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Wage and employment contracts as equilibria to a bargaining game : an empirical analysis 1987

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Wage and Employment Contracts as E q u i l i b r i a to a Bargaining Game: An Empirical Analysis by Denise J. Doiron B.A., University de Moncton, 197 9 .A., University of B r i t i s h Columbia, 1982 A Thesis Submitted in P a r t i a l Fulfillment of the Requirements for the Degree of Doctor of Philosophy in The Faculty of Graduate Studies (Department of Economics) We accept this thesis as conforming to the required standard The University of B r i t i s h Columbia October, 1987. (c) Denise J. Doiron, 1987. In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of (^C^/Hl^yCd^ The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 DE-6(3/81) i i A b s t r a c t The o b j e c t o f t h i s r e s e a r c h i s t o s tudy how u n i o n s and f i r m s d i v i d e the s u r p l u s o r r e n t s a v a i l a b l e t o them. Many i n s t r u m e n t s a r e used i n p r a c t i c e to make t h i s d i v i s i o n , but s t a n d a r d m i c r o d a t a o n l y i n c l u d e s t w o : wages a n d e m p l o y m e n t . I u s e a new a p p r o a c h t o s t u d y wage and employment c o n t r a c t s as I c o n s i d e r them e q u i l i b r i u m p o i n t s i n a n o n c o o p e r a t i v e b a r g a i n i n g game. T h i s w o r k i s a n e x t e n s i o n o f w a g e - e m p l o y m e n t d e t e r m i n a t i o n mode l s , the e x t e n s i o n b e i n g the i n c o r p o r a t i o n o f a b a r g a i n i n g mode l , s p e c i f i c a l l y , a R u b i n s t e i n b a r g a i n i n g game. G i v e n the o b j e c t i v e f u n c t i o n s o f the two p l a y e r s , the wage a n d e m p l o y m e n t e q u a t i o n s a r e s p e c i f i e d by t h e e q u i l i b r i u m c o n d i t i o n s f o r t h e game. A l s o , a d d i t i o n a l d e t e r m i n a n t s o f the c o n t r a c t s are i d e n t i f i e d . One o f the c h a r a c t e r i s t i c s o f the model i s t h a t the wage and employment c o n t r a c t s a r e a f f e c t e d by the r e l a t i v e s t r i k e c o s t s o f the two n e g o t i a t i n g p a r t i e s even i n the absence o f s t r i k e s . The d a t a i n v o l v e the B . C . wood p r o d u c t s i n d u s t r y and the IWA, a p o w e r f u l u n i o n b e l i e v e d to have been s u c c e s s f u l a t c a p t u r i n g r e n t s . The d a t a i n c l u d e i n p u t and output q u a n t i t i e s and p r i c e s and e q u a t i o n s r e p r e s e n t i n g i n p u t demands and output s u p p l y are e s t i m a t e d s i m u l t a n e o u s l y w i t h t h e n e g o t i a t e d wage a n d e m p l o y m e n t e q u a t i o n s . F o u r e s t i m a t i o n m o d e l s a r e d e r i v e d c o r r e s p o n d i n g t o two b a r g a i n i n g frameworks and two s e t s o f a s s u m p t i o n s on t h e i i i f i r m s ' t e c h n o l o g y . The two b a r g a i n i n g frameworks c o r r e s p o n d t o two p o l a r c a s e s t h a t have been assumed i n t h e wage- employment d e t e r m i n a t i o n l i t e r a t u r e : i n one c a s e , the wage i s s e t t h r o u g h b a r g a i n i n g w h i l e t h e employment l e v e l i s chosen by the f i r m , i n the second c a s e , b o t h the wage and employment l e v e l a r e n e g o t i a t e d . In one p a i r o f mode l s , o u t p u t i s t r e a t e d as exogenous to the b a r g a i n i n g w h i l e i n the second s e t o f mode l s , ou tput i s endogenous and c a p i t a l i s exogenous. The b a r g a i n i n g game i s s u c c e s s f u l l y implemented i n the s e n s e t h a t t e c h n o l o g y and u n i o n u t i l i t y p a r a m e t e r s a r e g e n e r a l l y r e a s o n a b l e and comparable t o p r e v i o u s e s t i m a t e s . A l s o , t h e d e t e r m i n a n t s o f r e l a t i v e s t r i k e c o s t s e n t e r s i g n i f i c a n t l y i n the e s t i m a t i o n . The u n i o n i s seen t o c a r e about employment as w e l l as t h e wage w i t h s l i g h t l y more w e i g h t b e i n g p l a c e d on t h e e m p l o y m e n t l e v e l . R e n t m a x i m i z a t i o n i s a l w a y s r e j e c t e d . B a r g a i n i n g powers a r e c a l c u l a t e d a t each d a t a p o i n t and r e s u l t s i n d i c a t e t h a t the 1980's r e c e s s i o n i n c r e a s e d the r e l a t i v e power o f the u n i o n . The hypotheses o f e q u a l b a r g a i n i n g powers and complete u n i o n b a r g a i n i n g power a r e t e s t e d a n d r e j e c t e d . A l s o , t h e p r o p o r t i o n o f r e n t s c a p t u r e d by the f i r m i s found to be a poor i n d i c a t o r o f i t s b a r g a i n i n g power. A l t h o u g h t h e q u a l i t a t i v e r e s u l t s mentioned above are r o b u s t a c r o s s t h e f o u r m o d e l s , p a r a m e t e r v a l u e s a r e g e n e r a l l y s e n s i t i v e to b o t h the t e c h n o l o g y assumptions and i v the b a r g a i n i n g f r a m e w o r k . I g n o r i n g t h e s i m u l t a n e i t y o f wages, employment and o t h e r v a r i a b l e s chosen by the f i r m can be v e r y m i s l e a d i n g . F i n a l l y , the model i n which b o t h wages and employment a r e n e g o t i a t e d c o n s i s t e n t l y per forms b e t t e r t h a n the framework i n which employment i s u n i l a t e r a l l y s e t by the f i r m . V T a b l e o f C o n t e n t s A b s t r a c t i i L i s t o f T a b l e s v i i L i s t o f F i g u r e s v i i i Acknowledgements i x C h a p t e r 1: I n t r o d u c t i o n 1 C h a p t e r 2: Review o f the L i t e r a t u r e 14 C h a p t e r 3: The Model 36 3.1 The B a r g a i n i n g Game 37 3.2 A p p l i c a t i o n o f the B a r g a i n i n g Game to F i r m - Union C o n t r a c t N e g o t i a t i o n s 50 3.3 The F i r m ' s Techno logy and O b j e c t i v e s 58 3.4 Union O b j e c t i v e s 62 C h a p t e r 4: The Data and the E m p i r i c a l S p e c i f i c a t i o n o f the Model 64 4.1 The E s t i m a t i o n Models 64 4.2 The Data 77 4 . 2 . 1 The I n s t i t u t i o n a l S e t t i n g 79 4 . 2 . 2 I n d u s t r y P r i c e and Q u a n t i t y Data . . . 85 4 . 2 . 3 The A l t e r n a t i v e Wage 89 4 . 2 . 4 S t r i k e C o s t s 91 C h a p t e r 5: E s t i m a t i o n R e s u l t s 9 6 5.1 Exogenous Output Model 98 5 . 1 . 1 The F i r m s ' Techno logy 98 5 . 1 . 2 Union P r e f e r e n c e s 106 5 . 1 . 3 The C o n t r a c t Curve and the B a r g a i n i n g Se t s 107 v i 5 . 1 . 4 B a r g a i n i n g Powers 108 5 . 1 . 5 Comparing the COOP and LDEM Models . . 116 5.2 Exogenous C a p i t a l Model 117 5 . 2 . 1 The F i r m s ' Techno logy 117 5 . 2 . 2 U n i o n P r e f e r e n c e s 123 5 . 2 . 3 The C o n t r a c t Curve and the B a r g a i n i n g Se t s 125 5 . 2 . 4 B a r g a i n i n g Powers 127 5 . 2 . 5 Comparing the COOP and LDEM Models . . 1 3 0 5.3 Summary o f R e s u l t s 133 C h a p t e r 6: C o n c l u s i o n 138 B i b l i o g r a p h y 142 Data Sources and C o n s t r u c t i o n 147 A . l P r i c e and Q u a n t i t y I n d i c e s 147 A . 1.1 Output 148 A . 1.2 M a t e r i a l s and S u p p l i e s 149 A . l . 3 F u e l s and E l e c t r i c i t y 149 A . 1.4 Labour 151 A . 1.5 C a p i t a l S e r v i c e s 154 A . 1.6 Input C o s t Shares and P r o f i t s 163 A . 2 The A l t e r n a t i v e Wage 167 A . 3 S t r i k e C o s t s 172 v i i L i s t o f T a b l e s T a b l e I : E s t i m a t i o n Models Under the Assumpt ion o f an Exogenous Output P r o f i t F u n c t i o n . . . . 72 T a b l e I I : E s t i m a t i o n Models Under the Assumpt ion o f an Exogenous C a p i t a l P r o f i t F u n c t i o n 74 T a b l e I I I : D e s c r i p t i v e S t a t i s t i c s o f V a r i a b l e s . . . . 79 T a b l e I V : Exogenous Output E s t i m a t i o n R e s u l t s . . . . 1 0 0 T a b l e V : P r o p o r t i o n o f T o t a l Rents C a p t u r e d by the F i r m . C o o p e r a t i v e Model w i t h Exogenous Output 115 T a b l e V I : Exogenous C a p i t a l E s t i m a t i o n R e s u l t s . . . 119 T a b l e V I I : P r o p o r t i o n o f T o t a l Rents C a p t u r e d by the F i r m C o o p e r a t i v e Model w i t h Exogenous C a p i t a l 132 T a b l e V I I I : P r o p o r t i o n o f T o t a l Rents C a p t u r e d by the F i r m Labour Demand Model w i t h Exogenous C a p i t a l 133 T a b l e I X : Hours per Worker per Year i n the B . C . Wood P r o d u c t s I n d u s t r y 154 T a b l e X: Share o f P r o d u c t i o n Workers i n O v e r a l l Labour i n the B . C . Wood P r o d u c t s I n d u s t r y 156 T a b l e X I : P r o f i t s Net o f C a p i t a l S e r v i c e s and Input C o s t Shares i n the B . C . Wood P r o d u c t s I n d u s t r y 166 T a b l e X I I : Wage D i s t r i b u t i o n A c r o s s B . C 171 T a b l e X I I I : I n t e r i o r and C o a s t a l W e i g h t s , and A l t e r n a t i v e Wages 17 4 v i i i L i s t o f F i g u r e s F i g u r e 1: B a r g a i n i n g Frameworks 17 F i g u r e 2: P e r f e c t E q u i l i b r i a w i t h A l t e r n a t i n g O f f e r s and C o s t s o f De lay 39 F i g u r e 3: Labour Demand Curves and the C o n t r a c t C u r v e . Exogenous Output E s t i m a t i o n . . . . 105 F i g u r e 4: U n i o n B a r g a i n i n g Power. Exogenous Output E s t i m a t i o n 113 F i g u r e 5: Labour Demand Curves and the C o n t r a c t C u r v e . Exogenous C a p i t a l E s t i m a t i o n 12 3 F i g u r e 6: U n i o n B a r g a i n i n g Power. Exogenous C a p i t a l E s t i m a t i o n 130 i x Acknowled gement s I r e c e i v e d many h e l p f u l comments f r o m K e n n e t h C . B inmore , R ober t C . A l l e n , Mukesh Eswaran , Kenneth W h i t e , and s e v e r a l c o l l e a g u e s b o t h a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a and t h e U n i v e r s i t y o f Western O n t a r i o . I would e s p e c i a l l y l i k e t o thank B i l l Schworm and the members o f my committee - C r a i g R i d d e l l , T e r e n c e Wales , T r a c y L e w i s , and C h a r l e s B l a c k o r b y . F i n a n c i a l s u p p o r t from the S . S . H . R . C . i s g r a t e f u l l y acknowledged. 1 C h a p t e r 1 I n t r o d u c t i o n The o b j e c t o f t h i s r e s e a r c h i s t o s tudy how u n i o n s and f i r m s d i v i d e the s u r p l u s or r e n t s a v a i l a b l e t o them. Many i n s t r u m e n t s are used i n p r a c t i c e to make t h i s d i v i s i o n , but s t a n d a r d m i c r o d a t a o n l y i n c l u d e s t w o : wages a n d e m p l o y m e n t . I u s e a new a p p r o a c h t o s t u d y wage and employment c o n t r a c t s as I c o n s i d e r them e q u i l i b r i u m p o i n t s i n a n o n c o o p e r a t i v e b a r g a i n i n g game. T h i s w o r k i s a n e x t e n s i o n o f w a g e - e m p l o y m e n t d e t e r m i n a t i o n mode l s , the e x t e n s i o n b e i n g the i n c o r p o r a t i o n o f a b a r g a i n i n g g a m e . 1 I n wage-employment d e t e r m i n a t i o n mode l s , m i c r o d a t a on wage -employment c o n t r a c t s u s u a l l y between a s i n g l e u n i o n and i n d u s t r y are . s t u d i e d . C o n t r a r y t o P h i l l i p s ' c u r v e m o d e l s o f wage d e t e r m i n a t i o n , t h e s e s t u d i e s are based on r i g o r o u s models o f u n i o n o b j e c t i v e s and f i r m t e c h n o l o g i e s . I t i s r e c o g n i z e d t h a t n e g o t i a t e d a g r e e m e n t s a r e . t h e r e s u l t s o f f i r m - u n i o n b a r g a i n i n g and c o n s e q u e n t l y , f a c t o r s a f f e c t i n g the b a r g a i n i n g r e l a t i o n s h i p o r e i t h e r p a r t y ' s o b j e c t i v e s c a n a l s o i n f l u e n c e t h e c o n t r a c t . I n p r e v i o u s wage -employment d e t e r m i n a t i o n s t u d i e s , e i t h e r a p a r t i c u l a r w a g e - e m p l o y m e n t o u t c o m e was n o t ^•Examples o f wage-employment d e t e r m i n a t i o n s t u d i e s a r e : Brown and A s h e n f e l t e r ( 1 9 8 6 ) , C a r d ( 1 9 8 6 ) , C a r r u t h and O s w a l d ( 1 9 8 3 ) , D e r t o u z o s and P e n c a v e l (1981) , E b e r t s and Stone (1986) , F a r b e r (1978) , MaCurdy and P e n c a v e l (19 8 6 ) , M a r t i n e l l o (1984) . 2 p r e d i c t e d o r one o f the agents was a l l o w e d t o impose h i s p r e f e r r e d c h o i c e . W i t h a b a r g a i n i n g g a m e , a w a g e - employment outcome i s p r e d i c t e d w i t h o u t t h i s e x t r e m e a s s u m p t i o n on the b a r g a i n i n g powers o f the a g e n t s . G i v e n the o b j e c t i v e f u n c t i o n s o f the two p l a y e r s , t h e wage and e m p l o y m e n t e q u a t i o n s a r e s p e c i f i e d by t h e e q u i l i b r i u m c o n d i t i o n s f o r t h e game. A l s o , t h e game i s h e l p f u l i n i d e n t i f y i n g a d d i t i o n a l d e t e r m i n a n t s o f the c o n t r a c t s . The use o f game t h e o r e t i c models i n e m p i r i c a l r e s e a r c h i s s t i l l v e r y new. There are s e v e r a l reasons f o r t h i s . The t h e o r e t i c a l models are themselves f a i r l y r e c e n t and a l s o , t h e y e a s i l y become v e r y complex. C h a r a c t e r i z a t i o n o f the e q u i l i b r i a o f t e n r e q u i r e s s e v e r e l y s i m p l i f y i n g a s s u m p t i o n s e s p e c i a l l y when a d d i n g t h e r e q u i r e m e n t t h a t t h e s e t o f p o s s i b l e e q u i l i b r i u m p o i n t s be s m a l l . The f a c t t h a t t h e e q u i l i b r i a are o f t e n v e r y s e n s i t i v e to p a r t i c u l a r parameter v a l u e s o f the game m a g n i f i e s t h e d i f f i c u l t i e s . F i n a l l y , when d o i n g e m p i r i c a l a p p l i c a t i o n s t h e r e i s the a d d i t i o n a l prob lem t h a t v a r i a b l e s t h a t a r e c r u c i a l t o t h e game a r e o f t e n not o b s e r v a b l e ( e . g . p r i o r b e l i e f s ) . The paper by F u d e n b e r g , L e v i n e and Rudd (1985) i s the o n l y o t h e r example o f the use o f a n o n c o o p e r a t i v e b a r g a i n i n g game t o s tudy f i r m - u n i o n n e g o t i a t i o n s . They emphasize the p r e d i c t i o n o f s t r i k e l e n g t h s r a t h e r than the d i s t r i b u t i o n o f the s u r p l u s a l t h o u g h t h e i r m o d e l a l s o p r e d i c t s t h e wage r a t e . T h e i r f ramework i s v e r y d i f f e r e n t f r o m t h e one 3 adopted h e r e . They assume t h a t employment i s exogenous to the n e g o t i a t i o n p r o c e s s , t h a t the u n i o n c a r e s o n l y about the l e v e l o f the wage r a t e and o n l y the u n i o n can make o f f e r s . A l s o , t h e i r d a t a c o v e r s e v e r a l u n i o n s b a r g a i n i n g w i t h f i r m s i n d i f f e r e n t i n d u s t r i e s . No v a r i a t i o n i s a l l owed i n u n i o n b e h a v i o r , f i r m b e h a v i o r , and i n the b a r g a i n i n g framework i n w h i c h t h e y n e g o t i a t e . T h e s e a s s u m p t i o n s c o n f l i c t w i t h r e s u l t s o f t h e e m p i r i c a l s t u d i e s o f wage and employment d e t e r m i n a t i o n mentioned above. F i n a l l y , a paper by G u l and Sonnensche in (1985) r a i s e s q u e s t i o n s c o n c e r n i n g the v a l i d i t y o f t h e i r u n d e r l y i n g m o d e l . 2 The game I use i s a v e r s i o n o f the R u b i n s t e i n game as i t was f i r s t p r e s e n t e d i n R u b i n s t e i n (1982) and extended i n B i n m o r e (1987b and 1987C). R u b i n s t e i n ' s b a r g a i n i n g model has the advantage o f a l l o w i n g b o t h p a r t i e s t o make o f f e r s , a p r a c t i c e w h i c h i s g e n e r a l l y o b s e r v e d i n c o l l e c t i v e n e g o t i a t i o n s . In t h i s s t u d y , e s t i m a t i o n models are d e r i v e d u n d e r t h e a s s u m p t i o n s o f p e r f e c t i n f o r m a t i o n , c o n t i n u o u s t ime and d i s c o u n t i n g c o s t s . (The r o l e o f c o n t i n u o u s t i m e and d e l a y c o s t s i s e x p l a i n e d i n C h a p t e r 3. ) The r e s u l t i n g e q u i l i b r i u m i s un ique and i t can be w r i t t e n as the s o l u t i o n t o an o p t i m i z a t i o n p r o b l e m . More s p e c i f i c a l l y , i t can be r e p r e s e n t e d by a g e n e r a l i z e d Nash b a r g a i n i n g s o l u t i o n w i t h 2 G u l and S o n n e n s c h e i n (1985) a r g u e t h a t e q u i l i b r i a i n v o l v i n g d e l a y s ( s t r i k e s ) can o n l y o c c u r i n d i s c r e t e t ime games , w h e r e a s F u d e n b e r g , L e v i n e , and Rudd (1985) have a c o n t i n u o u s t ime mode l . 4 the we ights on the p l a y e r s ' ga ins i n u t i l i t y b e i n g f u n c t i o n s o f the c o s t s o f d e l a y . T h i s i s i m p o r t a n t as i t a l l o w s f o r q u i t e g e n e r a l s p e c i f i c a t i o n s o f t h e p l a y e r s ' o b j e c t i v e f u n c t i o n s . The d e r i v e d e q u i l i b r i u m wage and employment e q u a t i o n s r e p r e s e n t a r e l a t i o n s h i p be tween t h e o b s e r v e d c o n t r a c t , t h e parameters o f the u n i o n u t i l i t y , the f i r m ' s p r o f i t f u n c t i o n , and the c o s t s o f d e l a y i n g t h e a g r e e m e n t . In t h i s framework, c o s t s o f d e l a y are s t r i k e c o s t s and they measure the b a r g a i n i n g powers o f the n e g o t i a t i n g p a r t i e s . Because o f the p a r t i c u l a r v e r s i o n o f the game which was chosen and the consequent r e p r e s e n t a t i o n o f the e q u i l i b r i u m as a g e n e r a l i z e d Nash b a r g a i n i n g s o l u t i o n , t h i s s tudy i s i n some s e n s e c o m p a r a b l e t o t h e w o r k by S v e j n a r ( 1 9 8 6 ) . S v e j n a r s t u d i e s wages and employment l e v e l s i n 12 i n d u s t r i e s i n the U . S . Wage and employment e q u a t i o n s a r e d e r i v e d from a g e n e r a l i z e d N a s h b a r g a i n i n g s o l u t i o n i n w h i c h u t i l i t y we ights are exogenous ly de termined b a r g a i n i n g p o w e r s . I n one s e t o f e s t i m a t e s , the b a r g a i n i n g powers are assumed to be f i x e d . In a second s e t o f e s t i m a t e s , t h e b a r g a i n i n g p o w e r s a r e r e p r e s e n t e d by l i n e a r f u n c t i o n s o f s e v e r a l e x o g e n o u s f a c t o r s : C O L A c l a u s e s , wage c o n t r o l s a n d g u i d e l i n e s , the r e g i o n a l unemployment r a t e , and the r a t e o f i n f l a t i o n . T h i s s t u d y o f f e r s s e v e r a l a d v a n t a g e s over S v e j n a r ' s r e s e a r c h . The f a c t t h a t the wage and employment e q u a t i o n s a r e g e n e r a t e d by t h e e q u i l i b r i u m t o a non c o o p e r a t i v e 5 b a r g a i n i n g game i m p l i e s t h a t t h r e a t p o i n t s and b a r g a i n i n g powers h a v e n a t u r a l i n t e r p r e t a t i o n s based on the model o f t h e u n d e r l y i n g n e g o t i a t i o n p r o c e s s . 3 F o r e x a m p l e , b a r g a i n i n g powers are measured by r e l a t i v e s t r i k e c o s t s o f t h e p l a y e r s . A l s o , my m o d e l l i n g o f u n i o n p r e f e r e n c e s i s more g e n e r a l and output s and i n p u t s o t h e r t h a n l a b o u r a r e n o t t r e a t e d as e x o g e n o u s t o t h e b a r g a i n i n g p r o c e s s . F i n a l l y , o n l y one i n d u s t r y i s c o n s i d e r e d i n t h i s s t u d y . R e s u l t s f r o m wage -employment s t u d i e s c o n c e r n i n g workers ' o b j e c t i v e s , a n d S v e j n a r ' s e s t i m a t e s i n v o l v i n g f i x e d b a r g a i n i n g powers show l a r g e v a r i a t i o n s a c r o s s i n d u s t r i e s . However, i n h i s subsequent m o d e l l i n g o f b a r g a i n i n g p o w e r s , S v e j n a r a s s u m e s t h a t t h e c o e f f i c i e n t s o f t h e f a c t o r s a f f e c t i n g t h e b a r g a i n i n g p o w e r s a r e c o n s t a n t a c r o s s i n d u s t r i e s , and , w i t h the e x c e p t i o n o f COLA c l a u s e s , t h e r e a r e no u n i o n or i n d u s t r y s p e c i f i c d e t e r m i n a n t s . I c o n s i d e r the b a r g a i n i n g r e l a t i o n s h i p between a s i n g l e u n i o n , the I n t e r n a t i o n a l Woodworkers o f A m e r i c a (IWA) and the B . C . wood p r o d u c t s i n d u s t r y over the p e r i o d 1963-1983. T h i s u n i o n i s a good c a n d i d a t e f o r t h i s t y p e o f r e s e a r c h i n t h e s e n s e t h a t i t i s a s t a b l e , p o w e r f u l o r g a n i z a t i o n b e l i e v e d t o have been s u c c e s s f u l i n c a p t u r i n g r e n t s i n the B . C . l u m b e r and plywood i n d u s t r y . The e x i s t e n c e o f r e n t s 3 S v e j n a r (1986 ) j u s t i f i e s the use o f the g e n e r a l i z e d Nash b a r g a i n i n g s o l u t i o n by a Z e u t h e n - H a r s a n y i n e g o t i a t i o n m o d e l . However t h i s model i s based on the assumpt ion o f i r r a t i o n a l b e h a v i o r o f the p l a y e r s over t i m e . 6 not c a p t u r e d by government i n the B r i t i s h C o l u m b i a f o r e s t r y s e c t o r has been a r g u e d by s e v e r a l o b s e r v e r s and i s t h e r e s u l t o f a r e l a t i v e l y low stumpage fee f o r the h a r v e s t i n g o f t i m b e r on Crown L a n d s . M o r e o v e r , because o f the h i g h l e v e l o f v e r t i c a l i n t e g r a t i o n i n the s e c t o r and government p o l i c i e s c o n c e r n i n g the c a l c u l a t i o n o f stumpage fees and tax r a t e s , l o g g i n g c o m p a n i e s h a v e i n c e n t i v e s t o p a s s on a v a i l a b l e r e n t s t o t h e i r o p e r a t i o n s i n the wood p r o d u c t s i n d u s t r y i n the form o f low p r i c e s f o r l o g s . T h i s d a t a s e t a l s o has the advantage o f i n c l u d i n g i n p u t and o u t p u t q u a n t i t i e s and p r i c e s . My system o f e q u a t i o n s w i l l i n c l u d e i n p u t demands and the output s u p p l y i n a d d i t i o n t o t h e wage and employment e q u a t i o n s . C o m p e t i t i o n i s assumed i n t h e o u t p u t and n o n l a b o u r i n p u t s m a r k e t s . The a s s u m p t i o n o f an e x o g e n o u s p r i c e f o r m a t e r i a l s i s v e r y r e s t r i c t i v e g i v e n the r o l e o f l o g p r i c e s as t r a n s f e r p r i c e s . N e v e r t h e l e s s , the assumpt ion i s m a i n t a i n e d i n o r d e r t o a v o i d the m o d e l l i n g o f the whole f o r e s t r y s e c t o r . C o m p e t i t i o n i n the o u t p u t m a r k e t i s n o t u n r e a s o n a b l e f o r t h i s i n d u s t r y g i v e n t h a t a l a r g e p o r t i o n o f t h e p r o d u c t s a r e s o l d i n h i g h l y c o m p e t i t i v e i n t e r n a t i o n a l m a r k e t s . A l s o , t h e r e a r e i n d i c a t i o n s t h a t f i r m s s e l l i n g t h e i r p r o d u c t s i n Canada are f a c e d w i t h s t r o n g c o m p e t i t i o n from the U n i t e d S t a t e s . T h i s i n d u s t r y was s t u d i e d i n M a r t i n e l l o (1984) who c o n s i d e r s two p o s s i b l e b a r g a i n i n g frameworks. In one c a s e , t h e u n i o n u n i l a t e r a l l y c h o o s e s t h e wage w h i l e t h e f i r m 7 imposes i t s c h o i c e o f employment l e v e l a f t e r the wage i s s e t by the u n i o n . In the second mode l , the u n i o n and the f i r m s b a r g a i n e f f i c i e n t l y over both wages and employment. In such a framework, the r e s u l t i n g c o n t r a c t i s l o c a t e d on the P a r e t o f r o n t i e r which i s the l o c u s o f tangency p o i n t s between u n i o n i n d i f f e r e n c e c u r v e s and f i r m s ' i s o - p r o f i t c u r v e s . T h i s f r o n t i e r i s c a l l e d t h e c o n t r a c t c u r v e . I n M a r t i n e l l o (1984) , the c o n t r a c t c u r v e i s s p e c i f i e d and e s t i m a t e d but no e x p l a n a t i o n i s p r o v i d e d f o r the l o c a t i o n o f t h e p a r t i c u l a r c o n t r a c t w h i c h i s o b s e r v e d . O n e c o n t r i b u t i o n o f M a r t i n e l l o ' s work was the t r e a t m e n t o f i n p u t demands and o u t p u t s u p p l i e s as endogenous and hence as de termined i n p a r t by the b a r g a i n i n g outcome. As mentioned above, I a l s o adopt t h i s method. Other than the d i f f e r e n c e s i n the b a r g a i n i n g framework, t h i s s t u d y d i f f e r s f r o m M a r t i n e l l o ( 1 9 8 4 ) i n t h e s p e c i f i c a t i o n o f the u n i o n ' s and f i r m s ' o b j e c t i v e s (which are more s i m p l e and s t r a i g h t f o r w a r d 4 ) and i n the d a t a s e t . A l t h o u g h t h e raw i n d u s t r y d a t a i s t h e same, i m p o r t a n t changes are made i n the t rea tment o f the d a t a and the sample p e r i o d i s extended to i n c l u d e the e a r l y 1980's (see Appendix A f o r d e t a i l s ) . 4 I n p a r t i c u l a r , M a r t i n e l l o e x p r e s s e d t h e u n i o n o b j e c t i v e s i n terms o f employment and c o m p e n s a t i o n (wage t imes employment) r a t h e r than the u s u a l r e p r e s e n t a t i o n which i s done i n terms o f wages and employment. 8 I assume the u n i o n has a CES u t i l i t y f u n c t i o n d e f i n e d over wages and employment w h i l e the f i r m s maximize p r o f i t s s u b j e c t t o a C o b b - D o u g l a s t e c h n o l o g y . F o u r m o d e l s a r e e s t i m a t e d based on d i f f e r e n t t e c h n o l o g i c a l and b a r g a i n i n g a s s u m p t i o n s . Two o f the models are based on the assumpt ion t h a t the f i r m s and the u n i o n b a r g a i n over the wage o n l y w i t h t h e employment l e v e l t h e n b e i n g c h o s e n o p t i m a l l y by the f i r m . T h i s i m p l i e s t h a t the c o n t r a c t w i l l be l o c a t e d on the l a b o u r demand c u r v e . The o t h e r two models are e f f i c i e n t c o n t r a c t i n g m o d e l s i n w h i c h t h e wage and t h e employment l e v e l s a r e j o i n t l y de termined by b a r g a i n i n g . In each o f the two b a r g a i n i n g frameworks, the two models t h a t are e s t i m a t e d d i f f e r w i t h r e s p e c t t o assumptions c o n c e r n i n g the adjustment o f i n p u t s and output t o the l a b o u r c o n t r a c t . S p e c i f i c a l l y , i n one c a s e , o u t p u t i s t r e a t e d as exogenous w h i l e a l l i n p u t s a r e c h o s e n o p t i m a l l y as f u n c t i o n s o f t h e n e g o t i a t e d c o n t r a c t . I n t h e s e c o n d c a s e , o u t p u t i s endogenous and c a p i t a l i s now independent o f the wage employment c o n t r a c t . E a c h o f t h e f o u r systems o f s i m u l t a n e o u s , n o n l i n e a r , s t r u c t u r a l e q u a t i o n s i s e s t i m a t e d by a FIML p r o c e d u r e . The e s t i m a t e s o f t h e parameters o f the u n i o n u t i l i t y f u n c t i o n are q u i t e r o b u s t t o the changes i n the t e c h n o l o g y and t h e b a r g a i n i n g framework. The e s t i m a t e s imply t h a t the u n i o n c a r e s about both wages and employment w i t h r e l a t i v e l y more w e i g h t b e i n g p l a c e d on employment. The d i f f e r e n c e i n the w e i g h t s p l a c e d on wages and employment i s s m a l l e r when 9 o u t p u t i s t r e a t e d as endogenous and i n f a c t , the h y p o t h e s i s o f e q u a l we ights cannot be r e j e c t e d i n t h a t c a s e . The u n i o n i n d i f f e r e n c e c u r v e s a r e c o n v e x w i t h an e l a s t i c i t y o f s u b s t i t u t i o n o f .87 on average when output i s endogenous and o f a p p r o x i m a t e l y 1.0 when o u t p u t i s e x o g e n o u s . I n t h e l a t t e r c a s e , a C o b b - D o u g l a s r e p r e s e n t a t i o n o f the u n i o n p r e f e r e n c e s c a n n o t be r e j e c t e d . F o r a l l m o d e l s , t h e h y p o t h e s i s o f r e n t m a x i m i z a t i o n i s r e j e c t e d a t the 1% l e v e l o f s i g n i f i c a n c e . When o u t p u t i s t r e a t e d as e x o g e n o u s , t h e u n i o n b a r g a i n i n g power as measured by the weight g i v e n t o u n i o n u t i l i t y i n the Nash b a r g a i n i n g s o l u t i o n i s on average .86 (out o f a t o t a l o f 1 ) . I t f a l l s s l i g h t l y i n t h e 1 9 7 0 ' s f o l l o w e d by a r a p i d i n c r e a s e i n the 1980 ' s . When o u t p u t i s t r e a t e d as endogenous, u n i o n b a r g a i n i n g power i s c l o s e r to the f i r m s ' power. S p e c i f i c a l l y , i t averages .53 i n the case o f b a r g a i n i n g on the l a b o u r demand and .32 when c o n t r a c t s a r e l o c a t e d on the c o n t r a c t c u r v e . The t ime p r o f i l e i s a l s o d i f f e r e n t from the exogenous output e s t i m a t i o n i n t h a t u n i o n b a r g a i n i n g power now r i s e s s l o w l y i n the 1970 ' s . In a l l f o u r mode l s , t h e h y p o t h e s e s o f c o m p l e t e u n i o n power and e q u a l u n i o n a n d f i r m p o w e r a r e t e s t e d a n d r e j e c t e d . F i n a l l y , t h e r e s u l t s s u g g e s t t h a t t h e 1 9 8 0 ' s r e c e s s i o n c a u s e d a d e t e r i o r a t i o n i n t h e f i r m s ' b a r g a i n i n g p o s i t i o n s i n c e i n a l l m o d e l s , t h e b a r g a i n i n g power o f t h e u n i o n i n c r e a s e s s h a r p l y . 10 T h e p r o p o r t i o n o f r e n t s c a p t u r e d by t h e f i r m i s c a l c u l a t e d when p o s s i b l e a n d i s c o m p a r e d t o t h e f i r m b a r g a i n i n g p o w e r . 5 The p r o p o r t i o n o f r e n t s i s o f t e n used t o measure b a r g a i n i n g power and i t i s i n t e r e s t i n g t o see whether i t i s a good measure s i n c e r e n t m a x i m i z a t i o n i s not a c c e p t e d as a good d e s c r i p t i o n o f u n i o n b e h a v i o u r i n t h i s s t u d y . T h e two m e a s u r e s t u r n o u t t o be c o n s i d e r a b l y d i f f e r e n t . F o r example , i n the e f f i c i e n t c o n t r a c t i n g mode l , when o u t p u t i s exogenous, the p r o p o r t i o n o f r e n t s c a p t u r e d by the f i r m i s on average 42% compared t o a b a r g a i n i n g power o f 16%, and when output i s endogenous, the two measures are 77% and 68% r e s p e c t i v e l y . F u r t h e r m o r e , the t ime p r o f i l e s o f the two measures are no t m o n o t o n i c a l l y r e l a t e d . As ment ioned p r e v i o u s l y , i n R u b i n s t e i n ' s b a r g a i n i n g t h e o r y , the b a r g a i n i n g powers o f the p l a y e r s a r e f u n c t i o n s o f t h e i r r e l a t i v e c o s t s o f d e l a y or s t r i k e c o s t s . In t h i s s t u d y , these s t r i k e c o s t s are a l l owed to v a r y over t ime and a c r o s s g r o u p s o f f i r m s a c c o r d i n g t o e x o g e n o u s f a c t o r s . T h e s e f a c t o r s a r e commonly u s e d i n t h e e m p i r i c a l s t r i k e l i t e r a t u r e as d e t e r m i n a n t s o f s t r i k e c o s t s . I n a l l f o u r mode l s , the h y p o t h e s i s t h a t the s t r i k e c o s t s d i d not mat ter i s r e j e c t e d . 6 However, the c o e f f i c i e n t s on the s t r i k e c o s t 5 T h e b a r g a i n i n g power o f t h e f i r m s i s e q u a l to one minus the u n i o n ' s b a r g a i n i n g power as d e s c r i b e d above. 6 T h e t e s t t h a t c o s t s do not a f f e c t the l a b o u r c o n t r a c t i s i d e n t i c a l t o the t e s t t h a t the u n i o n s t r i k e c o s t s a r e zero i . e . a l l c o e f f i c i e n t s i n the term r e p r e s e n t i n g r e l a t i v e 1 1 v a r i a b l e s are s e n s i t i v e to the b a r g a i n i n g framework and the t e c h n o l o g i c a l a s s u m p t i o n s and t h e i r s t a n d a r d e r r o r s are o f t e n l a r g e . In the e f f i c i e n t c o n t r a c t i n g mode l , the f i r m s ' r e l a t i v e s t r i k e c o s t s a r e n e g a t i v e l y and s i g n i f i c a n t l y a f f e c t e d by i n t e r e s t r a t e s and c a p i t a l u t i l i z a t i o n r a t i o s . E f f e c t s o f i n v e n t o r y l e v e l s and l a b o u r market c o n d i t i o n s depend on the t e c h n o l o g y a s sumpt ions . P a r t o f the problem o f l a r g e s t a n d a r d e r r o r s i s c a u s e d by t h e c o n s i d e r a b l e amount o f m u l t i c o l l i n e a r i t y w h i c h i s p r e s e n t among t h e s e v a r i a b l e s . A t t e m p t s t o f i n d b e t t e r d a t a f a i l e d as o t h e r v a r i a b l e s w h i c h were u s e d d i d n o t p r o v i d e a d d i t i o n a l i n f o r m a t i o n . A l s o , a t t e m p t s t o e s t i m a t e s e p a r a t e l y the s t r i k e c o s t s o f the f i r m and the u n i o n were not s u c c e s s f u l . When o u t p u t i s t r e a t e d as e x o g e n o u s , the l i k e l i h o o d v a l u e i n c r e a s e s and the p r e d i c t i o n o f employment i m p r o v e s c o n s i d e r a b l y b u t t h e r e s u l t i n g l a b o u r c o e f f i c i e n t ( t h e l a b o u r c o s t share) i s i m p l a u s i b l y l o w . I n t h e e f f i c i e n t c o n t r a c t i n g m o d e l t h i s i m p l i e s a s m a l l m a r g i n a l revenue p r o d u c t o f l a b o u r . P a r t o f the p r o b l e m i s c a u s e d by t h e l a r g e amount o f c o r r e l a t i o n between employment and o u t p u t . T h i s r e s u l t s i n a l a r g e s t a n d a r d e r r o r on t h e employment c o e f f i c i e n t . However, even when u s i n g the upper bound o f a c o n f i d e n c e i n t e r v a l , the l a b o u r c o e f f i c i e n t e s t i m a t e i n the c o o p e r a t i v e m o d e l i s v e r y s m a l l . O t h e r w i s e , t h e s t r i k e c o s t s are s e t t o z e r o . 12 t e c h n o l o g i c a l p a r a m e t e r s ( e . g . demand e l a s t i c i t i e s ) seem r e a s o n a b l e and they are comparable to p r e v i o u s e s t i m a t e s . C o n s i s t e n t l y throughout the e s t i m a t i o n , the e f f i c i e n t c o n t r a c t i n g model performs b e t t e r i n the sense o f g e n e r a t i n g a h i g h e r l i k e l i h o o d v a l u e . However, the parameter e s t i m a t e s seem t o be more s e n s i t i v e to t e c h n o l o g i c a l assumpt ions than t o t h e b a r g a i n i n g f r a m e w o r k u s e d . T h i s h a s s e r i o u s i m p l i c a t i o n s f o r t h e i n t e r p r e t a t i o n o f r e s u l t s i n wage- employment d e t e r m i n a t i o n s t u d i e s where the t e c h n o l o g y i s not m o d e l l e d r i g o r o u s l y . O v e r a l l , the b a r g a i n i n g game by R u b i n s t e i n proves t o be t r a c t a b l e and amenable t o e m p i r i c a l r e s e a r c h . In g e n e r a l , t h e e s t i m a t i o n y i e l d s r e a s o n a b l e t e c h n o l o g i c a l parameters and many o f the r e s u l t s c o n c e r n i n g t h e u n i o n u t i l i t y a r e comparable t o p r e v i o u s f i n d i n g s . F u r t h e r m o r e , new i n s i g h t s a r e p r o v i d e d on b a r g a i n i n g powers and t h e measurement o f s t r i k e c o s t s . T h i s t h e s i s i s o r g a n i z e d as f o l l o w s . A rev iew o f the l i t e r a t u r e i s p r o v i d e d i n t h e n e x t c h a p t e r . T h i s i s f o l l o w e d i n C h a p t e r 3 by a d e s c r i p t i o n o f the b a r g a i n i n g game and i t s a p p l i c a t i o n t o c o n t r a c t n e g o t i a t i o n s . The m o d e l l i n g o f t h e u n i o n a n d f i r m s ' o b j e c t i v e s i s a l s o d i s c u s s e d i n C h a p t e r 3 . C h a p t e r 4 i s composed o f two p a r t s : f i r s t , the models t o be e s t i m a t e d are d e r i v e d based on the assumpt ions g i v e n i n the p r e v i o u s c h a p t e r , and s e c o n d l y , a s h o r t d i s c u s s i o n o f t h e d a t a i s p r o v i d e d . E s t i m a t i o n 13 r e s u l t s a r e p r e s e n t e d i n C h a p t e r 5 and f i n a l l y , c o n c l u d i n g r e m a r k s a r e made i n C h a p t e r 6 . D e t a i l s c o n c e r n i n g d a t a s o u r c e s and m a n i p u l a t i o n s are p r o v i d e d i n Appendix A . 14 C h a p t e r 2 R e v i e w o f t h e L i t e r a t u r e I n t h i s s e c t i o n , a n o v e r v i e w o f t h e l i t e r a t u r e i n r e l e v a n t a r e a s i s p r e s e n t e d . S i n c e my w o r k t o u c h e s u p o n s e v e r a l a r e a s o f r e s e a r c h , t h i s i s by n o means a n e x h a u s t i v e r e v i e w . T h e r e a r e b a s i c a l l y t w o m a j o r l i t e r a t u r e s i n v o l v e d : w a g e - e m p l o y m e n t d e t e r m i n a t i o n m o d e l s a n d n o n c o o p e r a t i v e b a r g a i n i n g g a m e s . I w i l l s t a r t by d i s c u s s i n g t h e f i r s t a s i t w i l l s e r v e t o m o t i v a t e t h e c h o i c e o f a b a r g a i n i n g m o d e l . O t h e r t o p i c s w h i c h w i l l b e m e n t i o n e d i n c l u d e : m o d e l s o f u n i o n b e h a v i o u r , c o o p e r a t i v e b a r g a i n i n g g a m e s a n d s t r i k e t h e o r y . I n w a g e - e m p l o y m e n t d e t e r m i n a t i o n (W-E) m o d e l s , m i c r o d a t a o n w a g e - e m p l o y m e n t c o n t r a c t s b e t w e e n a u n i o n a n d a p a r t i c u l a r i n d u s t r y a r e s t u d i e d . C o n t r a r y t o P h i l l i p s ' c u r v e m o d e l s o f wage d e t e r m i n a t i o n , t h e s e s t u d i e s a r e b a s e d o n r i g o r o u s m o d e l s o f u n i o n o b j e c t i v e s a n d f i r m t e c h n o l o g i e s . I t i s a l s o r e c o g n i z e d t h a t n e g o t i a t e d a g r e e m e n t s a r e t h e r e s u l t o f f i r m - u n i o n b a r g a i n i n g a n d c o n s e q u e n t l y , f a c t o r s a f f e c t i n g e i t h e r p a r t y ( e . g . t h e f i r m ' s p r o d u c t m a r k e t c o n d i t i o n s a n d t h e u n i o n ' s p r e f e r e n c e s ) c a n i n f l u e n c e t h e o u t c o m e . W a g e - e m p l o y m e n t m o d e l s h a v e t h r e e c o m p o n e n t s e a c h o f w h i c h i s a n a r e a o f r e s e a r c h i n i t s e l f . T h e y a r e : t h e m o d e l l i n g o f u n i o n g o a l s , f i r m o b j e c t i v e s a n d c o n s t r a i n t s , a n d t h e b a r g a i n i n g f r a m e w o r k . F i r m s a r e u s u a l l y a s s u m e d t o 15 maximize p r o f i t s . The r e p r e s e n t a t i o n o f t h e t e c h n o l o g y v a r i e s a l o t a c r o s s s t u d i e s . Examples w i l l be g i v e n l a t e r on i n t h i s c h a p t e r . T h e m o d e l l i n g o f u n i o n b e h a v i o u r h a s b e e n a c o n t r o v e r s i a l i s s u e i n i n d u s t r i a l r e l a t i o n s ever s i n c e t h e 1940 ' s . The q u e s t i o n i s : can we model u n i o n o b j e c t i v e s by a common w e l l - b e h a v e d u t i l i t y f u n c t i o n o r i s t h e u n i o n ' s d e c i s i o n - m a k i n g too complex to be even approximated by such a f o r m u l a t i o n ? I n most c a s e s , economists have assumed the e x i s t e n c e o f a w e l l - d e f i n e d u t i l i t y f u n c t i o n w i t h o u t s p e c i f y i n g t h e u n d e r l y i n g p r o c e s s g e n e r a t i n g i t . Two e x c e p t i o n s are Oswald (1982) and B l a i r and Crawford ( 1984 ) who i n v e s t i g a t e t h e i m p l i c a t i o n s on u n i o n p r e f e r e n c e s o f v a r i o u s assumptions c o n c e r n i n g w o r k e r s ' p r e f e r e n c e s and t h e p o l i t i c a l p r o c e s s under which the u n i o n o p e r a t e s . To d a t e , the r e s u l t s have been d i s c o u r a g i n g i n the sense t h a t o n l y i n v e r y s p e c i a l c a s e s i s i t p o s s i b l e t o g e n e r a t e a w e l l - b e h a v e d u n i o n u t i l i t y f u n c t i o n from the u n d e r l y i n g w o r k e r s ' p r e f e r e n c e s . F o r e x a m p l e , a r e n t m a x i m i z i n g u t i l i t y f u n c t i o n c a n be g e n e r a t e d by a u n i o n who maximizes a r e p r e s e n t a t i v e w o r k e r ' s e x p e c t e d u t i l i t y i f t h i s expected u t i l i t y i s e q u a l t o the w o r k e r ' s expected income and i f a l l workers i n the u n i o n ' s f i x e d membership have an e q u a l chance o f b e i n g employed. In t h i s s t u d y , I assume the e x i s t e n c e o f a w e l l - b e h a v e d u n i o n u t i l i t y f u n c t i o n , but I b e l i e v e t h e r e i s a l o t o f i m p o r t a n t 16 work t o be done i n t h i s a r e a . (See F a r b e r (1986 ) f o r a d i s c u s s i o n o f t h e i s s u e s i n v o l v e d ) . Two d i f f e r e n t b a r g a i n i n g s e t - u p s have been c o n s i d e r e d i n W-E s t u d i e s . In the f i r s t one, i t i s assumed t h a t the u n i o n and the f i r m b a r g a i n over wages o n l y , the employment l e v e l b e i n g c h o s e n by t h e f i r m . T h i s i m p l i e s t h a t t h e c o n t r a c t w i l l be l o c a t e d on the l a b o u r demand c u r v e . In the s e c o n d f r a m e w o r k b o t h wages and e m p l o y m e n t l e v e l s a r e n e g o t i a t e d . E f f i c i e n t b a r g a i n i n g t h e n y i e l d s outcomes s i t u a t e d on a c o n t r a c t c u r v e (the P a r e t o f r o n t i e r ) which i s d e f i n e d by the l o c u s o f tangency p o i n t s between the u n i o n ' s i n d i f f e r e n c e c u r v e s and the f i r m ' s i s o - p r o f i t c u r v e s . T h i s c o n t r a c t c u r v e w i l l i n g e n e r a l be t o the r i g h t o f the l a b o u r demand c u r v e i n wage-employment s p a c e . T h i s i s e a s i l y seen from F i g u r e l ( f o l l o w i n g p a g e ) . In F i g u r e 1, D i s a l a b o u r demand, F i s an i s o - p r o f i t c u r v e , 0 i s a u n i o n i n d i f f e r e n c e c u r v e , and C i s t h e c o n t r a c t c u r v e . I s o - p r o f i t c u r v e s a r e h o r i z o n t a l a t t h e p o i n t o f i n t e r s e c t i o n w i t h the l a b o u r demand and they are n e g a t i v e l y s l o p e d t o the r i g h t o f the demand. U n l e s s t h e u n i o n i n d i f f e r e n c e c u r v e s are h o r i z o n t a l ( i n which case the u n i o n does n o t c a r e a b o u t t h e employment l e v e l ) , t h e i r tangency p o i n t s w i t h i s o - p r o f i t c u r v e s w i l l be to the r i g h t o f t h e l a b o u r demand. 