Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Wage and employment contracts as equilibria to a bargaining game : an empirical analysis Doiron, Denise J. 1987

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1987_A1 D64.pdf [ 7.95MB ]
Metadata
JSON: 831-1.0097185.json
JSON-LD: 831-1.0097185-ld.json
RDF/XML (Pretty): 831-1.0097185-rdf.xml
RDF/JSON: 831-1.0097185-rdf.json
Turtle: 831-1.0097185-turtle.txt
N-Triples: 831-1.0097185-rdf-ntriples.txt
Original Record: 831-1.0097185-source.json
Full Text
831-1.0097185-fulltext.txt
Citation
831-1.0097185.ris

Full Text

Wage and Employment Contracts as E q u i l i b r i a t o a Bargaining Game: An E m p i r i c a l A n a l y s i s by Denise J . Doiron .A.,  B.A., U n i v e r s i t y de Moncton, 197 9 U n i v e r s i t y of B r i t i s h Columbia, 1982 A Thesis Submitted  in Partial  F u l f i l l m e n t of the Requirements f o r the Degree of Doctor of Philosophy in The F a c u l t y of Graduate Studies (Department of Economics) We accept t h i s t h e s i s as conforming to the r e q u i r e d standard  The U n i v e r s i t y of B r i t i s h  Columbia  October, 1987. (c) Denise J . Doiron, 1987.  In  presenting  degree at  this  the  thesis  in  University of  partial  fulfilment  of  British Columbia, I agree  freely available for reference and study. I further copying  of  department publication  this or of  thesis for by  his  or  her  representatives.  that the  for  (^C^/Hl^yCd^  an advanced  Library shall make  It  is  granted  by the  understood  that  this thesis for financial gain shall not be allowed without  The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3  DE-6(3/81)  requirements  it  agree that permission for extensive  scholarly purposes may be  permission.  Department of  the  head of copying  my or  my written  ii Abstract  The o b j e c t firms  divide  instruments  the  I  employment  wage  work  and  contracts  of  are  an  demands  the  estimation bargaining  approach  them.  to  them  study  and Many  division,  two:  but  wages  and  wage  and  equilibrium  of  extension  being  functions  for  the  contracts  points  by  the  frameworks  data  and are and  specified Also,  strike  products  to  estimated  sets  by  the  additional One o f  have  costs  the  of  the  strikes. industry  been input  and  successful and  output  representing  input  simultaneously  with  equations.  Four  corresponding of  the  wage and employment  include  derived  two p l a y e r s ,  absence o f  employment  two  the  the  equations  are  incorporation  identified.  relative  believed  and  supply  of  B . C . wood  The  prices  models  that  the  a Rubinstein bargaining  game.  even i n the  union  wage  the  wage-employment  are  are  t h e model i s  rents.  negotiated  to  make t h i s  includes  equations  involve  and o u t p u t  to  specifically,  parties  and  how u n i o n s  available  consider  objective  IWA, a p o w e r f u l capturing  study  extension  the  affected  data  quantities  I  to  b a r g a i n i n g game.  is  of  two n e g o t i a t i n g  the  as  conditions  characteristics  The  new  employment  determinants  rents  only  a  models,  Given the  equilibrium  at  use  a b a r g a i n i n g model,  game.  the  data  a noncooperative  determination  or  is  in practice  contracts  This  research  surplus  micro  employment.  of  this  are used  standard  in  of  assumptions  to on  two the  iii firms' to  technology.  two  polar  employment is  set  chosen  the  the is  is  firm,  level  set  have  in  are as  of  been  assumed  literature:  bargaining  treated  second  that  determination  employment output  cases  through by  T h e two b a r g a i n i n g f r a m e w o r k s c o r r e s p o n d  the  one  while  the  second  case,  negotiated. exogenous  models,  in  output  the is  the  case,  both one  wage  of  bargaining  endogenous  wage  level  the  pair  wage-  the  employment  In  to  in  is and  models,  while  and  in  capital  exogenous. The  sense  b a r g a i n i n g game  that  generally Also,  the  technology reasonable  in  the  employment  weight  being  maximization calculated 1980's  as  at  recession  proportion poor  power of  Although robust  across  generally  to  relative  previous strike  on  the  the  with  employment  rejected.  the  relative  captured  its  the the  sensitive  tested  and by  the  enter  seen to  care  slightly  more  level.  Rent  indicate  power  e q u a l b a r g a i n i n g powers are  are  B a r g a i n i n g powers  and r e s u l t s  of  the  rejected. is  are  that  union  Also, found  the  union.  and c o m p l e t e  firm  the  estimates.  costs  wage  as  in  parameters  well  data point  rents  i n d i c a t o r of  utility  The u n i o n i s  increased  The h y p o t h e s e s o f bargaining  of  implemented  estimation.  always  each  union  and c o m p a r a b l e  placed is  successfully  and  determinants  significantly about  is  to  the be  a  b a r g a i n i n g power.  qualitative four to  results  models,  both  the  mentioned  parameter  technology  above  values  assumptions  are are and  iv the  bargaining  wages, be  framework.  employment  and o t h e r  very misleading.  and than  employment the  by t h e  are  framework  firm.  Ignoring variables  Finally,  the  negotiated in  which  the chosen  model  by t h e  i n which  consistently  employment  simultaneity  is  firm  both  performs  of can  wages better  unilaterally  set  V  Table of  Contents  Abstract  i i  List  of  Tables  List  of  Figures  vii viii  Acknowledgements  ix  Chapter  1:  Introduction  Chapter  2:  Review o f  Chapter  3:  The M o d e l  1  the  Literature  14 36  3.1  The B a r g a i n i n g Game  37  3.2  A p p l i c a t i o n o f t h e B a r g a i n i n g Game t o Union Contract N e g o t i a t i o n s  3.3  The F i r m ' s Technology  3.4  Union Objectives  Chapter the  4:  Firm50  and O b j e c t i v e s  58 62  The D a t a and t h e  Empirical Specification  of  Model  64  4.1  The E s t i m a t i o n M o d e l s  64  4.2  The D a t a  77  Chapter 5.1  5:  4.2.1  The I n s t i t u t i o n a l  4.2.2  Industry  4.2.3  The A l t e r n a t i v e  4.2.4  Strike  Estimation  Price  Setting  and Q u a n t i t y  79 Data  . . .  Wage  89  Costs  91  Results  96  Exogenous Output Model 5.1.1 5.1.2 5.1.3  85  98  The F i r m s ' T e c h n o l o g y Union Preferences The C o n t r a c t C u r v e and t h e Sets  98 106 Bargaining 107  vi  5.2  5.1.4  B a r g a i n i n g Powers  5.1.5  Comparing the  108  COOP and LDEM M o d e l s  .  Chapter  117  5.2.1  The F i r m s ' T e c h n o l o g y  117  5.2.2  Union Preferences  123  5.2.3  The C o n t r a c t C u r v e and t h e  Bargaining 125  5.2.4  B a r g a i n i n g Powers  5.2.5  Comparing the  Summary o f 6:  127  COOP and LDEM M o d e l s  Results  Conclusion  Data Sources  .  .130 133 138  Bibliography  A.l  116  Exogenous C a p i t a l Model  Sets  5.3  .  142 and C o n s t r u c t i o n  Price  and Q u a n t i t y  147 Indices  147  A . 1.1  Output  148  A . 1.2  Materials  A.l. 3  Fuels  A . 1.4  Labour  151  A . 1.5  Capital Services  154  A . 1.6  Input  and E l e c t r i c i t y  Cost  A. 2  The A l t e r n a t i v e  A. 3  Strike  Costs  and S u p p l i e s  Shares  Wage  and P r o f i t s  149 149  163 167 172  vii List Table Table  I: II:  of  Tables  E s t i m a t i o n M o d e l s Under t h e A s s u m p t i o n o f an E x o g e n o u s O u t p u t P r o f i t F u n c t i o n . . . . Estimation  Models  Under t h e  Exogenous C a p i t a l P r o f i t Table  III:  74  Exogenous Output E s t i m a t i o n R e s u l t s . P r o p o r t i o n o f T o t a l R e n t s C a p t u r e d by the F i r m . C o o p e r a t i v e Model w i t h Exogenous Output  .  Table VI:  Exogenous C a p i t a l E s t i m a t i o n  .  Table VII:  P r o p o r t i o n o f T o t a l R e n t s C a p t u r e d by F i r m C o o p e r a t i v e Model w i t h Exogenous Capital  Table  IX:  Table X:  an  Function .  Table VIII:  of  of  .  Table IV: Table V:  Descriptive Statistics  Assumption  72  Variables  Results  .  .  79  .  .100  115 .  .  119  the 132  P r o p o r t i o n o f T o t a l R e n t s C a p t u r e d by t h e F i r m L a b o u r Demand M o d e l w i t h E x o g e n o u s Capital  133  H o u r s p e r Worker p e r Products Industry  154  Year i n the  B . C . Wood  Share o f P r o d u c t i o n Workers i n O v e r a l l L a b o u r i n t h e B . C . Wood P r o d u c t s Industry  156  P r o f i t s Net o f C a p i t a l S e r v i c e s and I n p u t C o s t S h a r e s i n t h e B . C . Wood P r o d u c t s Industry  166  Table XII:  Wage D i s t r i b u t i o n  171  Table XIII:  I n t e r i o r and C o a s t a l A l t e r n a t i v e Wages  Table XI:  Across  B.C  Weights,  and 17 4  viii List  of  Figures  Figure  1:  B a r g a i n i n g Frameworks  Figure  2:  Perfect E q u i l i b r i a with Alternating and C o s t s o f D e l a y  Figure Figure  Figure  Figure  3: 4:  5:  6:  17 Offers 39  L a b o u r Demand C u r v e s and t h e C o n t r a c t Curve. Exogenous Output E s t i m a t i o n . U n i o n B a r g a i n i n g Power. Estimation  Exogenous  .  .  105  Output 113  L a b o u r Demand C u r v e s and t h e Exogenous C a p i t a l E s t i m a t i o n U n i o n B a r g a i n i n g Power. Estimation  .  Contract Curve. 12 3  Exogenous C a p i t a l 130  ix A c k n o w l e d gement s I  received  many  helpful  Binmore,  Robert C. A l l e n ,  several  colleagues  Columbia  and  especially committee Charles  the  like -  to  Craig  Blackorby.  gratefully  comments  from  Mukesh E s w a r a n , K e n n e t h W h i t e ,  both  at  the  University  University  of  thank  Schworm and t h e  Bill  Riddell,  Western  Terence  Wales,  F i n a n c i a l support  acknowledged.  Kenneth  of  Ontario.  from t h e  and  British I  members  Tracy  C.  would of  Lewis,  S.S.H.R.C.  my and is  1  Chapter  1  Introduction The o b j e c t firms  divide  instruments  the  I  determination of  a  micro  between  a  Phillips'  studies firm  an the  game.  either  to  includes approach  to  them.  to  them  and Many  division,  two:  extension  of  extension  being  but  wages  and  wage  and  study  equilibrium  points  In  and  models  It  is  results  factors  wage-employment the  incorporation  wage-employment  determination  industry of  affecting  usually Contrary  determination,  these  of union objectives  recognized of  contracts  are .studied.  wage  on r i g o r o u s m o d e l s  party's  how u n i o n s  make t h i s  wage-employment  union  are.the  consequently,  study  available  consider  1  on  technologies.  agreements  or  is  curve  are based  I  to  b a r g a i n i n g game.  data  single  new  as  is  rents  only  a  models,  bargaining  models,  to  use  contracts  work  or  in practice  data  a noncooperative This  research  surplus  micro  employment.  in  this  are used  standard  employment  of  that  negotiated  firm-union bargaining the  objectives  bargaining  can  also  and  and  relationship  influence  the  contract. In either  previous a  wage-employment  particular  determination  wage-employment  outcome  studies, was  not  ^•Examples o f wage-employment d e t e r m i n a t i o n s t u d i e s a r e : Brown and A s h e n f e l t e r (1986), Card ( 1 9 8 6 ) , C a r r u t h and O s w a l d ( 1 9 8 3 ) , D e r t o u z o s a n d P e n c a v e l ( 1 9 8 1 ) , E b e r t s and S t o n e ( 1 9 8 6 ) , F a r b e r ( 1 9 7 8 ) , MaCurdy and P e n c a v e l (19 8 6 ) , M a r t i n e l l o (1984).  2 predicted  or  one  of  preferred  choice.  employment  outcome  assumption  on  the  objective  employment  the  the  agents  With is  a  was  allowed  bargaining  predicted  of  equations  are  specified  by  Also,  game  identifying  a d d i t i o n a l determinants o f the  is  still  v e r y new.  theoretical they  equilibria especially possible  when  of  are the  doing  problem often  requires adding  often  points very  empirical  that  (e.g.  o n l y o t h e r example o f t h e use game  to  study  prediction the  surplus  rate.  of  firm-union  Their  to  their  framework  are  is  in  research  for this.  that  The  and  is to  The also,  of  the  assumptions the  fact  the  set  that  particular  crucial  and  helpful  recent  there  of the  parameter Finally, additional  the  game  are  beliefs).  Levine of  is  difficulties.  and Rudd  (1985)  is  the  a noncooperative bargaining  negotiations.  s t r i k e lengths  although  the  prior  p a p e r by F u d e n b e r g ,  reasons  small.  sensitive  that  wage  equilibrium  simplifying  applications  variables  the  Given  empirical  requirement be  extreme  Characterization  severely the  in  wage-  agents.  the  his  contracts.  fairly  complex.  game m a g n i f i e s  not observable The  themselves  very  equilibrium  equilibria  when  are  become  often  models  There are s e v e r a l  models  easily  values  game t h e o r e t i c  the  a  this  players,  for  of  game.  two  the  conditions  The u s e  the  the  of  impose  game,  without  b a r g a i n i n g powers  functions  to  They  emphasize  the  r a t h e r than the d i s t r i b u t i o n of model very  also  predicts  different  from  the the  wage one  3 adopted the  here.  negotiation  level  of  Also,  their  in  They  the  behavior, which  data  rate cover  of  (1985)  was  game  first  Binmore has  the  I  and  advantage  negotiations.  time and  and  an  is  represented  by  in  union in  with  and  employment  a paper  by G u l and  concerning the  validity  2  a version  of  the  R u b i n s t e i n game  (1982)  Rubinstein's  study, of  costs.  explained  problem.  a generalized  and e x t e n d e d  estimation  (The  t o make o f f e r s ,  i n Chapter  in  of  are  derived  continuous  continuous  3. )  The as  time  resulting  the  specifically,  Nash b a r g a i n i n g  a  collective  models  c a n be w r i t t e n More  in  information, role  as  b a r g a i n i n g model  observed  perfect  u n i q u e and i t  optimization  firms  conflict  wage  Finally,  generally  discounting  equilibrium to  is  is  allowed  allowing both p a r t i e s  In t h i s  costs  of  in Rubinstein  assumptions  delay  is  the  offers.  bargaining with  assumptions  questions  1987C).  of  which  the  is  presented  (1987b  practice  under  use  o n l y about  to  b a r g a i n i n g framework  studies  raises  their underlying model. The  it  and i n t h e  above.  exogenous  u n i o n c a n make  unions  These  d e t e r m i n a t i o n mentioned Sonnenschein  the  No v a r i a t i o n  empirical  is  the union cares  several  behavior,  the  employment  and o n l y  negotiate.  of  that  that  industries.  firm  they  results  process,  wage  different  assume  solution it  can  solution  be  with  G u l and S o n n e n s c h e i n (1985) a r g u e t h a t e q u i l i b r i a involving delays (strikes) can only occur i n d i s c r e t e time g a m e s , w h e r e a s F u d e n b e r g , L e v i n e , and Rudd (1985) have a continuous time model. 2  4 the of  w e i g h t s on t h e the  quite  costs  of  equations  profit  the  as  and t h e  sense  Svejnar in  of  the  the  are  one  of  set  the of  the  work  wages and employment  guidelines,  exogenously  In  are  exogenous  bargaining  a  second  of  by  factors:  by  COLA  regional  of  the  costs  firm's  and  they  parties.  game w h i c h was equilibrium  this  study  Svejnar  levels  i n 12  is  in  (1986). industries  a r e d e r i v e d from a in  which  bargaining  estimates,  the  functions  clauses,  wage rate,  utility  powers.  are  linear  unemployment  observed  agreement.  the  b a r g a i n i n g powers  set  represented  the  the  solution  determined the  the  the n e g o t i a t i n g  representation  to  employment  the  strike  for  objective  and  delaying are  functions allows  union u t i l i t y ,  delay of  it  between  particular version of  estimates,  fixed.  as  Nash b a r g a i n i n g s o l u t i o n ,  Nash  being  players'  U . S . Wage and employment e q u a t i o n s  weights  powers  of  consequent  studies  important of  costs  costs  comparable  generalized  be  of  and t h e  the  a generalized  some  is  relationship  b a r g a i n i n g powers  Because chosen  a  in u t i l i t y  e q u i l i b r i u m wage  parameters  framework,  measure t h e  This  derived  represent  function,  this  gains  specifications  The  contract,  In  delay.  general  functions.  players'  assumed  In to  bargaining of  several  controls and t h e  rate  and of  inflation. This research. are  study  offers  The f a c t  generated  by  that the  several the  advantages  wage  over  Svejnar's  and employment  equations  e q u i l i b r i u m to  a  non  cooperative  5 bargaining powers the  have  implies  natural  underlying  bargaining the  game  more  general  not  treated  threat  are  Also,  exogenous  to  only  one  Results  from  wage-employment  bargaining  and powers  However,  in  Svejnar  assumes  affecting  industry  his  industries,  and,  with  the  union, the  consider the  This  union is  the  sense  B.C.  to  lumber  products  powers  have and  labour  bargaining this  study. workers'  involving across  of  of  in  fixed  industries.  bargaining of  powers,  the  factors  constant  across  COLA c l a u s e s ,  it been  is  a  plywood  over  for  in  industry.  America  the  this  stable,  successful  there  determinants.  Woodworkers o f  industry  are  process.  concerning  are  exception  a good c a n d i d a t e  that  than  b a r g a i n i n g r e l a t i o n s h i p between a  International  B . C . wood  believed  the  strike  coefficients  a r e no u n i o n o r i n d u s t r y s p e c i f i c I  other  variations  bargaining  example,  is  show  the  of  union preferences  estimates  that  model  For  3  considered  modelling  the  of  studies  large  on  bargaining  costs  Svejnar's  subsequent  the  of  the  is  and  relative  inputs  Finally,  objectives,  by  my m o d e l l i n g and  based  process.  measured  and o u t p u t s as  points  interpretations  negotiation  powers  players.  that  (IWA)  period  type  of  single and  1963-1983. research  in  powerful  organization  capturing  rents  The e x i s t e n c e  of  in  the  rents  Svejnar (1986 ) j u s t i f i e s the use o f the g e n e r a l i z e d N a s h b a r g a i n i n g s o l u t i o n by a Z e u t h e n - H a r s a n y i n e g o t i a t i o n model. H o w e v e r t h i s m o d e l i s b a s e d on t h e a s s u m p t i o n o f i r r a t i o n a l behavior o f the p l a y e r s over time. 3  6  not  captured  sector  has  result of  of  of  on  Crown  logging  available industry  the  in  prices.  i n p u t demands  and t h e  output  assumption  of  restrictive  given  an  Nevertheless,  the  the  modelling  of  the  output  that  considers  the  union  whole  is  not  is  competition  possible  output  as  on  of  input  equations in  addition  markets.  avoid  Competition  products  United  sold  there  in are  i n Canada  are  States.  Martinello  b a r g a i n i n g frameworks.  in  industry  are  Also,  from the  wage  very  prices.  i n order to  this  is The  is  transfer  for  markets.  the  pass  products  materials  products  chooses  tax  Competition  sector.  in  and  including  their  studied  unilaterally  wood  inputs  for  the  high  government  fees  supply  unreasonable  selling  was  of  maintained  of  the  to  My s y s t e m  forestry  the  logs.  log prices  portion  firms  for  price  of  and  the  equations.  international  industry two  role  in  is  harvesting of  stumpage  nonlabour  assumption  large  with strong This  the  the  competitive  indications faced  a  and  exogenous  market  that  highly  employment  the  because  advantage  and  the  of  forestry  and  incentives  low p r i c e s the  for  sector  operations  a l s o has  and  the  have  their  form o f  fee  Moreover, in  Columbia  observers  stumpage  calculation  quantities  wage  assumed  given  low  British  several  Lands.  to  data set  include  by  the  integration  rents  output  in  companies  i n the  This  to  relatively  concerning the  rates,  will  argued  vertical  policies  and  been  a  timber  level  by g o v e r n m e n t  (1984)  who  In  one  case,  while  the  firm  7 imposes  its  by t h e  choice  union.  of  In the  bargain e f f i c i e n t l y a framework, the frontier  indifference  (1984),  adopt t h i s  Although changes period  as  A for  is  firms'  wage i s  u n i o n and t h e  contract  for  the  located points  curve.  specified the  One  treatment  endogenous  Pareto  curves. In  of  such  between u n i o n This  Martinello  and e s t i m a t e d  location  set  firms  In  on t h e  iso-profit  observed.  differs of  simple the  differences  the  and  raw  from  the  b u t no  particular  contribution  of  input  and h e n c e  as  As m e n t i o n e d  extended  of  demands  and  determined above,  I  in  also  b a r g a i n i n g framework,  and  firms'  straightforward )  and  4  industry  to  i n the  Martinello  union's  a r e made i n t h e is  the  method.  study  more  the  tangency  b a r g a i n i n g outcome.  specification are  of  curve is  is  Other than the this  the  work was  supplies  by t h e  and  provided  which  Martinello's  part  locus  called  is  contract  output  the  contract  explanation  model,  after  o v e r b o t h wages and e m p l o y m e n t .  curves  is the  second  resulting contract  which i s  frontier  employment l e v e l  data  treatment  i n c l u d e the  is of  the the  early  (1984)  in  objectives in  the  same,  (which  data  set.  important  d a t a and t h e 1980's  the  (see  sample  Appendix  details).  In particular, Martinello expressed the union objectives i n terms o f employment and c o m p e n s a t i o n (wage t i m e s employment) r a t h e r t h a n t h e u s u a l r e p r e s e n t a t i o n w h i c h i s done i n t e r m s o f wages and e m p l o y m e n t . 4  8 I over  assume  wages  subject  and  to  estimated  the  the  on  level  implies  demand  contracting levels  the  defined  maximize  profits  Four  technological a r e based  then  that  curve.  models  in  being  the  with respect  of  inputs  in  one c a s e ,  and o u t p u t output  chosen  on t h e  In  is  Each  is  wage o n l y  the  contract w i l l  be l o c a t e d  on  the  the  wage  models and  of  the  estimates  of  the  robust  is  the  framework.  cares  b o t h wages  about  weight weights  being  placed  placed  of  on  on  the  of  changes  estimated  the is  adjustment  all  inputs  negotiated  endogenous  the in  nonlinear,  union u t i l i t y the  with  that  and the  is  the  union  relatively  The d i f f e r e n c e  employment  The  function  technology imply  and  contract.  by a FIML p r o c e d u r e .  employment  and  of  the  Specifically,  simultaneous,  employment.  wages  are  wage employment  The e s t i m a t e s and  that  output  of  estimated  employment  In each o f  exogenous w h i l e  case,  systems  the  bargaining  as  efficient  concerning the  functions  parameters to  are  labour contract.  treated  four  equations  two m o d e l s  assumptions  now i n d e p e n d e n t  structural  quite  the  second  with the  which  as  assumption  by  two  the  bargaining  optimally  other  to  are  chosen  The  optimally  contract. capital  to  models  and  a r e j o i n t l y d e t e r m i n e d by b a r g a i n i n g .  differ  are  firms  technology.  models  two b a r g a i n i n g f r a m e w o r k s ,  are  the  function  f i r m s and t h e u n i o n b a r g a i n o v e r t h e  This  labour  while  different  Two o f  employment  firm.  a CES u t i l i t y  Cobb-Douglas  based  the  has  employment  a  assumptions. that  union  in  smaller  more the when  9 output of  is  treated  substitution  of  case,  preferences hypothesis  .87  a  are  and i n  convex  fact,  i n that with  1.0  when  output  is  the  hypothesis  case.  The u n i o n  an  on a v e r a g e when o u t p u t  elasticity  of  endogenous  and  is  exogenous.  Cobb-Douglas representation  cannot of  rent  be  rejected.  maximization is  For  of  a l l  rejected  In the  the  union  models,  at  the  the  1% l e v e l  significance. When  output  bargaining  power  utility  in  (out  a  of  followed  the  the  is as  of  1).  power.  different  four  on t h e  from t h e  bargaining  power  models,  equal  union  the and  rises  firm  increases  results  models,  sharply.  of  power suggest in  the  the  to  union  average  slightly  in  the  1980's.  1970's  is  .53  .32  closer i n the  when  the  complete are that  1970's.  tested the  firms'  to  contracts  i n that  union  is  case  The t i m e p r o f i l e i s  in  .86  When o u t p u t  averages  slowly  hypotheses  deterioration all  it  union  on  exogenous o u t p u t e s t i m a t i o n  caused  in  given  b a r g a i n i n g power  contract curve.  now  the  is  l a b o u r demand and  the  since  weight  i n the  union  Finally, a  exogenous,  the  falls  Specifically,  b a r g a i n i n g on t h e  are located  It  increase  endogenous,  firms'  by  as  Nash b a r g a i n i n g s o l u t i o n  total  as  treated  measured  by a r a p i d  treated  of  curves  approximately  latter  of  endogenous  e q u a l w e i g h t s c a n n o t be r e j e c t e d  indifference  of  as  also union  In  all  power  and  and  rejected.  1980's  recession  bargaining  b a r g a i n i n g power  of  position  the  union  10 The  proportion  calculated  when  bargaining  power.  to  measure  whether  it  is  as  study.  The  of  and  firm  measures  exogenous,  and when o u t p u t  is  two m e a s u r e s As  theory, of  the  their  study, across These  relative  these  factors  literature models, is  as  the  rejected.  costs  strike  groups  of are  of  costs firms  out  be  that the  used  of the  used  strike  this  considerably  rents  captured  a b a r g a i n i n g power  the  two m e a s u r e s time p r o f i l e s  of  to  bargaining  are  costs.  vary over exogenous  the  functions In  this  time  and  factors.  empirical  costs.  In  costs  d i d not  strike  coefficients  on t h e  strike  all  four matter  strike  T h e b a r g a i n i n g power o f t h e f i r m s i s e q u a l to m i n u s t h e u n i o n ' s b a r g a i n i n g power as d e s c r i b e d a b o v e . 5  are  related.  to in  in  c o n t r a c t i n g model,  strike  are allowed  determinants  However,  to  players  or  according  often  behaviour  Rubinstein's the  delay  commonly  hypothesis 6  union  Furthermore, the  of  firm  not  endogenous,  b a r g a i n i n g powers  the  rent maximization is  proportion of  in  is  is  see  efficient  previously,  to  firm  to  are not monotonically  mentioned  the  interesting  42% compared t o  77% and 68% r e s p e c t i v e l y . the  rents  is  turn  the  on a v e r a g e  it  of  i n the  by  compared  since  description  two  is  is  and  a good m e a s u r e  is  captured  The p r o p o r t i o n o f  5  F o r example,  output  16%,  possible  a good  different.  by t h e  rents  b a r g a i n i n g power  accepted  when  of  cost one  T h e t e s t t h a t c o s t s do n o t a f f e c t t h e l a b o u r c o n t r a c t i s i d e n t i c a l to the t e s t that the u n i o n s t r i k e c o s t s are zero i . e . a l l c o e f f i c i e n t s i n the term r e p r e s e n t i n g r e l a t i v e 6  11  variables  are  sensitive  technological often  large.  relative  In the  strike  costs  interest  Effects  of  inventory  of  large  amount  technology  which  information. costs  value  the  output  increases  considerably labour  cost  product large  of  coefficient.  strike  better  did  correlation  in  a  large  set  of  standard  is  labour very  zero.  conditions problem  considerable among  In  as  the  is  likelihood improves  the  coefficient  upper  (the  efficient  caused  the  the  successful.  marginal  on  small.  other  additional  the  employment  error  these  coefficient  problem  between  ratios.  employment  small  e v e n when u s i n g  the  to  the  firms'  separately  exogenous,  a  the  failed  estimate  as  implies of  are  the  provide  low.  model  the  data  not  to  of  present  implausibly  of  are  is  is  interval,  costs  by  labour  Part  errors  market  Part  resulting  However,  cooperative  which  prediction  this  the  significantly  and t h e u n i o n were n o t  the  labour.  results  labour  caused  find  treated  and  utilization  the  model  amount  confidence  but  and  attempts  is and  capital  is  used  firm  share)  contracting  This  of  and  assumptions.  to  Also,  standard  negatively and  errors  were  their  framework  c o n t r a c t i n g model,  levels  Attempts  variables  When  are  multicollinearity  variables.  strike  and  rates  standard  of  bargaining  efficient  by  on t h e  the  assumptions  affected  depend  to  and  revenue by  the  output.  employment bound o f  estimate  in  Otherwise,  a  the the  12  technological reasonable  parameters  and t h e y  Consistently  (e.g.  demand  are comparable to  throughout  the  likelihood value.  seem t o  be  to  bargaining  the  more  implications employment modelled  for  the  and  estimation  and  many  of  comparable  efficient  sense o f  generating  technological  estimates  assumptions  This of  s t u d i e s where  to  to  yields  the  provided  has  serious  results  the  than  in  technology  wageis  not  reasonable  results  previous on  empirical  research.  technological  concerning findings.  bargaining  In  the  union  and  the  be  general,  parameters  utility  F u r t h e r m o r e , new  powers  to  are  insights  measurement  of  costs.  This  thesis  literature  is  followed  in  game  its  and  modelling discussed  is  organized  provided  Chapter  3 by  the  union  i n Chapter 3.  the  in  application of  assumptions short  the  b a r g a i n i n g game by R u b i n s t e i n p r o v e s  amenable  the  first,  estimates.  parameter  used.  seem  rigorously.  tractable  strike  the  interpretation  determination  Overall,  are  to  framework  the  i n the  However,  sensitive  previous  estimation,  c o n t r a c t i n g model performs b e t t e r a higher  elasticities)  as  follows.  the a  to  next  contract firms'  Chapter 4 i s  models  to  be  estimated  given  in  the  previous  discussion  of  the  chapter.  description  and  data  is  A review  of  the  the  This  is  bargaining  negotiations. objectives  composed  are  of  of  derived  chapter,  and  provided.  The  is two  based  also parts: on  secondly,  the a  Estimation  13 results remarks sources  are are  presented made  in  in  Chapter  Chapter  and m a n i p u l a t i o n s  6.  5  and  finally,  Details  are provided  concluding  concerning  i n Appendix A .  data  14 Chapter Review of In  this  relevant several  section,  areas  is  areas of  review.  There  it  will  Other  are  union  basically  I  will  is  two  which  behaviour,  the  will  work  models by  and  involved:  noncooperative first  a bargaining include:  bargaining  upon  exhaustive  d i s c u s s i n g the of  in  touches  literatures  mentioned  cooperative  literature  by no means a n  choice  be  the my  major  start  motivate  of  Since  determination  to  topics  overview  presented.  games.  serve  an  Literature  research, this  wage-employment bargaining  the  2  games  as  model.  models and  of  strike  theory.  data  In  wage-employment  determination  on  wage-employment  contracts  particular curve on  industry  models  of  r i g o r o u s  models It  agreements  the  are  consequently,  is  is  an  modelling and t h e  of  of  area union  bargaining  of  models  have  firm  framework.  to  that  either  micro and  Phillips' are  based  and  f i r m  negotiated  bargaining party  and  a  (e.g.  the  and the  union's  outcome.  research  goals,  union  o b j e c t i v e s  c o n d i t i o n s the  a  studies  firm-union  affecting  can influence  these  recognized of  models,  Contrary  union  also  market  Wage-employment which  studied.  result  factors  product  preferences)  between  wage d e t e r m i n a t i o n ,  technologies.  f i r m ' s  are  (W-E)  in  three  components  itself.  objectives Firms  are  They and  usually  each are:  of the  constraints, assumed  to  15 maximize  profits.  varies  lot  a  on i n t h i s The  across  studies.  modelling  1940's.  representation  of  the  Examples w i l l  technology  be  given  later  chapter.  controversial  a  The  issue  of  in  The q u e s t i o n  too  behaviour  industrial is:  common w e l l - b e h a v e d  decision-making  union  relations  has  ever  been since  the  c a n we m o d e l u n i o n o b j e c t i v e s  utility  complex  function  to  or  be e v e n  is  the  a  by  union's  a p p r o x i m a t e d by  such  a formulation? I n most c a s e s , a  well-defined  economists  utility  underlying process (1982)  and B l a i r  implications concerning under been  is  utility For  union  it  a  ( 1984 )  from rent  sense to  the  that  utility  worker's  expected  income  if  utility  I  assume  function,  but  the I  very  workers  believe  of  there  is in  union  preferences. can  equal the  to  of  the  union's  being employed.  a lot  be  worker's  a well-behaved is  have  special  function  utility  all  existence  process  a representative  expected and  assumptions  well-behaved  m e m b e r s h i p h a v e an e q u a l c h a n c e o f study,  in  the  results  u n d e r l y i n g workers'  expected  this  a  the  investigate  the  of  a r e Oswald  political  only  generate  by a u n i o n who m a x i m i z e s  fixed  the  maximizing u t i l i t y  this  specifying  various  To d a t e ,  generated  if  who  of  and  operates. the  existence  Two e x c e p t i o n s  preferences  possible  function  example,  in  without  it.  preferences  union  discouraging  cases  generating  workers' the  function  and C r a w f o r d  on  which  h a v e assumed t h e  In  union  important  16 work  to  be  done  discussion Two in  of  in  the  this  issues  different  W-E s t u d i e s .  