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Production functions for apple orchard systems in the Okanagan valley of British Columbia McNeill, Roger Charles 1977

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PRODUCTION FUNCTIONS FOR APPLE ORCHARD SYSTEMS IN THE OKANAGAN VALLEY OF BRITISH COLUMBIA  by  ROGER CHARLES McNEILL B.A., U n i v e r s i t y o f B r i t i s h Columbia, 1973  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE  STUDIES  Department of A g r i c u l t u r a l Economics  We accept  t h i s t h e s i s as conforming  to the r e q u i r e d  standard  THE UNIVERSITY OF BRITISH COLUMBIA November, 1977  (c)Roger  C h a r l e s M c N e i l l , 1977  In p r e s e n t i n g t h i s  thesis  in p a r t i a l  fulfilment of  the requirements f o r  an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, the I  Library shall f u r t h e r agree  for  freely available  that permission  for  r e f e r e n c e and  f o r e x t e n s i v e copying o f  this  that  study. thesis  s c h o l a r l y purposes may be granted by the Head of my Department or  by h i s of  make i t  I agree  this  representatives. thesis  It  is understood that  f o r f i n a n c i a l gain shall  not be allowed without my  written permission.  Department of  A g r i c u l t u r a l Economics  The U n i v e r s i t y o f B r i t i s h 2075 Wesbrook P l a c e V a n c o u v e r , Canada V6T 1W5  Date  A p r i l 26, 1978  Columbia  copying or p u b l i c a t i o n  ABSTRACT  The b a s i c o b j e c t i v e of t h i s t h e s i s was  to e s t i m a t e  disaggregated  p r o d u c t i o n f u n c t i o n s f o r apple o r c h a r d systems i n the Okanagan area of B r i t i s h Columbia. and  Because of the complexity  of the p r o d u c t i o n  r e l a t i v e l y r e c e n t t e c h n o l o g i c a l developments, i t was  considered  t h a t 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 would be u s e f u l i n a i d i n g allocation.  In o r d e r to be u s e f u l a t the farm l e v e l i t was  t h a t the model i n c o r p o r a t e f a c t o r s of major importance i n decisions.  P a r t i c u l a r emphasis was  p l a c e d on o r c h a r d  process  resource necessary  managerial  establishment  a l t e r n a t i v e s r e l a t i n g to the p l a n t i n g concept which i n c l u d e d d e n s i t y , t r e e d e s i g n and  rootstock.  a l s o of major i n t e r e s t . disaggregated  and  Weather v a r i a b l e s and The  i n t e r a c t i o n s were  c o n c e p t u a l model was  therefore highly  i n c l u d e d a l a r g e number of v a r i a b l e s .  of these v a r i a b l e s was  Measurement  based on d a t a o b t a i n e d from an o r c h a r d  survey  p l u s r e c o r d s of e x p e r i m e n t a l b l o c k s a t the Summerland Research S t a t i o n . Problems i n e s t i m a t i o n a r o s e due atory v a r i a b l e s . problems.  The  Two first  to the l a r g e number of  explan-  b a s i c methods were used i n d e a l i n g w i t h i n v o l v e d a s e q u e n t i a l t e s t i n g procedure  these whereby  groups of e x p l a n a t o r y v a r i a b l e s were entered s e p a r a t e l y i n t o m u l t i p l e r e g r e s s i o n s w i t h y i e l d per a c r e as the dependent v a r i a b l e . of each group were r e t a i n e d i n the f i n a l model.  The  Subsets  second method  i n v o l v e d the e s t i m a t i o n of s e p a r a t e f u n c t i o n s f o r each t r e e - s i z e c a t e g o r y , thereby  e l i m i n a t i n g r o o t s t o c k and r e l a t e d  explanatory v a r i a b l e s .  interactions  as  In both cases weather v a r i a b l e s were p r e -  s e l e c t e d based on the r e s u l t s of a s e p a r a t e l y estimated which used o n l y weather i n f l u e n c e s as e x p l a n a t o r y  r e g i o n a l model  variables.  iii The  s t a t i s t i c a l r e s u l t s showed t h a t the p r o d u c t i o n  b e s t be r e p r e s e n t e d  by  separate  f u n c t i o n s f o r each t r e e - s i z e  I n t e r a c t i o n s proved to be s i g n i f i c a n t and a t o r y power to the model.  f u n c t i o n could  added c o n s i d e r a b l e  Weather v a r i a b l e s were a l s o  category. explan-  significant,  e s p e c i a l l y at the r e g i o n a l l e v e l where a l a r g e amount of v a r i a t i o n i n average y i e l d s c o u l d be The  estimated  explained  production  streams over a 20 year p e r i o d .  by blossom time i n f l u e n c e s .  f u n c t i o n s were used to p r e d i c t y i e l d I t was  shown under c e r t a i n c o n d i t i o n s  t h a t the p o t e n t i a l e x i s t s f o r much h i g h e r y i e l d s and  p r o f i t s from h i g h  d e n s i t y systems than from low  d e n s i t y systems.  functions  showed the h i g h e r v a r i a b i l i t y  of y i e l d s from h i g h d e n s i t y systems  greater responsiveness implying  to v a r i a b l e i n p u t s and  The  and  exogenous f a c t o r s ,  t h a t a g r e a t e r management e f f o r t i s r e q u i r e d i n t h e i r  Other a p p l i c a t i o n s of the p r o d u c t i o n  also  f u n c t i o n s were  i n c l u d i n g p o s s i b i l i t i e s of p r e d i c t i n g t o t a l h a r v e s t  operation.  discussed  volume from  observed blossom time weather v a r i a b l e s , e v a l u a t i o n of weather r e l a t e d t e c h n o l o g y , and  d i r e c t i o n s of f u t u r e s c i e n t i f i c and  economic  research.  iv TABLE OF CONTENTS  Chapter I  INTRODUCTION 1.1  II  1  Background  Information  2  1.1.1  The Okanagan Region  1.1.2 1.1.3 1.1.4  H i s t o r y o f F r u i t Growing i n t h e Region Economic Importance E x t e r n a l and C u l t u r a l B e n e f i t s  1.2  The Problem  1.3  Attempts  2 .  Setting  5  t o A i d Resource A l l o c a t i o n  1.3.1 1.3.2  Role of S c i e n t i f i c Research Role of Economic Research  1.3.3  The P r o d u c t i o n F u n c t i o n Approach  2 4 4  6 6 7 . . . .  8  1.4  S p e c i f i c O b j e c t i v e s of t h e T h e s i s  9  1.5  Research Procedure  10  1.6  Guide t o T h e s i s  13  THE ECONOMIC MODEL 2.1  2.2  2.3  2.4  14  The P r o d u c t i o n F u n c t i o n  14  2.1.1 2.1.2  Parameters Stages o f P r o d u c t i o n  15 15  2.1.3  Other C h a r a c t e r i s t i c s  16  F u n c t i o n a l Forms  17  2.2.1  Homogeneous F u n c t i o n s  18  2.2.2  Non-homogeneous F u n c t i o n s  20  Producer Behaviour 2.3.1 2.3.2  P r o f i t Maximization C o n s t r a i n e d Output M a x i m i z a t i o n  2.3.3  C o n s t r a i n e d Cost M i n i m i z a t i o n  23  . . . .  24 25 26  Implications f o r Estimation  27  2.4.1 2.4.2 2.4.3  27 28 29  V a r i a t i o n i n Input L e v e l s M u l t i c o l l i n e a r i t y o f Inputs Simultaneous E q u a t i o n B i a s  2.4.4 2.4.5 III  Left-out Variables Summary of Implications f o r Estimation . . .  THE CONCEPTUAL MODEL AND MEASUREMENT OF VARIABLES 3.1  Management  3.2 P h y s i c a l Features and Fixed Inputs 3.2.1 3.2.2 3.2.3 3.2.4 3.2.5 3.2.6 3.2.7 3.2.8 3.2.9 3.2.10 3.2.11 3.2.12 3.3  Soil Frost S u s c e p t i b i l i t y Frost Prevention System P o l l i n a t i o n Method Rootstock Density Spur-type Tree Design Variety Age of Trees Machinery Inputs I r r i g a t i o n System  ....  31 32 34 35 37 37 38 39 39 40 41 42 42 43 43 44 46  V a r i a b l e Inputs  46  3.3.1 3.3.2 3.3.3 3.3.4  Fertilizer Pesticides Irrigation Labour  46 48 49 50  3.4 Weather Variables  53  3.4.1 3.4.2 3.4.3 3.4.4 3.4.5 3.4.6 3.4.7 3.4.8  Blossom Influences Spring Frost Temperature Sunlight Wind Rain Growing Season Influences Cold Winter Temperatures  53 54 56 56 57 58 58 59  3.5  Y i e l d Per Acre  60  3.6  Summary  61  3.7 Data Sources  64  I-V  ESTIMATION OF THE  67  4.1  Estimation Strategy  67  4.2  R e s u l t s f o r the Weather Model  72  4.2.1  Estimations Excluding Sunlight  75  4.2.2 4.2.3  Estimations Including Sunlight E f f e c t of Weather on D i f f e r e n t Grades of Apples C o n c l u s i o n s Regarding the Weather Model . .  77  4.2.4 4.3  The  Complete Orchard  4.3.1 4.3.2 4.3.3 4.4  L e v e l Model . .  79 81 82  Robustness of the E s t i m a t e s M u l t i c o l l i n e a r i t y Problems E f f e c t s of D i s a g g r e g a t i o n  .  85 88 91  T r e e - s i z e and V a r i e t y F u n c t i o n s  92  4.4.1 4.4.2  93  4.4.3  V  PRODUCTION FUNCTION  R e s u l t s f o r the T r e e - s i z e F u n c t i o n s . . . . Robustness of T r e e - s i z e Category Estimates . . . . . V a r i e t y Functions  4.5  C o n c l u s i o n s Regarding  4.6  Importance of Weather V a r i a b l e s  107  4.7  Importance of I n t e r a c t i o n s  109  APPLICATION OF THE 5.1  Methodology  103 103  ESTIMATED PRODUCTION FUNCTIONS  Adjustments i n Orchard E s t a b l i s h m e n t Operation 5.1.1 5.1.2 5.1.3  104  . . . 112  and  R e l a t i v e P r o d u c t i v i t y of Orchard Systems R e l a t i v e P r o f i t a b i l i t y of Orchard Systems Other F a c t o r s I n f l u e n c i n g the Choice Between Systems  112  114 116 119  5.2  E v a l u a t i o n of T e c h n o l o g i c a l Innovations  121  5.3  Predicting Yields  122  vii  VI  SUMMARY, CONCLUSIONS AND IMPLICATIONS FOR FUTURE RESEARCH . . . . . . 6.1  Summary  6.2  Conclusions Research 6.2.1 6.2.2 6.2.3 6.2.4 6.2.5  123 123  For For For For For  and I m p l i c a t i o n s f o r F u r t h e r 128 the the the the the  Orchardist Government M a r k e t i n g Agency Scientist Economist  128 130 131 131 133  BIBLIOGRAPHY . .  138  APPENDIX A . . . . .  142  APPENDIX B . . .  149  viii  LIST OF TABLES  3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 4.1 4.2 4.3 4.4 4.5 4.6 4.7 5.1 5.2 5.3 6.1 A.l A. 2 A. 3 A. 4 B. l B.2 B.3 B.5  Index o f S o i l Type Based on Farmer's E s t i m a t e o f T e x t u r e . . Tree S i z e Index Based on R o o t s t o c k Type Indexed Age of Trees Based on Rootstock C l a s s i f i c a t i o n . . . Temperatures Below Which Damage Occurs D u r i n g Blossom Period A l t e r n a t i v e Measures o f F r o s t D u r i n g Bloom A l t e r n a t i v e Measures of Temperature D u r i n g Bloom A l t e r n a t i v e Measures of S u n l i g h t During Bloom A l t e r n a t i v e Measures of R a i n f a l l D u r i n g Bloom . E s t i m a t e d F u n c t i o n s f o r Weather M o d e l — E x c l u d i n g Sunlight E s t i m a t e d F u n c t i o n s f o r Weather M o d e l — I n c l u d i n g Sunlight E s t i m a t e d F u n c t i o n s f o r Weather M o d e l — D i f f e r e n t Grade C a t e g o r i e s C o l l i n e a r i t y w i t h an I n t e r a c t i o n E s t i m a t e d F u n c t i o n s f o r Complete Orchard L e v e l Model . . . . E s t i m a t e d F u n c t i o n s f o r Dwarf and Semi-dwarf C a t e g o r i e s . . E s t i m a t e d F u n c t i o n s f o r Standard and Semi-standard Categories P r e s e n t Value o f P r o d u c t i o n from Major Apple P r o d u c t i o n Systems f o r 20 y e a r s P r e s e n t Values of Costs and Returns f o r Apple Systems . . . L e v e l and V a r i a b i l i t y of Apple Y i e l d s from Four A l t e r n a t i v e Systems over a 20 y e a r P e r i o d Summary o f S t a t i s t i c a l R e s u l t s Dwarf P r o d u c t i o n Semi-Dwarf P r o d u c t i o n — l b s p e r a c r e Semi-Standard P r o d u c t i o n — l b s p e r a c r e . . . Standard P r o d u c t i o n — l b s per a c r e Per Acre Costs and R e t u r n s — D w a r f P e r A c r e Costs and R e t u r n s — S e m i - d w a r f Per A c r e Costs and R e t u r n s — S e m i - s t a n d a r d Per Acre Costs and R e t u r n s — S t a n d a r d  38 41 45 54 55 56 57 58 76 78 80 83 86 95 98 115 118 119 127 145 146 147 148 150 151 152 153  ix  LIST OF FIGURES  3.1 3.2 4.1  F a c t o r s i n Apple P r o d u c t i o n Comparison of concepts, r e q u i r e d measure and measures Overview of the E s t i m a t i o n Procedure  36 actual 63 70  X  ACKNOWLEDGEMENTS  I wish t o express my s i n c e r e a p p r e c i a t i o n t o Dr. John Graham, my t h e s i s a d v i s o r , f o r h i s guidance The  i n the undertaking  of t h i s  o r g a n i z a t i o n and p r e s e n t a t i o n o f t h e f i n a l manuscript  g r e a t l y improved by h i s suggestions..  research.  has been  Acknowledgements must be made t o  o t h e r members of t h e t h e s i s committee i n c l u d i n g Dr. G. Kennedy f o r h i s o r i g i n a l c o n c e p t u a l i z a t i o n o f t h e problem and many p r a c t i c a l  suggestions,  Dr. R. B a r i c h e l l o f o r h i s v a l u a b l e comments on methodology, and Dr. R. A l l e n f o r h i s review on s h o r t n o t i c e .  Mr. Maurice Welsh, h o r t i c u l t u r i s t  w i t h t h e B.C. M i n i s t r y o f A g r i c u l t u r e p r o v i d e d i n f o r m a t i o n on t e c h n i c a l a s p e c t s of apple p r o d u c t i o n , p a r t i c u l a r l y i n t h e a r e a of weather v a r i a b l e s , which g r e a t l y f a c i l i t a t e d t h i s r e s e a r c h . Thanks a r e extended t o A g r i c u l t u r e Canada f o r p r o v i s i o n o f f i n a n c i a l and r e s e a r c h support.  I am indebted t o Mr. A. Andison  of that  o r g a n i z a t i o n f o r h i s work i n c o l l e c t i o n and c o l l a t i o n o f t h e d a t a . The  c o n t i n u i n g support  and encouragement o f many p a s t and p r e s e n t  members of the Department of A g r i c u l t u r a l Economics a t U.B.C. has been deeply  appreciated.  CHAPTER I  INTRODUCTION  The  Okanagan t r e e - f r u i t  a b l e economic r e s e a r c h have been c a r r i e d out  i n d u s t r y has  been the  subject  i n the l a s t t h r e e decades. concerning  of  consider-  Some major  the s t r u c t u r e and  studies  performance of  the  i n d u s t r y by Hudson (1973) and MacPhee (1958) from which recommendations have been made on how  to improve the incomes of the growers.  r e c e n t major study by Hudson recommends, among other receive d i r e c t personal weaknesses.  In order  assistance  have i n f o r m a t i o n  statistical  the  importance of g e o g r a p h i c a l  by D o r l i n g  (1975), Lee  (1972) , and  In 1975,  of the v a r i a b l e s i n f r u i t p r o d u c t i o n  factors. Campbell  surveys  and  corresponding y i e l d s . The  on many  information  p r e s e n t e d i n a form t h a t enables growers and  h o r t i c u l t u r a l p r a c t i c e s and  i n p u t l e v e l s (Kennedy, Andison and  T h i s t h e s i s has  and  This  s i o n p e r s o n n e l to make judgements on the r e l a t i v e p r o d u c t i v i t y of  forthcoming).  the  information  d a t a base i s undergoing c o n t i n u a l u p d a t i n g each season. been c o l l a t e d and  staff  the Economics Branch of A g r i c u l t u r e Canada  began c o n s t r u c t i o n of a d e t a i l e d d a t a base c o n t a i n i n g  has  systems,  aimed at improving t h i s knowledge through o r c h a r d analysis.  managerial  industry f i e l d  on the r e l a t i v e p r o d u c t i v i t y of o r c h a r d  economic r e s e a r c h  (1976) has  growers  t h i s recommendation i t i s n e c e s s a r y f o r them to  e f f e c t s of i n p u t v a r i a t i o n , and Recently  and  most  things, that  to improve t e c h n o l o g i c a l and  f o r government o f f i c i a l s  to e f f e c t i v e l y c a r r y out  The  extenvarious  Graham,  taken the o b j e c t i v e somewhat f u r t h e r 1  by  2 u s i n g r e g r e s s i o n a n a l y s i s to e s t i m a t e u s i n g the same body of d a t a . apple p r o d u c t i o n for  can be e s t i m a t e d ,  functions f o r apples,  impact of each recorded hence p r o v i d i n g b e t t e r  v a r i a b l e on information  management p r a c t i c e s as w e l l as p r o v i d i n g some d i r e c t i o n f o r f u r t h e r  economic and  1.1  The  production  scientific  Background 1.1.1  The  research.  Information i  Okanagan Region  In t h i s t h e s i s the Okanagan r e g i o n r e f e r s to the Canadian p o r t i o n of the Okanagan V a l l e y and  the a d j a c e n t  Similkameen V a l l e y .  is  l o c a t e d i n the south  at  Osoyoos on the American b o r d e r from where i t branches out  c e n t r a l i n t e r i o r of B r i t i s h Columbia,  f o l l o w i n g the Okanagan system of l a k e s and the Similkameen V a l l e y . about 100  The  producing  m i l e s n o r t h to Vernon, w h i l e  kameen V a l l e y i s c o n f i n e d to a 1.1.2 The  short  ing  settlements  north,  r i v e r s and n o r t h - e a s t  through  a r e a of the Okanagan V a l l e y runs the producing  area of the  b e l t between Keremeos and  p l a n t i n g s i n the r e g i o n were a s s o c i a t e d w i t h h i s t o r i c a l such as the Oblate M i s s i o n i n Kelowna i n 1862  E l l i s Ranch i n P e n t i c t o n i n 1869. kameen were i n 1867, the 1890's and planted  began around The  beginning  i n d u s t r y i s of h i s t o r i c a l s i g n i f i c a n c e f o r a number of  first  which was  region  Simil-" Cawston.  H i s t o r y of F r u i t Growing i n the Region  The  in  This  The  first  p l a n t i n g s i n the  and  reasons. pioneerthe  Simil-  w h i l e o t h e r p a r t s of the Okanagan r e g i o n opened  e a r l y 1900's except f o r the southern i n the 1920's.  area around O l i v e r  S i g n i f i c a n t commercial  production  1900.  