A R A S p r o c e d u r e was u s e d t o e n s u r e c o m p a t i b i li t y . ' r h i s i s a n a r e a where f u r t h e r work needs t o be done.
111. EQUATION FORMULATION AND ESTIMATION A. P e r s o n a l Consumption E x p e n d i t u r e s
T h e r e a r e numerous forms o f consumption f u n c t i o n s i n e x i s t e n c e . For use
i n i n p u t - o u t p u t work, one o f t h e most u s e f u l forms i s t h a t developed b y Almon (1979) which has t h e f o l l o w i n g m a j o r p r o p e r t i e s :
-
homogeni t y o f degree z e r o i n a l l p r i c e s and income-
c o m m o d i t i e s s h o u l d be c o m p l e m e n t s f o r some goods and s u b s t i t u t e s f o r o t h e r s .-
a s y m p t o t i c c o n s u m p t i o n p a t t e r n depends, a s i n c o m e i n c r e a s e s , o n r e l a t i v e p r i c e s . The system r e q u i r e s t h a t we l i s t our commodities by g r o u p and subgroup, i.e.Groue
----
T r a n s p o r t a t i o n Food
Subgroue
--- ---
Public, P r i v a t e P r o t e i n , n o n - p r o t e i n, Beverages, Tobacco
The form of t h e e q u a t i o n f o r good i i n g r o u p G and subgroup S i s :
Ci = Cbli
+
b . t+
b+
b 4 i ~ ( y / p ) l 2 1 3 1where
Ci = consumption p e r c a p i t a i n c o n s t a n t p r i c e s o f good i i n y e a r t y = d i s p o s a b l e income p e r c a p i t a i n c u r r e n t p r i c e s i n y e a r t P i = t h e p r i c e i n d e x o f good i y e a r t.
-
l i n Sj
= a l l j P j
where s i s t h e budget s h a r e o f commodity j i n t h e base year, and j
and b ' s and ' s a r e p a r a m e t e r s t o be e s t i m a t e d s t a t i s t i c a l l y .
N o t e t h a t b 3 was n o t e s t i m a t e d b u t r a t h e r , e c o n o m e t r i c a l l y , we f i r s t e s t i m a t e d t h e income e l a s t i c i t y o f each p r o d u c t . Since t h e b ' s a r e d i r e c t l y
3
o b t a i n a b l e f r o m t h e i n d i v i d u a l e l a s t i c i t y e s t i m a t e s ( e l a s t i c i t y
-
-
= b3c
Y 1, we t h e n summed t h e b ' s t o s e e how c l o s e we w e r e t o t h eay
c
3c o r r e c t t o t a l e x p e n d i t u r e i n 1975 ( t h e base y e a r ) . Since o u r sum was low, a l l o f o u r i n d i v i d u a l e s t i m a t e s o f b were s c a l e d upwards by 11 p e r c e n t i n o r d e r
3
t o match t h e c o r r e c t t o t a l s p e n d i n g r a t e . Why s h o u l d we r e s o r t t o s u c h a method when e m p i r i c a l e s t i m a t i o n i s so obvious? Two reasons b o t h econometric, a r e p u t f o r w a r d . The f i r s t i s t h a t i n c o m e a n d t i m e a r e g e n e r a l l y v e r y c o l i n e a r and hence we would have s i g n i f i c a n t problems i n p i n p o i n t i n g t h e e x a c t e f f e c t s o f each. The second i s t h a t income development p l a y s a m a j o r r o l e i n f o r e c a s t i n g . However, t h e l e v e l o f income encountered i n t h e f o r e c a s t was never e x p e r i e n c e d i n t h e past. Hence we c o u l d e s t i m a t e income p a r a m e t e r s t h a t f i t w e l l h i s t o r i c a l l y , b u t f o r e c a s t p o o r l y . Our " h a n d - p i c k e d " c o e f f i c i e n t s c o u l d c e r t a i n l y be improved b y r e f e r r i n g them t o c r o s s - s e c t i o n d a t a where much g r e a t e r ranges o f income c o u l d be s t u d i e d . That work must be l e f t t o o t h e r s .
