Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Wage and employment determination in a unionized industry : the IWA in the B.C. wood products industry 1984

You don't seem to have a PDF reader installed, try download the pdf

Item Metadata

Download

Media
UBC_1984_A1 M37_8.pdf
UBC_1984_A1 M37_8.pdf [ 5.7MB ]
UBC_1984_A1 M37_8.pdf
Metadata
JSON: 1.0096593.json
JSON-LD: 1.0096593+ld.json
RDF/XML (Pretty): 1.0096593.xml
RDF/JSON: 1.0096593+rdf.json
Turtle: 1.0096593+rdf-turtle.txt
N-Triples: 1.0096593+rdf-ntriples.txt
Citation
1.0096593.ris

Full Text

WAGE AND EMPLOYMENT DETERMINATION IN A UNIONIZED INDUSTRY: THE IWA IN THE B .C . WOOD PRODUCTS INDUSTRY By FELICE F. MARTINELLO B .A . ( H o n . ) , The U n i v e r s i t y o f Western O n t a r i o , 1978 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES (Depar tment o f Economic s ) We a c c ep t t h i s t h e s i s as c o n f o r m i n g t o t he r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA A p r i l 1984 Q F e l i c e F. M a r t i n e l l o , 1984 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the requirements f o r an advanced degree a t the U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying o f t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the head o f my department o r by h i s o r her r e p r e s e n t a t i v e s . I t i s understood t h a t copying o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department o f Economics The U n i v e r s i t y o f B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date 28 September 19 i i A b s t r a c t A new da t a s e t i s o l a t 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 Ame r i c a and t h e B r i t i s h Co lumb ia wood p r o d u c t s i n d u s t r y 1 9 6 3 - 7 9 . Two n o n - n e s t e d mode ls o f 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 a r e d e r i v e d , s p e c i f i e d , and e s t i m a t e d u s i n g t h e new da t a s e t . In one model (monopoly un i on mode l ) t h e un i on chooses t h e wage u n i l a t e r a l l y t o max im i ze i t s o j e c t i v e f u n c t i o n s u b j e c t t o t h e i n d u s t r y l a b o u r demand f u n c t i o n . The i n d u s t r y chooses employment s u b j e c t t o t h e un i on wage and an i n e f f i c i e n t wage-employment package r e s u l t s . In t h e o t h e r model ( c o o p e r a t i v e un i on mode l ) t h e un i on and i n d u s t r y b a r g a i n about wages and employment and r e a c h , by some u n s p e c i f i e d means, an e f f i c i e n t wage-employment p a c k a g e . The e s t i m a t e d un i on o b j e c t i v e f u n c t i o n i s i n c r e a s i n g i n r e a l wages and employment and d e c r e a s i n g i n t h e w o r k e r s ' r e a l a l t e r n a t i v e wage . At t h e mean o f t h e d a t a t h e e s t i m a t e d e l a s t i c i t y o f s u b s t i t u t i o n between r e a l wages and employment i s 0.7 and t h e un i on i s i n d i f f e r e n t t o a 1.5% d e c r e a s e i n employment and a 1% i n c r e a s e i n r e a l wages . P o p u l a r h ypo the se s about un ion b e h a v i o u r ( r e n t m a x i m i z a t i o n and wage b i l l m a x i m i z a t i o n ) a r e r e j e c t e d as a r e h ypo t he s e s t h a t t h e un ion i s i n d i f f e r e n t t o t h e a l t e r n a t i v e wage and t h e l e v e l o f emp loyment . The e s t i m a t e d p r o d u c t i o n t e c h n o l o g y shows t h a t l a b o u r i s s u b s t i t u t a b l e w i t h m a t e r i a l s and c a p i t a l , and m a t e r i a l s and c a p i t a l a r e c omp l emen t s . I n d u s t r y c o s t f u n c t i o n s a r e not concave i n i n p u t p r i c e s , but i n p u t demand f u n c t i o n s s l o p e down. The e s t i m a t e d e l a s t i c i t y o f t h e demand f o r l a b o u r i s l e s s than minus one i n t h e i i i monopo ly un i on model so t h e un i on i s o p e r a t i n g on an e l a s t i c p o r t i o n o f t h e demand f o r l a b o u r f u n c t i o n . The c o o p e r a t i v e un i on model i s a rgued t o be t h e a p p r o p r i a t e model s i n c e i t p r e d i c t s an e f f i c i e n t ou t come . T h i s p r e f e r e n c e f o r t h e c o o p e r a t i v e un i on model i s s u p p o r t e d by t h e da t a when t h e two mode ls a r e t e s t e d a g a i n s t one a n o t h e r . i 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 L i s t o f F i g u r e s v i i i Acknow ledgements i x Chap 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: Su r vey o f L i t e r a t u r e 3 Chap t e r 3 : The Data 23 I n s t i t u t i o n a l S e t t i n g 23 Labour 26 C a p i t a l S e r v i c e s 26 M a t e r i a l s 30 Ou tpu t 31 A l t e r n a t i v e Wage 32 S c a l i n g t h e Da ta 33 Two F laws i n t h e Data 35 C h a p t e r 4: The Wood P r o d u c t s Te chno l ogy 36 T r a n s l o g S p e c i f i c a t i o n 37 C o n d i t i o n a l C o s t F u n c t i o n S p e c i f i c a t i o n 40 D i s c u s s i o n and Compar i son o f t h e R e s u l t s w i t h o t h e r S t u d i e s 49 V Chap te r 5: Un ion M o d e l s : Cos t M i n i m i z a t i o n 53 Monopo ly Un ion Model 61 C o o p e r a t i v e Un ion Model 72 Non -Cons t an t R e t u r n s t o S c a l e 80 Summary 88 Append i x t o C h a p t e r 5 91 Chap t e r 6: Un ion M o d e l s : P r o f i t M a x i m i z a t i o n 97 Monopo ly Un i on Model 99 C o o p e r a t i v e Un ion Model 106 Summary I l l Append i x t o Chap t e r 6 112 C h a p t e r 7: On C h o o s i n g a T rue Model 116 Nes ted Tes t 121 L i k e l i h o o d Compa r i son T e s t 123 Non-nes ted Tes t 125 Summary 128 Chap t e r 8 : C o n c l u s i o n 130 A p p e n d i x : More on t h e Da ta 133 B i b l i o g r a p h y 141 v i L i s t o f T a b l e s Tab l e I : E s t i m a t e d C o e f f i c i e n t s o f t h e T r a n s l o g Co s t F u n c t i o n 41 Tab l e I I : E s t i m a t e d C h a r a c t e r i s t i c s o f t h e T e c h n o l o g y : T r a n s l o g Co s t F u n c t i o n and Exogenous Wages 42 Tab l e I I I : E s t i m a t e d C o e f f i c i e n t s o f t h e C o n d i t i o n a l Co s t F u n c t i o n 46 Tab l e IV : E s t i m a t e d C h a r a c t e r i s t i c s o f t h e T e c h n o l o g y : C o n d i t i o n a l Co s t F u n c t i o n and Exogenous Wages 47 Tab l e V: C o l l e c t i v e Agreements f o r t h e Coas t and I n t e r i o r Reg i on s 56 Tab l e V I : E s t i m a t e d C o e f f i c i e n t s o f t h e Monopo ly Un i on Model 66 Tab l e V I I : E s t i m a t e d C h a r a c t e r i s t i c s o f Un ion P r e f e r e n c e s and P r o d u c t i o n T e c h n o l o g y : Monopo ly Un ion Model and No Dummy V a r i a b l e s 67 Tab l e V I I I : E s t i m a t e d C h a r a c t e r i s t i c s o f Un ion P r e f e r e n c e s and P r o d u c t i o n T e c h n o l o g y : Monopo ly Un ion Model w i t h Dummy V a r i a b l e s 68 Tab l e IX : Max im i zed Va l ue s o f t h e Log L i k e l i h o o d s o f t h e Un i on M o d e l s : C o n s t a n t R e t u r n s t o S c a l e 70 Tab l e X: E s t i m a t e d C o e f f i c i e n t s o f t h e C o o p e r a t i v e Un i on Model 75 Tab l e X I : E s t i m a t e d C h a r a c t e r i s t i c s o f Un ion P r e f e r e n c e s and P r o d u c t i o n T e c h n o l o g y : C o o p e r a t i v e Un ion Model and No Dummy V a r i a b l e s 76 Tab l e X I I : E s t i m a t e d C h a r a c t e r i s t i c s o f Un ion P r e f e r e n c e s and P r o d u c t i o n T e c h n o l o g y : C o o p e r a t i v e Un ion Model w i t h Dummy V a r i a b l e s 77 Tab l e X I I I : E s t i m a t e d C o e f f i c i e n t s : Non -Cons t an t R e t u r n s t o S c a l e w i t h Dummy V a r i a b l e s 84 Tab l e X IV : E s t i m a t e d C h a r a c t e r i s t i c s o f Un ion P r e f e r e n c e s and P r o d u c t i o n T e c h n o l o g y : Monopo ly Un ion Model w i t h Non -Cons t an t Re t u r n s t o S c a l e and Dummy V a r i a b l e s 85 v i i T ab l e XV: E s t i m a t e d C h a r a c t e r i s t i c s o f Un ion P r e f e r e n c e s and P r o d u c t i o n T e c h n o l o g y : C o o p e r a t i v e Un ion Model w i t h Non -Cons t an t Re tu rn s t o S c a l e and Dummy V a r i a b l e s 86 Tab l e XV I : Max im i z ed Va l ue s o f t h e Log L i k e l i h o o d s o f t h e Un ion M o d e l s : Non -Cons t an t R e t u r n s t o S c a l e w i t h Dummy V a r i a b l e s 87 Tab l e X V I I : E s t i m a t e d C o e f f i c i e n t s o f t h e Monopoly and C o o p e r a t i v e Un ion M o d e l s : P r o f i t M a x i m i z a t i o n 103 Tab l e X V I I I : E s t i m a t e d C h a r a c t e r i s t i c s o f Un ion P r e f e r e n c e s and P r o d u c t i o n T e c h n o l o g y : Monopo ly Un ion Model w i t h P r o f i t M a x i m i z a t i o n 104 Tab l e X IX : E s t i m a t e d C h a r a c t e r i s t i c s o f Un ion P r e f e r e n c e s and P r o d u c t i o n T e c h n o l o g y : C o o p e r a t i v e Un ion Model w i t h P r o f i t M a x i m i z a t i o n 110 T ab l e XX: Means and S t anda rd D e v i a t i o n s o f t h e Data . . . 134 v i i i L i s t o f F i g u r e s F i g u r e 1 5 F i g u r e 2 17 F i g u r e 3 59 F i g u r e 4 64 F i g u r e 5 119 F i g u r e 6 135 F i g u r e 7 136 i x Ackn owTedgemen t s I wou ld l i k e t o thank t h e members o f my commi t tee - E r w i n D i e w e r t , C r a i g R i d d e l l , and Ken W h i t e , f o r t h e i r sage a d v i c e and h e l p f u l s u g g e s t i o n s . I wou ld a l s o l i k e t o thank Karen K a l d e r b ank f o r he r a s s i s t a n c e w i t h t h e c o l l e c t i o n o f t h e da t a and Dav i d Ryan f o r h i s a s s i s t a n c e w i t h t h e n o n - l i n e a r m o n i t o r s o f t w a r e and e s t i m a t i o n . F i n a n c i a l s u p p o r t f rom t he S . S . H . R . C . i s g r a t e f u l l y a c know l edged . 1 Chap t e r 1 I n t r o d u c t i o n In a u n i o n i z e d i n d u s t r y t h e un i on i s t he s o l e and e x c l u s i v e r e p - r e s e n t a t i v e o f l a b o u r . I n d i v i d u a l w o r k e r s and f i r m s do no t n e g o t i a t e c o n d i t i o n s o f emp loyment . F i rms a r e f o r c e d t o n e g o t i a t e t h e c o n d i t i o n s o f employment w i t h t h e un i o n and t h e n e g o t i a t e d t e rms c o ve r a l l wo r k e r s i n t h e i n d u s t r y ( b a r g a i n i n g u n i t ) . Workers a r e f o r c e d t o a c c e p t t h e n e g o t i a t e d c o n d i t i o n s o r work o u t s i d e t h e i n d u s t r y . T h e o r e t i c a l mode l s o f t h e b e h a v i o u r o f u n i o n s and f i r m s i n t h i s s i t u a t i o n abound . However , l i t t l e e m p i r i c a l work has been done on t h e s e m o d e l s . * The pu r po se o f t h i s t h e s i s i s t o pu t mode ls o f t h e b e h a v i o u r o f u n i o n s and f i r m s t o an e m p i r i c a l t e s t . Two p o p u l a r mode ls o f 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 a r e p r e s e n t e d , s p e c i f i e d , and e s t i m a t e d u s i n g annua l d a t a on t h e I n t e r n a t i o n a l Woodworkers o f Ame r i c a (IWA) and 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 , 1963 -79 . The f i r s t model i s a monopo ly u n i o n mode l , where t h e un i o n chooses t h e wage t o max im i z e i t s o b j e c t i v e f u n c t i o n s u b j e c t t o t he i n d u s t r y ' s demand f o r l a b o u r f u n c t i o n . The f i r m choose s t h e l e v e l o f employment s u b j e c t t o 2 t h e un i on wage and an i n e f f i c i e n t outcome r e s u l t s . The s e cond m o d e l , h e r e i n r e f e r r e d t o as t h e c o o p e r a t i v e u n i o n model assumes t h a t t he un i on and i n d u s t r y b a r g a i n about wages and employment t o r each an 1. F a r b e r ( 1 9 7 8 ) , De r t o u z o s and Pen cave l ( 1 9 8 1 ) , de M e n i l ( 1 9 7 1 ) , P e n c a v e l ( 1 9 8 1 ) , and MaCurdy and Pencave l (1983) a r e n o t a b l e e x c e p t i ons . 2 . See , f o r e xamp l e , C a r t t e r ( 1 9 5 9 ) , pp . 77-94 f o r an e x p o s i t i o n o f monopoly m o d e l s . 2 outcome on t h e c o n t r a c t c u r v e , t h e r e b y i n s u r i n g an e f f i c i e n t ou tcome.^ The e s t i m a t i o n o f t h e mode ls p r o v i d e s e s t i m a t e s o f t h e IWA's p r e f e r e n c e s and a l l o w s common p r o p o s i t i o n s about un ion p r e f e r e n c e s t o be t e s t e d . The e s t i m a t i o n o f t h e mode l s a l s o p r o v i d e s e s t i m a t e s o f t h e t e c h n o l o g y o f t h e B .C . wood p r o d u c t s i n d u s t r y . Once t h e mode ls a r e e s t i m a t e d , t h e e m p i r i c a l p e r f o rmance o f each i s e v a l u a t e d . The mode ls a r e compared t o see wh i ch i s t h e t r u e model o f t h e o b s e r v e d b e h a v i o u r o f t h e IWA and wood p r o d u c t s i n d u s t r y i n B .C . C h a p t e r 2 p r e s e n t s a s u r v e y o f t h e t h e o r e t i c a l and e m p i r i c a l l i t e r a t u r e on un i on mode ls w h i l e Chap t e r 3 p r o v i d e s s o u r c e s , d e s c r i p - t i o n s and d e f i n i t i o n s o f t h e d a t a used i n t h e s t u d y . E s t i m a t e s o f t h e t e c h n o l o g y o f t h e B .C . wood p r o d u c t s i n d u s t r y , under t h e a s s u m p t i o n s o f exogenous i n p u t p r i c e s and p r i c e t a k i n g b e h a v i o r , a r e r e p o r t e d i n Chap t e r 4 . Chap t e r s 5 and 6 show t he d e r i v a t i o n , s p e c i f i c a t i o n and e s t i m a t i o n r e s u l t s o f t h e two un ion mode ls assuming c o s t m i n i m i z i n g and 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 by t h e i n d u s t r y . C h a p t e r 7 p r e s e n t s t h e a t t emp t t o choose between t he two un i on mode ls and c o n c l u s i o n s a r e drawn i n Chap t e r 8 . 3 . S e e , f o r e xamp l e , De Men i l ( 1 9 7 1 ) , pp . 1-27 or H a l l and L i l i e n (1979 ) f o r an e x p o s i t i o n o f a c o o p e r a t i v e m o d e l . 3 Chapter 2 Survey of the Literature This chapter surveys the theoretical and empirical l i terature on economic models of union behaviour. A truly exhaustive survey requires a study of bargaining and strike theories. These topics are outside the scope of this project and will therefore be mentioned brief ly rather than surveyed careful ly. The economic models of unions can be divided into two categories: monopoly models and cooperative models. The monopoly model is simply the standard textbook model of monopoly behaviour. The model can be written as a constrained maximization problem where the union maximizes some objective function of wages, employment, and other variables, subject to a market opportunities set defined by the demand for labour function. The demand for labour function which constrains the union's behaviour is the horizontal sum of the demand for labour functions of firms within the union's bargaining unit. If the union is the bargaining agent for all labour in an industry, the union is constrained by the industry demand for labour function. If the union only bargains for the workers in a single firm, then that firm's demand for labour function is the constraint in the union's maximization problem. The union, in this category of models, unilaterally chooses the wage which maximizes its objective function. The demanders of union labour accept the union wage as an exogenous parameter and choose the level of employment which yields them the highest level of profit possible given that union wage. This amount of employment is shown by the demand for labour function. Thus, the union chooses the wage 4 wh i ch max im i ze s i t s o b j e c t i v e f u n c t i o n s u b j e c t t o t h e a p p r o p r i a t e demand f o r l a b o u r f u n c t i o n . In F i g u r e 1, DD i s t h e a p p r o p r i a t e demand f o r l a b o u r f u n c t i o n ; T Q , and T 2 a r e i s o p r o f i t c u r v e s ; u^ and u 1 a r e un i o n i n d i f f e r e n c e c u r v e s ; and CC i s t h e c o n t r a c t c u r v e . A c c o r d i n g t o t h e monopo ly m o d e l , t h e u n i o n choose s a wage ŵ  and t h e f i r m s r e a c t t o w, by emp l o y i n g u n i t s o f l a b o u r . F o r m a l l y , t h e monopoly model can be w r i t t e n Max[U(X) : w e Z ] , where Z = [w : L (w ,Y ) > 0, w > 0 ] , U(X) i s t h e u n i o n ' s o b j e c t i v e f u n c t i o n , X i s a v e c t o r o f v a r i a b l e s ( u s u a l l y i n c l u d i n g w and L ( w , Y ) ) , w i s t h e a ve r age r a t e o f c ompensa t i on p a i d t o l a b o u r , L ( w , Y ) i s t h e demand f o r l a b o u r f u n c t i o n , and Y i s a v e c t o r o f exogenous v a r i a b l e s wh i ch a f f e c t t h e demand f o r l a b o u r f u n c t i o n . D i f f e r e n t t y p e s o f monopoly mode ls a r e d i f f e r e n t i a t e d f r om one ano t h e r by t h e o b j e c t i v e f u n c t i o n [ U ( X ) ] wh i ch i s s p e c i f i e d . The most commonly c i t e d monopoly model i s t h e r e n t m a x i m i z a t i o n model where U(X) = [w - A ] L , ( 2 . 1 ) A i s t h e o p p o r t u n i t y c o s t o f l a b o u r ' s t i m e and L i s t h e amount o f 1 l a b o u r e m p l o y e d . ' 1. C a r t t e r ( 1 9 5 9 ) , p. 80 , Dun lop ( 1 9 4 4 ) , p . 4 1 , Rosen ( 1 9 7 0 ) , R e y n o l d s ( 1 9 8 1 ) , and McDona ld and So low ( 1 9 8 1 ) , pp . 897 -899 a l l d i s c u s s t h i s m o d e l . McDona ld and Solow (1981) a c t u a l l y s p e c i f y 5 FIGURE 1 6 An o f t e n s u g g e s t e d e x t e n s i o n t o t h e r e n t m a x i m i z a t i o n model i s t o have t h e un i on max im i z e r e n t s minus t h e c o s t o f p r o v i d i n g un i on 2 s e r v i c e s . Hence , t h e u n i o n ' s maximand i s U(X) = [w - A]L - C ( L , P ) ( 2 . 2 ) where C ( L , P ) i s t h e minimum c o s t o f p r o v i d i n g un i o n s e r v i c e s t o L u n i o n members g i v e n i n p u t p r i c e s P. F i n a l l y , e q u a t i o n 2 .1 n e s t s a n o t h e r p o p u l a r monopoly m o d e l , t h e wage b i l l m a x i m i z a t i o n m o d e l . In t h i s c a s e , t h e u n i o n ' s o b j e c t i v e f u n c t i o n i s g i v e n by U(X) = wL. ( 2 . 3 ) The m i c r o f o u n d a t i o n s and i n t e r p r e t a t i o n o f t h e r e n t m a x i m i z a t i o n mode l s have been t h e s u b j e c t o f much c o n t r o v e r s y . R e yno l d s ( 1981 , p. 164) s u g g e s t s t h a t t h e r e n t m a x i m i z a t i o n models a r e r e a s o n a b l e be cause u n i o n d e c i s i o n makers want t o max im i z e t h e amount o f w e a l t h U(X) = ( L / N ) [ U ( w ) - D ] + [ ( N - L ) / N ] U ( A ) where N i s t h e number o f un i on members, D i s t h e d i s u t i l i t y o f wo r k , U(w) i s t h e u t i l i t y f u n c t i o n o f e v e r y u n i o n member, and employment i s a l l o c a t e d t o un i o n members by a l o t t e r y . M a x i m i z i n g t h e McDona ld and So low o b j e c t i v e f u n c t i o n i s e q u i v a l e n t t o m a x i m i z i n g U(X) = [ U ( w ) - D - U ( A ) ] L = [U(w) - U 0 ] L s i n c e N and D a r e assumed t o be exogenous t o t h e u n i o n . 2 . See , f o r i n s t a n c e , Rosen ( 1 9 7 0 ) , p. 269 , Lewis ( 1 9 5 9 ) , and M a r t i n ( 1 9 8 0 ) , pp . 5 8 - 6 0 . 3 . C a r t t e r (19.59), p. 8 2 , Rees ( 1 9 7 7 ) , p . 5 . Note t h a t t h i s model i s d i f f e r e n t f r om D u n l o p ' s ( 1 9 4 4 ) , p.. 36 famous model i n t h a t t h e r e does not e x i s t a wage-membersh ip f u n c t i o n wh i ch c o n s t r a i n s t h e u n i o n ' s c h o i c e s . 7 wh i c h can be d i s t r i b u t e d t o t h e m s e l v e s o r o t h e r s . R e y n o l d ' s b a s i c p r em i s e i s t h a t t h e model can p roduce c o r r e c t c o n c l u s i o n s w i t h o u t s p e c i f y i n g t h e r e c i p i e n t s o f t h e r e n t s wh i ch t h e un ion e a r n s . T h i s p r em i s e i s somewhat d i f f i c u l t t o m a i n t a i n g i v e n t h e work o f M a r t i n (1980) who e x p l o r e s ve r y c a r e f u l l y how t he a s s i gnmen t o f t h e r i g h t s t o earn r e n t s can a f f e c t t h e b e h a v i o r o f a u n i o n . Two a l t e r n a t e and ex t reme a s s i g nmen t s o f t h e r i g h t s t o earn r e n t s wh i ch p r e d i c t and , t h e r e f o r e , j u s t i f y t h e r e n t m a x i m i z a t i o n m o d e l s , have been s ugge s t ed by L ew i s ( 1959 , p p . 1 9 7 - 1 9 8 ) . The f i r s t i s t h e boss dom ina ted un ion ( o r r a c k e t ) where t h e un i on boss makes a l l t h e d e c i s i o n s and ea rn s a l l t h e r e n t s . The boss chooses t h e un ion wage wh i ch max im i ze s un i on r e n t s i n o r d e r t o max im i ze h i s i n c o m e . The un i on can be t h o u g h t o f as a f i r m wh i ch h i r e s l a b o u r a t i t s o p p o r t u n i t y c o s t and r e - s e l l s i t t o f i r m s a t t h e un ion r a t e . The d i f f e r e n c e between t h e un i on r a t e and l a b o u r ' s o p p o r t u n i t y c o s t i s e x t r a c t e d t h r o u g h i n i t i a t i o n f e e s and un ion d u e s . The second a s s i gnmen t o f t h e r i g h t s t o earn r e n t s i s t h e wo r ke r dom ina ted un i on where wo rke r s s h a r e a l l t h e r e n t s amongst t h e m s e l v e s . The w o r k e r s s e t t h e un i on wage t o max im i ze t o t a l r e n t s so as t o m a x i - m i ze t h e i r income f rom t h e r e n t s . Un ion l e a d e r s can be c o n s i d e r e d emp loyees o f t h e w o r k e r s , b e i n g p a i d t h e marke t wage f o r t h e i r s k i l l s , and wo r k i n g t o n e g o t i a t e and e n f o r c e t h e wage chosen by t h e w o r k e r s . N e i t h e r o f t h e two ex t reme a s s i g nmen t s o f r i g h t s wh i ch j u s t i f y t h e r e n t m a x i m i z a t i o n mode ls appea r t o c o r r e s p o n d t oo w e l l w i t h t h e e s t a b l i s h e d f o l k l o r e about t h e n a t u r e o f u n i o n s . As a r e s u l t , t h e r e n t m a x i m i z a t i o n mode ls have been c r i t i c i z e d by many a u t h o r s w i t h Ross (1948) be i ng t h e most i n f l u e n t i a l . 8 The c o n c e p t o f a "bos s dom ina t ed u n i o n " i s r e j e c t e d c o m p l e t e l y by Ross (1948 , pp . 22 , 2 8 ) , Dunlop (1944 , p. 3 2 ) , C a r t t e r ( 1959 , p . 78) and o t h e r s . They m a i n t a i n t h a t u n i o n s do no t p u r c h a s e l a b o u r f o r r e s a l e t o f i r m s and c a n n o t , t h e r e f o r e , be m o d e l l e d as f i r m s . Hence , t h e boss dom ina t ed j u s t i f i c a t i o n o f r e n t m a x i m i z a t i o n mode ls i s r e j e c t e d by t h o s e c r i t i c s . The wo r k e r dom ina t ed ex t r eme appea r s t o be much c l o s e r t o Ro s s ' (and o t h e r c r i t i c s ' ) n o t i o n o f t h e n a t u r e o f un i on s t han t h e boss dom ina t ed e x t r e m e . However , t h r e e s t r o n g arguments a r e made a g a i n s t t h e r e a s o n a b l e n e s s o f t h e wo r ke r dom ina ted j u s t i f i c a t i o n o f a r e n t m a x i m i z i n g u n i o n . The f i r s t argument p o i n t s ou t t h a t u n i o n w o r k e r s 4 a r e no t a homogeneous g r o u p . The r e a r e rank and f i l e members and un i on l e a d e r s who have been e l e c t e d t o o f f i c e by t h e members, but who rema in a p a r t o f t h e u n i o n . F u r t h e r , w i t h i n each o f t h o s e g roups t h e r e e x i s t o t h e r subgroups o f members wh i ch a r e d i f f e r e n t f r om one a n o t h e r . Ross (1948 , p p . 31 -32 ) m a i n t a i n s t h a t t h e d i f f e r e n t g roups have d i f f e r e n t and o f t e n c o n f l i c t i n g g o a l s f o r t h e u n i o n . T h i s p r ob l em becomes much more s e r i o u s when one r e c o g n i z e s t h a t a un i on p roduces many l o c a l p u b l i c good s . The p r i v a t e c o s t s and b e n e f i t s o f c h o i c e s d i f f e r a c r o s s g r o u p s , and t h e s e p r i v a t e c o s t s and 5 b e n e f i t s a r e d i f f e r e n t f rom t h e c o l l e c t i v e c o s t s and b e n e f i t s . Ross (1948) a rgues t h a t i t i s u n r e a s o n a b l e t o b e l i e v e t h a t t h e c o n f l i c t i n g p r e f e r e n c e s o f d i f f e r e n t g r o u p s , as w e l l as t h e 4 . See Ross ( 1 9 4 8 ) , p p . 3 1 - 3 2 . 5 . See Ross ( 1 9 4 8 ) , pp . 2 3 - 2 4 . Ross r e f e r s t o t h e c o l l e c t i v e g o a l s ( i . e . , t h e c o l l e c t i v e c o s t s and b e n e f i t s ) as t h e i n s t i t u t i o n a l g o a l s and p o i n t s out t h e d i f f e r e n c e between t h e member 's o r l e a d e r ' s p r i v a t e g o a l s and t h e i n s t i t u t i o n a l o r c o l l e c t i v e g o a l s . 9 d i f f e r e n c e s between p r i v a t e and c o l l e c t i v e i n c e n t i v e s , can be accommodated and e x p r e s s e d by t he s i m p l e r e n t m a x i m i z i n g o b j e c t i v e f u n c t i o n . The second argument f o l l o w s f rom t he f i r s t . G i v en t h a t t h e r e e x i s t d i f f e r e n t g roups w i t h i n t h e un i on wh i ch have d i f f e r e n t g o a l s , some s o r t o f p r o c e s s or sys tem i s needed t o choose wh i ch g o a l s t h e un i on a c t u a l l y p u r s u e s . The p a r t i c u l a r p r o c e s s o r sys tem used t o r e - c o n c i l e t h e c o n f l i c t i n g g o a l s a f f e c t s t h e b e h a v i o u r of t h e un i on and must t h e r e f o r e , be e x p l i c i t l y i n c l u d e d i n any model o f u n i o n b e h a v i o u r . The r en t m a x i m i z a t i o n mode ls do not model t h i s d e c i s i o n p r o c e s s so i t i s a g a i n a rgued t h a t t h e r e n t m a x i m i z a t i o n mode ls a r e i n a d e q u a t e mode ls o f un i on b e h a v i o u r . The t h i r d argument a s s e r t s t h a t u n c e r t a i n t y about t h e u l t i m a t e employment e f f e c t s o f n e g o t i a t e d wage r a t e s makes i t i m p o s s i b l e f o r t h e un i o n t o c o n s i d e r t h e employment e f f e c t s o f wage b a r g a i n s . ^ Ross ( 1948 , p p . 79 -80) a s s e r t s t h a t t h e d e c i s i o n makers w i t h i n t he un i on a re unab l e o r u n w i l l i n g t o a d j u s t ob se r ved employment f o r any changes i n exogenous v a r i a b l e s wh i ch may have o c c u r r e d . Hence , t h e d e c i s i o n - makers o b s e r v e no r e l a t i o n between wages and employment and n e g l e c t t h e employment e f f e c t s o f n e g o t i a t e d wage r a t e s . To summar i z e , Ross (among o t h e r s ) r e j e c t s t h e i d e a t h a t un i o n s can be f r u i t f u l l y mode l l e d as r e n t m a x i m i z i n g a g e n t s . Ross r e j e c t s c o m p l e t e l y t h e n o t i o n o f a boss dom ina ted un i on and a rgues c o n v i n c - 6 . See A t h e r t o n ( 1 9 7 3 ) , p. 20 and Ross ( 1 9 4 8 ) , p p . 32 , 3 7 - 4 0 . 7 . See Ross ( 1 9 4 8 ) , pp . 7 9 - 8 0 . 10 i n g l y t h a t a wo r ke r dom ina ted un i on w i l l no t behave as i f i t were m a x i m i z i n g an o b j e c t i v e f u n c t i o n l i k e e q u a t i o n 2 . 1 . The f i n a l word on t h e t h e o r e t i c a l r e a s o n a b l e n e s s o f r en t m a x i - m i z i n g mode l s w i l l be g i v en t o M a r t i n ( 1 9 8 0 ) . E s s e n t i a l l y , M a r t i n a r gue s t h a t i f t h e r i g h t s t o r e n t s a r e t r a n s f e r a b l e , and i f enough e f f i c i e n t ma r ke t s e x i s t , t hen a l l t h e o b j e c t i o n s o u t l i n e d above a re overcome by t h e ma rke t s and t h e un i on w i l l max im i ze t o t a l r e n t s . For e xamp l e , c o n s i d e r M a r t i n ' s s i m p l e s t c a s e . M a r t i n ( 1980 , p. 13) s p e c i f i e s t h a t i f (a) t h e r i g h t s t o r e n t s a r e a s s i g n e d t o un i on mem- be r s and a r e t r a n s f e r a b l e , (b) an e f f i c i e n t marke t f o r t h o s e r i g h t s e x i s t s , ( c ) m o n i t o r i n g l e a d e r s i s c o s t l e s s , and (d) an e f f i c i e n t marke t f o r l e a d e r s e x i s t s , t hen t h e un ion w i l l behave so as t o m a x i - m i z e t h e t o t a l r e n t s a c c r u i n g t o t h e u n i o n . A number o f mode ls wh i ch n e s t t h e r e n t m a x i m i z a t i o n model have been put t o an e m p i r i c a l t e s t by De r t ou zo s and Pencave l (1981) and Pencave l ( 1 9 8 1 ) , u s i n g annua l d a t a f rom a number o f newspaper p r i n t i n g o p e r a t i o n s i n v o l v i n g 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 ) . On ly t h e r e s u l t s o b t a i n e d f rom t he C i n c i n n a t i Pos t l o c a l ( 1946 -1965) a r e r e p o r t e d , s i n c e t h e d a t a f rom t he o t h e r newspapers a r e no t as good as t h e e x c e l l e n t d a t a on t h e C i n c i n n a t i P o s t . D e r t o u z o s and Pencave l (1981) a rgue t h a t t h e monopoly model i s a p p r o p r i a t e f o r t h e ITU because t h e un ion h o l d s a much s t r o n g e r b a r - g a i n i n g p o s i t i o n than t he newspapers and s t r i k e s a r e uncommon. The u n i o n ' s dominance o c c u r s because o f t h e n ewspape r ' s v u l n e r a b i l i t y t o s t r i k e s . T h i s v u l n e r a b i l i t y r e s u l t s f rom t h e e x i s t e n c e o f v e r y c l o s e s u b s t i t u t e s f o r a d v e r t i s e r s ( e . g . , r a d i o o r f l y e r s ) and t h e i m p o s s i - b i l i t y o f b u i l d i n g up an i n v e n t o r y o f o u t p u t . The ITU i s a l s o v e r y d e m o c r a t i c and t h e members a r e q u i t e homogeneous ( i . e . , t h e y a r e a l l 11 p r i n t e r s ) . T h e r e f o r e t h e r e s h o u l d be few d i v e r g e n t p r e f e r e n c e s between members and l e a d e r s and between d i f f e r e n t g roups o f members. Th r ee b a s i c mode ls a r e e s t i m a t e d . The f i r s t model s p e c i f i e s t h e f o l l o w i n g S t one -Gea r y o b j e c t i v e f u n c t i o n f o r t h e u n i o n , and c o s t m i n i m i z i n g demand f o r l a b o u r f u n c t i o n : U (w /p , L ) = ( w / p - A ) e ( L - B ) 1 _ 9 ( 2 . 4 ) L = bg + b 1 ( w / r 1 ) + b 2 ( r 2 / r 1 ) + b 3 Q + b 4 D ( 2 . 5 ) where p i s an i n de x o f consumer p r i c e s , Q i s ou t pu t measured by a d v e r t i s i n g l i n a g e , r 1 i s t h e p r i c e o f n e w s p r i n t , i s t h e w h o l e s a l e p r i c e i n de x o f mach i ne r y and equ i pmen t , and D i s a dummy v a r i a b l e wh i ch r e f l e c t s t h e e f f e c t s o f mergers w i t h o t h e r n ewspape r s . C l e a r l y e q u a t i o n 2 .4 n e s t s bo th t h e r e n t m a x i m i z a t i o n and w a g e - b i l l m a x i m i z a - t i o n m o d e l s . Reduced form e q u a t i o n s f o r w and L a r e d e r i v e d and FIML e s t i m a t e s o f t h e pa r ame te r s a r e o b t a i n e d . The e s t i m a t e d 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 un i on p r e f e r e n c e s between r e a l wages and emp l o y - ment , e v a l u a t e d a t t h e same mean, i s . 6 9 . F u r t h e r , i t i s e s t i m a t e d t h a t 0 < 9 < . 5 , i n d i c a t i n g t h a t t h e un ion i s no t i n d i f f e r e n t t o t h e l e v e l o f emp loyment , and A > 0 . The wage b i l l m a x i m i z a t i o n hypo- t h e s i s , e = .5 and A = B = 0, i s r e j e c t e d u s i n g a l i k e l i h o o d r a t i o t e s t ; as i 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 , 9 = . 5 , B = 0; where A i s d e f i n e d as a l i n e a r f u n c t i o n o f t h e h o u r l y e a r n i n g s o f n o n - s u p e r - v i s o r y w o r k e r s i n t h e r e t a i l t r a d e . The second model s p e c i f i e s t h e f o l l o w i n g l o g - l i n e a r r educed form e q u a t i o n s f o r lnw and I n L : 12 lnw = a Q + a j l n p + a 2 l n r 1 + a 3 l n r 2 + a 4" lnQ + a g D ( 2 . 6 ) InL = b n + b . l n p + b . l n r . + b_ l n r _ + b . l nQ + b D. ( 2 . 7 ) E q u a t i o n s 2.6 and 2.7 a re e s t i m a t e d u s i n g OLS and FIML t e c h n i q u e s , and y i e l d e s t i m a t e s o f t h e e l a s t i c i t i e s o f wages and employment w i t h r e s p e c t t o t h e exogenous v a r i a b l e s . The t h i r d model i s nove l i n t h a t t h e l o g o f t h e f i r s t o r d e r c o n - d i t i o n o f t h e m a x i m i z a t i o n p rob l em i s e s t i m a t e d r a t h e r than t h e r e d u - ced fo rm e q u a t i o n s . An a d d i l o g o b j e c t i v e f u n c t i o n i s s p e c i f i e d ; U (w /p , L ) = K + ya+xrV/p)1"^ ( l - y ) ( l + T 1 ) " 1 L 1 + T 1 ( 2 . 8 ) where K = - u ( l + X)" 1- (1 - y ) ( l + n ) " 1 , 0 < y < 1, and X, n < 0 . I f X = TI a CES f u n c t i o n i s o b t a i n e d w h i l e X = n = -1 i m p l i e s a Cobb- Doug las f u n c t i o n a l f o r m . The advan t age o f t h e a d d i l o g s p e c i f i c a t i o n i s t h a t t h e l o g o f 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 i s l i n e a r i n l nw , l n p , and I n L . The f i r s t o r d e r c o n d i t i o n o f t h e m a x i m i z a t i o n p rob lem i m p l i e s t h a t 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 e q u a l s t h e s l o p e o f t h e demand f o r l a b o u r f u n c t i o n . The s l o p e o f t h e demand f o r l a b o u r f u n c t i o n i s s p e c i f i e d t o be ( e ° ^ ) / r ^ . Hence t h e f i r s t o r d e r c o n d i t i o n can be r e w r i t t e n as l nw /p = ( l / x ) ( l n [ ( l - y ) / y ] + l n p / r . + n lnL + oQ) . ( 2 . 9 ) N o n - l i n e a r 2SLS i s used t o e s t i m a t e t h e pa r ame te r s o f e q u a t i o n 2 . 9 . 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 o f un i on p r e f e r e n c e s between r e a l 13 wages and employment i s e s t i m a t e d t o be .469 a t t h e sample mean, w h i l e t h e e s t i m a t e s o f u , A, n, and a a r e . 9 1 , - 2 . 1 4 6 , . 1 6 7 , and - . 