Production Function Estimation With Industry Capacity Data

( N r o B T S P r o d u c t i o n F u n c t i o n E s t i m a t i o n w i t h I n d u s t r y (cid:3) C a p a c i t y D a t a P l u t a r c h o s S a k e l l a r i s U n i v e r s i t y o f M a r y l a n d a n d B o a r d o f G o v e r n o r s o f t h e F e d e r a l R e s e r v e S y s t e m A u g u s t 1 6 , 2 0 0 0 A b s t r a c t T h i s p a p e r i n t r o d u c e s a n e w d a t a s e t f o r t h e a n a l y s i s o f p r o d u c t i v i t y i n U .S . m a n u f a c t u r i n g . I t c o n s i s t s o f d a t a o n p r o d u c t i o n a n d i n p u t l e v e l s w h e n t h e p l a n t s i n a n i n d u s t r y o p e r a t e a t c a p a c i t y . T h e e s t i m a t e s a r e c o n s i s t e n t w i t h t h o s e o b t a i n e d u s i n g d a t a o n a c t u a l o p e r a t i o n s f r o m t h e A S M . A s a n a p p l i c a t i o n , I u s e t h i s d a t a t o e s t i m a t e t h e r a t e o f g r o w t h o f t e c h n o l o g i c a l c h a n g e t h a t i s e m b o d i e d i n e q u i p m e n t c a p i t a l . T h e e s t i m a t e s i m p l y a l a r g e r r o l e o f e q u i p m e n t i n v e s t m e n t a n d e m b o d i e d t e c h n o l o g i c a l c h a n g e o n e c o n o m i c g r o w t h t h a n i s c o n v e n t i o n a l l y a s s u m e d . K e y w o r d s : p r o d u c t i v e c a p a c i t y , c a p a c i t y u t i l i z a t i o n , p r o d u c t i v i t y g r o w t h , e m b o d i e d t e c h o l o g i c a l c h a n g e , p r o d u c t i o n f u n c t i o n . J E L c o d e s : D 2 4 , E 2 2 . (cid:3) D e p a r t m e n t o f E c o n o m ic s , U n iv e r s it y o f M a r y la n d , C o lle g e P a r k , M D 2 0 7 4 2 p l u t a r c h @ e l e c t r a . u m d . e d u ) . I w o u ld lik e t o t h a n k C a r o l C o r r a d o fo r m a n y d is c u s s io n s , o r m a n M o r in a n d C h a r lie G ilb e r t fo r g u id a n c e w it h t h e d a t a , a n d O ja s D e s a i, a n d S u s a n P o la t z f o r e s e a r c h a s s is t a n c e . S o m e o f t h e c a p a c it y d a t a u s e d in t h is p a p e r w e r e c o lle c t e d u n d e r t h e p r o v is io n s f T it le 1 3 U .S . C o d e a n d a r e o n ly a v a ila b le a t t h e C e n t e r fo r E c o n o m ic S t u d ie s ( C E S ) , U .S . C e n s u s u r e a u . T h e r e s e a r c h in t h is p a p e r w a s c o n d u c t e d b y t h e a u t h o r a s a r e s e a r c h a s s o c ia t e a t t h e C E S . h e v ie w s e x p r e s s e d h e r e d o n o t r e p r e s e n t t h o s e o f t h e B o a r d o f G o v e r n o r s o f t h e F e d e r a l R e s e r v e y s t e m , it s s t a (cid:11) , o r t h e U .S . C e n s u s B u r e a u . 1

1 I n t r o d u c t i o n T h i s p a p e r i n t r o d u c e s a n e w d a t a s e t f o r t h e a n a l y s i s o f p r o d u c t i v i t y i n U . S . m a n u f a c t u r i n g . I t c o n s i s t s o f d a t a o n p r o d u c t i o n a n d i n p u t l e v e l s w h e n t h e p l a n t s i n a n i n d u s t r y o p e r a t e a t c a p a c i t y . T h i s d a t a o r i g i n a t e s i n t h e S u r v e y o f P l a n t C a p a c i t y ( S P C ) a n d i s p a r t l y u s e d b y t h e F e d e r a l R e s e r v e B o a r d t o c a l c u l a t e i n d u s t r i a l c a p a c i t y u t i l i z a t i o n . I d e m o n s t r a t e h e r e t h a t t h e i m p l e m e n t a t i o n o f e c o n o m e t r i c p r o d u c t i o n f u n c t i o n s u s i n g t h i s d a t a l e a d s t o r e s u l t s c o m p a r a b l e t o t h o s e o b t a i n e d w i t h t h e c o n v e n t i o n a l d a t a o n a c t u a l o p e r a t i o n s s u c h a s t h o s e i n t h e N B E R - C E S M a n u f a c t u r i n g P r o d u c t i v i t y d a t a b a s e t h a t o r i g i n a t e m o s t l y i n t h e A n n u a l S u r v e y o f M a n u f a c t u r e s . A n a d v a n t a g e o f t h e d a t a s e t u s e d h e r e i s t h a t i t c o n t a i n s i n f o r m a t i o n o n c a p i t a l u t i l i z a t i o n a s c a p t u r e d b y i t s w o r k q u a r t e r . V a r i o u s s t u d i e s h a v e a r g u e d t h a t f a i l u r e t o a c c o u n t f o r 1 v a r i a b l e c a p i t a l u t i l i z a t i o n c o n t a m i n a t e s m e a s u r e s o f t e c h n o l o g i c a l c h a n g e . A s a n a p p l i c a t i o n , I u s e t h i s d a t a t o e s t i m a t e t h e r a t e o f g r o w t h o f t e c h n o l o g i c a l c h a n g e t h a t i s e m b o d i e d i n e q u i p m e n t c a p i t a l . T h e f u n d a m e n t a l i d e a t h a t m o r e r e c e n t v i n t a g e s o f c a p i t a l m a y e m b o d y t e c h n o l o g i c a l a d v a n c e s t h a t m a k e t h e m \ b e t t e r " t h a n 2 o l d e r v i n t a g e s w a s i n t r o d u c e d b y J o h a n s e n ( 1 9 5 9 ) a n d S o l o w ( 1 9 6 0 ) . A n i m p o r t a n t i m p l i c a t i o n o f t h i s i d e a i s t h a t i n v e s t m e n t i s e s s e n t i a l i n o r d e r t o r e a p t h e b e n e (cid:12) t s f r o m s o m e p a r t o f t e c h n o l o g i c a l p r o g r e s s . A s e r i e s o f r e c e n t p a p e r s h a s e x p l o r e d t h e i m p o r t a n c e o f e m b o d i e d t e c h n o l o g i c a l c h a n g e f o r e c o n o m i c g r o w t h . H u l t e n ( 1 9 9 2 ) a n d G r e e n w o o d e t a l . ( 1 9 9 7 ) , a m o n g o t h e r s , c a l i b r a t e t h e r a t e o f g r o w t h o f e m b o d i e d t e c h n o l o g i c a l c h a n g e u s i n g p r o d u c e r d u r a b l e e q u i p m e n t p r i c e i n d e x e s c o n s t r u c t e d b y G o r d o n ( 1 9 9 0 ) t o r e (cid:13) e c t i m p r o v e m e n t s i n q u a l i t y . T h e y c o m p a r e t h e s e t o o Æ c i a l i n d e x e s a s s u m e d t o c o n t a i n n o q u a l i t y a d j u s t m e n t a n d a r r i v e a t a n e s t i m a t e o f a b o u t 3 t o 3 . 5 p e r c e n t p e r y e a r . 1 T h e o r ig in a l c o n c e r n w a s v o ic e d b y J o r g e n s o n a n d G r ilic h e s ( 1 9 6 7 ) . M o r e r e c e n t c o n t r ib u t io n s a r e s u r v e y e d in F e r n a ld a n d B a s u ( 1 9 9 9 ) a n d B e a u lie u a n d M a t t e y ( 1 9 9 6 ) . 2 \ B e t t e r " , o r e q u iv a le n t ly \ o f h ig h e r q u a lit y " , m e a n s d is p la y in g h ig h e r p r o d u c t iv it y a ft e r a d ju s t in g f o r w e a r a n d t e a r . 2