union  and  level  being  firm  the  framework  negotiated. situated  by  the  defined  by  indifference contract  curve,  0  contract point  is  of  union  the  union  sloped  to  not  points  with  l a b o u r demand.  assumed  only,  considered  the  that  then  Pareto  that  firm's  yields  which  This  is  is  union's  curves.  right of  space.  are  outcomes  between t h e  the  the  levels  iso-profit  be t o  the  In  frontier)  points  the  employment  implies  employment  a l a b o u r demand, indifference  with the  curves  care  a  This  the  labour  easily  seen  page).  Iso-profit  indifference  tangency of  a  intersection  does  (the  i n general  D is  curve.  negatively union  1,  is  This  and  tangency  (following  Figure  for  l a b o u r demand c u r v e .  i n wage-employment  from F i g u r e l  been  wages  firm.  curve  and t h e  curve w i l l  (1986 )  have  it  bargaining  of  curves  demand c u r v e  In  locus  over  wages  Efficient  the  one,  on t h e  both  on a c o n t r a c t  set-ups  first  bargain  chosen  Farber  involved).  c o n t r a c t w i l l be l o c a t e d second  (See  bargaining  In  the  area.  curves the  right are  about  are  the  iso-profit  C  is  the  horizontal  at  the  they  are  Unless  the  demand.  and  ( i n which case  employment curves  iso-profit  and  demand  horizontal  the  an  curve,  labour of  F is  will  level), be  to  the  the  their right  17  Figure  1  B a r g a i n i n g Frameworks  Wage  Employment  In the utility wage), is  case  takes the  of  the  form E»(W-W^)  contract  determined  a rent maximizing union  by  curve i s equating  where  alternative  wage  This  employment  maximizes  of  independent serves Note  to  that  bargaining  of  divide under over  contracts  will  level  also  is  the  negotiated  the  rents  the both  wages  total  between t h e  and  A  union  alternative level  product  in Figure  rents  of l).  and  is  The  contract  wage  union  and t h e  firm.  rent  maximization  employment,  i n the  competitive  of  revenue  point E  wage.  assumptions  be e f f i c i e n t the  (see  the  the  T h e employment  marginal  labour with the level  is  vertical. the  (i.e.  sense t h a t employment  and  the  resulting  the  employment  level.  This  18 property  is  called  Ashenfelter Note  that  predicted  Figure  1 is  the  to  This  based  of  cooperative  on  (e.g.  (1984)),  no  the  underlying  instruments monopoly  (e.g.  model  particular  studies  Once  derived make  and  of  impose  wage.  and  contract curve  his  The  called  the  choice.  point  monopoly  curve  the  is  wage is  endogeneity  of  variables the  (also  exogenous the  wage  but,  choice  Pencavel  (1986)).  is  assumed,  the  the  model.  explained.  as  and  the  the M in  model  not  treated  explaining  requires  is  c o n t r a c t u n d e r s u c h an  instrumental  None o f  preferences  estimated.  technology  estimation  to  the  relevant  contract  wage  unions  specified,  inferences  firm's  Brown  there of  the  Unless  prediction  specification  wage-employment  is  a  of  a  of  a  determination  such a model.  union  been  the  or the  model  contract  include  the  the  MaCurdy of  bargaining model.  have  use  on t h e  free  is  model),  either  by  demand o r  a predicted  Econometrically,  is  by  on a l a b o u r demand m o d e l ,  framework  based  Martinello  is  choose  an example  recognized  labour  agent  studies  studies  called  one  assumed  assumption. the  either  no p a r t i c u l a r outcome  i n the  is  In  in  unless  union  efficiency"  (1986).  curve models,  Usually,  "strong  about  wage  and  the  and  employment  The e s t i m a t i o n union  are  used  to  profit  and  function  equations  results  objectives,  and p r o d u c t m a r k e t .  results  firm's  are used possibly  are to the  I n some W-E s t u d i e s , evaluate  bargaining  19 frameworks locating  i.e.  the  outcomes  curve,  or  demand  curve.  The United U.S.  at  the  first  the  union  the  median  workers  the  Great  due  functions  In  utilitarian  of  of  rule. so  American  (1981),  a labour  coal  the  develop  National  industry  (1978),  union Again  of  that of  that the  the  union  have  that  in the  demand  the  labour  demand  of  costs.  if  are  labour  over  The  workers  aversion  utility  it  found  adopted to  a  be  risk  (ITU) l o c a l s  in a  counterparts.  been  (1984a),  Mineworkers  labour  as  workers  a model  a  risk  behaves  determination Pencavel  is  assumed  adjustment  relative  U.S.  is  T y p o g r a p h i c a l Union  cities  the  utility  that  of  to  adjustment  the  than t h e i r  the  in  and  and e s t i m a t e  it  subject  partial of  result  Union  modelling  for  labour  involved  expected  central  demand  on t h e  studies  by  employment.  constant  the  wage-employment Pencavel  the  presence  with  but l e s s  explained  which suggests  (1983)  their  The I n t e r n a t i o n a l number  His  wages  allow  and  such  maximizes  w e i g h t on  choose  the  curve,  bituminous  As i n F a r b e r  they to  for  averse  and O s w a l d  identical  averse  used  it  risk  wage p o l i c y  however,  better  p r e f e r r e d wage l e v e l  member.  substantial  can  is  a contract  set  if  quite  Britain.  data  assumes t h e monopoly m o d e l h o l d s  as  aged  constraint.  are  data  acts  are  union  time  on  union's  (1978)  Carruth of  the  M i n e W o r k e r s and t h e  Farber  places  whether  the  subject  studies.  of  several  Dertouzos  and P e n c a v e l  (1984b)  and all  20 assume  the  monopoly  difference union  in  locals'  locals.  of  In  the  next  the  cooperative (1986)  models  employment  the  is  choose i t s  to  the  If  employment  ratio  term appears rate  that  of  the  is  of  term  of  economic  suggest  that  in  the  across as  the  rents  are  most  cases,  of  Brown rents  test  contract  find  that  that the  could  description (1986)  set  wage e q u a t i o n  of  test  this  mean  rent  the  that  revenue  contracting,  i n the  form o f  assumed  important  in  for the  the  affect  ITU's  based is  input p r i c e ratios marginal  is  on  in  is  between wages and  form  wage  wages  also  maximizing firm  efficient  be  both  is  contracts  it  or  whether  (the  input's  to  and  to  Ashenfelter  wage  will  functional  and  alternative  a profit  by  contract  the  good  same  are performed  efficient  and P e n c a v e l ' s  found  tests  by  substitution  is  such  However,  a  chosen  i n the  preferences  data.  They  input levels  general  extra  the  suggests  not  found  of  vary  and  major  specification to  nested  contract  MaCurdy  to  A quite  studies,  inefficient.  observation  marginal  bill  The  a r e p l a c e d on e m p l o y m e n t .  curve) .  maximization behaviour.  union  ITU maximizes  which  are  are  determined  or  demand  industry  These  results  to  the is  (efficiency)  employment  two  the  applicability  assume  labour  The  bargaining.  in  of  wage  h i g h weights  the  evaluate  the  forms  of  is  objectives.  rejected.  relatively  the  models  Popular  maximization often  the  model  the  on free  equal  product. an  extra  union's  employment, the  MRS and  estimation.  21 They  conclude  constraint  is  that  unlikely  Martinello International locals  of  outcome  i n the  (1984)  on  ITU  of  the  industry.  function  which  The u n i o n  is  quadratic  tests  suggest  the  is  in  labour the  to and  efficient  concerned  wage  alternative  wage.  tested  rejected.  more  and  rigorous  particular, levels  to  it  represent  that  labour Also,  profit  functional The  study  are  general  firms'  all  to maximize  the  support the  maximizing  a  wood  utility  contracting The u n i o n  levels  firm  and  the  maximization  are  functional  technology. adjusts  rather  than  forms  other  input  fixing  them  are  adopted  curvature properties and  a In  Unfortunately,  behaviour  is  Martinello involves  firm's  technology.  by C a r d i n the assumed  rents.  (1986) U.S.  to  This  i n Brown and A s h e n f e l t e r additional  by  the  contract  rent  the  his  to his  associated choice  of  forms.  seven a i r l i n e s they  assumed  and  study  is  e s t i m a t e s do n o t with  The of  the  employment  B o t h wage b i l l  modelling  the  exogenously.  and  the  compensation.  t h a n t h e monopoly m o d e l .  both  of  Columbia have  model performs b e t t e r with  demand  particular  British  assumed  in  that  labour  behaviour  America,  IWA b a r g a i n i n g w i t h  products  the  negotiations.  studies  Woodworkers  the  Non-nested  an  effect  of  the  involves  a i r l i n e mechanics  Several unions  behave  are  identically,  involved  in  s i m i l a r to  (1986),  to  extended  alternative  wage  on  but  particular,  framework, which i s is  in  allow the  that  for  level  an of  22 employment.  More  specifically,  faces  adjustment  profit  maximizing l e v e l  employment  costs  implies  that  even  constraint,  of  alternative  assumes  labour  employment  are functions  binding the  of  its  and f u t u r e wage r a t e s .  f u t u r e wage r a t e s which  in  Card  if  input  is  firm  that  the  a function  of  past  current alternative  the  labour  demand  contracts  wage.  so  the  Moreover, expectations  of  employment  that  will  However,  he  is  a  functions  finds  that  an  unrestrictive  function  for  where  neither  the  monopoly model  (with the  d y n a m i c l a b o u r demand)  nor the  rent  maximizing contract The  last  reviewed school  is  curve  wage-employment  by E b e r t s  that  after  effect  attributes  the  sizes. on  behaviour  of  approach i s stock  agreements  efficient  bargaining  contracts  of  chooses signed  to  test  model  in  they in  a  1976  the  to  1982  be  public  reject  labour  the  demand  between  wage  clauses  such  find  expected  the  as  job  provisions. (1987)  to  the  data  framework That  to  non-employment  response  whether or  a  i n Abowd  employment. from  on  and l e a v e  taken  values  (1986)  protection  changes  study  involves  relationship  fringe benefits  collective  unilaterally  located  By c o n t r a s t ,  salary  and  Stone  positive  employment  s u c h as  A different  a  (1986)  and  are  better.  determination  Stone  Eberts  outcomes  and  on c l a s s  negative  and  finding  compensation limits  c u r v e a r e imposed p e r f o r m s  teachers.  hypothesis  employment  wages  curve  be  of  uses  signing  of  supports  an  where  data  who  the  firm  consists  involving  of  U.S.  23 manufacturing traded  and  stocks.  maximizers. serve  non-manufacturing  to  A l l  Abowd  finds  distribute  shareholders  but  stockholders information  unions  do  not  the  hypothesis  and  the  firms  of  a common  bargaining  and  different  implications changes  stockholders'  wealth.  There models  of  involve  are  bargaining  important  influence  determinants example, into  with  account  new  affect the  use  effects  the have  between  wealth  results  and  support  the  model.  extensions  determination  extension  the  shed  model  to  some o f  of  the  empirical w h i c h would  effects  of  information.  Not  may  with  unions  frameworks  members'  modelling  model.  identify it  explicit  the  Abowd' s  contracting  possible  consistent for  to  private)  relationship  empirical  efficient  and p r i v a t e  the  union  The  various  more  Another  but  for  in  is  contracting  and  information  set  In  rent  workers  (possibly  This  together.  wage-employment  uncertainty  to  the  unions'  be  agreements  to  provide  information  inefficient  unexpected  of  the  to  rents  publicly  to  collective  labour costs.  efficient  predictions  seem  with  assumed  the  firms'  concerning  on f u t u r e  are  that  the  firms  only  can  of  is  the  incorporation  a b a r g a i n i n g model  additional  light  on  the  wage-employment of  a  bargaining  of  the  exogenous  way  game,  alternative  be  we  wage  used  used As  could or  a  factors  previously  contracts.  of  an take  labour  24 market the  conditions  relative  problem  of  of has  type  the  the  bargaining the  games)  in  of  its  characteristics  on  focal-point  the  solution  observed the  study  In  any  lack  of  to  type ought  be.  of  description  (e.g.  In that  like  of  the  that  process  best-known  proposed  satisfies  the  Independence linear  by  four of  axioms  of  irrelevant  transformations.  It  models.  on t h e  Unless  one  basis relies  prescribe  than  what  than negotiated models  what it  is  agents  outcomes.  contain  arrive  at  in empirical studies  no the of  7  bargaining model  is  The Nash b a r g a i n i n g symmetry,  Pareto  alternatives be  The  a r e more a p p r o p r i a t e f o r  these  can  The  cooperative  chosen  models  settings.  Nash.  explicit  two t y p e s . (or  rather  to use  axiomatic J .  is  by w h i c h  non-experimental bargaining  on  mentioned.  models  sense they  fact  of  appropriate  these  arbitration decisions the  is  symmetry).  look  influence  agents.  h a v e been o f  arguments, to  its  importance  of  axiomatic  s o l u t i o n makes them d i f f i c u l t  first  the  w h i c h a p a r t i c u l a r outcome  case,  The  the  process  b a r g a i n i n g models  consists  wage by of  W-E s t u d i e s ,  been  Historically, first  contract  bargaining strengths  I n most modelling  on t h e  and  written  as  the  one  solution  optimality, invariance the  to  solution  S e e R o t h (1979) and R i d d e l l (1981) f o r d i s c u s s i o n s o f various solution concepts. There is a substantial l i t e r a t u r e on e x p e r i m e n t a l b a r g a i n i n g s t u d i e s i n w h i c h various bargaining s o l u t i o n s are t e s t e d . F o r example, see C o u r s e y (1982) and R o t h and Schoumaker ( 1 9 8 3 ) . 7  25 to  the  maximization  utility  increments  relaxed,  empirical and  Examples  Svejnar  while  periods  in his  study  latest  study,  contracts  in  exogenously  across is  possibly  power  two  determined  time  the the  U.S.  increased  with  the  a  Nash  whether  looks  at  industries  is  allowed  with  sample  i n the  is  assumed being  powers  workers  that  presence  to  be  form  of  coefficient.  utilities  show  the  wage and  U n i o n s a r e assumed  b a r g a i n i n g powers results  in  (1973),  assumes  are  of  Results  suggest  highly  variable  very  sizes.  solution of  I n some o f allowed  the  union  COLA  risk  imprecise,  are  of  the  functions  estimates  are  An  with  symmetric Nash b a r g a i n i n g  the  players'  solution  test  (1986)  o f v e r y s m a l l sample  work, and  of  is  holds.  Unfortunately,  parameters because  to  b a r g a i n i n g powers.  and t h e  the  this  (1971)  solution  bargaining  symmetry  Hamermesh  aversion  players'  to  players'  o f U . S . m a n u f a c t u r i n g wages  aversion risk  rejected.  empirical over  the  industries  aversion  Menil  Svejnar  bargaining  relative  often  risk  of  (1971),  industries.  relative Nash  on  the  but  two If  attached  attempt  several  the  points.  Nash b a r g a i n i n g s o l u t i o n  constant  that  Svejnar  of  use  Menil  solution  rent maximizers  weights  the  de  varying across  asymmetric  be  1986).  his  employment  de  threat  can  of  are  Hamermesh and  In  product  (1980,  (symmetric)  a  weights  research  bargaining  the  over t h e i r  different  u t i l i t i e s .  of  to  the vary  bargaining  clauses  and  26 inflation  and d e c r e a s e d  during periods  of price controls  and  h i g h unemployment. In the  second  type  process  is  described.  relied  on  ad  rationality Examples  hob  of  are  which p l a y e r s and  even  past  is  the  of  issue  contracting do n o t level  between  proceeding bargaining  observe is  requirements presented  and  it  and  so  I  the  want  to  unions  observe  imperfect  not  as  a  the non-  players.  on  mention  related  in  the  fact  contracts and  the  manning evidence  contract been  a good  we  employment  with  monitoring for  that  are concerned  have  The  implicit  i n which the  reasons  (1979)  a  non-  literature.  explicitly  information,  S e e F o l e y and Maunders t h i s type of model.  in  literature  engage  provisions,  possible  only  i n my e m p i r i c a l w o r k .  framework due t o  why  these  is  opponent's  modelled  suggests that unions  Several  8  the  transmission.  (Bayesian-Nash)  examine  We do  employment?  of  rational  seniority  also  models  about  their  i m p l i c i t contract  in this  levels,  involve  been  firm-union contracts  above  employment  information  has  games,  the  specified.  such  assumptions  behaviour.8  to  firms  arises  negotiation  very recently,  e r r o r s ^about  o f model I use  whether  the  by J . C r o s s and Z e u t h e n - H a r s a n y i i n  future  work n a m e l y , of  and  bargaining  type  cooperative area  own  game  Before  agents  models  that  cooperative This  But, u n t i l  make s y s t e m a t i c  their  decade  bargaining model,  and u n s a t i s f a c t o r y  the  the  of  with for  provided; costs  and  description  27 transaction contracts  costs. will  be  which n o t h i n g  is  include  kind  some  efficiency.  and  these  and  relevancy. The fairly  is  contracts  that  structure  results  known  which ensure the  Efficiency the  far  about  in  and above  on  so  but  will  efficiency.  imply the  little  scheme  resulting  level  c o n t r a c t i n g over  ensure  however,  the  have  employment  compensation  could  good  A lot  1 1  where that  on n o n - c o o p e r a t i v e  these will  and S a m u e l s o n  (1983)  in  players  the  of  i n e f f i c i e n t  the  players (or w i l l  present  form  are  their  of  model  empirical  b a r g a i n i n g games  work  is  set  bargain over not)  a one  submit  s i d e d u n c e r t a i n t y about the and  mean t h a n We c a n  the  implicit  literature  which  not  1 0  game  one  of  very  recent.  seller  about  compatibility  contracts;  specific  the  said  agreement  incentive  does  inefficient.  Also,  9  negotiated  This  be  a  the  traded.  buyer-  price  offers.  opponent's  There  valuation of  outcomes  of  Chatterjee  period buyer-seller  sealed  (no^trade)  in  is  can  game  is  two-  the  good  occur  in  equilibrium. F u d e n b e r g and T i r o l e  (1983),  and F u d e n b e r g , L e v i n e and T i r o l e multi-stage 9  one.  See Hall  1 0  In  imperfect  and L i l i e n  See Azariadis  (1979)  (1981)  for a  S o b e l and T a k a h a s h i (1983)  extend  the  information f o r examples  of  game t o  a  environments this.  survey.  S e e McLennan (1982) f o r a g e n e r a l d e f i n i t i o n b a r g a i n i n g p r o b l e m i n a game t h e o r e t i c f r a m e w o r k . i : L  (198 3)  of  the  28 learning  will  players  have  observable It  is  also  the  so  Takahashi  that  with  the  imperfect  the  The  rejecting  them.  there  time,  but  where  there  game was  the  This  certainty  Considerable (1984)  model  the  beliefs.  agree  look  is  early  at  while  an  a  two-  Sobel  and  infinite-horizon Fudenberg,  (with  Levine  one-sided  the  that  alternate this  presented  the  in  the  involves  the  a  pie  of  in Rubinstein  games,  fixed  pie,  shrinks  over  offers  and  concerns  the  making  initial  results  makes or  bargaining  in Rubinstein  his  for  (1982) the  for one-  (1985).  these  a l s o Cramton  of  of  accepting  uncertainty  than  of  in  In the next set  so  He e x t e n d s  seller  always  splitting  delay  exception  the  consists  good.  rather  the  only  the  extensions (see  to  their  there  infinite-horizon  uncertainty  first  case  to  case.  (1983)),  now  costs  case.  sided uncertainty  i n Cramton  uncertainty  uncertainty,  set.  that  (1983)  the  of  players  delay  models  incentives  games  over  costs  opponent's  opponents'  strategy  Also,  is  effect  the  results.  bargain  the  on t h e i r  have  generalize  buyer's  are  the  uncertainty  valuation of  players  strategies,  account  these  the  Samuelson  offers.  their  and T i r o l e ;  preceding  and  Again  to  extend  information  opponent's  have  players  one-sided  (1983)  Chatterjee  two  into  two-sided  (1983)  and T i r o l e  In  take  Fudenberg  game  for  choosing  fundamental  game.  period  game  to  In  behaviour w i l l  discounting in  occur.  models  (1985)).  were In h i s  provided thesis,  29 Cramton  looks  at  equilibrium horizon (the the  a game between  are  cases,  characterized  for  one-sided,  u n c e r t a i n t y always good),  offers,  there  is  and  have of  measure In  requiring  a is  that  also  evidence  relaxed  in  McLennan  valuation of  as w e l l  time  as  models  above  functions  one  case  i f  onewhere  of  the They  also  in  in  write  the  solution  of  models.  to  be  these  Discount a  important models  is  factors  stationarity  found c r u c i a l  that  my w o r k .  the  use  are  easy  of  the is  and to  in the  solution  later,  Another  this  common  discounting  as  time  manipulate  and  they  to  characteristic  that  Rubinstein  i n h i s model.  bargaining  characteristics  for  of  (1987C)  seen  to  feature  classes  be  that  function  view  an a s y m m e t r i c N a s h b a r g a i n i n g As w i l l  the  amounts  This  Binmore  in  assume  or a l i n e a r  earlier.  the  identical  share  this  assumption  examples  that  with  we  determined,  reviewed  is  and p i e  context,  being  models  as  of  The  infinite  game  out  have  in  restrictive  (1982).  some  (1982)  very  some  Rubinstein  the  the u n i o n maximize r e n t s  empirical  also  the opponent's  objective  firm-union  a  costs.  and  and no u n c e r t a i n t y  continuous  of  (dollars  thereof,  feature  for  feature  cardinal  employment  turns  two-sided,  involves  finally  important  other).  for  finite  The  no f i r s t mover a d v a n t a g e .  An  units  for  f o r games w i t h a l t e r n a t i n g o f f e r s  sided  agents  a b u y e r and a s e l l e r .  games  mentioned  above  have  a r e d e s i r a b l e f o r a p p l i e d work on  two firm-  30 union  contracts:  equilibrium  (i)  is  often  flexibility  i n the  throughout  the  studying the  a  game.  lengths  only  (if  observations). involving  It  inefficient  to  In  study  This  however,  the  cooperative  recent  reputation  the to  it  is  the  as  of  when  reflect have  information  and  Players  strategies  in  the  strike of  models  possibility also  players  are  tractability.  contracts that  one  offers  rather  the  offers  restricted  by  can  observe  such  as  wage  in  non-  area of  games  design  under  this). been  made  i n the  mechanism engage and  of  numbers  the  on t h e  and when  equilibria  offers  possible  developments  building  of  lot  the  the  important  course  a  bargaining  reasons is  in  hence  strikes  N o t a l l b a r g a i n i n g games O s b o r n e (1985) and C r a w f o r d 1 2  that  and  focus  model s h o u l d  information.  lot  found  relative  case  on  is  than  the  the  because  data  b a r g a i n i n g games e s p e c i a l l y  imperfect  imperfect  on  a  (the  important  rather than h e a v i l y  (Of  restrictions  Many  of  due  endogenously  then the  the  rather  or  is  is  especially  information  influence.  exogenous  with  often  small  there  industry  in  surplus  and t h e r e f o r e ,  be d e t e r m i n e d  is  and  restrictions  make.  than s t r i k e s  controls  is  (ii)  is  a g e n t s c a n make i n i t i a l l y ,  This  1 2  outcomes  severe  outside  the  because  asymmetric  allowed  e.g.  the  equilibria  unique)  contained  of  this  of  p a r t i c u l a r union  information  include  set  offers  distribution  of  the  in  sophisticated  implications  have t h e s e (1981).  of  the  characteristics  31 structure  of  studied.  the  However,  sophisticated become data  contract  very on  structure.  complex  the  framework  is  increase  the  firm  is  about  the  i n the  imperfect of  prior  time  the  more  equilibria  more  the  detailed  information  Strikes  occur  offered for  a function  the  a  the  wage  the  is in  the  wage  signed)  R o t h (1985)  special  for  simple  to  a recent  game their  size  or  being  increment  firm's  my  of  offers, rejects  e q u i l i b r i u m because  takes  schedule  the  firm.  form o f  are updated  the can  a  the over  (acceptance  estimate.  survey.  uncertain  reflects  actions form o f  to the  schedule  concession  sufficiently  In  absolute  union  union  This  the  bargaining  (1985).  and how t h e s e b e l i e f s  of  To  O n l y t h e u n i o n makes contract  schedule.  beliefs  using  (the  the  formulated  non-existent.  and Rudd  information,  Because  beliefs),  See  these  explicitly  bargain over  union observes the  rejection).  1 3  study  r e a l wage.  a strike).  union's  (the  and  an  Levine,  accepts  value  on  empirical  Fudenberg,  concession  as  require better,  practically  equilibrium strategy  wage  as  is  only  either  there  of  because the  process  based  a u n i o n and a f i r m  the  The  and w o u l d  work  game  knowledge  is  application  are  1 3  bargaining  (there  e q u i l i b r i u m outcomes  very d i f f i c u l t  bargaining  Empirical  paper,  the  empirical  games i s  the  on  or  uncertainty be  written  32 Concession strikes  in  the  Farber  (1978).  papers  in  is  it  difficult  in  is a  Their  as  paper,  worker  (the  This  due  is  of  in  concession to  only  the fact  that  leaders  i.e.  the  previous  contract  involving  more  than  union  interest  the  to  one  is  are  In  lack  thereof) the  model,  requirements.  downward  not  it  (or  Levine  disadvantage  involves  contract  have  economic  structure,  negotiations.  they  not  an  Fudenberg,  the  schedule  workers  are  have  rationality  game  union  parameters.  a p p l i c a b i l i t y of  in  those  of  since  of and  In such a framework,  these  the  in  the  Rudd,  information  (1967)  model  estimated  always  study  different  the  stringent  are  the  political  best  work,  in  Johnson  reasonableness  previous  strikes  and t h e  contract  the  and  re-election).  and  used  quite  some i n f o r m a t i o n on t h e  However,  game,  setting  workers'  Levine  particular  Rudd  Ashenfelter  evaluate  interpretation. provides  been  specifically  (e.g.  to  have  involves  i n the  goals  Fudenberg,  of  The  More  acting  different  work  that  behaviour. always  schedules  the  of  and the  sloping).  1 4  rules  of  the  negotiation  of  one  able  to  To a l l o w  learn  for  negotiation,  from  strategies  a  supergame  w o u l d be r e q u i r e d . The work seems  to  be  by G u l and S o n n e n s c h e i n  a basic  flaw  in  the  (1985)  Fudenberg,  indicates Levine  and  S e e E a t o n (1978) f o r an i n t e r e s t i n g v a r i a n t o f A s h e n f e l t e r and J o h n s o n m o d e l i n w h i c h i t i s t h e w o r k e r s b e n e f i t from s t r i k e s . 1 4  what Rudd  the who  33 model. while  Fudenberg, results  Levlne  by  Gul  inefficient  outcomes  equilibrium  points  and Rudd and  (i.e. in  strikes)  discrete  aspect  Fudenberg,  L e v i n e and Rudd has  A l l inputs levels) wage.  their  fixed  This  The model unions  is  and i n d u s t r i e s  Once s i g n e d ,  (iv)  This  means  will  be  the  with  that  the  by  output of  the from  models. on many  allowance  different  for  variance  technology  parameters.  assumed  last  expected  value  to of  forever.  the  contract  overstated.  The i n f o r m a t i o n s t r u c t u r e i s allow  the  weaknesses:  independently  w i t h no  is  as  adopted  (and t h e r e f o r e  data  or firm  the  model  e m p i r i c a l evidence  using  contract  that  Concerning  following  determination  in union preferences (iii)  the  exogenously,  estimated  suggest  games.  work,  conflicts  wage-employment (ii)  time  the  time  c a n o n l y be g e n e r a t e d  i n c l u d i n g employment  are  continuous  Sonnenschein  empirical  (i)  of  assume  for  firm  uncertainty is  assumed  very simple  regarding to  know  strike  and d o e s costs.  everything  not Also  about  the  union. For  my  Rubinstein First, the  it  empirical game.  is  union's  There  possible and  work,  to  firm's  I  use  are  two  use  more  a model  main  reasons  general  objective  based  on  for  this.  formulations  functions  the  of  without  34  complicating that  the  analysis  too  much.  in practice,  both n e g o t i a t i n g  As m e n t i o n e d  above,  Rubinstein's models  is  game  the  incentives  to  other  presence  of  players  to  delay agree  industry  which  is  and  costs  delay  a r e measured  area of  Most on t h e the  of  the  effects  of  Although  these and  costs  highly  are  the  will  early  by  which  in  delays strike  be d i s c u s s e d  studies  types in  of  on  the  the  strikes,  these ceteris  on l e n g t h  include  and  Reder  and  Addison  players  Examples and  Newmann  (1981),  the  of  strikes. of  were  increases  to the  strike. amount  and l e a d these  (1980)  Mauro  two  a model  paribus,  increase  strikes.  level  relationships  will  of  and/or  the  of  u n c e r t a i n environments  i n f o r m a t i o n between t h e  focused Firstly,  occurrence of  d i d not  that,  costs.  have  environment  to  last  c h a p t e r and  More r e c e n t l y ,  economic  generally  costs  In  strikes The  in this  willing  Siebert  to  costs.  less  (1980)  game.  lead  strikes  the  provide  relationships.  strike  related  of  offers.  e m p i r i c a l work on s t r i k e  arguments  probability  Kennan  costs);  is  clear  bargaining  make p a r t i e s  asymmetric  higher  the  hence  in  of  in  costs  here,  are modelled.  studies  by  Also  two  strikes  justified strike  of  parties  bargaining  the  variations  uncertainty  negotiating  is  empirical  estimation  frequency of of  studied  research which w i l l  t o w h i c h I now t u r n  is  do make  non-cooperative  the  of  parties  it  a fundamental c h a r a c t e r i s t i c o f  and  the  Secondly,  to  a  studies (strike  (1982),  and  35 Lacroix costs  (1983)  (uncertainty),  main  considered  costs  of are  variations  in  well  as  studied Tracy  in  here,  (1986)  the  during  of  also  strikes  strike  discount  of  strike of  factors  which the of  total  of  players.  is  to  is  and  specific  stoppages),  as  the  the  industry  as  study,  per  available  of is  considered.  measure  lost  level  rents  this  discount  and the  not  lost  of  of  as  of  rents  rents  measures  single  In  rents  by t h e the  size  are used  level  a  effect  strikes.  minus  firm  ability  work  Since  the  the  intensity  the  such  costs  one  The a b s o l u t e  be a f f e c t e d  indicate  of  been  Industry  capital  power  type  have  (unemployment),  during  union  considers  (i.e.  as  industry.  factor of  such  share  for  inventories),  (which  latter  proportion  players). will  (both  that  costs  variations.  used  the  the  explanatory determinants  workers  market  measures  unionization  of  the  costs  borrowing of  also  its  strike  levels  shipments  keep  of  of  cyclical  variables  to  measures  rates,  opportunity measures  determinants  are  (interest  in  (1986)  and u n c e r t a i n t y ) . The  firm  and T r a c y  an the  variations time  period  factors  of  due  strikes  to  as w e l l  as  the  the  36 Chapter 3 The M o d e l The  study  involves  the  bargaining: goals of  of  negotiated  modelling the  will  question  of  be  is  the  curve)? all  It  about  i.e.  a  to  negotiate  the the  3 components  is  of  of  but  first  I  the  level  of  union's right  of  Each  address  the  employment. by t h e  firm,  of (a  2 that a  firm's  employment  point if  on  the  to  optimal a  contract  l a b o u r demand c u r v e .  point  curves  The  will  resulting  employment  level  will  be g r e a t e r  than the  f i r m would l i k e  the  that  the  marginal  revenue  product  employment l e v e l  will  be s m a l l e r t h a n t h e  sense  Although specify  the  directly  level  (e.g.  be  collective of  affecting  provisions). could  the  used  employment,  non-linear  they  employment  Moreover, to  agreements  obtain  there an  are  compensation  at  in  that  wage. under  study  do c o n t a i n (e.g.  other  efficient  at  contract,  tangency  indifference  or  thereby  the union cares  Pareto  corresponds  the  firm  level  level,  and t h e  the  l a b o u r demand c u r v e ,  seen i n Chapter  which  collective  on t h e  contract  employment  contracts  and c o n s t r a i n t s ,  turn  the  efficient  was the  in  contract  contract  between lie  an  employment  employment u n i l a t e r a l l y c h o s e n  parties  attaining  and  bargaining relationship.  negotiation  i n which case the do  the  and t h e  studied  the  Specifically,  of  union objectives  and t e c h n o l o g y ,  these  wage  job  of  not  provisions security  instruments  level  schemes).  do  which  employment  A priori,  the  37 efficient is  some  c o n t r a c t i n g model indication  players  from  constraint costs be  or  argue  In g e n e r a l , two  this  contracting,  the  Pareto  costs.  argument  find  and l i t t l e  is  In t h i s contract  the  is  not to  do  can  be  i n choosing models of  been  model  evaluated  by  a  are the  as  can well.  between implicit  efficiency on t h e  very  empirical  of  model  and  forms  of  specific  relevancy.  l a b o u r demand and t h e  cooperative  two  constraints  structure  have  the  Such  demand m o d e l  specific  their  both the  these  helpful  impose  point.  