0 4 5 r e s p e c t i v e l y . C l e a r l y , t h e e s t i m a t e s do not s a t i s f y a l l t h e r e s t r i c t i o n s i m p l i e d by e q u a t i o n 2 . 8 . A number o f mode ls wh i ch i n c o r p o r a t e a s p e c t s o f t h e a rguments a g a i n s t r e n t m a x i m i z a t i o n mode ls have been p r o p o s e d . B e r k o w i t z (1954) and A t h e r t o n (1973 , p p . 71 -80 ) p ropose a model where t h e i n s t i t u t i o n a l goa l o f t he un ion i s a l l o w e d t o be d i f f e r e n t f rom un i on members ' g o a l s , and t h e i n s t i t u t i o n a l goa l i s p u r s u e d . The un i on max im i z e s i t s ne t revenue or p r o f i t s u b j e c t t o t h e c o n s t r a i n t t h a t t h e un i o n r e t a i n s t h e b a r g a i n i n g r i g h t s o f t h e w o r k e r s . The u n i o n ' s o b j e c t i v e f u n c t i o n can be w r i t t e n U ( w , L , D , S ) = wDL - C ( L , P , S ) , ( 2 . 1 0 ) where D i s t h e p r o p o r t i o n o f w o r k e r ' s e a r n i n g s c o l l e c t e d as due s , S i s t h e l e v e l o f s e r v i c e s p r o v i d e d by t h e un i on t o each w o r k e r , C ( L , P , S ) i s t h e minimum c o s t o f p r o v i d i n g s e r v i c e s S t o L wo r ke r s g i v e n i n p u t p r i c e s P, and D and S must be such t h a t t h e un i on i s no t d e c e r t i f i e d by t h e w o r k e r s . A t h e r t o n (1973 , p p . 8 0 - 157 ) a l s o p roposes a number o f more g ene r a l mode ls where t h e membersh ip i s no t homogeneous, and t h e s t r i k e l e n g t h needed t o a c h i e v e b a r g a i n i n g outcomes i s i n c l u d e d i n t h e economic c a l c u l u s . The un ion i s a s s i g n e d l e x i c o g r a p h i c p r e f e r e n c e s o ve r w i n n i n g ( d e ) c e r t i f i c a t i o n e l e c t i o n s and e a r n i n g p r o f i t s and i s assumed t o max im i z e i t s u t i l i t y . The model i s e x t ended t o i n c l u d e u n c e r t a i n t y about exogenous v a r i a b l e s so t h a t t h e un ion max im i ze s 14 some l e x i c o g r a p h i c c o m b i n a t i o n o f t h e p r o b a b i l i t y o f t h e l e a d e r ' s r e - e l e c t i o n and e xpe c t e d p r o f i t s . U n f o r t u n a t e l y t h e m o d e l ' s l e v e l o f a b s t r a c t i o n i s v e r y h i g h and no t e s t a b l e p r e d i c t i o n s a r e made. F u r t h e r , A t h e r t o n (1973) does not show t h a t any o f t h e v o t i n g e q u i l i b r i a e x i s t . F a r b e r (1978) d e v e l o p s a much s i m p l e r model where t h e p r e f e r e n c e s o f l e a d e r s and members a r e a l l o w e d t o d i f f e r and un i on members a r e n o t homogeneous. A l l wo r k e r s a r e e q u a l l y r i s k a v e r s e and f a c e a once and f o r a l l l o t t e r y f o r un i on j o b s . Workers who win un ion j o b s r e c e i v e un i o n wages w h i l e w o r k i n g , p en s i o n b e n e f i t s when r e t i r e d and h e a l t h and w e l f a r e b e n e f i t s when t hey a r e wo r k i n g and when t h e y a r e r e t i r e d . The u t i l i t y o f wo r k e r s i s a f u n c t i o n o f t h e p r e s e n t v a l u e o f t h e i r income s t r eam and b e n e f i t s p a c k age , so young and o l d w o r k e r s v a l u e t h e same wage, h e a l t h and p en s i o n b e n e f i t s package d i f f e r e n t l y . I t i s assumed t h a t un i on l e a d e r s max im i z e t h e p r o b a b i l i t y o f t h e i r r e - e l e c t i o n . T h e r e f o r e , u n i o n l e a d e r s choose a wage and h e a l t h and p en s i o n b e n e f i t s package wh i ch max im i z e s t h e median aged w o r k e r ' s e x p e c t e d u t i l i t y s u b j e c t t o t h e demand f o r un i on l a b o u r f u n c t i o n . The v a l u e o f t h e p en s i o n and h e a l t h and w e l f a r e b e n e f i t s i s assumed t o be equa l t o t h e c o n t r i b u t i o n s made t o t h e h e a l t h and p en s i o n funds by t h e e m p l o y e r . The emp loye r c o n t r i b u t e s a f i x e d cha rge per u n i t o u t p u t , so t h e un i on l e a d e r s a c t u a l l y choose t h e wage and ou t pu t t a x wh i ch max im i z e s t h e median aged w o r k e r ' s u t i l i t y . F a r b e r (1978) e s t i m a t e s h i s model u s i n g annua l da t a on t h e U n i t e d Mine Workers (UMW) i n t h e coa l i n d u s t r y ( 1 9 4 7 - 1 9 7 3 ) . F a r b e r ( 1978 , p . 926) a r gues t h a t t h e monopo ly model i s a p p r o p r i a t e because t h e un i on was dominant i n a coa l i n d u s t r y made up o f many sma l l f i r m s . 15 Hence i t i s p l a u s i b l e t o assume t h a t t h e un i on s e t s t h e wage u n i l a t e r a l l y . The e s t i m a t e d i ndex o f r e l a t i v e r i s k a v e r s i o n i s 2 . 9 8 , i n d i c a - t i n g t h a t t h e mine wo r ke r s were r i s k a v e r s e . G i ven t h e l o t t e r y f o r u n i o n j o b s t h i s i n d i c a t e s t h a t t h e un ion behaved as i f i t c o n s i d e r e d Q t h e employment e f f e c t s o f wage demands. The u n i o n ' s d i s c o u n t r a t e i s e s t i m a t e d t o be 3.5%-4.5%, and non taxed payments i n k i n d were v a l u e d 40% h i g h e r than wage paymen t s . F a r b e r ( 1978 , p . 932) does a dd r e s s t h e i s s u e o f whe the r t h e v o t i n g e q u i l i b r i u m e x i s t s . A s u f f i c i e n t c o n d i t i o n f o r t h e e x i s t e n c e o f t h e m a j o r i t y v o t i n g e q u i l i b r i u m i s t h a t t h e v o t e r ' s p r e f e r e n c e s be s i n g l e peaked ove r a s i n g l e v a r i a b l e . F a r b e r (1978 , p. 932) a r gues t h a t un i o n member 's p r e f e r e n c e s w i l l be s i n g l e peaked ove r t h e s e t o f wages and ou t pu t t a x e s wh i ch a r e P a r e t o o p t i m a l ( f rom t he un i on member ' s p o i n t o f v i e w ) . U n f o r t u n a t e l y B l a i r and C r aw fo r d (1983) p rove t h a t t h e v o t i n g e q u i l i b r i u m s p e c i f i e d i n F a r b e r (1978) does not e x i s t . A f i n a l g roup o f monopoly mode l s wh i ch do not be l ong i n t h e two above men t i oned g roups ( i . e . , t h o s e based on r e n t m a x i m i z a t i o n and t h o s e based on t h e c r i t i c i s m s o f t h e r e n t m a x i m i z a t i o n mode l s ) w i l l now be s u r v e y e d . Monopoly mode ls a r e i n c l u d e d i n t h i s group i f t h e i r o b j e c t i v e f u n c t i o n s a r e c o n s i d e r e d r e a s o n a b l e but a r e no t d e r i v e d f rom any a s sump t i o n about t h e n a t u r e o f u n i o n s . T h i s c o n t r a s t s w i t h t h e mode l s above whose o b j e c t i v e f u n c t i o n i s d e r i v e d (however r o u g h l y ) f rom t h e p r e f e r e n c e s o f agen t s w i t h i n t h e u n i o n . 8 . Whether i t i s a p p r o p r i a t e t o say t h a t t h e un i on c o n s i d e r s em- p l o ymen t e f f e c t s , o r t h e c o l l e c t i v e b a r g a i n i n g f ramework m e r e l y c au se s un i on s t o a c t as i f t h e y c o n s i d e r e d employment e f f e c t s (as d i s c u s s e d by Reder ( 1952 ) ) i s no t known. 16 The s i m p l e s t mode ls i n t h i s g roup a r e t h o s e s u r v e yed by C a r t t e r (1959 , p p . 8 3 - 9 0 ) . The un ion i s assumed t o max im i z e wages , emp loy - ment , t h e wage b i l l p l u s p r i v a t e o r p u b l i c unemployment i n s u r a n c e , un i on membe r sh i p , o r some a r b i t r a r y , i n c r e a s i n g , q u a s i c o n c a v e , f u n c - t i o n o f wages and emp loyment . A t h e r t o n ( 1973 , p p . 41 -70) p r e s e n t s a monopoly model wh i c h i s i n t e r e s t i n g i n t h a t t he un ion f a c e s two c o n s t r a i n t s : a demand f o r l a b o u r f u n c t i o n and a s t r i k e l e n g t h f u n c t i o n . The u n i o n ' s o b j e c t i v e f u n c t i o n i s an a r b i t r a r y i n c r e a s i n g f u n c t i o n o f a f t e r - t a x r e a l income and emp loyment , and a d e c r e a s i n g f u n c t i o n o f t h e l e n g t h o f s t r i k e endured b e f o r e a s e t t l e m e n t i s r e a c h e d . The un ion s t i l l chooses t h e wage u n i l a t e r a l l y . However , a s s o c i a t e d w i t h each wage r a t e i s a l e v e l o f emp loyment , g i v en by t h e demand f o r l a b o u r f u n c t i o n , and a s t r i k e o f a c e r t a i n l e n g t h ( p o s s i b l y z e r o ) , g i v e n by t h e s t r i k e 9 l e n g t h f u n c t i o n . The un ion choose s t h e wage wh i ch max im i ze s i t s o b j e c t i v e f u n c t i o n s u b j e c t t o t h e two c o n s t r a i n t s . A l l t h e above men t i oned mode l s s p e c i f y t h e un ion maximand as a f u n c t i o n o f t h e l e v e l s o f wages , emp loyment , and o t h e r v a r i a b l e s . C a r t t e r (1959 , p p . 89 -92 ) s p e c i f i e s a un i on o b j e c t i v e f u n c t i o n wh i ch i s a f u n c t i o n o f t h e changes i n t h e l e v e l s o f wages and employment f r om a s t a t u s quo p o i n t . The s t a t u s quo p o i n t i s t h e u n i o n ' s o p t i m a l wage-employment c o m b i n a t i o n i n t h e p r e v i o u s t ime p e r i o d . C a r t t e r ( 1959 , p p . 89 -90 ) a s s e r t s t h a t i n t e r n a l p o l i t i c a l c o n s i - d e r a t i o n s make t h e un i on u n w i l l i n g t o t r a d e wages f o r employment o r 9 . How t h e s t r i k e l e n g t h f u n c t i o n i s d e r i v e d f rom a t h e o r y o f t h e f i r m , o r why t h e f i r m endu re s a s t r i k e o f a g i v e n l e n g t h o n l y t o y i e l d t o t h e same wage demand e v e n t u a l l y , i n a model w i t h p e r - f e c t i n f o r m a t i o n , i s no t s p e c i f i e d . 17 FIGURE 2 18 v i c e - v e r s a . O t h e r t h i n g s e q u a l , t h e u n i o n r e q u i r e s l a r g e i n c r e a s e s i n wages t o compensate i t f o r sma l l d e c r e a s e s i n employment and l a r g e i n c r e a s e s i n employment t o compensa te i t f o r s m a l l d e c r e a s e s i n wages . In o t h e r wo r d s , t h e un i o n i n d i f f e r e n c e c u r v e s i n wage - emp l oy - ment space a r e a lmo s t L e o n t i e f i n s h a p e . C a r t t e r (1959) f u r t h e r a s s e r t s t h a t when t h e demand f o r l a b o u r i n c r e a s e s ( o t h e r t h i n g s e q u a l ) t h e u n i o n p r e s s e s f o r l a r g e wage i n c r e a s e s a t t h e expense o f sma l l i n c r e a s e s i n emp loyment . When t h e demand f o r l a b o u r d e c r e a s e s ( o t h e r t h i n g s e q u a l ) t h e u n i o n a c c e p t s l a r g e d e c r e a s e s i n employment i n o r d e r t o s u f f e r o n l y sma l l d e c r e a s e s i n wages . A t y p i c a l i n d i f - f e r e n c e map f o r a u n i o n o f t h i s s o r t i s shown i n F i g u r e 2 i n wage- employment s p a c e . R e f e r r i n g t o F i g u r e 2, u ^ u^, and u^ a r 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 e p r e v i o u s p e r i o d ' s demand f o r u n i o n l a b o u r f u n c t i o n i s shown by D Q , p o i n t " c " i s t h e s t a t u s quo p o i n t , and "wpp" i s t h e u n i o n ' s wage p r e f e r e n c e p a t h . I f D̂  r e p r e s e n t s t h e demand f o r un i on l a b o u r i n t h e p r e s e n t p e r i o d , then t h e un i on w i l l max im i z e i t s o b j e c t i v e f u n c t i o n by c h o o s i n g wage w^. P o i n t " d " w i l l be t h e s t a t u s quo p o i n t nex t p e r i o d . I f r e p r e s e n t s t h e p r e s e n t demand f o r u n i o n l a b o u r t h en t h e u n i o n w i l l c hoose w 2 and p o i n t " g " w i l l be nex t p e r i o d ' s s t a t u s quo p o i n t . The s u r v e y o f monopoly mode ls i s c omp l e t e save f o r a few g e n e r a l comments. F i r s t , a l l t h e mode ls o u t l i n e d above c o u l d be e x t ended so t h a t t h e f i r m and t h e u n i o n b a r g a i n o v e r wages w h i l e t h e f i r m s t i l l chooses t h e l e v e l o f emp loyment . Any s o r t o f b a r g a i n i n g model o r model o r a r b i t r a t i o n scheme c o u l d be u s e d . * 0 The f i n a l outcome wou l d 10 . The b a r g a i n i n g model o f H i c k s ( 1 9 6 3 ) , t h e A s h e n f e l t e r and J ohn son (1969) v a r i a t i o n o f t h e H i c k s (1963) m o d e l , o r t h e Nash a r b i t r a t i o n scheme c o u l d a l l be u s e d . 19 l i e on t h e demand f o r l a b o u r c u r v e , somewhere between t he u n i o n ' s op t imum, t h e p o i n t r eached i n t h e mode ls above , and t h e f i r m ' s op t imum, t h e p o i n t where t h e s u p p l y o f l a b o u r c u r v e ( i n t h e absence o f a u n i o n ) i n t e r s e c t s t h e demand f o r l a b o u r c u r v e . S e c ond , t h e monopoly mode ls y i e l d i n e f f i c i e n t o r P a r e t o i n f e r i o r s o l u t i o n s . R e f e r r i n g t o F i g u r e 1, i t i s c l e a r t h a t a l l t h e wage- employment c o m b i n a t i o n s i n t h e shaded l e n s a r ea a r e P a r e t o s u p e r i o r t o p o i n t " e " , t h e monopoly model s o l u t i o n . ^ T h i s f e a t u r e d i s t i n - g u i s h e s t h e monopoly mode ls f r om t h e o t h e r c a t e g o r y o f m o d e l s ; t h e c o o p e r a t i v e m o d e l s . In c o o p e r a t i v e mode ls t he un ion and t h e demanders o f un i on l a b o u r i d e n t i f y t h e i r c o n t r a c t c u r v e and c hoo s e , by some means o r a n o t h e r , a wage-employment c o m b i n a t i o n on t h a t c o n - t r a c t c u r v e . Hence , an e f f i c i e n t outcome i s a c h i e v e d . To r e a ch a p o i n t on t h e c o n t r a c t c u r v e t h e un ion and f i r m s must b a r g a i n o v e r more t han j u s t t h e l e v e l o f wages . The f i r m s must be f o r c e d o f f t h e i r demand f o r l a b o u r f u n c t i o n . T h e r e f o r e , a b a r g a i n wh i c h d e t e r m i n e s both t h e l e v e l o f wages and t h e l e v e l o f employment must be s t r u c k between the un ion and t h e f i r m s i n o r d e r t o keep t h e 12 f i r m s o f f t h e i r demand f o r l a b o u r f u n c t i o n s . 1 1 . The monopoly model s o l u t i o n i s i n e f f i c i e n t and t h e l e n s o f P a r e t o s u p e r i o r wage employment c o m b i n a t i o n s e x i s t s as l o ng as t h e l e v e l s e t s o f t h e un i on o b j e c t i v e f u n c t i o n a r e no t L e o n t i e f i n s h a p e , o r (as p o i n t e d out by Pencave l ( 1 9 8 1 ) , p . 13 as l o ng as t h e u n i o n ' s o b j e c t i v e f u n c t i o n i s not i ndependen t o f t h e l e v e l o f emp loyment . 12 . A f o rma l p r e s e n t a t i o n o f t h e c o o p e r a t i v e model r e q u i r e s a d e f i - n i t i o n o f t h e c o n t r a c t c u r v e and t h e s p e c i f i c a t i o n o f a mechan ism wh i ch chooses a un i que p o i n t on t h a t c o n t r a c t c u r v e . W h i l e t h e f o rme r i s s t r a i g h t f o r w a r d , t h e l a t t e r r e q u i r e s t h e i n v o c a t i o n o f a b a r g a i n i n g scheme wh i ch i s , as no ted e a r l i e r , o u t s i d e t h e scope o f t h i s s u r v e y . Hence a f o rma l s t a t emen t o f t h e c o o p e r a t i v e model w i l l no t be p r e s e n t e d . 20 McDona ld and So low (1981) and de M e n i l (1971) p r e s e n t v e r y s i m i l a r c o o p e r a t i v e models where t h e u n i o n ' s o b j e c t i v e f u n c t i o n i s a f u n c t i o n o f t h e r e n t s a c c r u i n g t o l a b o u r and an a r b i t r a t i o n r u l e i s 13 used t o choose a p o i n t on t h e c o n t r a c t c u r v e . The un i o n and f i r m r e a c h t h e i r c o n t r a c t c u r v e by b a r g a i n i n g o v e r bo th t h e l e v e l o f wages and t h e l e v e l o f emp loyment , de Men i l (1971) d e r i v e s a wage e q u a t i o n f r om h i s model and e x t e nd s i t i n t o a P h i l l i p s c u r v e w i t h b a r g a i n i n g r e l a t e d v a r i a b l e s on t h e r i g h t hand s i d e . The e x t ended P h i l l i p s c u r v e i s t h en e s t i m a t e d u s i n g d a t a on h e a v i l y u n i o n i z e d two d i g i t U .S . m a n u f a c t u r i n g i n d u s t r i e s . McDonald and Solow (1981) d e r i v e t h e c o m p a r a t i v e s t a t i c r e s pon s e s o f t h e i r model t o v a r i a t i o n s i n t h e demand f o r l a b o u r due t o t h e b u s i n e s s c y c l e . H a l l and L i l i e n (1979) a l s o p r opo se a model where t h e u n i o n m a x i - m i zes t h e r e n t s a c c r u i n g t o l a b o u r . T h e i r model i s n o ve l i n t h a t t h e u n i o n and f i r m s do no t b a r g a i n d i r e c t l y about t h e l e v e l o f emp loy - ment . I n s t e a d , t h e un i on s and f i r m s r each t h e i r c o n t r a c t c u r v e by c h o o s i n g a c ompensa t i o n f u n c t i o n (where t o t a l c ompen sa t i o n p a i d t o l a b o u r i s some f u n c t i o n o f employment) wh i ch s u p p o r t s an e f f i c i e n t e q u i l i b r i u m . The c ompensa t i on f u n c t i o n i s chosen so t h a t when bo th s i d e s choose t h e i r o p t i m a l l e v e l s o f employment ( i . e . , when bo th s i d e s max im i z e t h e i r o b j e c t i v e f u n c t i o n s ) s u b j e c t t o t h e c ompensa t i o n f u n c t i o n , bo th s i d e s choose t h e same l e v e l o f emp loyment . Hence , an e f f i c i e n t s o l u t i o n i s r e a c h e d . H a l l and L i l i e n ' s (1979) model does not p r e d i c t a u n i q u e ou t come . No b a r g a i n i n g mechanism i s s p e c i f i e d t o choose a p a r t i c u l a r p o i n t on 13 . McDona ld and So low (1981) a c t u a l l y s p e c i f y a d i f f e r e n t o b j e c t i v e f u n c t i o n f o r t h e u n i o n . However , t h a t o b j e c t i v e f u n c t i o n i m p l i e s r e n t m a x i m i z a t i o n i n t h e i r mode l . See f o o t n o t e 1. 21 t h e c o n t r a c t c u r v e . The model i s u sed t o e x p l a i n some s t y l i z e d f a c t s o f c o l l e c t i v e b a r g a i n i n g when t h e r e i s u n c e r t a i n t y about t h e demand and s u p p l y o f l a b o u r . In c o n c l u s i o n , one f i n d s two t y p e s o f u n i o n mode l s i n t h e l i t e r a - t u r e : monopoly mode ls wh i ch y i e l d i n e f f i c i e n t s o l u t i o n s , and c o o p e r a t i v e mode l s wh i c h y i e l d e f f i c i e n t s o l u t i o n s . G i v en t h e u s u a l n e o c l a s s i c a l p a r a d i g m , one wou ld e xpe c t t h e monopoly model t o be d i s c a r d e d i n f a v o u r o f t h e c o o p e r a t i v e mode l . The a b i l i t y o f economic agen t s t o e x p l o i t a l l g a i n s f rom t r a d e i s a c e n t r a l t e n n e n t o f a lmo s t a l l t e x t b o o k e c o n o m i c s . However , an argument wh i c h a p p e a l s t o f a c t o r s assumed away i n t h e n e o c l a s s i c a l pa rad igm s u g g e s t s t h a t t h e monopoly model may be t h e more a p p r o p r i a t e o f t h e two m o d e l s . T h i s argument c l a i m s t h a t un i o n s and f i r m s w i l l not have enough i n f o r m a t i o n abou t t h e o t h e r s i d e ' s o b j e c t i v e f u n c t i o n t o e x p l o i t a l l 14 t h e g a i n s f r om t r a d e . T h i s l a c k o f i n f o r m a t i o n may a r i s e f r om t h e c o s t s o f t r a n s m i t t i n g and r e c e i v i n g i n f o r m a t i o n . However , t h e b l u f f s , t h r e a t s , d e c e p t i o n s , and o t h e r b a r g a i n i n g t a c t i c s u sed by both s i d e s t o g a i n b a r g a i n i n g advan tages w i l l c o n t r i b u t e a g r e a t d e a l o f u n c e r t a i n t y and f a l s e i n f o r m a t i o n . Thu s , one can e x p e c t i m p e r f e c t i n f o r m a t i o n between u n i o n s and f i r m s and t h i s i m p e r f e c t i n f o r m a t i o n may c au se u n i o n s and f i r m s t o be u n a b l e t o e x p l o i t a l l o f t h e a v a i l a b l e g a i n s f rom t r a d e . W h i l e t h e above argument does r a i s e a v a l i d c r i t i c i s m a g a i n s t t h e c o o p e r a t i v e m o d e l , i t does n o t h i n g t o sugges t why one s h o u l d e xpe c t t h e monopo ly model t o be a p p r o p r i a t e . I m p e r f e c t i n f o r m a t i o n may i n deed cause un i on s and f i r m s t o d e v i a t e f rom an e f f i c i e n t s o l u t i o n . 14 . See Pen cave l ( 1 9 8 1 ) , p. 13 . 22 However , t h e argument does no t e x p l a i n why i m p e r f e c t i n f o r m a t i o n s h o u l d imp l y t h e monopoly s o l u t i o n . F u r t h e r , t h e same argument may be used a g a i n s t t h e monopoly m o d e l . U n c e r t a i n t y , i m p e r f e c t i n f o r m a t i o n , o r a t t emp t s a t d e c e p t i o n by t h e f i r m may cause t h e un i on t o m i s p e r c e i v e t h e demand f o r l a b o u r f u n c t i o n and choose a s u b o p t i m a l wage r a t e . T h e r e f o r e , i m p e r f e c t i n f o r m a t i o n does not a i d t h e c h o i c e 15 o f t h e more a p p r o p r i a t e m o d e l . 1 5 . One c o u l d a r g u e : (a) bo th mode l s a r e r e a s o n a b l e a p r i o r i , (b) t h e monopo ly model has l owe r i n f o r m a t i o n r e q u i r e m e n t s t han t h e c o o p e r a t i v e m o d e l , ( c ) f i r m s and un ion po s s e s s o n l y i m p e r f e c t i n f o r m a t i o n . T h e r e f o r e t h e monopoly model i s more a p p r o p r i a t e . I ag ree w i t h (b) and ( c ) , but am un conv i n c ed t h a t (a) i s t e n a b l e . 23 Chap te r 3 The D a t a 1 T h i s c h a p t e r o u t l i n e s t h e d e f i n i t i o n s and s o u r c e s o f t h e raw d a t a , and d e s c r i b e s how t h e f i n a l d a t a s e t i s p r oduced f r om t h e raw d a t a . The da t a s e t c o n s i s t s o f annua l o b s e r v a t i o n s on e s t a b l i s h m e n t s ( m i l l s ) i n t h e f o l l o w i n g B r i t i s h Co l umb i a wood p r o d u c t s i n d u s t r i e s : ( i ) s a w m i l l s and p l a n i n g m i l l s ( S . I . C . 2 5 1 3 ) , ( i i ) s h i n g l e m i l l s ( S . I . C . 2 5 1 1 ) , and ( i i i ) v enee r and p l ywood m i l l s ( S . I . C . 2 5 2 0 ) . O b s e r v a t i o n s f rom 1963 t o 1979 were c o l l e c t e d . F o r t u n a t e l y , s e p a r a t e d a t a a r e a v a i l a b l e f o r i n t e r i o r and c o a s t s a w m i l l s , y i e l d i n g a t o t a l o f 4 x 17 = 68 o b s e r v a t i o n s i n t h e d a t a s e t . A l l d a t a ( u n l e s s o t h e r w i s e s p e c i f i e d ) a r e p u b l i s h e d i n t h e S t a t - i s t i c s Canada p u b l i c a t i o n Annua l Census o f Manu f a c t u r e s " S a w m i l l s and P l a n i n g M i l l s and S h i n g l e M i l l s " ( C a t a l o g u e 35 -204) and " P l ywood and Veneer M i l l s " ( C a t a l o g u e 3 5 - 2 0 6 ) . 2 I n s t i t u t i o n a l S e t t i n g The B r i t i s h Co l umb i a wood p r o d u c t s i n d u s t r y i s l a r g e and v e r y a c t i v e i n w o r l d m a r k e t s . B .C . s a w m i l l s p roduce a lmos t 70% o f t h e s o f t w o o d l umber sawn i n Canada and e x p o r t a lmo s t 80% o f t h e i r o u t p u t . These e x p o r t s , i n t u r n , a c coun t f o r a l i t t l e l e s s t h an 10% o f w o r l d t r a d e i n s o f twood l u m b e r . 1. I wou l d l i k e t o t hank Ka ren K a l d e r b a n k ( S t a t i s t i c s Canada , Van - c o u v e r ) and Pau l M a r t i n ( S t a t i s t i c s Canada , Ot tawa) f o r t h e i r i n v a l u a b l e a s s i s t a n c e w i t h t h e c o l l e c t i o n o f t h e d a t a . 2 . A l l o f t h e d a t a r e p o r t e d i n t h i s s e c t i o n on B .C . and C a n a d i a n p r o d u c t i o n , e x p o r t s and marke t s h a r e s , a r e f ound i n P e a r s e ( 1 9 7 6 ) , Volume 2, Append i c e s A , B, C, and E; Pea r se ( 1 9 8 0 ) , p p . 1 -30; and I n d u s t r y , T r ade and Commerce ( 1 9 7 8 ) , pp . 1 -50 . 24 The s h i n g l e i n d u s t r y i n B . C . p r oduce s 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 made i n Canada and i s No r th A m e r i c a ' s ma jo r p r o - d u c e r . A h i g h p r o p o r t i o n o f t h e i n d u s t r y ' s o u t p u t i s e x p o r t e d , m a i n l y t o t h e U n i t e d S t a t e s . B . C . a l s o has 80% o f t h e Canad i a n c a p a c i t y f o r t h e p r o d u c t i o n o f s o f twood p lywood and v e n e e r . E x p o r t s a r e not as i m p o r t a n t t o t h e p l ywood m i l l s s i n c e h i g h t a r i f f s t h r o u g h o u t t h e w o r l d have s t i f l e d t r a d e . However , B .C . p l ywood m i l l s s t i l l e x p o r t about 20% o f t h e i r o u t p u t . The B .C . wood p r o d u c t s i n d u s t r y can be d e s c r i b e d as c o n c e n t r a t e d s i n c e most o f t h e m i l l s a r e owned and o p e r a t e d by a sma l l number o f l a r g e i n t e g r a t e d f i r m s . T h i s i s e s p e c i a l l y t r u e f o r s a w m i l l s and p lywood m i l l s . However , i t i s not u n r e a s o n a b l e t o assume t h a t t h e i n d u s t r y i s a p r i c e t a k e r i n o u t p u t ma r ke t s s i n c e so much o f t h e i n d u s t r y ' s o u t pu t i s s o l d i n w o r l d m a r k e t s . I ndeed , Pea r se ( 1980 , p. 23) w r i t e s : " F o r e s t p r o d u c t s p r oduced i n B r i t i s h Co l umb i a a r e , f o r t h e most p a r t , 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 . " I t i s much more u n r e a s o n a b l e t o assume t h a t t h e i n d u s t r y i s a p r i c e t a k e r i n t h e marke t f o r m a t e r i a l s . Import t a r i f f s on roundwood ( l o g s ) p r o t e c t l o g g i n g o p e r a t o r s f r om c o m p e t i t i o n . A l s o , bo th t h e l o g g i n g o p e r a t i o n s and t h e m i l l s t h e y d e l i v e r t h e i r o u t pu t t o , a r e u s u a l l y owned and o p e r a t e d by t h e same l a r g e , v e r t i c a l l y i n t e g r a t e d f i r m . T h e r e f o r e , t h e marke t f o r roundwood i s v e r y l i m i t e d and l o g g i n g o p e r a t i o n s may not s e l l roundwood t o m i l l s a t t h e f i r m ' s t r u e shadow p r i c e . T h i s may be done t o d e c r e a s e t h e r o y a l t i e s o r s tumpage f e e p a i d by t h e l o g g i n g o p e r a t i o n s t o t h e B . C . gove rnmen t . T h i s stumpage f e e i s s e t equa l t o t h e r ema i nde r o f t h e v a l u e o f t i m b e r 25 minus t h e c o s t s o f p r o d u c t i o n . Hence , l o g g i n g o p e r a t i o n s and m i l l s owned by t h e same f i r m , may t r a d e a t f a l s e p r i c e s i n o r d e r t o d e c r e a s e t h e p r o f i t a b i l i t y o f t h e l o g g i n g o p e r a t i o n s . T h i s , i n t u r n , wou ld d e c r e a s e t h e stumpage f e e and i n c r e a s e t h e o v e r a l l p r o f i t - a b i l i t y o f t h e f i r m . In s p i t e o f t h e a bo v e , p r i c e t a k i n g b e h a v i o u r i n t h e m a t e r i a l s marke t i s assumed i n o r d e r t o keep t h e a n a l y s i s s i m p l e . V i r t u a l l y a l l l a b o u r emp loyed i n t h e B . C . wood p r o d u c t s i n d u s t r y i s o r g a n i z e d by t h e I n t e r n a t i o n a l Woodworkers o f Amer i ca ( IWA) . S i n c e t h e i n d u s t r y i s so c o n c e n t r a t e d t h e un i o n has been a b l e t o keep t h e i n d u s t r y u n i o n i z e d ove r t h e who le p e r i o d o f t h e s t u d y . The IWA 3 c l a i m s t h a t 95-98% o f ou t pu t i s p roduced by IWA members . The b a r g a i n i n g s t r u c t u r e i s c e n t r a l i z e d . Un ion r e p r e s e n t a t i v e s f rom IWA Reg i ona l C o u n c i l #1 n e g o t i a t e a c o a s t mas t e r 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 emp loyed i n t h e c o a s t r e g i o n , w i t h t h e 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 ma s t e r i s t h en used as a b a s i s f o r mas t e r ag reement s between IWA r e g i o n a l c o u n c i l s and emp loye r a s s o c i a t i o n s i n t h e 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 t h e c o l l e c - t i v e agreements c o n t a i n un i o n shop p r o v i s i o n s . 3 . A s m a l l p a r t o f t h e r e m a i n i n g 2-5% o f o u t p u t i s p r oduced by w o r k e r s o r g a n i z e d by t h e C a r p e n t e r ' s Un i on o r t h e P u l p , P a p e r , and woodworkers o f Canada (PPWC), a r e c e n t l y fo rmed u n i o n . The r e s t o f t h e o u t p u t i s p r oduced by u n o r g a n i z e d w o r k e r s . The re a r e a few sma l l u n o r g a n i z e d s a w m i l l s and s h i n g l e m i l l s , and t h e r e i s a c o o p e r a t i v e p l ywood m i l l . 26 Labour The l a b o u r i n p u t (L) i s measured i n t hou sand s o f man-hours p a i d 4 f o r m a n u f a c t u r i n g a c t i v i t y . T o t a l c ompensa t i on p a i d t o l a b o u r i s t o t a l wages p a i d t o p r o d u c t i o n and r e l a t e d wo r ke r s f o r 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 ou sand s o f c u r r e n t d o l l a r s . T o t a l c ompensa t i o n 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 , b onu se s , and p a i d v a c a t i o n s and o t h e r payments f o r work no t p e r f o r m e d . The a v e r age nomina l r a t e o f c ompensa t i on p a i d t o l a b o u r (w) i s s i m p l y t o t a l nom- i n a l c ompensa t i o n p a i d t o l a b o u r d i v i d e d by t h e l a b o u r i n p u t . T o t a l r e a l c ompensa t i on p a i d t o l a b o u r (B) i s t o t a l c ompensa t i on d i v i d e d by t h e Canad i an consumer p r i c e i n d e x ( p ) . C a p i t a l S e r v i c e s The c o n s t r u c t i o n o f p r i c e and q u a n t i t y v a r i a b l e s f o r c a p i t a l s e r v i c e s p roved t o be q u i t e d i f f i c u l t s i n c e c a p i t a l s t o c k f o r f o u r d i g i t S . I . C . i n d u s t r i e s , by p r o v i n c e , i s no t t a b u l a t e d by S t a t i s t i c s Canada . Agg rega t e c a p i t a l s t o c k f o r t h e who le B .C . wood p r o d u c t s i n d u s t r y (two d i g i t S . I . C . ) a r e t h e most d i s a g g r e g a t e d d a t a a v a i l - a b l e . However , t h e a g g r e g a t e da t a on c a p i t a l s t o c k and d a t a on ene rgy c on sump t i on can be comb ined t o p roduce p r i c e and q u a n t i t y s e r i e s f o r c a p i t a l s e r v i c e s . L e t t h e p r o d u c t i o n f u n c t i o n f o r t h e wood p r o d u c t s i n d u s t r y be a f u n c t i o n o f l a b o u r ( L ) , m a t e r i a l s (M) , f l o w o f c a p i t a l s e r v i c e s f r om 4. Man -hou r s p a i d i n c l u d e s t i m e p a i d bu t no t wo r k ed , e . g . 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 . D u r i n g t h e p e r i o d o f i n t e r e s t t h e wo r k e r s r e c e i v e d two more s t a t u t o r y h o l i d a y s and l o n g e r v a c a - t i o n s , so t h e d a t a o v e r s t a t e s t h e t r u e l a b o u r i n p u t , e s p e c i a l l y i n l a t e r y e a r s . A d j u s t i n g t h e l a b o u r i n p u t v a r i a b l e f o r t h e e x t r a t i m e o f f l e f t t h e e s t i m a t e d u n i o n mode ls v i r t u a l l y unchanged . T h e r e f o r e t h e ad j u s tmen t was d ropped and t h e raw d a t a was u s e d . 27 t h e c a p i t a l s t o c k (S) wh i c h i s assumed t o be a c o n s t a n t p r o p o r t i o n o f t h e c a p i t a l s t o c k , and consump t i on o f f u e l s and e l e c t r i c i t y ( E ) , i . e . , where i i s t h e r unne r f o r t h e f o u r o b s e r v a t i o n s ( c o a s t 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 , p l ywood m i l l s ) o b s e r v e d a t each t ime t . Assume f ( ) i s weak l y s e p a r a b l e o v e r S. and and c a n , t h e r e f o r e , be w r i t t e n Q u - F ( L 1 t . H K(S , E 1 t ) ) where K ( S ^ , E ^ t ) i s t h e f l o w o f c a p i t a l s e r v i c e s as a f u n c t i o n o f ene rgy c on sump t i on and t h e s t o c k o f c a p i t a l . S p e c i f y a c o n s t a n t r e t u r n s t o s c a l e CES p r o d u c t i o n f u n c t i o n f o r c a p i t a l s e r v i c e s K i t = ( 6 E i t 6 + t 1 " « > S U B > " 1 / B < 3 ' 3 > Cos t m i n i m i z a t i o n i m p l i e s t h e f o l l o w i n g f i r s t o r d e r c o n d i t i o n p u / p n = M p n / M P i t = ^ / ( i - 6 ) ] [ s n / E i t ] e + 1 E s where P^ t i s t h e p r i c e o f ene rgy and i s t h e u s e r c o s t o f c a p i t a l . 28 T h e r e f o r e , E s < 3 + U~l s i t = E n ^ 1 ~ 6 ) p i t / 6 P i t ] < 3 - 4 > - I n E S . = ( 3 + D ' H n t d - 6 ) / 6 ) + l n \ E. (P* /P* ) ( B + X ) 1 ( 3 . 5 ) i = l i = l 4 5 E E S^. i s a v a i l a b l e f o r a l l t f rom S t a t i s t i c s Canada . P H t i s a i = l i r i r 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 o f t h e p r i c e s o f g a s o l i n e , f u e l o i l , l i q u e f i e d p e t r o l e u m g a s e s , n a t u r a l g a s , and e l e c t r i c i t y . ^ E ^ i s t h e t o t a l c o s t o f f u e l and e l e c t r i c i t y d i v i d e d by P^ t and i s , t h e r e - f o r e , an i m p l i c i t F i s h e r i d e a l i n d e x o f t h e q u a n t i t y o f ene rgy u s e d , s P^ t i s o b t a i n e d by m u l t i p l y i n g t h e sum o f t h e Canad i an i n t e r e s t r a t e 5 . S t a t i s t i c s Canada , F i x e d C a p i t a l F l ows and S t o c k s : B r i t i s h C o l u m b i a , C a t a l o g u e u - z n , u n p u b l i s h e d , i y » u . Note t h a t S t a t i s t i c s Canada r e p o r t s a g g r e g a t e c a p i t a l s t o c k f o r t h e e n t i r e wood p r o d u c t s i n d u s t r y , i n c l u d i n g wooden box m a n u f a c t u r e s , c o f - f i n and c a s k e t m a n u f a c t u r e s , and m i s c e l l a n e o u s wood i n d u s t r i e s . 