e f f o r t s of e a r l y f r u i t  growers i n the r e g i o n to o b t a i n  o r d e r l y market scheme are of h i s t o r i c a l s i g n i f i c a n c e .  up  The  an  Okanagan  3 U n i t e d Growers Co-op was  formed i n 1914  o r d e r l y market s t r a t e g y and was support  s u c c e s s f u l i n o b t a i n i n g governmental  f o r a compulsory marketing  M a r k e t i n g Act passed and by the B.C. extent due iation.  i n 1927,  w i t h the o b j e c t of d e v e l o p i n g an  association.  superceded  The B.C.  i n 1934  by F e d e r a l L e g i s l a t i o n  N a t u r a l Products M a r k e t i n g A c t of 1937  to the c o n s i s t e n t e f f o r t s and T h i s o r i g i n a l a c t and  Produce  was  to a l a r g e  l o b b y i n g of the growers' a s s o c -  subsequent l e g i s l a t i o n have s i n c e p l a y e d  a major r o l e i n the i n s t i t u t i o n a l framework of Canadian a g r i c u l t u r e . The  i n d u s t r y ' s i n t e r a c t i o n w i t h the F e d e r a l Research  Summerland has been adopted up  i n 1914  resulted  i n important  l o c a l l y , n a t i o n a l l y and  t e c h n o l o g i c a l advances which have internationally.  The  station  under the f e d e r a l e x p e r i m e n t a l farm system has devoted  d e a l of i t s r e s e a r c h e f f o r t s to pomology. w i t h p r o d u c t i v e and marketing industry.  Station i n  of the r e g i o n .  The  dealt  problems of the l o c a l a p p l e growing  to the a r e a and h a v i n g good market acceptance. was  a great  Much of the study has  Work has been c a r r i e d out i n d e v e l o p i n g new  v a r i e t y developed  set-  the Spartan v a r i e t y , now  varieties  adapted  The most n o t a b l e  new  a major commercial v a r i e t y  s t a t i o n ' s r e s e a r c h i n t o s t o r a g e systems, spray  equipment, i r r i g a t i o n systems and  f r o s t p r e v e n t i o n has r e s u l t e d  a p p l i c a t i o n s f o r the l o c a l i n d u s t r y . s t o c k s , h i g h e r d e n s i t y p l a n t i n g s and the s t a t i o n ' s r e s e a r c h .  The  i n several  t r e n d s towards dwarfing r o o t -  spur-type  t r e e s was  i n f l u e n c e d by  In the area of t r e e n u t r i t i o n , r e s e a r c h c o n c e r n -  i n g boran and n i t r o g e n i s c r e d i t e d w i t h r e v i t a l i z i n g the i n d u s t r y i n the 1930's.  More r e c e n t r e s e a r c h i n food p r o c e s s i n g has r e s u l t e d i n a b e t t e r  q u a l i t y of j u i c e , new and new  j u i c e b l e n d s , a v a r i e t y of p r o c e s s e d a p p l e  products  p r o c e s s i n g equipment.  The r e s e a r c h s t a t i o n has attempted  to make t h e i r r e s u l t s  and  c  4 recommendations a v a i l a b l e t o o r c h a r d i s t s b u l l e t i n s and a l i b r a r y 1.1.3  through f r e e  publications,  service.  Economic Importance  About 33,000 a c r e s were p l a n t e d 1973 t r e e census (Hudson, 1973). (25,000 a c r e s ) i s p l a n t e d  with f r u i t  trees according to the  About 73 p e r c e n t of t h i s  w i t h apple t r e e s .  On t h e b a s i s  total of t h e 1972-  1973 crop year Hudson has c a l c u l a t e d t h a t t h e t r e e - f r u i t i n d u s t r y vides  pro-  a base f o r an annual c o n t r i b u t i o n of over 50 m i l l i o n d o l l a r s t o t h e  r e g i o n ' s economy, c a l c u l a t e d by adding 17 m i l l i o n d o l l a r s net r e t u r n s t o growers from B.C. Tree F r u i t s , 3 m i l l i o n d o l l a r s from r o a d s i d e s a l e s , 14 m i l l i o n d o l l a r s f o r payment i n a d m i n i s t r a t i o n ,  s e l l i n g and p a c k i n g , 12  m i l l i o n d o l l a r s worth of processed f r u i t p r o d u c t s and 6 m i l l i o n d o l l a r s worth of t r a n s p o r t a t i o n  of t h e produce.  About 64% of t h i s v a l u e was  a t t r i b u t a b l e t o a p p l e s and a p p l e p r o d u c t s . The Delicious and  v a r i e t i e s of apples produced i n order of importance a r e t h e Red s t r a i n s , M c i n t o s h , Spartan, Golden D e l i c i o u s , Winesap, Newton,  Tydeman E a r l y .  planted  The annual p r o d u c t i o n p o t e n t i a l f o r t h e a r e a  has been e s t i m a t e d a t 9 t o 10 m i l l i o n b u s h e l s  1.1.4 The  External tree-fruit  and C u l t u r a l  (Swales, 1971).  Benefits  i n d u s t r y has a v a l u e t o t h e r e g i o n  measured i n market terms a l o n e .  External  benefits  t h a t cannot be  from the i n d u s t r y  o c c u r because o f the o r c h a r d s e t t i n g and i t s e f f e c t on t h e l a n d s c a p e o f the  region.  The t o u r i s t i n d u s t r y  i s a major b e n e f i c i a r y and t h e  o r c h a r d s e t t i n g i s a common theme of t o u r i s t - t r a d e a d v e r t i s i n g . same e x t e r n a l i t i e s which b e n e f i t residents The  tourism also benefit  The  the permanent  of the area. industry  i s a l s o of some c u l t u r a l importance i n the r e g i o n .  5 Because of the l o n g h i s t o r y of f r u i t  growing i n the Okanagan i t has  become the theme of s e v e r a l annual community f e s t i v i t i e s . is  a l s o of importance as a way  The  psychic  of l i f e  income which i s d e r i v e d  The  to o r c h a r d i s t s and  from t h i s way  of l i f e  industry  their  families.  i s an  important  s o c i a l b e n e f i t from the i n d u s t r y not measurable i n market terms.  1.2  The  Problem S e t t i n g  A b a s i c problem i n the i n d u s t r y i s low has  been d i s c u s s e d  has  been r e c o g n i z e d  years.  Low  by Hudson (1973), D o r l i n g by  the B.C.  farm incomes may  farm incomes. (1975), and  f a i r l y conservative i n the  geographic  s u p p l i e s on the world market and  t r a c e d to low  or n e g a t i v e  returns  Smith isolation  Hudson o u t l i n e s f u r t h e r reasons  D o r l i n g ' s work i n t h i s area has  o f t e n be  Smith (1976) and  r e s u l t from a number of causes.  from markets as b e i n g b a s i c causes.  inputs.  problem  F r u i t Growers A s s o c i a t i o n f o r s e v e r a l  s t a t e s changes i n market demands f o r v a r i e t i e s and  i n c l u d i n g increased  This  returns  to other  increasing costs  shown t h a t low  incomes  to management a f t e r  factors.  He  discusses  of  can  allowing  a phenomenon  industry:  Many f r u i t growers would tend to d i s c o u n t t h e i r own and f a m i l y l a b o u r as w e l l as i n t e r e s t on investment through the l i f e of a tree f r u i t enterprise. From a p r a c t i c a l s t a n d p o i n t they o f t e n have no c h o i c e i f they wish to stay i n f r u i t growing. (Dorling, 1975, p. 21) Poor management r e t u r n s may of the grower but The will  orchard use  i n h i s orchard,  of h i s o r c h a r d  so much to the  shortcomings  r a t h e r to the c o m p l e x i t y of the p r o d u c t i o n  manager must f i r s t  freestanding.  not be due  process.  d e c i d e what l o n g - r u n p l a n t i n g concept  i . e . , density, rootstock,  hedgerow, t r e l l i s ,  T h i s d e c i s i o n must be based on the g e o g r a p h i c a l which i n c l u d e f r o s t  incidence,  aspect,  s o i l and  he or  factors frost  risk  c  6 as w e l l as h i s own  c a p i t a l and  time l i m i t a t i o n s .  d e c i d e what s h o r t - t e r m i n p u t s to use and of  both s h o r t and  c a t e d and  difficult  developed.  The  His  allocation  of these i n p u t s .  advantages and disadvantages  T h i s assessment i s c o m p l i -  e v a l u a t e d and  of new  i n n o v a t i o n s have not  the knowledge t h e r e o f  to s i n g l e out the e f f e c t of any  upon p r o d u c t i o n .  disseminated.  one of these  alternatives  Furthermore, t h e r e i s reason to b e l i e v e t h a t s e v e r a l  i n t e r a c t i o n s o c c u r , where the l e v e l of one v a r i a b l e a f f e c t s the product  of another.  s e v e r a l i n p u t s and to  the r e s u l t a n t impact  t r e e replacement  age upon p r o d u c t i o n and  upon p r o d u c t i o n , i t i s d i f f i c u l t error-.  The  orchard  problem i s a l s o complex, as the e f f e c t s of  replacement  c o s t s must be c o n s i d e r e d .  b a s i c problem i n the i n d u s t r y i s how business  marginal  Because of the time l a g between the a p p l i c a t i o n of  a r r i v e a t o p t i m a l l e v e l s of i n p u t s by t r i a l and  renewal and  the  as t h e r e are many i n p u t s , many of which were r e c e n t l y  always been adequately is difficult  to what l e v e l .  l o n g term i n p u t s depends on h i s assessment of  r e l a t i v e marginal products  It  Each year he must  Thus a  to e f f e c t i v e l y manage a complex  i n a t e c h n o l o g i c a l l y dynamic s e t t i n g .  The next  section dis-  cusses attempts to overcome some of these management problems and improve growers  1.3  1  to  incomes.  Attempts to A i d Resource A l l o c a t i o n 1.3.1  Role of S c i e n t i f i c  Research  S c i e n t i f i c r e s e a r c h at the Summerland Research S t a t i o n c o n t i n u e s to  study technology  Much of t h e i r e f f o r t  aimed at s p e c i f i c problems i n the l o c a l i n d u s t r y . i s i n "pure r e s e a r c h " which i s aimed a t i n c r e a s i n g  the g e n e r a l u n d e r s t a n d i n g of  pomology.  and  filling  i n gaps i n knowledge i n the  field  However, g e n e r a l areas of r e s e a r c h have u s u a l l y been  7 c l o s e l y r e l a t e d t o t h e problem areas o f t h e i n d u s t r y . s t a t i o n has t a c k l e d t h e problem o f marketing  F o r example t h e  a l a r g e , seasonal  i c a l l y i s o l a t e d crop by r e s e a r c h i n t o s t o r a g e systems.  geograph-  They have h e l p e d  a l l e v i a t e t h e w i n t e r i n j u r y problem by t h e i r r e s e a r c h i n t o cover and w i n t e r - h a r d y  crops  v a r i e t i e s , and t h e i r c o n t i n u i n g r e s e a r c h i n t o new  v a r i e t y development i s i n l i n e w i t h s a t i s f y i n g t h e changing  demands o f  consumers. 1.3.2  Role o f Economic Research  A major a r e a o f r e s e a r c h by economists has been i n t h e g e n e r a l of p r o d u c t i o n economics.  T h i s area o f study o f f e r s f o u r p o t e n t i a l  area areas  f o r i n c r e a s i n g growers' incomes, p a r t i c u l a r l y i f economists can c o o r d i n a t e t h e i r work w i t h t h a t o f s c i e n t i s t s and e x t e n s i o n  personnel.  These areas i n c l u d e t h e f e a s i b i l i t y and t h e a d o p t i o n o f new the r e l a t e d problem o f o r c h a r d renewal,  technology,  the a l l o c a t i v e e f f i c i e n c y of the  growers and t h e a l l o c a t i o n o f r e s o u r c e s towards f u r t h e r t e c h n o l o g i c a l research. nology,  When c o n s i d e r i n g t h e f e a s i b i l i t y and a d o p t i o n o f new t e c h -  several:.of ..the r e l a t i v e l y new and r e c e n t i n p u t s such as d w a r f i n g  r o o t s t o c k s , h i g h d e n s i t y p l a n t i n g s , t r i c k l e and overhead i r r i g a t i o n  sys-  tems, f r o s t p r e v e n t i o n systems and new v a r i e t i e s should be c o n s i d e r e d . Some i n i t i a l work by D o r l i n g (1975) has been c a r r i e d out on t h e compari s o n o f y i e l d s and p r o f i t a b i l i t y between h i g h d e n s i t y and standard systems, but he found the sampling  t h a t d i f f e r e n c e s were n o t easy t o i d e n t i f y , u s i n g  coverage a f f o r d e d by h i s study.  o r c h a r d replacement,  Regarding  t h e second a r e a ,  r e s e a r c h has been c a r r i e d out i n d e v e l o p i n g a l i n e a r  programming model g i v i n g o p t i m a l replacement  strategies  ( M a r s h a l l , 1975).  T h i s work has been h i n d e r e d by a l a c k o f knowledge as t o m a r g i n a l products  o f s e v e r a l i n p u t s and v a r i a b l e s .  Research i n t o t h e t h i r d  area,  8 the a l l o c a t i v e e f f i c i e n c y of growers, can examine both the e x i s t e n c e of d i s e q u i l i b r i u m i n i n p u t l e v e l s among growers and at the f a c t o r s which result  i n growers b e i n g b e t t e r a b l e to a l l o c a t e e f f i c i e n t l y .  by Campbell  (1976) has  u c t s of p e s t i c i d e s and  Some work  shown t h a t e s t i m a t e s of the m a r g i n a l v a l u e f e r t i l i z e r s are s i g n i f i c a n t l y h i g h e r than  p r i c e s of these i n p u t s .  The  the  f o u r t h a r e a , a l l o c a t i o n of r e s o u r c e s f o r  t e c h n o l o g i c a l research concerning e x p l o r e d by economists.  prod-  the l o c a l i n d u s t r y has not been  Research can be c a r r i e d out i n t o  technical  p r o d u c t i o n problems of the l o c a l a r e a , to study the impact t i o n i f c o n s t r a i n t s a r e removed.  Weather and  upon produc-  s o i l v a r i a b l e s would  the main p r o d u c t i o n c o n s t r a i n t s i n t h i s c a t e g o r y .  By d e t e r m i n i n g  be the  impact  of these v a r i a b l e s on p r o d u c t i o n the p o t e n t i a l b e n e f i t of t e c h -  nology  concerning  these v a r i a b l e s i s measured.  These b e n e f i t s can  weighed a g a i n s t the c o s t s of the t e c h n o l o g i c a l r e s e a r c h and i t i e s of i t s success 1.3.3  be  the p r o b a b i l -  i n overcoming the c o n s t r a i n i n g f a c t o r s .  The P r o d u c t i o n F u n c t i o n Approach  P r o d u c t i o n f u n c t i o n s t u d i e s may areas mentioned above.  New  i n e x p e r i m e n t a l b l o c k s and  be of v a l u e i n a l l f o u r of  technology  has been i n c o r p o r a t e d as i n p u t s  i n some commercial o r c h a r d s .  e s t i m a t i o n of a p r o d u c t i o n f u n c t i o n the m a r g i n a l p r o d u c t s i n p u t s can be measured and  Through the of t h e s e  new  compared w i t h the p r i c e of i n c o r p o r a t i n g them.  In the a r e a of o r c h a r d renewal, the m a r g i n a l product  the  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  of a l l the new  y i e l d which i s e s p e c i a l l y important  i n p u t s and  the e f f e c t of age  i n the t r e e replacement  give  on  decision.  In the a r e a of a l l o c a t i v e e f f i c i e n c y , the estimated p r o d u c t i o n f u n c t i o n s will and  i n d i c a t e i f growers are u s i n g i n p u t s to p r o f i t maximizing i f any  levels  i n p u t adjustment i n the i n d u s t r y can improve incomes.  In  9 the a r e a of measuring p o t e n t i a l t e c h n o l o g i c a l r e s e a r c h b e n e f i t s , the main use of an estimated p r o d u c t i o n f u n c t i o n i s the measure i t g i v e s of the impact  of s o i l and weather v a r i a b l e s upon p r o d u c t i o n . A p r o d u c t i o n f u n c t i o n which i s u s e f u l to areas mentioned above,  should be based on data where i n p u t s have been d i s a g g r e g a t e d components.  into basic  For example, the c a p i t a l i n p u t must be broken down i n t o  p l a n t i n g concept,  i r r i g a t i o n system, d e n s i t y and  should be c l a s s i f i e d  i n t o s o i l type, aspect and  s i z e of t r e e s . frost risk.  The  Land data  c o l l e c t e d by A g r i c u l t u r e Canada supplemented w i t h r e g i o n a l weather d a t a i s more d i s a g g r e g a t e d previous studies.  and  i n c l u d e s more v a r i a b l e s than data used i n  T h i s t h e s i s attempts to e s t i m a t e such a p r o d u c t i o n  f u n c t i o n u s i n g t h i s data and  apply i t i n comparisons of the  t e c h n o l o g i c a l a l t e r n a t i v e s i n apple production.  The  study w i l l a l s o  examine p o s s i b l e i n p u t adjustment w i t h i n the i n d u s t r y , the between i n p u t s and  1.4  the impact  of weather and  soil  available  interaction  variables.  S p e c i f i c O b j e c t i v e s of the T h e s i s The b a s i c o b j e c t i v e of t h i s t h e s i s i s : 1.  To e s t i m a t e p r o d u c t i o n f u n c t i o n s f o r the main v a r i e t i e s of a p p l e s produced i n the Okanagan area of B r i t i s h  The  Columbia.  f o l l o w i n g s u b - o b j e c t i v e s f o l l o w from the b a s i c o b j e c t i v e : 2.  To i d e n t i f y key c l i m a t i c v a r i a b l e s w h i c h . a f f e c t a p p l e product i o n i n the a r e a .  3.  To i d e n t i f y and measure the i n t e r a c t i o n s between f a c t o r s i n apple production.  4.  To i n t e r p r e t the estimated p r o d u c t i o n f u n c t i o n s i n the f o l l o w ing  terms:  10 (a)  the c h o i c e among a v a i l a b l e t e c h n o l o g i e s or o r c h a r d  (b)  to a s s e s s the r e l a t i v e p r o d u c t i v i t y of v a r i o u s o r c h a r d systems b e i n g used f o r apple p r o d u c t i o n i n the  1.5  (c)  p o s s i b l e i n p u t adjustment i n the i n d u s t r y  (d)  d i r e c t i o n of r e s e a r c h to develop new  Research  systems  area  technology.  