I t i s a p r o p e r t y o f t h e s e f u n c t i o n s t h a t t h e e l a s t i c i t i e s w i t h r e s p e c t t o o f t h e demand f o r a l l goods n o t i n t h e same g r o u p w i t h i a r e t h e same, s a y
ni L i k e w i s e , t h e e l a s t i c i t i e s w i t h r e s p e c t t o p o f a l l o t h e r goods i n t h e i same s u b g r o u p w i t h p r o d u c t i a r e t h e same, s a y ni, S a s a r e a l l t h e e l a s t i c i t i e s w i t h i n t h e same g r o u p b u t n o t i n t h e subgroup ( i f any), say ni. 9
F i n a l l y , t h e e l a s t i c i t y o f i t s own p r i c e i s d i f f e r e n t . The s t a t i s t i c a l
e s t i m a t e s o f t h e s e t h r e e o r f o u r e l a s t i c i t i e s (depending o n whether o r n o t a g r o u p h a s s u b g r o u p s ) a r e shown i n T a b l e 1, w h i c h a l s o shows t h e i n c o m e e l a s t i c i t i e s , t h e t i m e c o e f f i c i e n t s (a 1 as a p e r c e n t a g e o f t h e v a l u e o f Ci i n
2
t h e l a s t y e a r o f data, t h e average a b s o l u t e p e r c e n t a g e e r r o r (AAPE), and t h e a u t o c o r r e l a t i o n o f t h e r e s i d u a l s (RHO). The p r i c e e l a s t i c i t i e s shown i n t h e t a b l e m u s t be r e a d i n t h e f o l l o w i n g way. The f i r s t , l a b e l e d "own" i s t h e e l a s t i c i t y o f a commodity's demand w i t h r e s p e c t t o i t s own p r i c e . The n e x t ,
l a b e l e d " g r o u p " i s t h e e l a s t i c i t y o f t h e demand f o r o t h e r i t e m s i n t h e same g r o u p
--
b u t n o t i n t h e same subgroup--
w i t h r e s p e c t t o t h e commodity p r i c e . The t h i r d e l a s t i c i t y , t h e one l a b e l e d "subgroup" i s t h e e l a s t i c i t y of o t h e r i t e m s i n t h e s u b g r o u p w i t h r e s p e c t t o t h e c o m m o d i t y ' s p r i c e . A p o s i t i v e ( n e g a t i v e ) v a l u e o f g r o u p o r s u b g r o u p e l a s t i c i t y i n d i c a t e s s u b s t i t u t i o n ( c o m p l e m e n t a r i t y ) u i t h i n g r o u p o r subgroup. The f o u r t h e l a s t i c i t y , l a b e l e d" g e n e r a l " , shows t h e e l a s t i c i t y o f a l l o t h e r commodities w i t h r e s p e c t t o t h e commodity's p r i ce.
The Food g r o u p i l l u s t r a t e s t h e w o r k i n g o f t h e s y s t e m . A1 1 i t e m s w e r e s u b s t i t u t e s . I n t h e B e v e r a g e s and Tobacco subgroup, however, t h e i t e m s a r e complements t o each o t h e r .
B. I n v e s t m e n t and C o n s t r u c t i o n E q u a t i o n s
I n v e s t m e n t d a t a f o r 34 i n d u s t r i e s , s e p a r a t i n g p l a n t and equipment, e n a b l e us t o s t u d y t h e e s s e n t i a l s o f i n v e s t m e n t behavior; t h e c a p i t a l o u t p u t r a t i o and t h e p a t t e r n o f t h e l a g between i n c r e a s e s i n o u t p u t s and t h e i n c r e a s e i n c a p i t a l s t o c k t h e y s t i m u l a t e .
The i n v e s t m e n t e q u a t i o n f o r m u l a t e s g r o s s i n v e s t m e n t o n t h e sum o f replacement p l u s e x p a n s i o n i n v e s t m e n t .