4 T h e r e f o r e , t h e S t a t i s t i c s Canada s e r i e s used o v e r s t a t e s I S i + . i = l u However , t h e two s e r i e s s h o u l d not be t o o f a r a p a r t s i n c e wooden box , c o f f i n and c a s k e t , and m i s c e l l a n e o u s a r e q u i t e s m a l l compared t o s a w m i l l s , s h i n g l e m i l l s , and p lywood m i l l s . In f a c t , S . I . C . 252 , 2513 and 2511 made up 92% o f t h e v a l u e added o f t h e wood p r o d u c t s i n d u s t r y , on a v e r a g e . 6 . S t a t i s t i c s Canada , Consumpt i on o f P u r c ha s ed Fue l and E l e c t r i c i t y by t h e M a n u f a c t u r i n g , M i n i n g , L o g g i n g , and E l e c t r i c Power I n d u s t r i e s , C a t a l o g u e 5 7 - 2 0 8 , 1975 -79 ; u n p u b l i s h e d d a t a , 1963 - ~TT. See D i e w e r t (1976) f o r d e f i n i t i o n s o f i n d i c e s . 29 (McLeod , Young, We i r 10 i n d u s t r i a l s bond y i e l d ) and t h e d e p r e c i a t i o n r a t e ( c a p i t a l c onsumpt i on a l l o w a n c e 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 d i v i d e d by m i d - y e a r g r o s s c a p i t a l s t o c k ) t i m e s t h e C anad i a n p r i c e i n d e x o f b u i l d i n g c o n s t r u c t i o n , e n g i n e e r i n g c o n s t r u c t i o n , m a c h i n e r y , and equ ipment f o r t h e wood p r o d u c t s i n d u s t r y . 7 S i n c e c a p i t a l p r i c e i n d i c e s and d e p r e c i a t i o n r a t e s a r e not a v a i l a b l e f o r t h r e e and f o u r d i g i t S . I . C . i n d u s t r i e s , P.. i s t h e u s e r c o s t o f c a p i t a l f o r t h e who le wood p r o d u c t s i n d u s t r y . T h e r e f o r e i t i s assumed t h a t s a w m i l l s , s h i n g l e m i l l s , and p l ywood m i l l s a l l f a c e t h e same u se r c o s t o f c a p i t a l , i . e . , P - t = P^ t i ,m = 1,4 and t = 1 ,17 . 2 A s t o c h a s t i c e r r o r t e rm e t , e t ~ N ( 0 , a ) , i s added on t o e q u a t i o n 3 . 5 , and maximum l i k e l i h o o d e s t i m a t e s o f s and 6 a r e o b t a i n e d . The e s t i m a t e o f 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 between ene rgy and c a p i t a l s t o c k o b t a i n e d f rom e q u a t i o n 3.5 i s 0 . 1 , wh i ch i s c o n s i s t e n t w i t h o t h e r e s t i m a t e s f ound i n t h e l i t e r a t u r e ( s e e , f o r e x amp l e , McFadden ( 1 978b ) , Dhrymes and Kurz ( 1 9 6 4 ) , o r Fuss ( 1 9 7 7 ) ) . 7 . The bond y i e l d i s f ound i n t h e Bank o f Canada R e v i e w . The c a p i - t a l c on sump t i on a l l o w a n c e and m i d - y e a r g r o s s s t o c k a r e r e p o r t e d i n S t a t i s t i c s Canada , C a t a l o g u e 1 3 - 2 1 1 , u n p u b l i s h e d 1980 . The p r i c e i n d e x f o r c a p i t a l i s p u b l i s h e d i n S t a t i s t i c s Canada , F i x e d C a p i t a l F l ows and S t o c k s , C a t a l o g u e 13-211 and 1 3 - 5 68 , v a r i o u s y e a r s . 30 The e s t i m a t e s o f 6 and g a r e s u b s t i t u t e d i n t o e q u a t i o n 3 .4 t o g p roduce p r e d i c t e d c a p i t a l s t o c k s f o r each o f t h e o b s e r v a t i o n s . The e s t i m a t e s o f S.. f r om e q u a t i o n 3 .4 a r e t h e n s u b s t i t u t e d i n t o e q u a t i o n 3 .3 ( a l o n g w i t h t h e e s t i m a t e s o f 6 and e) t o p r oduce e s t i m a t e s o f t h e f l o w o f c a p i t a l s e r v i c e s , K ^ . 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 f ound by d e r i v i n g t h e u n i t c o s t f u n c t i o n dua l t o e q u a t i o n 3 . 3 , 3 + 1 1 _ J _ _ J _ 3 TTT s 6 + 1 3 + 1 r 8 + 1 where r̂  i s t h e c o s t o f one u n i t o f c a p i t a l s e r v i c e s . E s t i m a t e s o f E s r . j t a r e t hen c a l c u l a t e d by s u b s t i t u t i n g P^, P^ and t h e e s t i m a t e s o f 6 and 6 i n t o e q u a t i o n 3 . 6 . Hence e s t i m a t e s o f t h e p r i c e and 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 a r e o b t a i n e d f o r a l l o b s e r v a t i o n s . M a t e r i a l s 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 o f t h e p r i c e o f m a t e r i a l s (m) i s c o n s t r u c t e d f o r each o f t h e o b s e r v a t i o n s f rom d e t a i l e d d a t a on t h e 9 q u a n t i t y and v a l u e o f m a t e r i a l s and s u p p l i e s u s e d . The m a t e r i a l s p r i c e i n d e x f o r s a w m i l l s i s s i m p l y t h e p r i c e o f roundwood ( l o g s ) 8 . S i n c e p r e d i c t e d v a l u e s o f t h e dependent v a r i a b l e a r e u s e d , a measu re o f goodness o f f i t o f t h e s t o c h a s t i c v e r s i o n o f e q u a t i o n 3 .5 i s d e s i r a b l e . The a ve r age p e r c e n t a g e d i f f e r e n c e between t h e a c t u a l and p r e d i c t e d dependen t v a r i a b l e i s 5%. 9 . S t a t i s t i c s Canada , C a t a l o g u e 35 - 204 , and u n p u b l i s h e d S t a t i s t i c s Canada d a t a . 31 w h i l e t h e p r i c e i n d e x f o r s h i n g l e m i l l s i s an i n d e x o f t h e p r i c e s o f roundwood, and u n f i n i s h e d s h i n g l e s and shakes f rom o t h e r e s t a b l i s h - men t s . The m a t e r i a l s p r i c e i n d e x f o r p l ywood m i l l s a g g r e g a t e s t h e p r i c e s o f d i f f e r e n t s p e c i e s o f roundwood (Doug las f i r , b a l s a l m and hem lo c k , s p r u c e and p i n e ) and t h e p r i c e o f g l u e . An i m p l i c i t F i s h e r i d e a l i n d e x o f t h e q u a n t i t y o f m a t e r i a l s and s u p p p i e s used (M) i s o b t a i n e d by d i v i d i n g t o t a l c o s t o f m a t e r i a l s and s u p p l i e s used by t h e m a t e r i a l s p r i c e i n d e x . Ou tpu t D e t a i l e d d a t a on t h e v a l u e and q u a n t i t y o f t h e d i f f e r e n t t y p e s o f s h i pmen t s made by t h e i n d u s t r i e s a re 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 o u t pu t p r i c e i n de x ( q ) . * ° The ou t pu t p r i c e i n d e x f o r c o a s t s a w m i l l s a g g r e g a t e s t h e p r i c e s o f rough and p l a n e d sawn l u m b e r , pu l p c h i p s , and s h i n g l e s and shakes w h i l e t h e i n t e r i o r s a w m i l l s p r i c e i n d e x a g g r e g a t e s t h e p r i c e s o f rough and p l a n e d sawn l umbe r , and p u l p c h i p s . The o u t p u t p r i c e i n d e x f o r s h i n g l e m i l l s i n d e x e s t h e p r i c e s o f shakes and two t y p e s o f s h i n g l e s w h i l e t h e p lywood m i l l s ' i n d e x a g - g r e g a t e s t h e p r i c e s o f s o f twood v e n e e r , Doug l a s f i r p l ywood and o t h e r t y p e s o f p l ywood . The t o t a l v a l u e o f o u t p u t i s d e f i n e d t o be t h e ne t v a l u e o f sh i pmen t s ( i . e . , e x c l u d i n g d i s c o u n t s and r e t u r n s ) p l u s t h e v a l u e o f 10 . S t a t i s t i c s Canada , C a t a l o g u e 35 - 204 , and u n p u b l i s h e d S t a t i s t i c s Canada d a t a . 32 t h e change i n i n v e n t o r i e s . Thu s , t h e v a l u e o f o u t p u t e q u a l s t h e sum o f v a l u e added , t h e c o s t o f m a t e r i a l s and s u p p l i e s , and t h e c o s t o f f u e l and e l e c t r i c i t y . An i m p l i c i t F i s h e r i d e a l i n d e x o f t h e q u a n t i t y o f o u t pu t (Q) i s o b t a i n e d by d i v i d i n g t o t a l v a l u e o f o u t pu t by t h e o u t p u t p r i c e i n d e x . A l t e r n a t i v e Wage The b e s t a l t e r n a t i v e wage o f IWA members i s d e f i n e d t o be t h e amount an a ve r age B .C . i n d u s t r i a l wo r ke r wou ld r e c e i v e i f t h e y s e p a - r a t e d f r om t h e i r c u r r e n t emp loyment . The a l t e r n a t i v e wage i s a w e i g h t e d ave rage o f : ( i ) what wo r ke r s r e c e i v e i f t h e y f i n d o t h e r work i m m e d i a t e l y - t h e B . C . a v e r age week l y wage f o r t h e i n d u s t r i a l c o m p o s i t e ; ( i i ) what wo r ke r s r e c e i v e i f t hey s u f f e r a s p e l l o f unemployment and q u a l i f y f o r unemployment i n s u r a n c e ( U l ) - t h e B . C . a ve r age week l y payment o f U l ; and ( i i i ) what wo r ke r s r e c e i v e i f t h e y 11 s u f f e r a s p e l l o f unemployment and do not q u a l i f y f o r U l - n o t h i n g . The w e i g h t on a ve r age week l y i n d u s t r i a l wage (w l ) i s t h e p r o b a - b i l i t y o f w o r k i n g , wh i ch i s d e f i n e d t o be B .C . employment d i v i d e d by B . C . l a b o u r f o r c e . The w e i g h t on t h e U l payment (w2) i s (1 - w l ) t i m e s t h e p r o b a b i l i t y o f q u a l i f y i n g f o r U l . The p r o b a b i l i t y o f q u a l i - f y i n g f o r U l i s d e f i n e d t o be t h e number o f weeks o f U l p a i d i n B . C . 12 d i v i d e d by t h e number o f weeks o f unemployment i n B . C . The w e i g h t 1 1 . I n d u s t r i a l c o m p o s i t e a v e r age week l y wage i s p u b l i s h e d i n S t a t - i s t i c s Canada , Employment E a r n i n g s and H o u r s , C a t a l o g u e 7 2 - 002 . The U l a v e r age week l y payment i s r e p o r t e d i n S t a t i s t i c s Canada , S t a t i s t i c a l Repo r t on t h e O p e r a t i o n o f t h e Unemployment I n s u r - ance A c t , C a t a l o g u e 7 3 - 0 0 1 . 12 . Employment , l a b o u r f o r c e and unemployment a r e r e p o r t e d i n S t a t i s t i c s Canada , H i s t o r i c a l Labou r F o r c e S t a t i s t i c s , C a t a l o g u e 7 1 - 2 0 1 . Number o f weeks o f U l p a i d a r e r e p o r t e d i n S t a t i s t i c s C anada , C a t a l o g u e 7 3 - 0 0 1 . 33 on t h e no wo r k , no U l s t a t e i s (1 - w l - w 2 ) , but i t i s m u l t i p l i e d by z e r o so i t d r ops o u t . The bes t r e a l a l t e r n a t i v e wage (A) i s t h e a l t e r n a t i v e wage d i v i d e d by t h e C anad i a n consumer p r i c e i n d e x . S c a l i n g t h e Data The re a r e two r e a s on s f o r s c a l i n g t h e d a t a . F i r s t , s c a l i n g i s done t o e n su r e t h a t t h e e s t i m a t e d pa r ame te r s a r e between one and minus one . T h i s r ea son i s i m p o r t a n t o n l y i f a n o n - l i n e a r o p t i m i z a - t i o n r o u t i n e i s used t o e s t i m a t e t h e p a r a m e t e r s . S c a l i n g t h e d a t a t o keep t h e e s t i m a t e d p a r ame t e r s i n t h e u n i t s i m p l e x i n c r e a s e s t h e p r o - b a b i l i t y t h a t t h e o p t i m i z i n g r o u t i n e w i l l c o n v e r g e , and h e l p s a v o i d p rob l ems o f f a l s e c o n v e r g e n c e . The se cond r e a s on f o r s c a l i n g i s t o e n s u r e t h a t t h e d a t a u sed t o c a l c u l a t e pa r ame te r e s t i m a t e s , t r u l y r e f l e c t t h e w o r l d . Many o f t h e d a t a a r e j u s t i n d e x numbers wh i c h can be a r b i t r a r i l y s c a l e d up and down. T h e r e f o r e s c a l i n g must be done so t h a t p r o f i t i s g r e a t e r t h a n o r equa l t o z e r o f o r most o b s e r v a t i o n s , and each i n p u t ' s s h a r e o f t o t a l c o s t i s c l o s e t o i t s t r u e s h a r e . C l e a r l y a r e s e a r c h e r must t a k e a l e x i c o g r a p h i c app roach and s c a l e t o s a t i s f y t h e second r ea son f i r s t . The s c a l i n g done t o p roduce t h e f i n a l d a t a s e t w i l l no t be r e p o r t e d h e r e . However, w i t h t h e s c a l i n g u s e d , p r o f i t i s g r e a t e r t h a n z e r o f o r most y e a r s w i t h 1970 , 1974, and 1975 b e i n g t h e w o r s t y e a r s . Ave raged ove r a l l o b s e r v a t i o n s , t h e s ha r e o f c a p i t a l i s 0 . 1 5 , t h e s h a r e o f l a b o u r i s 0 . 2 5 , and t h e s h a r e o f m a t e r i a l s i s 0 . 5 9 . The ITC r e v i ew r e p o r t s t h a t c o s t s o f m a t e r i a l s make up o n e - h a l f t o t w o - t h i r d s o f t o t a l c o s t , w h i l e t h e p r i n c i p a l s t a t i s t i c s o f t h e i n d u s t r i e s show t h a t t h e s h a r e o f m a t e r i a l s d i v i d e d by t h e s h a r e o f 34 l a b o u r a v e r age s 2 . 4 4 . T h e r e f o r e i t seems t h a t t h e s c a l i n g s a t i s - f i e s t h e v e r y i m p o r t a n t second c r i t e r i o n . Two F l aws i n t h e Da ta Sma l l e s t a b l i s h m e n t s a r e g i v e n s p e c i a l t r e a t m e n t by S t a t i s t i c s Canada . S p e c i f i c a l l y , sma l l e s t a b l i s h m e n t s i n c l u d e t h e c o s t o f f u e l and e l e c t r i c i t y w i t h t h e c o s t o f m a t e r i a l s and s u p p l i e s . A l s o , a l l p r i n c i p l e s t a t i s t i c s , e x c ep t f o r number o f wo r k i n g owners and p a r t - n e r s , a r e c l a s s i f i e d t o m a n u f a c t u r i n g a c t i v i t y . T h i s p r e s e n t s no p rob l em f o r s a w m i l l s and p lywood m i l l s s i n c e t h o s e i n d u s t r i e s a r e made up o f l a r g e e s t a b l i s h m e n t s . However , s h i n g l e m i l l s t e n d t o be s m a l l e r and t h e d i f f e r e n t c o n v e n t i o n s f o r sma l l e s t a b l i s h m e n t s may show up i n t h e d a t a . U n f o r t u n a t e l y t h e r e i s no way t o e i t h e r d e t e r - mine t h e s e r i o u s n e s s o f t h e p r o b l e m , o r a d j u s t t h e d a t a f o r t h e d i f - f e r e n t c o n v e n t i o n . The se cond f l a w i s m i s s i n g d a t a . The 1970 u n p u b l i s h e d d e t a i l e d d a t a on t h e c o m p o s i t i o n o f s h i p m e n t s , m a t e r i a l s , and ene rgy a r e u n - a v a i l a b l e f o r B . C . p l ywood m i l l s w h i l e t h e c o m p o s i t i o n o f m a t e r i a l s and ene rgy a r e u n a v a i l a b l e f o r B .C . s h i n g l e m i l l s . These d a t a a r e n e c e s s a r y f o r t h e c o n s t r u c t i o n o f t h e p r i c e i n d i c e s . Fo r each m i s s i n g p i e c e o f d a t a t h e B .C . s ha r e o f t h e Canad i an t o t a l i s c a l c u l a t e d f o r 1969 and 1971 . The s h a r e s a r e a v e r a g e d and t h a t a ve r age B .C . s h a r e , m u l t i p l i e d by t h e 1970 Canad i an t o t a l , 13 . I n d u s t r y , T r a d e , and Commerce, Rev iew o f t h e F o r e s t P r o d u c t s I n d u s t r y , ( 1 9 7 8 ) , p. 9 . A l s o , S t a t i s t i c s Canada , C a t a l o g u e 3 5 - 206 and 35 - 204 , 1964 - 79 . 35 y i e l d s t h e 1970 B..C. f i g u r e . The p r o c e d u r e i s a r b i t r a r y . However , f o r many i t e m s , t h e B .C . t o t a l s f o r 1969 and 1971 a r e v i r t u a l l y 100% o f t h e Canad i an t o t a l s , so i t i s no t u n r e a s o n a b l e t o assume t h e 1970 s ha r e s a r e a lmos t 100% a l s o . 36 Chap te r 4 The Wood P r o d u c t s Te chno l ogy Th i s c h a p t e r p r o v i d e s a c h a r a c t e r i z a t i o n o f t h e t e c h n o l o g y o f t h e B . C . wood p r o d u c t s i n d u s t r y a s sum ing exogenous i n p u t p r i c e s and p r i c e t a k i n g b e h a v i o u r i n a l l i n p u t m a r k e t s . The pa r ame te r s o f t h e t e c h n o l o g y a r e e s t i m a t e d i n d e p e n d e n t l y f r om any un i o n o b j e c t i v e f u n c t i o n p a r a m e t e r s . Thus , t h e pa r ame te r e s t i m a t e s a r e e q u i v a l e n t t o e s t i m a t e s wh i c h wou l d be o b t a i n e d i f p e r f e c t c o m p e t i t i o n i n t h e i n p u t marke t s was assumed. Cos t m i n i m i z i n g b e h a v i o u r i s assumed, and a l l a d j u s tmen t * 5 c o s t s a r e assumed t o be such t h a t e q u i l i b r i u m l e v e l s o f i n p u t s a r e a c h i e v e d w i t h i n one y e a r - t h e t i m e p e r i o d o f each o b s e r - v a t i o n i n t h e d a t a . T h e r e f o r e , t h e i n d u s t r y i s on i t s l o n g r un c o s t c u r v e , and a c o s t f u n c t i o n can be used t o c h a r a c t e r i z e t h e t e c h n o l o g y o f t h e i n d u s t r y . D e f i n e a c o s t f u n c t i o n f o r t h e i n d u s t r y C ( r ,m ,w ,Q ) = Min {rK + mM + wL : ( K ,M , L ,Q ) eT} ( 4 . 1 ) K , L ,M where r ,m , and w a r e p r i c e s o f c a p i t a l s e r v i c e s , m a t e r i a l s and l a b o u r ; K ,M , L , and Q a r e q u a n t i t i e s o f c a p i t a l s e r v i c e s , m a t e r i a l s , l a b o u r and o u t p u t ; and T i s t h e p r o d u c t i o n p o s s i b i l i t i e s s e t . * The p r o d u c t i o n p o s s i b i l i t i e s s e t i s t h e s e t o f a l l f e a s i b l e i n p u t s 1. The u s e f u l and c o n v e n i e n t p r o p e r t i e s o f t h e c o s t f u n c t i o n a r e w e l l documented and w i l l no t be d i s c u s s e d h e r e . S e e , f o r e x a m p l e , D i e w e r t (1974) and ( 1 9 7 8 a ) . 37 2 and o u t p u t s , and i t i s assumed t o be w e l l b ehaved . Two d i f f e r e n t f u n c t i o n a l fo rms a r e used t o s p e c i f y t h e c o s t f u n c - t i o n . Both c o s t f u n c t i o n s a r e e s t i m a t e d and t h e r e s u l t s a r e r e p o r t e d b e l o w . T r a n s l o g S p e c i f i c a t i o n S p e c i f y a t r a n s l o g c o s t f u n c t i o n l n C ( r , m , w , Q ) = CXQ + ct^lnr + o^lnm + ct3l nw 2 1 2 + ^ Y 3 3 ( 1 n w ) 2 1 2 + nQ + - e 2 ( l n Q ) + a ^ l n r 1 nQ + B 1 2 l n m InQ + B 1 3 l n w InQ + av I n t + a v j n r I n t + w, J n m I n t + u>..~lnw I n t a^int + ux^inr int + (D^mm mu + u> 3̂ 2 . See D i e w e r t ( 1 9 7 4 ) , p. 134 f o r a r i g o r o u s s t a t emen t o f t h e p r o - p e r t i e s a s s i g n e d t o T when c o n s t a n t r e t u r n s t o s c a l e i s impo sed . G e n e r a l l y T i s assumed t o be c l o s e d , bounded, and c o n v e x . The re i s a l s o f r e e d i s p o s a l . No te t h a t f o r t h e t r a n s l o g s p e c i f i c a t i o n T i s not assumed t o be a c one , w h i l e t h e c o n d i t i o n a l c o s t f u n c - t i o n s p e c i f i c a t i o n does assume t h a t T i s a c o n e . 38 where + + = 1 Y l l + Y 1 2 + Y 1 3 = 0 Y 1 2 + Y 2 2 + Y 2 3 = 0 Y 1 3 + Y 2 3 + Y 3 3 = ° S l l + 6 1 2 + *13 = ° M l l + " 12 + u 1 3 = ° and t i s a t r e n d v a r i a b l e . The t r a n s l o g c o s t f u n c t i o n p r o v i d e s a s e cond o r d e r a p p r o x i m a t i o n t o an a r b i t r a r y c o s t f u n c t i o n . Note t h a t t h e c o s t f u n c t i o n a l l o w s b i a s e d t e c h n i c a l change and does no t f o r c e t h e t e c h n o l o g y t o be h o m o t h e t i c o r e x h i b i t c o n s t a n t r e t u r n s t o s c a l e . S h e p h a r d ' s lemma i m p l i e s t h e f o l l o w i n g s h a r e e q u a t i o n s rK/C = s K = Oj + Y n l n r + Y 1 2 l n m + Y ^ l n w + 3 n l n Q + w n l n t ( 4 . 3 ) mM/C = s M = + Y 1 2 l n r + Y 2 2 l n m + Y 2 3 l n w + 8 1 2 l n Q + u ^ l n t ( 4 . 4 ) wL/C = s L = + Y 1 3 l n r + Y 2 3 l n m + Y 3 3 l n w + 3 1 3 l n Q + w ^ l n t . ( 4 . 5 ) 39 S i n c e t h e s h a r e s sum t o one , o n l y two o f t h e s h a r e e q u a t i o n s can be i n c l u d e d i n a sy s tem o f e s t i m a t i n g e q u a t i o n s . A maximum l i k e l i - hood e s t i m a t i o n t e c h n i q u e s h o u l d be used t o e s t i m a t e t h e p a r ame t e r s o f t h e t e c h n o l o g y , so as t o make t h e e s t i m a t e s i n v a r i a n t t o t h e s h a r e e q u a t i o n d r o p p e d . S t o c h a s t i c e r r o r t e rms e ^ e^, e^> where ( e ^ e,,, e 3 ) ~ N(0,E), a r e added t o e q u a t i o n s 4 . 2 , 4 . 4 and 4 . 5 r e s p e c t i v e l y . E r r o r t e rms c o r r e s p o n d i n g t o t h e same o b s e r v a t i o n a r e a l l o w e d t o be c o r r e l a t e d w i t h one a n o t h e r , w h i l e e r r o r t e rms c o r r e s p o n d i n g t o d i f f e r e n t o b s e r - v a t i o n s a r e assumed t o be i ndependen t o f each o t h e r . Thus , t h e s t o - c h a s t i c v e r s i o n s o f 4 . 2 , 4 . 4 and 4 . 5 f o rm a s e e m i n g l y u n r e l a t e d r e g r e s s i o n s y s t e m . Note howeve r , t h a t t h e r e i s o n l y v e r y l i m i t e d con temporaneous c o r r e l a t i o n , s i n c e t h e d a t a i s p o o l e d c r o s s s e c t i o n and t i m e s e r i e s , and not t i m e s s e r i e s . Dummy v a r i a b l e s f o r o b s e r v a t i o n s on s h i n g l e m i l l s and p l ywood m i l l s a r e a l s o added t o e q u a t i o n s 4 . 2 , 4 . 4 , and 4 . 5 . T h i s c o v a r i a n c e app r oa ch t o p o o l e d c r o s s - s e c t i o n and t i m e s e r i e s d a t a a c c o u n t s f o r u n s p e c i f i e d , c o n s t a n t , a c r o s s i n d u s t r y d i f f e r e n c e s i n t h e i n p u t s h a r e s . The e s t i m a t e s a r e a s y m p t o t i c a l l y e q u i v a l e n t t o e s t i m a t e s o b t a i n e d f rom t he e r r o r components a p p r o a c h . The s t o c h a s t i c v e r s i o n s o f e q u a t i o n s 4 . 2 , 4 . 4 , and 4 . 5 ( w i t h t h e dummy v a r i a b l e s ) a r e t h en e s t i m a t e d as a s e em ing l y u n r e l a t e d r e g r e s s i o n sys tem u s i n g t h e i t e r a - t i v e Z e l l n e r p r o c e d u r e . T h i s p r o c e d u r e y i e l d s e s t i m a t e s a s y m p t o t i - c a l l y e q u i v a l e n t t o maximum l i k e l i h o o d e s t i m a t e s . The e s t i m a t e d c o e f f i c i e n t s and t h e i r a s y m p t o t i c t - s t a t i s t i c s a r e r e p o r t e d i n T ab l e I . T ab l e I I shows t h e m a t r i x o f e s t i m a t e d p r i c e e l a s t i c i t i e s and o t h e r c h a r a c t e r i s t i c s o f t h e e s t i m a t e d t e c h n o l o g y , e v a l u a t e d a t t h e mean o f t h e d a t a . L e t t e r s u b s c r i p t s on C r e p r e s e n t p a r t i a l d e r i - 40 v a t i v e s o f t h e c o s t f u n c t i o n , where t h e arguments o f t h e d e r i v a t i v e s a r e o m i t t e d f o r c o n v e n i e n c e . A number o f h y p o t h e s i s t e s t s a r e p e r f o rmed on t h e e s t i m a t e d s y s t em u s i n g l i k e l i h o o d r a t i o t e s t s . The hypo these s o f no b i a s i n t e c h n i c a l change ( < ^ = <̂ 2 = 0 ) , no t e c h n i c a l change (u^ = a>^ = (0̂ 2= a^3= 0 ) , and h o m o t h e t i c i t y o f t h e p r o d u c t i o n t e c h n o l o g y ( e ^ = hz= B 1 3 = °^ a r e a 1 1 r e J e c t e d e a s i l y , even a t t h e 99.5% c o n f i d e n c e l e v e l . The r e j e c t i o n o f no b i a s i n t e c h n i c a l change means t h a t H i c k s ' n e u t r a l t e c h n i c a l change i s r e j e c t e d . The r e j e c t i o n o f h o m o t h e t i c i t y means t h a t a c o n s t a n t r e t u r n s t o s c a l e s p e c i f i c a t i o n o f t h e p r o d u c - t i o n t e c h n o l o g y i s a l s o r e j e c t e d . C o n d i t i o n a l C o s t F u n c t i o n S p e c i f i c a t i o n The t e c h n o l o g y o f t h e B . C . wood p r o d u c t s i n d u s t r y i s r e - e s t i m a t e d u s i n g a c o s t f u n c t i o n d e r i v e d f rom a c o n d i t i o n a l c o s t f u n c t i o n s u g g e s t e d by D i e w e r t (1974 , p. 1 3 7 ) . T h i s unusua l s p e c i f i c a t i o n i s used s i n c e t h e same c o n d i t i o n a l c o s t f u n c t i o n i s used t o r e p r e s e n t t h e p r o d u c t i o n t e c h n o l o g y o f t h e i n d u s t r y i n t h e u n i o n m o d e l s . Hence , one can ob s e r v e t h e e f f e c t s o f l e t t i n g t h e wage be endogenous and j o i n t l y e s t i m a t i n g p r o d u c t i o n and u n i o n p r e f e r e n c e p a r ame t e r s on t h e e s t i m a t e d p r o d u c t i o n t e c h n o l o g y w i t h o u t t h e p o s s i b i l i t y t h a t any d i f f e r e n c e s a r e due t o t h e use o f d i f f e r e n t f u n c t i o n a l f o r m s . 3 . The r e s t r i c t e d , max im i z ed l o g l i k e l i h o o d s f o r each o f t h e hypo- t h e s e s a r e 4 5 9 . 0 4 , 458 . 88 and 4 5 4 . 6 3 , r e s p e c t i v e l y . 41 TABLE I E s t i m a t e d C o e f f i c i e n t s o f t h e T r a n s ! o g Co s t F u n c t i o n A s y m p t o t i c t - s t a t i s t i c s a r e i n p a r e n t h e s e s ct0 0.5812 (3.995) 0.2559 (5.712) ct2 0.3548 (9.335) cu 0.3893 (12.25) Y n 0.1359 (7.879) Y 1 2 -0.1191 (-9.556) Y 1 3 -0.0169 (-0.976) Y 2 2 0.211 (15.091) Y 2 3 -0.0191 (-12.0) Y 3 3 0.1088 (5.042) B : 0.9072 (11.945) B2 0.0133 (0.5) B n ^-0.0049 (-0.314) B 0.0614 (4.828) B 1 3 -0.0565 (-4.876) 0.0543 (4.084) u 0.0254 (4.899) a>12 -0.0121 (-2.507) a>13 -0.0133 (-3.903) N a t u r a l l o g o f l i k e l i h o o d f u n c t i o n = 470.07 42 TABLE I I E s t i m a t e d C h a r a c t e r i s t i c s o f t h e T e chno l o g y : T r a n s l o g Co s t F u n c t i o n and Exogenous Wages A l l e s t i m a t e s a r e e v a l u a t e d a t t h e mean o f t h e d a t a . M o n o t o n i c i t y C p = 3 . 3 8 , C m = 6 . 6 9 , C w = 3 . 7 2 , C Q = 4 . 1 C u r v a t u r e The d e t e r m i n a n t s o f t h e m ino r s o f t h e h e s s i a n o f t h e c o s t f u n c t i o n a r e : 0 . 0 0 1 , - 0 . 0 1 4 , 0 . 0 . S u b s t i t u t i o n The m a t r i x o f p r i c e e l a s t i c i t i e s i s r m w K 0 .0006 - 0 . 1 3 3 0 . 132 M - 0 . 0 3 4 - 0 . 0 4 6 0 . 080 L 0 .097 0 .228 - 0 . 3 2 5 The e l a s t i c i t i e s o f s u b s t i t u t i o n a r e : CTKL = 0 * ^ 6 , = 0 . 3 6 6 , CT^ = - 0 . 2 1 3 R e t u r n s t o O u t l a y a lnC/.a lnQ = 0 .96 T h e r e f o r e t h e e l a s t i c i t y o f s c a l e i s 1.041 and t h e r e a r e i n c r e a s i n g r e t u r n s t o o u t l a y . T e c h n i c a l Change ( 3 s K / 3 t ) ( t / s K ) = 0 . 159 ( 3 s M / 3 t ) ( t / s M ) = - 0 . 0 2 ( a s L / a t ) ( t / s L ) = - 0 . 0 6 1 (ac/at ) ( t/c) = 0 . 043 43 Assume t h e p r o d u c t i o n p o s s i b i l i t i e s s e t i s a cone so t h a t t h e p r o d u c t i o n t e c h n o l o g y 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 . D e f i n e a c o n d i t i o n a l c o s t f u n c t i o n D ( r , m , L , Q ) = Min {rK + mM : ( K , M , L , Q ) e T } , ( 4 . 6 ) K,M where D ( r , m , L , Q ) i s t h e minimum c o s t o f m a t e r i a l s and c a p i t a l r e q u i r e d t o p roduce o u t p u t Q, g i v e n a f i x e d l a b o u r i n p u t L, and i n p u t p r i c e s r and m. McFadden ( 1978a , p. 61) n o t e s t h a t a c o n d i t i o n a l c o s t f u n c t i o n i s minus a v a r i a b l e p r o f i t f u n c t i o n where t h e o u t p u t s and some o f t h e i n p u t s o f t h e v a r i a b l e p r o f i t f u n c t i o n a r e f i x e d . T h e r e f o r e , a d j u s t i n g f o r t h e s i g n change and l e t t i n g ou t pu t be a n e g a t i v e i n p u t , D ( r , m , L , Q ) p o s s e s s e s t h e p r o p e r t i e s o f v a r i a b l e p r o f i t f u n c t i o n s o u t l i n e d i n D i ewe r t (1974 , p. 1 3 6 ) . For our pu rposes we need o n l y no te t h a t D^ < 0 and D ^ > 0 ' An o r d i n a r y c o s t f u n c t i o n , p o s s e s s i n g a l l t h e u s u a l p r o p e r t i e s and c h a r a c t e r i z i n g t h e p r o d u c t i o n p o s s i b i l i t i e s s e t , can be d e f i n e d : C ( r ,m ,w ,Q ) = Min {D ( r ,m , L ,Q ) + wL} . ( 4 . 7 ) L 4 . T h i s t y p e o f c o s t f u n c t i o n i s a l s o r e f e r r e d t o as a r e s t r i c t e d c o s t f u n c t i o n , o r j o i n t c o s t f u n c t i o n . Fo r p r o f i t f u n c t i o n s t h e names a r e c o n d i t i o n a l , r e s t r i c t e d , o r v a r i a b l e , p r o f i t f u n c t i o n . 5 . D i ewe r t ( 1 9 7 4 ) , p. 136 shows t h a t a v a r i a b l e p r o f i t f u n c t i o n i s n o n i n c r e a s i n g and concave i n i t s f i x e d i n p u t s . S i n c e t h e c o s t f u n c t i o n i s minus t h e p r o f i t f u n c t i o n and i n p u t s a r e measured as n e g a t i v e numbers i n D i e w e r t , bu t as p o s i t i v e numbers h e r e , D() i s n o n i n c r e a s i n g i n L. L i k e w i s e , t h e c o s t f u n c t i o n i s convex i n i t s f i x e d i n p u t s , so D ^ > 0 whe the r l a b o u r i s measured as a n e g a t i v e number o r n o t . See C h a p t e r 5 f o r a c omp l e t e l i s t o f t h e p r o p e r t i e s o f D ( r , m , L , Q ) . 44 The f i r s t o r d e r c o n d i t i o n f o r t h e minimum i s D L ( r , m , L , Q ) + w = 0 ( 4 . 8 ) and t h e second o r d e r c o n d i t i o n i s s a t i s f i e d s i n c e > 0 . L e t L * ( r ,m ,w ,Q ) be t h e amount o f l a b o u r wh i ch s a t i s f i e s t h e f i r s t o r d e r c o n d i t i o n ( 4 . 8 ) a nd , t h e r e f o r e , m i n i m i z e s e q u a t i o n 4 . 7 w i t h r e s p e c t t o L. Hence , C ( r ,m ,w ,Q ) = D ( r , m , L * ( r , m , w , Q ) , Q ) + w L * ( r , m , w , Q ) . ( 4 . 9 ) The c o s t m i n i m i z i n g demand f u n c t i o n s f o r c a p i t a l and m a t e r i a l s a r e d e r i v e d by u s i n g S h e p h a r d ' s lemma on t h e c o s t f u n c t i o n g i v e n by e q u a t i o n 4 . 9 . T h e r e f o r e , K*( r ,m,w,Q) - 9 C ( r , m , w , Q ) / 9 r - 3D ( r ,m , L ,Q ) / 3 r |^_^* ( 4 . 1 0 ) and M*(r ,m,w,Q) = 3C(r ,m,w,Q)/am = 3 D ( r , m , L , Q ) / a m | L = L * ( 4 . 1 1 ) by t h e e n v e l o p e t h e o r e m . The c o s t m i n i m i z i n g demand f o r l a b o u r f u n c t i o n i s g i v e n i n i m p l i c t f o rm by e q u a t i o n 4 . 8 . S p e c i f y t h e c o n d i t i o n a l c o s t f u n c t i o n t o be 45 D ( r , m , L , Q ) = c n r L + c ^ r Q + c 2 1 m L + c^mQ + 2 b 1 2 ( r + m + 2 X ) ( L Q ) a + 2 a 1 2 X Z ( 4 . 1 2 ) where X = ( - r 2 + - m 2 ) * and Z = L + Q + 2(1 .0)* . Note t h a t e q u a t i o n 2 2 4 . 1 2 p r o v i d e s a s e cond o r d e r a p p r o x i m a t i o n t o an a r b i t r a r y c o n d i - t i o n a l c o s t f u n c t i o n g i v e n a c o n s t a n t r e t u r n s t o s c a l e t e c h n o l o g y and no t e c h n i c a l c h a n g e . E q u a t i o n s 4 . 8 , 4 . 1 0 , 4 . 1 1 , and 4 . 12 i m p l y t h e f o l l o w i n g s i m u l - t aneous sys tem o f c o s t m i n i m i z i n g i n p u t demand f u n c t i o n s : K = c n L + c 1 2 Q + 2 b 1 2 ( L Q ) s ( l + r /X ) + a 1 2 r Z / X ( 4 . 1 3 ) M = c 2 1 L + c 2 2 Q + 2 b 1 2 ( L Q ) i ( l + m/X) + a 1 2 m Z / X ( 4 . 1 4 ) L~* = -[w + c n r + c 2 1 m + 2 a 1 2 X ] [ b 1 2 ( r + m + 2X)Q* + 2 a 1 2 X Q * ] _ 1 ( 4 . 1 5 ) S t o c h a s t i c e r r o r t e rms e^, e 2 > e^, where ( e ^ , e 2 , e 3 ) ~ N ( 0 , E) , a r e added on t o e q u a t i o n s 4 . 1 3 , 4 . 1 4 , and 4 .15 r e s p e c t i v e l y . The e r r o r s t r u c t u r e i s t h e same as t h e one s p e c i f i e d f o r t h e t r a n s l o g c o s t f u n c t i o n . E r r o r t e rms c o r r e s p o n d i n g t o t h e same o b s e r v a t i o n a r e a l l o w e d t o be c o r r e l a t e d w i t h one a n o t h e r , w h i l e e r r o r t e rms c o r r e s - pond ing t o d i f f e r e n t o b s e r v a t i o n s a r e assumed t o be i n dependen t o f each o t h e r . 6 . D i e w e r t ( 1 9 7 4 ) , p . 138 . 46 TABLE I I I E s t i m a t e d C o e f f i c i e n t s o f t h e C o n d i t i o n a l C o s t F u n c t i o n A s y m p t o t i c t - s t a t i s t i c s a r e i n p a r e n t h e s e s c l l 0 . 7090 ( 1 . 6 39 ) C 1 2 1 .0541 ( 7 . 8 25 ) C 2 1 1 .5352 ( 2 . 912 ) C 2 2 1 .1151 ( 11 . 198 ) b 1 2 - 0 . 8 6 4 9 ( - 3 . 6 8 3 ) a 1 2 0 .4406 ( 3 . 9 56 ) N a t u r a l l o g o f l i k e l i h o o d f u n c t i o n = 2 9 3 . 4 2 4 7 . 47 TABLE IV E s t i m a t e d C h a r a c t e r i s t i c s o f t h e T e c h n o l o g y : C o n d i t i o n a l Cos t F u n c t i o n and Exogenous Wages A l l e s t i m a t e s a r e e v a l u a t e d a t t h e mean o f t h e d a t a . M o n o t o n i c i t y C u r v a t u r e The d e t e r m i n a n t s o f t h e m ino r s o f t h e h e s s i a n o f t h e c o s t f u n c t i o n a r e : - 0 . 2 3 5 , - 0 . 0 6 3 , 0 . 0 . S u b s t i t u t i o n The m a t r i x o f p r i c e e l a s t i c i t i e s i s C p = 3 . 1 3 , C m = 7 . 1 0 , C w = 3 . 5 0 , C Q = 4 . 3 2 . r m w K M L - 0 . 1 3 7 2 - 0 . 0 6 6 5 0 .2907 0 .2576 0 . 0185 0 .1368 0 . 3948 0 .0479 - 0 . 4 2 7 4 The e l a s t i c i t i e s o f s u b s t i t u t i o n a r e : ov, = 1 . 8 1 , a M , = 0 . 2 1 9 , a. KM 0 .414 48 Dummy v a r i a b l e s f o r o b s e r v a t i o n s on p l ywood m i l l s and s h i n g l e m i l l s a r e added on t o each s t o c h a s t i c i n p u t demand e q u a t i o n t o ' a c c o u n t f o r u n s p e c i f i e d , c o n s t a n t , a c r o s s i n d u s t r y d i f f e r e n c e s i n i n p u t demands. F u l l i n f o r m a t i o n maximum l i k e l i h o o d e s t i m a t e s o f t h e p a r ame t e r s o f t h e c o n d i t i o n a l c o s t f u n c t i o n a r e o b t a i n e d f r om t h e s t o c h a s t i c s y s tem o f i n p u t demand f u n c t i o n s . The e s t i m a t e s and t h e i r a s y m p t o t i c t - s t a t i s t i c s a r e r e p o r t e d i n T a b l e I I I . G i ven t h e maximum l i k e l i h o o d e s t i m a t e s o f t h e p a r ame t e r s o f t h e c o n d i t i o n a l c o s t f u n c t i o n , an e s t i m a t e o f t h e o r d i n a r y c o s t f u n c t i o n i s d e r i v e d u s i n g e q u a t i o n s 4 . 8 and 4 . 9 . The o r d i n a r y c o s t f u n c t i o n p r o v i d e s e s t i m a t e s o f t h e c h a r a c t e r i s t i c s o f t h e p r o d u c t i o n t e c h - n o l o g y . The m a t r i x o f e s t i m a t e d p r i c e e l a s t i c i t i e s and o t h e r c h a r a c - t e r i s t i c s o f t h e e s t i m a t e d t e c h n o l o g y , e v a l u a t e d a t t h e mean o f t h e d a t a , a r e r e p o r t e d i n T a b l e IV . In t h e work shown above , i n p u t demand f u n c t i o n s a r e e s t i m a t e d f rom poo l e d c r o s s s e c t i o n and t i m e s e r i e s d a t a . I m p l i c i t i n t h e above i s t h e a s s ump t i o n t h a t t h e p a r ame t e r s o f t h e t e c h n o l o g y a r e t h e same i n a l l t h r e e i n d u s t r i e s a f t e r t h e a d j u s tmen t s made by t h e dummy v a r i a b l e s . These p o o l i n g r e s t r i c t i o n s a r e t e s t e d and o v e r w h e l m i n g l y r e j e c t e d by a l i k e l i h o o d r a t i o t e s t pe r f o rmed on t h e c o n d i t i o n a l c o s t f u n c t i o n s p e c i f i c a t i o n o f t h e t e c h n o l o g y . I t s h o u l d be no ted t h a t t h e e r r o r s t r u c t u r e appended t o e q u a t i o n s 4 . 