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UBC Theses and Dissertations

Export supply and import demand elasticities Lawrence, Denis Anthony 1987

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EXPORT SUPPLY AND IMPORT DEMAND ELASTICITIES By DENIS ANTHONY LAWRENCE B.Ec.(Hons . ) , A u s t r a l i a n N a t i o n a l  U n i v e r s i t y , 1977  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE  REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY  in THE  FACULTY 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  THE  standard  UNIVERSITY OF BRITISH COLUMBIA May 1987  (c) Denis Anthony Lawrence, 1987  A 6  In p r e s e n t i n g  t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of  requirements f o r an advanced degree a t the  the  University  o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make it  f r e e l y a v a i l a b l e f o r reference  and  study.  I further  agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may department o r by h i s o r her  be granted by the head o f representatives.  my  It is  understood t h a t copying or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l gain  s h a l l not be  allowed without my  permission.  Department o f  Economics  The U n i v e r s i t y of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date  1 June  1987  written  ABSTRACT The aim of which has  this thesis  been undertaken  u s i n g the  measuring export supply and and  imports are d i v i d e d  of e l a s t i c i t i e s  The  GNP  domestic  function  GNP  In  the second  then  In  represented  the  this  fixed  the  a  of  aggregate profit  output net  supply  outputs  are  supply. C a p i t a l  to  is for  1980.  four export and  components are i n c l u d e d by the use of aggregator p r o c e s s . The  thesis  of input-output data  Canada are used c o v e r i n g the p e r i o d 1961 In the f i r s t model estimated,  the  restricted net  sales  input. Time-series  two-stage e s t i m a t i o n  to  f u n c t i o n model.  aggregate  and domestic  o£  output. The  by  derivation  study  e x p o r t s , imports, labour t r e a t e d as a  approach  imports as an input to the  exports are an  be  facilitating  elasticities.  part  i s allowed f o r i n the GNP  f u n c t i o n framework t r e a t s  can  function  research  i n t o s e v e r a l components and d e t a i l e d s e t s  technology while  technology  the e m p i r i c a l  import demand r e s p o n s i v e n e s s . Exports  produced.  imperfect adjustment  i s to extend  four  import  f u n c t i o n s and  r e c e n t l y developed  a  Symmetric  G e n e r a l i s e d McFadden f u n c t i o n a l form which permits i m p o s i t i o n  of  the c o r r e c t c u r v a t u r e c o n d i t i o n s  is  used  at  both  aggregate in 1970 was  the  aggregator  while r e t a i n i n g and  GNP  function  export own-price supply e l a s t i c i t y was  while  the aggregate  -1.62. Increases  i n the  were found to decrease the  import  flexibility levels.  The  found to be  1.67  own-price demand  p r i c e s of both  imports and  f o r labour  was  labour  supply of exports while exports  found to be complementary to the output of domestic The demand  elasticity  found to  (ii)  be  were  s a l e s supply.  more e l a s t i c  than  in  e a r l i e r studies  and a  responsiveness  ln  general  the  own-price e l a s t i c i t i e s components were  t r e n d towards  Canadian for  stable  economy  the  and  four  was  export  of reasonable  increasing  price  observed. and  four  magnitude.  The import  A l l the  export and import components were found to be complementary. To remove the extended  to  assumption  two l a r g e r  function  models  aggregate  imports  outputs. Using  of  s e p a r a b i l i t y , modelling  disaggregated Generalised  containing  four  export  ( e x p o r t s ) , labour  this  procedure  export and import components was  McFadden  (import)  and domestic  more  was GNP  components, s a l e s as  net  between  the  substitution  found.  A p l a n n i n g p r i c e model whereby the producers' n o t i o n a l p r i c e adjusts  gradually  to  imperfect adjustment  actual is  price  in  that  the  traded  to p r i c e changes o n l y  over  period.  Finally, indicated  that  adjustment  was  an adjustment the  also variable  c o s t s model  effect  was estimated  allowing  import demand  for  i n the  was observed  short-run  labour demand. An i n c r e a s e i n  which  imperfect  between long-run  and  responsiveness  were  Considerable s u b s t i t u t a b i l i t y  the long-run  and  t h i s produced  between  labour  s i n c e labour  in  labour demand  c a p i t a l stock  i n c r e a s e d and  s h o r t - r u n labour i n c r e a s e .  (iii)  but  i n the  substituted  was  overshooting  export p r i c e s thus caused a  short-run increase was  of  use. D i f f e r e n c e s  supply and  r e l a t i v e l y small. in  main  on input  s h o r t - r u n export  and c a p i t a l  indicated  p a r t i c u l a r l y important  goods s e c t o r . Exports f u l l y a d j u s t e d an extended  changes  large  long-run  f o r much  of  of  the the  TABLE OF CONTENTS Abstract  ii  List  of  Tables  v  List  of  Figures  vii  Acknowledgement  viii  Chapter  1.  INTRODUCTION  1  Chapter  2.  PREVIOUS  5  Chapter  3.  A F L E X I B L E AGGREGATOR FUNCTION MODEL  STUDIES  13  3.1  The GNP F u n c t i o n Framework  13  3.2  Aggregator  20  3.3  Elasticities  3.4  Results  27  3.5  Conclusions  35  Chapter  4.  Functions Produced  26  F L E X I B L E DISAGGREGATED MODELS  48  4.1  The G e n e r a l i s e d  4.2  Results  52  4.3  Conclusions  57  Chapter  5.  A PLANNING  McFadden GNP F u n c t i o n  PRICE MODEL  5.1  The P l a n n i n g P r i c e  5.2  Results  Chapter  6.  49  65  Approach  65 69  AN ADJUSTMENT COSTS  MODEL  6.1  A Theoretical  6.2  An E c o n o m e t r i c A d a p t a t i o n  84  6.3  Results  90  6.4  Conclusions  96  Chapter 7.1  7.  CONCLUSIONS  E x t e r n a l Adjustment  80  AND FURTHER RESEARCH  Further Research  Model  80  105 107  Bibliography  111  A p p e n d i x 1.  DATA  Appendix  PRIMAL VERSUS  2.  Costs  116 DUAL ESTIMATION  ( iv)  129  LIST OF TABLES 37  Table 3. 1  SGM Parameter  Estimates  Table 3. 2  GNP F u n c t i o n E l a s t i c i t i e s  Table 3. 3  Export Supply  Elasticities  39  Table 3. 4  Import Demand  Elasticities  40  Table 3. 5  Labour Demand  Elasticities  41  Table 3. 6  Domestic Sales Supply  Table 3. 7  1970 Export Aggregator  Elasticities  43  Table 3. 8  1970 Import Aggregator  Elasticities  43  Table 3. 9  Export Component Own Supply  of T r a n s f o r m a t i o n  Elasticities  Table 3. 11 Import Component Own Demand  42  Elasticities  Table 3. 10 1970 Export Component Cross Supply  Elasticities  Elasticities  Table 3. 12 1970 Import Component Cross Demand  38  Elasticities  44 45 46 47  Table 4.1  GM Parameter Estimates  Table 4. 2  Export Model Own P r i c e  Table 4. 3  1970 Cross E l a s t i c i t i e s  Table 4 .4  Import Model Own P r i c e  Table 4. 5  1970 Cross E l a s t i c i t i e s  Table 5. 1  G e n e r a l i s e d L e o n t i e f Parameter Estimates  76  Table 5. 2  1970 Net Output Supply  77  Table 6. 1  Dynamic Parameter  Table 6. 2  1965 Net Output P r i c e  Elasticities  100  Table 6 .3  1970 Net Output P r i c e  Elasticities  101  Table 6. 4  1978 Net Output P r i c e  Elasticities  102  Table 6. 5  C a p i t a l - N e t Output Cross  Table 6. 6  Scale and T e c h n i c a l Change E l a s t i c i t i e s  59 Elasticities - Export Model Elasticities - Import Model  Elasticities  Estimates  Table Al .1 Aggregate P r i c e I n d i c e s  (v)  Elasticities  61 62 63 64  99  103 104 122  Table A l . 2 Aggregate Q u a n t i t i e s  i n M i l l i o n s of 1961 D o l l a r s  Table A l . 3 Export Component P r i c e  Indices  Table A l . 4 Export Component Q u a n t i t i e s  123 124  in Millions 125  of 1961 D o l l a r s Table A l . 5 Import Component P r i c e  Indices  Table A l . 6 Import Component Q u a n t i t i e s  126  in Millions 127  of 1961 D o l l a r s Table A l . 7 Adjustment Costs Model C a p i t a l Data  128  Table A2 .1 MACE Data  144  Table A2. 2 Cost F u n c t i o n C o e f f i c i e n t s  146  Table A2. 3 F i t s and Tests  147  Table A2 .4 E l a s t i c i t i e s of S u b s t i t u t i o n  148  Table A2. 5 Own P r i c e E l a s t i c i t i e s  150  (vi)  of Demand  LIST OF FIGURES F i g u r e 5.1  Adjustment of P l a n n i n g P r i c e s  78  F i g u r e 5.2  Adjustment of Q u a n t i t i e s  79  (vii)  ACKNOWLEDGEMENT in  completing  I am i n d e b t e d .  this  thesis  I would l i k e  Diewert,  John H e l l i w e l l ,  h e l p and  encouragement.  daughter,  Amanda,  provided did  not  to  thank  for  live  particular financial  to  my the  see  my  employer,  are  numerous p e o p l e  t h a n k my t h e s i s  T e r r y Wales and B r i a n I  their  encouragement  to  there  also  thank  my  to  whom  of  Erwin  Copeland for  their  committee  wife,  s u p p o r t and p a t i e n c e .  Mirinda,  and  My p a r e n t s  also  and s u p p o r t and p a r t i c u l a r l y my mother studies the  Industries  s u p p o r t d u r i n g the  completed.  Australian Assistance p e r i o d of  (viii)  Finally,  I would  Public Service,  Commission, my  studies.  for  and  who like in  generous  1.  INTRODUCTION T r a d i t i o n a l e m p i r i c a l trade models have t y p i c a l l y  attempted  to model export supply and import demand r e l a t i o n s by the use l i n e a r or l o g - l i n e a r  functions  of r e a l  income  traded goods r e l a t i v e to the p r i c e of domestic  and the p r i c e o f s u b s t i t u t e s . These  models have assumed t h a t e x p o r t s , imports and domestic be aggregated  goods  and have ignored much of the i n f o r m a t i o n  on the i n d u s t r i a l  s t r u c t u r e of  equation methods  has f u r t h e r  knowledge a v a i l a b l e  on the  the economy. The ignored  o b j e c t i v e of t h i s t h e s i s i s to extend of e m p i r i c a l trade  much of  properties  work which has  use of the  of demand  industrial  structure  of  single  theoretical  systems.  approximate the w e l l developed The  using  models  economy  and  more  and import  f u n c t i o n framework f i r s t function  closely  l i t e r a t u r e on trade theory.  framework  demand i s implemented treats  captured by by K o h l i  imports  using the  GNP  (1975, 1978).  The  as an input  p r o d u c t i o n technology and exports as an output of the thus e n a b l i n g the and demand The  with  i n f l u e n c e of the i n d u s t r i a l s t r u c t u r e of the economy on  export supply  GNP  The  the r e l a t i v e l y s m a l l amount  been undertaken  the  can  available  which i n t e g r a t e the supply of exports and demand f o r imports the  of  d e r i v a t i o n of an  to  the  technology  i n t e g r a t e d system of  supply  equations.  responsiveness of export supply and import demand i n the  Canadian economy i s c h a r a c t e r i s e d by a d e t a i l e d s e t of e l a s t i c i t y e s t i m a t e s . These e l a s t i c i t i e s provide i n f o r m a t i o n on the response of the economy to changes and  i n traded and non-traded  f a c t o r endowments. As such,  goods  the e l a s t i c i t i e s may be  1  prices thought  of as being analogous  to the standard trade t h e o r y r e s u l t s  except  that they show a more complex s e t of responses as we move o u t s i d e the standard 2x2x2 model and a l l o w f o r j o i n t p r o d u c t i o n . The e l a s t i c i t y estimates f o r exports and to be  of most  interest  in  f o r e c a s t i n g the  exogenous changes. For  i n s t a n c e , the  board  export s u b s i d y on  import t a r i f f  and domestic to the changes  or  outputs and  fixed  factor  on  the  imports are e f f e c t s of  e f f e c t s of  an a c r o s s  the  exports  import demand can be c a l c u l a t e d  (subject  supply). Similarly, to  factors  the can  effect be  favourable t a x a t i o n treatment  or  of i n t e r e s t  such  (eg. due  i n c r e a s e d u n i o n i s a t i o n ) on  supply of the v a r i o u s outputs and e x p o r t s , and elasticity  of  calculated.  A l t e r n a t i v e l y , the e f f e c t of changes i n f a c t o r p r i c e s  w i l l a l s o be  various  the supply of  return  be c a l c u l a t e d . The  likely  to those  the  import demand  estimates presented i n t h i s constructing larger  to  can study  applied  g e n e r a l e q u i l i b r i u m models of the Canadian economy. The GNP  f u n c t i o n framework of K o h l i i s extended  of d i r e c t i o n s  in  this thesis. F i r s t l y ,  each d i s a g g r e g a t e d i n t o s e v e r a l or  restricted  profit  unmanageable as more output and can be f a c i l i t a t e d applied  by  functional  by  Fuss forms  are  components explored  of  components. While the u s u a l  GNP  used  rapidly  becomes  input c a t e g o r i e s are allowed aggregator  which  have  f u n c t i o n s as recently  this first  developed  potentially  superior  t r a d i t i o n a l translog function.  allowing i s the  approach  Furthermore,  c u r v a t u r e p r o p e r t i e s to the now a l t e r n a t i v e means  are  the use of (1977).  number  imports  function  exports and  in a  for several  use of  2  export  An  and  import  l a r g e r disaggregated  models  which overcome the aggregator the f u l l  restrictive separability  f u n c t i o n approach  assumptions  but a t the expense of not  of the including  s e t of net outputs i n the one model.  The  second avenue e x p l o r e d  adjustment  in  the  GNP  l s the allowance  function  model.  This  for is  i n i t i a l l y by the use of p l a n n i n g p r i c e s as developed (1976, 1977). M o d e l l i n g i s then extended adjustment  model  as  developed  by  Imperfect  facilitated by  Woodland  t o an e x p l i c i t c o s t s  Berndt,  Fuss  and  of  Waverman  (1977). The data  used  i n the study are t i m e - s e r i e s of  data f o r Canada c o v e r i n g  the p e r i o d 1961 t o  a v a i l a b l e f o r 37 d i f f e r e n t output groups  and s i x  function  models.  end-users  and  The  four  1980. The data  i n d u s t r i e s but are aggregated  input groups output  types  input-output  for estimation  groups  are  of exports  sales  while  to  the advantage of  being d e t a i l e d , w e l l  developed  GNP  domestic  input  groups  c o n s i s t of four c a t e g o r i e s of imports, labour and c a p i t a l . t h i s data s e t i s l i m i t e d to 20 o b s e r v a t i o n s ending  five  of the to  the  are  While  i n 1980 i t has and  internally  c o n s i s t e n t f o r the e n t i r e p e r i o d . A brief  review of  previous empirical  s u p p l y and import demand i s presented this thesis.  The  flexible  r e s u l t s are presented and  export  i n the f o l l o w i n g chapter of  aggregator  i n Chapter  s t u d i e s of  function  model  and i t s  3 f o l l o w e d by the l a r g e r  import d i s a g g r e g a t e d models  i n Chapter  4.  Chapters  export 5 and  6  c o n t a i n p r e s e n t a t i o n s of the p l a n n i n g p r i c e and adjustment  costs  models, r e s p e c t i v e l y . F i n a l l y ,  areas  for future research i d e n t i f i e d  c o n c l u s i o n s are i n Chapter  3  drawn and  7. The data used  i n the  study are described contains  the  estimation  results  and l i s t e d of  a  i n Appendix 1  study  routes.  4  comparing  while primal  Appendix and  2  dual  2.  PREVIOU S A  STUDIES  b r i e f review of  import  demand  responsiveness  underlying theory chapter. In theory,  theoretical  of the  o n l y over  and  and  their  of i n t e r n a t i o n a l  spite  i tis  p r e v i o u s s t u d i e s of  well  i n t e g r a t e d approach  relationship  trade i s  developed  t h e l a s t decade  empirical  export supply to  presented  literature  u n d e r l y i n g t r a d e t h e o r y c a n be  this  on trade  and a h a l f t h a t  developments  the l i n k  the  in  have  enabled  both  a more  t o m o d e l l i n g a c t u a l e x p o r t s u p p l y and  demand. A good r e v i e w o f  and  import  between e m p i r i c a l s t u d i e s  found  i n Woodland  (1982,  and  Chapter  12) . Many t r a d i t i o n a l demand a n d domestic from  modelled  empirical  s t u d i e s c o n c e n t r a t e d on  imports as  final  p r o d u c t i o n s e c t o r . Assuming  other  modelled  commodities  as  afunction  goods and d o m e s t i c  demanded  goods n o t  of import  entering  that imports are then  import  p r i c e s , the  other  i n c o m e . I m p o r t demand was o f t e n m o d e l l e d  as a  i n spite  that this  cannot  maximising  be  d e r i v e d from  under v e r y r e s t r i c t i v e i n an  analogous  o t h e r goods from t h e r e s t  export  fact  behaviour  manner  u s i n g income a n d  the p r i c e o f  of the world. T y p i c a l of these (1969) i n w h i c h  studies  demand f u n c t i o n s  i m p o r t s a n d e x p o r t s f o r 26 c o u n t r i e s were e s t i m a t e d  the p e r i o d -1.46  utility  of the  c i r c u m s t a n c e s . E x p o r t demand c a n be  was t h a t o f H o u t h a k k e r a n d Magee for both  c a n be  p r i c e s of  r e l a t i o n s h i p of these v a r i a b l e s  modelled  the  separable  demand  log-linear  except  import  and  1951-66. F o r income  price  Canada a n  elasticity  elasticity  was  of  import p r i c e  1.20 -0.59  5  elasticity  were o b t a i n e d and  the  while  export  for of the  income  e l a s t i c i t y 1.41. Canadian  In  another  study Rhomberg  export demand e l a s t i c i t y t o be around  demand e l a s t i c i t y to be around demand  -1  (1964)  found  -2 and the  import  u s i n g a l i n e a r v e r s i o n of  the  relationship. An a l t e r n a t i v e s p e c i f i c a t i o n  for imports was used by Gregory  of the consumer demand  model  (1971). By assuming a CES u t i l i t y  f u n c t i o n the l o g a r i t h m of the r a t i o of import t o domestic becomes a analogous  function  of  the l o g a r i t h m  of  relative  demand  prices.  procedure w i t h i n a producer model was used by  Marsden and Z e i t s c h  (1977)  imported and domestic The CES f u n c t i o n  i n p u t s to v a r i o u s A u s t r a l i a n was a l s o used by  that the q u a n t i t y of a country's t o t a l  between  industries.  Hickman and Lau  (1973)  postulates  Imports i s a CES  function  of the q u a n t i t i e s of imports from each c o u n t r y . The import index i s  a l s o assumed  sourced from principles  to  c o u n t r i e s on  implicit  be a  CES  the b a s i s  i n the p r i c e  d i f f e r e n t c o u n t r i e s i n each  imports  of the  minimisation  cost  index. The model i s  of s u b s t i t u t i o n  linearised lags  demand f o r Canada  model  a  of 0.59 was  are from  market are obtained and  used  export demand f u n c t i o n s f o r  each  country. Using trade data f o r the p e r i o d 1961-69 and an e x p e c t a t i o n s dynamic  are  between imports  import  i n the d e r i v a t i o n of aggregate  price  f u n c t i o n and  f a c t o r s such as t r e n d s , e x p e c t a t i o n s and adjustment  allowed f o r . E l a s t i c i t i e s  An  Alaouse,  t o estimate the s u b s t i t u t i o n  w i t h i n an import a l l o c a t i o n model. T h i s type of model  and  the  s h o r t run  elasticity  adaptive  of  o b t a i n e d . The corresponding  run e l a s t i c i t y was estimated to be 0.84.  6  export long  The  first  e m p i r i c a l s t u d i e s to model import demand w i t h i n an  i n t e g r a t e d p r o d u c t i o n s e c t o r model were those of Denny (1972) and Burgess to  (1974a,  use  1974b). These s t u d i e s  flexible  functional  were a l s o among the  forms.  Burgess  (1974a)  first assumes  s e p a r a b i l i t y of the t r a n s f o r m a t i o n f u n c t i o n and models output a f u n c t i o n of the inputs of imports, c a p i t a l and t r a n s l o g share equations i s estimated  labour. A s e t of  f o r the US  f o r the  1947-68. The e l a s t i c i t y of demand f o r imports ranges -2.0.  An i n c r e a s e i n the p r i c e of imports was  wage/rental  p r i c e of c a p i t a l  Burgess  (1974b)  the  justified  aggregate  models import  production  by the argument t h a t  intermediate i n p u t s  which  to go  the use  of  are assumed to be an This  to the  undergo  further  processing consumer  and commercial  channels  output  (consumer  investment goods), three input ( l a b o u r , c a p i t a l and  imports)  t r a n s l o g cost f u n c t i o n model  substitution  f o r the  possibilities.  s u b s t i t u t a b l e with labour and p r i c e e l a s t i c i t y of the demand -0.66. Burgess j o i n t cost  (1976)  U.S.  f o r the Imports  were  found  to  f o r imports ranges from -0.51  uses a d i f f e r e n t  f u n c t i o n and  p e r i o d 1929-69  complementary to c a p i t a l . The  f u n c t i o n a l form f o r  d i f f e r e n t output  non-durables, and non-governmental the US  uses a two  is  constitute  consumer. Even imports of  through d i s t r i b u t i o n  a  input  assumption  i n many cases imports  before r e a c h i n g f i n a l demand. Burgess and  from -1.6  found to reduce  demand by  process.  have to  before being s u p p l i e d to the goods have  period  ratio.  t r a n s l o g j o i n t c o s t f u n c t i o n . Imports into  as  groups  be own to the  (durables  and  s e r v i c e s and s t r u c t u r e s )  for  f o r the s h o r t e r p e r i o d 1948-69. Import  7  to  demand e l a s t i c i t i e s  range for  from -0.19 labour  to -1.6  and  and  complements  r e l a t i o n s h i p s , however, p r i c e s are exogenously An  approach  c o u n t r y assumption price-taker  imports were found to be to  assume  that  more in  which the  imports and  to world p r i c e s  T h i s i s the  b a s i s of  (1975, 1978).  output  i n keeping with  substitution and  input  the n e o c l a s s i c a l  small  domestic  levels  behaves as  the q u a n t i t i e s of f a c t o r s  factor  f u n c t i o n approach  are a g a i n  treated  exogenously in  endowments.  used by  as an  a  prices  import demand can then move  s u b j e c t to domestic  the GNP  Imports  country  import markets would have  g i v e n . Domestic export s u p p l y and response  These  given.  i n both export and  for outputs and  capital.  substitutes  input  Kohli to  the  p r o d u c t i o n technology and exports are t r e a t e d as an output of the technology,  ie.  domestic  goods. T h i s assumption  consumers  may  destined  for  technology by the which  has  use of a  imports as v a r i a b l e assumed to This i s  domestic  consumption  a similar  for  export  consumption.  Kohli  translog restricted  goods,  investment  with t h e i r  models  profit  goods,  and c a p i t a l  prices adjusting  representation  fact  through d i f f e r e n t channels  net outputs. Labour  be f i x e d  no demand  be j u s t i f i e d by a p p e a l i n g to the  that export goods t y p i c a l l y proceed those  have  to Samuelson's  to the  function  exports  and  inputs  are  endogenously. (1953-4)  GNP  f u n c t i o n i n t r a d e t h e o r y . Supply equations f o r consumption goods, investment  goods and e x p o r t s , a  demand equation f o r imports  Inverse demand equations f o r labour and c a p i t a l are d e r i v e d the GNP  function.  These were  among the f i r s t  8  s t u d i e s to  and from model  domestic  export supply s u b j e c t to a given world p r i c e r a t h e r than  modelling the r e s t o£ the world's demand f o r a country's exports, Kohli  (1978)  estimated h i s model f o r Canadian data f o r  p e r i o d 1949-72 and found the imports  to  vary  e l a s t i c i t y of  between  supply of  E x p o r t s , consumption substitutes response  own-price e l a s t i c i t y of demand -0.9  and  -1.0  exports to  and  the  and  the  vary between  investment  goods  were  for  own  price  1.5 and found  2.2. to  i n p r o d u c t i o n and the wage r a t e was found to f a l l  to an i n c r e a s e i n import p r i c e s and r i s e  be in  i n response  to  an i n c r e a s e i n export p r i c e s . C a p i t a l r e n t a l p r i c e s responded  in  the opposite d i r e c t i o n . prices  increased  the  consumption goods  demand  prices  c a p i t a l s t o c k s reduced noted that  Increases i n investment  a model  reduced  imports  increases  in  demand.  Increases  in  and imports.  I t should  be  this w i l l  the Rybczynski  export  while  import  both exports  such as  r e s u l t s s i m i l a r to  for  goods and  not n e c e s s a r i l y  Theorem  produce  in traditional  theory as j o i n t p r o d u c t i o n i s allowed i n the GNP  function  trade model.  A l s o , the model i s o n l y p a r t i a l e q u i l i b r i u m i n that no balance of payments or exchange r a t e adjustment no e x p l a n a t i o n of the  earlier  mechanisms are i n c l u d e d  the c a p i t a l accumulation  study,  Kohli  (1975),  an  process i s made.  attempt  was  made  and In to  d i s a g g r e g a t e imports and exports by the use of t r a n s l o g submodels but c u r v a t u r e c o n d i t i o n s were not s a t i s f i e d and the submodels d i d not perform  well.  A r e c e n t a p p l i c a t i o n of the Diewert and Morrison (1986). a fixed  input and  GNP  f u n c t i o n model i s that  In t h i s study c a p i t a l  constant r e t u r n s  9  to s c a l e  i s treated  are imposed.  of as The  economy's outputs while  its  are modelled  variable  inputs  imports of petroleum, and  as  are  domestic Imports  l a b o u r . The  sales  and  excluding  exports  petroleum,  normalised q u a d r a t i c p r o f i t  f u n c t i o n i s used which  permits the c o r r e c t c u r v a t u r e  conditions  to be  the  model with  minimal  flexibility  model  i s applied  to  imposed on  p r o p e r t i e s . The  1967-82. Export supply e l a s t i c i t i e s non-petroleum  import  demand  import demand  -0.87.  were  Exports  domestic  sales  Non-petroleum petroleum  found  and  imports  exports. A r e l a t i v e l y labour of  around  e l a s t i c i t i e s was In  to  were  were  range  range  be  highly  period  to 0.60  while  -0.74  to  from -0.14  to  substitutable with  with  with  labour.  labour  domestic  price e l a s t i c i t y  obtained.  the  from  complementary  substitutable  high own was  for  from 0.52  complementary with  -1.0  to  e l a s t i c i t i e s range  highly  imports  US data  elasticities  -1.12. Petroleum  cost  A series  while  sales  and  of demand  for  of  devaluation  and  consumption  a l s o presented.  order to  s e c t o r s and t h e i r  model both  the p r o d u c t i o n  i n f l u e n c e on export  one has to move i n t o the  supply and  import  demand  realm of g e n e r a l e q u i l i b r i u m models.  A  s m a l l s c a l e g e n e r a l e q u i l i b r i u m model i n which the consumption as w e l l as the p r o d u c t i o n balance of payments  sector i s e x p l i c i t l y  mechanism i s  model i s h i g h l y aggregated importables  and  t h a t of  modelled  for  domestic the  exportables).  1952-71  The  with o n l y three goods (non-tradeables, Unlike  p r o d u c t i o n . The model was  period  the  Clements (1980).  the  Burgess  models, imports and exports are assumed t o be p e r f e c t for  as i s  but  relatively  Kohli  substitutes  estimated using U.S.  performed  10  and  data  poorly.  A  s i m u l a t i o n of the e f f e c t of imposing a 10 per cent import indicated that r e a l p e r i o d s and r e a l  exports would be  imports would  y e a r s . Dynamics  enter  20 per cent  be 32  the model  per cent  tariff  lower  in  lower a f t e r  v i a intertemporal  a l l 12  optimising  behaviour by consumers. Applied general s i m u l a t i o n s of  e q u i l i b r i u m models have o f t e n been used  the  exogenous shocks  effects  of  different  trade  policies  and  on the supply of exports and demand f o r imports.  Most a p p l i e d g e n e r a l e q u i l i b r i u m m o d e l l i n g , however, has been a "large  scale"  o b j e c t i v e of  in  basis  with  these s t u d i e s  many  and  exogenous changes on the economy once a l l the flow on e f f e c t s  of  worked through. T h i s  solution  solution. Typical  assess the  The of  the post-shock  been to  industries. impact  the change have been  has  goods  on  of  Boadway and Treddenick  of the  complete  these l a r g e r (1978) of  scale  i s done by  comparing  model with  the  models a r e  those  the Canadian  base of  economy and the  ORANI model of Dixon, Parmenter, Ryland and Sutton (1977) of the A u s t r a l i a n economy. Boadway and of  reducing  Canadian  trade  r e d u c t i o n i n aggregate e x p l o i t i n g monopoly tertiary  industries  manufacturing wage/rental  and  Treddenick  taxes  f i n d t h a t the  to zero  would  be  effect  a  small  u t i l i t y due t o the r o l e of trade taxes  power.  The  and  have  primary  tariff an  was  adverse  industries  found  to  impact  while  in  benefit  on  most  raising  the  s t a r t of a  new  ratio.  The model of  Harris  (1984) r e p r e s e n t s the  g e n e r a t i o n of g e n e r a l e q u i l i b r i u m models which i n c o r p o r a t e recent developments i n the f i e l d s  of i n d u s t r i a l o r g a n i s a t i o n and  11  trade  t h e o r y . By a l l o w i n g  for internal  d i f f e r e n t i a t i o n Harris d i f f e r markedly from  instance,  the  Canadian economy  those of models  can  based on the  neoclassical  to s c a l e and p e r f e c t  competition.  