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

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WAGE AND EMPLOYMENT DETERMINATION IN A UNIONIZED THE IWA IN THE B . C .  WOOD PRODUCTS  INDUSTRY:  INDUSTRY  By FELICE B.A.  (Hon.),  F.  MARTINELLO  The U n i v e r s i t y  A THESIS SUBMITTED  of  Western  IN PARTIAL  Ontario,  FULFILLMENT OF  THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n THE FACULTY OF GRADUATE (Department  We a c c e p t  this  to the  of  Economics)  thesis  required  as  Q  Felice  F.  conforming  standard  THE UNIVERSITY OF B R I T I S H April  STUDIES  COLUMBIA  1984  Martinello,  1984  1978  In p r e s e n t i n g requirements  this thesis f o r an  of  British  it  freely available  agree t h a t  in partial  advanced degree a t  Columbia,  Library  shall  for reference  and  study.  I  f o r extensive copying of  p u r p o s e s may  department or  by  h i s or  be  her  g r a n t e d by  f i n a n c i a l gain  shall  not  be  Economics  The U n i v e r s i t y o f B r i t i s h 1956 Main Mall V a n c o u v e r , Canada V6T 1Y3  Date  2 8 September 19  of  Columbia  make  further this  thesis  head o f  this  my  It is thesis  a l l o w e d w i t h o u t my  permission.  Department o f  the  representatives.  copying or p u b l i c a t i o n  the  University  the  for scholarly  for  the  I agree that  permission  understood that  f u l f i l m e n t of  written  ii Abstract  A new d a t a Woodworkers industry  1963-79.  estimated  the behaviour  in  a unionized  union  inefficient  subject  chooses  industry  employment  union model)  and e m p l o y m e n t  set.  to the  wage-employment  (cooperative  industry subject  package  the  between  wages.  hypotheses the  level  and d e c r e a s i n g  real  that  the  substitutable  results.  function  its  function.  In t h e o t h e r bargain  union  is  model  about  wages  efficient  union  indifferent  real  elasticity  i n employment  maximization) is  increasing  in the workers'  about  production  with materials  technology  and c a p i t a l ,  are complements.  Industry  prices,  demand f u n c t i o n s  elasticity  t o maximize  is  0.7  in  real  alternative of  and t h e  union  and a 1% i n c r e a s e  behaviour  in  (rent  are rejected  as  are  to the a l t e r n a t i v e  wage  and  employment.  The e s t i m a t e d  but  union  t o t h e u n i o n wage and an  wages and employment  hypotheses  and wage b i l l  of  and  (monopoly  u n i o n and i n d u s t r y  t o a 1.5% d e c r e a s e  Popular  maximization  specified,  l a b o u r demand  A t 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  indifferent  real  employment  package.  wages and e m p l o y m e n t  is  are d e r i v e d ,  In one model  The e s t i m a t e d union o b j e c t i v e  substitution  products  and r e a c h , by some u n s p e c i f i e d m e a n s , an  wage-employment  wage.  International  C o l u m b i a wood  c h o o s e s t h e wage u n i l a t e r a l l y  function  The i n d u s t r y  of the  Two n o n - n e s t e d m o d e l s o f wage and  u s i n g t h e new d a t a  the  ojective  isolates  o f A m e r i c a and t h e B r i t i s h  determination  model)  set  input  cost  o f t h e demand f o r  functions  labour  shows t h a t  and m a t e r i a l s are not  s l o p e down. is  labour  less  and  concave  The  is capital  in  input  estimated  than minus  one i n  the  i i i  monopoly  u n i o n model  o f t h e demand f o r  labour  The c o o p e r a t i v e model  since  it  the cooperative models  so t h e u n i o n  on an e l a s t i c  is  argued t o  be t h e  outcome.  This  an e f f i c i e n t  u n i o n model  are tested  operating  portion  function.  u n i o n model  predicts  is  against  is  one  supported another.  appropriate  preference  by t h e d a t a when t h e  for two  i v  Table of  Contents  Abstract  ii  List  of Tables  vi  List  of  vii i  Figures  Acknowledgements  ix  Chapter  Introduction  1  C h a p t e r 2:  Survey  3  Chapter  The D a t a  1:  3:  Institutional  of L i t e r a t u r e  23  Setting  23  Labour  26  Capital  Services  26  Materials  30  Output  31  Alternative  Wage  32  S c a l i n g t h e Data  33  Two F l a w s C h a p t e r 4:  in the  Data  The Wood P r o d u c t s  Translog  35 Technology  Specification  Conditional  Cost  Function  36 37  Specification  D i s c u s s i o n and C o m p a r i s o n o f Results with other Studies  40  the 49  V  Chapter  5:  Union M o d e l s :  Cost  Minimization  53  Monopoly U n i o n Model  61  Cooperative  72  U n i o n Model  Non-Constant  Returns t o Scale  80  Summary  88  Appendix t o Chapter Chapter  6:  5  Union M o d e l s :  91 Profit  Maximization  97  Monopoly U n i o n Model  99  Cooperative  106  U n i o n Model  Summary  Ill  Appendix to Chapter 6  112  Chapter  7:  On C h o o s i n g a T r u e Model  116  Nested Test  121  L i k e l i h o o d Comparison Test  123  Non-nested  125  Test  Summary Chapter  8:  Appendix:  128 Conclusion  More on t h e D a t a  Bibliography  130 133 141  vi  List  Table  Table  Table  Table  Table  Table  Table  Table  Table  Table  Table  Table  Table  Table  of  Tables  I:  II:  III:  IV:  V:  VI:  VII:  VIII:  IX:  X:  XI:  XII:  XIII:  XIV:  Estimated C o e f f i c i e n t s Cost Function  of the  Translog 41  Estimated C h a r a c t e r i s t i c s of the Technology: T r a n s l o g C o s t F u n c t i o n and Exogenous Wages  42  Estimated C o e f f i c i e n t s Cost Function  46  of  the  Conditional  Estimated C h a r a c t e r i s t i c s of the Technology: C o n d i t i o n a l C o s t F u n c t i o n and Exogenous Wages  47  Collective Interior  56  Agreements Regions  Estimated C o e f f i c i e n t s U n i o n Model  for  of  the Coast  the  and  Monopoly 66  E s t i m a t e d C h a r a c t e r i s t i c s of Union 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 : Monopoly Union Model and No Dummy V a r i a b l e s  67  E s t i m a t e d C h a r a c t e r i s t i c s of and P r o d u c t i o n T e c h n o l o g y : Model w i t h Dummy V a r i a b l e s  68  Union P r e f e r e n c e s Monopoly Union  M a x i m i z e d 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 the Union Models: Constant Returns t o Scale  70  Estimated C o e f f i c i e n t s U n i o n Model  75  of the  Cooperative  E s t i m a t e d C h a r a c t e r i s t i c s of Union 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 U n i o n Model and No Dummy V a r i a b l e s  76  E s t i m a t e d C h a r a c t e r i s t i c s of Union 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 : Cooperative U n i o n Model w i t h Dummy V a r i a b l e s  77  Estimated C o e f f i c i e n t s : Non-Constant t o S c a l e w i t h Dummy V a r i a b l e s  84  Returns  E s t i m a t e d C h a r a c t e r i s t i c s of Union 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 : Monopoly Union Model w i t h 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 n d Dummy V a r i a b l e s  85  vii  Table  Table  Table  Table  Table  Table  XV:  XVI:  XVII:  XVIII:  XIX:  XX:  E s t i m a t e d C h a r a c t e r i s t i c s of Union 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 : Cooperative U n i o n Model w i t h 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 and Dummy V a r i a b l e s  86  M a x i m i z e d 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 the Union Models: Non-Constant Returns t o S c a l e w i t h Dummy V a r i a b l e s  87  E s t i m a t e d C o e f f i c i e n t s of t h e Monopoly C o o p e r a t i v e Union Models: Profit Maximization  103  and  E s t i m a t e d C h a r a c t e r i s t i c s of Union 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 : Monopoly Union Model w i t h P r o f i t M a x i m i z a t i o n  104  E s t i m a t e d C h a r a c t e r i s t i c s of Union 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 : Cooperative U n i o n Model w i t h P r o f i t M a x i m i z a t i o n  110  Means and S t a n d a r d  134  Deviations  of the  Data  ...  vi i i List  of  Figure  Figures 1  5  Figure 2  17  Figure 3  59  Figure 4  64  Figure 5  119  Figure 6  135  Figure  136  7  ix  A c k n owTedgemen t s  I would l i k e Erwin  Diewert,  and h e l p f u l  t o thank  Craig  t h e members o f my c o m m i t t e e  Riddell,  suggestions.  and Ken W h i t e ,  I would a l s o  for  her a s s i s t a n c e w i t h the c o l l e c t i o n  his  assistance  Financial  with the n o n - l i n e a r  support  like  their  t o thank  sage  Karen  advice Kalderbank  o f t h e d a t a and D a v i d Ryan  monitor  from the S . S . H . R . C .  for  -  is  software  gratefully  and  for  estimation.  acknowledged.  1  Chapter 1 Introduction  In a u n i o n i z e d resentative  of  industry  labour.  the  union  Individual  the s o l e  workers  and e x c l u s i v e  and f i r m s  of  employment.  conditions  of  e m p l o y m e n t w i t h t h e u n i o n and t h e n e g o t i a t e d  all  workers  forced to accept  in  the  are forced to  do n o t  conditions  cover  Firms  is  industry  (bargaining  the negotiated conditions  negotiate  unit).  o r work  rep-  negotiate  the terms  Workers  are  outside  the  and f i r m s  in  industry. Theoretical situation  abound.  these models.* behaviour  models  of  However,  annual  unions  industry  d a t a on t h e  wood p r o d u c t s is  little  empirical  The p u r p o s e o f t h i s and f i r m s  Two p o p u l a r m o d e l s unionized  of the behaviour of unions  is  International in  Woodworkers  British  Columbia,  determination and e s t i m a t e d of America  1963-79.  a monopoly u n i o n model, where t h e union chooses  maximize  its  objective  labour function.  function  subject  to the  The f i r m c h o o s e s t h e l e v e l  of  the  in  a  test.  o f wage a n d e m p l o y m e n t specified,  has been done on  t o put models  t o an e m p i r i c a l  are presented,  industry  thesis  work  this  using  (IWA)  and  The f i r s t  t h e wage  industry's  the  model  to  demand  o f employment  for  subject  to  2 t h e u n i o n wage and an i n e f f i c i e n t model, the  herein  outcome  results.  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 and i n d u s t r y  bargain  The  u n i o n model  second assumes  a b o u t wages and employment t o  that  reach  1.  F a r b e r ( 1 9 7 8 ) , D e r t o u z o s and P e n c a v e 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 M a C u r d y a n d P e n c a v e l ( 1 9 8 3 ) a r e n o t a b l e e x c e p t i ons.  2.  See, f o r example, monopoly m o d e l s .  Cartter  (1959),  pp.  77-94 f o r  an e x p o s i t i o n  an  of  2  outcome on t h e  contract  curve,  thereby  insuring  an  efficient  outcome.^ The e s t i m a t i o n  of the models  preferences  and a l l o w s  be t e s t e d .  The e s t i m a t i o n  the technology  of the  provides  common p r o p o s i t i o n s  B.C.  model in  evaluated.  wood p r o d u c t s  industry.  The m o d e l s  provides  the empirical  a r e compared t o of the  of the  union  also  of the observed behaviour  IWA's  preferences estimates  performance  see w h i c h i s  of  of  the  IWA and wood p r o d u c t s  to  true  industry  B.C. Chapter  literature tions  2 presents  a survey  and d e f i n i t i o n s  assumptions  of  exogenous  reported  Chapter  specification  4.  B.C.  wood p r o d u c t s  input  and e s t i m a t i o n  cost minimizing  and p r o f i t  Chapter 7 presents and c o n c l u s i o n s  prices  Chapters  maximizing  a r e drawn i n  industry,  empirical  sources,  study.  behavior,  are  derivation,  by t h e  assuming  industry.  t o c h o o s e b e t w e e n t h e two u n i o n  Chapter  of  the  o f t h e two u n i o n m o d e l s behaviour  descrip-  Estimates  under  and p r i c e t a k i n g  5 and 6 show t h e  results  the attempt  and  Chapter 3 provides  of the data used i n the  of the  in  of the t h e o r e t i c a l  on u n i o n m o d e l s w h i l e  the technology  3.  about  of the models  Once t h e m o d e l s a r e e s t i m a t e d , each i s  estimates  models  8.  S e e , f o r e x a m p l e , De M e n i l ( 1 9 7 1 ) , p p . 1-27 o r H a l l ( 1 9 7 9 ) 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 .  and  Lilien  3  Chapter 2 Survey of the Literature  This chapter surveys the theoretical economic models of union behaviour.  and empirical l i t e r a t u r e on  A truly exhaustive  requires a study of bargaining and strike theories.  survey  These topics are  outside the scope of this project and will therefore be mentioned briefly  rather than surveyed  carefully.  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. the union is the bargaining agent for all  If  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, u n i l a t e r a l l y wage which maximizes its objective function.  chooses the  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 p r o f i t possible given that union wage.  This amount of employment is shown  by the demand for labour function.  Thus, the union chooses the wage  4  which maximizes demand f o r  labour  In F i g u r e TQ,  and T  curves; model,  its  and CC i s  DD i s  isoprofit the  units  Formally,  is  variables  another  m o s t commonly  According to the  c a n be  > 0, w > 0 ] , U(X) of  variables rate  of  labour function,  which a f f e c t  by t h e  labour  are union  1  a wage w^ and t h e f i r m s  the average  Different  appropriate  react  function;  indifference monopoly t o w,  by  written  : weZ],  a vector  t h e demand f o r  demand f o r  u^ and u  curve.  t h e m o n o p o l y model  X is  to the  labour.  w h e r e Z = [w : L ( w , Y )  L(w,Y)), w is  curves;  contract  of  Max[U(X)  function,  subject  the appropriate  the union chooses  employing  function  function.  1,  are  2  objective  types  the  is  the u n i o n ' s  (usually  i n c l u d i n g w and  compensation and Y i s  demand f o r  labour  objective  paid to  a vector  of  labour,  exogenous  function.  o f monopoly models a r e d i f f e r e n t i a t e d  objective  function  c i t e d m o n o p o l y model  [U(X)] which is  the  L(w,Y)  is  f r o m one  specified.  rent maximization  The model  where  U(X)  A is  the o p p o r t u n i t y  labour  1.  = [w - A ] L ,  cost  of  (2.1)  labour's  t i m e and L i s  t h e amount  of  1 employed.'  C a r t t e r ( 1 9 5 9 ) , p. 8 0 , D u n l o p ( 1 9 4 4 ) , p . 4 1 , R o s e n ( 1 9 7 0 ) , R e y n o l d s ( 1 9 8 1 ) , and M c D o n a l d a n d S o l o w ( 1 9 8 1 ) , p p . 8 9 7 - 8 9 9 a l l discuss t h i s model. McDonald 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  suggested extension t o the rent maximization  t o have t h e u n i o n maximize  rents  minus  the cost  of  model  providing  is  union  2 services.  Hence, the u n i o n ' s  U(X)  where C ( L , P )  is  = [w - A ] L -  popular  In t h i s  case,  models 164)  prices  of  providing  P.  Finally,  objective  union  function  services  equation  2.1  maximization is  given  the  model.  by  and i n t e r p r e t a t i o n  rent  of  the  o f much c o n t r o v e r s y . maximization  models  rent  maximization  Reynolds  are  where N i s w o r k , U(w) employment Maximizing equivalent  p.  wealth  + [(N-L)/N]U(A)  t h e number o f u n i o n members, D i s t h e d i s u t i l i t y o f 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 i s a l l o c a t e d t o u n i o n members by a l o t t e r y . t h e M c D o n a l d and S o l o w o b j e c t i v e f u n c t i o n i s to maximizing U(X)  since  = (L/N)[U(w)-D]  (1981,  reasonable  b e c a u s e u n i o n d e c i s i o n m a k e r s w a n t t o m a x i m i z e t h e amount o f  U(X)  L  (2.3)  foundations  that  to  nests  = wL.  h a v e been t h e s u b j e c t  suggests  (2.2)  m o n o p o l y m o d e l , t h e wage b i l l  the union's  U(X)  The m i c r o  input  is  C(L,P)  t h e minimum c o s t  u n i o n members g i v e n another  maximand  = [U(w)-D-U(A)]L  N and D a r e assumed t o  = [U(w)  -  U ]L 0  be e x o g e n o u s t o t h e p.  269,  Lewis  union.  2.  S e e , f o r i n s t a n c e , Rosen ( 1 9 7 0 ) , M a r t i n (1980), pp. 58-60.  (1959),  and  3.  C a r t t e r (19.59), p. 8 2 , Rees ( 1 9 7 7 ) , p . 5 . N o t e t h a t t h i s model i s d i f f e r e n t f r o m 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-membership f u n c t i o n w h i c h c o n s t r a i n s the union's choices.  7  w h i c h c a n be d i s t r i b u t e d premise  that  t h e model  specifying  the  recipients  premise  somewhat d i f f i c u l t  (1980) to  is  to themselves  is  who e x p l o r e s  earn  rents  rents  rents which the  to maintain  carefully  given  of a  and, t h e r e f o r e ,  the  boss dominated  justify  the decisions  (or  racket)  and e a r n s  all  the  income.  union  The u n i o n c a n be t h o u g h t  opportunity  difference extracted  cost  and r e - s e l l s  between t h e u n i o n through  initiation  The s e c o n d a s s i g n m e n t dominated  u n i o n where w o r k e r s  The w o r k e r s mize t h e i r employees skills,  set  in  of the workers,  The  boss  chooses  first  makes the his  as a f i r m w h i c h h i r e s  labour  at  it  to  rate.  The  firms  at the  fees  and u n i o n rights  share a l l  opportunity  cost  is  dues.  t o earn  the  union  rents  Union l e a d e r s  rents  is  amongst rents  and e n f o r c e  the  worker  themselves.  so as t o  can be  maxi-  considered  b e i n g p a i d t h e m a r k e t wage f o r  and w o r k i n g t o n e g o t i a t e  earn  of  and l a b o u r ' s  rents.  rights  maximization  order to maximize  t h e u n i o n wage t o m a x i m i z e t o t a l  income from t h e  to  197-198).  The b o s s  rate  of the  rights  where t h e u n i o n  rents.  rents  Martin  of the  rent  (1959, pp.  union  This  union.  which  h a v e been s u g g e s t e d by L e w i s  without  t h e work o f  of the  predict  basic  union e a r n s .  how t h e a s s i g n m e n t  the behavior  u n i o n wage w h i c h m a x i m i z e s  its  conclusions  and e x t r e m e a s s i g n m e n t s  the  all  can a f f e c t  of the  correct  Reynold's  Two a l t e r n a t e  models, is  very  can p r o d u c e  or o t h e r s .  their  t h e wage c h o s e n  by  the  workers. Neither the  o f t h e two e x t r e m e a s s i g n m e n t s  rent maximization  established  folklore  models  (1948)  unions.  have been c r i t i c i z e d  b e i n g t h e most  influential.  rights  which  correspond too well  about t h e n a t u r e of  rent m a x i m i z a t i o n models Ross  appear t o  of  justify  with  As a r e s u l t ,  by many a u t h o r s  the the  with  8  The c o n c e p t o f by Ross p. for  (1948,  pp.  to  rejected  28),  dominated union" i s Dunlop  (1944,  They m a i n t a i n t h a t  firms  Hence, t h e boss is  22,  78) and o t h e r s . resale  a "boss  and c a n n o t ,  therefore,  do n o t  (1959,  purchase  be m o d e l l e d  of  completely  32), Cartter  unions  dominated j u s t i f i c a t i o n  by t h o s e  p.  rejected  as  labour  firms.  rent maximization  models  critics.  T h e w o r k e r d o m i n a t e d e x t r e m e a p p e a r s t o be much c l o s e r (and o t h e r  critics')  dominated extreme. the  notion  of  However,  reasonableness  the  m a x i m i z i n g u n i o n . The f i r s t  of  Ross'  unions  than the  boss  t h r e e s t r o n g arguments  a r e made  against  of the worker  nature  to  dominated j u s t i f i c a t i o n  argument p o i n t s  out t h a t  of a  union  rent  workers  4 a r e n o t a homogeneous union  leaders  remain a p a r t there  exist  another.  have d i f f e r e n t This a union benefits  of the u n i o n . subgroups  (1948,  and f i l e  to o f f i c e  Further,  within  members  by t h e m e m b e r s , each of t h o s e  o f members w h i c h a r e d i f f e r e n t  pp. 31-32)  and o f t e n  maintains  conflicting  goals  that for  but  many l o c a l  choices  differ  public across  goods. groups,  who  groups from  the d i f f e r e n t the  and  one  groups  union.  p r o b l e m becomes much more s e r i o u s when one r e c o g n i z e s  produces of  There a r e rank  who h a v e been e l e c t e d  other  Ross  group.  The p r i v a t e  costs  and t h e s e p r i v a t e  that  and costs  and  5 benefits  are d i f f e r e n t  Ross conflicting  (1948)  from the  argues t h a t  preferences (1948),  of  pp.  it  collective is  different  costs  and  benefits.  unreasonable to believe groups,  as w e l l  as  that  the  the  4.  See Ross  31-32.  5.  See Ross ( 1 9 4 8 ) , p p . 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 a n d 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 o u t t h e d i f f e r e n c e b e t w e e n t h e m e m b e r ' 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 goals.  9  differences  between p r i v a t e  a c c o m m o d a t e d and e x p r e s s e d  and c o l l e c t i v e by t h e  simple  incentives,  can  rent maximizing  be  objective  function. The s e c o n d a r g u m e n t exist  different  some s o r t union  of  groups  process  actually  concile  is  The t h i r d  again of  argument  effects  of  in  pp. 79-80)  unable or exogenous  makers  process  in  variables  t h e employment  To s u m m a r i z e , c a n be f r u i t f u l l y the  Ross  See A t h e r t o n  7.  See Ross  (1973),  (1948),  that  pp.  of  union  reand  union  do n o t model  this  decision  r e n t m a x i m i z a t i o n models  uncertainty  wage r a t e s makes  adjust  effects  of  about the it  are  wage b a r g a i n s . ^  for  (among o t h e r s ) as r e n t  p.  79-80.  Ross  union  any  changes  and  decisionneglect  rates.  rejects  maximizing  the  idea that  agents.  dominated union  20 and Ross  for  the  Hence, t h e  b e t w e e n wages and employment wage  ultimate  impossible  o b s e r v e d employment  negotiated  modelled  of t h e  t h e d e c i s i o n makers w i t h i n  n o t i o n of a boss  6.  any model  w h i c h may h a v e o c c u r r e d .  of  the  behaviour.  that  no r e l a t i o n effects  the  t h e employment  to  goals,  or system used t o  the behaviour  included  negotiated  unwilling  observe  completely  affects  asserts  asserts  there  needed t o choose which g o a l s  argued t h a t  union  the union to consider  are  goals  Given that  u n i o n w h i c h have d i f f e r e n t  The p a r t i c u l a r  be e x p l i c i t l y  i n a d e q u a t e models  (1948,  the  The r e n t m a x i m i z a t i o n m o d e l s  so i t  employment  from the f i r s t .  or system i s  the c o n f l i c t i n g  behaviour. process  within  pursues.  must t h e r e f o r e ,  follows  Ross  and a r g u e s  (1948), pp.  32,  unions rejects  convinc-  37-40.  10  ingly  that  a worker dominated union w i l l  m a x i m i z i n g an o b j e c t i v e The f i n a l m i z i n g models argues  that  efficient  function  bers  (1980).  if  be g i v e n  the  rights exist,  that  to  rents  then  all  and t h e  Martin's  if  (a)  to Martin  the  and a r e t r a n s f e r a b l e ,  market  (c) for  monitoring  leaders  mize the t o t a l  (b)  rents  then  is  A number o f m o d e l s w h i c h n e s t been p u t t o an e m p i r i c a l Pencavel  (1981),  printing  operations  (ITU).  Only the  (1946-1965) are not  are  using  annual  involving  results  data the  reported,  appropriate  for  the  position  union's  dominance occurs  strikes.  This  substitutes of  democratic  for  the  argue that union  advertisers  results (e.g.,  up an i n v e n t o r y  (1981)  have and  newspaper  Post  Union  local  newspapers Post.  t h e m o n o p o l y model  holds  flyers) The  homogeneous  bar-  a r e uncommon.  The  vulnerability  from the e x i s t e n c e  of output.  is  a much s t r o n g e r  and s t r i k e s  radio or  and t h e members a r e q u i t e  maxi-  model  Typographical  because of the newspaper's  vulnerability  building  and P e n c a v e l  d a t a on t h e C i n c i n n a t i  than the newspapers  rights  efficient  rent maximization  from the C i n c i n n a t i  (1981)  For  13)  b e h a v e s o as t o  f r o m a number o f  ITU b e c a u s e t h e  gaining  an  s i n c e t h e d a t a from the o t h e r  and P e n c a v e l  are  rents.  for those  and ( d )  International  obtained  above  union.  by D e r t o u z o s  as g o o d a s t h e e x c e l l e n t  Dertouzos  bility  test  enough  (1980, p.  market  union w i l l  accruing to the  Martin  a r e a s s i g n e d t o u n i o n mem-  costless,  the  maxi-  and i f  outlined  Martin  an e f f i c i e n t  leaders  exists,  rents  were  rent  maximize t o t a l  case.  to  it  Essentially,  the objections  simplest rights  of  are t r a n s f e r a b l e ,  union w i l l  if  2.1.  will  consider  exists,  equation  reasonableness  markets  specifies  b e h a v e as  word on t h e t h e o r e t i c a l  o v e r c o m e by t h e m a r k e t s example,  like  not  of  very  and t h e ITU i s  (i.e.,  close  impossi-  also  they  to  very  are  all  11  printers).  Therefore  there  s h o u l d be few d i v e r g e n t  b e t w e e n members and l e a d e r s  and b e t w e e n d i f f e r e n t  Three b a s i c models are e s t i m a t e d . following  Stone-Geary  minimizing  objective  demand f o r  U(w/p,L)  labour  e  an i n d e x  consumer  r  is  price  index  of machinery  which  reflects  equation  2.4  tion models. estimates of  that  of  union  of  test;  the  rent  visory  workers  in the  The s e c o n d model equations  for  l n w and  Q is  preferences  that  the  output  function retail  the  a dummy  wholesale  variable  and w a g e - b i l l  Clearly maximiza-  The e s t i m a t e d  between  real  Further,  union  is  is  employ-  estimated  indifferent  maximization  hourly  9 = . 5 , B = 0; earnings  of  to  the  hypo-  using a l i k e l i h o o d  hypothesis,  of the  not  it  FIML  elasticity  wages and  .69.  and  ratio where A  non-super-  trade.  specifies InL:  is  by  f o r w and L a r e d e r i v e d  rejected  maximization  measured  with other newspapers.  The wage b i l l  is  (2.5)  4  and D i s  are obtained.  and A > 0 .  d e f i n e d as a l i n e a r  3  rent maximization  e = .5 and A = B = 0 ,  as i s  prices,  a t t h e same m e a n , i s  employment,  cost  + b Q + b D  1  of mergers  parameters  and  the  (2.4)  and e q u i p m e n t ,  both the  specifies  the union,  the p r i c e of newsprint,  0 < 9 < .5, indicating  thesis,  is  of the  evaluated  level  2  Reduced form e q u a t i o n s  substitution  ment,  1  the e f f e c t s  nests  2  of  linage,  model  members.  1 _ 9  + b (r /r )  1  advertising  for  groups of  function:  L = bg + b ( w / r )  where p i s  function  = (w/p-A) (L-B)  1  The f i r s t  preferences  the following  log-linear  reduced  form  12  lnw = a  Q  + ajlnp  + a lnr  InL = b  n  + b.lnp + b.lnr.  2  + a lnr  1  3  2.6 and 2.7 a r e e s t i m a t e d  and y i e l d  estimates  The t h i r d model dition  of the maximization  U(w/p,L)  objective  first  y)(l  marginal labour  con-  than t h e r e d u specified;  (2.8)  1 + T 1  + n ) " , 0 < y < 1, a n d X, n < 0 . 