TABLE 1.
C s o c l c r s u b s r a u c c c r m o d i t y f l ~ i i c k r - u i r o n f i : c h , - u a r e n e i c - r
m i l c h , k a s s e b u t t e r s p c i s r f e t t e b r c l r h a c k r a r e r k r r t o f f r l n y e n u e s d o h s t z u c k e r
s o r s t . n a n r u n g s r i t t o 1 a l k o n o l f r . 5 e t r r e n k e k r f f e o , t e e
a l t o h o l . g e t r a a n k e t e t a k u a r e n
O s e c t c r S u b g r o u p c c r m o d i t y k l o i d u n g s c t u h e
m i e t q n e l e k t r i z i t z s t y 2 5
koP l e n h e i r o r l
i s e c t o r s u b g r o u p c o n m o d ~ t y
f 0 0 4 t i r e i n 1 o f l a s t y r .
-1.6 -1 .L -2.1 1 . 2 -5.5 -0.e 1 . 2 - 2 . 1 0.7 -1.4.
.
o.e1 . 2 1 . 2 -0.1 -1.2 1.4
o r n -C .703 -C.977 -0.874 -0.929 -C .932 -C.934 - C . 839 -C.965 -0.924 -0.920 - C . 900 -C .934 - C . 458 -C.447 -0.535 -C.481
e 1 a : t i c i t i e s s c b g r c u o g e n n r s l
C.194 0.020
C.ClC 0.001
0.01? 0.001
0.C5F 0.006
C.C22 0.0'32
C.C2C 0.002
0 . 1 1 5 0.C10 C . C C F O.CO1
C.O!C O.CO3
C.O!4 0.003
C.054 0.005
C.02C 0 . 0 0 2
-.O?C 0.004
-.GI9 0.002
-.lC7 0.014
-.053 0.007
c l o t h i n g
i n c o m e t i m s i n X p r i c e e l a s t i c i t i e s elasticity o f l a s t y r . o u n s r o u p s u b g r o u p g e n e r a l
1 . C O O -0.4 -C.231 -0.232 0.028
o . e e 9 -3.2 -0.036 -c.037 0.004
h o u s i n g
i n c o i e t i m e ~ n X p r i c e e l a s t i c i t i e s e l a s t i c i t y o f l a s t y r . omn g r o u p s u b g r o u p g e n e r a l
1.111 0.1 -C.257 C.011 0.034
1.445 0. .! -0.206 0 . 0 9 2
-
0.0061.556 0.4 -C.267 C.OC1 0.002
0 . -21. e - C . Z ~ S C . O C O 0.001
0.667 1.4 -C.267 C.OC1 0.004
z z p e r h o
c s p e r h o
~ P P Q r h o
home ~ o o d s & s e r v i
i n c o m e t i m e i n X p r i c e e l a s t i c i t i e s ? c u e r h o e l a s t i c i t y o f l a s t y r . o u n g r o u p s u b f r o u p s e n e r a 1
1 . 1 1 1 -0.2 -C.7.51 C.EL1 O.12E 0 . J 1 8 2.4 0.29
1 . e 8 9 -2.t -C.b38 C.34e 0.C51 0.007 1 . 9 0.47
0 . - a m c ban
L u u o
. . .
N r W a
. . .
r(
CrNP-rnrn*>
L . - O U O O O O O O O U C . . . m O O o O O
"lo m
r(
Q L U w m o o
c q o 0
-
m 0 0 O
* e
C a
..
3r(
S n n * N N Y I L ' 3 C I O Q O c Y a 0 0 0 0 0 0
c . . .
0 0 0 0 C 0 0 m m
O
n ~ ~r u
0 0 3 0 0
o o q
. .
'3 20 0 0 0 0
r a
- 3
U O v m U v Q
." L U h U . - ' , C 0.-orb-.-
" l a . . . - 3 1 I I O U r( "3
N Y O N V I N C O N.- 0 0 -
. . .
- 0 0 0 1 1 1m o a Q Y I U N h U N
r r - N O O U U
. . .