the e f f e c t of a move t o m u l t i l a t e r a l f r e e trade was estimated as  aggregate welfare using  an 8.6 per  the model based  cent gain  on s c a l e economies  product d i f f e r e n t i a t i o n compared to only gain  product  f i n d s t h a t the r e s u l t s of s i m u l a t i o n s  assumptions of constant r e t u r n s For  economies of s c a l e and  a 2.4 per cent  on in and  welfare  from the model based on n e o c l a s s i c a l assumptions. While l a r g e s c a l e g e n e r a l e q u i l i b r i u m models are capable  producing more d e t a i l e d they a r e  typically  forms t o enable demand  based on  relatively  smaller  within  are the  also  usually  models.  scale  simplistic  t h e i r implementation. Export  elasticities  estimated  r e s u l t s than many  models  functional  supply and  assumed  Furthermore,  of  import  rather while  than recent  developments i n i n d u s t r i a l o r g a n i s a t i o n  t h e o r y have opened up new  areas of a p p l i e d  developments i n e m p i r i c a l  research,  other recent  techniques mean t h a t many u s e f u l s t u d i e s using new  models w i t h i n means  of  the n e o c l a s s i c a l  incorporating  relatively flexible adjustment  will  many  functional  enable  thesis  within  a  framework. In goods  forms and  modellers  e l a s t i c i t y e s t i m a t e s . I t i s these this  remain to be  to  undertaken particular,  and  factors  models  of  imperfect  more  detailed  produce  using  avenues which are explored  neoclassical  production  sector  in  model.  Although the r e s u l t s w i l l be of i n t e r e s t l n t h e i r own r i g h t , they may a l s o  provide  improved  e l a s t i c i t y estimates  larger scale general e q u i l i b r i u m  models.  12  f o r input  to  3 .  A. F L E X I B L E  FUNCTION  used and  In  this  to  provide  import  several detailed  MODEL.  Chapter  sets  elasticity  the  GNP f u n c t i o n  estimates  demand  export  AGGREGATOR  and of  of  the  estimates  for  and  exogenous shocks  are  3.1  The  Framework  GNP F u n c t i o n  The of  GNP f u n c t i o n  profit  maximising  competition  in  import  demands  and  import  prices  assumed to  to  their  be  the  model firms  are and  mobile  factors  available  The  non-increasing  marginal  be  bounded  The  competitive  available  technology,  import  while  thus  various  and  supply  functions producing  implications  of  these  policy  changes  economy i s  made u p  under  conditions Output  factor with  market  returns  to scale,  of for  factor  endowments  GNP and  output  prices  are equal be  disposal,  transformation, endowments.  be r e p r e s e n t e d  o f maximising  mixes  Factors  free  given then  and  assumed to  and  can  factor  is  substitution finite  perfect  given  quantities. their  of  levels  profits  technology  rates  problem  the  aggregate  equilibrium  t o the  of  maximise  firms  from above  solution  the  markets.  chosen to  b y constant  to  effects  operating  characterised  and  Finally,  export  aggregator  included  assumes t h a t  between  shadow p r i c e s .  elaborated  discussed.  goods and  and  Byusing  components are  elasticities.  is  r e s p o n s i v e n e s s of  i n Canada. import  framework  subject given  as  the  to  the  output  and  prices. Exports  are  treated  as  an  imports  are  treated  as  an  Chapter,  treating  imports  output input.  a s inputs  13  of  the  As n o t e d  production in  the  t o production  sector  preceding may  be  justified  by  intermediate consumer  appealing inputs  goods  channels separate  and  s t i l l  before goods  restrictive  goods  the  perfectly While demand  approach  by  including  d i f f i c u l t  to  resulting  model  prices the  effects  the  price  the  of  of  is  assumed  that  at  existing  response  firms  to  an  made  the  price  of  domestic  for  forces  which  for  of  payments  explain  the  process  x  (entries  prices  by  the  effect  sales tend  and of  no  vector  for  sector  p>>0,  nature.  be as  amount of  being of  the  change  is  be  usually the  By h o l d i n g  a l l  as  not  For  and  is  output  income  effect  captured  as  no  rewards  on  factor  Also,  no  allowance  is  disequilibrium at  it  sales  in  made  a l l  instance,  changes  is  not  that  domestic  will  import  and  exogenous  consumer  eliminate  this  made  in  stage  the to  accumulation.  net  the  in  even  and  is  captured.  attempt  outputs,  which  other  exports.  sector  procedure  not  or  as  will  of  to  highly  supply  as  is  demand  misspecified  output.  capital  N variable  positive the  the  export  retail  exports  partly  a l l  price  are  "final"  demand  may  are  and  c l a s s i f i e d  this  taken  any  Not  would  balance  is  s e l l  exogenous  is  Denoting  changes  price.  allowance  be  domestic  production  of  are  Treating  consumers  equilibrium  sales  can  no  model  imports  distribution  which  the  will  exogenous  which  goods  to  cost  partial  domestic  us  imports  consumption  the  model  the  on  the  model,  fixed,  the  enables  concentrating  e x p l i c i t l y  is  sector  with  many  consumer.  domestic  production  that  through  there  as  substitutable  this  go the  which  fact  those  to  reaching for  the  even  have  necessarily from  to  output  quantities  negative M fixed  14  for input  by  inputs),  the net  quantities  vector output by  the  vector  z,  fixed  input  shadow p r i c e s by  T,  and the  the  can  production  possibility  represented  by the f o l l o w i n g r e s t r i c t e d p r o f i t  (3.1)  set  by the v e c t o r w technology  be  (GNP) f u n c t i o n :  G(p;z) = max. { p'x : (z;x) belongs t o T, p>>0 }. x  The  restricted profit  and  convex  i n net output  (decreasing) be  f u n c t i o n (3.1)  p r i c e s and  monotonically  input  quantities.  functions are discussed  The  f u n c t i o n i n the trade  Woodland  (1982).  I.e.,  model  of  restricted  theory context  while by  assumption;  i n both i t s  import  markets. The q u a n t i t y of imports i s then determined by  domestic i n d u s t r y demand c o n d i t i o n s while i s determined by  domestic supply  assumption f o r Canada  the q u a n t i t y of exports  conditions.  was t e s t e d by  who found they could not  The s m a l l  the r e s t r i c t e d  country  Appelbaum and K o h l i  (1979)  r e j e c t the p r i c e t a k i n g assumption f o r  imports but found t h a t i t was r e j e c t e d f o r Canadian If  in  profit  i s described  the small country  i s a p r i c e taker  will  increasing  i n Diewert (1973, 1974)  i s a l s o based on  t h a t the home country  export  properties  in detail  the GNP  The  increasing  i n the p r i c e s of v a r i a b l e outputs ( i n p u t s ) . I t  l i n e a r l y homogeneous, concave and m o n o t o n i c a l l y  fixed  and  w i l l be l i n e a r l y homogeneous  profit  exports.  function i s differentiable  r e s p e c t t o p then the net output supply  f u n c t i o n s can be  with  derived  by a p p l y i n g H o t e l l i n g ' s (1932) Lemma: (3.2)  x(p,z) = v G ( p ; z ) p  Furthermore, i f the r e s t r i c t e d p r o f i t with r e s p e c t t o the f i x e d  function i s  differentiable  input q u a n t i t i e s , z, then the  demand f u n c t i o n s f o r the f i x e d  inputs may be obtained by: 15  inverse  w(p,z) = V G ( p ; z )  (3.3)  2  In t h i s study the aggregate only fixed capital  input. P r o f i t  stock  accumulation  the  the  i s maximised each p e r i o d s u b j e c t to  the  available  i s not  given  so  wage  treatment  the  Labour  choose how  exogenous  unemployment, t h i s  and  modelled.  i n p u t ; i . e . , producers at  c a p i t a l stock i s t r e a t e d as  process  is treated  of  capital  as a  variable  much labour they wish to employ rate.  of  With  the  labour appears  than the a l t e r n a t i v e of assuming  existence more  t h a t the labour stock  of  plausible is  fully  employed with the wage r a t e becoming an endogenous v a r i a b l e . Constant  returns  the c a p i t a l s t o c k . The be represented by  to s c a l e are a l s o assumed with r e s p e c t restricted  a unit  p r o f i t function  maximum amount of revenue the of c a p i t a l .  If  p r o f i t f u n c t i o n (3.1) can  the c a p i t a l  p r o p o r t i o n then the economy's net same p r o p o r t i o n . helps  avoid  aggregating  The  the over  conceptual  Essentially  there remains  for c o n s i s t e n t  were i n c r e a s e d  of  However,  which  can  as Blackorby  the  a  unit given the  to  scale  occur  when  and  Schworm  f o r c o n s i s t e n t aggregation  technology are h i g h l y  a trade-off  aggregation and  by  constant r e t u r n s  problems  (1984) p o i n t out, the requirements the e x i s t e n c e of an aggregate  which r e p r e s e n t s  revenue would i n c r e a s e by  assumption  producers.  then  economy can produce from one stock  the use  to  and  restrictive.  between the  requirements  of models  sufficiently  f l e x i b l e to capture s u b s t i t u t i o n p o s s i b i l i t i e s . The data used i n t h i s study are t i m e - s e r i e s of  input-output  data f o r the Canadian economy made a v a i l a b l e by S t a t i s t i c s Canada  16  and  c o v e r i n g the p e r i o d 1961  outputs  to 1980.  I n i t i a l l y four v a r i a b l e net  f o r the economy as a whole are  identified;  - the q u a n t i t y of domestic s a l e s ; - the q u a n t i t y of aggregate -  (minus) the q u a n t i t y of aggregate imports;  -  (minus) the q u a n t i t y of  Corresponding  index  by the is  outputs  d e r i v e d by  and  d i v i d i n g the  r e l e v a n t p r i c e index.  d e r i v e d as total  a residual  and  labour.  p r i c e i n d i c e s are s e t equal to 1.0  implicit quantities output  exports;  i n 1961  value of  and  the  the  net  An aggregate c a p i t a l  to equate  inputs under constant  the value  r e t u r n s and  price  of  the  total  quantity  of the c a p i t a l stock r e s c a l e d so t h a t the p r i c e index assumes the value  of  1.0  in  1961.  i n v a r i a n t to t h i s d e t a i l and To  The  e l a s t i c i t y estimates  c a p i t a l r e s c a l i n g . The  listed  i n Appendix  data are d e s c r i b e d  in  1.  profit  function  must be s p e c i f i e d  the system of d e r i v e d net output c h a r a c t e r i s t i c s of responses  the  e l a s t i c i t i e s and  are obtained  their  supply  production  e l a s t i c i t i e s d e r i v e d from  3.3  are  implement the model e m p i r i c a l l y a f u n c t i o n a l form f o r the  restricted  import  presented  and  estimation  of  f u n c t i o n s undertaken.  The  technology  from the  and  export  c a l c u l a t i o n of  the estimated  profit  i n t e r p r e t a t i o n are  various  function.  discussed  and  in  These Section  below. Desirable  c h a r a c t e r i s t i c s of  restricted profit  function  provide a  order  second  a functional  are t h a t  approximation  continuously d i f f e r e n t i a b l e p r o f i t  17  it to  be  form f o r  flexible an  the  (able  to  arbitrary  twice  f u n c t i o n ) , parsimonious  (have  the  minimal  number  and c o n s i s t e n t profit  with  function.  forms  have  relative  ease  properties  of  at a l l  problem,  the development  of  Diewert  profit  to  (3.4)  and b  t  t  and Wales  The  i j s  L  t  required  curvature  points.  conditions  for the unit  i i P i  =  i j  s  +  In  response  forms  have l e d  and  globally.  easily If  c a n be i m p o s e d although  profit  the with  non-linear  function  The 4 - v a r i a b l e  net output  Ziii  i  j  P P / ( Z i  *> Pit  j  +  b  l t  t o be e s t i m a t e d  j i =  s  adopted  (SGM)  net output  in  function SGM  unit  T p )  4 k  1  R  tt ^i=l  have been d e l e t e d  (  k  c  and the  subject  i P i s  )  - j' x  t  2  ^ i i ' ^it  to;  for a l l i , j ; and,  0  i s a time  and t h e exogenous  for  empirical  flexible  they  and  in  in functional  properties  (1/2)1^?.^  =  Z ti  variable  the  Leontief  have t o be u s e d .  (1987).  are parameters s  average  then  superscripts  (3.6)  suffer  a  is given by;  b  (3.5)  often  of  flexibility  Symmetric G e n e r a l i s e d McFadden  +  time  Generalised  which are  curvature  form  i s the  G(p,K)/K  where  functions  flexibility),  properties  their  satisfy  flexibility  techniques  function  they  are not s a t i s f i e d  functional  study  of  developments  of  conditions  regression The  recent  satisfying  cost  and  because  to  for  theoretical  (or any) of the o b s e r v a t i o n  to  minimal  required  the translog  failure  this  curvature  required  popular  from  as  the  parameters  implementation,  to  verified  free  While  become  applications  this  of  f  o  trend  parameters quantity  T  r  J=l/.-/4.  representing and  k  per unit  k,1=1,..,4.  18  C^^  technical  are set  of c a p i t a l  equal input  progress to  the  quantity  Diewert and for  Wales (1987) show that the SGM  form i s  flexible  a p r i c e v e c t o r p~ s a t i s f y i n g Sp~=0 . While the non-  symmetric  N  Generalised  McFadden  function  (analogous  q u a d r a t i c form used by Diewert and flexibility  properties  f l e x i b l e at j u s t one  in that  to  Morrison  i t is  the  normalised  (1986)) has  superior  not r e s t r i c t e d  p o i n t , the r e s u l t s obtained  to  being  are s e n s i t i v e to  the choice of the numeraire good which plays an asymmetric T h i s s e n s i t i v i t y i s e l i m i n a t e d by use D i f f e r e n t i a t i n g the net output p r i c e s supply  labour demand  function (3.4)  GNP  y i e l d s a domestic  f u n c t i o n , (minus) an function.  of the SGM  form.  with r e s p e c t to  supply  f u n c t i o n , an  import demand f u n c t i o n and  The  form  of  role.  these  net  the  export  (minus)  output  a  supply  functions i s ; (3.7)  / K = Zj=i SijPj/fZk :! T p ) - T ( Z f i Z j i i s p 4 2 2 2(Zk = i kPk^ i i it tt i* i ' 1 = 1,..,4. 4  X  i  k  T  The  +  b  +  v a r i a b l e net output  the c a p i t a l input e r r o r term i s terms f o r  the  observations  (3.5)  b  c  :  +  each equation. are  a multivariate  k j  assumed  k P j  )/  u  by the q u a n t i t y  The to  problems and v e c t o r s of be  of an  error  independently  normal d i s t r i b u t i o n  with  zero  matrix  estimating  restrictions  +  k  to reduce h e t e r o s k e d a s t i c i t y  covariance  The  t  R  quantity is divided  appended to  d i s t r i b u t e d with means and  t )  k  system c o n s i s t s  and  (3.6). The  of (3.7)  profit  s u b j e c t to  function (3.4)  i n c l u d e d i n the e s t i m a t i n g system as i t adds no new Maximum l i k e l i h o o d estimates be obtained  by u s i n g the  the SYSTEMS  command of  I t e r a t i v e Z e l l n e r technique  19  1978). I f  not  information.  of the system of equations  SHAZAM (White  is  the  (3.7)  can  available in  the matrix  of  estimated  coefficients  restricted prices  can  and  the  positive  can  be  shown t o  S matrix  is  not  function  be  estimated  reparameterised  Bramble  replaces  the  to  matrix  S=[s j]  and  (3.8)  S = AA'  Using  a  that  this  its  semi-definite be  then  globally  the  convex  in  technique  global  by  i  where due  is  definiteness.  ensure  positive  the  semi-definite  due  to  convexity.  product  of  a  Wiley, This  then  Schmidt technique  lower  triangular  transpose:  result  rows  using a  (1973)  matrix  three  is  p.  If it  profit  S  to  a Using  and  A =  ta^..]  /  i/J l*«»/4;  Lau  (1978),  general  way  this  columns  Diewert  procedure  of  and  =  and  3^=0  fori<j.  Wales  of  imposing  the  coefficients  (1987)  show  positive in  semi-  the  first  S become;  2 l l  a  (3.9)  [s  i : j  fourth  a  row  restrictions can  be  a  2 1  a  2  ] =  a  The  l l  a  1  a  1  l l  2  3 1  a  and  a  2  21 31 a  The  by  3 1  + a  32 22 a  of  S  a  are  the  ;i,j=l,2,3  21 31 32 22 2 2 2 31 32 33 a  2 2  a  +  + a  a  a  +  obtained  reparameterised  using  a  2 +a  1  column  (3.6).  estimated  a  1  l l  system  a  from  the  imposing  summing curvature  non-linear  regression algorithm  output  components  is  ensure  tractability  in  SHAZAM. 3.2  Aggregator  Functions  Aggregation part of  of  this  three not  procedure  any  input  empirical  conditions  lose  Hicks  any  of  of  is  study usually  under the  aggregation  and  which  available  where  the  to a  loss  of  information.  20  of  but  information.  aggregation  prices  a  a  will The group  be  the  cost  There  consistent  first of  necessary  of  these  goods  are or is  always  move can  i n exact then  be  Secondly,  formed  which  Leontief  quantity goods  p r o p o r t i o n . Aggregate p r i c e  and  behave  aggregation  price  always  will  indices  move  in  aggregation  are based  on  unlikely  t o be  met  The  third  basis for aggregation  quantities  indices  single  consistent of  good.  aggregate  a group  Clearly,  strict  of  Hicks  and  c o n d i t i o n s which  are  practice.  by  implying certain  is  t h e c o n d i t i o n o f h o m o g e n e o u s weak  to  Shephard  provides  p r o p e r t i e s f o r the  (1953),  quantity  for a  proportion.  Leontief  in  as  provides  when t h e  exact  and  a more g e n e r a l  functional  structure.  separability,  w h i c h a s s u m e s t h e GNP  case This  originally  function  c a n be  due  written  as: (3.10) w  h  e  r  e  R  G(p,z) =  (  R  n'"- '  R  1  and  p ,  for  the goods  n  fixed  z  = )  belong  m  V  =  (  V  to p,z,  i n group  inputs  G~(R,V)  in  1 V - - > ' respectively.  n while  group  m.  (  v m  )  z m  The  n  R  i s  R n  =  R  n Pn (  (P ) n  ><  is  a  V  m= m V  price  q u a n t i t y index  a  corresponding  ( z  m > index  f o r the  transformation  function i s : (3.11)  T(x,z)  where  Y= ( Y^, . . ., Y  index  which  (3.12)  where  (3.13)  n  (P ) n  , .. ) and  i s assumed  max. x n  R  = T~(Y,V) =  i  p x n  = is  a  G(p,z)  Y  n  n n  Y^  t o be  (  x n  )  *-  s  linearly  : Y (x ) n  0  = Y  n  revenue  n  Y  or aggregator  = max. = max.  h o m o g e n e o u s . We  p x R  R n  n  function.  Thus,  : T~(Y (x ),...,V)=0 1  n  ( P  n  then  quantity have:  : Y ( x / Y ) = l } = Y R (p ) n n n n n n  n  /  corresponding  n e  }  n  max. { p x / Y ,,, *n n n n n  X  ^  )  21  Y  : n  n  T~(Y,V)=0  }  }  = which  is  a  valid  G~(R,V) GNP  function  in  the  H o t e l l i n g ' s Lemma and the standard GNP applied  (Woodland 1982, The  aggregates  to  which  f u n c t i o n p r o p e r t i e s can be  p.368).  important i m p l i c a t i o n  of weak  separability is  that  o p t i m i s a t i o n proceeds by a two-stage  p r o c e s s . F i r s t , the  q u a n t i t y of the aggregate i s chosen  and then the optimal mix  that  aggregate  of  aggregate  is  independent of the q u a n t i t i e s of the other aggregates. Thus,  the  mix of t h a t aggregate  the  mix  of  between  the  other  s e p a r a b i l i t y which  two  chosen.  components  The  marginal  of  one  i s independent of both aggregates.  forms  f u n c t i o n s as proposed (and  is  of  rate  substitution  quantity  optimal  the l e v e l and  It  is  this  the b a s i s  of  the use  by Fuss (1977)  aspect  of  of  weak  aggregator  to accommodate many  input  output) components. With the  use of  i n c o r p o r a t i o n of available  impossible,  many inputs  degrees  multicollinearity  flexible  of  and outputs  freedom  problems  t o overcome.  functional  and  which  The  forms the  r a p i d l y exhausts creates  are  increased  explicit  significant  difficult,  if  computational burden  a l s o an important c o n s i d e r a t i o n . The use of aggregator permits the use of f l e x i b l e  not is  functions  f u n c t i o n a l forms f o r the GNP  a t the aggregate l e v e l a l o n g with f l e x i b l e aggregator  the  function  functions.  The response a t the most d i s a g g r e g a t e d l e v e l can be obtained by: (3.14)  X w  m  n  = 9G/9p  n  = OG~/3R .9R /9p  = 8G/8z  m  = 9G~/av .9V /8z .  n  m  22  n  m  n  m  The c o s t property weak  of t h i s  procedure  o£ weak  i s , of  s e p a r a b i l i t y . An  separability  i s that  the  components w i t h i n one aggregate  course, acceptance  of the  unfortunate i m p l i c a t i o n  substitutability  of  with another aggregate  any  is  In t h i s  study the aggregator  disaggregate t o t a l  exports  and  sales  to  aggregate.  f u n c t i o n procedure total  two  equal.  Thus, imports o f , say, t r a c t o r s and h a i r p i n s might be assumed be e q u a l l y s u b s t i t u t a b l e with the domestic  of  imports  i s used  each  into  to four  components. The four export components a r e ; Group 1 : A g r i c u l t u r a l and F o r e s t r y Products; Group 2 : M i n e r a l s and Energy  Products;  Group 3 : Motor V e h i c l e s , T e x t i l e s and E l e c t r i c a l Products; and Group 4 : Heavy I n d u s t r i a l and S e r v i c e Products. The  four import components a r e ;  Group 1 : A g r i c u l t u r a l , F o r e s t r y and S e r v i c e Products; Group 2 : Metals and Energy Group 3 : Machinery,  Products;  E l e c t r i c a l and T e x t i l e Products; and  Group 4 : Motor V e h i c l e s , Chemicals and Other The  four  export and  input-output movements  industries  over  aggregation.  import groups  the  The  20  were formed  according year  composition  to  period, of  each  e x p l a i n e d and p r i c e s and q u a n t i t i e s l i s t e d Making use of  the assumption  Products. by  aggregating  similarity  of  price  the  of  Hicks  of  basis  the  components  is  i n Appendix 1.  t h a t the Y ( x ) f u n c t i o n s a r e n  n  l i n e a r l y homogeneous the f o l l o w i n g Symmetric G e n e r a l i s e d McFadden  23  unit  revenue  functions  are  used  for  the  export  and  import  aggregates; (3.15)  = d/2)Z" i Z i  R(p,X)/X  i  + ^1=1 Z - i b i, .1p ^ 1. time  total  exports  have  (imports)  to  Ziii  (3.17) The  variable t  and  the  s  exogenous  T  (import)  component  export  (import)  quantity  for  given (3.18)  X . / X = Z.i (  Ci  of  V k  the  Convexity  and b  t  are  f c t  j=l,..,4.  C\  technical  are  quantity  implies of  set  progress  equal  per u n i t  that  total  The  By estimated  2  +  b  total  in prices the  vectors  independently with zero  )  i i  +  b  T p ) R  it  exports  f c  +  c a n be  -  k  the  to  of  export  exports  b  t t  c  i  t  2  the total  (import)  (imports)  the  terms  u  X is  imposed on t h e  error  Z.i  +  (import)  S matrix along of  TAZ^  (imports)  corresponding export  reparameterising (3.9).  per u n i t  8 , ^ / ( 2 ^  ±  q u a n t i t y of  index  i  are  by;  2  The  b  represents  k,i=l,..,4.  maximising behaviour  quantities  ,  X  i , j ; and,  and  k  export  component  b.^  trend representing  average  Profit  ,  deleted,  2  to;  for  parameters  Cp.)t  4  for a l l  a time  k  v < c  s^  subject  k  + b..(>~tt i --.l  F  = 0  i j  is  b i. t. p i. t  a g a i n been  Sj^j = Sjj^  T p )  k  and t h e  be e s t i m a t e d  (3.16)  SijPiPj/(27 ii  1  4  superscripts  parameters  j  + ^ F i.=,l  4  where  1  i  and c o v a r i a n c e  estimating parameters  in  the  s  l  - '  component aggregator  same  are  j  lines  again  P 4  a  P  )/  j  Divisia  quantities. functions as  (3.8)  assumed  normal  k  to  by and be  distribution  m a t r i x SL-  system  (3.15),  l  k  d e r i v e d as  d i s t r i b u t e d with a m u l t i v a r i a t e  means  '  s  ±  (3.18)  an e s t i m a t e  24  and of  substituting the  aggregate  the unit  price  is  obtained.  procedure  A  p r o p e r t y of  ls  that  although  components of  the  aggregate  aggregate  itself  procedure  aggregate  the are  two-stage  prices  of  exogenous,  optimisation  the  Individual  the p r i c e  of the  i s not exogenous because the c h o i c e of input and  output mix w i l l determine the  the  the aggregate  empirically  price  an  i s required.  estimated p r i c e  of the  p r i c e . Thus, t o implement  instrumental Fuss  variable  proposes  aggregate  obtained  i n equations  similar  the  f o r the  use  of the  by s u b s t i t u t i n g  the  t o (3.18)  the  parameters  estimated  aggregator  f u n c t i o n . T h i s i s used as an i n s t r u m e n t a l v a r i a b l e f o r  the aggregate  price  in  the  second  stage  of  into  the e s t i m a t i o n  p r o c e s s . Fuss j u s t i f i e s the use of the estimated aggregate as an i n s t r u m e n t a l v a r i a b l e t h a t the t r a n s l o g price  i n h i s case by a p p e a l i n g t o the  aggregator  f u n c t i o n i s exact f o r the  index of the components as e s t a b l i s h e d by Diewert The e s t i m a t i o n procedure  q u a n t i t y equations  substituted aggregate  import p r i c e s . i s the e s t i m a t i o n  (3.7) d e r i v e d from  The  prices. Application produces  of  The r o l e  this  (3.15) where the  of  (1976).  stage  of the  i n f o r m a t i o n maximum  instrument f o r each  25  supply function  export and  estimation  weak s e p a r a b i l i t y  are  v a r i a b l e s f o r the  of the net output  conditional  unit  stage  the SGM r e s t r i c t e d p r o f i t  estimates which a r e f u l l  (Fuss 1977).  Divisia  components.  first  second  u s i n g the i n s t r u m e n t a l v a r i a b l e s f o r aggregate  fact  estimate the  i n the  to obtain instrumental  and  e s t i m a t i o n procedure equations  estimates obtained  i n (3.15)  export  i s thus to f i r s t  (3.18) f o r the export and import  Next, the parameter  price  can be  aggregate  import  procedure likelihood seen  depends o n l y  from on  the p r i c e s of the components of t h a t aggregate. weak s e p a r a b i l i t y the p r i c e s of enter  (3.15)  and the  In the absence of  the other aggregates  above e s t i m a t i o n  would  procedure would  also  not  be  consistent. 3.3 E l a s t i c i t i e s The invariant  Produced  elasticities normalised  elasticities  may  be  form  presented  analogous  in  to  either the  a  scale  Allen-Uzawa  of s u b s t i t u t i o n or i n the standard net output  elasticity  form. The s c a l e  matrix of  elasticities  invariant e l a s t i c i t i e s  of t r a n s f o r m a t i o n  price  are a symmetric  between  net  outputs  ( n o r m a l i s a t i o n s of 3x /"2>p ) g i v e n by: n  (3.19)  n  ET = G.Gpp/(G .Gp) p  where G  p  = diag. ^ 7 G ( p ; z ) .  The d i a g o n a l elements  p  of ET are a l l  non-negative. The more f a m i l i a r the response j's  net output p r i c e e l a s t i c i t i e s  of net output  represent  i ' s q u a n t i t y to changes i n net  output  price:  (3.20)  E- . = d i n x . / d l n p. = s.ET. .  where s.. i s the  share of net output  the e l a s t i c i t i e s  s a t i s f y the f o l l o w i n g adding up r e s t r i c t i o n s ; Z}ii  (3.21) . Due  to the  j in restricted profit  E . j = 0.  maintained h y p o t h e s i s of  s c a l e the net output s u p p l y e l a s t i c i t i e s all  and  constant returns  with r e s p e c t t o  capital  take the value 1.0. T h i s a l s o means t h a t the e l a s t i c i t i e s  complementarity function  and  studies  intensity  are  not  normally  presented.  obtained  These  in  elasticities  v a r i o u s summation r e s t r i c t i o n s which a p p l y t o them are  26  to  of  profit and  presented  i n Diewert  (1974). For  restricted  profit  empirical applications  f u n c t i o n and  i n t e r p r e t a t i o n s of the  e l a s t i c i t i e s not i n the trade and V l a s t u i n While  of the  associated  model context see McKay,  Lawrence  (1982, 1983).  the e l a s t i c i t i e s above r e f e r to aggregate  imports, and  translog  the  second  stage of  s e t s of e l a s t i c i t i e s are of exports and  exports  and  the e s t i m a t i o n procedure,  two  obtained f o r the i n d i v i d u a l  imports. In  the case of c r o s s - p r i c e  components elasticities  between export components, f o r i n s t a n c e , from the f i r s t estimation  (equation  elasticities extending  given  a  equation  (3.18))  we  fixed  level  (3.14)  e l a s t i c i t i e s between export  obtain  we  of  cross-price  aggregate  obtain  components i  and  j  (3.22)  =  K  where E^j  i  j  +  X E  i  j  s  exports.  the  K j  E  x  x  i s the c r o s s - p r i c e e l a s t i c i t y between i and exports, S j  constant l e v e l of aggregate  By  supply  s u b j e c t to  input q u a n t i t y as f o l l o w s :  of  supply  cross-price  constant f i x e d c a p i t a l E  stage  j given  a  i s the share of export  j  if in t o t a l  exports  and  E x  aggregate  exports  for  a given  extending  (3.22) to the import components p r i c e e l a s t i c i t i e s  all  the  export  and  the  i s  X  import  fixed  components  own-price capital  input  are obtained  d i r e c t l y comparable with the p r i c e e l a s t i c i t i e s output c a t e g o r i e s obtained from the second 3.4  elasticity  of  level.  which  By for are  f o r the other net  stage of e s t i m a t i o n .  Results I n i t i a l e s t i m a t i o n of the l i n e a r systems i n (3.18) and  produced  coefficient  definite  for  the  matrices S  export  and  which were  import 27  not p o s i t i v e  aggregators  and  the  (3.7) semiGNP  f u n c t i o n . In  each  case  one  eigenvalue of  the  S  matrix  n e g a t i v e . Subsequent e s t i m a t i o n was, t h e r e f o r e , undertaken the n o n - l i n e a r r e s u l t s of  reparameterised  these n o n - l i n e a r  asymptotic  model  imposing  r e g r e s s i o n s and  t - v a l u e s are presented  using  curvature.  the  was  The  corresponding  i n Table 3.1. In each case  the  D a v i d s o n - F l e t c h e r - P o w e l l a l g o r i t h m i n the SHAZAM package was used and the systems converged  from the d e f a u l t c o e f f i c i e n t  starting  values of 1.0 w i t h i n 200 i t e r a t i o n s . L i m i t e d experimentation d i f f e r e n t s t a r t i n g values produced The  low R-square  aggregator  value f o r the  model i s  v a r i a b l e with the  due t o  the same parameter  Group 3 equation  lack of v a r i a t i o n  q u a n t i t y r a t i o being  estimates.  