1 3 , 4 . 14 and 4 . 1 5 i s r a t h e r a r b i t r a r y . Add i ng e r r o r t e rms i s u s u a l l y j u s t i f i e d by as sum ing some s o r t o f o p t i m i z a t i o n e r r o r . As sum ing t h a t o b s e r v e d l e v e l s o f i n p u t s a r e n o r m a l l y d i s t r i b u t e d a round t h e i r o p t i m a l l e v e l s (as i n e q u a t i o n s 4 .13 and 4 . 14 ) i s g e n e r - a l l y a c c e p t e d and i n t u i t i v e l y r e a s o n a b l e . However , a s sum ing t h a t t h e i n v e r s e o f t h e squa r e r o o t o f t h e o b s e r v ed l a b o u r i n p u t i s n o r m a l l y 49 d i s t r i b u t e d a round t h e i n v e r s e o f t h e s qua r e r o o t o f t h e o p t i m a l l a b o u r i n p u t (as i n e q u a t i o n 4 . 15 ) i s not as w e l l a c c e p t e d o r as i n t u i t i v e l y r e a s o n a b l e . The v e r y same argument a p p l i e s t o t h e dummy v a r i a b l e s wh i ch e n t e r l i n e a r l y i n t h e i n p u t demand e q u a t i o n s . The a d d i t i v e e r r o r s t r u c t u r e and t h e l i n e a r s p e c i f i c a t i o n f o r t h e dummy v a r i a b l e s a r e used f o r c o n v e n i e n c e . However, i t s h o u l d be n o t e d t h a t t h e r e s u l t s a r e no t t o o d i f f e r e n t f r om t h e ones o b t a i n e d f rom t he t r a n s l o g c o s t f u n c t i o n s p e c i f i c a t i o n , w i t h i t s more c o n v e n - t i o n a l e r r o r s t r u c t u r e . Hence , a l t h o u g h i t i s unknown what r e s u l t s wou ld be o b t a i n e d w i t h a d i f f e r e n t e r r o r s t r u c t u r e , t h e r a t h e r a r b i - t r a r y s p e c i f i c a t i o n may not t a i n t t h e e s t i m a t e s t o o s t r o n g l y . D i s c u s s i o n and Compa r i son o f t h e R e s u l t s w i t h o t h e r S t u d i e s . ^ Compar ing t h e r e s u l t s r e p o r t e d above w i t h t h e r e s u l t s o f o t h e r s t u d i e s o f t h e Canad i an m a n u f a c t u r i n g s e c t o r i s d i f f i c u l t f o r a num- b e r o f r e a s o n s . F i r s t , o t h e r s t u d i e s b reak i n p u t s up i n t o d i f f e r e n t s ub - g a g g r e g a t e s t han t h e ones used a b o v e . Second , t h e o t h e r s t u d i e s u s e d a t a on t h e who l e Canad i an m a n u f a c t u r i n g s e c t o r , w h i l e t h e r e s u l t s g i v e n above r e f e r t o o n l y a sma l l p a r t o f t h a t s e c t o r . The o t h e r 7 . O t h e r s t u d i e s o f t h e Canad i a n m a n u f a c t u r i n g s e c t o r a r e : Denny and May ( 1 9 7 7 ) , Denny and May ( 1 9 7 8 ) , Fuss ( 1 9 7 7 ) , K o t o w i t z ( 1 9 6 8 ) , Tsurumi (1970) and Woodland ( 1 9 7 5 ) . 8 . For e xamp l e , Denny and May (1978) s p e c i f y l a b o u r and c a p i t a l t o be i n p u t s , but b reak each o f t h e i n p u t s i n t o two s u b - a g g r e g a t e s . They s p e c i f y t h a t ou t pu t i s a f u n c t i o n o f f o u r i n p u t s : p r o d u c - t i o n l a b o u r , n o n - p r o d u c t i o n l a b o u r , s t r u c t u r e s , and e q u i p m e n t . T h e r e f o r e , c ompa r i s on s between t h e i r f o u r i n p u t model and t h e t h r e e i n p u t model shown above a r e d i f f i c u l t . 50 s t u d i e s a l s o use d a t a f r om an e a r l i e r t i m e p e r i o d t h a n t h e one used h e r e . F i n a l l y , c a p i t a l s e r i c e s i s d e f i n e d q u i t e d i f f e r e n t l y i n t h i s 9 work t han i n o t h e r s t u d i e s . However , I b e l i e v e i t i s w o r t h w h i l e t o r e p o r t o t h e r e s t i m a t e s f ound i n t h e l i t e r a t u r e . Bo t h o f t h e e s t i m a t e d c o s t f u n c t i o n s s a t i s f y t h e i r m o n o t o n i c i t y p r o p e r t i e s . T h i s i s a l s o t r u e i n o t h e r s t u d i e s o f Canad i an manu f a c - t u r i n g . U n f o r t u n a t e l y , t h e e s t i m a t e d c o s t f u n c t i o n s do no t s a t i s f y t h e c u r v a t u r e p r o p e r t y and a r e not concave w i t h r e s p e c t t o i n p u t p r i c e s . However , t h e own and c r o s s p r i c e e l a s t i c i t i e s o f t h e i n p u t demand f u n c t i o n s a r e v e r y c l o s e t o p o s s e s s i n g t h e p r o p e r t i e s t h a t c o n c a v i t y o f t h e c o s t f u n c t i o n imposes on them, so t h e c o s t f u n c t i o n s canno t be t oo f a r f rom b e i n g c o n c a v e . Woodland (1975) a l s o f i n d s t h a t t h e c o s t f u n c t i o n i s no t c o n c a v e , bu t t h e p r i c e e l a s t i c i t i e s a r e not u n r e a s o n a b l e . The c o s t f u n c t i o n s o f t h e o t h e r s t u d i e s s a t i s f y t h e c u r v a t u r e p r o p e r t y . The e s t i m a t e d own p r i c e e l a s t i c i t i e s o f c a p i t a l and m a t e r i a l s a r e q u i t e s m a l l . When one o f t h e e l a s t i c i t i e s has t h e wrong s i g n i t i s v e r y c l o s e t o z e r o . O t he r s t u d i e s f i n d t h e s e e l a s t i c i t i e s t o be somewhat h i g h e r . For e xamp l e , Denny and May (1977) f i n d e s t i m a t e d p r i c e e l a s t i c i t i e s o f c a p i t a l and m a t e r i a l s o f - 1 . 1 and - 0 . 5 , w h i l e Fuss (1977) e s t i m a t e s them t o be - 0 . 7 and - 0 . 3 5 8 . C a p i t a l and m a t e r i a l s a r e complements w i t h e s t i m a t e s o f be tween - 0 . 2 and - 0 . 5 . 1 0 No o t h e r s t u d y c o r r o b o r a t e s t h i s r e s u l t F o r 9 . See C h a p t e r 3 f o r d e t a i l s o f t h e d e f i n i t i o n o f c a p i t a l s e r - v i c e s . 10 . The ranges g i v e n he re a r e ve r y rough and a r e i n t e n d e d o n l y t o g i v e t h e g e n e r a l c h a r a c t e r o f t h e r e s u l t s . 51 examp l e , Denny and May (1977) e s t i m a t e a t o be 1 .8 . Fuss ( 1 9 7 7 ) , KM howeve r , f i n d s t h a t ene rgy and m a t e r i a l s a r e complements and c a p i t a l , i n t h i s s t u d y , i s d e f i n e d t o i n c l u d e e n e r g y . C a p i t a l and l a b o u r a r e s u b s t i t u t e s . U n f o r t u n a t e l y , t h e e s t i m a t e s o f a , , a r e q u i t e f a r a p a r t , so 0 .5 < a < 2 i s t h e n a r r o w e s t e s t i - K L K L mated range t h a t can be g i v e n f o r 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 between c a p i t a l and l a b o u r . T h i s r a t h e r w i de range e x t e nd s q u i t e f a r above t h e upper l i m i t f ound i n t h e l i t e r a t u r e . Fo r e xamp l e , Tsurumi ( 1 9 7 0 ) , Fuss ( 1 9 7 7 ) , and Woodland (1975) e s t i m a t e t o be 1 .0 , 0 . 8 and 0 .295 r e s p e c t i v e l y w h i l e K o t o w i t z (1968) g i v e s an e s t i m a t e d r ange o f 0 .3 < < ,̂L < 0 . 5 . On t h e o t h e r hand , Denny and May (1977) e s t i m a t e ov, t o be between - 0 . 3 and - 0 . 5 3 and c l a i m t h a t t h i s s t r i k i n g l y d i f - f e r e n t r e s u l t o c c u r s because t h e y do no t u se a v a l u e added f r amewo rk . T h i s s t udy does not use a v a l u e added f ramework e i t h e r , but f i n d s t h a t c a p i t a l and l a b o u r a r e s u b s t i t u t e s and not comp lemen t s . Labour and m a t e r i a l s a r e s u b s t i t u t e s w i t h a... e s t i m a t e d t o be LM between 0 .2 and 0 . 4 . Both Fuss (1977) and Denny and May (1977) a l s o f i n d l a b o u r and m a t e r i a l s t o be s u b s t i t u t e s , but Denny and May (1977) r e p o r t a much h i g h e r e s t i m a t e d 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 1 . 2 . The own p r i c e e l a s t i c i t y o f t h e demand f o r l a b o u r i s e s t i m a t e d t o be between - 0 . 3 and - 0 . 5 . T h i s i s s l i g h t l y b i g g e r t han t h e - 0 . 1 5 r e p o r t e d i n Hamermesh's (1976) i n f l u e n t i a l s t u d y . Woodland (1975) a l s o e s t i m a t e s a s m a l l e r e l a s t i c i t y ( - 0 . 0 9 9 6 ) , w h i l e Fuss (1977) and Denny and May (1977) r e p o r t e s t i m a t e d e l a s t i c i t i e s o f - 0 . 4 9 and - 0 . 7 4 r e s p e c t i v e l y . T h e r e f o r e , t h e p r i c e e l a s t i c i t y r e p o r t e d he re i s not i n c o n s i s t e n t w i t h o t h e r e s t i m a t e s f ound i n t h e l i t e r a t u r e . 52 H o m o t h e t i c i t y o f t h e p r o d u c t i o n t e c h n o l o g y i s r e j e c t e d w i t h t h e t r a n s l o g c o s t f u n c t i o n and i n c r e a s i n g r e t u r n s t o o u t l a y a r e f o u n d . The e l a s t i c i t y o f s c a l e i s e s t i m a t e d t o be 1 . 041 . Most o t h e r s t u d i e s impose c o n s t a n t r e t u r n s t o s c a l e , but Woodland (1975) a l s o r e j e c t s h o m o t h e t i c i t y and f i n d s i n c r e a s i n g r e t u r n s t o o u t l a y . F i n a l l y , bo th t h e h ypo the se s o f no t e c h n i c a l change and H i c k s ' n e u t r a l t e c h n i c a l change a r e r e j e c t e d . T e c h n i c a l change i s l a b o u r and m a t e r i a l s s a v i n g and c a p i t a l u s i n g . F u r t h e r , t h e e s t i m a t e o f t h e e l a s t i c i t y o f c o s t s w i t h r e s p e c t t o t i m e i s 0 . 0 4 3 , so t h e ne t r e s u l t o f t i m e i s n e g a t i v e t e c h n i c a l c hange . N e g a t i v e t e c h n i c a l change i s no t t o o s u r p r i s i n g s i n c e Woodland (1975) a l s o r e p o r t s n e g a t i v e t e c h - n i c a l c hange . Pea r ce (1980 , p. 10) s t a t e s : " T e c h n i c a l i n n o v a t i o n s , s t i m u l a t e d by t h e d e c l i n i n g s i z e and q u a l i t y o f t i m b e r a v a i l a b l e , have s t i m u l a t e d t h e c o n v e r s i o n o f m i l l s t o h i g h vo lume , sma l l l o g ' p r o c e s s i n g sy s tems wh i c h have e n a b l e d t h e I n t e r i o r [ B . C . s a w m i l l i n g ] i n d u s t r y t o a c h i e v e h i g h e r l e v e l s o f wood u t i l i z a t i o n and g r e a t l y imp roved l a b o u r p r o d u c t i v i t y . " The c o a s t r e g i o n has a l s o s u f f e r e d f rom d e c l i n i n g s i z e and q u a l i t y o f wood s t o c k s . Hence , i t seems t h a t a l t h o u g h t h e d e c l i n i n g s i z e and q u a l i t y o f m a t e r i a l s a v a i l a b l e has s p a r k ed m a t e r i a l s and l a b o u r s a v i n g , and c a p i t a l u s i n g t e c h n i c a l change ; t h e u l t i m a t e e f f e c t o f t h e d e t e r i o r a t i o n o f t h e wood s t o c k s i s t o i n c r e a s e c o s t s o v e r t i m e . 53 Chap t e r 5 Un ion M o d e l s : Co s t M i n i m i z a t i o n In t h i s c h a p t e r two d i f f e r e n t mode ls o f 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 a r e d e r i v e d , s p e c i f i e d and e s t i m a t e d . The e s t i m a t e d pa r ame te r s o f t h e mode ls p r o v i d e e s t i m a t e s o f t h e p r e f e r e n c e s o f t h e u n i o n and show how e s t i m a t e s o f t h e p r o d u c - t i o n t e c h n o l o g y can change when t h e wage i s endogenous t o t h e model and p r o d u c t i o n and un i o n p r e f e r e n c e p a r ame t e r s a r e e s t i m a t e d j o i n t l y w i t h i n a s p e c i f i c model o f u n i o n and f i r m b e h a v i o r . In o r d e r t o f a c i l i t a t e t h e a n a l y s i s , t h e f o l l o w i n g a s s u m p t i o n s a r e made. A l . A l l d i v e r g e n t p r e f e r e n c e s and g o a l s h e l d by d i f f e r e n t g roups w i t h i n t h e un i on can be accommodated and e x p r e s s e d by a s i n g l e un i o n o b j e c t i v e f u n c t i o n . A2 . The un i o n has o r g a n i z e d and b a r g a i n s f o r a l l w o r k e r s i n t h e i n d u s t r y and i s s e c u r e . The u n i o n has a u n i o n shop so a l l wo r k e r s a r e un i on members, and no un i on member w o r r i e s abou t b e i n g r e p l a c e d by a nonun i on w o r k e r . A 3 . The i n d u s t r y ' s c o s t f u n c t i o n i s i ndependen t o f t h e u n i o n ' s b e h a v i o u r . Hence t h e u n i o n c anno t e n f o r c e j o b r e s t r i c t i o n s wh i ch i n t u r n a f f e c t t h e i n d u s t r y ' s demand f o r l a b o u r . A4 . The f i r m s i n t h e i n d u s t r y and t h e u n i o n o p e r a t e i n a s t a t i c w o r l d . Un ion p r e f e r e n c e s a r e a tempora l and any a d j u s t m e n t c o s t s i n c u r r e d by t h e u n i o n o r t h e i n d u s t r y a r e such t h a t e q u i l i b r i u m i s a c h i e v e d w i t h i n one o b s e r v a t i o n (one y e a r ) . F u r t h e r , t h e l a b o u r c o n t r a c t does not impose any dynamic c o n s t r a i n t s on e i t h e r p a r t y . 54 A5 . Bo th t h e u n i o n and t h e f i r m s i n t h e i n d u s t r y have p e r f e c t i n f o r m a t i o n . A6 . The i n d u s t r y i s a p r i c e t a k e r i n t h e ma r ke t s f o r c a p i t a l s e r v i c e s and m a t e r i a l s , and i t m i n i m i z e s t h e c o s t s o f t h o s e i n p u t s s u b j e c t t o an exogenous o u t p u t c o n s t r a i n t . A 7 . The p r o d u c t i o n p o s s i b i l i t i e s s e t i s a c one , so t h e t e c h n o - l o g y 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 . The p r o d u c t i o n p o s s i b i l i t i e s s e t a l s o s a t i s f i e s t he o t h e r p r o p e r t i e s ( c l o s e d , bounded , non -emp ty , c onvex , f r e e d i s p o s a l ) g i v e n i n D i ewe r t (1974 , p. 1 3 4 ) . The r e a s o n a b l e n e s s o f some o f t h e a s s ump t i o n s has been d i s c u s s e d e l s e w h e r e . Chap t e r two s u r v e y s t h e l i t e r a t u r e on t h e r e a s o n a b l e n e s s o f s p e c i f y i n g a s i m p l e o b j e c t i v e f u n c t i o n t o r e p r e s e n t t h e p r e f e r - ences o f a un i on wh i ch i s not homogeneous and wh i ch i s run a c c o r d i n g t o a p o l i t i c a l s y s t e m . C h a p t e r t h r e e d i s c u s s e s t h e r e a s o n a b l e n e s s o f assuming p r i c e t a k i n g b e h a v i o r i n t h e m a t e r i a l s marke t g i v e n t h e c o n c e n t r a t e d , v e r t i c a l l y i n t e g r a t e d i n d u s t r i a l s t r u c t u r e o f t h e B . C . wood p r o d u c t s i n d u s t r y . A s s ump t i o n A4 s h o u l d a l s o be d i s c u s s e d . The w e l l e s t a b l i s h e d impo r t a n c e o f " c a t c h up" i n e m p i r i c a l s t u d i e s o f wage d e t e r m i n a t i o n p r o v i d e s s t r o n g e v i d e n c e t h a t m u l t i - y e a r c o l l e c t i v e ag reement s do impose dynamic c o n s t r a i n t s on f i r m s and u n i o n s . There wou ld be no p r o b l e m i f t h e IWA and t h e f o r e s t p r o d u c t s i n d u s t r y n e g o t i a t e d o n l y one y e a r c o l l e c t i v e ag r eemen t s , s i n c e each c o n t r a c t wou ld c o v e r o n l y one o b s e r v a t i o n . T a b l e V r e p o r t s t h e c o l l e c t i v e ag reements nego- t i a t e d i n t h e c o a s t and i n t e r i o r r e g i o n s ove r t h e p e r i o d o f i n t e r e s t and shows t h a t t h e c o n t r a c t s a r e d e f i n i t e l y no t r e n e g o t i a t e d f o r 55 e v e r y o b s e r v a t i o n ( y e a r ) . Most o f t h e c o n t r a c t s have two y e a r d u r a - t i o n s , so a s i n g l e c o n t r a c t d e t e r m i n e s t h e c o n d i t i o n s o f employment f o r more t h an one o b s e r v a t i o n . No dynamic c o n s t r a i n t s f r om m u l t i - y e a r c o n t r a c t s c o u l d be r a t i o n a l i z e d by assuming t h a t bo th t h e un i on and t h e i n d u s t r y have p e r f e c t f o r e s i g h t . In t h a t c a s e t h e c o n d i t i o n s o f employment f o r t h e second and t h i r d y e a r s o f t h e c o l l e c t i v e agreement a r e e x a c t l y t h e same as what t h e y wou l d be i f t h e u n i o n and t h e i n d u s t r y c o u l d r e n e g o t i a t e t h e te rms i n t h a t second o r t h i r d y e a r . C l e a r l y , a s s ump t i o n A4 i s a v e r y s t r o n g and r e s t r i c t i v e assump- t i o n wh i ch i s m a i n t a i n e d o n l y because i t keeps t h e a n a l y s i s t r a c t - a b l e . U n f o r t u n a t e l y , t h e e f f e c t s ( i f any) o f t h i s a s s ump t i o n on t h e e s t i m a t e s p r e s e n t e d be low a r e unknown. The c o n d i t i o n a l c o s t f u n c t i o n D ( r , m , L , Q ) = Min {rK + mM : ( K , M , L , Q ) e T } , ( 5 . 1 ) K,M d e s c r i b e d i n c h a p t e r 4 and dua l t o t h e c o n s t a n t r e t u r n s t o s c a l e t e c h n o l o g y , i s u sed t o c h a r a c t e r i z e t h e p r o d u c t i o n t e c h n o l o g y . As no ted i n c h a p t e r 4 , a c o n d i t i o n a l c o s t f u n c t i o n p o s s e s s e s a l l t h e p r o p e r t i e s o f minus a v a r i a b l e p r o f i t f u n c t i o n where a l l o u t p u t s and some i n p u t s a r e f i x e d . 2 1. The i n t e r i o r r e g i o n i s t h e s o u t h e r n i n t e r i o r r e g i o n . No i n f o r - ma t i on i s p r o v i d e d f o r t h e n o r t h e r n i n t e r i o r r e g i o n s i n c e i t has o n l y r e c e n t l y been fo rmed i n t o a s i n g l e b a r g a i n i n g u n i t , and s i n c e i t i s v e r y sma l l compared t o t h e s o u r t h e r n i n t e r i o r and c o a s t r e g i o n s . 2 . See McFadden ( 1 978a ) , p. 68 , and remember t h a t o u t p u t s a r e n e g a - t i v e i n p u t s and v i c e - v e r s a . 56 TABLE V C o l l e c t i v e Agreements f o r t h e Coas t and I n t e r i o r Reg i on s Coas t June 15 1962 t o June 14 1964 1964 t o " 1966 1966 t o " 1968 1968 t o " 1970 1970 t o " 1972 1972 t o " 1974 1974 t o " 1975 1975 t o " 1977 1977 t o " 1979 1979 t o " 1981 I n t e r i o r September 1 1962 t o Augus t 31 1964 September 1 1964 t o Augus t 31 1967 September 1 1967 t o June 30 1970 J u l y 1 1970 t o J une 30 1972 1972 t o " 1974 1974 t o " 1975 1975 t o " 1977 1977 t o " 1979 1979 t o " 1981 57 T h e r e f o r e , as shown by D i e w e r t (1974 , p. 1 3 6 ) , D ( r , m , L , Q ) p o s s e s s e s t h e f o l l o w i n g p r o p e r t i e s . ( i ) D ( r , m , L , Q ) i s a n o n - n e g a t i v e f u n c t i o n f o r r,m > 0 , L,Q > 0 but bo th L and Q canno t equa l z e r o . ( i i ) D ( r , m , L , Q ) i s homogeneous o f deg r ee one i n r and m. T h i s p r o p e r t y i s imposed by t h e f u n c t i o n a l f o rm u s e d . ( i i i ) D ( r , m , L , Q ) i s c oncave and c o n t i n u o u s i n r and m. ( i v ) D ( r , m , L , Q ) i s homogeneous o f deg ree one i n L and Q. (v ) D ( r , m , L , Q ) i s n o n - i n c r e a s i n g i n L (D^<0) and non - d e c r e a s i n g i n Q (DQ > 0 ) . ( v i ) D ( r , m , L , Q ) i s convex and c o n t i n u o u s i n L and Q, wh i c h i m p l i e s D ^ > 0 . F i n a l l y i t i s p r o v ed i n t h e a p p e n d i x t o t h i s c h a p t e r t h a t : ( v i i ) D ( r , m , L , Q ) i s n o n - d e c r e a s i n g i n r and m. A f u n c t i o n a l f o rm s u g g e s t e d by D i e w e r t (1974 , p. 137) i s u sed t o s p e c i f y D ( r , m , L , Q ) : D ( r , m , L , Q ) = c ^ r L + c 1 2 r Q + c 2 1 m L + c^rnQ + 2 b 1 2 ( r + m + 2 X ) ( L Q ) * + 2 a 1 2 X Z , ( 5 . 2 ) 1 2 1 2 1 1 where X = ( - r + - m ) 2 a n d Z = L + Q + 2 ( L Q ) 2 . As no t ed i n 2 2 C h a p t e r 4 , t h i s f u n c t i o n a l f o rm p r o v i d e s a s e cond o r d e r a p p r o x i m a t i o n t o an a r b i t r a r y c o n d i t i o n a l c o s t f u n c t i o n , g i v e n t h e c o n d i t i o n s on t h e t e c h n o l o g y and no t e c h n i c a l c hange . T o t a l e x p e n d i t u r e s made by t h e i n d u s t r y f o r i n p u t s ( E ) , g i v e n i n p u t p r i c e s , o u t p u t and t h e l a b o u r i n p u t , a r e 58 E ( r , m , w , L , Q ) = wL + D( r , m , L , Q ) , ( 5 . 3 ) where wL i s t o t a l c ompensa t i on p a i d t o l a b o u r , and w i s t o t a l compen- s a t i o n p a i d t o l a b o u r d i v i d e d by t h e t o t a l amount o f l a b o u r emp loyed ; i . e . , t h e a ve r age c ompensa t i on p a i d t o a u n i t o f l a b o u r . I s o - e x p e n d i t u r e c u r v e s i n compensa t i on -emp loymen t space a r e shown i n F i g u r e 3 by t h e f a m i l y o f c u r v e s EE , and a r e d e f i n e d by wL = pB = E - D ( r , m , L , Q ) ( 5 . 4 ) where E i s a c o n s t a n t and p i s t h e Canad ian consumer p r i c e i n d e x . CI e a r l y , 3 (wL ) / a t = -D L > 0 , and 8 2 ( w L ) / S t 2 = - D L L < 0 , so t h e i s o - e x p e n d i t u r e c u r v e s a r e i n c r e a s i n g and concave f u n c t i o n s o f emp loyment . Note t h a t t h e s l o p e o f t h e i s o - e x p e n d i t u r e c u r v e i s i n dependen t o f wL, i m p l y i n g t h a t t h e i s o - e x p e n d i t u r e c u r v e s a r e p a r - a l l e l f r om be l ow . Assume u n i o n p r e f e r e n c e s a r e d e f i n e d o v e r t o t a l r e a l compensa- t i o n p a i d t o l a b o u r (B , B = wL/p where p i s t h e Canad i an consumer p r i c e i n d e x ) , and t h e amount o f l a b o u r emp loyed ( L ) . Assume u n i o n p r e f e r e n c e s a r e c o n d i t i o n a l upon t h e bes t r e a l a l t e r n a t i v e wage a v a i l a b l e t o l a b o u r ( A ) . The b e s t r e a l a l t e r n a t i v e wage a v a i l a b l e t o 59 FIGURE 3 wL 60 l a b o u r i s a l s o t h e r e a l o p p o r t u n i t y c o s t o f w o r k i n g i n a u n i o n j o b , and i t i s assumed t o be t h e same f o r a l l w o r k e r s . L e t u n i o n p r e f e r e n c e s be c h a r a c t e r i z e d by t h e f u n c t i o n U ( B , L ; A ) where U u > 0 , U. < 0, and U ( B , L ; A ) i s q u a s i c o n c a v e i n r e a l compensa- D L t i o n and l a b o u r . Thu 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 between r e a l c ompensa t i on and l a b o u r i s an i n c r e a s i n g f u n c t i o n o f l a b o u r and t h e u n i o n r e q u i r e s e v e r i n c r e a s i n g i n c r e a s e s i n r e a l c ompen sa t i o n t o compensate i t f o r one more man-hour o f wo r k . T y p i c a l u n i o n i n d i f - f e r e n c e c u r v e s , g i v e n t h e a l t e r n a t i v e wage and t h e p r i c e l e v e l , a r e shown i n nomina l compensa t i on -emp loymen t space by t h e c u r v e s uu i n F i g u r e 3 . A p o s s i b l e r a t i o n a l i z a t i o n f o r t h e q u a s i c o n c a v i t y assump- t i o n i s t h a t t h e un i on i n c u r s i n c r e a s i n g r e a l c o s t s i n p r o v i d i n g u n i o n s e r v i c e s as t h e number o f man-hours worked i n c r e a s e s . A n o t h e r i s t h a t t h e s u p p l y o f l a b o u r c u r v e i s upward s l o p i n g and e v e r i n c r e a s i n g r a t e s o f r e a l c ompensa t i o n a r e r e q u i r e d f o r more l a b o u r t o be s u p p l i e d . The a ve r age r e a l r a t e o f c ompensa t i on (w/p) i s d e f i n e d t o be B /L . T h e r e f o r e we can d e f i n e S p e c i f y , U ( B , L ; A ) = i k B + ( 5 . 5 ) <j>(w/p,L;A) = U ( w L / p , L ; A ) = U ( B , L ; A ) ( 5 . 6 ) where <j> Vp > 0 and <}>. > 0 i f w/p > -U . /U 61 *L < 0 i f w/p < - U L / U B . Monopo ly Un ion Model In t h e monopoly u n i o n model (MUM) t h e un i o n choose s t h e a v e r age nomina l r a t e o f c ompensa t i on p a i d t o each wo rke r u n i l a t e r a l l y , i n o r d e r t o max im i z e U ( B , L ; A ) . The i n d u s t r y t h en choose s t h e c o s t m i n i - m i z i n g l e v e l o f employment g i v e n by i t s demand f o r l a b o u r f u n c t i o n and t h e u n i o n wage. Hence t h e u n i o n chooses t h e wage wh i c h max im i z e s U ( B , L ; A ) s u b j e c t t o t h e i n d u s t r y ' s demand f o r l a b o u r f u n c t i o n . T h i s model con fo rms t o t h e c o n v e n t i o n a l w isdom abou t 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 . Un ions a f f e c t wages , but f i r m s choose t h e l e v e l o f employment u n i l a t e r a l l y , s u b j e c t t o t h e n e g o t i a t e d wage. The i n d u s t r y ' s demand f o r l a b o u r f u n c t i o n i s g i v e n by t h e s o l u - t i o n t o t h e m i n i m i z a t i o n p rob l em Min { E ( r , m , w , L , Q ) } = Min {wL + D ( r , m , L , Q ) } . ( 5 . 7 ) L L The f i r s t o r d e r c o n d i t i o n i s w + D L ( r , m , L , Q ) = 0 ( 5 . 8 ) wh i ch i s a l s o t h e i n d u s t r y ' s demand f o r l a b o u r f u n c t i o n w r i t t e n i n i m p l i c i t f o r m . The second o r d e r c o n d i t i o n i s s a t i s f i e d s i n c e D^> 0 . M u l t i p l y e q u a t i o n 5.8 by L/p and s u b s t i t u t e t h e p r o du c t ( t he u n i o n ' s c o n s t r a i n t ) i n t o t h e u n i o n ' s o b j e c t i v e f u n c t i o n . The u n i o n ' s max im i - z a t i o n p rob l em can t hen be w r i t t e n 62 Max {U(-LD / p , L ; A ) } L wh i ch y i e l d s t h e f i r s t o r d e r c o n d i t i o n 311/St = U B ( - D L - L D L L ) / p + U L = 0 + D L + L D L L = p U L / U B . ( 5 . 9 ) The second o r d e r c o n d i t i o n o f t h e u n i o n ' s m a x i m i z a t i o n p r ob l em i n v o l v e s t h e t h i r d d e r i v a t i v e o f t h e c o n d i t i o n a l c o s t f u n c t i o n , so t h e u sua l c u r v a t u r e p r o p e r t i e s o f U ( B , L ; A ) and D ( r , m , L , Q ) a r e no t enough t o e n su r e a maximum. However , t h e t h i r d d e r i v a t i v e o f t h e f u n c t i o n a l fo rm used t o s p e c i f y D ( r , m , L , Q ) ( e q u a t i o n 5 . 2 ) , i s s u ch t h a t t h e s e cond o r d e r c o n d i t i o n i s a lway s s a t i s f i e d . See t h e appen - d i x t o t h i s c h a p t e r f o r t h e d e t a i l s on t h e second o r d e r c o n d i t i o n . E q u a t i o n s 5 .8 and 5.9 d e f i n e t h e compensa t i on -emp loymen t s o l u - t i o n t o t h e monopoly m o d e l . P o i n t 'm ' i n F i g u r e 4 shows t h i s s o l u - t i o n i n nomina l c ompensa t i on - emp loymen t s p a c e . EE a r e i s o - e x p e n d i t u r e c u r v e s , uu a r e un i o n i n d i f f e r e n c e c u r v e s ( g i v e n t h e a l t e r n a t i v e wage and t h e p r i c e l e v e l ) , D i s t h e demand f o r l a b o u r c u r v e and oa i s t h e c ompensa t i on f u n c t i o n whose s l o p e e q u a l s t h e nom ina l wage. F i rms choose employment t o m i n i m i z e e x p e n d i t u r e s ub - j e c t t o oa and t h e un i on choose s oa t o max im i ze i t s o b j e c t i v e f u n c t i o n . C o s t m i n i m i z i n g i n p u t demand f u n c t i o n s f o r c a p i t a l and m a t e r i a l s can be d e r i v e d f rom t h e c o n d i t i o n a l c o s t f u n c t i o n as t h ey were i n c h a p t e r 4. D e f i n e an o r d i n a r y c o s t f u n c t i o n , wh i c h i s a l s o dua l t o t h e t e c h n o l o g y , 63 C ( r ,m ,w ,Q ) = M in {wL + D ( r , m , L , Q ) } = wL* ( r ,m ,w ,Q) L + D ( r , m , L * ( r , m , w , Q ) , Q ) ( 5 . 1 0 ) where L* ( r ,m ,w ,Q ) i s t h e s o l u t i o n t o e q u a t i o n 5 . 8 . S h e p a r d ' s lemma, a p p l i e d t o e q u a t i o n 5 . 1 0 , i m p l i e s K*( r ,m,w,Q) = 8 C ( r , m , w , Q ) / 3 r = 8 D ( r , m , L , Q ) / 8 r j ( 5 . 1 1 ) f[_=L* and M*(r ,m,w,Q) = 3C ( r ,m ,w ,Q ) / an = 9 D ( r , m , L , Q ) / 9 m | ( 5 . 1 2 ) IL=L* by t h e e n v e l o p e t h e o r e m . E q u a t i o n s 5 . 2 , 5 . 5 , 5 . 8 , 5 . 9 , 5 . 1 1 , 5 .12 imp l y t h e f o l l o w i n g n o n l i n e a r s y s t em o f e q u a t i o n s : K = c n L + c 1 2 Q + 2 b 1 2 ( L Q ) i ( l + r /X ) + a 1 2 r Z / X ( 5 . 13a ) M = c 2 1 L + c 2 2 Q + 2 b 1 2 ( L Q ) 2 ( l + m/X) + a 1 2 m Z / X ( 5 . 13b ) -w = c n r + c 2 1 m + b 1 2 ( Q / L ) i ( r + m + 2X) + 2 a 1 2 X ( l + ( Q / L ) i ) ( 5 . 1 3 c ) L 2 = L - c ^ r - c 2 1 m - 2 a 1 2 X + p ( u 2 + u 2 2 L + u 1 2 B + u 2 3 A ) ( 5 . 1 3d ) ( u x + u n B + u 1 2 L + u ^ A ) " 1 ] ! ; - b 1 2 Q * ( r + m + 2X) + a ^ X Q * ] . .r 64 FIGURE 4 65 E q u a t i o n s 5 .13a and b a r e t h e c o s t m i n i m i z i n g i n p u t demand f u n c t i o n s g i v e n by 5.11 and 5 . 1 2 . E q u a t i o n 5 .13c i s t h e i n v e r s e demand f o r l a b o u r f u n c t i o n g i v e n by 5 .8 and 5 .13d i s t h e f i r s t o r d e r c o n d i t i o n o f t h e u n i o n ' s m a x i m i z a t i o n p rob l em g i v e n by 5 . 9 . There a r e f o u r endogenous v a r i a b l e s : K, M, w, and L. No rma l l y d i s t r i b u t e d e r r o r t e rms a r e added on to e q u a t i o n s 5 .13 and t h e i d e n t i f y i n g r e s t r i c t i o n , u^ = 1, i s imposed on un i o n p r e f e r e n c e s . E r r o r t e rms c o r r e s p o n d i n g t o t h e same o b s e r v a t i o n a r e a l l o w e d t o be c o r r e l a t e d w i t h one a n o t h e r , w h i l e e r r o r t e rms c o r r e s - pond ing t o d i f f e r e n t o b s e r v a t i o n s a r e assumed t o be i n dependen t o f one a n o t h e r . T h i s means t h a t t h e e r r o r t e rms appended t o e q u a t i o n s 5.13 a r e c o r r e l a t e d w i t h one a n o t h e r o n l y f o r a g i v e n t i m e and i n d u s - t r y . The re i s no c o r r e l a t i o n a c r o s s t i m e o r a c r o s s i n d u s t r i e s . U n f o r t u n a t e l y , n u m e r i c a l p rob l ems p r e v e n t e d t h e e s t i m a t i o n o f t h e c omp l e t e s y s t em o f e q u a t i o n s ( 5 . 1 3 ) , so t h e r e s t r i c t i o n u ^ = u 1 3 = 0 1 S i [ T 1 P 0 S e c ' o n u n i ° n p r e f e r e n c e s . F u l l i n f o r m a t i o n maximum l i k e l i h o o d (FIML) e s t i m a t e s o f t h e p a r ame t e r s o f t h e r e s t r i c t e d sys tem a re o b t a i n e d and r e p o r t e d (w i t h t h e i r a s y m p t o t i c t - s t a t i s t i c s ) i n T a b l e V I . In o r d e r t o a d j u s t f o r c o n s t a n t , a c r o s s i n d u s t r y d i f f e r e n c e s i n e q u a t i o n s 5 . 1 3 , t h e comp l e t e s y s t em i s r e - e s t i m a t e d w i t h dummy v a r i - a b l e s f o r o b s e r v a t i o n s on p l ywood m i l l s and s h i n g l e m i l l s added on t o each e q u a t i o n . The FIML e s t i m a t e s , and t h e i r a s y m p t o t i c t - s t a t i s t i c s a r e a l s o r e p o r t e d i n T a b l e V I . C h a r a c t e r i s t i c s o f t h e e s t i m a t e d u n i o n p r e f e r e n c e s and p r o d u c - t i o n t e c h n o l o g y , e v a l u a t e d a t t h e sample means, a r e r e p o r t e d i n T a b l e V I I . T a b l e V I I I r e p o r t s t h e e s t i m a t e d c h a r a c t e r i s t i c s when t h e dummy v a r i a b l e s a r e i n c l u d e d i n e q u a t i o n s 5 . 1 3 . L e t t e r s u b s c r i p t s on U and 66 TABLE VI E s t i m a t e d C o e f f i c i e n t s o f t h e Monopo ly Un i on Model A s y m p t o t i c t - s t a t i s t i c s a r e i n p a r e n t h e s e s No Dummy V a r i a b l e s '11 : 12 : 21 : 22 >12 '12 J 13 *22 '23 - 0 . 2 3 1 9 0 . 6963 0 .0329 0 .9336 - 0 . 2 3 7 8 0 .1328 1.0 - 0 . 1 297 0 . 0 - 0 . 0 1 2 4 0 .0 - 0 . 0 0 1 2 - 0 . 3 3 6 8 N a t u r a l l o g o f 1 i k e l i h o o d f u n c t i o n ( - 3 . 6 5 7 ) ( 2 3 . 5 67 ) ( 0 . 7 09 ) ( 2 1 . 3 61 ) ( - 1 1 . 1 8 1 ) ( 3 . 8 60 ) ( - 1 . 6 9 ) ( 2 . 0 98 ) ( - 0 . 0 6 2 ) ( - 6 . 4 3 6 ) 352 .804 C o r r e l a t i o n C o e f f i c i e n t s between a c t u a l and 0 . 9 3 , 0 . 9 9 , p r e d i c t e d v a l u e s o f 0 . 9 6 , 0 . 9 9 K,M,w, and L~* Dummy V a r i a b l e s f o r O b s e r v a t i o n s on S h i n g l e M i l l s and P l ywood M i l l s 0 .0482 ( - 0 . 7 2 9 ) 0 . 6368 ( 25 . 040 ) 0 . 0393 ( 1 . 0 31 ) 0 . 9675 ( 2 9 . 0 72 ) 0 .2527 ( - 1 1 , 7 8 8 ) 0 . 1365 ( 4 . 8 84 ) 1.0 0 .1921 ( - 1 . 8 6 0 ) 0 .0040 ( - 1 . 0 6 9 ) 0 .0160 ( 2 . 5 8 3 ) 0 .4449 ( - 5 0 . 4 1 9 ) 0 .0542 ( - 4 . 0 9 9 ) 0 .0856 ( 1 . 8 9 7 ) 424 . 618 0 . 9 3 , 0 . 9 9 , 0 . 9 6 , 0 . 9 9 67 TABLE V I I E s t i m a t e d C h a r a c t e r i s t i c s o f Un i on P r e f e r e n c e s and P r o d u c t i o n T e c h n o l o g y : Monopo ly Un ion Model and No Dummy V a r i a b l e s A l l e s t i m a t e s a r e e v a l u a t e d a t t he mean of t h e d a t a Un ion P r e f e r e n c e ^ M o n d t o n i c i t y U B = 0 . 9 5 7 , U L = - 0 . 8 4 4 , U A = - 1 . 1 6 3 , <|>w/p = 3 . 3 0 5 , <f>L = 1.201 C u r v a t u r e De t e rm i nan t o f b o r d e r ed h e s s i a n o f t h e u n i o n ' s o b j e c t i v e f u n c t i o n = 0 . 0 2 1 . M R S B L - 0 . 8 8 2 , M R S w / p L = 0 . 3 6 3 , a w / p L = 0 . 7 6 8 . P r o d u c t i o n Techno l ogy , M o n o t o n i c i t y C p = 3 . 1 3 0 , C m = 6 . 7 6 2 , C w = 4 . 0 1 0 , C Q = 4 . 3 25 C u r v a t u r e D e t e r m i n a n t s o f m i no r s o f t h e h e s s i a n o f t h e c o s t f u n c t i o n a r e : - 0 . 8 7 9 , - 0 . 1 7 2 , 0 .0 The m a t r i x o f p r i c e e l a s t i c i t i e s i s r m w K - 0 . 5 1 4 - 0 . 7 4 6 1.260 M - 0 . 1 9 3 - 0 . 1 7 5 0 . 368 L 0 .928 1.049 - 1 . 9 7 7 The e l a s t i c i t i e s o f s u b s t i t u t i o n a r e : CTKL = 5 ' 7 8 ' °ML = 1 ' 6 8 ' CTKM = - 1 ' 2 0 68 TABLE V I I I E s t i m a t e d C h a r a c t e r i s t i c s o f Un i on P r e f e r e n c e s and P r o d u c t i o n T e c h n o l o g y : Monopo ly Un i on Model w i t h Dummy V a r i a b l e s A l l e s t i m a t e s a r e e v a l u a t e d a t t h e mean o f t h e d a t a Un ion P r e f e r e n c e s M o n o t o n i c i t y U B = 0 . 2 0 8 , U L = - 0 . 1 0 5 , U A = - 2 . 9 5 9 , <|>w/p = 0 . 7 1 8 , $ L = 0 . 341 C u r v a t u r e De t e rm inan t o f b o r d e r e d h e s s i a n o f t h e u n i o n ' s o b j e c t i v e f u n c t i o n = 0 .0017 M R S B L = 0 . 