U U * O O N m a a n U J W U L L . . a m o uI I
L L . .
.
a 0 u u v
C h m P - o n a h . - n e e o o o o * P -
. . .
C
U U U U O O . r ) I t I I I C
cl-8- a w e
O O r 0 0
. .
I I
k P L C u W O O
u n a w
where
V = g r o s s i n v e s t m e n t
g
=
replacement c a p i t a l s t o c k r a t i o s k = c a p i t a l o u t p u t r a t i ow
=
Lag w e i g h t-
iQ t
=
smoothed o u t p u t = .5 t +3Qtel+
2Qt-2I n t h e f i r s t term, k t t approximates t h e c u r r e n t c a p i t a l s t o c k and g i s t h e r a t e o f i t s replacement. I n t h e s e c o n d t e r m kAQt shows t h e amount o f c a p i t a l needed t o accommodate t h e o u t p u t expansion i n year t and wi shows t h e f r a c t i o n o f t h a t c a p i t a l bought i n t h e ith year a f t e r t.
We c o n s t r a i n t h e sum o f t h e Lag w e i g h t , sims, t o u n i t y b y s e t t i n g 1
w 2 = l - C w Thus, t h e a c t u a l r e g r e s s i o n e q u a t i o n e s t i m a t e d i s i =O i '
H e r e we must r e i t e r a t e t h a t we a r e o n l y t r y i n g t o g e t t h e e s s e n t i a l s and t h a t t h e f i t s of t h e r e g r e s s i o n e q u a t i o n s c o u l d be improved.
Table 2 shows t h e r e s u l t s f o r equipment i n v e s t m e n t . T a b l e 3 shows t h e r e s u l t s f o r p l a n t ( c o n s t r u c t i o n ) investment.
The c o l u m n s o f t h e t a b l e s show t h e r e s u l t s f o r each equation. Most a r e c l e a r
--
column " r h o " i s t h e a u t o c o r r e l a t i o n c o e f f i c i e n t and t h e c o l u m n"AAPE" i s t h e annual average percentage e r r o r . The f i t s were remarkably good.
Only f i v e o f t h e 34 i n d u s t r i e s had AAPS1s above 25 percent; most were near 10 percent. Many o f t h e c a p i t a l o u t p u t r a t i o s were c o n f u s i n g
--
why t h a t o f I r o n and s t e e l ( 1 2 ) i s s o Low and t h a t O f f i c e m a c h i n e s (14) so high, we cannot e x p l a i n . Resident i a l c o n s t r u c t i o n is, a t present, exogenous.m
. . .
~ o a ~ o m o ~ m a ~ ~ m ~ m ~ - m m ~ o ~ ~ ~ m u ~ m O ~ r ' l b O - N m N m ~ N ( r m m m 9 a - O ( r N 9 h F u m O ( r ( r N m m 9 9N N N U N - N r ' l r r r q r N 9 7 r ' l - r r N - r ' l r'l r r r
0 N 0 0 9. r'l O * mo.
b 0 7 e W 0 N N e b
N N F N 0 N N N 7 -
m . . .
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
u m a . r ( c a - r( n a a G u m 0
Y ) O L O @ J L Q W L L C X d 4 4
C * 10 m a 0 > J a 8 0 d 9 ) J U l n * C
L I L Q d Q J C Q l Q X O C C 3 3 C 4 L H 10
4 9 ) C P C O 9 ) H N - i \ J J a 9) a . 4 L W C H 3 d > 3 \ O N J C L L C X C O I O L I C R O Q ~ L > d -4 d x - L m + r r r . c ( . 4 3 c ~ m m n u .4 C
H + 4 - 4 - @ d Z m m U C d W 3 W O O L 1 0 U Q 10
~4 o r E m d . 4 c U - v - Q m c n ~ .r0( 3 c c m c c a
a o m c C T Q L L O ~ ~ ~\ J~~ LI L W
L C ~ Q ~ O U L ~ W L Q L ~ ~o Uo L ~ ~
9 ) E m L L w m a L at ~ 4 . > 4~ c~ c r u d m d r o m + ~E 3 n o x L - I W Q X W a @ . - ( + +
~ C U mLm r c ~ . c ( u a + c ( m m m u r a m m >
O n l W a L l w . d E c ( P L u X X C n J C L W C 1 0 . 4
. d + m ~ + - ~ w n o m ~ w w w ~ m m m ~ ~ ~ + ~
O H E n m C w + . a l C a Q c ( + n Q w n z > Y H u l a
N r l
7 N
m N
. .