i n the  i n the  almost  with  import  dependent  constant f o r the  entire period. The  s c a l e i n v a r i a n t e l a s t i c i t i e s of t r a n s f o r m a t i o n  from the  GNP  function,  the  process,  are  presented  in  transformation for  import own  followed by  those  for  elasticities  f o r domestic  indicating l i t t l e largest  cross  price  items.  interpreted  Table  Of  stage 3.2.  of  The  demand are  export own  the  elasticities  largest  supply.  estimation  The  in  of  magnitude  transformation  s a l e s own supply are p a r t i c u l a r l y s m a l l responsiveness  transformation  exports and imports these  second  derived  for  elasticities  this are  output. those  The  between  i n d i c a t i n g r e l a t i v e p r i c e s e n s i t i v i t y between  more i n t e r e s t ,  conventional  however,  price  elasticities.  e l a s t i c i t i e s w i l l now be d i s c u s s e d i n net output c a t e g o r i e s .  28  are the  more  easily  These  price  t u r n f o r each of the  four  Export s u p p l y  e l a s t i c i t i e s are presented  own-price e l a s t i c i t y  of  aggregate  export  i n Table 3.3.  supply i n c r e a s e s  1.26 t o 2.29 over the p e r i o d . In 1970 an export p r i c e of  1  per cent  would have  brought  The  forth  from  i n c r e a s e of  an i n c r e a s e  in  total  exports of 1.67 per c e n t . These f i n d i n g s are c o n s i s t e n t with relatively  elastic  export  (1978) f o r Canada but supply e l a s t i c i t i e s  supply e l a s t i c i t i e s  l a r g e r than  of Diewert  found  the comparable  and Morrison  by  Kohli  U.S.  (1986).  the  export  A one  per  cent i n c r e a s e i n the p r i c e of the inputs labour and imports would reduce  export supply by 1.09 and 1.57 per cent, r e s p e c t i v e l y ,  1970. An i n c r e a s e i n the p r i c e  of domestic  s a l e s of 1 per  in  cent,  on the other hand, would i n c r e a s e exports by approximately  1  per  cent. In Allen  the p r o f i t  f u n c t i o n c o n t e x t , two goods are Hicks  (1938) s u b s t i t u t e s i f the  profit  f u n c t i o n with  Complementary  respect to  goods  have  a  d e r i v a t i v e . The e l a s t i c i t i e s  the  of a p r i c e same  sign  positive  profit  pattern  labour and complements  as  the  From the import e l a s t i c i t e s i t can be seen t h a t -0.98 t o  prices i s  -2.40. In  i n Table 3.3 are a  second  f u n c t i o n m u l t i p l i e d by  the  They w i l l hence  corresponding  second  both  have order  imports  and  sales.  import own-price  1970 a  1 per  import p r i c e s due t o , say, an a c r o s s - t h e - b o a r d  29  negative. price  of demand presented  the aggregate  the  order  thus s u b s t i t u t e s f o r  f o r domestic  d e r i v a t i v e of  second  and a p o s i t i v e q u a n t i t y .  d e r i v a t i v e s . Exports are  range from  t h e i r two  presented  order p r i c e d e r i v a t i v e of the ratio  cross p a r t i a l  (1946)-  i n Table 3.4 elasticities  cent i n c r e a s e t a r i f f would  in have  reduced  total  response  import  demand  by 1.62  per  cent.  of import demand to changes i n the t o t a l  c o n s i d e r a b l y higher than  the e a r l i e r Canadian  elastic  import  price i s  r e s u l t s of  (where labour was  t r e a t e d as a  r e s u l t s of Diewert  and Morrison where the e l a s t i c i t y has a  c l o s e r to one. Import demand  fixed  This  input) and  a l s o the  f a l l s when labour p r i c e s  In 1970, 1 per cent i n c r e a s e s i n export and domestic would have i n c r e a s e d  import demand  by 1.67 and  Kohli U.S. value  increase.  sales prices  0.72 per  cent,  r e s p e c t i v e l y . Import demand would have f a l l e n by 0.78 per cent i n response  to a 1 per cent  e l a s t i c i t i e s are a the r a t i o of a  i n c r e a s e i n labour p r i c e s . Since  second order p r i c e  p r i c e to a negative  opposite s i g n to the corresponding Consequently,  imports  derivative multiplied  q u a n t i t y they w i l l second order p r i c e  are s u b s t i t u t e s  these  have  by the  derivative.  with domestic  sales  and  complementary t o labour. A apparent 3.5. -0.21  n o t i c e a b l e t r e n d of in  The in  the labour  i n c r e a s i n g p r i c e responsiveness  demand e l a s t i c i t i e s  own-price e l a s t i c i t y 1962  to  -2.23  of labour  i n 1980.  r e f l e c t s a c t u a l p r i c e responsiveness a  growing  role  f o r wage  If  in  demand i n c r e a s e s this  result  Table from  accurately  i n the economy then there i s  moderation  unemployment problems. In 1970  presented  is  a 1 per  in  overcoming  current  cent r e d u c t i o n i n  wages  would have i n c r e a s e d labour demand by 0.88 per cent. By 1980  the  resulting  per cent wage  cut  per cent. I t i s p o s s i b l e t h a t  the  i n c r e a s e i n labour  had more than doubled  t o 2.23  demand from a 1  Canadian economy has become more p r i c e r e s p o n s i v e and f l e x i b l e i n recent decades due to i n c r e a s i n g openness i n i n t e r n a t i o n a l  30  trade  and d e r e g u l a t i o n . The c r o s s labour demand e l a s t i c i t i e s a l s o a  pattern  of  increasing  responsiveness  show  highlighting  the  importance of other p r i c e s on labour demand as w e l l . In 1970 a per cent i n c r e a s e i n export and domestic  s a l e s p r i c e s would  increased labour demand by 0.66 and 0.46 per cent, The  positive  value  r e s p e c t to the domestic  of  the e l a s t i c i t y  domestic  sales  price  price  i n c r e a s e d markedly  responsiveness over the  cent i n c r e a s e i n  the p r i c e of  negligible  on  impact  price  with and  domestic  cent  increases  s a l e s would sales  increased  0.50 per cent.  respectively.  An  i n c r e a s e d domestic complementarity  in  the p r i c e s  increase  also  this started  of domestic  would have  s a l e s supply by  has  from  from Table 3.6, i n 1962 a 1 per  the output  increase  sales  in  the  s a l e s supply by  have had but by  the  of  imports  export  price  of  sales  i n response to and  labour,  would  have  0.26 per cent r e f l e c t i n g  between exports and domestic  a  1980  quantity  In 1970 domestic  supply would have f a l l e n by 0.12 and 0.31 per cent 1 per  demand  t h a t labour  of domestic  p e r i o d although  very low l e v e l s . As can be seen  domestic  respectively.  labour  indicates  have  s a l e s are s u b s t i t u t e s . The  such a  of  1  the  sales.  Having d e r i v e d these p r i c e e l a s t i c i t i e s i t i s of i n t e r e s t to examine t h e i r  i m p l i c a t i o n s f o r the e f f e c t s of v a r i o u s  p r i c e changes on the economy. by  10  per  cent  liberalisation elasticities,  or  due move  imports  I f import  to,  say,  a  to  free  trade  would i n c r e a s e  p r i c e s were t o  substantial  by  then,  trade using  16 per  cent,  exogenous decrease barrier mid-point exports  would i n c r e a s e by 11 per cent and labour demand would i n c r e a s e by  31  2 per c e n t .  Domestic  lowering  of  sales  s u p p l y would f a l l  to  the  to  increase  by 10 p e r c e n t  due t o ,  in  foreign  trade  or an  barriers  Canadian products imports would  would  by a b o u t  elasticity  2.5  components  the  estimation  the  GNP  outputs  to  a  aggregator  of  the  fixed  elasticities  aggregate 1970.  function  and so  the  supply  year  are  elasticities  to  w h i c h show  capital  show  that  the  if  the  the  export  F o r e s t r y Product exports  Vehicle, 0.16  per  would have  M i n e r a l s and E n e r g y  Textile cent,  and  of  of  all  respectively.  32  quantity  are  elasticities  are  first  stage  response  of  of  The  export  to  maintain a  by 0.23  all  by 0.08  Service would cases  and  per  cent  per c e n t .  exports fall the  net  Agricultural  then,  increase  of with  to  exports  In  export  Agricultural  and  Electrical  four  q u a n t i t y of  exports  Heavy I n d u s t r i a l  the  price  quantity,  of  set  specifi-  account  input a v a i l a b l e .  constant  quantities  the  that  d i r e c t l y comparable  by 1 p e r c e n t  of  would  however,  to  i n the  increased  and t h a t  demand  supply  export These  used not  for  and F o r e s t r y P r o d u c t s total  cent,  on any one  take  for  16 p e r  sales  heavily  to  were  reduction  and l a b o u r  likely sensitivity  fixed  for  process  subject  by  s h o u l d be n o t e d ,  failure  prices  w o r l d demand  increase  too  response  influences.  aggregator  function  in  per cent  be b a s e d  in  a substantial  Domestic  It  and t h e  i n T a b l e 3.7  from the  say,  increase  cent.  to  Canadian export  by 16  elasticities  subject  If  would  per c e n t .  d a t a used  equilibrium  presented  per  s h o u l d not  The p r i c e  derived  6  e s t i m a t e s due  and  general  exports  increase  by  policy analysis  cation  then  also  increase  increase  import p r i c e s .  slightly  and  The Motor  by 0.23  quantities  and of  A g r i c u l t u r a l and F o r e s t r y exports and M i n e r a l s and Energy move together and  i n the  opposite d i r e c t i o n  V e h i c l e , T e x t i l e and E l e c t r i c a l  to  exports  those of  Motor  exports and Heavy I n d u s t r i a l  and  Service exports. The c o r r e s p o n d i n g import are presented i n Table 3.8. price  responsiveness  constant t o t a l the other  Service falls  These e l a s t i c i t i e s  among  import  f o r 1970  show very  components  to  little  maintain  a  q u a n t i t y of imports but are a l s o not comparable to  elasticities  elasticities  aggregator e l a s t i c i t i e s  presented  nor r e a d i l y  show that i f the p r i c e  imports  interpreted.  The  of A g r i c u l t u r a l , F o r e s t r y and  i n c r e a s e d by 1 per cent there would be n e g l i g i b l e  i n A g r i c u l t u r a l , F o r e s t r y and S e r v i c e imports and V e h i c l e s ,  Chemical level.  and Other  imports t o maintain  There would be  and Energy  offsetting negligible  imports and Machinery,  Of most  a constant t o t a l  i n t e r e s t are  e l a s t i c i t i e s derived  from  Electrical  the  increases in and T e x t i l e  export and  equation (3.22).  import  import These  Metals  imports. component  elasticities  show the component response s u b j e c t to a f i x e d aggregate  capital  input and are thus d i r e c t l y comparable with the other net e l a s t i c i t i e s derived  from the  export component own-price the c r o s s e l a s t i c i t i e s price  elasticities  exports range  stage  f o r 1970 are presented  of  of e s t i m a t i o n .  supply  i n Table 3.10.  for Agricultural  and  from 0.62 to 0.86. Those f o r Motor V e h i c l e , exports range  Energy exports  and Heavy  slightly  less  The  e l a s t i c i t i e s appear i n Table 3.9 while  and E l e c t r i c a l  exhibit  second  output  from 0.53  Industrial  price  t o 0.76.  and S e r v i c e  responsiveness  33  with  The  Forestry Textile  Minerals exports  and each  elasticities  ranging from 0.40  t o 0.77  and 0.41 t o  0.64, r e s p e c t i v e l y .  The  i n t e r e s t i n g r e s u l t e v i d e n t i n the t a b l e of c r o s s e l a s t i c i t i e s t h a t a l l the  cross e l a s t i c i t i e s  are p o s i t i v e .  Hence, the  is four  export components can be c o n s i d e r e d complementary i n s u p p l y as an Increase i n the p r i c e of any one component w i l l i n the q u a n t i t i e s of  a l l four export  lead t o i n c r e a s e s  components s u b j e c t to the  f i x e d c a p i t a l s t o c k . T h i s e x p l a i n s why the own-price of the components are a l l l e s s than the e l a s t i c i t y total  elasticities  of supply  exports obtained from the GNP f u n c t i o n . When the  export  price  increases  the  e f f e c t i v e l y i n c r e a s e and  prices  of  a l l four  hence compounding  come i n t o p l a y . I f the p r i c e  aggregate components  cross price  of j u s t one component  is  effects increased  then these compounding c r o s s e f f e c t s  are not p r e s e n t . The  i m p l i c a t i o n of these r e s u l t s  i f the p r i c e of one  i s that  component, say, A g r i c u l t u r a l due to f o r e i g n trade  and F o r e s t r y  b a r r i e r s or dumping  for  Products,  other export  is  reduced  then the other  export  components w i l l a l s o be a d v e r s e l y a f f e c t e d . Finally, presented  import component own-price demand e l a s t i c i t i e s  i n Table  3.11 and  cross e l a s t i c i t i e s  i n Table  are 3.12.  A g r i c u l t u r a l , F o r e s t r y and S e r v i c e imports e x h i b i t the most p r i c e responsiveness with while Machinery,  elasticities  Electrical  ranging from  and T e x t i l e  -0.36  to  imports e x h i b i t the l e a s t  responsiveness with a range of -0.27 t o -0.41. Metals and imports  and  Vehicle,  Chemicals  i n t e r m e d i a t e responsiveness -0.42 to -0.67,  and  with ranges  r e s p e c t i v e l y . Again a l l  Other  imports  of -0.21  Energy exhibit  t o -0.80  c r o s s import  e l a s t i c i t i e s are negative i n d i c a t i n g a complementarity  34  -0.75  and  component among  the  import groups. Hence, i f a 10 per cent t a r i f f  had been p l a c e d  on  Machinery,  Electrical  and T e x t i l e  imports i n 1970 the imports  of  Machinery,  Electrical  and T e x t i l e  Products would have f a l l e n  by  3.7 per c e n t , have f a l l e n  A g r i c u l t u r a l , F o r e s t r y and  by  2.6 per cent  V e h i c l e , Chemicals and Other  S e r v i c e imports  and Metals and  Energy  would  imports  imports would have f a l l e n  and  by 3.1 per  cent and 1.7 per cent, r e s p e c t i v e l y . 3.5 C o n c l u s i o n s These r e s u l t s f u n c t i o n approach and  input  illustrate  within a  the importance  such as the  aggregator  i n a l l o w i n g the i n c o r p o r a t i o n of s e v e r a l  categories  illustrate  the u s e f u l n e s s of the  GNP  f u n c t i o n model.  of r e c e n t l y developed  Symmetric G e n e r a l i s e d McFadden  output  They  functional  also forms  i n implementing  the  aggregator f u n c t i o n model with the c o r r e c t c u r v a t u r e requirements imposed. While the aggregate  or  elasticities  second  stage  comparable e l a s t i c i t i e s  the  general  level  trend  towards  labour demand e l a s t i c i t y . in  the  related to  failure  capacity u t i l i s a t i o n  similar  to  (eg. K o h l i ( 1 9 7 8 ) ) ,  they  rapidly  increasing  i s p a r t i c u l a r l y apparent  data,  the  to  imposition  o r , of course,  of a c t u a l s u b s t i t u t i o n the  generally  price f o r the  T h i s tendency may be the consequence of  requirements on the model, reflection  the model a t the  t e n d e n c i e s . The major anomaly present  responsiveness over time. T h i s  shortcomings  are  i n other s t u d i e s  do e x h i b i t some troublesome is  obtained from  take  might  possibilities. account of  of  curvature  be an  I t may a l s o  declining  r a t e s towards the end of the p e r i o d .  35  accurate be  capital Another  potential between  anomaly i n the r e s u l t s a l l export  responses are further  and  separability approach, f o r two  components  and  measured r e l a t i v e  to a  the p o t e n t i a l  cause of  examine  results  in  particular  assumption  the f o l l o w i n g flexible  aggregator  i s the complementarity  to  in  components  fixed c a p i t a l  the  the  disaggregated  models which  approach.  36  role  aggregator  of t h i s t h e s i s  presents do  not  when  input.  these f e a t u r e s  ascertain  implicit Chapter  import  observed  of of  To the the  function results use  the  TABLE 3.1 SGM PARAMETER ESTIMATES Coefficlent  R  2  Export  Aggregator  Import  Aggregator  GNP F u n c t i o n  a  l l  -0.2652 (-3.62)  -0.0052 (-0.17)  0.9169 (5.31)  a  12  •0.0796 (-1.40)  0.0523 (1.85)  -0.5440 (-6.86)  a  13  0.1826 (2.66)  0.1318 (0.93)  -0.4119 (-4.88)  a  22  •0.1057 (-1.58)  -0.0350 (-25.5)  0.4221 (4.70)  a  23  0.1926 (1.42)  -0.0890 (-92.8)  -0.4512 (-2.67)  a  33  •0.0095 (-0.00)  -0.0000 (-0.00)  -0.0000 (-0.00)  b  ll  b  lt  b  tt  b  22  b  2t  b  33  b  0.4095 (27.37) -0.1246 (-9.99 ) 0.0094 (1.61)  -0.3486 (-28.78) 0.0104 (0.80) 0.0174  (12.51)  0.5432 (18.19) 0.3497 (7.74) -0.0633 (-3.36)  0.2999 (58.29)  -0.2394 (-62.93)  -0.3325 (-26.9)  -0.0691 (-10.06)  0.0480 (14.78)  -0.1280 (-5.81)  0.1270 (5.45)  -0.2054 (-31.2)  -1.4233 (-68.3)  3t  0.1693 (8.15)  0.0131 (2.47)  0.0473 (0.70)  b  44  0.1692 (36.05)  -0.2277 (-21.08)  2.3446 (46.1)  b  4t  0.0269 (3.76)  -0.0489  0.1341 (1.51)  (-4.66)  Values  Equation 1  0.7650  0.4052  0.7605  Equation 2  0.8977  0.9007  0.9121  Equation 3  0.7701  0.0166  0.9859  Equation 4  0.7085  0.5948  0.4890  Log  261.38  275.25  182.55  Likelihood  't Values i n parentheses are assymptotic t - v a l u e s . The c o e f f i c i e n t s u b s c r i p t s and equation numbers 1,..,4 r e f e r t o Groups 1,..,4, r e s p e c t i v e l y . 3 The c o e f f i c i e n t s u b s c r i p t s and equation numbers 1,..,4 r e f e r t o E x p o r t s , Imports, Labour and Domestic S a l e s , r e s p e c t i v e l y . 37  3.2  TABLE  GNP FUNCTION ELASTICITIES OF TRANSFORMATION  1962  XX 2.5643  XM 2.8611  XL 0.4974  XD 0.1297  MM 4.8283  1964  2.6340  3.0708  0.5896  0.2015  5.3129  1966  2.4235  2.7104  0.6382  0.2249  4.5329  1968  2.4597  2.5911  0.7703  0.2931  4.0931  1970  2.7651  2.7867  1.0177  0.4248  4.1704  1972  2.2500  1.9265  1.0549  0.3910  2.5755  1974  2.1969  2.0809  1.0900  0.4098  3.0177  1976  2.8083  2.4428  1.6868  0.6799  3.1997  1978  2.7395  2.6139  1.7616  0.7050  3.7070  1980  3.0694  3.4598  2.0327  0.8596  5.5805  Year  1962  ET L 0.2177  MD 0.1841  0.1660  LD 0.0171  ' T 0.0075  1964  0.3209  0.2741  0.2095  0.0368  0.0163  1966  0.3224  0.2432  0.2701  0.0614  0.0209  1968  0.3702  0.2440  0.3840  0.1128  0.0380  1970  0.5060  0.3116  0.5729  0.2008  0.0752  1972  0.3429  0.1218  0.8337  0.3122  0.1169  1974  0.4371  0.1965  0.8794  0.3123  0.1115  1976  0.7022  0.3064  1.5577  0.6113  0.2402  1978  0.8485  0.4009  1.7039  0 .6399  0.2424  1980  1.3446  0.7533  1.8792  0.6907  0.2684  Year  ET  M  ET  ET  ET  ET  The s u b s c r i p t s X,M,L and D r e f e r and Domestic S a l e s , r e s p e c t i v e l y . 1  38  ET  ET  LL  to E x p o r t s , Imports,  ET  E  D D  Labour  TABLE 3.3 EXPORT SUPPLY Year  E  XX  E  ELASTICITIES  XM  E  1  XL  E  XD  1962  1.2666  -0.9014  -0.6381  0.2730  1964  1.3415  -0.9977  -0.7719  0.4281  1966  1.3406  -0.9465  -0.8850  0.4909  1968  1.4569  -0.9731  -1.1515  0.6677  1970  1.6657  -1.0852  -1.5704  0.9898  1972  1.4404  -0.7445  -1.5694  0.8736  1974  1.5666  -0.8813  -1.5647  0.8794  1976  1.9560  -1.0483  -2.3551  1.4475  1978  2.0125  -1.1460  -2.2722  1.4056  1980  2.2967  -1.4871  -2.4181  1.6085  The s u b s c r i p t s X,M,L and D r e f e r and Domestic S a l e s , r e s p e c t i v e l y . 1  39  to E x p o r t s , Imports,  Labour  TABLE 3 . 4 IMPORT DEMAND E L A S T I C I T I E S  Year  E  MX  E  MM  E  ML  E  MD  1962  1.4132  -1.5212  -0 .2794  0.3874  1964  1.5639  -1.7262  -0.4201  0.5824  1966  1.4993  -1.5830  -0.4471  0.5308  1968  1.5347  -1.5371  -0.5534  0.5558  1970  1.6787  -1.6240  -0.7808  0.7261  1972  1.2333  -0.9954  -0.5101  0.2722  1974  1.4839  -1.2781  -0.6274  0.4217  1976  1.7014  -1.3732  -0.9804  0.6522  1978  1.9203  -1.6252  -1.0944  0.7993  1980  2.5888  -2.3987  -1.5996  1.4095  1 The s u b s c r i p t s X , M , L and D r e f e r and D o m e s t i c S a l e s , respectively.  40  to  Exports,  Imports,  Labour  TABLE 3.5 LABOUR DEMAND ELASTICITIES Year  E  LX  E  LM  E  1  LL  E  LD  1962  0.2457  -0.0686  -0.2129  0.0359  1964  0.3003  -0.1043  -0.2743  0.0782  1966  0.3531  -0.1126  -0.3745  0.1341  1968  0.4562  -0.1390  -0.5741  0.2569  1970  0.6131  -0.1970  -0.8839  0.4679  1972  0.6753  -0.1325  -1.2403  0.6974  1974  0.7773  -0.1851  -1.2624  0.6702  1976  1.1748  -0.3013  -2.1748  1.3013  1978  1.2941  -0.3720  -2.1978  1.2757  1980  1.5210  -0.5780  -2.2355  1.2925  1 The s u b s c r i p t s X,M,L and D r e f e r and Domestic S a l e s , r e s p e c t i v e l y .  41  to E x p o r t s , Imports,  Labour  TABLE 3.6 DOMESTIC SALES SUPPLY ELASTICITIES Year  E  DX  E  DM  E  DL  1  E  DD  1962  0.0641  -0.0580  -0.0219  0.0158  1964  0.1026  -0.0891  -0.0482  0.0346  1966  0.1244  -0.0849  -0.0852  0.0457  1968  0.1736  -0.0916  -0.1686  0.0866  1970  0.2559  -0.1213  -0.3099  0.1753  1972  0.2503  -0.0471  -0.4645  0.2612  1974  0.2922  -0.0832  -0.4483  0.2393  1976  0.4736  -0.1315  -0.8535  0.5114  1978  0.5180  -0.1758  -0.8254  0.4832  1980  0.6432  -0.3238  -0.8217  0.5023  1 The s u b s c r i p t s X,M,L and D r e f e r and Domestic S a l e s , r e s p e c t i v e l y .  42  to E x p o r t s , Imports,  Labour  TABLE 3.7 1970 EXPORT AGGREGATOR With  ELASTICITIES ' 1  Respect to P r i c e of  AF  ME  VTE  HIS  AF  0 .2238  0.0610  -0 .1383  -0 .1465  Chanqe l n  ME  0 .0743  0.0646  -0 .1220  -0 .0169  Q u a n t i t y of  VTE  -0 .1675  -0.1213  0 .2335  0 .0553  HIS  -0 .2282  -0.0217  0 .0711  0 .1788  Export component response subject to a fixed q u a n t i t y of aggregate e x p o r t s . 2 Export components are A g r i c u l t u r a l and F o r e s t r y Products (AF), M i n e r a l s and Energy Products (ME), Motor V e h i c l e s , T e x t i l e and E l e c t r i c a l Products (VTE), and Heavy I n d u s t r i a l and S e r v i c e Products (HIS). x  TABLE 3.8 1970 IMPORT AGGREGATOR ELASTICITIES  '  With Respect to P r i c e of AFS AFS  MN  MET  VCO  -0 .0000  0 .0002  0.0004  -0 .0006  Chanqe i n  MN  0 .0004  -0 .0203  -0.0429  0 .0629  Q u a n t i t y of  MET  0 .0010  -0 .0505  -0.1066  0 .1561  VCO  -0 .0009  0 .0462  0.0975  -0 .1428  1 Import component response subject to a fixed q u a n t i t y of aggregate imports. 2 Import components are A g r i c u l t u r a l , F o r e s t r y and S e r v i c e Products (AFS), Metals and Energy Products (MN), Machinery, E l e c t r i c a l and T e x t i l e Products (MET), and V e h i c l e s , Chemicals and Other Products (VCO).  43  TABLE 3.9 EXPORT COMPONENT OWN Year  E  AF  E  SUPPLY ELASTICITIES ' 1  ME  E  VTE  E  HIS  1962  0.6955  0.4377  0.5837  0.4122  1964  0.7395  0.4270  0.5344  0.4364  1966  0.6949  0.3997  0.5585  0.4392  1968  0.6147  0.4316  0.6888  0.4437  1970  0.6556  0.4966  0.7262  0.4881  1972  0.6399  0.3937  0.6425  0.4630  1974  0.6864  0.4815  0.5876  0.4693  1976  0.7630  0.5692  0.7312  0.5387  1978  0.7892  0.5582  0.7554  0.5492  1980  0.8594  0.7655  0.6631  0.6369  Export component response s u b j e c t to f i x e d capital input available. 2 Export components are A g r i c u l t u r a l and F o r e s t r y Products (AF), M i n e r a l s and Energy Products (ME), Motor V e h i c l e s , T e x t i l e and E l e c t r i c a l Products (VTE), and Heavy I n d u s t r i a l and S e r v i c e Products (HIS).  44  TABLE 3.10 1970 EXPORT COMPONENT CROSS SUPPLY ELASTICITIES ' 1  With Respect  t o P r i c e of  AF  ME  VTE  HIS  AF  0.6556  0.4930  0.3544  0.1628  Chanqe i n  ME  0.5061  0.4966  0.3707  0.2924  Q u a n t i t y of  VTE  0.2643  0.3106  0.7262  0.3646  HIS  0.2036  0.4103  0.5638  0.4881  1 Export component response s u b j e c t to f i x e d capital input available. 2 Export components are A g r i c u l t u r a l and F o r e s t r y Products (AF), M i n e r a l s and Energy Products (ME), Motor V e h i c l e s , T e x t i l e and E l e c t r i c a l Products (VTE), and Heavy I n d u s t r i a l and S e r v i c e Products (HIS).  45  TABLE 3.11 IMPORT COMPONENT OWN DEMAND Year  E  AFS  MN  E  ELASTICITIES / 1  E  MET  2  E  VCO  1962  -0.6287  -0.3410  -0.3789  -0.4765  1964  -0.7009  -0.3822  -0.4113  -0.5186  1966  -0.6191  -0.3287  -0.3911  -0.5255  1968  -0.5530  -0.3069  -0.3593  -0.5973  1970  -0.5977  -0.3348  -0.3715  -0.5900  1972  -0.3631  -0.2070  -0.2851  -0.4300  1974  -0.4374  -0.3613  -0.2789  -0.4569  1976  -0.4528  -0.3831  -0.2766  -0.5150  1978  -0.5304  -0.4153  -0.3114  -0.6240  1980  -0.7551  -0.8013  -0.3978  -0.6777  Import component response s u b j e c t to fixed capital input available. 2 Import components are A g r i c u l t u r a l , F o r e s t r y and S e r v i c e Products (AFS), Metals and Energy Products (MN), Machinery, E l e c t r i c a l and T e x t i l e Products (MET), and V e h i c l e s , Chemicals and Other Products (VCO). x  46  TABLE  3.12 1,2  1970 IMPORT COMPONENT CROSS DEMAND E L A S T I C I T I E S With Respect MN  AFS  to  P r i c e of MET  VCO  AFS  -0 .5977  -0 .3142  -0 . 2645  -0 . 4476  Chanqe in...  MN  -0 .5973  -0 .3348  -0 .3078  -0 .3842  Q u a n t i t y of  MET  -0 .5967  -0 . 3649  -0 . 3715  -0 . 2909  VCO  -0 .5986  -0 .2682  -0 .1674  -0 .5900  Import component response s u b j e c t to fixed capital input available. 2 Import components are A g r i c u l t u r a l , Forestry and Service Products (AFS), Metals and Energy Products (MN), M a c h i n e r y , E l e c t r i c a l and T e x t i l e P r o d u c t s (MET), and V e h i c l e s , Chemicals and O t h e r P r o d u c t s ( V C O ) . 1  47  4.  FLEXIBLE In  DISAGGREGATED  MODELS  order to compare the r e s u l t s obtained from the aggregator  f u n c t i o n model  with those  s e p a r a b i l i t y assumption,  of  a model  not  several f l e x i b l e  were i n v e s t i g a t e d . I n i t i a l attempts  making use  of  disaggregated  models  t o estimate a f u l l model with  the four export components, the four import components, s a l e s and  domestic  labour as v a r i a b l e net outputs i n the one model  proved  u n s u c c e s s f u l as the e s t i m a t i n g system of ten equations would converge. Attempts the system proposed  to  economise on the  by the  use of  by Diewert  and  unsuccessful. Semi-flexible  quadratic price c o e f f i c i e n t  than f u l l  i n the  s e m i - f l e x i b l e system further reinforce procedure  when  also  forms, by  is  t o be the  m u l t i p l i e d together to form  the  converge.  the t r a c t a b i l i t y  there  in  reducing  a t the expense  would not  not  forms as  proved  t o t a l number o f of a c h i e v i n g  In t h i s case, however, even a  d e a l i n g with  p a r t i c u l a r l y when  functional  matrix, reduce the  system but  flexibility.  (1986)  functional  s i z e of the t r i a n g u l a r m a t r i c e s  parameters  number of parameters  semi-flexible Wales  the  of the  many output a limited  This  less  four-column  would appear  aggregator  to  function  and  input  categories,  number  of  observations  available. To f u r t h e r i n v e s t i g a t e the r e l a t i o n s h i p s between the and  import components  and the other  smaller disaggregated these the  four export  a l o n g with aggregate second,  models were  aggregate estimated.  components were  imports, domestic  the four import  48  net outputs, In the  t r e a t e d as s a l e s and  components, aggregate  export  net  first  of  outputs  l a b o u r . In  exports,  two  the  domestic  s a l e s and  labour were taken to  be the net outputs. By  these two disaggregated models i t i n f o r m a t i o n on the and  w i l l be p o s s i b l e to g a i n  r e l a t i o n s h i p s between  the import components and  examining  the export  more  components  on the s t a b i l i t y of the  estimated  e l a s t i c i t i e s to changes i n s p e c i f i c a t i o n of the model. 4.1  The  G e n e r a l i s e d McFadden GNP  The  GNP  f u n c t i o n framework o u t l i n e d  is a g a i n used  factor  i n the previous  i n the models presented here. The  r e g a r d i n g p r o f i t maximising and  Function  markets, and  firms,  the  same  Chapter  assumptions  perfect competition i n  c h a r a c t e r i s t i c s of  the  goods  aggregate  technology s e t are made. Imports are again assumed to be an input to  the  production sector  while  exports are  an output  of  the  p r o d u c t i o n s e c t o r not consumed d o m e s t i c a l l y . Aggregate c a p i t a l i s again assumed to be the o n l y f i x e d s c a l e are imposed  with r e s p e c t to  outputs are i n c l u d e d i n each these are (exports),  the 4  export  domestic  c a p i t a l . Seven  (import)  sales  (second)  components, aggregate  and  labour.  Imports  and the same data  to net  model imports  and  labour  s e t as that  of  3 i s used.  On the is  aggregate  model. In the f i r s t  q u a n t i t i e s are again negative Chapter  input and constant r e t u r n s  b a s i s of these assumptions the aggregate  represented  by  the  following  Generalised  technology  McFadden  GNP  function; (4.1)  G(p,K)/K = (1/2) +  where time  Zili  Ijfi b  i  t  s u p e r s c r i p t s have  P  i  t  +  b i j  p p /p i  j  b ^ C Z i l !  again  7  C  + lilx i P i  )t  been d e l e t e d  biPi  2  and  parameters s a t i s f y the f o l l o w i n g symmetry r e s t r i c t i o n s ;  49  the  b^  (4.2) The and  bj^j = b j j  f o r a l l i , j = 1,..,6.  v a r i a b l e t i s a time trend r e p r e s e n t i n g t e c h n i c a l the exogenous parameters  are s e t equal to the average  output q u a n t i t y per u n i t of c a p i t a l As noted  progress net  input q u a n t i t y f o r 1=1,..,7.  i n the preceding Chapter,  the G e n e r a l i s e d  McFadden  (GM) r e s t r i c t e d p r o f i t f u n c t i o n i s s e n s i t i v e t o the c h o i c e of the numeraire  good  (good  7  Symmetric G e n e r a l i s e d overcomes t h i s  as  specified  McFadden  (SGM)  s e n s i t i v i t y the  in  (4.1)).  