Procedure  There a r e two this thesis.  The  b a s i c areas of r e s e a r c h which a r e undertaken i n first  area i s the s t a t i s t i c a l p o r t i o n of the r e s e a r c h  which d e a l s w i t h the f i r s t  objective;  the e s t i m a t i o n of p r o d u c t i o n  f u n c t i o n s f o r i n d i v i d u a l v a r i e t i e s of a p p l e s . c o n f i n e d to the f i v e most important  The  varieties:  estimations are  Mcintosh,  Statistical  Spartan,  Newton, Winesap and  the D e l i c i o u s s t r a i n s .  methods are  used to measure and  i d e n t i f y the e f f e c t s of c l i m a t i c v a r i a b l e s and  inter-  a c t i o n s between f a c t o r s of p r o d u c t i o n . The  second a r e a of r e s e a r c h i s i n the i n t e r p r e t a t i o n of the  mated f u n c t i o n s and the two  i t d e a l s w i t h s a t i s f y i n g the f o u r t h o b j e c t i v e .  areas of r e s e a r c h , more emphasis i s put on the  portion.  The  i n t h i s t h e s i s and  procedure  tion functions.  of  f o r meeting o b j e c t i v e one has  s t e p i s an examination  the f e a s i b i l i t y  statistical  are s u b j e c t t o the success of  c o n f i d e n c e t h a t can be p l a c e d i n the s t a t i s t i c a l  first  Of  i n t e r p r e t a t i o n s of the f u n c t i o n s as o u t l i n e d i n o b j e c t i v e  f o u r are secondary  The  esti-  and  research. three steps.  The  of the economic theory r e l e v a n t to produc-  T h i s theory i s reviewed of econometric  f o r i m p l i c a t i o n s concerning  e s t i m a t i o n and  the d e s i r a b l e p r o p e r t i e s  the mathematical form of the p r o d u c t i o n f u n c t i o n .  Secondly,  a  c o n c e p t u a l model of a p p l e p r o d u c t i o n which o u t l i n e s the f a c t o r s i n a p p l e  11 production  and t h e i r i n f l u e n c e upon output i s p r e s e n t e d .  emphasis i s p l a c e d statistical  Particular  on c l i m a t i c v a r i a b l e s and i n t e r a c t i o n s .  representation  o f the c o n c e p t u a l  estimated by r e g r e s s i o n a n a l y s i s .  Ordinary  Thirdly, a  model i s developed and and r e s t r i c t e d l e a s t  squares r e g r e s s i o n i s a p p l i e d t o d a t a p r e v i o u s l y c o l l a t e d by A g r i c u l t u r e Canada, supplemented by r e g i o n a l weather The  major o b s t a c l e  problem of h a n d l i n g  i n estimation  of t h e s t a t i s t i c a l model i s t h e  an extremely l a r g e number o f f a c t o r s  important on a p r i o r i  grounds i n the c o n c e p t u a l  are used i n d e a l i n g w i t h t h i s problem. the model on a p r i o r i minor importance.  data.  or s t a t i s t i c a l  model.  The f i r s t  considered Two s t r a t e g i e s  strategy  i s t o reduce  grounds by l e a v i n g out v a r i a b l e s o f  T h i s p a r i n g down i s c a r r i e d out f o r two c l a s s e s o f  f a c t o r s , weather v a r i a b l e s and i n t e r a c t i o n s . r e g i o n a l averages of p r o d u c t i o n  A s e p a r a t e model u s i n g  and o n l y weather f a c t o r s as  explanatory  v a r i a b l e s i s e s t i m a t e d and used t o s e l e c t , a subset o f weather f a c t o r s t o be  included  i n t h e s t a t i s t i c a l model.  Important i n t e r a c t i o n s a r e chosen  through a step-wise p r o c e s s i n e s t i m a t i o n .  Some other v a r i a b l e s a r e  dropped from the model as they prove i n s i g n i f i c a n t runs.  through a number o f  Although t h e p a r i n g down s t r a t e g y i s a r e a s o n a b l e econometric  procedure i t s use i s l i m i t e d i n t h e case o f t h i s r e s e a r c h ,  as i t l e a d s  to some c o n f l i c t w i t h the o b j e c t i v e s of t h e t h e s i s .  The o b j e c t i v e s  aimed a t i n c l u d i n g a l a r g e number o f f a c t o r s i n o r d e r  that the estimated  f u n c t i o n s be u s e f u l on an i n d i v i d u a l o r c h a r d the model i n f o r m a t i o n  b a s i s , and i n p a r i n g down  i s l o s t about f a c t o r s which a r e o f s p e c i a l i n t e r e s t .  Thus a second s t r a t e g y f o r o b t a i n i n g a manageable s t a t i s t i c a l model i s used. and  T h i s s t r a t e g y i s to sub-group the d a t a i n t o t r e e - s i z e c a t e g o r i e s  e s t i m a t e models f o r each c a t e g o r y .  I n so d o i n g t h e t r e e - s i z e  12 v a r i a b l e and a l l of i t s i n t e r a c t i o n s can be e l i m i n a t e d from each F u r t h e r p a r t i t i o n i n g o f t h e data by s o i l type and g e o g r a p h i c a l i s a l s o c o n s i d e r e d but i s not c a r r i e d out due t o data The  second and t h i r d o b j e c t i v e s concern  equation.  location  limitations.  the i d e n t i f i c a t i o n and  measurement o f c l i m a t i c v a r i a b l e s and i n t e r a c t i o n s .  The importance of  these f a c t o r s based on s t a t i s t i c a l s i g n i f i c a n c e , s t a b i l i t y o f c o e f f i c i ents and the c o n s i s t e n c y w i t h a p r i o r i e x p e c t a t i o n s The  f o u r t h o b j e c t i v e concerns i n t e r p r e t a t i o n s of t h e estimated  functions.  The f i r s t  of v a r i o u s o r c h a r d standard  i s discussed.  i n t e r p r e t a t i o n concerns the r e l a t i v e p r o d u c t i v i t y  systems based on r o o t s t o c k :  and s t a n d a r d .  O p t i o n a l management and p h y s i c a l f e a t u r e s  w i t h i n each o f these c a t e g o r i e s a r e c o n s i d e r e d productivity.  dwarf, semi-dwarf, semi-  As equations  a r e estimated  i n terms o f r e l a t i v e  f o r each o f these f o u r c a t e -  g o r i e s , i n t e r - e q u a t i o n comparisons become the b a s i s f o r a s s e s s i n g t h e r e l a t i v e p r o d u c t i v i t y of each system.  I n these comparisons,  a r e g e n e r a l l y s e t a t mean l e v e l s , although  inputs  age o f t r e e s i s allowed t o  v a r y i n o r d e r t o show r e l a t i v e p r o d u c t i v i t i e s o f t h e systems a t v a r i o u s ages.  The second i n t e r p r e t a t i o n d e a l s w i t h the c h o i c e between t h e f o u r  s p e c i f i c t r e e s i z e systems. on t h e i n p u t s and o u t p u t s ,  In t h i s i n t e r p r e t a t i o n , p r i c e s are placed and a rough comparison o f t o t a l revenue and  t o t a l c o s t f o r each system i s g i v e n .  The t h i r d  i n t e r p r e t a t i o n which  concerns p o s s i b l e i n p u t adjustment i n t h e i n d u s t r y concerns annual variable inputs. product  W i t h i n each e q u a t i o n  the r a t i o o f t h e m a r g i n a l  o f each v a r i a b l e i n p u t t o i t s p r i c e i s c a l c u l a t e d .  ratio i s significantly different the r e s u l t  When t h i s  from u n i t y an a n a l y s i s i s made whether  i s due t o d i s e q u i l i b r i u m o r b i a s e s i n e s t i m a t i o n .  The  f o u r t h i n t e r p r e t a t i o n which c o n s i d e r s d i r e c t i o n o f r e s e a r c h t o develop  13 new  technology,  a s s e s s e s p o t e n t i a l g a i n s from removing weather and  c o n s t r a i n t s and d i s c u s s e s new  1.6  i n p u t s which c o u l d be  soil  developed.  Guide to T h e s i s The next chapter d i s c u s s e s an economic model of the p r o d u c t i o n  f u n c t i o n i n c l u d i n g the parameters and Models of producer  behaviour  f u n c t i o n a l form  and t h e o r e t i c a l i s s u e s a r e p r e s e n t e d .  chapter t h r e e a s p e c i f i c c o n c e p t u a l model i s developed b a s i s of t e c h n i c a l d a t a important The correspondence discussed.  i n p u t s and  between the i d e a l measures and  on grouped d a t a and  production functions. e s t i m a t e d model.  Chapter  In  the  chosen.  the a v a i l a b l e d a t a i s for a regional  f o r t h r e e c a t e g o r i e s of farm  level  f i v e d e a l s w i t h the i n t e r p r e t a t i o n of the  The m a r g i n a l v a l u e p r o d u c t s of i n p u t s are compared  w i t h t h e i r m a r g i n a l c o s t s to see i f t h e r e i s any ibrium.  where on  i n t e r a c t i o n s are  In chapter f o u r r e s u l t s a r e p r e s e n t e d  weather model based  specifications.  i n d i c a t i o n of d i s e q u i l -  P o s s i b l e b i a s e s i n the estimated c o e f f i c i e n t s a r e o u t l i n e d .  P r o d u c t i v i t y and p r o f i t a b i l i t y of d i f f e r e n t o r c h a r d systems i s compared. The  f i n a l c h a p t e r p r e s e n t s a summary of the study, c o n c l u s i o n s and  implications for further research.  CHAPTER I I  THE  ECONOMIC MODEL  The purpose of t h i s chapter i s to review economic t h e o r y i n o r d e r to examine the g e n e r a l n a t u r e of the p r o d u c t i o n p r o c e s s ,  mathematical  r e p r e s e n t a t i o n s of t h i s p r o c e s s and  i m p l i c a t i o n s that a r i s e f o r estima-  t i o n of p r o d u c t i o n f u n c t i o n s .  first  The  s e c t i o n of t h i s  chapter  examines the c l a s s i c a l t h e o r y of the p r o d u c t i o n f u n c t i o n . c h a r a c t e r i s t i c s of p r o d u c t i o n f u n c t i o n s and t h i s research are o u t l i n e d . and  Different  Mathematical  t h e i r r e l e v a n c e i n terms of  f u n c t i o n a l forms a r e  reviewed  c o n s i d e r e d as to t h e i r a b i l i t y to i n c o r p o r a t e the r e q u i r e d p a r a -  meters and an a p p r o p r i a t e form i s chosen f o r use i n s t a t i s t i c a l tion.  The  second  estima-  s e c t i o n of t h i s chapter d e a l s w i t h a s p e c t s of p r o -  ducer behaviour which have i m p l i c a t i o n s f o r e s t i m a t i n g the p r o d u c t i o n function.  P r o f i t maximization,  output m a x i m i z a t i o n  and c o s t  t i o n models are p r e s e n t e d and problems i n e s t i m a t i o n , which may a result  2.1  of o p t i m i z i n g behaviour  minimizaarise  as  are discussed.  The P r o d u c t i o n F u n c t i o n The  economic d e f i n i t i o n of a p r o d u c t i o n f u n c t i o n i s "a  (or t a b l e or mathematical from any  specified  equation)  showing the maximum amount of  s e t of i n p u t s " (Ferguson,  e s t i m a t i o n of a mathematical  schedule  1969,  p. 116).  output  In the  p r o d u c t i o n f u n c t i o n i t i s assumed t h a t such  a f u n c t i o n e x i s t s , t h a t i t i s continuous and t h a t the i n p u t s a r e c o n t i n u o u s l y v a r i a b l e and 14  twice d i f f e r e n t i a b l e substitutable.  and  15 2.1.1  Parameters  In mathematical f o r m u l a t i o n s of p r o d u c t i o n f u n c t i o n s f o u r g e n e r a l economic parameters can be c o n s i d e r e d (1) e f f i c i e n c y of technology of s c a l e , ity.  (Arrow et a l . , 1961).  ( s h i f t parameters),  These a r e :  (2) t e c h n i c a l economies  (3) degree of f a c t o r i n t e n s i t y , and (4) f a c t o r  substitutabil-  These parameters might not e x p l i c i t l y appear i n t h e e q u a t i o n as  they may have a v a l u e o f zero o r one i n d i f f e r e n t The  e f f i c i e n c y of technology  f u n c t i o n without  f u n c t i o n a l forms.  parameter s h i f t s the whole p r o d u c t i o n  a f f e c t i n g t h e other parameters.  A change i n t h i s  parameter over time i s a r e f l e c t i o n o f the change i n technology where a g r e a t e r output  can be a c h i e v e d u s i n g the same l e v e l of i n p u t s .  The  economy o f s c a l e parameter r e f l e c t s t h e e f f e c t s o f i n c r e a s i n g a l l i n p u t s by an equal p r o p o r t i o n . parameter showing t h e impact  The degree of f a c t o r i n t e n s i t y i s a  o f an i n p u t r e l a t i v e t o o t h e r i n p u t s w h i l e  the s u b s t i t u t a b i l i t y parameter i n d i c a t e s the degree o f s u b s t i t u t a b i l i t y between i n p u t s . The parameter o f primary factor intensity.  concern  i n t h i s study i s t h e degree of  By measuring t h e impact  o f an i n p u t r e l a t i v e t o  o t h e r i n p u t s some i n f e r e n c e as t o the a l l o c a t i o n o f r e s o u r c e s can be made. 2.1.2 The  Stages  of Production  t h e o r y o f the c l a s s i c a l t h r e e stages of p r o d u c t i o n has been  w e l l expounded  (Brennan, 1970;  Ferguson, 1969;  Henderson & Quandt, 1971).  The main i m p l i c a t i o n from t h i s t h e o r y i s t h a t producers  should be i n t h e  second stage where both t h e average and m a r g i n a l p r o d u c t s o f a l l i n p u t s are d e c r e a s i n g , and the m a r g i n a l product some cases where t h e producer  i s positive.  There may be  i s not i n t h e second s t a g e .  A production  16 f u n c t i o n n o t having c o n s t a n t r e t u r n s t o s c a l e and w i t h c e r t a i n i n p u t c o n s t r a i n t s may r e s u l t  i n t h e producer  b e i n g i n stage one or t h r e e .  Given l i m i t a t i o n s t o t h e a v a i l a b i l i t y o f r e s o u r c e s o r i n d i v i s i b i l i t i e s i n r e s o u r c e s the producer stage f o r a l l i n p u t s . i t may prevent  might not be a b l e t o move i n t o the second  I f t h e r e i s an upper l i m i t on a c e r t a i n  the o p e r a t o r from u s i n g enough t o move i n t o t h e a r e a o f  diminishing returns.  He might be a b l e t o compensate by r e d u c i n g  of o t h e r i n p u t s , but i f these a r e f i x e d unable  resource,  levels  ( b u i l d i n g s or land) he w i l l be  t o move from t h e uneconomic r e g i o n o f t h e p r o d u c t i o n f u n c t i o n .  This result  c o u l d a l s o occur because of an i n d i v i s i b l e i n p u t , such as a  t r a c t o r which i s too l a r g e and crushes cannot move from the t h i r d  some of t h e c r o p .  The producer  stage o f n e g a t i v e r e t u r n s t o t h e second  stage  of p o s i t i v e and d i m i n i s h i n g r e t u r n s because the t r a c t o r i s n o t d i v i s i b l e into smaller units. The  c o n c l u s i o n from t h e stages o f p r o d u c t i o n t h e o r y i s t h a t produc-  ers w i l l g e n e r a l l y be i n t h e second stage a l t h o u g h  the p o s s i b i l i t y  exists  t h a t they may be i n e i t h e r o f t h e other stages under c e r t a i n c o n d i t i o n s . 2.1.3  Other  Characteristics  There a r e a number of f u n c t i o n a l c h a r a c t e r i s t i c s of mathematical production functions. output  elasticity,  These i n c l u d e homogeneity, r e t u r n s t o s c a l e ,  e l a s t i c i t i e s o f s u b s t i t u t i o n and r a t e o f t e c h n i c a l  s u b s t i t u t i o n , shape o f i s o q u a n t s , c o n v e x i t y o r c o n c a v i t y o f t h e f u n c t i o n and  interactions.  In regards  a r e no s p e c i f i c requirements  to the o b j e c t i v e s of t h i s t h e s i s  f o r any o f these c h a r a c t e r i s t i c s  t h a t i n t e r a c t i o n s be r e p r e s e n t e d as e x p l i c i t r e s t r i c t i o n s on the s i g n s o f these  terms.  there  except  terms and t h a t t h e r e be no  17 2.2  Functional The  Forms  b a s i c requirements of the f u n c t i o n a l form of the  f u n c t i o n f o r t h i s study i s t h a t i t be a b l e to i n c o r p o r a t e of e x p l a n a t o r y explicitly isoquants  v a r i a b l e s and  i d e n t i f i e d and  measured.  which are convex  c o s t combinations of i n p u t s e s s e n t i a l t h a t i t has  allow  a l a r g e number  i n t e r a c t i o n s between these to  towards the o r i g i n thus a l l o w i n g to be c a l c u l a t e d .  decreasing  be  I t i s d e s i r a b l e t h a t i t have for least  I t i s p r e f e r a b l e but  marginal products for inputs.  mathematical c h a r a c t e r i s t i c s such as homogeneity and s u b s t i t u t i o n are not  production  of d i r e c t concern and  not  Other  elasticity  of  are not used as c r i t e r i a i n  the s e l e c t i o n of a f u n c t i o n a l form. I t was  difficult  to f i n d a f u n c t i o n a l form which was  both  to e s t i m a t e and  had  form e v e n t u a l l y  chosen can handle l a r g e numbers of i n p u t s ,  specific  practical  a l l of the d e s i r a b l e mathematical p r o p e r t i e s .  i n t e r a c t i o n s to be  i d e n t i f i e d and  between some p a i r s of i n p u t s but  does not  t e s t e d , has  The  allows  convex  e x h i b i t decreasing  isoquants marginal  products. F u n c t i o n a l forms may a c t e r i s t i c s but Jorgenson and  be  c l a s s i f i e d according  to a number of  a convenient c l a s s i f i c a t i o n i s t h a t of  Lau  (1973).  Two  Christenson,  c l a s s e s are c o n s i d e r e d :  f u n c t i o n s w i t h constant  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 , and  f u n c t i o n s which are not  always homogeneous and  constant  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 .  