1  X = n = -1 implies  specification  is linear  If  a Cobb-  equals  i s that  problem i m p l i e s  that the  t h e s l o p e o f t h e demand f o r  The s l o p e o f t h e demand f o r l a b o u r  t o be ( e ° ^ ) / r ^ .  the log of the  i n l n w , l n p , a n d I n L . The  of the maximization  rate of substitution  specified  with  form.  condition  function.  is  1  i s obtained while  rate of s u b s t i t u t i o n  order  function  order  1  The a d v a n t a g e o f t h e a d d i l o g marginal  rather  1  1  functional  the log of the f i r s t  ya+xrV/p) "^ ( l - y ) ( l + T ) " L  u  X = TI a CES f u n c t i o n  techniques,  o f wages and employment  problem i s estimated  w h e r e K = - ( l + X ) " - (1 -  Douglas  in that  An a d d i l o g  = K +  (2.7)  variables.  i s novel  ced form e q u a t i o n s .  (2.6)  g  u s i n g OLS and FIML  of the e l a s t i c i t i e s  t o t h e exogenous  4  + b _ l n r _ + b . l n Q + b D.  Equations  respect  + a "lnQ + a D  2  Hence t h e f i r s t  function  order condition  is  c a n be  r e w r i t t e n as  lnw/p = ( l / x ) ( l n [ ( l - y ) / y ]  Non-linear  + lnp/r.  2SLS i s u s e d t o e s t i m a t e  The e l a s t i c i t y  of substitution  + nlnL + oQ).  the parameters  o f union preferences  (2.9)  of equation 2 . 9 . between  real  13  wages and employment while  the  estimates  -.045  respectively.  restrictions  is of  e s t i m a t e d t o be u,  A,  n, and a a r e  Clearly,  implied  .469 at t h e  (1954)  rent maximization and A t h e r t o n  institutional members'  goal  goals, its  the union  retains  objective  function  net  U(w,L,D,S)  where D i s is  the  level  C(L,P,S) given  the  is  of  the  and t h e  maximizes  models  union  the bargaining  services  decertified  by t h e  workers.  is  arguments  Berkowitz where  pursued.  needed t o a c h i e v e  is  from  The  of the w o r k e r s .  about  its  union  union that  The  union's  (2.10)  earnings  collected  by t h e u n i o n t o e a c h  providing  is  also not  services  utility.  is  lexicographic  S to L  variables  workers  the union  is  so t h a t  in the  is  profits  and  extended to the union  not  general length  economic  preferences  and e a r n i n g  S  worker,  and t h e s t r i k e  included  The model  as d u e s ,  a number o f more  homogeneous,  elections  exogenous  proposes  outcomes  assigned  (de)certification  assumed t o m a x i m i z e  of  pp.80-157)  bargaining  The u n i o n  the  to the c o n s t r a i n t  and D and S must be s u c h t h a t  models where t h e membership  uncertainty  goal  rights  provided  P,  winning  of the  p r o p o s e a model  subject  of w o r k e r ' s  prices  (1973,  the  written  input  calculus.  aspects  = wDL - C ( L , P , S ) ,  proportion  and  all  a l l o w e d t o be d i f f e r e n t  revenue or p r o f i t  t h e minimum c o s t  Atherton  is  institutional  c a n be  satisfy  have been p r o p o s e d .  (1973, pp. 71-80) of  do n o t  .167,  2.8.  A number o f m o d e l s w h i c h i n c o r p o r a t e against  .91, -2.146,  the estimates  by e q u a t i o n  sample mean,  over is include  maximizes  14  some l e x i c o g r a p h i c election  and e x p e c t e d  abstraction Further,  is  very  Atherton  equilibria  exist.  Farber  (1978)  of  combination  leaders  of the p r o b a b i l i t y  profits.  Unfortunately  h i g h and no t e s t a b l e  (1973)  does not  develops  show t h a t  All  and f o r  all  receive  u n i o n wages w h i l e w o r k i n g ,  health  and w e l f a r e  retired. of  their  is  income  union j o b s .  benefits  of workers  is  re-election.  Therefore,  benefits  leaders union  a function package,  leaders  pension  and h e a l t h  output,  employer.  so t h e union  which maximizes Farber  926)  leaders  estimates  (UMW) i n  argues t h a t  u n i o n was d o m i n a n t  the  contributes  h i s model  a coal  industry  are  workers  differently. of  their  labour  worker's function.  benefits  health  a fixed  and  is  assumed  and p e n s i o n charge  per  funds  unit  c h o o s e t h e wage and o u t p u t  tax  utility.  u s i n g annual  industry  t h e m o n o p o l y model in  union  made t o t h e  actually  coal  package  and  value  so y o u n g and o l d  and w e l f a r e  t h e median aged w o r k e r ' s  (1978)  Mine Workers p.  The e m p l o y e r  jobs  and when t h e y  t h e m e d i a n aged  The v a l u e  by t h e  a once  c h o o s e a wage and h e a l t h  t o t h e demand f o r  to the c o n t r i b u t i o n s  are  when r e t i r e d  maximize the p r o b a b i l i t y  subject  be e q u a l  preferences  of the present  benefits  expected u t i l i t y  to  voting  a v e r s e and f a c e  are working  package which maximizes  of the  made.  where t h e  benefits  re-  of  and u n i o n members  risk  pension  same w a g e , h e a l t h and p e n s i o n union  level  W o r k e r s who w i n u n i o n  when t h e y  s t r e a m and b e n e f i t s  assumed t h a t  pension  for  The u t i l i t y  value the It  lottery  are equally  are  any o f t h e  a much s i m p l e r model  workers  leader's  the model's  predictions  and members a r e a l l o w e d t o d i f f e r  n o t homogeneous.  of the  d a t a on t h e  (1947-1973). is  appropriate  Farber  (1978,  because  made up o f many s m a l l  United  the  firms.  15  Hence i t  is  plausible  t o assume t h a t  the union  sets  the  wage  unilaterally. The e s t i m a t e d ting  that  union  index  of  t h e mine w o r k e r s  jobs  this  indicates  relative were  that  risk  risk  aversion  averse.  the union  is  2.98,  Given the  b e h a v e d as i f  indica-  lottery it  for  considered  Q t h e employment is  effects  estimated to  be 3.5%-4.5%,  v a l u e d 40% h i g h e r Farber voting  that  t h a n wage  (1978, p.  equilibrium  of the majority single  o f wage d e m a n d s .  932)  voting equilibrium  u n i o n member's  wages and o u t p u t point  prove t h a t  of  which  view).  the voting  the  is  in  kind  rate  were  will  are  i s s u e of whether  condition  that  variable.  preferences  taxes  payments  discount  payments.  A sufficient  peaked over a s i n g l e  member's  and n o n t a x e d  does a d d r e s s  exists.  The u n i o n ' s  be s i n g l e  Blair  specified  existence  preferences  (1978, p.  932)  (from the  and C r a w f o r d  in  Farber  be  argues  peaked o v e r t h e  Pareto optimal  equilibrium  the  the v o t e r ' s  Farber  Unfortunately  for  the  set  of  union (1983)  (1978)  does  not  exist. A final  g r o u p o f m o n o p o l y m o d e l s w h i c h do n o t  above m e n t i o n e d groups those  b a s e d on t h e c r i t i c i s m s  now be s u r v e y e d . objective  functions  the models roughly)  those  preferences  of  rent maximization included  reasonable  about t h e n a t u r e  a b o v e whose o b j e c t i v e  from the  are  are considered  in the  b a s e d on r e n t m a x i m i z a t i o n  of the  Monopoly models  f r o m any a s s u m p t i o n  8.  (i.e.,  belong  of  is  group  but a r e not  unions.  function agents  in t h i s  models)  This  derived  within  the  if  two  and will their  derived  contrasts  with  (however  union.  W h e t h e r i t i s a p p r o p r i a t e t o s a y t h a t t h e u n i o n c o n s i d e r s employment e f f e c t s , or t h e c o l l e c t i v e b a r g a i n i n g framework m e r e l y c a u s e s u n i o n 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 ( a s d i s c u s s e d by R e d e r ( 1 9 5 2 ) ) i s n o t k n o w n .  16  The s i m p l e s t (1959,  models  pp. 83-90).  in t h i s  The u n i o n  m e n t , t h e wage b i l l  plus  private  union membership,  or  tion  employment.  o f wages and Atherton  interesting labour  in  that  is  the union  and a s t r i k e  an a r b i t r a r y  and employment,  level  of  strike  a certain  is  given  unemployment  increasing,  function. function  function  employ-  still  real  zero),  given  income  strike  chooses  a s s o c i a t e d w i t h e a c h wage r a t e  (possibly  for  objective  length of  labour  is  a demand  of a f t e r - t a x  r e a c h e d . The u n i o n  func-  which  The u n i o n ' s  of the  Cartter  insurance,  a m o n o p o l y model  by t h e demand f o r  length  by  quasiconcave,  two c o n s t r a i n t s :  length  However,  employment,  of  faces  increasing  endured b e f o r e a s e t t l e m e n t wage u n i l a t e r a l l y .  or public  presents  and a d e c r e a s i n g  surveyed  assumed t o m a x i m i z e w a g e s ,  some a r b i t r a r y ,  (1973, pp. 41-70)  function  function  is  group are those  is  function,  by t h e  the a  and a  strike  9 length  function.  objective All  is  function  of  the  (1959,  a function  from a s t a t u s  Cartter derations  levels  t o t h e two  of wages,  pp. 89-92)  quo p o i n t .  make t h e u n i o n  levels  that  variables. function  o f wages and  quo p o i n t  previous  asserts  unwilling  and o t h e r  a union o b j e c t i v e  the  in the  pp. 89-90)  t h e u n i o n maximand as a  employment,  The s t a t u s  combination  (1959,  in  its  constraints.  specify  specifies  of t h e changes  wage-employment  9.  subject  c h o o s e s t h e wage w h i c h m a x i m i z e s  t h e above mentioned models  function Cartter  The u n i o n  is  time  the  employment  union's  optimal  period.  internal  t o t r a d e wages  which  political  for  consi-  employment  or  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 r o m 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 e n d u r e 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 not s p e c i f i e d .  17  FIGURE 2  18  vice-versa.  Other t h i n g s  i n wages t o increases wages.  compensate  equal)  that  increases  order to  union  labour  small  point  wage p r e f e r e n c e  in the  objective  function  quo p o i n t  next  present  If  labour then the union w i l l period's  status  The s u r v e y comments. that  model  10.  quo  the  level  (other  things  all  of  or a r b i t r a t i o n  at t h e expense labour in  2, u ^  u^,  If  and u^ a r e  union  union  and  "wpp"  t h e demand maximize  "d" will  the present  and p o i n t  labour  quo p o i n t ,  then the union w i l l  represents  indifwage-  D^ r e p r e s e n t s  Point  employment  2 in  demand f o r  path.  of  decreases  A typical  shown i n F i g u r e  the status  of monopoly models  First,  increases  "c" is  2  wage-employfurther  period's  choose w  in  (1959)  i n wages.  is  Figure  period,  in  large  be t h e  be  its  status  demand f o r  "g" will  for  union  next  point.  the models  t h e f i r m and t h e u n i o n  chooses  sort  and  Cartter  by c h o o s i n g wage w^.  period.  curves  large decreases  decreases  the previous Q  the union's  labour  increases  decreases  When t h e demand f o r  Referring to  shown by D ,  small  l a r g e wage i n c r e a s e s  a union of t h i s  curves,  for  large  i n employment  indifference  the union accepts  only  space.  is  for  requires  decreases  i n shape.  employment.  suffer  indifference  is  in  equal)  f e r e n c e map f o r employment  the union  Leontief  the union presses  function  small  when t h e demand f o r  (other things in  for  the union  i n employment t o compensate i t  ment s p a c e a r e a l m o s t  small  it  In o t h e r w o r d s ,  asserts  equal,  is  complete save f o r  outlined  a few  general  a b o v e c o u l d be e x t e n d e d  b a r g a i n o v e r wages w h i l e t h e f i r m  employment.  Any s o r t  of  scheme c o u l d  be u s e d . *  0  bargaining The f i n a l  model outcome  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 a n d J o h n s o n (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 , or t h e 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 .  so  still or would  Nash  19  lie  on t h e demand f o r  labour  optimum,  the  point  reached  optimum,  the  point  where t h e  of a union)  intersects  Second, solutions. employment to  point  guishes  curve  labour  to  Figure in the  1,  models. union  identify  o v e r more t h a n j u s t  which determines be s t r u c k  demand f o r  their  This  the level labour  inferior  the  Pareto  wagesuperior  feature  distin-  of models; and  combination  the  the  c u r v e and  choose,  on t h a t  con-  achieved.  curve the union of wages.  function.  and t h e  absence  Pareto  and f i r m s  The f i r m s must  Therefore,  o f wages and t h e l e v e l  union  the  all  union  contract  outcome i s  contract  both the l e v e l  between t h e  that  the  a wage-employment  on t h e  or  from the other category models  firm's  (in  area are  solution.^  In c o o p e r a t i v e labour  clear  shaded l e n s  H e n c e , an e f f i c i e n t  their  it  union's  curve.  is  To r e a c h a p o i n t  must  labour  Referring  t h e monopoly models  off  of  and t h e  inefficient  curve.  forced  supply  above,  t h e monopoly models y i e l d  by some means o r a n o t h e r ,  bargain  in the models  " e " , t h e m o n o p o l y model  demanders o f  somewhere between t h e  t h e demand f o r  combinations  cooperative  tract  curve,  firms  in  a  of  order to  must be  bargain employment keep  the  12 firms  off  their  demand f o r  labour  functions.  11.  The m o n o p o l y 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 e m p l o y m e n t c o m b i n a t i o n s e x i s t s as l o n g as t h e l e v e l s e t s of the union o b j e c t i v e f u n c t i o n are not L e o n t i e f i n s h a p e , o r ( a s p o i n t e d o u t by P e n c a v e l ( 1 9 8 1 ) , p . 13 as l o n g 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 n o t i n d e p e n d e n t o f t h e l e v e l of employment.  12.  A f o r m a 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 m e c h a n i s m w h i c h c h o o s e s a u n i q u e p o i n t on t h a t c o n t r a c t c u r v e . While the former i s s t r a i g h t f o r w a r d , the l a t t e r r e q u i r e s the i n v o c a t i o n o f a b a r g a i n i n g scheme w h i c h i s , as n o t e d e a r l i e r , o u t s i d e the scope of t h i s s u r v e y . Hence a f o r m a l s t a t e m e n t o f t h e c o o p e r a t i v e model w i l l n o t be p r e s e n t e d .  20  M c D o n a l d and S o l o w similar  cooperative  function  of the  (1981)  a n d de M e n i l  models where t h e  rents  accruing to  (1971)  union's  present  objective  very  function  l a b o u r and an a r b i t r a t i o n  is  rule  a is  13 used t o  choose a p o i n t  reach t h e i r and t h e  level  from h i s related curve U.S.  contract of  model  on t h e  demand f o r  the  de M e n i l  it  into  right  static labour  model  due t o t h e  business  cycle.  (1979)  accruing to  ment.  the  Instead,  also  labour.  function  labour  of  equilibrium. sides  choose t h e i r  optimal  sides  maximize t h e i r  function,  both s i d e s  efficient  solution  and L i l i e n ' s  No b a r g a i n i n g 13.  is  choose the  wages  equation  Phillips  (1981)  digit  derive  to variations  function of  is  in  novel  about t h e l e v e l  (where t o t a l  levels  objective  of  bargaining  u n i o n i z e d two  reach t h e i r  employment)  The c o m p e n s a t i o n  curve with  T h e i r model  and f i r m s  choosing a compensation some f u n c t i o n  a wage  firm  which is  same l e v e l  curve  by  paid  to  efficient  c h o s e n s o t h a t when (i.e.,  subject of  when  t o the  the  employ-  compensation  employment  functions)  of  an  maxi-  in that  contract  supports  the  the  p r o p o s e a model w h e r e t h e u n i o n  bargain d i r e c t l y  unions  derives  M c D o n a l d and S o l o w  of t h e i r  and L i l i e n rents  The u n i o n and  The e x t e n d e d  responses  do n o t  Hall  a Phillips  hand s i d e .  industries.  u n i o n and f i r m s  is  (1971)  t h e n 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  comparative  mizes  curve.  c u r v e by b a r g a i n i n g o v e r b o t h t h e l e v e l  and e x t e n d s  manufacturing  Hall  contract  employment,  variables  is  on t h e  both  both  compensation  employment.  Hence,  an  reached. ( 1 9 7 9 ) model  mechanism i s  does not p r e d i c t  specified  to  a unique  choose a p a r t i c u l a r  outcome. point  on  M c D o n a l d and S o l o w ( 1 9 8 1 ) 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 function for the union. 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 rent maximization i n t h e i r model. See f o o t n o t e 1.  21  the contract of  curve.  collective  and s u p p l y  is  used t o e x p l a i n  b a r g a i n i n g when t h e r e  of  one f i n d s  c o o p e r a t i v e models which y i e l d  discarded economic  paradigm,  of  almost  to  factors  all  inefficient  efficient  one w o u l d e x p e c t  to exploit  textbook  all  t h e m o n o p o l y model argument  gains  economics.  assumed away i n  information  about  of union models  the  facts  demand  solutions.  Given the to  The a b i l i t y  from t r a d e  is  litera-  and  t h e m o n o p o l y model  usual be  of  a central  tennent  However,  an a r g u m e n t w h i c h  appeals  the n e o c l a s s i c a l  paradigm suggests  that  may be t h e more a p p r o p r i a t e claims  in the  solutions,  i n favour of the c o o p e r a t i v e model. agents  This  uncertainty  two t y p e s  monopoly models which y i e l d  neoclassical  is  some s t y l i z e d  labour.  In c o n c l u s i o n , ture:  The model  that  about the o t h e r  unions  side's  of t h e two  and f i r m s  objective  will  not  function  models.  have  enough  to exploit  all  14 the gains costs  from t r a d e .  of t r a n s m i t t i n g  bluffs,  threats,  both s i d e s  to  information  available  bargaining  and f a l s e  gains  and o t h e r  does  Thus, and t h i s  raise  does  t h e m o n o p o l y model  to  be a p p r o p r i a t e .  See P e n c a v e l  will  from the  u s e d by  contribute  a great  one c a n e x p e c t imperfect all  the  deal  imperfect  information of  the  trade.  it  14.  However,  bargaining t a c t i c s  advantages  model,  indeed cause unions  may a r i s e  t o be u n a b l e t o e x p l o i t  W h i l e t h e above argument cooperative  information  information.  and f i r m s  and f i r m s from  of  information.  between u n i o n s  may c a u s e u n i o n s  lack  and r e c e i v i n g  deceptions,  gain  of uncertainty  This  nothing to  and f i r m s  (1981),  p.  to 13.  a valid  suggest  against  why one s h o u l d  Imperfect  deviate  criticism  information  f r o m an e f f i c i e n t  the  expect may  solution.  22  However, should  t h e argument  does n o t  i m p l y t h e monopoly  be u s e d a g a i n s t information,  solution.  t h e monopoly m o d e l .  or attempts  at  deception  t o m i s p e r c e i v e t h e demand f o r wage r a t e .  explain  Therefore,  labour  imperfect  why i m p e r f e c t  Further,  information  t h e same a r g u m e n t may  Uncertainty,  imperfect  by t h e f i r m may c a u s e t h e function  information  and c h o o s e a  does not  union  suboptimal  aid the  choice  15 o f t h e more a p p r o p r i a t e  15.  model.  One c o u l d a r g u e : (a) both models a r e r e a s o n a b l e a p r i o r i , ( b ) t h e m o n o p o l y model has l o w e 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 h a n 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 u n i o n p o s s e s s o n l y imperfect information. T h e r e f o r e t h e m o n o p o l y model i s more appropriate. I a g r e e w i t h ( b ) and ( c ) , b u t am u n c o n v i n c e d t h a t (a) i s t e n a b l e .  23  Chapter  3 The  This data,  outlines  and d e s c r i b e s  data.  The d a t a  (mills) (i)  chapter  set  consists  (S.I.C.  2511),  Observations  f r o m 1963 t o for  istics  (unless  raw  produced from the  observations  on  2513),  raw  establishments  C o l u m b i a wood p r o d u c t s  (S.I.C.  industries:  shingle  mills  v e n e e r and plywood m i l l s  (S.I.C.  2520).  1979 w e r e c o l l e c t e d .  interior  and c o a s t  in the data  otherwise  Canada p u b l i c a t i o n  is  of the  (ii)  o f 4 x 17 = 68 o b s e r v a t i o n s data  and s o u r c e s  data set  annual  British  and ( i i i )  data are a v a i l a b l e  All  of  and p l a n i n g m i l l s  1  definitions  how t h e f i n a l  in the following  sawmills  the  Data  Planing Mills  and S h i n g l e M i l l s "  Veneer M i l l s "  (Catalogue  Institutional  Setting  sawmills, yielding  separate a  total  set.  specified)  Annual  Fortunately,  are published  Census of Manufactures (Catalogue 35-204)  in the  Stat-  "Sawmills  and " P l y w o o d  and and  35-206).  2 The B r i t i s h active  C o l u m b i a wood p r o d u c t s  in world markets.  B.C.  sawmills  industry  trade  in turn,  in softwood  account  for  large  produce almost  s o f t w o o d l u m b e r sawn i n C a n a d a a n d e x p o r t These e x p o r t s ,  is  and  70% o f  a l m o s t 80% o f t h e i r  a little  less  than  10% o f  very the output. world  lumber.  1.  I would l i k e t o thank Karen Kalderbank ( S t a t i s t i c s Canada, Vanc o u v e r ) and P a u l M a r t i n ( S t a t i s t i c s C a n a d a , O t t a w a ) 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 the c o l l e c t i o n of the 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 market s h a r e s , a r e f o u n d i n P e a r s e ( 1 9 7 6 ) , Volume 2, A p p e n d i c e s A , B, C, and E; P e a r s e ( 1 9 8 0 ) , p p . 1 - 3 0 ; and I n d u s t r y , T r a d e a n d Commerce ( 1 9 7 8 ) , p p . 1 - 5 0 .  24  The s h i n g l e shingles ducer.  industry  i n B.C.  and s h a k e s made i n A high proportion  mainly  to the  B.C.  United  also  softwood  trade.  Canada and i s  virtually  output  However,  of the  is  cedar  major  pro-  exported,  States.  has 80% o f t h e C a n a d i a n c a p a c i t y  since  all  North A m e r i c a ' s  of the i n d u s t r y ' s  p l y w o o d and v e n e e r .  plywood m i l l s  produces  Exports  high t a r i f f s  B.C.  a r e not  throughout  plywood m i l l s  still  for the production as  important  to  t h e w o r l d have  export  about  of  the  stifled  20% o f  their  output. The B . C .  wood p r o d u c t s  s i n c e most o f large  the m i l l s  integrated  plywood m i l l s . industry  is  industry's p. for  a price output  23) w r i t e s :  is  This it  is  is  especially  not  i n output markets  sold  in world markets.  sold  products in  true for  unreasonable  taker  "Forest  t h e most p a r t ,  c a n be d e s c r i b e d as  concentrated  a r e owned and o p e r a t e d by a s m a l l  firms.  However,  industry  sawmills  and  t o assume t h a t  the  since  s o much o f  Indeed,  produced i n B r i t i s h  highly  competitive  number  of  the  Pearse  (1980,  Columbia  are,  international  markets." It price  is  much more u n r e a s o n a b l e t o assume t h a t  taker  (logs)  i n the market  protect  for  materials.  logging operators  logging  operations  shadow p r i c e .  may n o t s e l l  the  they  output  to,  are  logging operations  stumpage  set  equal  to the  their  vertically very  roundwood t o m i l l s  T h i s may be done t o  is  deliver  roundwood i s  f e e p a i d by t h e fee  roundwood  both  owned and o p e r a t e d by t h e same l a r g e , for  a  Also,  usually  the market  on  is  from c o m p e t i t i o n .  operations  Therefore,  industry  Import t a r i f f s  logging  firm.  and t h e m i l l s  the  decrease  the  t o the B.C.  remainder  integrated  limited  and  at the f i r m ' s  royalties government.  of the value  of  or  true  stumpage This  timber  25  minus t h e c o s t s owned by t h e  of p r o d u c t i o n .  same f i r m ,  may t r a d e  decrease the p r o f i t a b i l i t y would decrease the ability  In s p i t e  market  is  at  logging operations  false  prices  in  and i n c r e a s e  keep t h e  in  turn,  profit-  price taking  order to  mills  to  This,  the o v e r a l l  of the above,  assumed i n  and  order  of the l o g g i n g o p e r a t i o n s .  stumpage f e e  of the f i r m .  in the materials  Hence,  behaviour  analysis  simple. Virtually is  organized  Since the the  all  l a b o u r employed i n t h e B.C.  by t h e  industry  industry  International is  Woodworkers  wood p r o d u c t s of  America  industry  (IWA).  s o c o n c e n t r a t e d t h e u n i o n has been a b l e t o  unionized  over the whole p e r i o d of t h e  study.  keep  The IWA  3 claims  that  95-98% o f  The b a r g a i n i n g f r o m IWA R e g i o n a l covering  all  employer's  northern  IWA r e g i o n a l interior  p r o d u c e d by  is  #1 n e g o t i a t e  known as  a coast  Forest  and s o u t h e r n  contain  union  shop  representatives  master  contract,  region, with  All  (FIR).  agreements  associations  regions.  the  Relations  f o r master  and e m p l o y e r interior  Union  Industrial  t h e n u s e d as a b a s i s councils  IWA m e m b e r s .  centralized.  employed i n t h e c o a s t  association is  is  structure  Council  workers  The c o a s t m a s t e r between  output  in  the  of the  collec-  tive  agreements  provisions.  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 o d u c e d 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 U n i o n o r t h e P u l p , P a p e r , and w o o d w o r k e r s o f Canada (PPWC), a r e c e n t l y f o r m e d 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 o d u c e d by u n o r g a n i z e d w o r k e r s . There a r e a few s m a 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 plywood m i l l .  26  Labour The l a b o u r  input  (L)  is  measured i n thousands  of man-hours  paid  4 f o r manufacturing total  wages p a i d t o  activity all  activity.  vacations nominal  production  in thousands  wages b e f o r e  of  of  payments  compensation  compensation paid t o labour  and r e l a t e d w o r k e r s  current  deductions,  and o t h e r  rate  Total  dollars.  Total  for  includes  bonuses,  paid  payments,  f o r work  not performed. labour  (w) i s  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  real  compensation  paid to  t h e Canadian consumer p r i c e  Capital  total  services  proved to  S.I.C.  of  Aggregate  industry  (two d i g i t  price  be q u i t e  industries,  Canada.  nom-  input.  compensation  Total  divided  by  (p).  and q u a n t i t y  difficult  by p r o v i n c e ,  capital  stock  S.I.C.)  for  since is  variables capital  the whole B.C.  the aggregate  energy  consumption  c a n be c o m b i n e d t o p r o d u c e  series  for  services.  