form used  non-symmetric  While  in  Chapter  GM form  imposed i s precluded  SGM model of  by the  t h i s s i z e with  equation  3  i s more  t r a c t a b l e when e s t i m a t i n g a l a r g e model. In f a c t , i n the context e s t i m a t i o n of an  the  present  curvature  size constraint  i n the  n o n - l i n e a r a l g o r i t h m of the SHAZAM package. Domestic s a l e s s u p p l y was used as the  numeraire good i n both  here. The GM form has the form of not  the GM models  estimated  f u r t h e r s l i g h t advantage over the  being l i m i t e d t o  being f l e x i b l e a t  j u s t one  SGM  price  vector. By a p p l y i n g  H o t e l l i n g ' s Lemma  output s u p p l y equations (4.3) X j / K = Zjli  b  b  (4.4) x /K = - ( l / 2 ) Z ! Z = b i  s e t of net  i s obtained;  ijPj/P7 +  ?  the f o l l o w i n g  1  j  1  i + it D  i j  t  +  b  t t i  P P / 7 + b i  j  P  c  t  2  +  + b  ?  ? t  u  i ' i=l/./6;  t + b  t f c  C t 7  2  + u  ?  The v e c t o r s of e r r o r terms f o r the o b s e r v a t i o n s are again assumed to  be  independently  d i s t r i b u t i o n with  distributed  zero  means  and  with  a  multivariate  c o v a r i a n c e • matrix  normal The  e s t i m a t i n g system thus c o n s i s t s of (4.3) and (4.4) s u b j e c t to the symmetry r e s t r i c t i o n s  (4.2).  50  I f the  matrix of  positive semi-definite  estimated q u a d r a t i c  then the  g l o b a l l y convex i n p r i c e s s e m i - d e f i n i t e then Wiley, Schmidt  and  again  Bramble  i  restricted profit  (Diewert  I t can  terms B = [ b j ] i s  1985). I f  function i s  B i s not  be reparameterised  technique of  replacing  positive  using B  the  by the  product of a lower t r i a n g u l a r matrix and i t s transpose; (4.5)  B = AA' where A = t a ^ j J  ; i , j = l , . . , 6 ; and a j = 0 f o r i < j . i  E s t i m a t i o n of the r e s u l t i n g system r e q u i r e s the use of n o n - l i n e a r regression  techniques.  For s i m p l i c i t y of  p r e s e n t a t i o n , o n l y the c o n v e n t i o n a l  net  output supply e l a s t i c i t i e s d e r i v e d from the estimated system  are  discussed  i n the  following  section.  The  conventional  price  e l a s t i c i t i e s a r e g i v e n by; (4.6)  E  i ; J  =  dinX  d i n p^ = D P ^ p ^ / X j ^  j /  where DP^j i s the second profit  f u n c t i o n and  X  ; i,j=l,..,7,  order p r i c e d e r i v a t i v e of the r e s t r i c t e d  i s the estimated q u a n t i t y of net output  i  obtained from the system of net output supply equations (4.4). In  the GM  case the  second  order  (4.7)  DP  (4.8)  DP  i ?  = -Z-j^! i j P j / P 7  (4.9)  DP  7 ?  = 1 ^  i:j  = b  i ; j  /p  7  for i,j=l,..,6;  b  b  2  i j P i P j  51  f  o  /p  i = l / . . , 6 ; and  r  3 7  .  ( 4 . 3 ) and  price derivatives  g i v e n by;  i  are  4.2  Results I n i t i a l estimation  (import) models without d i d not s a t i s f y the  of both the curvature  first  convexity i n prices  of zero f o r the q u a d r a t i c terms, and equal to  second  imposed produced systems  the n o n - l i n e a r a l g o r i t h m of SHAZAM was  parameters s e t  (export) and  p r o p e r t y . In a l l  used with s t a r t i n g  the constant and  values obtained  technology  from r e g r e s s i n g  r e p r e s e n t the p o l a r L e o n t i e f case where there i s no  values  substitution  s i x e i g e n v a l u e s of the estimated  matrix were n e g a t i v e , i n d i c a t i n g  that  the B matrix  f a i l e d to  B be  s e m i - d e f i n i t e . In the l i n e a r export model case three out  of the seven estimated Subsequent  own-price e l a s t i c i t i e s had  imposition  r e p a r a m e t e r i s i n g the  B  of  The  log  compared to  for  of the  the  the wrong s i g n .  requirements  slower  which c u r v a t u r e  likelihood  443.74  curvature  matrix produced  r e f l e c t i o n of the degree to be met.  these  l i n e a r export model converged r e l a t i v e l y  q u i c k l y but three out of the  positive  cases values  v a r i a b l e s a g a i n s t the dependent v a r i a b l e s . These s t a r t i n g  between net outputs. The  which  convergence,  initially  failed  n o n - l i n e a r system was  linear  system  by  without  a to  423.48  curvature  imposed. The  import model had  negative and wrong  two  sign.  Imposition  log  compared to imposed.  The  out of the s i x B matrix  of the estimated  convergence of the v a l u e s . The  two  of  510.05 fact  own-price e l a s t i c i t i e s had  curvature  n o n - l i n e a r model from  likelihood for that  of the  the the  again  led  to  the L e o n t i e f  system  non-linear  without  import  the  slower starting  n o n - l i n e a r system was  linear  52  eigenvalues  497.75  curvature  model's  log  likelihood for  the  the  is  closer  to  corresponding  import  model  requirements restriction parameter  the  case  estimates  for  variation  i n the  Own-price presented of  Agricultural  obtained  the  correspond 0.72  in  the  aggregator  the  of  of  exports  0.53  of  to  10.58.  to  export  magnitude  of  of  less  The  of  a  non-linear  in Table  observed  due  4.1.  to  lack  variables.  the  export  model  for  are  exports  closely  to  those  Chapter  The e x p o r t  model  3.  compared t o  elasticities. and  two  curvature  correspond  0.63  0.85  for  The e l a s t i c i t i e s  of  Energy  models,  compared t o  the  results  Vehicles, these  0.76.  f r o m 1.84  imposition  0.90  Minerals  model  model  are  the  of  that  Products  ranging  0.39  to  also  f r o m 0.39  to  0.76  to  in  the  in  the  model.  elasticities  in  to  between t h e  export  aggregator  from  model  case  fact  represents  dependent  the  the  presented  for  is  the  own s u p p l y e l a s t i c i t i e s  f r o m 0.70  The r e s e m b l a n c e case  are  estimates  aggregator  closely  meeting  import model.  ratio  The  than  reflects  R-square values are  quantity  exports  model  curvature  the  aggregator  range  for  of  of  to  b o t h models  4.2.  corresponding  supply  values  and F o r e s t r y P r o d u c t s  from the  elasticities  linear  closer  elasticity  in Table  the  model  imposition  A g a i n some low e q u a t i o n of  of  export came  and so in  that  In  unstable These  model's  were o b t a i n e d  Textile  down,  were  the  model,  and  export of  results  as i n the  stable  unreasonable are and  the  linear  and  magnitude  not of  model.  a  Use  result  of  a  these ranging  for  similar  In  ranged  however,  major c a u s e  are  elasticities  53  however,  and E l e c t r i c a l P r o d u c t s .  elasticities  performance  curvature  breaks  concern of  the  sign  and  different  numeraire  good  in  elasticities.  This  take  of  account  vehicle export  the result  the  exports  model may,  influence  indicates  of  a reasonable  compared t o model export  0.41  indicates  0.64  the  the  decreasing  component whereas  the  aggregator  export  over the  model  for both domestic  In t h e  domestic  of  much g r e a t e r  responsiveness  elasticity  range  aggregator  model.  of  beginning  1.15  to  Labour  m a g n i t u d e between a l t h o u g h the  sales  the  of  the  period.  demand e l a s t i c i t i e s model  although they  than those  of  aggregator  elasticities agreement  the for  with  the the  trend  the  at  on  of  components.  54  this slight  to  end  demand. indicates  0.51  of  of the  aggregate to  models  third  and  those  the are  the  period at  the  import of  somewhat  then,  for  an  similar  responsiveness  Overall,  the  increasing  are  average  e x p o r t and a g g r e g a t o r exception  export  model w i t h  0.02  the  greater  are  of  aggregator  export model's  model.  a  e x p o r t model  similar pattern  aggregator  1.81  for  indicates  elasticities  indicates  follow a  a  compared t o  models  The  The  s u p p l y and l a b o u r  the  demand  two  e x p o r t model  supply,  1.60  to  period.  sales  than  of  elasticities  model.  model  The  exports  responsiveness  indicates  responsiveness case  for  to  raised  and t e c h n o l o g y .  aggregator  of  The  which  magnitude r a n g i n g from 0.85  for  in responsiveness  Auto Pact  these  failure  P r o d u c t s a l t h o u g h the  a trend  increase  on  the  more r e s p o n s i v e n e s s  o r d e r of  to  of  effect  be due t o  given prices  Heavy I n d u s t r i a l and S e r v i c e are  little  in part,  manyfold for  model a l s o  had  the  higher  own-price largely  fourth  in  export  The  important d i f f e r e n c e between the export and  models becomes apparent the  year  1970  are  i n d i c a t e d that a l l  aggregator  i n Table 4.3 where c r o s s e l a s t i c i t i e s f o r  presented.  Whereas  4 export components  the  aggregator  model  were complementary,  export model i n d i c a t e s that exports of A g r i c u l t u r a l and  Forestry  Products are s u b s t i t u t a b l e with exports of V e h i c l e s , T e x t i l e Electrical  Products which are i n t u r n s u b s t i t u t a b l e with  of M i n e r a l s and Energy Products.  and  exports  Exports of M i n e r a l s and  Products are a l s o s u b s t i t u t a b l e with exports of Heavy and  the  Energy  Industrial  S e r v i c e Products. The d i s a g g r e g a t e d export model thus g i v e s a  quite d i f f e r e n t  impression  export components This d i f f e r e n c e  than does c a r r i e s over  of  the  relationships  the r e s t r i c t i v e to the  Electrical  aggregator  the  model.  r e l a t i o n s h i p s between  export components and the other aggregate V e h i c l e s , T e x t i l e and  between  the  net outputs. Exports of  Products  d i s p l a y the  opposite  r e l a t i o n s h i p to aggregate  imports, labour and domestic  sales  than  do the  components  model  and  other  aggregate  3  export  exports  between aggregate  in  the  in  aggregator  imports, labour and domestic  elasticities indicates  are greater  Agricultural, aggregator to  now to  the import  presented price  Forestry  and  in  4.4.  responsiveness Service  relationships  s a l e s are the same  model.  model, own Table  export  model.The  i n the export model as i n the aggregator Turning  the  Products  net output The  price  import  for than  model  imports does  of the  model with a range of -0.71 to -1.89 compared to -0.36  -0.76 f o r the aggregator  model. Imports of Metals and  Energy  Products, on the other hand, e x h i b i t l e s s p r i c e responsiveness i n  55  the  i m p o r t model  with e l a s t i c i t i e s  ranging  to  aggregator  compared t o  -0.21  -0.80  Machinery,  Electrical  i n the  and  Textile  but the  i n the  i m p o r t model  elasticities  model  does,  are  responsiveness  for  i m p o r t model d o e s both domestic export  while half  its  sales  coincide  domestic  increasing and  the  4 import  components  Vehicles,  C h e m i c a l s and O t h e r  all  largely  consistent are  exports,  same r e l a t i o n s h i p s  as  do  labour  the  demand  lie  approximately  and a g g r e g a t o r for  elasticities  aggregator  domestic  the  model  models. year  1970  are  indicate  that  all  the  exception  These model  The c r o s s  other  sales  i n the  56  both  elasticities  and the  found  aggregator  export  substitutable.  the  price  the  complementary.  i m p o r t components  between a g g r e g a t e the  with  as  P r o d u c t s and M a c h i n e r y ,  are  less  of  complementary with  Products which  i m p o r t components  between t h e  are  import  the  model's  those  export  4 . 5 . The c r o s s  The  for  elasticities  in Table  model  price responsiveness  with  of  bounds.  l a b o u r demand  supply  price  The  closely  sales  Vehicles,  aggregator  size  of  on a v e r a g e .  The i m p o r t  presented  thus  the  models.  i m p o r t model c r o s s  and T e x t i l e  i n the  t h a n does  half  -0.30  Imports  and  considerably  exports than  supply  way between t h o s e The  less  indicate  and a g g r e g a t o r  elasticities  indicate  aggregate  model w i t h e l a s t i c i t i e s  than  to  c o n s i d e r a b l y more  within reasonable  however,  model.  Products  C h e m i c a l s and O t h e r P r o d u c t s b o t h e x h i b i t responsiveness  from -0.08  Electrical results  finding  are that  elasticities  a g g r e g a t e s as  and l a b o u r a l l  aggregator  of  model.  well  as  indicate  4.3  Conclusions Examination  of the  d i s a g g r e g a t e d export and  import  which do not make use of the s e p a r a b i l i t y assumption apparent  advantages and disadvantages  f u n c t i o n model.  The  aggregator  model  s t a b l e estimates of the own-price e l a s t i c i t i e s import  components,  elasticities  but  f o r domestic  the e x c e p t i o n of  less  stable  aggregator  produces  of  the  is d i f f i c u l t  or most  three models agree  estimates.  One  feature  unstable, "best"  which  all  responsiveness of domestic  sales  labour demand. In f a c t , the models i n d i c a t e t h a t  rate p o l i c i e s  would now  labour demand and,  have a  major impact  on the  l a r g e changes i n the magnitude  of  that  relatively  s a l e s supply e l a s t i c i t i e s  should be placed  Rather, a range  of s p e c i f i c a t i o n s should  the s t a b i l i t y of the  on any one  s e t of  be t r i e d to  is  i n the  c o n c l u s i o n one must draw from t h i s i s t h a t  too much weight  area of  is  of v a r i o u s e l a s t i c i t i e s . T h i s  best i l l u s t r a t e d by the domestic  As expected,  level  three models i l l u s t r a t e  r e l a t i v e l y s m a l l changes i n s p e c i f i c a t i o n can produce  three models. The  wage  hence, on employment.  Another f e a t u r e which the  i n the  the  upon, however, i s t h a t there has been a marked  trend towards i n c r e a s i n g p r i c e supply and  With  e l a s t i c i t y estimates f o r  to judge which s p e c i f i c a t i o n produces the  accurate e l a s t i c i t y  and  price  labour demand.  t h i r d export component which are i m p l a u s i b l y l a r g e and it  more  f o r the export  estimates  s a l e s supply and  the export model  r e v e a l s some  r e l a t i v e to the  function  models  not  estimates. determine  results.  the major d i f f e r e n c e between the models cross e l a s t i c i t i e s .  57  In p a r t i c u l a r ,  the  comes export  model r e s u l t s  do not  i n d i c a t e complementarity  export components as found of these r e u l t s then,  it  i n the aggregator  over  the  basis  would appear that the aggregator  model  larger  d i f f i c u l t y producing s t a b l e other hand, the  component own-price  disaggregated  the  models  elasticity  which  models appear  to have  r e l a t i o n s h i p s between the  the c r o s s  Into account.  relationships  I f the main i n t e r e s t i s i n  the an  individual  components. Which of the two approaches i s used should take considerations  have  estimates f o r a l l net outputs. On  larger disaggregated  advantage In d e t e c t i n g  the  model. On the  has advantages i n producing s t a b l e estimates  between a l l  these  detecting  then the l a r g e r d i s a g g r e g a t e d model would  appear t o be more s u i t a b l e .  58  TABLE 4.1 GM PARAMETER ESTIMATES Export Coefficient a  1 1  Model  Import 1  Model  0.3784  0.6077  Export Coefficient  2  Model  Import 1  Model  2  a  55  0.0360  -0.1328  a  65  0.1165  -0.1268  66  0.0123  0.1616  0.6301  1.0301  a  21  0.1884  -0.2257  a  31  -0.3349  -0.0543  a  a  41  0.0774  -0.1761  b  a  51  -0.4376  -0.1101  b  2  0.5588  -0.2915  a  61  -0.8882  -0.9145  b  3  -1.1873  -0.1006  a  22  -0.1849  0.2669  b  4  0.0765  -0.2559  a  32  0.7611  0.0119  b  5  -0.8355  -0.1322  a  42  0.1562  -0.1131  b  6  -2.8092  -2.3840  a  52  0.1212  -0.0286  b  7  3.4573  2.6636  a  62  0.2803  -0.2785  b  lt  0.1038  0.5178  a  33  -0.2829  -0.0681  b  2t  0.0680  -0.0929  a  43  -0.0820  -0.0622  b  3t  0.2045  -0.0272  a  53  0.5151  -0.1998  b  4t  0.1827  -0.0605  a  63  -0.1768  0.5283  b  5t  -0.2679  -0.0983  a  44  -0.3573  -0.3628  b  6t  -0.3094  -0. 4292  a  54  0.0385  0.2103  b  7t  0.8264  1.0296  a  64  0.6002  0.0484  b  tt  -0.1439  -0.1583  Equation 1  0.1190  0.8147  Equation 5  0.9349  0.9550  Equation 2  0.1243  0.9316  Equation 6  0.9795  0.9802  Equation 3  0.9322  0.6754  Equation 7  0.7499  0.6070  Equation 4  0.9475  0.7721  R  2  l  Values  59  TABLE 4.1 (CONTINUED) The s u b s c r i p t s and equation numbers 1,..,7 r e f e r t o A r i c u l t u r a l and F o r e s t r y Product E x p o r t s , M i n e r a l s and Energy Product E x p o r t s , V e h i c l e s , T e x t i l e and E l e c t r i c a l Product E x p o r t s , Heavy I n d u s t r i a l and S e r v i c e Product E x p o r t s , Aggregate Imports, Labour and Domestic S a l e s , r e s p e c t i v e l y . 2 The s u b s c r i p t s and e q u a t i o n numbers 1,..,7 r e f e r t o Aggregate Exports, A g r i c u l t u r a l , F o r e s t r y and S e r v i c e Product Imports, Metals and Energy Product Imports, Machinery, E l e c t r i c a l and T e x t i l e Product Imports, V e h i c l e s , Chemical and Other Product Imports, Labour and Domestic S a l e s , r e s p e c t i v e l y . x  60  TABLE 4.2 EXPORT MODEL OWN Year  E  AF  E  ME  E  PRICE ELASTICITIES  VTE  E  HIS  E  M  1  E  L  E  D  1962  0 .7147  0. 4636  10 .5813  1. 8161  -2. 6624  -0 .9502  1. 0416  1964  0 .7087  0. 4414  6 .9753  1. 5493  -2. 5862  -0 .9960  1. 1553  1966  0 .6961  0. 4204  4 .9657  1. 3808  -2. 0776  -1 .0908  1. 1460  1968  0 .7255  0. 4267  3 .2552  1. 2787  -1. 8132  -1 .2627  1. 2462  1970  0 .7557  0. 4459  2 .5020  1. 2045  -1. 6876  -1 .4554  1. 3646  1972  0 .7176  0. 3913  2 .0495  1. 0465  -1. 0762  -1 .6191  1. 3573  1974  0 .7559  0. 4240  2 .4006  1. 0000  -1. 2253  -1 .5926  1. 2052  1976  0 .8024  0. 5132  1 .9087  1. 0106  -1. 2115  -1 .9671  1. 4234  1978  0 .8466  0. 6023  1 .8459  0. 8972  -1. 3623  -2 .1072  1. 5198  1980  0 .9023  0. 7216  1 .9225  0. 8451  -1. 7266  -2 .2312  1. 6016  1 The s u b s c r i p t s AF ME, VTE, HIS, D r e f e r to M, L and A r i c u l t u r a l and F o r e s t r y Product E x p o r t s , M i n e r a l s and Energy Product Exports, Vehicles, Textile and E l e c t r i c a l Product E x p o r t s , Heavy I n d u s t r i a l and S e r v i c e Product E x p o r t s , Aggregate Imports, Labour and Domestic S a l e s , r e s p e c t i v e l y .  61  TABLE 4.3 1970 CROSS ELASTICITIES Change i n Quantity  - EXPORT MODEL  1  With Respect t o P r i c e o f : AF  ME  VTE  HIS  M  L  D  o f : AF  0.756  0.384  -0.570  0.151  -0.988  -2.439  2.701  ME  0.447  0.446  -1.089  -0.088  -0.743  -1.887  2.914  VTE  -0.482  -0.661  2.502  0.432  0.400  2.930  -4.990  HIS  0.219  -0.109  0.741  1.205  -0.600  -2.312  0.856  M  0.522  0.337  -0.250  0.218  -1.688  -1.551  2.410  L  0.280  0.186  -0.398  0.183  -0.338  -1.455  1.542  D  0.204  0.189  -0.445  0.045  -0.345  -1.012  1.365  The l a b e l s AF, ME, VTE, HIS, M, L and D r e f e r to A r i c u l t u r a l and F o r e s t r y Product E x p o r t s , Minerals and Energy Product E x p o r t s , V e h i c l e s , T e x t i l e and E l e c t r i c a l Product Exports, Heavy I n d u s t r i a l and S e r v i c e Product E x p o r t s , Aggregate Imports, Labour and Domestic S a l e s , r e s p e c t i v e l y . 1  62  TABLE 4 . 4 IMPORT MODEL OWN PRICE Year  E  X  E  AFS  MN  E  E  ELASTICITIES  MET  E  VCO  1  E  L  E  D  1962  0 .7115  -1. 6126  -0 .1332  -3 .4082  -1 .8418  -0 .9207  0 .4987  1964  0 .6448  -1. 8946  -0 .1296  -3 .0592  -1 .5716  -0 .9680  0 .5511  1966  0 .5795  -1. 5893  -0 .1170  -2 .5197  -1 .2522  -1 .0612  0 .5891  1968  0 .5418  -1. 3762  -0 . 1084  -2 .3039  -1 .0780  -1 .2217  0 . 6746  1970  0 .5146  -1. 3613  -0 .1055  -2 .1502  -0 .9290  -1 .3998  0 .7818  1972  0 .4517  -0. 7099  -0 .0824  -1 .6090  -0 .7101  -1 . 5604  0 .8015  1974  0 .4688  -0. 8012  -0 .1447  -1 .7685  -0 .6626  -1 .6089  0 .8227  1976  0 . 4716  -0. 7293  -0 .1529  -1 .6312  -0 .6549  -1 .9516  0 .9877  1978  0 .4842  -0. 7921  -0 .1758  -1 .6337  -0 .7798  -2 .0249  1 .0130  1980  0 .5059  -0. 8581  -0 . 3010  -1 .6102  -0 .9053  -2 . 0682  1 .0286  1 The s u b s c r i p t s X, AFS, MN, MET, VCO, L and D r e f e r t o Aggregate Exports, A g r i c u l t u r a l , F o r e s t r y and S e r v i c e Product Imports, Metals and Energy Product Imports, Machinery, E l e c t r i c a l and T e x t i l e Product Imports, V e h i c l e s , Chemical and Other Product Imports, Labour and Domestic S a l e s , r e s p e c t i v e l y .  63  TABLE 4.5 1970 CROSS ELASTICITIES Change i n Quantity of; X  - IMPORT MODEL  1  With Respect t o P r i c e o f ; X  AFS  MN  MET  VCO  L  D  0.515  -0.264  -0.050  -0.139  -0.095  -1.088  1.122  AFS  1.107  -1.361  -0.137  -0.072  -0.142  -1.497  2.102  MN  0.412  -0.211  -0.106  -0.145  -0.245  -0.181  0.531  MET  1.377  -0.170  -0.176  -2.150  0.542  -2.568  3.145  VCO  0.530  -0.188  -0.167  0.305  -0.929  -0.335  0.785  L  0.448  -0.147  -0.009  -0.107  -0.025  -1.400  1.240  D  0.301  -0.134  -0.018  -0.085  -0.038  -0.808  0.782  The l a b e l s X, AFS, MN, MET, VCO, L and D r e f e r to Aggregate Exports, A g r i c u l t u r a l , F o r e s t r y and S e r v i c e Product Imports, Metals and Energy Product Imports, Machinery, E l e c t r i c a l and T e x t i l e Product Imports, V e h i c l e s , Chemical and Other Product Imports, Labour and Domestic S a l e s , r e s p e c t i v e l y . 1  64  5.  A  PLANNING  As  I CE  MODEL.  In other areas o£ economics I t i s important to a l l o w  imperfect imperfect regard  PR  adjustment  in  adjustment i s  to traded  the likely  goods due  between the d e c i s i o n to  GNP  function  to be  particularly  buy  leads to an  but then to a longer-term the r o l e  of slow  explanation,  or s e l l  initial  i n the  however, r e q u i r e s  here. Many Canadian  products which  have  increase supply  of, say, a  long lead  is available  the r e s u l t s of models  5.1  The  As a  and  the  adjust  the time  p r i c e s which  to when  function  l i k e l y to  miss traded  of t h i s  which attempt to i n c l u d e  modelling  attention is  fully  p e r i o d . Instead  than  decision  thesis dynamics  f u n c t i o n framework.  imperfect  the use  adjustment which  of "planning  prices"  developed by Woodland (1976,1977). Under t h i s approach do not  Its  primary  r e s u l t , GNP  f o l l o w i n g one  of  P r i c e Approach  An approach to received l i t t l e  are a l s o of  between the  adjustment w i t h i n the GNP  Planning  sector.  at work i n the economy's  goods s e c t o r . T h i s Chapter and  imperfect  goods  adjustment are  much of the u n d e r l y i n g dynamics  and  important example  p a r t i c u l a r mineral  models which assume instantaneous  present  exports  for sale.  balance  s o p h i s t i c a t e d model  times  and  J-curve e f f e c t whereby  traded  a more  in  involved  a good i n t e r n a t i o n a l l y  improvement i s an  adjustment  fact,  important  worsening of the trade  those presented  that supply  In  to the r e l a t i v e l y long lags  i t s u l t i m a t e d e l i v e r y to the end-user. The a devaluation  model.  for  to c u r r e n t  they a d j u s t  in turn  prices within  fully  to a c t u a l  as  producers observation  w i t h i n the p e r i o d to  adjust gradually  65  the  has  planning  prices.  This  behaviour may may  be  interpreted in  have to commit themselves  one  of two  ways. F i r s t l y ,  to input d e c i s i o n s before  p r i c e s are known or even i f c u r r e n t p r i c e s are known the wish to wait and a d j u s t i n g to  see  a new  new  expectations  price  of  to  p r i c e . This  i n the  future  if  current period  p r i c e movements.  input p r i c e s  remain a t t h a t l e v e l then and  s t a b l e . Thus,  optimal  i t may  i t s new  optimal  planning  of  planning  a q u a n t i t y adjustment  change to  quantities  not  a new  path.  l e v e l and  change t h e i r i f the  be p o s s i b l e  then costs  input mix  to  adjustment path  is  or p r o f i t a b l e  t h a t i n the  then  the q u a n t i t y  of the  to  fully  form of b u i l d i n g s , be  increased  adjustment  transformation  f r o n t i e r there w i l l be a normal  frontier.  are  path  will  However,  transformation  p r i c e path  that which  p r i c e v e c t o r w i l l be a dual r e p r e s e n t a t i o n  observationally equivalent  t o , an optimal  path.  66  in  towards  v e c t o r of p r i c e s f o r which  q u a n t i t y d e c i s i o n i s o p t i m a l . Hence, a planning  and  way,  gradually.  to each p o i n t on the boundary of the  approaches the new  a  their  l e v e l over a number of p e r i o d s . I f producers  boundary  corresponding  depending on  Either  Rather, c a p i t a l would  technically efficient f o l l o w the  likened  t h a t the use  gradually  adjust c a p i t a l , p a r t i c u l a r l y the c u r r e n t p e r i o d .  be  producers faced with adjustment  q u a s i - f i x e d inputs w i l l  approach the new  may  whereby producers a d j u s t o n l y part-way  dual r e p r e s e n t a t i o n of  instance,  may  current  An a l t e r n a t i v e i n t e r p r e t a t i o n i s  For  firm  fully  p r i c e s w i l l a d j u s t to a c t u a l p r i c e s o n l y  prices is a  current  i f p r i c e changes are permanent before  p a r t i a l adjustment process towards a  firms  of,  q u a n t i t y adjustment  The p l a n n i n g p r i c e approach attempts t o ensuring  model q u a n t i t y  technical  adjustment paths,  efficiency  disadvantage though t h a t an to  actual  prices  must  has the advantage, over  at  each  of  automatically  point.  It  has  adjustment r e l a t i o n s h i p of  be  specified  to  make  early  the  planning  the  approach  o p e r a t i o n a l . T h i s i n t r o d u c e s a degree of a r b i t r a r i n e s s . In t h i s a p p l i c a t i o n the f o l l o w i n g a d a p t i v e p r i c e  adjustment  model i s used: (5.1)  q  where the q  i  l t  - q ^ t ^ =  (p  D i  - q ^ t ^ )  i t  are p l a n n i n g p r i c e s and p  t  then adjustment of  p l a n n i n g to a c t u a l  a c t u a l p r i c e s . I f D ^=1  i t  prices i s instantaneous.  For the adjustment process t o be s t a b l e the adjustment ,must  then adjustment cyclical  (0,2). I f D  l i e i n the i n t e r v a l  i fD  to is  i  the  new  price  i n the range  parameters  i s i n the range  L  i s monotonic  (1,2). To  while  make t h i s  (0,1) i t is  mechanism  implementable the f o l l o w i n g v e r s i o n i s e s t i m a t e d : (5.2)  q  where the  base  i t  =  DiZ5 = 0  (l-Di) p -j  period  planning price  j  t  +  (l-DiJ^n q  i s treated  i Q  as  a  parameter and estimated a l o n g with the adjustment c o e f f i c i e n t D j . Embedding t h i s p r i c e form f o r  the  GNP  relationship within function  means  that  a standard  functional  non-linear  regression  techniques must be used. The D a v i d s o n - F l e t c h e r - P o w e l l n o n - l i n e a r a l g o r i t h m i n the SHAZAM package was a g a i n used. The p l a n n i n g  p r i c e model estimated uses a u n i t  Leontief restricted c o m p l e x i t y of  the  G e n e r a l i s e d McFadden  profit  function.  estimation forms  Given  procedure,  would be  67  Generalised  the computational  use  of  prohibitive,  the  SGM  or  particularly  given  the  SHAZAM price  size  facility. procedure  equations before  constant  form i s  because the  dependent  the  of  not  GNP to  possible size  capital  were a g g r e g a t e d  returns  to  scale  in  the  suited  to  terms  non-linear  the  variables  of  which are  quantity of The  restricted  of  3  the  into  exports,  G(p,Z)/Z  planning the  share  not  known  b  it 3i  subscripts  parameters  b^j s a t i s f y  The  net  differentiating X j i  /Z  <  have  the  _ b  net  are  i ; J  the  fixed  respect net  3  to  due  to  the  non-  labour  and  constant  aggregate  categories  quantity  capital the  I n p u t and  this  output  imposing  aggregate  Consequently,  t  +  of  were,  i m p o r t s and  fixed thus, the  £i=l  b  the  b  (  t  Z is as  i,j  supply equations  1/2  6  qi  prices + b  68  u  ii*i  +  2  the  aggregate  given  symmetry  for a l l  b (q / )  Leontief  +  2  itt 3i  following  to  Generalised  by:  been d e l e t e d ,  respect i5  given  unit  b^q^'V'  = bji  with  output  planning prices  output  = ZTj = i  is  Zi^Ej^  i n p u t and  (5.4)  to  Chapter  to  sales.  ^1 = 1 time  in  model a n a l o g o u s  SHAZAM p a c k a g e  (minus)  function =  model  a single  with  variable  profit  output  restriction.  Imposed  domestic  net  respect  The r e m a i n i n g 3 v a r i a b l e  quantity  (5.5)  with  using  equation  where  function  scale  linear  (5.3)  not  planning price  a four-variable  stage  returns  i n p u t was  the  equation  estimation.  second  input.  on e a c h  The t r a n s l o g  contain  Estimation the  constraint  by  (5.2).  fixed The  restriction;  = 1,2,3. derived  from  (5.3)  by  are; + b  i  t  t  + b  t ; 2  i  t  t  i=l,2,3.  The  e s t i m a t i n g system thus c o n s i s t s  prices are  given by  s u p p l y equations  (5.2).  (b — ,  D  adjustment c o e f f i c i e n t s  ii./  o£ (5.5)  The parameters b  i t  a n <  *  b  itt  '' **  ne  Pl  net  a n n i n  t o maximise the  Q  9  output price prices  concentrated  f u n c t i o n of (5.5).  E s t i m a t i o n of t h i s model enables the v a l i d i t y of the instantaneous by t e s t i n g whether p l a n n i n g and  0^=1  actual  q u a n t i t y adjustment e f f e c t s of  ( i e . 0<D  adjustment model normally  paths,  and will  price  <1) due  The r e l a t i o n s h i p  instantaneous be  plotted  increases.  f o r exports i  t e s t s t o be c a r r i e d out of  f o r 1=1,2,3.  prices,  simulated  planning p r i c e s prices  of the  planning  (D^) and the base p e r i o d p l a n n i n g  ( q ^ ) a r e a l l chosen s i m u l t a n e o u s l y likelihood  where the  One  and Imports  to the lags  and  by would  used  between imperfect  t r a c k i n g the expect  t o l a g behind  the  actual  i n v o l v e d between  producer  d e c i s i o n s and d e l i v e r y d a t e s . 