o f t e n prove to be  Functions  s p e c i a l cases of f u n c t i o n s  c e r t a i n parameters are  restricted.  do not  char-  (1) (2)  homogeneous generalized  always have  i n the f i r s t  group  i n the second group i f  18 2.2.1  Homogeneous F u n c t i o n s  L i n e a r Form. w i t h output Q may  The l i n e a r form c o n s i d e r i n g two  i n p u t s x^ and X 2  be p r e s e n t e d as:  Q = axj + b x .  (2.1)  2  S t r i c t l y speaking t h i s f u n c t i o n does not have a c o n s t a n t e l a s t i c i t y of s u b s t i t u t i o n a l t h o u g h under e q u i l i b r i u m c o n d i t i o n s where p r i c e r a t i o s of i n p u t s a r e e q u a l to t h e i r r a t i o of t e c h n i c a l 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 would be i n f i n i t e .  elasticity  I t i s p o s s i b l e f o r the e l a s t i c i t y of  s u b s t i t u t i o n to be zero under o t h e r c o n d i t i o n s . There are some t h e o r e t i c a l drawbacks to t h i s form.  I t has  con-  s t a n t m a r g i n a l p r o d u c t s f o r both i n p u t s a l t h o u g h over a s h o r t range of i n p u t v a r i a t i o n t h i s f e a t u r e might not be unreasonable.  T h i s type of  f u n c t i o n has n e g a t i v e l y s l o p e d s t r a i g h t l i n e i s o q u a n t s , thus the second order s u f f i c i e n t c o n d i t i o n s f o r c o s t m i n i m i z a t i o n and output maximizat i o n a r e not met origin.  as they r e q u i r e the i s o q u a n t s to be convex towards the  The l i n e a r form a l s o e x c l u d e s any i n t e r a c t i o n between i n p u t s  i m p l y i n g that the m a r g i n a l product of any i n p u t i s not dependent on the l e v e l s of o t h e r i n p u t s .  Because of these drawbacks, e s p e c i a l l y  l a c k of i n t e r a c t i o n s t h i s form was i n s t a n c e s as a comparison Cobb-Douglas. 1928)  the  not used i n t h i s study except i n some  to i n t e r a c t i v e  forms.  S i n c e i t s development i n 1928  (Cobb and  Douglas,  the Cobb-Douglas has been a p o p u l a r form f o r e m p i r i c a l e s t i m a t i o n s  of p r o d u c t i o n f u n c t i o n s .  The b a s i c form i s :  Q = k  a X l  x  b 2  .  (2.2)  19 The  f u n c t i o n i s homogeneous of degree a + b, e x h i b i t s d e c r e a s i n g  m a r g i n a l p r o d u c t s when a and b a r e l e s s than one and has an of s u b s t i t u t i o n always equal to one. the o r i g i n so the second  I t s i s o q u a n t s a r e convex towards  order conditions  t i o n or output maximization  elasticity  sufficient  are s a t i s f i e d .  f o r cost  minimiza-  The f u n c t i o n i s e a s i l y  estimated i n l o g form:  log Q = log k + a(log  X l  )  + b(log x ) .  (2.3)  2  The major drawback of t h i s form f o r use i n t h i s study a g a i n cerns i n t e r a c t i o n s .  The m a r g i n a l p h y s i c a l product  fl  The h i g h e r the l e v e l of x  2  = akx^  a  con-  (M.P.P.) of x^ i s :  ^"x2^.  (2.4)  the h i g h e r the M.P.P. of x j i n d i c a t i n g a  p o s i t i v e i n t e r a c t i o n between i n p u t s .  T h i s r e s t r i c t i o n on the s i g n of  the i n t e r a c t i o n s i s not d e s i r a b l e i n t h i s study as t h e r e i s reason to b e l i e v e t h a t s e v e r a l i n t e r a c t i o n s w i l l be n e g a t i v e .  The  Cobb-Douglas  f u n c t i o n a l s o r e s u l t s i n i n t e r a c t i o n s between every p a i r of i n p u t s .  For  t h i s r e s e a r c h i t i s more d e s i r a b l e to have a form which p r e s e n t s i n t e r a c t i o n s as d i s t i n c t  terms i n the e q u a t i o n which can be i n c l u d e d  or  left  out a c c o r d i n g to s t a t i s t i c a l s i g n i f i c a n c e . Constant developed  E l a s t i c i t y of S u b s t i t u t i o n  by Arrow, Chenery, Minhas and  (CES).  I t has the f o l l o w i n g  Q = g[a  function  Solow (1961) r e t a i n s a c o n s t a n t  e l a s t i c i t y of s u b s t i t u t i o n but does not r e s t r i c t one.  The CES  i t to b e i n g equal to  form:  X l  "  C  +  (1 - a ) x " ] " C  2  v / c  .  (2.5)  20 The  f u n c t i o n g i v e s an e x p l i c i t r e p r e s e n t a t i o n of the parameters mentioned  earlier.  The  t e c h n i c a l e f f i c i e n c y parameter i s g, the f a c t o r i n t e n s i t y  parameter i s a, the s u b s t i t u t a b i l i t y parameter i s c and v i s the parameter.  T h i s f u n c t i o n i s homogeneous of degree v, has  r e t u r n s f o r each i n p u t and has The extending  isoquants  main drawback of the CES  convex towards the  inputs.  l i n e a r i z e when transformed l o g a r i t h m i c a l l y and it.  2.2.2  The  origin.  an a p p r o x i m a t i o n must i t was  not  has  A transcendental  f u n c t i o n where a l o g v a l u e H a l t e r , C a r t e r and  f u n c t i o n i s e i t h e r an  exponential  Q = c  Hocking  a X  i  l  e  b  l  X  where e i s the n a t u r a l number and parameters.  (1957) d i s c u s s such a f u n c t i o n t h a t  l  x  of p r o d u c t i o n .  e  3 2 2  a^,  b 2 X 2  a ,  2  l o g Q = l o g c + a ^ l o g x i + b^xj + a l o g x 2  e l a s t i c i t y of s u b s t i t u t i o n . t h e r e f o r e was  and  c are  estimated  i n l o g form:  2  + b x . 2  2  (2.7)  e a s i l y handle a l a r g e number of i n p u t s .  homogeneity i s not a c o n c e p t u a l  form:  (2.6)  bj, b ,  2  I t takes the  .  T h i s f u n c t i o n i s e a s i l y estimated  T h i s f u n c t i o n a l form can  logarith-  of an independent v a r i a b l e i s i n the equa-  a l l t h r e e of the c l a s s i c a l stages  terms and  con-  i n t h i s work.  f u n c t i o n where independent v a r i a b l e s appear i n the exponent or a  tion.  be  Non-homogeneous f u n c t i o n s  Transcendental.  mic  in  f u n c t i o n does not  Because of these d i f f i c u l t i e s  s i d e r e d a p r a c t i c a l form f o r use  diminishing  f o r t h i s study i s the d i f f i c u l t y  i t to i n c l u d e more than two  used when e s t i m a t i n g  scale  problem i n the study nor  Non-  i s the v a r i a b l e  However, i t l a c k s e x p l i c i t i n t e r a c t i o n  not used i n t h i s  study.  Generalized  Power F u n c t i o n  (GPF).  A power f u n c t i o n  represents  the dependent v a r i a b l e as a f u n c t i o n of the independent v a r i a b l e ( s ) taken to a c e r t a i n power. DeJanvry  A g e n e r a l i z e d power f u n c t i o n d i s c u s s e d  (1972) i n c l u d e s as s p e c i a l cases the Cobb-Douglas and  scendental  k  f (x)  k=l  where f ^ ( ) x  a n  d  S^( ) x  a  r  g (x) v  e  K  degree i n the arguments of  which has  k elements.  i s s i m i l a r to e q u a t i o n  (2.7)  i n t e r a c t i o n s and  but  l o g x.'s are i n c l u d e d .  interactions i s l e f t  The  choice  In l o g form t h i s  the c h o i c e t o the r e s e a r c h e r . expectations  nomials f ^ ( )  The  any  a n  g^(x).  power f u n c t i o n .  t h i s work, two  other  give  In order  to  any  utilize  are needed to s p e c i f y the  form i s so g e n e r a l  p a r t i c u l a r i n t e r a c t i v e form w i l l  generalized  are  d  I t does not  c h a r a c t e r i s t i c s on the form of the i n t e r a c -  the form c e r t a i n a p r i o r i x  of  i n t h i s study as i t a l l o w s  i n t e r a c t i o n terms i n the e q u a t i o n .  leaves  kind  the  open.  r e s t r i c t i o n s or impose any t i o n s , but  equation  squared terms of  of the degree and  T h i s form warrants c o n s i d e r a t i o n f o r use explicit  (2.8)  k  p o l y n o m i a l s of any  e  .  K  the i n p u t v e c t o r x and  for  tran-  functions:  Q = A n x ^  x.'s and  the  by  poly-  that i t i s l i k e l y  i n f a c t be a s p e c i a l case of  that the  B e f o r e d e c i d i n g on a s p e c i f i c form f o r  i n t e r a c t i v e forms, both s p e c i a l cases of the  GPF  discussed. Transcendental Logarithmic  (Trans-log).  developed from a T a y l o r expansion of the CES  This and  f u n c t i o n a l form  under c e r t a i n  restric-  t i o n s w i l l g i v e an a p p r o x i m a t i o n of the CES  l i n e a r i n i t s parameters.  I t was  (1971) i n an a n a l y s i s of  first  used by G r i l i c h e s and  Ringstad  was  22 Norwegian  manufacturing.  With two  i n p u t s x i and x  log Q = ailog X ! + a l o g x 2  2  i t takes  2  the form:  + a log x log x 3  2  3  + ai+Clog x )  2  x  + a (log x ) . 2  5  2  (2.9)  This f u n c t i o n i s a polynomial ables. and  I t i s a s p e c i a l case of the GPF where the p o l y n o m i a l  g, (x) =  0,  i s s i m i l a r to the q u a d r a t i c form which f o l l o w s . Quadratic.  and  form of the l o g s of the i n p u t v a r i -  This f u n c t i o n i s a polynomial  form of the inputs-X]^  x : 2  Q = aixi + a x 2  2  + a xix  When t h e r e are more than two  3  + ai^x^ + a s x . 2  2  (2.10)  2  2  i n p u t s t h e r e w i l l be an i n t e r a c t i o n between  every p a i r of i n p u t s and a squared  term f o r each i n p u t .  T h i s form i s  capable of r e p r e s e n t i n g a l l t h r e e c l a s s i c a l stages of p r o d u c t i o n as i t has  i n c r e a s i n g , d e c r e a s i n g , and n e g a t i v e m a r g i n a l  the input  products  depending  on  levels.  The major drawback of t h i s form i s the l a r g e number of parameters t h a t have to be estimated when more than two  i n p u t s are  considered.  Every time a v a r i a b l e i s added to the f u n c t i o n the number of terms, i n c l u d i n g square and of v a r i a b l e s .  c r o s s terms i n c r e a s e s by two  p l u s the p r e s e n t  In the c o n c e p t u a l model o u t l i n e d i n the next  chapter  t h e r e are 16 i n p u t s so a f u l l q u a d r a t i c e q u a t i o n would have 168 The  number  terms.  same problem a r i s e s w i t h the t r a n s - l o g when used i n i t s complete  form. The  two  forms c l o s e s t to meeting the requirements  for this  23 research  are the  t r a n s - l o g and  both these forms i s the To  the  p a r t l y overcome t h i s problem the  actions  and  eliminating  forms can be m o d i f i e d by  estimated.  eliminating  some of them would be u s e f u l i n r e d u c i n g  forms a l l o w f o r an  estimated.  Both the  quadratic  ated.  The  group of squared terms can  quadratic  others being  eliminated,  certain elimin-  although i n  form t h i s e l i m i n a t i o n r e s u l t s i n m a r g i n a l p h y s i c a l  becoming constant r a t h e r e x a c t l y what the the t r a n s - l o g  a l s o be  than d e c r e a s i n g or i n c r e a s i n g .  e f f e c t s w i l l be  function,  i f the  the  inputs  through an examination of the t e c h n i c a l p r o c e s s a subset of chosen a p r i o r i , the  the  and  i n t e r a c t i o n between every p a i r of  important i n t e r a c t i o n s can be  the  main problem w i t h  Most of the terms of the p o l y n o m i a l are i n t e r -  f u n c t i o n to a form t h a t can be trans-log  The  l a r g e number of parameters t h a t must be  some of the parameters.  but  quadratic.  products  I t ' i s not  clear  squared terms are removed from  although decreasing marginal products could  still  occur without them. In s e v e r a l  trial  squared terms and fit  w i t h only a few  selected  than a s i m i l a r l y m o d i f i e d t r a n s - l o g  modified quadratic  form was  estimated production  2.3  e s t i m a t i o n s the q u a d r a t i c  the  i n t e r a c t i o n s provided a  function.  chosen as the  form without  On  this basis  f u n c t i o n a l form f o r  better the  the  functions.  Producer Behaviour The  production function represents a t e c h n i c a l l y e f f i c i e n t  When producer behaviour i s c o n s i d e r e d the p o r t i o n of the  surface  surface. which  r e p r e s e n t s economic e f f i c i e n c y as w e l l as t e c h n i c a l e f f i c i e n c y becomes of primary s i g n i f i c a n c e .  I t i s u s u a l l y assumed t h a t producers attempt  to operate at such a r e a s on the  s u r f a c e where the outputs are  produced  w i t h the l e a s t c o s t combination of i n p u t s . t h i s a r e a may  Under e q u i l i b r i u m c o n d i t i o n s  o n l y be a s i n g l e p o i n t or l o c u s of p o i n t s .  The  tendency  f o r a c t u a l o b s e r v a t i o n s of i n p u t s and c o r r e s p o n d i n g outputs to be on or near these e c o n o m i c a l l y e f f i c i e n t  areas has important i m p l i c a t i o n s f o r  e s t i m a t i o n of t h e p r o d u c t i o n f u n c t i o n . Three models of producer behaviour where producers o p e r a t e a t e c o n o m i c a l l y e f f i c i e n t p o i n t s have been w e l l developed i n the l i t e r a t u r e and a r e b r i e f l y d i s c u s s e d below. 2.3.1  Profit  Maximization  In t h i s model where i n p u t and output p r i c e s a r e c o n s t a n t , producers w i l l operate a t a s i n g l e p o i n t on the p r o f i t maximized, i n p u t c o s t s a r e minimized  f u n c t i o n where p r o f i t i s  f o r the p a r t i c u l a r l e v e l of o u t p u t ,  and output i s maximized f o r the p a r t i c u l a r l e v e l of c o s t .  The  profit  f u n c t i o n ir can be s t a t e d a s :  IT = P f ( x i , x ) - r i x i 2  where f ( x rj  and r  2  l 5  - r x 2  2  - B.  (2.11)  x ) i s the p r o d u c t i o n f u n c t i o n , P i s the p r i c e of the output, 2  a r e i n p u t p r i c e s and B i s the f i x e d c o s t .  The f i r s t  c o n d i t i o n s f o r p r o f i t m a x i m i z a t i o n r e q u i r e t h a t Pf^ = r where f j and f  2  a r e t h e m a r g i n a l p r o d u c t s of x^ and x . 2  1  and P f The  order 2  =• r  second  order c o n d i t i o n s r e q u i r e that  "2  dx  2 2  p f  n  < 0,  pf  2 2  < 0,  (2.12)  2  25 These c o n d i t i o n s decreasing  and  s t a t e t h a t the m a r g i n a l v a l u e  t h a t the p r o d u c t i o n  p r o d u c t s of both i n p u t s  f u n c t i o n be  strictly  neighbourhood of the p r o f i t maximizing p o i n t . tions preclude  order  still  any  modified  second  decreasing,  However, t h i s form was  to r e p r e s e n t  given  chosen mainly  a complex s h o r t run s i t u a t i o n .  It  q u i t e p o s s i b l e t h a t o r c h a r d i s t s are a t t e m p t i n g to maximize  p r o f i t s over the long run and still  The  s a t i s f y the  c o n d i t i o n s , as m a r g i n a l p h y s i c a l p r o d u c t s are not  t h a t the squared terms are z e r o .  is  does not  condi-  f u n c t i o n i s of  than or e q u a l to one.  form chosen f o r t h i s r e s e a r c h  because of i t s a b i l i t y  concave i n the  second order  p r o f i t m a x i m i z a t i o n i f the p r o d u c t i o n  homogeneous form of degree g r e a t e r quadratic  The  be  any  resulting implications for  estimation  hold. 2.3.2  Constrained  Output M a x i m i z a t i o n  T h i s model i s r e l e v a n t where producers have a g i v e n use  i n production.  put  subject  cost outlay  to  With p r i c e s f i x e d they are assumed to maximize o u t -  to t h i s c o s t  constraint.  maximize  Q =  f(fi,f ) 2  (2.13) subject  The fl/f  2  first  = ri/r  2  order  or  to  conditions = £zl 2' r  C = r^xi + r x 2  2  +  B.  f o r output to be maximized are These c o n d i t i o n s  t e c h n i c a l s u b s t i t u t i o n which i s the s l o p e to the  that  s t a t e t h a t the r a t e of  isoquant  must be  equal to  the p r i c e r a t i o at the m a x i m i z a t i o n p o i n t . The  second order  c o n d i t i o n s r e q u i r e t h a t the r e l e v a n t  H e s s i a n determinant be p o s i t i v e .  This condition requires  of change of the s l o p e of an isoquant the isoquants  must be  bordered t h a t the  rate  must be p o s i t i v e which means t h a t  convex towards the o r i g i n i n the neighbourhood of  26 the output maximization 2.3.3 If  point.  C o n s t r a i n e d Cost M i n i m i z a t i o n a producer  quota he may  has a p r e s c r i b e d l e v e l of output  such as an order or  attempt to minimize the c o s t of p r o d u c i n g  then becomes one  it.  H i s problem  of c o n s t r a i n e d m i n i m i z a t i o n .  minimize  C = rixi  s u b j e c t to  Q =  + r x 2  2  + B (2.14)  f(xi,x ), 2  where C i s the c o s t f u n c t i o n , Q i s the p r e s c r i b e d l e v e l of output  and  f ( x i , x . ) i s the p r o d u c t i o n f u n c t i o n . 2  In t h i s model the f i r s t  and  second order c o n d i t i o n s f o r m i n i m i z a t i o n  are the same as the output maximization  problem.  The  s u b s t i t u t i o n must be equal to the p r i c e r a t i o and convex towards the  r a t e of  technical  the i s o q u a n t s must  be  origin.  T h i s model i s not e s p e c i a l l y r e l e v a n t to the Okanagan t r e e - f r u i t i n d u s t r y as t h e r e i s no quota or c o n t r a c t system.  There may  be some  cases where o r c h a r d i s t s themselves s e t a c e r t a i n l e v e l of p r o d u c t i o n a goal.  