O C I
D
m - N ~ Q ~ ~ O O - m em m
m N O O r ' l 0 U 0 m 0 r ' l ~ m h U 9 9 U r ' l U 4 U ~ r ' l r ' l N Ur'l
. . .
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 L C c o r n
C. F o r e i g n Trade E q u a t i o n s Merchandise I m p o r t s
The e q u a t i o n g i v e n below i s s i m i l a r t o t h a t used f o r t h e U.S.A., Canada, F r a n c e and B e l g i u m . O n l y a b r i e f e x p l a n a t i o n and t h e e m p i r i c a l r e s u l t s a r e g i v e n here.
'The e q u a t i o n f o r m f o r e a c h c o m m o d i t y ( d r o p p i n g c o m m o d i t y a n d t i m e s u b s c r i p t s ) i s :
where
M i s t h e volume o f i m p o r t s o f t h e commodity
U i s t h e d o m e s t i c demand
-
o u t p u t+
i m p o r t s-
e x p o r t s P i s t h e p r i c e t e r mwhere
- 9
-
E = f o r e i g n p r i c e 'fm 5 l
'm 'dm mwhere
Pdm i s t h e d o m e s t i c p r i c e i n d e x i n c o u n t r y m.
s is t h e s h a r e o f i m p o r t s f r o m c o u n t r y m o f t o t a l i m p o r t s o f t h e m
commodity
E i s an i n d e x o f t h e p r i c e o f m's c u r r e n c y i n DM m
Pd i s t h e d o m e s t i c p r i c e i n d e x o f t h e commodity i n t h e FRG
m = Canada, U.S.A., Japan, Belgium, France, I t a l y , N e t h e r l a n d s , U.K., and t h e Rest o f t h e World
w's a r e w e i g h t s f o r Lagged p r i c e s . The w e i g h t s a r e d e r i v e d f r o m Nyhus (1975)
.
Where e s t i m a t e s o f t h e c o e f f i c i e n t b were negative, a t i m e t r e n d e q u a t i o n was estimated. I t s f o r m i s
knM = a
+
b t i m e+
cP (9I n e s t i m a t i n g t h e p r i c e parameter n, we s t a r t e d w i t h a n a p r i o r i v a l u e and t h e n maximized t h e f o l l o w i n g u t i l i t y f u n c t i o n .
-2 I n
-
apri1 1
U = R-
.05I I
apri11
T a b l e 4 shows t h e r e s u l t s o f t h e e s t i m a t i o n . One can see t h a t o u r a p r i o r i e s t i m a t e s were sometimes a c c e p t e d and sometimes r e j e c t e d . The demand e l a s t i c i t y i s f o r t h e y e a r 1 9 7 5 o n l y , a n d i s n o t a n average f o r t h e whole p e r i o d . Assuming t h a t d o m e s t i c demand grows, t h e f o r m o f t h e e q u a t i o n has t h e p r o p e r t y t h a t t h e p o i n t e l a s t i c i t i e s o f demand t e n d t o w a r d u n i t y w i t h t h e i m p o r t f r a c t i o n o f d o m e s t i c demand b e i n g t h e c o e f f i c i e n t b. U s i n g 1975 weights, t h e a g g r e g a t e p r i c e e l a s t i c i t y was -.94 and t h e a g g r e g a t e demand e l a s t i c i t y was 1.30.