e p f a t 2 T w M e c d a i v t o p T h e a p p r o a c h i n t h i s p a p e r i s t o e s t i m a t e d i r e c t l y t h i s r a t e o f g r o w t h u s i n g a n c o n o m e t r i c p r o d u c t i o n f u n c t i o n f r a m e w o r k . I n t h e l a n g u a g e o f t h e d u a l i t y t h e o r y o f r o d u c t i o n , I w o r k w i t h t h e p r i m a l p r o b l e m w i t h o u t r e l y i n g o n m e a s u r e s o f p r i c e s . T h e r a m e w o r k u s e d h e r e h a s b e e n p r o p o s e d b y N e l s o n ( 1 9 6 4 ) a n d t h e e s t i m a t e s o b t a i n e d r e m u c h h i g h e r t h a n t h e p r i c e - b a s e o n e s i n d i c a t i n g a n e v e n l a r g e r r o l e f o r e m b o d i e d e c h n o l o g i c a l c h a n g e t h a n i s c o n v e n t i o n a l l y a c c e p t e d . T h e F r a m e w o r k h e p r o d u c t i o n o f g r o s s o u t p u t i n a n i n d u s t r y i s d e s c r i b e d b y t h e f o l l o w i n g e q u a t i o n : Y = Z f ( U K ; L ; M ) ( 1 ) t t t t t t h e r e , Z i s a f a c t o r t h a t c a p t u r e s d i s e m b o d i e d t e c h n o l o g i c a l c h a n g e , L i s l a b o r i n p u t , t t s e i s m a t e r i a l s i n p u t , K = K + K i s t h e s u m o f t h e c a p i t a l s t o c k o f s t r u c t u r e s a n d t t t t q u i p m e n t r e s p e c t i v e l y , a n d U i s t h e r a t e o f u t i l i z a t i o n o f c a p i t a l i n p r o d u c t i o n . T h e t a p i t a l s t o c k s a r e t h e o u t c o m e o f p a s t i n v e s t m e n t d e c i s i o n s b y i n d u s t r y (cid:12) r m s a n d o f e p r e c i a t i o n d u e t o u s e a c c o r d i n g t o t h e f o l l o w i n g e q u a t i o n s : 1 s s s (cid:0) K = ( 1 d ) I ; ( 2 ) (cid:0) (cid:0) t t i t i = 1 i X n d 1 e e e (cid:0) (cid:0) K = ( 1 d (cid:0) ) I (cid:0) q : ( 3 ) t i t t i t i = 1 i X I t i s a s s u m e d t h a t i n v e s t m e n t , I , b e c o m e s p r o d u c t i v e w i t h a l a g o f o n e p e r i o d , t h a t s , t h e r e i s \ t i m e t o b u i l d " . T h e i n d e x q m e a s u r e s t h e t e c h n i c a l e Æ c i e n c y o f d i (cid:11) e r e n t i n t a g e s o f e q u i p m e n t . N o t e t h a t i n e q u a t i o n ( 1 ) I a m m a k i n g t h e a s s u m p t i o n t h a t h e r e i s n o e m b o d i e d t e c h n o l o g i c a l c h a n g e i n s t r u c t u r e s . T h e p r o d u c t i o n f u n c t i o n g i v e n b y ( 1 ) i s e s s e n t i a l l y a d e s c r i p t i o n o f h o w a m i x f i n p u t s , o n e o f t h e m b e i n g t e c h n o l o g y , l e a d s t o a c e r t a i n a m o u n t o f o u t p u t b e i n g r o d u c e d . I t i s c o n v e n t i o n a l l y u s e d t o d e s c r i b e a c t u a l , t h a t i s o b s e r v e d , o p e r a t i o n s 3