Let the production function  of  labour  stock  d a t a on c a p i t a l  function  (L), materials  for  stock price  of  capital for  products  data  and  capital  four  Statistics  and d a t a  t h e wood p r o d u c t s  (M), flow  by  wood  a r e t h e most d i s a g g r e g a t e d  However,  capital  for  not t a b u l a t e d  able.  4.  total  Services  The c o n s t r u c t i o n  digit  index  is  average  simply  compensation  (B)  and  The  inal  labour  manufacturing  compensation  overtime  paid to  is  availon  quantity  industry  be a  services  from  Man-hours p a i d i n c l u d e s t i m e p a i d but not worked, e . g . vacat i o n s and s t a t u t o r y h o l i d a y s . During the period of i n t e r e s t the w o 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 data 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 in later years. Adjusting the labour input v a r i a b l e f o r the 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 models v i r t u a l l y unchanged. T h e r e f o r e t h e a d j u s t m e n t was d r o p p e d and t h e raw d a t a was u s e d .  27  the c a p i t a l  stock  ( S ) w h i c h i s a s s u m e d t o be a c o n s t a n t  the c a p i t a l  stock,  and c o n s u m p t i o n o f f u e l s  proportion  and e l e c t r i c i t y  of  (E),  i .e.,  where i  i s the runner  interior time  sawmills,  f o r the four  shingle m i l l s ,  observations  (coast  plywood m i l l s )  sawmills,  observed at  each  t. Assume f ( )  therefore,  Q  s e p a r a b l e o v e r S.  1  . H  t  where K ( S ^ , E ^ )  K(S  ,E  1 t  energy consumption and t h e s t o c k Specify  a constant  (  =  6  E  i t  Cost m i n i m i z a t i o n  p  returns  of  services  as a f u n c t i o n  of  capital.  to scale  CES p r o d u c t i o n  function  services  i t  K  and c a n ,  ))  i s the flow of c a p i t a l  t  capital  and  be w r i t t e n  - F ( L  u  i s weakly  u/ n  E w h e r e P^ capital.  p  t  =  M p  6  +  t  1  "  «> U >" S  implies  n/  M P  it  B  < ' >  1 / B  3  the f o l l o w i n g  =  first  order  ^/(i - 6)][s /E ]  i s t h e p r i c e o f energy and  n  s  e  +  condition  1  i t  i s the user cost  of  3  for  28  Therefore,  s  it  =  -In  E  n^  ES. i=l  1  ~  6  E ) i t p  = (3+  /  6  P  s i t  <  3  U~  +  l  < - >  ]  3  D'Hntd -  6)/6)  + l n \ E. i=l  (P* / P *  from S t a t i s t i c s  Canada.  4  E S^. i=l i  is  available  for  all  ideal  price  petroleum gases,  the t o t a l  cost  fore,  5.  B  P  of  an i m p l i c i t  is  +  fuel  index  of t h e p r i c e s  natural  gas,  and e l e c t r i c i t y  Fisher  ideal  o b t a i n e d by m u l t i p l y i n g  index  of  by P ^  of the q u a n t i t y  a  fuel E^  oil, is  there-  of energy  t h e sum o f t h e C a n a d i a n  (3.5)  r  and i s ,  t  1  is  H t  gasoline,  and e l e c t r i c i t y . ^ divided  X )  E i  liquefied  t  5  (  r  chained Fisher  s P^  t  )  4  used,  interest  rate  S t a t i s t i c s C a n a d a , F i x e d C a p i t a l F l o w s and S t o c k s : British Columbia, Catalogue u - z n , unpublished, iy»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 . Therefore,  the  Statistics  Canada s e r i e s  used o v e r s t a t e s  4  I S . i=l H o w e v e r , t h e two s e r i e s s h o u l d n o t be t o o f a r a p a r t s i n c e wooden b o x , c o f f i n a n d 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 c o m p a r e d t o s a w m i l l s , s h i n g l e m i l l s , and p l y w o o d m i l l s . In fact, S.I.C. 2 5 2 , 2 5 1 3 and 2511 made up 92% o f t h e v a l u e a d d e d 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 . i + u  6.  S t a t i s t i c s C a n a d a , C o n s u m p t i o n o f P u r c h a s e d F u e 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 , a n d E l e c t r i c P o w e r I n d u s t r i e s , Catalogue 57-208, 1975-79; unpublished d a t a , 1963~TT. See D i e w e r t ( 1 9 7 6 ) 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, rate  Y o u n g , W e i r 10 i n d u s t r i a l s  (capital  industry price  index  capital  of  building  price  indices  for  assumed t h a t  digit  t  for  = P^  of  industries,  P..  industry.  is  the  Canadian  construction,  a r e not  industry.  shingle m i l l s ,  capital,  i,m  t  rates  depreciation  products  times  engineering  and d e p r e c i a t i o n  sawmills,  wood  stock)  t h e wood p r o d u c t s  S.I.C.  and t h e  the B.C.  capital  t h e w h o l e wood p r o d u c t s  same u s e r c o s t  P-  gross  for  construction,  and e q u i p m e n t  and f o u r  capital  allowance  d i v i d e d by m i d - y e a r  machinery,  three  consumption  bond y i e l d )  the  Since  7  available user  cost  Therefore  and p l y w o o d m i l l s  it  for of  is  all  face  the  i.e.,  = 1,4  and t  = 1,17.  2 A stochastic 3.5,  term e , t  and maximum l i k e l i h o o d  estimate  of the e l a s t i c i t y  stock  obtained  other  estimates  (1978b),  7.  error  e  ~ N(0,a ),  t  estimates of  from e q u a t i o n  of  is  Dhrymes and K u r z  (1964),  between energy  0 . 1 , which  found i n the l i t e r a t u r e  a d d e d on t o  equation  s and 6 a r e o b t a i n e d .  substitution 3.5  is  (see,  or Fuss  is for  and  consistent example,  The capital  with  McFadden  (1977)).  The bond y i e l d i s f o u n d i n t h e Bank o f Canada R e v i e w . The c a p i t a l consumption 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 in S t a t i s t i c s Canada, Catalogue 13-211, unpublished 1980. The p r i c e index 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, Fixed C a p i t a l F l o w s and S t o c k s , C a t a l o g u e 1 3 - 2 1 1 and 1 3 - 5 6 8 , v a r i o u s years.  30  The e s t i m a t e s  of  6 and g a r e s u b s t i t u t e d  into equation  3.4  to g  produce  predicted  estimates 3.3  of  S..  capital  stocks  from e q u a t i o n 3.4  (along with the estimates  flow  of  capital  The p r i c e function  services,  of  dual  for  capital  of  each of  the o b s e r v a t i o n s .  are then s u b s t i t u t e d  6 and e)  into  The equation  t o produce estimates  of  the  K^. services  to equation  is  f o u n d by d e r i v i n g  the unit  cost  3.3,  3 + 1 _ J _ _ J _ 3 + 1 r 8 + 1  1  TTT  where  r^  is  the cost  of  s  6  +  1  one u n i t  of  capital E  r.j  t  are then  6 and  6 into  of c a p i t a l  calculated equation  services  by s u b s t i t u t i n g  3.6.  P^,  Hence e s t i m a t e s  are obtained f o r  all  services.  3  Estimates  of  s P^  and t h e e s t i m a t e s  of the p r i c e  and  of  quantity  observations.  Materials A chained Fisher is  constructed  for  ideal  each of  price the  index of the p r i c e  observations  of m a t e r i a l s  from d e t a i l e d  d a t a on  (m) the  9 quantity price  and v a l u e  index f o r  of m a t e r i a l s  sawmills  is  and s u p p l i e s  simply  the price  used. of  The  roundwood  materials (logs)  8.  S i n c e p r e d i c t e d v a l u e s of t h e dependent v a r i a b l e are u s e d , a measure of goodness of 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 v e r a g e p e r c e n t a g e d i f f e r e n c e b e t w e e n t h e a c t u a l and p r e d i c t e d d e p e n d e n t v a r i a b l e i s 5%.  9.  S t a t i s t i c s Canada, Catalogue Canada d a t a .  35-204,  and u n p u b l i s h e d  Statistics  31  while the price  index  for  shingle mills  r o u n d w o o d , and u n f i n i s h e d  shingles  is  an i n d e x o f t h e p r i c e s  and s h a k e s  from o t h e r  of  establish-  ments. The m a t e r i a l s prices  of  hemlock,  price  different  index f o r  species  s p r u c e and p i n e )  An i m p l i c i t  Fisher  (M) i s  of  plywood m i l l s  roundwood  and t h e p r i c e  ideal  supppies  used  supplies  u s e d by t h e m a t e r i a l s  index  of  (Douglas of  fir,  the  balsalm  and  glue.  the q u a n t i t y  o b t a i n e d by d i v i d i n g t o t a l price  aggregates  of m a t e r i a l s  cost  and  of m a t e r i a l s  and  index.  Output Detailed of  shipments  Fisher coast pulp  ideal  d a t a on t h e v a l u e a n d q u a n t i t y made by t h e output  sawmills chips,  industries  price  index  aggregates  and s h i n g l e s  index aggregates  are used t o  (q).*°  the prices  of  of  construct  The o u t p u t  price  a  types  chained  index  for  r o u g h a n d p l a n e d sawn  and s h a k e s w h i l e t h e  the prices  of the d i f f e r e n t  interior  lumber,  sawmills  r o u g h a n d p l a n e d sawn l u m b e r ,  and  price pulp  chi ps. The o u t p u t shakes  price  and two t y p e s  gregates  the prices  types  plywood.  of  The t o t a l shipments  10.  index for of  of  value of  (i.e.,  shingle mills  shingles  while  softwood veneer,  output  excluding  is  the prices  the plywood m i l l s ' Douglas  fir  and r e t u r n s )  35-204,  index  plywood and  d e f i n e d t o be t h e n e t  discounts  S t a t i s t i c s Canada, Catalogue Canada d a t a .  indexes  plus  value  agother  of  the value  and u n p u b l i s h e d  of  of  Statistics  32  t h e change i n of  value  fuel of  inventories.  added, the cost  and e l e c t r i c i t y .  output  output  (Q) i s  price  Alternative  Thus,  of m a t e r i a l s  An i m p l i c i t  obtained  Fisher  by d i v i d i n g  ideal  total  and t h e  the cost  index of the  value of  sum of  quantity  output  by  the  defined to  be  the  Wage alternative  amount an a v e r a g e B . C .  wage o f  industrial  r a t e d from t h e i r  current  weighted average  of:  work  - the B.C.  immediately (ii)  unemployment  and s u p p l i e s ,  equals  index.  The b e s t  composite;  the value of output  average weekly  receive  if  receive  if  they  unemployment  Ul;  and  (iii)  if  insurance  find  the  suffer  they  wage i s  they  a v e r a g e w e e k l y wage f o r  for  of  receive  The a l t e r n a t i v e  what w o r k e r s  what w o r k e r s  payment  worker would  employment.  (i)  and q u a l i f y  IWA members i s  a  other  industrial  a spell (Ul)  what w o r k e r s  sepa-  of  - the  receive  B.C.  if  they 11  suffer  a spell  The w e i g h t bility  o f unemployment  on a v e r a g e w e e k l y  of w o r k i n g , which  B.C.  labour  force.  times  the p r o b a b i l i t y  fying  for  U l is  and do n o t q u a l i f y  is  industrial  defined to  The w e i g h t  be B . C .  for  Ul.  Ul -  (wl)  is  employment  on t h e U l payment  of q u a l i f y i n g  defined to  wage  for  (w2)  is  nothing. the  divided (1 -  The p r o b a b i l i t y  be t h e number o f w e e k s o f  probaby  wl)  of  quali-  U l paid in  B.C.  12 divided  by t h e  number o f weeks  of  unemployment  in  B.C.  The  weight  11.  I n d u s t r i a l c o m p o s i t e a v e r a g e w e e k 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 C a n a d a , Employment E a r n i n g s a n d H o u r s , C a t a l o g u e 7 2 - 0 0 2 . The U l a v e r a g e w e e k 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 C a n a d a , S t a t i s t i c a l R e p o 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 , Catalogue 7 3 - 0 0 1 .  12.  Employment, l a b o u r S t a t i s t i c s Canada, 71-201. Number o f Canada, Catalogue  f o r c e and u n e m p l o y m e n t a r e r e p o r t e d i n H i s t o r i c a l Labour Force S t a t i s t i c s , Catalogue 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 73-001.  33  on t h e no w o r k , z e r o so i t  no U l  drops  state  out.  is  (1 - w l  The b e s t  real  - w2),  but  alternative  it  is  wage  (A)  alternative  wage d i v i d e d by t h e C a n a d i a n c o n s u m e r p r i c e  Scaling the  Data  T h e r e a r e two r e a s o n s done t o e n s u r e t h a t minus one. tion  This  routine  is  the  for  important  used t o e s t i m a t e  keep t h e e s t i m a t e d p a r a m e t e r s bability  that  problems  of  the o p t i m i z i n g  false  parameter  data are j u s t down.  index  Therefore  or equal total  is  Clearly to  here.  The  scaling  s c a l i n g must  the  industries  simplex  is  and  optimiza-  Scaling the increases  converge,  is  truly  t o ensure that reflect  data  the  and h e l p s  to  pro-  avoid  its  true  second  profit  reason  the  most y e a r s  with  1970,  is  reports  of t o t a l  show t h a t  cost,  the  s c a l e d up a n d is  share  approach  1974,  data set w i l l used, p r o f i t  costs  not  is  than of  and  the  share of  of m a t e r i a l s  while the principal  capital  share of m a t e r i a l s  is  make up  statistics  divided  by t h e  be  greater  and 1975 b e i n g t h e  and t h e s h a r e of m a t e r i a l s that  greater  and e a c h i n p u t ' s  scaling  observations,  0.25,  the  first.  with  labour  Many o f  to  share.  However,  all  the data used  the w o r l d .  be done so t h a t  done t o p r o d u c e t h e f i n a l  ITC r e v i e w  to two-thirds  a non-linear  numbers w h i c h c a n be a r b i t r a r i l y  Averaged over  the share of  if  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  satisfy  than zero f o r years.  routine will  scaling  a r e b e t w e e n one  parameters.  in the unit  estimates,  close to  The s c a l i n g reported  the  t o z e r o f o r most o b s e r v a t i o n s ,  cost  scale  only  the  convergence.  The second r e a s o n f o r calculate  parameters  is  by  index.  scaling the data. F i r s t ,  estimated  reason i s  multiplied  worst is  0.15,  0.59. one-half of  the  share  of  34  labour averages fies  the  very  Two F l a w s  are c l a s s i f i e d  made up o f smaller  small  except  sawmills  the scaling  include  of m a t e r i a l s for  activity. since  However,  conventions  for  there  of  the  is  missing data.  by  satis-  Statistics  the cost  and s u p p l i e s .  number o f w o r k i n g  Unfortunately  seriousness  treatment  establishments  large establishments.  those  shingle small is  and  industries mills  no are  tend to  establishments  the data  all  part-  presents  no way t o e i t h e r  problem, or a d j u s t  fuel  Also,  owners  This  of  for  be  may deter-  the  dif-  convention.  The second f l a w  d a t a on t h e c o m p o s i t i o n available  for  and e n e r g y necessary  B.C.  is  of  are u n a v a i l a b l e for  shipments,  plywood m i l l s for  the construction  For each m i s s i n g total  given special  and p l y w o o d m i l l s  and t h e d i f f e r e n t  mine t h e  seems t h a t  criterion.  to manufacturing  show up i n t h e d a t a .  ferent  are  with the cost  statistics,  problem f o r  it  Data  Specifically,  principle  second  establishments  and e l e c t r i c i t y  ners,  Therefore  important  in the  Small Canada.  2.44.  calculated B.C.  piece  for  share,  of  The 1970 u n p u b l i s h e d materials,  and e n e r g y  while the composition  B.C.  shingle  mills.  of the p r i c e  multiplied  share  The s h a r e s  by t h e  are  un-  materials  These d a t a  are  indices.  data the B.C.  1969 a n d 1 9 7 1 .  of  detailed  of the  Canadian  are averaged  1970 C a n a d i a n  and  that  average  total,  13.  I n d u s t r y , T r a d e , a n d Commerce, R e v i e w 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, Catalogue 35206 and 3 5 - 2 0 4 , 1 9 6 4 - 7 9 .  35  yields  t h e 1970 B..C.  f o r many i t e m s ,  figure.  the B.C.  of the Canadian t o t a l s , shares  are almost  The p r o c e d u r e  totals so i t  100% a l s o .  is  for  is  arbitrary.  1969 and 1971 a r e  However,  virtually  100%  n o t u n r e a s o n a b l e t o assume t h e  1970  36  Chapter  4 The Wood P r o d u c t s  This B.C.  chapter  provides  wood p r o d u c t s  taking  behaviour  technology function  a characterization  industry  in  all  are estimated  parameters.  was a s s u m e d .  input  markets.  independently  Thus,  adjustment* costs  Cost  the  inputs  are achieved w i t h i n  vation  in the data.  curve,  and a c o s t  of the  industry.  Define  a cost  Therefore,  for the  and w a r e p r i c e s  labour  The p r o d u c t i o n  1.  {rK + mM + wL :  of  and T i s  possibilities  the set  the  in the  a s s u m e d , and  on i t s  characterize  levels each  long the  to  input all of  obser-  run  cost  technology  (K,M,L,Q)eT}  services,  of c a p i t a l  production is  price  are e q u i v a l e n t  p e r i o d of  is  and  the  industry  capital  and Q a r e q u a n t i t i e s  and o u t p u t ;  industry  is  of  objective  equilibrium  - the time  function  where  K,M,L,  the  of  competition  behaviour  c a n be u s e d t o  =  labour;  estimates  perfect  function  C(r,m,w,Q)  r,m,  Min K,L,M  one y e a r  prices  f r o m any u n i o n  parameter  minimizing  input  The p a r a m e t e r s  a r e a s s u m e d t o be s u c h t h a t  5  of the t e c h n o l o g y  assuming exogenous  e s t i m a t e s w h i c h w o u l d be o b t a i n e d i f markets  Technology  the set  (4.1)  materials services,  possibilities of a l l  and materials, set.*  feasible  The u s e f u l a n d 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 w e l l d o c u m e n t e d a n d w i l l n o t be d i s c u s s e d h e r e . e x a m p l e , D i e w e r t (1974) and ( 1 9 7 8 a ) .  inputs  function are See, f o r  37  and o u t p u t s ,  and i t  Two d i f f e r e n t tion.  Both c o s t  is  assumed t o be w e l l  functional functions  forms  behaved.  2  a r e used t o s p e c i f y  are estimated  the cost  and t h e r e s u l t s  are  func-  reported  below.  Translog  Specification Specify  lnC(r,m,w,Q)  a translog  cost  function  = CXQ + ct^lnr + o^lnm + ct l nw 3  2  1  + ^  +  1 nQ + -  Y  3 3  (1nw)  2  2 e (lnQ) 2  + a^int av I n t + + ux^inr avjnr  2.  2  + a^lnr  1 nQ + B  1 2  l n m InQ + B  1 3  l n w InQ  Iint nt + + (D^mm w, J n m Imu nt + + u>^ u>..~lnw I n t 3  S e e 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 e m e n 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 i m p o s e d . G e n e r a l l y T i s assumed t o be c l o s e d , b o u n d e d , and c o n v e x . There is also free disposal. Note 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 n o t assumed t o be a c o n e , 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 d o e s assume t h a t T i s a c o n e .  38  where  +  Y  ll  Y  Y  S  M  and t  is a trend  second order the cost  the technology  13  ll  ll  variable.  approximation  function  1 2  allows  +  +  12  Y  + Y  Y  +  6  +  +  +  12  13  Y  +Y  2 2  23  +  = 1  *13  +  u  0  2 3  33  Y  +  "12  =  13  The t r a n s l o g  =0  °  =  =  =  °  °  cost  t o an a r b i t r a r y  biased technical  function  cost  provides  function.  Note  c h a n g e and does n o t  t o be h o m o t h e t i c o r e x h i b i t  constant  lemma i m p l i e s  share  returns  a that  force  to  scale.  Shephard's  rK/C  = Oj + Y l n r  = s  K  mM/C = s  M  =  + Y  wL/C = s  L  =  + Y  n  1 2  1 3  the following  + Y lnm + Y^lnw 1 2  + w lnt  (4.3)  lnQ  + u^lnt  (4.4)  lnQ  + w^lnt.  (4.5)  n  + Y lnm  lnw  + 8  lnr  + Y lnm + Y lnw  + 3  2 3  +  Y  + 3 lnQ  lnr  2 2  2 3  3 3  equations  1 2  1 3  n  39  Since the shares be i n c l u d e d  sum t o o n e ,  i n a system of  o n l y two o f t h e s h a r e e q u a t i o n s  estimating  equations.  A maximum  h o o d 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 u s e d t o e s t i m a t e t h e of the t e c h n o l o g y , equation  s o as t o make t h e e s t i m a t e s  error  terms e ^  a r e added t o e q u a t i o n s  4.2,  e^> w h e r e  e^,  4.4  and 4 . 5  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 w i t h one a n o t h e r ,  while  e r r o r terms  a r e assumed t o be i n d e p e n d e n t  chastic  versions  regression  of 4 . 2 ,  system.  contemporaneous  4.4  correlation,  series,  and 4 . 5  Note h o w e v e r ,  share  unspecified,  for observations  constant,  shares.  The e s t i m a t e s  obtained  from the e r r o r  of equations  4.2,  4.4,  across  This  Table  II  4.4,  very  and  sto-  section  in the to  estimates versions  are  system u s i n g the estimates The  on C r e p r e s e n t  then itera-  asymptoti-  estimated  are reported  of e s t i m a t e d p r i c e  for  input  The s t o c h a s t i c  estimates.  subscripts  covariance  data accounts  equivalent  regression  plywood  This  of the estimated technology,  Letter  obser-  limited  pooled cross  differences  asymptotic t - s t a t i s t i c s  and o t h e r c h a r a c t e r i s t i c s  only  and 4 . 5 .  procedure y i e l d s  shows t h e m a t r i x  t h e mean o f t h e d a t a .  is  approach.  t o maximum l i k e l i h o o d  and t h e i r  there  ( w i t h t h e dummy v a r i a b l e s )  tive  coefficients  correlated  unrelated  on s h i n g l e m i l l s  industry  unrelated  equivalent  terms  Thus, the  form a seemingly  and t i m e s e r i e s  components  procedure.  Error  of each o t h e r .  4.2,  e s t i m a t e d as a s e e m i n g l y Zellner  3  respectively.  are a s y m p t o t i c a l l y  and 4 . 5  ~ N(0,E),  e,,, e )  a r e a l l o w e d t o be  that  a r e a l s o added t o e q u a t i o n s  I.  to the  series.  approach t o pooled c r o s s - s e c t i o n  Table  invariant  (e^  since the data i s  and n o t t i m e s  Dummy v a r i a b l e s  cally  parameters  corresponding to d i f f e r e n t  vations  mills  likeli-  dropped.  Stochastic  and t i m e  can  in  elasticities evaluated partial  at deri-  40  vatives are  of the cost  omitted  for  technical  hz  =  B  13  =  hypothesis  likelihood  change  (0^2= a^3= 0 ) , °^  a  (<^  tests  ratio <^2  =  e  a  1  1  r  J  e  e  c  t  a r e p e r f o r m e d on t h e  tests.  e  The h y p o t h e s e s  0),  =  and h o m o t h e t i c i t y r  of the  derivatives  convenience.  A number o f system using  f u n c t i o n , where t h e arguments  of  no t e c h n i c a l  the  easily,  d  of  no b i a s  change  production  even at t h e  estimated  (u^ = a>^ = (e^  technology 99.5%  in  =  confidence  level. The r e j e c t i o n neutral  technical  means t h a t tion  of  change  a constant  technology  Conditional  is  Cost  using a cost  also  Hence,  the estimated differences  The r e j e c t i o n  of  Hicks'  homotheticity  of the  produc-  rejected.  Specification  derived (1974,  wood p r o d u c t s  technology  p.  137).  This  cost  of  is  without  different  re-estimated  function  used t o  in the union  letting  is  specification  models. endogenous  parameters  the p o s s i b i l i t y functional  is  represent  t h e wage be  and u n i o n p r e f e r e n c e  technology  a r e due t o t h e u s e o f  cost  unusual  function  of t h e i n d u s t r y  production  production  industry  from a c o n d i t i o n a l  same c o n d i t i o n a l  estimating  c h a n g e means t h a t  to scale specification  one c a n o b s e r v e t h e e f f e c t s  and j o i n t l y  3.  rejected.  of the B.C.  s u g g e s t e d by D i e w e r t  the production  in technical  returns  function  the  is  Function  The t e c h n o l o g y  used s i n c e  no b i a s  that  on any  forms.  The r e s t r i c t e d , m a x i m i z e d l o g l i k e l i h o o d s f o r e a c h o f t h e t h e s e s a r e 4 5 9 . 0 4 , 4 5 8 . 8 8 and 4 5 4 . 6 3 , r e s p e c t i v e l y .  hypo-  41  TABLE  Estimated C o e f f i c i e n t s  Asymptotic  t-statistics  ct  of the Trans!og Cost  (3.995)  0.2559  (5.712)  ct  2  0.3548  (9.335)  cu  0.3893  Y  n  0.1359  (7.879)  Y  12  -0.1191  (-9.556)  Y  13  -0.0169  (-0.976)  Y  22  0.211  (15.091)  Y  2 3  -0.0191  Y  3 3  0.1088  (5.042)  B  :  0.9072  (11.945)  0.0133  (0.5)  B B  2  (12.25)  (-12.0)  ^-0.0049  (-0.314)  0.0614  (4.828)  -0.0565  (-4.876)  0.0543  (4.084)  0.0254  (4.899)  a>  -0.0121  (-2.507)  a>  -0.0133  (-3.903)  n  B B  1 3  u 12  13  Function  parentheses  0.5812  0  Natural  are in  I  l o g of l i k e l i h o o d  function  = 470.07  42  TABLE  II  Estimated C h a r a c t e r i s t i c s Translog Cost  All  estimates  Function  are evaluated  of the  Technology:  and Exogenous  a t t h e mean o f  Wages  the  data.  Monotonicity C  = 3.38,  p  C  m  = 6.69,  C  w  = 3.72,  C  Q  = 4.1  Curvature The d e t e r m i n a n t s o f t h e m i n o r s function are: 0.001, -0.014, 0.0.  of  the hessian  of  the  cost  Substitution The m a t r i x  of  price  elasticities  r K M L  m  0.0006 -0.034 0.097  Returns  to  KL  w  -0.133 -0.046 0.228  The e l a s t i c i t i e s CT  is  =  of  substitution  0*^6,  0.132 0.080 -0.325 are:  = 0 . 3 6 6 , CT^ = - 0 . 2 1 3  Outlay alnC/.alnQ = 0.96  Therefore the e l a s t i c i t y returns to outlay.  Technical  of  scale  is  1.041  and t h e r e  Change (3s /3t)(t/s )  = 0.159  (3s /3t)(t/s )  = -0.02  (as /at)(t/s )  = -0.061  K  M  L  (ac/at)(t/c)  K  M  L  = 0.043  are  increasing  43  Assume t h e p r o d u c t i o n production  technology  conditional  cost  D(r,m,L,Q)  = Min K,M  possibilities  exhibits  {rK + mM :  is  (K,M,L,Q)  t h e minimum c o s t  r e q u i r e d t o p r o d u c e o u t p u t Q,  a cone so t h a t  returns  to scale.  the  Define  a  e T},  (4.6)  of m a t e r i a l s  given a f i x e d  and  labour  capital  input  L,  and  input  r and m.  McFadden  ( 1 9 7 8 a , p.  minus a v a r i a b l e inputs  is  function  where D ( r , m , L , Q )  prices  constant  set  profit  of the v a r i a b l e  adjusting  for  D(r,m,L,Q) outlined note t h a t  the  sign  possesses  in  61)  Diewert  function profit  and c h a r a c t e r i z i n g  where t h e o u t p u t s  function  the properties (1974,  cost  p.  136).  of  variable  function  and some o f  are f i x e d . output  cost  is  the  Therefore, be a n e g a t i v e  profit  input,  functions  F o r o u r p u r p o s e s we need  only  > 0'  function,  the  a conditional  c h a n g e and l e t t i n g  D^ < 0 and D ^  An o r d i n a r y  notes t h a t  possessing a l l  production  C(r,m,w,Q)  = Min L  the usual  possibilities  set,  {D(r,m,L,Q)  + wL}.  properties  can be  defined:  (4.7)  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 , or j o i n t cost f u n c t i o n . For p r o f i t f u n c t i o n s the 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 e w e 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 c o n c a v e i n i t s f i x e d i n p u t s . Since the cost f u n c t i o n i s m i n u s 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 m e a s u r e d a s n e g a t i v e numbers i n D i e w e r t , b u t a s 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 , the 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 , s o D ^ > 0 w h e t h e r l a b o u r i s m e a s u r e d as a n e g a t i v e number o r n o t . S e e C h a p t e r 5 f o r a c o m p l e t e l i s t o f t h e p r o p e r t i e s of D ( r , m , L , Q ) .  44  The f i r s t  order condition  f o r t h e minimum  D (r,m,L,Q) L  and t h e  second order  L*(r,m,w,Q) condition to  condition  be t h e amount (4.8)  of  is  is  + w = 0  satisfied  (4.8)  > 0.  