there  information, monitoring  notions  results  known a b o u t paper,  or  performance  but  optimal  labour  that  compatibility  contracts  the  unless  which p r o h i b i t s  However,  Turning  we  attractive  imperfect  against  models.  incentive  a  c o u l d be due t o  to  more  a constraint  reaching  transaction  used  the  of  is  efficient  estimated. use  of  a  Their  non-nested  test.  3.1  T h e B a r g a i n i n g Game This  first  section  b a r g a i n i n g model  and draws  (1987C).  followed  the  It  is  contains heavily in  empirical application of  description  from t h e  section the  a  3.2  game t o  by  of  the  work by B i n m o r e a discussion  of  firm-union contract  negotiations. The  bargaining  theoretic bargaining  form over  in  is  of  the  Rubinstein  the  division  type  first  (1982). of  a  pie.  presented Two In  in  game  players  are  the  original  38 paper, the  the  size  bargaining  linear  with  units  of  this  is  (1980)  case.  Other  adopt  the  specified  hearing reject  his it.  than  at  at  Both the do  final not  threats  I  follow on  the  hypothesis Binmore  is  the  to  take  rules  as  of  Binmore  a  the  a more special  game  and  preferences  as  making p r o p o s a l s . player  has  he  can  preferred  that  to  game ends and t h e make by  a  for  p r e f e r r e d to  After  accept  any  time  the  same  or  proposal  new  to  the  incurs costs t,  is  proposal.  both players  Moreover, each p l a y e r so  without  an  by  agreement  agreement  signed  t.  players  are  agreement  believe  the  rejects,  outcome.  after  a  [1982].  he a c c e p t s ,  is  identical  use  players'  each  agreement  I  was  specifically,  be t e s t e d  the  offer,  t  More  function  opponent's  he  assigning  study,  in  time  are  this  of  negotiations  maximizing,  alternate  If  frontier  in empirical studies.  In  this,  agreement  any t i m e  rent  players  If  no-agreement  to  players.  union u t i l i t y  in Rubinstein  feasible  signed  the  the  the  r e s t r i c t i o n c o u l d be r e l a x e d  restrictions  two  delaying  be  rejected this  of  Rent m a x i m i z a t i o n w i l l  implemented. Any  to  (i.e.  amounts  two  complication.  form.  The  the  fixed  start  This  to  that  was  the  union  and a l l o w  general  at  often  showed  much  result  the  pie  -1).  utility  most  the  set  slope  forces  which  too  of  and n o t  idle  such  rational;  how i t  threats  that  it  i.e.,  made  would  they  care  is  reached.  by  their  in  fact  only Also,  opponent not  be  in  about they (idle the  39 player's such be of  best  interest  rationality,  sub-game  any  perfect  rationality  Figure  2 is  to  to  them o u t ) .  e q u i l i b r i u m to  as  defined  and  used  carry  of  by  time  illustrate  the  the  face  of  game w i l l  have  to  Selton.  costs this  Figure  In  The  are  powerful  the  Figure  present  2,  value  along the  axes.  and B i i s  the  of  feasible  bargaining Suppose  the  present  utilities The p o i n t  2  value  of  the  set  player  shifts F  is  at  in the  time  over one  the  players  functions are  bargaining set  i .  The f r o n t i e r because  make  a  of  or  measured  no-agreement  the  time to  Delay  objective  two  ( F , U) i s  Pareto f r o n t i e r of  agreements)  ones.  point.  Perfect E q u i l i b r i a with A l t e r n a t i n g O f f e r s and C o s t s o f  In  assumptions  point,  (the  set  B^ o f  the  delay  proposal  costs. at  time  40  t  + 1.  He  agreement  Bt+2,  anticipates  is  reached  i n period  U 2 because  U2 is  t  can  get  is  for  the  game  at  time  for  any p r o p o s a l he makes  at t  than  U"2/ he  slightly still the  starting  could  less  include  + 1.  the  Player  since  this  starting of  is  at  equilibrium call  the  of  player U  by  the proposed p a y o f f U would a c c e p t  type  not  of  that  greater  offering  to  it.  U would  Therefore  + 1 will  at time t  reasoning  accept  minimum Using  we h a v e  points  now  proposal  he  relevant  part  move  to  he  the  [(F,U)  to  find  can  receive  Bt+2  set  a  not  lower  to player U at  any p a y o f f  l i m i t e d the set  Using the  [(F,U):Ui$  back  should  he a l s o  player. limit  opponent  F knows  off  no  his  + 1 giving U a payoff better  i f  less  for  and t h e of  time  than U  the  game  rationality  possible  perfect  : U_£ U ^ U 2 , F]_£ F ^ F ] w h i c h I Q  PEt+iWe  since  Player  equilibrium payoffs  U will  the p l a y e r s ,  that  t h e most  + 2.  himself  same  + 2.  t  knows  g i v i n g U more t h a n U 2 .  bound t o t h e p e r f e c t t  + l ,  equilibrium points  any p o i n t  We c a n u s e  t  Furthermore,  of perfect  he  t h e maximum p a y o f f  to U such that  exceed U 2 .  set  make  3  a n <  set  of  one  make  the  of  at  time  same  Bt.+2 type  possible  a n <  of  3  Q  time  t  as  equilibria  a  above, at  denoted P E t -  what  that  + 1 is  he knows F i s  reasoning  perfect  deciding  He k n o w s  at  U £ u , F i * F ^ F ] which i s 0  U is  t.  bargaining set  anticipates the  period.  the PEt+i  rational we c a n  time  t  to  41  If  we  were  to  go  relevant  bargaining  expect  limit  to  to  look  single in  at  finite  the  time,  2,  Figure  game  is  more  time  the  bargaining  game  surprising  given  that  the  and  discount for  i  the  large  which and  game homogeneous  form  can't  at  by  a  Sutton of  to  Let  the  the  clear  is  way  that  in  only,  in  of  back  from  time  on  Pareto  all  the  time  the  the  more  usually  is  costs  is  essentially  to  periods.  of  Suppose  players  on  infinite  equilibria  implication  and  the  games.  imposed  1 5  If  0  is  a  occurs  (Fj_, U ) .  limiting  result  to  Figure 2 ,  in  point  t  our  number  generalization  for  that  one  the  This  across  (1984).  this  with proper r e s t r i c t i o n s  its  discounting  factors  = u,f.  is  interesting  Suppose  is  the could  shrinks  time  work  is  we  set  It of  in infinitely-repeated  illustrated Shaked  we  unique.  stationarity  make t h e  U) .  limit  Bt+3,  It  assume  consist  equilibrium  structure  of  will  however,  is  more.  point.  (F,  and  using  bargaining  u n i q u e PE p o s s i b l e  point;  The  point  infinite,  costs  the  + 2  t  + 2 by  t  specifically  the  disagreement  encountered  where  PE s e t s  the  at  time  disagreement  is  the  particular the  case the  Bt+3  set  set  to  PE-t+i and PE-t e v e n  the  point,  back  the  argument  the  d ,df u  U and  frontier  This  are  delay  is  well  used  costs  in take  the  respective  F,  with  0 ^ d^ £ 1  in  current  values  S h a k e d and S u t t o n c o n s i d e r t h e c a s e o f t h e s p l i t t i n g o f a f i x e d p i e o f s i z e one i . e . the b a r g a i n i n g f r o n t i e r i n c u r r e n t v a l u e s U and F i s t h e u n i t s i m p l e x . 1 5  (i.e. U/d F  time  0 values)  = U(F/dft).  t u  = U  _ 1  (U)  Let  at  player  perfect  U = U(F)  Also,  assume  U be  the  level  for  first U in  equilibrium points  rather  than  giving  him  = 0)  t  more  then  h i m more t h a n U 2 a t  level  of  utility  and  for  for  he  himself  F±  player  U  - 1  (U2/d )] u  U: F i  for  the to  for  that  the  same as  the  two  players' di  Given  the  2  player  the  nature  optimization  that  accept that  1,  F at  at  set = 2  t  any  offer  F will  never  By d e f i n i n g  time  the  i n the  game s t a r t i n g  = l .  player  x U  U at  - 1  a maximum  U2 also  defines  1 w h i c h we  time  -  a  can  Since  t  8-1  of  problems,  for the the  = 1,  t  = 0 to  2  at  u )  Q  limits  = U(Fi)  the  = U [df  .  at  x  are  ,i)  time  time  player  U  this  guarantee  as:  (u /d  functions  p l a y e r F can  at  that U2  (remember  u  game s t a r t i n g  = u  (U2/d )  rewritten  game s t a r t i n g  i  PE2 (i.e.  implies  game s t a r t i n g  utility  with  so  t:  U 2 denotes  If  surely  U at  = df  w h i c h c a n be  Notice  the  t  values).  -S^Bol  factor  time  ic  i n present  maximum p a y o f f  at  invertible  set  will  time  of u t i l i t y  by u s i n g  F i are  general  U is  the  ic  retrieve  in  mover.  U2 which  than  offer  minimum l e v e l  and  = 0.  t  maximum u t i l i t y of  be  t  2 is  =  = 0 except  scaled  U and  t  i  equilibrium maximum p a y o f f  down = f as to  a  that  by  for  exactly  a  the fixed  player  series  player  U  F. of for  43  the  game s t a r t i n g a t  for  the  t  = 2 is  game s t a r t i n g a t  Substituting  the  = 0 , or U2 = d  t  concept  of  the  to  p l a y e r U at  game h a v e  minimum  (2)  time 0 . to  is  u  U  o  )  Q  .  w  equilibria to  player  is  d  solve  Note t h a t  satisfied  equilibrium  (  perfect  a l l o w e d us  payoff  equation the  of  U .  2 u  (1) yields:  in  5-1  The  s c a l e d down maximum p a y o f f  U. at  and t h e  for the  maximum p a y o f f  we c a n do t h e  In one  fact, point  if  same f o r  U is  only  structure  respect  to  are  assumed  the  value  player time  i  t.  the  of  It  (A-l)  U  contract. from the  assumed  of  the  this  players  Specifically,  over  time  Let  and  Ui(C,t)  for  i=u,f,  these  be  and f o r  the  ±  (C,t )  > U (C,t )  1  i  2  if  t  1  <  C signed all  t . 2  > 0.  U (C,t ) i  1  -  U.(C,t-1)] < 0.  > U ( C , t +l) i  ±  iff  U (C,t ) i  2  > U (C,t +l) i  with  utility  (C,t)  9[U.(C,t) i  with costs  increasing  b a r g a i n (or c o n t r a c t )  that  game by  }.  3U.  (A-4)  delay.  the  (A-2)  (A-3)  of  preferences  stationary  is  £ { 0 , 1 , 2  on t h e  be  receives  therefore  unique.  costs  to  the  concave,  and  As m e n t i o n e d p r e v i o u s l y , R u b i n s t e i n s o l v e d imposing  homogeneity  2  at  tj,t2,t  44  Assumption contract that  (A-l)  is  time  (A-4)  implies  measured costs  that  (A-4)'  if  This  is  to  period  the  is  e  that  same a t  will  be  Assumption  (A-4)  that  some  with  forms  of  time  per time  In costs,  -  order let  costs  to  delays  A n example  strike;  e.g.,  i,  (A-3)  contract  units  and  The l a s t  assumption  t.  for  times. in  in  of  the  waiting  (Note  the  permitted:  or  i  value.  a  to  the  t+1)  of  contract  an e x t r a  that  value  restrictive.  U ( C ) d^  are  of  that  follows:  player  all  (A-2)  (A-3) the  implies  contract).  B i n m o r e (1987a)  (A-4),  there  discounting  are  and  time  shows  only  fixed  two  costs  i.e.  parties  party  a  very  the  improvement  strengthening  period,  U^Ct)  of  increasing is  as  i  the  compensate  in  + e ,  i  independent  says  necessary  that  = u (C  1  costly,  stationary.  differently  U (C,t)  t h e n ei  are  is  which are v a l u a b l e  increasing  costs  c a n be e x p r e s s e d  time  in units  are  time  that  give  strikes  negotiating  fixed  a  of  and  costs  proportion  a strike  of  2-year  fixed  = U (C) -  i  examples  be  of  U (C,T)  six  of  fixed  discounting  that  the  worth V i n  would  be t h e  V in  each  would  ±  and  suppose  contract  months  D t.  i  loss  period mean  two total  to  each  of  the  losing  1/4  45 of  V, a strike  suppose  that  forward  in  contract  if  parties  but  in  that  after  the  have they  costs  types  of  is  it  is  higher  strikes,  the  becomes  more  encurred  as  In fully  equilibrium  easily  for  0,  the  pushed  value  During  the  contract  the  of  the  strike,  the  later  deplete  in  the  form o f  that  the  the  When  agreement  potential  and  fixed  this In  value  is  signed  For  longer  contract  costs  of  strikes  contract  production levels. the  In  discounting.  potential  after  savings,  time.  seem p l a u s i b l e .  unique,  it  but  u  £ Df,  are  value  probably  if  D  u  = Df,  Q  of  discount  at  time  i ,  that  a  the (2)  = 1-F ) . Q  equilibrium is there  which could occur l a t e r  are  i n the  Equilibria  perfect  equation  U(F )  Perfect  with  player (Note  the  of  case  occurs  from  frontier:  set  game  the  say  derived  D  the  the  In  mover,  bargaining if  still  is  opportunity cost  of  (1-dj)/(1-d^dj).  costs,  contract  Now  incurring  take  (1982)  pie.  is  f i r s t  is  V, etc.  well.  fixed  =  the  of  or  implausible  Rubinstein  Si  1/2  b o r r o w money  average  characterized a  is  costs  recovery  of  strike.  recovered  than  loss  strike, V  the  possible  completely  through  a  are  delay  both  the  to  example,  (V)  of  and  of  short,  time  is  value  are  the  there  the  reality,  and  year,  might  any c a s e ,  receiving  one  time  signed  two  last  of  0,  share  costs,  of  the  gives the  In  the  the  fixed  case  unique  of  to pie  e q u i l i b r i u m share  multiple game.  information  and i t  and  is  Si pie  fixed  and o c c u r s  at  e q u i l i b r i a some  46 Rubinstein with  (1985)  one-sided  opponent's  Crampton  points  role  agreement  With  asymmetric  in providing  models  the  be  to  equilibria  depend  structure  such  are  as  at  the  however,  quite  prior  derived  on  the  from  in  delay  delays  for  the  and  we  of  the  can play  the  which  a  simple  Furthermore,  of  of  information  even f o r v e r y  aspects  in  set  beginning  complex.  beliefs  a  the  Rubinstein  asymmetries  information,  crucially  on  are  to  gain  signed  information;  equilibria  of  game  concerning  results  sensitive  nothing to  f o r the  Not s u r p r i s i n g l y , t h e  absence  is  results  information  very  the  there  the  Further  (1984b). is  In  information,  1 6  and  his  information  imperfect  (1984a)  structure.  game.  costs.  with  equilibrium  expect  imperfect  time  bargaining  generalizes  the  information no  data  are  available. It above,  is  important to  there  is  negotiations. the  first  F o r example,  mover  in  the  is  above,  (l-d)/(l-d )  =  Unless there  that  in  the  an a d v a n t a g e i n b e i n g t h e  information Si  note  greater  one  discounting half  where d = d i  are i n s t i t u t i o n a l f a c t o r s  described  f i r s t mover i n  share o f the p i e  game w i t h than  2  the  results  when d i = dj  S i going and  the to  perfect  = dj .  (From  and 0 < d < l ) .  determining the  first  I do n o t t h i n k t h e e q u i l i b r i a i n v o l v i n g d e l a y w h i c h can occur i n the case o f equal f i x e d c o s t s u n d e r p e r f e c t i n f o r m a t i o n a r e good m o d e l s o f d e l a y s i n b a r g a i n i n g s i n c e , i n s u c h a f r a m e w o r k , t h e r e i s n o t h i n g t o be g a i n e d b y d e l a y i n g t h e agreement. R a t h e r , t h e y i n d i c a t e a need f o r some s t r e n g t h e n i n g o f t h e e q u i l i b r i u m c o n c e p t i n t h a t c a s e . 1  6  47 mover,  we w o u l d e x p e c t  first.  In t h i s  sense,  One way t o interval  first limit  of  offers at  each  Note  offer  is  game i s  incomplete.  that  zero.  It  most  recent  has  to  made.  advantage  in  time  game when t i m e  order  of  the  time the  being  the  game  (new)  moves  is  be  the  between  a game  where  offer  opponent.  the  or  words,  make a  his  goes  In  intervals  i n t e r p r e t e d as  by  who  small.  continuous  rejected  In other  allow  no  is  proposal  be  to  become  can e i t h e r  the  is  to  c a n be  a player  bargain over  feature  this  time  important that offer  the  there  discrete to  to  proposals  game  instant, the  is  each  the  tend  accept it  time  mover.  players  deal with this  between  continuous  the  or  However, respected;  accepted  before  another  simultaneous  offers  are  not  allowed. There is  is  appealing.  information, interval  unique  reason  For the Binmore  between moves  equilibrium movers  another  points  is  with  (1987b) approaches  the  other a  and  continuous  discounting showed to  corresponding to  approach each solution  game  why  at  generalized  the  the  as  the  two  limit,  Nash  and  that  zero,  time  perfect the  two  possible the  model  time  perfect first  resulting  b a r g a i n i n g (GNB)  48 solution  with weights  only.  T h e GNB s o l u t i o n  1 7  being  u ,u u  (U - T )  of  c a n be w r i t t e n  a max  functions  the as  discount  the  rates  solution  to:  B  (3)  a.p (U -T )'  u  f  s.t  1  f  (U ,U-)£ u  f  where Ui  is  the u t i l i t y  of player i ,  Ti  is  the u t i l i t y  of player i  the  given  a^ i s  weight  interpreted B  is  the  Note convex  as  the  bargaining that  any  can  solution  with  Therefore,  since  is  solution. be  functions  of  the  all  on be  the  of  results  that  is  the  the the  disagreement of  choice  however, the  time  Pareto  written  efficient,  as of  the  point  player  i  (often  i)  0  unique  frontier  the  costs,  of  the  a generalized  Nash  appropriate weights.  perfect  e q u i l i b r i u m to  information)  is  also  a GNB  appropriate weights  parameters  representing delay  parameters  the  utility  (with p e r f e c t  In g e n e r a l ,  functions  at  set.  bargaining  t h e R u b i n s t e i n game  = u,f  b a r g a i n i n g power o f p l a y e r  point  bargaining set  it  to  i  of  the  first  bargaining perfect  the  set.  game, mover, The  i.e. and  will the the  Binmore  equilibrium for  the  T h e N a s h b a r g a i n i n g s o l u t i o n i s a c o o p e r a t i v e game s o l u t i o n concept which s a t i s f i e s the f o u r f o l l o w i n g axioms: i n d e p e n d e n c e o f i r r e l e v a n t a l t e r n a t i v e s , symmetry, P a r e t o e f f i c i e n c y , invariance to (increasing) afine transformation. It c a n be w r i t t e n a s t h e s o l u t i o n t o t h e optimization problem (3) w i t h a i = a2 = . 5 . A generalized Nash b a r g a i n i n g s o l u t i o n i s a Nash b a r g a i n i n g s o l u t i o n without t h e symmetry r e q u i r e m e n t . 1 7  49 continuous  time  GNB s o l u t i o n  game  with  discounting  with a zero threat  point  can  be  written  and w i t h t h e  as  a  following  weights:  a  u  lnd  =  where d i  lnd^ + lnd  u  is  the  (Note t h a t be  reached  an i n f i n i t e  in  if  an  of  result the  and  the  time  order  to  the  contract to  the  player  n  c  f  i.  were p o s i t i v e ,  it  would  game w o u l d no l o n g e r  game  derive are  wage  for the  the  it  have  union  is  estimating this  at  0 be:  U (C)  let  U  u  u  C, w i l l  = U[U"1(U (C))/d ]. U  derive  f  rent  one  the  for is  maximizer unless  frontier  = U(Uf(C))  contract.  t i m e game,  costs, a  as  general  model  equation:  d U (C)  under  discounting  employment  to  In comparison,  To s e e  and  equilibrium  equations  the  empirical  possible  used. time  the  the  functions.  with  discrete  following  makes  assume  for  writing  employment  to  bargaining set  denotes  because  the u t i l i t y  forced  approximations the  of  important  problem  wage  discrete  is  game  of  in  point  and t h e  u  \ i + lnd  lnd  factor  threat  time  f  =  horizon.)  specifications  practically  discount  the  optimization  estimating  f  finite  Binmore's application  ^ a  of  where C  The e q u i l i b r i u m be t h e  solution  50 Rent  maximization  equation is  3.2  causes  then e a s i l y  Application Contract There  of  U to  be  linear  and  the  above  solved.  the  Bargaining  Game  to  Firm-Union  the  Rubinstein  Negotiations  are  several  bargaining  game.  In  discussed  in  crucial  this  the  elements  section,  context  in  these  of  assumptions  firm-union  are  contract  negotiations. First, once  an o f f e r  before a  the  players  is  wage-employment or  collective moves offer  to  rejects  to  the  the  it  made.  is  next  union.  must be a c c e p t e d  to  this  round  if  and  the  do  make  party  case of  is  offers.  Also,  generally  other party  (see  Secondly, the  collective  agreement  Craig  both is  negotiations  before  the  of  the  on the  to  (1986), firm  delayed.  study,  end  expected  the  firm is  a new  then  accepts,  elicit  a  counter  preferable  both firms  the  a  to  since,  a move  response  the  and u n i o n s by  from  a  the  7). union  incur  costs  bargaining process  contract  a  bargaining  makes  negotiations,  and t h e  existing  offers  o n l y c a n make o f f e r s  Chapter  in  it  and  rejected  firm  rejects,  bargaining, during  the  If  it  or  the union  firm,  framework  b a r g a i n i n g m o d e l s where one s i d e in  the  contract.  signed;  This  i n making o f f e r s  For example,  contract  agreement  on  alternate  has b e e n made,  another o f f e r  accepts  must  start  contract,  several  negotiating  if  under months teams  51 a r e composed disputes rather game  of  permanent  are s e t t l e d  begins 0).  first  offer  incurred,  at  of  At this  time  either  accepted)  or there  is  The  increase  until  an  signed.  Note  that  offer  i n the u t i l i t y  players  are  (e.g.  without  a  allowed work  as  the  punishment  d a t a on t h e  gains  the  requiring  1 8  This  kind  of  be  major element  bargaining horizon.  from  will  of  use  and  of  is  the  (the  of delay  are  the  threat of  the  players trade.  that  S e e Hart  the  to  and t h e i r  are  than  continued  work  working  the  the  the  model  timing  strategy  of  require  costs.  T h e r e a r e no e x o g e n o u s  stop bargaining while budget  union  survive  cannot  for a step i n t h i s  there  still  such  after  direction.  the  factors  are  constraints a strike  of the  in Rubinstein bargaining is  F o r example,  (1986)  rather  Also,  other  associated  is  negotiating  but  and  costs  contract  complicate used  bear  the  parties.  simply  would  contract  signed  and  delay  threats  or  part  bargaining  m a i n t a i n i n g the  of  lockouts)  previous  continue  costs  slowdown  would  the  and  and b o t h p a r t i e s  accepted  to  various threats  The t h i r d  forcing  the  or  F u r t h e r m o r e , e m p i r i c a l a p p l i c a t i o n would  1 8  infinite  of  that  an a g r e e m e n t  functions  contract).  considerably  players.  is  costs  embedded  parties,  (strikes  a strike/lockout  the  two  i n w h i c h c a s e no c o s t s  included i n the  not  the  assumed  expiry  strike/lockout  are not  stoppage  is  time  costs.  teams  It  the  is  of  by work s t o p p a g e s  than a r b i t r a t i o n .  (time  the  employees  as the  52 depletion assumed  of  its  strike  that  the  union could  indefinitely game  in  total on  the  the  of  rounds  would  be  precluded.  b o r r o w money  Rather,  to  to  the  players.  negotiation  before  a  impossible  and  breakdown  is  itself  a  finite  absence o f  on in  distinguish  is  it  c r u c i a l l y on  In the  rounds  final  to  sustain  The a l t e r n a t i v e  e q u i l i b r i u m w o u l d depend  available  length  possible  are  during a strike.  which  time  fund  the  the data  number  of  bargaining,  it  between  various  equilibria. Finally, rational care  in  only  utility major  and  the  two  the  sense  about  the  they  do  improvement  process  in  which  irrationality  final not  which  make  opponent's (See  behaviour  Foley  in  section  agreement idle  past  models  players.  well-known  even  of  and Maunders  (1979)  of  mistakes own  for  This  the on  they  associated  threats).  examples  their  extremely (i.e.  its  The models  systematic or  are 3.1  and  e q u i l i b r i u m depended  the are  partners  believe  over  Zeuthen-Harsanyi parties  described  the  of  bargaining  is  a  negotiation some by  form  Cross  bargaining about  future  of and in  their  behaviour.  a description  of  these  models.) Although underlying is  chosen  regarding time  as  these  are  the  Rubinstein bargaining, will the  depend  information  a discrete  on  the  fundamental the  or continuous  p a r t i c u l a r game  maintained  structure  assumptions  and  variable.  the  which  assumptions modelling  of  53 It  was  asymmetric the or  mentioned information  lockout.  the  when  information  with  Furthermore,  the  outside study but  such  of  for  The  question  The  discussions  at  the  mature  have  with  they  some  after  types  dealing  with  made  on  opponent). to  certain beliefs  available.  these  the  are j u s t  more  imperfect  of  is  of  strike  and u p d a t i n g  research,  strikes  are  sensitive  beliefs  a  substantially  one-sided  very  arises  the  only  3  assumption  a union of  the they  strikes  the to  A  problems,  complications too  great  and  together  do).  i  for  the  involving  long  time  suggest  that  they  and  markets  indication  and  period at  under  a  A further union  set  of  representing  technology  the  contract  data  association  firms'  Over  applicability  the  negotiator  between  strikes.  e m p l o y e e s o c c u r r e d due t o  to  employer  believe  of  as  bargaining  relationship  incidence  (1963-83)  for  been  knowledge  least  this  then  IWA and  and  (or  that  f o r w h i c h no d a t a  information  industry  a good  imply  assumptions  possible  involve of  allowing  information.  the  have  two  allowing  a strong  study.  will  that  signed  (e.g.  forming p r i o r  purposes  assume p e r f e c t  contracts  simplifying  only  section  general  equilibrium is  as  by  in  structure  strikes the  previous  equilibrium is  e q u i l i b r i u m paths  introduced  such  the  very  information  behavior  are  However,  even  the  will  equilibrium points  complex  the  in  least  negotiations.  the  firm  under 10%  of is  study of  the  54 The  choice  of  whether  to  continuous  variable  players  commit t h e m s e l v e s  if  to  the  not  u n i o n has  consider  present have  no  model, model  new  will  data  other has  a way  a  offer  should  stand  on  this  for  utility  functions. union  is  benefits  and  in  first  being  first  The  absence  of  such disputes  are  small,  has  shown  that  can  sometimes  T h i s means  be  that can  tractable.  With time  The u s e me t o u s e that  the  the  of  the  these  in  the  as  a  However, one  is  Nash  in  take  it  the  case are  expect  the  going  first.  time  periods  not  important.  section,  of  first  there  Binmore  time  bargaining  considerations  time  time  the  continuous  the  continuous  the  I  and s i m i l a r  if  of  that  the  its  appropriate  would  previous  the  will  then  generally  keeping  of  it  A discrete  specification  while  specification  costs  the  privilege  e q u i l i b r i u m to  used  is  suggests  Binmore r e s u l t ;  delay  that  Unfortunately,  mover a d v a n t a g e  written  be  it  the  p l a y e r with the  mover,  a more g e n e r a l  objectives  continuous  first  mentioned the  the  mover.  b a r g a i n over  as  that  or  example,  month,  choosing  practice,  to  Furthermore,  next  of  For  firm  come i n t o p l a y .  players  the  ability  offers.  the  when  two  i.e.  their  the  a discrete  even w i t h e q u a l time c o s t s  the  to  on  as  a long time.  characteristic  an a d v a n t a g e  large  to  before  considerations  the  the  depend  time  convincing the  offer  move h a s  that  of  model  solution.  the  players'  estimating mind,  game  I  model  adopt  a  game.  is  not  sufficient  is  also  necessary  form  of  discount  to to  allow assume  factors.  55 Although am  to  this  use  costs  in  is  the  or combinations  When  choosing  formed  guarantee plays.  by  threat  opponent losses  the  can  is  (-oo,-™)  keep  the  i.e.  it  is  little  costs.  costs,  possibilities, point. that  what  The  discounting  the  two  strategy  players even  an  important  The t h r e a t  disadvantage the  utilities.  horizon,  very  I  (4)  on n e g o t i a t i n g  or negative  infinite  have  time  if  f  levels  no m a t t e r  costs  the  fact,  d£  ±  utility  have  form:  D t]  in  I  fixed  implied threat  themselves  point  the  of  to  among t h e s e  the  Fixed  limited  -  ±  is  bargaining,  of  = [U (C)  consideration  restrictive,  specification  practically  U^Ct)  is  seem u n d u l y  Rubinstein  flexibility choice  might  players  their  that  implied  that  their  extremely  large  With d i s c o u n t i n g c o s t s the  can  opponent  the  believe  with  point  assumed  that  threat  specify  a zero disagreement  and an  point  is  (0,0). It for  the  will the is  is  firm  although  overestimate short  more  income  run.  has  not  point.  been  the  as  inconsistent  with  example,  fixed  costs,  profit  level  at  point  a measure  of  a disagreement  contract  suppose  any  of  a  in  union  alternative However,  an a l t e r n a t i v e  assumption that  the  this  least  for the  point.  wage s u c h as  the  point  of  a zero t h r e a t  Generally,  used  presence  guaranteed  Specifying  on t h e  For  in  the  unusual.  constraint is  n o t uncommon t o  zero  contract  a  wage  threat  giving  the  56 workers  less  than  the  union.  the  alternative  Also,  than  the  zero  threat  be  the  best  alternative  during  wage,  a strike,  they  earn  alternative  point,  normalized to  the  equal  the  equilibrium contract  in this  the  constraint  wage  Utility  the  to  the  which  of  the  pay.  greater  a  would  employment  Furthermore,  m o d e l would h a v e t o  be  less  with  union  of;zero  earn  is  consistent  point strike  do n o t  to  or  satisfy  equal  to  the  1 9  functions  with both fixed following  equal  pay  To be  zero  at  unacceptable  workers  function  the  wage.  the  utility  an i n c o m e  that  is  a strike  income.  and  alternative  level  wage  of  the  form  of  equation  and d i s c o u n t i n g t i m e c o s t s w i l l  threat  point  as  the  strike  (4)  above  approach the  length  becomes  infinite:  lnd Although resulting it  lnd  u  this  specification  estimating  requires  f  better  model i s data  on  is  less  restrictive,  substantially  strike  costs,  more c o m p l e x and in  The e q u i l i b r i u m of the bargaining e x a m p l e c a n be w r i t t e n as t h e s o l u t i o n t o : 1 9  A  max  U  u  u  A Uf  f  s.t.  (U ,Uf)£ u  the  particular, game  in  on  this  _ B , U £ 0 , Uf^O u  Uu.Uf where B i s t h e s e t formed by t h e u t i l i t y p a i r s c o r r e s p o n d i n g to a l l possible c o n t r a c t s g i v i n g the u n i o n at l e a s t the a l t e r n a t i v e wage, and U t a k e s t h e f o r m U ( W , E , ) - U with U r e p r e s e n t i n g t h e u t i l i t y r e c e i v e d from t h e s t r i k e p a y . u  U  S  s  57  exogenous the  factors  Dj^'s and  which  the  helpful  costs that the  the  data  is  simplest  a r e assumed the  on  strike  between  costs  among t h e s e  specifications.  fairly limited.  Consequently,  formulation costs  factors  final  (i)  is  chosen  are set  and  not Also,  in  this  discounting  equal to  c a n be d i f f e r e n t  is  zero).  for  the  Note  firm  and  remarks  Although  not  necessary  convexity  of  the  bargaining  In  general,  functions  guarantee  a convex  bargaining  contract  error  is  each data (ii) previous  by in is  convex  standard players  The u s u a l allowing  empirical the is  will  and t h e  the  set.  contract  which  parameters  of  set  problems  or expected  set  made  is  objective  observed  be  it  uniqueness.  causes  should  concerning  the  game:  equilibria,  the  discriminate  union.  bargaining  an  to  literature  (fixed  discount  Two  the  the  i n choosing  available  paper,  one  d^'s.  Unfortunately, very  enable  ex  post  set  does  not  practice  players  generally  this  be  factors  to  If  assumption  the will  to  randomize  because the  the ante  contain  with  game. be  ex  will  correlated of  the  convexifying  applications contract.  on  sufficient of  of  ensure  restrictions  are  the  existence  random, our o b s e r v a t i o n  exogenous and  for  I  the  assume  checked  at  point. The game m o d e l s contracts  can  one  affect  contract the  negotiation  present  only  negotiations  and only  58 through  the  building  strategy  This  would  itself  3.3  exogenous  require  a  this of  Supergame  notation). labour  (E),  can  be  to  sensitivity In the materials while  to  first  and  the  1  P^  materials services,  by  a  supplies is  time  Q  2  is  the  and T is  3  period  of  the  it  is  to  is  exogenously  to  , E) = RO x T  price  time  of  R  1  output,  Q3 i s  index,  and  _  process  two  both  the  Two models the  R  2  )  x  output  labour  labour  1  capital  concerning  that  to  x p[  inputs:  function.  determined.  respect  above  labour contract C.  assumed  adjusted  3  and  These  the  the  production  assumptions  and o u t p u t  with  (Q2)<•  supplies that  in  Q i using  estimated.  sets  supplies, a  allowed.  independent  (Uf(C)  is  P  P2 is  capital  X Q  the  the  quantity  the  R's  are  profit  written  R 2  and  contract  The  and  Cobb-Douglas p r o d u c t i o n f u n c t i o n  P ,  not  time  Cobb-Douglas  are  are  the  output  assumed  model,  restricted  (T, P ,  where  is  inputs  capital  function dual  It  and  different  of  is  each  function  produces  frameworks  correspond  where  characterize  materials  represented  different  contracts  reputation  Objectives  utility  firm  (Q3).  services  we  firm's  The  complex  game.  section  the  A  several  T h e F i r m ' s T e c h n o l o g y and  portion  r  covering  a bargaining  In  TT  factors.  of  R  3  and as:  x E  price  R  e  of  capital  functions  of  59 the  underlying production  profit of  elasticity  labour.  profits  and  R2  while  restricted  capital  is  the  (1-R2)  profits.  capital over  expected  that  while  =  2  - R 2 X RO x T  and t h e Q  to  1  x RO x T  in  the  processes. other  In  areas  explain of  the  of  R  function  P** " *  2  x P~  1  2  R 2  output  the  labour  work,  only.  x P is  of  R 2  x Q  Although this  demand  input  R 3  production  the  when t r e a t i n g that  one  x E  x E  is  literature find  it  and o u t p u t  industry  difficulties  assuming  to  labour  It  correspond  considered  researchers  than  costs  factor.  