b u t t p i h w a C A t w a o u u t i t d o e s n o t h a v e t o b e l i m i t e d t o s u c h a n a p p l i c a t i o n . I n p a r t i c u l a r , (cid:12) r m s d o n o t s u a l l y o p e r a t e a t f u l l c a p a c i t y b u t (cid:12) n d t h e m s e l v e s u t i l i z i n g o n l y p a r t o f t h e i r c a p a c i t y 3 o p r o d u c e o u t p u t . S u p p o s e t h a t (cid:12) r m s o r p l a n t s g a v e u s i n f o r m a t i o n o n t h e i n p u t s h e y w o u l d c h o o s e i f t h e y w e r e t o o p e r a t e a t c a p a c i t y a n d h o w m u c h o u t p u t t h e y w o u l d r o d u c e a s a r e s u l t ( a t c u r e n t l e v e l s o f t e c h n o l o g y ) . C o n c e p t u a l l y , t h e f u n c t i o n a l f o r m n ( 1 ) s h o u l d d e s c r i b e o p e r a t i o n s a t c a p a c i t y a s w e l l . T h u s , t h e (cid:12) r m s i n t h e i n d u s t r y a v e t h e c a p a c i t y t o p r o d u c e a c c o r d i n g t o t h e f o l l o w i n g e q u a t i o n : c c c c Y = Z f ( U K ; L ; M ) ( 4 ) t t t t t t c c h e r e L a n d M a r e t h e l e v e l s o f l a b o r a n d m a t e r i a l i n p u t s w h e n c a p i t a l i s u t i l i z e d c t c a p a c i t y . N o t e t h a t c a p i t a l u t i l i z a t i o n a t c a p a c i t y , U , m a y n o t b e e q u a l t o o n e . t a p a c i t y u t i l i z a t i o n i s t h e n d e (cid:12) n e d a s c c u = Y = Y : ( 5 ) t t t s s u m i n g t h a t t h e p r o d u c t i o n f u n c t i o n i s C o b b - D o u g l a s , (cid:11) (cid:12) (cid:13) f ( K ; L ; M ) = K L M ; ( 6 ) h e n e q u a t i o n ( 4 ) b e c o m e s : c c c c l o g ( Y ) = (cid:11) l o g ( U ) + (cid:11) l o g ( K ) + (cid:12) l o g ( L ) + (cid:13) l o g ( M ) + l o g ( Z ) ; ( 7 ) t t t t t t h e r e 1 s s s (cid:0) l o g ( K ) = l o g ( 1 d ) I ( 8 ) (cid:0) (cid:0) 1 t t i t ! = 1 i X n d 1 e e e (cid:0) (cid:0) 1 l o g ( K ) = l o g ( 1 d (cid:0) ) I (cid:0) 1 q : ( 9 ) t t t i t ! = 1 i X T h e (cid:12) r s t t a s k o f t h i s p a p e r i s t o e s t i m a t e ( 7 ) t o g e t h e r w i t h ( 8 ) a n d ( 9 ) u s i n g d a t a n c a p a c i t y o p e r a t i o n s . T h e s e e s t i m a t e s a r e t h e n c o m p a r e d t o r e s u l t s f r o m e s t i m a t i n g 3 S e e C o r r a d o a n d M a t t e y ( 1 9 9 7 ) fo r a d is c u s s io n o f v a r io u s is s u e s s u r r o u n d in g v a r ia b le c a p a c it y t iliz a t io n a s w e ll a s a r e v ie w o f r e la t e d s t u d ie s . 4

( t o T r p w q c I l a n i i 3 T t c t o 1 ) i n l o g s t o g e t h e r w i t h ( 8 ) a n d ( 9 ) . T h e s e t w o a p p r o a c h e s s h o u l d b e e q u i v a l e n t , h e m a i n d i (cid:11) e r e n c e b e i n g t h a t t h e t w o d a t a s e t s d e s c r i b e d i (cid:11) e r e n t l e v e l s o f p r o d u c t i o n p e r a t i o n s . h e A g e o f t h e C a p i t a l S t o c k N e l s o n ( 1 9 6 4 ) r e s t r i c t s e m b o d i e d t e c h n o l o g i c a l c h a n g e t o h a v e a c o n s t a n t g r o w t h a t e a n d d e r i v e s a r e l a t i o n s h i p b e t w e e n t h i s r a t e a n d t h e e (cid:11) e c t o f a v e r a g e c a p i t a l a g e o n (cid:0) 1 r o d u c t i v i t y . L e t q = q = ( 1 + (cid:21) ) ; f o r a l l t . T h e n , o n e c a n s h o w t h a t , a p p r o x i m a t e l y , t t t e e t e e (cid:0) (cid:0) (cid:0) 0 ( 1 d ) I q = B ( 1 + (cid:21) ) k k [ 1 + (cid:21) ( a a ) ] ; ( 1 0 ) K = (cid:0) (cid:0) t i t t i t i t t = 1 i X t (cid:0) e e e h e r e k k = ( 1 d ) I d e n o t e s t h e s t o c k o f c a p i t a l e q u i p m e n t u n a d j u s t e d f o r = 1 (cid:0) (cid:0) t i t i t i P u a l i t y c h a n g e , a i s t h e a v e r a g e a g e o f t h e e q u i p m e n t s t o c k a t t i m e i , a n d B i s a i 0 o n s t a n t t h a t d e p e n d s o n (cid:21) a n d a : (cid:0) (cid:0) 0 0 S u b s t i t u t i n g f r o m ( 1 0 ) i n t o ( 7 ) a n d a p p r o x i m a t i n g l o g ( 1 + (cid:21) ( a a ) ) w i t h (cid:21) ( a a ) , t t o b t a i n c c s e c c (cid:0) 0 o g ( Y ) = (cid:11) l o g ( U ) + (cid:11) l o g ( K + k k ) + (cid:12) l o g ( L ) + (cid:13) l o g ( M ) + (cid:12) (cid:21) ( a a ) + l o g ( Z ) ; t t t t t t t t ( 1 1 ) f t e r s u p p r e s s i n g a l i n e a r t i m e t r e n d t e r m . A c c o r d i n g t o N e l s o n ’ s ( 1 9 6 4 ) f r a m e w o r k e g a t i v e e (cid:11) e c t s o f a v e r a g e c a p i t a l s t o c k a g e o n p r o d u c t i v i t y p r o v i d e e v i d e n c e o f e m b o d m e n t . F u r t h e r m o r e , t h e n e g a t i v e o f t h e c o e Æ c i e n t o n t h e a g e t e r m f r o m s u c h r e g e s s i o n s e q u a l t o t h e s h a r e o f c a p i t a l t i m e s t h e r a t e o f e m b o d i e d t e c h n o l o g i c a l c h a n g e . D a t a h i s p a p e r u s e s d a t a o n a c t u a l a n d c a p a c i t y o p e r a t i o n s o f m a n u f a c t u r i n g i n d u s t r i e s a t h e t h r e e - d i g i t S I C l e v e l . T h e d a t a c o v e r t h e y e a r s 1 9 7 4 t o 1 9 8 8 a n d a r e a g g r e g a t e s o m p u t e d f r o m p l a n t - l e v e l d a t a c o n t a i n e d i n t h e S u r v e y o f P l a n t C a p a c i t y ( S P C ) a n d h e A n n u a l S u r v e y o f M a n u f a c t u r e s ( A S M ) . S o m e r e g r e s s i o n s u s e o n l y d a t a f r o m a c t u a l p e r a t i o n s a n d t h o s e s p a n t h e y e a r s 1 9 5 8 t o 1 9 9 6 . 5