5 0 3 , M R S w / p L = 0 . 4 8 9 , a w / p L = 0 . 7 3 7 . P r o d u c t i o n Te chno l og y M o n o t o n i c i t y C p = 3 . 2 4 2 , C m = 6 . 9 8 2 , C w = 3 . 6 18 , C Q = 4 .327 C u r v a t u r e D e t e r m i n a n t s o f m i no r s o f t h e h e s s i a n o f t h e c o s t f u n c t i o n a r e : - 0 . 3 9 9 , - 0 . 1 1 8 , 0 .0 The m a t r i x o f p r i c e e l a s t i c i t i e s i s r m w K - 0 . 2 3 3 - 0 . 5 6 8 0 . 801 M - 0 . 1 4 7 - 0 . 1 9 8 0 . 345 L 0 .590 0 .983 - 1 . 5 7 3 The e l a s t i c i t i e s o f s u b s t i t u t i o n a r e : °KL " 3 - 6 8 ' <k = 1 - 5 8 ' °KM " - ° - 9 1 69 C r e p r e s e n t p a r t i a l d e r i v a t i v e s o f t h e u n i o n o b j e c t i v e f u n c t i o n and t h e i n d u s t r y c o s t f u n c t i o n r e s p e c t i v e l y . A number o f h y p o t h e s i s t e s t s a r e pe r f o rmed on t h e e s t i m a t e d s y s - tems u s i n g l i k e l i h o o d r a t i o t e s t s . The r e s t r i c t e d and u n r e s t r i c t e d max im i z ed v a l u e s o f t h e l o g l i k e l i h o o d f u n c t i o n a r e r e p o r t e d i n T ab l e I X . The h y p o t h e s i s t h a t t h e u n i o n max im i z e s t h e wage b i l l (u^ = u l l = u 1 2 = u 1 3 = u 2 2 = u 2 3 = ^ a n c ' n y P o t n e s i s t n a t t n e u n i o n max im i z e s r e n t s ( u 2 = u ^ = u^ 2 = u i 3 = u 2 2 = u > u i = " u 2 3 ^ a r e k ° t n r e j e c t e d , even a t t h e 99.5% c o n f i d e n c e l e v e l . The h y p o t h e s i s t h a t t h e u n i o n ' s o b j e c t i v e f u n c t i o n i s i ndependen t o f t h e a l t e r n a t i v e wage ( u 1 3 = u 2 3 = 0) i s a l s o r e j e c t e d a t t h e 99.5% c o n f i d e n c e l e v e l . The same r e s u l t s a r e o b t a i n e d f r om t h e u n r e s t r i c t e d s y s t em when t h e dummy v a r i a b l e s a r e i n c l u d e d i n t h e e s t i m a t i n g e q u a t i o n s . The h y p o t h e s i s t h a t t h e u n i o n max im i ze s some f u n c t i o n o f t h e wage, and i s i n d i f f e r e n t t o t h e l e v e l o f employment (<j>̂  = 0) c anno t be t e s t e d d i r e c t l y . However t h e e s t i m a t e d s t a n d a r d e r r o r o f t h e e s t i m a t e o f i s 0 .0785 i n t h e r e s t r i c t e d model w i t h o u t dummy v a r i - a b l e s and 0 .0274 i n t h e u n r e s t r i c t e d model w i t h dummy v a r i a b l e s . S i n c e t h e two e s t i m a t e s o f <j>̂  a r e 1.201 and 0 .341 r e s p e c t i v e l y , i t i s c l e a r t h a t <j>̂  = 0 i s o v e r w h e l m i n g l y r e j e c t e d i n bo th m o d e l s . I t i s v e r y i n t e r e s t i n g t o compare t h e e s t i m a t e s o f t h e p r o d u c - t i o n t e c h n o l o g y f rom t he monopoly un i on model w i t h t h e e s t i m a t e s o b t a i n e d i n c h a p t e r f o u r , where a l l i n p u t p r i c e s a r e assumed t o be exogenous and p r o d u c t i o n pa r ame t e r s a r e not e s t i m a t e d j o i n t l y w i t h any un i o n p r e f e r e n c e p a r a m e t e r s . The u n i o n model shows much l a r g e r ( i n a b s o l u t e v a l u e ) p r i c e e l a s t i c i t i e s and e l a s t i c i t i e s o f s u b s t i t u - t i o n . Hence , t h e u n i o n model s u g g e s t s much g r e a t e r s u b s t i t u t a b i 1 i t y 70 TABLE IX Max im i z ed V a l u e s o f t h e Log L i k e l i h o o d s o f t h e Un ion M o d e l s : C on s t an t R e t u r n s t o S c a l e Monopo ly Un ion Model C o o p e r a t i v e Un i on Model No Dummy Dummy V a r i a b l e s V a r i a b l e s u n = u 1 3 = 0 No Dummy Dummy V a r i a b l e s V a r i a b l e s U n r e s t r i c t e d 352 .804 424 .618 395 .357 4 36 . 4 35 Wage b i l l m a x i m i z a t i o n h y p o t h e s i s 266 .213 351 .682 296 .294 375 . 199 Rent m a x i m i z a t i o n h y p o t h e s i s 260 .439 307 .385 309 .193 389 . 333 Un ion p r e f e r e n c e s i n d ependen t o f t h e a l t e r n a t i v e wage h y p o t h e s i s 336 .245 408 .967 380 .627 434 . 991 "11 = u 1 3 = 0 372 . 048 71 between t h e f a c t o r s o f p r o d u c t i o n and g r e a t e r r e s p o n s i v e n e s s t o p r i c e changes t h an t h e model wh i ch i s c o n s i s t e n t w i t h p e r f e c t c o m p e t i t i o n i n a l l i n p u t m a r k e t s . The most s t r i k i n g d i f f e r e n c e i s i n t h e e s t i m a t e o f t h e p r i c e e l a s t i c i t y o f t h e demand f o r l a b o u r f u n c t i o n . The t r a n s l o g c o s t f u n c t i o n , t h e c o n d i t i o n a l c o s t f u n c t i o n e s t i m a t e d i n c h a p t e r 4 , and a lmos t a l l o f t h e e s t i m a t e s f ound i n t he l i t e r a t u r e , show t h e p r i c e e l a s t i c i t y o f t h e demand f o r l a b o u r t o be s m a l l e r t h a n 0 . 5 ( i n ab so - l u t e v a l u e ) . In t h e monopoly un i on m o d e l , however , t h e e s t i m a t e d e l a s t i c i t y jumps t o an a b s o l u t e v a l u e g r e a t e r t h an 1 . 5 . O t h e r e v i - dence o f t h i s phenomenon i s f ound i n t h e l i t e r a t u r e . De r t ou zo s and P en c a ve l (1981) a l s o f i n d t h a t a monopo ly un i o n model y i e l d s a v e r y h i g h e s t i m a t e o f t h e e l a s t i c i t y o f t h e demand f o r l a b o u r . They r e p o r t a n e g a t i v e e s t i m a t e d e l a s t i c i t y r a n g i n g f r om 1.8 t o 1 .0 , w i t h a v a l u e o f 1.23 a t t h e means o f t h e v a r i a b l e s . T h e r e f o r e i t seems t h a t e s t i m a t e s o f p r o d u c t i o n t e c h n o l o g y a r e ve r y s e n s i t i v e t o t h e e x p l i c i t m o d e l i n g o f un i on b e h a v i o r i n t h e l a b o u r m a r k e t . I f t h e MUM has any v a l i d i t y (compared t o t h e assump- t i o n o f p e r f e c t c o m p e t i t i o n i n t h e l a b o u r ma r ke t ) t h en t h e e s t i m a t e s o f p r i c e e l a s t i c i t i e s and e l a s t i c i t i e s o f s u b s t i t u t i o n f ound i n t h e l i t e r a t u r e s h o u l d be s e r i o u s l y q u e s t i o n e d . In Canada , most manu- f a c t u r i n g i n d u s t r i e s a r e o r g a n i z e d by u n i o n s wh i c h have a s i g n i f i c a n t impac t on t h e i n d u s t r i e s ' l a b o u r m a r k e t . E s t i m a t e s o f t h e Canad i an m a n u f a c t u r i n g s e c t o r ' s t e c h n o l o g y c o u l d be v e r y d i f f e r e n t f r om t h e ones found i n t h e l i t e r a t u r e i f t h e u n i o n s ' b e h a v i o r had been m o d e l l e d and wages were assumed t o be endogenous . T h i s seems t o be e s p e c i a l l y t r u e f o r t he p r i c e e l a s t i c i t y o f t h e demand f o r l a b o u r , w h i c h i s so i m p o r t a n t f o r p o l i c y a p p l i c a t i o n s . 72 C o o p e r a t i v e Un ion Model In t h e c o o p e r a t i v e u n i o n model (CUM) t h e i n d u s t r y and un i o n use some u n s p e c i f i e d means t o choose a compensa t i on -emp loymen t c o m b i n a - t i o n wh i c h l i e s on t h e c o n t r a c t c u r v e . I t i s i m p o r t a n t t o r e a l i z e t h a t t h e compensa t i on -emp loymen t s o l u t i o n t o t h e model i s not on t h e f i r m ' s demand f o r l a b o u r f u n c t i o n . The f i r m emp loys more l a b o u r t h a n i t wou ld l i k e t o , g i v e n t h e n e g o t i a t e d wage. C l e a r l y , t h e two s i d e s must b a r g a i n abou t more t h a n j u s t t h e a ve r age r a t e o f c ompensa t i o n ( t he wage) t o f o r c e t h e f i r m o f f i t s demand f o r l a b o u r f u n c t i o n . The u n i o n and f i r m c o u l d use many d i f f e r e n t mechanisms t o r e a ch a p o i n t on t he c o n t r a c t c u r v e . For e xamp l e , t hey c o u l d n e g o t i a t e work r u l e s wh i c h t i e t h e amount o f l a b o u r emp loyed t o o u t p u t o r t h e u se o f some o t h e r i n p u t . Ano t he r a l t e r n a t i v e i s t o n e g o t i a t e c ompensa t i on r u l e s wh i c h a r e no t homogeneous o f deg r ee one i n t h e amount o f l a b o u r employed (see Chap t e r 7 ) . Assume, f o r t h e sake o f e x p o s i t i o n , t h a t t h e u n i o n and f i r m b a r g a i n d i r e c t l y abou t t h e l e v e l o f wages and t h e l e v e l o f emp loyment . Note t h a t t h i s a s sump t i on i s c o m p l e t e l y i n n o cuou s and does not a f f e c t t h e e s t i m a t i n g e q u a t i o n s . The e s t i m a t i n g e q u a t i o n s s i m p l y s p e c i f y a p o i n t on t h e c o n t r a c t c u r v e . How t h e p o i n t on t h e c o n t r a c t c u r v e i s r e a ched o r s u p p o r t e d i s no t s p e c i f i e d . The i n d u s t r y ' s e x p e n d i t u r e on i n p u t s i s g i v e n by E ( r , m , w , L , Q ) = wL + D ( r , m , L , Q ) ( 5 . 3 ) and an i s o - e x p e n d i t u r e c u r v e can be w r i t t e n wL = pB = E - D ( r , m , L , Q ) ( 5 . 4 ) 73 where E i s a c o n s t a n t . By s u b s t i t u t i n g t h e c o n s t r a i n t ( e q u a t i o n 5 .4 ) i n t o t h e u n i o n ' s o b j e c t i v e f u n c t i o n U ( B , L ; A ) , t h e m a x i m i z a t i o n p rob l em wh i ch c h a r a c - t e r i z e s t h i s model can be w r i t t e n Max {U(E/p - D ( r , m , L , Q ) / p , L ; A ) } . The f i r s t o r d e r c o n d i t i o n i s 3U/3L = - U B D L / p + U L = 0 D L = p U L / U B . ( 5 . 1 4 ) The c u r v a t u r e p r o p e r t i e s o f D ( r , m , L , Q ) and U ( B , L ; A ) e n s u r e t h a t t h e s e cond o r d e r c o n d i t i o n i s s a t i s f i e d . See t h e a p p e n d i x t o t h i s c h a p t e r f o r t h e d e t a i l s on t h e second o r d e r c o n d i t i o n . E q u a t i o n s 5.4 and 5 .14 d e f i n e t h e compensa t i on -emp loymen t s o l u - t i o n t o t h e CUM. P o i n t " d " i n F i g u r e 4 i s a p o s s i b l e s o l u t i o n t o t h e c o o p e r a t i v e model i n nom ina l c ompensa t i on -emp loymen t s p a c e , where c c i s t h e c o n t r a c t c u r v e . I t i s i m p o r t a n t t o no t e t h a t t h e CUM i s no t c o m p l e t e l y s p e c i - f i e d . The b a r g a i n i n g mechanism used by t h e two p a r t i e s t o choose t h e i n d u s t r y ' s l e v e l o f e x p e n d i t u r e and t h e u n i o n ' s l e v e l o f u t i l i t y i s l e f t u n s p e c i f i e d . The model does not p r e d i c t where on t h e c o n t r a c t c u r v e t h e s o l u t i o n w i l l be; i t o n l y p r e d i c t s t h a t t h e s o l u t i o n w i l l be on t h e c o n t r a c t c u r v e . The un i on and i n d u s t r y s i m p l y choose t h e 74 ob s e r v ed l e v e l o f e x p e n d i t u r e and no a c coun t i s g i v e n t o t h e d e t e r - m inan t s o f t h a t l e v e l o f e x p e n d i t u r e . Co s t m i n i m i z i n g demands f o r c a p i t a l and m a t e r i a l s , c o n d i t i o n a l upon ou t pu t and t h e l a b o u r i n p u t chosen w i t h t h e u n i o n , a r e d e r i v e d by a p p l y i n g S h e p a r d ' s lemma t o t h e c o n d i t i o n a l c o s t f u n c t i o n : K * ( r , m , L , Q ) = 3 D ( r , m , L , Q ) / 3 r ( 5 . 1 5 ) and M* ( r ,m , L ,Q ) = 3 D ( r , m , L , Q ) / 3 m . ( 5 . 1 6 ) E q u a t i o n s 5 . 2 , 5 . 5 , 5 . 4 , 5 . 1 4 , 5 . 1 5 , and 5.16 imp l y t h e f o l l o w i n g n o n l i n e a r s i m u l t a n e o u s s y s t em o f e q u a t i o n s : K = c n L + c 1 2 Q + 2 b 1 2 ( L Q ) * ( l + r /X ) + a ^ r Z / X ( 5 . 17a ) M = c 2 1 L + c 2 2 Q + 2 b 1 2 ( L Q ) i ( l + m/X) + a 1 2 m Z / X ( 5 . 17b ) -w = - E / L + c ^ r + c 1 2 r Q / L + c^m + c 2 2 m Q / L + 2 b 1 2 ( r + m + 2 X ) ( Q / L ) i + 2 a 1 2 X ( l + Q/L + 2 ( Q / L ) * ) ( 5 . 1 7 c ) L~2 = C - C ^ r ~ cz\m - 2a^ 2 X + ( u 2 + u 2 2 L + u ^ B + u ^ A ) - 1 * _ 1 p ( u x + u n B + u 1 2 L + u 1 3 A ) ] [ b 1 2 Q 2 ( r + m + 2X) + 2 a 1 2 X Q 2 ] . ( 5 . 1 7d ) 75 TABLE X E s t i m a t e d C o e f f i c i e n t s o f t h e C o o p e r a t i v e Un ion Model A s y m p t o t i c t - s t a t i s t i c s a r e i n p a r e n t h e s e s No Dummy V a r i a b l e s '11 : 12 : 21 : 2 2 hz J 12 '11 J 12 J 13 '22 J 23 0 .3847 0 .6444 0 .4800 0 . 9465 - 0 . 3938 0 .2123 1.0 -0 .4616 0 .0648 -0 .0924 -0 .4660 0 .0947 0 .2474 N a t u r a l l o g o f 1 i k e l i h o o d f u n c t i o n ( 1 . 6 47 ) ( 1 0 . 645 ) ( 2 . 4 9 4 ) ( 1 3 . 563 ) ( - 3 . 4 8 9 ) ( 3 . 4 31 ) ( - 2 . 9 8 9 ) ( 2 . 6 32 ) ( - 2 . 0 5 3 ) ( - 2 4 . 4 5 8 ) ( 1 . 4 72 ) ( 3 . 7 99 ) 395 .357 C o r r e l a t i o n C o e f f i c i e n t s between a c t u a l and 0 . 9 3 , 0 . 9 9 , p r e d i c t e d v a l u e s o f 0 . 9 2 , 0 . 9 9 Dummy V a r i a b l e s f o r O b s e r v a t i o n s on S h i n g l e M i l l s and P l ywood M i l l s K,M,w, and L 2 0.2069 0 .5991 0 .3027 0 .9079 -0 .3005 0 .1682 1.0 -0 .3513 0 .0514 -0 .0879 -0 .3520 0 .0781 0 .1735 ( 1 . 6 0 4 ) ( 1 0 . 706 ) ( 2 . 7 6 9 ) ( 2 2 . 260 ) ( - 4 . 1 3 9 ) ( 3 . 6 81 ) ( - 2 . 1 2 5 ) ( 1 . 8 22 ) ( - 1 . 4 8 7 ) ( - 4 . 4 4 7 ) ( 0 . 8 6 5 ) ( 2 . 7 0 9 ) 436 . 435 0 . 9 3 , 0 . 9 9 , 0 . 9 2 , 0 . 9 9 76 TABLE XI E s t i m a t e d C h a r a c t e r i s t i c s o f Un i on P r e f e r e n c e s and P r o d u c t i o n T e c h n o l o g y : C o o p e r a t i v e Un ion Model and No Dummy V a r i a b l e s A l l e s t i m a t e s a r e e v a l u a t e d a t t h e mean o f t h e d a t a Un ion P r e f e r e n c e s Monoton i c i t y U B = 0 . 2 9 9 , U L = - 0 . 3 5 6 , U A = - 2 . 5 5 4 , $ w / = 1 .046 , $ L = 0 . 286 C u r v a t u r e De t e rm i nan t o f b o r d e r ed h e s s i a n o f t h e u n i o n ' s o b j e c t i v e f u n c t i o n = 0 . 003 P r o d u c t i o n T e chno l o g y Monoton i c i t y D p = 3 . 4 24 , D m= 7 . 0 47 , D Q = 4 . 0 3 2 , D L = - 1 . 7 1 4 , D L [_= 0 .796 C u r v a t u r e D e t e r m i n a n t s o f m ino r s o f t h e h e s s i a n o f t h e c o n d i t i o n a l c o s t f u n c t i o n a r e : 0 . 1 7 9 , 0 .0 M R S m = 1 .192 , MRS w/p L = 0 . 2 7 3 , a. w/p L = 0 . 599 The m a t r i x o f p r i c e e l a s t i c i t i e s i s r m K K M 0 .105 - 0 . 0 2 7 0 .105 0 .027 ffKM = - 0 . 1 6 77 TABLE X I I E s t i m a t e d C h a r a c t e r i s t i c s o f Un ion P r e f e r e n c e s and P r o d u c t i o n T e c h n o l o g y : C o o p e r a t i v e Un ion Model w i t h Dummy V a r i a b l e s A l l e s t i m a t e s a r e e v a l u a t e d a t t h e mean o f t h e d a t a Un ion P r e f e r e n c e s M o n o t o n i c i t y U B = 0 . 4 2 5 , U L = - 0 . 4 0 5 , U A = - 1 . 9 7 6 , <|)w/p = 1 . 4 81 , <|>L = 0 . 505 C u r v a t u r e De t e rm i nan t o f b o r d e r ed h e s s i a n o f t h e u n i o n ' s o b j e c t i v e f u n c t i o n = 0 . 008 M R S B L = 0 . 9 5 5 , M R S w / p L = 0 . 3 4 1 , a w / p L = 0 . 6 7 5 . P r o d u c t i o n Te chno l og y M o n o t o n i c i t y D p = 3 . 4 44 , Dm= 7 . 1 29 , D Q = 4 . 0 3 1 , D L = - 1 . 6 1 5 D L L = 0 . 598 C u r v a t u r e D e t e r m i n a n t s o f m i no r s o f t h e h e s s i a n o f t h e c o s t f u n c t i o n a r e : 0 . 1 7 7 , 0 .0 The m a t r i x o f p r i c e e l a s t i c i t i e s i s r m K M 0 .104 -0 .027 •0.104 0 .027 - 0 . 1 6 78 E q u a t i o n s 5 .17a and b a r e t h e c o s t m i n i m i z i n g , c o n d i t i o n a l , i n p u t demand f u n c t i o n s g i v e n by 5.15 and 5 . 16 . E q u a t i o n 5 .17c i s t h e i s o - e x p e n d i t u r e c u r v e ( 5 . 4 ) chosen by t h e i n d u s t r y and u n i o n , d i v i d e d by t h e amount o f l a b o u r employed and 5.17d i s t h e f i r s t o r d e r c o n d i t i o n ( 5 . 1 4 ) t o t h e m a x i m i z a t i o n p r o b l e m . The re a r e f o u r endogenous v a r i - a b l e s ; K,M, w, and L. N o r m a l l y d i s t r i b u t e d e r r o r t e rms wh i c h a r e c o r r e l a t e d when t h e y c o r r e s p o n d t o t h e same o b s e r v a t i o n and i ndependen t when t hey c o r - r e spond t o d i f f e r e n t o b s e r v a t i o n s a r e added on t o e q u a t i o n s 5.17 and an i d e n t i f y i n g r e s t r i c t i o n , u^ = 1 i s imposed on un i o n p r e f e r e n c e s . FIML e s t i m a t e s o f t h e p a r ame t e r s o f t h e s y s t em a r e r e p o r t e d , a l o n g w i t h t h e i r t - s t a t i s t i c s , i n T ab l e X. The sys tem i s r e - e s t i m a t e d w i t h dummy v a r i a b l e s f o r s h i n g l e m i l l s and p l ywood m i l l s added on t o each e q u a t i o n and t h e pa r ame te r e s t i m a t e s a r e a l s o r e p o r t e d i n T ab l e X. C h a r a c t e r i s t i c s o f t h e e s t i m a t e d un i o n p r e f e r e n c e s and p r odu c - t i o n t e c h n o l o g y , w i t h and w i t h o u t dummy v a r i a b l e s and e v a l u a t e d a t t h e samp le means, a r e r e p o r t e d i n T a b l e s XI and X I I . I t i s c l e a r t h a t t h e dummy v a r i a b l e s do not a f f e c t t h e e s t i m a t e s o f t h e c h a r a c - t e r i s t i c s v e r y much, even t hough t h e h y p o t h e s i s t h a t t h e dummy v a r i - a b l e s have z e r o c o e f f i c i e n t s canno t be a c c e p t e d . The wage b i l l and r e n t m a x i m i z a t i o n h ypo t he s e s abou t u n i o n p r e f - e r en c e s a r e o v e r w h e l m i n g l y r e j e c t e d , bo th w i t h and w i t h o u t dummy v a r i a b l e s , u s i n g l i k e l i h o o d r a t i o t e s t s ( s ee T a b l e I X ) . The hypo - t h e s i s t h a t un i on p r e f e r e n c e s a r e i ndependen t o f t h e a l t e r n a t i v e wage i s a l s o o v e r w h e l m i n g l y r e j e c t e d i n t h e model w i t h o u t dummy v a r i a b l e s , but i t can o n l y be r e j e c t e d a t t h e 75% c o n f i d e n c e l e v e l i n t h e model w i t h dummy v a r i a b l e s . 79 The e s t i m a t e d v a l u e s and s t a n d a r d e r r o r s o f ^ a r e 0 . 286 and 0 .059 w i t h o u t t h e dummy v a r i a b l e s and 0 .505 and 0 .162 w i t h t h e dummy v a r i a b l e s , so t h e h y p o t h e s i s t h a t t h e u n i o n i s i n d i f f e r e n t t o t h e l e v e l o f employment i s a l s o r e j e c t e d i n both c a s e s . F i n a l l y , t h e h y p o t h e s i s t h a t t h e t e c h n o l o g y i s L e o n t i e f ^ °MK = ° ' ^12 = a 1 2 = ^ ^ S t e s t e d ^ n a s i g h t l y m o d i f i e d v e r s i o n o f t h e CUM. The r e s t r i c t e d max im i z ed v a l u e o f t h e l o g l i k e l i h o o d f u n c - t i o n i s 2 7 8 . 4 7 8 . The l o g l i k e l i h o o d o f t h e u n r e s t r i c t e d model r e a ched 3 1 2 . 3 , a l t h o u g h t h e maximum v a l u e was not f o u n d . T h e r e f o r e , i n s p i t e o f a ve r y low e s t i m a t e o f o M V I L e o n t i e f t e c h n o l o g y i s r e j e c t e d d e c i s i v e l y . The wrong s i g n s on t h e e s t i m a t e d p r i c e e l a s t i c i t i e s a r e due t o t he s t r o n g r e s t r i c t i o n s economic t h e o r y and t h e f u n c t i o n a l f o rm p l a c e on t h e p r o d u c t i o n t e c h n o l o g y i n t h e CUM. A l t h o u g h t h e r e a r e t h r e e i n p u t s , t h e l a b o u r i n p u t i s d e t e r m i n e d by some mechanism o u t s i d e t h e m o d e l , so t h e i n d u s t r y has o n l y two v a r i a b l e i n p u t s ; c a p i t a l and m a t e r i a l s . Economic t h e o r y i n s i s t s t h a t w i t h o n l y two i n p u t s , t h e i n p u t s must be s u b s t i t u t e s and t h e c r o s s p r i c e e l a s t i c i t i e s must be p o s i t i v e . Economic t h e o r y a l s o i n s i s t s t h a t t h e own p r i c e e l a s t i - c i t i e s must be n e g a t i v e . I t t u r n s ou t t h a t , c o n s i s t e n t w i t h economic t h e o r y , t h e f u n c t i o n a l f o rm f o r c e s t h e c r o s s p r i c e e l a s t i c i t y t o have t h e o p p o s i t e s i g n f r om t h e own p r i c e e l a s t i c i t y i n t h e two i n p u t c a s e . In f a c t , as can be seen f rom t he e s t i m a t e s , t h e f u n c t i o n a l f o rm f o r c e s t h e c r o s s p r i c e e l a s t i c i t i e s t o be e x a c t l y equa l t o minus t h e own p r i c e e l a s t i c i t i e s . ' U n f o r t u n a t e l y , a l l t h e work r e p o r t e d above i n d i c a t e s t h a t c a p i t a l and m a t e r i a l s a r e complements and no t s u b s t i t u t e s . That f a c t i s c o r r o b o r a t e d once a g a i n by t h e n e g a t i v e c r o s s p r i c e e l a s t i c i t i e s shown i n T a b l e s XI and X I I . G i v e n t h e f u n c - 80 t i o n a l f o r m , t h e n e g a t i v e c r o s s p r i c e e l a s t i c i t i e s imp l y p o s i t i v e own p r i c e e l a s t i c i t i e s and t h e m a t r i x o f p r i c e e l a s t i c i t i e s has a l l t h e wrong s i g n s . I t seems c l e a r t h a t t h e two i n p u t p r o d u c t i o n t e c h n o l o g y s p e c i f i e d i n t h e CUM i s j u s t not r i c h enough t o accommodate t h e com- p l e m e n t a r i t y o f c a p i t a l and m a t e r i a l s f ound i n t h e d a t a , and v e r y q u e s t i o n a b l e e s t i m a t e s r e s u l t . Non C o n s t a n t R e t u r n s t o S c a l e II .II .I— — —— —— — . i 4 S i n c e t h e work i n C h a p t e r 4 shows t h a t c o n s t a n t r e t u r n s t o s c a l e i s not an a c c e p t a b l e c h a r a c t e r i z a t i o n o f t h e p r o d u c t i o n t e c h n o l o g y , t h e MUM and CUM a r e r e - e s t i m a t e d u s i n g a c o n d i t i o n a l c o s t f u n c t i o n wh i ch does not c o n s t r a i n t h e t e c h n o l o g y t o c o n s t a n t r e t u r n s t o s c a l e . The MUM and CUM rema in e x a c t l y as t h e y a r e shown above . On l y t h e s p e c i f i c a t i o n o f D ( r , m , L , Q ) c h a n g e s . D ( r , m , L , Q ) r e t a i n s a l l o f t h e p r o p e r t i e s o u t l i n e d above e x c e p t homogene i t y o f deg r ee one i n Q and L. The new s p e c i f i c a t i o n o f D ( r , m , L , Q ) s t i l l e n su r e s t h a t t h e s e cond o r d e r c o n d i t i o n s o f t h e un i o n mode l s a r e s a t i s f i e d . By u s i n g t h e same g ene r a l f u n c t i o n a l fo rm ( D i e w e r t , 1974 , p . 137) and a d d i n g one more f i x e d i n p u t wh i c h i s c o n s t a n t and d e f i n e d equa l t o minus one , one can s p e c i f y D ( r , m , L , Q ) = c rL + c rQ + c r + c mL + c^mQ + c ^ m + 2 [ b 1 2 ( L Q ) * + ' b 1 3 L * + b 2 3 Q 2 ] [ r + m + 2X] + 2a ' 1 2 XZ ( 5 . 1 8 ) where X = ( - r 2 + - m 2 ) 2 and Z = 1 + L + Q + 2 ( ( L Q ) 2 + L* + Q 2 " ) . 2 2 81 In t h e MUM e q u a t i o n s , 5 . 5 , 5 . 8 , 5 . 9 , 5 . 1 1 , 5 . 1 2 , and 5 .18 i m p l y t h e f o l l o w i n g s i m u l t a n e o u s sys tem o f e q u a t i o n s : K = C 1 3 + C 1 1 L + C 1 2 Q + 2 [ b 1 2 ( L Q ) 4 + b 1 3 L i + b 2 3 Q i ] [ l + r / X ] + a 1 2 r Z / X ( 5 . 19a ) M = c 2 3 + c ^ L + c 2 2 Q + 2 [ b 1 2 ( L Q ) i + b 1 3 L 2 + b 2 3 Q i ] [ l + m/X] + a 1 2 m Z / X ( 5 . 1 9 b ) -w = c n r + c 2 1 m + [ b 1 2 ( Q / L ) 4 + b^L^Hr + m + 2X] ( 5 . 1 9 c ) + 2 a 1 2 X ( l + L~2 + (Q / L ) * ) L 2 = [ - c ^ r _ c 2 1 m _ 2 a 1 2 X + p ( u 2 + u 2 2 L + u-^B + u 2 3 A ) ( u -^ + u-^L + u ^ B + u^ 3 A) 1 i - 1 [ - ( b 1 2 Q 2 + b 1 3 ) ( r + m + 2X) + a 1 2 X ( l + Q 2 ) ] . ( 5 . 1 9d ) In t h e CUM e q u a t i o n s 5 . 5 , 5 . 4 , 5 . 14 , 5 . 1 5 , 5 . 1 6 , and 5.18 i m p l y t h e f o l l o w i n g s i m u l t a n o u s e q u a t i o n s s y s t em : K = c 1 3 + c n L + c 1 2 Q + 2 [ b 1 ? ( L Q ) 2 + b ^ L 2 + b^cnCl + r / X ] + a 1 ? r Z / X ( 5 . 20a ) 82 M = C 2 3 + C 2 1 L + C 2 2 Q + 2 [ b 1 2 ( L Q ) 2 + b ^ L 2 + b „ Q 2 ] [ l + m/X] + a 1 9 m Z / X ] ( 5 . 2 0b ) '13 u 2 3 12' -w = - E / L + c n r + c1 2rO/L + c ^ r / L + c ^ m + c 2 2 m Q / L + c 2 3 m / L + 2 [ b 1 2 ( Q / L ) i + b ^ ' 2 " + b ^ Q V 1 ] [ r + m + 2X] + 2 a 1 2 X Z / L ( 5 . 2 0 c ) L~ 2 = E-c^r - c 2 1 m - 2 a 1 2 X + p ( u 2 + u 2 2 L + u 1 2 B + u 2 3 A ) '12 ^ u l + U 1 2 L + U 1 3 A + u i i B ) _ 1 ^ i vn - 1 [ ( b 1 2 Q 2 + b 1 3 ) ( r + m + 2X) + 2 a 1 2 X ( l + Q 2 ) ] . ( 5 . 2 0 d ) No rma l l y d i s t r i b u t e d e r r o r s and dummy v a r i a b l e s f o r o b s e r v a t i o n s on s h i n g l e and p l ywood m i l l s a r e added on t o each e q u a t i o n i n t h e two sys tems and t h e i d e n t i f y i n g r e s t r i c t i o n u^= 1 i s impo sed . The e r r o r s t r u c t u r e s p e c i f i e d f o r t h e c o n s t a n t r e t u r n s t o s c a l e mode ls i s u sed a g a i n h e r e . E r r o r s c o r r e s p o n d i n g t o t h e same o b s e r v a t i o n a r e c o r r e l a t e d w h i l e e r r o r s c o r r e s p o n d i n g t o d i f f e r e n t o b s e r v a t i o n s a r e i n d e p e n d e n t . U n f o r t u n a t e l y n u m e r i c a l p rob l ems p r e v e n t e d t h e e s t i m a t i o n o f t h e CUM ( e q u a t i o n s 5 .20) so t h e r e s t r i c t i o n u l l = u 1 3 = ^ ^ s i m P 0 S e c l o n u n i o n p r e f e r e n c e s i n t h e CUM. The FIML e s t i m a t e s o f t h e p a r ame t e r s and t h e i r a s y m p t o t i c t - s t a t i s t i c s a r e r e p o r t e d i n T ab l e X I I I . The c h a r a c t e r i s t i c s o f t h e 83 e s t i m a t e d u n i o n p r e f e r e n c e s and p r o d u c t i o n t e c h n o l o g y a r e r e p o r t e d i n T a b l e s XIV and XV. The r e s u l t s o f h y p o t h e s i s t e s t s p e r f o rmed on t h e CUM and MUM a r e r e p o r t e d i n T a b l e X V I . The wage b i l l and r e n t m a x i - m i z a t i o n h y p o t h e s e s , as w e l l as t h e h y p o t h e s i s t h a t u n i o n p r e f e r e n c e s a r e i n dependen t o f t h e a l t e r n a t i v e wage, a r e a l l o v e r w h e l m i n g l y r e j e c t e d i n bo th t h e CUM and MUM. The e s t i m a t e d s t a n d a r d e r r o r s o f t h e e s t i m a t e s o f ^ a r e 0 . 026 i n t h e MUM and 0 .37 i n t h e CUM. S i n c e t h e two e s t i m a t e s o f <(>L a r e 0 .369 and - 1 . 0 r e s p e c t i v e l y , t h e h y p o - t h e s i s t h a t ^ e q u a l s z e r o can be r e j e c t e d i n bo th mode ls a t t h e 99% c o n f i d e n c e l e v e l . A l l o w i n g t h e t e c h n o l o g y t o e x h i b i t n o n - c o n s t a n t r e t u r n s t o s c a l e a f f e c t s t h e magn i t udes o f many o f t h e e s t i m a t e d c h a r a c t e r i s t i c s bu t changes few o f t h e q u a l i t a t i v e r e s u l t s . On t h e p r o d u c t i o n s i d e l a b o u r i s s t i l l e s t i m a t e d t o be a s u b s t i t u t e f o r c a p i t a l s e r v i c e s and m a t e r i a l s , and c a p i t a l s e r v i c e s and m a t e r i a l s a r e s t i l l e s t i m a t e d t o be comp lemen t s . In t h e MUM howeve r , n o n - c o n s t a n t r e t u r n s t o s c a l e d e c r e a s e s bo th t h e e s t i m a t e d s u b s t i t u t a b i 1 i t y between c a p i t a l s e r - v i c e s and l a b o u r and t h e e s t i m a t e d c o m p l e m e n t a r i t y between c a p i t a l s e r v i c e s and m a t e r i a l s . The e s t i m a t e d e l a s t i c i t i e s o f t h e demand f o r l a b o u r f u n c t i o n and t h e demand f o r c a p i t a l s e r v i c e s f u n c t i o n a r e a l s o much l o w e r . In t h e CUM, s p e c i f y i n g n o n - c o n s t a n t r e t u r n s t o s c a l e i n c r e a s e s t h e e s t i m a t e d c o m p l e m e n t a r i t y o f c a p i t a l s e r v i c e s and ma t e - r i a l s s l i g h t l y . On t h e u n i o n s i d e , t h e m o n o t o n i c i t y and q u a s i c o n c a v i t y p r o p e r - t i e s o f t h e un i o n o b j e c t i v e f u n c t i o n , i n r e a l c ompensa t i on - emp l oymen t s p a c e , a r e m a i n t a i n e d i n bo th n o n - c o n s t a n t r e t u r n s t o s c a l e m o d e l s . In t h e CUM, t h e a ve r age r e a l wage i s l e s s t h an t h e e s t i m a t e d a v e r a g e 84 TABLE X I I I E s t i m a t e d C o e f f i c i e n t s : Non -Cons t an t R e t u r n s t o S c a l e Wi th Dummy V a r i a b l e s A s y m p t o t i c t - s t a t i s t i c s a r e i n p a r e n t h e s e s Monopo ly Un ion Model C o o p e r a t i v e Un ion Model '11 : 12 : 13 : 21 : 22 : 23 '12 >13 '23 l 12 lll J 12 J 13 ] 22 J 23 0 .201 0 .8349 -2 .4014 0 . 1051 1 .0054 1.2816 -0 . 2889 -0 .0836 -0 .1279 0 . 1383 1.0 0 .0848 •0.0065 0 .0193 •0.4505 •0.0571 •0.0381 N a t u r a l l o g o f 1 i k e l i h o o d f u n c t i o n ( 2 . 1 87 ) ( 1 2 . 6 79 ) ( - 1 . 6 3 8 ) ( 1 . 4 61 ) ( 1 6 . 9 57 ) ( 0 . 7 7 8 ) ( - 9 . 9 7 0 ) ( - 3 . 1 1 8 ) ( - 0 . 5 9 6 ) ( 3 . 0 16 ) ( 0 . 6 28 ) ( - 3 . 1 0 1 ) ( 4 . 5 18 ) ( - 1 0 2 . 0 5 ) ( - 4 . 8 1 2 ) ( - 0 . 6 2 9 ) 454 . 701 C o r r e l a t i o n C o e f f i c i e n t s between a c t u a l and 0 . 9 5 , 0 . 9 9 , p r e d i c t e d v a l u e s o f 0 . 9 5 , 0 . 9 9 K,M,w, and L 0 . 1385 1.2147 0 .2971 1.4534 1.2054 -0 .8227 - 0 . 7819 -0 .2914 0 .0489 0 .3046 1.0 -1 .0218 0 . 0 -0 .0806 0 . 0 0 .2402 -0 .9576 ( 0 . 4 33 ) ( 8 . 4 68 ) ( 2 . 3 90 ) ( 3 . 4 80 ) ( 1 3 . 440 ) ( - 4 . 8 1 7 ) ( - 4 . 7 2 4 ) ( - 3 . 0 8 6 ) ( 1 . 3 76 ) ( 4 . 6 28 ) ( - 2 . 7 9 7 ) ( - 9 . 6 4 7 ) ( 2 . 5 2 9 ) ( - 3 . 6 5 8 ) 450 . 939 0 . 9 4 , 0 . 9 9 , 0 . 9 1 , 0 . 9 9 85 TABLE XIV E s t i m a t e d C h a r a c t e r i s t i c s o f Un ion P r e f e r e n c e s and P r o d u c t i o n T e c h n o l o g y : Monopo ly Un ion Model w i t h Non -Con s t an t R e t u r n s t o S c a l e and Dummy V a r i a b l e s A l l e s t i m a t e s a r e e v a l u a t e d a t t h e mean o f t h e d a t a Un ion P r e f e r e n c e s M o n o t o n i c i t y U B = 0 . 1 9 2 , U L = - 0 . 0 4 1 , U A = - 3 . 4 2 7 , $ w / = 0 . 6 6 , 4>L = 0 . 369 C u r v a t u r e De t e rm inan t o f b o r d e r ed h e s s i a n o f t h e u n i o n ' s o b j e c t i v e f u n c t i o n = 0 . 0 0 1 8 . M R S B L = 0 . 2 1 5 , M R S w / p L = 0 . 5 5 9 , a w / p L = 0 . 7 7 3 . P r o d u c t i o n Te chno l og y M o n o t o n i c i t y C p = 2 . 1 2 2 , C m = 7 . 3 63 , C w = 3 . 6 1 9 , C Q = 4 .401 C u r v a t u r e D e t e r m i n a n t s o f m i no r s o f t h e h e s s i a n o f t h e c o s t f u n c t i o n a r e : - 0 . 1 0 8 , - 0 . 1 0 3 , 0 .0 The m a t r i x o f p r i c e e l a s t i c i t i e s i s m w K M L -0 .063 -0 .109 0 .358 -0 .423 - 0 . 219 0 .937 0 .487 0 . 328 - 1 . 2 9 5 The e l a s t i c i t i e s o f s u b s t i t u t i o n a r e ; «!„. " 2 ' 2 3 - <k " i - 5 1 - °KM " - ° - 6 8 86 TABLE XV E s t i m a t e d C h a r a c t e r i s t i c s o f Un ion P r e f e r e n c e s and P r o d u c t i o n T e c h n o l o g y : C o o p e r a t i v e Un ion Model w i t h Non -Con s t an t R e t u r n s t o S c a l e and Dummy V a r i a b l e s A l l e s t i m a t e s a r e e v a l u a t e d a t t h e mean o f t h e d a t a Un ion P r e f e r e n c e s M o n o t o n i c i t y UB=0.722, U L = - 2 . 5 4 2 , U A = - 3 . 3 0 7 , <j> w / p=2.492, ^ = - 1 . 0 0 5 C u r v a t u r e De t e rm i nan t o f b o r d e r ed h e s s i a n o f t h e u n i o n ' s o b j e c t i v e f u n c t i o n = 0 . 171 M R S B L = 3 . 5 2 2 , M R S w / p L = - 0 . 4 0 3 , a w / p L = 0 . 4 0 1 . P r o d u c t i o n Te chno l og y M o n o t o n i c i t y D = 3 . 3 2 , D = 7 . 2 5 , D = 5 . 0 5 , D = - 5 . 4 7 , D, = 1.87 r m Q L LL C u r v a t u r e D e t e r m i n a n t s o f m i no r s o f t h e h e s s i a n o f t h e c o n d i t i o n a l c o s t f u n c t i o n a r e : 0 . 2 7 , 0 .0 The m a t r i x o f p r i c e e l a s t i c i t i e s i s r m K 0 .158 - 0 . 1 5 8 M - 0 . 0 4 1 0 . 041 a = - 0 . 2 5 KM 87 TABLE XVI Max im i z ed V a l u e s o f t h e Log L i k e l i h o o d s o f t h e Un ion M o d e l s : Non -Cons t an t R e t u r n s t o S c a l e w i t h Dummy V a r i a b l e s Monopo ly Un ion C o o p e r a t i v e Un ion Model Model u n = u 1 3 = 0 U n r e s t r i c t e d 454 .701 450 . 939 Wage b i l l m a x i m i z a t i o n 410 .902 407 . 863 h y p o t h e s i s Rent m a x i m i z a t i o n 314 .757 417 . 987 h y p o t h e s i s Un ion p r e f e r e n c e s 431 .554 443 . 0 22 i n d e p e n d e n t o f t h e a l t e r n a t i v e wage h y p o t h e s i s U l l = U 1 3 = ° 432 .436 88 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 l a b o u r and r e a l c o m p e n s a t i o n , so t h e e s t i m a t e o f <f>̂  i s l e s s t h an z e r o . As no ted a bo v e , t h i s r e s u l t c a n n o t be r e j e c t e d a t t h e 99% c o n f i d e n c e l e v e l and i t means t h a t t h e e s t i m a t e d 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 r e a l wages and employment i s n e g a t i v e . I t a l s o means t h a t t h e e s t i m a t e o f 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 between r e a l wages and employment i s d i f f i c u l t t o i n t e r p r e t . In t h e MUM, t h e e s t i m a t e d un i o n o b j e c t i v e f u n c t i o n i s s t i l l i n c r e a s i n g i n r e a l wages and employment and t h e e s t i m a t e d mar - g i n a l r a t e o f s u b s t i t u t i o n i s s l i g h t l y h i g h e r t h an t h e c o n s t a n t r e t u r n s t o s c a l e e s t i m a t e s . The e s t i m a t e d e l a s t i c i t y o f s u b s t i t u t i o n between r e a l wages and employment i s u n a f f e c t e d , i n t h e MUM, by non- c o n s t a n t r e t u r n s t o s c a l e i n t h e p r o d u c t i o n t e c h n o l o g y . Summary The e s t i m a t e s shown above s a t i s f y a lmo s t a l l t h e r e s t r i c t i o n s p l a c e d upon t h e u n i o n ' s p r e f e r e n c e s and t h e p r o d u c t i o n t e c h n o l o g y . G i v e n t h e mode l , t h e s e r e s u l t s p r o v i d e d e t a i l e d answers t o q u e s t i o n s about t h e IWA's p r e f e r e n c e s and t h e p r o d u c t i o n t e c h n o l o g y i n t h e p e r i o d s t u d i e d . The e s t i m a t e s o f t h e o b j e c t i v e f u n c t i o n used t o c h a r a c t e r i z e t h e IWA's p r e f e r e n c e s a r e i n c r e a s i n g i n t o t a l r e a l c o m p e n s a t i o n , d e c r e a s i n g i n man-hours o f wo r k , d e c r e a s i n g i n t h e r e a l a l t e r n a t i v e wage, and q u a s i c o n c a v e i n r e a l c ompensa t i on and h o u r s . When w r i t t e n as a f u n c t i o n o f t h e r e a l wage and man-hours o f work t h e e s t i m a t e d un i on o b j e c t i v e f u n c t i o n i s g e n e r a l l y i n c r e a s i n g i n bo th t h e r e a l wage and man -hou r s . The e s t i m a t e d e l a s t i c i t y o f s u b s t i t u t i o n between r e a l wages and man-hours ranges between 0 .6 and 0 . 