x Q f  1  M a r t i n e l l o (1984)  products  restricted  the  commonly made i n e s t i m a t i o n s  form  later,  scaling  the  is  the  supplies:  functional  seen  in  profit  model,  behaviour  prices wood  is  to  are gross of  and R e < l .  bargaining process. it  is  elasticity  material  shifts  a  R3  profit  R2<0,  1  (1-R2)  of  profits  X P* "* ^  1  =  assumption,  B.C.  R  curve:  the  use  and  supply  second  ratio  RO i s  restricted  the  revenues  R l measures  demand f o r m a t e r i a l s  Q  the  R 3 , R e , R0>0,  this  of  (Restricted  time  parameters.  and Re i s  ratio is  costs).  process  To  of  function  but  used  output  as  output  is  a  exogenous restrictive  of as  production well  quantities  a  as  difficult  in to  by  the  studied  the  more  flexible  had  similar  here  endogenous. an  e  e  as  who a l s o  with  R  R  exogenous  As w i l l  be  variable  60 does  improve  however,  it  The  2  where  3  is  function  profit  the  1  function  price  B's  1  of  is  the  i f  the  B  x P^~  1  B3  is  share of  that  labour  of  the  output  the  It  is  contract  demand f o r m a t e r i a l s  equal is  E  dfx  is  B e  shifts that  of  a  the  the  cost  on  the  B2 > 0,  and  B2  B  demand f o r c a p i t a l  1  x P~  cost the  model),  share labour  the  BO i s  wage  a  scaling  production  process  Be < 0 ,  function  B 3  x P  B 3  is  elasticity  labour  labour.  time  capital  and s u p p l i e s .  situated  in  T is  and B3 > 0.  TTB c o r r e s p o n d  supplies:  x BO x T  Bl = B3 x BO x T  share  cooperative  profit  and  m  3  i n the  expected  restricted  = (1-B3)  3  = 2,3,  and Be i s  Be w i l l  and B l m e a s u r e s  over time.  x P* x  i  materials  shadow p r i c e o f  parameter  B 3 )  cost  equal the  not  Q  model  the u n d e r l y i n g production  will  the  second  of  (e.g.  and  the  are functions  Otherwise  2  in  for  cost  Note  T  demand.  Q  study;  i ,  elasticity  labour.  To  this  input  parameters.  cost  only  in  c r e a t e s new p r o b l e m s .  1  and t h e  (1-B3)  employment  as:  1  b  index  of  P , P , P , Q , E ) = P Q - BO x  TT (T,  of  also  prediction  restricted  written  the  the  x Q  B  2  x E  B  e  services:  „(1-B3) „(B3-1) x P^ ' x P3  x  ^B2  Re x E .  the  61 It  is  assumed  exogenous,  i.e.  competitive. price  most  international assumption since  owned  by  the  the  prices  input  output  is  section  output  sold  However,  the  companies  and  in  the  the  also  4.2  for  a more  f o r the  of  in  this  in  are  competitive  the  market  materials  data  set  logging.  detailed  are  output  competitive  case  engage  wage  markets  in highly  lumber m i l l s  who  the  seem u n r e a s o n a b l e  restrictive of  except  are (See  description  of  industry) In  to  the  markets.  some  4,  all  does not  of  may be  price  Chapter  that  This  since  that  its  bargaining with  maximize  written  Uj  for  the Uj  when  R  case  1  2  3  i n which c a p i t a l  is  the  firm  function  b  is  other  the  1  is  assumed  can  then  be  than  (W,E)  standard  for  W is are  3  X Q  - WX E  3  and  the  wage  subsumed  on  and  exogenous  the  left-hand  simplicity.  convexity  will  P  ,E) - W X E  3  exogenous.  equations  functions  2  -  exogenous,  (W,E) = T T ( T , P , Q , P , P  Under utility  utility  (W,E) = TT ( T , P , P , Q , E )  output  of  Its  union,  as:  variables side  profits.  the  assumptions,  have t h e  following  both  of  these  properties:  l a b o u r demand c u r v e W BE  < 0 to the r i g h t o f demand c u r v e  the  labour  62  0  <  -E  < 0  f  9W where 3.4  i  The  2,  issue attempts  utilitarianism common i n t h i s behaved  to  process  the  p  cases of  p = -1,  the  (1-6)  (See is  on  the  function  the  by  (W ).  over  This  A  a  voting  results.  defined  wage  and  existence of  (W-W )  p  A  or  As a  is  well-  wages,  function  -1/p  )  function:  Cobb D o u g l a s : E ( W - W ) (  f o r example,  based  I assume  linear u t i l i t y 6  1 - 5  A  utility  f u n c t i o n by  majority  general  in  is  (5)  formulation include:  economists  maximizing  few,  a  mentioned  preferences as  been  CES f o r m :  p = 0 and 6 = . 5 , Some  As  has  a union objective  alternative  this  the  p = 0,  +  decades.  such  yielded  utility  and t h e  objectives  members'  literature,  = (6E  u  to j u s t i f y  have  take  U (C)  union  several  union  concave  employment,  of  for  representation  Special  = 0  9W  9W9E  modelling  individual  assumed  f  Objectives  contentious  the  -1  = R,B.  Union  Chapter  =  rent maximization: are  of  function  the  6E +  be  A  ) E(W-W ). A  opinion  should  (1-6)(W-W )  that  imposed  a a  rent  priori.  Brown and A s h e n f e l t e r  (1986).)  assumption  u n i o n maximizes  that  the  This  claim the  average to  worker's  be e q u a l t o  this  3- x W + E  where not  E is  know  assumption  constraint  during  rent  equal  equilibrium  of  assumed  utility  the  the  definition  the  wage has  union  level  constraint  contracts.  wage.  strong of  I  the  are  in  do  this  empirical  hypothesis choose  to  is  use  a  the u n i o n which  case. been  At  incorporated  than the  will  imposed threat  be  This  zero  a  point and  the  their  best  can  set  as  that  union u t i l i t y  the  in  implies  earning  assumption  W^W& t o  I  supports  tested  rather  set.  workers  This  is  a special  alternative  income.  it  which  function of  employment  the  u n i o n membership.  Therefore,  bargaining  the  strikes,  adding  usually  maximization  alternative  the  u  by m o d i f y i n g t h e  by  the  function on  alternative  and  the  the  when  rejected.  the  U (C)=0),  wage w i l l  is  income:  evidence  r e n t m a x i m i z a t i o n as  utility  (where  and E i s  furthermore,  form o f  Note t h a t the  expected  empirical  always  more g e n e r a l includes  any  unions,  virtually  which  (1—3-) w E  and  of  utility  worker's  employment of  studies  expected  be  avoided  as  follows:  of  possible  64 This  formulation allows  pay  less  the  estimation,  imposed  than  but  it  the  alternative  the will  for the  constraint be c h e c k e d  possibility  wage. on at  the  However, contract  each data  of to  a  simplify  wage  point.  strike  is  not  65 Chapter T h e D a t a and t h e E m p i r i c a l As  described  involves  the  cooperative  in  the  the  for  functions.  For purposes  confusion,  I  derivation This  is  data.  is  four  the  different  two  a  of  the  4.2  the  b a r g a i n i n g models  are  section  four  firm  of  profit  a v o i d any  (4.1),  to  estimation  by a b r i e f  description  study  models:  possible  separate  Model  this  o f c o m p a r i s o n and a l s o t o  in section  A detailed  the  models.  discussion data  the  of  the  sources  and  p r o v i d e d i n Appendix A .  The E s t i m a t i o n Models Chapter  negotiating function  from  of  am d e v o t i n g  followed  In  which  each  chapter,  demand  and p r e s e n t a t i o n  calculations  4.1  of  labour  estimated  S p e c i f i c a t i o n of the  previous  estimation  and  4  the  3  engaged  assumptions  objective  is  are  signed. imposed  in  a  each  U (W,E) u  = (6E"  P  two  the  (A-l)  is  time to  of  b a r g a i n i n g game.  a at  (A-4)  the  two  These  function  is  time at which the  agreement  is  consider  the union which i s  the  objective  reached.  We c a n t h e n  the  and  preferences  player's  to  of  the  Rubinstein  imply t h a t  C=(W,E)  Assumptions on  of  The u n i o n u t i l i t y  contract  separable with respect  function  functions  were s p e c i f i e d .  labour  contract  chapter  players  the  parties  of  the  3,  the  time  independent  specified  + (1-6)(W-W )" A  P  )~  utility  as:  1 / p  (1)  66  Similarly, of  the  the  firm's  profits  different output firm's  we c a n c o n s i d e r objective  achieved  are  exogenous  utility  U (W,E) = P x Q  time  which  is  assumed  labour contract  studied.  to  independent  the  in  to  equal  C=(W,E).  Firstly,  bargaining  portion  Two  the  level  of  which  case  the  is:  B  x  function  under the  frameworks  is  the  r  BO x T  B 1  x P' '"* 1  ^  x  x Q  B 2  x E  B e  - WxE  = n (T, P ,Q ,P ,P ,E) - W x E B  and,  1  secondly,  the  uJ(W,E) = RO x T = n  where  capital  x pJ  1  2  3 >  E)  T is  indices  materials  - P  of  parties  between  utilities.  depend  on  the  profit  will  More  has  unionized  i  - P x Q ~W x E 3  R's  with  3  are  i=l  for  specifications  union total  industries,  production  vectors  for c a p i t a l  precisely, of  R e  exogenous:  P^ and Q i a r e t h e  and i=3  according to  c a s e f o r most u n i o n i z e d here  and  employment  employment  vary  x E  as  3  above  the  R 3  treated  x Q - Wx E  trend,  and s u p p l i e s  is  x Q  input/output  A problem with the discrepancy  3  R 2  B's  a time  of  input  x P  1 _ R 2 )  vectors  coefficients,  for  R 1  3  2  (T, P , P , Q  R  the  quantity  1  level the  workers  output,  is  the  possible the  union u t i l i t y while  the As  i n d u s t r y under and  i=2  services.  employment. the  p r i c e and  affecting  members  of  two will  firm's is  the study  non-unionized  67 administrative obvious  and  solution  workers  as  a  Empirically, this the  new  at  for  costs  production  does n o t  in  the  labour  the  of  set,  of  This  is  -  (T, P  L  BxT  P ,  F  B 1  P ,  2  3  a  to  E) -  B  3  )  x  order  fraction  measured  15%.  only  (  of  to  non-production  is  in  by  labour  The  expressed  x P 2 "  because  In  production  to  of  non-production  fixed  fraction  equal  functions  [  and  process.  addition  information  details.)  as  p r o d u c t i o n workers  = 1.15 x  b  considered  and  the  calculations,  non-production  sample  employment  profit  the  non-production  production  data  p r o v i d e more  costs.  utility  TI  the  this  Appendix  are  ratio  =  least  in  treat  A for  labour  U*(W,E)  input  to  (See  them  possible  problem i s  between p r o d u c t i o n  include  over  this  Theoretically,  correlation  employment.  average  to  personnel.  separate  input  large  sales  the  costs  firm's  terms  of  two  of  the  -  WxE]  (2)  -  „ WxE]  (3)  become:  *  *  QJ B  E  B  e  1.15 x W x E  and T R/r, T  ^ \  U_(W,E)  ,  ,  c  = 1.15 x  r  „ R l [RxT  „(1-R2) x P,  m  = n (T, P ,P ,Q ,E) R  where  1  BO B = :—— 1.15  Given costs,  and  2  J  and  the  3  -  R2 x P„  „R3 x Q_  „Re x E  -  P^Q^ r^fi  1.15 x W x E  „ RO R = -—— 1.15  assumptions  perfect  of  information,  continuous I  can  use  time,  discounting  Binmore's  result  68 (see  Chapter  cooperative  3)  and  m o d e l as  write the  the  solution  lndf max u W,E  (W,E)  l  n  d  u  +  l  n  9lnU  the  for  the  following:  lndu d  f  lA(W,E)  (W,E) 9W  l  n  d  u  +  l  n  d  f ( 4  , x • lndu  )  u  l  x  9E where  du  discount The  is  the  and i  order conditions  verify  that  i)  The f i r m ' s union on  point  of  the  to:  origin.  lndu  for the  factor,  are  df  is  the  used  firm's  generate  Instead  of  wage  checking in  (4),  I  point:  curves. curve  to  p r o b l e m as w r i t t e n  curves  iso-utility  This  9E  equations.  The b a r g a i n i n g f r o n t i e r the  f  conditions  iso-profit  contract  9lnU (W,E)  f  f o r each data  indifference  the  d  9W  discount  estimating  will  n  1  = B o r R.  first-order  employment  second  union's  factor  9lnui(W,E)  L n a r  3lnU (W,E)  ii)  to  contract  U  withF.O.C:  and  labour  in  are  This  less  convex  ensures that  (W,E)  space  is  than the  a  the  point  tangency  curves. in  frontier  ( U , Uf) u  is  space i s  derived  concave  from t h e  to  solution  69  max U ( W , E ) W,E  s.t.  U  where for  i  = R o r B and  the  bargaining  In  between  (i)  and  employment,  the  as  .  . t  h  utility  and  u  i n U , we  have  (0^),  the  u  U^:  U  u  (ii)  are  and e a s i e r the  e q u i l i b r i u m to  the  solution  stronger  firm  the  than  to  is  check.  unilaterally  bargaining  game  to:  „ i lndu+lndf U (W,E) /  T  ,_.  (5)  T  u  „ F  of  lndu  ^vlndu+lndf (W,E) / I T  . . . subject  l  U  a r e more i n t u i t i v e  lndf  W  a given l e v e l  l a b o u r demand m o d e l where  be g e n e r a t e d  max U W  f  frontier.  but they  the  chooses  is  U  (W,E) and s u b s t i t u t i n g  conditions  necessary  can  for  relationship  The  I  firm.  Solving a  ui(W,E)  . to  3U* ( W , E )  _  .o.c.:  where  f  —  9  l  E(W)  constraint, substitution  0  n  D  U  u  is i  (  W  '  E  (the firm p  r  )  the  n  [1  l  B,  t  8  MRS x  M  +  f  R  q  labour  = R or for the  o  chooses  9E(W),  demand  and  employment t o maximize  0  lndf  x —  function  MRS i s  the  union;  p+i i.e.  MRS  = -  9  1  n  U  f  which  -  (  W  '  E  )  solves  marginal  rate  the of  70 For  the  set  is  l a b o u r demand m o d e l , the  Condition for  labour  (ii)  this  optimization added  problem  l a b o u r demand  and  (5)  labour  similar  that  to  the  can  be  demand  of  i n terms  somewhat  model  can  problem  f>  of  be  /E  is  derived  that  (ii)  in  but  combination  (4)  = " uW  point  f r o m an  with  lie  the  on  the  demand  and  the  optimization  be  the  Specifically,  as  the  added  located  model,  problems  solution  constraint  on  the  the  to that  labour  first  (4) the the the  demand  derivative  of  /E < 0  U  -  the  with  contract  labour  written  u  f E E  frontier  misleading.  where U w i s t h e p a r t i a l o f U d e r i v a t i v e has t h e s i g n o f t h e U  utilities.  each data  the  F o r the cooperative bargaining frontier is ( 0  in  at  (W,E)  2 0  °u  bargaining  2  wage-employment  the  expressed  the  curve. 0  models  optimization  curve  of  a l s o be c h e c k e d  formulation  cooperative  frontier  The b a r g a i n i n g  constraint  The  demand  above w i l l  model.  the  (l/E-U  u E W  /U  )  u W  2  w . r . t . t h e wage. The following expression:  u  x  (U  u W  /U  u W W  )  +  U  U E E  /U  second  W  In p a r t i c u l a r , in this model, a sufficient (but not necessary) c o n d i t i o n f o r concavity of the b a r g a i n i n g set is t h a t t h e c o n t r a c t c u r v e be p o s i t i v e l y sloped. F o r t h e l a b o u r demand m o d e l , t h e f i r s t d e r i v a t i v e of t h e b a r g a i n i n g f r o n t i e r i s t h e s l o p e o f t h e l a b o u r demand curve which is negative. C o n c a v i t y o f t h e l a b o u r demand c u r v e would e n s u r e c o n v e x i t y o f t h e b a r g a i n i n g s e t but in g e n e r a l , the second d e r i v a t i v e o f the f r o n t i e r w i l l have the s i g n o f the f o l l o w i n g expression: UWW  U  x  (UfEE)  2  +  U  U E E + UWE  + (1/E + U f  U  E E  /Uf  E E  )  x  Uf  X U  u E  E E  /(E  -  U  u  W  X Uf  X UfEE).  E E  /E  71  curve.  In  utilities  other for  bargaining frontiers care  the  set are  labour  for  is  the  nested case.  if  solutions  do n o t  (5)  which i s  of  include  (as  a subset)  l a b o u r demand b a r g a i n i n g s e t .  no  parameter  restrictions  cooperative  bargaining  l a b o u r demand m o d e l . The  system  of  cooperative  and t h e  assumption  of  assumption error  of  terms  will  (The  two  u n i o n does  the  l a b o u r demand  However,  the  to  set  i f  of  is  as  the  is the  These  solutions  frontier there  imposed  solutions  such  this  (4)  along the  which,  not  on  inside  solutions  of are the the  to  the  both  the  2 1  estimating  equations  l a b o u r demand m o d e l s  exogenous exogenous  and y  the  In other words,  yield  set  if  of  of  bargaining set.  composed o f t h e p o i n t s  model,  the  space  subset  solutions  model  the  cooperative  if  model.  possible  cooperative  a  the  model.  may seem as  cooperative  The s e t the  and o n l y  in  is  cooperative  It  i n the  of  bargaining set demand m o d e l  the  identical  frontier  to  the  about employment.)  model not  words,  has  output  capital been  in in  are given under  Table Table  substituted  for  I  II. for  and u n d e r The the  (b' s  the the are  expression  T h e r e a r e two e x c e p t i o n s t o t h i s c o r r e s p o n d i n g t o t h e two t r i v i a l m o d e l s i n w h i c h t h e u n i o n d o e s n o t c a r e a b o u t employment and t h e f i r m s h a v e c o m p l e t e b a r g a i n i n g p o w e r . In the l a t t e r case, the competitive s o l u t i o n holds i n the labour market. 2 1  72 Table Estimation Assumption  Models  of  Utility  VVV  Union:  Firms:  II  Functions  t  t  =  Cooperative  cB *lt  _ "  P  W  t  "  l t  (  5  E  t  P  +  ~~1?15  1.15E.  ~  Bl +  B  T  t  <h *4t  "  cB  Q  2t  o 3t  Q  "  d "  8  3  the  beginning  (  V At  t  2t  W  of  negotiations)  ) _ P  P  t  ) ^  E  t  P  Q  B  1  B  P  e  p  +  3 t  Q  l t  E  t  "  1  "  1 5  Vt  2t  (  -  P  (l-B3)  p  2t  „  3 t  P  1  l t  B  3 P  Q  P 3t )  B3 E  3t  1  At  r B ^ B T F P ' t t 2t E  B2  t  W -W  "  Output  Function  (Be-l)  F E  .lndu.  *3t  the  Model  l t  Q  (at ( 1 - 5 )  =  Under  an E x o g e n o u s  Profit  I  I  .lndu.  l t  (  B  3  _  1  ) Q  0 l t  B  2  „  .  73 Table I  III.  P  „ "  t  W  Bl  2  t  "  where  Q  Q  _ 2t  "  3t  "  (r ^),. lndf t 1  3  P  Q  At  _  1"  Y T  E  t  ,lndu.  (  +  W  Be  l  +  (  l n d f t }  ]  y  ,„  in7f \  r_L . ,lndiK , / t  . +  -W  t  (  (  w t  -  „ w  A t  V]  . )  E.  E  ,„,Bl ,(Be-l) B2 ,(l-B3) ,B3 BT E P T  r t  t  T  B  (B.-l)W  +  ( 1 - B 3 ) B3 B2 2t 3 t l t  T  ^-*W  (  W  1  t  t  , . (Be)  +  1  P  / t t  ,  (Be-1) E  t t  = W  , roB *3t -  *4t  t  B T  O  lt^lt  -T7Ur  "  +  .mB •  Continued  L a b o u r Demand M o d e l  mB  •it  -  )  T  3 f c  ,_. , Bl ,Be ,P3„B2 -B3 t 3t lt 2t T  m  T  T  E  t  T  t  B T  =  t  E  t  T >  P  P  Q  P  2t  P  (FO + F I  + Ul  x  Z  3t  + F2 x  t  x UIC  Q  + U2 x  f c  lt  IN7  t 4  + F3 x  DEM )  CU t  + UO x  UN  t  2  t  and kB <t>. = error J t  term for  j=l,...,4; B  IV.  t=l,...,84;  = exogenous  Predicted B > 0 BL. ? B2 > 0 B3 > 0 Be < 0  equation  output  Signs Y  (for 6 1 > . —  j ,  observation  k=cooperative  profit  model or  kB;  labour  demand  function.  both models): . FO 6 FI < F2 > F3 n  (c)  t,  ? 0 0 ?  UO > 0 Ul < 0 U2 < 0  (m);  74 Table Estimation of  I  Utility  R U (W T T  Fxrms:  II <t> •it  / t I  £  T >  "  W t  W  -  R T R  T  Functions  of  =  (  6  ^ v E ) =  t  E  P  (  Q  _ l t  -  6  )  (  W  (  1  ~  P  R  2  )  ) _ P  negotiations)  ^  )  P  3t -j-^  Q  3t  , . 1.15  -  Model  Q  E  -W  t  s  T  p  +  +  At  P  P  t  -lndu.  T  E  Q  1  , Rl ,Re„R2„-R2„R3 t t 2 t l t 3t m  3t 3t 1.15 E P  P  P  beginning  V At  R 1 R 2 ( 1 - R 2 ) R3 ( R e - 1 ) t 2 t l t 3t t  „ „ . '  1  the  R l R 2 ( 1 —R2) . R 3 R e RT^ P ^ -  T  ,lndu  =  (at  +  W  , cR *4t  Assumption Function  Cooperative cR  Models Under t h e  an Exogenous C a p i t a l P r o f i t  VVV  Union:  II  Q  ...  „  .  75 Table II III.  Continued  L a b o u r Demand M o d e l  p .mR •it  -  o  / w -w  3t 3t  .  w  w •  t -rm; +  1  ^  1  /  (Re-nv  +  t  (  y t  l  \  p + 1  At^  E  I  t  _ +  /lndu,  t (Wt  ,„ (  V At  , w -w -  .mR • 2  T I  W  T  6 ^ - 0  •3t  •4t  "  =  where  R T  Q  Q  T  2t  « lt  Rl„R2 (l-R2)-R3„(Re-l) 2 t i t 3t t  B  t  R  n  p  , , (Re)  / T  -  +  +  "  Q  I  I  T  t  T  1  (7^7),. lndr t  T,ON R  2  =  T  E  t  /i "  ,  +  1  2  E  1  )  t  R  1  P  E  R  e  2t  P  (  R  t  _  P  lt  1  .  /  y  t  \  p + 1  At E  )  E.  t  R  t  2  .lndu,  +  , „Rl ,(Re-l) ,R2 ,(l- 2)„R3 RT ; ^ P P j ^Q  r R 2 ^ R T  (  E  ,  w  )  P  (  1  -  R  0  2  )  Q  3t  3  t  B  3  -. Rl Re -.R2_~R2 B3 t t 2 t l t 3t m  T 7  1  E  P  (FO + F l  + Ul  x  x  r t  P  Z  Q  + F2 x  t  UIC  t  + U2 x  INV  t  + F3 x  DEM )  CU t  + UO x  UN  t  2  t  and kR <|>. = error J  term  j=l,...,4;  for  t=l,...,84;  R = exogenous  IV.  equation  capital  j ,  observation  k=cooperative profit  (c)  n  P  or  model  kR;  labour  demand  function.  P r e d i c t e d Signs (for both models): R > 0 S . FO ? R l ? 1 - 5 F1<0 R2 < 0 > F2 > 0 R3 > 0 " F3 ? Re > 0 Y  t,  UO > 0 U1<0 U2 < 0  (m);  76 5/(1-6).  Unless  description and  B).  explicitly  applies  to  both  and r e p r e s e n t  equations. the f i r s t  is  the constraint,  models,  the f i r s t  from t h e f i r s t negotiated  equations  i.e.  represent  a  n  two  f o r i=R equations  equations  and  to  employment  ( 5 ) , and t h e s e c o n d  equation  t h e l a b o u r demand e q u a t i o n .  In both  to  labour  demand  models,  F o r t h e exogenous o u t p u t  the input  cB (<i>2t  supplies  (i.e.  order  wage  following  equation  and t h e  appear.  the  the f i r s t  order condition  cooperative  they  functions  F o r t h e l a b o u r demand m o d e l s ,  is  the  the  otherwise,  profit  For the cooperative  <J>^£ a n d (j>2^ a r e d e r i v e d (4)  stated  mB ^ ^3t^  demand a  n  (  ^ ^  functions o  r  two  profit  extra  function,  f o r m a t e r i a l s and  Pital  services  cB (<J>|. and  profit  function  TTB(T,  c a  4  mB 4>^.)  derived  4  from t h e r e s t r i c t e d  P 2 , P 3 ,E).  Ql, they  represent  (<t>  and 4)^)  R  3  derived P3,  from  Q3, E).  output well  will  is  functional the  first  order  to  the input  profit  for materials  supply  function  the restricted  profit  function  is  adjust  assumed  that  level  forms order  adopted  note here,  conditions  reduced  forms  to  that it  is  the  even  R  mR  TTR(T,  P]_,  o f employment  with  cooperative  P 2 ,  i n p u t s and as  quantities. the  not possible  f o r W and E .  supplies  (<1>J and <t> )  and t h e e x o g e n o u s i n p u t o r o u t p u t to  function,  and  t h e endogenous  to the negotiated  important  get  demand  capital  and t h e o u t p u t  It  as p r i c e s It  F o r t h e exogenous  ,  to  simple solve  models  We a r e f o r c e d  in to  estimate as  to  structural  the  particular  conditions  which  considerations the  equations.  are  equations,  The q u e s t i o n  2 2  representations  should  be  important: and  the  used the  of for  arises  first  order  estimation.  degree  intuitive  the  then  of  Two  nonlinearity  explanation  for  in the  ci location on t h e  of  error  location  and B , t h e zero  the  for  of  term.  the  (RHS) o f  wage-employment Specifically,  between  the  players  multiplied  pairs  the  marginal  rates  by  i  the  frontiers.  For both  i=R and B ,  simply the respect to  inverse of W. ^^t'  the a  n  <t>^  on  first ^ ^2t  decisions  the  a  = R  equal  contract difference  of  measures  RHS o f  made  will  the  s  equilibrium along the  is  For both i  substitution  employment.  of  quantity  which  equation  located  of  location  input  this  RHS o f  made on t h e  the  an e r r o r  2  bargaining frontiers.  r i g h t hand s i d e  curve.  <J>^. i s  the  this  the the  two error  bargaining equation  is  o r d e r c o n d i t i o n t o (4) with a d d i t i v e e r r o r s made t o r  in  e  the  profit  maximization  CR  problem  while  quantity. model the  is  4t  is  an  For purposes given  RHS o f  labour  <t>  the  <J>^ i s  demand  m  of  error  comparison,  same s t r u c t u r e , the  equation  derived d i r e c t l y  additive  i.e.  bargaining in  from the  this first  case,  made the for  to  the  output  labour  demand  both  frontier and t h e  i=R and B ,  which  is  RHS o f  4> £  order condition  to  the m  is  (5).  T h e p r o b l e m i s t h a t b o t h t h e l e v e l s and t h e g r a d i e n t s of the u t i l i t y functions appear i n the first order conditions, and t h e r e i s a n e c e s s a r y l i n e a r i t y imposed i n t h e p r o f i t f u n c t i o n s by t h e t e r m - W E . 2 2  78 It  is  interesting  to  note  the  differences  cooperative  and l a b o u r demand m o d e l s .  by  authors  several  in  the  two b a r g a i n i n g f r o n t i e r s addition  in  the  representing union. two  the  (between (fc^ and <J> £)  first  marginal  equations  this  time  <J>^ and  to  i  m  cooperative  the  been  difference  model  rate  of  case  the  <J> £ m  labour  is  s  also  between  the  simply  the  of  a  demand  term  of  difference the  the  mentioned  substitution  With R u b i n s t e i n b a r g a i n i n g , the  2 3  term,  past  As has  between  in  addition  model.  the the of  This  a  term  equals  3  l  n  U  u  x 3E(W)  When c h o o s i n g labour  4.2  optimal  demand m o d e l ,  indirect effect  the  effect  on t h e  of  .  aw  9E  the  wage  through negotiations  players  will  take  into  t h e wage on t h e u n i o n u t i l i t y  employment  in  the  account  the  through  its  used  the  level.  The Data Table  estimation discussion sources  III  presents  a list  of  along with d e s c r i p t i v e will  include  only  and c o n s t r u c t i o n as  the  variables  statistics.  brief  following  descriptions  of  data  are given  i n the  form  T h i s was u s e d i n McCurdy and P e n c a v e l w h i c h o f t h e two m o d e l s p e r f o r m e d b e t t e r .  (1986)  to  a data appendix,  2 3  details  The  in  of  Appendix A .  test  79 Table  III  Descriptive Statistics  Description  of Variables  Var.  Mean  Min.  Max.  W  4.5209  2.7233  5.9169  0.95098  E  2.3132  3.7705  0.72052  Qj  38.4844  15.1218 96.0790  17.6237  6.6975 63.7650  11.8151  Standard Deviation  1.  Real compensation p a i d per hour of employment  2.  Hours of employment ( i n 10 M ' s )  3.  Q u a n t i t y of output (shipments) ( i n lOM's)  4.  Q u a n t i t y of m a t e r i a l s and s u p p l i e s ( i n lOM's)  Q2  23.8612  5.  Q u a n t i t y of c a p i t a l s e r v i c e s ( i n lOM's)  Q3  2.4203  0.6656  8.0661  1.7983  6.  Real p r i c e of output index  P^  1.2085  0.7626  2.4285  0.3574  7.  R e a l p r i c e of m a t e r i a l s and s u p p l i e s index  P2  1.1305  0.4909  2.4053  0.3750  8.  Real p r i c e of c a p i t a l s e r v i c e s index  P3  0.9255  0.3545  1.6422  0.2630  9.  Real a l t e r n a t i v e wage i n B . C . (Employment weighted average of the m a n u f a c t u r ing and s e r v i c e i n d u s t r i e s in B . C . )  3.4165  2.4554  3.9879  0.4748  10.  Rate of i n t e r e s t (McLeod, Young, Weir 10 i n d u s t r i a l bond r a t e )  Z  9.5876  5.3700 16.3201  2.9958  11.  A v g . change i n the v a l u e of i n v e n t o r i e s over the previous 5 years ( i n 0,000's of d o l l a r s )  INV  0.7925  -1.5592  8.1721  1.6409  12.  U t i l i z a t i o n r a t e i n the wood p r o d u c t s i n d u s t r y i n Canada  CU  9.0158  7.0150  9.8150  0.7308  13.  Unemployment r a t e  UN  0.07285  0.04198 0.13823  0.0228  14.  Measure of the g e n e r o s i t y of the unemployment insurance  UIC  0.3964  0.1203  0.6676  0.2258  15.  P r o p o r t i o n of t o t a l females and males under 25 i n t o t a l labour force i n B . C .  DEM  0.4929  0.4169  0.5415  0.0395  in B.C.  0.8324  80 4.2.1  The I n s t i t u t i o n a l The  data  America over part  and  the of  involves  the  sector.  of  products  1963-1983.  The  of wood  shingle  total  shingles  softwood  and  are  shakes,  and  elsewhere  in  they  forestry  is  for  virtually of  sector  account in  and  a large about  all  the  for the  composed  and p l y w o o d  of  is  forestry  activity  produce  bulk  Columbia  industry  industries)  industry  industry is  Canada.  (1978),  concentration  in  the  been  trend  has  centralized  place.  the  of  veneer part  of  two  thirds  the  cedar  national  softwood  the  rapid  Major  technological intensive  especially  factors change  the  growth  and  operations.  of  the (See  top  In the  construction in the  the  for  a movement B.C. interior  15  lumber  the past  of  Trade,  level 20  larger,  and  this  toward  1970's trend  more  sawmills  and  of  years,  B.C. interior  1960's  responsible  in B.C.  Industry,  Furthermore,  increasing.  toward  mills,  of  in B.C.  pg.32.)  B.C. is  more c o n c e n t r a t e d  Most  i n Canada a r e based  Commerce  of  the  of  output.  producers  most  British  i n B . C . , the  responsible as  Woodworkers  products  of  mills  lumber,  The wood p r o d u c t s  and  shake  output  in  manufacturing  products  and  Canadian  Canada's  than  T h e wood  total  The B . C . m i l l s  plywood  industry  and p a p e r and a l l i e d  one-half  sawmills,  the  International  The m a n u f a c t u r i n g i n d u s t r i e s  province.  mills.  the  dominant i n d u s t r i a l s e c t o r  (wood p r o d u c t s almost  wood  period  the  Setting  more where took  include capitalplywood  81 mills  which  are  believed  to  standards,  have  adopted  processing  small  dimension  productivity labour of  through  content),  by-products  environmental of  the  B.C.  B . C . lumber  single  due  to  and  grading  as  North  America,  sample  period,  is 80%  of  been  was  virtually  total  U.S. and  is  domestic on  bulk,  the  output,  competitive close  due t o  the  (1986),  capital  New  content  output. United  States sizes  throughout and  The  over  l u m b e r was  on  U.S.  U.S.  20.4% lumber  demand  and t r a d e  the  free  province's  The p r o v i n c e ' s  on e x c h a n g e r a t e s to  The  unrestricted  U.S.  dependent  costs  oriented.  minimal,  softwood  pg.5.)  very  transportation  low v a l u e While  sell  U . S . consumption o f  consequently  control.  the  is  of  industry  recovery  standardized  share  Percy  for the  Lumber g r a d e s ,  l u m b e r between Canada and t h e  (See  reducing  their  markets.  of  1978.  increased  export  is  trade  in  of  (thereby  the  highly  documentation  there  world  capable  have  quality  B . C . lumber  have  customs  by  well.  p r o x i m i t y and e a s e o f procedures  they  increased  almost for  better  facilities i n the  industry  market  Also,  of  have  export  efficient  automation  and ah i n c r e a s e  sawmills  largest  logs.  installation  standards  very  technologies  larger  production process  The  the  new  be  of  and  barriers, the  high  commodity.  sawmills  sell  international to  80% o f  fact  that  most  of  markets,  their  output  their  product  plywood inside  mills  Canada.  in  highly  in B.C. This  is  many o f C a n a d a ' s m a j o r t r a d i n g p a r t n e r s  82 in  forest  their  domestic  example, about in  in  in  In f a c t ,  1975.  be  that  the  it  is  belieyed  Trade,  of  logs,  1979  the  timber  intervention  fee  is  these firms  than  was  Percy takes  for  to  operations  pass  by  takes of  products  as  the  form  on  incentives timber  form o f  of  provide  year  stumpage  logs  fees  are higher  to  rents  the the  to  the  1972  government  i n the the  wood  rates. logging  stumpage  logs.  vertically  logs.  for  total  between  price of  a low p r i c e f o r  which  industries.  and t a x  and  their  policy.  inputs  of  Indirect  of  industry,  logs  products  per  (See  provincial  wood  pg.4) .  a function  continue  government  as  rates  then;  market.  unprocessed  to  with  consumption  since  exported  form o f tax  1970's  40.)  wood  0.9%  ( 1986),  the  give  i n the  pg.  manufacturing industries  calculated policies  domestic  the  industry  In p a r t i c u l a r , e f f e c t i v e sector  the  export  harvest  the  declined  affected  of  in  was  competitor  United States w i l l  of  average  a major  for For  on p l y w o o d  domestic  and p a p e r and a l l i e d  an  (see  in  intervention  wood p r o d u c t s  provincial  23% o f  the  market  forestry  example,  that  as  market  somewhat  tariffs.  tariff  emerged  almost  largely  on  the  U.S.  plywood  factor  input  government  constrain  through  and Commerce ( 1 9 7 8 ) ,  is  restrictions  the  U.S.  have  a competitive  Direct  and  70's,  softwood  Imports  The m a j o r  For  producers  imports representing  Industry,  the  late  Canadian  however, to  plywood  the  20%.  the  U.S.  products provide v a r y i n g degrees o f p r o t e c t i o n  Both  integrated products  83 That captured  there  are  rents  by g o v e r n m e n t  has  in been  i n c l u d i n g C o p i t h o r n e (1979), Haley the  (1980)  Pacific  Until  compares Northwest  recent  bid,  changes,  and t h e y  were  product prices lumber in  the  forestry  argued  Haley  B . C . stumpage  fees  and  U.S.  finds  the  U . S . stumpage  not  allowed  have  B.C. constitute  also an  several  (1980),  to  with  (1986).  those  fees  implicit  lower  subsidy  in  by w i n n i n g  v a r y w i t h changes  argued t h a t  set  much l a r g e r .  set  contract.  not  observers  and P e r c y  f e e s were  o c c u r r i n g during the  producers  by  industry  in  U.S.  end-  softwood  stumpage for  rates  Canadian  producers. Copithorne  (1979)  argues  that  sawmilling  and  logging  in  B.C. relative  industries  in  Ontario  is  indicative  i n t o wage l e v e l s . be  other  explanations  instability Evidence sector  of is  estimates the  in  also that  for  than  provided in  1979,  sector  and a l l i e d  in  58.8%  of  industries)  in  leakage that for  not  in  of  rents  there  could  example,  more  efficiency.  the  rents  logging,  wages  corresponding  (1985).  total  were  a  higher  wages  Allen  (including  of  wages;  and  average  to  however,  higher  employment,  larger  forestry  paper  He a c k n o w l e d g e s  higher  B.C.  (1986)  available  captured  products by  4  forestry  Percy  wood  2  in and  the B . C .  government.  T h e h y p o t h e s i s o f h i g h e r e f f i c i e n c y i s s u p p o r t e d by r e s u l t s o f a s t u d y o f r e g i o n a l p r o d u c t i v i t y done by Denny e t al. (1981). 2 4  84 Expected products recent  industry years  province lower  future  may  growth  are  that  bleak.  