s t t a p 1 C t m o o t i e t p o r a c ( p c T h e S P C c o l l e c t s d a t a o n f o u r t h - q u a r t e r p r o d u c t i o n l e v e l s a n d o p e r a t i o n s o n a s u b a m p l e o f p l a n t s i n t h e A n n u a l S u r v e y o f M a n u f a c t u r e s ( A S M ) . F r o m 1 9 7 4 t o 1 9 8 8 h e r e w e r e t h r e e p a n e l s i n t h e y e a r s 1 9 7 4 - 7 8 , 1 9 7 9 - 8 3 , a n d 1 9 8 4 - 8 8 . O n a v e r a g e , e i g h t o n i n e t h o u s a n d p l a n t s p e r y e a r w e r e s u r v e y e d f o r t h e S P C a b o u t a c t u a l , p r e f e r r e d , n d p r a c t i c a l o p e r a t i o n s . F o r e a c h o f t h e t h r e e p a n e l s , t h e r e w e r e s i x t o s e v e n t h o u s a n d l a n t s t h a t p r o v i d e d d a t a f o r t h e e n t i r e p e r i o d . T h e S P C w a s m o d i (cid:12) e d f o l l o w i n g t h e 9 8 8 s u r v e y a n d s o m e o f t h e v a r i a b l e s u s e d i n t h e a n a l y s i s h e r e b e c a m e u n a v a i l a b l e . a p a c i t y D e (cid:12) n i t i o n s T h e c o n c e p t s o f c a p a c i t y c o n v e y e d t o t h e s u r v e y r e s p o n d e n t s a r e d e (cid:12) n e d a s f o l l o w s . P r a c t i c a l C a p a c i t y : \ T h e g r e a t e s t l e v e l o f o u t p u t t h i s p l a n t c a n a c h i e v e w i t h i n h e f r a m e w o r k o f a r e a l i s t i c w o r k p a t t e r n , a n o r m a l p r o d u c t m i x , a n d t h e s c h e d u l e , a c h i n e r y , a n d e q u i p m e n t a l r e a d y i n p l a c e a n d r e a d y t o o p e r a t e . " P r e f e r r e d L e v e l o f O p e r a t i o n s : \ A n i n t e r m e d i a t e l e v e l o f o p e r a t i o n s b e t w e e n a c t u a l p e r a t i o n s a n d p r a c t i c a l c a p a c i t y t h a t y o u w o u l d p r e f e r n o t t o e x c e e d b e c a u s e o f c o s t s r o t h e r c o n s i d e r a t i o n s . I m p l i c i t i n t h e i d e a o f a p r e f e r r e d l e v e l o f o p e r a t i o n s i s t h e h e o r y t h a t t h e r e i s a p r e f e r r e d l e v e l o f o p e r a t i o n s a t w h i c h p r o (cid:12) t s a r e m a x i m i z e d . T h i s s a l e v e l w h e r e m a r g i n a l r e v e n u e e q u a l s m a r g i n a l c o s t s . T h e p r e f e r r e d l e v e l s h o u l d n o t x c e e d p r a c t i c a l c a p a c i t y . " T h e s e c o n d d e (cid:12) n i t i o n i s t h e o n e I u s e i n t h i s p a p e r a s i t c o r r e s p o n d s q u i t e c l o s e l y 4 o e c o n o m i c c o n c e p t s o f c a p a c i t y . S u r v e y r e s p o n d e r s i n d i c a t e t h e l e v e l o f p r o d u c t i o n , r o d u c t i o n w o r k e r h o u r s , a n d t h e w o r k w e e k o f c a p i t a l b o t h f o r a c t u a l a n d c a p a c i t y p e r a t i o n s f o r t h e f o u r t h q u a r t e r o f t h e y e a r . C a p a c i t y u t i l i z a t i o n i s d e (cid:12) n e d a s t h e a t i o o f p r o d u c t i o n l e v e l s a t a c t u a l a n d c a p a c i t y o p e r a t i o n s . W o r k w e e k i s c a l c u l a t e d s h o u r s w o r k e d p e r d a y t i m e s t h e d a y s w o r k e d p e r w e e k . 4 T h is is a ls o t h e d e (cid:12) n it io n u s e d b y t h e F e d e r a l R e s e r v e B o a r d ( F R B ) in c o n s t r u c t in g e s t im a t e s o f a p a c it y u t iliz a t io n . S e e C o r r a d o a n d M a t t e y ( 1 9 9 7 ) f o r a d e s c r ip t io n o f F R B m e t h o d s a n d D o y le 1 9 9 9 ) fo r e v id e n c e t h a t t h e \ p r e fe r r e d " m e a s u r e o f c a p a c it y a lig n s w e ll w it h e c o n o m ic c o n c e p t s o f r o d u c t iv e c a p a c it y t h a t in c o r p o r a t e c o s t c o n s id e r a t io n s . P r a c t ic a l c a p a c it y , o n t h e o t h e r h a n d , s e e m s lo s e r t o a n e n g in e e r in g n o t io n o f c a p a c it y b e s t d e s c r ib e d a s \ r u n n in g t h e m a c h in e s a ll o u t ." 6

t B h B A u q a a 4 I e a o n m o c r c E a T h e v a r i a b l e s f o r c a p a c i t y u t i l i z a t i o n , c a p i t a l i n p u t , a n d a c t u a l w o r k w e e k a r e f r o m h e F R B . A l l o t h e r d a t a u s e d h e r e i s f r o m t h e N B E R - C E S P r o d u c t i v i t y D a t a b a s e ( s e e a r t e l s m a n a n d G r a y , 1 9 9 6 ) e x c e p t f o r c a p a c i t y l e v e l s o f t h e w o r k w e e k a n d p r o d u c t i o n o u r s , w h i c h a r e a v a i l a b l e o n l y a t t h e C e n t e r f o r E c o n o m i c S t u d i e s ( C E S ) o f t h e C e n s u s u r e a u . T h e p r o c e d u r e I u s e t o c o n s t r u c t i n d u s t r y a g g r e g a t e s i s d e s c r i b e d i n t h e D a t a p p e n d i x . C a p a c i t y o u t p u t i s c o n s t r u c t e d a s t h e r a t i o o f g r o s s o u t p u t t o c a p a c i t y t i l i z a t i o n . I a l s o u s e a s e t o f i n s t r u m e n t a l v a r i a b l e s i n s o m e e s t i m a t i o n s . T h i s c o n s i s t s o f u a r t e r l y i n n o v a t i o n s t o t h e F e d e r a l F u n d s r a t e ( l a g g e d o n e y e a r ) a n d a m e a s u r e o f c t i v i t y i n \ d o w n s t r e a m i n d u s t r i e s . " T h e l a s t o n e i s a v a i l a b l e a t t h e 3 - d i g i t S I C l e v e l n d f o r y e a r s 1 9 7 8 t o 1 9 9 4 o n l y . E m p i r i c a l R e s u l t s p r e s e n t r e s u l t s p o o l i n g a l l i n d u s t r i e s t o g e t h e r . T a b l e 1 c o n t a i n s t h e r e s u l t s o f O L S s t i m a t i o n o f a p r o d u c t i o n f u n c t i o n . T h e (cid:12) r s t t w o c o l u m n s u s e d a t a o n c a p a c i t y o p e r t i o n s w h i l e t h e n e x t t w o u s e d a t a o n a c t u a l o p e r a t i o n s . T w o s p e c i (cid:12) c a t i o n s a r e u s e d : n e t h a t a l l o w s f o r v a r i a t i o n s i n t h e w o r k w e e k o f c a p i t a l a n d a n o t h e r o n e t h a t d o e s o t . R e g r e s s i o n s i n c l u d e i n t e r c e p t a n d l i n e a r t i m e t r e n d . T h e r e s u l t s a r e r o u g h l y c o n s i s t e n t a c r o s s t h e t w o d a t a s e t s . T h e c o e Æ c i e n t o n a t e r i a l s s e e m s t o b e l a r g e r t h a n e x p e c t e d , a t l e a s t j u d g e d b y t h e m a t e r i a l s ’ s h a r e i n u t p u t . C o n t r o l l i n g f o r v a r i a t i o n i n c a p i t a l u t i l i z a t i o n h a s t h e e (cid:11) e c t o f r e d u c i n g t h e o e Æ c i e n t o n c a p i t a l t h o u g h i t d o e s s o m u c h m o r e f o r d a t a o n a c t u a l o p e r a t i o n s . A e l a t e d o b s e r v a t i o n i s t h a t t h e c o e Æ c i e n t o n t h e w o r k w e e k i s v e r y c l o s e t o t h a t o n a p i t a l w i t h c a p a c i t y d a t a b u t i n s i g n i (cid:12) c a n t w i t h a c t u a l - o p e r a t i o n s d a t a . n d o g e n e i t y b i a s I t i s w e l l - k n o w n t h a t t h e r e m a y b e b i a s e s i n O L S e s t i m a t i o n o f p r o d u c t i o n f u n c t i o n s , s i n T a b l e 1 , d u e t o e n d o g e n e i t y . M o r e c o n c r e t e l y , t h e p r o d u c t i v i t y s h o c k , l o g ( Z ) , t 7