17 F i g u r e 1 B a r g a i n i n g Frameworks Wage Employment In the case o f a r e n t m a x i m i z i n g u n i o n ( i . e . t h e u n i o n u t i l i t y t a k e s the form E»(W-W^) where i s the a l t e r n a t i v e wage), the c o n t r a c t c u r v e i s v e r t i c a l . The employment l e v e l i s d e t e r m i n e d by e q u a t i n g the m a r g i n a l revenue p r o d u c t o f l a b o u r w i t h the a l t e r n a t i v e wage (see p o i n t E A i n F i g u r e l ) . T h i s l e v e l o f employment m a x i m i z e s t o t a l r e n t s a n d i s i n d e p e n d e n t o f t h e n e g o t i a t e d wage. The c o n t r a c t wage s e r v e s t o d i v i d e the r e n t s between the u n i o n and t h e f i r m . N o t e t h a t u n d e r t h e a s s u m p t i o n s o f r e n t m a x i m i z a t i o n and b a r g a i n i n g over b o t h wages and e m p l o y m e n t , t h e r e s u l t i n g c o n t r a c t s w i l l be e f f i c i e n t i n t h e sense t h a t the employment l e v e l i s a l s o t h e c o m p e t i t i v e employment l e v e l . T h i s 18 p r o p e r t y i s c a l l e d " s t r o n g e f f i c i e n c y " by B r o w n a n d A s h e n f e l t e r (1986) . Note t h a t i n e i t h e r the l a b o u r demand o r the c o n t r a c t c u r v e mode l s , no p a r t i c u l a r outcome on the r e l e v a n t c u r v e i s p r e d i c t e d u n l e s s one a g e n t i s f r e e to impose h i s c h o i c e . U s u a l l y , i n the s t u d i e s based on a l a b o u r demand mode l , the u n i o n i s a s s u m e d t o c h o o s e t h e wage. The p o i n t M i n F i g u r e 1 i s an example o f a p r e d i c t e d c o n t r a c t under such an a s s u m p t i o n . T h i s framework i s c a l l e d the monopoly mode l . I n t h e s t u d i e s b a s e d on t h e c o n t r a c t c u r v e m o d e l ( a l s o c a l l e d c o o p e r a t i v e m o d e l ) , t h e wage i s n o t e x p l a i n e d . E c o n o m e t r i c a l l y , e i t h e r t h e wage i s t r e a t e d as e x o g e n o u s ( e . g . M a r t i n e l l o (1984) ) , or the endogene i ty o f the wage i s r e c o g n i z e d by the use o f i n s t r u m e n t a l v a r i a b l e s b u t , t h e r e i s no u n d e r l y i n g m o d e l e x p l a i n i n g t h e c h o i c e o f t h e i n s t r u m e n t s ( e . g . MaCurdy and P e n c a v e l ( 1 9 8 6 ) ) . U n l e s s a m o n o p o l y m o d e l o f u n i o n s i s assumed, the p r e d i c t i o n o f a p a r t i c u l a r c o n t r a c t r e q u i r e s t h e s p e c i f i c a t i o n o f a b a r g a i n i n g mode l . None o f the wage-employment d e t e r m i n a t i o n s t u d i e s i n c l u d e such a mode l . Once u n i o n p r e f e r e n c e s and the f i r m ' s p r o f i t f u n c t i o n h a v e been s p e c i f i e d , wage and employment e q u a t i o n s a r e d e r i v e d and e s t i m a t e d . The e s t i m a t i o n r e s u l t s a r e used to make i n f e r e n c e s about u n i o n o b j e c t i v e s , and p o s s i b l y t h e f i r m ' s t e c h n o l o g y and p r o d u c t market . In some W-E s t u d i e s , e s t i m a t i o n r e s u l t s a r e u s e d t o e v a l u a t e b a r g a i n i n g 19 frameworks i . e . w h e t h e r t h e d a t a i s b e t t e r e x p l a i n e d by l o c a t i n g the outcomes on a c o n t r a c t c u r v e , a l a b o u r demand c u r v e , or a t the u n i o n ' s p r e f e r r e d wage l e v e l on the l a b o u r demand c u r v e . The f i r s t d a t a s e t used f o r such s t u d i e s i n v o l v e d the U n i t e d Mine Workers and the b i tuminous c o a l i n d u s t r y i n the U . S . F a r b e r (1978) assumes the monopoly model h o l d s and t h a t the u n i o n a c t s as i f i t maximizes the expected u t i l i t y o f t h e m e d i a n aged member. H i s c e n t r a l r e s u l t i s t h a t the workers are q u i t e r i s k averse which sugges ts t h a t the u n i o n p l a c e s s u b s t a n t i a l weight on employment. C a r r u t h and Oswald (1983) d e v e l o p and e s t i m a t e a model o f the wage p o l i c y o f the N a t i o n a l Union o f Mineworkers i n G r e a t B r i t a i n . As i n F a r b e r (1978) , i t i s assumed t h a t the u n i o n c a n c h o o s e wages s u b j e c t t o a l a b o u r demand c o n s t r a i n t . I n t h e i r m o d e l l i n g o f t h e l a b o u r demand h o w e v e r , t h e y a l l o w f o r p a r t i a l adjustment o f l a b o u r over t ime due t o the presence o f adjustment c o s t s . The workers a r e i d e n t i c a l w i t h c o n s t a n t r e l a t i v e r i s k a v e r s i o n u t i l i t y f u n c t i o n s a n d t h e u n i o n b e h a v e s as i f i t a d o p t e d a u t i l i t a r i a n r u l e . A g a i n the workers are found t o be r i s k a v e r s e but l e s s so than t h e i r U . S . c o u n t e r p a r t s . The I n t e r n a t i o n a l T y p o g r a p h i c a l Union (ITU) l o c a l s i n a number o f Amer ican c i t i e s have been the s u b j e c t o f s e v e r a l w a g e - e m p l o y m e n t d e t e r m i n a t i o n s t u d i e s . D e r t o u z o s and P e n c a v e l (1981) , P e n c a v e l (1984a) , and P e n c a v e l (1984b) a l l 20 assume t h e m o n o p o l y m o d e l o f b a r g a i n i n g . T h e m a j o r d i f f e r e n c e i n t h e m o d e l s i s i n t h e s p e c i f i c a t i o n o f the u n i o n l o c a l s ' o b j e c t i v e s . These are found t o v a r y a c r o s s l o c a l s . P o p u l a r f o r m s o f u n i o n p r e f e r e n c e s such as the m a x i m i z a t i o n o f t h e wage b i l l and o f e c o n o m i c r e n t s a r e o f t e n r e j e c t e d . The r e s u l t s suggest t h a t i n most c a s e s , r e l a t i v e l y h i g h weights are p l a c e d on employment. In the next two s t u d i e s , n e s t e d t e s t s are performed to e v a l u a t e t h e a p p l i c a b i l i t y o f e f f i c i e n t c o n t r a c t o r c o o p e r a t i v e m o d e l s t o t h e d a t a . Brown and A s h e n f e l t e r (1986) assume t h e ITU m a x i m i z e s r e n t s and t e s t w h e t h e r e m p l o y m e n t i s d e t e r m i n e d b y t h e a l t e r n a t i v e wage ( e f f i c i e n c y ) o r the c o n t r a c t wage (the c o n t r a c t i s on t h e l a b o u r demand c u r v e ) . They f i n d t h a t b o t h wages a f f e c t employment w h i c h s u g g e s t s t h a t t h e c o n t r a c t s i n t h i s i n d u s t r y a r e i n e f f i c i e n t . However, i t c o u l d a l s o mean r e n t m a x i m i z a t i o n i s n o t a g o o d d e s c r i p t i o n o f t h e I T U ' s b e h a v i o u r . MaCurdy and P e n c a v e l ' s (1986) t e s t i s based on the o b s e r v a t i o n t h a t a p r o f i t m a x i m i z i n g f i r m t h a t i s f r e e to choose i t s i n p u t l e v e l s w i l l s e t i n p u t p r i c e r a t i o s e q u a l to the r a t i o o f the same i n p u t ' s m a r g i n a l revenue p r o d u c t . I f employment i s chosen by e f f i c i e n t c o n t r a c t i n g , an e x t r a term appears i n the wage e q u a t i o n i n the form o f the u n i o n ' s m a r g i n a l r a t e o f s u b s t i t u t i o n between wages and employment, A q u i t e g e n e r a l f u n c t i o n a l form i s assumed f o r the MRS and the e x t r a term i s found to be i m p o r t a n t i n the e s t i m a t i o n . 21 T h e y c o n c l u d e t h a t an o u t c o m e on t h e l a b o u r demand c o n s t r a i n t i s u n l i k e l y i n the ITU n e g o t i a t i o n s . M a r t i n e l l o ( 1 9 8 4 ) s t u d i e s t h e b e h a v i o u r o f t h e I n t e r n a t i o n a l Woodworkers o f A m e r i c a , i n p a r t i c u l a r the l o c a l s o f the IWA b a r g a i n i n g w i t h the B r i t i s h Co lumbia wood p r o d u c t s i n d u s t r y . The u n i o n i s assumed to have a u t i l i t y f u n c t i o n w h i c h i s q u a d r a t i c i n l a b o u r and c o m p e n s a t i o n . N o n - n e s t e d t e s t s s u g g e s t t h a t t h e e f f i c i e n t c o n t r a c t i n g model per forms b e t t e r than the monopoly mode l . The u n i o n i s c o n c e r n e d w i t h b o t h wage and employment l e v e l s and t h e a l t e r n a t i v e wage. Both wage b i l l and r e n t m a x i m i z a t i o n are t e s t e d and r e j e c t e d . The s tudy by M a r t i n e l l o i n v o l v e s a more r i g o r o u s m o d e l l i n g o f t h e f i r m ' s t e c h n o l o g y . I n p a r t i c u l a r , i t i s assumed t h a t the f i r m a d j u s t s o t h e r i n p u t l e v e l s t o t h e l a b o u r c o n t r a c t r a t h e r t h a n f i x i n g t h e m e x o g e n o u s l y . A l s o , g e n e r a l f u n c t i o n a l forms a r e adopted to r e p r e s e n t t h e f i r m s ' t e c h n o l o g y . U n f o r t u n a t e l y , h i s e s t i m a t e s do no t s u p p o r t the c u r v a t u r e p r o p e r t i e s a s s o c i a t e d w i t h p r o f i t m a x i m i z i n g b e h a v i o u r a n d h i s c h o i c e o f f u n c t i o n a l forms . The s tudy by C a r d (1986) i n v o l v e s a i r l i n e mechanics i n seven a i r l i n e s i n the U . S . S e v e r a l u n i o n s are i n v o l v e d but they a r e a l l assumed t o behave i d e n t i c a l l y , i n p a r t i c u l a r , t o maximize r e n t s . T h i s framework, which i s s i m i l a r to t h a t i n Brown and A s h e n f e l t e r (1986) , i s extended to a l l o w f o r an a d d i t i o n a l e f f e c t o f the a l t e r n a t i v e wage on t h e l e v e l o f 22 employment. More s p e c i f i c a l l y , Card assumes t h a t the f i r m f a c e s a d j u s t m e n t c o s t s i n i t s l a b o u r i n p u t so t h a t t h e p r o f i t m a x i m i z i n g l e v e l o f employment i s a f u n c t i o n o f p a s t employment and f u t u r e wage r a t e s . M o r e o v e r , e x p e c t a t i o n s o f f u t u r e wage r a t e s are f u n c t i o n s o f c u r r e n t a l t e r n a t i v e wages w h i c h i m p l i e s t h a t e v e n i f t h e l a b o u r demand c u r v e i s a b i n d i n g c o n s t r a i n t , employment c o n t r a c t s w i l l be f u n c t i o n s o f t h e a l t e r n a t i v e w a g e . H o w e v e r , he f i n d s t h a t an u n r e s t r i c t i v e f u n c t i o n f o r employment where n e i t h e r t h e monopoly model (wi th the dynamic l a b o u r demand) nor the r e n t m a x i m i z i n g c o n t r a c t c u r v e are imposed per forms b e t t e r . T h e l a s t wage -employment d e t e r m i n a t i o n s t u d y t o be rev iewed i s by E b e r t s and Stone (1986) and i n v o l v e s p u b l i c s c h o o l t e a c h e r s . E b e r t s and S t o n e (1986) r e j e c t t h e h y p o t h e s i s t h a t outcomes a r e l o c a t e d on a l a b o u r demand c u r v e a f t e r f i n d i n g a p o s i t i v e r e l a t i o n s h i p between wage c o m p e n s a t i o n and employment p r o t e c t i o n c l a u s e s s u c h as l i m i t s on c l a s s s i z e s . By c o n t r a s t , they f i n d the expected n e g a t i v e e f f e c t on s a l a r y o f changes i n non-employment j o b a t t r i b u t e s such as f r i n g e b e n e f i t s and l e a v e p r o v i s i o n s . A d i f f e r e n t approach i s t aken i n Abowd (1987) who uses the b e h a v i o u r o f s t o c k v a l u e s i n response t o the s i g n i n g o f c o l l e c t i v e agreements t o t e s t whether the d a t a s u p p o r t s an e f f i c i e n t b a r g a i n i n g m o d e l or a framework where the f i r m u n i l a t e r a l l y c h o o s e s e m p l o y m e n t . T h a t d a t a c o n s i s t s o f c o n t r a c t s s i g n e d f r o m 1976 t o 1982 i n v o l v i n g U . S . 23 m a n u f a c t u r i n g and n o n - m a n u f a c t u r i n g f i r m s w i t h p u b l i c l y t r a d e d s t o c k s . A l l u n i o n s a r e a s s u m e d t o be r e n t m a x i m i z e r s . Abowd f i n d s t h a t t h e c o l l e c t i v e a g r e e m e n t s s e r v e t o d i s t r i b u t e t h e f i r m s ' r e n t s t o w o r k e r s and s h a r e h o l d e r s b u t do n o t seem t o p r o v i d e i n f o r m a t i o n t o s t o c k h o l d e r s c o n c e r n i n g t h e u n i o n s ' ( p o s s i b l y p r i v a t e ) i n f o r m a t i o n on f u t u r e l a b o u r c o s t s . T h i s i s c o n s i s t e n t w i t h t h e h y p o t h e s i s o f a common i n f o r m a t i o n s e t f o r t h e u n i o n s and the f i r m s b a r g a i n i n g t o g e t h e r . I n Abowd' s m o d e l t h e e f f i c i e n t a n d i n e f f i c i e n t c o n t r a c t i n g f r a m e w o r k s have d i f f e r e n t i m p l i c a t i o n s f o r t h e r e l a t i o n s h i p b e t w e e n u n e x p e c t e d c h a n g e s i n u n i o n m e m b e r s ' w e a l t h a n d s t o c k h o l d e r s ' w e a l t h . The e m p i r i c a l r e s u l t s s u p p o r t t h e p r e d i c t i o n s o f the e f f i c i e n t c o n t r a c t i n g mode l . T h e r e a r e v a r i o u s p o s s i b l e e x t e n s i o n s t o e m p i r i c a l models o f wage-employment d e t e r m i n a t i o n some o f which would i n v o l v e m o r e e x p l i c i t m o d e l l i n g o f t h e e f f e c t s o f u n c e r t a i n t y and p r i v a t e i n f o r m a t i o n . A n o t h e r i m p o r t a n t e x t e n s i o n i s the i n c o r p o r a t i o n o f a b a r g a i n i n g mode l . Not o n l y can a b a r g a i n i n g model be used t o i d e n t i f y the i n f l u e n c e o f a d d i t i o n a l e x o g e n o u s f a c t o r s b u t i t may s h e d new l i g h t on t h e way p r e v i o u s l y u s e d d e t e r m i n a n t s a f f e c t wage -employment c o n t r a c t s . A s an e x a m p l e , w i t h the use o f a b a r g a i n i n g game, we c o u l d take i n t o a c c o u n t e f f e c t s o f t h e a l t e r n a t i v e wage o r l a b o u r 24 market c o n d i t i o n s on the c o n t r a c t wage by i t s i n f l u e n c e on the r e l a t i v e b a r g a i n i n g s t r e n g t h s o f the a g e n t s . In most o f the W-E s t u d i e s , the importance o f e x p l i c i t m o d e l l i n g o f t h e b a r g a i n i n g p r o c e s s i s m e n t i o n e d . The p r o b l e m h a s b e e n t h e l a c k o f a p p r o p r i a t e m o d e l s . H i s t o r i c a l l y , b a r g a i n i n g models have been o f two t y p e s . The f i r s t t y p e c o n s i s t s o f a x i o m a t i c m o d e l s ( o r c o o p e r a t i v e games) i n which a p a r t i c u l a r outcome i s chosen on the b a s i s o f i t s c h a r a c t e r i s t i c s ( e . g . symmetry) . U n l e s s one r e l i e s on f o c a l - p o i n t t y p e arguments , these models p r e s c r i b e what t h e s o l u t i o n o u g h t t o l o o k l i k e r a t h e r t h a n what i t i s observed t o be . In t h a t sense they are more a p p r o p r i a t e f o r the s tudy o f a r b i t r a t i o n d e c i s i o n s than n e g o t i a t e d outcomes. I n a n y c a s e , t h e f a c t t h a t t h e s e m o d e l s c o n t a i n no d e s c r i p t i o n o f the p r o c e s s by w h i c h a g e n t s a r r i v e a t t h e s o l u t i o n makes them d i f f i c u l t t o use i n e m p i r i c a l s t u d i e s o f n o n - e x p e r i m e n t a l b a r g a i n i n g s e t t i n g s . 7 The best -known a x i o m a t i c b a r g a i n i n g m o d e l i s t h e one f i r s t p r o p o s e d by J . N a s h . The Nash b a r g a i n i n g s o l u t i o n s a t i s f i e s the f o u r axioms o f symmetry, P a r e t o o p t i m a l i t y , I n d e p e n d e n c e o f i r r e l e v a n t a l t e r n a t i v e s and i n v a r i a n c e to l i n e a r t r a n s f o r m a t i o n s . I t can be w r i t t e n as the s o l u t i o n 7 S e e Roth (1979) and R i d d e l l (1981) f o r d i s c u s s i o n s o f v a r i o u s s o l u t i o n c o n c e p t s . T h e r e i s a s u b s t a n t i a l l i t e r a t u r e on e x p e r i m e n t a l b a r g a i n i n g s t u d i e s i n w h i c h v a r i o u s b a r g a i n i n g s o l u t i o n s are t e s t e d . F o r example, see Coursey (1982) and Roth and Schoumaker (1983) . 25 t o t h e m a x i m i z a t i o n o f t h e p r o d u c t o f t h e two p l a y e r s ' u t i l i t y increments over t h e i r t h r e a t p o i n t s . I f symmetry i s r e l a x e d , d i f f e r e n t weights can be a t t a c h e d t o the p l a y e r s ' u t i l i t i e s . E x a m p l e s o f t h e u s e o f t h i s s o l u t i o n i n e m p i r i c a l r e s e a r c h are de M e n i l (1971) , Hamermesh ( 1 9 7 3 ) , and S v e j n a r (1980, 1986) . de M e n i l (1971) assumes a Nash b a r g a i n i n g s o l u t i o n i n h i s s tudy o f U . S . m a n u f a c t u r i n g wages w h i l e Hamermesh and S v e j n a r a t t e m p t t o t e s t whether the (symmetric) Nash b a r g a i n i n g s o l u t i o n h o l d s . In h i s l a t e s t s t u d y , S v e j n a r (1986) l o o k s a t wage and employment c o n t r a c t s i n s e v e r a l U . S . i n d u s t r i e s w i t h sample p e r i o d s v a r y i n g a c r o s s i n d u s t r i e s . Unions a r e assumed to be r e n t max imizers but r i s k a v e r s i o n i s a l l o w e d i n the form o f a c o n s t a n t r e l a t i v e r i s k a v e r s i o n c o e f f i c i e n t . A n asymmetr ic N a s h b a r g a i n i n g s o l u t i o n i s assumed w i t h t h e w e i g h t s on t h e two p l a y e r s ' u t i l i t i e s b e i n g f u n c t i o n s o f exogenous ly de termined b a r g a i n i n g powers . R e s u l t s s u g g e s t t h a t t h e r e l a t i v e b a r g a i n i n g powers a r e h i g h l y v a r i a b l e a c r o s s i n d u s t r i e s and the symmetric Nash b a r g a i n i n g s o l u t i o n i s o f t e n r e j e c t e d . U n f o r t u n a t e l y , e s t i m a t e s o f r i s k a v e r s i o n p a r a m e t e r s o f t h e w o r k e r s a r e v e r y i m p r e c i s e , p o s s i b l y because o f v e r y s m a l l sample s i z e s . In some o f the e m p i r i c a l work, the b a r g a i n i n g powers are a l l o w e d t o v a r y o v e r t i m e and t h e r e s u l t s show t h a t the u n i o n b a r g a i n i n g power i n c r e a s e d w i t h t h e p r e s e n c e o f COLA c l a u s e s a n d 26 i n f l a t i o n and d e c r e a s e d d u r i n g p e r i o d s o f p r i c e c o n t r o l s and h i g h unemployment. In the second type o f b a r g a i n i n g mode l , the n e g o t i a t i o n p r o c e s s i s d e s c r i b e d . B u t , u n t i l v e r y r e c e n t l y , such models r e l i e d on ad hob and u n s a t i s f a c t o r y assumptions about the r a t i o n a l i t y o f t h e a g e n t s and i n f o r m a t i o n t r a n s m i s s i o n . Examples are the models by J . C r o s s and Z e u t h e n - H a r s a n y i i n which p l a y e r s make s y s t e m a t i c e r r o r s ^about t h e i r opponent ' s and e v e n t h e i r own f u t u r e b e h a v i o u r . 8 i t i s o n l y i n the p a s t decade t h a t b a r g a i n i n g has been m o d e l l e d as a n o n - c o o p e r a t i v e game between r a t i o n a l (Bayes ian-Nash) p l a y e r s . T h i s i s the type o f model I use i n my e m p i r i c a l work. B e f o r e p r o c e e d i n g t o e x a m i n e t h e l i t e r a t u r e on n o n - c o o p e r a t i v e b a r g a i n i n g games, I want t o m e n t i o n a r e l a t e d a r e a o f work namely , the i m p l i c i t c o n t r a c t l i t e r a t u r e . The i s s u e o f w h e t h e r f i r m s and u n i o n s e n g a g e i n i m p l i c i t c o n t r a c t i n g a r i s e s i n t h i s framework due t o the f a c t t h a t we do not observe f i r m - u n i o n c o n t r a c t s i n which the employment l e v e l i s s p e c i f i e d . We do observe c o n t r a c t s w i t h manning r e q u i r e m e n t s and s e n i o r i t y p r o v i s i o n s , and t h e e v i d e n c e p r e s e n t e d above a l s o suggests t h a t u n i o n s are concerned w i t h employment l e v e l s , so why n o t e x p l i c i t l y c o n t r a c t f o r e m p l o y m e n t ? S e v e r a l p o s s i b l e reasons have been p r o v i d e d ; these i n v o l v e i m p e r f e c t i n f o r m a t i o n , m o n i t o r i n g c o s t s and 8 S e e F o l e y and Maunders (1979) f o r a good d e s c r i p t i o n o f t h i s t y p e o f mode l . 27 t r a n s a c t i o n c o s t s . T h i s does not mean than the r e s u l t i n g c o n t r a c t s w i l l be i n e f f i c i e n t . We can have c o n t r a c t s i n which n o t h i n g i s s a i d about the employment l e v e l but which i n c l u d e some k i n d o f compensat ion scheme t h a t w i l l ensure e f f i c i e n c y . 9 A l s o , i m p l i c i t c o n t r a c t i n g over and above the n e g o t i a t e d agreement c o u l d ensure e f f i c i e n c y . E f f i c i e n c y and i n c e n t i v e c o m p a t i b i l i t y imply s t r u c t u r e on the form o f t h e s e c o n t r a c t s ; h o w e v e r , t h e r e s u l t s so f a r a r e m o d e l s p e c i f i c and v e r y l i t t l e i s known a b o u t t h e i r e m p i r i c a l r e l e v a n c y . 1 0 The l i t e r a t u r e on n o n - c o o p e r a t i v e b a r g a i n i n g games i s f a i r l y r e c e n t . 1 1 A l o t o f t h e work i s s e t i n a b u y e r - s e l l e r game where these p l a y e r s b a r g a i n over t h e p r i c e o f the one good t h a t w i l l (or w i l l not ) be t r a d e d . C h a t t e r j e e and Samuelson (1983) p r e s e n t a one p e r i o d b u y e r - s e l l e r game i n w h i c h the p l a y e r s submit s e a l e d o f f e r s . There i s two- s i d e d u n c e r t a i n t y about the opponent ' s v a l u a t i o n o f the good a n d i n e f f i c i e n t ( n o ^ t r a d e ) o u t c o m e s c a n o c c u r i n e q u i l i b r i u m . Fudenberg and T i r o l e (1983) , S o b e l and T a k a h a s h i (198 3) and F u d e n b e r g , L e v i n e and T i r o l e (1983) extend the game to a m u l t i - s t a g e o n e . I n i m p e r f e c t i n f o r m a t i o n e n v i r o n m e n t s 9 S e e H a l l and L i l i e n (1979) f o r examples o f t h i s . 1 0 S e e A z a r i a d i s (1981) f o r a s u r v e y . i : L S e e McLennan (1982) f o r a g e n e r a l d e f i n i t i o n o f the b a r g a i n i n g prob lem i n a game t h e o r e t i c framework. 28 l e a r n i n g w i l l o c c u r . I n c h o o s i n g t h e i r s t r a t e g i e s , t h e p l a y e r s h a v e t o t a k e i n t o a c c o u n t t h e e f f e c t t h e i r o b s e r v a b l e b e h a v i o u r w i l l have on t h e i r opponents ' b e l i e f s . I t i s a l s o f u n d a m e n t a l t o t h e s e m o d e l s t h a t t h e r e i s d i s c o u n t i n g so t h a t p l a y e r s have i n c e n t i v e s to agree e a r l y i n t h e game. Fudenberg and T i r o l e ; (1983) l o o k a t a two- p e r i o d game w i t h t w o - s i d e d u n c e r t a i n t y w h i l e S o b e l and T a k a h a s h i (1983) e x t e n d t h e mode l to an i n f i n i t e - h o r i z o n game f o r the o n e - s i d e d u n c e r t a i n t y c a s e . F u d e n b e r g , L e v i n e and T i r o l e (1983) g e n e r a l i z e the i n f i n i t e - h o r i z o n o n e - s i d e d i m p e r f e c t i n f o r m a t i o n r e s u l t s . I n t h e p r e c e d i n g games ( w i t h t h e e x c e p t i o n o f C h a t t e r j e e and S a m u e l s o n ( 1 9 8 3 ) ) , o n l y t h e s e l l e r makes o f f e r s . The b u y e r ' s s t r a t e g y c o n s i s t s i n a c c e p t i n g o r r e j e c t i n g them. A l s o , the u n c e r t a i n t y always i n v o l v e s the opponent ' s v a l u a t i o n o f the good. In the next s e t o f games, two p l a y e r s b a r g a i n o v e r t h e s p l i t t i n g o f a f i x e d p i e , A g a i n t h e r e a r e c o s t s o f d e l a y so t h a t the p i e s h r i n k s over t i m e , but the p l a y e r s now a l t e r n a t e i n m a k i n g o f f e r s and where t h e r e i s u n c e r t a i n t y , t h i s u n c e r t a i n t y concerns the opponent ' s d e l a y c o s t s r a t h e r than the i n i t i a l b a r g a i n i n g s e t . T h i s game was f i r s t p r e s e n t e d i n R u b i n s t e i n (1982) f o r the c e r t a i n t y c a s e . He extends h i s r e s u l t s f o r t h e o n e - s i d e d u n c e r t a i n t y case i n R u b i n s t e i n (1985) . C o n s i d e r a b l e e x t e n s i o n s o f these models were p r o v i d e d i n Cramton (1984) (see a l s o Cramton (1985) ) . In h i s t h e s i s , 29 Cramton l o o k s a t a game between a buyer and a s e l l e r . The e q u i l i b r i u m a r e c h a r a c t e r i z e d f o r f i n i t e and i n f i n i t e h o r i z o n c a s e s , f o r o n e - s i d e d , t w o - s i d e d , and no u n c e r t a i n t y ( the u n c e r t a i n t y always i n v o l v e s the opponent ' s v a l u a t i o n o f the g o o d ) , f o r games w i t h a l t e r n a t i n g o f f e r s as w e l l as one- s i d e d o f f e r s , and f i n a l l y f o r c o n t i n u o u s t ime models where t h e r e i s no f i r s t mover advantage . An i m p o r t a n t f e a t u r e o f the above models i s t h a t the agents h a v e c a r d i n a l o b j e c t i v e f u n c t i o n s w i t h i d e n t i c a l u n i t s o f measure ( d o l l a r s i n one case and p i e s h a r e i n the o t h e r ) . I n a f i r m - u n i o n c o n t e x t , i f we a s s u m e t h a t e m p l o y m e n t i s a l s o b e i n g d e t e r m i n e d , t h i s amounts t o r e q u i r i n g t h a t the u n i o n maximize r e n t s or a l i n e a r f u n c t i o n t h e r e o f , a v e r y r e s t r i c t i v e a s s u m p t i o n i n v i e w o f t h e e m p i r i c a l e v i d e n c e r e v i e w e d e a r l i e r . T h i s f e a t u r e i s r e l a x e d i n some o f the examples i n Binmore (1987C) and i n M c L e n n a n ( 1 9 8 2 ) . They a l s o w r i t e t h e s o l u t i o n t o t h e R u b i n s t e i n game as an asymmetric Nash b a r g a i n i n g s o l u t i o n f o r some c l a s s e s o f models . As w i l l be s e e n l a t e r , t h i s t u r n s o u t t o be i m p o r t a n t f o r my w o r k . A n o t h e r common f e a t u r e o f these models i s the use o f d i s c o u n t i n g as t i m e c o s t s . D i s c o u n t f a c t o r s are easy t o m a n i p u l a t e and they a l s o have a s t a t i o n a r i t y c h a r a c t e r i s t i c t h a t R u b i n s t e i n (1982) found c r u c i a l i n h i s mode l . T h e b a r g a i n i n g games m e n t i o n e d a b o v e h a v e t w o c h a r a c t e r i s t i c s t h a t are d e s i r a b l e f o r a p p l i e d work on f i r m - 30 u n i o n c o n t r a c t s : ( i ) the s e t o f e q u i l i b r i a i s s m a l l ( t h e e q u i l i b r i u m i s o f t e n u n i q u e ) ( i i ) t h e r e i s a l o t o f f l e x i b i l i t y i n the o f f e r s the agents can make i n i t i a l l y , and t h r o u g h o u t t h e g a m e . 1 2 T h i s i s e s p e c i a l l y i m p o r t a n t when s t u d y i n g a p a r t i c u l a r u n i o n and i n d u s t r y b e c a u s e a l o t o f t h e i n f o r m a t i o n c o n t a i n e d i n t h e d a t a i s f o u n d i n t h e d i s t r i b u t i o n o f t h e s u r p l u s r a t h e r t h a n i n t h e s t r i k e l e n g t h s ( i f o n l y b e c a u s e o f t h e r e l a t i v e numbers o f o b s e r v a t i o n s ) . I t i s o f t e n the case t h a t b a r g a i n i n g models i n v o l v i n g asymmetric i n f o r m a t i o n and hence the p o s s i b i l i t y o f i n e f f i c i e n t outcomes o r s t r i k e s as e q u i l i b r i a a l s o i n c l u d e s e v e r e r e s t r i c t i o n s on the o f f e r s the p l a y e r s are a l l o w e d to make. T h i s i s due t o reasons o f t r a c t a b i l i t y . In t h i s s tudy however, the focus i s on the c o n t r a c t s r a t h e r t h a n s t r i k e s and t h e r e f o r e , i t i s i m p o r t a n t t h a t the o f f e r s be de termined endogenously r a t h e r than h e a v i l y r e s t r i c t e d by o u t s i d e i n f l u e n c e . ( O f c o u r s e when o n e c a n o b s e r v e exogenous r e s t r i c t i o n s on the p o s s i b l e o f f e r s such as wage c o n t r o l s t h e n the model s h o u l d r e f l e c t t h i s ) . Many r e c e n t d e v e l o p m e n t s h a v e b e e n made i n n o n - c o o p e r a t i v e b a r g a i n i n g games e s p e c i a l l y i n the area o f games w i t h i m p e r f e c t i n f o r m a t i o n and m e c h a n i s m d e s i g n u n d e r i m p e r f e c t i n f o r m a t i o n . P l a y e r s engage i n s o p h i s t i c a t e d r e p u t a t i o n b u i l d i n g s t r a t e g i e s and i m p l i c a t i o n s o f t h e 1 2 N o t a l l b a r g a i n i n g games have these c h a r a c t e r i s t i c s e . g . Osborne (1985) and Crawford (1981) . 31 s t r u c t u r e o f the c o n t r a c t on the e q u i l i b r i u m outcomes a r e s t u d i e d . H o w e v e r , e m p i r i c a l a p p l i c a t i o n o f t h e s e more s o p h i s t i c a t e d games i s v e r y d i f f i c u l t because the e q u i l i b r i a become v e r y complex and would r e q u i r e b e t t e r , more d e t a i l e d d a t a o n t h e b a r g a i n i n g p r o c e s s a n d t h e i n f o r m a t i o n s t r u c t u r e . 1 3 E m p i r i c a l w o r k b a s e d o n an e x p l i c i t l y f o r m u l a t e d b a r g a i n i n g game i s p r a c t i c a l l y n o n - e x i s t e n t . T o my knowledge the o n l y e m p i r i c a l s tudy u s i n g a b a r g a i n i n g game framework i s F u d e n b e r g , L e v i n e , and Rudd (1985) . In t h e i r p a p e r , a u n i o n and a f i r m b a r g a i n over the a b s o l u t e s i z e o f the i n c r e a s e i n the r e a l wage. Only the u n i o n makes o f f e r s , the f i r m e i t h e r a c c e p t s ( the c o n t r a c t i s s igned) or r e j e c t s ( t h e r e i s a s t r i k e ) . S t r i k e s o c c u r i n e q u i l i b r i u m because t h e r e i s i m p e r f e c t i n f o r m a t i o n , the u n i o n b e i n g u n c e r t a i n about the v a l u e o f the o f f e r e d wage increment t o the f i r m . The e q u i l i b r i u m s t r a t e g y f o r the u n i o n takes the form o f a wage c o n c e s s i o n s c h e d u l e . T h i s s c h e d u l e r e f l e c t s t h e u n i o n ' s p r i o r b e l i e f s and how these b e l i e f s are updated over t ime as the u n i o n observes the f i r m ' s a c t i o n s (acceptance or r e j e c t i o n ) . Because o f the s p e c i a l form o f the u n c e r t a i n t y ( the b e l i e f s ) , the wage c o n c e s s i o n s c h e d u l e can be w r i t t e n as a f u n c t i o n s u f f i c i e n t l y s i m p l e to e s t i m a t e . 1 3 S e e Roth (1985) f o r a r e c e n t s u r v e y . 32 C o n c e s s i o n s c h e d u l e s have been used i n the s tudy o f s t r i k e s i n the work o f A s h e n f e l t e r and Johnson (1967) and F a r b e r ( 1 9 7 8 ) . The s e t t i n g i s q u i t e d i f f e r e n t i n those p a p e r s i n t h a t i t i n v o l v e s a p o l i t i c a l m o d e l o f u n i o n b e h a v i o u r . More s p e c i f i c a l l y t h e u n i o n l e a d e r s are not always a c t i n g i n the workers ' b e s t i n t e r e s t s i n c e they have d i f f e r e n t g o a l s ( e . g . r e - e l e c t i o n ) . In such a framework, i t i s d i f f i c u l t t o e v a l u a t e t h e e s t i m a t e d p a r a m e t e r s . I n F u d e n b e r g , L e v i n e a n d R u d d , t h e s e h a v e an e c o n o m i c i n t e r p r e t a t i o n . T h e i r r e a s o n a b l e n e s s ( o r l a c k t h e r e o f ) p r o v i d e s some i n f o r m a t i o n on the a p p l i c a b i l i t y o f the mod e l , i n p a r t i c u l a r o f the s t r i n g e n t r a t i o n a l i t y r e q u i r e m e n t s . However, as i n p r e v i o u s work, i n the F u d e n b e r g , L e v i n e and Rudd p a p e r , s t r i k e s are always to the d i s a d v a n t a g e o f t h e w o r k e r ( t h e c o n c e s s i o n s c h e d u l e i s downward s l o p i n g ) . 1 4 T h i s i s due to the i n f o r m a t i o n s t r u c t u r e , the r u l e s o f the game, and the f a c t t h a t the game i n v o l v e s n e g o t i a t i o n o f one c o n t r a c t o n l y i . e . the workers are no t a b l e t o l e a r n f r o m p r e v i o u s c o n t r a c t n e g o t i a t i o n s . To a l l o w f o r s t r a t e g i e s i n v o l v i n g more t h a n one c o n t r a c t n e g o t i a t i o n , a supergame would be r e q u i r e d . The work by G u l and Sonnensche in (1985) i n d i c a t e s what seems to be a b a s i c f law i n the F u d e n b e r g , L e v i n e and Rudd 1 4 S e e E a t o n (1978) f o r an i n t e r e s t i n g v a r i a n t o f the A s h e n f e l t e r and Johnson model i n which i t i s the workers who b e n e f i t from s t r i k e s . 33 mode l . F u d e n b e r g , L e v l n e and Rudd assume c o n t i n u o u s t i m e w h i l e r e s u l t s by G u l a n d S o n n e n s c h e i n s u g g e s t t h a t i n e f f i c i e n t outcomes ( i . e . s t r i k e s ) can o n l y be genera ted as e q u i l i b r i u m p o i n t s i n d i s c r e t e t ime games. C o n c e r n i n g the e m p i r i c a l a s p e c t o f t h e i r w o r k , t h e m o d e l a d o p t e d by F u d e n b e r g , L e v i n e and Rudd has the f o l l o w i n g weaknesses: ( i ) A l l i n p u t s i n c l u d i n g employment (and t h e r e f o r e output l e v e l s ) are f i x e d exogenous ly , i n d e p e n d e n t l y o f t h e wage . T h i s c o n f l i c t s w i t h e m p i r i c a l e v i d e n c e from wage-employment d e t e r m i n a t i o n mode l s . ( i i ) The model i s e s t i m a t e d u s i n g d a t a on many d i f f e r e n t u n i o n s and i n d u s t r i e s w i t h no a l l o w a n c e f o r v a r i a n c e i n u n i o n p r e f e r e n c e s or f i r m t e c h n o l o g y p a r a m e t e r s . ( i i i ) Once s i g n e d , the c o n t r a c t i s assumed to l a s t f o r e v e r . T h i s means t h a t the expected v a l u e o f t h e c o n t r a c t w i l l be o v e r s t a t e d . ( i v ) The i n f o r m a t i o n s t r u c t u r e i s v e r y s i m p l e and does not a l l o w f o r u n c e r t a i n t y r e g a r d i n g s t r i k e c o s t s . A l s o t h e f i r m i s assumed t o know e v e r y t h i n g a b o u t the u n i o n . F o r my e m p i r i c a l w o r k , I u s e a m o d e l b a s e d on t h e R u b i n s t e i n game. T h e r e a r e two m a i n r e a s o n s f o r t h i s . F i r s t , i t i s p o s s i b l e to use more g e n e r a l f o r m u l a t i o n s o f t h e u n i o n ' s a n d f i r m ' s o b j e c t i v e f u n c t i o n s w i t h o u t 34 c o m p l i c a t i n g the a n a l y s i s too much. S e c o n d l y , i t i s c l e a r t h a t i n p r a c t i c e , bo th n e g o t i a t i n g p a r t i e s do make o f f e r s . As mentioned above, a fundamental c h a r a c t e r i s t i c o f the R u b i n s t e i n ' s game and o t h e r n o n - c o o p e r a t i v e b a r g a i n i n g m o d e l s i s t h e p r e s e n c e o f d e l a y c o s t s w h i c h p r o v i d e i n c e n t i v e s to the p l a y e r s to agree e a r l y i n the game. I n the i n d u s t r y which i s s t u d i e d h e r e , d e l a y s l e a d to s t r i k e s and c o s t s o f d e l a y are measured by s t r i k e c o s t s . The l a s t a r e a o f r e s e a r c h which w i l l be d i s c u s s e d i n t h i s c h a p t e r and to which I now t u r n i s the e m p i r i c a l work on s t r i k e c o s t s . Most o f the e m p i r i c a l s t u d i e s on s t r i k e s have focused on the e s t i m a t i o n o f two types o f r e l a t i o n s h i p s . F i r s t l y , the e f f e c t s o f v a r i a t i o n s i n s t r i k e c o s t s on l e n g t h a n d / o r f r e q u e n c y o f s t r i k e s are m o d e l l e d . More r e c e n t l y , t h e l e v e l o f u n c e r t a i n t y i n t h e e c o n o m i c e n v i r o n m e n t o f t h e two n e g o t i a t i n g p a r t i e s i s r e l a t e d t o the o c c u r r e n c e o f s t r i k e s . A l t h o u g h t h e s e s t u d i e s g e n e r a l l y d i d not i n c l u d e a model o f b a r g a i n i n g and hence o f s t r i k e s , these r e l a t i o n s h i p s were j u s t i f i e d by the arguments t h a t , c e t e r i s p a r i b u s , i n c r e a s e s i n s t r i k e c o s t s w i l l make p a r t i e s l e s s w i l l i n g t o s t r i k e . A l s o h i g h l y u n c e r t a i n environments w i l l i n c r e a s e the amount o f asymmetric i n f o r m a t i o n between the p l a y e r s and l e a d to a h i g h e r p r o b a b i l i t y o f s t r i k e s . Examples o f these s t u d i e s a r e Kennan (1980) and R e d e r and Newmann (1980) ( s t r i k e c o s t s ) ; S i e b e r t and A d d i s o n ( 1 9 8 1 ) , Mauro ( 1 9 8 2 ) , and 35 L a c r o i x (1983) ( u n c e r t a i n t y ) , and T r a c y (1986) (both s t r i k e c o s t s and u n c e r t a i n t y ) . The m a i n d e t e r m i n a n t s o f s t r i k e c o s t s t h a t have been c o n s i d e r e d a r e m e a s u r e s o f b o r r o w i n g c o s t s f o r t h e f i r m ( i n t e r e s t r a t e s , l e v e l s o f i n v e n t o r i e s ) , m e a s u r e s o f o p p o r t u n i t y c o s t s o f t h e w o r k e r s ( u n e m p l o y m e n t ) , a n d m e a s u r e s o f c y c l i c a l v a r i a t i o n s . I n d u s t r y s p e c i f i c v a r i a b l e s a r e a l s o u s e d s u c h as c a p i t a l i n t e n s i t y a n d v a r i a t i o n s i n shipments (which i n d i c a t e the a b i l i t y o f the f i r m t o keep i t s market share d u r i n g work s t o p p a g e s ) , as w e l l as m e a s u r e s o f u n i o n power s u c h as t h e l e v e l o f u n i o n i z a t i o n i n the i n d u s t r y . S i n c e a s i n g l e i n d u s t r y i s s t u d i e d h e r e , the l a t t e r type o f e f f e c t i s no t c o n s i d e r e d . T r a c y (1986) a l s o c o n s i d e r s t h e s i z e o f t h e r e n t s as an e x p l a n a t o r y f a c t o r o f s t r i k e s . I n t h i s s t u d y , t h e d e t e r m i n a n t s o f s t r i k e c o s t s are used to measure v a r i a t i o n s i n t h e p r o p o r t i o n o f r e n t s which i s l o s t per t ime p e r i o d d u r i n g s t r i k e s ( i . e . one minus the d i s c o u n t f a c t o r s o f the p l a y e r s ) . The a b s o l u t e l e v e l o f r e n t s l o s t due t o s t r i k e s w i l l be a f f e c t e d by the t o t a l r e n t s a v a i l a b l e as w e l l as the d i s c o u n t f a c t o r s o f the p l a y e r s . 