the  decline  timber  reductions  use.  would  wood p r o d u c t s traditional will  viability largely 1970's  on  a  (see  distinction  preferable plywood  except  for  output  in  also  competition i n plywood  the  and to  if  modelling  output  price  is  data  above  and  coastal  available,  Secondly,  interior the  unreasonable  mills,  the  firms  competitive that  international plywood  output markets.  from t h e  sell  that  These  the  United States,  late  pg.43). has  several  First,  the  sawmills  is  it  be  would  and  coastal  given of  markets.  are:  the  depends  in  most  mills  from  plywood  assumption  not  the  imports  mills  industry.  between  of  on l u m b e r  the  were  from  competition  coastal  to  non-timber  believed  described of  and  contraction  is  indications  imports  for  the  due  For coastal  It  interior  well.  in their  stands  in  in  future  and Commerce ( 1 9 7 8 ) ,  setting  as  concerns  program u n d e r t a k e n  distinguish  highly  the  base  markets.  B . C . wood  harvested  restrictions  high-cost  Trade,  more  plywood  forest  worse.  generally  between  mills  exogenous  are  are  modernization  for  in  a corresponding  institutional  important  the  output  industry,  implications  timber  second-growth  and U . S .  affect  the  of  the  been  Expected increased  prospects  of  The  in  cause  markets  the  from  industry.  adversely  mills,  volume  volumes  for  T h e r e have  significantly  significant This  prospects  face an  and t h e  of  an  that, their There s t i f f  increase extensive  85 m o d e r n i z a t i o n program undertaken i n the believed plywood  to  be  the  there  timber  Moreover, their  This  assumption  have  of  an  is  95-99% o f  produced  The IWA i s in  keeping  of  is  the  coastal  substantial  portion  exogenously  the  the  provincially  study  over  on  government.  these  form o f  price  of  rents  low  determined  materials  price avoid  to  materials is  Nevertheless,  i n order to  of  not the  materials  modelling  well  (see  of  B . C . wood p r o d u c t s Martinello  period  industry under  (1984),  According  virtually  study. to  It  America  o r g a n i z e d u n i o n w h i c h has  products  centralized.  bargaining setting.  Woodworkers  i n the  IWA members  the  pass  i n the  collective  output  wood  to  by  the  in B.C.  the  a large,  captured  the  International  by  unionized  that  a  competition.  sector  the  not  operations  in this  forestry  by  are  implies  I now t u r n t o  that  viability  that  incentives  through  maintained  claimed  the  evidence  rents  firms  determined  whole  is  wood p r o d u c t s  prices.  is  for  1970's which  mills.  Thirdly, of  crucial  late  is  (IWA)  industry pg.23). succeeded  completely  Bargaining  Martinello  is  (1984),  p . 23 : "Union representatives f r o m IWA R e g i o n a l C o u n c i l #1 n e g o t i a t e a c o a s t m a s t e r c o n t r a c t , c o v e r i n g a l l w o r k e r s employed i n the c o a s t r e g i o n , with the e m p l o y e r ' s a s s o c i a t i o n known as F o r e s t I n d u s t r i a l Relations (FIR). The c o a s t m a s t e r i s t h e n u s e d as a b a s i s f o r m a s t e r a g r e e m e n t s between IWA r e g i o n a l c o u n c i l s and e m p l o y e r a s s o c i a t i o n s i n t h e n o r t h e r n i n t e r i o r and s o u t h e r n i n t e r i o r r e g i o n s . A l l of  86 the c o l l e c t i v e provisions." Centralized either be  bargaining  the union or the  industry-wide  firms.  On t h e  experiencing firm  is  firms  other  the  in  the shows  strikes  that  large  the  fact  share  the  advantage  work s t o p p a g e costs  that  all  that  each  data  affecting  will  on  all are  individual  strike in  of  firms  to  engaged  and work s t o p p a g e s  shop  relative  Individual IWA has  union  strike  implies  market  the  to  A general  work s t o p p a g e  industry.  be  impose  hand,  its  contain  can  firms.  and w i l l  maintaining  industry wide  agreements  the  both  other  for  the  industry-  a s m a l l number  of  firms. During  the  sample  length,  years  in  years  long.  The t i m i n g  which  is  addressed  not  the  p e r i o d , most remaining of  in  of  ones  contracts this  study  the  contracts  being  either  is but  future  research.  4.2.2  I n d u s t r y P r i c e and Q u a n t i t y D a t a The  was  cumulated  adopted data. and  raw d a t a  some o f  and his  input  analyzed  that  firms'  and  output  by  methodology  The major d i f f e r e n c e s  in  profits;  are taken the  the  into  capital  which  in  is  quantity  (1984).  data  this  account  services  study,  i n the input  3  issue for  prices I  of  set  or  left  and  treatment  between t h e  1  an i m p o r t a n t  Martinello  i n M a r t i n e l l o ' s work a r e :  p r o d u c t i o n workers of  on  were 2  the  also raw  used  here  the  non-  calculation quantity  and  87  price  are  on more of  detailed  by  shares  the  to  in  firms  coastal  ( w h i c h was  the in  wood  the  mills  cover  21 y e a r s  data  and  the  candidate  for  the  section,  industry  in B . C . offers  and be  t h e wood p r o d u c t s some o f  the  84  why  that  the  data  a  good  in  the  resources  and t h a t ,  at  least  have succeeded  in  rents. of  this  data  lies  parameters  in  output  the  input  and  the m o d e l l i n g of it  virtually all  involves workers  the  the  input  i n c l u d e d i n the  with  since  and  The  natural  will  straight-forward  the  shingle  IWA i s  i n d u s t r y , B . C . unions  these  and  Columbia.  mentioned  rents  of  observations.  the As  the  inputs  mills.  bargaining equations  Finally,  representing  of  study.  shows  The t e c h n o l o g y  employment  prices.  veneer  natural  4 groups:  sawmills,  and  shares  consists  British  into  time  extend  other  in  divided  substantial  advantage  consistent  industry  reasons  evidence  The d a t a  employment,  interior  (the I  based  the  cost  here  finally,  are  at  input  adopted  used);  are  and  available  1980-1983.  present  previous  output data.  not  1963-1983 f o r a t o t a l several  Another  are  plywood  are  capturing  not  products  the  procedure  arbitrary  on wages,  There  in  are  industry  sawmills,  shake  the  include  observations  output  different  study);  by  period  annual  a  Martinello  given  sample  by  data  Martinello's  chosen  The  generated  be  and wage  constrained quantities  bargaining setting  only i n the  2  agents; industry,  the and  to and is IWA the  88 Forest firms  Industrial Relations i n the  One o f  the drawbacks o f time-series  the  focus  the  modelling of  of  this  a r e assumed t o  The  dates  that  the  however, this  study the  restrictive.  The  of  reduce  data.  modelled  person-hour. vacations  were  extensions  in  this  a  available  2 years  to  the present of is  includes  and o t h e r payments  this  Note  that  requires  For  issues  reasons are  However,  collective  not I  do  bargaining  study.  data  actually  length,  sharing  these  so  basis,  in  half.  research. of  contract.  contract  one  and  parameters  per  are  and r i s k  aspects  simple  firms.  annual o b s e r v a t i o n s .  disadvantage  This  by  requirements,  variable  to  on a v e r a g e size  kept  than  contracts  converted  interesting  T h e wage  rather  uncertainty  and d a t a  them  annual  Since  contracts,  technology  groups o f  the  rather than  simplicity  Another  be  the  is  across  my s a m p l e  data  and p o s s i b l e  of  contracts  contract  consider  are  could  modelling of  explicitly  all  pooled  observations.  on wage and employment  Specifically,  explicit  of  is  signature  since  d a t a stems f r o m t h e  nature of the  be c o n s t a n t  data  this  production process  observations  would  representing  industry.  cross-section  hence  Association  concerns  compensation  overtime payments, f o r work n o t  the  wage  per  paid  bonuses,  paid  performed.  To t h e  89 extent that this  these fringe  variable will The  of  labour  is  about  members) as  well.  of  hours  not  the  the  it  number o f  possibly,  The f i r m s worked,  firm  hours  per  per worker  as  two  were  In  would  it  assumed  parties  and  arise  intend  at  work the  per is  of  the  dispersion order  adding least  at  to  used; then  number  workers  a  third  the  are  time  keep hours p e r worker  the  and  fixed,  however,  and  are  process,  are  the  around the  avoid  union  total  worker  and  of  per worker  workers  sample  union  worker  production hours  the  per  bargaining variables.  over  from  that, to  number  that  number o f  hours  of  measurement  number  of  with  the  2 5  wage-employment  hours  variable,  the  in  both  number  the  the  which u n i t  are  the  (i.e.  firm's  the  for  period,  wage.  the  argued  and t h e  about  separate  fact,  be  the  the  If  treat  important,  which  in  care  calculated  Appendix A .  is  hours  worker  to  can  the  i n the  in  concerned  no d i f f e r e n c e  is  very  if  over  by  of units  workers  be  workers.  procedure  worker  will  or,  will  makes  measured  issue  about  substitutes  number o f  then  It  increased variations  is  important  studies.  and,  the  labour  The c h o i c e  an  the  perfect  then  of  paid.  determination cares  o v e r s t a t e the  quantity  person-hours  benefits  if  correct the  hours  Hours provided mean i s  per in not  complications  bargaining  variable,  of negotiation,  the  fixed.  M a r t i n e l l o (1984) c o r r e c t e d t h e d a t a f o r i n c r e a s e s i n v a c a t i o n s and h o l i d a y s and f o u n d h i s e s t i m a t e s v i r t u a l l y unchanged (see M a r t i n e l l o (1984), p g . 2 4 ) . 2 5  90 Most o f using on  data  the  i n p u t and o u t p u t  from the  quantities  materials were  the  and s u p p l i e s ,  used  to  only  plywood  mills).  shingle  and  aggregate  data  for  the  on  mills)  capital  stock,  capital  index.  4.2.3  the  of  shipments indices  each  is  is  firms  of  firms  aggregated.  of  the  and  (sawmills  and  A  disaggregate  constructed  indices  The p r i c e  formulation  and  of  and  available  (veneer  disaggregated  price  Appendix A f o r  alternative  hourly  assuming the i)  of  using fuels  a  and  constructed  capital  can  the  be  services  calculated  details).  T h e A l t e r n a t i v e Wage The  real  in  (see  for  data  each  price  stocks  group  the  user  directly  in  and  ideal  indices  capital  services  and  implicit  included  Fisher  3 groups  are  quantity  is  Detailed  and e l e c t r i c i t y ,  fourth  The o t h e r  capital  of  items  chained  electricity cost  of  constructed  groups.  shake  of  were  manufacturing.  i m p l i c i t quantity  Unfortunately,  measure  fuels  construct  and o u t p u t  separately  of  and v a l u e s  and c o r r e s p o n d i n g input  census  variables  to  earnings  (including  worker i s  work  B.C.  wage measure  in  and t o  earnings  in  the  faced  service  earn the these  is pay  with the or  based for  on  the  expected  time  not  worked)  following  manufacturing  employment w e i g h t e d industries.  This  options: industries  average will  in  hourly  occur  with  91 probability labour ii)  to  p  average  unemployment  which takes  UI  benefits.  probability latter  paid  in  (1-p) is  is  into 2  a  similar  rather  interior my  (W)  contract.  I  found  of  W  scaling taxation  occur  number o f  total  with  getting weeks  number o f  wage m e a s u r e the  A  real that  to  UI.  of  UI  weeks  of  the  one  a  1964  in  that  for  services  convert  the  in  the  is of  T h e r e s u l t i n g UI payment i s c o n s i s t e n t w i t h t h e measures o f the revenues o f the f i r m .  the  wage  group  and 1965.  conducted  occupations  below  one  constraint  several  i n t e r i o r were  being  earnings  alternative for  > W in  surveys  collar  used  to  difference  earnings  in  2 6  i n the  the  the and  alternative  dollars.  W^ a s  However, blue  the  (1984),  than  1971  sawmills,  definition  the  to  by a  p r o b a b i l i t y of  as  by  The CPI i s  (constant)  wage  equal  will  B . C . i n d u s t r i a l composite  When c o m p a r i n g t h i s union  event  alternative  total  manufacturing.  (UI)  in B.C.  he u s e d  alternative  the  calculated  by M a r t i n e l l o  wage t o  sectors/total  i n B . C . adjusted  This  times  constructed the  these  account changes  6  B . C . divided  unemployment This  in  insurance  h o u r l y UI payment  factor  The  (employment  force)  collect  of  =  in  on  i n the  (WA) t o  the  firms,  the  of  This the  negotiated  1 9 6 0 ' s on wages  B . C . show  provincial  violates  average  that  wages  while  the  a p r e - t a x payment. This a l t e r n a t i v e e a r n i n g s and  92 southern  coastal  occupations Later  show  Results  interior  maintained  4.2.4  weight the  on t h e  this  withstand  a  players  absence Table  for  the  the  for  the  coast  is  were  which  these the  in  were  average.  the  used  to  regional construct to  the  The r e s u l t i n g wages were  used  interior  applied  and c o a s t a l  sawmills  reach 1 i n the mid-70's  rest  same  of  the  interior 1.045.  sample  is  .91  (See  the  and a r e  period.  and  the  The  maximum  Appendix f o r  more  r e g i o n a l wages and w e i g h t s . )  of  study,  time  term  A large focused  determinants strikes.  costs  or the  ability  strike/lockout  measure  and a f f e c t  the  equilibrium  strikes.  In  I and T a b l e I I ,  by t h e  have  weights  for  above  differences  surveys  above.  for  S t r i k e Costs In  the  little  These weights  there  for  details  wages  wages  consistently  these  describe  respectively.  weight  of  W  alternative  minimum  very  coastal  A  offered  were  and  provincial as  which  surveys  wages.  areas  the  the  the  players  to  b a r g a i n i n g power  of  contract  empirical  relative  of  even  models  strike costs  in  the  given  in  a r e measured  (lndu/lndf). proportion of on of  the  Although model  relationship  was  empirical  estimation  strike  bargaining  the  costs  studies  hence  justified  by  a the  on  relationships  and t h e  these  and  of  studies  frequency did  model  of  argument  not  strikes between  or l e n g t h include  strikes, that  of a the  (ceteris  93 paribus) less  higher  willing  Kennan  strike  to  (1980)  strike.  of  costs  has  variables  regression  equation.  the  fruitful.  (  )  limited  sign It  adopted  =  (  F  0  to of  In the  I have  IndT t  +  is  t=l,  FO i s  a  ...  84.  The  first  strike  costs  1  x  I  t  of  the  ad h o c  some  T  t  impact  +  F  2  in  a  are  technology  of  identification and  to  (often  x  I  N  t  V  t  +  could  3  x  c  u  be  strike  formulation:  F  the  linear)  research  simple  2 7  t  + U x DEM )  denotes  measure  They  work  a r i g o r o u s model o f  + Ul x UIC t  of  impact  an a r e a where  and  3 variables time.  N  type  parties  (1980).  following  constant,  over  have  bargaining  this  the  absence o f the  F  to  the  + UO x U N where  of  modelling  believed  of  costs,  make  Examples  the  been  prediction  very  will  and R e d e r and Neumann  Unfortunately, strike  costs  2  t  the  variations  observation,  i n the  firms'  are:  A l i n e a r f o r m f o r ( l n d u / l n d f ) was a l s o e s t i m a t e d w i t h very l i t t l e d i f f e r e n c e i n the estimates f o r the cooperative models ( e x c e p t f o r t h e s t r i k e c o s t p a r a m e t e r s w h i c h were correspondingly larger). F o r the monopoly models, the l i n e a r f o r m y i e l d e d some v a l u e s f o r ( l n d u / l n d f ) w h i c h were negative. F o r c i n g t h e t e r m t o be g r e a t e r t h a n z e r o by s q u a r i n g i m p r o v e d t h e l i k e l i h o o d o f t h e monopoly m o d e l s f r o m t h e e s t i m a t i o n o f t h e l i n e a r f o r m c o n s t r a i n e d t o be g r e a t e r than zero. A l l m o d e l s were a l s o e s t i m a t e d w i t h an added exogenous v a r i a b l e i n the s p e c i f i c a t i o n o f the s t r i k e c o s t s r e p r e s e n t i n g wage a n d p r i c e c o n t r o l s . A dummy v a r i a b l e t a k i n g t h e v a l u e o f 1 i n 1976, 1977, and 1978 was added b u t had v e r y l i t t l e e f f e c t on t h e e s t i m a t e s . More d e t a i l is g i v e n on t h i s i n C h a p t e r 5. 2 7  94  INT-t = T h e  nominal  expected  reflecting  borrowing relative  costs  strike  INV-t = The c h a n g e over a  the  firm  market  latter  insurance force  -  u  building its  strike  years  was  tightness,  up  measured rate will  the  (UN) and t h e vary  More at  yiUlC-t above,  -  U 2  D  E  M  t '  UO m e a s u r e s  UI = UO x  expected  since  The a v e r a g e  over  the  smooth  the  out  variable.  very  2 8  i n the  opportunity  l a b o u r market  conditions.  tightness  of  of  changes  let u  w i l l In  the +  the effect  labour the  unemployment.  in  unemployment of  the  natural  y^UICt be  the  between  composition  the  averaged  be  in this  equal  t i g h t n e s s  increase  will  to  to  i n the  t  in  difference  precisely,  time  an i n c r e a s e  inventories  natural rate  according  <  firm.  changes  in  is  inventories  costs. used  0  will  F2 > 0 i s  (1982),  by  the of  F l  that firm  its  measure  and S m i t h  market  (lndu/lndf)  of  5 years.  (UIC) and c h a n g e s  -  the  value  t h r o u g h changes  unemployment  UN-t  of  costs  the  3 variables  (DEM).  Labour  fact  yearly variations  unemployment The  the  large  Riddell is  interest.  5  labour  Following  of  past  The l a s t of  in  last  reducing  cost  rate  +  labour  rate  of  W2  t«  D E M  measured  by  formulation  of  of  U2 = UO x \i2 and t h e  labour  market  t e r m UO x p  is  T h e e s t i m a t i o n r e s u l t s d e t e r i o r a t e d s l i g h t l y when t h e c h a n g e i n i n v e n t o r i e s o v e r t h e l a s t y e a r was u s e d i n s t e a d o f the average over the l a s t 5 y e a r s . 2 8  95 included  i n the  constant  FO.  The v a r i a b l e s  are  measured  as  follows: UN-t =  T h e unemployment since  the  inversely as  term  the  of  related  labour  relative  A measure insurance the  into  in  covered  DEM-t =  of  A g a i n U2 < 0 i s unemployment Some o f measures  of  t h e models  a  the  the  of  labour  the  unemployment as  benefits  to  factor of  follows:  covered  times  the the  which  available  for  B.C.)  expected  since  and DEM w i l l  of  ages  labour the  force Ul < 0  unemployment  and men u n d e r force  in B.C.  natural rate  be p o s i t i v e l y  were a l s o e s t i m a t e d as  takes  U i > 0).  all  total  ratio  unemployment labour  women o f  by  average  the  natural rate  such  increasing  force  Canada  (i.e.  and  opportunity  of  i n the  borrowing costs  tightness  is  union.  taxation  the  expected  p^DEMt)  thereby  scaling  not  -  constructed  in  with UlCt  age  falls,  proportion  The p r o p o r t i o n o f 25 y e a r s  is  the  the  since  increase  market  of  insurance  by U l was  expected  will  It  insurance  (The  y^UICt  generosity  of  account  UO > 0 i s  decreases costs  B . C . times  benefits.  is  the  proportion  wage  labour  also  unemployment  u -  tightness  program.  unemployment of  to  strike  of  in B.C.  (UN-t -  l a b o u r market  cost  UlC-t =  rate  using  mortgage  of  related. additional  rates  for  the  96 workers  and  estimates  demand were  reported here. du  and  strike  df  loan  not  Also,  failed.  costs,  it  two e l e m e n t s o f  for  greatly all  the  impossible  ratio  lndu. lndf  the  affected  attempts  Given  was the  rates  at  and  However, they  distinguishing  limited to  firm.  data  estimate  are  the not  between  available separately  on the  97  Chapter Estimation  Each of  the  structural estimated  four  equations  using  to  be  No  of  errors  i.i.d.  first  if  <t>^yf i s  model k j ,  year y,  and g r o u p o f  ^iyf  l  y =  vary  are  the  I  and  II  was  imposed  on  the  across  4 groups  order the  equations.  of  firms  for  lyf  N(v  for  k j S  4x4  }  i=l  .4;  (cooperative),  m (labour  demand);  f  = 1 (coastal sawmills), 2 (interior 3 ( s h i n g l e m i l l s ) , 4 ( p l y w o o d and mills).  serial  correlation  equations  time  by t h e  models  i ,  then  = B (exogenous o u t p u t p r o f i t f u n c t i o n ) , R (exogenous c a p i t a l p r o f i t f u n c t i o n ) ;  across  is  equation  j  across  are  autocorrelation  error  f,  nonlinear,  1964,...,1983;  k = c  The  i.i.d.  Tables  errors  firms  i(y-l)f  is  in  the  but  Specifically,  lyf  4 simultaneous,  across  allowed.  where:  of  restrictions  matrix  The c o n t e m p o r a n e o u s  Results  presented  FIML.  variance-covariance  assumed  systems  5  periods. (see  but  coefficient  not  across  I  and I I ) ,  k  groups  A l t h o u g h no c o n s t a n t  Tables  r ^  sawmills), veneer  is  allowed  of  firms  term i s  consistent  to nor  predicted  errors  were  98 found the  and t h e  estimation. The  except dummy  four  for  groups to  exist  separate to  of  value. should  in their  across  improved  means  for  these  be added t o for  the  for  models  models was  sets  where  groups  of  to  of  firms  improved  the  terms t o  get  It on that  allow  firms,  addition  constant  very  required  be d i f f e r e n t  this  the  across  the d i f f e r e n c e s that  I  for have  described  i n terms a  a  interior  reached.  are  (Note  on  of  proved  the  coefficients  interior  models  e s t i m a t i o n which i s  proved to and  identical  B and R d i f f e r e d  data  all  the  as  one  convergence  technologies.  terms  error  terms  of  estimate  These  extensive  The r e p o r t e d  constant  value  f i r m s t o model a d e q u a t e l y  terms  (v^)  treated  factors  and no  I n t e r i o r sawmills  constant  terms  four estimation  to  firms.  estimate  constant  sample  are  the  made  add 8 new p a r a m e t e r s t o  here.) the  takes  scaling  t h o u g h more  each group o f might  which  term or the  difficult as  firms  A t t e m p t s were  four  seems  of  inclusion in a l l  variable  constant  constant  2 9  groups  the  sawmills.  the  introduction of  of  separate  likelihood  dummy  variable  the appropriate  sawmills.  T o g e n e r a t e t h e c o n s t a n t t e r m s as p a r t o f t h e m o d e l r e q u i r e s more g e n e r a l s p e c i f i c a t i o n s of the technology. However, this would a l s o result i n more c o m p l i c a t e d bargaining equations. In p a r t i c u l a r , the f i r s t equations o f t h e s y s t e m s g i v e n i n T a b l e s I and I I w o u l d be s u b s t a n t i a l l y more c o m p l e x . This is l e f t for future research. 2 9  99 Estimation output the  are  case of  5.1  presented  where  in  under the  IV p r e s e n t s is  estimated  treated  as  cooperative  ( f r o m now on COOP)  comparison,  of  The F i r m s '  for  the  either For  model  LDEM m o d e l is  not  are  on t h e  time  model. on  5.2.  and  case  bargaining  for  labour  the  both  demand  in this  the (from  table.  3 0  but  for  and l a b o u r demand m o d e l s ,  this  the  only very s m a l l ,  has  the  no  the  of  the  expected  effect  is  is  also  negative  more the  exponent  effect  production  in  function. effect  important  labour  the  exception  labour  significant  COOP m o d e l , it  with  t r e n d B l and t h e  location  l a b o u r has  costs and,  the  for  the  results  significant  Time  the  both models,  restricted  in  are given  cooperative  coefficients  COOP  for  Technology  the  exponent  the  exogenous  The r e s u l t s  coefficients  the  now on LDEM) b a r g a i n i n g m o d e l s  technology  of  in section  exogenous  For  both  section.  are given  process.  For  assumption  Output Model  output  5.1.1  the  next  exogenous c a p i t a l  Exogenous Table  results  in  on the  coefficient  imprecise.  F r o m T a b l e X I i n t h e A p p e n d i x , we c a n s e e t h a t the s i z e o f t h e s h i n g l e and s h a k e m i l l s i n t e r m s o f c o s t s a n d r e v e n u e s i s s m a l l e r t h a n t h e o t h e r t h r e e g r o u p s o f f i r m s by a f a c t o r o f t h e o r d e r o f 10. To s i m p l i f y t h e estimation, a l l q u a n t i t y d a t a c o n c e r n i n g s h i n g l e m i l l s was m u l t i p l i e d by 10. The i m p l i c a t i o n s o f t h i s i s t h a t t h e e s t i m a t e d B , R , and y s h o u l d be m u l t i p l i e d by i n B 2 + B e - l , and 10~P r e s p e c t i v e l y i n order to get the a p p r o p r i a t e parameters f o r shingle m i l l s . 3 0  R  #  1  0  2  +  R  e  _  1  100 T a b l e IV Exogenous Output E s t i m a t i o n (asymptotic t ' s  Cooperative I.  Union  U t i l i t y  y  2.43168  implied 6 =  i n parenthesis)  Model  Labour I.  (12.345)* y  Results  .7086  Demand  Union  U t i l i t y  y  5.88248  implied 6 =  II.  IV.  (1.323)  Technology  B Bl B2 B3 Be  III.  0.04670  II.  0..36868 0..00353 1..09337 0..03008 - 0 . .01260  Strike  p  (6. (0. (28. (4. (-0.  228)* 155) 211)* 296)* 787)  Costs  -0.04792  .8547  (-1.637)  Technology  B Bl B2 B3 Be  III.  (8.142)* y 1+y  i+y p  Model  Strike  2,.21139 0..00826 0..81466 0..01572 - 0 , . 18179  (4. (0. (15. (3. (-14.  221)* 717) 825)* 939)* 386)*  Costs  F0 FI F2 F3  1.99872 -0.28815 0.05858 -0.26947  (1.602) (-10.948)* (3.141)* (-5.243)*  F0 FI F2 F3  -6.69166 -0.01315 -0.15232 0.13628  (-3.343)* (-0.375) (-8.251)* (1.419)  U0 Ul U2  -4.4653 2.85672 5.08272  (-1.569) (5.445)* (1.600)  U0 Ul U2  -2.52046 -1.12130 13.20971  (-1.047) (-1.717) (2.534)  F i r s t Order Correlation  eq.l eq.2 eq.3 eq.4  Serial Coefficients  0.62005 0.17802 0.18805 0.12803  (11.340)* (2.209)* (2.310)* (1.172)  IV.  F i r s t Order Correlation  eq. 1 eq.2 eq. 3 eq. 4  Serial  0.23388 0.25721 0.29529 0.17485  (3.809)* (4.206)* (3.639)* (1.700)  101  Table Cooperative V.  Continued  Model  Labour  Constants eq. 1 eq. 2 eq. 3 eq.4  Interior  Sawmills  of  (6.137)* (-7.032)* (-6.376)* (-3.926)*  eq.l eq.2 eq.3 eq.4  Dummy  1.71361 -0.36749 -3.30972 -3.10524  of the In l i k e l i h o o d  Number  Interior  (5.580)* (-2.956)* (-4.132)* (-12.140)*  eq. 1 eq.2 eq. 3 eq.4  Value -3286.8887  observations  84  -W -E 3  R^ b e t w e e n p r e d i c t e d a n d a c t u a l reduced sample 1964 - 1979  -W -E -Q -Q  3  Note:  (1)  at  of  Dummy  2.09485 -0.71870 -0.40284 -3.28161  (0.878) (-2.719)* (-0.511) (-12.726)*  -3315.1120  observations  -W -E -Q  2  -Q3  in  R^ in  84  5% i n 2 - t a i l e d  0.7334 0.3367 0.9574 0.5978  between p r e d i c t e d and a c t u a l reduced sample 1964-1979  -W -E -Q -Q  0.9244 0.3527 0.9454 0.6954  2  Sawmills  (2.680)* (-3.500)* (5.979)* (-3.677)*  between p r e d i c t e d and actual  0.6415 0.2896 0.9481 0.6341  -Q2 -Q  8.52566 -1.05901 12.71037 -0.84391  of the In likelihood  Number  R/ between p r e d i c t e d and actual (1)  * significant  Demand M o d e l  Constants  1.79659 -1.69284 -3.67800 -0.87202  eq. 1 eq.2 eq. 3 eq. 4  Value  IV  2  3  0.8861 0.1732 0.9418 0.7151  tests  F o r t h e c o o p e r a t i v e m o d e l , one observation, s h i n g l e m i l l s i n 1982 , was d e l e t e d i n t h e R calculation.  2  102  For input  comparison  coefficients  unrestricted  it  is  perhaps  i n terms  cost  U  N  (Q ,P ,P ,W) 1  2  Note  that  W,  (predicted) COOP to  Constant  the  since  right  of  - B L  x T ^  shadow  actual  model  the  for  -  3  cost  to  shares of  express  the  wage  in the  QJ -  price  in  that  -B2  (  8  the  labour  -(1-B3)  underlying  -B3.  \ \  1  of  P ^ "  labour,  LDEM m o d e l  case,  the  demand  is but  contract curve.  1  . Be . ' W ^ "  equal  the  w £ W in  the  can The  be  located  cost  shares  Shares  COOP Model  LDEM Model  Labour  .0124  .1538  .23  .31  Materials and Supplies  .9579  .8329  .55  .63  Capital  .0297  .0133  .21  .06  M a r t i n e l l o (1984), Appendix A  The  small  labour values  curve,  be  for  the  located  but,  with  shares of  Reference Shares in the Literature*  Actual Shares  Average Cost Over Sample**  pg.31.  estimation  surprising could  '  to  Input  smaller  1  are:  CUN  Cost  *see **see  the  function:  , C  of  more u s e f u l  than  the  exogenous are  far  ignoring  commonly  labour  COOP model to  the  output  reported  exponents.  since right  econometric  the of  issues,  yields  level the the  due  This of  much to  is  the not  employment  labour  demand  LDEM m o d e l  is  103 equivalent  to  exception  that  rather are  compensated The  compared t o when  they  wage  by  is  now  large  shares  general estimates  are  compared t o  estimations  chosen  forces.  very  capital  function  shares  actual  labour  for  are not  average  shares  materials  extremely  but they  the  through bargaining  The s m a l l  seem  with  small  and when  so s u r p r i s i n g  cost  shares  over  I  take  advantage  specification  and  sample. In  my  the  t h a n by c o m p e t i t i v e  supplies.  the  standard cost  order to  simple  look  at  scale  Cobb-Douglas  effects,  derive  of the  underlying production function parameters:  COOP:  Q, -  LDEM:  In  Q  the  the  COOP to  model, scale  Again,  LDEM m o d e l  product  of  perhaps  while  0  since  that  labour to  is  the  also  0  3  1  2  0  1  x  Q  x  Q ^  8  8  x  1  2  0  8  2  technology the  Q ° x  7  x  5  Q °  1  9  3  3  E ' x  exhibits is  1  5  2  for  1  the  LDEM  expected  wage.  output  3  decreasing  true  the  5  2  the marginal  resemble the  0  E *  on l a b o u r i s  model f o r c e s  that  2  3  reverse  closely is  7  2  in  revenue What  elasticity  is of  l a r g e r i n t h e LDEM m o d e l .  LDEM m o d e l ,  revenue  for  COOP m o d e l .  technology  0  a higher coefficient  marginal the  --  the  surprising  materials In  T  = Constant x T - -  l  returns model.  Constant x  the  product of  indicate  wage  labour.  The r e s u l t s that  for  is  the  forced This  for COOP  the  to  is  reflect  not  the  exogenous  model,  the  the case  output  wage  is  104 considerably labour. the  in  than  only  model is  is  the  the  COOP m o d e l , is  0.12.  revenue  It  constant  in  chapter,  estimated  when  for  explanation  is  the that  variable  increases  the  the  which  sample  revenue  that  used  the  for  labour  in  take  somewhat In  for  into  output revenue  As  (see  inclusion  introduces inaccuracy  the  two  mean o f  the  estimated the  c o r r e l a t i o n are  not  structure  be as  seen  later  5).  output  the  the  are  larger,  One  possible  quantity  multicollinearity in of  in  endogenous,  labour  Figure of  the  The  of  will  of  marginal  (These  1  treated  COOP  interval  one.  at  serial  products  COOP m o d e l  3  labour  the  average  than  account  and  is  3.  the  and t h e u p p e r bound  evaluated  Figure  terms  the  is  product of  the  less  of  labour over  (4.5).  estimate  Be,  is  calculations.)  marginal  especially  and  the  product  e v e n when a 95% c o n f i d e n c e  is  of  do n o t  3.3 4 32  labour coefficient  illustrated  i.e.  exogenous  but  values)  relationships  this  is  marginal true  revenue  revenue p r o d u c t o f  l a b o u r demand c u r v e s  are  included  is  f o r the  product  estimated  error  marginal  wage o v e r  average  imprecise,  absolute  data  the  LDEM m o d e l  average  the  calculated  (in  than  The average m a r g i n a l  sample  lower  larger  estimates  as  the  of  an  data  labour  T h e l a b o u r demand c a l c u l a t i o n s f o r t h e COOP m o d e l e x c l u d e t h e o b s e r v a t i o n f o r s h i n g l e m i l l s , 1982. To o b t a i n p r e d i c t e d v a l u e s f o r wages and e m p l o y m e n t , a s y s t e m o f 2 n o n - l i n e a r e q u a t i o n s must be s o l v e d f o r e a c h d a t a p o i n t . T h i s s y s t e m c o u l d n o t be s o l v e d w i t h any r e a s o n a b l e d e g r e e of accuracy f o r t h i s o b s e r v a t i o n . 3 1  105 Figure  3  L a b o u r Demand C u r v e s Contract  Curve.  and  Exogenous Output  the Estimation.  "1971 d o l l a r s p e r man-hour  ' \  l a b o r demand ( l a b o r demand model)  contract  curve  l a b o r demand ( c o o p e r a t i v e model)  0.0  o.s  -r  -  1.0  I  1.5  2.0  2.5  I  3.0  Employment ( i n l O M ' s man-hours)  i  3.5  I  4.0  106 productivity. and  (The  employment Studies  case  where  monopoly the  of  the  using the  a  sample  special  union  model),  the  at  the  general  estimates  literature  where  elasticities  are  .9876  for  Furthermore, are zero.  given  lie  this  to  the  of  large  absolute  (ITU).  the  LDEM  chooses price  value)  model,  the  These  impacts  remains union  LDEM.  wage  (the  the  smaller  (1984)  equal  who  for  1.5  find  a  and  value  International  be  compared  than  ignored.  .8462  when when  estimated  all  for  who for  .5  in  In t h i s  the  elasticities  the  they  LDEM m o d e l .  bargaining  (lndu/lndf)  with  study,  i n between t h e s e v a l u e s ;  true i.e.  to  should  are  somewhere  COOP m o d e l  for  the  elasticities  (1981)  data  elasticities  case the  .8405 f o r  case  the  output  .7371).  and P e n c a v e l of  union  the  In t h a t  COOP and  of  between  Examples a r e M a r t i n e l l o  (in  mean  Union  is  yielded  IWA, and D e r t o u z o s 1.23  coefficient  unilaterally  have  elasticity  Typographical  the  over  l a b o u r demand c u r v e .  finds the  correlation  is are  powers  fixed 1.033  at for  107 5.1.2  that (6  Union For  both  the  union puts  > .5).  