5.2 R e s u l t s The  maximum  Generalised Leontief p r i c e s are both  likelihood models  presented  parameter  using a c t u a l  i n Table  5.1.  estimates prices  and  f o r the planning  Both estimated  profit  f u n c t i o n s are p o s i t i v e a t a l l o b s e r v a t i o n p o i n t s and s a t i s f y curvature  requirements  of  being  convex  i n prices  the  at a l l  o b s e r v a t i o n p o i n t s . The g r a d i e n t s with r e s p e c t to p r i c e s have the c o r r e c t s i g n s and  so both  estimated  behaved. The  n o n - l i n e a r model  estimates  the  values  of  f o r the  was  Instantaneous  profit estimated  adjustment  p r i c e and technology  69  f u n c t i o n s are using model  the  well  linear  as  starting  parameters i n the  planning  p r i c e model along with values of  0.8  and  1.0  f o r the  c o e f f i c i e n t s and base p e r i o d p l a n n i n g p r i c e s , The  first  result  from 1.0 The  i n d i c a t i n g that  (subject  to  the  between the two  to  i s of  different importance.  c o e f f i c i e n t s are  period  planning  value of 43.58  log l i k e l i h o o d values)  the  strongly rejected important  has a  Chi-square value  Consequently,  base  of 11.34  equal  prices  hypothesis by  allow  the for  of  (twice the  degrees  instantaneous  model.  This  imperfect  production sector a c t i v i t i e s . This  test.  difference  result  of  cent  freedom.  adjustment  indicates  adjustment  to  being  compared to a 1 per  with 3  the  adjustment  be t e s t e d by use of the l i k e l i h o o d r a t i o  test s t a t i s t i c  critical  imperfect adjustment  t h a t a l l adjustment  u n r e s t r i c t e d ) may The  i . e . , are the  i n the p l a n n i n g p r i c e model s i g n i f i c a n t l y  hypothesis  unity  respectively.  of i n t e r e s t to be examined i s whether  two models are s i g n i f i c a n t l y d i f f e r e n t ; coefficients  adjustment  that  when  is  it  is  modelling  i s not unexpected  but  i t remains to e s t a b l i s h whether the p l a n n i n g p r i c e model p r o v i d e s reasonable estimates of the imperfect adjustment As the  base p e r i o d p l a n n i n g p r i c e s  model examination  are estimated  of  the estimated  base p e r i o d  r e l a t i o n s h i p between  actual prices  and  p r i c e s e r i e s p r o v i d e s one of  the model.  In the  input-output data  estimated model the  are o n l y  reasonable to assume would be  c l o s e to  the  t h a t the a c t u a l and probably  70  planning While  onwards  prices prevailing in  s l i g h t l y below  the  planning  base p e r i o d  1961  this  reasonableness  f o r the year 1960.  a v a i l a b l e from  in  values and  estimated  method of checking the  p r i c e r e f e r s t o the p l a n n i n g p r i c e  process.  the 1961  the  it  is 1960  price  index values of 1.0.  The  imports i s indeed 0.95 expected a  base p e r i o d  p l a n n i n g p r i c e estimated  which seems v e r y c l o s e  to what might  p r i o r i . The  estimate  of 0.64  domestic s a l e s p l a n n i n g  price is  somewhat below  expected. The  of  for  estimate  planning price  appears to  higher than the p r i o r to  1.89  the  a c t u a l export  prices l i k e l y  the  impressions. The but  from 0.92 2.94. actual  observation  base  be  period  considerably  to have  prevailed  period  to 2.85  compared to  range  of 1.00  f o l l o w but  to  l e s s resemblance  higher than a c t u a l p r i c e s  comparisons would appear  The  0.97  first  these  f o r both imports and  three estimated parameters  planning  of the  the  prices, being  period  and These  l e s s r e l i a n c e can  with regard to  be  exports than  its  i n t e r e s t i n the model  are  c o e f f i c i e n t s . Using  one  domestic s a l e s .  parameters I n d i c a t e  there i s a  compared to  second h a l f of the p e r i o d .  p l a n n i n g p r i c e adjustment  p r i c e s change when  to  behind  export p r i c e s ,  half  to i n d i c a t e that  model's r e s u l t s  i n t e r p r e t a t i o n , these  Export  to a c t u a l  parameter estimates of most  those of the  confirm  lag further  to 2.94  3.74.  f o r the  lower than a c t u a l p r i c e s f o r the  predictions  to  the a c t u a l p r i c e range of 1.00  import p r i c e s , ranging from  on the  tend  behind the a c t u a l p r i c e s e r i e s , ranging  Import p l a n n i n g p r i c e s a l s o  however, bear  estimated p l a n n i n g p r i c e  p l a n n i n g p r i c e s e r i e s f o r domestic s a l e s c l o s e l y  lags s l i g h t l y  actual price  placed  period  what might  being  be  1961.  for  follows  base  export  be unreasonable,  Comparisons of the a c t u a l p r i c e and series  f o r the  for  how  change i n the  a l l l i e in  71  quickly  planning  actual price.  the range (0,2)  The  required  for  s t a b i l i t y of  the adjustment p r o c e s s .  lie  i n the range  (0,1)  cases  is  monotonic  rather  adjustment c o e f f i c i e n t those  f o r the  supply i s  two  than  traded  to  As  all three  expected,  the  s a l e s i s c l o s e r to u n i t y than  goods i n d i c a t i n g  respond  import  adjustment i n a l l  cyclical.  f o r domestic  q u i c k e r to  export supply and  i n d i c a t i n g that  Furthermore, they  t h a t domestic  actual price  sales  changes than  is  use. Indeed, s t a r t i n g from a p o s i t i o n of  long run e q u i l i b r i u m where the i n i t i a l  a c t u a l and  planning p r i c e s  are e q u a l , an i n c r e a s e i n the  a c t u a l p r i c e of domestic  sales  of  ten  per cent would lead to  i n c r e a s e i n the p l a n n i n g p r i c e  of  7.7  per cent i n the f i r s t  p r i c e s to  the a c t u a l  an  p e r i o d . The adjustment of the  p r i c e changes  graphed i n F i g u r e 5.1.  under these  In the case of domestic  p r i c e approaches the new  planning  conditions  is  s a l e s the p l a n n i n g  a c t u a l p r i c e r e l a t i v e l y q u i c k l y with  the  adjustment e f f e c t i v e l y being complete w i t h i n 5 y e a r s . In the i n c r e a s e 3.4  case of imports  per cent i n the f i r s t  cent i n c r e a s e  in  the  actual  adjustment i s l i k e l y due a s s o c i a t e d with imported initial  price  coefficient  is  10  f a c t , the p l a n n i n g  export  year  price  purchases.  i n response  of  The  planning price  imports.  to a 10 This  The  lags  time elapsed between  export  price  per  slower  order and d e l i v e r y  the e f f e c t i v e adjustment of the years.  would  the  import  adjustment  i s r e l a t i v e l y s m a l l i n d i c a t i n g t h a t adjustment of the  p l a n n i n g p r i c e to the  first  year  to the longer  p r i c e i n c r e a s e and  planning  the import  p r i c e would  i n response  price.  Even  actual price  15  very s l u g g i s h indeed.  o n l y i n c r e a s e 0.7  to a 10 per after  is  cent  years  72  per cent  i n c r e a s e i n the  only  two-thirds  In the  actual of  the  adjustment  would  adjustment  of  have  taken  exports  b r i n g i n g a new  may  p l a c e . While  be  realistic  it  seems  manufacturing exports  and  less  very  sluggish  f o r ventures  mine on stream or expanding  uncleared l a n d ,  this  such  cropping into  plausible  for  the  increasing production  as  virgin,  output  from  of  existing  mines and a g r i c u l t u r a l l a n d . The  alternative  interpretation  p l a n n i n g p r i c e s are simply p a r t q u a n t i t y adjustment initial  prices,  of the model  magnitude  c h a r a c t e r i s t i c s of the  GNP  of the  to  interpret  the i n d i v i d u a l  directly  in  terms  their  the  price  the  changes  t h i s context i t  adjustment  implications  and  for  the  quantity  paths. To g a i n a b e t t e r understanding of the  adjustment  process a s e r i e s of s i m u l a t i o n s were c a r r i e d out.  per cent and  output was  then remain a t  these p r i c e changes on net to  the i n i t i a l  period  the aggregate  fixed  presented i n  Figure  monotonic i n each  The  In  domestic  10 of  subject  a constant l e v e l  of  r e s u l t s of these s i m u l a t i o n s quantity  adjustment  are  paths  from the monotonic  are  rather  of the three p l a n n i n g p r i c e s . the p r i c e  of  s a l e s supply  i n e x p o r t s . Adjustment  years with most of  The  The e f f e c t s  output s u p p l y were s i m u l a t e d  case which f o l l o w s  An i n c r e a s e  decrease  t h i s higher l e v e l .  i n p u t . The 5.2.  quantity  assumed to i n c r e a s e by  technology l e v e l and  than c y c l i c a l adjustment  increases in  in turn  is  coefficients  adjustment  p r i c e of each net  a  path w i l l depend on  f u n c t i o n . Within  difficult  of  the  of the dual r e p r e s e n t a t i o n of  path. The adjustment  the  i s that  domestic s a l e s and  import use  leads and  i s e f f e c t i v e l y complete  the adjustment  occurring  in  i n the f i r s t  73 t  to  to  a  five three  y e a r s . An i n c r e a s e  i n import  import demand and f a l l s is  effectively  p r i c e s leads  to a  large f a l l  i n s u p p l y of the two outputs.  Adjustment  complete i n t e n years with most of the  having taken p l a c e i n the f i r s t  adjustment  f i v e y e a r s . An i n c r e a s e i n export  p r i c e s leads t o i n c r e a s e s i n export supply and import demand a fall  in  domestic  however, with the  sales  in  s u p p l y . Adjustment  process s t i l l  being  i s very  incomplete  and  sluggish,  after  fifteen  years. Finally,  the net  the two models that the  output supply e l a s t i c i t i e s  are presented  in  Table 5.2. I t  instantaneous adjustment  the one p e r i o d response planning price  obtained  should be  model e l a s t i c i t i e s  t o a change i n  model e l a s t i c i t i e s  larger  than  elasticities  the  r e p r e s e n t the  because  p l a n n i n g p r i c e case. the p l a n n i n g  price  more  i s allowed  The c r o s s e l a s t i c i t i e s case  with the  s a l e s supply are  case but s l i g h t The  exception  of  Chapter  of  a  substantially adjustment for  i n the  that  in  between  c o n s t a n t . Exports  s u b s t i t u t e s i n the p l a n n i n g  price  complements i n the instantaneous adjustment  case.  instantaneous  corresponds  to  are a l s o l a r g e r  exports and imports which remains approximately and domestic  the  Accordingly,  instantaneous  adjustment  represent  response  own e l a s t i c i t i e s are a l l  corresponding  noted  a c t u a l p r i c e s while  change i n the p l a n n i n g p r i c e , not the a c t u a l p r i c e . the p l a n n i n g p r i c e model  from  adjustment  elasticities  sign  to t h a t of the instantaneous adjustment  GNP  pattern function  3 although the two s e t s of e l a s t i c i t i e s show responses  s u b j e c t t o d i f f e r e n t c o n d i t i o n s being h e l d f i x e d .  74  In c o n c l u s i o n , then, the p l a n n i n g p r i c e model has served demonstrate when  the importance  modelling  production  imperfect adjustment than f o r those  o£  a l l o w i n g f o r Imperfect  sector  i s more  s u p p l y but may o v e r s t a t e  s a l e s . The  f o r import demand the importance  i n the case of export s u p p l y . To f u r t h e r imperfect adjustment  in  It  adjustment  appears  important f o r t r a d e d goods  s u p p l y i n g domestic  present p l a u s i b l e r e s u l t s  response.  adjustment  following chapter.  75  sectors  and domestic  to  sales  adjustment  i n v e s t i g a t e the r o l e  export s u p p l y and  s o p h i s t i c a t e d model of imperfect  that  model appears  of imperfect  to  import demand a  of more  i s presented i n the  TABLE GENERALISED  LEONTIEF  5.1 PARAMETER  Instantaneous C o e f f i c i e n t  Adjustment  b  DD  1.0320  b  DM  -0.1287  b  DX  (2.10)  2  P l a n n i n g P r i c e  Model  2 .1937  (8.37) (-1.44)  0.0241  (0.04)  -0 .7681  (-4.68)  kMM  0.2807  (5.70)  0 .4843  MX  -0.2825  (-1.70)  -0 .3159  (3.95) (-2.15)  b  X X  0.4468  (0.62)  0 .9386  b  D t  0.2417  (3.72)  -0 .0530  (-0.56)  b  M t  -0.0836  (-4.24)  -0 .1908  (-2.31)  b  X t  0.2081  b  D t t  -0.0609  b  M t t  0.0123  b  X t t  -0.0466  (2.90) (-1.76)  D  D  M  D  X  -0 .0414  (4.93) (-1.79)  0 .0241  (1.18)  (-1.18)  0 .0101  (0.31)  0 .6397  (2.23)  0 .9595  (6.33)  1 .8897  (4.48)  0 .7683  (1.35)  0 . 3403  (6.33)  0 .0666  (59.71)  ^XO D  0 .3971  (4.95)  (1.21)  <3M0  Values  E q u a t i o n  D  E q u a t i o n  M  E q u a t i o n  X  Log  '  -0 .1668  ^DO  2  1  (-0.96)  b  R  E S T I M A T E S  L i k e l i h o o d  0.9216  0.9565  0.8494  0.9819  0.9216  0.9884  186.28  76  208.07  TABLE 5.2  (CONTINUED)  The s u b s c r i p t s and e q u a t i o n l a b e l s D, M and X r e f e r to Domestic S a l e s , Imports and E x p o r t s , r e s p e c t i v e l y . 2 Values i n parentheses are asymptotic t - v a l u e s . TABLE 5.2 1970 NET OUTPUT SUPPLY ELASTICITIES" Instantaneous Adjustment  Model  With Respect to P r i c e of : X  M  D  Chanqe i n  X  0. 4236  -0.4613  0.0377  Quantity of:  M  0. 7445  -1.0934  0.3488  D  0. 0106  -0.0610  0.0504  Planning Price  Model  With Respect to P l a n n i n g P r i c e of X  D  Chanqe i n  X  1.4674  -0.4362  -1.0312  Q u a n t i t y of  M  0.9342  -1.3874  0.4531  D  -0.3832  -0.0786  0.4619  The l e t t e r s X, M and Sales, r e s p e c t i v e l y . 1  M  D r e f e r to E x p o r t s , Imports and  77  Domestic  FIGURE 5.1 ADJUSTMENT OF PLANNING PRICES a) 10% Increase i n Domestic Sales P r i c e Price 1.101  Actual Price Planning Price  1  2  3  b) 10% Increase  1  2  3  4  5  i n Import  4  5  c) 10% Increase i n Export  6  7  10  11  12  13  14  Yrs 15  10  11  12  13  14  Yrs 15  10  11  12  13  14  Yrs 15  Price  6  7  Price  78  FIGURE 5.2 ADJUSTMENT OF QUANTITIES a) 10% I n c r e a s e - i n -Domestic Sales P r i c e Q u a n t i t y Index 1.10  _Domest i c .1 mports  1.00  I n s t a n t . Adjustment Imperfect Adjustment _Exports  0.90 8  9  10  11  12  13  b) 10% Increase i n Import P r i c e Q u a n t i t y Index 1.00  14  Yrs 15  _Domest i c _Exports  x  8 c) 10% Increase i n Export Q u a n t i t y Index 1.20  9  10  11  12  13  _I mports Yrs 14 15  Price .Imports "Exports  1.10  1.00  0.90 9  79  10  11  12  13  Domestic Yrs 14 15  6-  AN  ADJUSTMENT  An approach  to  COSTS  m o d e l l i n g Imperfect  MODEL adjustment  which  proven t o be more popular than the p l a n n i n g p r i c e model i n the  previous  Chapter  e x p l i c i t l y allow  i s the  for costs  development  of adjustment  of  outlined  models  w i t h i n an  has  which  optimising  framework. The aim of these models can be d e s c r i b e d as  modelling  s h o r t and  framework  long run  f a c t o r demands  where the ( c o s t l y ) r a t e of an  endogenous  choice  adjustment  variable  i n t e r r e l a t e d . Shocks which r e s u l t of long-run e q u i l i b r i u m are short-run  equilibrium  is  i s allowed f o r .  unified  of q u a s i - f i x e d  and f a c t o r  factors  demands  maintained  at  of s h o r t - r u n  At the same  are  although  a l l times,  i e . the  demands f o r  variable  time output f e a s i b i l i t y  maintained and the  Le C h a t e l i e r p r i n c i p l e  long-run own-price  e l a s t i c i t i e s are  is satisfied  greater i n  than the c o r r e s p o n d i n g s h o r t - r u n own-price  value  e l a s t i c i t i e s . By u s i n g c o s t s model i t  should be p o s s i b l e to g a i n a b e t t e r understanding of the r o l e  adjustment  costs  is  whereby  absolute  an e m p i r i c a l model d e r i v e d from such an adjustment  imperfect adjustment  is  i n a l l f a c t o r demands being out  c o n s i s t e n t with the models  phenomenon of " o v e r s h o o t i n g " factors  within a  of  i n the GNP f u n c t i o n framework. A t h e o r e t i c a l  model  is  b r i e f l y outlined  in  the  following  s e c t i o n and an econometric a d a p t a t i o n i s then presented. 6.1 A T h e o r e t i c a l E x t e r n a l Adjustment The  t h e o r e t i c a l model used  t h a t of  Berndt, Fuss  section  draws  Waverman model i s  i n t h i s a p p l i c a t i o n i s s i m i l a r to  and Waverman  on t h e i r i n turn  Costs Model  (1977, Chapter  presentation.  The  d e r i v e d from Lucas'  80  4) and  Berndt,  Fuss  (1967) model  this and of  e x t e r n a l adjustment c o s t s where z) a r e f i x e d to  quasi-fixed  factors  (denoted  i n the s t o r t - r u n but can be v a r i e d over time  positive,  increasing  marginal adjustment  marginal  costs  of  c o s t s a r e denoted by  C  m  subject  adjustment. (z ) m  by  The  where z  m  d z / d t and where; m  (6.1)  C ( 0 ) = 0 , C ' ( z ) > 0 , C » ( z ) > 0 ; m=l,..,M. m  m  m  m  m  Firms a r e assumed t o know the p r i c e s of v a r i a b l e net outputs with c e r t a i n t y and have s t a t i c expectations Adjustment production  c o s t s are e x t e r n a l  i s unaffected  outputs and f i x e d  value of  current  by changes i n the q u a s i - f i x e d  factors  i s a f f e c t e d . Time paths f o r v a r i a b l e  inputs  net r e c e i p t s  those p r i c e s .  i n the sense that  although future p r o d u c t i o n net  regarding  are chosen t o maximise the  given  the  initial  stock  of  present  quasi-fixed  i n p u t s . The present value of net r e c e i p t s i s ; (6.2)  V(0) = / ° ° 0  e " R ( t ) dt r t  where r i s the a p p r o p r i a t e net  discount  i s the value of  receipts. Using  a restricted  standard p r o p e r t i e s concavity  in z  profit  (6.3)  R(t)  first  function  of H o t e l l i n g ' s  and denoting  H(p,z), the revenue f u n c t i o n  The  r a t e and R(t)  Lemma,  the r e s t r i c t e d  which s a t i s f i e s convexity profit  the  i n p and  function  by  (R(t)) can be w r i t t e n as;  = H ( p ( t ) , z ( t ) ) - zjlx  C (z (t)). m  order c o n d i t i o n with respect  m  t o the q u a s i - f i x e d  inputs  from the maximisation of the present value of net r e c e i p t s i s now given by; (6.4)  H  - rC '(z )  z  m  m  + C "(z )z m  m  m  m  81  = 0 ;rd = l,..,M.  A stationary  solution for  the  quasi-fixed  inputs  exists  when  ZjjfZnfO and hence s a t i s f i e s ; (6.5)  H ( p , z ) - r C ' ( 0 ) = 0. Z m  m  T h i s c o n d i t i o n can be shown that  in  a  steady  quasi-fixed  input  state  to be e q u i v a l e n t the  equals  marginal  net s u p p l i e s  of the  obtained  substituting  the  by  quasi-fixed  inputs  Lucas shows  value  i t s marginal  steady s t a t e  to the  v a r i a b l e net state  i n t o the r e s t r i c t e d p r o f i t  p a r t i a l adjustment l i t e r a t u r e  product  accumulation  steady  that t h i s model  of  the  cost.  The  outputs can values  of  be the  function.  can be l i n k e d  (where  requirement  to the ad  a c t u a l stocks  are  hoc  adjusted  part-way towards some optimal l e v e l each p e r i o d ) by the s h o r t - r u n demand f o r q u a s i - f i x e d  inputs d e r i v e d  from (6.4) and (6.5)  being  an approximate s o l u t i o n to a l i n e a r d i f f e r e n t i a l equation system. In the case system t o  of one q u a s i - f i x e d which  (6.4) and  input the d i f f e r e n t i a l  (6.5)  are an  approximate  equation solution  reduces t o ; (6.6)  z = B~(z~(t)  - z(t))  where z~ i s the steady s t a t e q u a s i - f i x e d  input  l e v e l and B~ i s an  endogenous adjustment parameter given by; (6.7)  B~ = -(1/2) [r - { r  2  - 4H"(z~)/C"(0)}  1 / 2  ].  Since H l s concave i n z and C"(0)>0, B~ must l i e between zero and one  so t h a t the  a c t u a l stock  monotonically. Further, r a p i d l y then B~  as  approaches  marginal adjustment  approaches zero  adjustment parameter i s  the steady s t a t e  and no  also affected  r e s t r i c t e d p r o f i t f u n c t i o n and the  82  costs  stock  increase  adjustment occurs. by the  curvature  interest rate  of  (a decrease  The the in  I  the  interest rate acts  result,  the  to increase  the  parameter  is  adjustment  adjustment speed). As determined  a  within  the  Implemented e m p i r i c a l l y the  zero  economic model. Before t h i s model can  be  d e p r e c i a t i o n assumption has of adjustment  to be r e l a x e d ,  f u n c t i o n must  have to be chosen f o r  the u n i t s of the  be s p e c i f i e d  and  cost  functional adjustment  cost  f u n c t i o n s . To s i m p l i f y the p r e s e n t a t i o n ,  i t w i l l be assumed  that  there  To  is  only  depreciation depreciates (6.8)  one  it  the r e s t r i c t e d p r o f i t and  forms  q u a s i - f i x e d input.  will  be  assumed  the  e x p o n e n t i a l l y a t the r a t e d. We  non-zero  quasi-fixed  input  then have;  the stock  of z. We  now  specify  as;  (6.9)  C(z)  = qy +  qD(z)  where q i s the a s s e t p r i c e of the q u a s i - f i x e d Using quasi-fixed  (6.9)  the c o s t  input  i s now  c o s t s are s p e c i f i e d The  for  z = y - dz  where y i s the gross a d d i t i o n to C(z)  that  allow  present  (6.10)  value  V(0) = / Q  of not  changing the  0  in  e  _ r t  l e v e l of  the c o s t of d e p r e c i a t i o n and terms of the  fixed  of net r e c e i p t s f u n c t i o n 0  input.  { H ( t ) - qdz  n o t i n g t h a t y=z+dz. I n t e g r a t i n g the  - qD(z)  adjustment  input's a s s e t (6.2)  now  - qz}  y^  0 0  e " q z dt = / ] r t  c  Substituting this (6.12)  qz(0)  C P  dt  l a s t term i n (6.10) by  e " r q z dt - q z ( 0 ) . r t  i n (6.10) y i e l d s ;  + V(0) = / v  G 0 u  = Jo®  e~ {H(t)_ rt  W(0)  83  dt  price.  becomes;  produces; (6.11)  the  - uz - qD(z)} dt  parts  where u=q(r+d) i s the user Maximising equivalent qz(0)  to  c o s t of the q u a s i - f i x e d  the present  maximising the  i s an i n i t i a l  value  of net  r i g h t hand  c o n d i t i o n . The f i r s t  receipts  s i d e of order  input. ls  (6.12)  now  since  condition for this  maximisation problem now becomes; (6.13)  dW(0)/dz - d{dW(0)/dz)/dt = 0  which i s ; (6.14) The  z  - u - rqD'(z) + qD"(z)z  H ( p , z ) - u - rqD»(0) = 0. z  adjustment parameter B~ i s now g i v e n by;  (6.16)  B~ = -(1/2) [r - i r  T h i s completes the and  =0.  steady s t a t e s o l u t i o n must then s a t i s f y ;  (6.15) The  H  the next task  2  -  4H (p,z)/(qD"(0))} z z  t h e o r e t i c a l external  i s to  1 / 2  1.  adjustment c o s t s  model  s p e c i f y an implementable v e r s i o n of the  model. 6.2 An Econometric In t h i s used i n  Adaptation  a p p l i c a t i o n the e x t e r n a l adjustment c o s t s model  conjunction  with  the four-net  aggregate model of Chapter 3 t o estimate long-run  output, o n e - f i x e d  input  s h o r t , intermediate  and  responses of net outputs to changes i n p r i c e s . The  four  net outputs are aggregate e x p o r t s ,  aggregate imports,  labour  domestic s a l e s . C a p i t a l l s again t r e a t e d as the s o l e f i x e d The  same assumptions r e g a r d i n g  competition of the  is  p r o f i t maximising f i r m s ,  and  input. perfect  i n goods and f a c t o r markets, and the c h a r a c t e r i s t i c s  aggregate  technology s e t a r e  assumed to be an input t o the p r o d u c t i o n an output of the p r o d u c t i o n  made. Imports s e c t o r while  are  again  exports are  s e c t o r not consumed d o m e s t i c a l l y . The  84  same data s e t i s capital  i s now  used  as i n Chapter 3  d e r i v e d e x p l i c i t l y r a t h e r than as a r e s i d u a l .  c a p i t a l asset p r i c e , listed  except t h a t the p r i c e  user cost  and  quantity  i n Appendix 1 along with the d i s c o u n t  The  aggregate technology  Generalised  and  represented  by the f o l l o w i n g f u n c t i o n as  (1985);  H(p,K) = a = l  b i P i + d/2)  + Zi=l b PiK i K  Zi=l Z j i l  + Zi=l b  i t  b  i j  p  b (Zn=l  K t  the  /p4 Pn)K  K K  Pn)t  t t  parameters again s a t i s f y  i P j  b (Zh=l  p i t + (1/2)  + b ( Z n = l Pn)Kt + (1/2) where the bj_j  The  rate.  McFadden or b i q u a d r a t i c r e s t r i c t e d p r o f i t  s p e c i f i e d by Diewert (6.17)  i s now  are d e s c r i b e d  of  2  2  following  symmetry  restrictions; (6.18)  b  f o r a l l i , j = 1,2,3.  = bji  i:j  A time trend i s again used to represent should  be  noted  McFadden GNP  function  thesis i n that r e s p e c t to  that  this  the  i n f o r m a t i o n on  from  returns  fixed capital the  to s c a l e are input  suggestion,  the second order c a p i t a l  and  of  the  those used  Generalised this  not  imposed  with  to  obtain  more  and,  following  weights on the p r i c e s  technology  terms  It  in  process  the  index.  earlier  i n order  c a p i t a l adjustment  Diewert's (1985, p.90)  the  specification  differs  constant  the technology  are s e t equal  in to  i n v e r s e of the base p e r i o d p r i c e s . By a p p l y i n g  H o t e l l i n g ' s Lemma  output supply equations (6.19)  i K  K t  X4 = b  4  + (1/2)  - (1/2)  s e t of  i s obtained;  X i = bi + Zj=i bijpj/p4 + b K + b + b Kt  (6.20)  the f o l l o w i n g  b tt  2  t  i t  t  + (1/2)  b  K K  ; 1=1,2,3;  3 3 Z i = l l j = l b i j p i p j / p 4 + b4 K + b4tt K  85  K  2  net  + (1/2) b I f the  matrix  K K  K  + b Kt  2  of  positive semi-definite  estimated  then the  g l o b a l l y convex i n p r i c e s s e m i - d e f i n i t e then Wiley, Schmidt product  B = AA  c o n c a v i t y i n the  q u a n t i t y of  the  positive  using  replacing  ; i , j = l,2,3  B  ; and a  i j  the  by the  = 0 for i < j .  McFadden GNP  the f i x e d  If  B i s not  is  A and i t s transpose;  of the G e n e r a l i s e d  be n e g a t i v e .  K K  of  ] Is  function  be reparameterised  technique  where A = la^]  1  In t h i s s p e c i f i c a t i o n  that b  1985). I f  of a lower t r i a n g u l a r matrix  (6.21)  terms B=tbjj  restricted profit  again  Bramble  t . 2  t t  quadratic  (Diewert  i t can  and  + (1/2) b  K t  capital  estimated  non-negative then c o n c a v i t y i n the c a p i t a l  b  function  input  requires  parameter  is  input q u a n t i t y can  be  K K  2  imposed by r e p l a c i n g parameter to be To capture  b^K  by  the term  -aj(K  where  a^K  i  s  a  estimated. c o s t s of adjustment a q u a d r a t i c approximation  is  used; (6.22) Using  D(K) = (1/2) d  K . 2  K K  (6.22) and the r e s t r i c t e d p r o f i t  f u n c t i o n (6.17) the  order c o n d i t i o n with r e s p e c t t o the f i x e d input 4 4 4 (6.23) Zi=l b P i + b ( Z i = i Pi)K + b ( £ K K  i K  " <3K(d KK) r  i = 1  P  i  )t - u  is; K  <3KdKKK = -  +  n  K  From (6.15) the steady (6.24) K~ = -(ZIi = i b  K t  (6.14)  first  s t a t e l e v e l of the c a p i t a l input i s now; + b ( Z i = i Pi>t - K > / ( b Z i = i P i ) u  i K P i  K t  K K  I t i s f u r t h e r assumed t h a t c u r r e n t p e r i o d p r o d u c t i o n a c t i v i t y a f f e c t e d by the c a p i t a l  stock e x i s t i n g a t  the beginning  p e r i o d and that changes made to the c a p i t a l stock period only  a f f e c t next  period's production.  86  i n the  is  of the current  T h i s enables  the  following discrete  approximation  to  the  flexible  accelerator  f o r m u l a t i o n to be used; (6.25)  K  t  - K t . ! = B~(K~  -  t  K^)  where; (6.26)  B~ = -(1/2) t r - { r  The output (6.27)  equations and the c a p i t a l adjustment Xi = bi +  Zjli  X4 = b  b  i j  p /p j  + (1/2) b  K t  1•  + b K  4  + b  i K  t  t t  i t  t  + ei  2  + (1/2) b  ±  K  t  = -(1/2) [r - { r (  £i = l  b  iKPi  +  b  2  - 4b 27 = KK  K t ^ i =l  i  Pi  (  R K  K  2  ; 1=1,2,3;  - (1/2) Z i = l Z j = l b i j P i P j / P 4 + *>iRK + b 2 2 + (1/2) b RK + b t K t + (1/2) b t t + e  K - K_  net  equation;  4  K  (6.29)  1/2  K K  complete e s t i m a t i n g system i s now g i v e n by the four  + b Kt (6.28)  - 4 b r i = i Pi/(qR^KK)>  2  ) i :  i t  t  4  Pi/(°. KK d  1  }}  1  /  2 ][  K  " K u  ) / ( b  KK^i =l P i  }  - K_ J + e . 1  R  The v e c t o r s of e r r o r terms f o r the o b s e r v a t i o n s are a g a i n assumed to  be  independently  distributed  with  a  multivariate  normal  d i s t r i b u t i o n with zero means and covariance matrix SiFrom  the parameters  elasticities  can  be  of the  derived  e s t i m a t i n g system  which  completely  a s e t of  describes  the  dynamic r e l a t i o n s h i p s w i t h i n the estimated system. In the case of v a r i a b l e net outputs, e l a s t i c i t i e s which c h a r a c t e r i s e the intermediate and long-run p r i c e s of  net  outputs  r e p r e s e n t s the response p r i c e change  response are  produced.  which occurs  when c a p i t a l  intermediate-run  of net  response  represents  87  output supply to the  The  short-run  response  i n l e s s than one p e r i o d to a  input l e v e l s  p e r i o d has elapsed and the c a p i t a l  short,  have not the  changed.  response  input has p a r t i a l l y  after  The one  adjusted.  The  long-run  capital state  response  input  r e p r e s e n t s the  l e v e l s have  complete  f u l l y adjusted  response  to their  after  new  steady  levels. The  (6.30)  s h o r t - r u n net output p r i c e e l a s t i c i t i e s are g i v e n log PJ)IR=K_  E S i j = (d l o g X i / d  In the G e n e r a l i s e d McFadden case t h i s  (6.31)  <Pj/ i>0*i/9pj)•  =  X  1  produces;  E S i j = ( P j / x i ) (bi j / p )  i,j=l,2,3;  ;  4  (6.32)  ES  i 4  = (p /Xi)(-Zj=l bjipj/p )  (6.33)  ES  4 4  = ( p / x ) (Zi=12Tjll b i j p i p j / p ) .  