For example i f an o r c h a r d i s t operates  a r o a d s i d e stand  f e e l s t h a t a s p e c i f i c q u a n t i t y of f r u i t w i l l maximize revenue, he aim to produce t h i s amount i n h i s own The it  as  and may  orchard.  c o s t m i n i m i z a t i o n model i s of t h e o r e t i c a l importance because  i s the d u a l problem of output m a x i m i z a t i o n .  The  s o l u t i o n to  either  problem r e p r e s e n t s an e c o n o m i c a l l y e f f i c i e n t p o i n t on the p r o d u c t i o n function. In summary, t h e o r e t i c a l models suggest to  operate a t e c o n o m i c a l l y  As output  t h a t producers w i l l  attempt  e f f i c i e n t p o i n t s on the p r o d u c t i o n f u n c t i o n .  i n c r e a s e s , w i t h p r i c e s c o n s t a n t , the l o c u s of e f f i c i e n t p o i n t s  27 will  form the expansion path.  expansion path can h i n d e r functions. cussed  2.4  The  tendency f o r producers to be on  the s t a t i s t i c a l e s t i m a t i o n of the  S p e c i f i c problems which may  the  production  a r i s e i n estimation are  dis-  i n the next s e c t i o n .  Implications for Estimation I f i t i s expected t h a t producers are attempting  economically  e f f i c i e n t p o i n t s on the p r o d u c t i o n  of problems i n e s t i m a t i o n may  arise.  i n t r o d u c e b i a s e s i n t o the estimated o b t a i n i n g p r e c i s e estimates  The  to operate  at  f u n c t i o n then a number  b e h a v i o u r of p r o d u c e r s  parameters or p r e s e n t  of these parameters.  may  problems i n  A l a c k of v a r i a t i o n  i n i n p u t l e v e l s , h i g h m u l t i c o l l i n e a r i t y between i n p u t s , simultaneous e q u a t i o n b i a s and attempting  left  to operate  a r e analyzed 2.4.1  out v a r i a b l e b i a s may at e c o n o m i c a l l y  occur because producers  efficient points.  These problems  i n the f o l l o w i n g s e c t i o n s . V a r i a t i o n i n Input  Levels  I t has been noted by G r i l i c h e s e s t i m a t i o n of p r o d u c t i o n  (1971) and  f u n c t i o n s c o u l d be  possess u n l i m i t e d c a p i t a l and  others that  impossible  are p r o f i t maximizing.  statistical  i f a l l producers As  each i n p u t would  be used to i t s optimum l e v e l , t h e r e would be no v a r i a t i o n i n i n p u t and  are  hence no  s t a t i s t i c a l e s t i m a t i o n would be p o s s i b l e .  The  only  levels causes  of i n p u t v a r i a t i o n under e q u i l i b r i u m c o n d i t i o n s would be p r i c e v a r i a t i o n of output  and  i n p u t s between r e g i o n s and  over time.  be v a r i a t i o n i n the p r i c e growers a s s i g n to t h e i r own c o u l d cause v a r i a t i o n i n o t h e r with  There w i l l l a b o u r , and  likely this  i n p u t l e v e l s i f t h e r e are i n t e r a c t i o n s  labour. In a d d i t i o n t h e r e may  be some d i f f e r e n c e s i n the p r i c e  expectations  of growers. inputs  Because o f a c o n s i d e r a b l e  l a g between a p p l i c a t i o n o f many  and the marketing of the output, growers use an expected output  p r i c e , when c o n s i d e r i n g  allocation decisions.  Those growers who have  high p r i c e expectations  w i l l tend t o use h i g h e r  i n p u t l e v e l s than those  w i t h low p r i c e  expectations.  O r c h a r d i s t s may not be u s i n g  i n p u t s a t p r o f i t maximizing l e v e l s  because of a l a c k o f knowledge of t h e i r m a r g i n a l p r o d u c t i v i t y .  This  l a c k of knowledge may occur because o f the s u b s t a n t i a l time l a g between use  o f i n p u t s and the r e s u l t i n g r e t u r n s .  include rootstock,  Inputs i n t h i s  d e n s i t y and p l a n t i n g system.  category  The grower would have  to wait s e v e r a l y e a r s between t h e p l a n t i n g d a t e and the f i r s t  season o f  commercial p r o d u c t i o n  inputs.  t o a s s e s s the e f f e c t s o f changing these  Because the concept of h i g h d e n s i t y p r o d u c t i o n the a r e a ,  i t would a l s o be d i f f i c u l t  o r c h a r d s i n terms of m a r g i n a l r e t u r n s  i s r e l a t i v e l y recent i n  f o r growers t o a s s e s s s u r r o u n d i n g t o these i n p u t s .  Complicating  h i s assessment o f these i n p u t s a r e t h e l a r g e number o f other influencing  variables  production.  For o l d e r and e s t a b l i s h e d i n p u t s , such as f e r t i l i z e r and p e s t i c i d e s , i t i s more l i k e l y t h a t o r c h a r d i s t s have a d j u s t e d l e v e l s , and a s m a l l e r v a r i a n c e  to e q u i l i b r i u m  in' t h e i r sample l e v e l s i s expected.  In summary, because o f the r e a l world d i f f e r e n c e s i n p r i c e s , p r i c e expectations  and l a c k o f knowledge, i t i s expected t h a t s u b s t a n t i a l  v a r i a t i o n i n input  l e v e l s w i l l e x i s t a l t h o u g h t h e r e should  be some  tendency f o r a l a c k o f v a r i a t i o n i n c e r t a i n i n p u t s , p a r t i c u l a r l y f o r o l d e r and e s t a b l i s h e d 2.4.2  inputs.  M u l t i c o l l i n e a r i t y o f Inputs  I f producers a r e p r o f i t maximizing, c o s t m i n i m i z i n g or output  maximizing  they w i l l be o p e r a t i n g on t h e i r expansion  path.  For a func-  t i o n w i t h an i n t e r a c t i o n between i n p u t s the e q u a t i o n o f the expansion path i s r ( a + c x ) - r i ( b + c x ) = 0. 2  2  (2.15)  2  T h i s e q u a t i o n i s d e r i v e d from an i n t e r a c t i v e p r o d u c t i o n f u n c t i o n g i v e n as:  Q = axi + bx  Equation  2  + cxix .  (2.16)  2  (2.15) can be r e a r r a n g e d to s o l v e f o r x : 2  x  2  = ( r i / r ) x ! + ( r ! / r ) c - ac. 2  As the parameters a and c and p r i c e s r ^ and r equation  (2.17)  2  2  are constant,  (2.17) i n d i c a t e s t h a t x\ i s a l i n e a r f u n c t i o n of x  t h a t the two i n p u t s a r e p e r f e c t l y c o r r e l a t e d . not imply t h a t t h e i n p u t r a t i o x ^ / x i n c r e a s e s the i n p u t r a t i o converges I t i s expected  Equation  meaning  2  (2.17) does  i s c o n s t a n t , but r a t h e r as output  2  on a c o n s t a n t equal to r / r ^ . 2  t h a t the problems of c o l l i n e a r i t y w i l l be  allevi-  a t e d somewhat by the p o i n t s mentioned e a r l i e r , namely, i n p u t p r i c e v a r i a t i o n , d i f f e r e n c e i n p r i c e e x p e c t a t i o n s , d i f f e r e n c e s i n expected m a r g i n a l p r o d u c t s and d i f f e r e n c e s i n v a l u e s a s s i g n e d to o p e r a t o r s '  own  labour. 2.4.3  Simultaneous  Equation Bias  I t has been shown by Hoch (1962) and o t h e r s t h a t under p r o f i t maximizing  b e h a v i o u r , w i t h or without  simultaneous  e q u a t i o n b i a s may  Douglas p r o d u c t i o n f u n c t i o n s .  output and c o s t c o n s t r a i n t s ,  o c c u r , i n the e s t i m a t i o n of CobbU s i n g a s i m i l a r d e r i v a t i o n i t can be  30 shown t h a t e s t i m a t i o n of the i n t e r a c t i v e form used a l s o be s u b j e c t to such b i a s . (2.16) can be expressed d i s t u r b a n c e term  be expressed  may  The p r o d u c t i o n f u n c t i o n as i n e q u a t i o n  as a s t a t i s t i c a l model by adding a random  U:  Q = ax]. + b x  A first  i n this thesis  + cx!xc  2  2  + U.  (2.18)  order c o n d i t i o n f o r p r o f i t maximization  P  = ri q d  can  1 X l  as:  P (a + cx ) q  S o l v i n g f o r a from e q u a t i o n  2  (2.16) and  = r .  (2.19)  x  s u b s t i t u t i n g into equation  (2.19)  results i n  P  S o l v i n g f o r x i and  q  [  ( Q  -  b  X  2  xi  C  X  1  X  2  )  + cx ] 2  =  r i  .  1  simplifying results i n :  xi  I f the v a l u e f o r Q from e q u a t i o n  = P (Q q  - bx )/ 2  r i  .  w i t h the d i s t u r b a n c e term.  (2.21)  (2.18) i s s u b s t i t u t e d i n t o  (2.21) then x i becomes p a r t i a l l y dependent on U and  i s thus  equation correlated  T h i s c o r r e l a t i o n v i o l a t e s one of the  assumptions of u s i n g l e a s t squares the parameters w i l l  (2.20)  e s t i m a t i o n and a b i a s e d e s t i m a t e of  occur.  T h i s s i m u l t a n e i t y w i l l not occur i f farmers base t h e i r p r o d u c t i o n d e c i s i o n s on expected v a l u e of output r a t h e r than a c t u a l v a l u e s , p r o v i d i n g t h a t the expected v a l u e i s not e x a c t l y equal to a c t u a l v a l u e . This i s l i k e l y  to be t r u e i n apple p r o d u c t i o n because of the l a g  between the a p p l i c a t i o n of i n p u t s and  the r e s u l t i n g output and  prices.  31 DeJanvry  (1972) has shown t h a t i f producers use expected  p r i c e s and out-  puts i n d e c i s i o n making then t h e G.P.F. can be estimated by o r d i n a r y l e a s t squares without f u n c t i o n used  simultaneous  equation b i a s .  As the i n t e r a c t i v e  i n t h i s t h e s i s i s a s p e c i a l case o f the G.P.F. the p r o o f  also holds f o r i t . 2.4.4  Left-out Variables  I f the p r o d u c t i o n f u n c t i o n i s c o n s i d e r e d as p a r t o f a system which a l s o i n c l u d e s the f i r s t  simultaneous  o r d e r p r o f i t maximizing  condition  t h a t the m a r g i n a l v a l u e product be equal t o t h e m a r g i n a l c o s t f o r each i n p u t , then p r o b a b l e b i a s w i l l be imparted of  t o the estimated  the p r o d u c t i o n f u n c t i o n i f v a r i a b l e s a r e l e f t  coefficients  out of the e s t i m a t i o n .  For example, management b i a s i s l i k e l y t o o c c u r , i f i t i s supposed t h a t t h e r e i s a p o s i t i v e i n t e r a c t i o n between management and other i n p u t s . In  t h i s case b e t t e r managers w i l l o b t a i n h i g h e r m a r g i n a l p r o d u c t s  i n p u t s and w i l l thus use more of them i n s a t i s f y i n g the f i r s t p r o f i t maximizing  conditions.  The r e s u l t  i s a positive  from  order  correlation  between management l e v e l s and l e v e l s o f other i n p u t s i m p a r t i n g an upward b i a s t o the i n p u t c o e f f i c i e n t s i f management i s l e f t tion.  out o f t h e e s t i m a -  S i m i l a r l y i f other i n p u t s , such as l a b o u r , have i n t e r a c t i o n s  w i t h other i n p u t s , l e a v i n g them out of t h e e s t i m a t i o n w i l l r e s u l t i n biased c o e f f i c i e n t s .  As l a b o u r most l i k e l y p o s i t i v e l y i n t e r a c t s w i t h  many i n p u t s , l e a v i n g i t out o f t h e e s t i m a t i o n w i l l p r o b a b l y  cause  f u r t h e r upward b i a s i n t h e c o e f f i c i e n t s . I f management and l a b o u r do not have i n t e r a c t i o n s w i t h o t h e r i n p u t s , then t h i s b i a s w i l l not o c c u r , a s i d e from the e f f e c t s of random c o r r e l a t i o n between the l e f t - o u t v a r i a b l e s and t h e i n c l u d e d v a r i a b l e s . In  t h i s case management and l a b o u r c o u l d be c o n s i d e r e d as s h i f t  vari-  32 a b l e s , s h i f t i n g the l e v e l s of output by an amount independent of l e v e l s of o t h e r 2.4.5  inputs.  Summary of I m p l i c a t i o n s  for  Estimation  The most s e r i o u s i m p l i c a t i o n f o r e s t i m a t i o n left-out variable bias. i n p u t s are not other  the  Because measurements of management and  a v a i l a b l e (chapter  inputs w i l l  i s the p r o b a b i l i t y of  t h r e e ) , the estimated  l i k e l y be b i a s e d .  As  upward b i a s i n the estimated  coefficients for  t h e r e i s probably  i n t e r a c t i o n between the l e f t - o u t v a r i a b l e s and  other  some p o s i t i v e  inputs a  general  parameters i s expected to o c c u r .  i n t e r p r e t a t i o n of these c o e f f i c i e n t s must be  subject  labour  Any  to t h i s b i a s .  However, an allowance can be made f o r the magnitude of the b i a s due the i n f l u e n c e of l a b o u r .  Because e s t i m a t i o n s  are based on short  d a t a , r e p r e s e n t i n g a p e r i o d of f o u r to f i v e y e a r s , p o r t i o n s between l a b o u r and  other  i n p u t s i s not unreasonable.  the estimated  coefficient  the i n p u t and  a s p e c i f i e d amount of labour  The  i n f l u e n c e of l a b o u r  assuming f i x e d  f o r an i n p u t r e p r e s e n t s  to  run pro-  Hence  the i n f l u e n c e of both  required for i t s a p p l i c a t i o n .  can then be removed from the c o e f f i c i e n t , where  necessary. The was  not  tendency of v a r i a b l e s to be c o r r e l a t e d or have low v a r i a t i o n  felt  to be  so s e r i o u s .  There are adequate reasons f o r  a s i g n i f i c a n t amount of i n p u t v a r i a t i o n and  d i f f e r e n c e s i n input  a l t h o u g h some tendency of v a r i a b l e s to move t o g e t h e r Thus m u l t i c o l l i n e a r i t y may certain  affect  will  still  the p r e c i s i o n of the e s t i m a t e s  expecting ratios, exist. to a  extent.  Because i t i s r e a s o n a b l e expected p r i c e s , the p r o d u c t i o n  to assume t h a t d e c i s i o n s are made on f u n c t i o n does not have to be  as p a r t of a simultaneous system.  considered  Thus o r d i n a r y l e a s t squares  estimation  33 can be used without  t h e p r o b a b i l i t y o f simultaneous  Some of t h e problems suggested care i n data c o l l e c t i o n . important  bias.  by t h e t h e o r y can be overcome  through  E f f o r t s were made t o o b t a i n d a t a on a l l  i n p u t s and w i t h s u b s t a n t i a l v a r i a t i o n i n i n p u t l e v e l s , i n o r d e r  to reduce b i a s e s and f a c i l i t a t e e s t i m a t i o n . and  equations  t h e concepts  represented a r e presented  D e t a i l s of t h e d a t a i n t h e next  chapter.  used  CHAPTER I I I  THE  The  CONCEPTUAL MODEL AND  MEASUREMENT OF  VARIABLES  purpose of t h i s chapter i s to i d e n t i f y the important v a r i a b l e s  i n apple p r o d u c t i o n and  to d i s c u s s the measures of these v a r i a b l e s which  a r e used i n the estimated model.  Because a primary  o b j e c t i v e of t h i s  r e s e a r c h i s to d i s t i n g u i s h between the e f f e c t s of o r c h a r d systems i n p u t s which a r e of importance to an o r c h a r d manager, the  conceptual  model i s q u i t e d e t a i l e d i n comparison to e a r l i e r s t u d i e s (Lee, Campbell, 1976).  and  1972;  In p a r t i c u l a r the c a p i t a l i n p u t i s broken down i n t o  many components i n c l u d i n g f e a t u r e s of the l a n d , d e n s i t y , r o o t s t o c k , v a r i e t y , p l a n t i n g concept,  age  of t r e e s , machinery and  irrigation  system.  Other f a c t o r s which i n f l u e n c e the c h o i c e of system i n c l u d i n g weather i n f l u e n c e s and  i n t e r a c t i o n s are a l s o presented  annual v a r i a b l e i n p u t s . gated and The  The  i n d e t a i l as are  the  c o n c e p t u a l model i s thus h i g h l y d i s a g g r e -  i s r e l e v a n t to a s m a l l homogeneous u n i t or o r c h a r d b l o c k . c o n c e p t u a l model c o n s i d e r s the major p r o d u c t i o n d e c i s i o n s i n  e s t a b l i s h i n g and  o p e r a t i n g an apple o r c h a r d .  extension l i t e r a t u r e , p a r t i c u l a r l y  I t i s l a r g e l y based  Swales (1971), who  c i p l e s of commercial apple growing f o r new  and  presents  on  prin-  experienced o r c h a r d i s t s .  A more or l e s s d e t a i l e d c o n c e p t u a l model c o u l d be u t i l i z e d depending  on  the o b j e c t i v e s of the r e s e a r c h .  one  For example, i n s c i e n t i f i c r e s e a r c h  would l i k e l y c o n c e i v e of a more d e t a i l e d model w i t h h i g h e r emphasis the b i o l o g i c a l f a c t o r s , w h i l e i n economic r e s e a r c h f o r p o l i c y 34  on  purposes,  35 the r e s e a r c h e r might o n l y c o n s i d e r major aggregated i n p u t s such as l a n d , l a b o u r and c a p i t a l .  I t i s considered  t h a t the d e t a i l of the c o n c e p t u a l  model i n t h i s r e s e a r c h i s c o n s i s t e n t w i t h  the o b j e c t i v e s which aim a t  s u p p l y i n g q u a n t i t a t i v e i n f o r m a t i o n on s p e c i f i c i n p u t s t o o r c h a r d i s t s and extension The  workers. v a r i a b l e s can be c l a s s i f i e d  i n t o f o u r groups which a r e  (1) management, (2) f i x e d i n p u t s and p h y s i c a l f e a t u r e s , (3) annual v a r i a b l e i n p u t s , and (4) weather i n f l u e n c e s . between them a r e shown i n f i g u r e 3.1. complexity  of the conceptual  and s o i l .  T h i s f i g u r e i l l u s t r a t e s the  model and the r e l a t i o n s h i p between i n p u t s .  