m s m n c i i c o t t p ( ( i d F s F d s q a b p a y b e c o r r e l a t e d w i t h t h e l e v e l o f i n p u t s . T o t h e e x t e n t t h a t t h i s s h o c k h a s l i m i t e d e r i a l c o r r e l a t i o n a n d c a p i t a l i s q u a s i - (cid:12) x e d t h e p r o b l e m i s m o s t s e v e r e f o r t h e l a b o r a n d a t e r i a l s i n p u t . P r e s e n t l y , t h e r e i s n o g o o d (cid:12) x f o r t h i s p r o b l e m . G r i l i c h e s a n d R i n g s t a d ( 1 9 7 3 ) h a v e p r o p o s e d a p r o c e d u r e t o e v a l u a t e t h e r o b u s t e s s o f O L S e s t i m a t e s t o e n d o g e n e i t y p r o b l e m s . T h e i r s u g g e s t i o n i s t o c o n s t r a i n t h e o e Æ c i e n t s o f l a b o r a n d m a t e r i a l s t o t h e i r s h a r e s i n t o t a l c o s t , c a l c u l a t e d f r o m a v a i l a b l e n d u s t r y d a t a , b u t a l l o w t h e c o e Æ c e n t o n c a p i t a l t o b e e s t i m a t e d . I u s e t h i s a p p r o a c h n o r d e r t o d e t e c t p o s s i b l e b i a s e s . A s m a y b e s e e n i n t h e (cid:12) r s t c o l u m n o f T a b l e 2 , t h e o e Æ c i e n t o n c a p i t a l d o e s n o t c h a n g e v e r y m u c h , w h i c h i s r e a s s u r i n g . T h e c o e Æ c i e n t n i t s w o r k w e e k , h o w e v e r , i n c r e a s e s b y 5 0 p e r c e n t a n d s o d o e s i t s s t a n d a r d e r r o r . S i n c e h e r e s u l t s a r e m i x e d , I e x p l o r e i n s t r u m e n t a l v a r i a b l e s a s a n a l t e r n a t i v e . S o m e r e s e a r c h e r s h a v e a d v o c a t e d t h e u s e o f i n s t r u m e n t a l v a r i a b l e s i n o r d e r t o i d e n i f y t h e p r o d u c t i o n f u n c t i o n c o e Æ c i e n t s . H a l l ( 1 9 9 0 ) a n d B u r n s i d e e t a l . ( 1 9 9 5 ) p r o o s e d v a r i o u s a g g r e g a t e - l e v e l i n s t r u m e n t s w h e r e a s S h e a ( 1 9 9 3 ) a n d B a r t e l s m a n e t a l . 1 9 9 4 ) c o n s t r u c t e d i n d u s t r y - s p e c i (cid:12) c i n s t r u m e n t s . I n p a r t i c u l a r , t h e B a r t e l s m a n e t a l . 1 9 9 4 ) i n s t r u m e n t i s a w e i g h t e d a v e r a g e m e a s u r e o f e c o n o m i c a c t i v i t y i n \ d o w n s t r e a m n d u s t r i e s " t h a t d e m a n d t h e o u t p u t o f t h e i n d u s t r y i n q u e s t i o n a s i n t e r m e d i a t e i n p u t . I c o n s i d e r t h e f o l l o w i n g l i s t o f v a r i a b l e s a s p o t e n t i a l i n s t r u m e n t s : t h e p r i c e o f o i l , e f e n s e s p e n d i n g , t h e p o l i t i c a l p a r t y o f t h e p r e s i d e n t , q u a r t e r l y i n n o v a t i o n s t o t h e e d e r a l F u n d s r a t e a n d d o w n s t r e a m d e m a n d l e v e l . T h e a g g r e g a t e - l e v e l i n s t r u m e n t s u (cid:11) e r f r o m v e r y l o w r e l e v a n c e t o t h e i n d u s t r y - s p e c i (cid:12) c i n p u t v a r i a b l e s . S h o c k s t o t h e e d e r a l F u n d s r a t e s e e m t o b e t h e l e a s t o (cid:11) e n d i n g o f t h e s e s o I u t i l i z e t h e m . T h e o w n s t r e a m d e m a n d v a r i a b l e i s v e r y r e l e v a n t , a s w o u l d b e e x p e c t e d , s i n c e i t i s i n d u s t r y p e c i (cid:12) c . T a b l e 3 s h o w s t h e (cid:12) r s t - s t a g e r e g r e s s i o n s w i t h t h e i n s t r u m e n t s e t o f f o u r u a r t e r s o f F e d e r a l F u n d s s h o c k s ( l a g g e d b y a y e a r ) a n d t h e d o w n s t r e a m - d e m a n d . T h e 2 s s o c i a t e d R s a n d F - s t a t i s t i c s a r e r a t h e r l o w f o r e s h a d o w i n g i m p r e c i s e , a n d p o s s i b l y i a s e d , e s t i m a t e s . O n e m a y w o n d e r , t h e n , w h e t h e r \ t h e c u r e m a y b e w o r s e f o r t h e a t i e n t t h a n t h e d i s e a s e . " 8