since  labour which s a t i s f i e s  and, t h e r e f o r e ,  minimizes  the  equation 4.7  Let  first with  order respect  L. Hence,  C(r,m,w,Q)  = D(r,m,L*(r,m,w,Q),Q)  The c o s t  minimizing  demand f u n c t i o n 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 equation  + wL*(r,m,w,Q).  for  (4.9)  capital  lemma on t h e c o s t  and  materials  function  given  4.9.  Therefore,  K * ( r ,m,w,Q)  -  9C(r,m,w,Q)/9r  -  3D(r,m,L,Q)/3r|^_^*  (4.10)  and  M*(r,m,w,Q)  = 3C(r ,m,w,Q)/am = 3 D ( r , m , L , Q ) / a m |  by t h e e n v e l o p e t h e o r e m . function  is  Specify  given in  The c o s t  implict  the c o n d i t i o n a l  minimizing  f o r m by e q u a t i o n cost  function  to  L = L  *  demand f o r 4.8. be  (4.11)  labour  by  45  D(r,m,L,Q)  = c rL + 2b  where X = ( - r 2 4.12  provides  tional  cost  n  M = c  2 1  L~*  (r  + c mL  + c^mQ  2 1  + m + 2X)(LQ)  + 2a XZ  a  (4.12)  1 2  + - m ) * and Z = L + Q + 2 ( 1 . 0 ) * . 2  2  2  function  Note t h a t  equation  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  given a constant  returns  to scale  condi-  technology  and  change.  Equations  K = c  1 2  a second order  no t e c h n i c a l  taneous  + c^rQ  n  4.8,  system of  4.10, cost  4.11,  and 4 . 1 2  minimizing  imply the f o l l o w i n g  input  demand  simul-  functions:  L  + c  1 2  Q  + 2b  1 2  (LQ) (l  + r/X)  + a  rZ/X  (4.13)  L  + c  2 2  Q + 2b  1 2  (LQ) (l  + m/X)  + a mZ/X  (4.14)  = -[w + c  n  r  + c  s  i  2 1  m + 2a  1 2  X][b  1 2  1 2  1 2  (r  + m + 2X)Q* + 2 a  1 2  XQ*]  _ 1  (4.15)  Stochastic  error  t e r m s e^, e  added on t o e q u a t i o n s structure  is  function.  4.13,  2 >  4.14,  e^, w h e r e and 4 . 1 5  t h e same as t h e one s p e c i f i e d  Error  terms  corresponding  to the  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 , ponding to  different  each  other.  6.  Diewert  (1974),  observations  p.  138.  ( e ^ , e , e ) ~ N ( 0 , E) , 2  3  respectively.  The  for the t r a n s l o g same o b s e r v a t i o n while error  a r e assumed t o  terms  are  error  cost are corres-  be i n d e p e n d e n t  of  46  TABLE Estimated C o e f f i c i e n t s  Asymptotic  c  C  C  C  b  a  Natural  l l 12 21 22  12  12  log of  III  of the C o n d i t i o n a l  t-statistics  are in  (1.639)  1.0541  (7.825)  1.5352  (2.912)  1.1151  (11.198)  -0.8649  (-3.683)  0.4406  (3.956)  function  Function  parentheses  0.7090  likelihood  Cost  = 293.4247.  47  TABLE  IV  Estimated C h a r a c t e r i s t i c s Conditional  All  estimates  Cost  of the  Technology:  F u n c t i o n and Exogenous  are evaluated at  t h e mean o f  the  Wages  data.  Monotonicity C  p  = 3.13,  C  m  = 7.10,  C  w  = 3.50,  C  Q  = 4.32.  Curvature The d e t e r m i n a n t s o f t h e m i n o r s o f function are: -0.235, -0.063, 0.0.  the hessian  of  the  Substitution The m a t r i x  of  price  elasticities  r K  M L  -0.1372 -0.0665 0.2907 The e l a s t i c i t i e s ov,  of  m  w  0.2576 0.0185 0.1368  0.3948 0.0479 -0.4274  substitution  = 1.81,  a , M  is  are:  = 0.219,  a. KM  0.414  cost  48  Dummy v a r i a b l e s mills  for  observations  a r e added on t o e a c h s t o c h a s t i c  account input  for  unspecified,  demands.  Full  constant,  information  parameters  of t h e c o n d i t i o n a l  stochastic  system of  input  asymptotic t - s t a t i s t i c s  conditional derived  input  across  cost  function  reported  equations  4.8  and 4 . 9 .  of  estimated  price  teristics  of the estimated technology,  data,  reported  In t h e work  in  Table  section  three  variables.  These p o o l i n g  by a l i k e l i h o o d  function  specification  should 4.14  usually  and 4 . 1 5  justified  Assuming t h a t around t h e i r ally  is  of the  of  rather  root  cost cost  the  function function tech-  and o t h e r  characthe  data.  estimated  Implicit  in  the  of the technology  adjustments  are  the  made by t h e dummy  a r e t e s t e d and  overwhelmingly  p e r f o r m e d on t h e c o n d i t i o n a l  error  structure  arbitrary. some s o r t of  (as  of  are  cost  technology.  observed l e v e l s  the square  the  test  the  a c c e p t e d and i n t u i t i v e l y  inverse  series  after  ratio  levels  their  e v a l u a t e d a t t h e mean o f  the parameters  by a s s u m i n g  optimal  elasticities  restrictions  be n o t e d t h a t  the  the  of  of the p r o d u c t i o n  demand f u n c t i o n s  and t i m e  industries  rejected  4.13,  input  the assumption that all  of  IV.  shown a b o v e ,  from pooled c r o s s  The o r d i n a r y  of the c h a r a c t e r i s t i c s  in  and  the parameters  using  The m a t r i x  It  of  '  III.  an e s t i m a t e o f t h e o r d i n a r y  nology.  same i n  The e s t i m a t e s  function,  estimates  above i s  estimates  are obtained from  in Table  estimates  shingle  differences  cost  provides  are  industry  demand f u n c t i o n s .  are  and  demand e q u a t i o n t o  maximum l i k e l i h o o d  G i v e n t h e maximum l i k e l i h o o d  is  on p l y w o o d m i l l s  in  appended t o  Adding e r r o r of  inputs  optimization  are normally  equations  terms  However,  the observed  labour  is  error. distributed  4 . 1 3 and 4 . 1 4 )  reasonable.  equations  is  gener-  assuming t h a t  input  is  the  normally  49  distributed labour  around t h e  input  intuitively variables  (as  in  reasonable.  The a d d i t i v e dummy v a r i a b l e s the  error  The v e r y  cost  Discussion  Hence, although  ber of  error  it  t o t h e dummy  specification it  with  its  convenresults  rather  strongly.  and C o m p a r i s o n o f t h e R e s u l t s w i t h o t h e r  Studies.^  results  the estimates  be  more  the  r e p o r t e d above w i t h t h e  of the Canadian m a n u f a c t u r i n g  sector  is  results  of  difficult  the  obtained  unknown w h a t  structure,  for  should  f r o m t h e ones  is  as  equations.  However,  specification,  may n o t t a i n t  accepted or  demand  and t h e l i n e a r  optimal  too  Comparing t h e studies  input  convenience.  function  of the  as w e l l  a r e not t o o d i f f e r e n t  structure.  specification  not  root  same a r g u m e n t a p p l i e s  w o u l d be o b t a i n e d w i t h a d i f f e r e n t trary  is  in the  structure  a r e used f o r results  of the square  4.15)  linearly  error  from the t r a n s l o g tional  equation  which enter  noted that  inverse  for  arbi-  other a num-  reasons.  First,  other  studies  break  inputs  up i n t o d i f f e r e n t  sub-  g aggregates  t h a n t h e ones u s e d a b o v e .  Second, the other  d a t a on t h e w h o l e C a n a d i a n m a n u f a c t u r i n g given  above  refer  to only  a small  part  sector,  of t h a t  studies  while the  sector.  The  use  results other  7.  Other studies of the Canadian manufacturing s e c t o r a n d May ( 1 9 7 7 ) , Denny a n d May ( 1 9 7 8 ) , F u s s ( 1 9 7 7 ) , ( 1 9 6 8 ) , T s u r u m i ( 1 9 7 0 ) and W o o d l a n d ( 1 9 7 5 ) .  are: Denny Kotowitz  8.  F o r e x a m p l e , Denny and May ( 1 9 7 8 ) 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 , b u t b r e a k e a c h 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 o u t p u t i s a f u n c t i o n o f f o u r i n p u t s : product 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 o m p a r i s o n s b e t w e e n 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 a b o v e a r e d i f f i c u l t .  50  studies here.  a l s o u s e d a t a f r o m an e a r l i e r Finally,  capital  serices  is  t i m e p e r i o d t h a n t h e one  defined quite  differently  used  in  this  9 work  than  report  in other  other  studies.  estimates  However,  found i n the  Both of the estimated cost properties. turing. the  This  prices.  property  However,  demand f u n c t i o n s concavity  that not  the cost  far  and a r e n o t  close  function  is  very  small.  The c o s t  price Fuss  When one o f  higher.  Capital between - 0 . 2  worthwhile  imposes  their of  to  monotonicity  Canadian  functions  manufac-  do n o t  respect  elasticities  possessing  functions  satisfy  to  input  of t h e  the p r o p e r t i e s  input that  on t h e m ,  so t h e c o s t  functions  Woodland  (1975)  finds  but t h e p r i c e of the o t h e r  Other  elasticities  also  elasticities  studies  of c a p i t a l  the e l a s t i c i t i e s studies  For example,  elasticities (1977)  is  are  satisfy  property.  close to zero.  somewhat  to  price  not concave,  T h e e s t i m a t e d own p r i c e quite  studies  concave with  from being concave.  function  satisfy  the estimated cost  are very  unreasonable.  the curvature  other  t h e own a n d c r o s s  of the c o s t  be t o o  in  it  literature.  functions  also true  Unfortunately,  curvature  cannot  is  I believe  has t h e w r o n g s i g n  f i n d these e l a s t i c i t i e s  Denny and May  of  capital  and m a t e r i a l s  estimates  them t o  be - 0 . 7  and m a t e r i a l s and - 0 . 5 .  9.  See C h a p t e r vices.  3 for  10.  The r a n g e s g i v e n give the general  1 0  and m a t e r i a l s  and  (1977) of  -1.1  find  details  study  is  be  estimated  and - 0 . 5 ,  while  -0.358.  are complements w i t h e s t i m a t e s No o t h e r  to  it  are  corroborates  of t h e d e f i n i t i o n  h e r e a r e v e r y r o u g h and a r e c h a r a c t e r of the r e s u l t s .  of  of  this  capital  result  ser-  intended only  to  For  51  example,  Denny a n d May  (1977)  a  estimate  t o be 1 . 8 .  Fuss  (1977),  KM  however, in this  finds study,  Capital of  a,,  that is  energy  defined to  and l a b o u r  are q u i t e  and m a t e r i a l s  far  are  include  substitutes.  apart,  so 0 . 5  capital,  Unfortunately,  < a  < 2 is  the  estimates  the narrowest  esti-  KL  mated r a n g e t h a t  c a n be g i v e n  between c a p i t a l  and l a b o u r .  above t h e upper  limit  (1970),  Fuss  and 0 . 2 9 5  (1977),  < <^,  < 0.5.  ov,  be b e t w e e n  L  result  This  study  that  capital Labour  does  not  the e l a s t i c i t y  This  while  literature. (1975)  Kotowitz  On t h e o t h e r and - 0 . 5 3  gives  and c l a i m t h a t  to  an e s t i m a t e d  this  added framework  (1977)  and not  estimate dif-  framework.  but  finds  complements.  a...  with  0.8 range  strikingly  either,  far  Tsurumi  be 1 . 0 ,  do n o t u s e a v a l u e a d d e d  are s u b s t i t u t e s  quite  For example,  estimate  (1968)  and l a b o u r a r e s u b s t i t u t e s  and m a t e r i a l s  substitution  h a n d , Denny and May  because they use a v a l u e  of  r a t h e r wide range extends  and Woodland  -0.3  occurs  for  found i n the  respectively  of 0.3  ferent  and  energy.  KL  to  are complements  estimated to  be  LM between 0.2  and 0 . 4 .  find  and m a t e r i a l s  labour  report  a much h i g h e r  The own p r i c e be b e t w e e n reported also  -0.3  Both Fuss  Denny and May respectively. inconsistent  t o be s u b s t i t u t e s ,  elasticity  and - 0 . 5 .  other  is  slightly  influential  elasticity  Therefore, with  This  report  of  substitution labour  bigger study.  (-0.0996),  price  estimates  elasticity  found i n the  is  of  also (1977)  1.2.  estimated  than the  -0.15  Woodland  (1975)  while  estimated e l a s t i c i t i e s  the  (1977)  b u t Denny and May  o f t h e demand f o r  (1976)  a smaller (1977)  and Denny and May  estimated e l a s t i c i t y  i n Hamermesh's  estimates  (1977)  of  Fuss  (1977)  -0.49  reported  here  literature.  and is  to  and -0.74 not  52  Homotheticity translog  cost  function  The e l a s t i c i t y impose  of  constant  homotheticity Finally, neutral  of the p r o d u c t i o n  returns  to  scale,  and f i n d s both the  hypotheses  change a r e  elasticity  of  costs  of time  negative  not too s u r p r i s i n g  but Woodland  increasing of  technical  change.  s i n c e Woodland  Pearce  (1980,  p.  10)  change  0.043,  also  studies  is  Hicks' labour  the estimate so t h e n e t  Negative t e c h n i c a l  (1975)  found.  rejects  c h a n g e and  Further,  to time is  also  the  outlay.  Technical  using.  respect  to  are  Most o t h e r  (1975)  no t e c h n i c a l  rejected.  and c a p i t a l with  returns  rejected with  to outlay  e s t i m a t e d t o be 1 . 0 4 1 .  saving  change.  returns  is  and m a t e r i a l s  nical  and i n c r e a s i n g  is  scale  technical  is  technology  reports  of  the  result  change  negative  is  tech-  states:  " 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 the c o n v e r s i o n of m i l l s t o high volume, small l o g ' p r o c e s s i n g systems which have e n a b l e d t h e I n t e r i o r [B.C. sawmilling] industry to achieve higher l e v e l s o f wood u t i l i z a t i o n a n d g r e a t l y i m p r o v e d l a b o u r productivity." The c o a s t  region  wood s t o c k s .  has a l s o  Hence,  quality  of m a t e r i a l s  saving,  and c a p i t a l  the d e t e r i o r a t i o n  of  it  suffered  seems t h a t  available  from d e c l i n i n g  size  and q u a l i t y  although the d e c l i n i n g  has s p a r k e d m a t e r i a l s  using technical t h e wood s t o c k s  change; is  to  size  of  and  and  labour  the ultimate  effect  of  over  time.  increase  costs  53  Chapter  5 Union M o d e l s :  In t h i s  chapter  determination estimated.  tion  The e s t i m a t e d  technology  and p r o d u c t i o n within  two d i f f e r e n t  in a unionized  of the preferences  industry  of the union  Minimization  models  parameters  o f wage and  are d e r i v e d , of  and u n i o n  a specific  model  provide  a n d show how e s t i m a t e s  preference of  employment  specified  the models  c a n c h a n g e when t h e wage i s  union  In o r d e r t o f a c i l i t a t e are  Cost  endogenous  parameters  and f i r m  the analysis,  and  estimates  of t h e  produc-  to the  model  are estimated  jointly  behavior. the following  assumptions  made. Al.  All  divergent  groups w i t h i n by a s i n g l e A2.  The u n i o n industry workers about  A3.  has o r g a n i z e d and i s  The f i r m s world. costs  for  all  and no u n i o n member  function  is  the  independent  in the industry  Union p r e f e r e n c e s  industry's  Further,  is  constraints  all  worries  job  the  union's  restrictions labour. in a  are  adjustment  contract  on e i t h e r  shop so  the  and t h e u n i o n o p e r a t e atemporal  achieved within  the labour  of  demand f o r  and any  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  equilibrium  in  worker.  Hence t h e u n i o n c a n n o t e n f o r c e affect  expressed  workers  The u n i o n h a s a u n i o n  b e i n g r e p l a c e d by a n o n u n i o n  in turn  different  function.  and b a r g a i n s  secure.  cost  h e l d by  c a n be accommodated and  a r e u n i o n members,  behaviour.  A4.  the union  and g o a l s  union o b j e c t i v e  The i n d u s t r y ' s  which  preferences  party.  a r e such  one o b s e r v a t i o n  does not  (one  i m p o s e any  static  that year).  dynamic  54  A5.  Both t h e u n i o n and t h e f i r m s  in the  industry  have  perfect  i nformati on. A6.  The i n d u s t r y services inputs  A7.  is  and m a t e r i a l s ,  subject  exhibits  possibilities (closed, in  of  Chapter  specifying  ences  system.  assuming  taking  satisfies  is  also  p.  industry.  not  the  up"  in  in the  a n d shows t h a t  on f i r m s  agreements,  and i n t e r i o r  the contracts  studies  multi-year  the  techno-  production  given  the  prefer-  run  according  reasonableness given  B.C.  o f wage  determination  agreements  industry  not  do  T h e r e w o u l d be n o negotiated  only  would cover  agreements  over the p e r i o d  are d e f i n i t e l y  of the  established  the c o l l e c t i v e  of  the  The w e l l  each c o n t r a c t  regions  is  discussed  reasonableness  structure  collective  products  has b e e n  market  and u n i o n s .  since  Table V reports  coast  and w h i c h  industrial  empirical  IWA a n d t h e f o r e s t  tiated  those  properties  represent  be d i s c u s s e d .  problem i f  one o b s e r v a t i o n .  so t h e  on t h e  in the m a t e r i a l s  constraints  collective  of  free disposal)  literature  homogeneous  impose dynamic  one y e a r  costs  The  the other  function to  integrated  strong evidence that  the  to scale.  some o f t h e a s s u m p t i o n s  A s s u m p t i o n A4 s h o u l d a l s o  provides  a cone,  convex,  capital  134).  behavior  wood p r o d u c t s  "catch  is  the  for  constraint.  Chapter three discusses  vertically  of  set  set  of  concentrated,  importance  output  returns  a simple objective  to a political  minimizes  constant  two s u r v e y s  of a union which  price  possibilities  (1974,  The r e a s o n a b l e n e s s elsewhere.  and i t  bounded, non-empty,  Diewert  i n the markets  t o an e x o g e n o u s  The p r o d u c t i o n logy  a price taker  of  renegotiated  only  negointerest for  55  every  observation  tions, for  (year).  so a s i n g l e  more t h a n one  Most  contract  determines  perfect  have two y e a r  the c o n d i t i o n s  of  from m u l t i - y e a r  by a s s u m i n g t h a t  foresight.  In t h a t  s e c o n d and t h i r d y e a r s  of  contracts  b o t h t h e u n i o n and t h e  case the c o n d i t i o n s  the  collective  of  agreement  able.  Clearly,  a s s u m p t i o n A4 i s  which  maintained  Unfortunately,  estimates  presented  The c o n d i t i o n a l  D(r,m,L,Q)  described  = Min K,M  in  technology, noted  some i n p u t s  cost  assump-  the a n a l y s i s  of t h i s  tract-  assumption  on  the  function  (K,M,L,Q)eT},  4 and d u a l  a variable  fixed.  year.  keeps  any)  the  could  s t r o n g and r e s t r i c t i v e it  the  unknown.  to the constant  4, a c o n d i t i o n a l  of minus are  below are  (if  used t o c h a r a c t e r i z e  in chapter  properties  because  the effects  {rK + mM :  chapter is  only  a very  for  are e x a c t l y  second or t h i r d  in that  have  employment  renegotiate  the terms  be  industry  t h e u n i o n and t h e i n d u s t r y  is  employment  could  same as what t h e y w o u l d be i f  tion  dura-  observation.  No d y n a m i c c o n s t r a i n t s rationalized  of t h e c o n t r a c t s  (5.1)  returns  to  scale  the production technology.  cost  profit  function  possesses  f u n c t i o n where a l l  all  As the  outputs  and  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 m a t i o n 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 f o r m e d 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 s m a 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 coast regions.  2.  See McFadden ( 1 9 7 8 a ) , p. 6 8 , t i v e i n p u t s and v i c e - v e r s a .  and remember t h a t  outputs  are  nega-  56  TABLE V Collective  Agreements  for  the Coast  and I n t e r i o r  Regions  Coast J u n e 15  1962  to  J u n e 14  1964  1964  to  "  1966  1966  to  "  1968  1968  to  "  1970  1970  to  "  1972  1972  to  "  1974  1974  to  "  1975  1975  to  "  1977  1977  to  "  1979  1979  to  "  1981  Interior September  1  1962  to  August  31  1964  September  1  1964  to  August  31  1967  September  1  1967  to  J u n e 30  1970  1970  to  J u n e 30  1972  1972  to  "  1974  1974  to  "  1975  1975  to  "  1977  1977  to  "  1979  1979  to  "  1981  July  1  57  Therefore, possesses (i)  the  as shown by D i e w e r t  following  D(r,m,L,Q) but  (ii)  property  is  a non-negative  is  is  function  equal  i m p o s e d by t h e  functional  (iv)  D(r,m,L,Q)  is  homogeneous  (v)  D(r,m,L,Q)  is  non-increasing  decreasing  i n Q (DQ > 0 ) .  D(r,m,L,Q)  is  (vii)  of  degree  in  L,Q  r a n d m.  > 0  This  used.  r and m.  one i n L and  Q.  i n L (D^<0) a n d n o n -  convex and c o n t i n u o u s  i n L a n d Q,  which  > 0.  proved i n the appendix t o t h i s  D(r,m,L,Q)  A functional specify  D^  is  r,m > 0 ,  form  c o n c a v e and c o n t i n u o u s  it  for  homogeneous o f d e g r e e one i n  is  Finally  D(r,m,L,Q)  zero.  D(r,m,L,Q)  implies  is  non-decreasing  in  chapter  that:  r and m.  f o r m s u g g e s t e d by D i e w e r t  (1974,  p.  137)  is  used  to  D(r,m,L,Q):  D(r,m,L,Q)  + 2b  1 2 1 2 where X = ( - r + - m ) 2 2 Chapter 4,  this  an a r b i t r a r y  the technology Total input  136),  (iii)  (vi)  to  p.  properties.  b o t h L and Q c a n n o t  D(r,m,L,Q)  (1974,  1 2  (r  1 2  rQ  + c mL  + c^rnQ  2 1  + m + 2X)(LQ)* + 2 a  1 2  XZ,  (5.2)  1  a n d Z = L  conditional  + Q + 2(LQ) . 2  form provides cost  a n d no t e c h n i c a l  output  + c  1 2  functional  expenditures  prices,  = c^rL  As n o t e d  a second order  function,  in  approximation  given the c o n d i t i o n s  on  change.  made by t h e  and t h e l a b o u r  industry input,  for  are  inputs  (E),  given  58  E(r,m,w,L,Q)  w h e r e wL i s sation i.e.,  total  paid to  Figure  paid to  compensation  curves  paid to a unit  of  curves  of  a constant  and p i s  the  total  labour  labour.  employed;  Isoin  by  D(r,m,L,Q)  Canadian  compen-  s p a c e a r e shown  E E , and a r e d e f i n e d  wL = pB = E -  (5.3)  and w i s  amount o f  i n compensation-employment  3 by t h e f a m i l y  where E i s  labour,  l a b o u r d i v i d e d by t h e t o t a l  the average  expenditure  compensation  = wL + D ( r , m , L , Q ) ,  (5.4)  consumer  price  index.  CI e a r l y ,  = -D  3(wL)/at  8 (wL)/St 2  so t h e  iso-expenditure  employment.  Note t h a t  independent allel  from  o f wL,  curves  price  = - D  2  L L  increasing  and  < 0,  and c o n c a v e  implying  that  the  iso-expenditure  functions curve  curves  of  is  are  par-  below.  paid to  labour  index),  preferences available  > 0,  the slope of the i s o - e x p e n d i t u r e  Assume u n i o n p r e f e r e n c e s tion  are  L  are defined over t o t a l  ( B , B = wL/p w h e r e p i s  a n d t h e amount o f  are c o n d i t i o n a l  to labour  (A).  the Canadian  l a b o u r employed  upon t h e  The b e s t  best  real  real  real  (L).  compensaconsumer  Assume  alternative  alternative  union  wage  wage a v a i l a b l e  to  59  FIGURE 3  wL  60  labour  is  also the real  and i t  is  assumed t o  Let where U  union > 0,  u  opportunity  be t h e  preferences U.  D  < 0,  same f o r  and U ( B , L ; A )  real  c o m p e n s a t i o n and l a b o u r  the union  tion  it  for  curves,  the  union s e r v i c e s is  that  the  increasing be  ever  is  job,  workers. by t h e f u n c t i o n  quasiconcave  rate of  in  real  increasing  increases  rationalization incurs  function in  of work.  real  U(B,L;A) compensa-  of  between labour  union  price  s p a c e by t h e  real  costs  level,  curves  in  rates  of  of  labour  real  curve  is  compensation  upward s l o p i n g  and  are required f o r  uu  are in  assump-  providing  as t h e number o f m a n - h o u r s w o r k e d i n c r e a s e s .  supply  Another  ever  more l a b o u r  supplied. Specify,  U(B,L;A)  = ikB + (5.5)  The a v e r a g e  real  T h e r e f o r e we c a n  rate  of  compensation  Vp  is  d e f i n e d t o be  B/L.  define  <j>(w/p,L;A)  w h e r e <> j  (w/p)  > 0 and  <}>. > 0 i f  = U(wL/p,L;A)  w/p > - U . /U  = U(B,L;A)  to  indif-  f o r the quasi concavity  increasing  and  compensation  Typical  wage a n d t h e  compensation-employment  union  substitution  an i n c r e a s i n g  one more m a n - h o u r  A possible  that  the marginal  given the a l t e r n a t i v e  nominal  3.  is  Thus,  requires  compensate  Figure  is  in a union  L  and l a b o u r .  shown i n  all  of working  be c h a r a c t e r i z e d  tion  ference  cost  (5.6)  to  61  *L  Monopoly Union  < 0 if  w/p  < -U /U . L  Model  In t h e m o n o p o l y u n i o n model nominal  rate  of  compensation  order t o maximize U ( B , L ; A ) . mizing  level  B  of  employment  (MUM) t h e u n i o n c h o o s e s t h e  p a i d t o each worker The i n d u s t r y  given  by i t s  unilaterally,  model  subject  conforms  determination firms  to the  to the conventional in a unionized  choose the l e v e l  negotiated  demand f o r  labour  Min L  function  industry.  Unions  demand f o r  order  labour function  {E(r,m,w,L,Q)}  condition  also  employment  wages,  subject  but  to  the  form.  Multiply  equation  = Min L  constraint)  demand f o r  The s e c o n d o r d e r 5.8  is  g i v e n by t h e  solu-  {wL + D ( r , m , L , Q ) } .  by L/p  into the union's  p r o b l e m c a n t h e n be  (5.7)  is  the i n d u s t r y ' s  implicit  zation  This  problem  L  is  affect  maximizes  function.  w i s d o m a b o u t wage a n d  w + D (r,m,L,Q)  which  labour  o f employment u n i l a t e r a l l y ,  to the m i n i m i z a t i o n  The f i r s t  demand f o r  mini-  wage.  The i n d u s t r y ' s tion  industry's  in  then chooses the c o s t  a n d t h e u n i o n w a g e . Hence t h e u n i o n c h o o s e s t h e wage w h i c h U(B,L;A)  average  = 0  labour  condition  and s u b s t i t u t e objective  written  is  (5.8)  function satisfied  the product  function.  written since (the  The u n i o n ' s  in  D^>  0.  union's maximi-  62  Max L  which y i e l d s  the  first  {U(-LD  order  /p,L;A)}  condition  311/St = U ( - D B  + D  The s e c o n d o r d e r involves  the t h i r d  the usual  condition  derivative  curvature  that dix  form used t o  the second order to this  chapter  Equations  5.8  for  tion  in  wage a n d t h e p r i c e  is  cost  (equation  problem  function,  not  of  the  is  such  See t h e  on t h e s e c o n d o r d e r  'm'  in  appen-  condition.  indifference D is  function  solu-  F i g u r e 4 shows t h i s  space.  EE a r e curves  solu-  iso-  (given  t h e demand f o r  whose s l o p e  the labour  equals  the  choose employment t o m i n i m i z e e x p e n d i t u r e  union chooses  oa t o m a x i m i z e  its  so  are  5.2),  always s a t i s f i e d .  level),  the compensation  t o oa and t h e  maximization  and D ( r , m , L , Q )  D(r,m,L,Q)  uu a r e u n i o n  Firms  (5.9)  B  the t h i r d d e r i v a t i v e  compensation-employment  alternative  ject  L  U(B,L;A)  Point  curves,  nominal wage.  = 0  L  d e f i n e t h e compensation-employment  expenditure  and oa i s  + U  the union's  the d e t a i l s  and 5.9  )/p  = pU /U .  L L  However,  condition  t o t h e monopoly m o d e l .  curve  of  specify  tion  nominal  of  L L  of the c o n d i t i o n a l  properties  e n o u g h t o e n s u r e a maximum. functional  + LD  L  LD  L  sub-  objective  f u n c t i on. Cost minimizing c a n be d e r i v e d c h a p t e r 4. the  input  from the  demand f u n c t i o n s  conditional  D e f i n e an o r d i n a r y  technology,  cost  cost  for  capital  function  and  materials  as t h e y w e r e  f u n c t i o n , which  is  also  in  dual  to  63  C(r,m,w,Q)  = Min L  {wL + D ( r , m , L , Q ) }  = wL*(r,m,w,Q)  + D(r,m,L*(r,m,w,Q),Q)  where L * ( r , m , w , Q )  is  the  applied to equation  K*(r,m,w,Q)  solution  5.10,  to  equation  (5.10)  5.8.  