8 , w i t h t h e e s t i - mates i n t h e CUM s l i g h t l y l o w e r t h a n t h e e s t i m a t e s i n t h e MUM. 89 Rea l wage b i l l m a x i m i z a t i o n and r e a l r e n t m a x i m i z a t i o n by t h e IWA a re bo th r e j e c t e d as i s t h e h y p o t h e s i s t h a t t h e IWA max im i z e s o n l y t h e r e a l wage and i s i n d i f f e r e n t t o t h e l e v e l o f emp loyment . F u r t h e r , t h e IWA's e s t i m a t e d o b j e c t i v e f u n c t i o n i s not i n dependen t o f t h e r e a l a l t e r n a t i v e wage as i t i s s p e c i f i e d . The r e s u l t s f o r t h e IWA a r e s u r p r i s i n g l y c l o s e t o t h e r e s u l t s D e r t o u z o s and P en c a ve l (1981) r e p o r t f o r t h e ITU i n t h e C i n c i n n a t i l o c a l . The I T U ' s e s t i m a t e d o b j e c t i v e f u n c t i o n i s a l s o i n c r e a s i n g i n t h e r e a l wage and l a b o u r i n p u t , d e c r e a s i n g i n t h e a l t e r n a t i v e wage , and t h e e s t i m a t e d e l a s t i c i t y o f s u b s t i t u t i o n between r e a l wages and employment i s 0 . 6 9 . F u r t h e r , t h e r e a l wage b i l l m a x i m i z a t i o n and r en t m a x i m i z a t i o n h ypo the se s a r e r e j e c t e d f o r t h e ITU , and t h e ITU i s no t i n d i f f e r e n t t o t h e l e v e l o f emp loyment . The IWA's e s t i m a t e d 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 r e a l wages and man-hours emp loyed i s about 0 .4 i n t h e MUM and 0 . 3 i n t h e CUM. T h i s low v a l u e i s t h e r ea son why t h e e l a s t i c i t y o f t h e demand f o r l a b o u r i s so h i g h i n t h e MUM. G i v e n t h e s c a l i n g o f t h e v a r i - a b l e s , a 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 0 .4 means t h a t t h e un i o n i s i n d i f f e r e n t between a d e c r e a s e i n employment o f one w o r k e r (2000 h ou r s ) and a 0.032<t i n c r e a s e i n t h e r e a l h o u r l y wage. Put a n o t h e r way, t h e u n i o n i s i n d i f f e r e n t t o one l e s s wo r k e r ( f o r a who l e y e a r ) o r a $64 .00 i n c r e a s e i n t h e r e a l g r o s s annua l pay o f a l l t h e r e m a i n i n g e m p l o y e e s . The c o r r e s p o n d i n g e l a s t i c i t y i s e s t i m a t e d t o be about - 1 . 5 , so t h e un i on i s i n d i f f e r e n t between a 1% r i s e i n r e a l wages and a 1.5% d e c r e a s e i n emp loyment . The e s t i m a t e s o f t h e p r o d u c t i o n t e c h n o l o g y show t h a t c a p i t a l and m a t e r i a l s a r e complements w h i l e a l l o t h e r p a i r s o f i n p u t s a r e s ub - s t i t u t e s . In bo th m o d e l s , t h e e s t i m a t e d c o s t f u n c t i o n s s a t i s f y t h e i r 90 m o n o t o n i c i t y p r o p e r t i e s , bu t a r e no t concave w i t h r e s p e c t t o i n p u t p r i c e s . U n f o r t u n a t e l y , t h e t e c h n o l o g y s p e c i f i e d f o r t h e CUM i s no t r i c h enough t o accommodate t h e c o m p l e m e n t a r i t y o f c a p i t a l s e r v i c e s and m a t e r i a l s , so t h e e s t i m a t e d m a t r i x o f i n p u t p r i c e e l a s t i c i t i e s has a l l t h e wrong s i g n s . In t h e MUM, a l l t h e e s t i m a t e d i n p u t demand f u n c t i o n s s l o p e down and t hey a r e much more e l a s t i c t h an t h o s e e s t i - mated i n c h a p t e r f o u r . Fo r e x amp l e , t h e e l a s t i c i t y o f t h e demand f o r l a b o u r f u n c t i o n i s e s t i m a t e d t o be about - 0 . 4 i n c h a p t e r f o u r w h i l e t h e e s t i m a t e s f r om t h e MUM range between - 1 . 3 and - 2 . 0 . Hence , t h e un i on i s on an e l a s t i c p a r t o f t h e demand f o r l a b o u r c u r v e i n t h e MUM. The e l a s t i c i t i e s o f s u b s t i t u t i o n e s t i m a t e d i n t h e MUM a r e a l s o much l a r g e r ( i n a b s o l u t e v a l u e ) t han t h o s e e s t i m a t e d i n c h a p t e r f o u r . Thu s , i t i s o b s e r v e d t h a t t h e e s t i m a t e s o f t h e p r o d u c t i o n t e c h n o l o g y a r e ve r y s e n s i t i v e t o t h e e x p l i c i t m o d e l l i n g o f un i on b e h a v i o r . The e s t i m a t e s o f t h e t e c h n o l o g y i n t h e MUM a r e a l s o s e n s i t i v e t o whe the r o r not c o n s t a n t r e t u r n s t o s c a l e i s imposed on t h e t e c h n o l o g y . F i n a l l y , as no t ed i n C h a p t e r 4 , t h e s p e c i f i c a t i o n o f t h e e r r o r s t r u c t u r e and t h e dummy v a r i a b l e s i s r a t h e r a r b i t r a r y . The s p e c i f i - c a t i o n was chosen f o r i t s s i m p l i c i t y i n an a l r e a d y messy s y s t em o f e q u a t i o n s , and not f o r any b e l i e f s about e r r o r s o r a c r o s s i n d u s t r y d i f f e r e n c e s i n t h e e s t i m a t i n g e q u a t i o n s . 91 Append i x t o Chap t e r 5 P r o o f t h a t D ( r , m , L , Q ) i s N o n - d e c r e a s i n g i n r and m For r ,m , > 0 and L,Q > 0 bu t bo th L and Q canno t be z e r o , l e t r 1 > r ° . D ( r 1 , m , L , Q ) = Min [ r \ + mM : ( K ,M , L ,Q ) e T} K,M = r^K* + mM* where K* and M* a r e t h e s o l u t i o n s t o t h e m i n i m i z a t i o n p rob l em > r °K* + mM* > Min {r°K + mM : ( K , M , L , Q ) e T } K,M = D ( r ° , m , L , Q ) T h e r e f o r e D ( r 1 , m , L , Q ) > D ( r ° , m , L , Q ) The same p r o o f can be used t o show D ( r , m , L , Q ) i s n o n - d e c r e a s i n g i n and D ( r , m , L , Q ) i s n o n - d e c r e a s i n g when bo th r and m i n c r e a s e . M a r g i n a l Ra te o f S u b s t i t u t i o n o f t h e Un ion O b j e c t i v e F u n c t i o n The u n i o n o b j e c t i v e f u n c t i o n i s U ( B , L ; A ) , where U. < 0 , and U D 0 . D e f i n e B = Z ( L ) such t h a t U ( Z ( L ) , L ; A ) = U ° . D i f f e r e n t i a t e t h e un i on o b j e c t i v e f u n c t i o n and o b t a i n : U B ( 3 Z ( L ) / 3 L ) + u L = 0 -»• 3Z ( L ) / 3L = 3B/3L = -U /U | U U L B. T h e r e f o r e , MRS = 3B/3L = -U /U (A5 . 1 ) BL | U U L B 92 Second O rde r C o n d i t i o n f o r t h e M a x i m i z a t i o n P r o b l e m i n t h e Monopo ly Un ion Model The m a x i m i z a t i o n p r ob l em i n t h e monopoly u n i o n model i s : Max {U(B , L ;A ) : w = -D, ( r , m , L , Q ) } ( A 5 . 2 ) w,L w h i c h , by s u b s t i t u t i n g t h e c o n s t r a i n t i n t o t h e o b j e c t i v e f u n c t i o n ( n o t i n g t h a t B = w L / p ) , can be r e w r i t t e n a s : Max { U ( - L D L ( r , m , L , Q ) / p , L ; A ) } . ( A 5 . 3 ) The f i r s t o r d e r c o n d i t i o n i s 3U/8L U B [ - D L - L D L L ] / p + U L = 0 ( A 5 . 4 ) ( D L + . L D L L ) / p = U L / U B ( A 5 . 5 ) The second d e r i v a t i v e o f A5 .3 i s 8 2 U / 3 L 2 = - [ D L + L D L 1 _ ] [ U B B ( 3 B / 3 L ) + U g L ] / p - U R [ 2D . . + LD. . ] /p + U. R ( 8 B / 9 L ) + U LL ( A 5 . 6 ) The second o r d e r c o n d i t i o n (A5 . 6 ) must be e v a l u a t e d a t a p o i n t where bo th t h e f i r s t o r d e r c o n d i t i o n A5 .5 and t h e c o n s t r a i n t (w = -D ) a r e s a t i s f i e d . The c o n s t r a i n t i m p l i e s 93 wL/p = B = - L D L / p * 33/3L = ( - D L - L D L L ) / p + 3B/3L = - U L / U g = ( - D L - L D L L ) / p . ( A 5 . 7 ) by t h e f i r s t o r d e r c o n d i t i o n . S u b s t i t u t e A5 .7 i n t o A5 .6 and o b t a i n a W = - ( U L / U B ) [ - U B B ( U L / U B ) + U B L ] - U B [ 2 D L L + L D L L L ] / p - uLB(uL/uB) + u L L [ U B B U L 2 " 2 U B L U L U B + U L L U B V * + U B [ - 2 D L L " L D L L I > V 2L-H - U B 3 [ - 2 D L L - L D L L L ] / p ] where H i s t h e d e t e r m i n a n t o f t h e bo r d e r ed h e s s i a n o f t h e u n i o n ' s o b j e c t i v e f u n c t i o n . I t i s assumed t h a t p > 0, I L > 0 and H > 0 s i n c e U ( B , L ; A ) i s b q u a s i c o n c a v e i n B and L. t T h e r e f o r e , a s u f f i c i e n t c o n d i t i o n f o r t h e 2 2 second o r d e r c o n d i t i o n t o be s a t i s f i e d (3U /3L < 0) i s - 2 D L L - L D L L L < 0 * 2 D L L > " L D L L L ( A 5 . 8 ) 94 R e p e a t i n g e q u a t i o n 5 .2 : D ( r , m , L , Q ) = c n r L + c 1 2 r Q + c 2 1 m L + c 2 2 m Q + 2 b 1 2 ( r + m + 2 X ) ( L Q ) 2 + 2 a 1 2 X Z ( A 5 . 9 ) where X = ( - r 2 + - m 2 ) 2 and Z = L + Q + 2 ( L Q ) 2 . 2 2 C l e a r l y , D L = c l l r + C 2 1 m + b 1 2 ^ r + m + 2 X ) ( Q / L ) 2 + 2 a 1 2 X ( l + ( Q / L ) 2 ) A - "3/2 * °LL = " [ 2 b 1 2 Q ^ r + m + 2 X ) + a i 2 X Q ' ] L * ° LLL = ^ 3 / 4 ) b i 2 Q ' ( r + m + 2 X ) + ( 3 / 2 ) a 1 2 X Q i ] L ~ 5 / 2 i 1 - 3 / 2 > L D L L L = [ ( 3 / 4 ) b 1 2 Q 2 ( r + m + 2X) + ( 3 / 2 ) a 1 2 X Q 2 ] L T h e r e f o r e , -LD - (3/2)D L L < 2D U, s i n c e > 0, e q u a t i o n (A5 . 8 ) i s s a t i s f i e d , and t h e se cond o r d e r c o n d i t i o n o f t h e m a x i m i z a t i o n i s s a t i s f i e d . 95 Second O rde r C o n d i t i o n f o r t h e M a x i m i z a t i o n P r o b l e m i n t h e C o o p e r a t i v e Un ion Model The m a x i m i z a t i o n p rob l em i n t h e c o o p e r a t i v e un i o n model i s Max {U(B , L ;A ) : B = E/p - D ( r , m , L , Q ) / p } , w,L w h i c h , by s u b s t i t u t i n g t h e c o n s t r a i n t i n t o U ( B , L ; A ) , can be r e w r i t t e n a s : Max {U(E/p - D ( r , m , L , Q ) / p , L ; A ) } . ( A 5 . 1 0 ) L The f i r s t o r d e r c o n d i t i o n i s : 3U/3L = - U g D L / p + U L = 0 ( A 5 . l l ) + D L / p = U L / U B . The second d e r i v a t i v e o f A5 .10 i s 3 2 U / 3 L 2 = - D L [ U B B ( 9B/3L) + U ^ / p - D^Ug/p + U L B ( 3 B / 3 L ) + U L t (A5 . 12 ) The c o n s t r a i n t (B = E/p - D ( r , m , L , Q ) / p ) and t h e f i r s t o r d e r c o n d i t i o n i m p l y 3B/3L = - D L / p = - U L / U B , 96 wh i ch when s u b s t i t u t e d i n t o A5 . 12 y i e l d s a W = - ( u L / u B ) [ - u B B ( u L / u B ) + u B L ] - U g D ^ / p - u L B ( u L / u B ) + u L L • U B " 2 [ U B B U L - 2 U L B U L U B + U L L U B " U B D L L / P ^ = U B " 2 [ - H - U B D L L / p ] < 0 where H i s t h e d e t e r m i n a n t o f t h e bo r de r ed h e s s i a n o f t h e u n i o n o b j e c t i v e f u n c t i o n , p > 0 , U > 0 D > 0 and H > 0 by a s s u m p t i o n . B L L T h e r e f o r e t h e s e cond o r d e r c o n d i t i o n o f t h e m a x i m i z a t i o n p r ob l em i s s a t i s f i e d . 97 Chap te r 6 Un ion M o d e l s : P r o f i t M a x i m i z a t i o n A l l t h e un i on mode ls p r e s e n t e d i n Chap t e r 5 assume t h a t t h e f i r m s i n t h e i n d u s t r y m i n i m i z e v a r i a b l e c o s t s s u b j e c t t o some e xo - g e n o u s l y g i v e n o u t pu t c o n s t r a i n t . I t i s somewhat n a i v e t o assume t h a t t h e l e v e l o f o u t p u t i s i n d ependen t o f t h e u n i o n ' s a c t i o n s , t h e wage, t h e l a b o u r i n p u t , and t h e p r i c e s o f c a p i t a l and m a t e r i a l s . Hence t h e MUM and CUM a r e r e - e s t i m a t e d i n t h i s c h a p t e r a s sum ing t h a t t h e i n d u s t r y i s a p r i c e t a k e r i n t h e ma rke t s f o r o u t p u t , c a p i t a l and m a t e r i a l s ; and t h a t t h e i n d u s t r y choose s o u t p u t , c a p i t a l , and mate- r i a l s t o max im i ze v a r i a b l e p r o f i t . A s s ump t i o n s A l t o A5 a r e s t i l l assumed t o be t r u e . The p r o d u c - t i o n t e c h n o l o g y i s assumed t o be w e l l behaved ( c l o s e d , bounded , n o n - empty , c onvex , f r e e d i s p o s a l ; see D i e w e r t (1974 , p . 1 34 ) ) bu t d e c r e a s i n g r e t u r n s t o o u t l a y a r e assumed so t h a t t h e i n d u s t r y ' s p r o - f i t f u n c t i o n e x i s t s i n t h e MUM. D e f i n e a v a r i a b l e p r o f i t f u n c t i o n V ( q , r , m , L ) = Max {qQ - rK - mM : ( K , M , L , Q ) e T} ( 6 . 1 ) Q.K .M where q i s t h e p r i c e o f o u t pu t and a l l t h e o t h e r n o t a t i o n i s t h e same as i n t h e e a r l i e r c h a p t e r s . V ( q , r , m , L ) i s t h e maximum p o s s i b l e revenue minus v a r i a b l e c o s t s , g i v e n t e c h n o l o g y and i n p u t and o u t p u t p r i c e s , when t h e l a b o u r i n p u t i s g i v e n e x ogenou s l y t o t h e i n d u s t r y . D i ewe r t (1974 , p. 136) shows t h a t v a r i a b l e p r o f i t f u n c t i o n s p o s s e s s t h e f o l l o w i n g p r o p e r t i e s . 98 ( i ) V ( q , r , m , L ) i s a n o n - n e g a t i v e f u n c t i o n f o r q , r , m , > 0 and L > 0 . ( i i ) V ( q , r , m , L ) i s homogenous o f deg r ee one i n q , r , and m. ( i i i ) V ( q , r , m , L ) i s convex and c o n t i n u o u s i n q , r , and m. ( i v ) V ( q , r , m , L ) i s n o n - d e c r e a s i n g i n L (V^> 0 ) . R e c a l l t h a t t h e i n p u t L i s no t d e f i n e d as a n e g a t i v e v a l u e h e r e . ( v ) V ( q , r , m , L ) i s concave and c o n t i n u o u s i n L, wh i c h i m p l i e s v L L < 0. Moreove r i t can be shown t h a t V ( q , r , m , L ) i s n o n - d e c r e a s i n g i n q and n o n - i n c r e a s i n g i n r and m. The p r o o f i s e x a c t l y a na l o gou s t o t h e p r o o f t h a t D ( r , m , L , Q ) i s n o n - d e c r e a s i n g i n r and m shown i n t h e append i x t o Chap t e r 5, so i t w i l l not be r e pea t ed h e r e . N o t i c e t h a t V ( q , r , m , L ) i s no t homogeneous o f d eg r ee one i n L s i n c e c o n s t a n t r e t u r n s t o s c a l e i s not imposed on t h e t e c h n o l o g y . A f u n c t i o n a l f o rm s u g g e s t e d by D i e w e r t (1974 , p. 137) i s u sed t o s p e c i f y V ( q , r , m , L ) : V ( q , r , m , L ) = c 1 2 q + c ^ r + c 3 2 m + c ^ q L + c 2 1 r L + c 3 1 m L + 2 ( a 1 2 X + a 1 3 Y + a 2 3 Z ) ( l + L + 2L 2") + 2 b 1 2 L * ( q + r + m + 2X + 2Y + 2Z) ( 6 . 2 ) / I 2 1 2A v ,1 2 1 2 J , , 1 2 1 2A , where X = ( - q + - r ) , Y = ( - q + - m ) 2 , Z = ( - r + - m ) z a n d 2 2 2 2 2 2 . a c o n s t a n t f i x e d i n p u t , d e f i n e d equa l t o minus one , i s i n c l u d e d t o 99 impose d e c r e a s i n g r e t u r n s t o o u t l a y on t h e t e c h n o l o g y dua l t o 6 . 2 . Note t h a t e q u a t i o n 6 .2 p r o v i d e s a second o r d e r a p p r o x i m a t i o n t o an a r b i t r a r y v a r i a b l e p r o f i t f u n c t i o n . D e f i n e a f u n c t i o n , G ( q , r , m , w , L ) , wh i c h i s equa l t o t o t a l p r o f i t and i s a f u n c t i o n o f i n p u t and ou t pu t p r i c e s and t h e amount o f l a b o u r emp l o yed , G ( q , r , m , w , L ) = V ( q , r , m , L ) - wL. ( 6 . 3 ) I s o - p r o f i t c u r v e s i n compensa t i on -emp loymen t space can be w r i t t e n pB = wL = V ( q , r , m , L ) - G, ( 6 . 4 ) where G i s a c o n s t a n t , 9(wL)/9L = v L > 0 , and 3 2 ( w L ) / 3L 2 = V L L < 0 . Un ion p r e f e r e n c e s a r e e x a c t l y t h e same as t h ey a r e i n Chap t e r 5 . Monopo ly Un ion Model T h i s model i s t h e v e r y same as t h e MUM shown i n C h a p t e r 5, e x c e p t now t he i n d u s t r y chooses Q ,K ,M , and L t o max im i ze p r o f i t s r a t h e r t h a n c h o o s i n g K ,M, and L t o m i n i m i z e c o s t s s u b j e c t t o a g i v e n l e v e l o f o u t p u t . 100 The i n d u s t r y ' s demand f o r l a b o u r f u n c t i o n i s t h e s o l u t i o n t o t h e m a x i m i z a t i o n p rob l em Max { G ( q , r , m , w , L ) } = Max { V ( q , r , m , L ) - w L } . L L The f i r s t o r d e r c o n d i t i o n i s V L ( q , r , m , L ) - w = 0 ( 6 . 5 ) wh i ch i s a l s o t h e i n d u s t r y ' s p r o f i t m a x i m i z i n g demand f o r l a b o u r f u n c t i o n w r i t t e n i n i m p l i c i t f o r m . The s e cond o r d e r c o n d i t i o n i s s a t i s f i e d s i n c e < 0. The u n i o n ' s m a x i m i z a t i o n p r ob l em i n t h e MUM i s Max { U ( L V , / p , L ; A ) } ( 6 . 7 ) L L s i n c e t h e c o n s t r a i n t i m p l i e s wL/p = L V L / p = B. The f i r s t o r d e r c o n - d i t i o n t o t h e m a x i m i z a t i o n p r ob l em i s 3U/3L = U g [ V L + L V L [ _ ] / p + U L = 0 V L + L V L L - - P U L / U B . ( 6 . 8 ) The second o r d e r c o n d i t i o n i n v o l v e s t h e t h i r d d e r i v a t i v e o f t h e v a r i - a b l e p r o f i t f u n c t i o n , so t h e u s u a l c u r v a t u r e p r o p e r t i e s o f U ( B , L ; A ) and V ( q , r , m , L ) a r e not enough t o gua r an t e e a maximum. F o r t u n a t e l y t h e t h i r d d e r i v a t i v e o f e q u a t i o n 6 . 2 , t h e f u n c t i o n a l f o rm used t o s p e c i f y V ( q , r , m , L ) , i s such t h a t t h e second o r d e r c o n d i t i o n i s a lway s s a t i s - 101 f i e d . See t h e a ppend i x t o t h i s c h a p t e r f o r t h e d e t a i l s on t h e s e cond o r d e r c o n d i t i o n . E q u a t i o n s 6 .8 and 6 .5 d e f i n e t h e compensa t i on -emp loymen t s o l u - t i o n t o t h e MUM. The p r o f i t m a x i m i z i n g s u p p l y f u n c t i o n and i n p u t demand f u n c t i o n s can be d e r i v e d f r om t h e v a r i a b l e p r o f i t f u n c t i o n . D e f i n e an o r d i n a r y p r o f i t f u n c t i o n p o s s e s s i n g a l l t h e u sua l p r o p e r - t i e s and dua l t o t h e t e c h n o l o g y n ( q , r , m , w ) = Max { V ( q , r , m , L ) - wL} L = V ( q , r , m , L * ( q , r , m , w ) ) - wL* ( q , r ,m ,w ) ( 6 . 9 ) where L * ( q , r , m , w ) i s t h e s o l u t i o n t o e q u a t i o n 6 . 5 . H o t e l l i n g ' s lemma a p p l i e d t o e q u a t i o n 6 .9 i m p l i e s Q* (q , r ,m ,w ) = 3 n ( q , r , m , w ) / 3 q = 3 V ( q , r , m , L ) / 3 q | L = L * , ( 6 . 1 0 ) K* (q , r ,m ,w ) = - 3 n ( q , r , m , w ) / 3 r = - 3 V ( q , r , m , L ) / 3 r | L = L * » ( 6 . 1 1 ) and M*(q , r ,m ,w) = - 3n (q , r ,m ,w) /3m = - 3 V ( q , r , m , L ) / 3 m . | L = L * ( 6 . 1 2 ) by t h e e n v e l o p e t h e o r e m . E q u a t i o n s 5 . 5 , 6 . 2 , 6 . 5 , 6 . 8 , 6 . 1 0 , 6 . 1 1 , and 6 .12 i m p l y t h e f o l l o w i n g s i m u l t a n e o u s s y s t em o f e q u a t i o n s : 102 Q = c 1 2 + c n L + q ( a 1 2 / X + a 1 3 / Y ) ( l + L + 2 L 2 ) + 2 b 1 2 L 2 (1 + q/X + q/Y) ( 6 . 13a ) •K = c 2 2 + c 2 1 L + r ( a 1 2 / X + a 2 3 / Z ) ( l + L + 2 L 2 ) + 2 b 1 2 L 2 ( l + r/X + r /Z ) ( 6 . 1 3b ) •M = c 3 2 + c 3 1 L + m ( a 1 3 / Y + a 2 3 / Z ) (1 + L •+ 2L 2") + 2 b 1 2 L 2 ( l + m/Y + m/Z) ( 6 . 1 3 c ) w = c 1 1 q + c 2 1 r + c 3 1 m + 2 ( a 1 2 X + a 1 3 Y + a 2 3 Z ) ( l + L 2 ) + b 1 2 L * (q + r + m + 2X + 2Y + 2Z) ( 6 . 13d ) -x - L 2 = [ c ^ q + c 2 1 r + c 3 1 m + 2 ( a 1 ? X + a 1 3 Y + a 2 3 Z ) + ' p ( u 2 + u 2 2 L + u 2 3 A + u 1 2 B ) ( u 1 + u n B + u 1 2 L + u ^ A ) " 1 ] [ a 1 2 X + a 1 3 Y + a 2 3 Z + - b 1 2 ( q + r + m + 2X + 2Y + 2 Z ) ] " 1 . ( 6 . 1 3e ) E q u a t i o n 6 .13a i s t h e s u p p l y c u r v e f o r ou t pu t g i v e n by 6 . 1 0 . E q u a t i o n s 6 .13b and c a r e t h e p r o f i t m a x i m i z i n g i n p u t demand f u n c - t i o n s g i v e n by 6 .11 and 6 . 1 2 . E q u a t i o n 6 .13d i s t h e i n v e r s e demand f o r l a b o u r f u n c t i o n g i v e n by 6 .5 w h i l e e q u a t i o n 6 .13e i s t h e f i r s t 103 T A B L E X V I I E s t i m a t e d C o e f f i c i e n t s o f t h e M o n o p o l y a n d C o o p e r a t i v e U n i o n M o d e l s : P r o f i t M a x i m i z a t i o n A s y m p t o t i c t - s t a t i s t i c s a r e i n p a r e n t h e s e s M o n o p o l y U n i o n M o d e l c 1 2 C 2 2 C 3 2 C l l C 2 1 C 3 1 3 1 2 3 1 3 3 2 3 b 1 2 J l l J 1 2 J 1 3 ' 2 2 2 3 7 . 3 0 8 7 - 5 . 3 7 2 7 - 5 . 8 5 3 7 0 . 0 8 0 5 1 . 0 5 0 8 - 0 . 3 5 8 0 - 0 . 0 5 3 8 0 . 2 7 8 0 0 . 0 0 8 4 - 0 . 0 8 3 1 1 . 0 - 2 . 4 3 3 2 0 . 0 0 . 0 1 5 7 - 0 . 3 4 2 8 0 . 2 7 4 9 0 . 2 8 0 5 N a t u r a l l o g o f 1 i k e l i h o o d f u n c t i o n ( 1 2 . 2 8 0 ) ( - 9 . 6 9 3 ) ( - 8 . 6 7 7 ) ( 0 . 3 8 7 ) (8.991), ( - 1 . 4 9 4 ) ( - 0 . 6 7 4 ) ( 2 . 0 9 2 ) ( 0 . 0 9 3 ) ( - 1 . 3 0 3 ) ( - 4 . 3 6 7 ) ( 2 . 0 1 7 ) ( - 2 1 . 5 8 7 ) ( 2 . 4 3 9 ) ( 1 . 5 1 2 ) 2 6 3 . 2 5 3 C o r r e l a t i o n C o e f f i c i e n t s b e t w e e n a c t u a l a n d 0 . 9 7 , - 0 . 8 4 , p r e d i c t e d v a l u e s o f 0 . 9 3 , 0 . 9 9 , - 0 . 8 3 K . M . w , a n d L~* C o o p e r a t i v e U n i o n M o d e l - 1 . 1 2 6 2 ( - 1 . 7 2 1 ) 0 . 9 8 1 2 ( 4 . 9 7 5 ) - 0 . 6 7 0 6 ( - 2 . 7 3 6 ) 2 . 6 6 1 0 ( 4 . 9 6 8 ) - 0 . 5 7 9 2 ( - 2 . 9 0 0 ) - 3 . 4 0 9 0 ( - 1 6 . 2 3 9 ) - 0 . 3 0 8 4 ( - 1 . 6 6 3 ) 0 . 8 8 5 3 ( 3 . 8 3 8 ) 0 . 2 1 4 7 ( 1 . 8 5 2 ) - 0 . 2 5 4 2 ( - 3 . 0 5 1 ) 1 . 0 6 . 2 4 5 5 ( 1 . 4 1 2 ) 0 . 7 5 9 8 ( 1 . 8 8 2 ) - 1 . 0 1 5 7 ( - 2 . 0 9 0 ) - 0 . 4 3 8 9 ( - 5 . 3 5 2 ) 1 . 0 6 7 3 ( 2 . 1 4 6 ) - 4 . 9 6 0 5 ( - 1 . 6 2 8 ) 2 8 1 . 3 2 4 0 . 9 8 , 0 . 8 4 , 0 . 9 9 , 0 . 9 1 , - 0 . 0 6 104 TABLE X V I I I E s t i m a t e d C h a r a c t e r i s t i c s o f Un ion P r e f e r e n c e s and P r o d u c t i o n T e c h n o l o g y : Monopo ly Un i on Model w i t h P r o f i t M a x i m i z a t i o n A l l e s t i m a t e s a r e e v a l u a t e d a t t h e mean o f t h e d a t a Un ion P r e f e r e n c e s M o n o t o n i c i t y U B = 0 . 4 2 4 , U L = - 0 . 8 5 3 , U A = - 1 . 5 3 9 , <|>w/p = 1 .466 , cpL = 0 . 055 C u r v a t u r e De t e rm i nan t o f b o r d e r ed h e s s i a n o f t h e u n i o n ' s o b j e c t i v e f u n c t i o n = - 0 . 0 6 . M R S B L = 2 . 0 1 1 , M R S w / p L = 0 . 0 3 7 , o w / p L = - 0 . 0 5 5 . P r o d u c t i o n Techno l ogy , M o n o t o n i c i t y n = 7 . 8 8 2 , n = - 4 . 4 7 1 , n = - 5 . 7 6 , n , = - 1 . 3 7 3 q ' r ' m w C u r v a t u r e De t e rm i n an t s o f m i no r s o f t h e h e s s i a n o f t h e p r o f i t f u n c t i o n a r e : - 0 . 3 1 6 , - 0 . 1 4 8 , 0 . 0 3 5 , 0 .0 The m a t r i x o f p r i c e e l a s t i c i t i e s i s r m w Q K M L -0 .155 1.628 -0 .019 - 1 . 930 -0 .237 2 .212 -0 .140 -2 .427 0 .011 - 0 . 5 4 3 - 0 . 0 4 9 0 . 593 0 . 382 -3 .297 0 .208 3 .764 The e l a s t i c i t i e s o f s u b s t i t u t i o n a r e : °KL = - 1 ' 5 4 ' °ML = ° * 0 9 7 ' CTKM = - ° ' ° 8 9 105 o r d e r c o n d i t i o n shown by 6 . 8 . N o r m a l l y d i s t r i b u t e d e r r o r t e rms a r e added on t o e q u a t i o n s 6 .13 and an i d e n t i f y i n g r e s t r i c t i o n , u^ = 1 i s imposed on un i o n p r e f e r e n c e s . The same e r r o r s t r u c t u r e i s s p e c i f i e d . E r r o r t e rms c o r r e s p o n d i n g t o t h e same o b s e r v a t i o n a r e c o r r e l a t e d w h i l e e r r o r t e rms c o r r e s p o n d i n g t o d i f f e r e n t o b s e r v a t i o n s a r e i n d e p e n d e n t . U n f o r t u n a t e l y n u m e r i c a l p rob l ems p r e v e n t e d t h e e s t i m a t i o n o f t h e comp l e t e s y s t e m , so t h e r e s t r i c t i o n u ^ = 0 i s imposed on u n i o n p r e - f e r e n c e s . FIML e s t i m a t e s o f t h e pa r ame te r s o f t h e r e s t r i c t e d s y s t em a r e r e p o r t e d w i t h t h e i r a s y m p t o t i c t - s t a t i s t i c s i n T a b l e X V I I . C h a r a c t e r i s t i c s o f t h e e s t i m a t e d un i on p r e f e r e n c e s and p r o d u c t i o n t e c h n o l o g y , e v a l u a t e d a t t h e samp le means, a r e r e p o r t e d i n T ab l e X V I I I . I t i s c l e a r t h a t t h e p r o f i t m a x i m i z i n g v e r s i o n o f t h e MUM does not p e r f o rm w e l l e m p i r i c a l l y . The e s t i m a t e d un i on o b j e c t i v e f u n c t i o n s a t i s f i e s a l l t h e m o n o t o n i c i t y p r o p e r t i e s , but i t i s no t q u a s i c o n c a v e and 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 between r e a l wages and l a b o u r i s much l owe r t h a n t h e o t h e r e s t i m a t e s . F u r t h e r , t h e e s t i m a t e d 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 s n e g a t i v e . On t h e p r o d u c t i o n s i d e t h e e s t i m a t e d s u p p l y c u r v e s l o p e s down w h i l e t h e e s t i m a t e d demand c u r v e s f o r c a p i t a l and l a b o u r s l o p e up . C a p i t a l and m a t e r i a l s a r e s t i l l e s t i m a t e d t o be comp l emen t s , bu t c a p i t a l and l a b o u r a r e a l s o e s t i - mated t o be complements and m a t e r i a l s and l a b o u r a r e e s t i m a t e d t o be b a r e l y s u b s t i t u t a b l e . M a t e r i a l s and l a b o u r a r e a l s o f ound t o be i n f e r i o r i n p u t s . The e s t i m a t e s o f t h e i n p u t p r i c e e l a s t i c i t i e s and t h e e l a s t i c i - t i e s o f s u b s t i t u t i o n o f t h e p r o d u c t i o n t e c h n o l o g y a r e a l l f u n c t i o n s o f t h e e s t i m a t e s o f c c c_. , a . _ , a 1 Q , a , and b . 106 T a b l e XVI I shows t h a t o n l y t h e e s t i m a t e s o f and have a s y m p t o t i c t - s t a t i s t i c s g r e a t e r t h an two , w i t h t h e a s y m p t o t i c t - s t a t i s t i c f o r t h e e s t i m a t e o f a ^ o n l y s l i g h t l y above t w o . T h u s , a l t h o u g h no c o n f i d e n c e i n t e r v a l s f o r t h e e s t i m a t e s o f t h e e l a s t i c i t i e s a r e computed , i t i s no t u n r e a s o n a b l e t o b e l i e v e t h a t t h e e s t i m a t e s have v e r y l a r g e c o n f i d e n c e i n t e r v a l s wh i ch i n c l u d e z e r o i n t h e i r range f o r any r e a s o n a b l e c o n f i d e n c e l e v e l . More c o n f i d e n c e can be p l a c e d i n t h e e s t i m a t e s o f t h e c h a r a c t e r - i s t i c s o f u n i o n p r e f e r e n c e s s i n c e a l l o f t h e e s t i m a t e s o f t h e p a r a - me te r s o f t h e un i on o b j e c t i v e f u n c t i o n ( e x cep t f o r t h e e s t i m a t e o f u 2 3 ) have a s y m p t o t i c t - s t a t i s t i c s g r e a t e r t h a n two . D e s p i t e t h i s , t h e e s t i m a t e o f i s 0 .07 and a 95% c o n f i d e n c e i n t e r v a l f o r <j>L i s - 0 .085 < ^ < 0 . 1 9 5 . T h e r e f o r e , one canno t say w i t h 95% c o n f i d e n c e t h a t t h e u n i o n i s no t i n d i f f e r e n t t o t h e l e v e l o f employment i n r e a l wage-employment s p a c e . C o o p e r a t i v e Un ion Model T h i s model i s e x a c t l y t h e same as t h e CUM shown i n C h a p t e r 5 e x cep t t h e i n d u s t r y chooses Q,K, and M t o max im i ze v a r i a b l e p r o f i t s r a t h e r t h an c h o o s i n g K and M t o m i n i m i z e v a r i a b l e c o s t s g i v e n a l e v e l o f o u t p u t . The i n d u s t r y ' s p r o f i t , g i v e n some q u a n t i t y o f l a b o u r i s G ( q , r , m , w , L ) = V ( q , r , m , L ) - wL ( 6 . 3 ) wh i ch i m p l i e s t h e f o l l o w i n g i s o - p r o f i t c u r v e wL = pB = V ( q , r , m , L ) - G ( 6 . 4 ) 107 where G i s c o n s t a n t . The CUM can be w r i t t e n as t h e m a x i m i z a t i o n p r ob l em Max {U (B , L ;A ) : B = V ( q , r , m , L ) / p - G/p} w,L = Max { U ( V ( q , r , m , L ) / p - G / p , L ; A ) } ( 6 . 1 4 ) L wh i ch i m p l i e s t h e f i r s t o r d e r c o n d i t i o n 3U/3L = U DV. /p + U. = 0 D L L + V L = - p U L / U R . ( 6 . 1 5 ) The c u r v a t u r e p r o p e r t i e s o f V ( q , r , m , L ) and U ( B , L ; A ) e n s u r e t h a t t h e s e cond o r d e r c o n d i t i o n i s s a t i s f i e d . See t h e a ppend i x t o t h i s c h a p t e r f o r t h e d e t a i l s o f t h e second o r d e r c o n d i t i o n . E q u a t i o n s 6 .4 and 6 . 15 d e f i n e t h e compensa t i on -emp loymen t s o l u - t i o n t o t h e CUM. As w i t h t h e CUM o u t l i n e d i n Chap t e r 5, t h e model i s n o t c o m p l e t e l y s p e c i f i e d . The model p r e d i c t s an outcome on t h e c o n t r a c t c u r v e , but i t does not p r e d i c t where on t h e c o n t r a c t c u r v e t h e f i n a l outcome w i l l b e . The s u p p l y f u n c t i o n , and v a r i a b l e p r o f i t m a x i m i z i n g demand f u n c - t i o n s f o r c a p i t a l and m a t e r i a l s , a l l c o n d i t i o n a l on t h e l a b o u r i n p u t chosen w i t h t h e u n i o n , a r e d e r i v e d by a p p l y i n g H o t e l l i n g ' s lemma t o t h e v a r i a b l e p r o f i t f u n c t i o n : Q * ( q , r , m , L ) = 3 V ( q , r , m , L ) / 3 q ( 6 . 1 6 ) 108 K * ( q , r , m , L ) = - 9 V ( q , r , m , L ) / 9 r ( 6 . 1 7 ) and M * ( q , r , m , L ) = - 9 V ( q , r , m , L ) / 9 m . ( 6 . 1 8 ) The e q u a t i o n s used t o a c t u a l l y e s t i m a t e t h e pa r ame t e r s o f t h e CUM a r e : ( i ) t h e i n p u t and o u t p u t f u n c t i o n s g i v e n by 6 . 1 3 a , b and c ; ( i i ) t h e i s o - p r o f i t c u r v e g i v e n by e q u a t i o n 6.4 d i v i d e d by l a b o u r w = -G/L + c q + c Z ] r + c 3 ] m + c ^ q / L + c ^ r / L + c ^ m / L + 2 ( a 1 2 X + a 1 3 Y + a 2 3 Z ) ( l + L _ 1 + 2L *) + 2 b 1 2 L _ i ( q + r + m + 2X + 2Y + 2 Z ) ; ( 6 . 19d ) and ( i i i ) t h e f i r s t o r d e r c o n d i t i o n t o t h e m a x i m i z a t i o n p r ob l em g i v e n by 6 .15 - i - L 2 = Lc-Qq + c 2 ^ r + c ^ m + 2 ( a^ 2 X + a^ 3Y + a 2 3 X ) + p ( u 2 + u 2 2 L + u 2 3 A + u 1 2 B ) ( u 1 + u 1 1 B + u ^ L + u ^ A ) " 1 ] [ 2 ( a 1 2 X + a 1 3 Y + a 2 3 Z ) + b 1 2 ( q + r + m + 2 X + 2 Y + 2 Z ) ] " 1 , ( 6 . 1 9 e ) 109 The u sua l e r r o r s t r u c t u r e i s appended on t o t h e e s t i m a t i n g equa - t i o n s ( 6 . 1 3 a , b and c , 6 .19d and e) and t h e same i d e n t i f y i n g r e s t r i c - t i o n (u^ = 1) i s imposed . FIML e s t i m a t e s o f t h e p a r ame t e r s a r e r e p o r t e d i n T a b l e X V I I , and c h a r a c t e r i s t i c s o f t h e e s t i m a t e d t e c h - no l ogy and un i o n p r e f e r e n c e s a r e r e p o r t e d i n T ab l e X I X . T a b l e XIX shows t h a t t h e CUM pe r f o rms no b e t t e r t h an t h e MUM. The e s t i m a t e d un i on o b j e c t i v e f u n c t i o n s a t i s f i e s t h e m o n o t o n i c i t y p r o p e r t i e s but i t i s d e c r e a s i n g i n t h e l e v e l o f employment i n r e a l wage-employment s p a c e . The e s t i m a t e and s t a n d a r d e r r o r o f ^ a r e - 1 . 7 7 8 and 1.0 r e s p e c t i v e l y , so a 95% c o n f i d e n c e i n t e r v a l f o r <|>L i s - 3 . 7 3 8 < <j>L < 0 . 1 8 2 . Thus , <j>̂  may be p o s i t i v e o r n e g a t i v e a t t h e 95% c o n f i d e n c e l e v e l . The n e g a t i v e e s t i m a t e o f <j>L means t h a t t h e e s t i m a t e d 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 r e a l wages and employment i s n e g a t i v e and 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 i s d i f - f i c u l t t o i n t e r p r e t . The e s t i m a t e d un i on o b j e c t i v e f u n c t i o n i s a l s o no t q u a s i concave i n r e a l c ompensa t i on - emp loymen t s p a c e . On t he p r o d u c t i o n s i d e , t h e e s t i m a t e d v a r i a b l e p r o f i t f u n c t i o n s a t i s f i e s t h e m o n o t o n i c i t y p r o p e r t i e s , but i t i s not concave w i t h r e s p e c t t o l a b o u r . The e s t i m a t e d s u p p l y f u n c t i o n s l o p e s up and t h e e s t i m a t e d demand c u r v e f o r m a t e r i a l s s l o p e s down, but t h e e s t i m a t e d demand c u r v e f o r c a p i t a l s e r v i c e s s l o p e s up . C a p i t a l s e r v i c e s and m a t e r i a l s a r e e s t i m a t e d t o be s u b s t i t u t e s r a t h e r t h a n complements f o r t h e f i r s t t i m e , a l t h o u g h t h e e s t i m a t e d 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 s v e r y c l o s e t o z e r o . F i n a l l y , c a p i t a l s e r v i c e s i s e s t i m a t e d t o be an i n f e r i o r i n p u t . 110 TABLE XIX E s t i m a t e d C h a r a c t e r i s t i c s o f Un i on P r e f e r e n c e s and P r o d u c t i o n T e c h n o l o g y : C o o p e r a t i v e Un ion Model w i t h P r o f i t M a x i m i z a t i o n A l l e s t i m a t e s a r e e v a l u a t e d a t t h e mean o f t h e d a t a Un ion P r e f e r e n c e s M o n o t o n i c i t y U B = 2 . 2 4 3 , U L = - 6 . 6 1 4 , U A = - 2 0 . 3 4 3 , <|>w/p = 7 . 9 2 5 , <|>L = - 1 . 7 7 8 C u r v a t u r e De t e rm i nan t o f b o r d e r e d h e s s i a n o f t h e u n i o n ' s o b j e c t i v e f u n c t i o n = - 8 . 4 7 . M R S B L = 2 . 9 4 8 , M R S w / p L = - . 2 2 4 , a w / p L = 0 . 125 P r o d u c t i o n Te chno l og y M o n o t o n i c i t y V q = 9 . 5 9 , V r = - 3 . 3 1 , V m = - 6 . 8 9 , V L = 4 . 4 9 , V L L = 0 . 123 C u r v a t u r e De t e rm i n an t s o f m i no r s o f t h e h e s s i a n o f t h e c o s t f u n c t i o n a r e : 0 . 4 2 4 , - 0 . 3 7 3 , 0 .0 The m a t r i x o f p r i c e e l a s t i c i t i e s i s m Q K M 0 .208 -0 .479 0 .493 0 .070 0 . 354 0 .032 - 0 . 2 7 8 0 . 125 - 0 . 