36 C h a p t e r 3 The Model The s tudy o f n e g o t i a t e d wage and employment c o n t r a c t s i n v o l v e s t h e m o d e l l i n g o f t h e 3 components o f c o l l e c t i v e b a r g a i n i n g : the u n i o n o b j e c t i v e s and c o n s t r a i n t s , the f i r m g o a l s and t e c h n o l o g y , and the b a r g a i n i n g r e l a t i o n s h i p . Each o f t h e s e w i l l be s t u d i e d i n t u r n but f i r s t I a d d r e s s t h e q u e s t i o n o f t h e n e g o t i a t i o n o f t h e l e v e l o f employment. S p e c i f i c a l l y , i s employment u n i l a t e r a l l y chosen by the f i r m , i n which case the c o n t r a c t i s on the l a b o u r demand c u r v e , or do the p a r t i e s n e g o t i a t e the l e v e l o f employment t h e r e b y a t t a i n i n g an e f f i c i e n t c o n t r a c t (a p o i n t on the c o n t r a c t c u r v e ) ? I t was seen i n C h a p t e r 2 t h a t i f the u n i o n c a r e s at a l l about the employment l e v e l , a P a r e t o o p t i m a l c o n t r a c t , i . e . a c o n t r a c t w h i c h c o r r e s p o n d s t o a t a n g e n c y p o i n t between the u n i o n ' s and the f i r m ' s i n d i f f e r e n c e c u r v e s w i l l l i e t o the r i g h t o f the l a b o u r demand c u r v e . The r e s u l t i n g employment l e v e l w i l l be g r e a t e r t h a n the f i r m would l i k e i n t h e s e n s e t h a t t h e m a r g i n a l r e v e n u e p r o d u c t a t t h a t employment l e v e l w i l l be s m a l l e r than the wage. A l t h o u g h the c o l l e c t i v e agreements under s tudy do n o t s p e c i f y the l e v e l o f employment, they do c o n t a i n p r o v i s i o n s d i r e c t l y a f f e c t i n g e m p l o y m e n t ( e . g . j o b s e c u r i t y p r o v i s i o n s ) . M o r e o v e r , t h e r e are o t h e r i n s t r u m e n t s which c o u l d be used to o b t a i n an e f f i c i e n t l e v e l o f employment ( e . g . n o n - l i n e a r c o m p e n s a t i o n s c h e m e s ) . A p r i o r i , t h e 37 e f f i c i e n t c o n t r a c t i n g model i s more a t t r a c t i v e u n l e s s t h e r e i s some i n d i c a t i o n o f a c o n s t r a i n t which p r o h i b i t s the two p l a y e r s f r o m r e a c h i n g a P a r e t o o p t i m a l p o i n t . S u c h a c o n s t r a i n t c o u l d be due t o i m p e r f e c t i n f o r m a t i o n , m o n i t o r i n g c o s t s o r t r a n s a c t i o n c o s t s . However, these c o n s t r a i n t s can be u s e d to argue a g a i n s t the l a b o u r demand model as w e l l . In g e n e r a l , t h i s argument i s not h e l p f u l i n c h o o s i n g between t h e two m o d e l s . T u r n i n g t o s p e c i f i c mode l s o f i m p l i c i t c o n t r a c t i n g , we f i n d t h a t n o t i o n s o f e f f i c i e n c y a n d i n c e n t i v e c o m p a t i b i l i t y do impose s t r u c t u r e on the forms o f the c o n t r a c t s but the r e s u l t s have been v e r y model s p e c i f i c and l i t t l e i s known about t h e i r e m p i r i c a l r e l e v a n c y . In t h i s p a p e r , bo th the l a b o u r demand and the e f f i c i e n t c o n t r a c t o r c o o p e r a t i v e m o d e l a r e e s t i m a t e d . T h e i r per formance c a n be e v a l u a t e d by t h e u s e o f a n o n - n e s t e d t e s t . 3 .1 The B a r g a i n i n g Game T h i s f i r s t s e c t i o n c o n t a i n s a d e s c r i p t i o n o f t h e b a r g a i n i n g model and draws h e a v i l y from the work by Binmore (1987C). I t i s f o l l o w e d i n s e c t i o n 3.2 by a d i s c u s s i o n o f the e m p i r i c a l a p p l i c a t i o n o f the game t o f i r m - u n i o n c o n t r a c t n e g o t i a t i o n s . The b a r g a i n i n g i s o f the type f i r s t p r e s e n t e d i n game t h e o r e t i c f o r m i n R u b i n s t e i n ( 1 9 8 2 ) . Two p l a y e r s a r e b a r g a i n i n g o v e r t h e d i v i s i o n o f a p i e . In the o r i g i n a l 38 p a p e r , the s i z e o f the p i e was f i x e d ( i . e . the f r o n t i e r o f t h e b a r g a i n i n g s e t a t t h e s t a r t o f t h e n e g o t i a t i o n s was l i n e a r w i t h s l o p e - 1 ) . T h i s amounts t o a s s i g n i n g i d e n t i c a l u n i t s o f u t i l i t y t o t h e two p l a y e r s . More s p e c i f i c a l l y , t h i s f o r c e s the u n i o n to be r e n t m a x i m i z i n g , a h y p o t h e s i s which i s most o f t e n r e j e c t e d i n e m p i r i c a l s t u d i e s . Binmore (1980) showed t h a t t h i s r e s t r i c t i o n c o u l d be r e l a x e d w i t h o u t t o o much c o m p l i c a t i o n . In t h i s s t u d y , I use the Binmore r e s u l t and a l l o w the u n i o n u t i l i t y f u n c t i o n t o t a k e a more g e n e r a l form. Rent m a x i m i z a t i o n w i l l be t e s t e d as a s p e c i a l c a s e . Other than t h i s , I f o l l o w the r u l e s o f the game and a d o p t t h e r e s t r i c t i o n s on t h e p l a y e r s ' p r e f e r e n c e s as s p e c i f i e d i n R u b i n s t e i n [1982] . The two p l a y e r s a l t e r n a t e i n making p r o p o s a l s . A f t e r h e a r i n g h i s opponent ' s o f f e r , each p l a y e r has t o a c c e p t or r e j e c t i t . I f he a c c e p t s , the game ends and the p r o p o s a l i s implemented . I f he r e j e c t s , he can make a new p r o p o s a l . Any f e a s i b l e agreement i s p r e f e r r e d by b o t h p l a y e r s to the no-agreement outcome. M o r e o v e r , each p l a y e r i n c u r s c o s t s by d e l a y i n g a g r e e m e n t so t h a t f o r any t i m e t , an agreement s i g n e d a t t ime t i s p r e f e r r e d to the same agreement s i g n e d a t any t ime a f t e r t . Both p l a y e r s a r e r a t i o n a l ; i . e . , they c a r e o n l y about the f i n a l agreement and not how i t i s r e a c h e d . A l s o , they do n o t b e l i e v e i d l e t h r e a t s made by t h e i r opponent ( i d l e t h r e a t s a r e s u c h t h a t i t w o u l d i n f a c t n o t be i n t h e 39 p l a y e r ' s bes t i n t e r e s t t o c a r r y them o u t ) . In t h e f a c e o f s u c h r a t i o n a l i t y , any e q u i l i b r i u m t o the game w i l l have to be sub-game p e r f e c t as d e f i n e d by S e l t o n . The assumptions o f r a t i o n a l i t y a n d o f t i m e c o s t s a r e p o w e r f u l o n e s . F i g u r e 2 i s used t o i l l u s t r a t e t h i s p o i n t . F i g u r e 2 P e r f e c t E q u i l i b r i a w i t h A l t e r n a t i n g O f f e r s and C o s t s o f D e l a y I n F i g u r e 2 , the p r e s e n t v a l u e o b j e c t i v e f u n c t i o n s or the p r e s e n t v a l u e u t i l i t i e s o f the two p l a y e r s a r e measured a l o n g t h e axes . The p o i n t ( F , U) i s the no-agreement p o i n t , and B i i s the P a r e t o f r o n t i e r o f t h e b a r g a i n i n g s e t ( the s e t o f f e a s i b l e agreements) a t t ime i . The f r o n t i e r B^ o f the b a r g a i n i n g s e t s h i f t s i n over t ime because o f d e l a y c o s t s . S u p p o s e p l a y e r F i s t h e one t o make a p r o p o s a l a t t ime 40 t + 1 . He a n t i c i p a t e s B t + 2 , a n < 3 he knows t h a t i f no agreement i s reached i n p e r i o d t + l , the most h i s opponent can get i s U 2 because U 2 i s the maximum p a y o f f o f p l a y e r U f o r the game s t a r t i n g a t t ime t + 2 . P l a y e r F knows t h a t f o r any p r o p o s a l he makes a t t + 1 g i v i n g U a p a y o f f g r e a t e r t h a n U"2/ he c o u l d make h i m s e l f b e t t e r o f f by o f f e r i n g s l i g h t l y l e s s t o U such t h a t the proposed p a y o f f t o U would s t i l l exceed U 2 . F u r t h e r m o r e , U would a c c e p t i t . T h e r e f o r e the s e t o f p e r f e c t e q u i l i b r i u m p o i n t s a t t ime t + 1 w i l l not i n c l u d e any p o i n t g i v i n g U more than U 2 . We can use the same type o f r e a s o n i n g t o f i n d a lower bound t o the p e r f e c t e q u i l i b r i u m p a y o f f s t o p l a y e r U a t t ime t + 1 . P l a y e r U w i l l n o t a c c e p t any p a y o f f l e s s than U s i n c e t h i s i s t h e minimum he c a n r e c e i v e f o r t h e game s t a r t i n g a t t + 2 . U s i n g the s e t B t+2 and the r a t i o n a l i t y o f the p l a y e r s , we have l i m i t e d the s e t o f p o s s i b l e p e r f e c t e q u i l i b r i u m p o i n t s t o [ ( F , U ) : U_£ U ^ U 2 , F]_£ F ^ F Q ] which I c a l l P E t + i - We now move b a c k one p e r i o d . U i s d e c i d i n g what p r o p o s a l he s h o u l d make a t t i m e t . He knows t h a t t h e r e l e v a n t p a r t o f the b a r g a i n i n g s e t a t t ime t + 1 i s PEt+i s i n c e he a l s o a n t i c i p a t e s Bt.+2 a n < 3 he knows F i s a r a t i o n a l p l a y e r . U s i n g the same type o f r e a s o n i n g as above , we can l i m i t t h e s e t o f p o s s i b l e p e r f e c t e q u i l i b r i a a t t ime t t o [ ( F , U ) : U i $ U £ u 0 , F i * F ^ F Q ] which i s denoted P E t - 41 I f we were t o go back t o t i m e t + 2 and l i m i t t h e r e l e v a n t b a r g a i n i n g s e t a t t + 2 by u s i n g B t + 3 , we c o u l d expec t t o l i m i t PE-t+i and PE-t even more. I t i s i n t e r e s t i n g to l o o k a t the case where the b a r g a i n i n g s e t s h r i n k s t o a s i n g l e p o i n t , the d i sagreement p o i n t . Suppose t h i s o c c u r s i n f i n i t e t i m e , more s p e c i f i c a l l y assume t h a t i n F i g u r e 2 , t h e s e t B t + 3 i s t h e p o i n t ( F , U) . I t i s c l e a r t h a t i n F i g u r e 2 , the PE s e t s w i l l c o n s i s t o f one p o i n t o n l y , i n p a r t i c u l a r the u n i q u e PE p o s s i b l e a t t ime t i s (Fj_, U 0 ) . I f t h e game i s i n f i n i t e , we c a n ' t work our way back from t h e d i sagreement p o i n t ; however, w i t h p r o p e r r e s t r i c t i o n s on the t i m e c o s t s t h e e q u i l i b r i u m t o t h e l i m i t i n g i n f i n i t e b a r g a i n i n g game i s u n i q u e . T h i s r e s u l t i s a l l the more s u r p r i s i n g g i v e n t h e l a r g e number o f e q u i l i b r i a u s u a l l y encountered i n i n f i n i t e l y - r e p e a t e d games. The s t r u c t u r e which i s imposed on t h e t i m e c o s t s i s t h a t o f s t a t i o n a r i t y and i t s i m p l i c a t i o n i s e s s e n t i a l l y to make the game homogeneous a c r o s s t ime p e r i o d s . T h i s i s w e l l i l l u s t r a t e d by a g e n e r a l i z a t i o n o f t h e argument used i n S h a k e d and S u t t o n ( 1 9 8 4 ) . 1 5 Suppose the d e l a y c o s t s take t h e f o r m o f d i s c o u n t i n g and d u , d f a r e t h e r e s p e c t i v e d i s c o u n t f a c t o r s f o r the p l a y e r s U and F , w i t h 0 ^ d^ £ 1 f o r i = u , f . L e t t h e P a r e t o f r o n t i e r i n c u r r e n t v a l u e s 1 5 S h a k e d and S u t t o n c o n s i d e r the case o f the s p l i t t i n g o f a f i x e d p i e o f s i z e one i . e . the b a r g a i n i n g f r o n t i e r i n c u r r e n t v a l u e s U and F i s the u n i t s i m p l e x . ( i . e . t ime 0 v a l u e s ) be U = U(F) and i n g e n e r a l a t t ime t : U / d u t = U ( F / d f t ) . A l s o , assume U i s i n v e r t i b l e so t h a t F = U _ 1 ( U ) a t t = 0 . L e t p l a y e r U be t h e f i r s t mover. I f U 2 denotes the maximum u t i l i t y l e v e l f o r U i n the s e t P E 2 ( i . e . i n the s e t o f p e r f e c t e q u i l i b r i u m p o i n t s f o r the game s t a r t i n g a t t = 2 r a t h e r t h a n t = 0 ) t h e n he w i l l s u r e l y a c c e p t any o f f e r g i v i n g h im more t h a n U 2 w h i c h i m p l i e s t h a t F w i l l never o f f e r him more than U 2 a t t ime t = l . By d e f i n i n g a maximum l e v e l o f u t i l i t y f o r p l a y e r U a t t ime 1 , U 2 a l s o d e f i n e s a minimum l e v e l o f u t i l i t y f o r p l a y e r F a t t ime 1 which we can ic ic r e t r i e v e by u s i n g U: F i = d f x U - 1 ( U 2 / d u ) (remember t h a t U 2 and F i a r e i n p r e s e n t v a l u e s ) . S i n c e p l a y e r F can guarantee h i m s e l f F± f o r the game s t a r t i n g a t t = 1 , t h i s l i m i t s the maximum p a y o f f t o p l a y e r U a t t = 0 t o U Q = U ( F i ) = U [ d f x U - 1 ( U 2 / d u ) ] which can be r e w r i t t e n as : - S ^ B o l - 8-1 ( u 2 / d u ) . , i ) N o t i c e t h a t the game s t a r t i n g a t t ime t = 2 i s e x a c t l y the same as the game s t a r t i n g a t t ime t = 0 except t h a t the two p l a y e r s ' u t i l i t y f u n c t i o n s a r e s c a l e d down by a f i x e d f a c t o r d i 2 w i t h i = u f o r p l a y e r U and i = f f o r p l a y e r F . G i v e n t h e n a t u r e o f t h e e q u i l i b r i u m as a s e r i e s o f o p t i m i z a t i o n p r o b l e m s , the maximum p a y o f f t o p l a y e r U f o r 4 3 t h e game s t a r t i n g a t t = 2 i s the s c a l e d down maximum p a y o f f f o r the game s t a r t i n g a t t = 0 , o r U 2 = d u 2 U Q . S u b s t i t u t i n g i n ( 1 ) y i e l d s : 5-1 ( d u U o ) . w The concept o f p e r f e c t e q u i l i b r i a and the homogeneity o f t h e game have a l l o w e d us t o s o l v e f o r the maximum p a y o f f t o p l a y e r U at t ime 0 . Note t h a t we can do the same f o r the minimum p a y o f f t o p l a y e r U . I n f a c t , i f U i s c o n c a v e , e q u a t i o n ( 2 ) i s s a t i s f i e d a t one p o i n t o n l y and t h e r e f o r e the e q u i l i b r i u m i s u n i q u e . As mentioned p r e v i o u s l y , R u b i n s t e i n s o l v e d t h i s game by impos ing s t r u c t u r e on the p r e f e r e n c e s o f t h e p l a y e r s w i t h r e s p e c t t o the c o s t s o f d e l a y . S p e c i f i c a l l y , t h e s e c o s t s a r e assumed to be s t a t i o n a r y over t ime and i n c r e a s i n g w i t h t h e v a l u e o f t h e c o n t r a c t . L e t U i ( C , t ) be t h e u t i l i t y p l a y e r i r e c e i v e s from the b a r g a i n (or c o n t r a c t ) C s i g n e d a t t ime t . I t i s assumed t h a t f o r i = u , f , and f o r a l l t j , t 2 , t £ { 0 , 1 , 2 } . ( A - l ) U± ( C , t 1 ) > U i ( C , t 2 ) i f t 1 < t 2 . 3U. ( C , t ) ( A - 2 ) > 0 . 9 [ U . ( C , t ) - U . ( C , t - 1 ) ] ( A - 3 ) i < 0 . ( A - 4 ) U i ( C , t 1 ) > U i ( C , t±+l) i f f U i ( C , t 2 ) > U i ( C , t 2 + l ) 44 Assumpt ion ( A - l ) i m p l i e s t h a t t ime i s c o s t l y , (A-2) t h a t the c o n t r a c t i s measured i n u n i t s which a r e v a l u a b l e t o i , (A-3) t h a t t ime c o s t s a r e i n c r e a s i n g i n t h e c o n t r a c t u n i t s and (A-4) t h a t t ime c o s t s are s t a t i o n a r y . The l a s t assumpt ion can be expres sed d i f f e r e n t l y as f o l l o w s : ( A - 4 ) ' i f U 1 ( C , t ) = u i(C + e i , t+1) t h e n ei i s independent o f t . T h i s s a y s t h a t t h e i m p r o v e m e n t i n t h e c o n t r a c t n e c e s s a r y t o compensate a p l a y e r f o r w a i t i n g an e x t r a t ime p e r i o d i s the same at a l l t i m e s . (Note t h a t (A-3) i m p l i e s t h a t e w i l l be i n c r e a s i n g i n the v a l u e o f the c o n t r a c t ) . Assumpt ion (A-4) i s v e r y r e s t r i c t i v e . Binmore (1987a) shows t h a t w i t h some s t r e n g t h e n i n g o f ( A - 4 ) , t h e r e are o n l y two forms o f t ime c o s t s p e r m i t t e d : d i s c o u n t i n g and f i x e d c o s t s p e r t ime p e r i o d , i . e . U ^ C t ) - U i ( C ) d^ or U i ( C , T ) = U i ( C ) - D ± t . I n o r d e r t o g i v e e x a m p l e s o f f i x e d and d i s c o u n t i n g c o s t s , l e t d e l a y s be s t r i k e s and s u p p o s e t h a t t h e two p a r t i e s are n e g o t i a t i n g a 2 -year c o n t r a c t worth V i n t o t a l v a l u e . An example o f f i x e d c o s t s would be the l o s s to each p a r t y o f a f i x e d p r o p o r t i o n o f V i n e a c h p e r i o d o f the s t r i k e ; e . g . , a s t r i k e o f s i x months would mean l o s i n g 1/4 45 o f V , a s t r i k e o f one y e a r , the l o s s o f 1/2 o f V , e t c . Now s u p p o s e t h a t i f t h e r e i s a s t r i k e , the c o n t r a c t i s pushed f o r w a r d i n t i m e and t h a t V i s s t i l l t h e v a l u e o f t h e c o n t r a c t s i g n e d a f t e r the s t r i k e . D u r i n g the s t r i k e , the two p a r t i e s might have t o borrow money o r d e p l e t e s a v i n g s , but i n any c a s e , they are i n c u r r i n g the o p p o r t u n i t y c o s t o f r e c e i v i n g the v a l u e o f the c o n t r a c t l a t e r i n t i m e . In t h i s l a s t example , d e l a y c o s t s take the form o f d i s c o u n t i n g . In r e a l i t y , b o t h types o f c o s t s seem p l a u s i b l e . When s t r i k e s a r e s h o r t , i t i s p o s s i b l e t h a t the p o t e n t i a l c o n t r a c t v a l u e (V) i s c o m p l e t e l y r e c o v e r e d a f t e r the agreement i s s i g n e d t h r o u g h h i g h e r than average p r o d u c t i o n l e v e l s . F o r l o n g e r s t r i k e s , t h e r e c o v e r y o f t h e p o t e n t i a l c o n t r a c t v a l u e b e c o m e s m o r e i m p l a u s i b l e and f i x e d c o s t s a r e p r o b a b l y e n c u r r e d as w e l l . In R u b i n s t e i n (1982) the s e t o f P e r f e c t E q u i l i b r i a i s f u l l y c h a r a c t e r i z e d f o r the game w i t h p e r f e c t i n f o r m a t i o n a n d a f i x e d p i e . I n t h e c a s e o f d i s c o u n t c o s t s , t h e e q u i l i b r i u m i s u n i q u e , i t o c c u r s a t t ime 0, and i t g i v e s to t h e f i r s t m o v e r , s a y p l a y e r i , a s h a r e o f t h e p i e S i = ( 1 - d j ) / ( 1 - d ^ d j ) . (Note t h a t the e q u i l i b r i u m share S i i s e a s i l y d e r i v e d f r o m e q u a t i o n (2) and t h e f i x e d p i e b a r g a i n i n g f r o n t i e r : U ( F Q ) = 1 - F Q ) . In the case o f f i x e d c o s t s , i f D u £ D f , the e q u i l i b r i u m i s un ique and o c c u r s a t t ime 0, but i f D u = D f , t h e r e are m u l t i p l e e q u i l i b r i a some o f which c o u l d o c c u r l a t e r i n the game. 46 R u b i n s t e i n (1985) g e n e r a l i z e s h i s r e s u l t s f o r the game w i t h o n e - s i d e d i m p e r f e c t i n f o r m a t i o n c o n c e r n i n g t h e o p p o n e n t ' s t i m e c o s t s . F u r t h e r r e s u l t s on R u b i n s t e i n b a r g a i n i n g w i t h i m p e r f e c t i n f o r m a t i o n a r e d e r i v e d i n Crampton (1984a) and (1984b). Not s u r p r i s i n g l y , the s e t o f e q u i l i b r i u m p o i n t s i s v e r y s e n s i t i v e t o t h e i n f o r m a t i o n s t r u c t u r e . I n t h e a b s e n c e o f a s y m m e t r i e s i n t h e i n f o r m a t i o n , t h e r e i s n o t h i n g to g a i n from a d e l a y and we e x p e c t t h e agreement t o be s i g n e d a t t h e b e g i n n i n g o f the g a m e . 1 6 W i t h a s y m m e t r i c i n f o r m a t i o n , d e l a y s can p l a y a r o l e i n p r o v i d i n g i n f o r m a t i o n ; however, even f o r v e r y s i m p l e models the e q u i l i b r i a are q u i t e complex. F u r t h e r m o r e , the e q u i l i b r i a depend c r u c i a l l y on a spec t s o f t h e i n f o r m a t i o n s t r u c t u r e s u c h as p r i o r b e l i e f s f o r w h i c h no d a t a a r e a v a i l a b l e . I t i s i m p o r t a n t t o no te t h a t i n the r e s u l t s d e s c r i b e d above , t h e r e i s an advantage i n b e i n g the f i r s t mover i n the n e g o t i a t i o n s . F o r example, the share o f the p i e S i g o i n g t o the f i r s t mover i n the game w i t h d i s c o u n t i n g and p e r f e c t i n f o r m a t i o n i s g r e a t e r than one h a l f when d i = dj . (From above , S i = ( l - d ) / ( l - d 2 ) where d = d i = dj and 0 < d < l ) . U n l e s s t h e r e are i n s t i t u t i o n a l f a c t o r s d e t e r m i n i n g the f i r s t 1 6 I do no t t h i n k the e q u i l i b r i a i n v o l v i n g d e l a y which can o c c u r i n the case o f e q u a l f i x e d c o s t s u n d e r p e r f e c t i n f o r m a t i o n are good models o f d e l a y s i n b a r g a i n i n g s i n c e , i n s u c h a f r a m e w o r k , t h e r e i s n o t h i n g t o be g a i n e d by d e l a y i n g t h e agreement. R a t h e r , they i n d i c a t e a need f o r some s t r e n g t h e n i n g o f the e q u i l i b r i u m concept i n t h a t c a s e . 47 mover, we would expect the p l a y e r s t o b a r g a i n over who goes f i r s t . In t h i s s ense , the game i s i n c o m p l e t e . One way to d e a l w i t h t h i s f e a t u r e i s t o a l l o w the t ime i n t e r v a l b e t w e e n p r o p o s a l s t o b e c o m e s m a l l . I n t h e c o n t i n u o u s t i m e game t h e r e i s no a d v a n t a g e i n b e i n g t h e f i r s t m o v e r . N o t e t h a t t h i s c o n t i n u o u s t ime game i s the l i m i t o f the d i s c r e t e t ime game when t ime i n t e r v a l s between o f f e r s tend t o z e r o . I t can be i n t e r p r e t e d as a game where a t each i n s t a n t , a p l a y e r can e i t h e r make a (new) o f f e r or a c c e p t the most r e c e n t p r o p o s a l by h i s opponent . However, i t i s i m p o r t a n t t h a t the o r d e r o f the moves be r e s p e c t e d ; e a c h o f f e r has t o be r e j e c t e d or accepted b e f o r e another o f f e r i s made. In o t h e r words , s imul taneous o f f e r s are not a l l o w e d . T h e r e i s another reason why the c o n t i n u o u s t ime model i s a p p e a l i n g . F o r the game w i t h d i s c o u n t i n g and p e r f e c t i n f o r m a t i o n , B i n m o r e ( 1 9 8 7 b ) showed t h a t as t h e t i m e i n t e r v a l between moves approaches to z e r o , the two p e r f e c t e q u i l i b r i u m p o i n t s c o r r e s p o n d i n g t o the two p o s s i b l e f i r s t movers approach each o t h e r and at the l i m i t , the r e s u l t i n g u n i q u e s o l u t i o n i s a g e n e r a l i z e d N a s h b a r g a i n i n g (GNB) 48 s o l u t i o n w i t h weights b e i n g f u n c t i o n s o f the d i s c o u n t r a t e s o n l y . 1 7 The GNB s o l u t i o n can be w r i t t e n as the s o l u t i o n t o : a a.p max (U - T ) u ( U f - T f ) ' 1 s . t ( U u , U - ) £ B (3) u u , u f where U i i s the u t i l i t y o f p l a y e r i , i = u , f T i i s the u t i l i t y o f p l a y e r i a t the d i sagreement p o i n t a^ i s the weight g i v e n to the u t i l i t y o f p l a y e r i ( o f t e n i n t e r p r e t e d as the b a r g a i n i n g power o f p l a y e r i ) B i s the b a r g a i n i n g s e t . N o t e t h a t any p o i n t on t h e P a r e t o f r o n t i e r o f t h e convex b a r g a i n i n g s e t can be w r i t t e n as a g e n e r a l i z e d Nash b a r g a i n i n g s o l u t i o n w i t h the c h o i c e o f a p p r o p r i a t e w e i g h t s . T h e r e f o r e , s i n c e i t i s e f f i c i e n t , the p e r f e c t e q u i l i b r i u m t o the R u b i n s t e i n game (w i th p e r f e c t i n f o r m a t i o n ) i s a l s o a GNB s o l u t i o n . In g e n e r a l , however, the a p p r o p r i a t e we ights w i l l be f u n c t i o n s o f a l l t h e parameters o f the game, i . e . the f u n c t i o n s r e p r e s e n t i n g d e l a y c o s t s , the f i r s t mover, and t h e p a r a m e t e r s o f t h e t i m e 0 b a r g a i n i n g s e t . The B i n m o r e r e s u l t s i s t h a t t h e u n i q u e p e r f e c t e q u i l i b r i u m f o r t h e 1 7 T h e N a s h b a r g a i n i n g s o l u t i o n i s a c o o p e r a t i v e game s o l u t i o n concept which s a t i s f i e s the f o u r f o l l o w i n g axioms: i n d e p e n d e n c e o f i r r e l e v a n t a l t e r n a t i v e s , symmetry, P a r e t o e f f i c i e n c y , i n v a r i a n c e t o ( i n c r e a s i n g ) a f i n e t r a n s f o r m a t i o n . I t c a n be w r i t t e n as t h e s o l u t i o n t o t h e o p t i m i z a t i o n p r o b l e m (3) w i t h a i = a2 = . 5 . A g e n e r a l i z e d N a s h b a r g a i n i n g s o l u t i o n i s a Nash b a r g a i n i n g s o l u t i o n w i t h o u t the symmetry r e q u i r e m e n t . 49 c o n t i n u o u s t ime game w i t h d i s c o u n t i n g can be w r i t t e n as a GNB s o l u t i o n w i t h a zero t h r e a t p o i n t and w i t h the f o l l o w i n g w e i g h t s : l n d ^ ^ n c \ i a u = l n d u + l n d f a f = l n d u + l n d f where d i i s the d i s c o u n t f a c t o r o f p l a y e r i . (Note t h a t i f the t h r e a t p o i n t were p o s i t i v e , i t would be reached i n f i n i t e t ime and the game would no l o n g e r have an i n f i n i t e h o r i z o n . ) B i n m o r e ' s r e s u l t i s i m p o r t a n t f o r t h e e m p i r i c a l a p p l i c a t i o n o f the game because w r i t i n g the e q u i l i b r i u m as an o p t i m i z a t i o n p r o b l e m m a k e s i t p o s s i b l e t o d e r i v e e s t i m a t i n g wage and employment e q u a t i o n s u n d e r g e n e r a l s p e c i f i c a t i o n s o f the u t i l i t y f u n c t i o n s . In c o m p a r i s o n , f o r t h e d i s c r e t e t i m e game w i t h d i s c o u n t i n g c o s t s , o n e i s p r a c t i c a l l y f o r c e d t o assume the u n i o n i s a r e n t maximizer i n o r d e r t o d e r i v e t h e e s t i m a t i n g m o d e l u n l e s s a p p r o x i m a t i o n s a r e u s e d . To see t h i s l e t the f r o n t i e r o f the b a r g a i n i n g s e t a t t ime 0 be: U U ( C ) = U ( U f ( C ) ) where C denotes the wage and employment c o n t r a c t . The e q u i l i b r i u m c o n t r a c t f o r the d i s c r e t e t ime game, C , w i l l be the s o l u t i o n t o the f o l l o w i n g e q u a t i o n : d u U u ( C ) = U [ U " 1 ( U U ( C ) ) / d f ] . 50 R e n t m a x i m i z a t i o n c a u s e s U t o be l i n e a r and t h e above e q u a t i o n i s then e a s i l y s o l v e d . 3.2 A p p l i c a t i o n o f t h e B a r g a i n i n g Game t o F i r m - U n i o n C o n t r a c t N e g o t i a t i o n s T h e r e a r e s e v e r a l c r u c i a l e lements i n the R u b i n s t e i n b a r g a i n i n g game. In t h i s s e c t i o n , t h e s e a s s u m p t i o n s a r e d i s c u s s e d i n t h e c o n t e x t o f f i r m - u n i o n c o n t r a c t n e g o t i a t i o n s . F i r s t , the p l a y e r s must a l t e r n a t e i n making o f f e r s and once an o f f e r has been made, i t must be accepted o r r e j e c t e d b e f o r e another o f f e r i s made. F o r example , the u n i o n o f f e r s a w a g e - e m p l o y m e n t c o n t r a c t t o t h e f i r m , t h e f i r m t h e n a c c e p t s o r r e j e c t s t h i s c o n t r a c t . I f i t a c c e p t s , a c o l l e c t i v e agreement i s s i g n e d ; i f i t r e j e c t s , b a r g a i n i n g moves on t o t h e n e x t r o u n d and t h e f i r m makes a c o u n t e r o f f e r t o the u n i o n . T h i s framework i s p r e f e r a b l e t o t h e b a r g a i n i n g models where one s i d e o n l y can make o f f e r s s i n c e , i n t h e case o f c o l l e c t i v e b a r g a i n i n g , b o t h f i r m s and un ions do make o f f e r s . A l s o , d u r i n g n e g o t i a t i o n s , a move by a p a r t y i s g e n e r a l l y expected to e l i c i t a r e s p o n s e f r o m t h e o t h e r p a r t y (see C r a i g (1986) , C h a p t e r 7 ) . S e c o n d l y , b o t h the f i r m and the u n i o n i n c u r c o s t s i f the agreement i s d e l a y e d . i n the b a r g a i n i n g p r o c e s s under s t u d y , n e g o t i a t i o n s on a new c o n t r a c t s t a r t s e v e r a l months b e f o r e the end o f the e x i s t i n g c o n t r a c t , n e g o t i a t i n g teams 51 are composed o f permanent employees o f the two p a r t i e s , and d i s p u t e s a r e s e t t l e d by work s toppages ( s t r i k e s o r l o c k o u t s ) r a t h e r t h a n a r b i t r a t i o n . I t i s assumed t h a t the b a r g a i n i n g game beg ins a t the t ime o f e x p i r y o f the p r e v i o u s c o n t r a c t ( t ime 0 ) . A t t h i s t ime e i t h e r an agreement i s s i g n e d (the f i r s t o f f e r i s accepted) i n which case no c o s t s o f d e l a y are i n c u r r e d , or t h e r e i s a s t r i k e / l o c k o u t and b o t h p a r t i e s bear c o s t s . The s t r i k e / l o c k o u t w i l l c o n t i n u e and t h e c o s t s i n c r e a s e u n t i l an o f f e r i s a c c e p t e d and t h e c o n t r a c t i s s i g n e d . Note t h a t the c o s t s o f m a i n t a i n i n g the n e g o t i a t i n g teams a r e no t i n c l u d e d i n the c o s t s o f d e l a y but a r e r a t h e r embedded i n the u t i l i t y f u n c t i o n s o f the p a r t i e s . A l s o , the p l a y e r s a r e n o t a l l o w e d t o u s e t h r e a t s o t h e r t h a n work s t o p p a g e ( e . g . work s lowdown o r s i m p l y c o n t i n u e d work ing w i t h o u t a c o n t r a c t ) . T h i s w o u l d c o m p l i c a t e t h e m o d e l c o n s i d e r a b l y as the k i n d o f t h r e a t used and the t i m i n g o f t h e p u n i s h m e n t w o u l d be p a r t o f t h e s t r a t e g y o f t h e p l a y e r s . 1 8 F u r t h e r m o r e , e m p i r i c a l a p p l i c a t i o n would r e q u i r e d a t a on t h e v a r i o u s t h r e a t s and t h e i r a s s o c i a t e d c o s t s . The t h i r d major element i n R u b i n s t e i n b a r g a i n i n g i s the i n f i n i t e b a r g a i n i n g h o r i z o n . There are no exogenous f a c t o r s f o r c i n g the p l a y e r s to s t o p b a r g a i n i n g w h i l e t h e r e are s t i l l g a i n s from t r a d e . F o r example, budget c o n s t r a i n t s such as r e q u i r i n g t h a t the u n i o n cannot s u r v i v e a s t r i k e a f t e r the 1 8 S e e H a r t (1986) f o r a s t ep i n t h i s d i r e c t i o n . 52 d e p l e t i o n o f i t s s t r i k e fund are p r e c l u d e d . R a t h e r , i t i s assumed t h a t the u n i o n c o u l d borrow money to s u s t a i n i t s e l f i n d e f i n i t e l y d u r i n g a s t r i k e . The a l t e r n a t i v e i s a f i n i t e game i n which the e q u i l i b r i u m would depend c r u c i a l l y on the t o t a l t ime a v a i l a b l e t o the p l a y e r s . In the absence o f d a t a on t h e l e n g t h o f n e g o t i a t i o n rounds and on the number o f p o s s i b l e rounds b e f o r e a f i n a l breakdown i n b a r g a i n i n g , i t w o u l d be i m p o s s i b l e t o d i s t i n g u i s h b e t w e e n v a r i o u s e q u i l i b r i a . F i n a l l y , t h e two b a r g a i n i n g p a r t n e r s a r e e x t r e m e l y r a t i o n a l i n the sense d e s c r i b e d i n s e c t i o n 3.1 ( i . e . t h e y c a r e o n l y a b o u t t h e f i n a l a g r e e m e n t and i t s a s s o c i a t e d u t i l i t y and they do not b e l i e v e i d l e t h r e a t s ) . T h i s i s a m a j o r i m p r o v e m e n t o v e r p a s t m o d e l s o f t h e n e g o t i a t i o n p r o c e s s i n which the e q u i l i b r i u m depended on some f o r m o f i r r a t i o n a l i t y o f t h e p l a y e r s . The m o d e l s by C r o s s and Z e u t h e n - H a r s a n y i are we l l -known examples o f b a r g a i n i n g i n w h i c h p a r t i e s make s y s t e m a t i c m i s t a k e s a b o u t t h e i r opponent ' s b e h a v i o u r or e v e n t h e i r own f u t u r e b e h a v i o u r . (See F o l e y and Maunders (1979) f o r a d e s c r i p t i o n o f these m o d e l s . ) A l t h o u g h t h e s e a r e t h e f u n d a m e n t a l a s s u m p t i o n s u n d e r l y i n g R u b i n s t e i n b a r g a i n i n g , the p a r t i c u l a r game which i s c h o s e n w i l l d e p e n d on t h e m a i n t a i n e d a s s u m p t i o n s r e g a r d i n g t h e i n f o r m a t i o n s t r u c t u r e and t h e m o d e l l i n g o f t ime as a d i s c r e t e or c o n t i n u o u s v a r i a b l e . 53 I t was mentioned i n the p r e v i o u s s e c t i o n t h a t a l l o w i n g asymmetr ic i n f o r m a t i o n w i l l i n g e n e r a l i m p l y t h a t some o f the e q u i l i b r i u m p o i n t s are c o n t r a c t s s i g n e d a f t e r a s t r i k e o r l o c k o u t . However, the e q u i l i b r i u m i s s u b s t a n t i a l l y more complex even when v e r y s i m p l i f y i n g assumptions a r e made on t h e i n f o r m a t i o n s t r u c t u r e ( e . g . o n e - s i d e d i m p e r f e c t i n f o r m a t i o n w i t h o n l y two p o s s i b l e t y p e s o f o p p o n e n t ) . F u r t h e r m o r e , the e q u i l i b r i u m i s v e r y s e n s i t i v e t o c e r t a i n b e h a v i o r such as forming p r i o r b e l i e f s and u p d a t i n g b e l i e f s o u t s i d e e q u i l i b r i u m paths f o r which no d a t a i s a v a i l a b l e . A s tudy o f s t r i k e s w i l l i n v o l v e d e a l i n g w i t h these p r o b l e m s , but f o r the purposes o f t h i s r e s e a r c h , t h e c o m p l i c a t i o n s i n t r o d u c e d by a l l o w i n g f o r s t r i k e s are j u s t too g r e a t and i assume p e r f e c t i n f o r m a t i o n . T h e q u e s t i o n t h e n a r i s e s as t o the a p p l i c a b i l i t y o f such a s t r o n g i n f o r m a t i o n assumpt ion t o the d a t a s e t under s t u d y . The IWA and the employer a s s o c i a t i o n r e p r e s e n t i n g the i n d u s t r y have been b a r g a i n i n g t o g e t h e r f o r a l o n g t ime and d i s c u s s i o n s w i t h a u n i o n n e g o t i a t o r suggest t h a t they have a good knowledge o f the f i r m s ' t e c h n o l o g y and markets (or a t l e a s t they b e l i e v e they d o ) . A f u r t h e r i n d i c a t i o n o f the mature r e l a t i o n s h i p between the u n i o n and t h e f i r m i s t h e i n c i d e n c e o f s t r i k e s . O v e r t h e p e r i o d u n d e r s t u d y (1963 -83 ) o n l y 3 s t r i k e s i n v o l v i n g a t l e a s t 10% o f t h e employees o c c u r r e d due t o c o n t r a c t n e g o t i a t i o n s . 54 The c h o i c e o f whether to model t ime as a d i s c r e t e or c o n t i n u o u s v a r i a b l e s h o u l d depend on t h e a b i l i t y o f t h e p l a y e r s t o commit themselves t o t h e i r o f f e r s . F o r example, i f the u n i o n has a way o f c o n v i n c i n g t h e f i r m t h a t i t w i l l n o t c o n s i d e r a new o f f e r b e f o r e the next month, then i t s p r e s e n t o f f e r w i l l s tand f o r a l o n g t i m e . U n f o r t u n a t e l y , I h a v e no d a t a on t h i s and when c h o o s i n g t h e a p p r o p r i a t e mode l , o t h e r c o n s i d e r a t i o n s come i n t o p l a y . A d i s c r e t e t ime model has the c h a r a c t e r i s t i c t h a t the p l a y e r w i t h the f i r s t move has an advantage even w i t h e q u a l t ime c o s t s and s i m i l a r u t i l i t y f u n c t i o n s . i n p r a c t i c e , i t i s g e n e r a l l y the case t h a t the u n i o n i s the f i r s t mover. However, i f t h e r e a r e l a r g e b e n e f i t s t o b e i n g f i r s t mover, one would expec t the two p l a y e r s t o b a r g a i n over the p r i v i l e g e o f g o i n g f i r s t . The absence o f such d i s p u t e s sugges ts t h a t the t ime p e r i o d s a r e s m a l l , i . e . the f i r s t mover advantage i s not i m p o r t a n t . F u r t h e r m o r e , as mentioned i n the p r e v i o u s s e c t i o n , Binmore has shown t h a t the e q u i l i b r i u m t o the c o n t i n u o u s t ime game c a n s o m e t i m e s be w r i t t e n as a N a s h b a r g a i n i n g s o l u t i o n . T h i s means t h a t a more g e n e r a l s p e c i f i c a t i o n o f the p l a y e r s ' o b j e c t i v e s c a n be used w h i l e k e e p i n g the e s t i m a t i n g model t r a c t a b l e . W i t h these c o n s i d e r a t i o n s i n m i n d , I a d o p t a c o n t i n u o u s t ime s p e c i f i c a t i o n o f the game. The use o f c o n t i n u o u s t ime i s no t s u f f i c i e n t to a l l o w me t o use the Binmore r e s u l t ; i t i s a l s o n e c e s s a r y t o assume t h a t the d e l a y c o s t s t a k e t h e f o r m o f d i s c o u n t f a c t o r s . 55 A l t h o u g h t h i s might seem u n d u l y r e s t r i c t i v e , i n f a c t , i f I am t o u s e R u b i n s t e i n b a r g a i n i n g , I h a v e v e r y l i t t l e f l e x i b i l i t y i n the s p e c i f i c a t i o n o f t h e t i m e c o s t s . The c h o i c e i s p r a c t i c a l l y l i m i t e d t o f i x e d c o s t s , d i s c o u n t i n g c o s t s o r c o m b i n a t i o n s o f the form: f U ^ C t ) = [ U ± ( C ) - D ± t ] d £ (4) When c h o o s i n g among these p o s s i b i l i t i e s , an i m p o r t a n t c o n s i d e r a t i o n i s the i m p l i e d t h r e a t p o i n t . The t h r e a t p o i n t i s f o r m e d by t h e u t i l i t y l e v e l s t h a t the two p l a y e r s can guarantee themse lves no mat ter what s t r a t e g y t h e i r opponent p l a y s . F i x e d c o s t s have the d i s a d v a n t a g e t h a t the i m p l i e d t h r e a t p o i n t i s ( -oo , -™) i . e . the p l a y e r s b e l i e v e t h a t t h e i r opponent can keep on n e g o t i a t i n g even w i t h ex treme ly l a r g e l o s s e s o r n e g a t i v e u t i l i t i e s . W i t h d i s c o u n t i n g c o s t s and an i n f i n i t e h o r i z o n , i t i s assumed t h a t the t h r e a t p o i n t i s ( 0 , 0 ) . I t i s no t uncommon t o s p e c i f y a z e r o d i sagreement p o i n t f o r the f i r m a l t h o u g h i n the presence o f f i x e d c o s t s , t h i s w i l l o v e r e s t i m a t e the guaranteed p r o f i t l e v e l a t l e a s t i n the s h o r t r u n . S p e c i f y i n g a zero t h r e a t p o i n t f o r the u n i o n i s more u n u s u a l . G e n e r a l l y , a measure o f the a l t e r n a t i v e income has been used as a d i sagreement p o i n t . However , a c o n s t r a i n t on the c o n t r a c t wage such as an a l t e r n a t i v e wage i s no t i n c o n s i s t e n t w i t h the a s s u m p t i o n o f a z e r o t h r e a t p o i n t . F o r example , suppose t h a t any c o n t r a c t g i v i n g the 56 workers l e s s t h a n the a l t e r n a t i v e wage i s u n a c c e p t a b l e t o t h e u n i o n . A l s o , d u r i n g a s t r i k e , the workers do not earn t h e a l t e r n a t i v e wage, they e a r n a s t r i k e pay which i s l e s s t h a n the b e s t a l t e r n a t i v e income. To be c o n s i s t e n t w i t h a z e r o t h r e a t p o i n t , the u t i l i t y f u n c t i o n o f the u n i o n would be n o r m a l i z e d t o e q u a l zero a t the p o i n t o f ; z e r o employment and an income l e v e l e q u a l t o t h e s t r i k e pay . F u r t h e r m o r e , t h e e q u i l i b r i u m c o n t r a c t i n t h i s model would have t o s a t i s f y t h e c o n s t r a i n t t h a t t h e wage be g r e a t e r o r e q u a l t o t h e a l t e r n a t i v e w a g e . 1 9 U t i l i t y f u n c t i o n s o f t h e f o r m o f e q u a t i o n (4) above w i t h b o t h f i x e d and d i s c o u n t i n g t ime c o s t s w i l l approach the f o l l o w i n g t h r e a t p o i n t as t h e s t r i k e l e n g t h becomes i n f i n i t e : l n d u l n d f A l t h o u g h t h i s s p e c i f i c a t i o n i s l e s s r e s t r i c t i v e , t h e r e s u l t i n g e s t i m a t i n g model i s s u b s t a n t i a l l y more complex and i t r e q u i r e s b e t t e r d a t a on s t r i k e c o s t s , i n p a r t i c u l a r , on 1 9 T h e e q u i l i b r i u m o f t h e b a r g a i n i n g game i n t h i s example can be w r i t t e n as the s o l u t i o n t o : A u A f _ max U u U f s . t . ( U u , U f ) £ B , U u £ 0 , Uf^O U u . U f where B i s t h e s e t formed by the u t i l i t y p a i r s c o r r e s p o n d i n g t o a l l p o s s i b l e c o n t r a c t s g i v i n g t h e u n i o n a t l e a s t t h e a l t e r n a t i v e wage, and U u t akes the form U U ( W , E , ) - U S w i t h U s r e p r e s e n t i n g the u t i l i t y r e c e i v e d from the s t r i k e pay . 