The  (6.34)  ;  2  4  by;  4  1=1,2,3;  3  4  4  4  long-run net output  p r i c e e l a s t i c i t i e s are g i v e n  by;  E L i j = (d l o g x^/d l o g Pj ) IK=K~ = ( P j / x i ) [ (9xi/9pj ) + O x i / 9 K ~ ) ( 9 K ~ / 9  Pj  ) ]  T h i s produces i n the G e n e r a l i s e d McFadden case; (6.35)  EL  i:J  =  E  S  ij "  << iK  +  b  b  +  b  KK  j K Zn=l  K  ^  Pn)Pj  t  ^  ^  l  /<bK Xi K  b  nRPn " K U  (Zn=l  Pn>  ;  2  1,j=l,..,4. The  i n t e r m e d i a t e - r u n e l a s t i c i t i e s a f t e r one  stock adjustment has taken place are g i v e n (6.36)  Elij  = ESij + K b "  b  j K  period's  by;  + bK K +bK t)(Zn=l b  i K  K  Zn=l  capital  t  n K  p  Pn)Pj/^b KKXi ( Z = l  - u  n  K  Pn> HBl  ;  2  n  i,j=l,..,4. where;  (6.37)  B l = B ~ ( l + dB~/dpj) = B~[l - b j ^ / U r  2  - 4^,^^^  9i/(^  K  K  ))  1  /  2  ^  K  K  }^  I t can be shown t h a t the own-price e l a s t i c i t i e s s a t i s f y the Le C h a t e l i e r p r i n c i p l e behaved and  the  i f the r e s t r i c t e d p r o f i t  function i s  a b s o l u t e value of the long-run e l a s t i c i t y  88  well will  exceed t h a t  of the  Intermediate-run  exceeds t h a t of the s h o r t - r u n price e l a s t i c i t i e s whereby s h o r t or the magnitude T h i s may  the  elasticity.  phenomenon of  which  With regard to  used l e s s  cross-  i n t e r m e d i a t e - r u n c r o s s - e l a s t i c i t i e s may  exceed  the c o r r e s p o n d i n g to an  output  long-run  price  cross-elasticity.  i n c r e a s e . The  i n c r e a s e i n output s u p p l y  but  to the  f i x i t y of c a p i t a l .  input has been  i n t e n s i v e l y and  response  i n the  t h i s w i l l have to be achieved by u s i n g some v a r i a b l e  the c a p i t a l  turn  allowed  a r i s e due  i n t e n s i v e l y due  ln  "overshooting" i s  of  t h i s w i l l be an  elasticity  to  short-run  inputs  more  In the long-run  when  i n c r e a s e d the v a r i a b l e  i n p u t s may  so the long-run c r o s s - e l a s t i c i t y may  be be  l e s s than the s h o r t - r u n c r o s s - e l a s t i c i t y . By d e f i n i t i o n a l l  short-run e l a s t i c i t i e s  involving  the p r i c e or q u a n t i t y of c a p i t a l are z e r o . However, and  long-run e l a s t i c i t i e s  user c o s t of  c a p i t a l can  between net output given  be o b t a i n e d .  q u a n t i t i e s and  EL  i u  The  q u a n t i t i e s and long-run  the user c o s t  the  elasticity  of c a p i t a l  is  = ( u / X i ) Caxi/'SUK) l =K~ K  K  = (u /Xi)[(b K  corresponding  (6.39)  EI The  i u  i K  + b  K K  K t  t ) / ( b K r j i l Pj)] ;i=l,.,4. K  i s given  by;  i u  i n t e r m e d i a t e - r u n response  long-run c r o s s - e l a s t i c i t y K  + b  = B~EL .  long and  EL i  K  intermediate-run e l a s t i c i t y  l e v e l s to changes i n net output  (6.40)  net output  intermediate  by;  (6.38)  The  between  either  of c a p i t a l  p r i c e s can a l s o be o b t a i n e d .  i s given  = (Pi/K)(dK~/dpi)  by; ;  89  i=l,..,4;  input The  = (P /K)[(Z i  The  corresponding  (6.41)  EI  4 j  1  b  Finally,  elasticities  on the response  technology.  The  E  R  T  V^/.ib^T^  !  )2}].  P j  by;  1 = 1,..,4. can  be  of p r o f i t s  derived to  which  provide  changes i n s c a l e  and  e l a s t i c i t y f o r r e t u r n s to s c a l e i s ; =  S  4  e l a s t i c i t y i s given  ;  R i  information  (6.42)  - b ^  K  intermediate-run  = Bl.EL  R i  - u  j K P j  [(dH(p,K)/dK).Kl/H(p,K).  T h i s e l a s t i c i t y shows the percentage change i n p r o f i t s  following  a one  value  percent  greater  change  than one  The  the c a p i t a l  then there  input.  E  Is  Is i n c r e a s i n g r e t u r n s to s c a l e .  T C  = (dH(p,K)/dt)/H(p,K) .  e l a s t i c i t y Is negative  increase  i n technology  there  a c t s to reduce  i s t e c h n i c a l r e g r e s s as  a better  understanding of  the  importance  dynamics of the adjustment process  an  profits.  From t h i s s e t of e l a s t i c i t i e s i t should  6.3  If i t s  t e c h n i c a l change e l a s t i c i t y i s given by ;  (6.43) If t h i s  in  be p o s s i b l e to of a l l o w i n g  w i t h i n the GNP  gain  for  the  f u n c t i o n model.  Results Initial  results  estimation  of the  which f a i l e d to meet  system (6.27)-(6 . 29)  convexity  produced  of the r e s t r i c t e d  profit  f u n c t i o n i n p r i c e s but which were concave i n the q u a n t i t y of  the  capital  the  input.  reparameterised  Subsequent  estimation  was  therefore  model imposing p r i c e c o n v e x i t y  resulting  maximum  likelihood  parameter  asymptotic  t - v a l u e s are presented  restricted  profit  i n Table  using  estimates 6.1.  90  (6.21). and  Concavity  f u n c t i o n In the q u a n t i t y of c a p i t a l  of  The their  of  input  the was  a g a i n s a t i s f i e d as i n d i c a t e d by the is  significantly  different  f u n c t i o n parameter dj<  i  from  negative value of b zero.  The  adjustment  p o s i t i v e and s i g n i f i c a n t l y  s  K  which  K K  costs  different  from zero as r e q u i r e d by economic t h e o r y . The estimated dependent v a r i a b l e s t r a c k the a c t u a l dependent v a r i a b l e values w e l l i n  a l l  cases and the equation R-square v a l u e s are r e p o r t e d i n Table 6.1. The values of B~, the p a r t i a l adjustment c a p i t a l s t o c k , produced  by the estimated  range from 0.07 t o 0.09, t a k i n g means t h a t the a c t u a l  coefficient  f o r the  system are s t a b l e  and  a value of 0.0727 i n 1970.  c a p i t a l stock a d j u s t s  o n l y seven  This  to  nine  per cent towards i t s steady s t a t e value i n one year. T h i s i m p l i e s r e l a t i v e l y slow adjustment  of the c a p i t a l s t o c k . As a r e s u l t  one  would expect s u b s t a n t i a l d i f f e r e n c e s between the estimated s h o r t run and long-run own-price e l a s t i c i t i e s either  strongly  substitutable  c a p i t a l . For  net outputs  capital  those  (ie.  which  or  which  f o r net outputs which are  strongly  complementary  are r e l a t i v e l y  are e i t h e r  weakly  independent  of  substitutable  or  weakly complementary with c a p i t a l ) the slow adjustment need not  imply  substantial differences  long-run own-price  to  between  of c a p i t a l  short-run  and  elasticities.  Due to the l a r g e volume  of output produced  by t h i s  model,  d e t a i l e d e l a s t i c i t y estimates are presented o n l y f o r three of the n i n e t e e n years f o r which output e l a s t i c i t i e s f o r the year s e r i e s a r e presented the middle  of the  i s obtained.  1965 near the  i n Table 6.2.  beginning of the  Those f o r the year 1970  t i m e - s e r i e s are presented  91  Net output  i n Table 6.3  price timenear while  those f o r 1978, a year near the end of the t i m e - s e r i e s , appear i n Table  6.4. The  estimated s h o r t - r u n export own-price e l a s t i c i t i e s are of  s i m i l a r magnitude to Chapter  those obtained  3. The s i g n i f i c a n t  i n the  difference i s that  export own-price e l a s t i c i t y tends t o decrease l i k e l y due imposed  to  here  the f a c t and  the  aggregate  that  i n t h i s case  variable  in  of the  over time. T h i s  constant r e t u r n s  dependent  model  is  are  not  being  the  estimating  equation i s the gross export q u a n t i t y r a t h e r than export q u a n t i t y per u n i t of c a p i t a l  input q u a n t i t y . T h i s would appear t o i n d i c a t e  t h a t more confidence estimated  long-run  can be placed export  i n mid-point  estimates.  own-price e l a s t i c i t i e s  are  The  somewhat  l a r g e r than the s h o r t - r u n e l a s t i c i t i e s but not t o the extent t h a t may have  been expected  beforehand.  long-run e l a s t i c i t y was 1.58 of  1.51.  T h i s would  appear to  indicate that  the  1970  B~ adjustment  the  elasticity relationship  i s not s t r o n g . As expected  of the estimated  intermediate-run e l a s t i c i t y  instance, i n  compared t o a s h o r t - r u n  between export s u p p l y and c a p i t a l the s m a l l value  For  coefficient  from the  i s c l o s e t o the s h o r t - r u n e l a s t i c i t y  value. The of  export c r o s s - e l a s t i c i t i e s produce a more i n t e r e s t i n g s e t  r e s u l t s . While  exports f a l l  p r i c e of imports the f a l l it  is in  the s h o r t - r u n  from imports and effect  is  to an i n c r e a s e i n the  s l i g h t l y l e s s i n the long-run  i n d i c a t i n g that  towards c a p i t a l  i s most pronounced i n  e l a s t i c i t y . While  i n response  some s u b s t i t u t i o n  occurs i n  the long-run.  the case of the labour  exports f a l l  i n response  92  t o an  than away This  cross-price increase  in  labour  prices  what  it  away  from  in  is  the  the  in  the  labour  Cross-price small  but  the  in  Import magnitude  obtained  to  those  in  between  Some  increase  with  Following  increase  indicating stock  in  long-run  the  further  increases.  in  from  sales  price  short-run)  following the  the  only  an  cross-  corresponding  half  of  in  the in  away  increased  and  capital  between import  cross-price to  imports  an  less  in  in  the  short-run.  the  in  export  import  as  are  short-run  the  more  and  import  however,  from  period  short-run  in  does  tend  little  increasing  it  similar  very  response  does  of  the is  imports  prices,  than  also  elasticities  difference  it  93  are  The  3.  that  labour  is  strong.  the  is  and  than  usage  This  long-run  occurs  substitution  Import  in  There  usage  long-run  the  half.  evident  import  and  an  is  that  slightly  first  larger  overshooting  intermediate  more  the  indicating  elasticities  of  domestic  zero  sign  second  Again a  the  elasticities  elasticities  elasticities.  drops  the  case  3.  estimated  long-run  price  in  the  independent.  to  evident  classic  relatively  Chapter  during  even  is  price.  in  is  capital  sales  Chapter  a  fifth  substitution  indicate  reduced  obtained  trend  one  to  near  differs  only  appear  are  own-price  during  This  respect  (being  in  magnitude  stabilise  own-price  which  and  is  substantial  represents  also  with  domestic  long-run  capital.  labour  short-run  decline  difference  would  exports  elasticity  elasticities  and  It  the  and  negative  increase  almost  towards  elasticities  that  then  indicating  between  indicating  to  short-run  intermediate-run  relationship  price  in  and  "overshooting".  are  reduction  the the  usage  short-run capital long-run  than  it  sales  is  i n the  short-run following  relatively  mid-point results  short-run  stable  value above,  the  larger  around  -1.50.  This  substitutable  with  more  i n the  the  capital  is  than  short-run  the  the  that  usage  has  approximately half  i n the  long-run  short-run  following  increases  c o n s i d e r a b l y more  short-run, price.  however,  This  production plausible domestic  is  given  domestic  higher value  slightly  relationship  elasticity  is  averaging  in  an  i n the  long-  prices.  indicate in  importance  i n the that  its  of  in  does  domestic  service  of  the usage  in  domestic  use  being  Labour  it  an  short-run.  run than  l o n g - r u n than increase  following  i n l a b o u r use is  import  once  considerable  labour  it  i n the  strongly  considerably  Again  increase  intensive  the  the  the sales sales  labour,  industries  a in  production.  The e s t i m a t e d somewhat  more  to  from  in labour prices  of  what  i n the  appear  relatively  sales  the  Increase  following  would  result  around the  an  the  declining  usage  are  near  elasticity,  increased.  i n the  slightly  which i s  own-price  an i n c r e a s e  with  usage d e c l i n e s  elasticities  As e x p e c t e d  labour  prices  only  domestic  l a b o u r and c a p i t a l a r e  of  been  evident  -1.0  3.  labour  in export  Labour  of  long-run  indicates  stock  value  i n Chapter  long-run following  overshooting increase  labour own-price  around the  obtained  substantially  is  i n the  price. The e s t i m a t e d  all  an i n c r e a s e  sales  than that of  0.85.  larger,  The  again  between d o m e s t i c  s h o r t - r u n own-price  obtained  in Chapter  long-run own-price indicating sales  94  a  elasticity  3 and  stable  elasticity  relatively  s u p p l y and c a p i t a l .  is weak  Domestic  sales supply  drops  slightly  f o l l o w i n g an  increase  in  export  p r i c e s but the c r o s s e l a s t i c i t y values are c l o s e to zero i n the s h o r t and  long-run. Domestic  s m a l l degree s h o r t and  increase l n  falls  import p r i c e s  i n domestic  net output and  the user c o s t of supply i n  i n the  long-run.  and q u a n t i t i e s  from the s m a l l value of B~,  c a p i t a l has a n e g l i g i b l e  the i n t e r m e d i a t e - r u n .  In  exports and  slightly  increase  impact  output, thus c o n f i r m i n g t h a t domestic  on net  labour  intensive  while  export  supply  i n t e n s i v e . Increases i n the user of  the other two The  however,  increase  in  net  c o e f f i c i e n t B~.  q u a n t i t y of  output  prices  the  is  sales  relatively  the c a p i t a l  capital usage  also  near  stock of zero  in  while  an i n c r e a s e  export in  the  sales  c a p i t a l stock.  As  expected  an i n c r e a s e i n import p r i c e s has a n e g l i g i b l e e f f e c t  on  and  even i n the  imports are almost  the  the  domestic  the c a p i t a l stock  decreases  an  adjustment  however, an i n c r e a s e i n  c a p i t a l stock  price actually  supply  relatively  to the s m a l l value of the p a r t i a l  In the long-run,  prices increases  is  an  imports.  on the  i n t e r m e d i a t e - r u n due  the  c o s t a c t t o i n c r e a s e the  i n p u t s , labour and  effect  is  output  of domestic  s a l e s output  in  an i n c r e a s e i n  the long-run,  the supply  between  are presented  i n c r e a s e i n the user c o s t of c a p i t a l a c t s to decrease of  the  equal.  long-run c r o s s - p r i c e e l a s t i c i t i e s  capital prices  Table 6.5. As expected  a  s a l e s s u p p l y occur f o l l o w i n g an i n c r e a s e  labour p r i c e s with the f a l l being l a r g e r Intermediate and  to  with  long-run c r o s s e l a s t i c i t i e s being approximately  Larger f a l l s in  f o l l o w i n g an  s a l e s supply a l s o  both  long-run i n d i c a t i n g that  capital  independent. The s t r o n g e s t r e l a t i o n s h i p i s  95  between c a p i t a l leading to a  and labour  substantial  with an  Increase  increase i n  labour  l n the c a p i t a l  prices  stock l n the  long-run. Finally,  the r e t u r n s  elasticities  a r e presented  elasticities  are  c a p i t a l stock  and  and  technical  6.6. The  i n the  there  of  scale  existing  are increasing  i n value over time. The  however, i n d i c a t e  change  r e t u r n s to  neighbourhood  indicate that  r e t u r n s t o s c a l e and i n c r e a s e change e l a s t i c i t e s ,  scale  i n Table  calculated  levels  to  t h a t there  technical  is  initially  t e c h n i c a l progress but then t e c h n i c a l r e g r e s s towards the end the  period.  There,  hence,  appears  d i s t i n g u i s h i n g the i n f l u e n c e s of change  with  the  elasticities  increasing  capturing  t e c h n i c a l change.  This  of  would  be  some  of  the  the  effects  account  of the  p e r i o d and the  elasticities. scale,  scale  due  declining towards  the r e t u r n s t o  this  represents  assumptions  of  a  the  contradiction  model  as  a  to and the  scale  To the extent t h a t there are i n c r e a s i n g r e t u r n s  however,  neoclassical  to  likely  f o r the  high values of  technical  returns  negative values of the t e c h n i c a l change e l a s t i c i t i e s end  difficulty  r e t u r n s t o s c a l e and  value  some  to  of  of  to the  competitive  e q u i l i b r i u m w i l l not e x i s t with i n c r e a s i n g r e t u r n s to s c a l e . 6.4  Conclusions The  adjustment c o s t s model presented  advantage of i n c o r p o r a t i n g the fixed  input  capital  as  adjustment process of the  the s o l u t i o n  o p t i m i s a t i o n problem where the r a t e fixed  input  i s endogenously  i n t h i s Chapter  to  Output  quasi-  e x p l i c i t . dynamic  of adjustment of the  determined.  96  an  has the  quasi-  feasibility  is  maintained allowed.  The  produced dynamic  while  by  short,  the  the  long-run  traded  adjustment  help  to  may  elasticities  in  weakly  related  import  demand  they the  ls  do  difference  between  negligible  for  to  as  and  and  of  for  out  sales  capital.  exports  short  of  the  areas  of  to  be  only  supply  As a  own-price  the  between  important  domestic  of  imports  turn  while  result  the  elasticities  and  is  model.  divergence  Exports  long-run  small  understanding  other  is  demands  elasticities  GNP f u n c t i o n  exports  the  process.  and  our  for  independent  short  imports  the  input  long-run  less  capital  almost  and  Indicate  point  dynamic  to  variable  increase  process within  results  sector  of  intermediate  model  adjustment  While and  overshooting  domestic  is  sales  supply. The is  on  important  input  increase in  labour usage  export  supply  with  stock  is  export usage of  is  importance  supply.  An  export  supply  it  goes  increase  in  of  dynamics  labour.  about  capital  input,  by  to  a  appears  to  make  a  producing  that  Hence,  intensiveness  domestic  sales  97  prices  model  short-run  more  labour  long-run  with  import  while  allowing  difference  supply.  the of  the  increased  difference  export by  a  the  little  process highlighted labour  the  extent  significant  this  While  for  lesser  make  in  using  in  substituted  price, increase.  into  the  for  brought  and  does  adjustment of  that  happens  adjustment  aspect the  fixed  also  an  which  the  the  is  increased  This  following  imperfect  input  allowing  particularly  usage.  actual  of  usage,  conjunction  capital  for  in  effect  to  the  Another  dynamic  domestic  actually  to  model sales  acts  to  decrease  the steady s t a t e c a p i t a l stock and  hence reduces  export  supply. While the adjustment c o s t s model may  appear to downplay  importance of a l l o w i n g f o r imperfect adjustment on export and  import  demand r e l a t i v e to  model of the preceding two  models have q u i t e d i f f e r e n t assumptions and  labour are aggregated together and  Hence the major  avenue of  adjustment c o s t s  hence the  usage as  the c a p i t a l  stock  p l a n n i n g p r i c e model. The  capital  inputs  price  are f i x e d  f r o n t i e r as  p l a n n i n g p r i c e model frontier both  increased, i s  f o r the  d u r a t i o n of  source  of  c o n s i d e r s adjustment  J-curve  experimentation  effect  i n net output  with  be necessary  input in  the price  w i t h i n a general  use and  simulation.  the s h i f t  of  the  dynamics, while  the  production  p r i c e s . In  principle,  simultaneously. models  to model imperfect  As a and  process  phenomena such as  the  adjustment  e q u i l i b r i u m context and  with r e s p e c t to import  98  the  labour  before the dynamic  To f u l l y understand  a l l o w f o r endogeneity  precluded  d i f f e r e n t dynamic  i t w i l l be necessary  on the demand s i d e  of labour  the  along the  forms of adjustment could be considered  i s f u l l y understood.  i n d i c a t e d by  t h a t both  c o s t s model views  the only  s e t s of assumptions w i l l  input.  i n the p l a n n i n g  i n c r e a s e , given  f o l l o w i n g changes  r e s u l t more  results  much g r e a t e r i n c r e a s e i n import  Furthermore, the adjustment production  is  e f f e c t of t h i s  model i s h i g h l i g h t e d by the f o l l o w i n g an export  the adjustment  the  capital  t r e a t e d as a f i x e d  dynamic adjustment  model, namely  price  be remembered t h a t  are not d i r e c t l y comparable. In the p l a n n i n g p r i c e model and  supply  the r e s u l t s of the p l a n n i n g  Chapter, i t must  the  and  export  prices.  to  TABLE 6.1 DYNAMIC PARAMETER Coeff i c l e n t  Estimate  t-value  Estimate  t-value  -1.3082  -4.7518  MK  0 .0527  1.4400  b  Mt  -1.0516  -4.7532  -4.2531  -4.4495  -0.0000  -0.0000  0.1486  4.3780  -2.0457  -8.2437  4.1866  4.2798  -0.0175  -0.2227  X  -0.1251  -0.1440  a  a  xx  -1.4685  -4.7798  b  a  XM  0.8951  5.7610  a  XL  0.3249  0.7640  b  L  b  XK  0.0758  1.2022  a  LL  b  xt  0.4740  0.8415  b  LK  b  KK  -0.0034  -2.1381  b  Kt  0.0334  2.2309  b  D  b  tt  -0.4001  -2.4949  b  DK  M  -0.9898  -2.5164  b  Dt  3.0128  5.0193  -0.2811  -0.8718  d  KK  1.6831  2.3937  MM  a  2  Coefficient  b  b  R  ESTIMATES  b  ML  Lt  Values  Equation X  0.9795  Equation D  0 .9842  Equation M  0.9851  Equation K  0 . 4667  Equation L  0.9701  Log L i k e l i h o o d  141.80  The s u b s c r i p t s and equation l a b e l s X, M, L, D, K and t r e f e r t o aggregate e x p o r t s , aggregate imports, labour, domestic sales, c a p i t a l and technology, r e s p e c t i v e l y . x  99  TABLE 6.2 1965 NET OUTPUT PRICE ELASTICITIES sticity  Short-run  1  Intermediate-run  Lonq-run  E  XX  2.2607  2.2692  2.3737  E  XM  -1.6610  -1.6584  -1.6265  E  XL  -0.5535  -0.5221  -0.1342  E  XD  -0.0462  -0.0634  -0.2752  MX  2.5377  2.5291  2.4236  MM  -2.0484  -2.0511  -2.0833  ML  -1.4070  -1.4387  -1.8306  MD  0.9177  0.9351  1.1491  E  LX  0.2206  0.2115  0.0998  E  LM  -0.3670  -0.3698  -0.4039  E  LL  -0.9296  -0.9632  -1.3778  E  LD  1.0760  1.0944  1.3208  E  DX  -0.0114  -0.0132  -0.0346  E  DM  -0.1487  -0.1492  -0.1557  E  DL  -0.6682  -0.6746  -0.7542  E  DD  0.8282  0.8318  0.8752  E  E  E  E  1 The s u b s c r i p t s X, M, L and D r e f e r to aggregate exports, aggregate imports, labour and domestic s a l e s , r e s p e c t i v e l y .  100  TABLE 6.3 1970 NET OUTPUT PRICE ELASTICITIES Elasticity  Short-run  1  Intermediate-run  Long-run  E  XX  1.5052  1.5105  1.5779  E  XM  -1.0609  -1.0600  -1.0479  E  XL  -0.4678  -0 .4404  -0.0934  E  XD  0.0236  0.0099  -0.1625  E  MX  1.6559  1.6502  1.5779  MM  -1.2823  -1.2833  -1.2962  ML  -1.1654  -1.1948  -1.5666  0.7918  0.8064  0.9911  E  E  E  MD  E  LX  0.1955  0.1884  0.0981  E  LM  -0.3121  -0.3134  -0.3296  E  LL  -1.0459  -1.0826  -1.5473  E  LD  1.1624  1.1807  1.4116  E  DX  0.0063  0.0053  -0.0069  DM  -0.1357  -0.1359  -0.1381  -0.7441  -0.7491  -0.8122  0.8735  0. 8760  0.9073  E  E  DL  E  DD  1 The s u b s c r i p t s X, M, L and D r e f e r to aggregate exports, aggregate imports, labour and domestic s a l e s , r e s p e c t i v e l y .  101  TABLE 6.4 1978 NET OUTPUT PRICE ELASTICITIES  1  Elasticity  Short-run  Intermediate-run  Lonq-run  E  XX  0.9846  0.9873  1.0238  E  XM  -0.6372  -0.6371  -0.6366  E  XL  -0.3216  -0.3051  -0.0840  E  XD  -0.0258  -0.0336  -0.1382  E  MX  1.0752  1.0722  1.0327  MM  -0.7644  -0.7645  -0.7651  ML  -0.7953  -0.8132  -1.0531  0.4845  0.4930  0.6065  E  E  E  MD  E  LX  0.1823  0.1771  0.1087  E  LM  -0.2671  -0.2672  -0.2682  E  LL  -1.0247  -1.0557  -1.4707  E  LD  1.1095  1.1242  1.3205  E  DX  -0.0096  -0.0101  -0.0179  -0.1064  -0.1064  -0.1065  -0.7255  -0.7290  -0.7758  0.8414  0.8431  0.8652  E  DM  E  DL  E  DD  1 The s u b s c r i p t s X, M, L and D r e f e r to aggregate exports, aggregate imports, labour and domestic s a l e s , r e s p e c t i v e l y .  102  TABLE 6.5 CAPITAL - NET OUTPUT CROSS Year  ELASTICITIES  1  Elasticity EI XU  EI MU  EI LU  EI DU  1965  -0.0251  0.0254  0.0268  0.0051  1970  -0.0199  0.0214  0.0267  0.0036  1978  -0.0114  0.0124  0.0215  0.0024  E L  XU  EL  MU  E L  LU  E L  DU  1965  -0.3378  0.3413  0.3611  0.0693  1970  -0.2742  0.2938  0.3672  0.0499  1978  -0.1650  0.1791  0.3097  0.0349  E I  KX  EI  KM  E I  KL  E I  KD  1965  0.0130  0.0040  0.0481  -0.0263  1970  0.0083  0.0015  0.0425  -0.0211  1978  0.0047  0.0001  0.0283  -0.0134  EL  R X  EL  KM  E L  KL  E L  KD  1965  0.1728  0.0528  0.6413  -0.3502  1970  0.1127  0.0202  0.5798  -0.2881  1978  0.0671  0.0010  0.4072  -0.1926  1 The s u b s c r i p t s X, M, L, D, U and K r e f e r t o aggregate aggregate imports, l a b o u r , domestic s a l e s , the user c a p i t a l and c a p i t a l input q u a n t i t y , r e s p e c t i v e l y .  103  exports, c o s t of  TABLE 6.6 SCALE AND TECHNICAL CHANGE ELASTICITIES Year  RTS  TC  1962  1.1229  0.0926  1964  1.1866  0.0593  1966  1.2817  0.0380  1968  1.4217  0.0193  1970  1.5936  0.0044  1972  1.6490  -0.0032  1974  1.8280  -0.0123  1976  1.9710  -0.0193  1978  1.9361  -0.0192  1980  1.9495  -0.0216  104  7 .  CONCLUSIONS  AND  FURTHER  RESEARCH The  results  understanding adjustment  of  in  presented the  the  responsiveness of changes. They  in  roles  this thesis  of  disaggregation  GNP  function  export  supply  have a l s o  have extended  approach and  pointed to  to  import  measuring to  of d i r e c t i o n s  import  the use  obtaining detailed  of the  has  r e c e n t l y developed  Generalised  a l l o w s i m p o s i t i o n of the  proved  sets  to  be an e f f e c t i v e  of e l a s t i c i t i e s  correct means  characterising  l e v e l export  e a r l i e r Canadian be somewhat  study, while higher  both imports  s u p p l y of exports  and  while exports were  study. Increases  were found  in  t o decrease  found to be  At the produced  for  s t a b l e and  the  than i n most e a r l i e r s t u d i e s and a the  observed.  disaggregated the export  of  the  labour  g e n e r a l t r e n d towards i n c r e a s i n g p r i c e responsiveness w i t h i n Canadian economy was  was  complementary  s a l e s supply. The demand f o r  to be more e l a s t i c  was  (1978)  import responsiveness  in this labour  with the output of domestic found  export  supply responsiveness  found to be of a s i m i l a r magnitude to t h a t found by K o h l i  was  of  import demand r e s p o n s i v e n e s s .  At the aggregate  p r i c e s of  in  f u n c t i o n method of i n c l u d i n g s e v e r a l export and  curvature conditions  found to  price  of the  McFadden f u n c t i o n a l form which  i n an  the  Combination  c a t e g o r i e s with  s u p p l y and  Imperfect  demand  a number  which f u r t h e r r e s e a r c h needs to be undertaken. aggregator  and  our  reasonable  and  l e v e l the  own-price  import components  magnitude. The  105  elasticities  were  disadvantage  generally of  the  aggregator  f u n c t i o n approach,  restrictive  assumption  however, i s t h a t i t r e l i e s on the  of  separability  s t r u c t u r e and  a l l export  were found to  be complementary  fixed capital  models  components along  contained  aggregate  impression of  components,  production  respectively, s u b j e c t to the  E x t e n s i o n of m o d e l l i n g to  which  with  the  with each other  input a v a i l a b l e .  disaggregated  different  and import  of  four  imports  the c r o s s  export  (exports)  larger (import)  produced  r e l a t i o n s h i p s between  a  export  (import) components with some s u b s t i t u t i o n becoming e v i d e n t . larger disaggregated  models  tended,  however,  to  The  produce  s t a b l e estimates of the component own-price e l a s t i c i t i e s  less  in  some  instances. The major c o n c l u s i o n , then, r e g a r d i n g d i s a g g r e g a t i o n i s t h a t the aggregator functional  f u n c t i o n approach,  forms  which  permit  when combined curvature  with  flexible  imposition,  is  an  e f f e c t i v e means of o b t a i n i n g i n f o r m a t i o n on the responsiveness of export and import components t o own-price changes. The aggregator function  approach  information  on  appears  cross  to  be  relationships  d i s a g g r e g a t e d models,  on  relative  in  advantage  the  other  providing  less  suited  to  providing  among  components.  hand,  appear  information  to  Larger have  on ,  a  cross  relationships. Combining  the  imperfect adjustment results  which  planning  with the  indicated  p a r t i c u l a r l y important p a r t i c u l a r t a k i n g an  p r i c e method GNP f u n c t i o n  that  of  allowing for  framework  imperfect  produced  adjustment  was  i n the traded goods s e c t o r with exports i n extended  period  106  to f u l l y  a d j u s t to  price  changes.  Extension  adjustment of  those  p r o c e s s . Both  were found to  of  the  however, i n strong  modelling  a  short-run.  the composition  of  r e s p e c t to  between  impression  import  were  labour  i n the s h o r t - r u n but  with in  the  planning price  c a p i t a l were t r e a t e d as f i x e d  avenue  variable  i n the s h o r t - r u n ,  of adjustment  model  where both  i n both the s h o r t and  important  to a l l o w f o r  understanding t h a t the  of  imperfect adjustment  export s u p p l y  r e s u l t s obtained  assumptions  made.  are  and  import  was  not  labour  and  long-run.  fuller  be s e n s i t i v e  to  but the with  d i f f e r e n t models and s e t s of assumptions w i l l be necessary  before  7.1  Further  is fully  more  it  experimentation  the dynamic process  Consequently,  to g a i n a  demand response  l i k e l y to  the with  The major c o n c l u s i o n s , then, from these r e s u l t s are t h a t is  a the  indicated considerable overshooting  demand. T h i s  to  found,  over time  and  variable  demand  i n the long-run  differences  capital  fixed  labour in  a different  input usage  i n the long-run, while labour was c o s t s model  sophisticated  export supply and  Important  long-run. Since c a p i t a l was  adjustment  more  be l i t t l e d i f f e r e n t  substitutability  available  to  c o s t s model, however, produced  the adjustment  responses  of  understood.  