v t s E m c o e a a v (cid:21) C d t t m p t T h e s e c o n d a n d t h i r d c o l u m n o f T a b l e 2 c o n (cid:12) r m t h i s f e a r w i t h e s t i m a t e s d i s p l a y i n g e r y h i g h s t a n d a r d e r r o r s . H o w e v e r , t h e a c t u a l e s t i m a t e s a r e n o t v e r y d i (cid:11) e r e n t f r o m 5 h o s e o f O L S . T h i s p r o v i d e s a n i n d i c a t i o n t h a t , p e r h a p s , t h e O L S e s t i m a t e s a r e n o t e v e r e l y b i a s e d . m b o d i e d T e c h n o l o g i c a l C h a n g e I p r o c e e d n o w t o e s t i m a t i n g (cid:21) , t h e r a t e o f e m b o d i e d t e c h n o l o g i c a l c h a n g e . T h e e s t i a t e o f (cid:21) , i s a b o u t 1 0 p e r c e n t , o b t a i n e d b y d i v i d i n g t h e c o e Æ c i e n t o n c a p i t a l a g e b y t h e o e Æ c i e n t o n c a p i t a l i n T a b l e 4 . T h i s e s t i m a t e i s m u c h l a r g e r t h a n t h e e s t i m a t e s b a s e d n c o m p a r i s o n s o f p r i c e i n d e x e s . I t i m p l i e s a l a r g e r r o l e o f e q u i p m e n t i n v e s t m e n t a n d m b o d i e d t e c h n o l o g i c a l c h a n g e o n e c o n o m i c g r o w t h t h a n i s c o n v e n t i o n a l l y a s s u m e d . I t l s o i m p l i e s t h a t t h e p r o d u c t i v e c a p i t a l s t o c k o f e q u i p m e n t i s c u r r e n t l y m i s m e a s u r e d s i t d o e s n o t r e (cid:13) e c t s u b s t a n t i a l i m p r o v e m e n t s i n q u a l i t y t h r o u g h i n v e s t m e n t i n n e w i n t a g e s . C l e a r l y , m o r e r e s e a r c h w o u l d b e u s e f u l i n a s s e s s i n g t h e r o b u s t n e s s o f t h e h i g h 6 e s t i m a t e f o u n d h e r e w i t h a l t e r n a t i v e d a t a a n d s p e c i (cid:12) c a t i o n s . o n c l u s i o n s S u m m i n g u p , t h e c o n c r e t e l e s s o n f r o m t h i s p a p e r i s t h a t d a t a o n i n d u s t r i a l p r o u c t i v e c a p a c i t y f r o m t h e S P C i s s u i t a b l e f o r p r o d u c t i o n f u n c t i o n e s t i m a t i o n . I n f a c t , h e e s t i m a t e s a r e q u i t e s i m i l a r t o t h o s e o b t a i n e d u s i n g d a t a o n a c t u a l o p e r a t i o n s f r o m h e A S M . T h i s (cid:12) n d i n g i s r e a s s u r i n g f o r u s e r s o f t h e F e d e r a l R e s e r v e B o a r d ’ s p u b l i s h e d e a s u r e s o f c a p a c i t y u t i l i z a t i o n , b a s e d o n t h e s a m e S P C d a t a . 5 A g a in t h e w o r s t o (cid:11) e n d e r is t h e c o e Æ c ie n t o f t h e w o r k w e e k . 6 S a k e lla r is a n d W ils o n ( 2 0 0 0 ) t a k e a s t e p in t h a t d ir e c t io n . T h e y c o n s t r u c t a la r g e d a t a s e t o f la n t o p e r a t io n s a n d e s t im a t e t h e g r o w t h r a t e o f e m b o d ie d t e c h n o lo g ic a l c h a n g e w it h o u t r e s o r t in g t o h e a p p r o x im a t io n s in h e r e n t in N e ls o n ’s ( 1 9 6 4 ) a p p r o a c h . 9

5 B S p D U S a R P P 1 C o I 8 R e f e r e n c e s a r t e l s m a n , E r i c J . , C a b a l l e r o , R i c a r d o , a n d L y o n s , R i c h a r d K . \ C u s t o m e r - a n d A m e r i c a n E c o n o m i c R e v i e w , u p p l i e r - D r i v e n E x t e r n a l i t i e s . " S e p t e m b e r 1 9 9 4 , 8 4 : 4 , p . 1 0 7 5 - 8 4 . B a r t e l s m a n , E r i c J . , a n d G r a y , W a y n e . \ T h e N B E R M a n u f a c t u r i n g P r o d u c t i v i t y a t a b a s e . " N B E R T e c h n i c a l W o r k i n g P a p e r 2 0 5 , O c t o b e r 1 9 9 6 . B e a u l i e u , J . J o s e p h , a n d M a t t e y , J o e . \ T h e W o r k w e e k o f C a p i t a l a n d C a p i t a l t i l i z a t i o n i n U . S . M a n u f a c t u r i n g . " M i m e o , B o a r d o f G o v e r n o r s o f t h e F e d e r a l R e s e r v e y s t e m , A u g u s t 1 9 9 6 . B u r n s i d e , C r a i g , E i c h e n b a u m , M a r t i n , a n d R e b e l o , S e r g i o . \ C a p i t a l U t i l i z a t i o n N B E R M a c r o e c o n o m i c s A n n u a l 1 9 9 5 n d R e t u r n s t o S c a l e . " I n e d i t e d b y J u l i o J . o t e m b e r g a n d B e n S . B e r n a n k e . C a m b r i d g e , M a : M I T P r e s s , 1 9 9 5 . J o u r n a l o f E c o n o m i c C o r r a d o , C a r o l , a n d M a t t e y , J o e . \ C a p a c i t y U t i l i z a t i o n . " e r s p e c t i v e s , W i n t e r 1 9 9 7 , 1 1 : 1 , p p . 1 5 1 - 1 6 7 . D o y l e , M a u r a P . \ T h e 1 9 8 9 C h a n g e i n t h e D e (cid:12) n i t i o n o f C a p a c i t y : A P l a n t L e v e l e r s p e c t i v e . " M i m e o , B o a r d o f G o v e r n o r s o f t h e F e d e r a l R e s e r v e S y s t e m , J a n u a r y 9 9 9 . F e r n a l d , J o h n , a n d B a s u , S u s a n t o . \ W h y i s P r o d u c t i v i t y P r o c y c l i c a l ? W h y D o W e a r e ? " B o a r d o f G o v e r n o r s o f t h e F e d e r a l R e s e r v e S y s t e m , I F D P n o . 6 3 8 , J u n e 1 9 9 9 . T h e M e a s u r e m e n t o f D u r a b le G o o d s P r i c e s . G o r d o n , R o b e r t J . C h i c a g o : U n i v e r s i t y f C h i c a g o P r e s s , 1 9 9 0 . G r e e n w o o d , J e r e m y ; H e r c o w i t z , Z v i ; a n d K r u s s e l l , P e r . \ L o n g - R u n I m p l i c a t i o n s o f A m e r i c a n E c o n o m i c R e v i e w , n v e s t m e n t - S p e c i (cid:12) c T e c h n o l o g i c a l C h a n g e . " J u n e 1 9 9 7 , 7 : 3 , p p . 3 4 2 - 3 6 2 . 1 0