57 exogenous f a c t o r s which enab le one to d i s c r i m i n a t e between the Dj^'s and d ^ ' s . U n f o r t u n a t e l y , t h e l i t e r a t u r e on s t r i k e c o s t s i s not v e r y h e l p f u l i n c h o o s i n g among these s p e c i f i c a t i o n s . A l s o , the a v a i l a b l e d a t a i s f a i r l y l i m i t e d . C o n s e q u e n t l y , i n t h i s p a p e r , the s i m p l e s t f o r m u l a t i o n i s chosen and d i s c o u n t i n g c o s t s are assumed ( f i x e d c o s t s are s e t e q u a l to z e r o ) . Note t h a t the d i s c o u n t f a c t o r s can be d i f f e r e n t f o r the f i r m and the u n i o n . Two f i n a l r e m a r k s s h o u l d be made c o n c e r n i n g t h e b a r g a i n i n g game: ( i ) A l t h o u g h i t i s n o t n e c e s s a r y f o r e x i s t e n c e o f e q u i l i b r i a , c o n v e x i t y o f t h e b a r g a i n i n g s e t does e n s u r e u n i q u e n e s s . I n g e n e r a l , s t a n d a r d r e s t r i c t i o n s on t h e o b j e c t i v e f u n c t i o n s o f the p l a y e r s a r e n o t s u f f i c i e n t t o guarantee a convex s e t . The u s u a l p r a c t i c e o f c o n v e x i f y i n g the b a r g a i n i n g s e t by a l l o w i n g t h e p l a y e r s t o r a n d o m i z e c a u s e s p r o b l e m s i n e m p i r i c a l a p p l i c a t i o n s b e c a u s e t h e observed c o n t r a c t i s the ex p o s t c o n t r a c t . I f the ex ante or expec ted c o n t r a c t i s random, our o b s e r v a t i o n w i l l c o n t a i n an e r r o r w h i c h w i l l g e n e r a l l y be c o r r e l a t e d w i t h t h e parameters and the exogenous f a c t o r s o f the game. I assume the s e t i s convex and t h i s a s s u m p t i o n w i l l be c h e c k e d a t each d a t a p o i n t . ( i i ) The game models one c o n t r a c t n e g o t i a t i o n o n l y and p r e v i o u s c o n t r a c t s can a f f e c t the p r e s e n t n e g o t i a t i o n s o n l y 58 t h r o u g h t h e e x o g e n o u s f a c t o r s . A c o m p l e x r e p u t a t i o n b u i l d i n g s t r a t e g y c o v e r i n g s e v e r a l c o n t r a c t s i s no t a l l o w e d . T h i s would r e q u i r e a Supergame where e a c h t i m e p e r i o d i s i t s e l f a b a r g a i n i n g game. 3.3 The F i r m ' s Techno logy and O b j e c t i v e s In t h i s s e c t i o n we c h a r a c t e r i z e the t i m e i n d e p e n d e n t p o r t i o n o f the f i r m ' s u t i l i t y f u n c t i o n (Uf(C) i n the above n o t a t i o n ) . The f i r m p r o d u c e s o u t p u t Q i u s i n g 3 i n p u t s : l a b o u r ( E ) , m a t e r i a l s a n d s u p p l i e s (Q2)<• and c a p i t a l s e r v i c e s ( Q 3 ) . I t i s assumed t h a t the p r o d u c t i o n p r o c e s s c a n be r e p r e s e n t e d by a C o b b - D o u g l a s f u n c t i o n . Two d i f f e r e n t f r a m e w o r k s a r e e s t i m a t e d . T h e s e two m o d e l s c o r r e s p o n d t o d i f f e r e n t s e t s o f assumptions c o n c e r n i n g t h e s e n s i t i v i t y o f i n p u t s and output t o the l a b o u r c o n t r a c t C . In the f i r s t mode l , i t i s assumed t h a t b o t h output and m a t e r i a l s and s u p p l i e s are a d j u s t e d t o the l a b o u r c o n t r a c t w h i l e c a p i t a l i s e x o g e n o u s l y d e t e r m i n e d . T h e p r o f i t f u n c t i o n r e s t r i c t e d w i t h r e s p e c t t o l a b o u r and c a p i t a l and d u a l t o the Cobb-Douglas p r o d u c t i o n f u n c t i o n i s w r i t t e n as : T T r ( T , P 1 , P 2 , Q 3 , E) = RO x T R 1 x p [ 1 _ R 2 ) x P R 2 X Q R 3 x E R e w h e r e P^ i s t h e p r i c e o f o u t p u t , P 2 i s t h e p r i c e o f m a t e r i a l s and s u p p l i e s , Q3 i s t h e q u a n t i t y o f c a p i t a l s e r v i c e s , T i s a t ime i n d e x , and the R ' s are f u n c t i o n s o f 59 the u n d e r l y i n g p r o d u c t i o n f u n c t i o n p a r a m e t e r s . R3 i s t h e p r o f i t e l a s t i c i t y o f c a p i t a l and Re i s t h e p r o f i t e l a s t i c i t y o f l a b o u r . R2 i s t h e r a t i o o f r e v e n u e s t o r e s t r i c t e d p r o f i t s w h i l e (1 -R2) i s t h e r a t i o o f m a t e r i a l c o s t s t o r e s t r i c t e d p r o f i t s . ( R e s t r i c t e d p r o f i t s are g r o s s o f l a b o u r and c a p i t a l c o s t s ) . R l measures s h i f t s i n the p r o d u c t i o n p r o c e s s o v e r t i m e w h i l e RO i s a s c a l i n g f a c t o r . I t i s expec ted t h a t R3 , Re , R0>0, R2<0, and R e < l . To t h i s r e s t r i c t e d p r o f i t f u n c t i o n c o r r e s p o n d t h e demand f o r m a t e r i a l s and s u p p l i e s : Q 2 = -R2 X RO x T R 1 X P * 1 " * 2 ^ P * * 2 " 1 * x Q f x E R e and the s u p p l y c u r v e : Q 1 = (1-R2) x RO x T R 1 x P ~ R 2 x P R 2 x Q R 3 x E R e i n the second mode l , ou tput i s c o n s i d e r e d as exogenous t o the b a r g a i n i n g p r o c e s s . A l t h o u g h t h i s i s a r e s t r i c t i v e a s s u m p t i o n , i t i s commonly made i n e s t i m a t i o n s o f p r o d u c t i o n p r o c e s s e s . In the l a b o u r demand l i t e r a t u r e as w e l l as i n o t h e r a r e a s o f w o r k , r e s e a r c h e r s f i n d i t d i f f i c u l t t o e x p l a i n the b e h a v i o u r o f i n p u t and output q u a n t i t i e s by the use o f p r i c e s o n l y . M a r t i n e l l o (1984) who a l s o s t u d i e d the B . C . wood p r o d u c t s i n d u s t r y b u t w i t h a more f l e x i b l e f u n c t i o n a l f o r m t h a n t h e o n e u s e d h e r e h a d s i m i l a r d i f f i c u l t i e s when t r e a t i n g output as endogenous. As w i l l be seen l a t e r , assuming t h a t output i s an exogenous v a r i a b l e 60 does improve the p r e d i c t i o n o f employment i n t h i s s t u d y ; however, i t a l s o c r e a t e s new p r o b l e m s . The r e s t r i c t e d p r o f i t f u n c t i o n i n the second model i s w r i t t e n as : T T b ( T , P 1 , P 2 , P 3 , Q 1 , E ) = P 1 Q 1 - BO x T B 1 x P ^ ~ B 3 ) x P * 3 x dfx E B e where i s the p r i c e o f i n p u t i , f o r i = 2 , 3 , T i s a t ime index and the B ' s are f u n c t i o n s o f the u n d e r l y i n g p r o d u c t i o n f u n c t i o n p a r a m e t e r s . B3 i s the c o s t share o f c a p i t a l and (1-B3) i s the c o s t share o f m a t e r i a l s and s u p p l i e s . B2 i s the c o s t e l a s t i c i t y o f output and Be i s the c o s t e l a s t i c i t y o f l a b o u r . Note t h a t Be w i l l e q u a l the l a b o u r c o s t s h a r e o n l y i f t h e l a b o u r c o n t r a c t i s s i t u a t e d on t h e l a b o u r demand. Otherwi se ( e . g . i n the c o o p e r a t i v e m o d e l ) , the wage w i l l no t e q u a l the shadow p r i c e o f l a b o u r . BO i s a s c a l i n g parameter and B l measures s h i f t s i n the p r o d u c t i o n p r o c e s s over t i m e . I t i s expected t h a t B2 > 0, Be < 0, and B3 > 0. To t h e r e s t r i c t e d p r o f i t f u n c t i o n TTB c o r r e s p o n d the demand f o r m a t e r i a l s and s u p p l i e s : Q 2 = (1-B3) x BO x T B 1 x P ~ B 3 x P B 3 x Q B 2 x E B e and the demand f o r c a p i t a l s e r v i c e s : m B l „ ( 1 - B 3 ) „ ( B 3 - 1 ) ^B2 Re Q 3 = B3 x BO x T x P^ ' x P 3 x x E . 61 I t i s assumed t h a t a l l p r i c e s e x c e p t t h e wage a r e e x o g e n o u s , i . e . t h a t t h e i n p u t and o u t p u t m a r k e t s a r e c o m p e t i t i v e . T h i s does no t seem u n r e a s o n a b l e f o r the output p r i c e s i n c e most o f the o u t p u t i s s o l d i n h i g h l y c o m p e t i t i v e i n t e r n a t i o n a l m a r k e t s . H o w e v e r , t h e c o m p e t i t i v e market a s sumpt ion may be r e s t r i c t i v e i n the case o f the m a t e r i a l s p r i c e s i n c e some o f the lumber m i l l s i n t h i s d a t a s e t are owned by c o m p a n i e s who a l s o e n g a g e i n l o g g i n g . ( S e e C h a p t e r 4 , s e c t i o n 4.2 f o r a more d e t a i l e d d e s c r i p t i o n o f the i n d u s t r y ) In i t s b a r g a i n i n g w i t h the u n i o n , the f i r m i s assumed t o m a x i m i z e p r o f i t s . I t s u t i l i t y f u n c t i o n c a n t h e n be w r i t t e n as : when o u t p u t i s e x o g e n o u s . W i s t h e wage and exogenous v a r i a b l e s o t h e r than (W,E) a r e subsumed on t h e l e f t - h a n d s i d e o f the e q u a t i o n s f o r s i m p l i c i t y . Under s t a n d a r d c o n v e x i t y a s s u m p t i o n s , b o t h o f t h e s e u t i l i t y f u n c t i o n s w i l l have the f o l l o w i n g p r o p e r t i e s : U j (W,E) = TT R ( T , P 1 , P 2 , Q 3 , E ) - P 3 X Q 3 - W X E f o r the case i n which c a p i t a l i s exogenous, and U j (W,E) = TT b (T , P 1 , Q 2 , P 3 , P , E ) - W X E BE W < 0 t o the r i g h t o f the l a b o u r demand c u r v e l a b o u r demand c u r v e 62 < 0 - E < 0 f = -1 f = 0 9W 9W9E 9W where i = R , B . 3 . 4 U n i o n O b j e c t i v e s T h e m o d e l l i n g o f u n i o n o b j e c t i v e s h a s b e e n a c o n t e n t i o u s i s s u e f o r s e v e r a l d e c a d e s . As m e n t i o n e d i n C h a p t e r 2, a t tempts t o j u s t i f y a u n i o n o b j e c t i v e f u n c t i o n by t h e i n d i v i d u a l u n i o n m e m b e r s ' p r e f e r e n c e s a n d by a r e p r e s e n t a t i o n p r o c e s s s u c h as m a j o r i t y v o t i n g o r u t i l i t a r i a n i s m h a v e y i e l d e d few, g e n e r a l r e s u l t s . As i s common i n t h i s l i t e r a t u r e , I assume the e x i s t e n c e o f a w e l l - b e h a v e d c o n c a v e u t i l i t y f u n c t i o n d e f i n e d o v e r w a g e s , employment, and the a l t e r n a t i v e wage ( W A ) . T h i s f u n c t i o n i s assumed t o take the CES form: S p e c i a l cases o f t h i s f o r m u l a t i o n i n c l u d e : p = - 1 , the l i n e a r u t i l i t y f u n c t i o n : 6E + (1-6)(W-W A ) p = 0, the Cobb Doug las : E 6 ( W - W A ) ( 1 - 5 ) p = 0 and 6 = . 5 , r e n t m a x i m i z a t i o n : E ( W - W A ) . Some e c o n o m i s t s a r e o f t h e o p i n i o n t h a t a r e n t m a x i m i z i n g u t i l i t y f u n c t i o n s h o u l d be i m p o s e d a p r i o r i . (See f o r example , Brown and A s h e n f e l t e r (1986) . ) T h i s c l a i m i s b a s e d on t h e a s s u m p t i o n t h a t t h e u n i o n maximizes the U u ( C ) = (6E p + (1-6) (W-WA) p ) - 1 / p (5) average w o r k e r ' s expec ted u t i l i t y which i s u s u a l l y assumed t o be e q u a l to t h i s w o r k e r ' s expected income: where E i s employment and E i s the u n i o n membership. I do n o t know o f any e m p i r i c a l e v i d e n c e w h i c h s u p p o r t s t h i s as sumpt ion and f u r t h e r m o r e , when i t i s t e s t e d i n e m p i r i c a l s t u d i e s o f u n i o n s , t h e r e n t m a x i m i z a t i o n h y p o t h e s i s i s v i r t u a l l y a l w a y s r e j e c t e d . T h e r e f o r e , I choose t o use a more g e n e r a l form o f the u t i l i t y f u n c t i o n o f the u n i o n which i n c l u d e s r e n t m a x i m i z a t i o n as a s p e c i a l c a s e . Note t h a t t h e a l t e r n a t i v e wage has been i n c o r p o r a t e d i n t h e u t i l i t y f u n c t i o n o f the u n i o n r a t h e r t h a n imposed as a c o n s t r a i n t on t h e b a r g a i n i n g s e t . A t t h e t h r e a t p o i n t (where U u ( C ) = 0 ) , the employment l e v e l w i l l be z e r o and the wage w i l l e q u a l t h e a l t e r n a t i v e wage. T h i s i m p l i e s t h a t d u r i n g s t r i k e s , t h e w o r k e r s a r e e a r n i n g t h e i r b e s t a l t e r n a t i v e income. T h i s s t r o n g assumpt ion can be avo ided by m o d i f y i n g the d e f i n i t i o n o f the u n i o n u t i l i t y as f o l l o w s : and by a d d i n g t h e c o n s t r a i n t W^W& t o the s e t o f p o s s i b l e e q u i l i b r i u m c o n t r a c t s . 3 - x W + (1—3-) w E E 64 T h i s f o r m u l a t i o n a l l o w s f o r the p o s s i b i l i t y o f a s t r i k e pay l e s s than the a l t e r n a t i v e wage. However, t o s i m p l i f y the e s t i m a t i o n , the c o n s t r a i n t on the c o n t r a c t wage i s not imposed but i t w i l l be checked a t each d a t a p o i n t . 65 C h a p t e r 4 The Data and t h e E m p i r i c a l S p e c i f i c a t i o n o f t h e Model As d e s c r i b e d i n t h e p r e v i o u s c h a p t e r , t h i s s t u d y i n v o l v e s t h e e s t i m a t i o n o f f o u r d i f f e r e n t m o d e l s : t h e c o o p e r a t i v e and t h e l a b o u r demand b a r g a i n i n g m o d e l s a r e e s t i m a t e d f o r e a c h o f t h e two p o s s i b l e f i r m p r o f i t f u n c t i o n s . F o r purposes o f compar i son and a l s o t o a v o i d any c o n f u s i o n , I am d e v o t i n g a s e p a r a t e s e c t i o n ( 4 . 1 ) , t o the d e r i v a t i o n and p r e s e n t a t i o n o f the f o u r e s t i m a t i o n m o d e l s . T h i s i s f o l l o w e d i n s e c t i o n 4.2 by a b r i e f d i s c u s s i o n o f the d a t a . A d e t a i l e d d e s c r i p t i o n o f t h e d a t a s o u r c e s and c a l c u l a t i o n s i s p r o v i d e d i n Appendix A . 4 .1 The E s t i m a t i o n Models I n C h a p t e r 3 , t h e o b j e c t i v e f u n c t i o n s o f t h e two n e g o t i a t i n g p a r t i e s were s p e c i f i e d . The u n i o n u t i l i t y i s a f u n c t i o n o f t h e l a b o u r c o n t r a c t C=(W,E) and the t ime at which t h e c o n t r a c t i s s i g n e d . Assumpt ions ( A - l ) t o ( A - 4 ) f r o m c h a p t e r 3 a r e imposed on the p r e f e r e n c e s o f the two p l a y e r s engaged i n a R u b i n s t e i n b a r g a i n i n g game. T h e s e a s s u m p t i o n s imply t h a t each p l a y e r ' s o b j e c t i v e f u n c t i o n i s s e p a r a b l e w i t h r e s p e c t to the t ime a t which the agreement i s r e a c h e d . We can then c o n s i d e r the t ime independent u t i l i t y f u n c t i o n o f the u n i o n which i s s p e c i f i e d as : U u ( W , E ) = ( 6 E " P + ( 1 - 6 ) ( W - W A ) " P ) ~ 1 / p (1) 6 6 S i m i l a r l y , we can c o n s i d e r the t ime independent p o r t i o n o f the f i r m ' s o b j e c t i v e f u n c t i o n which i s assumed t o e q u a l the p r o f i t s a c h i e v e d under the l a b o u r c o n t r a c t C=(W,E) . Two d i f f e r e n t frameworks are s t u d i e d . F i r s t l y , t h e l e v e l o f o u t p u t i s e x o g e n o u s t o t h e b a r g a i n i n g i n which case the f i r m ' s u t i l i t y i s : U B (W,E) = P x x Q r BO x T B 1 x P'1'"* x ^ x Q B 2 x E B e - W x E = n B (T, P1,Q1,P2,P3,E) - W x E and, s e c o n d l y , the c a p i t a l i n p u t i s t r e a t e d as exogenous: uJ(W,E) = RO x T R 1 x p J 1 _ R 2 ) x P R 2 x Q R 3 x E R e - P 3 x Q 3 ~ W x E = n R (T, P 1 , P 2 , Q 3 > E ) - P 3 x Q 3 - W x E w h e r e t h e v e c t o r s o f B ' s a n d R ' s a r e v e c t o r s o f c o e f f i c i e n t s , T i s a t ime t r e n d , P^ and Q i a r e the p r i c e and q u a n t i t y i n d i c e s o f i n p u t / o u t p u t i w i t h i = l f o r o u t p u t , i=2 f o r m a t e r i a l s and s u p p l i e s and i=3 f o r c a p i t a l s e r v i c e s . A problem w i t h the above s p e c i f i c a t i o n s i s the p o s s i b l e d i s c r e p a n c y between the employment l e v e l a f f e c t i n g the two p a r t i e s u t i l i t i e s . More p r e c i s e l y , t h e u n i o n u t i l i t y w i l l depend on the employment o f u n i o n members w h i l e the f i r m ' s p r o f i t w i l l v a r y a c c o r d i n g t o t o t a l employment. As i s the case f o r most u n i o n i z e d i n d u s t r i e s , the i n d u s t r y under s tudy here has u n i o n i z e d p r o d u c t i o n w o r k e r s and n o n - u n i o n i z e d 67 a d m i n i s t r a t i v e and s a l e s p e r s o n n e l . T h e o r e t i c a l l y , t h e o b v i o u s s o l u t i o n to t h i s problem i s t o t r e a t n o n - p r o d u c t i o n w o r k e r s as a s e p a r a t e i n p u t i n t h e p r o d u c t i o n p r o c e s s . E m p i r i c a l l y , a t l e a s t f o r t h i s d a t a s e t , the a d d i t i o n o f t h i s new i n p u t does no t p r o v i d e more i n f o r m a t i o n because o f the l a r g e c o r r e l a t i o n between p r o d u c t i o n and n o n - p r o d u c t i o n employment. (See A p p e n d i x A f o r d e t a i l s . ) I n o r d e r t o i n c l u d e them i n t h e p r o f i t c a l c u l a t i o n s , n o n - p r o d u c t i o n l a b o u r c o s t s a r e c o n s i d e r e d as a f i x e d f r a c t i o n o f p r o d u c t i o n l a b o u r c o s t s . T h i s f r a c t i o n i s measured by the average r a t i o o f n o n - p r o d u c t i o n t o p r o d u c t i o n l a b o u r c o s t s o v e r t h e s a m p l e and i s e q u a l t o 15%. The f i r m ' s two p o s s i b l e u t i l i t y f u n c t i o n s e x p r e s s e d i n t e r m s o f t h e employment o f p r o d u c t i o n workers o n l y become: U * ( W , E ) = 1 . 1 5 x [ - B x T B 1 x P ( 2 " B 3 ) x * QBJ * E B e - W x E ] ( 2 ) = T I b ( T , P L F P 2 , P 3 , E ) - 1 . 1 5 x W x E and T T R / r , ^ \ , , c r„ m R l „ ( 1 - R 2 ) R2 „ R 3 „ R e P ^ Q ^ „ U _ ( W , E ) = 1 . 1 5 x [ R x T x P , x P „ x Q_ x E - r^fi - W x E ] ( 3 ) = n R ( T , P 1 , P 2 , Q 3 , E ) - 1 . 1 5 x W x E BO J „ RO w h e r e B = : — — a n d R = - — — 1 . 1 5 1 . 1 5 G i v e n t h e assumptions o f c o n t i n u o u s t i m e , d i s c o u n t i n g c o s t s , and p e r f e c t i n f o r m a t i o n , I can use B i n m o r e ' s r e s u l t 68 ( see C h a p t e r 3) and w r i t e t h e l a b o u r c o n t r a c t f o r t h e c o o p e r a t i v e model as the s o l u t i o n t o the f o l l o w i n g : l n d f l n d u max u ( W , E ) l n d u + l n d f l A ( W , E ) l n d u + l n d f ( 4 ) W,E U 9lnU (W,E) , 9 l n u i ( W , E ) w i t h F . O . C : - x • L n a r 1 9W l n d u 9W 3 l n U u ( W , E ) l n d f 9 l n U f ( W , E ) x 9E l n d u 9E where du i s the u n i o n ' s d i s c o u n t f a c t o r , d f i s the f i r m ' s d i s c o u n t f a c t o r and i = B o r R. The f i r s t - o r d e r c o n d i t i o n s a r e used t o g e n e r a t e wage and employment e s t i m a t i n g e q u a t i o n s . I n s t e a d o f c h e c k i n g second o r d e r c o n d i t i o n s f o r the problem as w r i t t e n i n ( 4 ) , I w i l l v e r i f y t h a t f o r each d a t a p o i n t : i ) The f i r m ' s i s o - p r o f i t c u r v e s a r e l e s s convex than the u n i o n i n d i f f e r e n c e c u r v e s . T h i s ensures t h a t the p o i n t on t h e c o n t r a c t c u r v e i n (W,E) s p a c e i s a tangency p o i n t o f t h e i s o - u t i l i t y c u r v e s . i i ) The b a r g a i n i n g f r o n t i e r i n ( U u , Uf) space i s concave to the o r i g i n . T h i s f r o n t i e r i s d e r i v e d from the s o l u t i o n t o : 69 max U U ( W , E ) s . t . ui(W,E) I U f W,E where i = R o r B and i s a g i v e n l e v e l o f u t i l i t y f o r the f i r m . S o l v i n g f o r (W,E) and s u b s t i t u t i n g i n U u , we have a r e l a t i o n s h i p b e t w e e n U u a n d U ^ : U u ( 0 ^ ) , t h e b a r g a i n i n g f r o n t i e r . T h e c o n d i t i o n s ( i ) and ( i i ) a r e s t r o n g e r t h a n i s n e c e s s a r y but they a r e more i n t u i t i v e and e a s i e r t o c h e c k . In the l a b o u r demand model where the f i r m u n i l a t e r a l l y chooses employment, the e q u i l i b r i u m t o the b a r g a i n i n g game can be genera ted as the s o l u t i o n t o : l n d f l n d u / I T ^ v l n d u + l n d f „ i / T T l n d u + l n d f , _ . max U ( W , E ) U ( W , E ) (5) W u 3U* ( W , E ) . . . . f n ( t h e f i r m c h o o s e s e m p l o y m e n t t o m a x i m i z e s u b j e c t t o — 0 p r o f l t 8 0 . . „ _ 9 l D U u ( W ' E ) n M R q 9E(W), l n d f 9 1 n U f ( W ' E ) W l t h F . o . c . : [1 + MRS x x — = - - where E(W) i s the l a b o u r demand f u n c t i o n which s o l v e s the c o n s t r a i n t , i = R o r B , and MRS i s t h e m a r g i n a l r a t e o f s u b s t i t u t i o n f o r t h e u n i o n ; i . e . MRS p+i 70 F o r the l a b o u r demand mode l , the f r o n t i e r o f the b a r g a i n i n g s e t i s t h e l a b o u r demand c u r v e e x p r e s s e d i n u t i l i t i e s . C o n d i t i o n ( i i ) above w i l l a l s o be checked at each d a t a p o i n t f o r t h i s mode l . The b a r g a i n i n g f r o n t i e r i s d e r i v e d from an o p t i m i z a t i o n problem s i m i l a r to t h a t i n ( i i ) b u t w i t h t h e added c o n s t r a i n t t h a t t h e (W,E) c o m b i n a t i o n l i e on t h e l a b o u r demand c u r v e . 2 0 T h e f o r m u l a t i o n o f t h e l a b o u r demand a n d t h e c o o p e r a t i v e models i n terms o f the o p t i m i z a t i o n problems (4) and (5) c a n be somewhat m i s l e a d i n g . S p e c i f i c a l l y , t h e l a b o u r demand model can be w r i t t e n as the s o l u t i o n t o t h e o p t i m i z a t i o n problem (4) w i t h the added c o n s t r a i n t t h a t the wage-employment c o n t r a c t be l o c a t e d on t h e l a b o u r demand 2 0 F o r t h e c o o p e r a t i v e mode l , the f i r s t d e r i v a t i v e o f the b a r g a i n i n g f r o n t i e r i s ° u ( 0 f > = " UuW / E < 0 where U uw i s the p a r t i a l o f U u w . r . t . the wage. The second d e r i v a t i v e has the s i g n o f the f o l l o w i n g e x p r e s s i o n : U f E E / E - ( l / E - U u E W / U u W ) 2 x ( U u W / U u W W ) + U U E E / U W I n p a r t i c u l a r , i n t h i s m o d e l , a s u f f i c i e n t ( b u t n o t n e c e s s a r y ) c o n d i t i o n f o r c o n c a v i t y o f the b a r g a i n i n g s e t i s t h a t the c o n t r a c t c u r v e be p o s i t i v e l y s l o p e d . F o r t h e l a b o u r demand mode l , the f i r s t d e r i v a t i v e o f the b a r g a i n i n g f r o n t i e r i s the s l o p e o f the l a b o u r demand c u r v e w h i c h i s n e g a t i v e . C o n c a v i t y o f the l a b o u r demand c u r v e would ensure c o n v e x i t y o f the b a r g a i n i n g s e t b u t i n g e n e r a l , the second d e r i v a t i v e o f the f r o n t i e r w i l l have the s i g n o f the f o l l o w i n g e x p r e s s i o n : UUWW x ( U f E E ) 2 + U U E E + UUWE x U f E E - U u W X U f E E / E + ( 1 / E + U f E E / U f E E ) X U u E / ( E X U f E E ) . 71 c u r v e . In o t h e r words , the b a r g a i n i n g s e t i n the space o f u t i l i t i e s f o r t h e l a b o u r demand model i s a subse t o f the b a r g a i n i n g s e t f o r t h e c o o p e r a t i v e m o d e l . ( T h e two f r o n t i e r s a r e i d e n t i c a l i f and o n l y i f the u n i o n does not c a r e about employment.) I t may seem as i f the l a b o u r demand model i s n e s t e d i n the c o o p e r a t i v e mode l . However, t h i s i s n o t the c a s e . The s e t o f p o s s i b l e s o l u t i o n s t o (4) i s the f r o n t i e r o f t h e c o o p e r a t i v e model b a r g a i n i n g s e t . These s o l u t i o n s do not i n c l u d e (as a subse t ) the s e t o f s o l u t i o n s t o (5) which i s composed o f the p o i n t s a l o n g the f r o n t i e r o f t h e l a b o u r demand b a r g a i n i n g s e t . In o t h e r words , t h e r e are n o p a r a m e t e r r e s t r i c t i o n s w h i c h , i f i m p o s e d o n t h e c o o p e r a t i v e m o d e l , w i l l y i e l d s o l u t i o n s i n s i d e t h e c o o p e r a t i v e b a r g a i n i n g s e t s u c h as t h e s o l u t i o n s to the l a b o u r demand m o d e l . 2 1 T h e s y s t e m o f e s t i m a t i n g e q u a t i o n s f o r b o t h t h e c o o p e r a t i v e and the l a b o u r demand models are g i v e n under the a s s u m p t i o n o f e x o g e n o u s o u t p u t i n T a b l e I and under the as sumpt ion o f exogenous c a p i t a l i n T a b l e I I . The (b' s a r e e r r o r t e r m s and y has been s u b s t i t u t e d f o r the e x p r e s s i o n 2 1 T h e r e a r e two e x c e p t i o n s to t h i s c o r r e s p o n d i n g to the two t r i v i a l models i n which the u n i o n does no t c a r e a b o u t employment and the f i r m s have complete b a r g a i n i n g power. In t h e l a t t e r c a s e , t h e c o m p e t i t i v e s o l u t i o n h o l d s i n t h e l a b o u r m a r k e t . 72 T a b l e I E s t i m a t i o n Models Under t h e A s s u m p t i o n o f an Exogenous Output P r o f i t F u n c t i o n I U t i l i t y F u n c t i o n s (at the b e g i n n i n g o f n e g o t i a t i o n s ) U n i o n : V V V = ( 5 E t P + ( 1 - 5 ) ( V W A t ) _ P F i r m s : t t = ~~1?15 ~ t 2 t P 3 t Q l t E t "  1 " 1 5 V t I I C o o p e r a t i v e Mode l c B _ P l t Q l t B l F ( B e - l ) B 2 p ( l - B 3 ) B 3 * l t " W t " 1 . 1 5 E . + B T t E t Q l t P 2 t E 3 t W -W p + 1 . l n d u . t A t „ . l n d u . „ . * 3 t " Q 2 t " d " 8 3 ) ^ E t P 2 t P 3 t Q l t <h c B - o r B ^ B T B 1 F B e P ( 1 - B 3 ) P ( B 3 _ 1 ) 0 B 2 * 4 t " Q 3 t ' t E t P 2 t P 3 t Q l t 73 T a b l e I - C o n t i n u e d I I I . L a b o u r Demand Model P O W - W mB „ l t ^ l t , 1 t A t _ , l n d u . , „ „ . •it " W t " -T7Urt 1 + ( B . - l ) W T Y 1 " E t + (in7f \ ( w t - w A t ) E . B l ( B e - 1 ) ( 1 - B 3 ) B 3 B 2 . r_L . ,lndiK , / W t V ] + B T t E t P 2 t P 3 t Q l t + l B e + ( l n d f } t ] y ( E . m B t t / t , . T , „ , B l T , ( B e - l ) r t B 2 T , ( l - B 3 ) T , B 3 • 2 t = W t + ( B e ) B T t E t P 3 f c , roB _ T , _ . T , m B l T , B e T , P 3 „ B 2 T > - B 3 * 3 t - Q 2 t " ^-*Wt E t P 3 t Q l t P 2 t * 4 t " Q 3 t " ( B 3 ) B T t E t P 2 t P 3 t Q l t w h e r e (r 1^),. = ( F O + F I x Z + F 2 x I N 7 4 + F 3 x C U + UO x U N l n d f t t t t t + U l x U I C f c + U 2 x D E M t ) 2 a n d k B <t>. = e r r o r t e r m f o r e q u a t i o n j , o b s e r v a t i o n t , m o d e l k B ; J t j = l , . . . , 4 ; t = l , . . . , 8 4 ; k = c o o p e r a t i v e ( c ) o r l a b o u r d e m a n d ( m ) ; B = e x o g e n o u s o u t p u t p r o f i t f u n c t i o n . I V . P r e d i c t e d S i g n s ( f o r b o t h m o d e l s ) : B > 0 6 . n FO ? UO > 0 BL. ? Y 1 - 6 F I < 0 U l < 0 B2 > 0 > . F2 > 0 U2 < 0 B3 > 0 — F3 ? Be < 0 74 T a b l e I I E s t i m a t i o n Models Under t h e Assumpt ion o f an Exogenous C a p i t a l P r o f i t F u n c t i o n I U t i l i t y F u n c t i o n s (at the b e g i n n i n g o f n e g o t i a t i o n s ) U n i o n : V V V = ( 6 E t P + ( 1 - 6 ) ( V W A t ) _ P ) ^ T T R / t I ^ v R l R2 (1 —R2) . R 3 Re P 3 t Q 3 t , . F x r m s : U £ ( W T > E T ) = R T ^ P ^ - -j-^ - 1 . 1 5 I I C o o p e r a t i v e Model <t>cR - W - R T R 1 P R 2 ( 1 - R 2 ) R3 ( R e - 1 ) P 3 t Q 3 t • i t " W t R T t P 2 t P l t Q 3 t E t + 1 . 1 5 E t W -W p + 1 , l n d u s t A t - l n d u . . . . „ . , c R _ „ „ . T , m R l T , R e „ R 2 „ - R 2 „ R 3 * 4 t = Q l t ' ( 1 ~ R 2 ) t E t P 2 t P l t Q 3 t 75 T a b l e I I - C o n t i n u e d I I I . L a b o u r Demand Model p o / w -w \ p + 1 .mR 3 t w 3 t . ^ 1 / t At^ _ / l n d u , , „ , • i t •  wt+ -rm; 1 + ( R e - n v t y ( l t I Et+ (Wt ( V w A t ) , w -w \ p + 1 B R l „ R 2 n ( l - R 2 ) - R 3 „ ( R e - l ) , 1 . l n d u , . / t A t - R T t R 2 t p i t Q 3 t E t + + y E t E . .mR T I / T , , I , I „ R l T , ( R e - l ) T , R 2 T , ( l - R 2 ) „ R 3 • 2 T - W T - ( R e ) R T t E ; ^ P 2 t P j t ^ Q 3 t 6 ^ - 0 + r R 2 ^ R T R 1 E R e P ( R 2 _ 1 ) P ( 1 - R 2 ) 0 B 3 • 3 t " Q 2 t + t E t P 2 t P l t Q 3 t « / i T,ON 1 - . m R l T 7 R e 1 - . R 2 _ ~ R 2 r t B 3 • 4 t = Q l t " ( 1 " R 2 ) t E t P 2 t P l t Q 3 t w h e r e ( 7 ^ 7 ) , . = (FO + F l x Z + F 2 x I N V + F 3 x C U + UO x U N l n d r t t t t t + U l x U I C t + U2 x D E M t ) 2 a n d k R <|>. = e r r o r t e r m f o r e q u a t i o n j , o b s e r v a t i o n t , m o d e l k R ; J j = l , . . . , 4 ; t = l , . . . , 8 4 ; k = c o o p e r a t i v e ( c ) o r l a b o u r d e m a n d ( m ) ; R = e x o g e n o u s c a p i t a l p r o f i t f u n c t i o n . I V . P r e d i c t e d S i g n s ( f o r b o t h m o d e l s ) : R > 0 S . n FO ? UO > 0 R l ? Y 1 - 5 F 1 < 0 U 1 < 0 R2 < 0 > F2 > 0 U2 < 0 R3 > 0 P " F3 ? Re > 0 76 5 / ( 1 - 6 ) . U n l e s s e x p l i c i t l y s t a t e d o t h e r w i s e , the f o l l o w i n g d e s c r i p t i o n a p p l i e s t o both p r o f i t f u n c t i o n s ( i . e . f o r i=R and B ) . F o r the c o o p e r a t i v e models , the f i r s t two e q u a t i o n s <J>̂ £ and (j>2^ a r e d e r i v e d from the f i r s t o r d e r e q u a t i o n s to (4) and r e p r e s e n t t h e n e g o t i a t e d wage a n d e m p l o y m e n t e q u a t i o n s . F o r the l a b o u r demand mode l s , the f i r s t e q u a t i o n i s the f i r s t o r d e r c o n d i t i o n to ( 5 ) , and the second e q u a t i o n i s the c o n s t r a i n t , i . e . the l a b o u r demand e q u a t i o n . In both the c o o p e r a t i v e and t h e l a b o u r demand m o d e l s , two e x t r a e q u a t i o n s a p p e a r . F o r the exogenous o u t p u t p r o f i t f u n c t i o n , they r e p r e s e n t the i n p u t demand f u n c t i o n s f o r m a t e r i a l s and cB mB cB s u p p l i e s (<i>2t a n ^ ^ 3 t ^ a n ( ^ ^ o r c a P i t a l s e r v i c e s (<J>4|. and mB 4>4̂ .) d e r i v e d from the r e s t r i c t e d p r o f i t f u n c t i o n T T B ( T , , Q l , P 2 , P 3 , E ) . F o r the exogenous c a p i t a l p r o f i t f u n c t i o n , they r e p r e s e n t the i n p u t demand f o r m a t e r i a l s and s u p p l i e s (<t>3R and 4)^) and the output s u p p l y f u n c t i o n (<1>JR and <t>mR) d e r i v e d f r o m t h e r e s t r i c t e d p r o f i t f u n c t i o n T T R ( T , P]_, P 2 , P 3 , Q 3 , E ) . I t i s assumed t h a t the endogenous i n p u t s and o u t p u t w i l l a d j u s t t o the n e g o t i a t e d l e v e l o f employment as w e l l as p r i c e s and the exogenous i n p u t o r output q u a n t i t i e s . I t i s i m p o r t a n t t o n o t e t h a t e v e n w i t h t h e s i m p l e f u n c t i o n a l forms adopted h e r e , i t i s no t p o s s i b l e t o s o l v e t h e f i r s t o r d e r c o n d i t i o n s t o t h e c o o p e r a t i v e m o d e l s i n o r d e r t o get reduced forms f o r W and E . We are f o r c e d to e s t i m a t e s t r u c t u r a l e q u a t i o n s . 2 2 The q u e s t i o n then a r i s e s as t o the p a r t i c u l a r r e p r e s e n t a t i o n s o f t h e f i r s t o r d e r c o n d i t i o n s w h i c h s h o u l d be u s e d f o r e s t i m a t i o n . Two c o n s i d e r a t i o n s are i m p o r t a n t : the degree o f n o n l i n e a r i t y i n t h e e q u a t i o n s , a n d t h e i n t u i t i v e e x p l a n a t i o n f o r t h e c i l o c a t i o n o f the e r r o r t e r m . <J>2̂ . i s an e r r o r which i s made on the l o c a t i o n o f the b a r g a i n i n g f r o n t i e r s . F o r b o t h i = R and B , the r i g h t hand s i d e (RHS) o f t h i s e q u a t i o n w i l l e q u a l z e r o f o r wage -employment p a i r s l o c a t e d on t h e c o n t r a c t c u r v e . S p e c i f i c a l l y , t h e RHS o f i s t h e d i f f e r e n c e be tween t h e m a r g i n a l r a t e s o f s u b s t i t u t i o n o f t h e two p l a y e r s m u l t i p l i e d by employment. <t>̂  measures the e r r o r made on the l o c a t i o n o f the e q u i l i b r i u m a l o n g the b a r g a i n i n g f r o n t i e r s . F o r b o t h i=R and B , the RHS o f t h i s e q u a t i o n i s s i m p l y the i n v e r s e o f the f i r s t o r d e r c o n d i t i o n t o (4) w i t h r e s p e c t t o W. ^^t' a n ^ ^2t a r e a d d i t i v e e r r o r s made to t h e i n p u t q u a n t i t y d e c i s i o n s i n t h e p r o f i t m a x i m i z a t i o n C R p r o b l e m w h i l e <t>4t i s an a d d i t i v e e r r o r made t o the output q u a n t i t y . F o r purposes o f c o m p a r i s o n , t h e l a b o u r demand model i s g i v e n the same s t r u c t u r e , i . e . f o r b o t h i=R and B , t h e RHS o f <J>m^ i s t h e b a r g a i n i n g f r o n t i e r w h i c h i s t h e l a b o u r demand e q u a t i o n i n t h i s c a s e , and the RHS o f 4>m£ i s d e r i v e d d i r e c t l y from the f i r s t o r d e r c o n d i t i o n t o ( 5 ) . 2 2 T h e problem i s t h a t b o t h the l e v e l s and the g r a d i e n t s o f t h e u t i l i t y f u n c t i o n s a p p e a r i n t h e f i r s t o r d e r c o n d i t i o n s , and t h e r e i s a n e c e s s a r y l i n e a r i t y imposed i n the p r o f i t f u n c t i o n s by the term -WE. 78 I t i s i n t e r e s t i n g t o note the d i f f e r e n c e s between the c o o p e r a t i v e and l a b o u r demand mode l s . As has been mentioned by s e v e r a l a u t h o r s i n the p a s t the d i f f e r e n c e between the two b a r g a i n i n g f r o n t i e r s (between (fc^ and <J>m£) i s s i m p l y the a d d i t i o n i n t h e c o o p e r a t i v e m o d e l c a s e o f a t e r m r e p r e s e n t i n g t h e m a r g i n a l r a t e o f s u b s t i t u t i o n o f t h e u n i o n . 2 3 W i t h R u b i n s t e i n b a r g a i n i n g , the d i f f e r e n c e i n the two f i r s t e q u a t i o n s <J>̂  and <J>m£ i s a l s o the a d d i t i o n o f a t e r m , t h i s t i m e t o t h e l a b o u r demand m o d e l . T h i s t e r m e q u a l s 3 l n U u x 3E(W) . 9E aw When c h o o s i n g the o p t i m a l wage t h r o u g h n e g o t i a t i o n s i n the l a b o u r demand mode l , the p l a y e r s w i l l t a k e i n t o account the i n d i r e c t e f f e c t o f the wage on the u n i o n u t i l i t y t h r o u g h i t s e f f e c t on the employment l e v e l . 4 .2 The Data T a b l e I I I p r e s e n t s a l i s t o f the v a r i a b l e s used i n the e s t i m a t i o n a l o n g w i t h d e s c r i p t i v e s t a t i s t i c s . The f o l l o w i n g d i s c u s s i o n w i l l i n c l u d e o n l y b r i e f d e s c r i p t i o n s o f d a t a s o u r c e s and c o n s t r u c t i o n as d e t a i l s a r e g i v e n i n the form o f a d a t a a p p e n d i x , Appendix A . 2 3 T h i s was used i n McCurdy and P e n c a v e l (1986) t o t e s t which o f the two models performed b e t t e r . 79 T a b l e I I I D e s c r i p t i v e S t a t i s t i c s o f V a r i a b l e s D e s c r i p t i o n Var. 1. Real compensation paid W per hour of employment 2. Hours of employment E ( i n 10 M's) 3. Quanti ty of output Qj (shipments) ( i n lOM's) 4. Quanti ty of mater ia l s Q2 and suppl ies ( i n lOM's) 5. Quanti ty of c a p i t a l Q3 serv ices ( i n lOM's) 6. Real p r i c e of output index P^ 7. Real p r i c e of mater ia l s and P2 suppl ies index 8. Real p r i c e of c a p i t a l P3 serv ices index 9. Real a l t e r n a t i v e wage i n B . C . (Employment weighted average of the manufactur- ing and serv ice i n d u s t r i e s i n B . C . ) 10. Rate of i n t e r e s t (McLeod, Z Young, Weir 10 i n d u s t r i a l bond rate) 11. Avg. change in the value INV of inventor ies over the previous 5 years ( i n 0,000's of d o l l a r s ) 12. U t i l i z a t i o n rate in the wood CU products industry in Canada 13. Unemployment rate i n B . C . UN 14. Measure of the generos i ty UIC of the unemployment insurance 15. Propor t ion of t o t a l females DEM and males under 25 i n t o t a l labour force i n B . C . Mean Min. Max. Standard Deviation 4.5209 2.7233 5.9169 0.95098 2.3132 0.8324 3.7705 0.72052 38.4844 15.1218 96.0790 17.6237 23.8612 6.6975 63.7650 11.8151 2.4203 0.6656 8.0661 1.7983 1.2085 0.7626 2.4285 0.3574 1.1305 0.4909 2.4053 0.3750 0.9255 0.3545 1.6422 0.2630 3.4165 2.4554 3.9879 0.4748 9.5876 5.3700 16.3201 2.9958 0.7925 -1.5592 8.1721 1.6409 9.0158 7.0150 9.8150 0.7308 0.07285 0.04198 0.13823 0.0228 0.3964 0.1203 0.6676 0.2258 0.4929 0.4169 0.5415 0.0395 80 4 . 2 . 1 The I n s t i t u t i o n a l S e t t i n g The d a t a i n v o l v e s t h e I n t e r n a t i o n a l Woodworkers o f A m e r i c a and the wood p r o d u c t s i n d u s t r y i n B r i t i s h Columbia o v e r t h e p e r i o d 1963-1983. The wood p r o d u c t s i n d u s t r y i s p a r t o f the dominant i n d u s t r i a l s e c t o r i n B . C . , the f o r e s t r y s e c t o r . The m a n u f a c t u r i n g i n d u s t r i e s o f the f o r e s t r y s e c t o r (wood p r o d u c t s and paper and a l l i e d i n d u s t r i e s ) account f o r a l m o s t o n e - h a l f o f t o t a l m a n u f a c t u r i n g a c t i v i t y i n t h e p r o v i n c e . The wood p r o d u c t s i n d u s t r y i s c o m p o s e d o f s a w m i l l s , s h i n g l e and s h a k e m i l l s and plywood and veneer m i l l s . The B . C . m i l l s are r e s p o n s i b l e f o r a l a r g e p a r t o f the t o t a l C a n a d i a n output as they produce about two t h i r d s o f C a n a d a ' s s o f t w o o d l u m b e r , v i r t u a l l y a l l o f t h e c e d a r s h i n g l e s and shakes , and the b u l k o f the n a t i o n a l softwood plywood o u t p u t . The wood p r o d u c t s i n d u s t r y i s more c o n c e n t r a t e d i n B . C . t h a n e l s e w h e r e i n C a n a d a . Mos t o f t h e t o p 15 l u m b e r p r o d u c e r s i n Canada are based i n B . C . (See I n d u s t r y , T r a d e , and Commerce ( 1 9 7 8 ) , p g . 3 2 . ) F u r t h e r m o r e , t h e l e v e l o f c o n c e n t r a t i o n i n B . C . i s i n c r e a s i n g . In the p a s t 20 y e a r s , the t r e n d has been toward the c o n s t r u c t i o n o f l a r g e r , more c e n t r a l i z e d m i l l s , e s p e c i a l l y i n the B . C . i n t e r i o r where most o f t h e r a p i d g r o w t h o f t h e 1 9 6 0 ' s and 1 9 7 0 ' s t o o k p l a c e . M a j o r f a c t o r s r e s p o n s i b l e f o r t h i s t r e n d i n c l u d e t e c h n o l o g i c a l change and a movement t o w a r d more c a p i t a l - i n t e n s i v e o p e r a t i o n s . B . C . i n t e r i o r s a w m i l l s and plywood 81 m i l l s w h i c h a r e b e l i e v e d t o be v e r y e f f i c i e n t by w o r l d s t a n d a r d s , have adopted new t e c h n o l o g i e s b e t t e r c a p a b l e o f p r o c e s s i n g s m a l l d i m e ns i on l o g s . A l s o , they have i n c r e a s e d p r o d u c t i v i t y t h r o u g h l a r g e r a u t o m a t i o n ( thereby r e d u c i n g l a b o u r c o n t e n t ) , i n s t a l l a t i o n o f f a c i l i t i e s f o r the r e c o v e r y o f b y - p r o d u c t s and ah i n c r e a s e i n the q u a l i t y c o n t r o l . New e n v i r o n m e n t a l s t a n d a r d s have i n c r e a s e d the c a p i t a l c o n t e n t o f the p r o d u c t i o n p r o c e s s as w e l l . The B . C . lumber i n d u s t r y i s h i g h l y e x p o r t o r i e n t e d . B . C . s a w m i l l s e x p o r t a l m o s t 80% o f t h e i r o u t p u t . The l a r g e s t s i n g l e market f o r B . C . lumber i s the U n i t e d S t a t e s due to p r o x i m i t y and ease o f m a r k e t s . Lumber g r a d e s , s i z e s and g r a d i n g p r o c e d u r e s h a v e been s t a n d a r d i z e d t h r o u g h o u t N o r t h A m e r i c a , customs documentat ion i s m i n i m a l , and over the sample p e r i o d , t h e r e was v i r t u a l l y u n r e s t r i c t e d f r e e t r a d e o f lumber between Canada and the U . S . The p r o v i n c e ' s s h a r e o f t o t a l U . S . consumption o f softwood lumber was 20.4% i n 1978. (See Percy (1986) , p g . 5 . ) The p r o v i n c e ' s lumber i n d u s t r y i s c o n s e q u e n t l y v e r y dependent on U . S . demand and U . S . domes t i c o u t p u t , on exchange r a t e s and t r a d e b a r r i e r s , and on the t r a n s p o r t a t i o n c o s t s t o t h e U . S . o f t h e h i g h b u l k , low v a l u e commodity. W h i l e s a w m i l l s s e l l most o f t h e i r p r o d u c t i n h i g h l y c o m p e t i t i v e i n t e r n a t i o n a l m a r k e t s , p l y w o o d m i l l s i n B . C . s e l l c l o s e t o 80% o f t h e i r output i n s i d e Canada . T h i s i s due t o the f a c t t h a t many o f Canada' s major t r a d i n g p a r t n e r s 82 i n f o r e s t p r o d u c t s p r o v i d e v a r y i n g degrees o f p r o t e c t i o n f o r t h e i r d o m e s t i c p l y w o o d p r o d u c e r s t h r o u g h t a r i f f s . F o r example , i n the l a t e 7 0 ' s , the U . S . t a r i f f on p lywood was about 20%. In f a c t , the U . S . emerged as a major c o m p e t i t o r i n the C a n a d i a n softwood plywood market i n the 1970's w i t h U . S . impor t s r e p r e s e n t i n g a lmost 23% o f domest i c consumption i n 1975 . I m p o r t s have somewhat d e c l i n e d s i n c e t h e n ; however, i t i s b e l i e y e d t h a t the U n i t e d S t a t e s w i l l c o n t i n u e t o be a c o m p e t i t i v e f a c t o r i n the d o m e s t i c m a r k e t . (See I n d u s t r y , T r a d e , and Commerce (1978) , p g . 