I t a l s o i d e n t i f i e s major sources age  These f a c t o r s and i n t e r a c t i o n s  of i n t e r a c t i o n s , p a r t i c u l a r l y  Management, which i n t e r a c t s w i t h a l l o t h e r  shown as a s e p a r a t e  category  as i t t i e s t o g e t h e r  i n the f o l l o w i n g s e c t i o n s . versus  inputs, i s  the p r o d u c t i o n  Each c l a s s o f v a r i a b l e s as shown i n f i g u r e 3.1 i s d i s c u s s e d  rootstock,  process.  separately  The a c t u a l measures o f these v a r i a b l e s  t h e i d e a l o r r e q u i r e d measures a r e o u t l i n e d and a d e t a i l e d t a b u l a -  t i o n o f the v a r i a b l e s used f o r e s t i m a t i o n i s g i v e n l a t e r i n the c h a p t e r .  3.1  Management Two g e n e r a l a s p e c t s  considered.  The f i r s t  o f management i n a p p l e p r o d u c t i o n may be  aspect  i s the a b i l i t y to a l l o c a t e resources  e f f i c i e n t l y by u s i n g o p t i m a l l e v e l s o f i n p u t s . o b t a i n a h i g h e r output  A good manager c o u l d  u s i n g the same v a l u e o f i n p u t s as a poor manager  by a l l o c a t i n g h i s funds to o b t a i n the best combination o f i n p u t s . second aspect  o f management i s t h e a b i l i t y  of p h y s i c a l i n p u t s .  The  to increase the e f f e c t i v e n e s s  For example a good manager o b t a i n s a b e t t e r  q u a l i t y o f f r u i t because h i s p r u n i n g  techniques  a r e more e f f e c t i v e  than  36 j Management Weather Influences  «^  P h y s i c a l Features and F i x e d Inputs  blossom time influences  ^j s o i l  wind  Variable Inputs  quality  frost risk p o l l i n a t i o n method  rain temperature  rootstock  sunlight  density  frost growing season heat a c c u m u l a t i o n  spur-type j p l a n t i n g concept  winter k i l l severe c o l d  t  pruning thinning harvesting input associated  variety  age  machinery i n p u t s  irrigation  system  yield -«-»-  shows an i n t e r a c t i o n between i n p u t s  F i g u r e 3.1.  F a c t o r s i n Apple P r o d u c t i o n  the poor manager's, a l t h o u g h both may spend the same amount o f time pruning.  T h i s aspect o f management  i n c l u d e s a number o f f a c t o r s which  a r e not e a s i l y measurable as p h y s i c a l u n i t s .  The e f f e c t i v e n e s s o f  pesticide application, thinning, f e r t i l i z e r application,  irrigation,  f r o s t p r e v e n t i o n and l a b o u r s u p e r v i s i o n a l l come i n t h i s  category.  Because management a b i l i t y  i s a f f e c t e d by a number o f i n t a n g i b l e s and  qualitative variables i t i s d i f f i c u l t  t o c o n c e i v e of an i d e a l measure.  Such v a r i a b l e s as e d u c a t i o n and e x p e r i e n c e might prove t o be adequate proxy v a r i a b l e s . explicit  3.2  No d a t a was c o l l e c t e d on these a s p e c t s and no  r e p r e s e n t a t i o n i s i n c l u d e d i n t h e e s t i m a t e d models.  P h y s i c a l F e a t u r e s and F i x e d These i n p u t s a r e expected  years.  Inputs t o remain c o n s t a n t f o r a number of  They i n c l u d e g e o g r a p h i c a l f a c t o r s such as s o i l q u a l i t y and  f r o s t r i s k , concepts  of p l a n t i n g such as d e n s i t y , t r e e d e s i g n and  r o o t s t o c k and f i x e d i n p u t s such as i r r i g a t i o n system and machinery. 3.2.1 The  Soil q u a l i t y o f the s o i l f o r a p p l e p r o d u c t i o n i s determined  number o f f a c t o r s i n c l u d i n g depth, drainage  (Swales,  1971).  t i o n as c o r r e c t m o i s t u r e  result  t e x t u r e , a c i d i t y , a l k a l i n i t y and  Deep s o i l s a r e expected  t o i n c r e a s e produc-  l e v e l s can be more e a s i l y maintained  i s a g r e a t e r supply of n u t r i e n t s .  by a  and t h e r e  S o i l s w i t h l i g h t e r t e x t u r e should  i n h e a l t h i e r more p r o d u c t i v e t r e e s because they have b e t t e r  d r a i n a g e than h e a v i e r s o i l s .  S o i l s w i t h h i g h PH l e v e l s have  e f f e c t s on t h e a v a i l a b i l i t y of s o i l n u t r i e n t s and y i e l d be lower.  adverse  i s expected to  There i s a c o m p l i c a t e d i n t e r a c t i o n between these  soil  f e a t u r e s and f e r t i l i z e r a p p l i c a t i o n , an i n t e r a c t i o n w i t h r o o t s t o c k and  38 an i n t e r a c t i o n w i t h i r r i g a t i o n . input  These a r e d i s c u s s e d under t h e r e l e v a n t  category. An i d e a l measurement would c o n s i d e r s o i l depth,  and n u t r i e n t c o n t e n t . t e x t u r e based  The a c t u a l measure r e c o r d e d i s o n l y o f s o i l  on t h e farmer's  sandy, c l a y or rocky.  t e x t u r e , PH l e v e l  estimate.  An index based  T h i s i s a r e a s o n a b l e proxy  S o i l i s c l a s s i f i e d as e i t h e r on t e x t u r e was c o n s t r u c t e d .  f o r s o i l q u a l i t y , as other i n f l u e n c e s on  q u a l i t y are often associated with texture.  T a b l e 3.1.  The e f f e c t s of s o i l  texture  Index o f s o i l type based on farmer's e s t i m a t e of texture  Index  Texture  1  sandy  2  clay  3  rocky  are a l s o measured u s i n g dummy v a r i a b l e s which a l l o w t h e e f f e c t s o f each type of s o i l  t o be measured as a s h i f t v a r i a b l e u n r e s t r a i n e d by t h e  n a t u r e of t h e index. dummies because o f the c o e f f i c i e n t  I n some cases the index i s used m u l t i c o l l i n e a r i t y problems.  The expected  sign of  i s n e g a t i v e as c l a y and rocky s o i l s a r e c o n s i d e r e d t o  be l e s s p r o d u c t i v e than sandy 3.2.2  instead of the  soils.  Frost Susceptibility  Orchards  h i g h l y s u s c e p t i b l e t o f r o s t a r e expected  t o have l e s s  p r o d u c t i o n , a l l o t h e r t h i n g s b e i n g e q u a l , than l e s s s u s c e p t i b l e o r c h a r d s . T h i s v a r i a b l e i s expected  t o i n t e r a c t w i t h the w i n t e r h a r d i n e s s o f the  39 r o o t s t o c k and  tree size.  The  i n t e r a c t i o n i s expected to be,  s m a l l e r the t r e e s i z e , the g r e a t e r as a h i g h e r  c o n c e n t r a t i o n of the blossoms  w i l l be c l o s e to ground l e v e l and more s u b j e c t to s p r i n g This f r o s t and  frosts.  s u s c e p t i b i l i t y v a r i a b l e w i l l also i n t e r a c t with  amount of f r o s t p r o t e c t i o n used.  this  the k i n d  When e f f e c t i v e f r o s t p r e v e n t i o n i s  used, i t w i l l o b v i o u s l y l e s s e n the i n f l u e n c e of f r o s t pockets  and  channels. I d e a l l y a measure which takes drainage,  the exposure and  included. lows:  i n t o account f r o s t pockets,  the aspects  A c t u a l measurement i s based on a farmer's e s t i m a t e s  1—low, 2—moderate, 3 — h i g h . 3.2.3 The  Frost Prevention use  by l o w e r i n g fruit.  of the i n d i v i d u a l b l o c k s  The  the should as  be  fol-  expected s i g n i s n e g a t i v e .  System  of f r o s t p r e v e n t i o n  systems i s expected to i n c r e a s e y i e l d s  the i n c i d e n c e of f r o s t damage to buds, blossoms and  green  Smudge pots which heat the a i r near the ground's s u r f a c e  and  wind machines which break up n a t u r a l temperature i n v e r s i o n s a r e both used by growers.  Davies  (1974) has  shown the e f f e c t i v e n e s s of wind  machines i n i n c r e a s i n g temperatures at t r e e - l e v e l . used to r e p r e s e n t 3.2.4  these  systems and  are expected to have p o s i t i v e s i g n s .  P o l l i n a t i o n Method  Cross p o l l i n a t i o n i s e s s e n t i a l f o r f r u i t - s e t v a r i e t i e s and 1971).  Dummy v a r i a b l e s are  The  should  improve f r u i t - s e t  i n other v a r i e t i e s  i n c i d e n c e of p o l l i n a t o r t r e e s and  a c t i v i t y are both expected to i n c r e a s e  in self-unfruitful (Swales,  the amount of i n s e c t  production.  I d e a l l y t h e r e should be a measure i n c o r p o r a t i n g the number of p o l l i n a t o r t r e e s per a c r e , the number of bee-hives per a c r e and  the  p r o x i m i t y of n e i g h b o u r i n g  the  hives.  The  a c t u a l measure c o n s i d e r s  p o l l i n a t i o n method, e i t h e r bees or p o l l i n a t o r t r e e s . used the number of h i v e s per  acre i s given.  the model i s the number of h i v e s per a c r e p o l l i n a t o r t r e e s are u s e d ) .  The  The  (which i s zero  beehives.  are  v a r i a b l e entered  measure does not  which have both p o l l i n a t o r t r e e s and  Where bees  in  i f only  account f o r o r c h a r d s  The  expected s i g n i s  positive. 3.2.5 The  Rootstock e f f e c t of r o o t s t o c k  i s c o n t r o l of t r e e s i z e .  the r e l a t i v e t r e e s i z e produced by  the M a i l i n g and  s t o c k s which are the most common r o o t s t o c k Swales (1971). rootstock  Malling-Merton root-  i n the area  i s given  by the  to get a l a r g e r t r e e s i z e w i l l be p o s i t i v e . i n t e r a c t w i t h s o i l f a c t o r s i n i t s e f f e c t s on  d w a r f i n g r o o t s t o c k s , MIX  soils.  e s t i m a t e of  I t i s expected t h a t the e f f e c t s of y i e l d of v a r y i n g  R o o t s t o c k can The  An  The  and  M 26 b o t h s t u n t b a d l y  semi-dwarf M V I I has  the same problem, and  on l i g h t  soil.  There w i l l l i k e l y be  w i t h v a r i a b l e i n p u t s a l t h o u g h the s i g n and t i o n s are u n c e r t a i n .  P e s t i c i d e s may  shallow  i t i s expected  t h a t y i e l d s from these t h r e e r o o t s t o c k s w i l l be lower on l i g h t s o i l s than on h e a v i e r  yield.  shallow  several interactions  magnitude of these i n t e r a c -  have more e f f e c t on dwarf  trees  because the spray a p p l i c a t i o n w i l l r e a c h a l l p a r t s of a s m a l l  tree  e a s i e r than a l a r g e r t r e e .  require-  ments may  F e r t i l i z e r , p r u n i n g and  a l s o d i f f e r between s m a l l and  i s a l s o d i f f e r e n t f o r dwarf and t r e e s , as much e a r l i e r b e a r i n g  large trees.  thinning The  e f f e c t of  semi-dwarf t r e e s than f o r standard takes p l a c e i n the s m a l l e r  I n t e r a c t i o n s w i t h blossom f r o s t and  severe winter cold w i l l  c l o s e to ground l e v e l .  size  trees.  Smaller t r e e s are more s u s c e p t i b l e to blossom f r o s t because t h e i r soms are c o n c e n t r a t e d  age  occur. blos-  T h e i r r o o t s are more  41 s u s c e p t i b l e to w i n t e r - k i l l . An index of t r e e - s i z e based  on Swales' (1971) e s t i m a t e s has been  c o n s t r u c t e d as i n t a b l e 3.2.  T a b l e 3.2.  The  expected  Tree S i z e Index Based on R o o t s t o c k Type  Index  Rootstock  40  Standard  35  MM 104  32.5  MM 111  30  M  11  27.5  M  4  22.5  M  7  20  M  26  15  M  9  s i g n o f t h e index c o e f f i c i e n t  i s p o s i t i v e , but t h e r e  may be some range over which t h e m a r g i n a l p h y s i c a l product  i s negative  depending on the l e v e l of other v a r i a b l e s . Negative  i n t e r a c t i o n s w i t h s o i l t e x t u r e , blossom f r o s t and w i n t e r -  k i l l and p o s i t i v e i n t e r a c t i o n s w i t h age and p e s t i c i d e s a r e expected. I n t e r a c t i o n s w i t h f e r t i l i z e r , d e n s i t y and l a b o u r a r e a l s o p o s s i b l e a l t h o u g h t h e i r s i g n s a r e not known. 3.2.6 It  Density  i s expected  per a c r e w i l l decrease.  t h a t up t o a p o i n t , i n c r e a s i n g t h e number o f t r e e s  i n c r e a s e y i e l d p e r a c r e but beyond t h a t p o i n t y i e l d  will  At t h i s c r i t i c a l p o i n t t h e t r e e s become too crowded and  s u n l i g h t , sprays and a p p l i c a t i o n s o f f o l i a r n u t r i e n t s cannot  reach t h e  42 i n n e r and crowded p o r t i o n s by  of t h e t r e e s .  t r e e s i z e as w e l l as d e n s i t y — a n  This  crowding e f f e c t i s caused  o r c h a r d can be v e r y crowded w i t h  l a r g e t r e e s i n a p l a n t i n g of o n l y moderate d e n s i t y . between d e n s i t y and  magnitude.  and r o o t s t o c k  i s a g a i n hard t o s p e c i f y i n terms of s i g n  I f the density  o f a p l a n t i n g i s low,  of a l a r g e t r e e t o a standard p l a n t i n g would l i k e l y than t h e a d d i t i o n of a s m a l l crowded c o n d i t i o n s  This i n t e r a c t i o n  then t h e a d d i t i o n  increase  t r e e t o a dwarf p l a n t i n g .  increasing density  output more  However, i n  i n a standard p l a n t i n g c o u l d  a more n e g a t i v e e f f e c t on output than i n c r e a s i n g d e n s i t y  have  i n a dwarf  plant-  i n g so t h e i n t e r a c t i o n may be p o s i t i v e o r n e g a t i v e depending on t h e a c t u a l l e v e l of crowding. The accurately  number o f t r e e s p e r a c r e (the r e q u i r e d measure) has been r e c o r d e d f o r each b l o c k .  The expected s i g n i s p o s i t i v e b u t  l i k e t r e e - s i z e t h e r e may be some range over which the M.P.P. i s 3.2.7  Spur-type  Generally, The  s p u r - t y p e a r e about 60% of t h e s i z e o f non spur  trees.  dwarfing e f f e c t may r e s u l t i n a lower y i e l d p e r t r e e , but t h e  improved p o s i t i o n o f t h e f r u i t b e a r i n g  may compensate f o r t h i s .  the e f f e c t s of t h i s v a r i a b l e on output are not c l e a r . has  negative.  been used t o r e p r e s e n t  Thus  A dummy v a r i a b l e  t h e e f f e c t s o f spur-type t r e e s i n the  esti-  mated models. 3.2.8 The  Tree D e s i g n b a s i c d e s i g n s a r e e i t h e r hedgerow o r i n d i v i d u a l t r e e s  Hedgerows can e i t h e r be t r e l l i s e d o r f r e e - s t a n d i n g .  i n rows.  Hedgerow d e s i g n s ,  p a r t i c u l a r l y t r e l l i s e d hedgerows p r o v i d e g r e a t e r b e a r i n g  surface per  a c r e and a r e expected to r e s u l t i n h i g h e r y i e l d s . A dummy v a r i a b l e has been used f o r hedgerow p l a n t i n g t o a l l o w  for  43 a d i f f e r e n c e from the i n d i v i d u a l t r e e concept.  A s i d e from  multi-  c o l l i n e a r i t y problems t h i s i s p r o b a b l y the best method o f measuring t h e i n f l u e n c e o f the hedgerow p l a n t i n g concept.  The expected  sign i s  p o s i t i v e f o r the hedgerow dummy. 3.2.9 The  Variety e f f e c t s o f i n d i v i d u a l v a r i e t i e s on y i e l d are not w e l l known.  However, Golden D e l i c i o u s , Spartan and Winesap are c o n s i d e r e d h i g h l y productive.  Dummy v a r i a b l e s are used t o r e p r e s e n t the major v a r i e t i e s  which a r e Red D e l i c i o u s , Golden D e l i c i o u s , Spartan, Newton, Winesap and Tydeman Red.  I n d i v i d u a l f u n c t i o n s a r e a l s o e s t i m a t e d f o r some v a r i -  eties . 3.2.10 Yield  Age o f Trees i s expected  t o i n c r e a s e as t r e e s become o l d e r , l e v e l o f f  a f t e r a c e r t a i n age and e v e n t u a l l y s t a r t d e c l i n i n g . yield  (The age where  s t a r t s t o d e c l i n e i s u n c e r t a i n a l t h o u g h i t i s q u i t e o l d and i t i s  d o u b t f u l i f the sample c o n t a i n s many t r e e s o f t h i s age.) v a r i a b l e i n t e r a c t s w i t h the types o f r o o t s t o c k .  The age  Standard t r e e s on  s e e d l i n g r o o t s t o c k u s u a l l y are commercially non-bearing u n t i l s i x t h y e a r as i n d i c a t e d by Van Roechoudt's r e s u l t s standard t r e e s r e a c h commercial  (1962).  l e v e l s o f p r o d u c t i o n about  their Semi-  a year  e a r l i e r , w h i l e dwarf and semi-dwarf t r e e s come i n t o p r o d u c t i o n i n t h e i r t h i r d year. u n t i l about  F u l l p r o d u c t i o n from s t a n d a r d t r e e s w i l l not be reached t h e i r t w e l f t h y e a r , f o r semi-standard  reached around reached  t r e e s i t w i l l be  the t e n t h y e a r and f o r dwarf and semi-dwarf i t w i l l be  i n about  s i x years  (Van Roechoudt, 1962).  An a d d i t i o n a l f a c t o r t o be c o n s i d e r e d under age i s b i a n n u a l b e a r i n g where some t r e e s tend t o produce  a l t e r n a t i v e l y l i g h t and heavy  44 crops.  Golden D e l i c i o u s and Newton have s t r o n g t e n d e n c i e s  b i a n n u a l b e a r i n g , as w e l l as Tydeman t o a l e s s e r e x t e n t . b e a r i n g may occur t o some degree i n o t h e r v a r i e t i e s  towards Alternate  (Carlson et a l . ,  1974) . When t r e e s a r e i n t h e i r f o r m a t i v e l i t t l e o r no f r u i t .  (non-bearing)  I t f o l l o w s t h a t the y i e l d  stage they produce  from v e r y young t r e e s  should not be a f f e c t e d t o a l a r g e degree by f e r t i l i z e r , p e s t i c i d e , irrigation ing  and l a b o u r .  