Shepard's  lemma,  implies  = 8C(r,m,w,Q)/3r  = 8D(r,m,L,Q)/8rj  (5.11) f[_=L*  and  M*(r,m,w,Q)  = 3C(r,m,w,Q)/an = 9D(r,m,L,Q)/9m| IL=L*  by t h e e n v e l o p e Equations nonlinear  K = c  n  theorem. 5.2,  5.5,  system of  L  + c  L  + c  (5.12)  5.8,  5.9,  5.11,  5.12  imply  the  following  equations:  1 2  Q  + 2b  2 2  Q + 2b  1 2  (LQ) (l  1 2  (LQ) (l  i  + r/X)  + a  1 2  rZ/X  (5.13a)  .r M = c  2 1  -w = c  L  2  r  n  + c  = L-c^r  (u  x  2 1  m + b  - c  + u B n  2 1  m  + u  2  (Q/L) (r i  1 2  - 2a  1 2  L  1 2  X  + m/X)  + a mZ/X  + m + 2X)  + p(u  2  + u  + u^A)" ]!;- b  (5.13b)  1 2  2 2  1  1 2  + 2a  L + u  1 2  1 2  X(l  B  +  + u  2 3  Q * ( r + m + 2X)  (Q/L) )(5.13c) i  A)  (5.13d)  + a^XQ*]  .  64  FIGURE 4  65  Equations given  5.13a  by 5 . 1 1  and b a r e t h e c o s t  and 5 . 1 2 .  labour function of the u n i o n ' s endogenous  Normally and t h e  Equation  g i v e n by 5 . 8 maximization  variables:  K,  preferences.  and 5.13d  error  terms  different  one a n o t h e r . 5.13 try.  There  is  with  Unfortunately,  t h e complete system of u  13  =  0  i  1 S  likelihood  [ T 1  P  0 S e c  '  (FIML)  o  n  n  i°  5.13,  ables  observations  each e q u a t i o n .  the  condition  There are  four  for  5.13  union  same o b s e r v a t i o n  while  terms  error  terms  appended t o  and  of the parameters (with t h e i r  indus-  industries.  prevented the estimation  Full  of  equations  a given time  so t h e  are  corres-  be i n d e p e n d e n t  time or across  (5.13),  reported  tion  technology,  VII.  Table VIII are  for  constant,  complete  across  system i s  on p l y w o o d m i l l s  The FIML e s t i m a t e s , in Table  Characteristics  variables  order  for  restriction  information of the  u^  of =  maximum  restricted  asymptotic  t-statistics)  VI.  equations  are also  demand  i m p o s e d on  to the  only  problems  and r e p o r t e d  In o r d e r t o a d j u s t  for  is  preferences.  n  by 5 . 9 .  a r e assumed t o  across  equations  estimates  system are o b t a i n e d i n Table  u  u^ = 1,  one a n o t h e r  numerical  inverse  functions  a r e added o n t o e q u a t i o n s  the error  no c o r r e l a t i o n  the  demand  L.  terms  observations  input  the f i r s t  one a n o t h e r ,  T h i s means t h a t  are c o r r e l a t e d  is  corresponding  a l l o w e d t o be c o r r e l a t e d w i t h ponding to  is  problem given  restriction,  Error  5.13c  M, w, a n d  distributed  identifying  minimizing  industry  differences  re-estimated with and s h i n g l e m i l l s  and t h e i r  asymptotic  reports  included  in  vari-  a d d e d on  to  t-statistics  VI.  of the e s t i m a t e d union p r e f e r e n c e s  evaluated  dummy  in  at  the  sample means, a r e  reported  the estimated c h a r a c t e r i s t i c s equations  5.13.  Letter  and  producin  Table  when t h e dummy  subscripts  on U and  66  TABLE VI Estimated C o e f f i c i e n t s  Asymptotic  t-statistics  No Dummy  '11 :  :  :  12 21 22  >12  are  in  of t h e Monopoly Union  parentheses  Variables  (-3.657)  0.0482  (-0.729)  0.6963  (23.567)  0.6368  (25.040)  0.0329  (0.709)  0.0393  (1.031)  0.9336  (21.361)  0.9675  (29.072)  -0.2378  (-11.181)  0.2527  (-11,788)  0.1328  (3.860)  0.1365  (4.884)  -0.1297  1.0 (-1.69)  0.0  J  13  *22 '23  -0.0124  (2.098)  0.0  0.1921  (-1.860)  0.0040  (-1.069)  0.0160  (2.583)  0.4449  (-50.419)  -0.0012  (-0.062)  0.0542  (-4.099)  -0.3368  (-6.436)  0.0856  (1.897)  Natural log of 1ikelihood function  352.804  Correlation Coefficients between a c t u a l and 0.93,0.99, p r e d i c t e d values of 0.96,0.99 K , M , w , 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 M i l l s a n d Plywood M i l l s  -0.2319  1.0  '12  Model  L~*  424.618  0.93,0.99, 0.96,0.99  67  TABLE Estimated C h a r a c t e r i s t i c s Technology:  All  Union  VII  of Union Preferences  M o n o p o l y U n i o n Model  estimates  are evaluated  and  a n d No Dummy  at  t h e mean o f  Production  Variables  the  data  Preference^ Mondtonicity  U  B  = 0.957,  U  = -0.844,  L  U  A  = -1.163,  <|>  = 3.305,  w/p  <f> = L  1.201  Curvature Determinant of bordered function = 0.021. MRS  Production  B L  -  0.882,  hessian MRS  w / p  of  the u n i o n ' s  = 0.363,  L  a  w  /  p  objective  L  = 0.768.  Technology,  Monotonicity C  p  = 3.130,  C = 6.762, m  C  w  = 4.010,  C  Q  = 4.325  Curvature Determinants of minors of the are: - 0 . 8 7 9 , - 0 . 1 7 2 , 0.0  The m a t r i x  of  price  r K M L  the cost  elasticities  is w  -0.746 -0.175 1.049  The e l a s t i c i t i e s KL  of  m  -0.514 -0.193 0.928  CT  hessian  =  5  '  7  8  '  °ML  of =  1  '  1.260 0.368 -1.977  substitution 6  8  '  CT  KM  =  -  1  are: '  2  0  function  68  TABLE Estimated C h a r a c t e r i s t i c s Technology:  All  Union  VIII  of Union P r e f e r e n c e s  and  M o n o p o l y U n i o n Model w i t h Dummy  estimates  are evaluated  a t t h e mean o f  Production  Variables  the  data  Preferences Monotonicity  U  B  = 0.208,  U  = -0.105,  L  U  = -2.959,  A  <|>  = 0.718,  w/p  $  L  = 0.341  Curvature Determinant of bordered hessian f u n c t i o n = 0.0017 MRS  Production  B L  = 0.503,  MRS  w / p  of  the u n i o n ' s  =0.489,  L  a  w  /  C  Q  p  objective  L  = 0.737.  Technology  Monotonicity C  p  = 3.242,  C = 6.982,  C  m  w  = 3.618,  = 4.327  Curvature Determinants of minors of the h e s s i a n are: - 0 . 3 9 9 , - 0 . 1 1 8 , 0.0  The m a t r i x  of  price  r K M L  the cost  elasticities  m  -0.233 -0.147 0.590  3  -  6 8  '  <k  =  1  0.801 0.345 -1.573  of  substitution  -  '  5 8  is w  -0.568 -0.198 0.983  The e l a s t i c i t i e s  °KL "  of  °KM " - ° -  are: 9 1  function  69  C represent the  partial  industry  cost  derivatives  function  likelihood  maximized values Table  l l  =  ratio  tests tests.  The r e s t r i c t e d  u  12  =  13  u  =  u  that  22  23  u  ^  =  = u  same r e s u l t s variables  2  objective = 0)  2 3  = u^  a n c  are  is  n  be t e s t e d  included  is  and 0.0274  in the  that  is  exogenous  very  tion.  u  n  = 2  e  u  2  s  i  >  independent  s  t  u  level.  estimating  to the  in the  of  level  in  a  t  =  t  n  union  e  " 23^ u  of  1.201  overwhelmingly  four,  of  and p r o d u c t i o n  parameters. price  H e n c e , t h e u n i o n model  t n  that wage  level.  some f u n c t i o n  employment  dummy  and 0 . 3 4 1  input  The  a r e not  of  cannot the  dummy  vari-  variables.  of the  is  produc-  estimates  a r e assumed t o  shows much  and e l a s t i c i t i e s  s u g g e s t s much g r e a t e r  it  models.  estimated j o i n t l y  The u n i o n model  the  respectively,  in both  prices  of  (<j>^ = 0)  standard error  rejected  elasticities  k°  e  s y s t e m when t h e dummy  u n i o n model w i t h t h e  parameters  r  the a l t e r n a t i v e  t o compare t h e e s t i m a t e s  where a l l  a  The h y p o t h e s i s  r e s t r i c t e d model w i t h o u t  from the monopoly  value)  i  n  (u^ =  equations.  estimated  <> j^ are  interesting  in chapter  absolute  t  i n t h e u n r e s t r i c t e d model w i t h  any u n i o n p r e f e r e n c e (in  =  o  the union maximizes  0.0785  <> j^ = 0 i s  technology  obtained  is  However t h e  S i n c e t h e two e s t i m a t e s  It  i3  u  y P  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  indifferent  estimate of  tion  are reported  are obtained from the u n r e s t r i c t e d  directly.  clear that  = 2  function  also  The h y p o t h e s i s w a g e , and i s  = u^  '  e v e n a t t h e 99.5% c o n f i d e n c e  the u n i o n ' s  (u  =  rejected,  ables  unrestricted  t h e u n i o n m a x i m i z e s t h e wage b i l l  rents  1 3  function  and  sys-  IX.  maximizes  (u  and  a r e p e r f o r m e d on t h e e s t i m a t e d  of the l o g l i k e l i h o o d  The h y p o t h e s i s u  function  respectively.  A number o f h y p o t h e s i s tems u s i n g  of the union o b j e c t i v e  of  be  with larger  substitu-  substitutabi1ity  70  TABLE Maximized  IX  V a l u e s o f t h e Log L i k e l i h o o d s Constant  Returns to  Monopoly  Union  No Dummy Variables u = u =0 n  of t h e Union  Models:  Scale  Model  Dummy Variables  Cooperative Model No Dummy Variables  Union  Dummy Variables  1 3  Unrestricted  352.804  424.618  395.357  436.435  Wage b i l l m a x i m i z a t i o n hypothesis  266.213  351.682  296.294  375.199  Rent m a x i m i z a t i o n hypothesis  260.439  307.385  309.193  389.333  Union p r e f e r e n c e s independent of the a l t e r n a t i v e wage hypothesis  336.245  408.967  380.627  434.991  "11  =  u  13  =  0  372.048  71  between t h e f a c t o r s changes in all  of  production  t h a n t h e model input  which  of  function, almost  Pencavel  phenomenon i s  of  seems t h a t  to the e x p l i c i t If  tion  competition  literature facturing impact  industries  manufacturing ones  found  of  the  which  is  true  the  labour  the  so important  price  for  (in  if  Other  to  evi-  a  and very  They 1.0,  with  technology  union behavior  in  (compared t o t h e  market)  then the  are  the assump-  estimates  found i n  the  In C a n a d a , most manu-  Estimates  of  the  c o u l d be v e r y d i f f e r e n t  the unions'  elasticity  policy  abso-  Dertouzos  of s u b s t i t u t i o n  market.  technology  price  estimated  labour.  of production  questioned.  labour  literature  for  the  and  variables.  behavior  m o d e l l e d a n d wages w e r e a s s u m e d t o be e n d o g e n o u s . especially  than 0.5  r a n g i n g f r o m 1.8  modeling of  in  4,  show t h e  a r e o r g a n i z e d by u n i o n s w h i c h h a v e a  sector's  cost  in chapter  literature.  t h e demand f o r  and e l a s t i c i t i e s  industries'  in the  in the  estimates  s h o u l d be s e r i o u s l y  on t h e  price  price  The t r a n s l o g  literature,  t h e MUM has a n y v a l i d i t y  elasticities  of the  a m o n o p o l y u n i o n model y i e l d s  a t t h e means o f  sensitive  price  in the  found  it  perfect  function.  estimated e l a s t i c i t y  labour market.  of  to  competition  value g r e a t e r than 1.5.  of the e l a s t i c i t y  1.23  in the estimate  union model, however,  Therefore  of  perfect  l a b o u r t o be s m a l l e r  also find that  a negative  a value  with  function estimated  found  In t h e m o n o p o l y  (1981)  high estimate report  cost  j u m p s t o an a b s o l u t e  dence of t h i s  is  labour  o f t h e demand f o r  value).  elasticity  very  t h e demand f o r  of t h e e s t i m a t e s  elasticity lute  difference  the conditional  all  consistent  responsiveness  markets.  T h e most s t r i k i n g elasticity  is  and g r e a t e r  of  Canadian from  the  had b e e n  This  seems t o  t h e demand f o r  applications.  significant  be  labour,  72  Cooperative  Union  Model  In t h e c o o p e r a t i v e some u n s p e c i f i e d t i o n which that  the  firm's it  lies  u n i o n model  means t o  curve.  compensation-employment  would l i k e  to,  the  force  the  contract  which t i e other  curve.  firm off  input.  labour  its  employed  (see Chapter  7).  t h e u n i o n and f i r m b a r g a i n level  of  employment.  innocuous estimating  and d o e s  demand f o r  How t h e p o i n t  to  for  directly  simply  to  on  negotiate  reach a  the estimating  curve  a point is  is  sides  The  work  rules  or the use of compensation  some rules  labour  o f wages  that  and  The  contract  reached or supported  curve. is  not  specified. The i n d u s t r y ' s  expenditure  E(r,m,w,L,Q)  and an i s o - e x p e n d i t u r e  curve  on i n p u t s  is  given  = wL + D ( r , m , L , Q )  c a n be  by  (5.3)  written  wL = pB = E -  D(r,m,L,Q)  the  completely  equations. on t h e  than  point  the sake of e x p o s i t i o n ,  assumption  the  function.  could negotiate  about t h e l e v e l  this  specify  on t h e c o n t r a c t  not  compensation  labour  mechanisms  they  is  Assume,  Note t h a t  realize  t h e two  d e g r e e one i n t h e amount o f  not a f f e c t  equations  rate of  use  combina-  to is  Clearly,  employed t o output  Another a l t e r n a t i v e  w h i c h a r e n o t homogeneous o f  important  t o t h e model  the average  For example,  t h e amount o f  and u n i o n  The f i r m e m p l o y s more l a b o u r  u n i o n a n d f i r m c o u l d u s e many d i f f e r e n t on t h e  is  n e g o t i a t e d wage.  m u s t b a r g a i n a b o u t more t h a n j u s t ( t h e wage) t o  It  solution  labour function. given  industry  choose a compensation-employment  on t h e c o n t r a c t  demand f o r  (CUM) t h e  (5.4)  73  where E i s  a  constant.  By s u b s t i t u t i n g objective terizes  function  this  the constraint  U(B,L;A),  model  c a n be  Max  The f i r s t  order  (equation 5.4)  the maximization  {U(E/p -  condition  chapter  for  Equations tion  5.4  t o t h e CUM.  the It  fied.  contract is  left  + U  L  = 0  L  = pU /U .  L  L  (5.14)  B  D(r,m,L,Q)  satisfied.  on t h e  and U ( B , L ; A )  ensure  See t h e a p p e n d i x t o  second order  that  this  condition.  d e f i n e the compensation-employment  "d" in  i n nominal  Figure 4 is  a possible  compensation-employment  solution  soluto  the  s p a c e , where  cc  curve.  important  t o note t h a t  The b a r g a i n i n g  industry's  of  is  and 5 . 1 4 Point  c o o p e r a t i v e model is  properties  the d e t a i l s  charac-  is  D  condition  problem which  D(r,m,L,Q)/p,L;A)}.  B  t h e second order  union's  written  3U/3L = - U D / p  The c u r v a t u r e  into the  level  of  unspecified.  not  completely  m e c h a n i s m u s e d by t h e two p a r t i e s  expenditure The model  curve the 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  t h e CUM i s  be;  curve.  and t h e u n i o n ' s  does it  not  only  The u n i o n  predict  predicts  level  of  to  and i n d u s t r y  choose  utility  w h e r e on t h e that  speci-  is  contract  the solution simply  the  choose  will the  74  observed l e v e l minants  of  of t h a t  expenditure  level  of  a n d no a c c o u n t  and t h e  by a p p l y i n g  Shepard's  given to the  deter-  expenditure.  C o s t m i n i m i z i n g demands f o r upon o u t p u t  is  labour  input  capital  and m a t e r i a l s ,  chosen w i t h the u n i o n ,  lemma t o t h e c o n d i t i o n a l  cost  conditional are  derived  function:  K*(r,m,L,Q)  = 3D(r,m,L,Q)/3r  (5.15)  M*(r,m,L,Q)  = 3D(r,m,L,Q)/3m.  (5.16)  and  Equations  5.2,  nonlinear  simultaneous  K = c  n  M = c  2 1  5.14,  5.15,  system of  and 5 . 1 6  imply  the  following  equations:  + c  1 2  Q  + 2b  1 2  (LQ)*(l  + r/X)  + a^rZ/X  (5.17a)  L  + c  2 2  Q + 2b  1 2  (LQ) (l  + m/X)  + a mZ/X  (5.17b)  + c^r  + 2b  2  5.4,  L  -w = - E / L  L~  5.5,  = C  - C  p(u  1 2  ^  x  r  (r  + c  i  1 2  rQ/L  + c^m  + m + 2X)(Q/L)  ~ z\ c  m  + u B n  i  2  + u  1 2  L  + u  1 3  + c mQ/L 2 2  + 2a  - 2a^ X + ( u  A)  2  1 2  1 2  X(l  + u  -1  2 2  ][b  + Q/L + 2 ( Q / L ) * )  L + u^B  Q (r 2  1 2  (5.17c)  + u^A)  + m + 2X)  + 2a  * XQ ]  _  1  2  1 2  (5.17d)  .  75  TABLE X Estimated C o e f f i c i e n t s  Asymptotic  t-statistics  No Dummy  '11 :  :  :  12 21 22  hz J  12  are  in  of the Cooperative  J  J  12 13  '22 J  23  Natural  log  1 ikelihood  Variables  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 a n d Plywood M i l l s  0.3847  (1.647)  0.2069  (1.604)  0.6444  (10.645)  0.5991  (10.706)  0.4800  (2.494)  0.3027  (2.769)  0.9465  (13.563)  0.9079  (22.260)  -0.3938  (-3.489)  -0.3005  (-4.139)  0.2123  (3.431)  0.1682  (3.681)  1.0  -0.4616  (-2.989)  -0.3513  (-2.125)  0.0648  (2.632)  0.0514  (1.822)  -0.0924  (-2.053)  -0.0879  (-1.487)  -0.4660  (-24.458)  -0.3520  (-4.447)  0.0947  (1.472)  0.0781  (0.865)  0.2474  (3.799)  0.1735  (2.709)  of function  Correlation  and  values  K , M , w , and L  395.357  436.435  Coefficients  between a c t u a l predicted  Model  parentheses  1.0  '11  Union  2  of  0.93,0.99,  0.93,0.99,  0.92,0.99  0.92,0.99  76  TABLE XI Estimated C h a r a c t e r i s t i c s Technology:  All Union  of  Cooperative  estimates  Union P r e f e r e n c e s  U n i o n Model  are evaluated  and  Production  a n d No Dummy  a t t h e mean o f  Variables  the  data  Preferences Monotoni c i t y  U  B  = 0.299,  U  = -0.356,  L  U  A  = -2.554,  $  w /  = 1.046,  $  L  = 0.286  Curvature Determinant of bordered h e s s i a n f u n c t i o n = 0.003 MRS  Production  = 1.192,  m  MRS  w/p L  of the u n i o n ' s  objective  = 0.599 = 0 . 2 7 3 , a. w/p L  Technology  Monotoni c i t y D  p  = 3.424,  D = 7.047, m  D  Q  = 4.032,  D  L  = -1.714,  D _= L[  0.796  Curvature Determinants of minors function are: 0.179,  The m a t r i x  K M  of the 0.0  of  hessian  price  of the c o n d i t i o n a l  elasticities  r  m K  0.105 -0.027  0.105 0.027 ff  KM  = -0.16  is  cost  77  TABLE Estimated C h a r a c t e r i s t i c s Technology:  All Union  of  Cooperative  estimates  XII  Union P r e f e r e n c e s  and  U n i o n Model w i t h Dummy  a r e e v a l u a t e d a t t h e mean o f  Production Variables  the  data  Preferences Monotonicity  U  B  = 0.425,  U  = -0.405,  L  U  A  = -1.976,  <|)  = 1.481,  w/p  <|> = 0 . 5 0 5 L  Curvature Determinant of bordered f u n c t i o n = 0.008 MRS  Production  = 0.955,  B L  hessian  MRS  w / p  L  of the u n i o n ' s  = 0.341,  a  w  /  p  objective  = 0.675.  L  Technology  Monotonicity D  p  = 3.444,  D = 7.129,  D  of minors 0.0  of  the hessian  The m a t r i x  of  price  m  Q  = 4.031, D  L  = -1.615  D  L L  =  0.598  Curvature Determinants are: 0.177,  the  elasticities  r K M  of  m •0.104 0.027  0.104 -0.027 -0.16  cost  is  function  78  Equations  5.17a  and b a r e t h e c o s t m i n i m i z i n g ,  demand f u n c t i o n s expenditure  given  curve  t h e amount o f  by  (5.4)  labour  5.15  e m p l o y e d and 5 . 1 7 d  to the maximization  ables;  K , M , w, and  problem.  error  observations  an i d e n t i f y i n g  restriction,  FIML e s t i m a t e s  of the parameters  t-statistics,  dummy v a r i a b l e s equation  for  and t h e  that  the  ables  is but  also it  are  that  can o n l y  by  condition vari-  are a l s o  affect  cannot  be  rejected,  preferences  rejected  be r e j e c t e d  variables.  are  at  along  a d d e d on t o in  Table  and  XI and X I I .  the estimates that  It of  with each X.  produc-  and e v a l u a t e d is  at  clear  the  charac-  t h e dummy  vari-  accepted. hypotheses  about union  (see Table  independent  of  IX).  75% c o n f i d e n c e  pref-  dummy  The  hypo-  the a l t e r n a t i v e  i n t h e model w i t h o u t the  and  re-estimated  b o t h w i t h and w i t h o u t  ratio tests  cor-  preferences.  reported  dummy v a r i a b l e s  they  5.17  reported,  and plywood m i l l s  in Tables  do n o t  using l i k e l i h o o d union  divided  when t h e y  The s y s t e m i s  and r e n t m a x i m i z a t i o n  overwhelmingly  w i t h dummy  X.  estimates  reported  are overwhelmingly  variables, thesis  Table  coefficients  T h e wage b i l l  iso-  endogenous  i m p o s e d on u n i o n  v e r y much, even though t h e h y p o t h e s i s  have z e r o  erences  and i n d e p e n d e n t  of t h e system are  and w i t h o u t  dummy v a r i a b l e s  teristics  the  order  of the estimated union preferences  with  t h e sample means,  the f i r s t  There are f o u r  u^ = 1 i s  in  parameter  technology,  and u n i o n ,  a r e added o n t o e q u a t i o n s  shingle mills  Characteristics tion  is  t e r m s w h i c h a r e c o r r e l a t e d when  same o b s e r v a t i o n  respond to d i f f e r e n t  with t h e i r  is  5.17c  input  L.  distributed  correspond to the  Equation  c h o s e n by t h e i n d u s t r y  (5.14)  Normally  and 5 . 1 6 .  conditional,  dummy  level  wage  variables,  in the  model  79  The e s t i m a t e d 0.059 w i t h o u t variables, level  of  so t h e h y p o t h e s i s  employment  °'  =  tion  is  =  a  12  278.478.  spite  ^  =  ^  low e s t i m a t e  the  labour  materials.  economic  positive.  industry  Economic  both  indifferent  ^  n  sightly  a  to  the  cases.  the technology  is  Leontief  modified  version  of the u n r e s t r i c t e d  of  o  Leontief  M V I  the  of  func-  model Therefore,  technology  is  also It  that  insists  with  only  price that  that  elasticities  t h e own p r i c e  form f o r c e s  the cross  price  elasticity  elasticities  That  fact  elasticities  is  and m a t e r i a l s  corroborated  shown i n T a b l e s  with  to  have  input  equal  to  minus  reported  a r e complements by t h e  XI and X I I .  economic  functional  t h e work  once a g a i n  be  elasti-  i n t h e two  t o be e x a c t l y all  the  must  elasticity  the  the  and  two i n p u t s ,  consistent  capital  place  three  capital  out t h a t ,  e l a s t i c i t i e s . 'Unfortunately,  above i n d i c a t e s  inputs;  turns  price  form  to  by some m e c h a n i s m o u t s i d e  as can be s e e n f r o m t h e e s t i m a t e s ,  the cross  t h e own p r i c e  substitutes.  insists  a r e due  Although there are  two v a r i a b l e  s i g n f r o m t h e own p r i c e  In f a c t ,  price  determined  elasticities  and t h e f u n c t i o n a l  and t h e c r o s s  theory  functional  theory  i n t h e CUM.  has o n l y  must be n e g a t i v e .  form f o r c e s  cross  is  Economic t h e o r y  the opposite case.  input  must be s u b s t i t u t e s  theory,  in  on t h e e s t i m a t e d p r i c e  restrictions  so t h e  cities  is  likelihood  on t h e p r o d u c t i o n t e c h n o l o g y  inputs  the union  dummy  decisively.  strong  model,  and  and 0 . 1 6 2 w i t h t h e  tested  S  are 0.286  and 0 . 5 0 5  rejected that  ^  a l t h o u g h t h e maximum v a l u e was n o t f o u n d .  The w r o n g s i g n s  inputs,  that  of  maximized value of the l o g l i k e l i h o o d  The l o g  of a very  rejected  the  also  The r e s t r i c t e d  reached 312.3, in  is  the hypothesis  ^12  t h e CUM.  and s t a n d a r d e r r o r s  t h e dummy v a r i a b l e s  Finally, ^ °MK  values  and n o t negative  Given the  func-  80  tional price  form,  the negative  elasticities  wrong s i g n s . specified  in  It  cross  price  and t h e m a t r i x  of  seems c l e a r t h a t  price  just  plementarity  of  and m a t e r i a l s  questionable  estimates  Non C o n s t a n t  II .II .II— — —— —— R e t u r n s S i n c e t h e work  is  not  an a c c e p t a b l e  t h e MUM and CUM a r e w h i c h does  not  to  Scale  —  properties  .  L.  conditions  t o minus  as t h e y  above e x c e p t  D(r,m,L,Q)  = c  one can  rL + c  + 2[b  to  1 2  D(r,m,L,Q)  homogeneity  D(r,m,L,Q)  1 3  cost  function  returns  retains  to  Only all  scale. the  of  the  o f d e g r e e one i n Q a n d  still  functional  scale  ensures  that  the  second  satisfied. form  input which  (Diewert, is  1974,  constant  and  defined  specify  rQ + c  (LQ)* +'b  constant  to  technology,  a r e shown a b o v e .  of the union models a r e  one,  very  returns  of the p r o d u c t i o n  changes.  of  constant  using a conditional  1 3 7 ) a n d a d d i n g one more f i x e d  equal  and  com-  4  the technology  By u s i n g t h e same g e n e r a l p.  technology  i  re-estimated  The new s p e c i f i c a t i o n  order  own  the  accommodate t h e  found i n the d a t a ,  characterization  D(r,m,L,Q)  outlined  has a l l  production  enough t o  i n C h a p t e r 4 shows t h a t  constrain  of  positive  result.  The MUM and CUM r e m a i n e x a c t l y specification  rich  imply  elasticities  t h e two i n p u t  t h e CUM i s capital  not  elasticities  L*  r + c  + b  mL + c^mQ + c ^ m  Q ][r 2  2 3  + m + 2X] + 2a' XZ 1 2  (5.18)  where X = ( - r 2  2  + - m ) 2 2  2  and Z = 1 + L + Q + 2 ( ( L Q )  2  + L* + Q " ) . 2  81  In t h e MUM e q u a t i o n s , the f o l l o w i n g  K  =  C  13  +  2[b  M = c  2  1 2  -w = c  n  (LQ)  1 2  2  C  12  + b  4  (LQ)  1 2  2 1  X(l  + u  2  1 [- ( b  Q  1 2  +  1 3  L  2 2  2  L  1 3  + L~  2 1  + b  i  +  2  1 2  +  3  +  2[b  1 ?  c  n  L + c  (LQ)  2  + r/X] + a  rZ/X  (5.19a)  b Q i ] [ l + m/X] + a m Z / X  (5.19b)  2 3  1 2  1 2  1 2  4  +  b^L^Hr + m + 2 X ]  (5.19c)  X +  + u-^B + u A ) ( u - ^ + u-^L + u ^ B + u ^ A ) 2 3  b 1  3  ) (  1 2  3  + m + 2X) + a  r  the following simultanous  1  equations:  + (Q/L)*)  2  In t h e CUM e q u a t i o n s  K = c  Q ][l i  2 3  (Q/L)  m _ 2a  L  system of  Q +  m + [b  = [-c^r _ c  p(u  Q  2 2  + b  i  r + c  + 2a  L  L +  + c^L + c  3  2[b  11  C  simultaneous  5 . 5 , 5 . 8 , 5 . 9 , 5 . 1 1 , 5 . 1 2 , and 5 . 1 8 i m p l y  1 2  X(l  i  + Q )] 2  -  1  .  (5.19d)  5 . 5 , 5 . 4 , 5 . 1 4 , 5 . 1 5 , 5 . 1 6 , and 5 . 1 8 i m p l y equations  system:  Q +  + b^L  2  +  b^cnCl + r / X ] + a r Z / X 1 ?  (5.20a)  82  M  =  C  23  +  2[b  21  C  1 2  L  +  (LQ)  -w = - E / L  22  C  [ r + m + 2X] +  L~  = E-c^r  2  ^ l  - c  u  +  [(b  1 2  U  Q  12  systems  U  1 3  correlated  13  2 a' 1 2X  A  +  u  ii ) B  for  the  errors  u  13  =  ^ ^  s  m  0 S e c  l  T h e FIML e s t i m a t e s statistics  are  2 2  L + u  1 2  B  + u  2 3  A)  ^  1 2  X(l  ivn-1 + Q )] .  (5.20d)  2  and dummy v a r i a b l e s  for  observations  a r e a d d e d on t o e a c h e q u a t i o n restriction constant  u^= 1 i s  returns  numerical  CUM ( e q u a t i o n s  i P  + u  to  imposed. scale  corresponding to different  the  =  ]  1  reported  o  n  union  5.20)  models  prevented  so t h e  restriction  of the parameters i n Table  XIII.  is  error used  are  the  i n t h e CUM.  and t h e i r  two  are  observations  problems  preferences  in the The  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  estimation l l  1  errors  Unfortunately  of  _  2  + m + 2X) + 2 a  identifying  while  b ^ Q V  (5.20c)  + p(u  1 2  )(r  Errors  +  1 2  independent.  u  2  and plywood m i l l s  again here.  2 2  2a XZ/L  -  specified  + c^m + c mQ/L  + b^' "  i  (5.20b)  1 9  + c^r/L  (Q/L)  distributed  and t h e  structure  m  +  + b  2  Normally on s h i n g l e  L  2 1  1 2  + m/X] + a m Z / X ] 12'  2  u  12  + 2[b  2 3  + b„Q ][l 23  2  c rO/L  +  n  + c m/L  +  + b^L '13  2  c r  +  Q  asymptotic  The c h a r a c t e r i s t i c s  of  tthe  83  estimated union preferences Tables  XIV and X V .  The r e s u l t s  CUM a n d MUM a r e r e p o r t e d mization  hypotheses,  are independent rejected  in  confidence  in Table XVI.  as w e l l  of  ^ of  ^equals  <(> a r e L  zero  the magnitudes  is  labour  much l o w e r .  rials  standard errors  and - 1 . 