40 . ) The major i n p u t market o f the wood p r o d u c t s i n d u s t r y , t h a t o f l o g s , i s l a r g e l y a f f e c t e d by government p o l i c y . D i r e c t government i n t e r v e n t i o n takes the form o f p r o v i n c i a l r e s t r i c t i o n s o n t h e e x p o r t o f u n p r o c e s s e d l o g s w h i c h c o n s t r a i n the f o r e s t r y i n d u s t r y to p r o v i d e wood i n p u t s f o r the wood p r o d u c t s and paper and a l l i e d p r o d u c t s i n d u s t r i e s . F o r e x a m p l e , an a v e r a g e o f 0.9% p e r y e a r o f t h e t o t a l p r o v i n c i a l t i m b e r h a r v e s t was e x p o r t e d as l o g s between 1972 and 1979 (see P e r c y ( 1 9 8 6 ) , p g . 4 ) . I n d i r e c t g o v e r n m e n t i n t e r v e n t i o n takes the form o f stumpage fees and tax r a t e s . In p a r t i c u l a r , e f f e c t i v e tax r a t e s are h i g h e r i n the l o g g i n g s e c t o r t h a n f o r m a n u f a c t u r i n g i n d u s t r i e s and the stumpage f ee i s c a l c u l a t e d as a f u n c t i o n o f the p r i c e o f l o g s . Both these p o l i c i e s g i v e i n c e n t i v e s to the v e r t i c a l l y i n t e g r a t e d f i r m s t o p a s s on t i m b e r r e n t s t o t h e i r wood p r o d u c t s o p e r a t i o n s i n the form o f a low p r i c e f o r l o g s . 83 T h a t t h e r e a r e r e n t s i n t h e f o r e s t r y i n d u s t r y n o t c a p t u r e d by government has been argued by s e v e r a l o b s e r v e r s i n c l u d i n g C o p i t h o r n e (1979) , Ha ley (1980) , and P e r c y (1986) . H a l e y (1980) compares B . C . stumpage fees w i t h those s e t i n the P a c i f i c Northwest and f i n d s the U . S . f ees much l a r g e r . U n t i l r e c e n t changes , U . S . stumpage fees were s e t by w i n n i n g b i d , and they were not a l l owed t o v a r y w i t h changes i n end- p r o d u c t p r i c e s o c c u r r i n g d u r i n g the c o n t r a c t . U . S . softwood lumber p r o d u c e r s have a l s o argued t h a t lower stumpage r a t e s i n B . C . c o n s t i t u t e an i m p l i c i t s u b s i d y f o r C a n a d i a n p r o d u c e r s . C o p i t h o r n e ( 1 9 7 9 ) a r g u e s t h a t h i g h e r wages i n s a w m i l l i n g and l o g g i n g i n B . C . r e l a t i v e t o c o r r e s p o n d i n g i n d u s t r i e s i n O n t a r i o i s i n d i c a t i v e o f a l e a k a g e o f r e n t s i n t o wage l e v e l s . He acknowledges however, t h a t t h e r e c o u l d be o t h e r e x p l a n a t i o n s f o r h i g h e r wages; f o r example, more i n s t a b i l i t y i n e m p l o y m e n t , a n d h i g h e r e f f i c i e n c y . 2 4 E v i d e n c e o f l a r g e r than average wages i n the B . C . f o r e s t r y s e c t o r i s a l s o p r o v i d e d i n A l l e n ( 1 9 8 5 ) . P e r c y (1986) e s t i m a t e s t h a t i n 1979, 58.8% o f t o t a l r e n t s a v a i l a b l e i n t h e f o r e s t r y s e c t o r ( i n c l u d i n g l o g g i n g , wood p r o d u c t s and paper and a l l i e d i n d u s t r i e s ) were no t c a p t u r e d by the B . C . government. 2 4 T h e h y p o t h e s i s o f h i g h e r e f f i c i e n c y i s suppor ted by r e s u l t s o f a s tudy o f r e g i o n a l p r o d u c t i v i t y done by Denny e t a l . (1981) . 84 E x p e c t e d f u t u r e g r o w t h p r o s p e c t s f o r t h e B . C . wood p r o d u c t s i n d u s t r y are b l e a k . There have been c o n c e r n s i n r e c e n t y e a r s t h a t t h e vo lume o f t i m b e r h a r v e s t e d i n the p r o v i n c e may d e c l i n e s i g n i f i c a n t l y i n t h e f u t u r e due t o l o w e r t i m b e r v o l u m e s f r o m s e c o n d - g r o w t h s t a n d s and from s i g n i f i c a n t r e d u c t i o n s i n t h e f o r e s t b a s e f o r n o n - t i m b e r u s e . T h i s would cause a c o r r e s p o n d i n g c o n t r a c t i o n o f the wood p r o d u c t s i n d u s t r y . Expec ted i n c r e a s e d c o m p e t i t i o n from t r a d i t i o n a l markets and U . S . r e s t r i c t i o n s on lumber impor t s w i l l a d v e r s e l y a f f e c t output m a r k e t s . F o r c o a s t a l plywood m i l l s , t h e p r o s p e c t s are worse . I t i s b e l i e v e d t h a t the v i a b i l i t y o f the g e n e r a l l y h i g h - c o s t c o a s t a l m i l l s depends l a r g e l y on a m o d e r n i z a t i o n program u n d e r t a k e n i n the l a t e 1970's (see i n d u s t r y , T r a d e , and Commerce (1978) , p g . 4 3 ) . The i n s t i t u t i o n a l s e t t i n g d e s c r i b e d above has s e v e r a l i m p l i c a t i o n s f o r the m o d e l l i n g o f the i n d u s t r y . F i r s t , the d i s t i n c t i o n b e t w e e n i n t e r i o r and c o a s t a l s a w m i l l s i s i m p o r t a n t and i f more d a t a were a v a i l a b l e , i t w o u l d be p r e f e r a b l e t o d i s t i n g u i s h be tween i n t e r i o r and c o a s t a l p l y w o o d m i l l s as w e l l . S e c o n d l y , t h e a s s u m p t i o n o f an e x o g e n o u s o u t p u t p r i c e i s n o t u n r e a s o n a b l e g i v e n t h a t , e x c e p t f o r p l y w o o d m i l l s , t h e f i r m s s e l l most o f t h e i r o u t p u t i n h i g h l y c o m p e t i t i v e i n t e r n a t i o n a l m a r k e t s . There a r e a l s o i n d i c a t i o n s t h a t p l y w o o d m i l l s f a c e s t i f f c o m p e t i t i o n i n t h e i r output m a r k e t s . These a r e : an i n c r e a s e i n plywood impor t s from the U n i t e d S t a t e s , and the e x t e n s i v e 85 m o d e r n i z a t i o n program u n d e r t a k e n i n the l a t e 1970's which i s b e l i e v e d t o be c r u c i a l f o r t h e v i a b i l i t y o f the c o a s t a l plywood m i l l s . T h i r d l y , t h e r e i s e v i d e n c e t h a t a s u b s t a n t i a l p o r t i o n o f t h e t i m b e r r e n t s a r e n o t c a p t u r e d by g o v e r n m e n t . M o r e o v e r , f i r m s have i n c e n t i v e s to pass on these r e n t s to t h e i r wood p r o d u c t s o p e r a t i o n s i n the form o f low m a t e r i a l s p r i c e s . T h i s i m p l i e s t h a t the p r i c e o f m a t e r i a l s i s not d e t e r m i n e d t h r o u g h c o m p e t i t i o n . N e v e r t h e l e s s , t h e a s s u m p t i o n o f an exogenous ly de termined p r i c e o f m a t e r i a l s i s m a i n t a i n e d i n t h i s s tudy i n o r d e r to a v o i d m o d e l l i n g the whole f o r e s t r y s e c t o r i n B . C . I now t u r n t o the c o l l e c t i v e b a r g a i n i n g s e t t i n g . I t i s c l a i m e d by the I n t e r n a t i o n a l Woodworkers o f A m e r i c a (IWA) t h a t 95-99% o f the output i n the B . C . wood p r o d u c t s i n d u s t r y i s produced by IWA members (see M a r t i n e l l o (1984) , p g . 2 3 ) . The IWA i s a l a r g e , w e l l o r g a n i z e d u n i o n which has succeeded i n k e e p i n g the wood p r o d u c t s i n d u s t r y v i r t u a l l y c o m p l e t e l y u n i o n i z e d o v e r t h e p e r i o d u n d e r s t u d y . B a r g a i n i n g i s p r o v i n c i a l l y c e n t r a l i z e d . A c c o r d i n g t o M a r t i n e l l o ( 1 9 8 4 ) , p . 23 : " U n i o n r e p r e s e n t a t i v e s from IWA R e g i o n a l C o u n c i l #1 n e g o t i a t e a c o a s t master c o n t r a c t , c o v e r i n g a l l w o r k e r s e m p l o y e d i n t h e c o a s t r e g i o n , w i t h the e m p l o y e r ' s a s s o c i a t i o n known as F o r e s t I n d u s t r i a l R e l a t i o n s ( F I R ) . The c o a s t master i s then used as a b a s i s f o r master agreements between IWA r e g i o n a l c o u n c i l s and employer a s s o c i a t i o n s i n the n o r t h e r n i n t e r i o r and s o u t h e r n i n t e r i o r r e g i o n s . A l l o f 86 t h e c o l l e c t i v e a g r e e m e n t s c o n t a i n u n i o n s h o p p r o v i s i o n s . " C e n t r a l i z e d b a r g a i n i n g c a n be t o t h e a d v a n t a g e o f e i t h e r the u n i o n or the f i r m s . A g e n e r a l work s toppage w i l l be i n d u s t r y - w i d e and w i l l impose l a r g e s t r i k e c o s t s on a l l f i r m s . On t h e o t h e r h a n d , t h e f a c t t h a t a l l f i r m s a r e e x p e r i e n c i n g the work s toppage i m p l i e s t h a t each i n d i v i d u a l f i r m i s m a i n t a i n i n g i t s market share r e l a t i v e t o the o t h e r f i r m s i n t h e i n d u s t r y . I n d i v i d u a l s t r i k e d a t a f o r t h e i n d u s t r y shows t h a t the IWA has engaged i n b o t h i n d u s t r y - wide s t r i k e s and work s toppages a f f e c t i n g a s m a l l number o f f i r m s . D u r i n g the sample p e r i o d , most o f the c o n t r a c t s were 2 y e a r s i n l e n g t h , t h e r e m a i n i n g ones b e i n g e i t h e r 1 o r 3 y e a r s l o n g . The t i m i n g o f c o n t r a c t s i s an i m p o r t a n t i s s u e which i s no t addressed i n t h i s s tudy but which i s l e f t f o r f u t u r e r e s e a r c h . 4 . 2 . 2 I n d u s t r y P r i c e and Q u a n t i t y Data The raw d a t a on i n p u t and output q u a n t i t y and p r i c e s was c u m u l a t e d and a n a l y z e d by M a r t i n e l l o (1984) . I a l s o adopted some o f h i s methodology i n the t rea tment o f the raw d a t a . The major d i f f e r e n c e s between the d a t a s e t used here and t h a t i n M a r t i n e l l o ' s work a r e : i n t h i s s t u d y , the n o n - p r o d u c t i o n workers are taken i n t o account i n the c a l c u l a t i o n o f f i r m s ' p r o f i t s ; the c a p i t a l s e r v i c e s i n p u t q u a n t i t y and 87 p r i c e a r e generated by a d i f f e r e n t p r o c e d u r e and are based on more d e t a i l e d d a t a (which was not a v a i l a b l e a t the t ime o f M a r t i n e l l o ' s s t u d y ) ; t h e a r b i t r a r y i n p u t c o s t s h a r e s c h o s e n by M a r t i n e l l o a r e n o t a d o p t e d h e r e ( t h e n a t u r a l s h a r e s g i v e n by the d a t a are u s e d ) ; f i n a l l y , I e x t e n d t h e s a m p l e p e r i o d t o i n c l u d e 1980-1983. The d a t a c o n s i s t s o f a n n u a l o b s e r v a t i o n s on wages, employment, o t h e r i n p u t s and o u t p u t i n t h e wood p r o d u c t s i n d u s t r y i n B r i t i s h C o l u m b i a . The f i r m s i n the i n d u s t r y a r e d i v i d e d i n t o 4 g r o u p s : t h e c o a s t a l s a w m i l l s , t h e i n t e r i o r s a w m i l l s , the s h i n g l e and shake m i l l s and t h e p l y w o o d and v e n e e r m i l l s . The d a t a c o v e r 21 y e a r s 1963-1983 f o r a t o t a l o f 84 o b s e r v a t i o n s . T h e r e a r e s e v e r a l r e a s o n s why t h e IWA i s a g o o d c a n d i d a t e f o r t h e p r e s e n t s t u d y . As m e n t i o n e d i n t h e p r e v i o u s s e c t i o n , e v i d e n c e shows t h a t the n a t u r a l r e s o u r c e s i n d u s t r y i n B . C . o f f e r s s u b s t a n t i a l r e n t s and t h a t , a t l e a s t i n the wood p r o d u c t s i n d u s t r y , B . C . u n i o n s have succeeded i n c a p t u r i n g some o f these r e n t s . A n o t h e r advantage o f t h i s d a t a l i e s i n the i n p u t and o u t p u t d a t a . The t e c h n o l o g y parameters i n c l u d e d i n the wage and employment b a r g a i n i n g e q u a t i o n s w i l l be c o n s t r a i n e d to be c o n s i s t e n t w i t h t h e i n p u t and o u t p u t q u a n t i t i e s and p r i c e s . F i n a l l y , the m o d e l l i n g o f the b a r g a i n i n g s e t t i n g i s s t r a i g h t - f o r w a r d s i n c e i t i n v o l v e s o n l y 2 a g e n t s ; t h e IWA r e p r e s e n t i n g v i r t u a l l y a l l workers i n the i n d u s t r y , and the 88 F o r e s t I n d u s t r i a l R e l a t i o n s A s s o c i a t i o n r e p r e s e n t i n g a l l f i r m s i n the i n d u s t r y . One o f the drawbacks o f t h i s d a t a stems from the poo led c r o s s - s e c t i o n t i m e - s e r i e s n a t u r e o f the o b s e r v a t i o n s . S i n c e the focus o f t h i s s tudy i s on wage and employment c o n t r a c t s , the m o d e l l i n g o f the p r o d u c t i o n p r o c e s s i s kept s i m p l e and hence r e s t r i c t i v e . S p e c i f i c a l l y , the t e c h n o l o g y parameters are assumed to be c o n s t a n t a c r o s s groups o f f i r m s . The o b s e r v a t i o n s are annua l r a t h e r than p e r c o n t r a c t . The da te s o f s i g n a t u r e o f the c o n t r a c t s a r e a v a i l a b l e so t h a t t h e d a t a c o u l d be c o n v e r t e d t o a c o n t r a c t b a s i s , however, s i n c e c o n t r a c t s were on average 2 y e a r s i n l e n g t h , t h i s w o u l d r e d u c e my sample s i z e by one h a l f . Note t h a t e x p l i c i t m o d e l l i n g o f u n c e r t a i n t y and r i s k s h a r i n g r e q u i r e s c o n t r a c t d a t a r a t h e r than annua l o b s e r v a t i o n s . F o r reasons o f s i m p l i c i t y and d a t a r e q u i r e m e n t s , these i s s u e s a r e n o t e x p l i c i t l y m o d e l l e d i n t h i s r e s e a r c h . H o w e v e r , I do c o n s i d e r them i n t e r e s t i n g a spec t s o f c o l l e c t i v e b a r g a i n i n g and p o s s i b l e e x t e n s i o n s t o the p r e s e n t s t u d y . A n o t h e r d i s a d v a n t a g e o f t h i s d a t a c o n c e r n s t h e wage d a t a . The wage v a r i a b l e i s a c t u a l l y compensat ion per p a i d p e r s o n - h o u r . T h i s i n c l u d e s o v e r t i m e payments , bonuses , p a i d v a c a t i o n s and o t h e r payments f o r work not p e r f o r m e d . To the 89 e x t e n t t h a t these f r i n g e b e n e f i t s i n c r e a s e d over the p e r i o d , t h i s v a r i a b l e w i l l o v e r s t a t e the v a r i a t i o n s i n the w a g e . 2 5 The q u a n t i t y o f l a b o u r i s m e a s u r e d by t h e number o f p e r s o n - h o u r s p a i d . The c h o i c e o f u n i t s f o r the measurement o f l a b o u r i s an i m p o r t a n t i s s u e i n w a g e - e m p l o y m e n t d e t e r m i n a t i o n s t u d i e s . I t c a n be a r g u e d t h a t the u n i o n c a r e s about the number o f workers ( i . e . the number o f u n i o n members) a n d , p o s s i b l y , about the hours o f work per worker as w e l l . The f i r m s w i l l be concerned w i t h the t o t a l number o f hours worked, o r , i f hours and the number o f workers are no t p e r f e c t s u b s t i t u t e s i n the f i r m ' s p r o d u c t i o n p r o c e s s , t h e n the f i r m w i l l c a r e about b o t h the hours per worker and the number o f w o r k e r s . I f the hours per worker a r e f i x e d , t h e n i t makes no d i f f e r e n c e which u n i t i s u s e d ; however, i f t h e h o u r s p e r w o r k e r a r e v a r i a b l e , t h e n t h e c o r r e c t p r o c e d u r e i s t o t r e a t the number o f workers and the hours p e r worker as two s e p a r a t e b a r g a i n i n g v a r i a b l e s . Hours per worker were c a l c u l a t e d over the sample and are p r o v i d e d i n Appendix A . In f a c t , the d i s p e r s i o n around the mean i s not v e r y i m p o r t a n t , and i n o r d e r t o a v o i d t h e c o m p l i c a t i o n s which would a r i s e from add ing a t h i r d b a r g a i n i n g v a r i a b l e , i t i s assumed t h a t , a t l e a s t a t the t ime o f n e g o t i a t i o n , the p a r t i e s i n t e n d to keep hours per worker f i x e d . 2 5 M a r t i n e l l o (1984) c o r r e c t e d the d a t a f o r i n c r e a s e s i n v a c a t i o n s and h o l i d a y s and f o u n d h i s e s t i m a t e s v i r t u a l l y unchanged (see M a r t i n e l l o (1984) , p g . 2 4 ) . 90 Most o f the i n p u t and output v a r i a b l e s were c o n s t r u c t e d u s i n g d a t a from the census o f m a n u f a c t u r i n g . D e t a i l e d d a t a on t h e q u a n t i t i e s and v a l u e s o f i tems i n c l u d e d i n each o f m a t e r i a l s and s u p p l i e s , f u e l s and e l e c t r i c i t y , and shipments were u s e d t o c o n s t r u c t c h a i n e d F i s h e r i d e a l p r i c e i n d i c e s and c o r r e s p o n d i n g i m p l i c i t q u a n t i t y i n d i c e s f o r each o f the i n p u t and o u t p u t g r o u p s . U n f o r t u n a t e l y , d a t a on c a p i t a l s t o c k s i s a v a i l a b l e s e p a r a t e l y o n l y f o r the f o u r t h group o f f i r m s ( v e n e e r and plywood m i l l s ) . The o t h e r 3 groups o f f i r m s ( s a w m i l l s and s h i n g l e and shake m i l l s ) are a g g r e g a t e d . A d i s a g g r e g a t e m e a s u r e o f c a p i t a l s e r v i c e s i s c o n s t r u c t e d u s i n g t h e a g g r e g a t e c a p i t a l s t o c k , t h e d i s a g g r e g a t e d f u e l s a n d e l e c t r i c i t y q u a n t i t y and p r i c e i n d i c e s and a c o n s t r u c t e d u s e r c o s t o f c a p i t a l i n d e x . The p r i c e o f c a p i t a l s e r v i c e s i s i m p l i c i t i n t h e f o r m u l a t i o n and c a n be c a l c u l a t e d d i r e c t l y (see Appendix A f o r d e t a i l s ) . 4 . 2 . 3 The A l t e r n a t i v e Wage The a l t e r n a t i v e wage measure i s based on the expected r e a l h o u r l y e a r n i n g s ( i n c l u d i n g pay f o r t i m e n o t worked) assuming the worker i s faced w i t h the f o l l o w i n g o p t i o n s : i ) t o work i n the s e r v i c e o r m a n u f a c t u r i n g i n d u s t r i e s i n B . C . and t o e a r n the employment weighted average h o u r l y e a r n i n g s i n t h e s e i n d u s t r i e s . T h i s w i l l o c c u r w i t h 91 p r o b a b i l i t y p = (employment i n t h e s e s e c t o r s / t o t a l l a b o u r f o r c e ) i i ) t o c o l l e c t unemployment i n s u r a n c e (UI) e q u a l t o the average h o u r l y UI payment i n B . C . a d j u s t e d by a s c a l i n g f a c t o r which takes i n t o account changes i n the t a x a t i o n o f U I b e n e f i t s . 2 6 T h i s e v e n t w i l l o c c u r w i t h p r o b a b i l i t y (1-p) t imes the p r o b a b i l i t y o f g e t t i n g U I . The l a t t e r i s c a l c u l a t e d as the number o f weeks o f UI p a i d i n B . C . d i v i d e d by the t o t a l number o f weeks o f unemployment i n B . C . T h i s i s a s i m i l a r a l t e r n a t i v e wage measure t o the one c o n s t r u c t e d by M a r t i n e l l o (1984) , the d i f f e r e n c e b e i n g t h a t he used the t o t a l B . C . i n d u s t r i a l compos i te e a r n i n g s f o r the a l t e r n a t i v e r a t h e r t h a n e a r n i n g s i n s e r v i c e s a n d m a n u f a c t u r i n g . The CPI i s used t o c o n v e r t the a l t e r n a t i v e wage t o ( cons tant ) 1971 d o l l a r s . When comparing t h i s r e a l a l t e r n a t i v e wage (WA) t o the u n i o n wage (W) I found t h a t f o r one g r o u p o f f i r m s , t h e i n t e r i o r s a w m i l l s , W A > W i n 1964 and 1965. T h i s v i o l a t e s my d e f i n i t i o n o f W^ as a c o n s t r a i n t on t h e n e g o t i a t e d c o n t r a c t . However, surveys conducted i n the 1960's on wages i n s e v e r a l b l u e c o l l a r o c c u p a t i o n s i n B . C . show t h a t wages i n the i n t e r i o r were below the p r o v i n c i a l average w h i l e the 2 6 T h e r e s u l t i n g UI payment i s a p r e - t a x payment. T h i s i s c o n s i s t e n t w i t h the measures o f a l t e r n a t i v e e a r n i n g s and o f the revenues o f the f i r m . 92 s o u t h e r n c o a s t a l a r e a s o f f e r e d wages f o r t h e s e same o c c u p a t i o n s w h i c h were c o n s i s t e n t l y above t h e a v e r a g e . L a t e r s u r v e y s show v e r y l i t t l e d i f f e r e n c e s i n the r e g i o n a l wages . R e s u l t s o f t h e s e s u r v e y s were u s e d t o c o n s t r u c t i n t e r i o r and c o a s t a l w e i g h t s w h i c h were a p p l i e d t o t h e p r o v i n c i a l W A d e s c r i b e above. The r e s u l t i n g wages were used as a l t e r n a t i v e wages f o r the i n t e r i o r and c o a s t a l s a w m i l l s r e s p e c t i v e l y . These weights r e a c h 1 i n the m i d - 7 0 ' s and are m a i n t a i n e d t h e r e f o r the r e s t o f t h e s a m p l e p e r i o d . The minimum w e i g h t f o r t h e i n t e r i o r i s .91 and t h e maximum weight f o r the c o a s t i s 1 .045. (See the Appendix f o r more d e t a i l s on the r e g i o n a l wages and w e i g h t s . ) 4 . 2 . 4 S t r i k e C o s t s In t h i s s t u d y , t ime c o s t s or the a b i l i t y o f p l a y e r s to w i t h s t a n d a s t r i k e / l o c k o u t measure the b a r g a i n i n g power o f the p l a y e r s and a f f e c t the e q u i l i b r i u m c o n t r a c t even i n the a b s e n c e o f s t r i k e s . I n t h e e m p i r i c a l m o d e l s g i v e n i n T a b l e I and T a b l e I I , the r e l a t i v e s t r i k e c o s t s are measured by the term ( l n d u / l n d f ) . A l a r g e p r o p o r t i o n o f the e m p i r i c a l s t u d i e s on s t r i k e s have f o c u s e d on t h e e s t i m a t i o n o f r e l a t i o n s h i p s be tween d e t e r m i n a n t s o f s t r i k e c o s t s and the f r e q u e n c y or l e n g t h o f s t r i k e s . A l t h o u g h t h e s e s t u d i e s d i d n o t i n c l u d e a b a r g a i n i n g m o d e l a n d h e n c e a m o d e l o f s t r i k e s , t h e r e l a t i o n s h i p was j u s t i f i e d by t h e argument t h a t ( c e t e r i s 93 p a r i b u s ) h i g h e r s t r i k e c o s t s w i l l make b a r g a i n i n g p a r t i e s l e s s w i l l i n g to s t r i k e . Examples o f t h i s type o f work are Kennan (1980) and Reder and Neumann (1980) . U n f o r t u n a t e l y , t h e m o d e l l i n g o f t h e t e c h n o l o g y o f s t r i k e c o s t s has been l i m i t e d t o the ad hoc i d e n t i f i c a t i o n o f v a r i a b l e s b e l i e v e d t o have some i m p a c t and t o t h e p r e d i c t i o n o f the s i g n o f the impac t i n a ( o f t e n l i n e a r ) r e g r e s s i o n e q u a t i o n . I t i s an area where r e s e a r c h c o u l d be v e r y f r u i t f u l . In the absence o f a r i g o r o u s model o f s t r i k e c o s t s , I have adopted the f o l l o w i n g s i m p l e f o r m u l a t i o n : 2 7 (IndT)t = ( F 0 + F 1 x I N T t + F 2 x I N V t + F 3 x c u t + UO x U N t + U l x U I C t + U x DEM t ) 2 where FO i s a c o n s t a n t , and t d e n o t e s t h e o b s e r v a t i o n , t = l , . . . 84. The f i r s t 3 v a r i a b l e s measure v a r i a t i o n s i n the f i r m s ' s t r i k e c o s t s over t i m e . They a r e : 2 7 A l i n e a r form f o r ( l n d u / l n d f ) was a l s o e s t i m a t e d w i t h v e r y l i t t l e d i f f e r e n c e i n the e s t i m a t e s f o r the c o o p e r a t i v e m o d e l s ( e x c e p t f o r t h e s t r i k e c o s t parameters which were c o r r e s p o n d i n g l y l a r g e r ) . F o r t h e m o n o p o l y m o d e l s , t h e l i n e a r form y i e l d e d some v a l u e s f o r ( l n d u / l n d f ) which were n e g a t i v e . F o r c i n g t h e t e r m t o be g r e a t e r t h a n z e r o by s q u a r i n g improved the l i k e l i h o o d o f the monopoly models from the e s t i m a t i o n o f the l i n e a r form c o n s t r a i n e d t o be g r e a t e r t h a n z e r o . A l l m o d e l s were a l s o e s t i m a t e d w i t h an added exogenous v a r i a b l e i n the s p e c i f i c a t i o n o f the s t r i k e c o s t s r e p r e s e n t i n g wage and p r i c e c o n t r o l s . A dummy v a r i a b l e t a k i n g the v a l u e o f 1 i n 1976, 1977, and 1978 was added but had v e r y l i t t l e e f f e c t on the e s t i m a t e s . More d e t a i l i s g i v e n on t h i s i n C h a p t e r 5. 94 INT-t = T h e n o m i n a l r a t e o f i n t e r e s t . F l < 0 i s expected r e f l e c t i n g the f a c t t h a t an i n c r e a s e i n b o r r o w i n g c o s t s o f t h e f i r m w i l l i n c r e a s e r e l a t i v e s t r i k e c o s t s o f the f i r m . INV-t = The change i n the v a l u e o f i n v e n t o r i e s averaged over the l a s t 5 y e a r s . F2 > 0 i s expec ted s i n c e a f i r m b u i l d i n g up i t s i n v e n t o r i e s w i l l be r e d u c i n g i t s s t r i k e c o s t s . The average over the p a s t 5 y e a r s was u s e d t o smooth out the v e r y l a r g e y e a r l y v a r i a t i o n s i n t h i s v a r i a b l e . 2 8 The l a s t 3 v a r i a b l e s measure changes i n the o p p o r t u n i t y c o s t o f l a b o u r t h r o u g h changes i n l a b o u r market c o n d i t i o n s . F o l l o w i n g R i d d e l l and Smith (1982) , t i g h t n e s s o f the l a b o u r m a r k e t i s m e a s u r e d by t h e d i f f e r e n c e b e t w e e n t h e unemployment r a t e (UN) and the n a t u r a l r a t e o f unemployment. The l a t t e r w i l l v a r y a c c o r d i n g to changes i n unemployment i n s u r a n c e (UIC) and changes i n the c o m p o s i t i o n o f the l a b o u r f o r c e ( D E M ) . More p r e c i s e l y , l e t t h e n a t u r a l r a t e o f u n e m p l o y m e n t a t t i m e t e q u a l u + y ^ U I C t + W 2 D E M t « L a b o u r m a r k e t t i g h t n e s s w i l l b e m e a s u r e d b y UN-t - u - y i U l C - t - U 2 D E M t ' I n t h e f o r m u l a t i o n o f ( l n d u / l n d f ) above , UO measures the e f f e c t o f l a b o u r market t i g h t n e s s , UI = UO x U2 = UO x \i2 and the term UO x p i s 2 8 T h e e s t i m a t i o n r e s u l t s d e t e r i o r a t e d s l i g h t l y when the change i n i n v e n t o r i e s over the l a s t year was used i n s t e a d o f the average over the l a s t 5 y e a r s . 95 i n c l u d e d i n the c o n s t a n t F O . The v a r i a b l e s are measured as f o l l o w s : UN-t = The unemployment r a t e i n B . C . UO > 0 i s expected s i n c e t h e t e r m (UN-t - u - y ^ U I C t - p^DEMt) i s i n v e r s e l y r e l a t e d to l a b o u r market t i g h t n e s s and as l a b o u r market t i g h t n e s s f a l l s , the o p p o r t u n i t y c o s t o f l a b o u r a l s o d e c r e a s e s t h e r e b y i n c r e a s i n g the r e l a t i v e s t r i k e c o s t s o f the u n i o n . UlC-t = A m e a s u r e o f t h e g e n e r o s i t y o f the unemployment i n s u r a n c e program. I t i s c o n s t r u c t e d as f o l l o w s : t h e p r o p o r t i o n o f t h e l a b o u r f o r c e c o v e r e d by unemployment i n s u r a n c e i n Canada t imes t h e r a t i o o f unemployment i n s u r a n c e b e n e f i t s to the average wage i n B . C . t imes a s c a l i n g f a c t o r w h i c h t a k e s i n t o a c c o u n t t h e t a x a t i o n o f u n e m p l o y m e n t b e n e f i t s . (The p r o p o r t i o n o f t h e l a b o u r f o r c e c o v e r e d by U l was no t a v a i l a b l e f o r B . C . ) U l < 0 i s expected s i n c e the n a t u r a l r a t e o f unemployment w i l l i n c r e a s e w i t h U l C t ( i . e . U i > 0 ) . DEM-t = The p r o p o r t i o n o f women o f a l l ages and men under 25 y e a r s o f age i n the t o t a l l a b o u r f o r c e i n B . C . A g a i n U2 < 0 i s expected s i n c e the n a t u r a l r a t e o f unemployment and DEM w i l l be p o s i t i v e l y r e l a t e d . Some o f the models were a l s o e s t i m a t e d u s i n g a d d i t i o n a l measures o f borrowing c o s t s such as mortgage r a t e s f o r the 96 workers and demand l o a n r a t e s f o r the f i r m . However , t h e e s t i m a t e s w e r e n o t g r e a t l y a f f e c t e d and t h e y a r e n o t r e p o r t e d h e r e . A l s o , a l l a t tempts a t d i s t i n g u i s h i n g between du and d f f a i l e d . G i v e n t h e l i m i t e d d a t a a v a i l a b l e on s t r i k e c o s t s , i t was i m p o s s i b l e t o e s t i m a t e s e p a r a t e l y the two e lements o f the r a t i o l n d u . l n d f 97 C h a p t e r 5 E s t i m a t i o n R e s u l t s E a c h o f the f o u r systems o f 4 s i m u l t a n e o u s , n o n l i n e a r , s t r u c t u r a l e q u a t i o n s p r e s e n t e d i n T a b l e s I and I I was e s t i m a t e d u s i n g F I M L . No r e s t r i c t i o n s are imposed on t h e v a r i a n c e - c o v a r i a n c e m a t r i x o f the e r r o r s a c r o s s e q u a t i o n s . The contemporaneous e r r o r s a c r o s s the 4 groups o f f i r m s are assumed t o be i . i . d . b u t f i r s t o r d e r a u t o c o r r e l a t i o n i s a l l o w e d . S p e c i f i c a l l y , i f <t>̂ yf i s the e r r o r f o r e q u a t i o n i , model k j , y e a r y , and group o f f i r m s f , t h e n where: ^iyf l i ( y - l ) f l y f l y f i s i . i . d . N ( v k j S 4 x 4 } f o r i = l .4; y = 1 9 6 4 , . . . , 1 9 8 3 ; k = c ( c o o p e r a t i v e ) , m ( l a b o u r demand); j = B (exogenous output p r o f i t f u n c t i o n ) , R (exogenous c a p i t a l p r o f i t f u n c t i o n ) ; f = 1 ( c o a s t a l s a w m i l l s ) , 2 ( i n t e r i o r s a w m i l l s ) , 3 ( s h i n g l e m i l l s ) , 4 (plywood and veneer m i l l s ) . The s e r i a l c o r r e l a t i o n c o e f f i c i e n t r k ^ i s a l l owed to v a r y a c r o s s e q u a t i o n s but not a c r o s s g r o u p s o f f i r m s n o r a c r o s s t ime p e r i o d s . A l t h o u g h no c o n s t a n t term i s p r e d i c t e d by the models (see T a b l e s I and I I ) , c o n s i s t e n t e r r o r s were 98 found and t h e i n t r o d u c t i o n o f c o n s t a n t terms ( v ^ ) improved the e s t i m a t i o n . 2 9 The f o u r g r o u p s o f f i r m s a r e t r e a t e d as i d e n t i c a l except f o r the i n c l u s i o n i n a l l f o u r e s t i m a t i o n models o f a dummy v a r i a b l e w h i c h t a k e s the v a l u e o f one f o r i n t e r i o r s a w m i l l s . At tempts were made t o e s t i m a t e models where the c o n s t a n t term or the s c a l i n g f a c t o r s B and R d i f f e r e d a c r o s s t h e f o u r g r o u p s o f f i r m s . T h e s e m o d e l s p r o v e d v e r y d i f f i c u l t t o e s t i m a t e and no convergence was r e a c h e d . I t seems as though more e x t e n s i v e d a t a s e t s a r e r e q u i r e d on each group o f f i r m s t o model a d e q u a t e l y the d i f f e r e n c e s t h a t might e x i s t i n t h e i r t e c h n o l o g i e s . (Note t h a t t o a l l o w f o r s e p a r a t e c o n s t a n t terms a c r o s s a l l groups o f f i r m s , I have t o add 8 new parameters t o the e s t i m a t i o n which i s d e s c r i b e d h e r e . ) I n t e r i o r s a w m i l l s proved t o be d i f f e r e n t i n terms o f t h e s a m p l e e r r o r means and t h e a d d i t i o n o f a s e p a r a t e c o n s t a n t t e r m s f o r t h e s e f i r m s i m p r o v e d t h e l i k e l i h o o d v a l u e . The r e p o r t e d c o e f f i c i e n t s on t h i s dummy v a r i a b l e s h o u l d be added t o the c o n s t a n t terms t o get the a p p r o p r i a t e c o n s t a n t terms f o r i n t e r i o r s a w m i l l s . 2 9 T o g e n e r a t e the c o n s t a n t terms as p a r t o f the model r e q u i r e s more g e n e r a l s p e c i f i c a t i o n s o f t h e t e c h n o l o g y . H o w e v e r , t h i s w o u l d a l s o r e s u l t i n m o r e c o m p l i c a t e d b a r g a i n i n g e q u a t i o n s . In p a r t i c u l a r , the f i r s t e q u a t i o n s o f the systems g i v e n i n T a b l e s I and I I would be s u b s t a n t i a l l y more complex . T h i s i s l e f t f o r f u t u r e r e s e a r c h . 99 E s t i m a t i o n r e s u l t s under the assumpt ion o f exogenous o u t p u t a r e p r e s e n t e d i n the next s e c t i o n . The r e s u l t s f o r the case o f exogenous c a p i t a l are g i v e n i n s e c t i o n 5 . 2 . 5 .1 Exogenous Output Model T a b l e IV p r e s e n t s e s t i m a t e d c o e f f i c i e n t s f o r the case where o u t p u t i s t r e a t e d as e x o g e n o u s i n t h e b a r g a i n i n g p r o c e s s . F o r c o m p a r i s o n , t h e r e s u l t s f o r b o t h t h e c o o p e r a t i v e (from now on COOP) and the l a b o u r demand (from now on LDEM) b a r g a i n i n g models are g i v e n i n t h i s t a b l e . 3 0 5 . 1 . 1 The F i r m s ' Techno logy F o r b o t h the c o o p e r a t i v e and l a b o u r demand mode l s , the t e c h n o l o g y c o e f f i c i e n t s a r e s i g n i f i c a n t w i t h t h e e x c e p t i o n o f the exponent on the t ime t r e n d B l and the l a b o u r exponent f o r t h e COOP m o d e l . T ime has no s i g n i f i c a n t e f f e c t i n e i t h e r m o d e l on t h e l o c a t i o n o f the p r o d u c t i o n f u n c t i o n . F o r b o t h mode l s , l a b o u r has the expected n e g a t i v e e f f e c t on r e s t r i c t e d c o s t s but t h i s e f f e c t i s more i m p o r t a n t i n the LDEM model and , f o r the COOP mode l , the l a b o u r c o e f f i c i e n t i s no t o n l y v e r y s m a l l , i t i s a l s o i m p r e c i s e . 3 0 F r o m T a b l e XI i n the A p p e n d i x , we can see t h a t the s i z e o f the s h i n g l e and shake m i l l s i n terms o f c o s t s and revenues i s s m a l l e r than the o t h e r t h r e e groups o f f i r m s by a f a c t o r o f the o r d e r o f 10. To s i m p l i f y the e s t i m a t i o n , a l l q u a n t i t y d a t a c o n c e r n i n g s h i n g l e m i l l s was m u l t i p l i e d by 10. The i m p l i c a t i o n s o f t h i s i s t h a t the e s t i m a t e d B , R , and y s h o u l d be m u l t i p l i e d by i n B 2 + B e - l # 1 0 R 2 + R e _ 1 , and 10~P r e s p e c t i v e l y i n o r d e r t o get the a p p r o p r i a t e parameters f o r s h i n g l e m i l l s . 100 T a b l e IV Exogenous Output E s t i m a t i o n R e s u l t s ( a s y m p t o t i c t ' s i n p a r e n t h e s i s ) C o o p e r a t i v e M o d e l I . U n i o n U t i l i t y y 2.43168 (12.345)* impl ied 6 = y .7086 i+y p 0.04670 (1.323) L a b o u r D e m a n d M o d e l I . U n i o n U t i l i t y y 5.88248 (8.142)* impl ied 6 = y .8547 1+y p -0.04792 (-1.637) I I . T e c h n o l o g y B 0. .36868 (6. 228)* B l 0. .00353 (0. 155) B2 1. .09337 (28. 211)* B3 0. .03008 (4. 296)* Be -0. .01260 (-0. 787) I I . T e c h n o l o g y B 2, .21139 (4. 221)* B l 0. .00826 (0. 717) B2 0. .81466 (15. 825)* B3 0. .01572 (3. 939)* Be -0, . 18179 (-14. 386)* I I I . S t r i k e C o s t s F0 FI F2 F3 1.99872 -0.28815 0.05858 -0.26947 (1.602) (-10.948)* (3.141)* (-5.243)* U0 -4.4653 U l 2.85672 U2 5.08272 (-1.569) (5.445)* (1.600) I V . F i r s t O r d e r S e r i a l C o r r e l a t i o n C o e f f i c i e n t s e q . l 0.62005 eq.2 0.17802 eq.3 0.18805 eq.4 0.12803 (11.340)* (2.209)* (2.310)* (1.172) I I I . S t r i k e C o s t s F0 FI F2 F3 -6.69166 -0.01315 -0.15232 0.13628 (-3.343)* (-0.375) (-8.251)* (1.419) U0 Ul U2 -2.52046 -1.12130 13.20971 (-1.047) (-1.717) (2.534) I V . F i r s t O r d e r S e r i a l C o r r e l a t i o n eq. 1 eq.2 eq. 3 eq. 4 0.23388 0.25721 0.29529 0.17485 (3.809)* (4.206)* (3.639)* (1.700) 101 T a b l e I V C o n t i n u e d V . C o o p e r a t i v e M o d e l C o n s t a n t s L a b o u r D e m a n d M o d e l e q . 1 e q . 2 e q . 3 e q . 4 1 . 7 9 6 5 9 - 1 . 6 9 2 8 4 - 3 . 6 7 8 0 0 - 0 . 8 7 2 0 2 ( 6 . 1 3 7 ) * ( - 7 . 0 3 2 ) * ( - 6 . 3 7 6 ) * ( - 3 . 9 2 6 ) * C o n s t a n t s e q . l 8 . 5 2 5 6 6 e q . 2 - 1 . 0 5 9 0 1 e q . 3 1 2 . 7 1 0 3 7 e q . 4 - 0 . 8 4 3 9 1 ( 2 . 6 8 0 ) * ( - 3 . 5 0 0 ) * ( 5 . 9 7 9 ) * ( - 3 . 6 7 7 ) * I n t e r i o r S a w m i l l s Dummy e q . 1 e q . 2 e q . 3 e q . 4 1 . 7 1 3 6 1 - 0 . 3 6 7 4 9 - 3 . 3 0 9 7 2 - 3 . 1 0 5 2 4 ( 5 . 5 8 0 ) * ( - 2 . 9 5 6 ) * ( - 4 . 1 3 2 ) * ( - 1 2 . 1 4 0 ) * I n t e r i o r S a w m i l l s Dummy e q . 1 e q . 2 e q . 3 e q . 4 2 . 0 9 4 8 5 - 0 . 7 1 8 7 0 - 0 . 4 0 2 8 4 - 3 . 2 8 1 6 1 ( 0 . 8 7 8 ) ( - 2 . 7 1 9 ) * ( - 0 . 5 1 1 ) ( - 1 2 . 7 2 6 ) * V a l u e o f t h e I n l i k e l i h o o d - 3 2 8 6 . 8 8 8 7 V a l u e o f t h e I n l i k e l i h o o d - 3 3 1 5 . 1 1 2 0 N u m b e r o f o b s e r v a t i o n s 8 4 N u m b e r o f o b s e r v a t i o n s 8 4 R / b e t w e e n p r e d i c t e d a n d a c t u a l ( 1 ) b e t w e e n p r e d i c t e d a n d a c t u a l -W -E -Q2 - Q 3 0 . 6 4 1 5 0 . 2 8 9 6 0 . 9 4 8 1 0 . 6 3 4 1 -W -E -Q2 -Q3 0 . 7 3 3 4 0 . 3 3 6 7 0 . 9 5 7 4 0 . 5 9 7 8 R^ b e t w e e n p r e d i c t e d a n d a c t u a l i n r e d u c e d s a m p l e 1 9 6 4 - 1 9 7 9 -W -E -Q2 -Q3 0 . 9 2 4 4 0 . 3 5 2 7 0 . 9 4 5 4 0 . 6 9 5 4 R^ b e t w e e n p r e d i c t e d a n d a c t u a l i n r e d u c e d s a m p l e 1 9 6 4 - 1 9 7 9 -W -E -Q2 -Q3 0 . 8 8 6 1 0 . 1 7 3 2 0 . 9 4 1 8 0 . 7 1 5 1 * s i g n i f i c a n t a t 5% i n 2 - t a i l e d t e s t s Note : (1) F o r t h e c o o p e r a t i v e m o d e l , o n e o b s e r v a t i o n , s h i n g l e m i l l s i n 1982 , was d e l e t e d i n t h e R 2 c a l c u l a t i o n . 102 F o r compar i son i t i s perhaps more u s e f u l t o express the i n p u t c o e f f i c i e n t s i n terms o f c o s t shares o f the u n d e r l y i n g u n r e s t r i c t e d c o s t f u n c t i o n : , - B L ( - B 2 - ( 1 - B 3 ) - B 3 . . B e . C U N ( Q 1 , P 2 , P 3 , W ) - C o n s t a n t x T ^ Q J 8 - 1 \ \ P ^ " 1 ' W ^ " 1 ' N o t e t h a t W, t h e shadow p r i c e o f l a b o u r , i s e q u a l to the ( p r e d i c t e d ) a c t u a l wage i n the LDEM model but w £ W i n the C O O P model s i n c e i n t h a t c a s e , the c o n t r a c t can be l o c a t e d t o t h e r i g h t o f the l a b o u r demand c u r v e . The c o s t shares f o r C U N a r e : C o s t S h a r e s I n p u t COOP L D E M R e f e r e n c e S h a r e s A c t u a l A v e r a g e C o s t M o d e l M o d e l i n t h e L i t e r a t u r e * S h a r e s O v e r S a m p l e * * L a b o u r . 0 1 2 4 . 1 5 3 8 . 2 3 . 3 1 M a t e r i a l s . 9 5 7 9 . 8 3 2 9 . 5 5 . 6 3 a n d S u p p l i e s C a p i t a l . 0 2 9 7 . 0 1 3 3 . 2 1 . 0 6 * s e e M a r t i n e l l o ( 1 9 8 4 ) , p g . 3 1 . * * s e e A p p e n d i x A T h e e s t i m a t i o n w i t h e x o g e n o u s o u t p u t y i e l d s much s m a l l e r l a b o u r shares than are commonly r e p o r t e d due t o the s m a l l v a l u e s o f t h e l a b o u r e x p o n e n t s . T h i s i s n o t s u r p r i s i n g f o r the C O O P model s i n c e the l e v e l o f employment c o u l d be l o c a t e d f a r t o t h e r i g h t o f t h e l a b o u r demand c u r v e , b u t , i g n o r i n g econometr i c i s s u e s , the LDEM model i s 103 e q u i v a l e n t t o s t a n d a r d c o s t f u n c t i o n e s t i m a t i o n s w i t h t h e e x c e p t i o n t h a t t h e wage i s now chosen t h r o u g h b a r g a i n i n g r a t h e r than by c o m p e t i t i v e f o r c e s . The s m a l l l a b o u r shares a r e c o m p e n s a t e d by v e r y l a r g e s h a r e s f o r m a t e r i a l s and s u p p l i e s . The c a p i t a l s h a r e s seem e x t r e m e l y s m a l l when compared t o g e n e r a l e s t i m a t e s but they are no t so s u r p r i s i n g when they are compared to a c t u a l average c o s t s h a r e s o v e r the sample . In o r d e r t o l o o k a t s c a l e e f f e c t s , I t ake advantage o f my s i m p l e C o b b - D o u g l a s s p e c i f i c a t i o n a n d d e r i v e t h e u n d e r l y i n g p r o d u c t i o n f u n c t i o n p a r a m e t e r s : COOP: Q , - C o n s t a n t x T - - 0 0 3 2 x Q 2 8 8 7 1 x Q 3 ° 2 7 5 x E ' 0 1 5 5 LDEM: Q l = C o n s t a n t x T - - 0 1 0 1 x Q ^ 2 0 8 2 x Q 3 ° 1 9 3 x E * 2 2 3 1 I n t h e COOP m o d e l , t h e t e c h n o l o g y e x h i b i t s d e c r e a s i n g r e t u r n s t o s c a l e w h i l e t h e r e v e r s e i s t r u e f o r the LDEM m o d e l . A g a i n , a h i g h e r c o e f f i c i e n t on l a b o u r i s expected i n the LDEM model s i n c e t h a t model f o r c e s the m a r g i n a l revenue p r o d u c t o f l a b o u r t o c l o s e l y r e s e m b l e t h e wage. What i s p e r h a p s s u r p r i s i n g i s t h a t t h e o u t p u t e l a s t i c i t y o f m a t e r i a l s i s a l s o l a r g e r i n the LDEM mode l . I n t h e LDEM mode l , the wage i s f o r c e d t o r e f l e c t the m a r g i n a l revenue p r o d u c t o f l a b o u r . T h i s i s no t t h e c a s e f o r t h e COOP mode l . The r e s u l t s f o r the exogenous output t e c h n o l o g y i n d i c a t e t h a t f o r t h e COOP m o d e l , t h e wage i s 104 c o n s i d e r a b l y l a r g e r than t h e m a r g i n a l r e v e n u e p r o d u c t o f l a b o u r . The average m a r g i n a l revenue p r o d u c t o f l a b o u r over the sample i n the LDEM model i s 3.3 4 32 w h i c h i s somewhat lower than the average wage over the sample ( 4 . 