Merchandise E x p o r t s
The f o r m o f t h e e q u a t i o n i s i d e n t i c a l b u t t h e meaning o f t h e v a r i a b l e s i s d i f f e r e n t .
-
- 4 - 3 L O C Y
m c c C K . 4
0 W P r J d L U C
u w ..I L C - L r J c l r J C
C . ~ ~ J ~ O C J L ~ C W
a n
> ffi ...Iu A
Y e m m c
.-I G P I * a l + . O C tno
C U 0
+ U
m e tno
m
I1 4
e
CI
u l 0
+ u
C 0 L
a a
X
a
Y
C .-I
where
X i s t h e volume o f e x p o r t s o f a commodity D i s an i n d e x o f f o r e i g n demands d e f i n e d by:
where
I
i s t h e i n d u s t r i a l p r o d u c t i o n index o f c o u n t r y m and mv i s t h e share o f t h e t o t a l e x p o r t s g o i n g t o c o u n t r y m.
m
m i s Canada, U.S.A., Japan, Belgium, France, I t a l y , N e t h e r l a n d s , U.K., and Rest of t h e World.
where
P i s t h e domestic p r i c e i n d e x i n t h e FRG d
Pf i s an i n d e x o f c o m p e t i t o r s p r i c e s d e f i n e d by:
where
'dm i s t h e domestic p r i c e i n d e x o f t h e commodi t y i n c o u n t r y m Em i s t h e p r i c e o f m's c u r r e n c y
n m
~ o o ~ ~ a a ~ o r c u ~ ~ ~ ~ ~ ~ ~ n r n ~ ~
n i r n r 9 m O m ~ - u r m m a m a a h a a w
n m W 9 m m Q m 6 W W W m m 6 - a m O I W W - m
L . . . . . . . . . . . . . . . . . . . . . .
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Y Y Y Y Y Y Y Y Y Y Y Y Y
0 hnp,
. .
rr,.-urn
r u b I
-
I 0 r . l IY Y Y
0 0 0
m o o
Q Q C C
4 - U Q O
a r c u m 4
" l .
. .
C C I u 0 I N
-
30 07
a M
X
a
7 0 . F f . l
6 CI M 0
n m n u n a n m n
u
.-
. a . O . ah r N N C I M I C I U 0 . N . N . O . u
.
0. U O N U N
N - r F
Y Y Y Y Y Y Y Y Y
Y Y Y Y
~ -
L l n U ) m L
a m m o
E O 3 A
u i s t h e share o f w o r l d e x p o r t s o f t h e commodity by c o u n t r y m.
m
As w i t h m e r c h a n d i s e i m p o r t s , h e r e we u s e d an a p r i o r i e s t i m a t e o f t h e p r i c e e l a s t i c i t y n. The e s t i m a t i o n r e s u l t s a p p e a r i n T a b l e 5. T h e a g g r e g a t e e x p o r t p r i c e e l a s t i c i t y , u s i n g 1975 e x p o r t s a s weights, i s e s t i m a t e d t o be -.92 and t h e average demand e l a s t i c i t y t o be 1.38.
Nonmerchandi se Trade E q u a t i o n s
T r a n s p o r t a t i o n a n d s e r v i c e e x p o r t s and i m p o r t s were r e l a t e d v e r y s i m p l y as f o l l o w s :
where
Vik i s t h e f l o w o f e x p o r t s ( k = l ) o r i m p o r t (k=2) f o r a g i v e n y e a r Sk i s t h e merchandise t o t a l f o r e x p o r t s ( k = l ) o r i m p o r t s (k=2).
T a b l e 6 g i v e s a summary o f t h e r e s u l t s .
D. P r o d u c t i v i t y E q u a t i o n s
The e q u a t i o n f o r l a b o r p r o d u c t i v i t y f o r e a c h o f 3 8 i n d u s t r i e s i s f o r m u l a t e d t o show t h e e f f e c t s o f t e c h n o l o g i c a l c h a n g e a n d g r o w t h i n t h e economy. The f o r m i s
Log (E/Q) = bo + blt
+
b2Q (16)where
E = l e v e l o f employment i n an i n d u s t r y i n man y e a r s . Q = o u t p u t o f t h a t same i n d u s t r y .