LDEM  the  than  the of  LDEM and t h e  1% l e v e l  COOP m o d e l  of  cannot the  findings  reject  the  of  elasticity  of  Martinello  (1984)  the  ITU  rejected  for  Dertouzos It similar  in  technology exist. (.9554)  in  the  test  substitution (-.7)  both  that  reassuring  (1981) that  models  coefficients.  lower  than  result  is  of  is  of  rejected  at  as  t h e IWA.  parameter p  implies  The  that  w h i c h was  and M a r t i n e l l o union  given  the  substitution LDEM  and also  (1981)  y=l)  is  found  by  are  so  (1984).  preferences difference  some for model  take  f o u n d by  and P e n c a v e l (p = 0  we  resulting  l a r g e r than that  result  the  test  the union preferences  However,  for  the  function.  the  the  consistent  I T U as w e l l  This  for  the is  maximization a  on wages  greater  y=l)  and by D e r t o u z o s  models,  two  that  suggests  than  cases,  f r o m 0.  (-1)  Rent  is  LDEM m o d e l s ,  Cobb-Douglas  (.7).  both  This  different  The e l a s t i c i t y is  but  hypothesis  a  the  weights  i n v o l v i n g the  and P e n c a v e l  is  i n the  COOP and t h e  significantly  form  for  (i.e.  results  on employment  significance.  Again f o r both the not  COOP m o d e l ,  more w e i g h t  weights  with previous  is  3 2  The d i f f e r e n c e  equality the  Preferences  in  the  differences the  do  COOP  model  (1.0503)  which  T a k i n g i n t o account the s c a l i n g of the data for shingle m i l l s , the union u t i l i t y parameters y f o r those f i r m s i s 2 . 1 8 3 7 6 f o r t h e COOP m o d e l and 6.5687 f o r t h e LDEM model. None o f t h e q u a l i t a t i v e r e s u l t s d e s c r i b e d i n this section are affected when c o n s i d e r i n g t h e s e adjusted parameters f o r s h i n g l e m i l l s . 3 2  108 means  that  the  indifference  COOP m o d e l .  At the  increase  the  in  compensate workers in  in  the  wage  (above  union  for  a  compensate  the  union  These  data, the  contract  mean o f very  the  flat  data  i.e.  curve has  the  for  estimates  for  the been  data  points  contracts  than  the  recession, sawmills is  true  This  finding  threat can  for  be  which  wage.  specifically,  f r o m 1980  to  not  explained cause  possibility  the of  by  of  quickly  one  1.32% in  the  worker to  in  that  of  at  3.  away  elasticity  i n the the  for  1983  the  It  is  from  the  the  contract  COOP m o d e l and 2 o f p r e d i c t e d wage was  occurred d u r i n g the  the  and f o r  COOP m o d e l , the  and f o r  maintained the  increase  comparable  in  shingle  presence  threat  a negative  point  to  threat  of  study.  fixed  be point  mills  assumption  in this  less  the  lower 1980's  W<W^ f o r  LDEM m o d e l ,  c o n s i s t e n t with the  p o i n t which i s  equals  Figure  This  i n t e r i o r sawmills is  of  Bargaining Sets  move  LDEM m o d e l ,  alternative  number  3.44%.  data points  i n the  are  to  plotted  is  the  loss  0.44%  wage)  evaluated  curve over  4 of  the  a  COOP m o d e l  The a v e r a g e  For  1% i n  the  (.67%).  also  sample  alternative  the  in  would t a k e  a much l a r g e r  l a b o u r demand c u r v e . the  convex  same m e a s u r e  T h e C o n t r a c t C u r v e and t h e The  more  it  of  This  takes  model.  are  loss  COOP m o d e l .  i n M a r t i n e l l o (1984)  5.1.3  the  It  LDEM  found  the  mean o f  LDEM m o d e l .  wage t o the  the  curves  the  same  in  1982.  of  a  zero  However,  costs than  sounds  the  of  it  delay  zero.  plausible  The in  109 the  short  run  but  it  is  unlikely  survive prolonged periods Excluding the mills that  the  and the  in  LDEM  1982  the  models  are  COOP  convex that  model,  than  the  the  contract  convex  the  iso-profit  union  defined  curves.  (Note t h a t  LDEM  since  that  the  contract  5.1.4  in  determinants  significant  are  is  I  find  the  COOP  ensures  that  both  not  labour  Also,  everywhere This  by t a n g e n c y  this  shingle  31),  unique.  curves.  the  can  for less  ensures  points  of  the  an i s s u e  in  the  demand  curve  is  curve.)  Bargaining Powers The  case,  for This  curves  indifference  curve is  above p l u s  space  b a r g a i n i n g game i s  the  players  footnote  everywhere.  iso-utility model  (see  in utility  the  utility.  mentioned  COOP m o d e l  bargaining sets  e q u i l i b r i u m to  the  of negative  observations  for  that  and h a v e  3 3  of  the  the  firms'  expected  strike  signs  in  costs  the  COOP  are  all  model.  A 1 1 m o d e l s were a l s o e s t i m a t e d w i t h t h e a d d i t i o n o f a dummy v a r i a b l e r e p r e s e n t i n g t h e e f f e c t s o f wage a n d p r i c e c o n t r o l s on t h e r e l a t i v e s t r i k e c o s t s . T h i s dummy v a r i a b l e t a k e s t h e v a l u e o f one i n 1 9 7 6 , 1977, and 1978. In a l l cases, the c o e f f i c i e n t s on t h i s v a r i a b l e a r e s m a l l and n o t s i g n i f i c a n t l y d i f f e r e n t from z e r o . The o t h e r p a r a m e t e r s a r e p r a c t i c a l l y u n a f f e c t e d by t h e a d d i t i o n o f t h i s t e r m . The l i k e l i h o o d i s s l i g h t l y improved. Under t h e a s s u m p t i o n o f exogenous output, the log likelihood value for the c o o p e r a t i v e m o d e l i s - 3 2 8 5 . 9 3 4 0 and f o r t h e l a b o u r demand model, -3315.0744. T h e same v a l u e s u n d e r t h e a s s u m p t i o n o f exogenous capital are -3466.6705 and -3479.1330 respectively. The c o e f f i c i e n t s on t h e dummy v a r i a b l e a r e : f o r t h e e x o g e n o u s o u t p u t f r a m e w o r k , - 0 . 0 9 9 f o r COOP and 0 . 0 2 5 f o r LDEM, f o r t h e e x o g e n o u s c a p i t a l m o d e l , 0 . 0 1 8 for COOP and - 0 . 0 7 8 f o r LDEM. 3 3  110 An  increase  in  the  interest  relative  strike  costs  inventory  levels  over  by  a  fall  in  following related a  year.  to  of  costs the  of  over  coefficient  business  Here,  it  rate  union  has  strike  t  costs effects  is  on  rate  the  during  is  Tracy  the  negatively (1986)  found  firms'  strike  were meant t o  measure  i n the  cycle  absolute  on  level  has  sign  utilization  the  effects  variations  opposite  costs  varied  x UIC t  g§  also  x  to  level  capital on  strike  in  rents.  a  significant  that  in  In  COOP.  rate  have  smaller  time  according  and  spouse's  The e f f e c t above  the  income).  to  term:  DEM ]. t  enters  t h r o u g h W^, d i r e c t l y utility.  over  as m e a s u r e d by t h e  unemployment  over  accompanied  costs  in  effects.  U0[UN -  union's  the  and c a p i t a l  l a b o u r market t i g h t n e s s  and,  business  inventory  and  be  coefficient  the  insignificant  the  the  only  and  measure  and h e n c e  the  will  on  cycles  in  increase  strike  cycles  rise  an  costs.  cyclical  interest  that  strike  a  while  utilization  the  The  Note  relative  i n rents  cause  5 years  above  LDEM m o d e l ,  The  past  r a t i o measures and  will  firms  business  study,  costs.  utilization  the  relative  variations  strike  the  firm's  effect  In that  cyclical  of  The c a p i t a l  firms'  positive  costs.  the  rate  the  alternative  affects of  direct  the  constraint  unemployment effects  For both  the  wage  on  on  strike  on  COOP m o d e l  (e.g. and  Ill the  LDEM m o d e l ,  relative  union  bargaining tighter. errors model  of  the  the  In the  coefficient The where  term  the  union  costs  go  to  costs  (lndu/lndf)  .1222  power  when  likelihood  is  tests  monopoly  model  but  over  the  LDEM m o d e l .  below  (equal  value  of  is  all  equal  unions  to  the  .1943  to  the  a  is  the  power,  UIC  case  and  firms'  relative  strike  COOP m o d e l  efficient.  Both  F0 = 1  and  hypotheses do n o t  symmetric  Nash  less Log  hypothesis:  b a r g a i n i n g power) i.e.,  is  time  relatively  following  The e s t i m a t e s nor  natural  the  i n the  be  power;  0).  COOP  on DEM has  0,  the  The u n i o n has  bargaining  both models. of  has  the  by  when  were p e r f o r m e d on t h e union  the  insignificant.  ~  assumed  standard  while  bargaining  sample  are  on  coefficient  is  approaches  becomes  as in  union  UIC c o e f f i c i e n t  the  the  average  coefficients for  the  bounded  The  (the  rejected  imprecise  effects  that  hence  market  significant  is  all  it  contracts  ( l n d u / l n d f ) =1 other  as  the  (lndu/lndf)=0  only  and  has  0.  in  but  (lndu/lndf)  above  and  (positive)  t h e wrong s i g n  unbounded  implies  (and  labour  are  LDEM m o d e l ,  sign  has  the  effects  predicted  predicted  which  The U I C and DEM v a r i a b l e s  unemployment  significant.  sign  increase  when  these  large.  wrong  costs  falls)  However, are  the  strike  power  have  rate  UO has  support  and all were the  bargaining  solution. The implies  fact that  that the  the  value  union discount  of  (lndu/lndf)  rate  du i s  is  very  much l a r g e r  low than  112 the  discount  better  idea  value  of  factor of  utilities  equations  (4)  easier  to  bounded  above  and  The  f  term  a )  both  the  is  note  exogenous  .8913.  in  the  the  COOP  in  the  1960's l e v e l decrease  model, 1976 .  _ "  the  the  of  two (see  weights  below  by  The w e i g h t  union  four  "  (as  are zero,  on  the  groups  of  i n F i g u r e 4.  model. is  the  but  in  the  and  again  o r 1983. early  by  the  and  for  fall  in  the  '  union the  the  union  to  reach  80' s  but  its  utility model  the  For the  COOP m o d e l , for  the  high level  70's  in  LDEM  of  in  thing  the union i s  power  '70's  remained at  u  The f i r s t  in  bargaining  a  firms  average  .8 375  rises  b a r g a i n i n g power this  The  1  measured  b a r g a i n i n g power o f  a g a i n by 1982  Furthermore,  one.  the  is:  the  all  models,  started  bounded  the  solution  These  (lndu/lndf) + (lndu/lndf)  l  model  70's  on  a  (lndu/lndf)'  profits  for  output  For both  decreases its  +  power  how l a r g e  bargaining  are  have  i m p l i e d by  weights  4).  to  1  COOP and LDEM m o d e l s is  order  by:  firms'  plotted  In  the  sum t o  _  bargaining  u  weight  they  and t h e y  lndu lndu + l n d f  "  Nash  Chapter  " lndu + lndf " l  The  the  in as  lndf  df.  b a r g a i n i n g powers  the  (5)  given  w e i g h t on t h e  a  to  is  firms  calculated  in  by 1,  _ u  I  interpret  union u t i l i t y  the  relative  (lndu/lndf),  parties'  a  the  of  is  not  LDEM until caused  113  Figure 4 U n i o n B a r g a i n i n g Power. a. C o o p e r a t i v e  1964.0  1966.0  1968.0  Exogenous Output  Model  1970.0  I97J.0  1974.0  TIME  1976.0  1978.0  b. Labor Demand Model  shing mills  Estimation,  1980.0  1982.0  1984.0  interior sawmills  plywood and veneer mills  V  /  7'  A  ,  coastal V . sawmills 1964.0  ISS6.0  1968.0  1970.0  1972.0  1974.0  1978.0  1978.0  1980^0I98ZJ)TsW.O  114 solely  by t h e  The  union  and  U2  the  bargaining  set  at  '70's  increase  with  is  However,  it  does n o t fact,  the  easily  shown  the  to  see  the  and  labour  should  be  kept  a decrease  in  utility is  that  utility  by  was  of  looking  captured  at  bargaining  when  markets  the  that  a  over  by t h e  f i r m which are  given  i n Table V are  tight.  is  in  function, this  were  This  estimated  very  decrease  profits  union.  provincial  were  union u t i l i t y  the  in  estimated union  firms'  the  trend  sample.  increasing  the  and  UO, UI  subsequent  mind  the  downward  1981  '70's  in  above w i t h  a  the  booming  as  rate.  u  in  period.  increasing  perhaps  more  proportions listed  a  of  i n Table V  COOP m o d e l .  The ratio  2 years of  unemployment  slight  around  late  the  rents  fall  a  the  indicates than  for  last  union  faster  shows  sharp  on t h e  calculated  in  imply  What i t  power  surprising  was  coefficient  still  a  decreasing  economy  total  zero  i n the  It power  perverse  of  proportions estimated  evaluated  at  employment firms  on  average  especially  on  succeeded over  by  of  alternative  level  the  captured  the  profits  the  the  i n the  the  the wage  labour  firm  was  latter  of  divided  at  the  the  by  I  over  average  the  decade.  the  profits  find  40% o f  proportion  on  as  corresponding  curve.  slightly  Also,  larger  half  and  demand  in capturing period.  firms  calculated  in  the  of  that rents rents  1970's,  115  Table V Proportion  of Total  R e n t s C a p t u r e d by t h e  Firm.  C o o p e r a t i v e Model w i t h Exogenous Output  Year  Coastal  1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983  Interior Sawmills  Shingle  Sawmills  .31113 .33218 .35079 .42393 .36535 .28265 .29588 .32846 .43833 .44509 .18168 .45291 .41620 .44037 .51582 .45093 .17879 .29232 .27218 .33905  .59166 .57967 .58601 .57622 .55831 .43007 .50572 .56994 .55050 .49261 .39963 .60943 .56498 .51496 .55352 .45831 .45267 .55320 .63340 .65908  .39781 .43755 .43599 .42172 .38423 .20909 .24876 .34617 .38960 .36297 .29614 .54350 .43655 .39039 .47949 .44947 .34229 .39730 - (1) .40259  Mills  Plywood Veneer Mi!  .46465 .44462 .43327 .46698 .43616 .45712 .47370 .48529 .47539 .43178 .36443 .52181 .44838 .41167 .54334 .38503 .22093 .20498 .17610 .22517  G r a n d A v g . = .4223  Note:  (1)  P r e d i c t e d v a l u e s f o r wages and employment not be c a l c u l a t e d for this observation footnote 31).  could (see  116 It  is  interesting  proportion than  60%  measured  of on  (which  u  of  rents  because  space)  it  between  estimated  is  the  to  and is  is  by  the  a poor  than  curve  is  contract  curve.  T h e s e two m e a s u r e s  union  r e n t m a x i m i z i n g and i f  For  the  negative factor  for  than  most  B (2.21).  product  (MRP)  in  the  data  of  labour  COOP m o d e l  This  larger  coefficient  on  evident  from the  labour  the  still MRP's  turn,  higher  small is  and  due  causes the  be b i g and t h e  profits  to  MRP o f  due  cost  share,  larger  estimated  estimated  costs  profits  to  of  this  the to  the  factor  of materials  the  if  the  rents  are  scaling revenue  LDEM  model  reflect in  and  labour  of  union  along  large  However,  scaling  curve  the marginal in  the  efficient.  and  achieved  part  are,  is  forced  is  (Be).  a substantial the  is  value  the  much l a r g e r  labour  labour  to  earlier,  it  ( i n W,E  same o n l y  estimated  because  bargaining  measured  are the  as The  i s o - p r o f i t  contract  is  less  power  corresponding  distance  points  is  distance  the  As m e n t i o n e d  wage.  is  on t h e  LDEM m o d e l ,  union  The c o r r e c t  b a r g a i n i n g power  is  based  of  the  profit.  the  80% on a v e r a g e ) .  vertical  and  in  (which  bargaining  indicator  iso-profit  a zero  difference  union  union  on t h e  level  the  the  greater  based  profit  corresponding  note  captured  average)  by a  proportion power  rents  to  part  the by  this  This,  and c a p i t a l  in general,  was  coefficient  difference B.  a  in in to  negative.  117  5.1.5  Comparing the In  Table IV,  performs larger. with  in  This  has  data  set.  3 4  correlation the  R  s  2 1  are  clear  errors  from  model  the  could  and  of  LDEM m o d e l .  that  the  COOP m o d e l  employment  in  be  model  compare  the  values  and e m p l o y m e n t ,  the  the  without  the  The l i s t was  very  1980's. the  is  research  and a c t u a l  in  interesting  model  hypothesis  performs  appropriate  due t o  the  bargaining  transactions  could  set  F o r wages  value  my w h o l e to  model  years  of  poor  This  is  1980  to  reported i n Table IV.  more  made  contract  likelihood  interesting  better  tested nesting  over  two  the  environment  i n the  very  type  b a r g a i n i n g models.  the  recessions.  1980's  costly  (enforcement)  regime  w o u l d p r o b a b l y be r e q u i r e d as  while  general,  economic  employment  a switching  the  in  severe recession  and m o n i t o r i n g  by  that  during severe  changes which o c c u r r e d i n the  have  general  its  is  calculated  2  two p l a y e r s  terms  data  is  that  between p r e d i c t e d  showed  R 's  contract  large  This  the  efficient  throughout  larger  wages  the  true  It  suggests the  efficient  of  sense  been  actually  This  The  the  which are a l s o  LDEM  that  coefficients  predicting  1983  see  endogenous v a r i a b l e s .  prediction at  we  better  this  of  COOP and LDEM M o d e l s  in  costs.  model  or  a  A larger  well.  S i n c e b o t h m o d e l s h a v e t h e same number o f p a r a m e t e r s , the comparison o f the l i k e l i h o o d v a l u e s is equivalent to u s i n g t h e A k a i k e I n f o r m a t i o n C r i t e r i o n w i t h b o t h models b e i n g c o n s i d e r e d as n e s t e d i n a m o r e g e n e r a l m o d e l w h i c h c o u l d t a k e t h e form o f a convex c o m b i n a t i o n o f t h e two. 3 4  118  5.2  Exogenous C a p i t a l Table  models as  VI  and  presents  for  exogenous  Model  the to  case  the  coefficients  for  where  services  capital  bargaining  process.  chosen  o p t i m a l l y given the negotiated  5.2.1  The F i r m s ' For  both  coefficients  bargaining output are  the  COOP  similar  models.  That  estimation.  over  As input  LDEM m o d e l s ,  coefficients  was  not  the  cost  the  than  has  zero  are q u i t e  exogenous  shares  is  now  in  based  on t h e  in  the  It the  is  is two  exogenous  coefficients  implying  small  output  technology  zero.  are  case  trend  all  from  the  less  The e f f e c t s  for  treated  contract.  f u n c t i o n i n b o t h b a r g a i n i n g models  time.  are  Output  labour  different  The t i m e  significantly  production  and t h e  significantly  how  bargaining  Technology  are  surprising  both  which  that  the  shifting  in  however.  estimation,  I  derive  underlying unrestricted  the cost  function:  C  UN  ( Q  r  V  where t h e R  3' "  ?  )=  exponents  coefficients.  exogenous, differ  C o n s t a n t  from  the the  x  t C 1 x  Q"  x  PJ" "  are functions  Note shadow actual  that  since  price price  of of  0 3  of  0 6  x p^ x w  the  3  vector  capital capital capital  Ce  is  of  assumed  P3 will P 3 .  estimated  in  Also,  to  be  general W,  the  119  Table VI Exogenous C a p i t a l E s t i m a t i o n R e s u l t s (asymptotic t ' s i n parentheses)  Cooperative I.  Union  Utility  y  1.05352  implied  6 =  Model  Labour Demand Model  (7. 315)* y  Union  Utility  y  1.49223  implied  51303  8 =  i+y p  II.  0.14051  17.98817 -0.21048 -0.53964 0.59467 0.19463  III. S t r i k e  IV.  .59875  i+y (2. 786)*  Technology R Rl R2 R3 Re  (5.619)*  0.16808  II. (7. 436)* ( - 7 . 461)* (-9. ,294)* (9. 753)* (6. 873)*  Technology R Rl R2 R3 Re  Costs  (2.781)*  16.74362 -0.11640 -0.53247 0.44378 0.29027  Strike  (5. (-3. (-6. (6. (9.  854)* 772)* 970)* 063)* 971)*  073)* 300)* 296) 891)*  Costs  F0 Fl F2 F3  4.66183 -0.07521 -0.02315 -0.20538  (4. (-4. (-2. (-4.  548)* 041)* 064)* 869)*  F0 Fl F2 F3  -4.49366 0.05896 0.02169 0.22046  (-4. (2. (1. (3.  U0 UI U2  -7.99731 0.67511 -0.62665  ( - 5 . 357)* (2. 044)* ( - 0 . 276)  UO UI U2  9.08620 -0.21710 0.86142  (2. 647)* ( - 0 . 707) ( 0 . 329)  F i r s t Orde r S e r :i a 1 Correlation Coefficients eq.l eq.2 eq.3 eq.4  0.26175 0.45682 0.08056 0.27959  (3. (6. (1. (4.  599)* 606)* 228) 234)  IV.  F i r s t Order Correlation eq. eq. eq. eq.  1 2 3 4  0.32974 0.38440 0.04105 0.17203  Se r i a  (4. (6. (0. (2.  739)* 227)* 592) 716)*  120  Table Cooperative  IV  Model  Labour  Constants eq. eq. eq. eq.  1 2 3 4  Interior eq. eq. eq. eq.  Value  V.  1.02308 -1.33659 -9.26692 -4.99822  Sawmills  1 2 3 4  eq. 1 eq. 2 eq. 3  2.74521 0.39170 -3.91362 4.14343  Interior  (2.863)* (2.039)* (-1.386) (0.997)  eq. eq. eq. eq.  Number  Value  likelihood  -3466.7148  of observations  between actual  84  -W -E -Q  2  -Qi  -W -E -Q2  -Qi *significant  1 2 3 4  2.52769 0.44520 -5.25611 0.58108  -Q  2  -Qi  in  -3479.5348  84  0.7020 0.0055 0.5314 0.5591  between p r e d i c t e d and actual r e d u c e d s a m p l e 1964-1979  0.9346 -0.0589 0.5024 0.3829  a t 5% i n 2 - t a i l e d  (1.908) (1.242) (-1.324) (0.099)  predicted and  -W -E  in  (-0.069) (-3.102)* (-4.253)* (-0.307)  Dummy  of observations  between actual  0.6823 -0.0817 0.5829 0.5466  R.2 b e t w e e n p r e d i c t e d a n d a c t u a l r e d u c e d s a m p l e 1964 - 1979  Sawmills  of the In likelihood  Number  predicted and  Model  -0.10978 -0.97044 -7.89717 -1.12594  eq.4  Dummy  Demand  Constants  (0.703) (-8.483)* (-6.687)* (-1.825)  of the  In  Continued  -W -E -Q  2  -Qi tests  0.9390 -0.2929 0.4264 0.3729  121 shadow  price  of  labour  actual  wage  in  the  located  to  the  for  the  shares  will  COOP  right  of  in  general  model  the  since  labour  exogenous c a p i t a l  Cost  be  less  than  employment  demand  will  curve.  estimation  The  Labour  .1465  .2291  .23  .31  Materials and Supplies  .4061  .3504  .55  .63  Capital  .4475  .4204  .21  .06  the  labour  exogenous  reported  in  share  output  the  which  shares  in  exogenous o u t p u t  the  Assuming  the  for  this  and  seven times the  the  sample.  shadow The  firms  about  This  price  two  capital  input,  of  is  Also,  twice of  the the  suggests capital  a d j u s t m e n t s were  costless.  from the  vector  comparable  exogenous  increase  derived  is  larger  the  to  than  the  difference  models  is  in  shares in  smaller  the than  estimation.  size  underlying  Actual Average Cost Shares over Sample (see Appendix A)  substantially  bargaining  would  The  is  literature.  in  Reference Shares in the L i t e r a t u r e (see Martinello (1984), pg.31)  estimation  labour  cost  Shares  LDEM Model  The  be  are:  COOP Model  Input  the  size  in  larger  their  production of  of  actual  that  is  yields  large  the  share this  than  usage  function  technological  shares  reference  share  calculated  over  estimation,  the  the of  cost  actual  capital  price. if  the  parameters  are  coefficients:  122  COOP:  Q  LDEM:  l  Q  Both  = Constant  x T " '  = Constant  x T " '  x  production  returns output  to  over the  scale.  This but  increasing  materials  and  6  7  X Q '  7  6  average  the  sample  lower  X Q '  0  was  the  also  due t o  marginal  is  2.1803  than the  revenue for  (Notice  is  its  the  that  the  the  labour  is  in  in  both  forced  to  the  (Re).  estimated  LDEM  1  6  8  4  9  4  exogenous output on  in Figure  per  value.  hour In  (measured the  LDEM  because i t  does  error at  but  the the  to  The  mean  marginal wage.  1971  to of  output  revenue The COOP COOP  coefficient efficient,  labour  dollars)  for  model.  than the  be  of  quite  output  a larger  product  exogenous  the  otherwise  much h i g h e r  in  term.)  The l a b o u r demand  a r e assumed  revenue  for  the  exogenous  3 due  When c o n t r a c t s marginal  the  labour  3.6234  MRP i n  4.52  reflect  labour  $1.50  2  decreasing  and  evaluated  cases,  model  demand  of  the  l a b o u r demand i n F i g u r e 5 i s  average  E '  1  (MRP) o f  average  flatter  model  the  X  6  the  COOP m o d e l  i n F i g u r e 5.  somewhat  since  product  structure  counterpart  expected  on l a b o u r  E '  high coefficient  a v e r a g e wage o f  illustrated  model  of  9  X  exhibit  a very  data  product  8  2  exogenous  the  is  2  6  with  l a b o u r demand c u r v e s  This  X Q '  5  8  LDEM m o d e l  estimated  to  7  3  in  two  similar  4  X Q '  5  case  account  LDEM  3  0  the  take into  the  5  estimates  not  are  3  supplies.  The  is  0  returns  LDEM m o d e l .  model  3  function  COOP m o d e l  yielded  1  less  estimation,  is  on than this  123  5  Figure L a b o u r Demand C u r v e s  and t h e  Exogenous C a p i t a l 1971  Contract  Curve.  Estimation.  dollars  per man-hour  I  ( l a b o r .demand model)  4  \  y y  \\  /  /  /  /  y  /  contract  curve  \ \ / l a b o r demand ( c o o p e r a t i v e model)  0 0  i  0.5  i  1.0  i  1.5  Employment  i  2.0  ( i n lOM's  i  2.5  i  3.0  man-hours)  :  3.5  '  :  1—  4.0  124  same d i f f e r e n c e similarity model  $2.20  between  model  labour  and  slightly  lower  assumption COOP) .  of  Pencavel output  the  than  the  for for  estimates,  ability above,  to it  I  set  wage.  (lndu/lndf)  elasticities  I  are  model.  Letting  does  increase  the  efficient  elasticities Martinello  5.2.2  the  estimates  are  still  of  under  the  .9876  for  the by  As  two  ones  smaller  LDEM  found  Dertouzos  for  the  labour  results  and  demand union's  mentioned  unilaterally  labour  model demand  and 0 . 7 7 8 f o r  all  bargaining  elasticities  the  those  the  power  especially  however, than  by  exogenous  exogenous c a p i t a l  have  model,  and  estimated  COOP m o d e l  union  contracting  are  my s m a l l e r  the  demand  and D e r t o u z o s  Union In  labour  them  The r e s u l t i n g  the  the  of  union could  zero.  1.1644 f o r  LDEM  the  at  Both  and  the  re-estimated  set  the  a s s u m p t i o n s on t h e  For the  estimation. for  below  whether  different  that  bargaining  ( . 8 4 6 2 f o r LDEM and lie  greater  .7708  model.  ITU ( 1 . 2 3 ) .  wage.  assumed  are  IWA ( 1 . 5 )  verify  the  inefficient  elasticities  still  the  the  exogenous c a p i t a l  the  a r e due t o  was  choose the  and  COOP  estimates  (1981)  reflecting  elasticities  for  (1984)  elasticities  hour  exogenous o u t p u t  These  Martinello  i n the  demand  .8535  per  efficient  l a b o u r demands The  with  is  for  resulting  reported  by  Pencavel.  Preferences previous the  discussion,  firms'  technology  it  was were  seen very  that  the  different  125 depending  on  whether  exogenous  to  the  with  my  utility  two  utility  As utility  for  the  is  that  for  the be  models.  coefficient  on  the  coefficient  coefficient  of  and  employment LDEM  .487. .401  the  on  just  in  exogenous  I  is  .513  of  .71  exogenous  it  find  output  that  of  COOP and  with  a  (These for  the  output  in  COOP  1  model,  for the  greater  The  equals  output  employment  the  The  .8561.  significance  For  the  contracting  is  exogenous  F o r t h e LDEM m o d e l ,  the  similarities  substitution  slightly  respectively.  in  in  efficient  of  term.  coefficients  models  the  1% l e v e l  now  employment  .599  in  the  similar  exogenous o u t p u t c a s e .  elasticity  wage  the  consistent  however,  very  some  LDEM m o d e l ,  The w e i g h t is  be  as  differences.  in  the  the  is  are very s i m i l a r i n the  rejected  at  function  with  than i n the  and  rejected  utility  the  to  are  treated  study  coefficients,  substitution  .8768,  bargaining  to  found  important  technology  could not  now  find  more so of  hypothesis  are  that  estimates  parameter estimates  elasticity  which  were  was  This  m  Although there  parameter  LDEM m o d e l s ,  model  parameters  I also  capital  b a r g a i n i n g process.  scenarios.  estimates,  is  or  M a r t i n e l l o ' s f i n d i n g s . 35  union the  output  both union  than  the  model,  the  c o r r e s p o n d i n g wage these  coefficients  should  be compared  COOP  and  .85  estimation.)  for The  M a r t i n e l l o (1984) assumed a l l i n p u t s and t h e o u t p u t t o be endogenous i n h i s p r o f i t f u n c t i o n e s t i m a t i o n a n d he assumed an e x o g e n o u s o u t p u t i n h i s c o s t f u n c t i o n e s t i m a t i o n . 3 5  126 hypothesis accepted  of  at  equal  the  weights  5% l e v e l  on employment  of  significance  and  (W-W^)  is  now  for both bargaining  models. The  marginal rate of  workers  and wages  percentage  terms  .15  for  the  exogenous  in  the  the  in  capital, model  above  COOP m o d e l output  the  is  y=l)  is  was  also  5.2.3  the  the  and  small.  rejected true  mean o f  for  the  LDEM m o d e l .  it  i n the  the  both  the  The  contract  mean o f  the  steeper  than the  assumption contract  data  of  COOP  representation slopes  were  capital  is  curve for been  average  exogenous  of  curves  negative  and  have  large  in  and  small  of  curves at  large  positive  5.  for  (p=l  and This  data  data  value  at  is  case,  the  a  good as  points.  other  much the  sample  some  while  the  under  was  however, slopes  at  It  that  over the  all  exogenous  absolute  bargaining  estimated  the  as  in  exogenous  evaluated  Figure  Also,  contract  treated  COOP m o d e l  output.  the  two  a  estimation.  curve  mean  increase  maximization  contract  the  for  Bargaining Sets  plotted  at  positive  contract  the  As  is  union for  with  the  in  data  and LDEM m o d e l s .  exogenous o u t p u t  has  curve  in  rent  T h e C o n t r a c t C u r v e and t h e  the  However,  MRS's  the  a larger  compensate  Finally,  for  takes  workers.  in  expressed  the  LDEM m o d e l t o  difference  very  .20  wage  number o f  at  estimation,  number o f  between t h e  alternative  and c a l c u l a t e d  wage i n t h e  1% f a l l  substitution  When of  slopes  data  the  the are  points.  127  Over  the  sample,  sawmills  in  general,  the  bending the  if  1973  the  In was  ceteris is  exogenous the  This  also  exogenous c a p i t a l . than  the  1981  and  observations, both the  the  COOP  iso-profit  union  for the and  both  for  the  indifference  curves.  to  bargaining  solution  This  are  years  of  less  ensures  and  the  data  the  early of less  in  1980 ,  Ignoring  these  everywhere the  COOP  convex that  that  be  wage  wage i s  the  the  for  model,  than  second  problem d e s c r i b i n g  satisfied  will  assumption  sawmills  for  demand  predicted  are concave and,  zero,  (Re).  of  models.  to  curve  few  the  In  backward  labour  predicted  everywhere  maximization  a  interior  LDEM m o d e l s are  for  the  be  the  the  under  bargaining  to  interior 1968.  on l a b o u r  recession  bargaining sets  conditions  is  wage  curves  the  wage  case  in  contract  estimation,  the  the  mills  to  coefficient  Specifically,  alternative 1983  to  the  for  an MRS e q u a l  identical  output  -671.8  likely  With  3 6  alternative  is  more  paribus, the  corresponding  '80's.  be  from  shingle  is  small.  would  the  for  curve  MRS i s  smaller  than  varies  106.9  the  less  points  to  curve  Also,  flatter  slope  contract  contract  curve.  the  the  order Nash  equilibrium  unique.  More specifically, in this have a n e g a t i v e s l o p e i f J 6  will  model,  the  contract  curve  128 5.2.4  Bargaining Powers Contrary  parameters,  to  models.  different For  the  more same  The  results  are  also  same  that  with  coefficient  the  which  coefficients  for  the  has  a  the  counterparts  in  coefficients  in  both  u t i l i t y  strike two  costs  bargaining  between estimated  concerning  the  inventory  firm's  same  exception  the  the  the under  of  relative  in  the  the  has  costs.  determinants  exogenous  demographics  output  variable  perverse  but  insignificant  LDEM m o d e l  are  more d i f f e r e n t  the  large  exogenous  output  standard  estimations,  errors  their  the  inventory  strike  costs  firm  output  now  i n average  strike  as  the  exogenous  variable  an i n c r e a s e  the  in  given  in  results  as  the  increase  qualitatively  however,  the  concerning the u n i o n ' s  estimation  the  s i m i l a r i t i e s  implying that  will  on  union  assumptions.  the  except  and  b a r g a i n i n g model  model,  are  sign  holdings  their  the  COOP  costs  opposite  are  different  technological  estimation  The  very  There of  technology  coefficients  are  coefficients  strike  the  the  determinants  3 7  sign. from  estimation; on  variability  these is  not  so s u r p r i s i n g . The costs the  average  (lndu/lndf)  COOP m o d e l .  3 7  See  value of is  term measuring r e l a t i v e  .8949 f o r t h e  As was  footnote  the  33.  the  case  strike  LDEM m o d e l and 2 . 1 0 6 1 for  the  exogenous  for  output  129 estimation, contracts monopoly  The  the  firm  efficient. and  solution for  of  (as  the  the  to  different  firm  bargaining  costs, power  exogenous  LDEM m o d e l . is  in  these  5.1)  very  the  slowly  rapid  increase  in in  complete  LDEM m o d e l w h i l e 2/3  the  closer  to  weight  over the  the  .2.  In  late  1960's  early  the  i n the  union's  relative  i n the  COOP m o d e l .  .8375 r e s p e c t i v e l y  .5277  These  and  1970's  f o r the  union  i n 1984  power  according to its  maximum  compared t o  a  the is  utility  LDEM m o d e l and  exogenous o u t p u t  by  achieves  The a v e r a g e u n i o n  be  the  followed  The u n i o n  f o r the  should  COOP and  l a b o u r demand  the  r e l a t i v e u n i o n power a t  sample i s  the  affecting  cases  1980's.  COOP m o d e l .  Despite  COOP m o d e l e s t i m a t e ,  both  c o n t r o l o v e r wages  are  variables  similar  l a r g e r than the  also  They  6.  on  Nash  were  model.  in Figure  of  discount  The w e i g h t s  section  exogenous  is  larger  union i n the  capital  profile  time  averaging  the  p e r f o r m e d and  T h e u n i o n b a r g a i n i n g power i n t h e  rises  the  the  everywhere  difference  on t h e  over  of  Nash  and t h e  described  coefficients  strike  when  symmetric  the u n i o n .  f o r b o t h b a r g a i n i n g models  almost  Tests  the  are  power  for both bargaining models.  relative  functions  calculated  for  be  less  exogenous c a p i t a l e s t i m a t i o n y i e l d s  utility  model  to  ( l n d u / l n d f ) =1  are rejected  bargaining  the  relatively  (lndu/lndf)=0  solution  for  plotted  has  assumed  model  hypothesis  the  union  are  bargaining  factors  the  .8913  estimation.  .3220 and  130  6  Figure  Union Bargaining Exogenous C a p i t a l  Power.  