J F P t C o R P n 2 1 K f G r e e n w u n e 1 9 9 8 G r i l i c h u n c t i o n . H a l l , R r o d u c t i v i e r D i a m o H u l t e n a p i t a l . " J o h a n s f E c o n o m J o r g e n e v i e w o f N e l s o n r o j e c t i o n S a k e l l a o l o g i c a l C 0 0 0 . S h e a , J 0 8 : 1 , p p . S o l o w , a r l i n , a n o r d , C A : o o d , J e r e m y , a n d J o v a n o v i c , B o y a n . \ A c c o u n t i n g f o r G r o w t h . " M i m e o , . E c o n o m i e s o f S c a le a n d t h e F o r m o f t h e P r o d u c t i o n e s , Z v i , a n d R i n g s t a d , V . A m s t e r d a m : N o r t h - H o l l a n d , 1 9 7 1 . G r o w t h o b e r t E . \ I n v a r i a n c e P r o p e r t i e s o f S o l o w ’ s P r o d u c t i v i t y R e s i d u a l . " I n t y , U n e m p lo y m e n t : E s s a y s t o C e le b r a t e B o b S o lo w ’ s B i r t h d a y . E d i t e d b y P e n d . C a m b r i d g e , M a s s : M I T P r e s s , 1 9 9 0 , p p . 7 1 - 1 1 2 . , C h a r l e s . \ G r o w t h A c c o u n t i n g w h e n T e c h n i c a l C h a n g e i s E m b o d i e d i n A m e r i c a n E c o n o m i c R e v i e w , S e p t e m b e r 1 9 9 2 , 8 2 : 4 , p p . 9 6 4 - 9 8 0 . e n , L e i f . \ S u b s t i t u t i o n v e r s u s F i x e d P r o p o r t i o n C o e Æ c i e n t s i n t h e T h e o r y E c o n o m e t r i c a , i c G r o w t h . " A p r i l 1 9 5 9 , 2 7 , n o . 2 , p p . 1 5 7 - 1 7 6 . s o n , D a l e W . , a n d G r i l i c h e s , Z v i . \ T h e E x p l a n a t i o n o f P r o d u c t i v i t y C h a n g e . " E c o n o m i c S t u d i e s , 1 9 6 7 , 3 4 , p p . 2 4 9 - 2 8 3 . , R i c h a r d . \ A g g r e g a t e P r o d u c t i o n F u n c t i o n s a n d M e d i u m - R a n g e G r o w t h A m e r i c a n E c o n o m i c R e v i e w , s . " S e p t e m b e r 1 9 6 4 , 5 4 : 5 , p p . 5 7 5 - 6 0 6 . r i s , P l u t a r c h o s , a n d W i l s o n , D a n i e l . \ V i n t a g e C a p i t a l a n d E m b o d i e d T e c h h a n g e : P l a n t - L e v e l E s t i m a t e s . " M i m e o , U n i v e r s i t y o f M a r y l a n d , S e p t e m b e r Q u a r t e r ly J o u r n a l o f E c o n o m i c s , o h n . \ D o S u p p l y C u r v e s S l o p e U p ? " 1 9 9 3 , 1 - 3 2 . R o b e r t . \ I n v e s t m e n t a n d T e c h n o c a l P r o g r e s s . " I n K e n n e t h A r r o w , S a m u e l M a t h e m a t i c a l M e t h o d s i n t h e S o c i a l S c i e n c e s . d P a t r i c k S u p p e s , e d s . , S t a n - S t a n f o r d U n i v e r s i t y P r e s s , 1 9 6 0 , p p . 8 9 - 1 0 4 . 1 1 ,

Table 1. Estimates of Production Function Parameters: U.S. Manufacturing Industries (3-Digit SIC) Variables Capacity Operations Actual Operations A B C D Labor 0.201 0.257 0.250 0.254 (0.009) (0.009) (0.006) (0.007) Capital 0.185 0.137 0.133 0.127 (0.009) (0.011) (0.006) (0.008) Materials 0.614 0.665 0.638 0.639 (0.011) (0.012) (0.008) (0.008) Workweek of Capital 0.140 0.016 (0.016) (0.013) RMSE 0.243 0.241 0.191 0.191 # Observations 1988 2835 Note: The data used describe productive operations at capacity levels (columns A and B) or observed levels (columns C and D). The estimating equation is (7) in the text. The capacity-operations sample spans years 1974 to 1988, whereas the actual-operations sample spans years 1958 to 1996. Table 2. Estimates of Production Function Parameters: U.S. Manufacturing Industries (3-Digit SIC) Variables Restricted Shares Unrestricted Shares OLS IV IV Labor -- -- 0.312 (1.470) Capital 0.169 0.187 0.130 (0.014) (0.420) (0.966) Materials -- -- 0.526 (1.346) Workweek of Capital 0.214 0.388 0.355 (0.049) (1.380) (0.842) R-Squared 0.137 0.004 0.175 # Observations 1988 1434 1434 Note: The data used describe productive operations at capacity levels. The first two columns restrict the coefficients of labor and materials to their shares in total cost as calculated from available industry data. The instrument set used in IV estimation consists of a constant, trend, four quarterly shocks to the Federal Funds rate (lagged one year) and a measure of “downstream demand” for industry output. The sample for the OLS estimation is 1974 to 1988, whereas for the IV estimation it is 1978 to 1988. 12

Table 3. Instrument Relevance Endogenous Variable R-Squared F-value P-value Capital Workweek 0.010 2.520 0.020 Labor 0.020 4.902 0.000 Capital 0.009 2.241 0.037 Materials 0.007 1.687 0.121 Note: Relevance statistics of instrumental variables obtained by regressing various input variables on the instrument set. The instrument set includes a constant, trend, federal funds shocks (lagged), and a measure of “downstream demand”. Input variables are measured at capacity levels of operations. Table 4. Estimates of Embodied Technological Change: U.S. Manufacturing Industries (3-Digit SIC) Variables Labor 0.256 (0.009) Capital 0.139 (0.011) Materials 0.665 (0.012) Workweek 0.153 (0.016) Average Equipment Age -0.014 (0.005) RMSE 0.236 # Observations 1988 Note: OLS estimation of equation (11) in the text. All variables are measured at capacity levels. The sample spans years 1974 to 1988. 13