5 2 5 The e l a s t i c i t i e s o f s u b s t i t u t i o n a r e : a KM = ° ' 0 2 I l l Summary As no t ed i n t h e i n t r o d u c t i o n t o t h i s c h a p t e r , i t i s n a i v e t o b e l i e v e t h a t o u t pu t i s i n dependen t o f p r i c e s o r t h e b e h a v i o u r o f t h e u n i o n , as i s assumed i n c h a p t e r 5. The i n d u s t r y s u r e l y a d j u s t s t h e l e v e l o f o u t pu t i n r e spon se t o changes i n p r i c e s o r u n i o n p o l i c i e s . Hence , t h e u n i o n mode ls a r e r e - e s t i m a t e d a l l o w i n g t h e i n d u s t r y t o choose t h e l e v e l o f o u t pu t wh i ch max im i ze s i t s p r o f i t s r a t h e r t h a n t a k i n g o u t p u t as an exogenous c o n s t r a i n t . The change i n t h e a s s ump t i o n about i n d u s t r y b e h a v i o u r a f f e c t s t h e e s t i m a t e s o f u n i o n p r e f e r e n c e s . The e s t i m a t e d u n i o n o b j e c t i v e f u n c t i o n i s s t i l l i n c r e a s i n g i n r e a l c ompensa t i on and d e c r e a s i n g i n employment and t h e r e a l a l t e r n a t i v e wage. W r i t t e n as a f u n c t i o n o f r e a l wages and emp loyment , t h e e s t i m a t e d un i on o b j e c t i v e f u n c t i o n i s i n c r e a s i n g i n t h e r e a l wage but an i n c r e a s i n g o r d e c r e a s i n g f u n c t i o n o f t h e l e v e l o f emp loyment . Hence , t h e e s t i m a t e s o f 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 and t h e e l a s t i c i t i e s o f s u b s t i t u t i o n between r e a l wages and employment a r e r a t h e r u n i n f o r m a t i v e . F u r t h e r , t h e e s t i m a t e d un i o n o b j e c t i v e f u n c t i o n i s no t q u a s i c o n c a v e i n r e a l compensa t i on -emp loymen t space i n e i t h e r t h e MUM o r CUM. The p r o d u c t i o n s i d e i s a l s o a f f e c t e d by t h e change i n a s - sumpt i ons and v e r y poor r e s u l t s o b t a i n . E s t i m a t e d s u p p l y and demand f u n c t i o n s s l o p e t h e wrong way, i n p u t s a r e f ound t o be i n f e r i o r , and p a i r s of i n p u t s jump i n d i s c r i m i n a t e l y f rom complements t o s u b s t i t u t e s and v i c e - v e r s a . The o n l y r e a s o n a b l e i n f o r m a t i o n o b t a i n e d f r om t h e s e mode ls i s t h a t t h e demand f o r m a t e r i a l s s l o p e s down and l a b o u r and m a t e r i a l s a r e s u b s t i t u t e s . A l l o t h e r r e s u l t s c o n t r a d i c t e i t h e r economic t h e o r y , a l l o t h e r e v i d e n c e , o r b o t h . 112 Append i x t o Chap t e r 6 Second O rde r C o n d i t i o n f o r t h e U n i o n ' s M a x i m i z a t i o n P r o b l e m i n t h e MUM The u n i o n ' s m a x i m i z a t i o n p r ob l em can be w r i t t e n : Max {U (B , L ;A ) : w = V } ( A 6 . 1 ) Max {U(LV . /p , L ; A ) }. ( A 6 . 2 ) L L The f i r s t o r d e r c o n d i t i o n i s 9U/3L = U g [ V L + L V L L ] / p + U L = 0 V L + V L L = • P U L / U B ' ( A 6 , 3 ) The second d e r i v a t i v e o f e q u a t i o n A6 .2 i s 3 2 U / 3 L 2 = [ L V L L + V L ] [ U B B ( 3 B / 3 L ) + U g L ] / p + U g ( 2 V L L + L V L | _ L ) / p + U L B ( 3 B / 3 L ) + U L L . ( A 6 . 4 ) The s e cond o r d e r c o n d i t i o n (A6 . 4 ) must be e v a l u a t e d a t a p o i n t where bo th t h e f i r s t o r d e r c o n d i t i o n (A6 . 3 ) and t h e c o n s t r a i n t (w = V L ) a r e s a t i s f i e d . The c o n s t r a i n t i m p l i e s wL/p = B = L V L / p 113 • 3B/3L = (LV L [ _ + V L ) / p + 9B/2L = ( L V L L + V L ) / p = - U L / U g ( A 6 . 5 ) by t h e f i r s t o r d e r c o n d i t i o n . S u b s t i t u t e A6 .5 i n t o A6 .4 and o b t a i n 9 W = U B B ( U L / U R ) 2 - U B L ( U L / U B ) + U B ( 2 V L L + L V L L L ) / P - U L B A / l V + U L L = U B - 2 [ - H + U B 3 ( 2 V L L + L V L L L ) / p ] where H i s t h e d e t e r m i n a n t o f t h e b o r d e r ed h e s s i a n o f t h e u n i o n ' s o b j e c t i v e f u n c t i o n and p, IL and H a r e assumed t o be g r e a t e r t h a n D z e r o . T h e r e f o r e a s u f f i c i e n t c o n d i t i o n f o r t h e se cond o r d e r 2 2 c o n d i t i o n t o be s a t i s f i e d ( 8 U/3L < 0) i s 2 V L L + L V U L < 0 + L V L L L < " 2 V L L * ( A 6 , 6 ) R e p e a t i n g e q u a t i o n 6 . 2 , V ( q , r , m , L ) = c 1 2 q + c 2 2 r + c 3 2 m + c ^ q L + c 2 1 r L + c31mL + 2 ( a 1 2 X + a 1 3 Y + a 2 3 Z ) ( l + L + 2L*) + 2 b 1 9 L 4 ( q + r + m + 2X + 2Y + 2Z) 114 v ,1 2 1 2 . i v ,1 2 ^ 1 2 N i . _ , 1 2 1 2 . i where X = ( - q + - r ) , Y = ( - q + - m ) and Z = (— r + — m ) . 2 2 2 2 2 2 C I e a r l y , V L = C l l q + C 2 1 r + C 3 1 m + 2 ^ a l 2 X + a 1 3 Y + a 2 3 Z ^ X + L ^ + b 1 2 L _ i ( q + r + m + 2X + 2Y + 2Z) -3/2 . V L L = - ( a 1 2 X + a 1 3 Y + a ^ Z j L 1 -3/2 - b 1 9 ( q + r + m + 2X + 2Y + 2Z)L 2 L d * V L L L = ( 3 / 2 ) [ a l 2 X + a 1 3 Y + 3 2 3 Z + - b 1 9 ( q + r + m + 2 X + 2 Y + 2Z ) ] L 2 v c -5/2 . L V L L L = - ( 3 / 2 ) V L L . T h e r e f o r e , L V U L . - (3/2JV < - 2 V L L s i n c e < 0, e q u a t i o n A6 .6 i s s a t i s f i e d and t h e second o r d e r c o n d i t i o n o f t h e m a x i m i z a t i o n p r ob l em i s s a t i s f i e d . Second O rde r C o n d i t i o n f o r t h e M a x i m i z a t i o n P r ob l em i n t h e CUM The m a x i m i z a t i o n p r ob l em i n t h e CUM i s 115 Max {U(B , L ;A ) : B = V ( p , r , m , L ) / p - G/p} ( A 6 . 7 ) w ,L Max { U ( V ( q , r , m , L ) / p - G / p , L ; A ) } . ( A 6 . 8 ) L The f i r s t o r d e r c o n d i t i o n i s 3U/3L = U R V L / p + U L = 0 + V L = - p U L / U R . ( A 6 . 9 ) The second d e r i v a t i v e o f A6 . 8 i s 3 2 U/8L 2 = V L [ U B B ( 3B/3L) + U g J / p + U g V L L / p + U L B(3B/3L) + U L L (A6 . 10 ) The c o n s t r a i n t and t h e f i r s t o r d e r c o n d i t i o n i m p l y 3B/3L = V L / p = - U L / U B w h i c h , when s u b s t i t u t e d i n t o A 6 . 1 0 , y i e l d s 3 2 U / 3 L 2 = ( U L / U B ) [ U B B ( U L / U B ) - 2 U B L ] + U B V L | _ /p + U L |_ = U B " 2 ( - H + U B 3 V L L / p ) < 0 s i n c e p > 0 , U D > 0 , H > 0 and V . . < 0 . T h e r e f o r e t h e second o r d e r b L L c o n d i t i o n i s s a t i s f i e d . 116 Chap te r 7 On C h o o s i n g a T rue Model U n t i l now t h e CUM and MUM have been t r e a t e d as two e q u a l l y r e a - s o n a b l e and e q u a l l y l i k e l y a l t e r n a t i v e mode ls o f t h e b e h a v i o u r o f u n i o n s and f i r m s . However , t h e two mode ls a r e n o n - n e s t e d and p r e d i c t d i f f e r e n t ou t comes . I f one model i s t r u e , t h en t h e o t h e r model must be f a l s e . 1 Hence , i t i s d e s i r a b l e t o choose wh i c h o f t h e two mode ls i s t h e t r u e model o f t h e b e h a v i o u r o f un i on s and f i r m s . The pu rpo se o f t h i s c h a p t e r i s t o choose t h e model wh i c h i s c o n s i s t e n t w i t h t h e o b s e r v ed b e h a v i o u r o f t h e IWA and t h e wood p r o d u c t s i n d u s t r y i n B . C . , 1 963 - 79 . On a t h e o r e t i c a l b a s i s , g i v e n t h e a s sump t i o n s o u t l i n e d i n Chap t e r 5, t h e c h o i c e i s o b v i o u s . The CUM i s t h e c o r r e c t , o r more r e a s o n a b l e m o d e l , because i t p r e d i c t s an e f f i c i e n t P a r e t o o p t i m a l outcome w h i l e t h e MUM p r e d i c t s an i n e f f i c i e n t P a r e t o i n f e r i o r o u t - come. However , as no t ed i n C h a p t e r 2 , a rguments a p p e a l i n g t o f a c t o r s o u t s i d e t h e n e o c l a s s i c a l pa r ad i gm have been made s u g g e s t i n g t h a t t h e CUM i s n o t . s u c h a c l e a r f a v o u r i t e o v e r t h e MUM. These arguments b a s i c a l l y say t h a t w h i l e one e x p e c t s u n i o n s and f i r m s t o e x p l o i t a l l p o s s i b l e g a i n s f r om t r a d e and r e a ch e f f i c i e n t s o l u t i o n s , t h e outcome p r e d i c t e d by t h e CUM i s u n a t t a i n a b l e s i n c e t h e c o m p e t i t i v e b a r g a i n i n g r e l a t i o n s h i p makes t h e two p a r t i e s u n a b l e o r u n w i l l i n g t o convey enough i n f o r m a t i o n about t h e i r v a l u a t i o n s o f 1. T h i s i s no t a lway s t h e c a s e . F o r e xamp l e , i f 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 L e o n t i e f i n wage and employment s p a c e , o r i f t h e un i on i s i n d i f f e r e n t t o t h l e v e l o f employment , t h en t h e s o l u - t i o n s o f t h e MUM and CUM c o i n c i d e . 117 outcomes t o r e a c h a p o i n t on t h e c o n t r a c t c u r v e ( see P en cave l 1 981 ) . F u r t h e r , s i n c e c o n d i t i o n s change d u r i n g t h e l i f e o f a c o n t r a c t , i t i s n e c e s s a r y t o n e g o t i a t e a s e t o f c o n t i n g e n t c o n t r a c t s c o v e r i n g a l l p o s s i b l e changes i n i n p u t and ou t pu t p r i c e s and v a r i a b l e s a f f e c t i n g t h e u n i o n . Even i f a c o m p l e t e s e t o f c o n t i n g e n t c o n t r a c t s a r e nego- t i a t e d , t h e y s t i l l have t o be e n f o r c e d . P rob lems o b s e r v i n g and a c c u r a t e l y mea su r i n g t h e v a r i a b l e s d e s c r i b i n g t h e c o n t i n g e n c i e s l i m i t 9 t h e w o r k a b i l i t y o f t h e c o n t i n g e n t c o n t r a c t s . A mora l h a z a r d p r ob l em a l s o e x i s t s i f t h e u n i o n o r emp l o ye r s can i n f l u e n c e t h e p e r c e i v e d v a l u e o f t h e c o n t i n g e n c y v a r i a b l e s . These p rob l ems make a s o l u t i o n on t h e c o n t r a c t c u r v e seem u n l i k e l y and t hey a r e v a l i d c r i t i c i s m s c o u n t i n g a g a i n s t t h e r e a s - o n a b l e n e s s o f t h e CUM. However a l l t h e s e a rguments can be a p p l i e d w i t h equa l f o r c e a g a i n s t t h e MUM. Lack o f i n f o r m a t i o n about t h e i n d u s t r y ' s demand f o r l a b o u r f u n c t i o n o r f a l s e i n f o r m a t i o n s u p p l i e d by t h e f i r m can cause t h e un i o n t o choose a n o n - o p t i m a l wage. F u r t h e r , t h e demand f o r l a b o u r c u r v e s h i f t s and t w i s t s as p r i c e s change , j u s t as un i on i n d i f f e r e n c e c u r v e s change when t h e a l t e r n a t i v e wage, p r i c e l e v e l , o r t a x r a t e s c hange . So c o n t i n g e n t c o n t r a c t s a r e a l s o n e c e s s a r y i n t h e MUM, and t h a t l e a d s t o t h e same p rob l ems o f m e a s u r i n g t h e c o n t i n g e n c y v a r i a b l e s and mora l h a z a r d . T h e r e f o r e , w h i l e u n c e r t a i n t y , i m p e r f e c t i n f o r m a t i o n , and mora l h a z a r d a r e i m p o r t a n t f a c t o r s wh i c h ought t o be i n c l u d e d i n t h e u n i o n mode l s ; t h e y do not h e l p i n t h e c h o i c e between t h e MUM and CUM. 2 . See H a l l and L i l i e n (1979 , p. 870) f o r a d i s c u s s i o n o f t h e p r o b - lems o f c o n t i n g e n t c o n t r a c t s i n t h e CUM. 118 I t i s t r u e t h a t t h e i n f o r m a t i o n r e q u i r e m e n t s o f t h e CUM a r e g r e a t e r t han t h o s e o f t h e MUM s i n c e more t han j u s t t h e wage has t o be n e g o t i a t e d i n t h e CUM. I t i s a l s o t r u e i n g e n e r a l , t h a t one o b s e r v e s t h a t un i on s and f i r m s n e g o t i a t e t h e wage r a t e but f i r m s choose t h e l e v e l o f employment u n i l a t e r a l l y . D e s p i t e t h e s e f a c t s , e f f i c i e n t c o n t r a c t s can be a c h i e v e d by n e g o t i a t i n g work r u l e s o r , more i m p o r t a n t l y , by n e g o t i a t i n g c ompen sa t i o n f u n c t i o n s wh i c h a r e no t 3 homogeneous o f deg ree one i n t h e l e v e l o f emp loyment . R e f e r r i n g t o F i g u r e 5 a , i t i s easy t o see t h a t t h e c ompensa t i on f u n c t i o n oab , w i t h i t s c o m b i n a t i o n o f a lump sum payment oa and a wage equa l t o t h e s l o p e o f a b , r e s u l t s i n an e f f i c i e n t ou t come . The un i on a n d , f i r m b a r g a i n o n l y about c ompensa t i on and t h e f i r m chooses employment u n i l a t e r a l l y t o m i n i m i z e c o s t s , but an e f f i c i e n t s o l u t i o n r e s u l t s . Compensa t i on f u n c t i o n s l i k e oab a r e not uncommon. I f employment i s measured i n hou r s wo r k ed , oa can be payment f o r work not pe r f o rmed such as v a c a t i o n s o r s t a t u t o r y h o l i d a y s , w h i l e t h e s l o p e o f ab i s j u s t t h e h o u r l y wage . I f employment i s measured by number o f p eop l e w o r k i n g , h o l d i n g hou r s pe r wo r ke r f i x e d , and emp l o y - ment i s d e c r e a s i n g , t h en t h e c ompensa t i o n f u n c t i o n oab r e s u l t s f r om t he f i r m p a y i n g unemployment i n s u r a n c e b e n e f i t s o r s e v e r a n c e pay t o l a i d o f f w o r k e r s . In t h a t c a s e t h e wage seen by t h e f i r m i s t h e w o r k e r ' s wages minus what t h e f i r m wou ld pay i f t he wo r ke r was l a i d o f f . I f employment i s i n c r e a s i n g , l a b o u r i s homogeneous, and s e n i o r i t y p r o v i s i o n s e n su r e t h a t wo r ke r s w i t h more s e n i o r i t y c anno t be d i s p l a c e d by w o r k e r s w i t h l e s s s e n i o r i t y t h en t h e m a r g i n a l c o s t o f 3 . H a l l and L i l i e n (1979) show how non-homogeneous o f deg r ee one c o m p e n s a t i o n f u n c t i o n s can s u p p o r t e f f i c i e n t e q u i l i b r i a . i i 119 FIGURE 5 120 a w o r k e r i s l e s s t h a n t h e a v e r age c o s t . T h i s o c c u r s because t h e wo r ke r s w i t h more s e n i o r i t y ea rn h i g h e r wages and r e c e i v e more p a i d t i m e o f f and b e n e f i t s . Hence , t h e c ompensa t i o n f u n c t i o n l o o k s l i k e oa i n F i g u r e 5b and i t s u p p o r t s an e f f i c i e n t outcome when t h e f i r m choo se s employment u n i l a t e r a l l y t o m i n i m i z e c o s t s . O t he r common c o n t r a c t p r o v i s i o n s wh i ch make t h e compensa t i on f u n c t i o n n o n - l i n e a r a r e o v e r t i m e p remiums , c o n t r i b u t i o n s t o p e n s i o n f unds and o t h e r bene- f i t s , and s h i f t p remiums . So a l t h o u g h b a r g a i n i n g i n t h e CUM must be more c o m p l i c a t e d t h a n i n t h e MUM and must c o v e r more t h a n j u s t t h e wage, t h e b a r g a i n i n g n e c e s s a r y t o a c h i e v e an e f f i c i e n t outcome i s no t beyond t h e a b i l i t i e s o r even t h e common p r a c t i c e o f u n i o n s and f i r m s . Payment p r o v i s i o n s wh i ch make t h e c ompensa t i on f u n c t i o n not homo- geneous o f deg ree one , so t h a t e f f i c i e n t outcomes can be a c h i e v e d , a r e i n c l u d e d i n a lmos t a l l c o l l e c t i v e agreements c u r r e n t l y i n e f f e c t . T h e r e f o r e , any a rguments s t a t i n g t h a t e f f i c i e n t outcomes a r e not a c h i e v e d because t h e y a r e t o o d i f f i c u l t t o b a r g a i n f o r o r because u n i o n s and f i r m s do no t b a r g a i n abou t employment c anno t be a c c e p t e d as v a l i d a rguments a g a i n s t t h e CUM. A l t h o u g h I have a rgued t h a t f i r m s and un i on s c o u l d use n o n - l i n e a r c ompensa t i on f u n c t i o n s t o a c h i e v e e f f i c i e n t ou t comes , t h e CUM o u t l i n e d i n Chap t e r 5 assumes t h a t e f f i c i e n t outcomes a r e r e a ched by b a r g a i n i n g d i r e c t l y o v e r t h e a ve r age c o s t o f a u n i t of l a b o u r ( the wage) and t h e l e v e l o f emp loy - men t . T h i s a s s ump t i o n i s made t o keep t h e a n a l y s i s s i m p l e , and i t does not a f f e c t t h e pe r f o rmance o f t h e CUM. The CUM c o n s i s t s o f t h e demands f o r c a p i t a l s e r v i c e s and m a t e r i a l s , an i s o - e x p e n d i t u r e c u r v e and t he t angency c o n d i t i o n between t he i s o - e x p e n d i t u r e c u r v e and 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 . None o f t h e e q u a t i o n s i n t h e CUM change i f 121 a n o n - l i n e a r c ompensa t i on f u n c t i o n i s u sed t o a c h i e v e an e f f i c i e n t s o l u t i o n . The CUM shows o n l y t h e f i n a l outcome and i s i n dependen t o f how t h e outcome i s r ea ched o r s u p p o r t e d . One f i n a l r a t i o n a l e o f t h e MUM s h o u l d be m e n t i o n e d . F a r b e r ( 1978 , p. 926) s t a t e s t h a t t h e MUM i s a p p r o p r i a t e f o r t h e c o a l m i n i n g i n d u s t r y because t h e r e i s one powe r f u l un i on wh i ch can d i c t a t e i t s t e rms t o a l a r g e number o f s m a l l u n c o o r d i n a t e d f i r m s . The u n i o n a c t s as a m o n o p o l i s t i c s u p p l i e r o f l a b o u r t o t h e f i r m s . G i ven t h e u n i o n ' s power r e l a t i v e t o t h e f i r m s , why does t h e u n i o n d i c t a t e an i n e f f i - c i e n t s o l u t i o n i n s t e a d o f an e f f i c i e n t one where t h e un i o n i s b e t t e r o f f h o l d i n g t h e f i r m ' s w e l f a r e c o n s t a n t ? I f t h e u n i o n can d i c t a t e and e n f o r c e a l e v e l o f wages and p e n s i o n fund c o n t r i b u t i o n s a c r o s s a l l f i r m s , t h e r e i s no r e a son t o b e l i e v e t h a t t h e u n i o n wou l d no t d i c t a t e a c ompensa t i on f u n c t i o n ( i n c l u d i n g wages and p e n s i o n f u nd c o n t r i b u t i o n s ) wh i c h s u p p o r t s an e f f i c i e n t ou t come . To sum up , one must c o n c l u d e t h a t d e s p i t e t h e p o p u l a r i t y o f t h e MUM i n t h e l i t e r a t u r e and t h e a rguments o u t l i n e d above , t h e r e i s no good r eason f o r b e l i e v i n g t h a t un i o n s and f i r m s s e t t l e a t i n e f f i c i e n t outcomes l i k e t h o s e p r e d i c t e d by t h e MUM r a t h e r t h an t h e e f f i c i e n t outcomes p r e d i c t e d by t h e CUM. The nex t q u e s t i o n i s : does t h e d a t a b e a r ou t t h i s p r e f e r e n c e f o r t h e CUM o ve r t h e MUM? Tha t i s t o s a y : does t h e CUM p r o v i d e a b e t t e r model o f t he ob s e r v ed b e h a v i o u r o f t h e IWA and t h e B . C . f o r e s t p r o d u c t s i n d u s t r y i n t h e y e a r s 1963-79? Nes t ed T e s t An answer t o t h i s e m p i r i c a l q u e s t i o n can be f ound by n e s t i n g t h e two models i n s i n g l e e q u a t i o n as done by MaCurdy and Pencave l ( 1 9 8 3 ) . The MUM s o l u t i o n i s on t h e i n d u s t r y ' s demand f o r l a b o u r f u n c t i o n . In our model t h a t i m p l i e s 122 D, + w = 0 . ( 7 . 1 ) The CUM r e q u i r e s t h a t t h e s l o p e o f t h e u n i o n ' s o b j e c t i v e f u n c t i o n e q u a l s t h e s l o p e o f t h e i n d u s t r y ' s i s o - e x p e n d i t u r e c u r v e : E q u a t i o n 7.1 i s n e s t e d i n e q u a t i o n 7 . 2 . I t s h o u l d be e m p h a s i z e d , howeve r , t h a t t h e MUM and t h e CUM a r e n o n - n e s t e d m o d e l s . I f t h e mode ls a r e w r i t t e n out c o m p l e t e l y , r e s t r i c t i o n s imposed on one model c anno t p roduce t h e o t h e r m o d e l . I t j u s t t u r n s ou t ( f o r t u i t o u s l y ) t h a t t h e c o n s t r a i n t i n t h e MUM ( 7 . 1 ) i s n e s t ed i n t h e f i r s t o r d e r c o n d i t i o n o f t h e CUM ( 7 . 2 ) . The c omp l e t e mode ls c anno t be t e s t e d a g a i n s t one a n o t h e r i n a n e s t e d t e s t , but t h e v a l u e o f can be t e s t e d i n a s i n g l e e q u a t i o n ; t h e r e b y a l l o w i n g a h y p o t h e s i s t e s t o f t h e MUM g i v e n t h e a l t e r n a t i v e h y p o t h e s i s t h a t t h e CUM i s t r u e . The c o n s t a n t r e t u r n s t o s c a l e v e r s i o n o f D ( r , m , L , Q ) i s s p e c i - f i e d as i t i s i n C h a p t e r 5 ( e q u a t i o n 5 . 2 ) . U n f o r t u n a t e l y , n u m e r i c a l p rob l ems p r e v e n t e d t h e e s t i m a t i o n o f e q u a t i o n 7.2 when U ( B , L ; A ) i s s p e c i f i e d as i n C h a p t e r 5 ( e q u a t i o n 5 . 5 ) , so t h e f o l l o w i n g s p e c i f i c a - t i o n i s used D L " p U L / U B = °* ( 7 . 2 ) U ( B , L ; A ) = u n B + u,± + u 1 9 B L ( 7 . 3 ) where u 12 = -1 i s an i d e n t i f y i n g r e s t r i c t i o n . 123 N o n - l i n e a r 2SLS i s used t o e s t i m a t e e q u a t i o n 7.2 s i n c e i t i s j u s t one e q u a t i o n out o f a s i m u l t a n e o u s sys tem o f e q u a t i o n s . The i n s t r u m e n t a l v a r i a b l e s a r e : a c o n s t a n t , dummy v a r i a b l e s f o r t h e i n d u s t r i e s , a t r e n d t e r m , t h e t r e n d t e rm t i m e s t h e dummy v a r i a b l e s , t r e n d s q u a r e d , p r i c e o f o u t p u t , p r i c e o f c a p i t a l , and t h e s q u a r e s o f t h e p r i c e s . The l i k e l i h o o d r a t i o t e s t ana l ogue d e r i v e d i n G a l l a n t and J o r g e n s o n (1979) i s u sed t o t e s t t h e n u l l h y p o t h e s i s t h a t e q u a t i o n 7.1 i s t r u e s u b j e c t t o t h e a l t e r n a t i v e h y p o t h e s i s t h a t e q u a t i o n 7 .2 i s t r u e . The e s t i m a t e d t e s t s t a t i s t i c , wh i c h G a l l a n t 2 and J o r g en son p rove i s a s y m p t o t i c a l l y d i s t r i b u t e d as a x w i t h two deg ree s o f f r eedom (u^ = u^= 0 ) , i s 9 2 . 2 0 2 . Thus , t h e h y p o t h e s i s t h a t e q u a t i o n 7.1 and t h e MUM i s t r u e i s o v e r w h e l m i n g l y r e j e c t e d . The s p e c i f i c a t i o n o f U ( B , L ; A ) used f o r t h e h y p o t h e s i s t e s t ( e q u a t i o n 7 .3 ) i s a s p e c i a l c a s e o f t h e more g e n e r a l s p e c i f i c a t i o n used i n t h e un i on mode ls ( e q u a t i o n 5 . 5 ) . S i n c e e q u a t i o n 7.1 i s r e j e c t e d when t e s t e d a g a i n s t a r e s t r i c t e d v e r s i o n o f e q u a t i o n 7 . 2 , i t i s c l e a r t h a t e q u a t i o n 7.1 and t h e MUM a r e a l s o r e j e c t e d when t h e more g e n e r a l s p e c i f i c a t i o n o f U ( B , L ; A ) i s u s e d . L i k e l i h o o d Compa r i s on Te s t More s u p p o r t f o r t h e CUM i s f ound by compa r i ng t h e max im i z ed v a l u e s o f t h e l o g l i k e l i h o o d s o f t h e CUM and MUM. The l o g l i k e l i h o d o f t h e CUM i s a lway s a t l e a s t e l e v e n p o i n t s h i g h e r t h a n t h e l o g l i k e - l i h o o d o f t h e MUM f o r t h e c o s t m i n i m i z i n g models when one compares 124 mode ls w i t h an equa l number o f f r e e p a r a m e t e r s . Thus , t h e MUM can be r e j e c t e d i n f a v o u r o f t h e CUM. T h i s f o l l o w s because t h e MUM wou l d be c o n v i n c i n g l y r e j e c t e d i f i t was t e s t e d a g a i n s t a h y p o t h e t i c a l g e n e r a l model wh i c h n e s t s t h e two mode ls and has one more p a r a m e t e r . T h i s i s t r u e s i n c e t h e l o g l i k e l i h o o d o f t h e g ene r a l model must be 5 g r e a t e r t h an o r equa l t o t h e l o g l i k e l i h o o d o f t h e CUM. The advan t age o f t h i s t y p e o f t e s t i s t h a t i t compares t h e p e r - fo rmance o f t h e comp l e t e mode ls a g a i n s t one a n o t h e r . T h i s i s d i f - f e r e n t f r om t h e n e s t e d t e s t shown abo ve , where j u s t one e q u a t i o n f r om one model i s t e s t e d a g a i n s t a d i f f e r e n t e q u a t i o n f rom t h e o t h e r m o d e l . A n o t h e r d i f f e r e n c e between t h e two t e s t s s h o u l d be e m p h a s i z e d . The n e s t e d t e s t assumes t h a t t h e a l t e r n a t i v e h y p o t h e s i s , e q u a t i o n 7 .2 f r om t h e CUM, i s t r u e w i t h c e r t a i n t y . The c o n s i s t e n c y o r r e a s o n a b l e - ness o f t h e r e s t r i c t i o n s on t h e CUM (wh i ch y i e l d t h e MUM) i s t hen t e s t e d a g a i n s t t h e o b s e r v e d d a t a g i v e n t h e t r u t h o f t h e CUM - i . e . , g i v e n t h a t t h e d a t a a r e o r g a n i z e d a c c o r d i n g t o t h e a l t e r n a t i v e h ypo - t h e s i s . G i v en t h e q u a l i t a t i v e a rguments i n f a v o u r o f t h e CUM p r e - s e n t e d a t t h e b e g i n n i n g o f t h e c h a p t e r , i t may not be u n r e a s o n a b l e t o l e t t h e CUM be t h e a l t e r n a t i v e h y p o t h e s i s , wh i c h i s b e l i e v e d w i t h c e r t a i n t y . However , g i v e n t h e MUM's p o p u l a r i t y and a c c e p t a n c e i n t h e 4 . The d i f f e r e n c e i n t h e c o s t m i n i m i z i n g , c o n s t a n t r e t u r n s t o s c a l e mode l s i s 11 .8 p o i n t s w i t h dummy v a r i a b l e s and 19 p o i n t s w i t h o u t dummy v a r i a b l e s . The d i f f e r e n c e i s 18 p o i n t s i n t h e n o n - c o n s t a n t r e t u r n s t o s c a l e , c o s t m i n i m i z i n g m o d e l s . See Tab l e s IX and X V I . 5. J u s t i f y i n g t h e l i k e l i h o o d c ompa r i s on t e s t by t e s t i n g t h e mode l s a g a i n s t a h y p o t h e t i c a l g e n e r a l model was s u g g e s t e d t o me by James MacK innon i n p e r s o n a l c o r r e s p o n d e n c e . 125 l i t e r a t u r e , i t i s d e s i r a b l e t o choose t h e t r u e model w i t h a t e s t wh i ch does not we i gh t t h e r e s u l t so s t r o n g l y i n f a v o u r o f t h e CUM. The l i k e l i h o o d c ompa r i s on t e s t does no t assume t h a t a p a r t i c u l a r model i s t r u e a p r i o r i and t e s t o t h e r models a g a i n s t t h a t assumed t r u e mode l . I n s t e a d i t assumes t h a t t h e t r u e model i s i n c l u d e d i n t h e s e t o f a l t e r n a t i v e m o d e l s . A l o g l i k e l i h o o d a t l e a s t two p o i n t s h i g h e r t h an t h e l o g l i k e l i h o o d s o f t h e o t h e r mode ls i d e n t i f i e s t h e t r u e model f rom among a l l t h e f a l s e a l t e r n a t i v e s a t t h e 95% c o n f i d e n c e l e v e l . Thus t h e t e s t i s e s s e n t i a l l y model " d i s - c r i m i n a t i o n . " G i ven a f i x e d s e t o f a l t e r n a t i v e m o d e l s , wh i ch we b e l i e v e w i t h c e r t a i n t y c o n t a i n s t h e t r u e mode l , choose t h e t r u e model f rom among t he a l t e r n a t i v e s c o n t a i n e d i n t h e s e t . In g e n e r a l , i t i s p o s s i b l e t h a t no l o g l i k e l i h o o d i s s i g n i f i c a n t l y l a r g e r t h an a l l t h e o t h e r s , and no ' b e s t ' model i s f o u n d . T h i s o n l y means t h a t t h e r e i s no t enough i n f o r m a t i o n i n t h e mode ls t o d i s c r i m i n a t e one model f r om a l l t h e o t h e r s . S i n c e t h e r e i s no way t h a t a l l t h e a l t e r n a t i v e mode l s can be r e j e c t e d , t h e t e s t s t i l l assumes t h a t t h e t r u e model i s c o n t a i n e d i n t h e s e t o f a l t e r n a t i v e s . In our c a se t h e l i k e l i h o o d c o m p a r i s o n t e s t i m p l i c i t l y assumes t h a t one o f t h e CUM o r t h e MUM i s t r u e , and g i v e n o n l y t h o s e two a l t e r n a t i v e s , t h e CUM i s chosen o v e r t h e MUM. Non - ne s t ed T e s t The n o n - n e s t e d t e s t r e l a x e s t h e a p r i o r i a s s ump t i o n s abou t t h e t r u t h o f t h e mode ls s t i l l f u r t h e r . As i n t h e l i k e l i h o o d c o m p a r i s o n 6 . T h i s f o l l o w s because a l l t h e o t h e r mode ls wou l d be r e j e c t e d when t e s t e d a g a i n s t a h y p o t h e t i c a l g e n e r a l model w i t h one more p a r a m e t e r . 126 t e s t , no model i s assumed t o be t r u e a p r i o r i , and t h e a l t e r n a t i v e s may not c o n t a i n enough i n f o r m a t i o n t o r e j e c t any model as f a l s e . U n l i k e t h e l i k e l i h o o d c ompa r i s on t e s t , t h e t r u e model i s not assumed t o be i n t h e s e t o f a l t e r n a t i v e s w i t h c e r t a i n t y . In a n o n - n e s t e d h y p o t h e s i s t e s t a l l a l t e r n a t i v e mode l s may be a c c e p t e d as t r u e o r r e j e c t e d as f a l s e . The b a s i c p r o c e d u r e i s t o l e t t h e MUM and CUM be t h e n u l l and a l t e r n a t i v e h ypo the se s r e s p e c t i v e l y , and t o t e s t t h e n u l l h y p o t h e s i s g i v e n t h e a l t e r n a t i v e h y p o t h e s i s . Then t h e n u l l and a l t e r n a t i v e hypo the se s a r e r e v e r s e d and t h e t e s t i s r e p e a t e d . T h e r e f o r e one model may be a c c e p t e d , bo th mode l s may be a c c e p t e d , o r bo th mode ls may be r e j e c t e d . The a s s ump t i o n u n d e r l y i n g t h e p r o c e d u r e i s t h a t t h e r e i s no a l - t e r n a t i v e o r m a i n t a i n e d h y p o t h e s i s wh i ch i s b e l i e v e d t o be t r u e w i t h c e r t a i n t y . Tha t i s why bo th mode l s can be r e j e c t e d and why bo th mode ls a r e a l l o w e d t o be t h e a l t e r n a t i v e h y p o t h e s i s . Each model i s on an equa l f o o t i n g w i t h t h e o t h e r . F u r t h e r , each model i s t e s t e d a g a i n s t t h e o t h e r so t h a t t h e t e s t l o o k s f o r i n c o n s i s t e n c y o f t h e n u l l h y p o t h e s i s w i t h t h e d a t a i n d i r e c t i o n s s u g g e s t e d by t h e o t h e r m o d e l . The n o n - n e s t e d t e s t i s an h y p o t h e s i s t e s t on t h e " t r u t h " o f a model where no h ypo t he s e s abou t t h e t r u e model a r e b e l i e v e d w i t h c e r t a i n t y . 7 The n o n - n e s t e d t e s t i s done on t h e c o s t m i n i m i z i n g , c o n s t a n t r e t u r n s t o s c a l e v e r s i o n s o f t h e CUM and MUM (w i t h dummy v a r i a b l e s ) , 7 . The p r e c e d i n g d i s c u s s i o n and c o m p a r i s o n o f t e s t s i s t a k e n f r om P e s a r a n and Deaton (1978 , pp . 6 7 7 - 6 8 0 ) , D a s t o o r ( 1983 , p. 2 1 3 ) , and Dav i d s on and MacK innon (1982 , p. 5 5 1 ) . 1 2 7 u s i n g a v a r i a n t o f t h e J t e s t s u g g e s t e d by MacK i nnon , Wh i t e and Dav i d son ( 1 9 8 3 , p. 5 5 ) . S t o c h a s t i c v e r s i o n s o f t h e MUM and CUM mode l s a r e w r i t t e n i n i m p l i c i t f o rm as M ( K,M , w,L , e ; r , m , g , A , p ) = e and C ( K , M , w , L , Y ; r , m , Q , A , p ) = e r e s p e c t i v e l y , where 6 and y a r e t h e v e c t o r s o f pa r ame te r s t o be e s t i - mated and e i s t h e v e c t o r o f n o r m a l l y d i s t r i b u t e d e r r o r s . E r r o r t e rms c o r r e s p o n d i n g t o t h e same o b s e r v a t i o n a r e c o r r e l a t e d w h i l e e r r o r t e rms c o r r e s p o n d i n g t o d i f f e r e n t o b s e r v a t i o n s a r e i n d e p e n d e n t . Nest t h e two mode ls i n an a r t i f i c i a l compound model ( 1 - a ) M ( ) + a C ( ) = e . ( 7 . 4 ) To t e s t t h e n u l l h y p o t h e s i s t h a t t h e MUM i s t r u e g i v e n t h e a l t e r n a - t i v e h y p o t h e s i s t h a t t h e CUM i s t r u e , r e p l a c e y by i t s ML e s t i m a t e , o b t a i n e s t i m a t e s o f 3 and a and t e s t i f a = 0 . The a s y m p t o t i c t - s t a t i s t i c f o r t h e e s t i m a t e o f a i s 1 3 . 7 2 7 , so a i s s i g n i f i c a n t l y d i f f e r e n t f rom z e r o . The h y p o t h e s i s t h a t t h e MUM i s t r u e i s r e j e c t e d g i v e n t h e a l t e r n a t i v e h y p o t h e s i s t h a t t h e CUM i s t r u e . Thus t h e r e s u l t s o f t h e n e s t e d t e s t a r e c o n f i r m e d . R e v e r s i n g t h e n u l l and a l t e r n a t i v e h y p o t h e s e s , one o b t a i n s t h e a r t i f i c i a l compound model ( 1 - o)C() + aM() = e , ( 7 . 5 ) 128 where t h e n o t a t i o n i s t h e same as b e f o r e . R e p l a c e 8 by i t s ML e s t i - ma te , e s t i m a t e a and y and t e s t i f a = 0 . The a s y m p t o t i c t - s t a t i s t i c f o r t h e e s t i m a t e o f a i s 1 3 . 0 3 , so a i s s i g n i f i c a n t l y d i f f e r e n t f r om z e r o . The h y p o t h e s i s t h a t t h e CUM i s t r u e i s r e j e c t e d g i v e n t h e a l t e r n a t i v e h y p o t h e s i s t h a t t h e MUM i s t r u e . Dav i d son and MacK innon (1982) do show t h a t t h e J t e s t t e nd s t o r e j e c t t h e n u l l h y p o t h e s i s t o o o f t e n i n s m a l l s a m p l e s . However , t h e ve r y h i g h t - s t a t i s t i c s l e a v e no o t h e r c o n c l u s i o n t han t h e r e j e c t i o n o f bo th mode ls i n a n o n - n e s t e d t e s t . Summary I t i s a r gued t h a t t h e CUM i s t h e more a p p r o p r i a t e o r c o r r e c t o f t h e two models because one e x p e c t s un i on s and f i r m s t o e x p l o i t a l l p o s s i b l e g a i n s f r om t r a d e and r e a c h e f f i c i e n t ou t comes . Arguments e x p l a i n i n g why t h e CUM s o l u t i o n may be u n a t t a i n a b l e and t h e i n e f f i - c i e n t MUM s o l u t i o n may r e s u l t a r e f o und u n c o n v i n c i n g . T h i s p r e f e r e n c e f o r t h e CUM ove r t h e MUM i s s u p p o r t e d by t h e d a t a . When t h e CUM i s assumed t o be t r u e , t h e MUM i s f o und t o be i n - c o n s i s t e n t w i t h t h e da t a and t h e MUM i s r e j e c t e d . When t h e IWA and f o r e s t p r o d u c t s i n d u s t r y a r e assumed t o behave a c c o r d i n g t o one o f e i t h e r t h e CUM o r MUM, t h e CUM p r o v i d e s a b e t t e r model o f t h e d a t a t h a n t h e MUM. So i n a t e s t between t h e MUM and CUM, t h e MUM i s r e j e c t e d i n f a v o u r o f t h e CUM ( g i v e n t h e d a t a ) and t h e q u a l i t a t i v e a rguments f a v o u r i n g t h e CUM o ve r t h e MUM a r e c o n f i r m e d . However once we a l l o w t h a t n e i t h e r model may be t r u e , b o t h mode l s a r e r e j e c t e d . T h i s i s a l s o c o n s i s t e n t w i t h t h e a rguments p r e s e n t e d above . F a c t o r s such as a g g r e g a t i o n o f un i on members ' p r e - f e r e n c e s , u n c e r t a i n t y , i m p e r f e c t i n f o r m a t i o n , mora l h a z a r d , dynamic 129 c o n s t r a i n t s , n o n - p r i c e t a k i n g b e h a v i o u r , t h e c o s t s o f n e g o t i a t i o n s , and s t r i k e s a r e assumed away by bo th mode ls and t h e i r n e g l e c t l e s s e n s t h e v a l i d i t y o f bo th m o d e l s . The r e j e c t i o n o f bo th mode l s by t h e n on - n e s t e d t e s t o n l y shows t h a t more work needs t o be done on t h e s p e c i f i c a t i o n o f mode ls o f u n i o n and f i r m b e h a v i o u r . In c o n c l u s i o n , g i v e n t h e c h o i c e between t he CUM and MUM, t h e CUM must be chosen as t h e t r u e m o d e l . However , t h e n o n - n e s t e d t e s t shows t h a t t h e t r u t h o f e i t h e r model may not be ve r y g r e a t . 