Estimation.  a. C o o p e r a t i v e Model  coastal sawmills  shingle mills  plywood and veneer m i l l s 1364.0  1  1966.0  1  1968.0  1  1970.0  1  1972.0  1  ^974.0  —I  1976.0  1  1978.0  1  1960.0  1  1982.0  a _•u b. Labor  Demand Model coastal sawmills  interior sawmills  plywood and veneer m i l l s  1970.0  1972.0  1974.0  TIME  1  1984.0  131 It the  is  interesting  union  rents  and  firm  between  estimation, union  was  rents  it  it  as two  of  was  seen  to  the  the  contract  is  and  in  model  the  the  division  exogenous  bargaining  This  given  is  of  still  true  for  the  for  The p r o p o r t i o n o f  VIII  of  proportion of  i n Table VII for the  Table  of  output  power  when m e a s u r e d by t h e  capture.  firm  with  in  u n d e r exogenous c a p i t a l .  by t h e  b a r g a i n i n g powers  above  them.  that  underestimated  estimation  compare  measured  the  succeeded  captured  to  the  the rents  efficient  labour  demand  curve. On model the  average,  and  firms  83% i n  firm  as  the  captured  LDEM m o d e l .  measured  by  Nash b a r g a i n i n g s o l u t i o n the  LDEM m o d e l .  over  the  However,  with  proportion during  of  the  consistent  the  is  is  not  the  rents  evident  exception  years  rapid  Tables  interior firm  of  the  the  efficient  model value.  in  the When  for  contract sense  model  that  output  the  is  it no  VII  COOP  in  and  of the  VIII.  sawmills,  the  substantially  1980's  and  this  is  i n u n i o n b a r g a i n i n g power  C o m p a r i n g t h e COOP and LDEM M o d e l s case  utility  fell  5.2.5  the  the  COOP m o d e l and 47% i n  those years  was  Figure  its  during  As  (see  on  in  of  increase  in  i n u n i o n b a r g a i n i n g power  c a p t u r e d by t h e  recession  with the  weight  rise  rents  The b a r g a i n i n g power  68% i n t h e  The g e n t l e  1970's  77% o f  6).  exogenous performs  generates longer  output better a  used  estimation, than  higher as  an  the  LDEM  likelihood explanatory  132  Table VII P r o p o r t i o n o f T o t a l Rents  C a p t u r e d by t h e  C o o p e r a t i v e Model w i t h Exogenous  Firm  Capital  Year  Coastal Sawmills  Interior Sawmills  Shingle Mills  1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983  .74880 .80234 .81928 .81880 .80743 .79035 .78127 .80159 .83279 .83166 .82508 .83462 .78420 .80739 .79446 .78648 .73643 .72202 .68826 .60260  .82466 .88400 .89641 .88980 .87658 .84419 .87310 .88317 .88068 .86472 .87030 .90171 .86755 .86251 .85348 .83982 .91261 .98679 .90225 1.01554  .78684 .82541 .83191 .81860 .80092 .77868 .75429 .80895 .81736 .80659 .81825 .81784 .76305 .78170 .77085 .75432 .78749 .77092 .72923 .62893  .65592 .74559 .76808 .77545 .75927 .77011 .77290 .80389 .82067 .81259 .82484 .84606 .80948 .79832 .80681 .77218 .78223 .74739 .66790 .65400  Average  .78079  .8865  .78411  .76968  O v e r a l l A v e r a g e = .76692  Plywood Veneer  133  Table VIII P r o p o r t i o n o f T o t a l Rents  C a p t u r e d by t h e  L a b o u r Demand M o d e l w i t h E x o g e n o u s  Firm  Capital  Year  Coastal Sawmills  Interior Sawmills  Shingle Mills  1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983  .83630 .85970 .87056 .87158 .87050 .86362 .85637 .86852 .87147 .86502 .86398 .87227 .85015 .85565 .84673 .84156 .84015 .84198 .82862 .81952  .86966 .89976 .90588 .89942 .89194 .86426 .88969 .90226 .88892 .87651 .88497 .90417 .87767 .86819 .85904 .85597 1.10236 1.10372 .94375 1.07388  .86711 .91029 .88378 .88096 .87339 .85733 .85336 .87547 .86671 .85630 .86081 .87496 .83377 .83897 .83387 .82865 .85337 .85113 .83383 .80887  .79415 .82874 .84198 .85160 .85086 .86414 .86553 .88099 .87625 .87016 .87816 .88412 .86731 .86286 .85828 .85061 .86201 .85419 .83032 .84253  Average  .85471  .91810  .85711  .85574  O v e r a l l A v e r a g e = .82992  Plywood Veneer  134 variable,  the  Although  there  is  better  during as  at  the  i n the  1980's  one  COOP  models  labour;  as  an  however,  labour cost The  is  under  powers  labour  evidence  it  shares  technology  compared  yielded less  a flat  than  5%.  the  data  is  its  counterpart  estimation  is  employment  not  as  strong  the  coefficient  the  also  model yielded The  the  contract This  variable  did  respect  result  the  very  product of  of  for  small  labour  substitution  capital  curve with  an a v e r a g e  3 and  to  5.1.1.  exogenous  was  for  estimates.  the This  elasticity  of  evaluated  at  the  mean  of  it  be  compared  to  should  endogenous o u t p u t  illustrated  the  values  Figure  of  output.  increase  with  was  was  estimation  low  revenue  all  predicted  implausibly  curve  i n the  the  exogenous  especially  contract  drawn i n  which i s  of  reported i n section  marginal  to  i n the  assumption  explanatory  had  in  on l a b o u r w h i c h  standard error the  of  coefficients  and  a c c o m p a n i e d by a l a r g e m a r g i n a l r a t e union  LDEM m o d e l  i n wages and  significant  coefficients.  small  the  estimation.  the  were  a large  model  predictive  the  exception,  output  the  considerably.  Results  small with  Using  behavior  recession,  The e x c e p t i o n  very  worsens  some i n d i c a t i o n t h a t  p r e d i c t i n g the  estimation  sign.  still  employment  exogenous o u t p u t  With  the  is  Summary o f  5.3  4  prediction of  in Figure  -  exogenous 5.  capital  135 The curves  closeness  in Figure  technological output  is  utility  two  to  the This  the  the  labour  similarity in  In g e n e r a l , to  also  the  the  imposition is  demand  b a r g a i n i n g models  sensitive  qualitative were  the when  estimated  imposition  of  a  true  of  different  of  the  union  when  output of  bargaining  is  ranging  curves  from  exogenous,  .86  the  the  data  In  to  likelihood; Also, the  the  1.05.  supports  of  i.e., in  of  the  the  contract  union In  The  and  and  all  be  models,  for  union of  output  is  a Cobb-Douglas  efficient  contract  convex  treated  rejected.  in  the  model, as  sense  improved  rejected  c u r v e was w e l l - d e f i n e d  as  specification  always  is  the  either  has  bargaining variables  (lndu/lndf)=0  but  substitution  b a r g a i n i n g model  the  quite  exogenous,  elasticity When  is  estimation  rejected the  with  difference  wages  capital  Rent m a x i m i z a t i o n i s  introduction  exceptions,  all  with  the  models.  exogenous o u t p u t  cannot  hypothesis  be r e j e c t e d .  The  employment  i n the  models.  indifference  on  weights  across  on e m p l o y m e n t .  endogenous  the  concerning  b o t h wages and employment  placed  placed  and s i g n i f i c a n t  equality  about  being  weights  results  consistent  union cares  large  models.  the  more  than  the  function  between  the  in  endogenous.  been  a l a r g e r weight  that  an i n d i c a t i o n o f  framework.  of  the  cannot  of  parameters.  Many  cases,  as  output  bargaining  similarity  parameters  have  exogenous  utility  5 is  treated  parameters  and  in  all  with  few  the  locus  136 of  tangency  points  indifference of  curves  utilities  uniqueness  was  of  observations the  (i.e.  wage).  1980's  results  output  frequently  but  power  often  by  the  bargaining union early  used  as  by  weight  was the  was d e t e c t e d .  t r e n d was  zero  found  ensures  all  involved  point  than the  in  space  inconsistent  threat  the  exogenous  with  for  the  alternative  LDEM m o d e l  output,  predicted profits  this  due t o  for  c a p t u r e d by t h e  on t h e  profit  Although  firm  of  the  during  in  (interior relationship  of  function  the  the  firm, firm  b a r g a i n i n g power  reflected  no monotone  estimates  were  an i n d i c a t o r  the  solution.  1980's  general,  a  were  rents  b a r g a i n i n g power  captured  union  with model  the  low  on l a b o u r .  overestimated  defined  and  condition  The e x c e p t i o n s  of  with  The p r o p o r t i o n o f is  latter  and t h e y  yielded negative  coefficient  which  The  p r e d i c t e d wage was l e s s  Similar  endogenous  iso-profit  bargaining f r o n t i e r i n the  assumption  the  the  equilibrium.  the  maintained  union  and t h e  concave.  the in  between  rapid  union  sawmills between  exogenous  capital  bargaining  power  hypothesis  of  estimation  closer  equal  1970's.  to  the  the  the  two  in  the  of  the  firms'  power  in  measures large  a downward  measures  was  rents  yielded  and  as  Nash  excepted),  T h e endogenous  yielded  b a r g a i n i n g powers  in  firms  proportion of  b a r g a i n i n g power  i n d i c a t e d over the  the  years  The e x o g e n o u s o u t p u t e s t i m a t i o n the  bargaining  increase  recession the  a measure  output,  of  union  although  rejected  for  the both  137 bargaining  models.  There  upward t r e n d d u r i n g t h e It  is  1970's  increase in the  powers  all  severe  recession position  probability  of  the  across  profiles  models,  One p o s s i b l e  precarious  firms  time  i n u n i o n power d u r i n g t h e  cases.  and t h e  1980's  relatively worsening union.  of  of  union are  the  firms'  for  an  this  placed  If  unanticipated  and  where  if  could  be  found  is  is  in  the of  union  would  is  imply  relative  a  the  severity  a  to  the are  and  risk  aversion  to  test  this  used  that  that  the  sharing  uncertainty  is  an  increased  the  bargaining position  of  firms  possibility  sharing.  the  1960's  result  and g r e a t l y  risk  of  the  recession  1980's  Another  averse,  formulated  of  indication  1980's  early  risk  was  risk  A model  explicitly  the  bankruptcy.  more  evidence  over  the  reason  financially,  recession  some  although the magnitudes  and t h e i r  varied  also  1970's.  worth n o t i n g that  bargaining and  was  second  hypothesis. The the  coefficients  relative  strike  are seen to vary standard  rate  relative  strike  costs  (and h e n c e  In has  a  costs  the  significant of  the  utilization ratio.  depends  on t h e sign  technology on t h e  firm.  variables  the  and t h e y  efficient  capital  negative  exogenous  a c r o s s models  errors.  interest  on t h e  affecting  b a r g a i n i n g powers)  often  have v e r y h i g h  contracting model, positive  effect  The same i s  The e f f e c t assumptions.  of  inventory coefficient  on  the  true of  the  inventory  Note t h a t  the  build-up  although a  was p r e d i c t e d ,  a  138 positive  relationship  unanticipated  increases  unanticipated, hardship cost)  for  changes the  the  strike  standard large  variables  If  case they  can i n d i c a t e a  strong  of are  financial  (low  strike  are  highly  variable these  the  workers' but  Also, of  they  the  firms  not  were and  variables  costs.  to  workers  the  large is  the  among  the  Some  contribute made  of  with  especially  strike  did  attempts  coefficients  other  additional  estimate  the  separately  but  successful.  than  this  the a  estimation  that  the  during the  study,  labour  larger  indication  overall,  holdings.  the  of  factors  generating some  model  multicollinearity  Throughout better  the  than  One p r o b l e m w i t h  were u s e d  none were  rather  of  information. discount  inventory  demand  errors.  determinants  in  in  in inventories  variables  amount  plausible  position.  labour  cost  also  firms  bargaining In  is  the  demand  likelihood  especially although  labour  recession  of  model  model  in  value.  in  the  demand years  efficient  the  Finally  the  performed sense there  exogenous  COOP m o d e l  model  was  a  the  1980's.  performed better  of was  output better  predictor  139 Chapter 6 Conclusion  In model  this is  study,  used  Specifically, generate the  to  the  wage  a version  and  study  costs  of  the  the  employment of  the  contracts  Rubinstein  union-firm  equilibrium of  characteristics  and employment  of  the  estimating  negotiations.  game  negotiating  parties  is  used  equations.  r e s u l t i n g model  are affected  bargaining  is  by t h e  even  in  One  that  the  relative the  to of  wage  strike  absence  of  strikes. The the at  data  involves  IWA, a p o w e r f u l capturing  quantities demands the  negotiated  the  and  have  includes  equations  are  and  to  estimated  employment  can  scenarios  unilaterally  contract  case  frontier  industry  been input  and  successful and  output  representing  input  simultaneously  equations.  two p o l a r c a s e s have b e e n assumed:  resulting  each  data  products  with  In  the  on wage and employment d e t e r m i n a t i o n i n u n i o n i z e d  firm  second  believed  supply  wage  B . C . wood  The  prices  and o u t p u t  sectors,  union  rents.  and  literature  the  of  the the  are  level  on  the  of  and  framework  labour  employment  bargaining set  modelled  bargaining  technological  is  choose  is  the  estimated is  assumptions.  employment demand is  in  one  negotiated  and  the  in  the  and  the  curve.  this  paper.  under  two  case,  instance  curve,  contract  estimated In  i n one  all  Both Also,  sets  inputs  of are  140 chosen the In  optimally  level the  of  as  studies  estimated  of  output  here  is  quite  parameters  are  estimates.  employment thing are  is  ranging is  and i t  reasonable  union  study.  estimates  from  .86  to  rejected  as  bargaining  while  process.  capital  is  it  is  cares  the  e m p i r i c a l model that  and  union  and  comparable  about  both  wages  on e m p l o y m e n t .  to in and  The same  indifference  In a l l models,  the  utility  a standard r e s u l t  elasticity  appropriate  contract  reassuring  The u n i o n  of  1.05.  an  and  the  is  coefficients  the  i n the  contract  empirical union  F o r example,  that  with  the  endogenous  but w i t h a l a r g e r weight  found  convex  novel  generally  literature  labour  a b a r g a i n i n g game,  technology  this  is  previous  estimated  previous  the  negotiations.  the  included  of  exogenous t o  during  none  had  is  case,  fixed  Since  functions  output  second  treated  as  curves  of  substitution  rent  maximization  representation  of  union  behaviour. The firms strike costs  new  results  and t h e  u n i o n measured  costs.  In  all  significantly  individual  concern  affects  the  to  the  technology  assumptions.  b a r g a i n i n g powers  rejected  as  well  as  the  on  b a r g a i n i n g powers  functions the  sensitive  equal  as  models,  coefficients both  the  term  strike  (the  all  their  cost  cases  the  Nash b a r g a i n i n g  monopoly m o d e l  of  strike  However,  variables  framework  the  relative  representing  estimates.  bargaining In  of  of  are  and  the  hypothesis  of  solution)  is  unions  (in  which  141 the  union  has  suggest  complete  that  the  deterioration According performs is  chosen  by  the  than the  interpretation  modelled model  performs  labour  in  employment  the  different  this  of  of  study  Since  this  noncooperative  especially particular,  at  Also,  be e x p l i c i t l y and s t r i k e s  the  cost  concerning the  as  than  to  assumption uncertainty  formulated.  of  was  is  cooperative  some  indication  predicting the  a first  and  1980's.  in  several  attempt  the  the  at  the  empirical  game was  kept  assumptions  structure.  In  information could  and b e h a v i o u r  e q u i l i b r i u m outcomes.  that  wages  early  possible  information  not  the  restrictive  T h i s would  is  estimation)  symmetric  for  wage-employment  contracts,  of  the  implications  b a r g a i n i n g models t o  wage and employment  simple  are  with  assumptions  although  at  labour  to  technology  output  better  i n which  seem  of  there  model  consistent  serious  the  power.  estimates  recession years of  directions.  application  relaxed.  to  overall,  is  d u r i n g the  Extensions  which  exogenous  model  is  results  Finally,  better  demand  studies  in  rapid  contracting  parameter  the  studies  this  T h i s has  a  bargaining  technological  of  rigorously.  (especially  very  the  the  results  caused  efficient  Again,  framework.  determination  the  However, to  relative  Also,  l a b o u r demand m o d e l  firm.  sensitive  power).  recession  firms'  estimate,  the  bargaining  19 80 ' s  the  studies.  more  the  my  better  previous be  to  in  bargaining  towards  allow  for  risk  risk  be  could  sharing  Secondly, emphasized  the  strike  costs  believe  that  be  other  both  of  Rubinstein  contracts  and  this  study  and  firms.  the In  employment  only,  fringe  account.  Also,  this  bargaining  framework  nesting  and e f f i c i e n t  of  particular, costs,  between game  it  I  will  different  and  from p r o b l e m s empirical  particular, and  does the  has  possibly  well.  two  not  have  available  cases  models.  of  taken  include  polar  contracting  is  dimensions  are  not  which  wage-employment data  other  benefits  study  game  measuring  In  strike  bargaining  literature.  as  and  empirically  suffers  of  particular  modelling  b a r g a i n i n g games as  such  demand m o d e l s  this  modelling of  the  characteristic  wages  unions  discriminate  types of  of  better  to  determination on  for  through the  Thirdly, been  application  need for  possible  versions  the  a of  the into  general labour  143 Bibliography  Abowd, J . M . ( 1 9 8 7 ) , " C o l l e c t i v e B a r g a i n i n g and t h e D i v i s i o n o f t h e V a l u e o f t h e E n t e r p r i s e , " NBER W o r k i n g P a p e r No.2137. A l l e n , R . C . (1985), " T r a d e U n i o n s and t h e B . C . E c o n o m y , " B.C. Economic P o l i c y I n s t i t u t e Paper No. P - 8 5 - 0 4 , Department of Economics, University of British Columbia, Vancouver, B . C . A l l e n , R . C . and W . E . D i e w e r t ( 1 9 8 1 ) , " D i r e c t V e r s u s I m p l i c i t Superlative I n d e x Number F o r m u l a e , " T h e R e v i e w o f E c o n o m i c s and S t a t i s t i c s , V o l . 6 3 , N o . 3 . A s h e n f e l t e r , 0 . and G . E . J o h n s o n ( 1 9 6 9 ) , " B a r g a i n i n g T h e o r y , T r a d e U n i o n s , and I n d u s t r i a l S t r i k e A c t i v i t y , " A m e r i c a n Economic Review, V o l . 5 9 , N o . l . Azariadis, C . (1981), "Implicit Contracts and R e l a t e d T h e o r i e s : A S u r v e y , " i n Z . H o r n s t e i n e t . a l . ( e d . ) , The E c o n o m i c s o f t h e L a b o u r M a r k e t , L o n d o n , HMSO. Binmore, K. (1987a), B i n m o r e and P . Bargaining, Basil  "Nash B a r g a i n i n g T h e o r y I , " i n K . Dasgupta ( e d s . ) , The Economics of B l a c k w e l l , New Y o r k .  Binmore, K. (1987b), B i n m o r e and P . Bargaining, Basil  "Nash B a r g a i n i n g T h e o r y I I , " i n K . Dasgupta ( e d s . ) , The Economics of B l a c k w e l l , New Y o r k .  Binmore, K. (1987c), "Perfect Equilibria in Bargaining M o d e l s , " i n K . B i n m o r e and P . D a s g u p t a ( e d s . ) . The E o n o m i c s o f B a r g a i n i n g , B a s i l B l a c k w e l l , New Y o r k . Blair, D . H . and D . L . C r a w f o r d (1984), "Labor Union Objectives and C o l l e c t i v e Bargaining," Quarterly J o u r n a l o f Economics, V o l . 9 9 , N o . 3 . Brown, J . N . and 0. A s h e n f e l t e r , (1986), "Testing the Efficiency o f Employment C o n t r a c t s , " Journal of P o l i t i c a l Economy, V o l . 9 4 , N o . 3 . Card, D. (1986), "Efficient Contracts with Costly Adjustment: S h o r t - R u n Employment D e t e r m i n a t i o n for A i r l i n e M e c h a n i c s , " The A m e r i c a n Economic Review, Vol.76, No.5.  144 C a r r u t h , A . A . and A . J . Oswald ( 1 9 8 3 ) , " M i n e r ' s Wages i n Post-War B r i t a i n : An A p p l i c a t i o n o f A M o d e l o f T r a d e U n i o n B e h a v i o r , " The Economic J o u r n a l , V o l . 9 5 , No.380. Chatterjee, K . and W. S a m u e l s o n ( 1 9 8 3 ) , " B a r g a i n i n g U n d e r Incomplete Information", Operations Research, V o l . 3 1 . Copithorne, L. Disparities,  (1979), N a t u r a l R e s o u r c e s and R e g i o n a l Economic C o u n c i l o f Canada, Ottawa.  Coursey, D. (1982), "Bilateral Bargaining, Pareto O p t i o n a l i t y , and t h e E m p i r i c a l F r e q u e n c y o f I m p a s s e , " J o u r n a l o f E c o n o m i c B e h a v i o r and O r g a n i z a t i o n , V o l . 3 . C r a i g , A . (1986 ) , T h e S y s t e m Canad a , 2nd e d i t i o n , Scarborough, Ontario.  of I n d u s t r i a l Relations in Prentice-Hall, Canada,  C r a m t o n , D . C . ( 1 9 8 4 a ) , The R o l e o f Time and I n f o r m a t i o n Bargaining, Ph.D. Thesis, Stanford U n i v e r s i t y .  in  Cramton, D . C . (1984b), "Bargaining with incomplete Information: An I n f i n i t e - H o r i z o n with Two-Sided U n c e r t a i n t y , " The R e v i e w o f E c o n o m i c S t u d i e s , V o l . 5 1 , No.167. Crawford, V.P. Bargaining,"  (1981), "A T h e o r y o f D i s a g r e e m e n t Econometrica, V o l . 5 0 , No.3.  D e M e n i l , G. (1971), B a r g a i n i n g : Monopoly P o w e r , MIT P r e s s , C a m b r i d g e , M a s s .  Power  vs  in  Union  Denny, M. , M. F u s s , a n d J . D . May ( 1 9 8 1 ) , "Intertemporal Changes in Regional Productivity in Canadian Manufacturing," Canadian J o u r n a l o f Economics, Vol.14, No. 3. Dertouzos, J . N . and J . H . P e n c a v e l (1981), "Wage a n d Employment D e t e r m i n a t i o n U n d e r T r a d e U n i o n i s m : The International Typographical Union," Journal of P o l i t i c a l Economy, V o l . 8 9 , N o . 6 . E a t o n , C . ( 1 9 7 8 ) , "The W o r k e r and t h e P r o f i t a b i l i t y o f t h e S t r i k e , " I n d u s t r i a l and L a b o r R e l a t i o n s R e v i e w , V o l . 2 6 , No.l. E b e r t s , R . W . and J . A . S t o n e ( 1 9 8 6 ) , "On t h e C o n t r a c t C u r v e : A T e s t o f A l t e r n a t i v e Models o f C o l l e c t i v e B a r g a i n i n g , " J o u r n a l o f Labor Economics.  145 F a r b e r , H . S . ( 1 9 7 8 ) , " I n d i v i d u a l P r e f e r e n c e s and U n i o n Wage Determination: The Case o f t h e U n i t e d Mine Workers", J o u r n a l o f P o l i t i c a l Economy, V o l . 8 6 , N o . 5 . F a r b e r , H . S . ( 1 9 8 6 ) , "The / A n a l y s i s o f U n i o n B e h a v i o r , " in Ashenfelter and L a y a r d ( e d s . ) , Handbook o f L a b o r E c o n o m i c s , V o l . 1, N o r t h H o l l a n d , New Y o r k . F o l e y , B . J . and R . T . Maunders ( 1 9 7 9 ) , A c c o u n t i n g I n f o r m a t i o n Disclosure and C o l l e c t i v e B a r g a i n i n g , Holmes and M e i r P u b l i s h e r s , New Y o r k . F u d e n b e r g , D . , D . L e v i n e , and D . A . Rudd ( 1 9 8 5 ) , "Strike Activity a n d Wage S e t t l e m e n t s , " U n i v e r s i t y of C a l i f o r n i a mimeo. F u d e n b e r g , D . , D . L e v i n e , and J . T i r o l e ( 1 9 8 5 ) , "InfiniteH o r i z o n Models o f B a r g a i n i n g w i t h O n e - S i d e I n c o m p l e t e Information," i n A . R o t h ( e d . ) , Game T h e o r e t i c M o d e l s o f B a r g a i n i n g , Cambridge U n i v e r s i t y P r e s s . F u d e n b e r g , D . and J . T i r o l e ( 1 9 8 3 ) , " S e q u e n t i a l Bargaining Under Incomplete Information," Review o f Economic S t u d i e s , V o l . 50. Gul,  F . a n d H . S o n n e n s c h e i n ( 1 9 8 5 ) , " U n c e r t a i n t y Does N o t Cause D e l a y , " S t a n f o r d B u s i n e s s S c h o o l Working P a p e r .  H a l e y , D . ( 1 9 8 0 ) , "A R e g i o n a l C o m p a r i s o n o f Stumpage V a l u e s i n B r i t i s h C o l u m b i a and t h e U n i t e d S t a t e s Pacific Northwest," Forestry C h r o n i c l e , V o l . 5 6 . Hall,  R . E . and D . M . L i l i e n ( 1 9 7 9 ) , " E f f i c i e n t Wage U n d e r U n c e r t a i n S u p p l y and Demand," A m e r i c a n Review, V o l . 6 9 , N o . 5 .  Bargains Economic  H a m e r m e s h , D . S . ( 1 9 7 3 ) , "Who ' W i n s ' i n Wage B a r g a i n i n g ? , " I n d u s t r i a l and L a b o u r R e l a t i o n s R e v i e w , V o l . 2 6 , N o . 4 . Hart,  0. (1986), p a p e r #423.  "Bargaining  and S t r i k e s , "  MIT d i s c u s s i o n  I n d u s t r y , T r a d e , and Commerce ( 1 9 7 8 ) , R e v i e w o f t h e C a n a d i a n F o r e s t Products I n d u s t r y , Ottawa. K e n n a n , J . ( 1 9 8 0 ) , " P a r e t o O p t i m a l i t y and t h e E c o n o m i c s o f S t r i k e D u r a t i o n , " J o u r n a l o f Labor Research, Vol.1, No.l. Lacroix, R. (1983), "The E f f e c t s of Strikes C a h i e r 8405, U n i v e r s i t y o f M o n t r e a l .  on  Wages,"  146 M c C u r d y , T . and J . P e n c a v e l (1986), "Testing Between C o m p e t i n g M o d e l s o f Wage and Employment Determination i n U n i o n i z e d M a r k e t s , " J o u r n a l o f P o l i t i c a l Economy, Vol.94, No.3. M a r t i n e l l o , F . F . ( 1 9 8 4 ) , "Wage and Employment Determination in a Unionized Industry: T h e IWA i n t h e B . C . Wood Products Industry," Ph.D. Thesis, U n i v e r s i t y of B r i t i s h Columbia, Vancouver, Canada. Mauro, M . J . (1982), "Strikes Information," Industrial Vol.35, No.4.  as a R e s u l t of Imperfect and L a b o r R e l a t i o n s Review,  McLennan, A . (1982), "A N o n c o o p e r a t i v e D e f i n i t i o n o f Two Person B a r g a i n i n g , " Department of Economics and I n s t i t u t e f o r P o l i c y a n a l y s i s W o r k i n g P a p e r N o . 8303, University of Toronto, Toronto, Ontario. O s b o r n e , M . J . ( 1 9 8 5 ) , "The R o l e o f R i s k A v e r s i o n i n a S i m p l e B a r g a i n i n g Model," i n A. Roth ( e d . ) , Game-Theoretic Models o f B a r g a i n i n g , Cambridge U n i v e r s i t y P r e s s . O s w a l d , A . J . ( 1 9 8 2 ) , "The M i c r o e c o n o m i c T h e o r y o f t h e U n i o n , " Economic J o u r n a l , V o l . 9 2 No.367.  Trade  P e n c a v e l , J . ( 1 9 8 4 a ) , "The E m p i r i c a l P e r f o r m a n c e o f a M o d e l of Trade Union Behavior," i n J . Rosa ( e d . ) , The E c o n o m i c s o f L a b o r U n i o n s : New D i r e c t i o n s , RluwerN i j h o f f P u b l i s h i n g Company. Pencavel, J . (1984b), "The T r a d e - o f f Between Employment i n Trade Union Objectives," J o u r n a l o f Economics, V o l . 9 9 , N o . 2 .  Wages a n d Quarterly  P e r c y , M . ( 1 9 8 6 ) , F o r e s t Management and E c o n o m i c G r o w t h i n B r i t i s h C o l u m b i a , Economic C o u n c i l o f Canada, Ottawa. R e d e r , M.W. and G . R . Neuman The Case o f S t r i k e s , " Vol.88, No.5.  ( 1 9 8 0 ) , " C o n f l i c t and C o n t r a c t : J o u r n a l o f P o l i t i c a l Economy,  Riddell, W . C . (1981), "Bargaining American Economic Review.  Under  Uncertainty,"  R i d d e l l , W . C . and P . M . S m i t h ( 1 9 8 2 ) , " E x p e c t e d I n f l a t i o n and Wage Changes i n C a n a d a , 1 9 6 7 - 8 1 , " C a n a d i a n J o u r n a l o f Economics, V o l . 1 5 , No.3. Roth,  A . (1979), Axiomatic Springer-Verlag.  Models  of  Bargaining,  New Y o r k ,  147  Roth, A. (1985), Game-Theoretic Cambridge U n i v e r s i t y P r e s s .  Models  of  Bargaining,  Roth, A . and F . Schoumaker ( 1983 ) , "Expectations Reputations i n B a r g a i n i n g : An E x p e r i m e n t a l S t u d y , " American Economic Review, V o l . 7 3 , N o . 3 . R u b i n s t e i n , A . (1982), "Perfect E q u i l i b r i u m i n a Model," Econometrica, Vol.50, N o . l .  and The  Bargaining  R u b i n s t e i n , A . ( 1 9 8 5 ) , "A B a r g a i n i n g M o d e l w i t h I n c o m p l e t e I n f o r m a t i o n About Time P r e f e r e n c e s , " Econometrica, Vol.53, No.5. S h a k e d , A . and J . S u t t o n ( 1 9 8 4 ) , " I n v o l u n t a r y Unemployment as a P e r f e c t Equilibrium in a Bargaining Model," Econometrica, Vol.52, No.6. Sobel, J . and I . T a k a h a s h i ( 1 9 8 3 ) , "A M u l t i s t a g e M o d e l B a r g a i n i n g , " Review o f Economic S t u d i e s , V o l . 5 0 . Siebert, W . S . and J . T . A d d i s o n (1981), "Are A c c i d e n t a l ? " Economic J o u r n a l , V o l . 9 1 , No.362. Svejnar, J . (1980), "On E m p i r i c a l T e s t i n g o f Zeuthen B a r g a i n i n g S o l u t i o n , " Industrial R e l a t i o n s Review, V o l . 3 3 , N o . 4 .  of  Strikes  the Nashand L a b o r  S v e j n a r , J . ( 1 9 8 6 ) , " B a r g a i n i n g Power, F e a r o f D i s a g r e e m e n t and Wage S e t t l e m e n t s : T h e o r y a n d E m p i r i c a l E v i d e n c e from U . S . I n d u s t r y , " E c o n o m e t r i c a , V o l . 5 4 . T r a c y , J . S . ( 1 9 8 6 ) , "An I n v e s t i g a t i o n i n t o t h e Determinants o f U . S . S t r i k e A c t i v i t y , " A m e r i c a n Economic Review, Vol.76.  148 Appendix A Data Sources The  appendix  sources data the  provides  is  referred to  P r i c e and Q u a n t i t y In  this the  section, input  described.  through  manufacturing.  electricity. stock  data  provided  the  B . C . wood  output  is  for  interior  plywood  and v e n e e r  mills.  this  Canada's  services  4  sawmills,  Most o f  breakdown  are of  on  and v e n e e r for  shingle  the  35-204  data and  output mills  groups  and  capital is  firms:  mills, published  35-206  and  and  shingle  is  three  data  of  is of  fuels  This  and in  with  the  materials  and  the  breakdown  mills  which  I would l i k e t o thank F . M a r t i n e l l o f o r with unpublished industry data. 8  data  census  and  input.  following  of  j  are  i n conjunction with  exception  supplies  prices  and  used  catalogues  and  data  supplies,  Canada  materials  industry  and  Statistics  plywood  products  and h e n c e i n p u t s  the  sawmills,  for  the  and d r a w b a c k s ,  specified,  Statistics  coastal  supplies  of  text.  quantities  otherwise  form a c a p i t a l  the  the  data  3  materials  separately  advantages  Chapter 5 of  The l a t t e r to  of  broader d i s c u s s i o n  on i t s  Industry costs  labour,  description  Indices 8  and  Unless  collected  types:  For a  i n c l u d i n g comments  reader  namely  a detailed  and m a n i p u l a t i o n .  set  A.l  and C o n s t r u c t i o n  on are  p r o v i d i n g me  149 unpublished. costs  are  Also,  published  exceptions,  the  construct  price  Martinello  the  input, of  the  was  (1984)  also  used  between t h i s of  some  study  the  arbitrary  period  has  in  been  to  here. and  capital  n o n - p r o d u c t i o n workers  w h i c h was  sample  With  Martinello  construction  data  electricity  and  Martinello  extended  to  1980-1983.  Output Data  on  shipments  price  the is  index  implicit factor  to  and v a l u e  construct group  index  is  test.  1971 for  of  of  index  for  the  Fisher  can  be  Fisher  types ideal  1963-83.  by  Fisher's  price  dollars the  different  chained  derived  Finally,  use  quantity  a  the  firms  then  constant  the  of  weak  index  using  the  direct price  found  The  in  was CPI. index  Allen  and  (1981)) shingle  processed"  mills,  shingles  amounts  were  shingles  and  1982  to  each  reversal  implicit  For  used  for  (Justification  Diewert  quantity  quantity  converted  for  the  the  the years  and  in  and  57-208.  in  industry data  are  fuel  indices  inclusion of  include  of  used  the  Also,  on  catalogue  quantity  i n the  (1984).  A.1.1  in  and  (1984)  scaling  details  methodology  The d i f f e r e n c e s  services  the  and  used.  was  the  quantity  not  available  Similarly  shakes  in  1983  and  coastal the  the  and v a l u e in  were  amounts  "further  and t h e  quantity  sawmills  1981  1983  of  and v a l u e not  were  1982 of  available  assumed  to  150 remain  constant.  coastal  Also,  sawmills,  the  1981  was u s e d t o  this  1980  Quebec and B . C . and t h e in  for  same  figures  type  were  breakdown between  estimate  separate  of  output  in  aggregated  these  2  provincial  for  provinces  amounts  for  1980.  A.1.2  M a t e r i a l s and S u p p l i e s The  price  procedure  and q u a n t i t y  input.  and v a l u e  processing  in  corresponding linearly  to  Price following  amounts  estimate  and  and  mills  for  1980  were and  the m i s s i n g  quantity  indices  were  fuel  natural  gas,  and e l e c t r i c i t y .  this  1983,  I n 1982  the  generate  and  supplies  and 1982,  used  for  the  further  available.  were  The  interpolated  was  and 198 3,  assumed  to  in  and  1982  To e s t i m a t e price  calculated fuel  oils),  Several  is  was  the  averaged  as  the it  using  petroleum  1980  were  included i n  the  The v a l u e  same p r o p o r t i o n  did  on  average  q u a n t i t y of kerosene  over  the  (kerosene,  problems  available.  constitute 1983  oils  liquified  kerosene  f o r which only v a l u e  category  and 1 9 8 1 .  to  values.  heavy  kerosene  1981  not  1983  and  other  for  shakes  light  category  1980  shingle  used  materials  gasoline,  encountered.  of  the  was  Electricity  and data  for  breakdown:  diesel,  for  of  above  encountered,  shingle  F u e l s and  gases,  indices  One p r o b l e m was  quantity  A.l.3  described  and 1981  was  in  in 1982  divided  151 into  the  estimated  (Averages the  last  over  the  year's  19 80 for  aggregated  divided  into  contributions these  of  sawmills two  these  figures. groups  of  above  and price  divided  by  by  being the  calculated  as  equal  for  to  using  in  1979  according to  the  the  interior  separately  divided  estimated  total  by  into  the  in  1981  follows:  ,81  electricity  costs  TC  total  and e l e c t r i c i t y  I  interior  IC  all  fuels  81  costs  sawmills  sawmills  i.e.  i n t e r i o r plus  coastal  the  costs two  described groups,  (aggregate)  sawmills  ECT C  in  the  two  For example,  were  adjusting  total  values  for  given  relative  changes  the  was for  values  the  and  the  with  was  quantity.  