The c o e f f i c i e n t bl r e p r e s e n t s t e c h n o l o g i c a l change and b t h e s i z e o f t h e 2
economy. Because o f h i g h c o l l i n e a r i t y between t i m e and o u t p u t , t h e v a l i d i t y
. . .
3 O Q m u J F 0 u ~ 0 0 0 d m m + 9 h . r b O Icu
m - m m a a - u - F l n
> F a J - o . r l F m
O ? + + r . 7 O m U I U -
C + - m b + u - - C r CY
. . .
O C O O O O O O C O O I
o f t h e d i s t i n c t i o n i s s o m e t i m e s i n doubt. An a l t e r n a t i v e i n t e r p r e t a t i o n i s t h a t Q i s r e a l l y a p r o x y f o r c a p i t a l a c c u m u l a t i o n . Hence, b may b e
2
i n t e r p r e t e d w i t h t h i s a s s u m p t i o n a s t h e e f f e c t o f c a p i t a l a c c u m u l a t i o n on p r o d u c t i v i t y .
T a b l e 7 shows t h e r e s u l t s o f t h e e s t i m a t i o n . The n e g a t i v e o f t h e c o l u m n
" t i m e " shows t h e p e r c e n t p e r y e a r of exogenous l a b o r p r o d u c t i v i t y growth. The c o l u m n " o u t p u t L e v e l " shows t h e c o e f f i c i e n t b2, t h e n e g a t i v e o f which shows t h e percentage change i n p r o d u c t i v i t y a s s o c i a t e d w i t h a one p e r c e n t c h a n g e i n o u t p u t . Thus, f o r A g r i c u l t u r e ( s e c t o r 1) we show an exogenous g r o w t h of 4.6 p e r c e n t p e r y e a r and a 1.05 p e r c e n t g r o w t h f o r each one p e r c e n t g r o w t h i n t h e
l e v e l o f o u t p u t . The l a s t column, e m p l o y m e n t l e v e l , shows t h e r e l a t i v e i m p o r t a n c e of employment o f each i n d u s t r y i n t h e German economy.
E.
C o e f f i c i e n t ChangeChanges i n 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 c r u c i a l t o any m e a n i n g f u l s t u d y o f s t r u c t u r a l c h a n g e i n a n economy. The method chosen h e r e i s d e s i g n e d t o account f o r w i d e - s p r e a d , p e r v a s i v e c o e f f i c i e n t change i n a r a t h e r s i m p l e manner.
A l o g i s t i c c u r v e d e f i n e d by t h e d i f f e r e n t i a l e q u a t i o n
i s used. "c" d e n o t e s t h e c o e f f i c i e n t , "a" i t s asymptote a n d "b" a c o n s t a n t . Thus t h e r a t e of change o f t h e c o e f f i c i e n t slows as t h e c o e f f i c i e n t approaches i t s " s a t u r a t i o n " o r as i t n e a r s i t s minimum use p o i n t .
The s o l u t i o n of t h i s d i f f e r e n t i a l e q u a t i o n i s
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~ N O N N N ~ ~ S ~ ~ ~ ~ N @ N N O ~ ~ N ~ N ~ C U F O . ~ O . O ~ O O ~ . O N O I
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a x c . 4 D Z a a c c ~ - r ( . r ( r ~ m
. r ( U O C 4 L r n + ' Q O O U Q t n m a >
P J Q X Y ~ C ~ C ~ C Cc m . 4 O L r g L O b ) m Q a n r g . - I o > L 0 o Y r
a u r l r z ~ ~ r n ~ o W ~ z Ya m a
where A i s a c o n s t a n t o f i n t e g r a t i o n .
To a p p l y o r d i n a r y Least squares t h e e q u a t i o n i s r e a r r a n g e d as f o l l o w s :
an (:t- 1) = Ln A
-
b a t i f - a > 1C -
t
'The f i r s t i s used f o r r i s i n g c o e f f i c i e n t s ; t h e s e c o n d f o r d e c l i n i n g ones.