As t h e t r e e s become o l d e r and r e a c h t h e i r beartr  stage i t i s l i k e l y  t h a t the i n f l u e n c e of t h e v a r i a b l e i n p u t s w i l l be  much g r e a t e r .  However, t h e r e w i l l : l i k e l y be a lagged e f f e c t o f these  v a r i a b l e s , as maintenance o f t h e t r e e h e a l t h i n the f o r m a t i v e y e a r s  will  improve y i e l d s i n the b e a r i n g y e a r s . A measure which accounts  f o r the f o r m a t i v e , b e a r i n g and p o s t -  b e a r i n g stages of the t r e e s should be c o n s i d e r e d .  The a c t u a l age,  entered as an independent v a r i a b l e would r e s t r i c t  the r e g r e s s i o n to  e s t i m a t i n g an average c o e f f i c i e n t f o r each y e a r , when i t i s known t h a t an a d d i t i o n a l year d u r i n g the f o r m a t i v e stage has much l e s s impact an a d d i t i o n a l year d u r i n g t h e b e a r i n g stage. ally  c o r r e c t to r e s t r i c t  3.2.11  Machinery  The f o l l o w i n g index  ( t a b l e 3.3) from  (1962) i s used. Inputs  Machinery i n p u t s a r e expected Weed s p r a y i n g and mowing w i l l and  I t i s a l s o not conceptu-  the age o f d i f f e r e n t c a t e g o r i e s o f t r e e s i z e s  to have the same c o e f f i c i e n t . Van Roechoudt's r e s u l t s  than  t o i n c r e a s e y i e l d s i n s e v e r a l ways.  improve l i g h t  p e n e t r a t i o n a t lower  a i d i n the e f f i c i e n c y of p r u n i n g , t h i n n i n g and p e s t i c i d e  levels  application.  Mechanical  a i d s such as g i r e t t e s should improve the e f f e c t i v e n e s s o f  time spent  i n t h i n n i n g and p r u n i n g .  Higher  powered t r a c t o r s and  45 T a b l e 3.3.  Indexed Age of T r e e s Based on R o o t s t o c k C l a s s i f i c a t i o n  A c t u a l Age (years)  Indexed Standard  '  Age  Semi-Standard  Dwarf & Semi-Dwarf  3  0  0  0  3  0  0  1  4  0  0  2  5  0  1  3  6  1  2  4  7  2  3  4.5  8  3  4  5  9  4  4.5  5.5  10  5  5  6  11  6  5.5  6  12  7  6  6  13  7. 5  6  6  14  8  6  6  8. 5  6  6  9  6  6  15 16  higher a i r - v o l u m e - v e l o c i t y sprayers w i l l  improve the e f f e c t i v e n e s s of  pesticides. I d e a l l y a measure of the time and is required.  e f f e c t i v e n e s s of machinery  Proxy v a r i a b l e s such as s p r a y e r c a p a b i l i t y or  horsepower would l i k e l y However, no d a t a was  use  tractor  c a p t u r e some of the e f f e c t s of machinery.  o b t a i n e d f o r these v a r i a b l e s so they have not been  i n c l u d e d i n the s t a t i s t i c a l model.  There i s no evidence to  suggest  t h a t machinery i n p u t s a r e c o r r e l a t e d w i t h o t h e r i n p u t s , so no b i a s i s expected  to occur because of the e x c l u s i o n of t h i s  variable.  46 3-.-2.12  Irrigation  System  There a r e t h r e e major systems b e i n g used i n the a r e a which are overhead, p o r t a b l e s p r i n k l e r and t r i c k l e systems. of these systems are not w e l l known. represent  the more common p o r t a b l e  I f t h e r e were more i n f o r m a t i o n on the e f f e c t s o f t h e  systems i t would a l s o be d e s i r a b l e t o c o n s t r u c t an i r r i g a t i o n which c o u l d be used i f the dummies cause  multicollinearity  In summary, f i x e d i n p u t s are w e l l r e p r e s e n t e d data.  index  problems.  by the a v a i l a b l e  Through the use o f dummy v a r i a b l e s and i n d i c e s a l l f i x e d  inputs with  the e x c e p t i o n o f machinery can be r e p r e s e n t e d  mated models.  A l t h o u g h machinery i s an important  b i a s i n e s t i m a t i o n i s expected t o occur  3.3  effects  Dummy v a r i a b l e s have been used t o  overhead and t r i c k l e systems v e r s u s  sprinklers.  The r e l a t i v e  i n the  esti-  i n p u t no s y s t e m a t i c  as a r e s u l t o f i t s e x c l u s i o n .  V a r i a b l e Inputs V a r i a b l e i n p u t s are those where an annual d e c i s i o n i s made con-  c e r n i n g l e v e l s o f use. to remain constant  Whereas f i x e d i n p u t s would u s u a l l y be expected  over a number o f y e a r s , some v a r i a t i o n i s l i k e l y i n  the annual l e v e l s o f v a r i a b l e i n p u t s .  They i n c l u d e f e r t i l i z e r ,  trace  elements, p e s t i c i d e s , i r r i g a t i o n and l a b o u r . 3.3.1 The  Fertilizer e f f e c t s o f p l a n t food elements on y i e l d s and f r u i t q u a l i t y  v a r y depending on l o c a l s o i l c o n d i t i o n s .  However, a l l o r c h a r d  soils  i n B r i t i s h Columbia should b e n e f i t from a p p l i c a t i o n on n i t r o g e n and boron (Swales, 1971).  The t i m e l i n e s s and the q u a n t i t y o f n i t r o g e n  s u p p l i e d are both c o n s i d e r e d  important.  l a t e i t can cause poor f r u i t  colour  I f n i t r o g e n i s a p p l i e d too  (although  fruit  s i z e should be good) ,  as w e l l as making the t r e e s more s u s c e p t i b l e to w i n t e r i n j u r y . l i t t l e nitrogen coloured  i s a p p l i e d y i e l d s w i l l l i k e l y be  small f r u i t .  yields.  Too  l i g h t with highly  l i t t l e boron w i l l r e s u l t i n l i g h t  A p p l i c a t i o n of other  manganese can have b e n e f i c i a l e f f e c t s on y i e l d and  ing  on l o c a l s o i l d e f i c i e n c i e s .  pointed  out  misshapen  elements i n c l u d i n g z i n c , magnesium i r o n  and  Previous  quantity  depend-  r e g r e s s i o n a n a l y s i s on the e f f e c t s of f e r t i l i z e r  the p o s i t i v e i n f l u e n c e of f e r t i l i z e r on y i e l d s .  (1976) found t h a t the amount of f e r t i l i z e r a p p l i e d had i n f l u e n c e on the t o t a l v a l u e of the f r u i t , of f e r t i l i z e r on y i e l d s and/or q u a l i t y . r e s u l t using  I f too  quantity  rather  Campbell  a positive  indicating a positive effect Lee  than v a l u e  have  (1972) had  a similar  as the dependent v a r i a b l e .  The more f e r t i l e s o i l s by d e f i n i t i o n have more of the n u t r i e n t elements t h a t are r e q u i r e d production  f o r t r e e growth and  plant production.  Fruit  from n a t u r a l l y f e r t i l e s o i l s w i l l be expected to respond  l e s s to f e r t i l i z e r s o i l s w i t h a PH  than would p r o d u c t i o n  7.5  or h i g h e r would be  response to f e r t i l i z a t i o n than y i e l d correct f e r t i l i z e r  from poor s o i l s .  Y i e l d on  expected to have a  on lower. PH  greater  s o i l s because  reduces a l k a l i n i t y as w e l l as s u p p l y i n g  the  nutrient  elements. The complicated  i n t e r a c t i o n between s o i l f e r t i l i t y and and  d e f i c i e n t and  i t s e f f e c t s on output w i l l v a r y .  poorly drained  s o i l s may  nitrogen application i s C e r t a i n boron  respond p o o r l y  to  nitrogen  a p p l i c a t i o n because the n i t r o g e n w i l l not be u t i l i z e d by the The  trees.  response to n i t r o g e n w i l l p r o b a b l y be b e t t e r from s l i g h t l y  s o i l s , but  from v e r y  better  good s o i l s the response w i l l a l s o be poor, because  the n u t r i e n t elements are a l r e a d y  contained  i n the s o i l .  Thus  the  48 i n t e r a c t i o n between n i t r o g e n or n e g a t i v e ,  and  soil fertility  depending on the range of s o i l  can be  either positive  fertility.  I d e a l l y , a measure of each n u t r i e n t added i n c l u d i n g boron, z i n c , i r o n magnesium, manganese and The  measure used i n t h i s study i s the  of f e r t i l i z e r per concentrations  acre.  34%  fertilizers.  account f o r the r e l a t i v e  I t i s assumed t h a t most  the common ammonium n i t r a t e f e r t i l i z e r which i s  nitrogen. 3.3.2  Pesticides  The  e f f e c t i v e n e s s of the v a r i o u s  climatic conditions.  attention.  p e s t i c i d e s depends on  a r e a s m i t e s and  c o d l i n g moths r e q u i r e more  However, a l l areas are under some t h r e a t  as w e l l as o t h e r s i n c l u d i n g l e a f r o l l e r , a p h i d s , bud t h r i p s and  powdery mildew (B.C.M.A., 1975).  Jose s c a l e can occur i n some d i s t r i c t s .  from t h e s e p e s t s moth, l e a f hopper,  European f r u i t The  1975).  i n t e r v a l s depending on the Thus the o r c h a r d i s t  as the c o n c e n t r a t i o n  i n y i e l d , by  reducing The  An  fruit  of a p p l i c a t i o n s w i l l of c u l l s and  s t u d i e s by Campbell  quantity  to  season at (B.C.M.A.,  I t i s expected t h a t  the q u a n t i t y  have both confirmed t h i s e x p e c t a t i o n of p e s t i c i d e s on v a l u e and  and  can v a r y the number of a p p l i c a t i o n s as  of each a p p l i c a t i o n .  the h e a l t h of the t r e e .  the  stage of the buds and  i n e i t h e r the frequency or c o n c e n t r a t i o n increase  scale  most e f f i c i e n t way  d e a l w i t h these p e s t s i s to spray s e v e r a l times d u r i n g varying  local  Higher r a i n f a l l areas have h i g h e r o c c u r r e n c e s of  a p p l e scab w h i l e i n the d r y e r  San  required.  farmer's e s t i m a t e of t o t a l pounds  T h i s measure does not  of the a p p l i e d  o r c h a r d i s t s are u s i n g  potassium i s  nitrogen,  by  (1976) and  well  increases  l e a d to  an  maintaining Lee  (1972)  as they showed a p o s i t i v e i n f l u e n c e of y i e l d  respectively.  important v a r i a b l e r e l a t i n g to the e f f e c t i v e n e s s of  pesticides  49 i s the machinery used  i n spraying.  Sprayers capable o f a h i g h a i r  volume output as w e l l as h i g h a i r v e l o c i t i e s a r e thought e f f e c t i v e f o r c o n t r o l of c e r t a i n p e s t s , p a r t i c u l a r l y  to be more  San J o s e  scale.  These f e a t u r e s are n e c e s s a r y i n o r d e r to c o m p l e t e l y coat the f o l i a g e i n the upper and  i n n e r areas of the t r e e w i t h p e s t i c i d e .  tractor w i l l result  A h i g h e r powered  i n h i g h e r a i r volume and v e l o c i t y from the s p r a y e r ,  thus r e s u l t i n g i n b e t t e r pest c o n t r o l . I d e a l l y a measure a c c o u n t i n g f o r the amount and number of a p p l i c a t i o n s of each of the major chemicals should be i n c l u d e d . measure used was  The  actual  the o r c h a r d i s t ' s e s t i m a t e of the t o t a l v a l u e of p e s t i -  c i d e s a p p l i e d per a c r e .  In cases where t h i s was  not  available,  growers were asked whether they f o l l o w e d the recommendations s e t out i n the B.C.M.A. spray c a l e n d a r (B.C.M.A., 1975), or sprayed more or o f t e n than the g u i d e l i n e s suggested. lowed, the c o s t per a c r e was guidelines.  I f the recommendations were  s e t a t the average  c o s t of f o l l o w i n g  folthese  Cases where farmers d i d not f o l l o w the g u i d e l i n e s and  c o u l d not make an e s t i m a t e of the v a l u e per a c r e were r a r e and o b s e r v a t i o n s were excluded.  Many growers tended  these  t o say they f o l l o w e d  the recommendations when they were o n l y u s i n g them as a l b a s i c The r e s u l t  less  guide.  i s t h a t $65 per a c r e became the predominant v a l u e f o r p e s t i -  c i d e i n the d a t a w i t h l i t t l e v a r i a t i o n o c c u r r i n g .  Over l a r g e  sub-sets  of the d a t a p e s t i c i d e i s o f t e n c o n s t a n t or near c o n s t a n t . 3.3.3 The ture.  Irrigation importance  of i r r i g a t i o n i s i n the maintenance of s o i l mois-  Up t o a c e r t a i n p o i n t s o i l m o i s t u r e can be expected  p o s i t i v e i n f l u e n c e on f l o w e r i n i t i a t i o n , t r e e s i z e and ( C h i l d e r s , 1954)  and thus on y i e l d s and q u a l i t y .  fruit  to have a size  As the amount of  50 i r r i g a t i o n a f f e c t s s o i l m o i s t u r e i t i s expected ence y i e l d s and q u a l i t y .  that i t w i l l also  influ-  However, the i n f l u e n c e which i r r i g a t i o n  has  upon s o i l m o i s t u r e v a r i e s a c c o r d i n g to l o c a l s o i l and c l i m a t i c c o n d i tions.  Swales (1971) e s t i m a t e s t h a t the r a t e of i r r i g a t i o n t o m a i n t a i n  optimum s o i l m o i s t u r e v a r i e s from once every f o u r or f i v e days d u r i n g h o t , dry weather on l i g h t s h a l l o w s o i l s , d i s t r i c t s on heavy s o i l s . growing  to once a month i n the c o o l e r  I r r i g a t i o n i s most d e s i r a b l e d u r i n g the  season of the t r e e and f r u i t , and l e a s t d e s i r a b l e d u r i n g e a r l y  f a l l when i t can i n c r e a s e s u s c e p t i b i l i t y to w i n t e r The  i d e a l measurement should account  the amount of water a p p l i e d . was  cold.  f o r both the t i m e l i n e s s  No measure was  and  a v a i l a b l e so the v a r i a b l e  not i n c l u d e d i n the s t a t i s t i c a l models. 3.3.4  Labour  The amount of l a b o u r i s a s s o c i a t e d w i t h p r e v i o u s l y mentioned able i n p u t s — p e s t i c i d e s , f e r t i l i z e r expected  and  i r r i g a t i o n and  so would  to have some p o s i t i v e i n f l u e n c e on y i e l d s and  quality.  remaining l a b o u r used c o u l d m o s t l y be accounted  vari-  be The  f o r i n pruning, thinning  and h a r v e s t i n g . The reasons f o r p r u n i n g a r e t o l e t the s u n l i g h t and spray r e a c h the i n n e r branches t r e e s i z e and expected  of the t r e e s , to f a c i l i t a t e h a r v e s t i n g by  to e l i m i n a t e u n p r o d u c t i v e wood.  For these reasons  t h a t the amount of p r u n i n g l a b o u r (up to c e r t a i n l e v e l s )  p o s i t i v e l y i n f l u e n c e both q u a n t i t y and q u a l i t y of f r u i t . will  limiting it is will  The q u a n t i t y  i n c r e a s e because t h e r e w i l l be l e s s c u l l s as a r e s u l t of l i g h t  spray p e n e t r a t i o n , but a f t e r a c e r t a i n p o i n t w i l l d e c r e a s e , because the b e a r i n g a r e a of the t r e e decreases w i t h p r u n i n g . e f f e c t s of p r u n i n g on f r u i t  q u a l i t y would be expected  and  simply The  to c o n t i n u e t o be  51 p o s i t i v e to a h i g h e r  p o i n t than f o r q u a n t i t y .  In f a c t , a s t r i c t l y  p o s i t i v e r e l a t i o n s h i p can be expected between p r u n i n g and f r u i t but  quality w i l l f a l l  i n the very  l a r g e f r u i t s as the f l e s h  size,  will  become s o f t and the c o l o u r i n g poor. The  e f f e c t s of t h i n n i n g are s i m i l a r t o pruning.  I f no t h i n n i n g  i s done, q u a n t i t y w i l l be low because t h e r e w i l l be a l a r g e number o f small f r u i t c u l l s . and  quantity w i l l  As t h i n n i n g i n c r e a s e s , increase.  these c u l l s w i l l  After a c e r t a i n point quantity  decrease will  decrease as t h e t h i n n i n g w i l l be removing p o t e n t i a l l y commercial The  fruit.  amount o f t h i n n i n g w i l l be p o s i t i v e l y r e l a t e d t o f r u i t s i z e , but  when c a r r i e d t o excess w i l l r e s u l t i n o v e r l y l a r g e s o f t f r u i t o f poor quality. Within  a c e r t a i n range an i n c r e a s e  increase production.  Obviously  i n harvesting  labour  once the f r u i t has a l l been  will picked  labour w i l l have no a d d i t i o n a l p r o d u c t i v i t y , and we would not expect to observe t h i s excess o c c u r r i n g . the exact  amount of h a r v e s t i n g  a l t h o u g h i n a few i n s t a n c e s  In f a c t one would u s u a l l y observe  labour  necessary to harvest  t h e r e might not be enough s e a s o n a l  a v a i l a b l e and some of t h e crop w i l l remain u n h a r v e s t e d . a shortage of s e a s o n a l  labour  labour  When t h e r e i s  c e r t a i n o r c h a r d i s t s who have b e t t e r  t a c t s i n t h e i n d u s t r y or more e a s i l y h a r v e s t e d o b t a i n more and a b e t t e r q u a l i t y o f labour The  the crop  than  o r c h a r d s would  likely  others.  i d e a l measure of p r u n i n g and t h i n n i n g l a b o u r  should  include  both t h e time spent and the e f f e c t i v e n e s s o f these a c t i v i t i e s . accurate  measure was p o s s i b l e without s i g n i f i c a n t l y added  e f f o r t , so t h i s v a r i a b l e i s not i n c l u d e d  con-  i n estimations.  No  research This  input  may be somewhat a s s o c i a t e d w i t h the p l a n t i n g system and can be accounted  52 for  by assuming a f i x e d amount of l a b o u r  The  e x c l u s i o n of t h i s v a r i a b l e , i s a r e c o g n i z e d I d e a l l y t h e r e should  ing  be  i s r e q u i r e d f o r each system. weakness of the model.  some measure of the q u a l i t y of the  l a b o u r r a t h e r than the a c t u a l v a l u e p a i d f o r h a r v e s t i n g .  