5 ) . In the COOP mode l , the average m a r g i n a l revenue p r o d u c t o f l a b o u r i s o n l y 0 . 1 2 . I t i s t r u e t h a t the e s t i m a t e f o r the COOP model i s i m p r e c i s e , but even when a 95% c o n f i d e n c e i n t e r v a l i s c a l c u l a t e d f o r the l a b o u r c o e f f i c i e n t and the upper bound ( i n a b s o l u t e v a l u e s ) i s used f o r Be , the average m a r g i n a l r e v e n u e p r o d u c t o f l a b o u r i s l e s s t h a n o n e . The two e s t i m a t e d l a b o u r demand c u r v e s e v a l u a t e d a t the mean o f the d a t a a r e i l l u s t r a t e d i n F i g u r e 3. 3 1 ( T h e s e e s t i m a t e d r e l a t i o n s h i p s do no t take i n t o account the s t r u c t u r e o f the e r r o r i . e . c o n s t a n t t e r m s and s e r i a l c o r r e l a t i o n are not i n c l u d e d i n the c a l c u l a t i o n s . ) As w i l l be s e e n l a t e r i n t h i s c h a p t e r , when o u t p u t i s t r e a t e d as endogenous , the e s t i m a t e d m a r g i n a l revenue p r o d u c t s o f l a b o u r a r e l a r g e r , e s p e c i a l l y f o r the COOP model (see F i g u r e 5 ) . One p o s s i b l e e x p l a n a t i o n i s t h a t the i n c l u s i o n o f o u t p u t q u a n t i t y as an exogenous v a r i a b l e i n t r o d u c e s m u l t i c o l l i n e a r i t y i n the d a t a and i n c r e a s e s t h e i n a c c u r a c y o f t h e e s t i m a t e s o f l a b o u r 3 1 T h e l a b o u r demand c a l c u l a t i o n s f o r the COOP model e x c l u d e the o b s e r v a t i o n f o r s h i n g l e m i l l s , 1982. To o b t a i n p r e d i c t e d v a l u e s f o r wages and employment, a system o f 2 n o n - l i n e a r e q u a t i o n s must be s o l v e d f o r e a c h d a t a p o i n t . T h i s system c o u l d not be s o l v e d w i t h any r e a s o n a b l e degree o f a c c u r a c y f o r t h i s o b s e r v a t i o n . 105 "1971 d o l l a r s per man-hour F i g u r e 3 L a b o u r Demand C u r v e s and the C o n t r a c t C u r v e . Exogenous Output E s t i m a t i o n . ' labor demand \ (labor demand model) contract curve l a b o r demand ( c o o p e r a t i v e model) - r - 1.0 0.0 o.s I 1.5 I 3.0 2.0 2.5 Employment ( i n lOM 's man-hours) i 3.5 I 4.0 106 p r o d u c t i v i t y . (The c o r r e l a t i o n c o e f f i c i e n t between o u t p u t and employment over the sample i s . 7371) . S t u d i e s u s i n g a s p e c i a l c a s e o f t h e LDEM m o d e l , t h e c a s e where t h e u n i o n u n i l a t e r a l l y c h o o s e s the wage (the monopoly m o d e l ) , have y i e l d e d l a r g e p r i c e e l a s t i c i t i e s f o r the l a b o u r demand c u r v e . Examples are M a r t i n e l l o (1984) who f i n d s the e l a s t i c i t y ( i n a b s o l u t e v a l u e ) t o e q u a l 1 .5 f o r the IWA, and Dertouzos and P e n c a v e l (1981) who f i n d a v a l u e o f 1 .23 a t t h e mean o f t h e d a t a f o r t h e I n t e r n a t i o n a l T y p o g r a p h i c a l Union ( I T U ) . These s h o u l d be compared w i t h g e n e r a l e s t i m a t e s o f e l a s t i c i t i e s s m a l l e r t h a n .5 i n t h e l i t e r a t u r e where u n i o n impacts are i g n o r e d . In t h i s s t u d y , the e l a s t i c i t i e s l i e somewhere i n between these v a l u e s ; they a r e .9876 f o r the COOP model and .8462 f o r the LDEM mode l . F u r t h e r m o r e , t h i s remains t r u e when a l l b a r g a i n i n g powers a r e g i v e n t o t h e u n i o n i . e . when ( l n d u / l n d f ) i s f i x e d a t z e r o . In t h a t case the e s t i m a t e d e l a s t i c i t i e s are 1.033 f o r COOP and .8405 f o r LDEM. 107 5 . 1 .2 U n i o n P r e f e r e n c e s 3 2 F o r b o t h the LDEM and the COOP mode l , r e s u l t s suggests t h a t the u n i o n puts more weight on employment t h a n on wages (6 > . 5 ) . The d i f f e r e n c e i n the weights i s g r e a t e r f o r the LDEM t h a n the COOP mode l b u t i n b o t h c a s e s , t h e t e s t o f e q u a l i t y o f we ights ( i . e . the t e s t t h a t y=l) i s r e j e c t e d a t the 1% l e v e l o f s i g n i f i c a n c e . T h i s r e s u l t i s c o n s i s t e n t w i t h p r e v i o u s f i n d i n g s i n v o l v i n g the ITU as w e l l as the IWA. A g a i n f o r b o t h the COOP and the LDEM mode l s , the parameter p i s no t s i g n i f i c a n t l y d i f f e r e n t from 0. T h i s i m p l i e s t h a t we cannot r e j e c t the h y p o t h e s i s t h a t the u n i o n p r e f e r e n c e s take t h e f o r m o f a C o b b - D o u g l a s f u n c t i o n . T h e r e s u l t i n g e l a s t i c i t y o f s u b s t i t u t i o n (-1) i s l a r g e r than t h a t found by M a r t i n e l l o (1984) ( - .7 ) and by Dertouzos and P e n c a v e l (1981) f o r t h e I T U ( . 7 ) . R e n t m a x i m i z a t i o n (p = 0 and y = l ) i s r e j e c t e d f o r b o t h mode l s , a r e s u l t which was a l s o found by Der touzos and P e n c a v e l (1981) and M a r t i n e l l o (1984) . I t i s r e a s s u r i n g t h a t t h e u n i o n p r e f e r e n c e s are so s i m i l a r i n t h e two m o d e l s g i v e n t h e d i f f e r e n c e i n t h e t e c h n o l o g y c o e f f i c i e n t s . H o w e v e r , some d i f f e r e n c e s do e x i s t . The e l a s t i c i t y o f s u b s t i t u t i o n f o r the COOP m o d e l ( . 9 5 5 4 ) i s l o w e r t h a n f o r t h e LDEM m o d e l (1.0503) which 3 2 T a k i n g i n t o a c c o u n t t h e s c a l i n g o f t h e d a t a f o r s h i n g l e m i l l s , t h e u n i o n u t i l i t y p a r a m e t e r s y f o r t h o s e f i r m s i s 2.18376 f o r the COOP model and 6.5687 f o r the LDEM m o d e l . None o f the q u a l i t a t i v e r e s u l t s d e s c r i b e d i n t h i s s e c t i o n a r e a f f e c t e d when c o n s i d e r i n g t h e s e a d j u s t e d parameters f o r s h i n g l e m i l l s . 108 means t h a t the i n d i f f e r e n c e c u r v e s are more c o n v e x i n t h e COOP mode l . A t the mean o f the d a t a , i t would t a k e a 0.44% i n c r e a s e i n t h e wage (above t h e a l t e r n a t i v e wage) t o c o m p e n s a t e t h e u n i o n f o r a l o s s o f 1% i n t h e number o f workers i n the COOP mode l . T h i s same measure e q u a l s 1.32% i n the LDEM mode l . I t takes a much l a r g e r i n c r e a s e i n the wage to compensate the u n i o n f o r the l o s s o f one worker i n t h e LDEM m o d e l . T h e s e e s t i m a t e s a r e c o m p a r a b l e to t h a t found i n M a r t i n e l l o (1984) (.67%). 5 . 1 . 3 The C o n t r a c t C u r v e and the B a r g a i n i n g S e t s The c o n t r a c t c u r v e f o r the COOP model e v a l u a t e d a t the mean o f the d a t a has a l s o been p l o t t e d i n F i g u r e 3. I t i s v e r y f l a t i . e . t h e c o n t r a c t s move q u i c k l y away f r o m t h e l a b o u r demand c u r v e . The average e l a s t i c i t y o f the c o n t r a c t c u r v e over the sample i s 3.44%. F o r 4 o f the d a t a p o i n t s i n the COOP model and 2 o f the d a t a p o i n t s i n the LDEM mode l , the p r e d i c t e d wage was lower than the a l t e r n a t i v e wage. T h i s o c c u r r e d d u r i n g the 1980's r e c e s s i o n , s p e c i f i c a l l y , f o r the COOP mod e l , W<W^ f o r the s a w m i l l s from 1980 to 1983 and f o r the LDEM mode l , the same i s t r u e f o r i n t e r i o r s a w m i l l s and f o r s h i n g l e m i l l s i n 1982. T h i s f i n d i n g i s no t c o n s i s t e n t w i t h the assumpt ion o f a zero t h r e a t p o i n t which i s m a i n t a i n e d i n t h i s s t u d y . However, i t can be e x p l a i n e d by the presence o f f i x e d c o s t s o f d e l a y w h i c h c a u s e t h e t h r e a t p o i n t t o be l e s s than z e r o . The p o s s i b i l i t y o f a n e g a t i v e t h r e a t p o i n t sounds p l a u s i b l e i n 109 t h e s h o r t r u n b u t i t i s u n l i k e l y t h a t t h e p l a y e r s c a n s u r v i v e p r o l o n g e d p e r i o d s o f n e g a t i v e u t i l i t y . E x c l u d i n g the o b s e r v a t i o n s mentioned above p l u s s h i n g l e m i l l s i n 1982 f o r the COOP model (see f o o t n o t e 31) , I f i n d t h a t the b a r g a i n i n g s e t s i n u t i l i t y space f o r b o t h the COOP and LDEM models are convex everywhere . T h i s ensures t h a t the e q u i l i b r i u m t o the b a r g a i n i n g game i s u n i q u e . A l s o , f o r t h e COOP m o d e l , the i s o - p r o f i t c u r v e s are everywhere l e s s convex than the u n i o n i n d i f f e r e n c e c u r v e s . T h i s e n s u r e s t h a t the c o n t r a c t c u r v e i s d e f i n e d by tangency p o i n t s o f the i s o - u t i l i t y c u r v e s . (Note t h a t t h i s i s no t an i s s u e i n the LDEM model s i n c e i n t h a t c a s e , the l a b o u r demand c u r v e i s the c o n t r a c t c u r v e . ) 5 . 1 . 4 B a r g a i n i n g P o w e r s 3 3 The d e t e r m i n a n t s o f t h e f i r m s ' s t r i k e c o s t s are a l l s i g n i f i c a n t and have the expected s i g n s i n the COOP mode l . 3 3 A 1 1 models were a l s o e s t i m a t e d w i t h the a d d i t i o n o f a dummy v a r i a b l e r e p r e s e n t i n g the e f f e c t s o f wage and p r i c e c o n t r o l s on the r e l a t i v e s t r i k e c o s t s . T h i s dummy v a r i a b l e t a k e s the v a l u e o f one i n 1976 , 1977 , and 1978 . I n a l l c a s e s , the c o e f f i c i e n t s on t h i s v a r i a b l e are s m a l l and not s i g n i f i c a n t l y d i f f e r e n t from z e r o . The o t h e r parameters are p r a c t i c a l l y u n a f f e c t e d by the a d d i t i o n o f t h i s t e r m . The l i k e l i h o o d i s s l i g h t l y improved . Under the a s s u m p t i o n o f e x o g e n o u s o u t p u t , t h e l o g l i k e l i h o o d v a l u e f o r t h e c o o p e r a t i v e model i s -3285.9340 and f o r the l a b o u r demand mode l , -3315 .0744 . The same v a l u e s under the assumpt ion o f e x o g e n o u s c a p i t a l a r e - 3 4 6 6 . 6 7 0 5 a n d - 3 4 7 9 . 1 3 3 0 r e s p e c t i v e l y . The c o e f f i c i e n t s on the dummy v a r i a b l e a r e : f o r the exogenous o u t p u t f r a m e w o r k , - 0 . 0 9 9 f o r COOP and 0.025 f o r LDEM, f o r the exogenous c a p i t a l mod e l , 0.018 f o r COOP and - 0 . 0 7 8 f o r LDEM. 110 An i n c r e a s e i n the i n t e r e s t r a t e w i l l cause a r i s e i n t h e r e l a t i v e s t r i k e c o s t s o f t h e f i r m s w h i l e an i n c r e a s e i n i n v e n t o r y l e v e l s over the p a s t 5 y e a r s w i l l be accompanied by a f a l l i n t h e f i r m ' s r e l a t i v e s t r i k e c o s t s d u r i n g the f o l l o w i n g y e a r . The c a p i t a l u t i l i z a t i o n r a t e i s n e g a t i v e l y r e l a t e d t o f i r m s ' r e l a t i v e s t r i k e c o s t s . T r a c y (1986) found a p o s i t i v e e f f e c t o f b u s i n e s s c y c l e s on the f i r m s ' s t r i k e c o s t s . I n t h a t s t u d y , b u s i n e s s c y c l e s were meant t o measure c y c l i c a l v a r i a t i o n s i n r e n t s and hence i n the a b s o l u t e l e v e l o f s t r i k e c o s t s . H e r e , t h e c o e f f i c i e n t on t h e c a p i t a l u t i l i z a t i o n r a t i o measures b u s i n e s s c y c l e e f f e c t s on s t r i k e c o s t s over and above the c y c l i c a l v a r i a t i o n s i n r e n t s . In the LDEM mode l , o n l y the i n v e n t o r y l e v e l has a s i g n i f i c a n t c o e f f i c i e n t and i t has the o p p o s i t e s i g n t o t h a t i n COOP. The i n t e r e s t r a t e and c a p i t a l u t i l i z a t i o n r a t e have s m a l l e r and i n s i g n i f i c a n t e f f e c t s . The u n i o n s t r i k e c o s t s v a r i e d over t ime a c c o r d i n g to l a b o u r market t i g h t n e s s as measured by the t e r m : U 0 [ U N t - x U I C t - g§ x D E M t ] . Note t h a t unemployment a l s o e n t e r s t h e a l t e r n a t i v e wage measure and , t h r o u g h W^, d i r e c t l y a f f e c t s the c o n s t r a i n t on the u n i o n ' s u t i l i t y . The e f f e c t o f unemployment on s t r i k e c o s t s i s o v e r and above t h e d i r e c t e f f e c t s on ( e . g . e f f e c t s on s p o u s e ' s income) . F o r b o t h the COOP mode l and I l l the LDEM m ode l , UO has the wrong s i g n w h i c h i m p l i e s t h a t r e l a t i v e u n i o n s t r i k e c o s t s i n c r e a s e (and h e n c e u n i o n b a r g a i n i n g power f a l l s ) when t h e l a b o u r m a r k e t becomes t i g h t e r . However, these e f f e c t s a r e i m p r e c i s e as s t a n d a r d e r r o r s a r e l a r g e . The UIC and DEM v a r i a b l e s i n t h e COOP model have the p r e d i c t e d ( p o s i t i v e ) e f f e c t s on the n a t u r a l r a t e o f u n e m p l o y m e n t b u t o n l y t h e U I C c o e f f i c i e n t i s s i g n i f i c a n t . In the LDEM mode l , the c o e f f i c i e n t on DEM has t h e p r e d i c t e d s i g n a n d i s s i g n i f i c a n t w h i l e t h e U I C c o e f f i c i e n t has the wrong s i g n but i s i n s i g n i f i c a n t . The term ( l n d u / l n d f ) i s bounded below by 0 , t h e c a s e w h e r e t h e u n i o n h a s a l l t h e b a r g a i n i n g p o w e r , and i s unbounded above as i t a p p r o a c h e s ~ when t h e f i r m s ' t i m e c o s t s go t o 0 . The average v a l u e o f the r e l a t i v e s t r i k e c o s t s ( l n d u / l n d f ) over the sample i s .1943 i n the COOP model and .1222 i n the LDEM mode l . The u n i o n has r e l a t i v e l y l e s s power when c o n t r a c t s a r e assumed t o be e f f i c i e n t . L o g l i k e l i h o o d t e s t s were performed on the f o l l o w i n g h y p o t h e s i s : ( l n d u / l n d f ) = 0 (the u n i o n has a l l the b a r g a i n i n g power) and ( l n d u / l n d f ) = 1 ( e q u a l b a r g a i n i n g power; i . e . , F0 = 1 and a l l o t h e r c o e f f i c i e n t s e q u a l t o 0 ) . B o t h h y p o t h e s e s w e r e r e j e c t e d f o r b o t h mode l s . The e s t i m a t e s do no t s u p p o r t the monopoly model o f u n i o n s nor a s y m m e t r i c N a s h b a r g a i n i n g s o l u t i o n . T h e f a c t t h a t t h e v a l u e o f ( l n d u / l n d f ) i s v e r y low i m p l i e s t h a t the u n i o n d i s c o u n t r a t e du i s much l a r g e r than 112 the d i s c o u n t f a c t o r o f the f i r m s d f . In o r d e r t o have a b e t t e r i d e a o f the r e l a t i v e b a r g a i n i n g powers i m p l i e d by the v a l u e o f ( l n d u / l n d f ) , I c a l c u l a t e d the we ights on t h e two p a r t i e s ' u t i l i t i e s i n t h e N a s h b a r g a i n i n g s o l u t i o n (see e q u a t i o n s (4) and (5) i n C h a p t e r 4 ) . T h e s e w e i g h t s a r e e a s i e r t o i n t e r p r e t as t h e y a r e bounded b e l o w by z e r o , bounded above by 1, and they sum t o one. The weight on the u n i o n u t i l i t y i s g i v e n by: a _ l n d f _ 1 u " l n d u + l n d f " l + ( l n d u / l n d f ) ' The weight on the f i r m s ' p r o f i t s i s : l n d u _ ( l n d u / l n d f ) a f " l n d u + l n d f " l + ( l n d u / l n d f ) " 1 a u ' The b a r g a i n i n g power o f the u n i o n (as measured by the t e r m a u ) i s p l o t t e d f o r a l l f o u r groups o f f i r m s and f o r b o t h the COOP and LDEM models i n F i g u r e 4. The f i r s t t h i n g t o no te i s how l a r g e the b a r g a i n i n g power o f the u n i o n i s i n t h e e x o g e n o u s o u t p u t m o d e l . The a v e r a g e u n i o n u t i l i t y w e i g h t i n t h e COOP m o d e l i s .8 375 and i n the LDEM model .8913. F o r b o t h mode l s , the b a r g a i n i n g power o f the u n i o n d e c r e a s e s i n the 70's but r i s e s a g a i n i n the 80' s t o r e a c h i t s 1960's l e v e l a g a i n by 1982 or 1983. F o r the COOP mode l , t h e d e c r e a s e s t a r t e d i n the e a r l y '70 's but f o r the LDEM mode l , the b a r g a i n i n g power remained a t i t s h i g h l e v e l u n t i l 1976 . F u r t h e r m o r e , t h i s f a l l i n t h e 70's i s not caused 113 F i g u r e 4 U n i o n B a r g a i n i n g Power. Exogenous Output E s t i m a t i o n , a. Cooperative Model 1964.0 1966.0 1968.0 1970.0 I97J.0 1974.0 TIME 1976.0 1978.0 1980.0 1982.0 1984.0 b. Labor Demand Model i n t e r i o r sawmills shing mills plywood and veneer mills V 7 ' / A , coastal V . sawmills 1964.0 ISS6.0 1968.0 1970.0 1972.0 1974.0 1978.0 1978.0 1 9 8 0 ^ 0 I 9 8 Z J ) T s W . O 114 s o l e l y by the p e r v e r s e c o e f f i c i e n t on the unemployment r a t e . The u n i o n b a r g a i n i n g power c a l c u l a t e d as above w i t h UO, UI and U2 s e t a t z ero s t i l l shows a s l i g h t downward t r e n d i n t h e ' 7 0 ' s w i t h a s h a r p f a l l around 1981 and a subsequent i n c r e a s e i n the l a s t 2 y e a r s o f the sample . I t i s s u r p r i s i n g to see the e s t i m a t e d u n i o n b a r g a i n i n g power d e c r e a s i n g i n t h e l a t e ' 7 0 ' s when t h e p r o v i n c i a l economy was b o o m i n g and l a b o u r m a r k e t s were v e r y t i g h t . H o w e v e r , i t s h o u l d be kept i n mind t h a t a d e c r e a s e i n a u does n o t imply a d e c r e a s e i n the u n i o n u t i l i t y f u n c t i o n , i n f a c t , t h e u n i o n u t i l i t y was i n c r e a s i n g over t h i s p e r i o d . What i t i n d i c a t e s i s t h a t the f i r m s ' p r o f i t s were i n c r e a s i n g f a s t e r than the u t i l i t y o f the u n i o n . T h i s i s perhaps more e a s i l y shown by l o o k i n g a t t h e e s t i m a t e d p r o p o r t i o n s o f t o t a l r e n t s c a p t u r e d by the f i r m which are l i s t e d i n T a b l e V f o r the COOP mode l . The p r o p o r t i o n s g i v e n i n T a b l e V are c a l c u l a t e d as the r a t i o o f e s t i m a t e d p r o f i t s o f the f i r m s d i v i d e d by p r o f i t s e v a l u a t e d a t the a l t e r n a t i v e wage and at the c o r r e s p o n d i n g employment l e v e l on the l a b o u r demand c u r v e . I f i n d t h a t the f i r m s succeeded i n c a p t u r i n g s l i g h t l y over 40% o f r e n t s on average over the p e r i o d . A l s o , the p r o p o r t i o n o f r e n t s c a p t u r e d by the f i r m was l a r g e r on average i n the 1970's , e s p e c i a l l y i n the l a t t e r h a l f o f the decade . 115 T a b l e V P r o p o r t i o n o f T o t a l Rents C a p t u r e d by t h e F i r m . C o o p e r a t i v e Model w i t h Exogenous Output Y e a r C o a s t a l I n t e r i o r S h i n g l e P l y w o o d S a w m i l l s S a w m i l l s M i l l s V e n e e r M i ! 1964 .31113 .59166 .39781 .46465 1965 .33218 .57967 .43755 .44462 1966 .35079 .58601 .43599 .43327 1967 .42393 .57622 .42172 .46698 1968 .36535 .55831 .38423 .43616 1969 .28265 .43007 .20909 .45712 1970 .29588 .50572 .24876 .47370 1971 .32846 .56994 .34617 .48529 1972 .43833 .55050 .38960 .47539 1973 .44509 .49261 .36297 .43178 1974 .18168 .39963 .29614 .36443 1975 .45291 .60943 .54350 .52181 1976 .41620 .56498 .43655 .44838 1977 .44037 .51496 .39039 .41167 1978 .51582 .55352 .47949 .54334 1979 .45093 .45831 .44947 .38503 1980 .17879 .45267 .34229 .22093 1981 .29232 .55320 .39730 .20498 1982 .27218 .63340 - (1) .17610 1983 .33905 .65908 .40259 .22517 G r a n d A v g . = .4223 Note : (1) P r e d i c t e d v a l u e s f o r wages and employment c o u l d n o t be c a l c u l a t e d f o r t h i s o b s e r v a t i o n ( s e e f o o t n o t e 31) . 116 I t i s i n t e r e s t i n g t o n o t e t h e d i f f e r e n c e i n t h e p r o p o r t i o n o f r e n t s c a p t u r e d by t h e u n i o n ( w h i c h i s l e s s t h a n 60% on a v e r a g e ) and t h e u n i o n b a r g a i n i n g power as measured by a u (which i s g r e a t e r than 80% on a v e r a g e ) . The p r o p o r t i o n o f r e n t s i s a poor i n d i c a t o r o f u n i o n b a r g a i n i n g power because i t i s based on the v e r t i c a l d i s t a n c e ( i n W,E space) between the i s o - p r o f i t c u r v e c o r r e s p o n d i n g t o t h e e s t i m a t e d p r o f i t l e v e l a n d t h e i s o - p r o f i t c u r v e c o r r e s p o n d i n g t o a zero p r o f i t . The c o r r e c t v a l u e o f u n i o n b a r g a i n i n g power i s based on the d i s t a n c e measured a l o n g the c o n t r a c t c u r v e . These two measures are the same o n l y i f the u n i o n i s r e n t m a x i m i z i n g and i f the c o n t r a c t i s e f f i c i e n t . F o r the LDEM mode l , e s t i m a t e d p r o f i t s and r e n t s a r e n e g a t i v e f o r most d a t a p o i n t s due t o t h e l a r g e s c a l i n g f a c t o r B ( 2 . 2 1 ) . As mentioned e a r l i e r , the m a r g i n a l revenue p r o d u c t (MRP) o f l a b o u r i s much l a r g e r i n the LDEM model t h a n i n the COOP model because i t i s f o r c e d t o r e f l e c t the wage. T h i s h i g h e r MRP o f l a b o u r i s a c h i e v e d i n p a r t by a l a r g e r c o e f f i c i e n t on l a b o u r (Be ) . However, and t h i s was e v i d e n t from the l a b o u r c o s t s h a r e , t h i s l a b o u r c o e f f i c i e n t i s s t i l l s m a l l and a s u b s t a n t i a l p a r t o f the d i f f e r e n c e i n the MRP's i s due to the l a r g e r s c a l i n g f a c t o r B . T h i s , i n t u r n , causes the e s t i m a t e d c o s t s o f m a t e r i a l s and c a p i t a l t o be b i g and the e s t i m a t e d p r o f i t s a r e , i n g e n e r a l , n e g a t i v e . 117 5 . 1 . 5 Comparing t h e COOP and LDEM Models In T a b l e I V , we see t h a t the e f f i c i e n t c o n t r a c t model p e r f o r m s b e t t e r i n the sense t h a t i t s l i k e l i h o o d v a l u e i s l a r g e r . 3 4 T h i s has been t r u e throughout my whole r e s e a r c h w i t h t h i s d a t a s e t . I t i s i n t e r e s t i n g t o compare t h e c o r r e l a t i o n c o e f f i c i e n t s between p r e d i c t e d and a c t u a l v a l u e s o f the endogenous v a r i a b l e s . F o r wages and employment, the R 2 1 s a r e a c t u a l l y l a r g e r i n the LDEM mode l . The l i s t o f p r e d i c t i o n e r r o r s showed t h a t the COOP model was v e r y poor a t p r e d i c t i n g wages and employment i n the 1980 ' s . T h i s i s c l e a r f r o m t h e R 2 ' s c a l c u l a t e d w i t h o u t the y e a r s 1980 to 1983 which are a l s o r e p o r t e d i n T a b l e I V . T h i s sugges ts the i n t e r e s t i n g h y p o t h e s i s t h a t w h i l e the e f f i c i e n t c o n t r a c t model p e r f o r m s b e t t e r i n g e n e r a l , t h e LDEM m o d e l i s more a p p r o p r i a t e d u r i n g s e v e r e r e c e s s i o n s . The l a r g e changes which o c c u r r e d i n the economic environment o f the two p l a y e r s due to the s e v e r e r e c e s s i o n i n the 1980's c o u l d have made b a r g a i n i n g over employment v e r y c o s t l y i n t e r m s o f t r a n s a c t i o n s and m o n i t o r i n g (enforcement) c o s t s . T h i s c o u l d be t e s t e d by a s w i t c h i n g regime type model or a g e n e r a l model n e s t i n g the two b a r g a i n i n g mode l s . A l a r g e r d a t a s e t would p r o b a b l y be r e q u i r e d as w e l l . 3 4 S i n c e b o t h models have the same number o f p a r a m e t e r s , the compar i son o f the l i k e l i h o o d v a l u e s i s e q u i v a l e n t t o u s i n g t h e A k a i k e I n f o r m a t i o n C r i t e r i o n w i t h b o t h models b e i n g c o n s i d e r e d as n e s t e d i n a more g e n e r a l m o d e l w h i c h c o u l d take the form o f a convex c o m b i n a t i o n o f the two. 118 5.2 Exogenous C a p i t a l Model T a b l e VI p r e s e n t s c o e f f i c i e n t s f o r b o t h b a r g a i n i n g models and f o r the case where c a p i t a l s e r v i c e s a r e t r e a t e d as e x o g e n o u s t o t h e b a r g a i n i n g p r o c e s s . O u t p u t i s now chosen o p t i m a l l y g i v e n the n e g o t i a t e d l a b o u r c o n t r a c t . 5 . 2 . 1 The F i r m s ' Techno logy F o r b o t h the COOP and the LDEM mode l s , a l l t e c h n o l o g y c o e f f i c i e n t s are s i g n i f i c a n t l y d i f f e r e n t from z e r o . I t i s s u r p r i s i n g how s i m i l a r t h e c o e f f i c i e n t s a r e i n t h e two b a r g a i n i n g mode l s . That was no t the case i n the exogenous o u t p u t e s t i m a t i o n . The t ime t r e n d has c o e f f i c i e n t s which a r e s i g n i f i c a n t l y l e s s t h a n z e r o i m p l y 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 n b o t h b a r g a i n i n g models i s s h i f t i n g i n over t i m e . The e f f e c t s are q u i t e s m a l l however. As f o r t h e exogenous output e s t i m a t i o n , I d e r i v e the i n p u t c o s t shares based on the u n d e r l y i n g u n r e s t r i c t e d c o s t f u n c t i o n : C U N ( Q r V ? 3 ' " ) = C o n s t a n t x t C 1 x Q" x P J" 0 3" 0 6 x p̂ 3 x w C e where the exponents are f u n c t i o n s o f the v e c t o r o f e s t i m a t e d R c o e f f i c i e n t s . Note t h a t s i n c e c a p i t a l i s assumed t o be e x o g e n o u s , the shadow p r i c e o f c a p i t a l P 3 w i l l i n g e n e r a l d i f f e r from the a c t u a l p r i c e o f c a p i t a l P 3 . A l s o , W, the 119 T a b l e V I Exogenous C a p i t a l E s t i m a t i o n R e s u l t s ( a sympto t i c t ' s i n parenthese s ) Cooperative Model Labour Demand Model I. Union U t i l i t y II. III. IV. y 1.05352 (7. 315)* impl ied 6 = y 51303 i+y p 0.14051 (2. 786)* Technology R 17.98817 (7. 436)* Rl -0.21048 (-7. 461)* R2 -0.53964 (-9. ,294)* R3 0.59467 (9. 753)* Re 0.19463 (6. 873)* S t r i k e Costs F0 4.66183 (4. 548)* F l -0.07521 (-4. 041)* F2 -0.02315 (-2. 064)* F3 -0.20538 (-4. 869)* U0 -7.99731 (-5. 357)* UI 0.67511 (2. 044)* U2 -0.62665 (-0. 276) F i r s t O r d e r S e r : C o r r e l a t i o n C o e f f i c i e n t s e q . l 0.26175 (3. 599)* eq.2 0.45682 (6. 606)* eq.3 0.08056 (1. 228) eq.4 0.27959 (4. 234) i a 1 IV. Union U t i l i t y y 1.49223 implied 8 = i+y 0.16808 II. Technology (5.619)* .59875 (2.781)* R 16.74362 (5. 854)* Rl -0.11640 (-3. 772)* R2 -0.53247 (-6. 970)* R3 0.44378 (6. 063)* Re 0.29027 (9. 971)* S t r i k e Costs F0 -4.49366 (-4. 073)* F l 0.05896 (2. 300)* F2 0.02169 (1. 296) F3 0.22046 (3. 891)* UO 9.08620 (2. 647)* UI -0.21710 (-0. 707) U2 0.86142 (0. 329) F i r s t O r d e r S e r i a C o r r e l a t i o n eq. 1 0.32974 (4. 739)* eq. 2 0.38440 (6. 227)* eq. 3 0.04105 (0. 592) eq. 4 0.17203 (2. 716)* 120 T a b l e I V C o n t i n u e d C o o p e r a t i v e M o d e l C o n s t a n t s e q . 1 e q . 2 e q . 3 e q . 4 1.02308 -1.33659 -9.26692 -4.99822 (0.703) (-8.483)* (-6.687)* (-1.825) V . L a b o u r D e m a n d M o d e l C o n s t a n t s e q . 1 e q . 2 e q . 3 e q . 4 -0.10978 -0.97044 -7.89717 -1.12594 (-0.069) (-3.102)* (-4.253)* (-0.307) I n t e r i o r S a w m i l l s Dummy e q . 1 e q . 2 e q . 3 e q . 4 2.74521 0.39170 -3.91362 4.14343 (2.863)* (2.039)* (-1.386) (0.997) I n t e r i o r S a w m i l l s Dummy e q . 1 e q . 2 e q . 3 e q . 4 2.52769 0.44520 -5.25611 0.58108 (1.908) (1.242) (-1.324) (0.099) V a l u e o f t h e I n l i k e l i h o o d -3466.7148 V a l u e o f t h e I n l i k e l i h o o d -3479.5348 N u m b e r o f o b s e r v a t i o n s 84 N u m b e r o f o b s e r v a t i o n s 84 b e t w e e n p r e d i c t e d a n d a c t u a l -W -E - Q 2 -Qi 0.6823 -0.0817 0.5829 0.5466 b e t w e e n p r e d i c t e d a n d a c t u a l -W -E - Q 2 -Qi 0.7020 0.0055 0.5314 0.5591 R.2 b e t w e e n p r e d i c t e d a n d a c t u a l i n r e d u c e d s a m p l e 1964 - 1979 -W -E -Q2 -Qi 0.9346 -0.0589 0.5024 0.3829 b e t w e e n p r e d i c t e d a n d a c t u a l i n r e d u c e d s a m p l e 1964-1979 -W -E - Q 2 -Qi 0.9390 -0.2929 0.4264 0.3729 * s i g n i f i c a n t a t 5% i n 2 - t a i l e d t e s t s 121 shadow p r i c e o f l a b o u r w i l l i n g e n e r a l be l e s s t h a n t h e a c t u a l wage i n t h e COOP m o d e l s i n c e employment w i l l be l o c a t e d t o the r i g h t o f the l a b o u r demand c u r v e . The c o s t s h a r e s f o r the exogenous c a p i t a l e s t i m a t i o n a r e : C o s t Shares Input COOP Model Labour Materials and Supplies Capital .1465 .4061 .4475 LDEM Model .2291 .3504 .4204 Reference Shares in the Literature (see Martinello (1984), pg.31) .23 .55 .21 Actual Average Cost Shares over Sample (see Appendix A) .31 .63 .06 The l a b o u r share which i s s u b s t a n t i a l l y l a r g e r than i n the exogenous output e s t i m a t i o n i s comparable t o the shares r e p o r t e d i n the l i t e r a t u r e . A l s o , t h e d i f f e r e n c e i n t h e l a b o u r shares i n the two b a r g a i n i n g models i s s m a l l e r than i n the exogenous o u t p u t e s t i m a t i o n . Assuming c a p i t a l i s exogenous y i e l d s l a r g e c o s t shares f o r t h i s i n p u t , about t w i c e the s i z e o f the r e f e r e n c e share and seven t imes the s i z e o f the a c t u a l share c a l c u l a t e d over the sample . T h i s s u g g e s t s t h a t i n t h i s e s t i m a t i o n , t h e shadow p r i c e o f c a p i t a l i s l a r g e r than the a c t u a l p r i c e . The f i r m s w o u l d i n c r e a s e t h e i r u s a g e o f c a p i t a l i f t h e adjus tments were c o s t l e s s . T h e u n d e r l y i n g p r o d u c t i o n f u n c t i o n p a r a m e t e r s a r e d e r i v e d from the v e c t o r o f t e c h n o l o g i c a l c o e f f i c i e n t s : 122 COOP: Q l = C o n s t a n t x T " ' 1 3 6 7 X Q ' 3 5 0 5 X Q ' 3 8 6 2 X E ' 1 2 6 4 LDEM: Q x = C o n s t a n t x T " ' 0 7 6 0 X Q ' 3 4 7 5 X Q ' 2 8 9 6 X E ' 1 8 9 4 B o t h 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 e s e x h i b i t d e c r e a s i n g r e t u r n s t o s c a l e . T h i s was a l s o the case i n the exogenous o u t p u t COOP model but the LDEM model w i t h exogenous output y i e l d e d i n c r e a s i n g r e t u r n s due to a v e r y h i g h c o e f f i c i e n t on m a t e r i a l s and s u p p l i e s . T h e a v e r a g e m a r g i n a l revenue p r o d u c t (MRP) o f l a b o u r over the sample i s 2.1803 f o r the COOP model and 3.6234 f o r t h e LDEM mode l . ( N o t i c e t h a t the average MRP i n the LDEM model i s lower than the average wage o f 4.52 because i t does not t a k e i n t o account the s t r u c t u r e o f the e r r o r t e r m . ) The two e s t i m a t e d l a b o u r demand c u r v e s e v a l u a t e d a t the mean o f the d a t a a r e i l l u s t r a t e d i n F i g u r e 5. The l a b o u r demand f o r t h e LDEM m o d e l i s somewhat f l a t t e r b u t o t h e r w i s e q u i t e s i m i l a r t o i t s c o u n t e r p a r t i n the exogenous o u t p u t mode l . T h i s i s expec ted s i n c e i n b o t h c a s e s , the m a r g i n a l revenue p r o d u c t o f l a b o u r i s f o r c e d t o r e f l e c t the wage. The COOP model l a b o u r demand i n F i g u r e 5 i s much h i g h e r than the COOP model l a b o u r demand i n F i g u r e 3 due to a l a r g e r c o e f f i c i e n t on l a b o u r ( R e ) . When c o n t r a c t s a r e assumed t o be e f f i c i e n t , t h e e s t i m a t e d m a r g i n a l r e v e n u e p r o d u c t o f l a b o u r i s on average $1.50 per hour (measured i n 1971 d o l l a r s ) l e s s than t h e LDEM v a l u e . In the exogenous output e s t i m a t i o n , t h i s 123 F i g u r e 5 L a b o u r Demand C u r v e s and the C o n t r a c t C u r v e . Exogenous C a p i t a l E s t i m a t i o n . 1971 d o l l a r s per man-hour y y y / / / / / contract curve I 4 (labor .demand model) \ \ \ \ \ / l a b o r demand ( c o o p e r a t i v e m o d e l ) i i i i i i : : 1— 0 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 ' 4.0 Emp loymen t ( i n l O M ' s m a n - h o u r s ) 124 same d i f f e r e n c e i s $2.20 per h o u r r e f l e c t i n g t h e g r e a t e r s i m i l a r i t y be tween e f f i c i e n t and i n e f f i c i e n t b a r g a i n i n g model l a b o u r demands i n the exogenous c a p i t a l e s t i m a t i o n . The l a b o u r demand e l a s t i c i t i e s are .7708 f o r the LDEM m o d e l and .8535 f o r t h e COOP m o d e l . B o t h o f them a r e s l i g h t l y l o w e r t h a n t h e e l a s t i c i t i e s e s t i m a t e d under the assumpt ion o f exogenous output (.8462 f o r LDEM and .9876 f o r COOP) . These e s t i m a t e s s t i l l l i e below the ones found by M a r t i n e l l o (1984) f o r the IWA ( 1 . 5 ) and by D e r t o u z o s and P e n c a v e l (1981) f o r the ITU ( 1 . 2 3 ) . As f o r the exogenous o u t p u t e s t i m a t e s , I v e r i f y whether my s m a l l e r l a b o u r demand e l a s t i c i t i e s a r e due to d i f f e r e n t assumptions on the u n i o n ' s a b i l i t y to s e t the wage. F o r t h e two r e s u l t s m e n t i o n e d above , i t was assumed t h a t the u n i o n c o u l d u n i l a t e r a l l y choose t h e wage. I r e - e s t i m a t e d the exogenous c a p i t a l model w i t h ( l n d u / l n d f ) s e t a t z e r o . The r e s u l t i n g l a b o u r demand e l a s t i c i t i e s are 1.1644 f o r the COOP model and 0.778 f o r the LDEM m o d e l . L e t t i n g t h e u n i o n have a l l b a r g a i n i n g power does i n c r e a s e the l a b o u r demand e l a s t i c i t i e s e s p e c i a l l y f o r t h e e f f i c i e n t c o n t r a c t i n g m o d e l , h o w e v e r , t h e r e s u l t i n g e l a s t i c i t i e s a r e s t i l l s m a l l e r t h a n t h o s e r e p o r t e d by M a r t i n e l l o and Dertouzos and P e n c a v e l . 5 . 2 . 2 U n i o n P r e f e r e n c e s I n t h e p r e v i o u s d i s c u s s i o n , i t was s e e n t h a t t h e e s t i m a t e s o f t h e f i r m s ' t e c h n o l o g y were v e r y d i f f e r e n t 125 d e p e n d i n g on w h e t h e r o u t p u t o r c a p i t a l was t r e a t e d as e x o g e n o u s t o t h e b a r g a i n i n g p r o c e s s . T h i s i s c o n s i s t e n t w i t h M a r t i n e l l o ' s f i n d i n g s . 35 m t h a t s tudy however, the u n i o n u t i l i t y parameters were found to be v e r y s i m i l a r i n the two s c e n a r i o s . A l t h o u g h t h e r e are some s i m i l a r i t i e s i n my u t i l i t y parameter e s t i m a t e s w i t h t h e e x o g e n o u s o u t p u t e s t i m a t e s , I a l s o f i n d i m p o r t a n t d i f f e r e n c e s . As f o r the t e c h n o l o g y c o e f f i c i e n t s , I f i n d t h a t t h e u t i l i t y parameter e s t i m a t e s are v e r y s i m i l a r i n the COOP and LDEM mode l s , more so than i n the exogenous o u t p u t c a s e . The e l a s t i c i t y o f s u b s t i t u t i o n i n t h e e f f i c i e n t c o n t r a c t i n g model i s .8768, and f o r the LDEM mode l , i t i s .8561. The h y p o t h e s i s t h a t t h e e l a s t i c i t y o f s u b s t i t u t i o n e q u a l s 1 which c o u l d no t be r e j e c t e d i n the exogenous o u t p u t mode l , i s now r e j e c t e d a t t h e 1% l e v e l o f s i g n i f i c a n c e f o r b o t h b a r g a i n i n g mode l s . The weight on employment i n t h e u n i o n u t i l i t y f u n c t i o n i s now j u s t s l i g h t l y g r e a t e r t h a n t h e c o e f f i c i e n t on t h e wage t e r m . F o r t h e COOP m o d e l , t h e employment c o e f f i c i e n t i s .513 w i t h a c o r r e s p o n d i n g wage c o e f f i c i e n t o f .487 . F o r the LDEM mode l , these c o e f f i c i e n t s a r e .599 and .401 r e s p e c t i v e l y . (These s h o u l d be compared to employment c o e f f i c i e n t s o f .71 f o r the COOP and .85 f o r t h e LDEM models i n the exogenous output e s t i m a t i o n . ) The 3 5 M a r t i n e l l o (1984) assumed a l l i n p u t s and the output t o be endogenous i n h i s p r o f i t f u n c t i o n e s t i m a t i o n and he - assumed an exogenous output i n h i s c o s t f u n c t i o n e s t i m a t i o n . 126 h y p o t h e s i s o f e q u a l weights on employment and (W-W^) i s now a c c e p t e d a t the 5% l e v e l o f s i g n i f i c a n c e f o r b o t h b a r g a i n i n g mode l s . The m a r g i n a l r a t e o f s u b s t i t u t i o n between the number o f workers and wages above the a l t e r n a t i v e wage e x p r e s s e d i n p e r c e n t a g e terms and c a l c u l a t e d a t the mean o f the d a t a i s .15 f o r the COOP model and .20 f o r the LDEM mode l . As f o r the exogenous output e s t i m a t i o n , i t takes a l a r g e r i n c r e a s e i n the wage i n the LDEM model t o compensate the u n i o n f o r a 1% f a l l i n the number o f w o r k e r s . However, w i t h exogenous c a p i t a l , the d i f f e r e n c e i n the MRS's i n the two b a r g a i n i n g m o d e l i s v e r y s m a l l . F i n a l l y , r e n t m a x i m i z a t i o n (p=l and y=l) i s r e j e c t e d f o r b o t h the COOP and LDEM mode l s . T h i s was a l s o t r u e i n the exogenous output e s t i m a t i o n . 5 . 2 . 3 The C o n t r a c t Curve and t h e B a r g a i n i n g S e t s The c o n t r a c t c u r v e f o r the COOP model e v a l u a t e d a t the mean o f the d a t a has been p l o t t e d i n F i g u r e 5. I t i s much s t e e p e r t h a n t h e average c o n t r a c t c u r v e e s t i m a t e d under the a s s u m p t i o n o f exogenous o u t p u t . A l s o , f o r t h a t c a s e , the c o n t r a c t c u r v e a t t h e mean o f t h e d a t a was a g o o d r e p r e s e n t a t i o n o f the c o n t r a c t c u r v e s over the sample as the s l o p e s were p o s i t i v e and s m a l l a t a l l d a t a p o i n t s . When c a p i t a l i s t r e a t e d as e x o g e n o u s h o w e v e r , some o f t h e c o n t r a c t c u r v e s have l a r g e p o s i t i v e s l o p e s w h i l e s l o p e s are n e g a t i v e and l a r g e i n a b s o l u t e v a l u e a t o t h e r d a t a p o i n t s . 127 Over the sample , the s l o p e v a r i e s from -671 .8 f o r i n t e r i o r s a w m i l l s i n 1973 t o 106.9 f o r s h i n g l e m i l l s i n 1968. In g e n e r a l , the c o n t r a c t c u r v e i s more l i k e l y t o be b a c k w a r d b e n d i n g i f the MRS i s s m a l l . 3 6 W i t h an MRS e q u a l t o z e r o , the c o n t r a c t c u r v e would be i d e n t i c a l t o the l a b o u r demand c u r v e . A l s o , c e t e r i s p a r i b u s , the c o n t r a c t c u r v e w i l l be f l a t t e r the s m a l l e r i s the c o e f f i c i e n t on l a b o u r ( R e ) . I n the exogenous output e s t i m a t i o n , t h e p r e d i c t e d wage was l e s s t h a n the a l t e r n a t i v e wage f o r a few o f t h e d a t a p o i n t s c o r r e s p o n d i n g t o t h e r e c e s s i o n y e a r s o f t h e e a r l y ' 8 0 ' s . T h i s i s a l s o t h e c a s e u n d e r t h e a s s u m p t i o n o f exogenous c a p i t a l . S p e c i f i c a l l y , the p r e d i c t e d wage i s l e s s than the a l t e r n a t i v e wage f o r i n t e r i o r s a w m i l l s i n 1980 , 1981 and 1983 f o r b o t h b a r g a i n i n g mode l s . I g n o r i n g these o b s e r v a t i o n s , the b a r g a i n i n g s e t s a r e concave everywhere f o r b o t h the COOP and the LDEM models and , f o r the COOP mode l , the i s o - p r o f i t c u r v e s are everywhere l e s s c o n v e x t h a n t h e u n i o n i n d i f f e r e n c e c u r v e s . T h i s ensures t h a t second o r d e r c o n d i t i o n s t o the m a x i m i z a t i o n prob lem d e s c r i b i n g the N a s h b a r g a i n i n g s o l u t i o n are s a t i s f i e d and t h a t the e q u i l i b r i u m i s u n i q u e . J 6 M o r e s p e c i f i c a l l y , i n t h i s mode l , the c o n t r a c t c u r v e w i l l have a n e g a t i v e s l o p e i f 128 5 . 2 . 