x  where E C  by  a common p r i c e  aggregate  electricity  sawmills  of  involved)  and e l e c t r i c i t y  The a g g r e g a t e  quantity  assuming  instead  s m a l l numbers  calculated  by u s i n g  used  q u a n t i t y and v a l u e was  groups  time  respectively.  were  fuel  groups  proportions  sawmills  of  only.  two  The aggregate  years  interior  component's  the  values  of the  costs  and  p r o p o r t i o n s over  corresponding  of  each  1983  previous  total  coastal  onwards, the  this  the  for  two  and  v a l u e because  Although available  1982  the  value costs  would  be  152  and where t h e electricity calculated  s u p e r s c r i p t denotes the used  as  by  interior  year.  sawmills  The q u a n t i t y  in  1981  would  of be  follows:  81  where EQ = q u a n t i t y Finally, the  cost  the  costs  generated other  of  these  as  noted  fuel  for  of  electricity by  small  firms  was n o t  establishments  and  for  their  included.  quantity  of  labour  man-hours p a i d which i n c l u d e s vacations  worked  and s t a t u t o r y  own u s e  was  pg.32),  included  also,  any  in  power  f r o m wood w a s t e  N o t h i n g c o u l d be done  compensation  number o f  compensation payments,  paid  man-hours includes  bonuses,  work  not  performed.  1971  dollars using  paid  to  paid  all  is  measured  time p a i d but  holidays.  by p r o d u c t i o n w o r k e r s  total  the  supplies,  (see,  or  about  Labour The  as  (19 84)  omissions.  A.1.4  as  consumed  Martinello  materials  by t h e  sources  of  only.  the  not  to  worked  T h e wage  are  is  before and then  hours  to  by  Total overtime  payments  converted  such  divided  deductions, other  of  calculated  production workers.  vacations  The wage i s  number  these  p r o d u c t i o n workers  wages  the CPI.  Also,  by  for  constant  153 An i n t e r e s t i n g measure firm  for  will  the  labour  care  process  number  workers  membership constant If  of  then  it  labour  contract  be This  group o f  in  Table  to  the  due  In  order  at  the  treated  It  mean  be  firms  IX.  substantial to  The  of  time  of  the  composed  remainder  distribution.  or  to  its  with  the  closely  the  worker  are  which u n i t  is  separately the  worker  to  were  1983.  being  of  hours  concerns  of  administrative  workers  employed  these workers  are not  three  analysis  are  presented  The These  of  is  only could  assumed  industry  of  is  non-  in B . C . ,  sales of  that  worker  and o f f i c e  part  are  overtime.  treatment  in  for  numbers  work p e r  wood p r o d u c t s  the  year.  it  the  wage,  calculated  elimination  tractable,  the  these  these  per  then  the  They  worker  chosen.  The b a r g a i n i n g  complicate  the  the  issue  For the  mostly  Since  per  into  per  respect  to  analysis  important  the  per  the  occur during recessions.  Another  is  hours  number o f w o r k e r s .  bargaining,  labour.  more  of  that  inputed  dimensions,  with  the u n i t  concerned  s u r p r i s i n g how c l o s e  constant.  this  three  f r o m 1963  a  production  is  of  argued  work  the  obviously  sharing  keep  of  be  negotiated  hours  deviations  to  is  1,96 3 h o u r s  work  as  is  can  difference  have  would  choice  reflects  If  conducted  substantially. each  this  no  and t h e  It  union  union.  will  hours per worker,  variables.  the  workers  the  hours  since  makes  number o f  then  the  while  the  the  would  input.  about  production of  issue concerns  staff, and  t h e IWA,  154  T a b l e IX Hours p e r Worker p e r Year i n t h e B . C . Wood P r o d u c t s Year  Coastal Sawmills  Interior Sawmills  1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983  2054 2074 2047 2059 2067 2056 2050 2006 2022 1952 1992 1980 1940 2038 2046 2040 2038 2058 1845 1831 1943  1960 2026 2022 2006 2003 2040 2025 2003 2026 2017 1992 2074 2022 2035 1992 1992 2054 2056 1909 1836 1968  Industry  Shingle Sawmills 1891 1683 1959 1925 1944 1917 1921 1931 1952 1866 1888 1951 1926 1957 1988 2068 2063 1901 1918 1829 1879  O v e r a l l A v e r a g e = 196 3  Plywood & Veneer M i l l s  2005 1991 1972 1894 1968 1963 1912 1893 1993 1951 1968 1903 1753 1751 1982 1954 1908 1977 1842 1599 1953  155 they  should  figures are  an  firm  not  be  entering  the  additional  and  in  the  a  small  the  profit  of for  input  proportion  are  labour,  by a f a c t o r  1.15,  labour  input  provided  A.1.5  Capital  its of  (1984)  calculate by t h e  capital capital  the  stock  in  services process.  the  production  stock i.e.  and the  the  as:  However,  they  process be  with  by  of  costs  salaries the  of  of  the  included  I  to  wages  account  production  average i n v e r s e salaries  more  and t h e  decided  production  and  are  non-production  number  increasing  labour  proportion  and w a g e s .  labour  in  of  Data  the  total  i n Table IX.  of  adopted  the  following  procedure  quantity  and  price  the  It  is  assumed  conjunction which More  quantity  output  be w r i t t e n  the  the  mills.  production mills'  wage  Services  Martinello  used  and  should  labour  wages i n t o t a l  magnitude  input  costs  respectively.  relative  to  function.  production  total  and  on t h e  is  employment  Non-production labour costs  labour  of  production workers'  the  labour  correlated  non-production  order  the  of  number  highly  production  costs  in  calculations.  the  in  union u t i l i t y  non-production  importantly, labour  Included  the  are  then  that  used  fuels  group  of  is  separable and  mills  to  as  it  at  form  inputs  is  uses units  in  assumed  in  electricity i  capital  each m i l l  energy  specifically,  function of  with  of  time  in  the  the that  capital  consumed, t,  Q^t  can  156  Table X Share  of  Production  Labour i n the  Year  1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983  Workers  in  B . C . Wood P r o d u c t s  Proportion of Production Workers in Total Employment in %  Overall Industry  Proportion of Production Workers' Wages in Total S a l a r i e s and Wages in %  Coastal Sawmills  Interior Sawmills  Shingle Sawmills  Plywood SVeneer  91 90 90 90 91 91 90 87 87 87 87 85 82 86 86 87 87 85 85 85 86  92 86 88 88 89 89 90 87 87, 88 89 86 87 89 89 88 87 87 86 85 86  93 93 93 93 93 93 93 94 94 94 93 93 93 93 92 94 93 93 92 91 93  90 90 90 91 92 92 92 91 91 90 91 90 90 90 90 90 91 89 88 89 90  Coastal Sawmills  88 87 87 87 88 88 87 83 84 83 84 82 78 83 84 85 84 83 81 80 82  Interior Sawmills  Shingle Sawmills  88 82 85 85 85 85 87 85 84 85 85 85 85 88 87 86 85 85 82 82 84  overal I average = 86.6%  91 91 92 92 91 92 91 93 93 91 90 91 91 91 91 80 91 91 91 86 86  Plywood SVeneer  87 87 87 87 89 90 89 87 89 88 88 86 85 87 88 88 88 86 84 84 87  157  Q±t = where  it< it-  F  E  M  it-  < it-  K  s  F is  the  production  E  is  the  labour  M is  the  quantity  Y  it>>  function  input of materials  and  supplies  S i s t h e c a p i t a l s t o c k ( t h e c o n s t a n t 1971 d o l l a r m i d - y e a r n e t c a p i t a l s t o c k m e a s u r e c a l c u l a t e d by S t a t i s t i c s Canada) Y is  the  quantity  of  fuels  and  electricity  K i s t h e (common) a g g r e g a t o r f u n c t i o n w h i c h has as i t s image Kj_-t, t h e q u a n t i t y o f c a p i t a l s e r v i c e s u s e d as i n p u t . The of  aggregator  function  assumed  to  take  the  form  a CES:  K. Firms  = (QY-P +  t  are  assumed  S-P  d-a) to  separability  assumption,  optimization  problem.  the  K is  r  minimize can  The  be  first  1 / 6  costs  which,  represented stage  by  given a  consists  the  two-stage in  solving  following:  (1)  min Y  p?  Y  t  i  t  +  p?  S  t  l  t  subject  to  K  i  t  £ K  it' it S  where K i s Y Pit p..  a fixed '""  s  is in  level  pri  c  e  of  of  capital  fuels  and  services electricity  t h e u s e r c o s t o f c a p i t a l ( t o be d e t a i l later in this section)  described  158 From  the  relationship  first  is  order  conditions,  the  following  derived: 6+1 a (1-a)  where of  the  the  RHS i s  'it  Data to  price of  on  converted  This  s  while data of  y  K.  technical This  the  as to  stocks  and  were c a l c u l a t e d  1971  energy  coefficients  described  the  6 to  equation  can  be  can  be  consumption  a and B .  data  is  using  and v a l u e  available  provincial figures stocks  separately.  is  The p r i c e the  for  of  CPI.  the  of  Data  available  The m e t h o d o l o g y  energy on  in  for used  was  capital  stock,  catalogue  and  group  Canada a r e u s e d  are unpublished.  not  and e a c h  capital  Canada  i n u s i n g the energy  breakdown t h e  The q u a n t i t y  f o r each year  previously.  dollars  quantity  on c a p i t a l  firms  substitution  it  capital  (1984) c o n s i s t e d and  of  by i n d u s t r y c o m p i l e d by S t a t i s t i c s  construct p .  =  energy  firms  stocks  it  function  estimate the  of  Y  as:  (2)  used  it  the marginal rate  aggregator  rewritten  S  to  S and 13-211  Unfortunately the by  four  groups  Martinello  c o s t s and e s t i m a t e s o f a  aggregate c a p i t a l  stocks  figures  and  159 obtain four the  separate  groups only  of  capital firms.  available  product  industry  mills.  Since  used  given  was  then,  new  4  t  an  mills. to  for  each  of Martinello's  capital  separate  data  time  stocks  aggregate data  of  in  all  has  the  research,  B.C.'s  four  become  of  wood  groups  of  available  on  Following M a r t i n e l l o ' s procedure, estimate  1 , / (l-a)\ — — In [ ']+ $+1 [ a J  -  the  system  subscript denotes sawmills  u-jt i s -  the  1963  However, unsatisfactory  it  / '  of  equations  the  p+r-  ln  (  1 6+1  + u 2t  it;  t h e sum o v e r c o a s t a l and s h i n g l e m i l l s ; term f o r e q u a t i o n j  and  mills; interior  and y e a r  t;  1983. results  i n the  p  uIt  4 d e n o t e s p l y w o o d and v e n e e r  error  to  P  Y \ it s  V  2 i  t  +  8+1  x  i t  the  , _ In Y 4t  1 . (1-a) , „ „ , In + In Z &+1 a  In ( Z S ) = i  where  on  estimates  below:  l n S  (3)  (4)  this  At the  data  p l y w o o d and v e n e e r I  services  sense t h a t  -a->  of the  the  estimation  constant  term  were  160 had  a large standard error  were  extremely  term  and  the  variable. implied  a  different  assumptions  correlation  i n the  Assumed s e r i a l correlation in Ujt  Not of  that the  error  a  is  0,  choice  of  reasonable  I  assume  energy  and t h e  groups  of  firms  =  time  serial  50.11805 51.2876 51.5514 53.9046  no r o l e  In  to  used  a  the  stock  the  order I  i n the same i s avoid  (constant)  denoted  the  arbitrary simpler  shares  across  interior  ratio  the  input  constant  sawmills,  true of  different,  relative  are  calculation  the  for three  sawmills  and  by G i s  then  as:  I  S  itPft  ( 4 ) above. periods.  sawmills  of  0 .9839 .9998 1  a,  coastal  '  I  where t h e n o t a t i o n i s and  degree  to  0.17695 -0.12787 -2.0458 -0.1285  that  This  according  Value of the In likelihood function  1.  capital  mills.  calculated  is  the  constant  Implied a  input while  if  approach.  a  below  the  Asymptotic t ratio  energy p l a y s  stock a  reported  of  for a  term Ujt-  capital services  t  estimates  concerning  capital  G  Various  258.65 -2.5587 -5.5745 -226.42  if  shingle  r e s u l t i n g estimates  are  Estimated C o n s t a n t Term  f i r s t order second order t h i r d order fourth order  and t h e  and  the  Note The  Y  itPit  same as  that  is  aggregate  shingle  mills  t h a t used  is  allowed  capital then  i n equations ( 3 ) to  stock  broken  differ  across  measure  for  down i n t o  the  161 capital  stock  according  Git  shingle A  is  it =  G  mills  "  G  t  f °  G4t for  x  Y  i  r  it  '  Pit  x  = coastal  can  the  3  groups  of  firms  P?t  and  also  be  interior  calculated  which a separate  function  Cobb-Douglas. function  capital  Specifically,  I  5  K  if  constant  S^t  sawmills  and  for  plywood  and  stock  measure  a  n  &  Y  it  k  it -  = TT?—  =  it  takes  is  returns c  a  n  D  e  assumption o f the  assumed to  scale  recovered  form that then  an  of  S  ii"  the  from G j _ f  X l t )  (P?t)  f  r  o  i=l,2,3,4;  function X l t  This  (p!t)  and  implies:  t=1963,...,1983.  is: (  1  "  X  i  t  )  (Mt)-  X  it  a  this  assume:  dual u n i t cost P t  which  Y  cost minimizing behaviour.  ^it  with the  K (Sif it)  exhibits on  <>  consistent  Furthermore,  coefficients  (6)  it  procedure i s  aggregator  The  of  available. This  and  each  mills. ratio  veneer  for  to:  S  where  measures  ( l - X i t J - ^ i t )  162 Quantity calculated groups vary  as  was  of m i l l s  (and  in  (1984),  of  r  (3)  is  ( r  t  is  +  d e  the  poor  of  to  capital  think  this powers  is of  calculation  P^«  is  found  of in  In M a r t i n e l l o  Pt  x  interest Weir  rate  10  This  is  available  depreciation  as  the  ratio  allowance  of  to  the  by t h e bond in  which  is  mid-year series  for  are  Bank  in of  calculated  consumption gross  capital  unpublished.  allowance plywood  confidentiality  McLeod,  yield  the  capital  consumption  separately to  rate  the  Both these  capital  measured  industrial  the  due  6it  random e r r o r  and h e r e  capital  is  mills  I  four  as:  Pt>  available  the  predicted  explanatory  (1984)  Review,  The  of  by a l l o w i n g  between t h e  Canada  stock.  each  were  (4).  cost  Canada.  that  (1984).  the  calculated  "  for  services  some u n e x p l a i n e d  difference  Young,  dep  °f  and  user  (6)  Note  in Martinello  the  capital  calculating  "t  of  serious  services  Pit where  ne  for  and  Martinello  s u c h as  this  (5)  am n o t  because  A second  measure  I  hence K^t)  done  regressions  the  indices  and e a c h y e a r .  time,  preferable  capital  price  from equations  across  stocks  and  and  was  not  veneer  and h e n c e  was  163  p  1  calculated  for  industry.  It  the  four  is  the  the is  assumed  groups o f p r i c e  expenditures  on  total  B . C . woods to  be  product  equal  across  firms. in  1971$  plant  and  for  c a p i t a l  equipment  for  the  wood p r o d u c t s i n d u s t r y i n Canada p u b l i s h e d i n 13-211.  The  difference  study p ^  are two-fold.  measured  by  subtracted Secondly, is  the  In  from the  sum o f  price  index  used  by  Statistic's  of  However, sawmills to  assume  of  firms.  firms due  to  index  will a  this  be  the  aggregation  The u s e r  the  goods  of  mix  of  is  equal  the  stock.  for  each  of  investment.  those  c a p i t a l which  used  inflate  interior  for  and  costs.  which I  to  are  CPI  and  of  I  the  coastal  i n c a p i t a l stock measures,  index cost  in  Canada  different  this  c a p i t a l gains  different  to  price  in  current value c a p i t a l  due  and s h i n g l e m i l l s  cost  and d e p r e c i a t i o n  investment  to  user  change  interest of  the  expected  proportional  the  this  p?^. and  Firstly,  value c a p i t a l stock  theory,  groups  the  index  constant  between  I  three  have  groups  calculate  is  then:  c u r r e n t v a l u e Sit. x c o n s t a n t v a l u e S^t for  i  = interior mills;  or  i  = p l y w o o d and v e n e e r  and t  =  and  1963,...,1983.  ( r + dep  CPIt+i - CPIt CPI t  coastal mills,  sawmills  and  shingle  164  A.1.6  Input Cost Shares In t h i s  cost  section,  shares  because o f  of  the  First, the in  final  rule  indices  observations  for  0.25  to  two  statistics divided  indices services units and  this by  the  thirds. the  study,  I  input  their  input cost for  the  value  represented  price  and q u a n t i t y XI,  to  by  the  indices  stock  by u s i n g  value  of  0.15  for  to  this  profits  of  one  materials  units  will  the  capital also  have  the  fuel  for  recover  the  of  the  quantity  of  Trade  principal  of  b a s e w h i c h was u s e d  product  most  2.44.  example,  simple  of  share  share  For  indices the  the  bases.  is  for  from  natural  It  quantity  an I n d u s t r y ,  calculations  capital  hoc  materials.  the  (common) and  shares  used  an ad  positive  a materials  price  between  and  recover  and  constructed.  adopted  were  the  especially  and t h a t  price  labour averages  quantity  respectively.  Table  (1984)  i n d u s t r y shows t h a t of  study  output  gives  and  a difference  in this  and 0 . 5 9  Also,  share  electricity  In  out  profits  which  profits  i n p u t w h i c h was  and  that  of  interesting  were f o u n d c o m p a r a b l e  using  equal to  indices,  is  point  input  report  of  value  Martinello  for labour,  by t h e  In  to  and w h i c h y i e l d e d  Commerce  half  like  ensured  The s h a r e s and  This  services  (1984).  which  capital,  the  i n p u t - o u t p u t d a t a used  Martinello  scaling  inputs.  would  Profits  I examine  capital  I  and  and the  capital  price dollar  services  base. net  of  the  capital  165 services  input  are  presented  along  with  average  input  cost  shares. It of  is  the  6 out  data, of  the  the  4 groups for  s e e n f r o m T a b l e XI t h a t  of  firms  price  electricity,  costs  and  of  as  in  the  equal  for  the  electricity  costs It  study  data  the  With of  total  are  assumed  respect capital  to  indices  to  the the  statistics  used  in  this  for  this  data,  for  and  quantity variations  in  principal  the  same  data  had  the  as  the  prices the  product  inputs/output  that  shares,  the  reflect  will  input/output  d i v i d e d by t h e  cost  in  breakdown  Therefore,  for  the  the  omitted  for the  costs/revenue  input  price  these  yield  reported  in  were  of  not  detailed  reported  available.  services  the  and  shipments  does  in  fuel  The r e a s o n  The  and  remark i s  for  and  omitted  that  in  components  generated  was  in principal  and  data  in  costs.  revenues  real  1981  industry.  and  w h i c h was  all  and r e v e n u e s  data  were  for  indices  detailed  various  were n e g a t i v e sawmills  various  costs  p r i c e and q u a n t i t y  reported  share  the  breakdown p r o p o r t i o n a l l y  detailed of  on  but  supplies,  establishments  this  statistics.  and  all  One i m p o r t a n t  quantity  scaling  for  coastal  1970.  total  of  are p o s i t i v e  Profits  for  This  statistics  and  total  same  the  small  fuel  indices in  materials  omission  example,  in  and  revenues.  principal the  1982,  from d a t a  same t o t a l s  is  in  sawmills  The  constructed  profits  84 o b s e r v a t i o n s .  interior  order.  resulting  w i t h no a r b i t r a r y  we  study  as  base. find  that  which  is  the on  166 Table XI  a.  Profits  Net o f  Capital  Cost Shares  i n the  B . C . Wood P r o d u c t s  Services  and I n p u t Industry  Year  Coastal Sawmills  Interior Sawmills  1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983  5.0814 4.6299 4.4464 3 .9038 5.0662 9.9539 7.3163 2.7140 4.3482 6.8280 17.8310 7.7459 2.7964 5.9445 10.9838 13.7170 14.1214 4.4582 -0.6781 -2.6144 2.8261  5.3954 5.9050 5.5079 5.1897 4.2921 9.7280 6.8809 -0.7919 4.3150 14.9517 22.2486 6.3443 3.7848 12.4591 20.2602 27.5161 24.6231 9.9658 0.9772 -7.4137 6.6433  0.4839 0.1917 0.0798 0.1598 0.2146 0.7732 0.3570 0.0146 0.4380 0.9887 0.9518 0.2522 0.6186 0.9955 1.0770 1.1051 0.4968 0.6999 0.2111 -0.1204 0.0292  2.1561 2.0707 2.2390 1.8437 2.7318 2.7873 3.1189 0.5368 2.2939 4.3251 4.9872 2.3548 2.4648 4.1137 3.0932 6.2824 3.5657 1.8470 2.0271 -1.2103 0.7207  6.2581  8.9896  0.4770  2.5881  Average  O v e r a l l Average  b.  Average Input  Shingle Mills  P l y w o o d ai Veneer Mi:  = 4.5782  Shares  o f T o t a l Costs Labour  O v e r t h e Sample  Materials & Supplies  Period  Capital Services  C o a s t a l Sawmills I n t e r i o r Sawmills Shingle Sawmills P l y w o o d and V e n e e r M i l l s  0.25611 0 . 2 9 382 0.36352 0.32653  0.70713 0.61477 0.59451 0.61847  0.03676 0.09140 0.04196 0.05500  Average  0.31000  0.63372  0.05628  167 average  6% i s  This  made up by  is  on a v e r a g e ) is  much l o w e r  and t h e  interesting  this  respect.  larger  for  services  is  interior  a noticeable in  benefiting the  the  flaws  that  the  sawmills  and  that  are  for  more  the  two  the  the  in  sawmills  in  opposite  groups  with  the This  prices  are  of  true  of  capital sawmills,  Also,  there  materials  interior is  is  p r i c e and  of  of  intensive.  share is  price  price  price.  timber  It  services  the  two  the  areas  lower  that  while  (31%  (63%).  The r e s p e c t i v e  capital  difference  share  interior  capital  while  [15].  labour share  higher  on  and  sawmills  consistent  l a r g e amount o f h a r v e s t i n g and h e n c e  forest In  i)  from  the  and s u p p l i e s  show  the  hypothesis  due t o  materials  comparable  sawmills  supplies  both the  and s u p p l i e r s s h a r e .  indices  by M a r t i n e l l o  in  compare c o a s t a l  interior  quantity  used  increases  We f i n d  the m a t e r i a l s  is  to  than that  the  with coast  low y i e l d  of  lands.  conclusion,  i n the There  would  i n d u s t r y d a t a as is  impact  I  on  no  like  as  mention  compiled for t h i s  accounting  profits  to  of  corporate  a whole  and on  two  study.  taxes the  important  and  user  their  cost  of  capital. ii)  The a s s u m p t i o n o f very and  restrictive supplies  exogeneity of especially  since  companies which a l s o  some  in of  engage i n  the  input prices  the  case  the  mills  logging.  of are  c a n be  materials owned  by  168  A.2  T h e A l t e r n a t i v e Wage The a l t e r n a t i v e  wage W  W. = ( p „ x H E A E s+m vC  where  p^  + (l-p„)  the  the  service  the  employment  in  these  i-  s  the  B.C. wood  in  products  income as  vacations  is  the  to  pay  and the  unemployment the  unemployment weeks as  of  this  given  of  by  by  hourly  manufacturing in  in the  alternative  not  collecting  This  divided  total  worked  such  and h o l i d a y s .  benefits  of  in  divided  average  time  unemployed. weeks  of  wage m e a s u r e  for  p r o b a b i l i t y of  insurance  either  force.  weighted  industry,  includes  in  ratio  sectors  labour  services  Similarly  by t h e  two  provincial  employment  / CPI  manufacturing s e c t o r s  measured  total  follows  finding a job  is  earnings  PUi  or  as  x Ul) '  M T  This  the s+m  C  probability of  B.C.  H E  calculated  x p U1  x  o i i n  is  is  A  in  is  the  calculated  total  force  The in -  as  worker  of  total  B.C. is  is  t h e number  insurance number  B.C.  unemployment  (B.C. labour  that  unemployment  in B.C. weeks  of  number  of  calculated  B . C . employment)  *  52. Ul  is  the  average  insurance  h o u r l y payment o f  i n B . C . adjusted  unemployment  f o r tax  treatment.  169 (For  the  calculation  Riddell  and  resulting  factor  and  was  the  tax  [1982 ] .  UI payment  adjustment 1979  Smith  of  is  was  factor,  Note  pre-tax.  constant  that  the  Also,  available  assumed  see  only for  this up  to  1979  to  1983. ) CPI  They  the  Consumer P r i c e I n d e x  to  the  base o f  Both  HE  were  converted  average  s  +  other  and  m  weekly  manufacturing in  is  1965.  figure  This  is  alternative  reported  as  hourly  numbers  with  of  work  was u s e d  wage  few  the  as  in  goods i n  weekly the  1971.  figures.  use  of  B . C . manufacturing.  because  alternative  alternative  the  the  of  very  actual wage  this  are  finding of  wages  with  the  poor  turned  sawmills  the The  coverage  are  wage 0.01$  very in in  of  interior  p r o m p t e d me t o across  the  this  small.  1964  in  of  be and the  to  the  inconsistency  are  differences  sawmills  look  to  1964  wage  (The  and  province  o f d a t a were f o u n d :  out  interpretation  minimum a c c e p t a b l e  •70's. Three sources  wage  interior  occurrences  magnitudes  the  distribution  the  inconsistent  Arguably,  However,  were  r e a l wage i n  union.  between  a CPI b u n d l e o f  industries.  than the  and  to  hours  Surprisingly, greater  UI  w h i c h c o n v e r t s WA  0.03$ for in  and  in data  the  the  1965 ) . on  '60's  the and  170 i)  The A n n u a l B.C.  S a l a r y and Wage R a t e S u r v e y c o n d u c t e d  Bureau o f  1957-1966. along and  Wages  with  the  number  that  left  for  full-time  7 blue  Labour similar  iii)  to  occupations  Statistics employees different  Salary the  except  all  for  industries  It  interior  interior that The  a  sawmills gap  being  with  differences  in  to  through the  wages  the  the  conducted  by  The d a t a  is  of  the  coastal  whole  across  for  sets  for  of  data  during the and t h e the  early  4  saw  are '60's  coast  provincial '70's.  real  sample  areas  all  1984.  below  gone by t h e  behaviour  compared  remains  to  interior  consistently  almost  the  include  available  c a n be s e e n t h a t  the  consistent  not  were  centres.  for these three  with  is  did  Earnings  are  a gap between wages i n t h e  gap was  and  a more l i m i t e d number  Weekly  was  This  Office  considered  1971-1973.  there  average.  and  o f B . C . f r o m 1967  i n Table XII.  occupations  The wages  geographical  Average  Descriptive Statistics provided  not  and Wage R a t e s  period  (i)  Canada  regions  only  period  surveyed.  occupations.  and fewer  and  were  the  the  bonuses.  of  in  over  selected  employees  employees  over  that  of  for  occupations  or s p e c i a l  Canada  given  collar  The B . C . Survey  of  were  professional  overtime ii)  E c o n o m i c s and S t a t i s t i c s  by  wage mills  in  could  that be  This in  the  except case. due  to  Table XII Wage D i s t r i b u t i o n A c r o s s B . C .  a.  Government o f B . C . A n n u a l Wage R a t e S u r v e y . Employment weighted averages over 7 blue c o l l a r occupations. Sample p e r i o d 1 9 5 7 - 1 9 6 6 . 1  1957 - 1966  Metro. Vancouver  Metro. Victoria  Southern Interior  Northern Centres  Provincial Average  Average  2.21  2.24  Minimum  1.84  1.89  1.89  2.12  2.11  .8953  1.0521  1.67  1.86  1.85  .8685  Maximum  2.62  2.63  1.0049  2.25  2.53  2.51  .9177  1.0720  2  3  Int. Weight Co 1.3/Col.5  Coastal Weight Cols.1+2/Col.5  Notes: ioccupations: Labourer, Labour foreman. A u t o m o b i l e mechanic, Equipment o p e r a t o r (Heavy), d r i v e r , Medium t r u c k d r i v e r .  Southern  Penticton,  interior and V e r n o n .  Centres:  Northern Centres: Prince T e r r a c e , Q u e s n e l and S m i t h e r s . 3  b.  Labour Canada, B . C . Survey weighted averages over 3 Sample p e r i o d 1 9 7 1 - 7 3 .  1971 - 1973 Vancouver  Average  4.16 3.73 4.63  Minimum Maximum  Carpenter, Light truck  Kamloops,  Rupert,  Kelowna,  Prince  George,  o f Wage R a t e s . Employment blue c o l l a r occupations.  Victoria  Kamloops  Prince George  3.99 3.59 4.35  3.93 3.56 4.13  4.01 3.68 4.38  1  Provincial Average 4.02 3.64 4.37  Int. Weight Col.3/Col.5  Coastal Weight Cols.1+2/Col.5  .9796 .9410 1.0198  1.0128 1.0049 1.0281  Notes:  truck  ^-Occupations: L i g h t d r i v e r , Labourer.  and h e a v y  truck  driver,  Industrial  172 Table XII  c.  (Continued)  Statistics Canada, Average Weekly Earning. employees. I n d u s t r i a l Composite. Sample p e r i o d 1984. C a t . 72-002. Vancouver  Victoria  Kamioops  All 1967-  Prince George  Provincial  Int. Weight  Coastal Weight  Average  Col.3/Col.5  Cols.1+2/Col.5  1967-70 Average Minimum Maximum  121.27 109.69 113.91  107.60 97.49 17.31  107.05 93.40 18.44  127.15 115.36  115.77 103.99  .9237 .8982  .9888 .9807  139.26  127.23  .9424  .9962  1971-73 Average Minimum Maximum  161.48 148.86 174.47  137.99 128.39 148.75  149.96 133.38 162.11  165.22 143.10 181.82  165.66 138.43 166.79  .9755 .9635 .9912  .9751 .9549 1.0014  1974-84 Average Minimum Maximum  302.38 194.41 420.31  334.16 167.38 461.97  322.46 180.67 432.58  282.39 205.66 382.13  310.35 187.03 412.59  .9613 .9423 1.0187  .9699 .9569 .9856  173 imperfect living is  labour  f o r example.  larger  than  in  i n the  difference mix  mobility  of  the  is  We a l s o  data  total  or  on  find  blue  earnings  s u r p r i s i n g given  occupations  that  can  in  the  cost  i n Table XII that  selected  employees  not  differences  collar  data. the  this  there  differences between  place  to  gap  occupations  That  exist  of  is  in  the  a  the  various  centres. Although  I  any i n d i v i d u a l this  trend  by  linear  blue 1,  weights was  fixed  multiplied  similarly  of  by  wage for  the  A strike data  the  for  by  much i m p o r t a n c e  to  take  wages and  two  the  once  these  rest  of  XIII.  weight  alternative  coastal  areas in  the  reached These  interior  weight  to  sawmill and  I  sample.  wage  wages  B.C.  weights  the  on  account  weights  The  interior  into  across  average  alternative  coastal  given  the  the  Table  the  The r e s u l t i n g  Strike  of  Also,  in  faced  firms are also  A. 3  d i d want  interior  of  there  presented  alternative  I  the  occupations.  are  workers.  for  interpolation  were  to  equalization  weights  collar  they  want  observation,  of  constructed  d i d not  yield  the  workers  and  coastal for  the  sawmill 4  groups  i n Table A - 6 .  Costs  discussion costs  sources  can and  of  be  the  found  choice in  the  calculations  of  variables  text. are  In  given.  affecting  this  section,  The  following  174  Table Interior  Year  1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983  and C o a s t a l W e i g h t s ,  Weights Interior Coastal  0.9102 0.9179 0.9256 0.9334 0.9411 0.9488 0.9566 0.9643 0.9720 0.9798 0.9875 0.9952 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000  XIII  1.0449 1.0414 1.0378 1.0343 1.0307 1.0272 1.0236 1.0201 1.0165 1.0130 1.0094 1.0059 1.0023 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000  Coastal  Sawmills  2.81883 2.86624 2.97213 3.01436 2.92198 2.97409 3.09719 3.17544 3.37840 3.48673 3.55525 3.67669 3.87980 3.89204 3.98790 3.85113 3.78325 3.87554 3.90708 3.92880 3.79753  and A l t e r n a t i v e  A l t e r n a t i v e Wages I n t e r i o r Sawmills  2.45545 2.52633 2.65080 2.72030 2.66797 2.74710 2.89446 3.00174 3.23050 3.37246 3.47811 3.63758 3.87090 3.89204 3.98790 3.85113 3.78325 3.87554 3.90708 3.92880 3.79753  Wages  Shingle, Plywood & Veneer M i l l s  2.69771 2.75229 2.86387 2.91440 2.83494 2.89523 3.02578 3.11287 3.32356 3.44199 3.52214 3.65512 3.87090 3.89204 3.98790 3.85113 3.78325 3.87554 3.90708 3.92880 3.79753  175 v a r i a b l e s were u s e d costs  over  t o measure v a r i a t i o n s  in relative  strike  time:  INT = T h e  nominal  rate  m e a s u r e d by t h e yield in  average  the  INV = T h e  change  in  the  plus  of  in  inventories  costs  of  fuel  shipments  available  averaged  calculated  from  cat. is  35-204 equal  and e l e c t r i c i t y  in  35-206)  value  plus  minus  expressed  industry  and  to  the  terms  the  added  costs value  of  of of  '0,000's  current dollars  CU = T h e  Bank  available  of  Canada  from  the  capacity  Bank  of  r a t e was m u l t i p l i e d by 10 UN = T h e unemployment catalogue  insurance the  rate  in  utilization  Canada  review.  for estimation BC.  rate The  purposes  (Statistics  Canada  71-201).  UIC = A m e a s u r e  of  is  wood p r o d u c t s  supplies  INV i s  It  inventories  is  the  Canada  and  as  W e i r i n d u s t r i a l bond  of  This  change  materials  percent  Review.  value  Statistics  in  long-term.  5 years  BC ( S t a t i s t i c s  The  of  weighted  past  Principle  interest  McLeod Y o u n g ,  Bank o f Canada  over the  in  of  of  the  program.  labour  insurance unemployment  in  generosity_ It  is  force Canada  insurance  wage i n BC t i m e s  of  equal  the to  covered times benefits  unemployment  the  by the  proportion  unemployment r a t i o  of  to  the  average  a f a c t o r which takes  into  account  176 the  tax  treatment  tax  factor  is  alternative data  is  001.  the  same  in  only by  industrial  for the  total  available  from  with  under  25  which  is  under  25 was  the  in  Finally adjusted  The  not  exception  that  force  was  the  data  caused  correct adopted:  for  of  1966  for to  this  the  from  number -  to of  BC's  1963  to  the  major  1974 males  and  in  i n the  males  1965  25  is  Force  of  1966  under  following  under  Labour  Labour F o r c e Survey break  BC's  available  number  proportion  a noticeable  is  This data  from  the  for  wage  and men  f r o m 1963  1974  was  72-002.  the  males  7 3-  for  data,  ages  force  constant  insurance  wage  i n BC.  Also,  their  the  coverage  Canada's  available  which occurred i n the This  all  Statistics  in  average  firm  force  unpublished.  from  on  weekly  larger  BC's labour  assumed  labour  Canada  women o f  The  Canada c a t a l o g u e data  labour  used  Unemployment  average  of  benefits.  one  Canada c a t a l o g u e  DEM = The p r o p o r t i o n  Survey  the  the  composite,  from S t a t i s t i c s  i n the  as  Statistics  Unfortunately,  measured  was  unemployment  wage m e a s u r e .  given  available  25  of  it  total 1966 .  was  not  changes in  series.  procedure  1974. To was  177  where m.  =  m a l e s u n d e r 25 y e a r s i n area K i n year t  of  age  i n the  labour  v LF^. =  total  labour force  BC  =  British  C  =  Canada  t  =  1963  to  Columbia  1974.  i n area k i n year  t  force  

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0097185/manifest

Comment

Related Items