0  i n t h e CUM.  respectively, in  the  both models  the  preferences  The e s t i m a t e d  to exhibit  non-constant  the estimated results.  of Since  hypo-  a t t h e 99%  and m a t e r i a l s  In t h e MUM h o w e v e r ,  and t h e e s t i m a t e d  the  capital  are s t i l l  services  complementarity  of  estimated  to  to  between  scale ser-  capital  o f t h e demand function  returns  capital  side and  between c a p i t a l  non-constant  scale  services  returns  complementarity  In t h e CUM, s p e c i f y i n g estimated  for  non-constant  capital  to  characteristics  The e s t i m a t e d e l a s t i c i t i e s  and t h e demand f o r  returns  On t h e p r o d u c t i o n  be a s u b s t i t u t e  services  to  services  are  for also  scale and m a t e -  slightly. On t h e u n i o n s i d e ,  ties  union  in  maxi-  overwhelmingly  c a n be r e j e c t e d  estimated to  and m a t e r i a l s .  function  increases  that  and r e n t  wage, are a l l  both 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  and l a b o u r  services  0.369  o f many o f  and c a p i t a l  be c o m p l e m e n t s .  vices  hypothesis  reported  p e r f o r m e d on  The wage b i l l  i n t h e MUM and 0 . 3 7  few o f t h e q u a l i t a t i v e  still  materials,  decreases  tests  are  level.  but changes labour  as t h e  are 0.026  Allowing the technology affects  hypothesis  of the a l t e r n a t i v e  t h e two e s t i m a t e s that  of  b o t h t h e CUM and MUM.  the estimates  thesis  and p r o d u c t i o n t e c h n o l o g y  the monotonicity  of the union o b j e c t i v e  space,  are maintained  In t h e CUM, t h e  in  average  function,  in  and q u a s i c o n c a v i t y real  both non-constant real  wage i s  less  proper-  compensation-employment  returns  to scale  than the estimated  models. average  84  TABLE Estimated C o e f f i c i e n t s :  Non-Constant  W i t h Dummy  Asymptotic  t-statistics  Monopoly  :  :  :  :  12 13 21 22 23  '12 >13 '23 l  Union  0.201  '11 :  are  12  in  ll  J  J  ]  J  12 13 22 23  Natural  log  1ikelihood  to  Scale  Variables  Model  Cooperative  Union  Model  (2.187)  0.1385  (0.433)  0.8349  (12.679)  1.2147  (8.468)  -2.4014  (-1.638)  0.2971  (2.390)  0.1051  (1.461)  1.4534  (3.480)  1.0054  (16.957)  1.2054  (13.440)  1.2816  (0.778)  -0.8227  (-4.817)  -0.2889  (-9.970)  -0.7819  (-4.724)  -0.0836  (-3.118)  -0.2914  (-3.086)  -0.1279  (-0.596)  0.0489  (1.376)  0.1383  (3.016)  0.3046  (4.628)  1.0  0.0848  (0.628)  -1.0218  (-2.797)  •0.0065  (-3.101)  0.0193  (4.518)  •0.4505  (-102.05)  •0.0571  (-4.812)  0.2402  (2.529)  •0.0381  (-0.629)  -0.9576  (-3.658)  0.0 -0.0806  (-9.647)  0.0  of function  Correlation  and  values  K , M , w , and L  454.701  450.939  Coefficients  between a c t u a l predicted  Returns  parentheses  1.0  l  XIII  of  0.95,0.99,  0.94,0.99,  0.95,0.99  0.91,0.99  85  TABLE Estimated C h a r a c t e r i s t i c s Production  Technology:  Non-Constant  All Union  of Union P r e f e r e n c e s M o n o p o l y U n i o n Model  Returns to  estimates  XIV  S c a l e and Dummy  are evaluated  and with  Variables  a t t h e mean o f t h e  data  Preferences Monotonicity  U  B  = 0.192,  U  = -0.041,  L  U  A  = -3.427,  $  = 0.66,  w /  4> = 0 . 3 6 9 L  Curvature Determinant of bordered f u n c t i o n = 0.0018. MRS  Production  B L  = 0.215,  hessian MRS  w / p  of the  union's  = 0.559,  L  a  w  /  p  objective  L  = 0.773.  Technology  Monotonicity C  p  = 2.122,  C = m  7.363,  C  = 3.619,  w  C  Q  = 4.401  Curvature Determinants of minors of the hessian are: - 0 . 1 0 8 , - 0 . 1 0 3 , 0.0  The m a t r i x  of  price  of the  cost  elasticities  is  m K M L  -0.063 -0.109 0.358  0.487 0.328 -1.295  -0.423 -0.219 0.937  The e l a s t i c i t i e s  «!„. "  w  2  '  2 3  -  of  substitution  <k " i -  5  1  -  are;  °KM " - ° -  6 8  function  86  TABLE XV Estimated C h a r a c t e r i s t i c s Production  Technology:  Non-Constant  All  Union  estimates  of  Union P r e f e r e n c e s  Cooperative  U n i o n Model  R e t u r n s t o S c a l e and Dummy  are evaluated  and with  Variables  a t t h e mean o f t h e  data  Preferences Monotonicity  U =0.722, B  U =-2.542, L  U =-3.307, A  <j> =2.492, w/p  ^=-1.005  Curvature Determinant of bordered hessian of the u n i o n ' s f u n c t i o n = 0.171 MRS = 3.522, M R S = -0.403, a B L  Production  w / p  L  w / p  objective L  =  0.401.  Technology  Monotonicity D  = 3.32, r  D = 7.25, m  D  = 5.05, Q  D L  = - 5 . 4 7 , D, = LL  1.87  Curvature Determinants of minors of t h e h e s s i a n function are: 0 . 2 7 , 0.0  The m a t r i x  K M  of  price  of the c o n d i t i o n a l  elasticities  r  m  0.158 -0.041  -0.158 0.041 a  = -0.25 KM  is  cost  87  TABLE XVI Maximized Values Non-Constant  o f t h e Log L i k e l i h o o d s  of the Union  R e t u r n s t o S c a l e w i t h Dummy  Monopoly Union Model  Variables  C o o p e r a t i v e Union Model u = u = 0 n  1 3  Unrestricted  454.701  450.939  Wage b i l l m a x i m i z a t i o n hypothesis  410.902  407.863  Rent m a x i m i z a t i o n hypothesis  314.757  417.987  Union p r e f e r e n c e s independent of the a l t e r n a t i v e wage hypothesis  431.554  443.022  U  l l  =  U  13  =  °  432.436  Models:  88  marginal  rate  of  so t h e e s t i m a t e cannot  substitution of  <f>^ i s  be r e j e c t e d  ticity to  of  is  substitution  increasing  ginal  r a t e of to  in  of  zero.  substitution  It  As n o t e d a b o v e , level  and i t  between  real  a l s o means t h a t  between  real  real  is  wages  estimates.  returns  to  scale  and t h e  higher than the  i n the  is  unaffected,  production  the  and  is  elas-  difficult  function  estimated  The e s t i m a t e d e l a s t i c i t y  wages and e m p l o y m e n t  result  of the  wages and e m p l o y m e n t  slightly  this  means t h a t  the estimate  wages and employment  substitution  scale  between r e a l  than  compensation,  In t h e MUM, 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  still  constant  rate  negative.  interpret.  returns  less  a t t h e 99% c o n f i d e n c e  estimated marginal employment  b e t w e e n l a b o u r and r e a l  is  mar-  constant of  substitution  i n t h e MUM, by n o n -  technology.  Summary The e s t i m a t e s p l a c e d upon t h e  union's  Given the model, about  the  period  IWA's  shown a b o v e s a t i s f y  these  preferences  and t h e  are i n c r e a s i n g  and q u a s i c o n c a v e of the  union o b j e c t i v e  of work, in  real  function  wage a n d m a n - h o u r s .  mates  the  restrictions  production  technology.  p r o v i d e d e t a i l e d answers  of the o b j e c t i v e  i n man-hours  as a f u n c t i o n  real  and t h e  all  production  to  technology  questions in  the  studied.  decreasing wage,  results  preferences  The e s t i m a t e s IWA's  preferences  almost  real  function  in total  used t o c h a r a c t e r i z e  real  decreasing  compensation  is  generally  i n t h e CUM s l i g h t l y  ranges  o f work t h e  increasing  between 0.6  real  and h o u r s .  The e s t i m a t e d e l a s t i c i t y  wages and m a n - h o u r s  compensation,  in the  wage a n d m a n - h o u r s  the  of  in  alternative When  written  estimated  both t h e  real  substitution  and 0 . 8 ,  lower than the estimates  with the  i n t h e MUM.  between esti-  89  Real IWA a r e only  wage b i l l  both  the  maximization  rejected  real the  the  alternative  IWA's  The r e s u l t s Dertouzos local. the  indifferent  and P e n c a v e l  (1981)  estimated  is  0.69.  rent maximization not  indifferent The IWA's  Further,  hypotheses  to the level  for  This  ables,  is  so high  a marginal  indifferent  is  rate  a n o t h e r way, t h e u n i o n or a $64.00  about  -1.5,  so t h e  is  materials stitutes.  of  in the  is  of the  in the  Cincinnati  increasing  real  the  in  wage,  wages  and  and  I T U , and t h e  substitution  ITU  between  i n t h e MUM and 0 . 3  is  of the  o f one  real  elasticity  the  demand vari-  the union  is  worker  hourly  wage.  worker  annual  real  in  of the  0 . 4 means t h a t  gross  indifferent  in  results  maximization  t o one l e s s  real  (for  pay o f is  Put a whole  all  the  estimated to  b e t w e e n a 1% r i s e  in  be  real  employment.  production  a r e complements w h i l e a l l In b o t h m o d e l s ,  for  i n employment  The c o r r e s p o n d i n g  union  between  Given the s c a l i n g  indifferent  wages a n d a 1.5% d e c r e a s e The e s t i m a t e s  of  about 0.4  increase  increase  remaining employees.  rate  substitution  and a 0.032<t  of  employment.  i n t h e MUM. of  also  r e a s o n why t h e e l a s t i c i t y  between a d e c r e a s e  (2000 h o u r s )  year)  the  is  wage b i l l  rejected  of  employed i s  low v a l u e  labour  real  estimated marginal  w a g e s and m a n - h o u r s CUM.  the  to the  in the a l t e r n a t i v e  substitution  are  independent  ITU i n t h e  function  decreasing  of  employment.  not  close  f o r the  objective  and t h e e s t i m a t e d e l a s t i c i t y  the  IWA m a x i m i z e s of  is  by  specified.  report  input,  the  function  IWA a r e s u r p r i s i n g l y  wage a n d l a b o u r  employment  is  that  to the level  objective  wage as i t the  rent maximization  the hypothesis  estimated  for  The I T U ' s  real  is  wage a n d i s  Further, real  as  and r e a l  the  technology other  estimated  pairs cost  show t h a t  capital  of  are  inputs  functions  satisfy  and  subtheir  90  monotonicity prices. rich  properties,  Unfortunately,  but are not concave w i t h the technology  specified  enough t o accommodate t h e c o m p l e m e n t a r i t y  and m a t e r i a l s , has a l l  so t h e e s t i m a t e d m a t r i x  t h e wrong s i g n s .  functions  slope  mated i n c h a p t e r labour  function  the estimates  In t h e MUM, a l l  down and t h e y four. is  MUM.  The e l a s t i c i t i e s  part  (in absolute  Thus,  observed that  sensitive  estimates or not  Finally, structure  value)  to the e x p l i c i t  returns  to  differences  and n o t  for  its  in  input  is  chapter  four  curve  in  union  simplicity  any b e l i e f s  in the estimating  about  equations.  the  chapter  also four.  technology  behavior. to  The  whether  of the  arbitrary.  errors  in  the  technology.  the s p e c i f i c a t i o n  i n an a l r e a d y  for  while  Hence,  of the production  rather  esti-  i n t h e MUM a r e  i m p o s e d on t h e  is  demand  o f t h e demand  i n t h e MUM a r e a l s o s e n s i t i v e scale  services  than those  labour  of  not  elasticities  and - 2 . 0 .  estimated  modelling  as n o t e d i n C h a p t e r 4 ,  c a t i o n was c h o s e n f o r  price  than those estimated  and t h e dummy v a r i a b l e s  equations,  -0.4  input  t h e CUM i s  the estimated  demand f o r  the estimates  of the technology  constant  of the  of s u b s t i t u t i o n  much l a r g e r  are very  be a b o u t  to  capital  For example, the e l a s t i c i t y  on an e l a s t i c  is  of  input  f r o m t h e MUM r a n g e b e t w e e n - 1 . 3  is  for  a r e much more e l a s t i c  estimated to  union  it  of  respect  The  messy  or across  error  specifi-  system  of  industry  91  Appendix t o Chapter  Proof that For r  r,m,  D(r,m,L,Q)  > 0 a n d L,Q  is  Non-decreasing  > 0 but  in  r and m  both L and Q cannot  be z e r o ,  let  > r°.  1  D(r ,m,L,Q) 1  =  Min K,M  =  r^K*  + mM :  [r\  + mM*  ( K , M , L , Q ) e T}  w h e r e K* a n d M* a r e t h e s o l u t i o n s minimization  >  r ° K * + mM*  >  Min K,M  =  D(r°,m,L,Q)  {r°K + mM :  The same p r o o f  c a n be u s e d t o show D ( r , m , L , Q )  and D ( r , m , L , Q )  is  Marginal  > D(r°,m,L,Q)  non-decreasing  Rate of S u b s t i t u t i o n  The u n i o n o b j e c t i v e Define  B = Z(L)  union o b j e c t i v e  such t h a t and  is  non-decreasing  in  when b o t h r and m i n c r e a s e .  of the Union O b j e c t i v e  function  function  the  (K,M,L,Q)eT}  D(r ,m,L,Q) 1  to  problem  Therefore  0.  5  is  U(B,L;A),  U(Z(L),L;A)  w h e r e U.  = U°.  Function < 0,  and U  Differentiate  the  obtain:  U (3Z(L)/3L) B  -»• 3 Z ( L ) / 3 L  + u  L  = 3B/3L  = 0  = -U |U  U  /U L  B.  Therefore, MRS  = 3B/3L BL  |U  U  = -U /U L B  D  (A5.1)  92  Second O r d e r C o n d i t i o n i n t h e Monopoly  Union  {U(B,L;A)  which,  Max  : w = -D, ( r , m , L , Q ) }  B = wL/p),  order  U [-D  3U/8L  B  (D  L  +  L  . LD  L L  L L  )/p  The s e c o n d d e r i v a t i v e  8 U/3L  2  = -[D  L  ]/p  U  +  L  L  (A5.4)  = 0  (A5.5)  B  is  + LD _][U (3B/3L)  The s e c o n d o r d e r where both t h e f i r s t  + U  B B  R  ]/p  order  g L  ]/p  + U. ( 8 B / 9 L )  condition  (w = -D ) a r e s a t i s f i e d .  as:  (A5.3)  of A5.3  U [ 2 D . . + LD. .  function  is  = U /U  L 1  the o b j e c t i v e  L;A)}.  condition  - LD  into  c a n be r e w r i t t e n  L  is:  (A5.2)  the c o n s t r a i n t  {U(-LD (r,m,L,Q)/p,  The f i r s t  2  p r o b l e m i n t h e m o n o p o l y u n i o n model  by s u b s t i t u t i n g  (noting that  Problem  Model  The m a x i m i z a t i o n  Max w,L  for the Maximization  R  (A5.6)  -  + U  (A5.6)  LL  must be e v a l u a t e d  c o n d i t i o n A 5 . 5 and t h e The c o n s t r a i n t  implies  at a  constraint  point  93  wL/p = B = - L D / p L  *  33/3L = ( - D  +  3B/3L = - U / U L  by t h e f i r s t  aW  order  -  L  LD  L  B  BB L U  2  V L-H 2  B B  "  (U /U ) L  3 B  )/p.  (A5.7)  B  +  U  B L  A5.7 i n t o  ] - U [2D B  L L  A5.6 and o b t a i n  +  LD  L L L  ]/p  -  uLL  +  U  - U  L L  Substitute  BL L B  2 U  where H i s t h e d e t e r m i n a n t  It  - LD  L  condition.  u L B (u L /u B )  objective  )/p  = (-D  g  = -(U /U )[-U  [ U  L L  U  +  [-2D  U  LL B V* U  -  L L  LD  L L L  +  U  B [  2 D  LL  "  L  D  L L I >  ]/p]  of the bordered hessian  of the  union's  function. is  assumed t h a t  p > 0, I L > 0 and H > 0 s i n c e  U(B,L;A)  is  b quasiconcave  i n B and L.  second order  condition  t  Therefore,  a sufficient  t o be s a t i s f i e d -2D  *  L L  2 D  - LD  LL  > "  condition  2 2 (3U /3L < 0)  L L L  L D  for the  is  < 0  LLL  (A5.8)  94  Repeating equation  D(r,m,L,Q)  5.2:  = c r L n  + 2b  where X = ( - r 2  + c  1 2  (r  + m + 2X)(LQ)  1 2  + - m ) 2  2  2  rQ  + c mL  + c mQ  2 1  2 2  + 2a XZ  2  (A5.9)  1 2  and Z = L + Q + 2 ( L Q ) .  2  2  Clearly,  D  L  =  c  l l  r  +  21  C  m  +  b  12^  r  +  m  +  2 X  )(Q/ ) L  2  +  2  a  A-  *  °LL  *  °LLL  >  LD  "  =  [  12 ^  b  Q  2  r  +  ^ / ) i2 '  =  3  4  b  Q  (  m  +  2  r  +  m  X  )  +  +  2 X  a  i2  )  X Q  '  X(l  +  = [(3/4)b  XQ ]L~ i  1 2  5 / 2  1-3/2  Q (r  + m + 2X)  2  1 2  2  "3/2  i L L L  (Q/L) )  ] L  (3/2)a  +  1 2  +  (3/2)a  XQ ]L 2  1 2  Therefore,  -LD  - (3/2)D  LL  < 2D ,  equation  U  since  > 0,  (A5.8)  condition  of the maximization  is is  satisfied, satisfied.  and t h e  second  order  95  Second O r d e r C o n d i t i o n in the Cooperative  for the Maximization  Union  The m a x i m i z a t i o n  Max w,L  {U(B,L;A)  which,  Model  problem i n  : B = E/p  by s u b s t i t u t i n g  Problem  -  the cooperative  u n i o n model  is  D(r,m,L,Q)/p},  the c o n s t r a i n t  into  U(B,L;A),  c a n be  rewritten  as:  Max L  {U(E/p -  The f i r s t  D(r,m,L,Q)/p,  order  3U/3L = - U g D / p L  + D /p  condition  + U  2  is:  = 0  L  L  (A5.ll)  B  The s e c o n d d e r i v a t i v e  2  (A5.10)  = U /U .  L  3 U/3L  L;A)}.  = -D [U L  B B  of  A5.10  is  ( 9B/3L) + U ^ / p  - D^Ug/p + U ( 3 B / 3 L ) L B  + U  L  t  (A5.12)  The c o n s t r a i n t  (B = E/p  imply 3B/3L = - D / p L  = -U /U , L  B  -  D(r,m,L,Q)/p)  and t h e f i r s t  order  condition  96  w h i c h when s u b s t i t u t e d  a W  i n t o A5.12 y i e l d s  = -(uL/uB)[-uBB(uL/uB)  •  U  B "  2  [  U  B B  U  L  -  = U " [-H - U 2  B  where H i s t h e d e t e r m i n a n t objective  function,  B  B  satisfied.  U  D  L B  L L  U  L  U  B  +  U  LL  U  B  "  U  B  D  +  uLL  L /P^ L  /p] < 0  of the bordered hessian  p > 0, U  Therefore t h e second order  2  uBL] - UgD^/p - uLB(uL/uB)  +  > 0 D  of the union  > 0 a n d H > 0 by a s s u m p t i o n .  LL  condition  of the maximization  problem  is  97  Chapter  6 Union M o d e l s :  All firms  the  in the  union models industry  given  output  that  level  of output  the  wage, t h e  labour  presented  minimize  genously  input,  is  industry  materials; rials  is  and t h a t  to maximize Assumptions  tion  technology  empty,  convex,  decreasing fit  is  function  =  where q i s  the  as  Max Q.K.M  to outlay  revenue minus  of  of  capital  in this  and  assume  actions,  the  materials.  chapter  for  behaved  see D i e w e r t  assuming  output,  that  capital  capital,  (closed,  (1974,  a r e assumed so t h a t  and  and m a t e -  The  bounded,  p.134)) the  producnon-  but  industry's  pro-  when t h e l a b o u r  Diewert  (1974,  136)  function  rK - mM :  output  chapters.  prices,  the following  of t h e u n i o n ' s  to  a s s u m e d t o be t r u e .  be w e l l  profit  {qQ -  variable  p.  naive  some e x o -  i n t h e MUM.  price  in the e a r l i e r  to  the  profit.  free disposal;  Define a v a r i a b l e  V(q,r,m,L)  subject  chooses o u t p u t ,  t o A5 a r e s t i l l  exists  5 assume t h a t  somewhat  in the markets  assumed t o  returns  costs  is  prices  industry  variable Al  It  re-estimated  taker  the  Chapter  independent  and t h e  a price  in  Maximization  variable  constraint.  H e n c e t h e MUM and CUM a r e the  Profit  costs, input  and a l l  V(q,r,m,L)  e T}  the other is  is  (6.1)  notation  t h e maximum  given technology  shows t h a t  properties.  (K,M,L,Q)  variable  profit  the  same  possible  and i n p u t  given exogenously  is  and  to the functions  output  industry. possess  98  (i)  V(q,r,m,L)  is  a non-negative  function  for  q,r,m,  > 0 and L  > 0. (ii)  V(q,r,m,L)  is  homogenous o f d e g r e e one i n q , r ,  (iii)  V(q,r,m,L)  is  convex  (iv)  V(q,r,m,L)  is  non-decreasing  the (v)  input  V(q,r,m,L)  v < it  that  in  Chapter  V(q,r,m,L)  is  returns  scale  to  r and m.  D(r,m,L,Q)  appendix to  as a n e g a t i v e  Recall  value  i n L,  that  here.  which  is  5,  V(q,r,m,L)  The p r o o f  is  non-decreasing  so i t  will  is  not  non-decreasing  exactly in  analogous  implies  is  not  be r e p e a t e d h e r e .  i m p o s e d on t h e  i n q and to  r and m shown i n  n o t homogeneous o f d e g r e e one i n L s i n c e  A functional specify  and m.  i n L (V^> 0 ) .  c o n c a v e and c o n t i n u o u s  c a n be shown t h a t  non-increasing proof  is  not d e f i n e d  in q,r,  0.  LL  Moreover  L is  and c o n t i n u o u s  a n d m.  the  the  Notice  that  constant  technology.  f o r m s u g g e s t e d by D i e w e r t  (1974,  p.  137)  is  used  to  V(q,r,m,L):  V(q,r,m,L)  = c  1 2  q  + c^r  + c  + 2(a  1 2  X  + a  + a  + 2b  1 2  L*(q  /I 2 1 2A where X = ( - q + - r ) , Y 2 a constant  fixed  2 input,  v  1 3  Y  3 2  2 3  m + c^qL  Z)(l  + c  2 1  rL  2  (6.2)  ,1 2 1 2 J , , 1 2 = (-q + - m ) , Z = (- r 2  d e f i n e d equal  3 1  + L + 2L ")  + r + m + 2X + 2Y + 2Z)  2  + c mL  2 t o minus one,  2 is  1 2A , + - m ) a n d z  2  .  included  to  99  impose d e c r e a s i n g  returns  Note t h a t  equation  6.2  arbitrary  variable  profit  provides  Define a function, and i s  a function  of  to outlay  on t h e t e c h n o l o g y  a second order  to  approximation  6.2. to  an  function.  G(q,r,m,w,L),  input  dual  and o u t p u t  which i s prices  equal  to total  profit  and t h e amount o f  labour  employed,  G(q,r,m,w,L)  Iso-profit  = V(q,r,m,L)  curves  in  a  (6.3)  compensation-employment  pB = wL = V ( q , r , m , L )  where G i s  - wL.  -  s p a c e c a n be  written  G,  (6.4)  constant,  9(wL)/9L = v  L  > 0,  and  3 (wL)/ 3L 2  2  Union p r e f e r e n c e s  Monopoly Union T h i s model the  is  industry  c h o o s i n g K,M, output.  = V  L L  <  0.  are e x a c t l y  the  same as t h e y  are i n  Chapter  5.  Model the very  chooses  same as t h e MUM shown i n C h a p t e r  Q , K , M , and L t o m a x i m i z e  and L t o m i n i m i z e c o s t s  subject  profits  5,  except  rather  than  to a given level  of  now  100  The i n d u s t r y ' s the maximization  order  labour function  {G(q,r,m,w,L)}  condition  = Max L  also the  function written satisfied  industry's in  since  implicit  implies  to the maximization  V  The s e c o n d o r d e r  L  labour  condition  is  p r o b l e m i n t h e MUM i s  {U(LV,/p,L;A)}  L  problem  L L  -  of  L [  the  order  + U  L  con-  = 0  - U /U . P  so t h e usual  such t h a t  The f i r s t  is  L  involves  equation 6.2,  = B.  + LV _]/p  L  a r e not enough t o  derivative  (6.7)  L  wL/p = L V / p  LV  +  condition  function,  is  (6.5)  The s e c o n d o r d e r  g  V(q,r,m,L),  wL}.  form.  3U/3L = U [ V  third  -  m a x i m i z i n g demand f o r  maximization  s i n c e the c o n s t r a i n t  and V ( q , r , m , L )  {V(q,r,m,L)  profit  Max L  able profit  to  < 0.  The u n i o n ' s  dition  solution  - w = 0  L  is  the  is V (q,r,m,L)  which  is  problem  Max L  The f i r s t  demand f o r  (6.8)  B  the t h i r d curvature  derivative properties  of of  the  U(B,L;A)  g u a r a n t e e a maximum. F o r t u n a t e l y the functional  second order  form used t o  condition  is  vari-  always  the  specify satis-  101  fied.  See t h e a p p e n d i x t o t h i s  order  6.8  t o t h e MUM.  demand f u n c t i o n s Define ties  for  the d e t a i l s  on t h e  second  condition. Equations  tion  chapter  n(q,r,m,w)  maximizing  profit  function  Hotelling's  function  {V(q,r,m,L)  is  possessing  profit  all  and  solu-  input  function.  the usual  proper-  technology - wL}  = V(q,r,m,L*(q,r,m,w))  where L * ( q , r , m , w )  supply  c a n be d e r i v e d f r o m t h e v a r i a b l e  to the  = Max L  d e f i n e the compensation-employment  The p r o f i t  an o r d i n a r y  and d u a l  and 6.5  the  solution  - wL*(q,r,m,w)  to equation  6.5.  lemma a p p l i e d t o e q u a t i o n 6 . 9  Q*(q,r,m,w)  = 3n(q,r,m,w)/3q = 3 V ( q , r , m , L ) / 3 q |  K*(q,r,m,w)  = -3n(q,r,m,w)/3r  = -  (6.9)  implies  L = L  *,  3V(q,r,m,L)/3r|  (6.10)  *»  (6.11)  *  (6.12)  L = L  and  M*(q,r,m,w)  = - 3n(q,r,m,w)/3m = - 3 V ( q , r , m , L ) / 3 m . |  by t h e e n v e l o p e Equations following  L = L  theorem. 5.5,  6.2,  simultaneous  6.5,  6.8,  system of  6.10,  6.11,  equations:  and 6 . 1 2  imply  the  102  Q = c  +  1 2  + 2b  •K = c  c  L  1 2  L  n  L  + r(a  + 2b12L2(l  + r/X  •M = c  2 2  + c  3 2  2 1  3 1  L  1 1  q  + b  -L  -x  1 2  + c  L  '  + a  1 3  /Y)(l  + L + 2L ) 2  /X  (6.13a)  + a  2 3  /Z)(l  + L + 2L ) 2  + r/Z)  (6.13b)  + a  1 3  / Z ) (1 + L •+ 2L ") 2  2 3  + m/Y + m/Z)  r  + c  3 1  m + 2(a  (6.13c)  1 2  X  + a  1 3  Y  + a  2 3  Z)(l  + L  2  )  * ( q + r + m + 2X + 2Y + 2Z)  = [c^q  2  2 1  1 2  + m(a /Y  + 2b12L2(l  w = c  /X  1 2  (1 + q/X + q / Y )  2  + c  + q(a  p(u  2  [a  X  1 2  + c  + u  2 1  2 2  + a  r  + c  L + u  1 3  Y  3 1  2 3  + a  m + 2(a  A + u  2 3  Z  1 2  + -  1 ?  X  B)(u  b  1 2  + a  1  (q  (6.13d)  1 3  Y  + a  + u B n  2 3  + u  Z)  1 2  L  +  + u^A)" ] 1  + r + m + 2X + 2Y + 2 Z ) ] " . 1  (6.13e)  Equation Equations tions for  6.13a 6.13b  is  the supply  curve  for  and c a r e t h e p r o f i t  g i v e n by 6 . 1 1  labour function  and 6 . 1 2 .  output  g i v e n by  maximizing  Equation  6.13d  is  input  6.10. demand  the inverse  g i v e n by 6 . 5 w h i l e e q u a t i o n 6 . 1 3 e  is  the  funcdemand first  103  TABLE Estimated  Coefficients  of  the  Monopoly  Profit  Asymptotic  t-statistics  Monopoly 12  c  22  C  32  C  C  ll 21  C  31  C  3  12 13  3  23  3  b  12  are  Union  in  J  J  13  '22 23  Model  and  Cooperative  Union  Model  -1.1262  (-1.721)  -5.3727  (-9.693)  0.9812  (4.975)  -5.8537  (-8.677)  -0.6706  (-2.736)  0.0805  (0.387)  2.6610  (4.968)  1.0508  (8.991),  -0.5792  (-2.900)  -0.3580  (-1.494)  -3.4090  (-16.239)  -0.0538  (-0.674)  -0.3084  (-1.663)  0.2780  (2.092)  0.8853  (3.838)  0.0084  (0.093)  0.2147  (1.852)  -0.0831  (-1.303)  -0.2542  (-3.051)  1.0 (-4.367)  6.2455  (1.412)  0.7598  (1.882)  0.0157  (2.017)  -1.0157  (-2.090)  -0.3428  (-21.587)  -0.4389  (-5.352)  0.2749  (2.439)  1.0673  (2.146)  0.2805  (1.512)  -4.9605  (-1.628)  263.253  Correlation Coefficients between a c t u a l and 0.97,-0.84,  K.M.w,  Models:  (12.280)  Natural log of 1ikelihood function  predicted  Union  parentheses  0.0  12  Cooperative  7.3087  -2.4332  ll  and  Maximization  1.0  J  XVII  values L~*  of  0.93,0.99,-0.83  281.324  0.98,0.84,0.99, 0.91,-0.06  104  TABLE Estimated C h a r a c t e r i s t i c s Technology:  All  Union  of  XVIII  Union P r e f e r e n c e s  and  M o n o p o l y U n i o n Model w i t h P r o f i t  estimates  are evaluated  at  Production  Maximization  t h e mean o f  the  data  Preferences Monotonicity  U  B  = 0.424,  U  = -0.853, U  L  A  = -1.539,  <|>  = 1.466,  w/p  cp = 0 . 0 5 5 L  Curvature Determinant of bordered h e s s i a n of the u n i o n ' s function = -0.06. MRS = 2.011, M R S = 0.037, o B L  Production  w / p  L  w / p  objective L  = -0.055.  Technology,  Monotonicity n = 7.882, q '  n = -4.471, r '  n = -5.76, m  n , = -1.373 w  Curvature Determinants of minors of the hessian are: - 0 . 3 1 6 , - 0 . 1 4 8 , 0 . 0 3 5 , 0.0  The m a t r i x  of  price  of the p r o f i t  elasticities  r Q K M L  =  - ' 1  5  4  '  °ML  w 0.382 -3.297 0.208 3.764  0.011 -0.543 -0.049 0.593  The e l a s t i c i t i e s °KL  is  m  -0.237 2.212 -0.140 -2.427  -0.155 1.628 -0.019 -1.930  of =  °*  substitution 0 9 7  '  CT  KM  =  function  are:  -°'°  8 9  105  order condition a d d e d on t o  shown by 6 . 8 .  equations  6.13  Normally  distributed  and an i d e n t i f y i n g  i m p o s e d on u n i o n p r e f e r e n c e s .  The same e r r o r  structure  specified.  while  terms  to different  are  u^ = 1  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 corresponding  terms  restriction,  E r r o r terms error  error  are  is  is  correlated  observations  are  independent. Unfortunately complete  system,  ferences. are  so t h e  reported with t h e i r  technology, Table  of  the  is  satisfies  = 0 is  parameters  union  of  i m p o s e d on u n i o n  of the  asymptotic t - s t a t i s t i c s  the estimated  clear that  all  the p r o f i t  empirically.  restricted  in Table  preferences  and  the  pre-  system  XVII.  production  are reported  rate  of  of  substitution  estimated supply capital  in  is  slope  e s t i m a t e d t o be c o m p l e m e n t s , mated t o barely  be c o m p l e m e n t s  substitutable.  inferior  it  is  real  not  function  quasiconcave  wages and the  labour  estimated  On t h e p r o d u c t i o n  side  down w h i l e t h e e s t i m a t e d demand up.  