4 B a r g a i n i n g P o w e r s 3 7 C o n t r a r y t o t h e t e c h n o l o g y a n d u n i o n u t i l i t y p a r a m e t e r s , t h e c o e f f i c i e n t s o n t h e s t r i k e c o s t s d e t e r m i n a n t s a r e v e r y d i f f e r e n t i n t h e two b a r g a i n i n g m o d e l s . T h e r e a r e m o r e s i m i l a r i t i e s b e t w e e n t h e c o e f f i c i e n t s o f t h e same b a r g a i n i n g model e s t i m a t e d under d i f f e r e n t t e c h n o l o g i c a l a s sumpt ions . F o r t h e COOP m o d e l , t h e r e s u l t s c o n c e r n i n g the f i r m s t r i k e c o s t s a r e t h e same as f o r t h e e x o g e n o u s o u t p u t e s t i m a t i o n e x c e p t t h a t the i n v e n t o r y v a r i a b l e now has the o p p o s i t e s i g n i m p l y i n g t h a t an i n c r e a s e i n average i n v e n t o r y h o l d i n g s w i l l i n c r e a s e t h e f i r m ' s r e l a t i v e s t r i k e c o s t s . The r e s u l t s c o n c e r n i n g the u n i o n ' s s t r i k e c o s t s d e t e r m i n a n t s a r e a l s o q u a l i t a t i v e l y the same as i n the exogenous output e s t i m a t i o n w i t h the e x c e p t i o n o f the demographics v a r i a b l e c o e f f i c i e n t w h i c h has a p e r v e r s e but i n s i g n i f i c a n t s i g n . The c o e f f i c i e n t s i n the LDEM model a r e more d i f f e r e n t from t h e i r c o u n t e r p a r t s i n t h e e x o g e n o u s o u t p u t e s t i m a t i o n ; h o w e v e r , g i v e n t h e l a r g e s t a n d a r d e r r o r s o n t h e s e c o e f f i c i e n t s i n both e s t i m a t i o n s , t h e i r v a r i a b i l i t y i s not so s u r p r i s i n g . The average v a l u e o f the term measur ing r e l a t i v e s t r i k e c o s t s ( l n d u / l n d f ) i s .8949 f o r the LDEM model and 2.1061 f o r t h e COOP mode l . As was the case f o r the exogenous output 3 7 S e e f o o t n o t e 33. 129 e s t i m a t i o n , t h e u n i o n h a s r e l a t i v e l y l e s s p o w e r when c o n t r a c t s a r e a s s u m e d t o be e f f i c i e n t . T e s t s o f t h e m o n o p o l y m o d e l ( l n d u / l n d f ) = 0 a n d t h e s y m m e t r i c N a s h b a r g a i n i n g s o l u t i o n ( l n d u / l n d f ) =1 a r e performed and these h y p o t h e s i s are r e j e c t e d f o r both b a r g a i n i n g mode l s . The exogenous c a p i t a l e s t i m a t i o n y i e l d s l a r g e r d i s c o u n t f a c t o r s f o r the f i r m r e l a t i v e to the u n i o n . The weights on the u t i l i t y f u n c t i o n s o f the f i r m and the u n i o n i n the Nash b a r g a i n i n g s o l u t i o n (as d e s c r i b e d i n s e c t i o n 5.1) were a l s o c a l c u l a t e d f o r t h e e x o g e n o u s c a p i t a l m o d e l . They a r e p l o t t e d f o r b o t h b a r g a i n i n g models i n F i g u r e 6. D e s p i t e the d i f f e r e n t c o e f f i c i e n t s on the exogenous v a r i a b l e s a f f e c t i n g t h e s t r i k e c o s t s , t h e p r o f i l e o f t h e u n i o n ' s r e l a t i v e b a r g a i n i n g power over t ime i s v e r y s i m i l a r i n the COOP and LDEM mode l . The u n i o n b a r g a i n i n g power i n the l a b o u r demand model i s everywhere l a r g e r than the COOP model e s t i m a t e , the d i f f e r e n c e a v e r a g i n g . 2 . I n b o t h c a s e s t h e u n i o n power r i s e s s l o w l y i n t h e l a t e 1960's and 1970's f o l l o w e d by a r a p i d i n c r e a s e i n t h e e a r l y 1 9 8 0 ' s . T h e u n i o n a c h i e v e s a lmost complete c o n t r o l over wages i n 1984 a c c o r d i n g to the LDEM model w h i l e the r e l a t i v e u n i o n power a t i t s maximum i s c l o s e r to 2/3 i n the COOP mode l . The average u n i o n u t i l i t y weight over the sample i s .5277 f o r the LDEM model and .3220 f o r the COOP mode l . These s h o u l d be compared t o .8913 and .8375 r e s p e c t i v e l y f o r the exogenous output e s t i m a t i o n . 130 F i g u r e 6 U n i o n B a r g a i n i n g Power. Exogenous C a p i t a l E s t i m a t i o n . a. Cooperative Model coastal sawmills shingle m i l l s plywood and veneer m i l l s 1 1 1 1 1 1364.0 1966.0 1968.0 1970.0 1972.0 ^ 9 7 4 . 0 —I 1 1 1 1 1976.0 1978.0 1960.0 1982.0 1984.0 a _•-u b. Labor Demand Model coastal sawmills i n t e r i o r sawmills plywood and veneer m i l l s 1970.0 1972.0 1974.0 TIME 131 I t i s i n t e r e s t i n g to compare the b a r g a i n i n g powers o f t h e u n i o n and f i r m as measured above w i t h the d i v i s i o n o f r e n t s be tween t h e two o f t h e m . i n t h e exogenous output e s t i m a t i o n , i t was seen t h a t t h e b a r g a i n i n g power o f t h e u n i o n was u n d e r e s t i m a t e d when measured by the p r o p o r t i o n o f r e n t s i t succeeded to c a p t u r e . T h i s i s s t i l l t r u e f o r the e s t i m a t i o n under exogenous c a p i t a l . The p r o p o r t i o n o f r e n t s c a p t u r e d by the f i r m i s g i v e n i n T a b l e V I I f o r the e f f i c i e n t c o n t r a c t m o d e l and i n T a b l e V I I I f o r t h e l a b o u r demand c u r v e . On a v e r a g e , f i r m s c a p t u r e d 77% o f r e n t s i n the COOP model and 83% i n the LDEM model . The b a r g a i n i n g power o f t h e f i r m as measured by the weight on i t s u t i l i t y i n the Nash b a r g a i n i n g s o l u t i o n i s 68% i n the COOP model and 47% i n the LDEM mode l . The g e n t l e r i s e i n u n i o n b a r g a i n i n g power o v e r t h e 1 9 7 0 ' s i s n o t e v i d e n t i n T a b l e s V I I and V I I I . H o w e v e r , w i t h t h e e x c e p t i o n o f i n t e r i o r s a w m i l l s , t h e p r o p o r t i o n o f r e n t s c a p t u r e d by the f i r m f e l l s u b s t a n t i a l l y d u r i n g t h e r e c e s s i o n y e a r s o f t h e 1 9 8 0 ' s and t h i s i s c o n s i s t e n t w i t h the r a p i d i n c r e a s e i n u n i o n b a r g a i n i n g power d u r i n g those y e a r s (see F i g u r e 6 ) . 5 . 2 . 5 Comparing t h e COOP and LDEM Models As was the case f o r the exogenous o u t p u t e s t i m a t i o n , the e f f i c i e n t c o n t r a c t model performs b e t t e r than the LDEM model i n the sense t h a t i t g e n e r a t e s a h i g h e r l i k e l i h o o d v a l u e . When o u t p u t i s no l o n g e r u s e d as an e x p l a n a t o r y 132 T a b l e V I I P r o p o r t i o n o f T o t a l Rents C a p t u r e d by t h e F i r m C o o p e r a t i v e Model w i t h Exogenous C a p i t a l Year C o a s t a l I n t e r i o r S h i n g l e Plywood Sawmi l l s Sawmi l l s M i l l s Veneer 1964 .74880 .82466 .78684 .65592 1965 .80234 .88400 .82541 .74559 1966 .81928 .89641 .83191 .76808 1967 .81880 .88980 .81860 .77545 1968 .80743 .87658 .80092 .75927 1969 .79035 .84419 .77868 .77011 1970 .78127 .87310 .75429 .77290 1971 .80159 .88317 .80895 .80389 1972 .83279 .88068 .81736 .82067 1973 .83166 .86472 .80659 .81259 1974 .82508 .87030 .81825 .82484 1975 .83462 .90171 .81784 .84606 1976 .78420 .86755 .76305 .80948 1977 .80739 .86251 .78170 .79832 1978 .79446 .85348 .77085 .80681 1979 .78648 .83982 .75432 .77218 1980 .73643 .91261 .78749 .78223 1981 .72202 .98679 .77092 .74739 1982 .68826 .90225 .72923 .66790 1983 .60260 1.01554 .62893 .65400 Average .78079 .8865 .78411 .76968 O v e r a l l Average = .76692 133 T a b l e V I I I P r o p o r t i o n o f T o t a l Rents C a p t u r e d by t h e F i r m L a b o u r Demand Model w i t h Exogenous C a p i t a l Year C o a s t a l I n t e r i o r S h i n g l e Plywood Sawmi l l s Sawmi l l s M i l l s Veneer 1964 .83630 .86966 .86711 .79415 1965 .85970 .89976 .91029 .82874 1966 .87056 .90588 .88378 .84198 1967 .87158 .89942 .88096 .85160 1968 .87050 .89194 .87339 .85086 1969 .86362 .86426 .85733 .86414 1970 .85637 .88969 .85336 .86553 1971 .86852 .90226 .87547 .88099 1972 .87147 .88892 .86671 .87625 1973 .86502 .87651 .85630 .87016 1974 .86398 .88497 .86081 .87816 1975 .87227 .90417 .87496 .88412 1976 .85015 .87767 .83377 .86731 1977 .85565 .86819 .83897 .86286 1978 .84673 .85904 .83387 .85828 1979 .84156 .85597 .82865 .85061 1980 .84015 1.10236 .85337 .86201 1981 .84198 1.10372 .85113 .85419 1982 .82862 .94375 .83383 .83032 1983 .81952 1.07388 .80887 .84253 Average .85471 .91810 .85711 .85574 O v e r a l l Average = .82992 134 v a r i a b l e , the p r e d i c t i o n o f employment worsens c o n s i d e r a b l y . A l t h o u g h t h e r e i s s t i l l some i n d i c a t i o n t h a t the LDEM model i s b e t t e r a t p r e d i c t i n g the b e h a v i o r i n wages and employment d u r i n g the 1980's r e c e s s i o n , t h e e v i d e n c e i s no t as s t r o n g as i n the exogenous output e s t i m a t i o n . 5.3 Summary o f R e s u l t s W i t h one e x c e p t i o n , the t e c h n o l o g y c o e f f i c i e n t s i n a l l 4 e s t i m a t i o n models were s i g n i f i c a n t and had the p r e d i c t e d s i g n . The e x c e p t i o n i s the c o e f f i c i e n t on l a b o u r which was v e r y s m a l l w i t h a l a r g e s t a n d a r d e r r o r i n the e s t i m a t i o n o f t h e COOP m o d e l u n d e r t h e a s s u m p t i o n o f exogenous o u t p u t . U s i n g output as an e x p l a n a t o r y v a r i a b l e d i d i n c r e a s e t h e p r e d i c t i v e powers o f the model e s p e c i a l l y w i t h r e s p e c t to l a b o u r ; however, i t a l s o y i e l d e d i m p l a u s i b l y low v a l u e s f o r t h e l a b o u r c o e f f i c i e n t s . The r e s u l t was the v e r y s m a l l l a b o u r c o s t shares r e p o r t e d i n s e c t i o n 5 . 1 . 1 . T h e s m a l l m a r g i n a l r e v e n u e p r o d u c t o f l a b o u r was accompanied by a l a r g e m a r g i n a l r a t e o f s u b s t i t u t i o n f o r the u n i o n compared t o t h e exogenous c a p i t a l e s t i m a t e s . T h i s y i e l d e d a f l a t c o n t r a c t c u r v e w i t h an average e l a s t i c i t y o f l e s s than 5%. T h i s c o n t r a c t c u r v e e v a l u a t e d a t the mean o f the d a t a i s drawn i n F i g u r e 3 and i t s h o u l d be compared to i t s c o u n t e r p a r t i n the endogenous o u t p u t - exogenous c a p i t a l e s t i m a t i o n which i s i l l u s t r a t e d i n F i g u r e 5. 135 T h e c l o s e n e s s and s i m i l a r i t y o f t h e l a b o u r demand c u r v e s i n F i g u r e 5 i s an i n d i c a t i o n o f the s i m i l a r i t y i n the t e c h n o l o g i c a l parameters i n the two b a r g a i n i n g models when o u t p u t i s t r e a t e d as endogenous. In g e n e r a l , the e s t i m a t e d p a r a m e t e r s h a v e been more s e n s i t i v e to the i m p o s i t i o n o f e x o g e n o u s o u t p u t t h a n t o t h e i m p o s i t i o n o f a d i f f e r e n t b a r g a i n i n g f r a m e w o r k . T h i s i s a l s o t r u e o f t h e u n i o n u t i l i t y p a r a m e t e r s . Many o f t h e q u a l i t a t i v e r e s u l t s c o n c e r n i n g the u n i o n u t i l i t y f u n c t i o n were c o n s i s t e n t a c r o s s m o d e l s . I n a l l c a s e s , the u n i o n c a r e s about b o t h wages and employment w i t h a l a r g e r weight b e i n g p l a c e d on employment. The d i f f e r e n c e be tween w e i g h t s p l a c e d on employment and wages i s q u i t e l a r g e and s i g n i f i c a n t i n the exogenous output e s t i m a t i o n but when o u t p u t i s e n d o g e n o u s a n d c a p i t a l e x o g e n o u s , t h e e q u a l i t y o f t h e w e i g h t s c a n n o t be r e j e c t e d f o r e i t h e r b a r g a i n i n g m o d e l s . I n a l l m o d e l s , t h e u n i o n has convex i n d i f f e r e n c e c u r v e s w i t h t h e e l a s t i c i t y o f s u b s t i t u t i o n r a n g i n g f r o m .86 t o 1 . 0 5 . When o u t p u t i s t r e a t e d as exogenous, the h y p o t h e s i s o f a C o b b - D o u g l a s s p e c i f i c a t i o n cannot be r e j e c t e d . Rent m a x i m i z a t i o n i s always r e j e c t e d . The d a t a s u p p o r t s the b a r g a i n i n g m o d e l i n t h e s e n s e t h a t the i n t r o d u c t i o n o f the b a r g a i n i n g v a r i a b l e s improved t h e l i k e l i h o o d ; i . e . , ( l n d u / l n d f ) = 0 i s r e j e c t e d i n a l l m o d e l s . A l s o , i n t h e e f f i c i e n t c o n t r a c t mode l , w i t h few e x c e p t i o n s , the c o n t r a c t c u r v e was w e l l - d e f i n e d as the l o c u s 136 o f t a n g e n c y p o i n t s b e t w e e n t h e i s o - p r o f i t a n d u n i o n i n d i f f e r e n c e c u r v e s and the b a r g a i n i n g f r o n t i e r i n the space o f u t i l i t i e s was c o n c a v e . The l a t t e r c o n d i t i o n e n s u r e s un iquenes s o f the e q u i l i b r i u m . The e x c e p t i o n s a l l i n v o l v e d o b s e r v a t i o n s i n the 1980's and they were i n c o n s i s t e n t w i t h t h e m a i n t a i n e d a s s u m p t i o n o f a zero t h r e a t p o i n t f o r the u n i o n ( i . e . the p r e d i c t e d wage was l e s s than the a l t e r n a t i v e w a g e ) . S i m i l a r r e s u l t s were found i n the LDEM model w i t h endogenous o u t p u t b u t w i t h exogenous o u t p u t , t h i s m o d e l f r e q u e n t l y y i e l d e d n e g a t i v e p r e d i c t e d p r o f i t s due to the low c o e f f i c i e n t on l a b o u r . The p r o p o r t i o n o f r e n t s c a p t u r e d by the f i r m , a measure which i s o f t e n used as an i n d i c a t o r o f the f i r m b a r g a i n i n g power o v e r e s t i m a t e d t h e b a r g a i n i n g power o f the f i r m s as d e f i n e d by the weight on the p r o f i t f u n c t i o n i n t h e N a s h b a r g a i n i n g s o l u t i o n . A l t h o u g h the r a p i d i n c r e a s e i n the u n i o n b a r g a i n i n g power d u r i n g t h e r e c e s s i o n y e a r s o f t h e e a r l y 1 9 8 0 ' s was r e f l e c t e d i n t h e p r o p o r t i o n o f r e n t s c a p t u r e d by t h e f i r m ( i n t e r i o r s a w m i l l s e x c e p t e d ) , i n g e n e r a l , no monotone r e l a t i o n s h i p between the two measures was d e t e c t e d . The exogenous output e s t i m a t i o n y i e l d e d l a r g e e s t i m a t e s f o r t h e u n i o n b a r g a i n i n g power and a downward t r e n d was i n d i c a t e d over the 1970 ' s . The endogenous o u t p u t , e x o g e n o u s c a p i t a l e s t i m a t i o n y i e l d e d m e a s u r e s o f u n i o n b a r g a i n i n g power c l o s e r to t h e f i r m s ' power a l t h o u g h t h e h y p o t h e s i s o f e q u a l b a r g a i n i n g powers was r e j e c t e d f o r both 137 b a r g a i n i n g m o d e l s . T h e r e was a l s o some e v i d e n c e o f an upward t r e n d d u r i n g the 1970 ' s . I t i s worth n o t i n g t h a t a l t h o u g h the magnitudes o f the b a r g a i n i n g powers and t h e i r t ime p r o f i l e s o v e r t h e 1 9 6 0 ' s a n d 1 9 7 0 ' s v a r i e d a c r o s s m o d e l s , t h e i n d i c a t i o n o f an i n c r e a s e i n u n i o n power d u r i n g the 1980's r e c e s s i o n i s found i n a l l c a s e s . One p o s s i b l e reason f o r t h i s r e s u l t i s t h a t the s e v e r e r e c e s s i o n o f the e a r l y 1980's p l a c e d f i r m s i n a p r e c a r i o u s p o s i t i o n f i n a n c i a l l y , and g r e a t l y i n c r e a s e d the p r o b a b i l i t y o f b a n k r u p t c y . Another p o s s i b i l i t y i s t h a t the f i r m s and the u n i o n are r i s k s h a r i n g . I f the s e v e r i t y o f the 1980's r e c e s s i o n was u n a n t i c i p a t e d and i f the u n i o n i s r e l a t i v e l y more r i s k a v e r s e , r i s k s h a r i n g would imply a worsen ing o f the f i r m s ' b a r g a i n i n g p o s i t i o n r e l a t i v e t o the u n i o n . A m o d e l where u n c e r t a i n t y and r i s k a v e r s i o n are e x p l i c i t l y f o r m u l a t e d c o u l d be u s e d t o t e s t t h i s s e c o n d h y p o t h e s i s . T h e c o e f f i c i e n t s on the exogenous v a r i a b l e s a f f e c t i n g the r e l a t i v e s t r i k e c o s t s (and hence the b a r g a i n i n g powers) are seen t o v a r y a c r o s s models and they o f t e n have v e r y h i g h s t a n d a r d e r r o r s . In the e f f i c i e n t c o n t r a c t i n g m o d e l , t h e i n t e r e s t r a t e has a s i g n i f i c a n t p o s i t i v e e f f e c t on t h e r e l a t i v e s t r i k e c o s t s o f the f i r m . The same i s t r u e o f the c a p i t a l u t i l i z a t i o n r a t i o . The e f f e c t o f i n v e n t o r y b u i l d - u p depends on the t e c h n o l o g y a s sumpt ions . Note t h a t a l t h o u g h a n e g a t i v e s i g n on the i n v e n t o r y c o e f f i c i e n t was p r e d i c t e d , a 138 p o s i t i v e r e l a t i o n s h i p i s a l s o p l a u s i b l e i n t h e c a s e o f u n a n t i c i p a t e d i n c r e a s e s i n i n v e n t o r y h o l d i n g s . I f they are u n a n t i c i p a t e d , changes i n i n v e n t o r i e s can i n d i c a t e f i n a n c i a l h a r d s h i p f o r t h e f i r m s r a t h e r t h a n a s t r o n g (low s t r i k e c o s t ) b a r g a i n i n g p o s i t i o n . I n t h e l a b o u r demand m o d e l t h e c o e f f i c i e n t s o f the s t r i k e c o s t v a r i a b l e s a r e h i g h l y v a r i a b l e w i t h l a r g e s t a n d a r d e r r o r s . One problem w i t h these v a r i a b l e s i s the l a r g e amount o f m u l t i c o l l i n e a r i t y e s p e c i a l l y among t h e d e t e r m i n a n t s o f t h e w o r k e r s ' s t r i k e c o s t s . Some o t h e r v a r i a b l e s were used but they d i d not c o n t r i b u t e a d d i t i o n a l i n f o r m a t i o n . A l s o , a t t e m p t s were made t o e s t i m a t e t h e d i s c o u n t f a c t o r s o f the f i r m s and w o r k e r s s e p a r a t e l y b u t none were s u c c e s s f u l . T h r o u g h o u t t h i s s t u d y , the e f f i c i e n t model performed b e t t e r t h a n t h e l a b o u r demand m o d e l i n t h e s e n s e o f g e n e r a t i n g a l a r g e r l i k e l i h o o d v a l u e . F i n a l l y t h e r e was some i n d i c a t i o n e s p e c i a l l y i n t h e e x o g e n o u s o u t p u t e s t i m a t i o n t h a t a l t h o u g h t h e COOP model performed b e t t e r o v e r a l l , the l a b o u r demand m o d e l was a b e t t e r p r e d i c t o r d u r i n g the r e c e s s i o n y e a r s o f the 1980 ' s . 139 C h a p t e r 6 C o n c l u s i o n In t h i s s t u d y , a v e r s i o n o f the R u b i n s t e i n b a r g a i n i n g m o d e l i s u s e d t o s t u d y u n i o n - f i r m n e g o t i a t i o n s . S p e c i f i c a l l y , t h e e q u i l i b r i u m o f t h e game i s u s e d t o g e n e r a t e wage and employment e s t i m a t i n g e q u a t i o n s . One o f the c h a r a c t e r i s t i c s o f the r e s u l t i n g model i s t h a t the wage and employment c o n t r a c t s are a f f e c t e d by the r e l a t i v e s t r i k e c o s t s o f the n e g o t i a t i n g p a r t i e s e v e n i n t h e a b s e n c e o f s t r i k e s . The d a t a i n v o l v e s the B . C . wood p r o d u c t s i n d u s t r y and the IWA, a p o w e r f u l u n i o n b e l i e v e d t o have been s u c c e s s f u l a t c a p t u r i n g r e n t s . The d a t a i n c l u d e s i n p u t and o u t p u t q u a n t i t i e s and p r i c e s and e q u a t i o n s r e p r e s e n t i n g i n p u t demands and output s u p p l y are e s t i m a t e d s i m u l t a n e o u s l y w i t h t h e n e g o t i a t e d wage and employment e q u a t i o n s . I n t h e l i t e r a t u r e on wage and employment d e t e r m i n a t i o n i n u n i o n i z e d s e c t o r s , two p o l a r cases have been assumed: i n one i n s t a n c e t h e f i r m c a n u n i l a t e r a l l y c h o o s e e m p l o y m e n t and t h e r e s u l t i n g c o n t r a c t i s on the l a b o u r demand c u r v e , i n t h e s e c o n d c a s e the l e v e l o f employment i s n e g o t i a t e d and the f r o n t i e r o f the b a r g a i n i n g s e t i s the c o n t r a c t c u r v e . Both s c e n a r i o s are mode l l ed and e s t i m a t e d i n t h i s p a p e r . A l s o , each b a r g a i n i n g framework i s e s t i m a t e d u n d e r two s e t s o f t e c h n o l o g i c a l a s s u m p t i o n s . I n one c a s e , a l l i n p u t s are 140 chosen o p t i m a l l y as f u n c t i o n s o f the l a b o u r c o n t r a c t w h i l e the l e v e l o f o u t p u t i s exogenous t o the b a r g a i n i n g p r o c e s s . I n t h e second c a s e , o u t p u t i s endogenous and c a p i t a l i s t r e a t e d as f i x e d d u r i n g n e g o t i a t i o n s . S i n c e none o f the p r e v i o u s e m p i r i c a l u n i o n c o n t r a c t s t u d i e s had i n c l u d e d a b a r g a i n i n g game, the e m p i r i c a l model e s t i m a t e d here i s q u i t e n o v e l and i t i s r e a s s u r i n g t h a t the e s t i m a t e d t e c h n o l o g y c o e f f i c i e n t s a n d u n i o n u t i l i t y p a r a m e t e r s a r e g e n e r a l l y r e a s o n a b l e a n d c o m p a r a b l e t o p r e v i o u s e s t i m a t e s . F o r example, i t i s a s t a n d a r d r e s u l t i n t h i s l i t e r a t u r e t h a t the u n i o n c a r e s about b o t h wages and employment but w i t h a l a r g e r weight on employment. The same t h i n g i s found i n the s t u d y . The u n i o n i n d i f f e r e n c e curves a r e convex w i t h e s t i m a t e s o f the e l a s t i c i t y o f s u b s t i t u t i o n r a n g i n g from .86 t o 1 .05 . In a l l mode l s , r e n t m a x i m i z a t i o n i s r e j e c t e d as an a p p r o p r i a t e r e p r e s e n t a t i o n o f u n i o n b e h a v i o u r . The new r e s u l t s c o n c e r n the b a r g a i n i n g powers o f the f i r m s and the u n i o n measured as f u n c t i o n s o f t h e i r r e l a t i v e s t r i k e c o s t s . In a l l mode l s , the term r e p r e s e n t i n g s t r i k e c o s t s s i g n i f i c a n t l y a f f e c t s t h e e s t i m a t e s . H o w e v e r , i n d i v i d u a l c o e f f i c i e n t s o n s t r i k e c o s t v a r i a b l e s a r e s e n s i t i v e t o b o t h t h e b a r g a i n i n g f r a m e w o r k a n d t h e t e c h n o l o g y a s s u m p t i o n s . I n a l l c a s e s t h e h y p o t h e s i s o f e q u a l b a r g a i n i n g powers ( the Nash b a r g a i n i n g s o l u t i o n ) i s r e j e c t e d as w e l l as the monopoly model o f u n i o n s ( i n which 141 the u n i o n has complete b a r g a i n i n g p o w e r ) . A l s o , r e s u l t s s u g g e s t t h a t t h e 19 80 ' s r e c e s s i o n c a u s e d a r a p i d d e t e r i o r a t i o n i n t h e f i r m s ' r e l a t i v e b a r g a i n i n g p o w e r . A c c o r d i n g t o my e s t i m a t e , the e f f i c i e n t c o n t r a c t i n g model per forms b e t t e r than the l a b o u r demand model i n which l a b o u r i s c h o s e n by t h e f i r m . A g a i n , t h i s i s c o n s i s t e n t w i t h p r e v i o u s s t u d i e s . However, the parameter e s t i m a t e s seem to be more s e n s i t i v e to the t e c h n o l o g i c a l assumptions than to the b a r g a i n i n g framework. T h i s has s e r i o u s i m p l i c a t i o n s f o r t h e i n t e r p r e t a t i o n o f t h e r e s u l t s o f w a g e - e m p l o y m e n t d e t e r m i n a t i o n s t u d i e s i n w h i c h t h e t e c h n o l o g y i s n o t m o d e l l e d r i g o r o u s l y . F i n a l l y , a l t h o u g h t h e c o o p e r a t i v e model p e r f o r m s b e t t e r o v e r a l l , t h e r e i s some i n d i c a t i o n ( e s p e c i a l l y i n t h e e x o g e n o u s o u t p u t e s t i m a t i o n ) t h a t the l a b o u r demand m o d e l i s b e t t e r a t p r e d i c t i n g wages a n d employment d u r i n g the r e c e s s i o n y e a r s o f the e a r l y 1980 ' s . E x t e n s i o n s t o t h i s s t u d y a r e p o s s i b l e i n s e v e r a l d i f f e r e n t d i r e c t i o n s . S i n c e t h i s was a f i r s t at tempt a t the a p p l i c a t i o n o f n o n c o o p e r a t i v e b a r g a i n i n g models to e m p i r i c a l s t u d i e s o f wage and employment c o n t r a c t s , the game was kept v e r y s i m p l e a t t h e c o s t o f r e s t r i c t i v e a s s u m p t i o n s e s p e c i a l l y c o n c e r n i n g t h e i n f o r m a t i o n s t r u c t u r e . I n p a r t i c u l a r , the assumpt ion o f symmetric i n f o r m a t i o n c o u l d be r e l a x e d . A l s o , u n c e r t a i n t y and b e h a v i o u r towards r i s k c o u l d be e x p l i c i t l y f o r m u l a t e d . T h i s would a l l o w f o r r i s k s h a r i n g and s t r i k e s as e q u i l i b r i u m outcomes. S e c o n d l y , the a p p l i c a t i o n o f t h i s p a r t i c u l a r game has emphasized the need f o r b e t t e r m o d e l l i n g and m e a s u r i n g o f s t r i k e c o s t s f o r both u n i o n s and f i r m s . In p a r t i c u l a r , I b e l i e v e t h a t t h r o u g h the m o d e l l i n g o f s t r i k e c o s t s , i t w i l l be p o s s i b l e t o d i s c r i m i n a t e e m p i r i c a l l y between d i f f e r e n t v e r s i o n s o f t h e R u b i n s t e i n b a r g a i n i n g game and p o s s i b l y o t h e r t y p e s o f b a r g a i n i n g games as w e l l . T h i r d l y , t h i s s tudy s u f f e r s from p r o b l e m s w h i c h have b e e n c h a r a c t e r i s t i c o f t h e e m p i r i c a l wage -employment d e t e r m i n a t i o n l i t e r a t u r e . In p a r t i c u l a r , d a t a i s a v a i l a b l e on wages and employment o n l y , and o t h e r d imens ions o f the c o n t r a c t s s u c h as f r i n g e b e n e f i t s a r e n o t t a k e n i n t o a c c o u n t . A l s o , t h i s s t u d y does n o t i n c l u d e a g e n e r a l b a r g a i n i n g framework n e s t i n g the two p o l a r cases o f l a b o u r demand models and e f f i c i e n t c o n t r a c t i n g mode l s . 143 B i b l i o g r a p h y Abowd, J . M . (1987) , " C o l l e c t i v e B a r g a i n i n g and the D i v i s i o n o f t h e V a l u e o f t h e E n t e r p r i s e , " NBER Working Paper No .2137 . A l l e n , R . C . ( 1 9 8 5 ) , " T r a d e Unions and the B . C . Economy," B . C . E c o n o m i c P o l i c y I n s t i t u t e P a p e r N o . P - 8 5 - 0 4 , D e p a r t m e n t o f E c o n o m i c s , U n i v e r s i t y o f B r i t i s h C o l u m b i a , V a n c o u v e r , B . C . A l l e n , R . C . and W . E . Diewert (1981) , " D i r e c t V e r s u s I m p l i c i t S u p e r l a t i v e I n d e x Number F o r m u l a e , " The R e v i e w o f Economics and S t a t i s t i c s , V o l . 6 3 , N o . 3 . A s h e n f e l t e r , 0 . and G . E . Johnson (1969) , " B a r g a i n i n g T h e o r y , T r a d e U n i o n s , and I n d u s t r i a l S t r i k e A c t i v i t y , " Amer ican Economic Review, V o l . 5 9 , N o . l . A z a r i a d i s , C . ( 1 9 8 1 ) , " I m p l i c i t C o n t r a c t s and R e l a t e d T h e o r i e s : A S u r v e y , " i n Z . H o r n s t e i n e t . a l . ( e d . ) , The Economics o f the Labour M a r k e t , London , HMSO. B i n m o r e , K . ( 1 9 8 7 a ) , "Nash B a r g a i n i n g T h e o r y I , " i n K . B i n m o r e a n d P . D a s g u p t a ( e d s . ) , The E c o n o m i c s o f B a r g a i n i n g , B a s i l B l a c k w e l l , New Y o r k . B i n m o r e , K . ( 1 9 8 7 b ) , "Nash B a r g a i n i n g T h e o r y I I , " i n K. B i n m o r e a n d P . D a s g u p t a ( e d s . ) , The E c o n o m i c s o f B a r g a i n i n g , B a s i l B l a c k w e l l , New Y o r k . B i n m o r e , K . ( 1 9 8 7 c ) , " P e r f e c t E q u i l i b r i a i n B a r g a i n i n g M o d e l s , " i n K . B i n m o r e and P . D a s g u p t a ( e d s . ) . The Eonomics o f B a r g a i n i n g , B a s i l B l a c k w e l l , New Y o r k . B l a i r , D . H . a n d D . L . C r a w f o r d ( 1 9 8 4 ) , " L a b o r U n i o n O b j e c t i v e s a n d C o l l e c t i v e B a r g a i n i n g , " Q u a r t e r l y J o u r n a l o f Economics , V o l . 9 9 , N o . 3 . B r o w n , J . N . a n d 0 . A s h e n f e l t e r , ( 1 9 8 6 ) , " T e s t i n g t h e E f f i c i e n c y o f E m p l o y m e n t C o n t r a c t s , " J o u r n a l o f P o l i t i c a l Economy, V o l . 9 4 , N o . 3 . C a r d , D . ( 1 9 8 6 ) , " E f f i c i e n t C o n t r a c t s w i t h C o s t l y A d j u s t m e n t : S h o r t - R u n Employment D e t e r m i n a t i o n f o r A i r l i n e M e c h a n i c s , " The A m e r i c a n E c o n o m i c R e v i e w , V o l . 7 6 , N o . 5 . 144 C a r r u t h , A . A . and A . J . O s w a l d ( 1 9 8 3 ) , " M i n e r ' s Wages i n Pos t -War B r i t a i n : An A p p l i c a t i o n o f A Model o f Trade U n i o n B e h a v i o r , " The Economic J o u r n a l , V o l . 9 5 , No .380 . C h a t t e r j e e , K . and W. Samuelson (1983) , " B a r g a i n i n g U n d e r Incomple te I n f o r m a t i o n " , O p e r a t i o n s R e s e a r c h , V o l . 3 1 . C o p i t h o r n e , L . ( 1 9 7 9 ) , N a t u r a l R e s o u r c e s and R e g i o n a l D i s p a r i t i e s , Economic C o u n c i l o f Canada , Ot tawa. C o u r s e y , D . ( 1 9 8 2 ) , " B i l a t e r a l B a r g a i n i n g , P a r e t o O p t i o n a l i t y , and the E m p i r i c a l Frequency o f I m p a s s e , " J o u r n a l o f Economic B e h a v i o r and O r g a n i z a t i o n , V o l . 3 . C r a i g , A . (1986 ) , The S y s t e m o f I n d u s t r i a l R e l a t i o n s i n C a n a d a , 2 n d e d i t i o n , P r e n t i c e - H a l l , C a n a d a , S c a r b o r o u g h , O n t a r i o . Cramton , D . C . (1984a) , The R o l e o f Time and I n f o r m a t i o n i n B a r g a i n i n g , P h . D . T h e s i s , S t a n f o r d U n i v e r s i t y . C r a m t o n , D . C . ( 1 9 8 4 b ) , " B a r g a i n i n g w i t h i n c o m p l e t e I n f o r m a t i o n : An I n f i n i t e - H o r i z o n w i t h T w o - S i d e d U n c e r t a i n t y , " The Review o f Economic S t u d i e s , V o l . 5 1 , No .167 . C r a w f o r d , V . P . ( 1 9 8 1 ) , "A T h e o r y o f D i s a g r e e m e n t i n B a r g a i n i n g , " E c o n o m e t r i c a , V o l . 5 0 , N o . 3 . D e M e n i l , G . ( 1 9 7 1 ) , B a r g a i n i n g : M o n o p o l y Power vs Union Power, MIT P r e s s , Cambridge , Mass . D e n n y , M . , M. F u s s , and J . D . May ( 1 9 8 1 ) , " I n t e r t e m p o r a l C h a n g e s i n R e g i o n a l P r o d u c t i v i t y i n C a n a d i a n M a n u f a c t u r i n g , " Canad ian J o u r n a l o f E c o n o m i c s , V o l . 1 4 , No. 3. D e r t o u z o s , J . N . a n d J . H . P e n c a v e l ( 1 9 8 1 ) , "Wage and Employment D e t e r m i n a t i o n U n d e r T r a d e U n i o n i s m : The I n t e r n a t i o n a l T y p o g r a p h i c a l U n i o n , " J o u r n a l o f P o l i t i c a l Economy, V o l . 89, N o . 6 . E a t o n , C . (1978) , "The Worker and the P r o f i t a b i l i t y o f the S t r i k e , " I n d u s t r i a l and L a b o r R e l a t i o n s Review, V o l . 2 6 , N o . l . E b e r t s , R.W. and J . A . Stone (1986) , "On the C o n t r a c t C u r v e : A T e s t o f A l t e r n a t i v e Models o f C o l l e c t i v e B a r g a i n i n g , " J o u r n a l o f L a b o r Economics . 145 F a r b e r , H . S . 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P e n c a v e l ( 1 9 8 6 ) , " T e s t i n g B e t w e e n C o m p e t i n g Models o f Wage and Employment D e t e r m i n a t i o n i n U n i o n i z e d M a r k e t s , " J o u r n a l o f P o l i t i c a l Economy, V o l . 9 4 , N o . 3 . M a r t i n e l l o , F . F . (1984) , "Wage and Employment D e t e r m i n a t i o n i n a U n i o n i z e d I n d u s t r y : The IWA i n t h e B . C . Wood P r o d u c t s I n d u s t r y , " P h . D . T h e s i s , U n i v e r s i t y o f B r i t i s h C o l u m b i a , V a n c o u v e r , Canada. M a u r o , M . J . ( 1 9 8 2 ) , " S t r i k e s as a R e s u l t o f I m p e r f e c t I n f o r m a t i o n , " I n d u s t r i a l and L a b o r R e l a t i o n s Review, V o l . 3 5 , N o . 4 . M c L e n n a n , A . ( 1 9 8 2 ) , "A N o n c o o p e r a t i v e D e f i n i t i o n o f Two P e r s o n B a r g a i n i n g , " D e p a r t m e n t o f E c o n o m i c s a n d I n s t i t u t e f o r P o l i c y a n a l y s i s Working Paper No. 8303, U n i v e r s i t y o f T o r o n t o , T o r o n t o , O n t a r i o . Osborne , M . J . (1985) , "The R o l e o f R i s k A v e r s i o n i n a S imple B a r g a i n i n g M o d e l , " i n A . R o t h ( e d . ) , G a m e - T h e o r e t i c Models o f B a r g a i n i n g , Cambridge U n i v e r s i t y P r e s s . Oswald , A . J . (1982) , "The Microeconomic Theory o f the Trade U n i o n , " Economic J o u r n a l , V o l . 9 2 No .367 . P e n c a v e l , J . (1984a) , "The E m p i r i c a l Performance o f a Model o f T r a d e U n i o n B e h a v i o r , " i n J . R o s a ( e d . ) , The E c o n o m i c s o f L a b o r U n i o n s : New D i r e c t i o n s , R l u w e r - N i j h o f f P u b l i s h i n g Company. P e n c a v e l , J . 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( 1 9 8 5 ) , G a m e - T h e o r e t i c M o d e l s o f B a r g a i n i n g , Cambridge U n i v e r s i t y P r e s s . R o t h , A . a n d F . S c h o u m a k e r ( 1983 ) , " E x p e c t a t i o n s and R e p u t a t i o n s i n B a r g a i n i n g : An E x p e r i m e n t a l S t u d y , " The A m e r i c a n Economic Review, V o l . 7 3 , N o . 3 . R u b i n s t e i n , A . (1982) , " P e r f e c t E q u i l i b r i u m i n a B a r g a i n i n g M o d e l , " E c o n o m e t r i c a , V o l . 5 0 , N o . l . R u b i n s t e i n , A . (1985) , "A B a r g a i n i n g Model w i t h Incomplete I n f o r m a t i o n A b o u t T i m e P r e f e r e n c e s , " E c o n o m e t r i c a , V o l . 5 3 , N o . 5 . S h a k e d , A . and J . S u t t o n (1984), " I n v o l u n t a r y Unemployment as a P e r f e c t E q u i l i b r i u m i n a B a r g a i n i n g M o d e l , " E c o n o m e t r i c a , V o l . 5 2 , N o . 6 . S o b e l , J . and I . T a k a h a s h i (1983) , "A M u l t i s t a g e Model o f B a r g a i n i n g , " Review o f Economic S t u d i e s , V o l . 5 0 . S i e b e r t , W . S . a n d J . T . A d d i s o n ( 1 9 8 1 ) , " A r e S t r i k e s A c c i d e n t a l ? " Economic J o u r n a l , V o l . 9 1 , No .362 . S v e j n a r , J . ( 1 9 8 0 ) , "On E m p i r i c a l T e s t i n g o f t h e N a s h - Z e u t h e n B a r g a i n i n g S o l u t i o n , " I n d u s t r i a l and L a b o r R e l a t i o n s Review, V o l . 3 3 , N o . 4 . S v e j n a r , J . (1986) , " B a r g a i n i n g Power, F e a r o f Disagreement and Wage S e t t l e m e n t s : T h e o r y and E m p i r i c a l E v i d e n c e from U . S . I n d u s t r y , " E c o n o m e t r i c a , V o l . 5 4 . T r a c y , J . S . (1986) , "An I n v e s t i g a t i o n i n t o the Determinants o f U . S . S t r i k e A c t i v i t y , " A m e r i c a n Economic Review, V o l . 7 6 . 148 Appendix A Data Sources and C o n s t r u c t i o n The appendix p r o v i d e s a d e t a i l e d d e s c r i p t i o n o f d a t a s o u r c e s and m a n i p u l a t i o n . F o r a broader d i s c u s s i o n o f the d a t a s e t i n c l u d i n g comments on i t s advantages and drawbacks , the r e a d e r i s r e f e r r e d t o C h a p t e r 5 o f the t e x t . A . l P r i c e and Q u a n t i t y I n d i c e s 3 8 In t h i s s e c t i o n , the B . C . wood p r o d u c t s i n d u s t r y da ta n a m e l y t h e i n p u t and o u t p u t q u a n t i t i e s and p r i c e s a r e d e s c r i b e d . U n l e s s o t h e r w i s e s p e c i f i e d , t h i s d a t a i s c o l l e c t e d t h r o u g h S t a t i s t i c s C a n a d a ' s c e n s u s o f m a n u f a c t u r i n g . I n d u s t r y c o s t s and hence i n p u t s are o f t h r e e t y p e s : l a b o u r , m a t e r i a l s a n d s u p p l i e s , a n d f u e l s and e l e c t r i c i t y . The l a t t e r i s used i n c o n j u n c t i o n w i t h c a p i t a l s t o c k d a t a t o form a c a p i t a l s e r v i c e s i n p u t . T h i s d a t a i s p r o v i d e d s e p a r a t e l y f o r t h e f o l l o w i n g 4 groups o f f i r m s : c o a s t a l s a w m i l l s , i n t e r i o r s a w m i l l s , s h i n g l e m i l l s , and plywood and veneer m i l l s . Most o f the d a t a i s p u b l i s h e d i n S t a t i s t i c s C a n a d a c a t a l o g u e s 35-204 and 35-206 w i t h t h e e x c e p t i o n o f t h e b r e a k d o w n on o u t p u t and m a t e r i a l s and s u p p l i e s f o r plywood and veneer m i l l s and the breakdown on m a t e r i a l s a n d s u p p l i e s f o r s h i n g l e m i l l s w h i c h a r e j 8 I would l i k e to thank F . M a r t i n e l l o f o r p r o v i d i n g me w i t h u n p u b l i s h e d i n d u s t r y d a t a . 149 u n p u b l i s h e d . A l s o , t h e d e t a i l s on f u e l and e l e c t r i c i t y c o s t s a r e p u b l i s h e d i n c a t a l o g u e 5 7 - 2 0 8 . W i t h some e x c e p t i o n s , the methodology u s e d i n M a r t i n e l l o (1984) t o c o n s t r u c t p r i c e and q u a n t i t y i n d i c e s was a l s o used h e r e . The d i f f e r e n c e s i n the i n d u s t r y d a t a between t h i s s tudy and M a r t i n e l l o (1984) a r e i n t h e c o n s t r u c t i o n o f the c a p i t a l s e r v i c e s i n p u t , the i n c l u s i o n o f n o n - p r o d u c t i o n workers and t h e s c a l i n g o f the d a t a which was a r b i t r a r y i n M a r t i n e l l o ( 1 9 8 4 ) . A l s o , t h e s a m p l e p e r i o d has been e x t e n d e d t o i n c l u d e the y e a r s 1980-1983. A . 1 . 1 Output Data on the q u a n t i t y and v a l u e o f the d i f f e r e n t types o f shipments i s used t o c o n s t r u c t a c h a i n e d F i s h e r i d e a l p r i c e i n d e x f o r e a c h g r o u p o f f i r m s f o r 1 9 6 3 - 8 3 . The i m p l i c i t q u a n t i t y index i s t h e n d e r i v e d by F i s h e r ' s weak f a c t o r r e v e r s a l t e s t . F i n a l l y , t h e p r i c e i n d e x was c o n v e r t e d t o 1971 c o n s t a n t d o l l a r s u s i n g t h e C P I . ( J u s t i f i c a t i o n f o r the use o f the F i s h e r d i r e c t p r i c e index and i m p l i c i t q u a n t i t y i n d e x c a n be f o u n d i n A l l e n a n d D i e w e r t (1981)) F o r s h i n g l e m i l l s , the q u a n t i t y and v a l u e o f " f u r t h e r p r o c e s s e d " s h i n g l e s was not a v a i l a b l e i n 1983 and the 1982 amounts were u s e d . S i m i l a r l y t h e q u a n t i t y and v a l u e o f s h i n g l e s and shakes i n c o a s t a l s a w m i l l s were no t a v a i l a b l e f o r 1982 and 1983 and t h e 1981 amounts were assumed to 150 remain c o n s t a n t . A l s o , f o r t h i s same t y p e o f o u t p u t i n c o a s t a l s a w m i l l s , t h e 1980 f i g u r e s were a g g r e g a t e d f o r Quebec and B . C . and the breakdown between these 2 p r o v i n c e s i n 1981 was used t o e s t i m a t e s e p a r a t e p r o v i n c i a l amounts f o r 1980. A . 1 . 2 M a t e r i a l s and S u p p l i e s The p r o c e d u r e d e s c r i b e d above was u s e d t o g e n e r a t e p r i c e and q u a n t i t y i n d i c e s f o r the m a t e r i a l s and s u p p l i e s i n p u t . One problem was e n c o u n t e r e d , f o r 1981 and 1982, the q u a n t i t y and v a l u e o f s h i n g l e and shakes used f o r f u r t h e r p r o c e s s i n g i n s h i n g l e m i l l s were n o t a v a i l a b l e . The c o r r e s p o n d i n g amounts f o r 1980 and 1983 were i n t e r p o l a t e d l i n e a r l y to e s t i m a t e the m i s s i n g v a l u e s . A . l . 3 F u e l s and E l e c t r i c i t y P r i c e and q u a n t i t y i n d i c e s were c a l c u l a t e d u s i n g the f o l l o w i n g d a t a breakdown: g a s o l i n e , f u e l o i l s ( k e r o s e n e , d i e s e l , l i g h t and h e a v y f u e l o i l s ) , l i q u i f i e d pe tro l eum g a s e s , n a t u r a l gas , and e l e c t r i c i t y . S e v e r a l problems were e n c o u n t e r e d . In 1982 and 198 3, kerosene was i n c l u d e d i n the c a t e g o r y o t h e r f o r which o n l y v a l u e i s a v a i l a b l e . The v a l u e f o r kerosene was assumed t o c o n s t i t u t e the same p r o p o r t i o n o f t h i s c a t e g o r y i n 1982 and 1983 as i t d i d on average i n 1980 and 1981. To e s t i m a t e the q u a n t i t y o f kerosene i n 1982 and 1983, the p r i c e averaged over 1980 and 1981 was d i v i d e d 151 i n t o t h e e s t i m a t e d 1982 and 1983 v a l u e s r e s p e c t i v e l y . (Averages over the two p r e v i o u s y e a r s were used i n s t e a d o f t h e l a s t y e a r ' s v a l u e because o f the s m a l l numbers i n v o l v e d ) A l t h o u g h t h e t o t a l c o s t s o f f u e l and e l e c t r i c i t y was a v a i l a b l e f o r c o a s t a l and i n t e r i o r s a w m i l l s s e p a r a t e l y f o r 19 80 onwards, each component's q u a n t i t y and v a l u e was g i v e n f o r the aggregated s a w m i l l s o n l y . The aggregate v a l u e s were d i v i d e d i n t o t h e two g r o u p s by u s i n g t h e r e l a t i v e c o n t r i b u t i o n s o f these two groups i n 1979 and by a d j u s t i n g t h e s e p r o p o r t i o n s over t ime a c c o r d i n g t o the changes i n the c o r r e s p o n d i n g p r o p o r t i o n s c a l c u l a t e d w i t h t h e t o t a l c o s t s f i g u r e s . The aggregate q u a n t i t y was d i v i d e d i n t o the two groups o f s a w m i l l s by u s i n g the e s t i m a t e d v a l u e s d e s c r i b e d a b o v e and by a s s u m i n g a common p r i c e f o r the two g r o u p s , t h i s p r i c e b e i n g e q u a l t o t h e t o t a l ( a g g r e g a t e ) v a l u e d i v i d e d by the aggregate q u a n t i t y . F o r example , the c o s t s o f e l e c t r i c i t y f o r i n t e r i o r s a w m i l l s i n 1981 w o u l d be c a l c u l a t e d as f o l l o w s : x EC ,81 T C 81 where EC e l e c t r i c i t y c o s t s TC t o t a l f u e l s and e l e c t r i c i t y c o s t s I i n t e r i o r s a w m i l l s IC a l l s a w m i l l s i . e . i n t e r i o r p l u s c o a s t a l 152 and where t h e s u p e r s c r i p t denotes the y e a r . The q u a n t i t y o f e l e c t r i c i t y u s e d by i n t e r i o r s a w m i l l s i n 1981 w o u l d be c a l c u l a t e d as f o l l o w s : where EQ = q u a n t i t y o f e l e c t r i c i t y consumed F i n a l l y , as no ted by M a r t i n e l l o (19 84) ( s e e , p g . 