Research  At the most g e n e r a l l e v e l , further research i s make i t more  an Important  e x t e n s i o n of the  general e q u i l i b r i u m i n  explicit  modelling  allowance  for  of  the  exchange r a t e  GNP  adjustment  consumption to  warrants  f u n c t i o n framework  nature. T h i s would  domestic  107  area which  to  involve  sector  maintain balance  and of  payments e q u i l i b r i u m . The promising s t a r t With obvious  regard to  area  different  in this  for  the s p e c i f i c  to  is  assess  be p a r t i c u l a r l y  whether the t r e n d towards i n the aggregator  r e s u l t s of  research  forms  would  (1980) r e p r e s e n t s  a  direction.  further  functional  r e s u l t s . This  work of Clements  this thesis  experimentation the  robustness  interesting  In  an with  of  the  examining  i n c r e a s i n g p r i c e responsiveness  found  f u n c t i o n and disaggregated models i s r e p l i c a t e d  with other f l e x i b l e forms p e r m i t t i n g c u r v a t u r e i m p o s i t i o n such as the G e n e r a l i s e d Barnett  (Diewert and Wales  1987). E x t e n s i o n  the work t o d i f f e r e n t data s e t s may  permit s u c c e s s f u l  of s e m i - f l e x i b l e  as  Wales  (1986).  including a l l  f u n c t i o n a l forms This  the  procedure variable  r e l y i n g on the s e p a r a b i l i t y An important little  would  net  i n p u t s . In to  Although  adjustment  costs  framework  no  utilisation. c a p i t a l and  In other  model  made  changes  quasi-fixed  w i l l r e p r e s e n t an important it  be u t i l i s e d  is  reality  advantage  of  components  adjustment  c a p i t a l stock over  allowance  and  which has  attempts  approach  to  not  received  utilisation  constant to  in  changes capacity  inputs such  allowing  108  rate. for  optimising  in  capacity  utilisation  as some labour  in  and  of  types  t o output f l u c t u a t i o n s  for q u a s i - f i x i t y  the  allow  time w i t h i n an for  response  at a  i s c o r r e s p o n d i n g l y important that they be modelled  work. One  while  a l l the models presented here  i s assumed  of the  the  Diewert  for variable capacity  c a p i t a l stock  adjustment  by  estimation  assumption.  a t t e n t i o n i s allowance  the  have  output  area of input  r a t e s of the f i x e d  proposed  of  and  applied variable  utilisation  i s that  of H e l l i w e l l and  Denny (1980) attempt to  Chung (1986). E p s t e i n  endogenise u t i l i s a t i o n and  and  depreciation  d e c i s i o n s as s o l u t i o n s to o p t i m i s i n g problems. Recent increased present  most of the  applied  work.  material  in this  the v a l i d i t y of the along  the  t h i s t h e s i s on of  A  relatively  theory  v a r i a b l e net output,  testing  assumption  the m a t e r i a l presented  p r i c e model  leaving capital  T h i s would go some way  price-taking  adjustment. A simple  the p l a n n i n g  straight-forward  (1979).  e x i s t f o r extending  imperfect  have  assumption  t h e s i s would i n v o l v e  p e r f e c t competition  l i n e s of Appelbaum  Many avenues  extension  Industrial organisation  i n t e r e s t i n r e l a x i n g the p e r f e c t competition  in  extension  advances i n  first  step might  be  to i n c l u d e  labour as  a  as the  sole fixed  towards making the model more  input.  comparable  to the adjustment c o s t s model although as c u r r e n t l y s p e c i f i e d fixed  input remains f i x e d  model. More i n f o r m a t i o n  in  the long-run  on the  fixed  e x p l i c i t l y e s t i m a t i n g a "planning fixed  l n the p l a n n i n g  price  input could be obtained  shadow p r i c e " equation  the  for  by the  input. A number of  model presented internal  in  the  v a r i a t i o n s can be made to the adjustment in  Chapter  sense  that  quasi-fixed  input a f f e c t s  production.  The  Morrison The  in  and  model  Berndt  6. Adjustment a  change  in  current production  could  be extended  (1981) to i n c l u d e  two  assumption of s t a t i c p r i c e e x p e c t a t i o n s  109  costs  can  the  stock  as  along  be  quasi-fixed  made  of  w e l l as the  costs  the  future  lines  of  factors.  could be r e l a x e d  and  a v e r s i o n c o n s i s t e n t with the l i n e s of Morrison  r a t i o n a l e x p e c t a t i o n s estimated  (1985).  There are a l s o a l t e r n a t i v e models of the dynamic process which  should be  r e s t r i c t i o n s within Anderson and adjustment  process  which  t h a t of  impact  of  testing  i s developed  by  (1983). An a l t e r n a t i v e model of the dynamic  is  also  Pindyck  and  Further experimentation with these and our understanding  adjustment  framework f o r  dynamic system  derived e x p l i c i t l y  o p t i m i s a t i o n problem expectations i s  investigated. 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(1985), 'The Measurement of the Economic Benefits of I n f r a s t r u c t u r e S e r v i c e s ' , Department of Economics Working Paper No. 85-11, U n i v e r s i t y of B r i t i s h Columbia. Diewert, W.E. and C.J. Morrison (1986), 'Export Supply and Import Demand F u n c t i o n s : A P r o d u c t i o n Theory Approach', Department of Economics Discussion Paper No. 86-10, U n i v e r s i t y of B r i t i s h Columbia. Diewert, W.E. and L.A. Ostensoe (1986), 'Flexible Functional Forms f o r P r o f i t F u n c t i o n s and G l o b a l Curvature C o n d i t i o n s ' , NBER Working Paper S e r i e s . Diewert, W.E. and T.J. Wales (1986), * Semi f l e x i b l e Functional Forms', Department of Economics D i s c u s s i o n Paper No. 86-25, U n i v e r s i t y of B r i t i s h Columbia. Diewert, W.E. and T.J. Wales (1987), " F l e x i b l e F u n c t i o n a l Forms and G l o b a l Curvature C o n d i t i o n s " , Econometrica 55, 43-68. Dixon, P.B., B.R. Parmenter, G.J. 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(1978), " T e s t i n g and Imposing M o n t o n i c i t y , Convexity and Q u a s i c o n v e x i t y C o n s t r a i n t s " , i n M. Fuss and D. McFadden ( e d s . ) , P r o d u c t i o n Economics: A Dual Approach to Theory and A p p l i c a t i o n s , North-Holland, Amsterdam, pp.409-53. Lucas, R.E., Supply",  J r . (1967), "Adjustment Costs and the J o u r n a l of P o l i t i c a l Economy, 331-44.  Theory  of  McKay, L., D. Lawrence and C. Vlastuin (1982), "Production F l e x i b i l i t y and T e c h n i c a l Change i n A u s t r a l i a ' s Wheat/Sheep Zone", Review of Marketing and A g r i c u l t u r a l Economics 50, 9-26. McKay, L., D. Lawrence and C. V l a s t u i n (1983), " P r o f i t , Output Supply, and Input Demand F u n c t i o n s f o r M u l t i p r o d u c t Firms: The Case of A u s t r a l i a n A g r i c u l t u r e " , I n t e r n a t i o n a l Economic Review 24, 323-39 . Morrison, C.J. (1985), "On the Economic I n t e r p r e t a t i o n and Measurement of Optimal Capacity Utilisation with A n t i c i p a t o r y E x p e c t a t i o n s " , Review of Economic S t u d i e s 52, 295-310 . Morrison, C.J. and E.R. Berndt (1981), "Short-run Labour P r o d u c t i v i t y i n a Dynamic Model", J o u r n a l of Econometrics 16, 339-65. Ostensoe, L.A. (1986), 'Production Analysis for Applied General Equilibrium Modelling*, B.A.(Hons) t h e s i s , U n i v e r s i t y of B r i t i s h Columbia. Pindyck, R.S. and J . J . Rotemberg (1983a), "Dynamic F a c t o r Demands and the E f f e c t s of Energy P r i c e Shocks", American Economic Review 73, 1066-79. Pindyck, R.S. and J . J . Rotemberg (1983b), "Dynamic F a c t o r Demands under R a t i o n a l E x p e c t a t i o n s " , Scandinavian Journal of Economics 85, 223-38. Rhomberg, R.R. (1964), "A Model of the Canadian Economy under F i x e d and F l u c t u a t i n g Exchange Rates", J o u r n a l of Political Economy 72, 1-31. Samuelson, P.A. (1953-4), " P r i c e s of F a c t o r s and Goods i n General E q u i l i b r i u m " , Review of Economic Studies 21, 1-20. Shephard, R.W. (1953), Cost and P r o d u c t i o n F u n c t i o n s , U n i v e r s i t y Press, P r i n c e t o n .  114  Princeton  S t a t i s t i c s Canada (1983), "The Input-Output Structure of Canadian Economy i n Constant P r i c e s 1971-79", Catalogue 15-202E, M i n i s t e r of Supply and S e r v i c e s , Ottawa.  the No.  Wiley, D.E., W.H. Schmidt and W.J. Bramble (1973), " S t u d i e s of a Class of Covariance S t r u c t u r e Models", J o u r n a l of the American S t a t i s t i c a l A s s o c i a t i o n 68, 317-23. White, K.J. (1978), "A General Computer Program f o r Methods - SHAZAM", Econometrica 46, 239-40.  Econometric  Woodland, A.D. (1976), 'Modelling the P r o d u c t i o n Sector of an Economy: A S e l e c t i v e Survey and A n a l y s i s ' , Department of Economics Working Paper No. 76-21, U n i v e r s i t y of British Columbia. Woodland, A.D. (1977), " E s t i m a t i o n of a V a r i a b l e P r o f i t and of Planning Price Functions for Canadian Manufacturing, 1947-70", Canadian J o u r n a l of Economics 10, 355-77. Woodland, A.D. (1982), International Trade A l l o c a t i o n , North-Holland, Amsterdam.  115  and  Resource  P E N D I yC  AP  1  DATA The  data used  s e r i e s of annual Canada to UBC  i n t h i s study are d e r i v e d from a 20 year  input-output  i n 1984.  The  data made a v a i l a b l e by  Statistics  data c o n s i s t of c u r r e n t and  d o l l a r s e r i e s f o r 37 i n d u s t r i a l c l a s s i f i c a t i o n s . The used  by S t a t i s t i c s Canada i n  described  in detail  Statistics  Canada  methodology  Bureau of S t a t i s t i c s  Lai  (1982)  methodological problems encountered data with the  constant  p r e p a r i n g i t s input-output data  i n Dominion (1983).  time  N a t i o n a l Accounts  reviews  some  in reconciling  data  (1969) of  is and the  input-output  and compares the  Canadian  input-output t a b l e s to those of other c o u n t r i e s . For each i n d u s t r y data i s a v a i l a b l e f o r 8 primary i n t e r i n d u s t r y inputs and c o m p e t i t i v e and  2 outputs. The  non-competitive  imports,  Crown c o r p o r a t i o n s and government i n v e n t o r i e s of  raw  e i t h e r domestic several  i n d u s t r y are  inputs c o n s i s t of  inputs purchased  bodies, and  materials, inventories  machinery and equipment c a p i t a l , Outputs of each  primary  of  5 durable  c o n s t r u c t i o n c a p i t a l and  c l a s s i f i e d according  variables  are  also  to end  available  from  inputs;  finished  s a l e s or e x p o r t s . In a d d i t i o n to these  financial  i n p u t s , 36  goods, land. use,  variables, for  each  i n d u s t r i a l c l a s s i f i c a t i o n . To more c l o s e l y approximate the a c t u a l prices  faced  by  producers  d i s t r i b u t e d to other input and of d e t a i l  a v a i l a b l e on  these  financial  variables  output c a t e g o r i e s . Given the  the f i n a n c i a l  variables this  were lack  procedure  o f t e n i n v o l v e d r e l a t i v e l y ad hoc methods. For i n s t a n c e , commodity i n d i r e c t taxes were d i s t r i b u t e d a c r o s s the 36 i n t e r m e d i a t e s and  116  2  import  components  proportionate  total  intermediate  input  analogously d i s t r i b u t e d while s u b s i d i e s and  to 1971  u s i n g 1961  1971  as the  base year. 1971  obtained by d i v i d i n g The  construction  as the The and  two based  The  dollar  study the  The d i s c r e t e D i v i s i a  v a r i a b l e was competitive  Divisia  exact f o r  to 1980  the  A price  industry  and  an  listed recent  over  the  37  package.  has the advantage t h a t i t i s  the f l e x i b l e  translog  aggregator  s a l e s , aggregate  level.  a g g r e g a t i n g the  for  as  Ostensoe  i n d i c e s i n the SHAZAM  The  export  and  input-output  aggregate  import  c o m p e t i t i v e and  the d i s t i n c t i o n being  n e i t h e r r e l i a b l e nor u s e f u l . F i n a l l y , an aggregate  earlier  was  constant  data i s  Diewert  the  series  then serves  were aggregated  economy  obtained by  using  (1986).  data  import c a t e g o r i e s ,  categories l i s t e d  and  periods  s e r i e s by the  are Cas,  index procedure  obtained by  q u a n t i t y s e r i e s was  land  added to  labour hours v a r i a b l e s were taken d i r e c t l y from the to  and  i n Ostensoe (1986). Other  (Diewert 1976). The domestic  data aggregated  of were  s p l i c e d using  series  resulting  data s e t  i n d u s t r i e s by the use of  function  i n 1961.  constant d o l l a r  and Ostensoe  s u p e r l a t i v e , being  capital  1971  s e r i e s were  the nominal  a p p l i c a t i o n s u s i n g the  this  taxes  a v a i l a b l e f o r the  base year and  i t s construction described  (1986) and Diewert  indirect  share  output.  i m p l i c i t q u a n t i t y index.  In  other  d o l l a r s e r i e s are  1961  and  commodity's  r o y a l t i e s were, r e s p e c t i v e l y ,  The constant  dollar series.  value,  across  s u b t r a c t e d from domestic  o v e r l a p p i n g year  t o each  non-  considered  capital  stock  a g g r e g a t i n g the 5 durable  input  the 37  117  i n d u s t r i e s using  capital  stock p r i c e s  as weights.  Since constant  imposed i n t h i s study the user r e s i d u a l t o equate the v a l u e s  scale  s a l e s and  and imports, the  d i v i d e d by the c a p i t a l  are  c o s t of c a p i t a l was d e r i v e d as  the v a l u e s of outputs and i n p u t s . A f t e r  of domestic  v a l u e s of labour  returns to  exports and  a  adding  subtracting  the  r e s u l t i n g r e s i d u a l value  was  q u a n t i t y s e r i e s to  obtain a price  index  f o r the user c o s t of c a p i t a l . Subsequent r e s c a l l n g made the value of the p r i c e  index 1.0 i n 1961 and p r i c e times q u a n t i t y equal  the r e s i d u a l v a l u e . The four net outputs s a l e s and  p r i c e and q u a n t i t y  s e r i e s used  (aggregate e x p o r t s , aggregate  labour) and  the  fixed  input  imports,  c a p i t a l are  to  f o r the domestic  listed  in  Tables A l . l and A l . 2 , r e s p e c t i v e l y . The  technology index used throughout  trend ranging from a value s c a l i n g was chosen  t h i s t h e s i s was a  of 0.1 i n 1961  t o 2.0 i n 1980.  obtained by  This  so t h a t the squared value of the index was  the same maximum order of magnitude as the p r i c e The  time  four export  and  a g g r e g a t i n g the  which had s i m i l a r export  import component exports and  index s e r i e s . categories  imports of  and import p r i c e  industries  industries  t o g e t h e r . The composition of the four export component groups (and c o r r e s p o n d i n g 1-0 i n d u s t r y  i s as f o l l o w s ; Export Group 1 : A g r i c u l t u r a l and F o r e s t r y Products 1) A g r i c u l t u r e and F i s h i n g  7)  2) F o r e s t r y  11) Woods  4) Food and Beverages  13) Paper and A l l i e d  118  were  p a t t e r n s over the 20  year p e r i o d . Some e f f o r t was a l s o made to keep s i m i l a r  input-output i n d u s t r i e s  of  Leather  by  numbers)  Export Group 2 : M i n e r a l s and Energy 3)  Mines, Q u a r r i e s and  O i l Wells  15) Primary Metals  Products  21) Petroleum  and  Coal  33) E l e c t r i c Power  Export Group 3 ; Motor V e h i c l e s , T e x t i l e and E l e c t r i c a l  14) P r i n t i n g and P u b l i s h i n g  5)  Tobacco  6)  Rubber and  8)  Textiles  9)  Knitting  18) T r a n s p o r t Equipment  Plastic  19) E l e c t r i c a l 26) Railway  Mills  10) C l o t h i n g  32)  12) F u r n i t u r e and F i x t u r e s  34) Gas  Export Group 4 : Heavy I n d u s t r i a l and 16) Metal 17)  Products  Equipment  Transport  Telephones Distribution  S e r v i c e Products  28) Motor T r a n s p o r t  Fabricating  29) Urban T r a n s p o r t  Machinery  20) N o n - m e t a l l i c M i n e r a l s  30)  Storage  22)  31)  Broadcasting  35)  Trade  Chemicals  23) M i s c e l l a n e o u s  Manufacturing  25) A i r Transport  36) Finance, Insur. & R e a l t y  27) Water t r a n s p o r t  37) Commercial S e r v i c e s .  The  price  and  implicit  components are l i s t e d The  1-0  quantity series  for  i n Tables Al.3 and A1.4,  the  four  export  respectively.  I n d u s t r i a l composition of the four import components  i s as f o l l o w s ; Import Group 1 : A g r i c u l t u r a l , F o r e s t r y and S e r v i c e Products 1)  A g r i c u l t u r e and  2)  Forestry  4)  Food and  7)  Leather  26) R a i l T r a n s p o r t  Fishing  27) Water T r a n s p o r t 28) Motor T r a n s p o r t  Beverages  29) Urban Transport  119  11) Woods  30)  Storage  13) Paper and A l l i e d  35)  Trade  14) P r i n t i n g and P u b l i s h i n g  36) Finance, Insur. & R e a l t y  24) C o n s t r u c t i o n  37) Commercial S e r v i c e s  25) A i r Transport Import Group 2 ; Metals and Energy Products 3)  Mines, Q u a r r i e s and O i l Wells  21) Petroleum  and  Coal  15) Primary Metals  33) E l e c t r i c Power  16) Metal F a b r i c a t i n g  34) Gas  Import Group 3 : Machinery,  Distribution  E l e c t r i c a l and T e x t i l e  Products  5)  Tobacco  12) F u r n i t u r e and F i x t u r e s  6)  Rubber and P l a s t i c s  17)  8)  Textiles  19) E l e c t r i c a l  9)  Knitting Mills  31)  10) C l o t h i n g  32)  Import Group 4 : V e h i c l e s , Chemicals  Machinery  Broadcasting Telephones  and Other  18) T r a n s p o r t Equipment  22)  20) N o n - m e t a l l i c M i n e r a l s  23) Misc.  The  price  and  implicit  components are l i s t e d In the adjustment  Products  Chemicals  quantity series  i n Tables A1.5  Equipment  Manufacturing  for  and A1.6,  c o s t s model of Chapter  the  four  import  respectively. 6 constant  returns  to s c a l e with r e s p e c t t o c a p i t a l are not imposed. As a r e s u l t  an  e x p l i c i t asset  be  d e r i v e d . In  price  t h i s case  d i r e c t l y from the  and  user  cost for  the a s s e t  p r i c e of  input-output d a t a .  f i v e durable  inputs were aggregated  an aggregate  c a p i t a l asset p r i c e .  120  capital  have  c a p i t a l was  The a s s e t  to  derived  prices for  using a D i v i s i a  index to  the form  Derivation  of a  problems. Using a nominal i n c r e a s i n g user c o s t  user  cost for c a p i t a l  presents  d i s c o u n t r a t e tends t o produce  s e r i e s when c a p i t a l  more  rapidly  gains are not  allowed  f o r while u s i n g a r e a l d i s c o u n t r a t e produces negative user c o s t s i n more r e c e n t y e a r s .  To overcome t h i s problem  approach as used by Ostensoe average  of the nominal  (1986) was used whereby a  user  taken as the r a t e taken  t o produce  cost s e r i e s .  The  unweighted average  at  of the 90  monthly i n t e r v a l s .  used  index from  weighted  the nominal  a relatively  nominal  The  interest  stable, rate  day c o r p o r a t e  real  c o n s t r u c t e d by s u b t r a c t i n g the percentage price  hoc  and r e a l d i s c o u n t r a t e s i s used along with  appropriate depreciation rates non-negative  the same ad  interest  interest rate.  paper  rate  change i n the  was  was  consumer  The d i s c o u n t  rate  i n d e r i v i n g the user c o s t of c a p i t a l was obtained by p l a c i n g  a weight nominal  of 0.68  on the  real  Interest rate  and 0.32  on the  i n t e r e s t r a t e . The d i s a g g r e g a t e d data from which the user  c o s t s e r i e s was obtained a r e l i s t e d For c o n s i s t e n c y , the same weighted i n the e s t i m a t i n g system of Chapter  in detail average  average  6. The a s s e t p r i c e , user c o s t  discount rate.  121  (1986).  d i s c o u n t r a t e was used  and q u a n t i t y s e r i e s f o r c a p i t a l a r e presented with the weighted  i n Ostensoe  i n Table A1.7 along  TABLE A l . l AGGREGATE PRICE INDICES Year  Exports  Imports  1961  1.0000  1.0000  1962  1.0204  1963  Dom.  Labour  Capital  1.0000  1.0000  1.0000  1.1960  1.0071  1.0350  1.0667  1.0239  1.2399  1.0250  1.0747  1.1129  1964  1.0340  1.2723  1.0370  1.1101  1.1654  1965  1.0559  1.2728  1.0603  1.1684  1.2191  1966  1.0853  1.2957  1.1054  1.2664  1.2711  1967  1.1078  1.3132  1.1437  1.3564  1.2405  1968  1.1319  1.3150  1.1730  1.4581  1.3114  1969  1.1653  1.3447  1.2216  1.5748  1.3680  1970  1.2053  1.3939  1.2759  1.6931  1.3510  1971  1.2230  1.2108  1.3343  1.8360  1.4353  1972  1.2751  1.2494  1.3961  1.9738  1.5392  1973  1.4167  1.3670  1.5140  2.1892  1.7841  1974  1.7102  1.8005  1.7390  2.4937  1.9934  1975  1.9456  2.0591  1.9653  2.8539  2.1016  1976  2.0819  2.1346  2.1110  3.2378  2.2778  1977  2.2671  2.3861  2.2532  3.4999  2.3690  1978  2.5106  2.6657  2.4130  3.7063  2.5881  1979  2.8651  3.0923  2.6024  3.9336  2.9382  1980  3.2431  3.7384  2.9404  4.4886  3.1815  122  Sales  TABLE A1.2 AGGREGATE QUANTITIES Year  Exports  Imports  IN MILLIONS OF 1961 DOLLARS Dom.  Sales  Labour  Capital  1961  6445 .8  4272 . 8  29988. 3  18747. 4  13414.0  1962  6840 .8  3929 .6  32298. 7  19403. 0  13806.3  1963  7550 .8  4117 .6  33783. 9  19811. 5  14345.1  1964  8664 .6  4581 .1  35865. 0  20604 .1  14971.4  1965  8989 .3  5038 .3  39067. 5  21721. 4  15686.2  1966  10251 . 3  5607 .1  41243. 2  22439 . 1  16547.3  1967  11047 .8  5777 .0  41578. 5  22568. 9  17407.0  1968  12866 .7  6416 . 4  42976. 8  22459. 5  18139.0  1969  13743 .4  7097 .8  45548. 1  22984. 0  18943.8  1970  14960 .6  6939 .6  44712. 8  22782. 9  19862.8  1971  15672 .1  8923 .1  47519. 2  23056. 7  20507.3  1972  16891 .3  10010 .0  50745. 1  23808. 4  21365.4  1973  19083 .3  11191 .2  54886. 0  25095. 6  22360.1  1974  19287 .3  11883 .3  57993. 5  26230. 5  23591.0  1975  17699 .2  11169 .1  58963. 9  26236. 0  24954.1  1976  19292 .2  11688 .1  61903. 0  26563. 6  26291.6  1977  20802 .9  11825 .6  62552. 0  26848. 2  27827.7  1978  22603 .7  12499 .1  64277. 8  27685. 4  29333.9  1979  23949 .6  13296 .2  67519. 4  28674. 0  30773.8  1980  25055 .1  12613 .9  67671. 5  29153. 3  32132.0  123  TABLE A l . 3 EXPORT COMPONENT PRICE INDICES Textiles  Heavy Ind.  & Energy  & Electrical  & Services  Products  Products  Products  Products  1961  1.0000  1.0000  1.0000  1.0000  1962  1.0347  1.0212  0.9821  1.0099  1963  1.0458  1.0228  0.9683  1.0111  1964  1.0548  1.0356  0.9613  1.0324  1965  1.0764  1.0685  0.9645  1.0526  1966  1.1200  1.1013  0.9750  1.0667  1967  1.1420  1.1275  0.9852  1.0989  1968  1.1718  1.1480  1.0006  1.1308  1969  1.2218  1.1759  1.0236  1.1623  1970  1.2336  1.2583  1.0509  1.2042  1971  1.2518  1.2418  1.0764  1.2482  1972  1.3629  1.2697  1.0996  1.2950  1973  1.6445  1.4499  1.1361  1.3765  1974  1.9986  1.9430  1.2625  1.6014  1975  2.1906  2.3470  1.4058  1.8181  1976  2.2353  2.6105  1.5081  1.9618  1977  2.3731  2.9656  1.6420  2.0917  1978  2.6363  3.3414  1.8140  2.2630  1979  3.0640  3.9620  2.0077  2.5050  1980  3.3090  4.7162  2.2520  2.8385  Year  Agricultural  Minerals  & Forestry  124  MVs.  TABLE A 1 . 4 EXPORT COMPONENT QUANTITIES Aqr i c u l t u r a l Year  IN MILLIONS OF 1961 DOLLARS  Minerals  MVs.  Textiles  Heavy  Ind.  & Forestry  & Enerqy  & Electrical  & Services  Products  Products  Products  Products  1961  2763.9  1853.1  687.8  1141.0  1962  2767.9  2053.5  831.1  1191.3  1963  3074.8  2130.5  968.5  1383.2  1964  3502.0  2379.5  1215.0  1582.2  1965  3455.6  2477.3  1376.4  1707.4  1966  3700.7  2567.8  2127.4  1948.9  1967  3320.9  2802.2  3037.9  2087.3  1968  3448.6  3227.6  4230.8  2285.3  1969  3471.1  3129.7  4983.0  2575.4  1970  3788.9  3716.3  5075.1  2780.7  1971  4072,4  3617.7  5490.1  2938.4  1972  4306.0  3880.6  5914.6  3273.0  1973  4748.4  4572.1  6803.6  3536.2  1974  4834.7  4615.0  6594.8  3765.5  1975  4187.7  4034.8  6607.2  3577.6  1976  4789 .9  3980.2  7614.8  3864.9  1977  5343.8  4025.5  8365.9  4209.8  1978  5726 . 4  4135.5  9267.5  4870.5  1979  5955.1  4642.0  8836.5  5684.3  1980  6385.3  5209 .8  8126.7  6079 .3  125  TABLE A1.5 IMPORT COMPONENT PRICE INDICES Ag.,  Forestry  Metals &  Machinery,Elec,  Vehicles,  & Service  Energy  & Textile  Chem. &Other  Products  Products  Products  Products  1961  1.0000  1.0000  1.0000  1.0000  1962  1.3568  1.1344  1.0708  1.0642  1963  1.4575  1.1375  1.0836  1.0872  1964  1.5280  1.1587  1.0834  1.1017  1965  1.5174  1.1678  1.0835  1.1093  1966  1.5504  1.1940  1.0837  1.1332  1967  1.5516  1.2223  1.0915  1.1685  1968  1.5457  1.2270  1.0903  1.1783  1969  1.5768  1.2563  1.1103  1.2102  1970  1.6638  1.3221  1.1235  1.2316  1971  1.2443  1.2147  1.0643  1.1901  1972  1.3027  1.2526  1.0754  1.2208  1973  1.4509  1.3997  1.1803  1.2847  1974  1.7726  2.5983  1.3946  1.4764  1975  1.9386  3.1224  1.5062  1.7539  1976  1.9853  3.2792  1.5800  1.8102  1977  2.2172  3.6450  1.7327  2.0544  1978  2.4396  3.9983  1.9135  2.3807  1979  2.7455  5.0706  2.1486  2.6856  1980  3.0906  7.2636  2.3489  3.0792  Year  126  TABLE A 1 . 6 IMPORT  COMPONENT Q U A N T I T I E S  Aq., Year  &  Forestry Service  Products  IN MILLIONS  Metals & Enerqy Products  OF 1 9 6 1 DOLLARS  Machinery,Elec &  Textile  Products  Vehicles, Chem.  &Othe:  Products  1961  1821.8  923.9  773.7  753.5  1962  1431.3  885.4  777.0  865.9  1963  1426.1  958.0  832.5  952.1  1964  1548.8  1066.3  948.9  1087.9  1965  1655.8  1140.5  1039.1  1300.7  1966  1832.5  1196.0  1202.2  1494.5  1967  1915.7  1158.8  1214.4  1602.3  1968  1963.7  1286.9  1260.4  2078.5  1969  2175.4  1352.4  1448.2  2319.4  1970  2139 .7  1416.5  1404.3  2162.0  1971  3147.8  1707.7  1649.9  2568.4  1972  3501.9  1839 .6  1954.3  2898.7  1973  3831.3  2100.7  2118.8  3345.5  1974  4124.6  2162.1  2262.1  3598.3  1975  3901.7  2058.1  2053.7  3372.7  1976  4139.1  1958.6  2165.8  3804.6  1977  4193.2  1899.6  2154.3  4022.4  1978  4455.7  1956.5  2364.8  4242.8  1979  4773.7  2160.2  2755.9  4146.1  1980  4798.2  2069.4  2736.8  3528 .8  127  TABLE A1.7 ADJUSTMENT COSTS MODEL CAPITAL DATA Year  Asset P r i c e  User Cost  Capital Quantity  1  Discount Rate  1961  1.0000  0.0998  10.3960  0.0510  1962  1.0152  0.1012  10.7000  0.0501  1963  1.0395  0.0956  11.1176  0.0414  1964  1.0731  0.0977  11.6030  0.0405  1965  1.1250  0.0975  12.1570  0.0361  1966  1.1858  0.0977  12.8243  0.0321  1967  1.2299  0.1009  13.4906  0.0320  1968  1.2478  0.1186  14.0579  0.0458  1969  1.3084  0.1278  14.6816  0.0486  1970  1.3582  0.1240  15.3939  0.0414  1971  1.4393  0.1073  15.8934  0.0240  1972  1.5330  0.1033  16.5584  0.0170  1973  1.7104  0.1039  17.3293  0.0126  1974  2.0089  0.0950  18.2833  0.0011  1975  2.2797  0.1171  19.3397  0.0059  1976  2.5141  0.1747  20 . 3762  0.0264  1977  2.7302  0.1853  21.5668  0.0245  1978  2.9436  0.2474  22.7341  0.0427  1979  3.2096  0.2902  23.8500  0.0507  1980  3.4800  0.3251  24.9026  0.0540  1  In tens of  b i l l i o n s of 1961 d o l l a r s .  128  A P P E N D I X P R I M A L A2.1.  V E R S U S  D U A L  production  researchers  characteristics  models and  of  the  interested  price e l a s t i c i t i e s  available flexible  possibilities  between forms  Elasticities  of  able  inputs  such  as  Substitution  factors to  are more  of s u b s t i t u t i o n  forms, on the other function  up  model more  models.  In  Generalised  the  substitution  accurately  Cobb-Douglas the  the  than  and  Constant  case  of  the  of s u b s t i t u t i o n are r e s t r i c t e d  a significant  i n p u t s . The  hand, are able to  and  inputs.  t r a n s l o g and  much  be equal -  than two  The  usually  one. The CES form r e s t r i c t s the e l a s t i c i t i e s  p a i r s of  when there  are  to  f u n c t i o n a l forms have made  to  the  the  analyses.  structure  as the  Cobb-Douglas form a l l e l a s t i c i t i e s to the value  simple p o l i c y  of f l e x i b l e  are  modelling  economies as an input  the e l a s t i c i t i e s  forms such  which  tradidional  in  of demand between the v a r i o u s  Advances i n the f i e l d  (GL)  to  production  summarised by estimates of  Leontief  are  s t r u c t u r e of i n d u s t r i e s and  l a r g e r econometric  cost  E S T I M A T I O N  Introduction Applied  all  2  disadvantage  flexible  functional  t o approximate an  second-order  terms  between  and  arbitrary hence  to  approximate an a r b i t r a r y matrix of s u b s t i t u t i o n e l a s t i c i t i e s . The  Cobb-Douglas and CES forms a r e , however, s e l f - d u a l which  means t h a t both the p r o d u c t i o n  f u n c t i o n and the c o s t f u n c t i o n are  members of the same f a m i l y of f u n c t i o n a l forms. Hence the  choice  of whether  to  the  primal  (production  function)  is in  theory  model  the p r o d u c t i o n or d u a l  structure  by  (cost f u n c t i o n ) route  129  of  no  significance.  estimated  In  practice,  e l a s t i c i t i e s would  be observed  the b e h a v i o u r a l  implications  (Burgess  In the  1975).  however,  of  case  of  the  due  differences  in  to d i f f e r e n c e s  in  stochastic  the f l e x i b l e  specification  functional  forms  mentioned, however, the c h o i c e between primal and dual e s t i m a t i o n routes  i s no longer t r i v i a l  self-dual,  ie.  equivalent in  a translog  s i n c e these  f u n c t i o n a l forms are  cost function  the p r i m a l  does not  representation a  only  imply  differences  different stochastic  in  the  its  production  dual forms w i l l  elasticity  s p e c i f i c a t i o n s but  have as  translog  f u n c t i o n . Hence the c h o i c e between p r i m a l and  not  estimates  a l s o due  to  due  not to  different  u n d e r l y i n g p r o d u c t i o n s t r u c t u r e s being modelled. In s p i t e of the d i f f e r e n t e l a s t i c i t y estimates i s adopted  appears to  while  depend  magnitude  others  flexible  of  remain has  forms.  with  (1975) where t r a n s l o g p r o d u c t i o n were d e r i v e d f o r the different  to compare the from  exception and  same data and  is  from  functions for  three inputs  aggregate Canadian data  and  that  130  primal  and of  dual  Burgess  significantly  possibilities.  