Capital  but c a p i t a l  and m a t e r i a l s Materials  and m a t e r i a l s and l a b o u r  and l a b o u r  are  the  curves  still  are a l s o  esti-  are estimated t o  and l a b o u r a r e a l s o  found t o  be  be  inputs.  The e s t i m a t e s of  but  Further,  negative.  o f t h e MUM d o e s  union o b j e c t i v e  between  estimates.  curve slopes  and l a b o u r  properties,  substitution  much l o w e r t h a n t h e o t h e r  elasticity  maximizing version  The e s t i m a t e d  the monotonicity  and t h e m a r g i n a l  ties  u^  e v a l u a t e d a t t h e sample means,  perform well  for  prevented the e s t i m a t i o n  XVIII. It  not  of  problems  restriction  FIML e s t i m a t e s  Characteristics  is  numerical  of the input  substitution  of the estimates  of  of c  the c  price  production  elasticities technology  c_. , a . _ , a  1  Q  ,  a  and t h e are a l l  , and b  elasticifunctions  .  106  Table XVII  shows t h a t  asymptotic  t-statistics  statistic although  for  estimates  the estimates  greater  the estimate  no c o n f i d e n c e  elasticities  their  only  intervals  have v e r y  range f o r  large  any  it  More c o n f i d e n c e  meters  of the  2 3  )  have a s y m p t o t i c  the estimate of 0.085 that  < ^  < 0.195.  the union  is  wage-employment  Cooperative  except  the  not  which  all  the  (except  for  of  the  greater than two.  one c a n n o t  indifferent  include  of the estimates  say w i t h  to the level  the  zero  estimate  Despite for  of  this, <j> i s L  -  95% c o n f i d e n c e  o f employment  in  real  Model  is  industry  The i n d u s t r y ' s  exactly chooses  t h e same a s t h e CUM shown i n C h a p t e r Q,K,  profit,  and M t o m a x i m i z e  g i v e n some q u a n t i t y  G(q,r,m,w,L)  implies  in  para-  variable costs  the f o l l o w i n g  = V(q,r,m,L)  iso-profit  of  given a  - wL  labour  is  (6.3)  curve  wL = pB = V ( q , r , m , L )  - G  5  profits  output.  which  the  character-  of t h e  interval  r a t h e r t h a n 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 of  Thus,  level.  a n d a 95% c o n f i d e n c e  Therefore,  of  t-  space.  Union  T h i s model  0.07  above t w o .  in the estimates  function  t-statistics  is  intervals  confidence  since  union o b j e c t i v e  have  not 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  c a n be p l a c e d  of union preferences  slightly  the estimates  confidence  istics  u  only for  is  reasonable  and  than two, with the asymptotic  of a ^  are computed,  of  (6.4)  level  107  where G i s  constant.  T h e CUM c a n be w r i t t e n  Max w,L  {U(B,L;A)  = Max L  which  implies  as t h e m a x i m i z a t i o n  : B = V(q,r,m,L)/p  {U(V(q,r,m,L)/p  the f i r s t  order  -  G/p}  - G/p,L;A)}  (6.14)  condition  3U/3L = U V. / p + U. D  D  +  The c u r v a t u r e second order chapter  for  properties condition  the d e t a i l s  Equations tion  t o t h e CUM.  not completely contract the final  curve,  for  specified. but  it  =  = -pU /U . L  (6.15)  R  and U ( B , L ; A )  ensure that  See t h e a p p e n d i x t o  second order  t h e CUM o u t l i n e d The model not  condition.  i n Chapter  predicts  predict  the  this  d e f i n e t h e compensation-employment  5 , t h e model  an o u t c o m e on  w h e r e on t h e  soluis  the  contract  curve  be. and v a r i a b l e  and m a t e r i a l s ,  profit  L  = 0  L  V(q,r,m,L)  the  does  function,  chosen w i t h the u n i o n ,  Q*(q,r,m,L)  V  L  satisfied.  of  As w i t h  capital  the v a r i a b l e  is  and 6 . 1 5  outcome w i l l  The s u p p l y tions  6.4  of  problem  all  profit  m a x i m i z i n g demand  conditional  on t h e  labour  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  funcinput  lemma  function:  3V(q,r,m,L)/3q  (6.16)  to  108  K*(q,r,m,L)  = -9V(q,r,m,L)/9r  (6.17)  = -9V(q,r,m,L)/9m.  (6.18)  and  M*(q,r,m,L)  The e q u a t i o n s CUM a r e : (ii)  the  (i)  used t o  the input  iso-profit  + 2(a  + 2b  and ( i i i ) by  1 2  1 2  X  L  q + c  + a  _ i  (q  the f i r s t  1 3  estimate the  and o u t p u t  curve  w = -G/L + c  actually  given  Z ]  Y  by e q u a t i o n  + c  r  + a  2 3  functions  3 ]  m  given  + L  + c^r/L  + 2L  _ 1  by  the  b and  labour  *)  (6.19d)  to the maximization  problem  given  6.15  - i  -L  2  = Lc-Qq + c ^ r  + c ^ m + 2 ( a ^ X + a^ Y  2  p(u  2  [2(a  + u  1 2  X  2 2  2  L + u  + a  1 3  Y  2 3  A + u  + a  2 3  Z)  1 2  B)(u  + b  + a  3  1 2  1  (q  + u  1 1  B  c;  + c^m/L  + r + m + 2X + 2Y + 2 Z ) ;  order condition  of  by 6 . 1 3 a ,  6.4 d i v i d e d  + c^q/L  Z)(l  parameters  2 3  X)  + u^L  +  + u^A)" ]  + r + m + 2 X + 2 Y +  1  2Z)]" , 1  (6.19e)  109  The u s u a l tions  error  structure  ( 6 . 1 3 a , b and c ,  tion  (u^ = 1)  reported nology  is  imposed.  in Table XVII,  and u n i o n  Table  properties  - 1 . 7 7 8 and 1.0  is  space.  95% c o n f i d e n c e  estimated marginal  ficult  to  Thus,  rate  of  in  On t h e p r o d u c t i o n  labour.  <> j ^ may be p o s i t i v e estimate  for  capital  properties,  supply  materials  services  slopes  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  the  time,  very  although  close to zero.  inferior  input.  the estimated  Finally,  capital  are <|> i s L  <j> means t h a t  the  L  real  wages  is  and is  function  difis  also  space. profit  not  slopes  Capital  function  concave  down, but t h e  up.  ^  the  function  slopes  real  for  substitution  it  in  at  variable  but  of  interval  union o b j e c t i v e  materials first  of  of  error  or n e g a t i v e  between  the estimated  The e s t i m a t e d  e s t i m a t e d demand c u r v e f o r demand c u r v e  so a 95% c o n f i d e n c e  side,  monotonicity  o f employment  and s t a n d a r d  tech-  t h a n t h e MUM.  the  compensation-employment  the monotonicity  to  satisfies  substitution  are  XIX.  no b e t t e r  in the level  The e s t i m a t e d real  Table  equa-  restric-  of the estimated  in  n e g a t i v e and t h e e l a s t i c i t y  not quasi concave  respect  function  The n e g a t i v e  interpret.  satisfies  reported  The e s t i m a t e  level.  of the parameters  t h e CUM p e r f o r m s  respectively,  L  is  are  decreasing  < <j> < 0 . 1 8 2 .  same i d e n t i f y i n g  and c h a r a c t e r i s t i c s  preferences  it  wage-employment  employment  and e ) and t h e  union o b j e c t i v e  but  appended onto t h e e s t i m a t i n g  FIML e s t i m a t e s  X I X shows t h a t  The e s t i m a t e d  -3.738  6.19d  is  with  up and  the  estimated  services  and  r a t h e r t h a n complements  elasticity services  is  of  substitution  for is  e s t i m a t e d t o be an  110  TABLE Estimated C h a r a c t e r i s t i c s Technology:  All  Union  Cooperative  estimates  of  XIX  Union P r e f e r e n c e s  and  U n i o n Model w i t h P r o f i t  are evaluated  at  Production  Maximization  t h e mean o f t h e  data  Preferences Monotonicity U  B  = 2.243,  U  = -6.614,  L  U  A  = -20.343,  <|>  = 7.925,  w/p  <|> = L  -1.778  Curvature Determinant of bordered hessian function = -8.47. MRS  Production  = 2.948,  B L  MRS  w / p  L  of the u n i o n ' s  = -.224,  a  w  /  p  objective  = 0.125  L  Technology  Monotonicity  V  q  = 9.59,  V = -3.31, r  V  m  = -6.89,  V  L  = 4.49,  V  = 0.123  L L  Curvature Determinants are: 0.424,  of minors of - 0 . 3 7 3 , 0.0  The m a t r i x  the  of  hessian  price  of  the cost  elasticities  function  is m  Q K M  0.208 -0.479 0.493  -0.278 0.125 -0.525  0.070 0.354 0.032  The e l a s t i c i t i e s a  KM  of =  substitution °'  0  2  are:  Ill  Summary As n o t e d i n t h e i n t r o d u c t i o n believe union, level  that  output  as i s of  is  independent  assumed i n c h a p t e r  output  in  level  t a k i n g output  of  the estimates function  is  employment real  increasing  and t h e  real  of the rates  in the  level of  of  real  in  compensation-employment  the  are  space  side  materials  that  wage.  estimated  rather  in  results  The o n l y  is  economic t h e o r y ,  all  other  the the  industry  to  rather  than  affects objective  and d e c r e a s i n g  in  as a f u n c t i o n  of  Written  union o b j e c t i v e  function  All  other  evidence,  function  between  Further, in  the  real  t h e MUM o r CUM. by t h e c h a n g e Estimated  in  supply  asand  demand  a r e f o u n d t o be i n f e r i o r , from complements t o information  materials  slopes  results or  is  marginal  substitution  not q u a s i c o n c a v e  obtain. inputs  of  of the  uninformative.  either  reasonable  t h e demand f o r  are s u b s t i t u t e s .  of  policies.  behaviour  the estimates  jump i n d i s c r i m i n a t e l y  and v i c e - v e r s a .  to  adjusts  or union  compensation  also affected  s l o p e t h e wrong way,  is  poor  is  functions  models  real  function  and v e r y  inputs  surely  The e s t i m a t e d u n i o n  Hence,  sumptions  of  behaviour  profits  industry  and t h e e l a s t i c i t i e s  estimated union o b j e c t i v e  The p r o d u c t i o n  its  naive  wage b u t an i n c r e a s i n g o r d e c r e a s i n g  wages and e m p l o y m e n t  pairs  about  alternative  employment.  substitution  prices  is  constraint.  union preferences.  still  in  it  or the  The i n d u s t r y  5.  in the assumption  of  prices  which maximizes  wages and e m p l o y m e n t ,  increasing  real  output  chapter,  re-estimated allowing the  as an e x o g e n o u s  The c h a n g e  of  response t o changes  Hence, t h e u n i o n models a r e choose the  to this  both.  substitutes  obtained from  down and l a b o u r  contradict  and  either  these and  112  Appendix t o Chapter Second Order C o n d i t i o n  for the Union's  6  Maximization  Problem  i n t h e MUM  The u n i o n ' s  Max  {U(B,L;A)  Max L  maximization  : w = V }  {U(LV./p  9U/3L = U g [ V  V  , L ; A ) }.  L  +  order  (A6.2)  + LV  L  V  LL  =  L L  condition  ]/p  •P L U  The s e c o n d d e r i v a t i v e  2  (A6.1)  L  The f i r s t  3 U/3L  p r o b l e m c a n be w r i t t e n :  2  = [LV  L  L B  The s e c o n d o r d e r  B B  (  equation  (3B/3L)  + U  condition  order  = 0  L  B'  of  + U (3B/3L)  satisfied.  / U  + V ][U  L L  both the f i r s t  + U  is  L L  + Ug ]/p L  6  ,  3  )  is  + Ug(2V  L L  + LV _ )/p L |  .  L  (A6.4)  (A6.4)  condition  The c o n s t r a i n t  A6.2  A  must be e v a l u a t e d a t  (A6.3)  a point  and t h e c o n s t r a i n t  implies  wL/p = B = L V / p L  where  (w = V ) L  are  113  •  3B/3L = ( L V _ + V ) / p  +  9B/2L = ( L V  L[  by t h e  first  9  L  + V )/p  L L  order  W  = U  U  = U  where H i s objective  = -U /U  L  L  condition.  B B  (U /U ) L  LBA V /l  B  -  2  [ - H  the determinant function  +  U  +  and p ,  Substitute  - U  2  R  U  3 B  B L  (U /U ) L  B  +  L V  A6.5  into  +  U (2V  L  )/p]  B  L L +  A 6 . 4 and  obtain  LV  -  L L L  )/  P  LL ( 2 V  of IL  (A6.5)  g  L  the  L  L  L  bordered hessian  and H a r e a s s u m e d t o  of the  union's  be g r e a t e r  than  D  zero.  Therefore a s u f f i c i e n t  condition  to  condition  2 2 ( 8 U/3L < 0)  be s a t i s f i e d  2V  +  L V  LLL  Repeating  <  "  2 V  L L  +  LV  U L  the second  order  is <  0  LL*  (  equation  V(q,r,m,L)  for  = c  1 2  6  ,  6  )  6.2,  q  2(a  2b  A  + c  1 2  X  + a  L (q 4  1 9  2 2  r  1 3  +  Y  c m  + c^qL  + a  Z)(l  32  2 3  + c  rL  +  + L + 2L*)  +  2 1  + r + m + 2X + 2Y + 2Z)  c mL + 31  114  ,1 2 1 2.i ,1 where X = ( - q + - r ) , Y = ( - q 2 2 2 v  v  2 ^ 1 2 i +- m ) 2  . _ ,1 2 1 2.i and Z = (— r +— m ) . 2 2  N  CIearly, V  L  =  C  l l  q  +  C  21  r  +  C  31  m +  2  + b  1 2  ^ l2 a  L  _ i  X  +  (q  a  13  Y  +  a  23 ^ Z  X  +  ^  L  + r + m + 2X + 2Y + 2Z)  -3/2 . V  L  = -(a  L  X  1 2  1  V  =  (  - b 2  . L V  L  L  L  3  1 9 L  /  1 9 v  a  1 3  Y  a^ZjL  +  -3/2  - b 2  * LLL  +  ( q + r + m + 2X + 2Y + 2 Z ) L  d  2  )  [  a  l2  X  +  a  13  Y  +  3  23  Z  +  (q + r + m + 2 X + 2 Y +  2Z)]L  -5/2  c  = -(3/2)V  L L  .  Therefore,  L V  U  L  .  -(3/2JV  < -2V  L L  since  < 0, e q u a t i o n A6.6 i s s a t i s f i e d  condition  of the maximization  Second Order C o n d i t i o n The m a x i m i z a t i o n  problem i s  and t h e s e c o n d  order  satisfied.  f o r the Maximization p r o b l e m i n t h e CUM i s  P r o b l e m i n t h e CUM  115  Max w,L  {U(B,L;A)  Max L  : B = V(p,r,m,L)/p  {U(V(q,r,m,L)/p  The f i r s t  order  - G/p}  (A6.7)  - G/p,L;A)}.  condition  (A6.8)  is  3U/3L = U V / p + U R  +  V  L  2  2  = V [U L  L  (A6.9)  R  of A6.8  is  ( 3B/3L) + U g J / p  B B  = 0  L  = -pU /U .  The s e c o n d d e r i v a t i v e  3 U/8L  L  + UgV /p  + U (3B/3L) + U  L L  L B  L L  (A6.10)  The c o n s t r a i n t  and t h e f i r s t  order  condition  3B/3L = V / p L  which,  3 U/3L 2  when s u b s t i t u t e d  2  = (U /U )[U L  B  B B  = U " (-H + 2  B  since  p > 0, U  condition  is  D  b  > 0,  into A6.10,  (U /U ) L  U  B  3 B  V  L L  - 2U  /p)  = -U /U L  B  yields  ] + U V _/p + U _ B  L |  L|  < 0  H > 0 and V . .  satisfied.  B L  imply  LL  < 0.  Therefore the second  order  116  Chapter 7 On C h o o s i n g a T r u e  Until sonable unions  and f i r m s .  be f a l s e . is  now t h e CUM and MUM h a v e been t r e a t e d  and e q u a l l y  different  likely  outcomes. Hence,  1  chapter  alternative  However,  t h e t r u e model  of t h i s  Model  If it  of  is  is  true,  are non-nested  and  is  desirable  t o choose w h i c h of t h e two  the  behaviour  of  of the  of predict  t h e n t h e o t h e r model  unions  t o c h o o s e t h e model w h i c h  observed behaviour  rea-  models of t h e b e h a v i o u r  t h e two m o d e l s  one model  as two e q u a l l y  and f i r m s . is  The  consistent  IWA and t h e wood p r o d u c t s  must  models purpose  with  industry  in  the B.C.,  1963-79. On a t h e o r e t i c a l Chapter  5, t h e c h o i c e  reasonable model, outcome w h i l e come.  CUM i s  the  neoclassical  to exploit the  competitive unwilling  1.  to  The CUM i s  predicts  all  an i n e f f i c i e n t  favourite  arguments  possible  gains  while  optimal  inferior  appealing to  one e x p e c t s  f r o m t r a d e and r e a c h  by t h e CUM i s  relationship  enough  more  outfactors  that  the  unions  and  o v e r t h e MUM.  say t h a t  outcome p r e d i c t e d  convey  Pareto  Pareto  in or  p a r a d i g m have been made s u g g e s t i n g  basically  bargaining  outlined  the c o r r e c t ,  an e f f i c i e n t  as n o t e d i n C h a p t e r 2 ,  not.such a clear  solutions,  obvious.  because i t  These arguments firms  is  given the assumptions  t h e MUM p r e d i c t s  However,  outside  basis,  unattainable  makes t h e t w o p a r t i e s  information  about  efficient  their  since  unable  valuations  the or  of  T h i s i s not always t h e c a s e . For example, i f union 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 a n d e m p l o y m e n t s p a c e , o r i f t h e union i s i n d i f f e r e n t t o t h l e v e l of employment, then 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 Further,  reach a point  since  necessary possible  to negotiate changes  the union. tiated,  conditions  in  Even i f  they  accurately  still  on t h e c o n t r a c t change d u r i n g  a set  input  of  curve  the l i f e  contingent  and o u t p u t  a complete set  (see Pencavel of a c o n t r a c t ,  contracts  prices  measuring the v a r i a b l e s  is  all  affecting  contracts  Problems  it  covering  and v a r i a b l e s  of contingent  h a v e t o be e n f o r c e d .  1981).  are  observing  nego-  and  describing the contingencies  limit  9  the w o r k a b i l i t y also exists value  of  if  of  the  contingent  contracts.  the union or employers  the contingency  and t h e y  are v a l i d  onableness  o f t h e CUM.  with  force  equal  industry's  t h e MUM.  labour  change, wage, also  t h e demand f o r just  price  as u n i o n level,  necessary  labour  while  uncertainty,  important they  2.  factors  do n o t  rates  help  variables  imperfect  of  the  problem  perceived  against  curves  leads  seem  the  reas-  c a n be  and t w i s t s  the supplied  wage. as  c h a n g e when t h e So c o n t i n g e n t  applied  about  information  choose a non-optimal  prices alternative  contracts  t o t h e same p r o b l e m s  and m o r a l  information,  hazard.  and m o r a l  w h i c h o u g h t t o be i n c l u d e d in the choice  curve  information  or f a l s e  change.  i n t h e MUM, and t h a t  measuring the contingency  Lack  curve s h i f t s  indifference  or tax  counting  t h e s e arguments  function  by t h e f i r m c a n c a u s e t h e u n i o n t o Further,  on t h e c o n t r a c t  criticisms  However a l l  against  demand f o r  can i n f l u e n c e  hazard  variables.  T h e s e p r o b l e m s make a s o l u t i o n unlikely  A moral  are  of  Therefore,  hazard  in the union  are models;  b e t w e e n t h e MUM and CUM.  See H a l l and L i l i e n ( 1 9 7 9 , p. 8 7 0 ) f o r a d i s c u s s i o n l e m s 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.  of the  prob-  118  It greater  is  true that  than those of  negotiated that  and f i r m s  o f employment  contracts  It  is  also true  negotiate  o f t h e CUM a r e  but  that  firms  one  work  rules  compensation f u n c t i o n s  be  observes  choose  Despite these f a c t s ,  by n e g o t i a t i n g  by n e g o t i a t i n g  t h e wage has t o  in general,  t h e wage r a t e  unilaterally.  c a n be a c h i e v e d  importantly,  requirements  t h e MUM s i n c e more t h a n j u s t  i n t h e CUM.  unions  level  the information  the  efficient  or,  more  which are  not  3 homogeneous  of  degree  one i n t h e  Referring to Figure function  oab, w i t h  wage e q u a l union  its  bargain  employment u n i l a t e r a l l y Compensation  employment not  is  the laid  combination  only  about  just  people working,  workers.  In t h a t  provisions  3.  i i  chooses solution  uncommon.  If  oa c a n be payment f o r  statutory  holidays,  while  If  employment  is  hours  per worker  fixed,  f i r m w o u l d pay i f  ensure that  by w o r k e r s w i t h  benefits  work the  m e a s u r e d by and  employ-  oab r e s u l t s  from  the  increasing,  H a l l and L i l i e n ( 1 9 7 9 ) compensation functions  firm  The  c a s e t h e wage s e e n by t h e f i r m i s  employment  is  outcome.  b u t an e f f i c i e n t  oab a r e n o t  insurance  oa and a  pay  off.  be d i s p l a c e d  or  compensation  or severance  wages m i n u s what t h e  seniority  like  and t h e  then the compensation f u n c t i o n  worker's If  compensation  holding  f i r m p a y i n g unemployment off  i n an e f f i c i e n t  to minimize costs, functions  the  o f a lump sum payment  t h e h o u r l y wage.  decreasing,  employment.  easy t o see t h a t  results  s u c h as v a c a t i o n s  s l o p e o f ab i s  ment i s  is  of  measured i n hours worked,  performed  number o f  it  t o the slope of ab,  and,firm  results.  5a,  level  less  labour  workers  is  t h e w o r k e r was  homogeneous,  laid  and  w i t h more s e n i o r i t y  seniority  to  then the marginal  show how n o n - h o m o g e n e o u s o f d e g r e e can support e f f i c i e n t e q u i l i b r i a .  cannot cost  one  of  119  FIGURE 5  120  a worker workers  less  than the average c o s t .  w i t h more s e n i o r i t y  time off oa i n  is  and b e n e f i t s .  Figure  chooses  employment  contract  supports  and s h i f t  an e f f i c i e n t  more c o m p l i c a t e d t h a n  So a l t h o u g h  bargaining  beyond t h e a b i l i t i e s  o r e v e n t h e common p r a c t i c e  so t h a t  are  all  in  to achieve  firm  common non-linear  and o t h e r  in the  an e f f i c i e n t  w h i c h make t h e c o m p e n s a t i o n  geneous of degree one, included  like  almost  efficient  collective  of unions  outcomes  agreements  c a n be  is  and  not  be  the  outcome  function  bene-  CUM must  i n t h e MUM a n d m u s t c o v e r more t h a n j u s t necessary  provisions  Other  t o pension funds  paid  looks  function  wage, t h e b a r g a i n i n g  Payment  the  o u t c o m e when t h e  to minimize costs.  contributions  premiums.  because  function  w h i c h make t h e c o m p e n s a t i o n  a r e o v e r t i m e premiums, fits,  the compensation  unilaterally  provisions  occurs  e a r n h i g h e r wages and r e c e i v e more  Hence,  5b and i t  This  not  firms.  homo-  achieved,  currently  in  effect. Therefore, achieved unions  efficient  does  cost This  not  t h e CUM.  Although  outcomes,  the  are  in  is  made t o k e e p t h e a n a l y s i s  performance services  condition  indifference  curve.  ( t h e wage)  of  t h e CUM.  and m a t e r i a l s ,  between t h e  and t h e  are  be  accepted that to  5 assumes  level  over of  simple,  and  None o f t h e e q u a t i o n s  it  of  an i s o - e x p e n d i t u r e curve  the  employ-  The CUM c o n s i s t s  iso-expenditure  not  because  r e a c h e d by b a r g a i n i n g d i r e c t l y  assumption  capital  or  functions  Chapter  labour  the  for  I have a r g u e d  compensation  CUM o u t l i n e d  outcomes  cannot  of  and t h e t a n g e n c y union  bargain  of a u n i t  affect  demands f o r  against  outcomes  to  efficient  b a r g a i n a b o u t employment  c o u l d use n o n - l i n e a r  efficient  average ment.  arguments  stating that  are too d i f f i c u l t  do n o t  and u n i o n s  achieve that  because they  and f i r m s  as v a l i d firms  any a r g u m e n t s  the  curve  and  the  i n t h e CUM c h a n g e  if  121  a non-linear solution.  compensation  The CUM shows o n l y  how t h e o u t c o m e i s One f i n a l (1978,  p.  industry  function  reached or  rationale  926)  states  of  one p o w e r f u l  as a m o n o p o l i s t i c  supplier  small of  power r e l a t i v e  to the firms,  cient  instead  off  holding the firm's  and e n f o r c e all  of  firms,  dictate  a level there  is  MUM i n t h e  like  outcomes  predicted  bear out t h i s  those  constant?  If  Given the an  that  unions  for  better  dictate across  wages and p e n s i o n  forest  fund  the p o p u l a r i t y  of  the  o u t l i n e d above, there  is  no  and f i r m s  settle  question  t h e CUM o v e r t h e MUM? of  not  outcome.  despite  The n e x t  model  acts  union's  is  t h e union can  at  p r e d i c t e d by t h e MUM r a t h e r t h a n t h e by t h e CUM.  its  ineffi-  fund c o n t r i b u t i o n s  (including  and t h e arguments that  mining  The u n i o n  one w h e r e t h e u n i o n  an e f f i c i e n t  d o e s t h e CUM p r o v i d e a b e t t e r  Nested  the coal  uncoordinated firms.  conclude  preference  IWA and t h e B . C .  for  u n i o n w h i c h can d i c t a t e  an e f f i c i e n t  function  believing  of  Farber  no r e a s o n t o b e l i e v e t h a t t h e u n i o n w o u l d  literature  outcomes  appropriate  o f wages and p e n s i o n  one must  good r e a s o n f o r  independent  why d o e s t h e u n i o n d i c t a t e  which supports  To sum u p ,  efficient  be m e n t i o n e d .  labour to the f i r m s .  welfare  a compensation  contributions)  outcome and i s  t h e MUM s h o u l d  is  number o f  an  supported.  t h e MUM i s  terms t o a l a r g e  used t o a c h i e v e  final  that  because t h e r e  solution  the  is  is:  inefficient efficient  does t h e  That  is  to  the observed behaviour  data say:  of  products  industry  in the years  empirical  question  c a n be f o u n d by n e s t i n g  the  1963-79?  Test  An a n s w e r t o t h i s two m o d e l s (1983). function.  in  single  equation  The MUM s o l u t i o n In o u r model  is  that  as done by MaCurdy and  on t h e implies  industry's  Pencavel  demand f o r  labour  the  122  D,  The CUM r e q u i r e s  that  the  equals the slope of the  slope  7.1  however,  that  is  nested  in  L  "  cannot  produce t h e other model.  out  the c o n s t r a i n t  against tested  in a single  The c o n s t a n t  problems  is  B  function  curve:  (7.2)  °*  =  It  s h o u l d be  emphasized,  just is  in a nested t e s t , equation;  returns  in Chapter  as i n C h a p t e r  turns  out  nested  to  thereby  but  hypothesis scale  5 (equation of  the value  first  5.2).  5 (equation 5.5),  of  tested can  a hypothesis  of  be  test  D(r,m,L,Q)  is  specinumerical  7 . 2 when U ( B , L ; A )  so t h e f o l l o w i n g  12  = -1  is  an i d e n t i f y i n g  n  + u,± + u  restriction.  1 9  BL  is  specifica-  used  = u B  of  true.  Unfortunately,  equation  order  be  t h a t t h e CUM i s  version  the  (fortuitously)  in the  allowing  If  i m p o s e d on one model  The c o m p l e t e m o d e l s c a n n o t  U(B,L;A)  where u  objective  restrictions  It  prevented the e s t i m a t i o n  specified tion  is  / U  7.2.  i n t h e MUM ( 7 . 1 )  t h e MUM g i v e n t h e a l t e r n a t i v e  it  L  p U  completely,  o f t h e CUM ( 7 . 2 ) .  one a n o t h e r  f i e d as  union's  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 .  are w r i t t e n  condition  (7.1)  iso-expenditure  equation  models  that  of the  industry's  D  Equation  + w = 0.  (7.3)  123  Non-linear just  one e q u a t i o n  instrumental industries,  are:  system of  a constant,  price  of  output,  The l i k e l i h o o d  and Jorgenson 7.1  (1979) is  e q u a t i o n 7.2  is  true  is  price  ratio  test  used t o t e s t  subject  true.  of  to the  7.2  since  The e s t i m a t e d t e s t  variables,  in  hypothesis  alternative  the  and t h e s q u a r e s  analogue d e r i v e d  the null  is  The  for  t h e dummy  capital,  it  equations.  dummy v a r i a b l e s  a t r e n d term, the t r e n d term times  prices.  equation  used t o e s t i m a t e e q u a t i o n  out of a s i m u l t a n e o u s  variables  trend squared, the  2SLS i s  Gallant  that  hypothesis  statistic,  of  that  which  Gallant  2 and J o r g e n s o n degrees that  of  prove  freedom  equation  7.1  is  asymptotically  (u^ = u^= 0 ) , and t h e MUM i s  The s p e c i f i c a t i o n (equation  7.3)  used i n the  is  union models  clear  that  more g e n e r a l  Likelihood  specification  Comparison  More s u p p o r t values  of  the  o f t h e CUM i s lihood  (equation  7.1  log  Thus, the  of  U(B,L;A)  is  with  rejected.  of  test  specification  Since equation version  two  hypothesis  the hypothesis  and t h e MUM a r e a l s o  7.1  is  equation  rejected  when  7.2,  it  the  used.  Test  likelihoods  o f t h e MUM f o r  5.5).  a x  overwhelmingly  used f o r  a restricted  f o r t h e CUM i s  always  is  as  c a s e o f t h e more g e n e r a l  against  equation  92.202.  