T h e a p p l i c a t i o n o f t h e a b o v e e q u a t i o n s t o t h e d a t a p r e s e n t s some problems. Time s e r i e s on i n d i v i d u a l c o e f f i c i e n t s do e x i s t , b u t b e c a u s e t h e y w e r e n o t d e r i v e d f r o m b a s i c d a t a b u t r a t h e r f r o m a form o f t h e R A S method, we f e e l t h a t t h e e s t i m a t e s b a s e d o n t h e movements o f i n d i v i d u a l c e l l s o f t h e m a t r i x a r e p r o b a b l y n o t m e a n i n g f u l . T h e r e f o r e , we i n t r o d u c e a new C
i t r e f e r r i n g t o t h e e n t i r e row i as f o l l o w s :
tit
= U i t l V i t I i=1,...,
50.where
'it = a c t u a l i n t e r m e d i a t e use o f commodity i 'it = domestic o u t p u t o f ccmmodity i
'it = i n d i c a t e d u s e i f c o e f f i c i e n t s h a v e r e m a i n e d c o n s t a n t o v e r t h e e n t i r e p e r i o d
a
=
t h e m a t r i x o f d i r e c t c o e f f i c i e n t s f o r 1975 i jt h i t
=
i n d e x f o r t h e movement o f a l l t h e c o e f f i c i e n t s i n t h e i row.T a b l e 8 shows a summary o f t h e r e s u l t s . For each i n d u s t r y we see t h e p r e d i c t e d c o e f f i c i e n t change f o r t h e f i r s t t w o y e a r s o f t h e f o r e c a s t , t h e n t h e change f o r t h e l a s t two years. The e q u a t i o n e n s u r e s t h a t a 1 1 a b s o l u t e r a t e s o f c h a n g e a r e reduced and t h a t t h e d i r e c t i o n o f change i s h e l d c o n s t a n t . The t h i r d column o f n u m b e r s shows t h e f i t o f t h e e q u a t i o n a s i t p r e d i c t s t h e movements i n C
--
o r i n t h e l a s t column--
t h e f i t i n p r e d i t i n g Uit.i t
As we l o o k a t t h e f i r s t t w o columns we see t h a t s e v e r a l r a p i d changes i n t h e f i r s t p e r i o d slow d r a m a t i c a l l y a t t h e end. Gas (3) shows a n i n i t i a l n i n e p e r c e n t i n c r e a s e , b u t t h a t r a t e s f a l l s t o l e s s t h a n one p e r c e n t b y 1990.
P l a s t i c (10) has an i n i t i a l g r o w t h o f 1.5 p e r c e n t p e r y e a r which f a l l s t o l e s s t h a n - 2 p e r c e n t b y 1990.
For s e v e r a l equations, t h e f i t of Cit was v e r y good; f o r o t h e r s , v e r y p o o r . However, i t s h o u l d b e p o i n t e d o u t t h a t a p o o r f i t o f Cit does n o t n e c e s s a r i l y i m p l y a p o o r p r e d i c t i v e power. I n i n s t a n c e s o f s m a l l c o e f f i c i e n t c h a n g e s t h e e q u a t i o n f i t i s p o o r w h i l e t h e use l e v e l i s v e r y good. See, f o r example, S e c t o r s 2, 4, 18, 26, 47, and 48.
I V . A FORECAST
Any f o r e c a s t o f an economy u s i n g an e c o n o m e t r i c m o d e l i s t h e r e s u l t o f j o i n i n g t h e e q u a t i o n s used t o c e r t a i n assumptions. Assumptions may i n t e r a c t , w i t h each o t h e r , a s t h e y d o here, b u t t h e o u t l i n e o f t h e r e s u l t i s s t i 1 1 d e t e r m i n e d b y t h e i n t e r a c t i o n o f a s s u m p t i o n s a n d e q u a t i o n s . S i n c e t h e