Leontief  labour  f o r the p e r i o d 1954  dual  elasticities  to give  Generalised  (capital,  the  primal  Chung (1986) have r e c e n t l y c a l c u l a t e d translog  the  performance  cost function found  of  traditional  information regarding s u b s t i t u t i o n  F i s h e r and estimates  the  estimates One  the b i a s e s  c o n s i s t e n t l y use  been done  elasticity  functional  p r i m a r i l y on  Some authors  approach. L i t t l e work and  to d e r i v e  from the p r i m a l or d u a l form, which approach  i n d i v i d u a l researcher. approach  i m p l i c a t i o n s of choosing  and  elasticity production  energy)  to 1982.  using  The data  is  that  used  in  MacGregor and  the  MACE  Padmore,  macro  econometric  1984). T h i s  work  model  i s extended  Appendix where e l a s t i c i t y estimates are d e r i v e d GL c o s t  function  those d e r i v e d The  cost  models using  by F i s h e r and  function  developed Symmetric  the same data  is  Generalised  McFadden  and  this  extended  and with  specification.  to  (SGM)  compared  the  recently  functional  developed by Diewert and  Wales (1987). T h i s form has  advantages over e a r l i e r  flexible  s a t i s f y i n g g l o b a l curvature  in  from t r a n s l o g  Chung from the primal  estimation  (Helliwell,  f u n c t i o n a l forms  form  significant i n regard  c o n d i t i o n s . E l a s t i c i t y estimates  to are  found to be q u i t e s e n s i t i v e to the s p e c i f i c a t i o n used. The  methodology used i n the  estimation  i s o u t l i n e d i n the  are presented drawn i n the A2.2.  i n the  third  comparison of primal and  dual  f o l l o w i n g s e c t i o n while the r e s u l t s section. Finally,  conclusions  are  fourth section.  Methodology The  translog  and  GL  production  summarised below. More d e t a i l s can  be  function  estimation  found i n F i s h e r and  (1986) . A d e t a i l e d d i s c u s s i o n of the p r o p e r t i e s of the GL and  SGM  cost  f u n c t i o n s can  be  found  i n Diewert  is  Chung  translog, and  Wales  (1987) . A2.2.1 The The  Translog 3-factor  translog production  Form [capital  (K), labour  f u n c t i o n i s given  131  by;  (L) and  energy  (E)]  InQ = a (A2.1)  + a lnK  Q  + a lnL + a lnE + a t +  K  L  E  (1/2)a (InK)  t  + (l/2)a lnKlnL + a lnKlnE + (1/2)a (InL) K L  K E  L E  a where Q  tlnL  + a  i s output,  imposed.  The  + (1/2)a fe  2  E E  L t  + a  2  tt  K t  +  tlnK +  tlnE  E t  T is  translog  2  L L  a lnLlnE + (1/2)a (InE)  2  K K  a  time t r e n d  production  and symmetry  function  has  exhibits  been  constant  r e t u r n s to s c a l e i f :  (A2.2)  a  K  a  KK  a  +  a  +  L a  +  KL  + a  K L  a  KE  +  a  a  Kt  +  a  E =  a  +  a  +  a  +  a  Lt  KE  =  + a  L L  LE  1  EE  0  = 0  L E  =  0  Et =  0  If the t e s t f o r constant r e t u r n s to s c a l e (A2.2) i s accepted and p r o f i t maximisation (A2.1) can  be  is  assumed then the p r o d u c t i o n  estimated a l o n g  with  the f o l l o w i n g  function  cost  share  equations: (A2.3)  S S  The t h i r d  K  = a  L  = L  + a lnK  K  a  + a  K K  +  share  a  KL  l n K  +  a  equation  shares must sum to u n i t y .  LL  K L  l n L  is  lnL +  a  + a LE  l n E  excluded  K E  lnE +  a  Lt  + a  K t  t  f c  s i n c e the  three  factor  The t e s t f o r n e u t r a l t e c h n i c a l  change  is: (A2.4)  a  K t  Elasticities Hessian  L t  + a  E t  = 0  of s u b s t i t u t i o n are d e r i v e d from the  bordered  of the p r o d u c t i o n f u n c t i o n , G, as f o l l o w s :  (A2.5) where  + a  ES j = IGij|/|G| i;  IGjjl  i s the i , j c o f a c t o r of G. Own  demand are d e r i v e d as f o l l o w s :  132  price e l a s t i c i t i e s  of  (A2.6)  ED - . = S -ES . . ID  The  D  ID  t r a n s l o g c o s t f u n c t i o n may be represented  lnC(p,Q,t) = a  as f o l l o w s :  3 2 + Zi=i a i l n P i + a l n Q + a t + ( l / 2 ) a t +  0  Q  t  t t  (A2 . 7 )  where a i j = a j i f o r a l l i , j ; Zi=l a i = l , Zj=l a i j = 0 f o r i=l,2,3; 3 3 Z i = l a = 0 and Z i = l a = 0 . iQ  By a p p l y i n g (A2.8 )  it  Shephard's Lemma c o s t share equations are obtained:  Si(p,Q,t)  = a i + Z j = i a i j l n p j + aiQlnQ + a i t t ;  1=1,2,3.  Again the t h i r d share equation i s excluded so t h a t the e s t i m a t i n g system c o n s i s t s  of (A2.7)  constant  t o s c a l e can be made;  (A2.9) The  returns a  Q  = 1; a i  Q  and (A2.8).  = 0, 1=1,2,; a  Q  Q  The f o l l o w i n g  = 0; a  Q  t  test  for  = 0.  t e s t f o r n e u t r a l t e c h n i c a l change i s ;  (A2.10)  a t = 0; a i t = 0, 1=1,2; a t = 0; a t t = °Q  For the estimated c o s t f u n c t i o n t o s a t i s f y the of economic  theory  observation  points.  i t must In  be concave  the  translog  f o l l o w i n g matrix t o be negative point  in  requirements  prices at  case  this  a l l the  requires  s e m i - d e f i n i t e a t each  observation  (Diewert and Wales 1987);  (A2.ll)  ^ K K - S R + S K  ^ K L + S R S L  ^ K L + S R S L  ^ L L - S L + S L  A  K  E  +  S  K  S  E  A  L  E  +  S  L  S  A  a  K  E  LE  aEE  E  +  S  + s  - s  K  S  E  L E  E  s  + s  EE  Allen-Uzawa e l a s t i c i t i e s of s u b s t i t u t i o n a r e given by: (A2.12)  ESii = ( a n + S i - Si)/Si 2  133  2  the  E  s  i j  =  a j/(S Sj) + 1 i  i  P a r t i a l p r i c e e l a s t i c i t i e s are given by: (A2.13)  EDii = SiESii  ;  ED^ j = S j E S j . i :  A2.2.2 The G e n e r a l i s e d L e o n t i e f Form The  p r i m a l GL system estimated Q = aQ + a K K 2aKL(KL)  (A2.14)  1 / 2  + a L  aEEE + ( l / 2 ) a t t t  + a t + a K  +  KK  t  + aLLL + a L E ( L E )  1 / 2  +  1 / 2  + aKttK + a L t t L + a E t t E  2  1 / 2  1 / 2  E  + 2aKE(KE)  PK/PQ = aKK + l / 2 a K K "  The  + a E  1 / 2  L  1 / 2  by F i s h e r and Chung i s :  + aKL(L/K)  1 / 2  + aKE(E/K)  1 / 2  + aKtt  PL/PQ = aLL + l / 2 a L L  _ 1 / 2  + aKL(K/L)  1 / 2  + aLE(E/L)  1 / 2  + aLtt  PE/PQ = aEE + l / 2 a E E  - 1 / 2  + aKE(K/E)  1 / 2  + aLE(L/E)  1 / 2  + aEtt  t e s t f o r constant  (A2.15) The  a  Q  = a  K  GL c o s t  returns to scale i s :  = a  L  = a  E  = a  = a  t  t  t  = 0  f u n c t i o n as s p e c i f i e d by Diewert and Wales  can  be represented a s : C(p,Q,t) = Z i = l Z j i l a  Zlll  (A2.16)  a  where a ^ s a ^ ,  i j  f u n c t i o n would appear  i  1 / 2  j  Q  + Zi=l a  aitPltQ + a (Zi=l A t  QQ<Zi=l B  i P i  f o r i , j = l , 2 , 3 and  s p e c i f i e d constants.  (p p )  Since  )Q A  2  i 7  1 P i  C  1 P  i)Qt  B^, and Cj^ are  a l l the c o e f f i c i e n t s  i n the Input  +  )t +  + a t(Zi!l t  i P i  2  exogenously  of  the  demand f u n c t i o n s d e r i v e d  cost by  the use of Shephard's Lemma,  the c o s t f u n c t i o n and input  f u n c t i o n s cannot be estimated  as a t o t a l system. Consequently, i n  t h i s a p p l i c a t i o n the equations  was  following set  estimated:  134  of input-output  demand  coefficient  (A2.17) x ^ p ^ t J / Q  = Xjli aijtpj/pi) / 1  + a^BiQ + a ^ t Input-output c o e f f i c i e n t input  + a  i t  t  + a^-A^/Q  2  rather  than  problem  of  t e s t f o r the c o s t f u n c t i o n not being dependent on  time  demand  equations  + a^1  2  equations  were estimated  to  reduce  the  heteroskedasticity. The  t e s t f o r constant  (A2.18)  returns to scale i s :  a- = 0, 1=1,2,3; a x  The  = 0; a  t  Q  Q  = 0.  is: (A2.19)  a  Concavity  i t  of  = 0, 1=1,2,3; a the c o s t  at  each  f c t  = 0.  f u n c t i o n was examined by  whether the matrix of second order semi-definite  = 0; a  t  p r i c e d e r i v a t i v e s was  observation  point.  are, respectively,  derivatives  of  the  cost  A2 .2.3 The Symmetric G e n e r a l i s e d A problem  order  function.  price  in as  Partial (A2.13).  McFadden Form  o f t e n encountered by e m p i r i c a l s t u d i e s u s i n g  dual s p e c i f i c a t i o n i s  suspect  definition:  the f i r s t and second  e l a s t i c i t i e s were then computed u s i n g equation  concave  of  ESij = CCij/(CiCj)  where C i and C i j price  negative  Elasticities  s u b s t i t u t i o n were c a l c u l a t e d u s i n g the o r i g i n a l (A2.20)  determining  prices. they  t h a t the This  are not  estimated c o s t  renders derived  the from a  f u n c t i o n i s not  estimated cost  the t r a n s l o g ' s  elasticities  function  s a t i s f i e s the b a s i c requirements of economic theory. p o s s i b l e t o f o r c e the t r a n s l o g  the  which  While i t i s  form to be concave t h i s  destroys  f l e x i b i l i t y p r o p e r t i e s . The SGM form developed by  135  Diewert and Wales allows  us t o ensure g l o b a l c o n c a v i t y  with  flexibility  minimal  function  loss  of  properties.  in  The  prices  SGM  cost  i s given by: C(p,Q,t) = g(p)Q + Zi = i a ^ P i Q + Zi = i a ^ i +  Zi = i a ^ p ^ O + a ( Z i = i A ^ J t +  (A2.21)  t  a  where and  QQ £i=l (  B  iPi)Q  2  +  a  tt Zi=l  C  (  i P i  )Qt  2  g(p) = (1/2) p'Sp/(T p) f  the A^,  and  Again t h i s c o s t input demand  are exogenously  given.  f u n c t i o n cannot be estimated along  equations  so  the f o l l o w i n g  set  of  with i t s  input-output  c o e f f i c i e n t equations was used f o r e s t i m a t i o n : = Xj=iSijPj/(rk=lTkPk) " Ti(r =iFj=iSkjPkPj>/2(Ek=l T Pk) -1 2 (A2.22) + a i i +aiQ + a i t t + Ait/Q + BiQ + C i t + u i ; 1=1,2,3. 3 xi/Q  k  2  k  where s i j = s j i and Z i = l s i j = 0 f o r i , j = l , 2 , 3 . Using the s p e c i f i c a t i o n are s e t t o  unity to  (A2.22) the  produce a  (A2.22) a r e s e t equal to relevant cost  and a t t  more f l e x i b l e  (A2.18) and  not being (A2.19),  concave. I f semi-definite  it  is  dependent on  respectively.  semi-definite  then  not,  without  i  (A2.21)  n  form. The  T i in  the sample midpoint q u a n t i t i e s f o r the  i n p u t s . The t e s t s f o r c o n s t a n t s r e t u r n s  function  negative  a t / aQQ  the  the S  time a r e If  cost  matrix  losing  the  properties.  136  t o s c a l e and again  the  given  by  matrix  is  the [ S j j  ]  function  is  globally  made  negative  can  be  function's  flexibility  The equation  elasticities  of s u b s t i t u t i o n were a g a i n c a l c u l a t e d u s i n g  (A2.20) while the p r i c e  t u r n d e r i v e d u s i n g equation  e l a s t i c i t i e s of demand were  in  (A2.13).  A2.3. R e s u l t s D e t a i l e d r e s u l t s f o r the t r a n s l o g and GL p r o d u c t i o n f u n c t i o n e s t i m a t i o n can be found the c o s t  i n F i s h e r and Chung. Only the r e s u l t s f o r  function estimation  are presented  in detail  in  this  Appendix. In  undertaking the c o s t  converted to p r i c e  indices  f u n c t i o n e s t i m a t i o n the data  having a value of  o b s e r v a t i o n and corresponding  1.0 f o r the  were first  i m p l i c i t q u a n t i t i e s f o r each of the  inputs obtained by d i v i d i n g the input value by the r e l e v a n t p r i c e index. In the case of output the q u a n t i t y was normalised t o a value of 1.0 f o r the  first  found t o be i n v a r i a n t i n to  o b s e r v a t i o n . The t r a n s l o g form  terms of f i t and e l a s t i c i t i e s  s e n s i t i v e t o s c a l i n g . The data used are l i s t e d and Chung  specifications.  One  has  report results a  constant  component i n d e r i v i n g the  user c o s t while the  o p p o r t u n i t y c o s t component  which v a r i e s over  appears  to  be  no  theoretical  constant r e a l o p p o r t u n i t y  justification  c o s t of c a p i t a l  here are those f o r the t i m e - v a r y i n g c a p i t a l C o n c l u s i v e evidence of  capital  price  opportunity  cost  other has a time. Since for  f u n c t i o n t h i s was c o r r e c t e d f o r by  137  real there  imposing  the r e s u l t s  a  reported  price.  a u t o c o r r e l a t i o n was  three d u a l e s t i m a t i n g systems. In  quite  i n Table A2.1.  f o r two real  was  obtained  the s c a l i n g of the data but the GL form was found to be  Fisher  have  found  in a l l  the case of the t r a n s l o g  cost  use of the AUTO o p t i o n  which  imposes a  constant  across equations.  value  of  In the GL  not e a s i l y be c o r r e c t e d  trend  e x c e p t i o n of  autocorrelation  coefficient  and SGM cases a u t o c o r r e l a t i o n  f o r but d i d not  problem with the s c a t t e r of with the  the  could  appear t o be a  serious  r e s i d u a l s showing no marked  pattern  the c a p i t a l  equations where  a  cyclical  i n the r e s i d u a l s c o u l d be d i s c e r n e d . T h i s i s not s u r p r i s i n g  g i v e n the l i k e l y m i s s p e c i f i c a t i o n of the c a p i t a l equation due the f a i l u r e to take account  of i n v e n t o r y , u t i l i s a t i o n r a t e ,  other c o n s i d e r a t i o n s which a f f e c t the most durable The  to and  input.  estimated c o e f f i c i e n t s f o r the t r a n s l o g , GL and SGM c o s t  f u n c t i o n s and corresponding asymmtotic t - v a l u e s a r e presented  in  Table A2.2 f o r the t i m e - v a r y i n g c a p i t a l  price data. D e t a i l s  of  f o r constant r e t u r n s  to  (CRTS) and n e u t r a l t e c h n i c a l change (NTC) a r e presented  in  the f i t of the scale  f u n c t i o n s and the t e s t s  Table A2.3. The t r a n s l o g c o s t fit  t o the data, having a  l o g l i k e l i h o o d value of 421. In  of f i t the SGM system appears comparing the  f u n c t i o n appears t o give the  r e s u l t s of  best terms  to perform b e t t e r than the GL.  the  t e s t s f o r CRTS the  first  d i f f e r e n c e between the p r i m a l and d u a l systems becomes  In  major  apparent.  In a l l three d u a l systems the assumption of CRTS i s very s t r o n g l y r e j e c t e d whereas  i t i s accepted  function tests. I t  should be noted,  production function test i s conducted whereas  the  in  the  translog  production  however, t h a t the t r a n s l o g  f o r CRTS i s a r e l a t i v e l y weak one as i t  on the OLS estimate of the p r o d u c t i o n f u n c t i o n alone other  tests  e s t i m a t i n g systems. The  are  conducted  assumption of NTC  138  within  the  i s accepted  complete for  both  p r i m a l systems  but i s d e c i s i v e l y r e j e c t e d  for a l l  three  dual  systems. F i s h e r and Chung f i n d the t r a n s l o g and GL p r i m a l systems s a t i s f y the  necessary  curvature  conditions at  p o i n t s . S i m i l a r l y , the t r a n s l o g dual prices at a l l negative  semi-definite  however, does with the  at  not s a t i s f y  matrix  of  each  a l l observation  system i s concave i n  o b s e r v a t i o n p o i n t s with  the matrix  point.  concavity at  second-order p r i c e  The  to  input  (A2.ll)  GL , dual  being system,  a l l observation derivatives  points  not  being  negative s e m i - d e f i n i t e f o r 12 of the 29 o b s e r v a t i o n s . In c o n t r a s t the  S  matrix  in  the  SGM  s e m i - d e f i n i t e and hence the concave. Given at a l l the  case  was  estimated  found  to  be  negative  cost function i s  the f a i l u r e of the GL system t o s a t i s f y  o b s e r v a t i o n p o i n t s the  globally concavity  d e r i v e d e l a s t i c i t i e s must  be  t r e a t e d with s u s p i c i o n . The  Allen-Uzawa e l a s t i c i t i e s  p a i r of the three  inputs are presented  29 o b s e r v a t i o n s . In the case s u b s t i t u t i o n the  of s u b s t i t u t i o n between  i n Table A2.4 f o r 8 of the  of c a p i t a l - l a b o u r and c a p i t a l - e n e r g y  translog cost  function e l a s t i c i t i e s  generally  i n d i c a t e much l e s s scope f o r s u b s t i t u t i o n than does the production  function.  The  capital-labour e l a s t i c i t i e s  c o s t f u n c t i o n are only one f i f t h the magnitude of those production  of  g r e a t e s t scope production  translog from  the  from  the  f u n c t i o n . Labour-energy e l a s t i c i t i e s a r e approximately  the same f o r both the p r i m a l the h i g h e s t  each  the  and d u a l sources  translog cost  for substitution  function  i s between  as  function  elasticities,  i n d i c a t e d by  capital  139  but while t h i s  the  and l a b o u r .  is the  translog  Hence  the  d e t a i l s of  the  technology  t r a n s l o g estimates The  conveyed  by  the  primal  GL dual estimates  again g e n e r a l l y I n d i c a t e l e s s  capital-labour e l a s t i c i t i e s  t h a t there i s  and  for  energy. The  dual GL e s t i m a t e s ,  indicate  f o r s u b s t i t u t i o n . The  most scope f o r s u b s t i t u t i o n  GL p r i m a l estimates  energy are complements and  this  finding  c o n t r a r y to the  scope  estimates.  the dual GL system  almost n e g l i g i b l e scope  c o s t f u n c t i o n i n d i c a t e s the labour and  dual  differ greatly.  f o r s u b s t i t u t i o n between inputs than do the p r i m a l GL The  and  GL  between  indicate that  capital  i s r e i n f o r c e d by  the  t r a n s l o g r e s u l t s . While  the  dual GL s u b s t i t u t i o n e l a s t i c i t i e s are r e l a t i v e l y s t a b l e they must be t r e a t e d with  s u s p i c i o n due  to the f a i l u r e  of the  concavity  requirement. The translog  dual SGM dual  e l a s t i c i t i e s are  estimates  for  i n d i c a t e the g r e a t e s t scope energy as  did  the  dual  of s i m i l a r magnitude to  capital-labour  substitution  and  f o r s u b s t i t u t i o n between labour  and  translog estimates.  c a p i t a l - e n e r g y s u b s t i t u t i o n , however, the SGM through time from s l i g h t one  the  In  the  case  indicates a  of  change  s u b s t i t u t a b i l i t y to no r e l a t i o n s h i p  to  of i n c r e a s i n g complementarity. From the s u b s t i t u t i o n e l a s t i c i t i e s ,  t h a t the  impression  very s e n s i t i v e not  of the technology o n l y to  then,  one must  conclude  c h a r a c t e r i s t i c s conveyed i s  the c h o i c e between  p r i m a l and  dual  e s t i m a t i o n routes but a l s o to the choice of f u n c t i o n a l form. With the e x c e p t i o n of the dual GL estimates to c o n c a v i t y v i o l a t i o n s there estimates  ( t r a n s l o g or SGM,  is l i t t l e  which can be r u l e d out  due  to i n d i c a t e which s e t  of  p r i m a l or dual) should be p r e f e r r e d .  140  Moving to Table A2.5  own  price e l a s t i c i t i e s  each of the three Inputs are presented As  i n d i c a t e d by the  and GL  generally  The  energy  own  price  t r a n s l o g sources  elasticities  are  from  the  small  and  start  i n d i c a t e huge wage  c l o s e to the result  s m a l l as to  to a l l e v i a t e even s m a l l unemployment  estimates  i s r e a s s u r i n g as the two  in a l l  SGM  results  dual  capital being be  from the  levels. extremely  three cases.  This  produce s i m i l a r own  in  price  o n l y major d i f f e r e n c e between the d u a l t r a n s l o g  is  the SGM  finding that  c a p i t a l and energy  are  i n c r e a s i n g l y complementary whereas the t r a n s l o g f i n d s them to s u b s t i t u t e s . There i s c o n f l i c t i n g studies  as  to  GL  reductions  d u a l forms which perform best  terms of f i t and c u r v a t u r e requirements  and  and  off  p r i c e e l a s t i c i t y estimates are  dual t r a n s l o g  e l a s t i c i t i e s . The  changes.  t h a t t h i s s e t of e l a s t i c i t i e s must  c o s t f u n c t i o n are so  own  price  elasticities  dual GL  price e l a s t i c i t i e s  The dual SGM  less  price  t r e a t e d with s u s p i c i o n . Labour own  being necessary  translog  primal  e q u a l . The  implausibly  f u r t h e r evidence  labour  demand to own  are approximately  price e l a s t i c i t i e s positive,  of input  the dual  i n d i c a t e much  r e s p o n s i v e n e s s . The d u a l t r a n s l o g c a p i t a l and i n d i c a t e minimal response  for  f o r the same o b s e r v a t i o n s .  substitution e l a s t i c i t i e s  price e l a s t i c i t i e s  of demand  whether  capital  evidence and  from other  energy  are  be  empirical in  fact  complementary or s u b s t i t u t a b l e . A2 .4.  Conclusions The  f i n d i n g s .. of  Burgess which i n d i c a t e  t h i s study support the e a r l i e r t h a t the c h o i c e  e s t i m a t i o n routes i s not a  trivial  141  one.  findings  between p r i m a l and Rather,  quite  of  dual  different  impressions depending  of  on w h i c h  information sensitive sets  of  has  it  elasticity  view  prices  firm  used  may b e  the  are  of _its  is  committed whatever  the  primal  At recognised  a  to  beyond and  more to  price  the  certain clears be  primal  the  are  the  truly  firm's  very  translog SGM  cost the  to  but  then  made.  by  depend  the the  should  primal  the  firm. firm  dual  other  of  models.  which  should  on t h e and  is  given  its  quantity  it  should  or on If has  model  hand,  levels  market  more  inputs  robustness  sector  exogenous  If,  cost  choices  choice  is  highlight  of  control  quantity the  to  criteria  decisions  SGM  econometric  production  level  output  practical the  the  some  satisfy  most  while  lack  consider  appropriate.  m o d e l may  more that  basic  to  and  The  larger  quite  predict  estimation  to  to  energy.  serves  relative  be  options  for  they  and  This  input  model  variables  input be  the  as  translog  the  While  remaining  substitutes  the  useful  most  which  seem t o  accept then  of  faced  control would  At  to  highlights  it  as  to  fail  estimates  capital  complements.  when d e c i d i n g  means.  pair  results  estimates  Finally,  one's  as  they  the  obtained  Furthermore,  chosen.  conditions,  between  this  form  between while  be  appears  because  elastlcltly  curvature  them  Furthermore,  choice  will  adopted.  functional  instance,  similar  has  of  used  the  is  technology  discarded  relationships  function  technology  route  the  be  For  satisfy  sensitivity  dual  can  produce  both  function  on  particular  arbitrary.  different  be  estimation  conditions  functions  cost  the  results  largely  production  obtained  to  curvature  and  the  the  prepared  to  levels  appropriate.  level, and  142  however, dual  models  have  also  be  different  comparative  advantages  v a r i a b l e s . For of output accurate the d u a l  in  i n s t a n c e , i f one  levels  r e s u l t s . I f one model  is  is  likely  important  predicting  model i s l i k e l y  to  be  more  i s made and  accurate  the method of  cho ic e of f u n c t i o n a l  form, e t c . ) and  with d i f f e r e n t e s t i m a t i o n methods may  t h a t some  143  reasons obtained  (primal or  dual,  experimentation  be a p p r o p r i a t e  obtained.  hence,  f o r whatever  estimation  more  however,  and,  p o i n t to bear i n mind i s t h a t the r e s u l t s  of the r e s u l t s  certain  to give  interested in cost l e v e l s ,  w i l l be s e n s i t i v e to  the robustness  and  i s i n t e r e s t e d mainly i n f o r e c a s t s  then the p r i m a l  a p p r o p r i a t e . Whichever c h o i c e the  modelling  to determine  TABLE A 2 . 1 MACE DATA  Capital  Labour  Labour  Energy  Energy  Price  Quantity  Price  Quantity  Price  Quantity  1 .0000  1 .0000  5 .8912  1 .0000  15 . 3590  1 .0000  2 .1269  1955  1 .0945  1 .0481  6 .1646  1 .0253  15 .7400  0 .9951  2 .4860  1956  1 .1864  1 .1287  6 .4954  1 • 093_6  16 .3890  0 .9604  2 .7820  1957  1 .2137  1 .1950  6 .8532  1 .1440  16 .8338  0 .9825  3 .0051  1958  1 .2447  1 .2468  7 .1946  1 .1727  16 .7562  0 .9857  3 .1070  1959  1 .2892  1 .2767  7 .5389  1 .2087  17 .2674  0 .9050  3 . 4664  1960  1 .3233  1 .3157  7 .8683  1 .2464  17 .5751  0 .8753  3 .7356  1961  1 .3555  1 .3546  8 .1408  1 .2802  17 .8565  0 .8755  3 .9108  1962  1 .4357  1 .4112  8 .3940  1 .3228  18 .3813  0 .8681  4 .1749  1963  1 .5168  1 . 4630  8 .6693  1 .3692  18 .8528  0 .8608  4 . 4541  1964  1 .6099  1 .5026  9 .0063  1 .4312  19 .5810  0 .8848  4 .8503  1965  1 .7143  1 .5377  9 .4273  1 .5165  20 .3785  0 . 8707  5 .2459  1966  1 .8328  1 .5859  9 .9122  1 .6248  21 .2819  0 .8747  5 .6338  1967  1 .8860  1 .6306  10 .4008  1 .7459  21 .9057  0 .8888  6 .0376  1968  1 .9953  1 .6838  10 .8410  1 .8373  22 .3240  0 .9091  6 .5599  1969  2 .0953  1 .7787  11 .2888  2 .0112  23 .0340  0 .8969  6 .9819  1970  2 .1458  1 .8797  11 .7445  2 .1442  23 .2874  0 .9079  7 .4121  1971  2 .2950  1 .9572  12 .2232  2 .2969  23 .8680  0 .9503  7 .7892  1972  2 . 4190  2 .0465  12 .7750  2 .4786  24 .5353  0 .9571  8 .4472  1973  2 .6089  2 .1812  13 . 4246  2 .7204  25 .7767  1 .0223  8 .7976  1974  2 .7222  2 .4083  14 .1568  3 .1314  26 .8543  1 .2509  9 .3174  1975  2 .7996  2 .5916  14 .8831  3 .5865  27 .3125  1 .4768  9 .2115  1976  2 .9713  2 .6789  15 .6112  4 .1175  27 .8397  1 .6554  9 .7194  Output  Capital  Year  Quantity  1954  144  TABLE A2.1 (CONTINUED) Output  Capital  Year  Quantity  Pr i c e  1977  3.0418  2.7352  16.3232  4.4615  28.3814  1.8997  10.1380  1978  3.1701  2.8898  16.9430  4.7199  29 .3694  2.0830  10.4261  1979  3.2782  3.2439  17.5675  5.1023  30.5767  2.3172  10.7488  1980  3.3104  3.8424  18.2553  5.5827  31.5144  2.6869  11.0033  1981  3.4178  4.7141  18.9659  6.2671  32.3699  3.4063  10.8558  1982  3.2756  5.4384  19.5231  6.9630  31.2575  3.9482  10.9788  C a p i t a l Labour Quantity  Price  145  Labour Quantity  Enerqy Pr i c e  Enerqy Quantity  TABLE A2.2 COST FUNCTION COEFFICIENTS Transloq  Gen. L e o n t i e f  Sym. Gen. McFadden  ao  3.14  (248.3)  aRK  1 .22  (2.1)  S  KK  -2.45  (-0.4)  aK  0.26  (120.2)  aKL  0 .35  (1.3)  SKL  19.77  (1.3)  aL  0 .64  *  aKE  aE  0.10  (50.9)  aLL  5 .86  aQ  0.16  (1.3)  aLE  1 .67 . (9.9)  SLE  at  0.03  (4.8)  aEE  1 .09  (1.6)  aKK  0.16  (36.4)  aK  4 .80  aL  7 .29  K L -0.14  *  aKE -0.02  (-7.4)  a  a  a  a  a  a  a  E  -0 . 37 (-2.6) (7.7)  SKE  3.68  SLL -78.88  * (-3.5)  59 .12  *  SEE  -62.80  *  (8.9)  aKK  0.25  (0.2)  (8.9)  aK  5.24  (9.2)  -0.12  (-0.2)  AK  0.41  (1.9)  -0 .15 (-0.3)  aKt  0.17  *  aKt  L E -0.03  *  aLt  -0 .11 (-2.8)  BK  0 .12  (0.2)  0.05  (14.1)  aEt  -0 .09 (-2.9)  CK  0.004  (3.5)  KQ -0.11  (-6.9)  at  aLL  6.31  (1.0)  LL  EE  LQ  0.12  a£Q -0.01 3Rt  0.006  a  Lt  -0.008  a  Et  0.002  a  QQ  0.82  a  Qt  -0.03  att  RHO  O.001  * (-1.1)  0 .001 (0.03)  0 .66  (7.3)  QQ  -0 .80 (-1.6)  aL  9.40  (1.6)  att  0 .007 (4.5)  aLt  0 .20  (0.6)  a  (10.0)  AL  .-0.04  (-0.3)  BL  -0.61  (-0.9)  (4.4)  CL  -0.003 (-0.4)  (2.9)  aEE  *  4 .27  (2.0)  (-1.9)  aE  -1.11  (-0.5)  (1.1)  aEt  -0.01  (-0.1)  AE  0.04  (0.4)  BE  -1.04  (-2.7)  0.56  CE  0.002  Asymptotic t - v a l u e s l n parentheses * C o e f f i c i e n t d e r i v e d from summation r e s t r i c t i o n s  1 A r\  (0.7)  TABLE A2.3 FITS AND TESTS Translog  Log L i k e l i h o o d  GL  Primal  Dual  Primal  310.99  421.55  128.30  Test f o r CRTS  5.40  2  114.34  2  Test f o r NTC  3.18  4  75.50  2  Concavity V i o l a t i o n s !A11  0  1  32.08 .  0  3.80  5  0  3  SGM Dual  Dual  120.83  134.60  129.36  2  126.OO  3  78.46  2  112.60  3  12  0  GL p r i m a l r e s u l t s a r e not c o r r e c t e d f o r a u t o c o r r e l a t i o n  2  Critical  Chi-square  (0.99) = 15.09  3  C r i t i c a l Chi-square  (0.99) = 16.81  4  C r i t i c a l Chi-square  (0.99) =  5  C r i t i c a l Chi-square  (0.99) = 11.34  9.21  147  TABLE A2.4 ELASTICITIES OF SUBSTITUTION Translog Pr imai  Dual  Gen. L e o n t i e f Pr imai  SGMcFadden  Dual  Dual  Capital-Labour 1954  1.00  0.16  1.50  0.05  0.13  1958  0.99  0.19  1.66  0.05  0.16  1962  0.99  0.22  1.74  0.05  0.19  1966  0.99  0.21  1.82  0.05  0.21  1970  0.99  0.21  1.91  0.05  0.22  1974  0.99  0.17  1.99  0.06  0.23  1978  0.99  0.09  2.08  0.06  0.21  1982  1.00  0.18  2.17  0.06  0.20  Capital-Energy 1954  0.46  0.28  -0.36  -0.34  0.17  1958  0.42  0.29  -0.60  -0.30  0.04  1962  0.39  0.27  -0.82  -0.27  •0.08  1966  0.38  0.21  -0.94  -0.28  •0.16  1970  0.36  0.16  -1.12  -0.28  •0.24  1974  0.36  0.14  -1.21  -0.29  •0.28  1978  0.38  0.17  -1.34  -0.28  -0.27  1982  0.41  0.41  -1.52  -0.23  •0.14  148  TABLE A2.4 (CONTINUED) Translog Primal  Dual  Gen. L e o n t i e f Primal  SGMcFadden  Dual  Dual  Labour-Energy 1954  0.56  0.56  0.99  0.61  1.06  1958  0.54  0.52  1.04  0.57  0.88  1962  0.53  0.48  1.09  0.57  0.72  1966  0.53  0.47  1.10  0.59  0.64  1970  0.52  0.45  1.14  0.60  0.54  1974  0.53  0.49  1.19  0.61  0.55  1978  0.56  0.57  1.31  0.57  0.60  1982  0.59  0.58  1.44  0.55  0.67  149  TABLE A2.5 OWN  PRICE ELASTICITIES OF DEMAND  Translog Primal  Dual  Gen. L e o n t i e f Pr imal  SGMcFadden  Dual  Dual  Capital 1954  •0.57  •0.13  -0.91  0.002  •0 .10  1958  -0.61  -0.14  -0.99  -0.000  •0.11  1962  -0.68  -0.16  -1.05  -0.004  •0.11  1966  -0.70  -0.15  -1.06  -0.007  •0.12  1970  -0.67  •0.15  -1.07  •0.011  •0.12  1974  -0.68  -0.12  -1.09  -0.013  •0.13  1978  -0.62  •0.08  -1.18  •0 . 012  •0.11  1982  -0.68  -0.15  -1.33  -0.007  •0.10  Labour 1954  -0.38  -0.10  -0.52  -0.07  -0.13  1958  •0.35  •0.10  -0.56  •0.07  •0.13  1962  -0.32  -0.11  -0.57  -0.07  •0.12  1966  •0.31  0.10  -0.60  •0.07  •0.12  1970  -0.32  -0.10  -0.64  -0.07  -0.11  1974  •0.32  •0.09  -0.67  •0.07  •0.11  1978  -0.33  •0.08  -0.68  -0.07  -0.11  1982  -0.32  •0.12  -0.66  •0.08  -0.14  150  TABLE  Translog Primal  Dual  A2.5  (CONTINUED)  Gen. L e o n t i e f Primal  Dual  SGMcFadden Dual  Energy 1954  -0.36  - 0 . 42  -0.46  -0.31  -0.73  1958  -0.44  -0.40  -0.49  -0.28  -0.63  1962  -0.44  -0.37  - 0 . 47  -0.27  -0.52  1966  -0.46  -0.36  -0.44  -0.29  -0.47  1970  -0.46  -0.33  -0.42  -0.30  -0.39  1974  -0.41  -0.35  -0.43  -0.32  -0.41  1978  -0.42  -0.42  -0.47  -0.32  -0.47  1982  -0.44  -0.46  -0.59  -0.27  -0.47  151  

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