3 2 ) , t h e c o s t o f f u e l f o r s m a l l e s t a b l i s h m e n t s was i n c l u d e d i n t h e c o s t s o f m a t e r i a l s a n d s u p p l i e s , a l s o , any power genera ted by the f i r m s f o r t h e i r own use from wood waste or o t h e r s o u r c e s was no t i n c l u d e d . N o t h i n g c o u l d be done about t h e s e o m i s s i o n s . A . 1 . 4 L a b o u r The q u a n t i t y o f l a b o u r i s measured by the number o f man-hours p a i d which i n c l u d e s t ime p a i d but no t worked such as v a c a t i o n s and s t a t u t o r y h o l i d a y s . A l s o , t h e s e a r e hours worked by p r o d u c t i o n workers o n l y . The wage i s c a l c u l a t e d as t o t a l compensat ion p a i d t o p r o d u c t i o n workers d i v i d e d by t h e number o f man-hours p a i d to p r o d u c t i o n w o r k e r s . T o t a l compensat ion i n c l u d e s a l l wages b e f o r e d e d u c t i o n s , o v e r t i m e payments , bonuses , p a i d v a c a t i o n s and o t h e r p a y m e n t s f o r work not p e r f o r m e d . The wage i s then c o n v e r t e d t o c o n s t a n t 1971 d o l l a r s u s i n g the C P I . 81 153 An i n t e r e s t i n g i s s u e concerns the c h o i c e o f t h e u n i t o f measure f o r the l a b o u r i n p u t . I t can be a r g u e d t h a t t h e f i r m w i l l c a r e a b o u t t h e h o u r s o f work i n p u t e d i n t o i t s p r o d u c t i o n p r o c e s s w h i l e t h e u n i o n i s c o n c e r n e d w i t h t h e number o f w o r k e r s s i n c e t h i s r e f l e c t s more c l o s e l y t h e m e m b e r s h i p o f t h e u n i o n . I f t h e h o u r s p e r w o r k e r a r e c o n s t a n t t h e n i t makes no d i f f e r e n c e which u n i t i s chosen . I f the number o f workers i s n e g o t i a t e d s e p a r a t e l y then the l a b o u r c o n t r a c t w i l l have t h r e e d i m e n s i o n s , the wage, the hours per w o r k e r , and t h e number o f w o r k e r s . The b a r g a i n i n g w o u l d t h e n be c o n d u c t e d w i t h r e s p e c t t o t h e s e t h r e e v a r i a b l e s . T h i s would o b v i o u s l y c o m p l i c a t e t h e a n a l y s i s s u b s t a n t i a l l y . The h o u r s p e r worker were c a l c u l a t e d f o r each group o f f i r m s from 1963 t o 1983. They a r e p r e s e n t e d i n T a b l e I X . I t i s s u r p r i s i n g how c l o s e these numbers are t o the mean o f 1,96 3 hours per worker per y e a r . The o n l y s u b s t a n t i a l d e v i a t i o n s o c c u r d u r i n g r e c e s s i o n s . These c o u l d be due t o work s h a r i n g o r to the e l i m i n a t i o n o f o v e r t i m e . In o r d e r to keep the a n a l y s i s t r a c t a b l e , i t i s assumed t h a t a t the t ime o f b a r g a i n i n g , the hours o f work per worker i s t r e a t e d as a c o n s t a n t . A n o t h e r i m p o r t a n t i s s u e concerns the t r e a t m e n t o f n o n - p r o d u c t i o n l a b o u r . F o r the wood p r o d u c t s i n d u s t r y i n B . C . , t h i s i s composed m o s t l y o f a d m i n i s t r a t i v e and o f f i c e s t a f f , t h e r e m a i n d e r b e i n g w o r k e r s e m p l o y e d i n s a l e s a n d d i s t r i b u t i o n . S i n c e these workers are not p a r t o f the IWA, 154 T a b l e IX Hours p e r Worker p e r Year i n t h e B . C . Wood P r o d u c t s I n d u s t r y Year C o a s t a l I n t e r i o r S h i n g l e Plywood & Sawmi l l s Sawmi l l s Sawmi l l s Veneer M i l l s 1963 2054 1960 1891 2005 1964 2074 2026 1683 1991 1965 2047 2022 1959 1972 1966 2059 2006 1925 1894 1967 2067 2003 1944 1968 1968 2056 2040 1917 1963 1969 2050 2025 1921 1912 1970 2006 2003 1931 1893 1971 2022 2026 1952 1993 1972 1952 2017 1866 1951 1973 1992 1992 1888 1968 1974 1980 2074 1951 1903 1975 1940 2022 1926 1753 1976 2038 2035 1957 1751 1977 2046 1992 1988 1982 1978 2040 1992 2068 1954 1979 2038 2054 2063 1908 1980 2058 2056 1901 1977 1981 1845 1909 1918 1842 1982 1831 1836 1829 1599 1983 1943 1968 1879 1953 O v e r a l l Average = 196 3 155 t h e y s h o u l d n o t be I n c l u d e d i n t h e employment and wage f i g u r e s e n t e r i n g the u n i o n u t i l i t y f u n c t i o n . However, they a r e an a d d i t i o n a l i n p u t i n the p r o d u c t i o n p r o c e s s o f t h e f i r m and the n o n - p r o d u c t i o n l a b o u r c o s t s s h o u l d be i n c l u d e d i n the p r o f i t c a l c u l a t i o n s . N o n - p r o d u c t i o n l a b o u r c o s t s are a s m a l l p r o p o r t i o n o f t o t a l l a b o u r c o s t s a n d m o r e i m p o r t a n t l y , the number and the s a l a r i e s o f n o n - p r o d u c t i o n l a b o u r a r e h i g h l y c o r r e l a t e d w i t h the number and the wages o f p r o d u c t i o n l a b o u r , r e s p e c t i v e l y . I d e c i d e d t o a c c o u n t f o r n o n - p r o d u c t i o n l a b o u r by i n c r e a s i n g p r o d u c t i o n l a b o u r c o s t s by a f a c t o r o f 1 .15 , the average i n v e r s e p r o p o r t i o n o f p r o d u c t i o n w o r k e r s ' wages i n t o t a l s a l a r i e s and wages. Data on the r e l a t i v e magnitude o f p r o d u c t i o n l a b o u r i n the t o t a l l a b o u r i n p u t i s p r o v i d e d i n T a b l e I X . A . 1 . 5 C a p i t a l S e r v i c e s M a r t i n e l l o (1984) adopted the f o l l o w i n g p r o c e d u r e i n o r d e r t o c a l c u l a t e the q u a n t i t y and p r i c e o f t h e c a p i t a l i n p u t used by the m i l l s . I t i s assumed t h a t each m i l l uses i t s c a p i t a l s t o c k i n c o n j u n c t i o n w i t h energy t o form u n i t s o f c a p i t a l s e r v i c e s which are then used as i n p u t s i n the p r o d u c t i o n p r o c e s s . More s p e c i f i c a l l y , i t i s assumed t h a t the m i l l s ' p r o d u c t i o n f u n c t i o n i s s e p a r a b l e i n the c a p i t a l s t o c k and the q u a n t i t y o f f u e l s and e l e c t r i c i t y c o n s u m e d , i . e . the o u t p u t o f the group o f m i l l s i a t t ime t , Q^t can be w r i t t e n as : 156 T a b l e X Share o f P r o d u c t i o n Workers i n O v e r a l l Labour i n t h e B . C . Wood P r o d u c t s I n d u s t r y Year Proportion of Production Workers Proportion of Production Workers' Wages in Total Employment in % in Total Salar ies and Wages in % Coastal Interior Shingle Plywood Coastal Interior Shingle Plywood Sawmills Sawmills Sawmills SVeneer Sawmills Sawmills Sawmills SVeneer 1963 91 92 93 90 88 88 91 87 1964 90 86 93 90 87 82 91 87 1965 90 88 93 90 87 85 92 87 1966 90 88 93 91 87 85 92 87 1967 91 89 93 92 88 85 91 89 1968 91 89 93 92 88 85 92 90 1969 90 90 93 92 87 87 91 89 1970 87 87 94 91 83 85 93 87 1971 87 87, 94 91 84 84 93 89 1972 87 88 94 90 83 85 91 88 1973 87 89 93 91 84 85 90 88 1974 85 86 93 90 82 85 91 86 1975 82 87 93 90 78 85 91 85 1976 86 89 93 90 83 88 91 87 1977 86 89 92 90 84 87 91 88 1978 87 88 94 90 85 86 80 88 1979 87 87 93 91 84 85 91 88 1980 85 87 93 89 83 85 91 86 1981 85 86 92 88 81 82 91 84 1982 85 85 91 89 80 82 86 84 1983 86 86 93 90 82 84 86 87 overal I average = 86.6% 157 Q ± t = F i t < E i t - M i t - K < s i t - Y i t>> where F i s the p r o d u c t i o n f u n c t i o n E i s the l a b o u r i n p u t M i s the q u a n t i t y o f m a t e r i a l s and s u p p l i e s S i s t h e c a p i t a l s t o c k ( the c o n s t a n t 1971 d o l l a r m i d - y e a r ne t c a p i t a l s t o c k measure c a l c u l a t e d by S t a t i s t i c s Canada) Y i s the q u a n t i t y o f f u e l s and e l e c t r i c i t y K i s the (common) aggrega t or f u n c t i o n which has as i t s image Kj_-t, the q u a n t i t y o f c a p i t a l s e r v i c e s used as i n p u t . The a g g r e g a t o r f u n c t i o n K i s assumed to t a k e the form o f a C E S : K . t = (QY-P + d-a) S-P r 1 / 6 F i r m s are assumed t o m i n i m i z e c o s t s w h i c h , g i v e n t h e s e p a r a b i l i t y a s s u m p t i o n , can be r e p r e s e n t e d by a two-s tage o p t i m i z a t i o n p r o b l e m . The f i r s t s tage c o n s i s t s i n s o l v i n g the f o l l o w i n g : (1) min p ? t Y i t + p ? t S l t s u b j e c t t o K i t £ K Y i t ' S i t where K i s a f i x e d l e v e l o f c a p i t a l s e r v i c e s Y P i t '""s p r i c e o f f u e l s and e l e c t r i c i t y p . . i s the u s e r c o s t o f c a p i t a l ( to be d e s c r i b e d i n d e t a i l l a t e r i n t h i s s e c t i o n ) 158 F r o m t h e f i r s t o r d e r c o n d i t i o n s , t h e f o l l o w i n g r e l a t i o n s h i p i s d e r i v e d : a (1-a) S i t Y i t 6+1 where the RHS i s t h e m a r g i n a l r a t e o f t e c h n i c a l s u b s t i t u t i o n o f t h e a g g r e g a t o r f u n c t i o n K . T h i s e q u a t i o n c a n be r e w r i t t e n as : (2) ' i t = y i t D a t a on c a p i t a l s t o c k s and energy consumpt ion can be used to e s t i m a t e the c o e f f i c i e n t s a and B. The q u a n t i t y and p r i c e o f energy were c a l c u l a t e d f o r each y e a r and e a c h group o f f i r m s as d e s c r i b e d p r e v i o u s l y . The p r i c e o f energy was c o n v e r t e d t o 1971 d o l l a r s u s i n g the C P I . Data on c a p i t a l s t o c k s by i n d u s t r y c o m p i l e d by S t a t i s t i c s Canada a r e used to c o n s t r u c t the q u a n t i t y and v a l u e o f the c a p i t a l s t o c k , S and p s . T h i s d a t a i s a v a i l a b l e f o r Canada i n c a t a l o g u e 13-211 w h i l e t h e p r o v i n c i a l f i g u r e s are u n p u b l i s h e d . U n f o r t u n a t e l y d a t a on c a p i t a l s t o c k s i s no t a v a i l a b l e f o r the f o u r groups o f f i r m s s e p a r a t e l y . The m e t h o d o l o g y u s e d by M a r t i n e l l o (1984) c o n s i s t e d i n u s i n g the energy c o s t s and e s t i m a t e s o f a and 6 t o breakdown the aggregate c a p i t a l s t o c k s f i g u r e s and 159 o b t a i n s e p a r a t e c a p i t a l s e r v i c e s e s t i m a t e s f o r each o f the f o u r groups o f f i r m s . A t the t ime o f M a r t i n e l l o ' s r e s e a r c h , t h e o n l y a v a i l a b l e d a t a on c a p i t a l s t o c k s i n B . C . ' s wood p r o d u c t i n d u s t r y was an a g g r e g a t e o f a l l f o u r groups o f m i l l s . S i n c e t h e n , s e p a r a t e d a t a has become a v a i l a b l e on plywood and veneer m i l l s . F o l l o w i n g M a r t i n e l l o ' s p r o c e d u r e , I used t h i s new d a t a t o e s t i m a t e t h e s y s t e m o f e q u a t i o n s g i v e n below: (3 ) l n S 4 t - 1 , / ( l - a ) \ , _ — — In [ ']+ In Y $+1 [ a J 4t 8 + 1 + u It (4) In ( Z S i t ) = i 1 . (1-a) , „ „ , In x + In Z & + 1 a i t 1 / Y \ 6+1 ' P i t s V p i t ; + u 2t where the s u b s c r i p t 4 denotes plywood and veneer m i l l s ; 2 d e n o t e s t h e sum o v e r c o a s t a l and i n t e r i o r i s a w m i l l s and s h i n g l e m i l l s ; u-jt i s the e r r o r term f o r e q u a t i o n j and y e a r t ; t - 1963 t o 1983. H o w e v e r , 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 w e r e u n s a t i s f a c t o r y i n the sense t h a t the c o n s t a n t term p+r-ln ( - a - > 160 had a l a r g e s t a n d a r d e r r o r and the r e s u l t i n g e s t i m a t e s f o r a were e x t r e m e l y v a r i a b l e . V a r i o u s e s t i m a t e s o f the c o n s t a n t t e r m and t h e i m p l i e d a a r e r e p o r t e d b e l o w a c c o r d i n g t o d i f f e r e n t a s s u m p t i o n s c o n c e r n i n g t h e d e g r e e o f s e r i a l c o r r e l a t i o n i n the e r r o r term Ujt- Assumed s e r i a l E s t i m a t e d A s y m p t o t i c I m p l i e d V a l u e o f t h e I n c o r r e l a t i o n i n U j t C o n s t a n t Te rm t r a t i o a l i k e l i h o o d f u n c t i o n f i r s t o r d e r 2 5 8 . 6 5 0 . 1 7 6 9 5 0 5 0 . 1 1 8 0 5 s e c o n d o r d e r - 2 . 5 5 8 7 - 0 . 1 2 7 8 7 . 9 8 3 9 5 1 . 2 8 7 6 t h i r d o r d e r - 5 . 5 7 4 5 - 2 . 0 4 5 8 . 9 9 9 8 5 1 . 5 5 1 4 f o u r t h o r d e r - 2 2 6 . 4 2 - 0 . 1 2 8 5 1 5 3 . 9 0 4 6 Not t h a t i f a i s 0, energy p l a y s no r o l e i n the c a l c u l a t i o n o f the c a p i t a l s e r v i c e s i n p u t w h i l e the same i s t r u e o f the c a p i t a l s t o c k i f a i s 1. In o r d e r to a v o i d the a r b i t r a r y c h o i c e o f a r e a s o n a b l e a , I u s e d a d i f f e r e n t , s i m p l e r a p p r o a c h . I assume t h a t t h e r e l a t i v e i n p u t s h a r e s f o r energy and the c a p i t a l s t o c k are c o n s t a n t a c r o s s the t h r e e groups o f f i r m s c o a s t a l s a w m i l l s , i n t e r i o r s a w m i l l s and s h i n g l e m i l l s . T h i s ( cons tant ) r a t i o denoted by G i s then c a l c u l a t e d as : G t = I S i t P f t ' I Y i t P i t where the n o t a t i o n i s the same as t h a t used i n e q u a t i o n s ( 3 ) and ( 4 ) a b o v e . N o t e t h a t i s a l l owed to d i f f e r a c r o s s t i m e p e r i o d s . The a g g r e g a t e c a p i t a l s t o c k m e a s u r e f o r s a w m i l l s and s h i n g l e m i l l s i s t h e n b r o k e n down i n t o the 161 c a p i t a l s t o c k measures f o r each o f t h e 3 g r o u p s o f f i r m s a c c o r d i n g t o : S i t " G i t x Y i t x Pit ' P ? t where G i t = G t f ° r i = c o a s t a l and i n t e r i o r s a w m i l l s and s h i n g l e m i l l s . A r a t i o G4t c a n a l s o be c a l c u l a t e d f o r p lywood and veneer m i l l s f o r which a s e p a r a t e c a p i t a l s t o c k measure i s a v a i l a b l e . T h i s p r o c e d u r e i s c o n s i s t e n t w i t h the assumpt ion o f an a g g r e g a t o r f u n c t i o n K ( S i f Y i t ) which takes the form o f a C o b b - D o u g l a s . F u r t h e r m o r e , i f i t i s assumed t h a t t h i s f u n c t i o n e x h i b i t s c o n s t a n t r e t u r n s t o s c a l e t h e n t h e c o e f f i c i e n t s on S^t a n & Y i t c a n D e r e c o v e r e d f r o m G j _ f S p e c i f i c a l l y , I assume: <5> K i t - S i i " X l t ) and c o s t m i n i m i z i n g b e h a v i o u r . T h i s i m p l i e s : ^ i t = T T ? — f o r i = l , 2 , 3 , 4 ; and t = 1 9 6 3 , . . . , 1 9 8 3 . The d u a l u n i t c o s t f u n c t i o n i s : (6) P k t = ( P ? t ) X l t ( p ! t ) ( 1 " X i t ) ( M t ) - X i t ( l - X i t J - ^ i t ) 162 Q u a n t i t y and p r i c e i n d i c e s f o r c a p i t a l s e r v i c e s were c a l c u l a t e d from e q u a t i o n s (5) and (6) f o r each o f the f o u r groups o f m i l l s and each y e a r . Note t h a t by a l l o w i n g 6 i t t o v a r y a c r o s s t i m e , I am not c a l c u l a t i n g p r e d i c t e d c a p i t a l s t o c k s (and hence K^t) n e "t ° f some u n e x p l a i n e d random e r r o r as was d o n e i n M a r t i n e l l o ( 1 9 8 4 ) . I t h i n k t h i s i s p r e f e r a b l e b e c a u s e o f t h e p o o r e x p l a n a t o r y powers o f r e g r e s s i o n s such as (3) and ( 4 ) . A second s e r i o u s d i f f e r e n c e between the c a l c u l a t i o n o f c a p i t a l s e r v i c e s i n M a r t i n e l l o (1984) and here i s found i n the measure o f the u s e r c o s t o f c a p i t a l P ^ « In M a r t i n e l l o (1984) , t h i s i s c a l c u l a t e d as : P i t " ( r t + d e P t > x P t where r i s the i n t e r e s t r a t e measured by the McLeod, Y o u n g , W e i r 10 i n d u s t r i a l b o n d y i e l d i n C a n a d a . T h i s i s a v a i l a b l e i n the Bank o f Canada Review, dep i s the d e p r e c i a t i o n r a t e which i s c a l c u l a t e d as t h e r a t i o o f t h e c a p i t a l c o n s u m p t i o n a l l o w a n c e t o t h e m i d - y e a r g r o s s c a p i t a l s t o c k . Both these s e r i e s a r e u n p u b l i s h e d . The c a p i t a l c o n s u m p t i o n a l l o w a n c e was not a v a i l a b l e s e p a r a t e l y f o r plywood and v e n e e r m i l l s due t o c o n f i d e n t i a l i t y and hence was 163 c a l c u l a t e d f o r the t o t a l B . C . woods p r o d u c t i n d u s t r y . I t i s assumed t o be e q u a l a c r o s s the f o u r groups o f f i r m s . p 1 i s t h e p r i c e i n 1 9 7 1 $ f o r c a p i t a l e x p e n d i t u r e s on p l a n t and equipment f o r t h e wood p r o d u c t s i n d u s t r y i n Canada p u b l i s h e d i n 13-211. The d i f f e r e n c e between p?^. and the u s e r c o s t i n t h i s s tudy p ^ a r e t w o - f o l d . F i r s t l y , expected c a p i t a l g a i n s are m e a s u r e d by t h e p r o p o r t i o n a l c h a n g e i n t h e C P I and s u b t r a c t e d from the sum o f i n t e r e s t and d e p r e c i a t i o n c o s t s . S e c o n d l y , the p r i c e index o f inves tment goods which I used i s t h e i n d e x u s e d by S t a t i s t i c ' s C a n a d a t o i n f l a t e t h e c o n s t a n t v a l u e c a p i t a l s t o c k t o c u r r e n t v a l u e c a p i t a l s t o c k . I n t h e o r y , t h i s i n d e x w i l l be d i f f e r e n t f o r each o f the g r o u p s o f f i r m s due t o a d i f f e r e n t mix o f i n v e s t m e n t . H o w e v e r , due t o t h e a g g r e g a t i o n o f i n t e r i o r and c o a s t a l s a w m i l l s and s h i n g l e m i l l s i n c a p i t a l s t o c k measures , I have t o assume t h i s p r i c e index i s e q u a l f o r those t h r e e groups o f f i r m s . The u s e r c o s t o f c a p i t a l w h i c h I c a l c u l a t e i s t h e n : f o r i = i n t e r i o r a n d c o a s t a l s a w m i l l s and s h i n g l e m i l l s ; o r i = plywood and veneer m i l l s , and t = 1 9 6 3 , . . . , 1 9 8 3 . c u r r e n t v a l u e Sit . x (r + dep CPIt+i - C P I t c o n s t a n t v a l u e S^t C P I t 164 A . 1 . 6 I n p u t C o s t Shares and P r o f i t s In t h i s s e c t i o n , I examine the v a l u e o f p r o f i t s and the c o s t s h a r e s o f i n p u t s . T h i s i s i n t e r e s t i n g e s p e c i a l l y because o f the c a p i t a l s e r v i c e s i n p u t which was c o n s t r u c t e d . F i r s t , I would l i k e to p o i n t out a d i f f e r e n c e between the f i n a l i n p u t - o u t p u t d a t a used i n t h i s s tudy and t h a t used i n M a r t i n e l l o (1984) . M a r t i n e l l o (1984) adopted an ad hoc s c a l i n g r u l e f o r the i n p u t and o u t p u t p r i c e and q u a n t i t y i n d i c e s w h i c h ensured t h a t p r o f i t s were p o s i t i v e f o r most o b s e r v a t i o n s and which y i e l d e d i n p u t c o s t s h a r e s o f 0.15 f o r c a p i t a l , 0.25 f o r l a b o u r , and 0.59 f o r m a t e r i a l s . The shares were found comparable to an I n d u s t r y , Trade and Commerce r e p o r t w h i c h g i v e s a m a t e r i a l s share o f one h a l f t o two t h i r d s . A l s o , c a l c u l a t i o n s f r o m p r i n c i p a l s t a t i s t i c s o f the i n d u s t r y shows t h a t the share o f m a t e r i a l s d i v i d e d by the share o f l a b o u r averages 2 .44 . I n t h i s s t u d y , I r e c o v e r t h e n a t u r a l u n i t s o f t h e i n d i c e s by u s i n g t h e i r b a s e s . F o r e x a m p l e , t h e c a p i t a l s e r v i c e s i n p u t q u a n t i t y and p r i c e i n d i c e s w i l l a l s o have u n i t s e q u a l t o the (common) base which was used f o r the f u e l a n d e l e c t r i c i t y a n d c a p i t a l s t o c k q u a n t i t y and p r i c e i n d i c e s , r e s p e c t i v e l y . I t i s s i m p l e t o r e c o v e r the d o l l a r v a l u e r e p r e s e n t e d by t h e p r o d u c t o f the c a p i t a l s e r v i c e s p r i c e and q u a n t i t y i n d i c e s by u s i n g t h i s base . I n T a b l e X I , the v a l u e o f p r o f i t s ne t o f the c a p i t a l 165 s e r v i c e s i n p u t are p r e s e n t e d a l o n g w i t h average i n p u t c o s t s h a r e s . I t i s seen from T a b l e XI t h a t w i t h no a r b i t r a r y s c a l i n g o f the d a t a , the r e s u l t i n g p r o f i t s are p o s i t i v e f o r a l l but 6 out o f the 84 o b s e r v a t i o n s . P r o f i t s were n e g a t i v e f o r a l l 4 groups o f f i r m s i n 1982, f o r c o a s t a l s a w m i l l s i n 1981 and f o r i n t e r i o r s a w m i l l s i n 1970. One i m p o r t a n t remark i s i n o r d e r . The p r i c e a n d q u a n t i t y i n d i c e s f o r f u e l a n d e l e c t r i c i t y , m a t e r i a l s and s u p p l i e s , and s h i p m e n t s were c o n s t r u c t e d from d a t a on the v a r i o u s c o m p o n e n t s o f t h e s e c o s t s and revenues . T h i s d e t a i l e d d a t a does n o t y i e l d the same t o t a l s as the t o t a l c o s t s and revenues r e p o r t e d i n the p r i n c i p a l s t a t i s t i c s f o r the i n d u s t r y . The reason f o r t h i s i s the o m i s s i o n o f v a r i o u s d a t a i n the d e t a i l e d d a t a , f o r e x a m p l e , s m a l l e s t a b l i s h m e n t s are o m i t t e d i n the breakdown o f f u e l and e l e c t r i c i t y c o s t s . The p r i c e and q u a n t i t y i n d i c e s i n t h i s s tudy were generated to r e f l e c t v a r i a t i o n s i n t o t a l c o s t s and r e v e n u e s r e p o r t e d i n t h e p r i n c i p a l s t a t i s t i c s . I t was assumed t h a t the o m i t t e d d a t a had the same breakdown p r o p o r t i o n a l l y and t h e same p r i c e s as t h e d e t a i l e d d a t a which was a v a i l a b l e . T h e r e f o r e , the p r o d u c t o f the p r i c e and q u a n t i t y i n d i c e s f o r the i n p u t s / o u t p u t w i l l e q u a l the t o t a l r e a l c o s t s / r e v e n u e f o r t h a t i n p u t / o u t p u t as r e p o r t e d i n p r i n c i p a l s t a t i s t i c s d i v i d e d by the base . W i t h r e s p e c t t o i n p u t c o s t s h a r e s , we f i n d t h a t the share o f c a p i t a l s e r v i c e s used i n t h i s s t u d y w h i c h i s on 166 T a b l e XI a. C o s t P r o f i t s Net o f C a p i t a l S e r v i c e s and Input Shares i n t h e B . C . Wood P r o d u c t s I n d u s t r y Year C o a s t a l I n t e r i o r S h i n g l e Plywood ai Sawmi l l s Sawmi l l s M i l l s Veneer Mi: 1963 5.0814 5.3954 0.4839 2.1561 1964 4.6299 5.9050 0.1917 2.0707 1965 4.4464 5.5079 0.0798 2.2390 1966 3 .9038 5.1897 0.1598 1.8437 1967 5.0662 4.2921 0.2146 2.7318 1968 9.9539 9.7280 0.7732 2.7873 1969 7.3163 6.8809 0.3570 3.1189 1970 2.7140 -0 .7919 0.0146 0.5368 1971 4.3482 4.3150 0.4380 2.2939 1972 6.8280 14.9517 0.9887 4.3251 1973 17.8310 22.2486 0.9518 4.9872 1974 7.7459 6.3443 0.2522 2.3548 1975 2.7964 3.7848 0.6186 2.4648 1976 5.9445 12.4591 0.9955 4.1137 1977 10.9838 20.2602 1.0770 3.0932 1978 13.7170 27.5161 1.1051 6.2824 1979 14.1214 24.6231 0.4968 3.5657 1980 4.4582 9.9658 0.6999 1.8470 1981 -0 .6781 0.9772 0.2111 2.0271 1982 -2 .6144 -7 .4137 -0 .1204 -1 .2103 1983 2.8261 6.6433 0.0292 0.7207 Average 6.2581 8.9896 0.4770 2.5881 O v e r a l l Average = 4.5782 b . A v e r a g e Input Shares o f T o t a l C o s t s Over t h e Sample P e r i o d Labour C o a s t a l S a w m i l l s 0.25611 I n t e r i o r S a w m i l l s 0.29 382 S h i n g l e S a w m i l l s 0.36352 Plywood and Veneer M i l l s 0.32653 M a t e r i a l s & S u p p l i e s 0.70713 0.61477 0.59451 0.61847 C a p i t a l S e r v i c e s 0.03676 0.09140 0.04196 0.05500 Average 0.31000 0.63372 0.05628 167 average 6% i s much lower than t h a t used by M a r t i n e l l o [15 ] . T h i s i s made up by i n c r e a s e s i n both the l a b o u r share (31% on average) and the m a t e r i a l s and s u p p l i e s share (63%). I t i s i n t e r e s t i n g t o compare c o a s t a l and i n t e r i o r s a w m i l l s i n t h i s r e s p e c t . We f i n d t h a t the c a p i t a l s e r v i c e s s h a r e i s l a r g e r f o r i n t e r i o r s a w m i l l s w h i l e the o p p o s i t e i s t r u e o f the m a t e r i a l s and s u p p l i e r s s h a r e . The r e s p e c t i v e p r i c e and q u a n t i t y i n d i c e s show t h a t w h i l e t h e p r i c e o f c a p i t a l s e r v i c e s i s c o m p a r a b l e f o r t h e two g r o u p s o f s a w m i l l s , i n t e r i o r s a w m i l l s are more c a p i t a l i n t e n s i v e . A l s o , t h e r e i s a n o t i c e a b l e d i f f e r e n c e i n t h e p r i c e o f m a t e r i a l s and s u p p l i e s i n t h e two a r e a s w i t h t h e i n t e r i o r s a w m i l l s b e n e f i t i n g from the lower p r i c e . T h i s i s c o n s i s t e n t w i t h t h e h y p o t h e s i s t h a t t imber p r i c e s a r e h i g h e r on the c o a s t due t o the l a r g e amount o f h a r v e s t i n g and hence low y i e l d o f t h e f o r e s t l a n d s . I n c o n c l u s i o n , I would l i k e t o ment ion two i m p o r t a n t f laws i n the i n d u s t r y d a t a as compi l ed f o r t h i s s t u d y . i ) T h e r e i s no a c c o u n t i n g o f c o r p o r a t e taxes and t h e i r impact on p r o f i t s as a whole and on the u s e r c o s t o f c a p i t a l . i i ) The assumpt ion o f exogene i ty o f the i n p u t p r i c e s can be v e r y r e s t r i c t i v e e s p e c i a l l y i n the c a s e o f m a t e r i a l s and s u p p l i e s s i n c e some o f t h e m i l l s a r e owned by companies which a l s o engage i n l o g g i n g . 168 A . 2 The A l t e r n a t i v e Wage The a l t e r n a t i v e wage W A i s c a l c u l a t e d as f o l l o w s W. = ( p „ x H E o i i n + ( l - p „ ) x p M T x U l ) / CPI A v CE s+m x CU1 ' where p^ i s the p r o b a b i l i t y o f f i n d i n g a j o b i n e i t h e r the s e r v i c e or the m a n u f a c t u r i n g s e c t o r s i n B . C . T h i s i s measured by the r a t i o o f t o t a l employment i n these two s e c t o r s d i v i d e d by the t o t a l p r o v i n c i a l l a b o u r f o r c e . H E s+m i - s t h e employment w e i g h t e d a v e r a g e h o u r l y e a r n i n g s i n s e r v i c e s and m a n u f a c t u r i n g i n B . C . S i m i l a r l y t o the wage measure i n the wood p r o d u c t s i n d u s t r y , t h i s a l t e r n a t i v e income i n c l u d e s pay f o r t ime not worked such as v a c a t i o n s and h o l i d a y s . P U i i s the p r o b a b i l i t y o f c o l l e c t i n g unemployment i n s u r a n c e b e n e f i t s g i v e n t h a t the w o r k e r i s unemployed. T h i s i s c a l c u l a t e d as the number o f weeks o f unemployment i n s u r a n c e i n B . C . d i v i d e d by t h e t o t a l number o f weeks o f unemployment i n B . C . The t o t a l number o f weeks o f unemployment i n B . C . i s c a l c u l a t e d as ( B . C . l a b o u r f o r c e - B . C . employment ) * 52. U l i s the average h o u r l y payment o f unemployment i n s u r a n c e i n B . C . a d j u s t e d f o r tax t r e a t m e n t . 169 ( F o r the c a l c u l a t i o n o f the tax f a c t o r , see R i d d e l l and S m i t h [1982 ] . N o t e t h a t t h e r e s u l t i n g UI payment i s p r e - t a x . A l s o , t h i s adjustment f a c t o r was a v a i l a b l e o n l y up t o 1979 and was assumed c o n s t a n t f o r 1979 to 1983. ) CPI i s the Consumer P r i c e Index which c o n v e r t s WA t o the base o f a CPI bundle o f goods i n 1971. B o t h H E s + m and UI were r e p o r t e d as w e e k l y f i g u r e s . They were c o n v e r t e d t o h o u r l y numbers w i t h t h e u s e o f t h e a v e r a g e w e e k l y h o u r s o f work i n B . C . m a n u f a c t u r i n g . The m a n u f a c t u r i n g f i g u r e was used because o f v e r y poor coverage i n o t h e r i n d u s t r i e s . S u r p r i s i n g l y , t h e a l t e r n a t i v e wage t u r n e d out to be g r e a t e r t h a n the r e a l wage i n i n t e r i o r s a w m i l l s i n 1964 and 1965. T h i s i s i n c o n s i s t e n t w i t h the i n t e r p r e t a t i o n o f the a l t e r n a t i v e wage as t h e minimum a c c e p t a b l e wage t o t h e u n i o n . A r g u a b l y , the o c c u r r e n c e s o f t h i s i n c o n s i s t e n c y are few and the m a g n i t u d e s a r e v e r y s m a l l . (The d i f f e r e n c e s b e t w e e n t h e a c t u a l wage i n i n t e r i o r s a w m i l l s and t h e a l t e r n a t i v e wage a r e 0 .01$ i n 1964 and 0 .03$ i n 1965 ) . H o w e v e r , t h i s f i n d i n g prompted me t o l o o k f o r d a t a on the d i s t r i b u t i o n o f wages a c r o s s the p r o v i n c e i n the '60 's and • 7 0 ' s . T h r e e s o u r c e s o f d a t a were found: 170 i ) The A n n u a l S a l a r y and Wage Rate Survey conducted by the B . C . Bureau o f Economics and S t a t i s t i c s over the p e r i o d 1957-1966. Wages were g i v e n f o r s e l e c t e d o c c u p a t i o n s a l o n g w i t h the number o f employees s u r v e y e d . O f f i c e and p r o f e s s i o n a l o c c u p a t i o n s were no t c o n s i d e r e d and t h a t l e f t 7 b l u e c o l l a r o c c u p a t i o n s . The wages were f o r f u l l - t i m e e m p l o y e e s o n l y and d i d n o t i n c l u d e o v e r t i m e o r s p e c i a l bonuses . i i ) The B . C . Survey o f S a l a r y and Wage Rates conducted by Labour Canada over the p e r i o d 1971-1973. The d a t a i s s i m i l a r to t h a t i n ( i ) except f o r a more l i m i t e d number o f o c c u p a t i o n s and fewer g e o g r a p h i c a l c e n t r e s . i i i ) S t a t i s t i c s C a n a d a A v e r a g e W e e k l y E a r n i n g s f o r a l l e m p l o y e e s and a l l i n d u s t r i e s a r e a v a i l a b l e f o r 4 d i f f e r e n t r e g i o n s o f B . C . from 1967 t o 1984. D e s c r i p t i v e S t a t i s t i c s f o r these t h r e e s e t s o f d a t a are p r o v i d e d i n T a b l e X I I . I t can be seen t h a t d u r i n g the '60 's t h e r e was a gap between wages i n the i n t e r i o r and the c o a s t w i t h t h e i n t e r i o r b e i n g c o n s i s t e n t l y below the p r o v i n c i a l a v e r a g e . T h i s gap was a lmost gone by the e a r l y ' 7 0 ' s . T h i s i s c o n s i s t e n t w i t h t h e b e h a v i o u r o f the r e a l wage i n the i n t e r i o r s a w m i l l s compared to the c o a s t a l saw m i l l s except t h a t a gap remains t h r o u g h the whole sample i n t h a t c a s e . The d i f f e r e n c e s i n the wages a c r o s s areas c o u l d be due t o T a b l e X I I Wage D i s t r i b u t i o n A c r o s s B . C . a . Government o f B . C . A n n u a l Wage Rate S u r v e y . Employment w e i g h t e d a v e r a g e s o v e r 7 b l u e c o l l a r o c c u p a t i o n s . 1 Sample p e r i o d 1957-1966. 1957 - 1966 Metro. Metro. Southern Northern Provincia l Int. Weight Coastal Weight Vancouver V ic to r ia In ter ior 2 Centres 3 Average Co 1.3/Col.5 Cols.1+2/Col.5 Average 2.21 2.24 1.89 2.12 2.11 .8953 1.0521 Minimum 1.84 1.89 1.67 1.86 1.85 .8685 1.0049 Maximum 2.62 2.63 2.25 2.53 2.51 .9177 1.0720 N o t e s : i o c c u p a t i o n s : L a b o u r e r , L a b o u r f o r e m a n . C a r p e n t e r , A u t o m o b i l e mechan ic , Equipment o p e r a t o r (Heavy) , L i g h t t r u c k d r i v e r , Medium t r u c k d r i v e r . S o u t h e r n i n t e r i o r C e n t r e s : K a m l o o p s , K e l o w n a , P e n t i c t o n , and V e r n o n . 3 N o r t h e r n C e n t r e s : P r i n c e R u p e r t , P r i n c e G e o r g e , T e r r a c e , Quesne l and S m i t h e r s . b . Labour Canada , B . C . Survey o f Wage R a t e s . Employment w e i g h t e d a v e r a g e s o v e r 3 b l u e c o l l a r o c c u p a t i o n s . 1 Sample p e r i o d 1971-73. 1971 - 1973 Vancouver V ic to r ia Kamloops Prince Provincia l Int. Weight Coastal Weight George Average Co l .3 /Co l .5 Cols.1+2/Col.5 Average 4.16 3.99 3.93 4.01 4.02 .9796 1.0128 Minimum 3.73 3.59 3.56 3.68 3.64 .9410 1.0049 Maximum 4.63 4.35 4.13 4.38 4.37 1.0198 1.0281 Notes : ^-Occupations: L i g h t and heavy t r u c k d r i v e r , I n d u s t r i a l t r u c k d r i v e r , L a b o u r e r . 172 T a b l e X I I (Cont inued) c . S t a t i s t i c s C a n a d a , A v e r a g e W e e k l y E a r n i n g . A l l employees . I n d u s t r i a l Compos i t e . Sample p e r i o d 1967- 1984. C a t . 72-002. Vancouver V ic to r ia Kamioops Prince Provincia l Int. Weight Coastal Weight George Average Co l .3 /Co l .5 Cols.1+2/Col.5 1967-70 Average 121.27 107.60 107.05 127.15 115.77 .9237 .9888 Minimum 109.69 97.49 93.40 115.36 103.99 .8982 .9807 Maximum 113.91 17.31 18.44 139.26 127.23 .9424 .9962 1971-73 Average 161.48 137.99 149.96 165.22 165.66 .9755 .9751 Minimum 148.86 128.39 133.38 143.10 138.43 .9635 .9549 Maximum 174.47 148.75 162.11 181.82 166.79 .9912 1.0014 1974-84 Average 302.38 334.16 322.46 282.39 310.35 .9613 .9699 Minimum 194.41 167.38 180.67 205.66 187.03 .9423 .9569 Maximum 420.31 461.97 432.58 382.13 412.59 1.0187 .9856 173 i m p e r f e c t l a b o u r m o b i l i t y o r d i f f e r e n c e s i n t h e c o s t o f l i v i n g f o r example . We a l s o f i n d i n T a b l e X I I t h a t t h i s gap i s l a r g e r i n t h e d a t a on s e l e c t e d b l u e c o l l a r o c c u p a t i o n s t h a n i n the t o t a l employees e a r n i n g s d a t a . That t h e r e i s a d i f f e r e n c e i s no t s u r p r i s i n g g i v e n the d i f f e r e n c e s i n t h e m i x o f o c c u p a t i o n s t h a t c a n e x i s t be tween t h e v a r i o u s c e n t r e s . A l t h o u g h I d i d not want t o p l a c e to much importance on any i n d i v i d u a l o b s e r v a t i o n , I d i d want t o take i n t o account t h i s t r e n d o f e q u a l i z a t i o n o f t h e wages a c r o s s B . C . I c o n s t r u c t e d weights f o r the i n t e r i o r and the c o a s t a l areas by l i n e a r i n t e r p o l a t i o n o f the two average weights i n the b l u e c o l l a r o c c u p a t i o n s . A l s o , once these weights reached 1, they were f i x e d t h e r e f o r the r e s t o f the sample . These we ights are p r e s e n t e d i n T a b l e X I I I . The i n t e r i o r w e i g h t was m u l t i p l i e d by t h e a l t e r n a t i v e wage t o y i e l d t h e a l t e r n a t i v e wage f a c e d by i n t e r i o r s a w m i l l w o r k e r s and s i m i l a r l y f o r t h e c o a s t a l w e i g h t and c o a s t a l s a w m i l l w o r k e r s . The r e s u l t i n g a l t e r n a t i v e wages f o r the 4 groups o f f i r m s are a l s o g i v e n i n T a b l e A - 6 . A . 3 S t r i k e C o s t s A d i s c u s s i o n o f t h e c h o i c e o f v a r i a b l e s a f f e c t i n g s t r i k e c o s t s can be found i n the t e x t . I n t h i s s e c t i o n , d a t a s o u r c e s and c a l c u l a t i o n s a r e g i v e n . The f o l l o w i n g 174 T a b l e X I I I I n t e r i o r and C o a s t a l W e i g h t s , and A l t e r n a t i v e Wages Y e a r W e i g h t s A l t e r n a t i v e Wages I n t e r i o r C o a s t a l C o a s t a l S a w m i l l s I n t e r i o r S a w m i l l s S h i n g l e , P l y w o o d & V e n e e r M i l l s 1963 0.9102 1.0449 2.81883 2.45545 2.69771 1964 0.9179 1.0414 2.86624 2.52633 2.75229 1965 0.9256 1.0378 2.97213 2.65080 2.86387 1966 0.9334 1.0343 3.01436 2.72030 2.91440 1967 0.9411 1.0307 2.92198 2.66797 2.83494 1968 0.9488 1.0272 2.97409 2.74710 2.89523 1969 0.9566 1.0236 3.09719 2.89446 3.02578 1970 0.9643 1.0201 3.17544 3.00174 3.11287 1971 0.9720 1.0165 3.37840 3.23050 3.32356 1972 0.9798 1.0130 3.48673 3.37246 3.44199 1973 0.9875 1.0094 3.55525 3.47811 3.52214 1974 0.9952 1.0059 3.67669 3.63758 3.65512 1975 1.0000 1.0023 3.87980 3.87090 3.87090 1976 1.0000 1.0000 3.89204 3.89204 3.89204 1977 1.0000 1.0000 3.98790 3.98790 3.98790 1978 1.0000 1.0000 3.85113 3.85113 3.85113 1979 1.0000 1.0000 3.78325 3.78325 3.78325 1980 1.0000 1.0000 3.87554 3.87554 3.87554 1981 1.0000 1.0000 3.90708 3.90708 3.90708 1982 1.0000 1.0000 3.92880 3.92880 3.92880 1983 1.0000 1.0000 3.79753 3.79753 3.79753 175 v a r i a b l e s were used t o measure v a r i a t i o n s i n r e l a t i v e s t r i k e c o s t s over t i m e : INT = T h e n o m i n a l r a t e o f i n t e r e s t i n p e r c e n t as measured by the McLeod Young, Weir i n d u s t r i a l bond y i e l d average weighted l o n g - t e r m . I t i s a v a i l a b l e i n the Bank o f Canada Review. INV = T h e change i n t h e v a l u e o f i n v e n t o r i e s averaged over the p a s t 5 y e a r s T h i s i s c a l c u l a t e d from the P r i n c i p l e S t a t i s t i c s o f the wood p r o d u c t s i n d u s t r y i n BC ( S t a t i s t i c s Canada c a t . 35-204 and 35-206) The change i n i n v e n t o r i e s i s e q u a l to v a l u e added p l u s c o s t s o f f u e l and e l e c t r i c i t y p l u s c o s t s o f m a t e r i a l s a n d s u p p l i e s m i n u s t h e v a l u e o f shipments INV i s expres sed i n terms o f ' 0 , 0 0 0 ' s o f c u r r e n t d o l l a r s CU = T h e B a n k o f C a n a d a c a p a c i t y u t i l i z a t i o n r a t e a v a i l a b l e from t h e Bank o f C a n a d a r e v i e w . The r a t e was m u l t i p l i e d by 10 f o r e s t i m a t i o n purposes UN = The unemployment r a t e i n B C . ( S t a t i s t i c s Canada c a t a l o g u e 71-201) . UIC = A m e a s u r e o f t h e generos i ty_ o f the unemployment i n s u r a n c e program. I t i s e q u a l to the p r o p o r t i o n o f t h e l a b o u r f o r c e c o v e r e d by unemployment i n s u r a n c e i n C a n a d a t i m e s t h e r a t i o o f unemployment i n s u r a n c e b e n e f i t s t o t h e average wage i n BC t imes a f a c t o r which takes i n t o account 176 t h e tax t rea tment o f unemployment b e n e f i t s . The tax f a c t o r i s t h e same as t h e one u s e d i n t h e a l t e r n a t i v e wage measure. Unemployment i n s u r a n c e d a t a i s g i v e n i n S t a t i s t i c s Canada c a t a l o g u e 7 3- 0 0 1 . U n f o r t u n a t e l y , t h e d a t a on c o v e r a g e was a v a i l a b l e o n l y f o r C a n a d a The a v e r a g e wage i s m e a s u r e d by t h e a v e r a g e w e e k l y wage f o r B C ' s i n d u s t r i a l c o m p o s i t e , l a r g e r f i r m d a t a , a v a i l a b l e from S t a t i s t i c s Canada c a t a l o g u e 72-002. DEM = The p r o p o r t i o n o f women o f a l l ages and men under 25 i n the t o t a l l a b o u r f o r c e i n B C . T h i s d a t a i s a v a i l a b l e f r o m S t a t i s t i c s Canada ' s Labour F o r c e Survey w i t h the e x c e p t i o n o f the number o f males u n d e r 25 i n B C ' s l a b o u r f o r c e from 1966 to 1974 which i s u n p u b l i s h e d . A l s o , the number o f males under 25 was not a v a i l a b l e from 1963 - 1965 and i t was assumed t h a t t h e i r p r o p o r t i o n i n B C ' s t o t a l l a b o u r f o r c e was c o n s t a n t f r o m 1963 t o 1966 . F i n a l l y t h e d a t a f o r m a l e s u n d e r 25 was n o t a d j u s t e d from 1966 t o 1974 f o r the major changes which o c c u r r e d i n the Labour F o r c e Survey i n 1974. T h i s caused a n o t i c e a b l e break i n the s e r i e s . To c o r r e c t f o r t h i s t h e f o l l o w i n g p r o c e d u r e was adopted: 177 where m. = males under 25 y e a r s o f age i n the l a b o u r f o r c e i n a r e a K i n y e a r t v LF^. = t o t a l l a b o u r f o r c e i n a r e a k i n y e a r t BC = B r i t i s h Co lumbia C = Canada t = 1963 to 1974.

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