130 Chap te r 8 C o n c l u s i o n Two mode ls o f un i on and i n d u s t r y b e h a v i o u r a r e d e r i v e d , s p e c i - f i e d and e s t i m a t e d u s i n g annua l d a t a on t h e IWA and wood p r o d u c t s i n d u s t r y i n B . C . , 1 9 6 3 - 7 9 . D i f f e r e n t v e r s i o n s o f t h e mode ls a r e s p e c i f i e d and e s t i m a t e d a s sum ing c o s t m i n i m i z i n g and 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 by t h e f i r m s i n t h e i n d u s t r y and c o n s t a n t and n o n - c o n s t a n t r e t u r n s t o s c a l e . The t e c h n o l o g y o f t h e wood p r o d u c t s i n d u s t r y i s a l s o e s t i m a t e d i n d e p e n d e n t l y o f any un i o n o b j e c t i v e f u n c - t i o n p a r a m e t e r s , a s sum ing c o s t m i n i m i z i n g b e h a v i o r and exogenous wages . Thus , t h e e s t i m a t e s o f t h e t e c h n o l o g y a r e e q u i v a l e n t t o t h o s e w h i c h wou l d be o b t a i n e d i f p e r f e c t c o m p e t i t i o n i n a l l i n p u t ma r ke t s was assumed. The e s t i m a t e d u n i o n o b j e c t i v e f u n c t i o n i s f ound t o be i n c r e a s i n g i n t o t a l r e a l c o m p e n s a t i o n , d e c r e a s i n g i n employment and t h e r e a l a l t e r n a t i v e wage, and q u a s i c o n c a v e o v e r r e a l c ompensa t i on and emp loy - ment . W r i t t e n as a f u n c t i o n o f t h e a ve r age r a t e o f r e a l c ompen s a t i o n ( t h e r e a l wage) and emp loyment , t h e e s t i m a t e d u n i o n o b j e c t i v e f u n c - t i o n i s i n c r e a s i n g i n bo th r e a l wages and emp loyment , and 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 between r e a l wages and employment r anges f r om 0.6 t o 0 . 8 . The un i on i s f ound t o be i n d i f f e r e n t t o t h e f i r i n g o f one w o r k e r (2000 hou r s ) and a 0.032<t an hou r i n c r e a s e i n t h e r e a l wages o f a l l o t h e r w o r k e r s . In p e r c e n t a g e t e r m s , t h e u n i o n i s i n d i f - f e r e n t t o a 1.5% d e c r e a s e i n employment and a 1% i n c r e a s e i n t h e r e a l wage. Many p o p u l a r h ypo the se s about un i on p r e f e r e n c e s a r e t e s t e d . The h y p o t h e s i s t e s t s i n d i c a t e t h a t t h e IWA does not max im i z e r e n t s o r t h e wage b i l l and t h e IWA i s not i n d i f f e r e n t t o t h e l e v e l o f 131 employment o r t h e a l t e r n a t i v e wage a v a i l a b l e t o l a b o u r . The e s t i - mates o f un i on p r e f e r e n c e s a r e s u r p r i s i n g l y r o b u s t t o changes i n t h e model and t h e t e c h n o l o g y , a l t h o u g h t h e y a r e s e n s i t i v e t o whe t he r c o s t m i n i m i z i n g o r p r o f i t m a x i m i z i n g b e h a v i o r i s assumed. The e s t i m a t e s o f u n i o n p r e f e r e n c e s a r e a l s o v e r y s i m i l a r t o o t h e r e s t i m a t e s f o und i n t h e l i t e r a t u r e (see De r t ou zo s and Pencave l ( 1 9 8 1 ) ) . On t h e p r o d u c t i o n s i d e , t h e i n d u s t r y ' s e s t i m a t e d c o s t f u n c t i o n i s not concave i n p r i c e s and t h e i n d u s t r y ' s e s t i m a t e d p r o f i t f u n c t i o n i s no t convex i n p r i c e s . In t h e exogenous wage r a t e m o d e l , homothe- t i c i t y o f t h e p r o d u c t i o n t e c h n o l o g y i s r e j e c t e d as i s no t e c h n i c a l change and H i c k s ' n e u t r a l t e c h n i c a l c hange . C a p i t a l and m a t e r i a l s a r e e s t i m a t e d t o be complements w h i l e c a p i t a l and l a b o u r , and l a b o u r and m a t e r i a l s a r e f o und t o be s u b s t i t u t e s . The e s t i m a t e s o f t h e p r o d u c t i o n t e c h n o l o g y ^ a r e ve r y s e n s i t i v e t o whe the r o r no t t h e u n i o n ' s b e h a v i o u r i s e x p l i c i t l y m o d e l l e d . The e s t i m a t e s o f t h e s ub - s t i t u t a b i l i t y o f t h e f a c t o r s o f p r o d u c t i o n i n c r e a s e d r a m a t i c a l l y when wages a r e endogenous t o t h e model and p r o d u c t i o n and u n i o n p r e f e r e n c e pa r ame te r s a r e e s t i m a t e d j o i n t l y . W i t h r e g a r d t o t h e c h o i c e o f an a p p r o p r i a t e model o f u n i o n and f i r m b e h a v i o u r , i t i s c l e a r on bo th t h e o r e t i c a l and e m p i r i c a l g rounds t h a t i f one has t o choose between t h e MUM and t h e CUM, t h e CUM dom in - a t e s t h e MUM. I f , howeve r , one wants t o t e s t t h e " t r u t h " o f t h e mode l s e m p i r i c a l l y , w i t h no c e r t a i n m a i n t a i n e d o r a l t e r n a t i v e hypo - t h e s i s , t hen bo th t h e MUM and t h e CUM a re r e j e c t e d by a n o n - n e s t e d h y p o t h e s i s t e s t . The r e j e c t i o n o f bo th mode ls i n t h e n o n - n e s t e d t e s t u n d e r l i n e s some o f t h e f a u l t s of t h e work r e p o r t e d above . There i s t h e u b i q u i t o u s f a u l t o f a s sum ing away u n c e r t a i n t y and i m p e r f e c t i n f o r m a - 132 t i o n . Such i m p o r t a n t f a c t o r s as t h e c o s t s o f b a r g a i n i n g , b a r g a i n i n g s t r a t e g i e s , s t r i k e s , j o b r e s t r i c t i o n s , and d i v e r g e n t p r e f e r e n c e s w i t h i n t h e u n i o n a r e a l l assumed away. The dynamics o f t h e r e l a t i o n - s h i p between t he f i r m and t h e un i o n a r e a l s o i g n o r e d as i s t h e v e r t i - c a l i n t e g r a t i o n o f t h e f i r m s i n t h e i n d u s t r y and a number o f f l a w s i n t h e d a t a . From an e c o n o m e t r i c s t a n d p o i n t t h e e r r o r s t r u c t u r e i s a r b i t r a r y and t h e samp le i s t o o s m a l l t o p l a c e a l o t o f c o n f i d e n c e i n t h e a s y m p t o t i c p r o p e r t i e s o f t h e e s t i m a t e s . In s p i t e o f t h e f a u l t s l i s t e d a b o v e , a p o s i t i v e c o n t r i b u t i o n has been made. F i r s t , a new da t a s e t wh i c h i s o l a t e s t h e b e h a v i o u r o f a u n i o n and i t s u n i o n i z e d i n d u s t r y i s d e v e l o p e d . E m p i r i c a l work on un i on s has been h i n d e r e d by a l a c k o f da t a on t h e b e h a v i o u r o f u n i o n s and t h e f i r m s t h e y o r g a n i z e d . The d a t a u s u a l l y c o n t a i n some unknown mix o f un i on and non - un i o n wo r ke r s and un i on and n on - un i o n f i r m s . T h i s d a t a s e t p r o v i d e s o b s e r v a t i o n s on a s i n g l e un i o n and t h e f i r m s i t b a r g a i n s w i t h , w i t h ve r y l i t t l e c o n t a m i n a t i o n f rom n o n - u n i o n w o r k e r s and f i r m s . S e c o n d , e s t i m a t e s o f t h e IWA's p r e f e r e n c e s a r e o b t a i n e d t h e r e b y p r o v i d i n g an answer t o t h e v e r y o l d q u e s t i o n "What do un i on s m a x i - m i z e ? " . E s t i m a t e s o f t h e p r o d u c t i o n t e c h n o l o g y o f t h e B . C . wood p r o d u c t s i n d u s t r y a r e a l s o o b t a i n e d t h e r e b y add i ng t o t h e s t o c k o f know ledge abou t f a c t o r s u b s t i t u t i o n and show ing t h e s e n s i t i v i t y o f t h e t e c h n o l o g y e s t i m a t e s t o t h e e x p l i c i t 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 . F i n a l l y , t h e MUM, wh i c h i s so p o p u l a r i n t h e l i t e r a t u r e , i s r e - j e c t e d i n f a v o u r o f t h e CUM ( w i t h i t s e f f i c i e n t ou tcomes) when t h e two mode ls a r e compared t o one a n o t h e r . 133 Appendi x More on t h e Da ta The pu rpose o f t h i s a ppend i x i s t o p r o v i d e more i n f o m r a i t o n on t h e d a t a , t h e u n i o n and t h e i n d u s t r i e s . T a b l e XX shows t h e means- and s t a n d a r d d e v i a t i o n s o f t h e v a r i a b l e s i n t h e d a t a s e t and F i g u r e s 6 and 7 show t h e l e v e l s and movements o f r e a l wages and employment i n each o f t h e i n d u s t r i e s . F i g u r e 6 shows t h a t t h e r e a l wages t r e n d upwa rds . However , t h e r e i s s t i l l v a r i a t i o n i n each i n d u s t r y ' s r e a l wages a f t e r a c o n s t a n t t e r m and t r e n d i s removed (where each i n d u s t r y i s a l l o w e d a d i f f e r e n t c o n s t a n t and t r e n d ) . T h i s r e m a i n i n g v a r i a t i o n i s i n dependen t o f t h e c y c l e s o f t h e i n d u s t r y , where bo th o u t p u t and t h e p r i c e o f o u t p u t were used t o measure t h e i n d u s t r y ' s c y c l e . The r e a l wages o f each i n d u s t r y move c l o s e l y t o g e t h e r w i t h s i m p l e c o r r e l a t i o n c o e f f i c i e n t s r a n g i n g f rom .99 t o . 9 7 . Th i s i s no t s u r - p r i s i n g s i n c e t h e i n d u s t r i e s a r e v e r y s i m i l a r , i n t h e same p r o v i n c e , and t h e b a r g a i n i n g s t r u c t u r e i s c e n t r a l i z e d . B a r g a i n i n g t a k e s p l a c e w i t h t h e 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 i n g a c o l l e c t i v e agreement wh i c h ( e f f e c t i v e l y ] s e t s t h e wages f o r e ve r y wo rke r o r o c c u p a t i o n h i r e d by each i n d u s t r y . However , t h e r e a l wages o f each i n d u s t r y a r e d i f f e r e n t s i n c e each i n d u s t r y h i r e s a d i f f e r e n t mix o f o c c u p a t i o n s . The h y p o t h e s i s t h a t a l l t h e i n d u s t r i e s have t h e same mean o r t r e n d i s r e j e c t e d a t t h e 95% c o n f i d e n c e l e v e l . Real wages i n i n t e r i o r saw- 134 TABLE XX Means and S t a n d a r d D e v i a t i o n s o f t h e Da ta S t anda r d d e v i a t i o n s a r e i n p a r e n t h e s e s be low t h e mean. Coas t I n t e r i o r S h i n g l e P l ywood f a r i a b l e S a w m i l l s Sawmi11s M i l l s M i l l s q 1.94 1.50 2 .53 1.56 ( 0 . 9 9 ) ( 0 . 71 ) ( 1 . 5 2 ) ( 0 . 6 3 ) r 3 .30 3 .34 3 .79 3 .21 ( 1 . 4 3 ) ( 1 . 4 2 ) ( 1 . 6 0 ) ( 1 . 4 6 ) m 1.98 1.18 2 .24 1.63 ( 0 . 9 9 ) ( 0 . 5 3 ) ( 1 . 5 4 ) ( 0 . 5 0 ) w/p 4 . 32 3.97 4 .61 4 . 21 ( 0 . 8 8 ) ( 0 . 9 9 ) ( 0 . 8 2 ) ( 0 . 7 9 ) Q 34 . 55 41 . 99 2 .26 17 .05 ( 5 . 6 7 ) ( 1 2 . 0 5 ) ( 0 . 2 6 ) ( 2 . 7 9 ) M 20 .80 26 .97 1.38 8 .77 ( 3 . 8 7 ) ( 7 . 2 6 ) ( 0 . 2 1 ) ( 2 . 1 6 ) K 6 .54 14 . 53 0 .42 5 .33 ( 1 . 9 6 ) ( 5 . 8 3 ) ( 0 . 1 4 ) ( 1 . 5 6 ) L 24 . 93 28 . 06 2 .75 13 .33 ( 2 . 5 0 ) ( 5 . 2 4 ) ( 0 . 3 0 ) ( 0 . 9 3 ) A 3.67 _ - - ( 0 . 4 8 ) 135 FIGURE 6 Wages i n Cons t an t 1971 D o l l a r s CC i s c o a s t s a w m i l l s I I i s i n t e r i o r s a w m i l l s SS i s s h i n g l e m i l l s PP i s p lywood m i l l s $ pe r hour I 6 .00 4- I 1 4 1 1 1 < 1963 1965 1968 1971 1974 1977 1979 Year 136 FIGURE 7 Employment 0 0 0 ' s o f man hours 38000 34000 + CC i s c o a s t s a w m i l l s I I i s i n t e r i o r s a w m i l l s PP i s p lywood m i l l s SS i s s h i n g l e m i l l s Yea r 1972 137 m i l l s have t h e s t e e p e s t t r e n d f o l l o w e d by t h e r e a l wages i n c o a s t s a w m i l l s , s h i n g l e m i l l s and p l ywood m i l l s . The d a t a on i n p u t s and o u t p u t s show t h a t t h e i n d u s t r i e s a r e no t v e r y s t a b l e f rom y e a r t o y e a r w i t h p e r i o d s o f boom and b u s t . T h i s i s shown i n F i g u r e 7 where employment i n each i n d u s t r y i s p l o t t e d . There i s a g r e a t dea l o f v a r i a b i l i t y i n employment bo th w i t h and w i t h o u t i n d u s t r y t r e n d s removed, and o n l y employment i n i n t e r i o r s a w m i l l s has a s t a t i s t i c a l l y s i g n i f i c a n t t r e n d . The v a r i a t i o n r e m a i n i n g a f t e r t h e i n d u s t r y t r e n d i s removed i s p o s i t i v e l y c o r - r e l a t e d w i t h t h e p r i c e o f o u t pu t i n i n t e r i o r and c o a s t s a w m i l l s and s h i n g l e m i l l s , bu t not i n p l ywood m i l l s . Employment i n t h e i n d u s - t r i e s does not move t o g e t h e r . The s i m p l e c o r r e l a t i o n c o e f f i c i e n t s r ange f r om .37 between employment i n s h i n g l e m i l l s and i n t e r i o r saw- m i l l s and .77 between employment i n p lywood m i l l s and c o a s t s a w m i l l s . The h ypo t h e s e s t h a t each i n d u s t r y ' s employment has t h e same mean o r t r e n d i s r e j e c t e d a t t h e 95% l e v e l . In t h e work above , a l l f o u r i n d u s t r i e s a r e assumed t o have t h e same t e c h n o l o g y , a l t h o u g h d i f f e r e n t c o n s t a n t t e rms a r e p e r m i t t e d i n some o f t h e e s t i m a t i n g e q u a t i o n s . Even t hough t h e a g g r e g a t i o n o f t e c h n o l o g y a c r o s s i n d u s t r i e s i s r e j e c t e d by a h y p o t h e s i s t e s t ( u s i n g t h e model c o n t a i n e d i n C h a p t e r 4 ) , t h e a g g r e g a t i o n a s s ump t i o n i s easy t o d e f e n d . A l l o f t h e i n d u s t r i e s do b a s i c a l l y t h e same t h i n g . They p u r c h a s e l o g s and b o l t s ; saw, p ee l o r s p l i t them i n t o s m a l l e r p i e c e s and t hen do some f u r t h e r p r o c e s s i n g ; such as p l a n i n g , o r g l u i n g t h e p i e c e s . S i n c e t h e i n d u s t r i e s a r e s o s i m i l a r , t h e y a r e a l l i n c l u d e d 138 i n t h e same two d i g i t SIC l e v e l ( s e e , f o r e xamp l e , Woodland [ 1985 ] o r Denny and May [1977 and 1 9 7 8 ] ) . T h e r e f o r e t h e a g g r e g a t i o n o f t h r e e and f o u r d i g i t SIC i n d u s t r i e s i s no t u n r e a s o n a b l e when compared t o t h e s t a n d a r d s f ound i n t he l i t e r a t u r e . To c o n s i d e r t h e r e a s o n a b l e n e s s o f t h e a g g r e g a t i o n o f d i f f e r e n t g roups o f wo r ke r s and un i on l e a d e r s i n t o an e n t i t y p o s s e s s i n g a s i n g l e c o n s i s t e n t o b j e c t i v e f u n c t i o n one must know t h e c h a r a c t e r - i s t i c s o f t h e wo r ke r s and t h e l e a d e r s . Census d a t a shows t h a t , i n g e n e r a l , t h e w o r k e r s a r e no t w e l l e d u c a t e d , s l i g h t l y y o u n g e r t h an t h e a ve r age wo rke r i n t h e l a b o u r f o r c e and v i r t u a l l y a l l m a l e . They do s t r e n u o u s and dange rous s o r t s o f work i n f a i r l y u n p l e a s a n t c o n d i - t i o n s . Much o f t h e work i s c l a s s e d as u n s k i l l e d , but t h e r e a r e i n d u s t r y s p e c i f i c s k i l l s such as o p e r a t i n g l a r g e , e x p e n s i v e and s p e c i a l i z e d m a c h i n e r y . The un i o n l e a d e r s a r e s e c u r e and p o w e r f u l . S i n c e 1958 t h e IWA Reg i o n a l C o u n c i l #1 has gove rned t h e a c t i v i t i e s o f t h e IWA i n B r i t i s h C o l u m b i a . The members o f t h e r e g i o n a l c o u n c i l p o s s e s s most o f t h e power f o r c o l l e c t i v e b a r g a i n i n g and t h e o t h e r f u n c t i o n s o f t h e u n i o n . The r e i s l i t t l e t u r n o v e r on t h e r e g i o n a l c o u n c i l and t h e c o u n c i l l o r s e n j o y l o n g t e n u r e s on t h e c o u n c i l . D e s p i t e t h e c e n t r a l i z e d power s t r u c t u r e o f t h e u n i o n and t h e l a c k o f c o m p e t i t i o n and t u r n o v e r i n t h e l e a d e r s h i p , t h e IWA i s a r e l a - t i v e l y d e m o c r a t i c u n i o n w i t h l o t s o f p u b l i c d e b a t e . S i n c e t h e u n i o n i s an i n d u s t r i a l un i on r e p r e s e n t i n g a l l o f t h e d i f f e r e n t wo r k e r s i n t h e i n d u s t r i e s , c o n f l i c t s between d i f f e r e n t g roups w i t h i n t h e member- 139 s h i p a r e i n e v i t a b l e . However i n t h e IWA t h e a f f e c t e d g roups a r e v e r y v o c a l about t h e i r p l i g h t , and t h e l e a d e r s g e n e r a l l y l i s t e n and t a k e some r emed i a l a c t i o n . A good examp l e , common t o most i n d u s t r i a l u n i o n s , i s t h e s k i l l e d t r a d e s . A d d i t i v e ( r a t h e r t h an p e r c e n t a g e ) wage i n c r e a s e s have d e c r e a s e d t h e i r r e l a t i v e wage d i f f e r e n t i a l s . The t r a d e s have been ve r y v o ca l about t h e e r o s i o n o f t h e i r r e l a t i v e wages and t h e l e a d e r s have r e s ponded . Most o f t h e c o l l e c t i v e agreements c o n t a i n e x t r a i n c r e a s e s f o r t h e t r a d e s , and one c o l l e c t i v e agreement was even r e - opened i n t h e m i d d l e o f i t s t e r m t o a d j u s t t h e t r a d e s wage s c a l e s . Thus t h e r e a r e no w a r r i n g f a c t i o n s w i t h i n t h e u n i o n , o r l a r g e upheava l s c a u s i n g changes i n i d e o l o g y , d i r e c t i o n o r g o a l s . There i s s t a b l e and powe r f u l l e a d e r s h i p wh i c h seems t o r e spond c l o s e l y t o t h e member sh i p . Hence i t i s not u n r e a s o n a b l e t o t r e a t t h e un i o n as an e n t i t i y w i t h a s i n g l e c o n s i s t e n t o b j e c t i v e f u n c t i o n whose pa r ame te r s a r e c o n s t a n t o v e r t i m e . A n o t h e r i s s u e wh i c h must be a d d r e s s e d i s how t h e i n d u s t r y and un i on r each an outcome o f f t h e i n d u s t r y ' s demand f o r l a b o u r c u r v e , and on t h e c o n t r a c t c u r v e . One a l t e r n a t i v e i s t h e u n i o n and manage- ment j o i n t commi t t ees wh i ch a d m i n i s t e r t h e s awm i l l and p l ywood j o b e v a l u a t i o n p l a n s . However t h e s e p l a n s dea l m a i n l y w i t h j o b c l a s s i f i - c a t i o n and i t i s u n l i k e l y t h a t t h e y have a s i g n i f i c a n t e f f e c t upon t h e l e v e l o f emp loyment . The re a r e no o t h e r s i g n i f i c a n t j o b r e s t r i c - t i o n s so t h e un i on canno t c o n t r o l employment d i r e c t l y . A n o t h e r a l t e r n a t i v e i s t h e non-homogeneous o f deg ree one compen- s a t i o n f u n c t i o n s s p e c i f i e d i n t h e c o l l e c t i v e ag r e emen t s . The a g r e e - 140 merits s t a t e t h a t t h e i n d u s t r y must pay f o r v a c a t i o n s ; s t a t u t o r y h o l i d a y s ; m e d i c a l , d i s a b i l i t y , d ismemberment and l i f e i n s u r a n c e ; a d e n t a l p l a n ; p e r s o n a l s a f e t y equ i pmen t ; and s e v e r a n c e pay . These a r e a l l f i x e d c o s t s o f employment and t hey can be used t o s u p p o r t an outcome on t h e c o n t r a c t c u r v e as shown i n Chap t e r 7. The f i n a l i s s u e t o be a d d r e s s e d i s whe the r o r not each i n d u s t r y p r o v i d e s i n dependen t o b s e r v a t i o n s ( i n f o r m a t i o n ) on t h e p r o d u c t i o n t e c h n o l o g y and t h e un i on o b j e c t i v e f u n c t i o n . The i n d u s t r i e s a r e assumed t o have t h e same p r o d u c t i o n t e c h n o l o g y . However , each i n d u s - t r y chooses a d i f f e r e n t p o i n t on i t s p r o d u c t i o n t e c h n o l o g y f r o n t i e r because t h e y f a c e d i f f e r e n t i n p u t p r i c e s . Energy and m a t e r i a l s p r i c e s va r y because o f d i f f e r e n t l o c a t i o n s and t h e d i f f e r e n t b und l e s o f t r e e s and f u e l s u s e d . The p r i c e o f l a b o u r v a r i e s because t h e i n d u s t r i e s choose d i f f e r e n t m ixes o f o c c u p a t i o n s . Each i n d u s t r y o p e r a t e s a t a d i f f e r e n t p o i n t on t h e same p r o d u c t i o n t e c h n o l o g y , and t h i s p r o v i d e s i ndependen t o b s e r v a t i o n s on t h e p r o d u c t i o n t e c h n o l o g y as w e l l as i ndependen t o b s e r v a t i o n s o f d i f f e r e n t p o i n t s on t h e same un i on o b j e c t i v e f u n c t i o n . T h e r e f o r e each i n d u s t r y p r o v i d e s i n d e - pendent i n f o r m a t i o n on t h e p r o d u c t i o n t e c h n o l o g y and t h e un i on o b j e c t i v e f u n c t i o n . 141 B i b l i o g r a p h y Appe lbaum, A . (1979) " T e s t i n g P r i c e T a k i n g B e h a v i o r . " J o u r n a l o f E c o n o m e t r i c s 9, 283 -294 . A s h e n f e l t e r , O r l e y and George Johnson (1969) " B a r g a i n i n g T h e o r y , T r ade 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 i can Economic Rev iew 59 , 3 5 - 4 9 . A t h e r t o n , W.N. (1973) Theo r y o f Un ion B a r g a i n i n g G o a l s . ( P r i n c e t o n : P r i n c e t o n U n i v e r s i t y P r e s s ) . Bank o f Canada (1963 -79 ) Bank o f Canada Rev i ew . (O t t awa : Bank o f C a n a d a ) . B e r k o w i t z , M. (1954) "The Economics o f T rade Un ion O r g a n i z a t i o n and A d m i n i s t r a t i o n . " I n d u s t r i a l and Labo r R e l a t i o n s Rev i ew 7, 5 75 - 592 . B e r n d t , E .R. and D. Wood (1975) " T e c h n o l o g y , P r i c e s and The D e r i v e d Demand f o r E n e r g y . " Rev iew o f Economics and S t a t i s t i c s 57 , 2 59 - 268 . B i n s w a n g e r , H .P . (1974) "The Measurement o f T e c h n i c a l Change B i a s e s w i t h many F a c t o r s o f P r o d u c t i o n . " Amer i can Economic Rev iew 64 , 9 6 4 - 9 7 6 . B l a i r , D .H . and D .L . C r aw fo r d (1983) Labou r Un ion O b j e c t i v e s and C o l l e c t i v e B a r g a i n i n g . Mimeo R u t g e r s U n i v e r s i t y . C a r t t e r , A . M . (1959) Theo ry o f Wages and Employment . (Homewood, I l l i n o i s : Irwin"] - ; D a s t o o r , N. (1983) "Some A s p e c t s o f T e s t i n g Non-Nes ted H y p o t h e s e s . " J o u r n a l o f E c o n o m e t r i c s 2 1 , 213 - 228 . D a v i d s o n , R. and J . G . MacK innon (1981) " S e v e r a l T e s t s f o r Model S p e c i f i c a t i o n i n t h e P r e s e n c e o f A l t e r n a t i v e H y p o t h e s e s . " E c o n o m e t r i c a 4 9 , 7 8 1 - 7 9 3 . (1982) "Some Non-Nes ted H y p o t h e s i s T e s t s and t h e R e l a t i o n s Among Them." Rev iew o f Economic S t u d i e s 49 , 5 51 - 565 . de M e n i l , G. (1971) B a r g a i n i n g : Monopo ly Power V e r s u s Un ion Power . ( C amb r i d ge , M a s s . : MIT P r e s s ) . Denny, M. and Doug May (1977) "The E x i s t e n c e o f a Real V a l u e - A d d e d F u n c t i o n i n t h e Canad i a n M a n u f a c t u r i n g S e c t o r . " J o u r n a l o f E c o n o m e t r i c s 5, 5 5 - 6 9 . (1978) "A R e p r e s e n t a t i o n o f Canad i an M a n u f a c t u r i n g Te chno - l o g y . " A p p l i e d Economics 10, 3 05 - 317 . 142 D e r t o u z o s , J . and J . P en cave l (1981) "Wage and Employment D e t e r m i n a t i o n Under T rade U n i o n i s m . " J o u r n a l o f P o l i t i c a l Economy 89 , 1 162 - 1181 . Dhrymes, P. and M. Kurz (1964) " Te chno l ogy and S c a l e i n E l e c t r i c i t y G e n e r a t i o n . " E c onome t r i c a 32 , 287 - 315 . D i e w e r t , W.E. (1973) " F u n c t i o n a l Forms f o r P r o f i t and T r a n s f o r m a t i o n F u n c t i o n s . " J o u r n a l o f Economic Theo ry 6, 2 84 - 316 . (1974) " A p p l i c a t i o n s o f D u a l i t y T h e o r y . " In M.D. I n t r i l l i g a - t o r and D.A. K e n d r i c k ( e d s . ) , F r o n t i e r s o f Q u a n t i t a t i v e E c onom i c s . (New Yo r k : No r th Hoi l a n d ) . (1976) " E x a c t and S u p e r l a t i v e Index Numbers . " J o u r n a l o f E c o n o m e t r i c s 4 , 1 15 - 145 . (1978a) D u a l i t y App roaches t o M i c r o e c o n o m i c s . IMSSS T e c h n i c a l R epo r t #281, S t a n f o r d . (1978b) " S u p e r l a t i v e Index Numbers and C o n s i s t e n c y i n A g g r e g a t i o n . " E c onome t r i c a 46 , 8 83 - 900 . Dun l op , J . T . (1944) Wage D e t e r m i n a t i o n Under T rade Un ions (New Y o r k : Agu s t u s Ke ! l y ) . F a r b e r , H. (1978) " P r e f e r e n c e s and Un ion Wages . " J o u r n a l o f P o l i t i c a l Economy 86 , 9 2 3 - 9 4 2 . F u s s , M. (1977) "The Demand f o r Energy i n Canad i an M a n u f a c t u r i n g . " J o u r n a l o f E c o n o m e t r i c s 5, 8 9 - 1 1 6 . F u s s , M . , D. McFadden, and Y. Mundlak (1978) "A Su r vey o f F u n c t i o n a l Forms i n t h e Economic A n a l y s i s o f P r o d u c t i o n . " In M. Fus s and D. McFadden ( e d s . ) , P r o d u c t i o n E c o n o m i c s . (New Yo r k : No r t h H o l l a n d ) . G a l l a n t , A . R . and D. J o r gen son (1979) " S t a t i s t i c a l I n f e r e n c e f o r a Sys tem o f S i m u l t a n e o u s N o n - l i n e a r I m p l i c i t E q u a t i o n s i n t h e Con t e x t o f I n s t r u m e n t a l V a r i a b l e E s t i m a t i o n . " J o u r n a l o f E c o n o m e t r i c s 11 , 2 75 - 302 . G a v e r , K .M. and M.S. G e i s e l (1974) " D i s c r i m i n a t i n g Among A l t e r n a t i v e M o d e l s : B a y e s i a n and N o n - B a y e s i a n M e t h o d s . " In P. Zarembka ( e d . ) . F r o n t i e r s o f E c o n o m e t r i c s . (New Yo rk : Academic P r e s s ) . H a l l , R . E . and D. L i l i e n (1979) " E f f i c i e n t Wage B a r g a i n s Under U n c e r t a i n Supp l y and Demand." Amer i can Economic Rev i ew 69 , 8 6 8 - 8 7 9 . Hamermesh, D. (1976) " E c o n o m e t r i c S t u d i e s o f Labour Demand and T h e i r A p p l i c a t i o n t o P o l i c y A n a l y s i s . " J o u r n a l o f Human Re s ou r c e s 11 5 0 7 - 5 2 5 . 143 Hanoch , G i o r a (1975) "The E l a s t i c i t y o f S c a l e and t h e Shape o f Ave rage C o s t s . " Ame r i c an Economic Rev iew 6 5 , 4 9 2 - 4 9 7 . H i c k s , J . R . (1963) The Theo ry o f Wages. (London: M a c m i l l a n ) . I n d u s t r y , T rade and Commerce; Re sou r c e I n d u s t r i e s B ranch (1978) Rev iew o f t h e Canad i an F o r e s t P r o d u c t s I n d u s t r y . (O t t awa : Government o f C a n a d a ) . I n t e r n a t i o n a l Woodworkers o f A m e r i c a , Wes te rn Canad i an R e g i o n a l C o u n c i l #1 (1971) The IWA i n B r i t i s h C o l u m b i a . ( V an couve r : IWA). J o h n s o n , G. (1975) "Economic A n a l y s i s o f T rade U n i o n i s m . " Ame r i c an Economic Rev iew Pape r s and P r o c e e d i n g s 87 , 2 3 - 2 8 . K o t o w i t z , Y. (1968) " C a p i t a l - L a b o u r S u b s t i t u t i o n i n C anad i a n M a n u f a c t u r i n g 1926-39 and 1 9 4 6 - 6 1 . " Canad ian J o u r n a l o f Economics 1, 6 1 9 - 6 3 2 . L e o n t i e f , W. (1946) "The Pure Theory o f t h e Gua ran teed Annua l Wage C o n t r a c t . " J o u r n a l o f P o l i t i c a l Economy 54, 7 6 - 7 9 . L e w i s , H.G. (1959) " C o m p e t i t i v e and Monopoly U n i o n i s m . " In P. B r a d l e y ( e d . ) , The P u b l i c S t a k e i n Un ion Powe r . ( C h a r l o t t e s v i l l e : U n i v e r s i t y o f V i r g i n i a P r e s s ) . Ma cK i nnon , James , H. W h i t e , and R. Dav i d son (1983) " T e s t s f o r Model S p e c i f i c a t i o n i n t h e P r e s e n c e o f A l t e r n a t i v e H y p o t h e s e s . " J o u r n a l o f E c o n o m e t r i c s 2 1 , 5 3 - 7 0 . MaCurdy , Thomas and J . Pencave l (1983) T e s t i n g Between Compe t i ng Mode l s 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 . Re sea r ch Paper b t a n r o r o . M a r t i n , D. (1980) An Owner sh ip Theo ry o f t h e T rade U n i o n . ( B e r k e l e y : U n i v e r s i t y o t C a l i f o r n i a P r e s s ) . McDona l d , I . M . and R. So low (1981) "Wage B a r g a i n i n g and Emp loymen t . " Amer i c an Economic Rev i ew 71 , 8 96 - 908 . McFadden , D a n i e l (1978a) " C o s t , Revenue and P r o f i t F u n c t i o n s . " In M. Fus s and D. McFadden ( e d s . ) , P r o d u c t i o n E c o n o m i c s . (New Yo r k : No r th H o l l a n d ) . (1978b) " E s t i m a t i o n Te chn i que s f o r 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 and O the r P r o d u c t i o n P a r a m e t e r s . " In M. Fuss and D. McFadden ( e d s . ) , P r o d u c t i o n E c onom i c s . (New Yo r k : No r t h H o l l a n d ) . P e a r s e , P e t e r (1976) T imbe r R i g h t s and F o r e s t P o l i c y i n B r i t i s h C o l u m b i a . Repo r t o f t h e Roya l Commiss ion on F o r e s t R e s o u r c e s . ( V i c t o r i a : Government o f B r i t i s h C o l u m b i a ) . 144 (1980) The F o r e s t I n d u s t r i e s o f B r i t i s h C o l u m b i a : B . C . Te l S e r i e s i n B u s i n e s s Economics #1. ( Van couve r : B r i t i s h Co l umb i a T e l e phone Company) . P e n c a v e l , J . (1971) "The Demand f o r Un ion S e r v i c e s : An E x e r c i s e . " I n d u s t r i a l and Labo r R e l a t i o n s Rev iew 24 , 180 -190 . (1981) The E m p i r i c a l P e r f o rmance o f a Model o f T r ade Un i on B e h a v i o r . S t a n f o r d U n i v e r s i t y , mimeo. P e s a r a n , M.H. and A . S . Deaton (1978) " T e s t i n g Non -ne s t ed N o n l i n e a r R e g r e s s i o n M o d e l s . " E c o n o m e t r i c a 46 , 6 77 - 694 . Ramsey, J . B . (1974) " C l a s s i c a l Model S e l e c t i o n Through S p e c i f i c a t i o n E r r o r T e s t s . " In P. Zarembka ( e d . ) , F r o n t i e r s o f E c o n o m e t r i c s . (New Yo r k : Academic P r e s s ) . Rede r , M.W. (1952) "The Theory o f Un ion Wage P o l i c y . " Rev i ew o f Economics and S t a t i s t i c s 34 , 3 4 - 4 5 . - (1960) " Job S e c u r i t y and t h e Na tu re o f Un ion P o w e r . " I n d u s t r i a l and Labo r R e l a t i o n s Rev iew 13 , 3 49 - 362 . Ree s , A. (1977) The Economics o f T r ade U n i o n s . ( C h i c a g o : U n i v e r s i t y ot C h i c a g o P r e s s ) . R e y n o l d s , M.O. (1981) "Whatever Happened t o t h e Monopo ly Theory o f L abo r U n i o n s ? " J o u r n a l o f L abo r Re s ea r c h 2, 1 6 3 - 1 7 3 . Ro sen , S. (1970) "Un i on i sm and O c c u p a t i o n a l Wage S t r u c t u r e i n t h e U n i t e d S t a t e s . " I n t e r n a t i o n a l Economic Rev iew 11 , 2 69 - 286 . R o s s , A . M . (1948) T rade Un ion Wage P o l i c y . ( B e r k e l e y : U n i v e r s i t y o f C a l i f o r n i a P r e s s ) . R o t h e n b e r g , T . J . and C . T . Leende r s (1964) " E f f i c i e n t E s t i m a t i o n o f S i m u l t a n e o u s E q u a t i o n S y s t e m s . " E c onome t r i c a 39 , 5 7 - 7 6 . Sawa, T . (1978) " I n f o r m a t i o n C r i t e r i a f o r D i s c r i m i n a t i n g Among A l t e r n a t i v e R e g r e s s i o n M o d e l s . " E c onome t r i c a 46 , 1 273 - 1291 . S t a t i s t i c s Canada (1964 -79 ) " S a w m i l l s and P l a n i n g M i l l s and S h i n g l e M i l l s . " Annual Census o f M a n u f a c t u r e s , C a t a l o g u e 3 5 - 204 . (O t t awa : Government o f C a n a d a ) . ( 1964 -79 ) "Veneer and P lywood M i l l s . " Annua l Census o f M a n u f a c t u r e s , C a t a l g u e 3 5 - 2 06 . (O t t awa : Government o f C a n a d a ) . (1979) Concep t s and D e f i n i t i o n s o f t h e Census o f M a n u f a c t u r e s , C a t a l o g u e 3 1 - 5 2 8 . (O t t awa : Government o f C a n a d a ) . ( 1975 -79 ) Consumpt i on o f P u r c h a s e d Fue l and E l e c t r i c i t y by t h e M a n u f a c t u r i n g , M i n i n g , L o g g i n g , and E l e c t r i c Power I n d u s t r i e s , C a t a l o g u e 5 7 - 2 0 8 . (O t t awa : Government o f C a n a d a ) . 145 (1963 -79 ) Employment , E a r n i n g s and H o u r s , C a t a l o g u e 7 2 - 0 0 2 . (O t t awa : Government o f C a n a d a ) . ( 1972 -79 ) F i x e d C a p i t a l F l ows and S t o c k s , C a t a l o g u e 13 -211 and 13 -568 (O t t awa : Government o f C a n a d a ) . (1980) F i x e d C a p i t a l F l ows and S t o c k s : B r i t i s h C o l u m b i a , C a t a l o g u e 1 3 - 2 1 1 , u n p u b l i s h e d ) . ( 1973 ,1978 ) H i s t o r i c a l Labou r F o r c e S t a t i s t i c s , C a t a l o g u e 7 1 - 201 . (O t t awa : Government o f C a n a d a ) . ( 1963 -79 ) S t a t i s t i c a l R epo r t on t h e O p e r a t i o n o f t h e Unemployment I n s u r a n c e A c t , C a t a l o g u e 7 3 - 0 0 1 . (O t t awa : Government o f C a n a d a ) . T s u r u m i , H. (1970) " N o n l i n e a r Two-S tage L e a s t Squa res E s t i m a t i o n o f CES P r o d u c t i o n F u n c t i o n s A p p l i e d t o t h e Canad i a n M a n u f a c t u r i n g I n d u s t r i e s , 1926 -1939 , 1 9 4 6 - 1 9 6 7 . " Rev iew o f Economics and S t a t i s t i c s 52 , 200 - 207 . Wood land , A . D . (1975) " S u b s t i t u t i o n o f S t r u c t u r e s Equ ipment and L abo r i n C anad i a n P r o d u c t i o n . " I n t e r n a t i o n a l Economic Rev i ew 16, 171 -187 .

Cite

Citation Scheme:

    

Usage Statistics

Country Views Downloads
Japan 4 0
Canada 3 0
China 3 0
United States 2 2
City Views Downloads
Tokyo 4 0
Halifax 3 0
Beijing 2 0
Shenzhen 1 0
Sunnyvale 1 0
Ashburn 1 0

{[{ mDataHeader[type] }]} {[{ month[type] }]} {[{ tData[type] }]}

Share

Share to:

Comment

Related Items