Data Appendix This paper uses data at the three-digit SIC level. The data on actual levels of operations span the years 1958-96, whereas the data on capacity levels of operations span the years 1974-88. Survey of Plant Capacity (SPC) The data on capacity levels of operation come from the U.S. Census Bureau’s Survey of Plant Capacity (SPC). The SPC collects data on fourth-quarter production levels and operations on a sub-sample of plants in the Annual Survey of Manufactures (ASM). The ASM provides statistics about U.S. manufacturing plants on an annual basis, drawing upon data from a panel of respondents that is selected every five years. About three-quarters of plants in the SPC remain in the sample for an entire ASM panel. From 1974 to 1988, there were three panels in the years 1974-78, 1979-83, and 1984-88. On average, eight to nine thousand plants per year were surveyed for the SPC about actual, preferred, and practical operations (see Table 1). For each of the three panels, there were six to seven thousand plants that provided data for the entire period. The SPC was modified following the 1988 survey to include questions on full production capability instead of preferred and practical operations. Table 1: Capacity Definitions Capacity Definition Time Period Practical Capacity Greatest level of output this plant can achieve within the 1974-88 framework of a realistic work pattern, a normal product mix, and the schedule, machinery, and equipment already in place and ready to operate. Preferred Level of Operations An intermediate level of operations between actual operations 1974-88 and practical capacity that you would prefer not to exceed because of costs or other considerations. Implicit in the idea of a preferred level of operations is the theory that there is a preferred level of operations at which profits are maximized. This is a level where marginal revenue equals marginal costs. The preferred level should not exceed practical capacity. Full Production Capability The maximum level of production that this establishment could 1989-present reasonably expect to attain under normal operating conditions. Source: U.S. Census Bureau’s Survey of Plant Capacity MQ-C1 Form and Instructions Table 2: Assumptions Used in Computing Capacity Estimates Assumption Preferred Practical Full 1) Do not consider overtime pay, availability of labor, materials, utilities, etc. to be x x limiting factors. 2) Assume a product mix that was typical or representative of your production during x x x the current quarter. If your plant is subject to considerable short-run variation assume the product mix of the current period. 3a) Assume the number of shifts and hours of plant operation that can be reasonable x x attained by your plant in your community. 3b) Do not assume number of shifts and hours of plant operations under normal x conditions to be higher than that attained by your plant over the last five years. 4) Consider only the machinery and equipment in place and ready to operate. Do not x x x consider facilities or that would require extensive reconditioning before they can be made operable. 5) Assume normal downtime, maintenance, repair and cleanup. x x x 6) Do not assume increased use of production facilities outside the plant in excess of x x the proportion that would be normal during the time period covered by this survey. 7) Assume the availability of labor, materials, utilities, etc., sufficient to utilize the x x machinery and equipment that was in place at the end of the year. Source: U.S. Census Bureau’s Survey of Plant Capacity MQ-C1 Form and Instructions 1

ASM Variables Used: The following series are created from the National Bureau of Economic Research (NBER) / Center for Economic Studies (CES) Manufacturing Productivity Database for the years 1958 to 1994 and the Federal Reserve Board’s (FRB) ASM data for the years 1995 and 1996: cost of materials, cost of energy, gross output1, number of employees, number of production employees, inventories, new capital investment, payroll, shipments, value added, and wages. Price deflators for shipments, materials, energy, and new capital investment were also taken from the NBER-CES Manufacturing Database. Capital Input The following describes the construction of industry-level capital input. For each year, the industry-level capital expenditures are split among 35 asset categories. This is accomplished with an iterative matrix balancing (RASing) technique that employs the industry-level investment data as column controls and utilizes NIPA data on asset-level capital expenditures as row controls for the 35 asset categories. Data derived from BEA’s Capital Flows Tables (CFTs) provide initial asset-by-industry investment shares for the iterative procedure. For each industry, asset-level net capital stocks are created by adjusting for asset-specific physical depreciation as described in Gilbert and Mohr (1996). Industry-level capital input estimates are constructed as a rental price-weighted Tornqvist index of net capital stocks, q(i,t), in the 35 asset categories. The rental price is calculated using the following equation: p(i,t) = q(i,t)*[r(t)+(d(i,t)-f(i,t))]*[(1-u(t)z(i,t)-k(i,t))/(1-u(t))] q(i,t)=chain-weighted investment price deflator for asset i in time t d(i,t)=the rate of economic depreciation for asset i in time t f(i,t)=expected real capital gain for asset i in time t u(t)=corporate income tax k(i,t)=investment tax credit for asset i in time t z(i,t)=present value of expected tax depreciation Capacity Output Capacity equals gross output/capacity utilization. This paper uses a series that is constructed by overlaying full production capacity utilization rates (post 1988) with preferred utilization rates (pre-1989) and aggregating to the 3digit level using value added. Both are published by the Federal Reserve Board. Workweek of Capital at Capacity Workweek at capacity equals actual workweek (provided by Norman Morin at the FRB) over workweek utilization (constructed from SPC data at the CES). The workweek of capital was available from the SPC for the years 1974- 88 only. Actual workweek is defined as actual hours worked per day times the actual days worked per week. Capacity workweek was defined in a similar manner. Actual and preferred workweek were aggregated to the 4-digit industry level using the following weight for each plant: SPC weight * total employment (ASM) / shift; where shift is an assigned variable based on the reported actual workweek. If actual workweek is less than 58.5 hours then shift equals one; if actual workweek is greater than 58.5 hours and less than 101.5 hours then shift equals two; and if actual workweek is greater than 101.5 hours then shift equals three. The actual and preferred workweek were aggregated to the 3-digit level using value added weights. The ratio of actual to capacity workweek, in other words workweek utilization, was formed at the 3-digit level. Labor input at Capacity Labor input at capacity equals actual labor input (from the NBER-CES Productivity Database) over the labor utilization (constructed from SPC data at the CES). Actual labor input was imputed using the formula: (Productionworker Hours)*(Total Payroll/ Production-worker Payroll). Labor utilization refers to production-worker hours only as this is the only available information in the SPC data. Actual to capacity ratios were formed for production 1 Gross output is constructed by summing the value added series to the cost of materials series. 2

worker hours at the plant level. This production-worker-hours ratio was aggregated to the 4-digit level using the SPC weight. Actual employment hours (from the NBER-CES Database) were then used as weights to aggregate to the 3-digit level. Materials Input at Capacity The SPC does not contain information on materials use at capacity operations. I made the assumption that materials utilization was equal to labor utilization for each plant-year observation. Materials input at capacity, then, equals actual materials input (from the NBER-CES Productivity Database) over the labor utilization (constructed from SPC data at the CES). REFERENCES Gilbert, C.E. and Mohr, M. F. “Capital Stock Estimates for Manufacturing Industries: Methods and Data,” Federal Reserve Board, March 1996. 3