true  U(B,L;A)  a special  r e j e c t e d when t e s t e d is  of  is  distributed  at  least  the cost  f o u n d by c o m p a r i n g t h e  o f t h e CUM and MUM. eleven points minimizing  maximized  The l o g  likelihod  higher than the log  m o d e l s when one  like-  compares  124  models w i t h  an e q u a l  be r e j e c t e d  in  number o f  f a v o u r o f t h e CUM.  be c o n v i n c i n g l y  rejected  if  general  model w h i c h n e s t s  This  true  is  free  since the  it  parameters. This  follows  was t e s t e d  T h u s , t h e MUM c a n b e c a u s e t h e MUM w o u l d  against  a  hypothetical  t h e t w o m o d e l s a n d h a s one more  log  likelihood  of  the general  parameter.  model  must  be  5 greater  than or equal  to the  The a d v a n t a g e o f t h i s formance ferent  of the  is  complete models  tested  likelihood  type of t e s t  from the nested t e s t  one model  log  against  is  o f t h e CUM. that  it  one a n o t h e r .  shown a b o v e , w h e r e j u s t  against  a different  compares t h e  equation  This  is  per-  dif-  one e q u a t i o n  from the  from  other  model. Another  difference  The n e s t e d t e s t  assumes  f r o m t h e CUM, i s ness  of  the  given that thesis.  the  s h o u l d be e m p h a s i z e d . hypothesis,  The c o n s i s t e n c y  on t h e CUM ( w h i c h y i e l d  the observed data given the t r u t h  the data are organized  the beginning  of  the  t h e CUM be t h e a l t e r n a t i v e  certainty.  alternative  certainty.  Given the q u a l i t a t i v e  sented at let  that  true with  restrictions  tested against  between t h e two t e s t s  However,  or  equation  reasonable-  t h e MUM) i s  then  o f t h e CUM -  i.e.,  according to the a l t e r n a t i v e  arguments chapter,  7.2  hypo-  i n f a v o u r o f t h e CUM p r e it  hypothesis,  may n o t which i s  g i v e n t h e MUM's p o p u l a r i t y  be u n r e a s o n a b l e believed  to  with  and a c c e p t a n c e  in  the  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 m o d e l s i s 1 1 . 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 constant returns t o s c a l e , cost minimizing models. See T a b 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 o m p a r i s o n t e s t by t e s t i n g t h e m o d e 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 MacKinnon 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  literature, w h i c h does  it  is  d e s i r a b l e t o c h o o s e t h e t r u e model w i t h  not weight  The l i k e l i h o o d model  is  set  of  result  Instead  and t e s t it  alternative  crimination." believe with  level.  'best'  models  others.  in the  is  is  significantly This  of  is  the t e s t  no way t h a t still  alternatives.  implicitly  true,  only  assumes t h a t  particular assumed  included  least  two  in  points  alternatives  essentially models,  model  "dis-  w h i c h we  In g e n e r a l , l a r g e r than  o n l y means t h a t  all  at  choose t h e t r u e  in the s e t .  found.  that is  i n t h e models t o d i s c r i m i n a t e  comparison t e s t and g i v e n  is  Since there  set  the f a l s e  alternative  contained  model  c a n be r e j e c t e d ,  contained  of  at  a  models  the t r u e model,  no l o g l i k e l i h o o d  and no  the  set  contains  n o t enough i n f o r m a t i o n all  of t h e o t h e r  Thus t h e t e s t  f r o m among t h e a l t e r n a t i v e s  others,  likelihood  f r o m among a l l  Given a f i x e d  possible that  against  test  o f t h e CUM.  d o e s n o t assume t h a t  models. A log  certainty  favour  a s s u m e s t h a t t h e t r u e model  t h e t r u e model  t h e 95% c o n f i d e n c e  in  o t h e r models  higher than the log l i k e l i h o o d s identifies  so s t r o n g l y  comparison t e s t  true a priori  t r u e model. the  the  a  the  assumes t h a t  model it  all  is the  there  one model  is  from  alternative t h e t r u e model  In o u r c a s e t h e  is  likelihood  one o f t h e CUM o r t h e MUM i s  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  over  t h e MUM.  Non-nested  Test  The n o n - n e s t e d t e s t truth  6.  of  t h e models  still  relaxes  the a priori  further.  As  assumptions  in the l i k e l i h o o d  about  the  comparison  T h i s f o l l o w s b e c a u s e a l l t h e o t h e r m o d e l s w o u l d be r e j e c t e d 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 parameter.  when  126  test,  no model  may n o t  contain  Unlike the to  is  enough i n f o r m a t i o n  likelihood  be i n t h e  hypothesis rejected  a s s u m e d t o be t r u e a p r i o r i ,  set  test  as  all  model  comparison t e s t ,  alternatives alternative  procedure  hypotheses  given the alternative hypotheses  any model  are  is  to let  hypothesis.  That  and t o t e s t  the  Then t h e n u l l  and  is  repeated.  hypothesis  i s why b o t h m o d e l s  the other  so t h a t  with the data  model w h e r e no h y p o t h e s e s certai nty.  or  null  and  hypothesis  alternative  or both  one models  to  is  that  there  believed to  is  hypothesis.  Further, looks  for  an h y p o t h e s i s  both  is  inconsistency  on t h e  is  tested of  s u g g e s t e d by t h e  a b o u t t h e t r u e model  with  Each model  e a c h model  test  no a l -  be t r u e  c a n be r e j e c t e d a n d why  in directions  is  is  the other  " t r u t h " of  are believed  with  7  The n o n - n e s t e d t e s t  7.  the t e s t  The n o n - n e s t e d t e s t  which  alternative  footing with the other.  hypothesis  returns  non-nested  Therefore  b o t h m o d e l s may be a c c e p t e d ,  a r e a l l o w e d t o be t h e  on an e q u a l  model.  assumed  t h e MUM a n d CUM be t h e n u l l  r e v e r s e d and t h e t e s t  or maintained  certainty.  null  In a  not  rejected.  ternative  against  is  false.  m o d e l s may be a c c e p t e d a s t r u e  The a s s u m p 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  models  as  t h e t r u e model  with certainty.  respectively,  may be a c c e p t e d ,  may be  reject  alternatives  false.  The b a s i c alternative  of  to  and t h e  scale  versions  is of  done on t h e c o s t m i n i m i z i n g , the  CUM and MUM ( w i t h dummy  constant variables),  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 P e s a r a n a n d D e a t o n ( 1 9 7 8 , p p . 6 7 7 - 6 8 0 ) , D a s t o o r ( 1 9 8 3 , p. a n d D a v i d s o n a n d M a c K i n n o n ( 1 9 8 2 , p. 5 5 1 ) .  from 213),  a  127  using a variant Davidson  of the J t e s t  ( 1 9 8 3 , p.  models are w r i t t e n  Stochastic  55). in  s u g g e s t e d by M a c K i n n o n , W h i t e  implicit  versions  and  o f t h e MUM and C U M  f o r m as  M(K,M,w,L,e;r,m,g,A,p)  = e  C(K,M,w,L,Y;r,m,Q,A,p)  = e  and  respectively,  where  m a t e d and e i s  the vector of  terms  corresponding  error  terms  Nest  6 and y a r e t h e  to the  vectors  normally  same o b s e r v a t i o n  i n an a r t i f i c i a l  parameters t o  distributed errors.  corresponding to different  t h e two m o d e l s  of  are  tive  the  null  hypothesis  obtain  estimates  hypothesis that of  statistic  for  different  from z e r o .  t h e CUM i s  compound model  the estimate of  are  true  given the  r e p l a c e y by i t s if  a = 0.  that  alterna-  ML e s t i m a t e ,  The a s y m p t o t i c  a i s 1 3 . 7 2 7 , so a i s  hypothesis  Reversing the null artificial  true,  The h y p o t h e s i s  of the nested t e s t  (7.4)  t h e MUM i s  3 and a and t e s t  given the a l t e r n a t i v e results  that  while  independent.  (1 - a ) M ( ) + a C ( ) = e .  To t e s t  esti-  Error  are c o r r e l a t e d  observations  be  t h e MUM i s  t-  significantly true  t h a t t h e CUM i s t r u e .  is  Thus  rejected the  confirmed.  and a l t e r n a t i v e  hypotheses,  one o b t a i n s  compound model  ( 1 - o)C() + aM() = e ,  (7.5)  the  128  where t h e n o t a t i o n mate, for  estimate  a is  The h y p o t h e s i s  alternative  reject  that  hypothesis  high t - s t a t i s t i c s  both models  a = 0.  so a i s  t h e CUM i s  (1982)  no o t h e r  in a non-nested  8 by i t s  ML  The a s y m p t o t i c  is  esti-  t-statistic  different  rejected  given  from  the  true.  do show t h a t  too often  leave  Replace  significantly  true  t h e MUM i s  and M a c K i n n o n  the null  if  13.03,  that  hypothesis  Davidson  very  t h e same as b e f o r e .  a and y and t e s t  the estimate of  zero.  of  is  i n small  the J t e s t  samples.  conclusion  tends  to  However,  than the  the  rejection  test.  Summary It  is  argued 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  t h e two m o d e l s  b e c a u s e one e x p e c t s  possible  from t r a d e  gains  explaining cient  This data.  may r e s u l t  preference  for  When t h e CUM i s  consistent  with the  forest  products  either  the  rejected  in  arguments  are  above.  ferences,  uncertainty,  This  Factors  supported  rejected.  a better  ineffi-  by  the  f o u n d t o be  When t h e  model  in-  IWA and  of the  of  data  b e t w e e n t h e MUM and CUM, t h e MUM i s  f a v o u r i n g t h e CUM o v e r t h e MUM a r e  presented  Arguments  and t h e  t h e MUM i s  o f t h e CUM ( g i v e n t h e d a t a )  rejected.  all  a r e a s s u m e d t o b e h a v e a c c o r d i n g t o one  However o n c e we a l l o w t h a t models  of  unconvincing.  be t r u e ,  d a t a and t h e MUM i s  So i n a t e s t  favour  outcomes.  t h e CUM o v e r t h e MUM i s  CUM o r MUM, t h e CUM p r o v i d e s  t h a n t h e MUM.  to e x p l o i t  may be u n a t t a i n a b l e  are found  assumed t o  industry  and f i r m s  and r e a c h e f f i c i e n t  why t h e CUM s o l u t i o n  MUM s o l u t i o n  unions  or c o r r e c t  is  neither  model  also consistent  s u c h as a g g r e g a t i o n  imperfect  and t h e  qualitative  confirmed. may be t r u e , with the of  both  arguments  u n i o n members'  i n f o r m a t i o n , moral  hazard,  pre-  dynamic  129  constraints, and s t r i k e s  non-price taking  behaviour,  a r e assumed away by b o t h m o d e l s  the v a l i d i t y  of  non-nested t e s t specification  both m o d e l s . only  shows t h a t  more work  given the  choice  m u s t be c h o s e n as t h e t r u e m o d e l . the t r u t h  of e i t h e r  model  of  and t h e i r  The r e j e c t i o n  of models o f u n i o n and f i r m  In c o n c l u s i o n ,  that  the costs  of  negotiations, neglect  both models  needs t o  lessens  by  the  be done on  the  behaviour.  b e t w e e n t h e CUM and MUM, t h e CUM  However, t h e n o n - n e s t e d t e s t  may n o t  be v e r y  great.  shows  130  Chapter  8 Conclusion  Two m o d e l s  of  u n i o n and i n d u s t r y  f i e d and e s t i m a t e d industry  in  specified mizing  B.C.,  u s i n g annual 1963-79.  behaviour  by t h e  to scale.  industry  is  estimated  also  parameters,  IWA and wood  versions  Thus,  in the  industry  The t e c h n o l o g y independently  of  speci-  products  the models  the estimates if  of  and c o n s t a n t  o f t h e wood  of  assuming cost m i n i m i z i n g  w h i c h w o u l d be o b t a i n e d was  Different  firms  returns  wages.  d a t a on t h e  are d e r i v e d ,  are  and e s t i m a t e d a s s u m i n g c o s t m i n i m i z i n g and p r o f i t  constant  tion  behaviour  and n o n -  products  any u n i o n o b j e c t i v e  behavior  the technology  perfect  maxi-  and  func-  exogenous  are e q u i v a l e n t  competition  in all  function  found t o  to  input  those  markets  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  in total  real  alternative ment.  compensation,  w a g e , and q u a s i c o n c a v e  Written  as a f u n c t i o n  (the  real  tion  is  city  of s u b s t i t u t i o n  0.6 t o  wage)  0.8.  wages o f  in  both  is  (2000 hours)  t o a 1.5% d e c r e a s e  wage.  Many p o p u l a r  t h e wage b i l l  compensation rate  of  real  wages a n d e m p l o y m e n t be i n d i f f e r e n t  In p e r c e n t a g e t e r m s ,  indicate that IWA i s  not  real  and  employ-  compensation  and t h e ranges  to the  in the  the union  union preferences  funcelastifrom  firing  i n e m p l o y m e n t a n d a 1% i n c r e a s e about  increasing  union o b j e c t i v e  wages and e m p l o y m e n t ,  found to  hypotheses  and t h e  real  be  and t h e  a n d a 0.032<t an h o u r i n c r e a s e  ferent  tests  employment  the estimated  real  other workers.  The h y p o t h e s i s  over  in  the average  between r e a l  The u n i o n  all  of  and e m p l o y m e n t ,  increasing  one w o r k e r  decreasing  is  are  of  real is  indif-  in the  tested.  t h e IWA d o e s n o t m a x i m i z e r e n t s  indifferent  to the  level  real  of  or  131  employment mates o f model  or the a l t e r n a t i v e  union preferences  and t h e t e c h n o l o g y ,  minimizing  or p r o f i t  literature  side,  not  is  not convex i n p r i c e s . of the  in prices  production  change and H i c k s ' are estimated to and m a t e r i a l s production union's  neutral  is  of the  With  that  if  ates  t h e MUM.  models thesis,  it  function  profit  function  In t h e e x o g e n o u s wage r a t e m o d e l ,  very  rejected  as i s  Capital  capital  sensitive  technical  and  materials  and l a b o u r ,  and  The e s t i m a t e s  t o whether  of  or not  The e s t i m a t e s  factors  production  increase  and p r o d u c t i o n  homothe-  no  modelled.  of  found  (1981)).  estimated  change.  cost  labour the  the  of t h e  dramatically  and u n i o n  subwhen  preference  jointly.  clear  of  an a p p r o p r i a t e model  on b o t h t h e o r e t i c a l  of union  and e m p i r i c a l  and  grounds  one h a s t o c h o o s e b e t w e e n t h e MUM and t h e CUM, t h e CUM d o m i n If,  empirically, then  hypothesis  with  one w a n t s t o t e s t  no c e r t a i n  the  " t r u t h " of  the  maintained or a l t e r n a t i v e  CUM a r e  rejected  by a  hypo-  non-nested  test.  the f a u l t s  ubiquitous  however,  b o t h t h e MUM and t h e  The r e j e c t i o n some o f  is  to other estimates  industry's  technical  the  estimates  and t h e  regard to the choice  behaviour,  The  estimated cost  is  in  t o whether  industry's  technology  esti-  changes  explicitly  are estimated  firm  The  the  wages a r e e n d o g e n o u s t o t h e model parameters  to  assumed.  and P e n c a v e l  a r e f o u n d t o be s u b s t i t u t e s .  behaviour  stitutability  is  similar  be c o m p l e m e n t s w h i l e  technology^are  robust  are s e n s i t i v e  behavior  (see Dertouzos  is  ticity  concave  although they  are a l s o very  On t h e p r o d u c t i o n  to labour.  are s u r p r i s i n g l y  maximizing  of union preferences i n the  wage a v a i l a b l e  fault  of  of  both models  of  t h e work  i n the non-nested t e s t  reported  above.  a s s u m i n g away u n c e r t a i n t y  There i s  underlines the  and i m p e r f e c t  informa-  132  tion.  Such i m p o r t a n t  strategies,  as t h e c o s t s  of  bargaining,  job  restrictions,  and d i v e r g e n t  w i t h i n the union are a l l  assumed a w a y .  The d y n a m i c s  ship  strikes,  factors  between t h e  cal  integration  the  data.  and t h e sample i s  asymptotic In s p i t e  been made.  First,  This it  of  they  listed  which is  bargains  workers  with, with  and  isolates  of  in  is  confidence  in  the  contribution  has  behaviour  a  Empirical  work  d a t a on t h e b e h a v i o u r  The d a t a u s u a l l y  contain  little  on a s i n g l e contamination  union from  of on  of  unions  some unknown  and u n i o n and n o n - u n i o n  observations very  flaws  firms.  and t h e  firms  non-union  firms.  Second, providing  provides  a positive  developed. of  u n i o n and n o n - u n i o n w o r k e r s  data set  verti-  structure  to place a lot  above,  by a l a c k  organized.  the  estimates.  industry  has been h i n d e r e d  and a number o f  the e r r o r  is  relation-  industry  standpoint  the  of the  i g n o r e d as  in the  a new d a t a s e t  unionized  and t h e f i r m s mix of  properties  preferences  are a l s o  too small  of the f a u l t s  u n i o n and i t s unions  of the firms  From an e c o n o m e t r i c  arbitrary the  f i r m and t h e u n i o n  bargaining  estimates  of the  an a n s w e r t o t h e  mize?".  Estimates  products  industry  knowledge about the technology  IWA's  very  preferences  old question  factor  also  obtained  substitution  estimates  thereby  thereby  "What do u n i o n s  of t h e p r o d u c t i o n technology are  are obtained  of t h e B.C.  wood  stock  of  and showing t h e s e n s i t i v i t y  of  to the e x p l i c i t  adding t o the  maxi-  modelling  of  union  behaviour. Finally, jected  in  two models  t h e MUM, w h i c h  favour  is  so p o p u l a r  o f t h e CUM ( w i t h  a r e c o m p a r e d t o one  its  in the l i t e r a t u r e ,  efficient  another.  outcomes)  when  is  re-  the  133  Appendi x  More on t h e  The p u r p o s e  of t h i s  appendix  is  Data  to  p r o v i d e more i n f o m r a i t o n  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 . standard  deviations  of the  a n d 7 show t h e l e v e l s each of  the  variables  still  variation  t e r m and t r e n d constant cycles  is  of the  removed  wages t r e n d u p w a r d s .  industry,  wages o f  remaining  industry's  ranging  from  and t h e  bargaining  is  IWA R e g i o n a l  Council  h i r e d by e a c h i n d u s t r y .  However,  different  since  The h y p o t h e s i s rejected  each i n d u s t r y that  all  for  hires  is  independent of  different of  the  output  This  is  i n t h e same Bargaining  a collective  every worker or wages o f  a different  level.  together with  .97.  similar,  the real  the industries  a t t h e 95% c o n f i d e n c e  .99 t o  #1 n e g o t i a t i n g  t h e wages  there  constant  allowed a  and t h e p r i c e  centralized.  (effectively] sets  a  is  move c l o s e l y  are very  which  in  cycle.  since the industries structure  However,  wages a f t e r  variation  where both o u t p u t  each i n d u s t r y  coefficients  real  prising  with the  6  wages a n d e m p l o y m e n t  (where each i n d u s t r y  This  were used t o measure t h e  correlation  real  i n each i n d u s t r y ' s  and t r e n d ) .  The r e a l  real  and F i g u r e s  industries.  F i g u r e 6 shows t h a t t h e is  T a b l e XX shows t h e means- a n d  in the data set  a n d movements o f  on  not  simple sur-  province,  takes  place  agreement  occupation  each i n d u s t r y  mix o f  occupations.  h a v e t h e same mean o r t r e n d Real  wages i n  are  interior  saw-  is  134  TABLE XX Means and S t a n d a r d D e v i a t i o n s  Standard d e v i a t i o n s  are  in  of the  Data  p a r e n t h e s e s below t h e mean.  Shingle Mills  Plywood Mills  1.50 (0.71)  2.53 (1.52)  1.56 (0.63)  3.30 (1.43)  3.34 (1.42)  3.79 (1.60)  3.21 (1.46)  m  1.98 (0.99)  1.18 (0.53)  2.24 (1.54)  1.63 (0.50)  w/p  4.32 (0.88)  3.97 (0.99)  4.61 (0.82)  4.21 (0.79)  Q  34.55 (5.67)  41.99 (12.05)  2.26 (0.26)  17.05 (2.79)  M  20.80 (3.87)  26.97 (7.26)  1.38 (0.21)  8.77 (2.16)  K  6.54 (1.96)  14.53 (5.83)  0.42 (0.14)  5.33 (1.56)  L  24.93 (2.50)  28.06 (5.24)  2.75 (0.30)  13.33 (0.93)  A  3.67 (0.48)  Coast Sawmills  I n t e r i or Sawmi11s  q  1.94 (0.99)  r  fariable  _  -  -  135  FIGURE 6 Wages i n C o n s t a n t CC II SS PP  is is is is  1971  Dollars  coast sawmills i n t e r i o r sawmills shingle mills plywood m i l l s  $ per hour I  6 . 0 0 4-  I 1963  1  1965  4  1968  1  1971  1  1  1974  1977  <  1979 Year  136  FIGURE 7 Employment  CC II PP SS  is is is is  coast sawmills i n t e r i o r sawmills plywood m i l l s shingle mills  0 0 0 ' s o f man h o u r s 38000  34000 +  Year 1972  137  mills  have t h e s t e e p e s t  sawmills,  shingle mills  The d a t a on i n p u t s very  stable  is  without  deal  industry  trends  mills,  price  show t h a t periods  but  not  trend is in  d o e s n o t move t o g e t h e r .  The h y p o t h e s e s trend  is  that  rejected  In t h e w o r k  above,  same t e c h n o l o g y ,  technology t h e model to  All  logs  Since the  is  and  interior  variation cor-  sawmills  in the  and  indus-  coefficients  and i n t e r i o r and c o a s t  saw-  sawmills.  e m p l o y m e n t h a s t h e same mean  4),  saw, p e e l  or  terms  the  are p e r m i t t e d  Even t h o u g h t h e a g g r e g a t i o n by a h y p o t h e s i s  the aggregation do b a s i c a l l y or s p l i t  processing;  industries  a r e assumed t o have  constant  rejected  industries  and b o l t s ;  in  and c o a s t  correlation  is  plotted.  both w i t h  Employment  not  This  positively  plywood m i l l s  different  in Chapter  of the  removed i s  industries  equations.  and t h e n do some f u r t h e r pieces.  four  industries  contained  defend.  purchase  across  is  The  in shingle mills in  are  95% l e v e l .  all  although  some o f t h e e s t i m a t i n g  trend.  interior  each i n d u s t r y ' s  at the  coast  boom and b u s t .  employment  The s i m p l e  and . 7 7 b e t w e e n e m p l o y m e n t  of  employment  i n plywood m i l l s .  range from .37 between employment mills  in  significant  output  in  the industries  i n each i n d u s t r y  removed, and o n l y  of  wages  mills.  variability  the industry  r e l a t e d with the  tries  of  has a s t a t i s t i c a l l y  remaining after  shingle  and o u t p u t s  7 where employment  a great  sawmills  and p l y w o o d  from y e a r t o y e a r w i t h  shown i n F i g u r e There  t r e n d f o l l o w e d by t h e r e a l  the  s u c h as p l a n i n g , they  (using is  same t h i n g .  them i n t o  are so s i m i l a r ,  of  test  assumption  smaller  easy They  pieces  or g l u i n g  are a l l  in  the  included  138  i n t h e same t w o d i g i t  SIC l e v e l  (see, for  example,  Woodland [ 1 9 8 5 ]  Denny and May [ 1 9 7 7 and 1 9 7 8 ] ) .  Therefore  and f o u r d i g i t  n o t u n r e a s o n a b l e when c o m p a r e d  the  standards  SIC i n d u s t r i e s found i n  To c o n s i d e r t h e  the  is  reasonableness  of the aggregation  of workers  and u n i o n  leaders  single  consistent  objective  function  istics  of the workers the workers  average worker strenuous tions.  power f o r There i s enjoy  leaders  Council  is the  to  o f work  different  possessing  a  character-  d a t a shows t h a t ,  slightly  in f a i r l y  all  as u n s k i l l e d , large,  in  younger than male.  They  unpleasant  a r e s e c u r e and p o w e r f u l .  #1 has g o v e r n e d t h e a c t i v i t i e s  The members o f t h e collective little  the do  condi-  but t h e r e  are  expensive  and  on t h e  industries,  of the  IWA i n  possess  most o f  other  functions  of the  and t h e  council  power s t r u c t u r e in the  and t h e  IWA British the union.  councillors  lots  o f t h e u n i o n and t h e  leadership, of  representing  conflicts  1958 t h e  council.  democratic union with union  Since  council  on t h e r e g i o n a l  and t u r n o v e r  an i n d u s t r i a l  regional  bargaining  turnover  long tenures  competition  tively  Census  and v i r t u a l l y  classed  of  one must know t h e  s u c h as o p e r a t i n g  Despite the centralized of  three  machinery.  The u n i o n  Columbia.  skills  is  an e n t i t y  educated,  force  sorts  t h e work  specific  specialized  Regional  labour  into  leaders.  are not w e l l  and d a n g e r o u s  Much o f  industry  and t h e  in the  of  literature.  groups  general,  the aggregation  or  public all  the  debate.  IWA i s  rela-  Since the  of the d i f f e r e n t  between d i f f e r e n t  a  lack  union  workers  groups w i t h i n t h e  in  member-  139  ship  are  vocal  inevitable.  about  their  some r e m e d i a l  plight,  Additive  decreased t h e i r very  vocal  and t h e  IWA t h e a f f e c t e d  leaders  generally  groups  listen  are  and  very  take  action.  A good e x a m p l e , trades.  However i n t h e  common t o most  (rather  relative  about  have responded.  than  industrial  percentage)  of t h e i r  for  the t r a d e s ,  re-opened  in the middle  its  have have  contain  been  the trades  leaders  extra  a g r e e m e n t was  term to adjust  skilled  wages and t h e  agreements  and one c o l l e c t i v e  of  the  The t r a d e s  relative  Most of t h e c o l l e c t i v e  is  wage i n c r e a s e s  wage d i f f e r e n t i a l s .  the erosion  increases  unions,  even  wage  scales. 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 upheavals stable  causing  changes  and p o w e r f u l  in  ideology,  leadership  Hence i t  is  entitiy  a single  consistent  are constant Another union  over  r e a c h an outcome o f f curve.  committees  evaluation  plans.  and i t  level  tions  of  so t h e  Another sation  is  or g o a l s .  There  the union  f u n c t i o n whose  the  industry's  However t h e s e that  plans  they  how t h e  demand f o r  One a l t e r n a t i v e  which a d m i n i s t e r  unlikely  is  to as  is the  an  parameters  the  is  labour  mainly with  job  significant  union cannot  control  directly.  is  specified  the  non-homogeneous  in the c o l l e c t i v e  of  degree  agreements.  job  classifi-  effect  T h e r e a r e no o t h e r  alternative  curve,  and p l y w o o d  have a s i g n i f i c a n t  employment  and  t h e u n i o n and manage-  sawmill  deal  industry  employment.  functions  large  respond c l o s e l y  to treat  objective  i s s u e w h i c h must be a d d r e s s e d  ment j o i n t  the  unreasonable  or  time.  a n d on t h e c o n t r a c t  cation  direction  w h i c h seems t o  membership. with  not  w i t h i n the union,  upon  job  restric-  one  compen-  The  agree-  140  merits s t a t e holidays; dental all  that  the  medical,  plan;  fixed  industry  disability,  personal  costs  of  safety  provides  issue to  independent  technology  vacations;  dismemberment  equipment;  employment  o u t c o m e on t h e c o n t r a c t The f i n a l  must pay f o r  and t h e y  and l i f e  observations  is  function.  chooses  a different  because they prices  vary  of trees  operates this  because  at  objective  function.  mixes  point  locations  of  of  and  Therefore  are  each  technology  varies  frontier  because  points  each i n d u s t r y  on t h e p r o d u c t i o n t e c h n o l o g y  bundles the  industry  technology,  production  different  indus-  materials  Each  on t h e same p r o d u c t i o n  of  industry  and t h e d i f f e r e n t  on t h e  an  production  However,  occupations.  observations  each  on t h e  Energy  labour  are  7.  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