harvest-  Because  p i c k e r s are p a i d by the pound or b i n , u s u a l l y at common r a t e f o r area,  t h e r e w i l l be a h i g h c o r r e l a t i o n between the amount p a i d f o r  h a r v e s t i n g and likely  yields.  Harvesting  l a b o u r measured by v a l u e p a i d would  be a dominant v a r i a b l e i n the r e g r e s s i o n s , thus i m p a i r i n g  e s t i m a t i o n of other of h a r v e s t i n g  coefficients.  labour  i s i n c l u d e d i n the e s t i m a t i o n s .  s u b t r a c t i n g the h a r v e s t i n g  inputs.  e f f e c t s of  have taken p l a c e , of the  by  yields.  i s dependent on the amount of  to measure i t on a p e r - a c r e  b a s i s as are  inputs  other  A measure c o u l d be made on a per u n i t b a s i s such as the  taken to apply 100  The  c o s t s from the p r e d i c t e d v a l u e  Because i n p u t a s s o c i a t e d l a b o u r a p p l i e d , i t i s b e s t not  the  No measure of the amount or q u a l i t y  t h i s v a r i a b l e can be removed a f t e r the e s t i m a t i o n s  apply  the  time  a hundred g a l l o n s of spray m a t e r i a l or the time taken to  l b s of f e r t i l i z e r .  t h i s v a r i a b l e i s not  No measure was  recorded  i n c l u d e d i n the e s t i m a t i o n s .  f i x e d amount of l a b o u r per u n i t of i n p u t i s not t i o n over the s h o r t run,  and  consequently  It i s f e l t that  a  an unreasonable assump-  so the a n a l y s i s w i l l not be h i n d e r e d  by  the  e x c l u s i o n of t h i s v a r i a b l e . In summary, the v a r i a b l e i n p u t s are not as s t r o n g l y r e p r e s e n t e d the data as f i x e d i n p u t s .  Labour i s accounted f o r by assuming  fixed  p r o p o r t i o n s which i s r e a s o n a b l e  over the s h o r t run a l t h o u g h i t may  the p r e c i s i o n of the e s t i m a t e s .  Because of measurement problems  p e s t i c i d e data g e n e r a l no  i s i m p r e c i s e which might a l s o a f f e c t e s t i m a t i o n .  systematic  b i a s i s expected to occur  because of data  in  lower the In  problems  53 with v a r i a b l e inputs, unless  the assumption of f i x e d p r o p o r t i o n s of  i s i n c o r r e c t i n which case some c o e f f i c i e n t s may  3.4  show an upward b i a s .  Weather V a r i a b l e s Weather v a r i a b l e s present  a different  ment than the i n p u t s a l r e a d y d i s c u s s e d . weather f a c t o r s are important r i a t e measures of these it  labour  type of problem i n measure-  Although i t i s known which  i n tree f r u i t production  the most approp-  f a c t o r s a r e not always obvious.  For  example,  i s known t h a t below f r e e z i n g temperatures d u r i n g the blossom p e r i o d  have adverse e f f e c t s on the buds and the ensuing  crop, but  i n f l u e n c e of f r o s t  blossoms and  therefore w i l l  i t i s not known what the best measure of  is.  reduce  the  I t c o u l d be measured by the d u r a t i o n of c o l d  temperatures, the i n c i d e n c e of temperatures below a c e r t a i n l e v e l , or a combination of d u r a t i o n and  incidence.  S i m i l a r problems i n  determining  the i d e a l measurements of most of the o t h e r weather v a r i a b l e s a r e a l s o encountered.  A s e p a r a t e weather model, s e c t i o n 4.2,  i s estimated  the o b j e c t of s e l e c t i n g a s e t of a p p r o p r i a t e measures of weather ences and  a s s e s s i n g t h e i r impact at a r e g i o n a l l e v e l .  v a r i a b l e s were c o n s i d e r e d 3.4.1  Blossom  The  influ-  following  i n the model.  Influences  A number of f a c t o r s d u r i n g the green t i p t o green f r u i t i n f l u e n c e p o l l i n a t i o n and  fruit  s e t w i t h a r e s u l t i n g e f f e c t on  These f a c t o r s are f r o s t , temperature, s u n l i g h t , wind and The  with  stage  will  yield.  rain.  p e r i o d d u r i n g which the blossoms can be p o l l i n a t e d i s approx-  i m a t e l y f o u r to t e n days l o n g .  There i s a n a t u r a l compensation  effect  at work d u r i n g t h i s p e r i o d , i n t h a t the weather f a c t o r s which cause p o l l i n a t i o n to be poor, a l s o l e n g t h e n p o l l i n a t i o n p e r i o d .  However, i t  54 is  felt  t h a t a s h o r t blossom p e r i o d , w i t h weather s u i t a b l e f o r heavy  insect p o l l i n a t i o n a c t i v i t y with less suitable  i s p r e f e r a b l e to a l o n g e r blossom p e r i o d  weather.  P o l l i n a t i o n depends  f o r the most p a r t on honey bees, w i l d  solitary  bees and bumble bees, w i t h honey bees g e n e r a l l y d o i n g most of the p o l lination.  The weather v a r i a b l e s which a f f e c t  insects w i l l  the a c t i v i t i e s of t h e s e  thus i n f l u e n c e the amount of p o l l i n a t i o n and the f r u i t  yield. The p e r i o d s p r e c e d i n g and f o l l o w i n g t h e blossom stage a r e a l s o important because c o l d temperature can cause damage to the p i s t i l s  during  t h i s time. 3.4.2  Spring Frost  Spring f r o s t  c o n s t i t u t e s a major h a z a r d d u r i n g the blossom p e r i o d  of  the f r u i t .  of  the blossom, which i f i n j u r e d b e f o r e p o l l i n a t i o n , cannot be  ized  The major damage d u r i n g t h i s time o c c u r s on the p i s t i l  (Karmo et a l . , 1956).  A f t e r p o l l i n a t i o n the p i s t i l  s l i g h t l y more hardy, but s t i l l  fertil-  becomes  can be i n j u r e d by s u f f i c i e n t l y  cold  temperatures.  The p i s t i l  i s most s u s c e p t i b l e to i n j u r y d u r i n g the  bloom p e r i o d .  The f o l l o w i n g temperatures a r e the minimum temperatures  t h a t a p p l e blossoms can stand f o r 30 minutes, at v a r i o u s stages of development  (Davis,  Table  1974).  3.4.  Temperatures below which damage occurs d u r i n g blossom p e r i o d  showing  colour  25 F. duration  3 to 4 weeks  f u l l bloom 28 F. 4 to 10 days  green  fruit  29 F. 10 days to 2 weeks  full  55 Thus t h e r e i s a p e r i o d of about  35 t o 50 days where a s p r i n g  can cause blossom damage and a p o s s i b l e r e d u c t i o n i n y i e l d . of  The  i n f l u e n c e can be summarized as the frequency of c o l d below the  ical  frost factors crit-  temperatures, the i n t e n s i t y o f t h i s c o l d and the stage o f blossom  development. I d e a l l y a measure i n c l u d i n g both l e n g t h and i n t e n s i t y of f r o s t i n each o r c h a r d below c r i t i c a l should be i n c l u d e d .  l e v e l s a t each s t a g e of blossom  development  The a c t u a l measurements are as f o l l o w s .  s t a g e , green t i p , was  The  first  taken from 25 days b e f o r e the r e c o r d e d d a t a of  f u l l bloom to one day b e f o r e .  The second s t a g e , f u l l bloom was  from  one day b e f o r e the r e c o r d e d date t o 6 days a f t e r and the t h i r d s t a g e , green f r u i t , are  as  was  taken as the next 12 days.  The v a r i a b l e s  compiled  follows.  T a b l e 3.5.  Variable  A l t e r n a t i v e measures of f r o s t d u r i n g bloom  Explanation  Frost 1  Accumulated degrees from minimum temperatures below 27 F. 30 F. and 31 F. f o r the green t i p , f u l l bloom and green f r u i t stages respectively.  Frost 2  As i n F r o s t 1, but w i t h c r i t i c a l temperatures of 25 F. 28 F. and 29 F.  Frost 3  The number of days d u r i n g the whole p e r i o d on which any f r o s t occurred.  Temperatures  Expected  sign  were r e c o r d e d at r e g i o n a l weather s t a t i o n s .  56 3.4.3  Temperature  Honey bees a r e unable t o f l y a t temperatures below 55 F. and a r e .. not  c a p a b l e of c a r r y i n g out e f f e c t i v e p o l l i n i z a t i o n u n t i l t h e tempera-  t u r e reaches a t l e a s t  65 F. (Karmo, 1956).  Bumble bees a r e a b l e t o  p o l l i n i z e a t s l i g h t l y lower temperatures w h i l e w i l d bees need a s l i g h t l y warmer temperature. of  I t i s expected t h a t the frequency and the d u r a t i o n  temperature above 65F. and the amount by which t h i s temperature i s  exceeded w i l l have a p o s i t i v e i n f l u e n c e on y i e l d . I d e a l l y a measure f o r each o r c h a r d of t h e d u r a t i o n and i n t e n s i t y o f temperatures conducive t o i n s e c t p o l l i n a t i o n a c t i v i t y d u r i n g t h e f u l l bloom p e r i o d s h o u l d be used.  U n f o r t u n a t e l y , the exact l e n g t h of t h e f u l l  bloom p e r i o d f o r each year i s not known, so measures o f t h i s i n f l u e n c e a r e compiled over d i f f e r e n t  l e n g t h s s t a r t i n g a t the r e c o r d e d d a t a o f f u l l  bloom of t h e c l o s e s t r e c o r d i n g s t a t i o n . for  The measures below a r e r e c o r d e d  each r e g i o n , namely (1) Kelowna Westbank, (2) Penticton-Summerland-  Naramata, and (3) O l i v e r - O s o y o o s .  T a b l e 3.6.  A l t e r n a t i v e measures o f temperature d u r i n g bloom  Accumulated Temp 1  over 65 F.  degrees  (from d a i l y maximums) 5 day p e r i o d  Temp 2  it  7 day p e r i o d  Temp 3  II  10 day p e r i o d  Temp 4  II  3.4.4 It  5 day p e r i o d from 6th day to 10th day  Sunlight  has been observed t h a t bees p r e f e r b r i g h t sunny days t o o v e r -  c a s t days f o r a c t i v i t y  (even i f t h e r e i s no d i f f e r e n c e i n temperature)  (Karmo, et a l . , 1956).  I t i s t h e r e f o r e expected t h a t the amount of  b r i g h t sunlight occurring during influence  each o r c h a r d  i d e a l to c o n s i d e r measure of t h i s v a r i a b l e f o r  over the f u l l bloom p e r i o d .  The  measures a c t u a l l y  are s i m i l a r to those a l r e a d y d i s c u s s e d , as they are on  r e g i o n a l l e v e l and day  of f u l l  over d i f f e r e n t  sun 1  3.7.  hours of b r i g h t s u n l i g h t  2  sun  3  "  s  4  "  n  3.4.5  (Karmo, et a l . , 1956).  over 15 mph.,  -  5 day  period  7 day  period  10 day  period  5  Bloom  day p e r i o d from 6th to 10th day  of the g r e a t e s t i n f l u e n c e s on  w h i l e bumble bees can work i n s l i g h t l y s t r o n g e r  the frequency and i n f l u e n c e on  d u r a t i o n of winds over 15 mph.  winds  I t i s expected w i l l have a  that  negative  yield.  A measure of both the i n t e n s i t y and d u r i n g the blossom p e r i o d would be  d u r a t i o n of wind i n each ideal.  No  d a i l y data  a v a i l a b l e so a measure of t h i s v a r i a b l e i s not  estimations.  bee  Honey bees cannot work i n winds of  and w i l d bees must stop at a l e s s e r wind speed.  winds was  recorded  Wind  Wind i s thought to be one activity  s t a r t i n g on the f i r s t  A l t e r n a t i v e Measures of S u n l i g h t d u r i n g  sun  u  lengths  a  bloom.  Table  orchard  positively  yield.  A g a i n , i t would be  recorded  f u l l bloom p e r i o d w i l l  on  included i n  58 3.4.6  Rain  Heavy r a i n w i l l al.,  1956).  fall,  cause a l l types of bees t o cease working  O f t e n bees w i l l not resume work immediately  but w i l l w a i t u n t i l  the next day.  New  p o l l e n w i l l then be produced  r e q u i r e d f o r p r o d u c t i o n , any  after a rain-  R a i n can a l s o a f f e c t  a t i o n by r u i n i n g the p l o o e n on the a n t h e r s of p o l l i n a t i n g  (Karmo, et  pollin-  varieties.  by the blossom but i n the p e r i o d  i n s e c t a c t i v i t y w i l l have no e f f e c t .  i s h y p o t h e s i z e d t h a t the frequency and  It  i n t e n s i t y of r a i n f a l l d u r i n g the  f u l l bloom p e r i o d w i l l n e g a t i v e l y i n f l u e n c e y i e l d s .  It i s also  expected  t h a t the e a r l i e r a r a i n f a l l o c c u r s d u r i n g t h i s p e r i o d , the g r e a t e r w i l l be i t s e f f e c t s on  yield.  I d e a l l y a measure of the t o t a l r a i n f a l l o c c u r r i n g i n each o r c h a r d d u r i n g the f u l l bloom p e r i o d should be i n c l u d e d .  Because the exact  l e n g t h of the f u l l bloom p e r i o d i s not known, these v a r i a b l e s are a l s o compiled  over d i f f e r e n t  time p e r i o d s .  The  t o t a l s shown are r e c o r d e d f o r  the t h r e e r e g i o n s mentioned above.  T a b l e 3.8.  A l t e r n a t i v e measures of r a i n f a l l d u r i n g bloom  T o t a l p r e c i p i t a t i o n i n hundredths Rain 1  II  5 day p e r i o d  Rain 2  II  7 day p e r i o d  Rain 3 Rain 4 Rain 5  3.4.7  of an  inch  10 day p e r i o d 5 day p e r i o d from 6th day t o 10th day number of days where p r e c i p i t a t i o n o c c u r r e d i n 10 day p e r i o d  Growing Season I n f l u e n c e s  Temperature i s a primary f a c t o r  c o n t r o l l i n g the growth of p l a n t s  59 and heat u n i t a c c u m u l a t i o n has been demonstrated of  f r u i t m a t u r i t y (Ag. Canada, 1959).  a c c u m u l a t i o n d u r i n g t h e growing some compensation  as an a c c u r a t e p r e d i c t o r  While i t i s expected t h a t heat  season w i l l  influence y i e l d , there i s  f o r a l a c k o f heat i n t h a t the f r u i t  can be l e f t  l o n g e r on the t r e e i n o r d e r t o s i z e - u p and mature. A measure of t h e t o t a l heat accumulated the  h a r v e s t i n g stage would be i d e a l .  from the g r e e n - f r u i t to  A good a p p r o x i m a t i o n o f t h i s  measure can be made by c a l c u l a t i n g heat u n i t s f o r each r e g i o n and y e a r . However, heat u n i t s were not c a l c u l a t e d  i n t h i s r e s e a r c h , as tempera-  t u r e s f o r n e a r l y 4,000 days would have t o be compiled. 3.4.8  C o l d Winter  Temperatures  When w i n t e r temperatures a r e abnormally c o l d i n the Okanagan a r e a , s e v e r a l forms o f i n j u r y t o f r u i t hardy f r u i t for  t r e e s can o c c u r .  Apples a r e t h e most  and a temperature a t l e a s t as c o l d as -25°F.  s i g n i f i c a n t damage and a subsequent  (Mann, e t a l . , 1952).  i s necessary  drop i n p r o d u c t i o n t o occur  C o l d temperatures r a r e l y k i l l  the f r u i t  buds  d i r e c t l y , but s m a l l limb and twig i n j u r y r e s u l t s more o f t e n , c u t t i n g o f f c i r c u l a t i o n to the f r u i t b e a r i n g a r e a .  Large limb and t r u n k i n j u r y i s  o f t e n caused by s u n s c a l d on t h e southwest  s i d e o f t r e e s where t h e  a l t e r n a t e warming d u r i n g the day and severe f r e e z i n g a t n i g h t  causes  damage i n the bark, cambium and wood c o n d u c t i n g t i s s u e s . The r e s u l t of t h e s u n s c a l d i n g can be a weakened or d y i n g c o n d i t i o n of  the upper p o r t i o n of t h a t s i d e of the t r e e .  severe enough t o k i l l  Crown i n j u r y can be  the t r e e w i t h t h e damage near ground  a s s o c i a t e d w i t h the bud u n i o n of t h e t r e e .  Root  l e v e l and  i n j u r y can occur i n  s e v e r a l degrees, r a n g i n g from damage t o o n l y t h e s m a l l f e e d i n g r o o t s to k i l l i n g of a l l the r o o t s .  I n t h e former case the t r e e s r e c o v e r w i t h  o n l y some delayed f o l i a g e development w h i l e i n the l a t t e r case t h e t r e e s u s u a l l y d i e w i t h the coming o f s p r i n g .  I t i s expected  t h a t the f r e -  quency and i n t e n s i t y o f c o l d below -25°F. w i l l thus n e g a t i v e l y i n f l u e n c e y i e l d s i n the f o l l o w i n g season. During t h e p e r i o d covered by the sample t h e r e was no s e r i o u s amount of w i n t e r k i l l or used  i n t h e a r e a , so no measure o f t h i s v a r i a b l e was r e c o r d e d  i n estimations.  G e n e r a l l y t h e weather v a r i a b l e s a r e adequately r e p r e s e n t e d i n the data.  Measures a r e a v a i l a b l e f o r most o f t h e important  blossom  time  i n f l u e n c e s w h i l e no measure was r e q u i r e d f o r w i n t e r - k i l l v a r i a b l e s i n recent years.  The o n l y a r e a w i t h a l a c k o f d a t a i s growing  season  i n f l u e n c e s where t h e r e q u i r e d measurement i s not p r e s e n t l y a v a i l a b l e . Because weather v a r i a b l e s were r e c o r d e d a t r e g i o n a l weather  stations,  r a t h e r than on the a c t u a l o r c h a r d s i t e s , some i m p r e c i s i o n i n the e s t i mated c o e f f i c i e n t s f o r o r c h a r d l e v e l f u n c t i o n s may r e s u l t .  3.5  Y i e l d Per A c r e The  i d e a l measurement accounts  f r u i t per acre.  f o r both q u a l i t y and q u a n t i t y o f  Value p a i d to t h e farmer w i t h some adjustment  made  f o r y e a r l y p r i c e f l u c t u a t i o n s would be an a p p r o p r i a t e measure.  How-  ever, f o r the data from e x p e r i m e n t a l p l o t s t h e r e i s no q u a l i t y  grading  and v a l u e s cannot  be a s s i g n e d .  I t was e s s e n t i a l t o i n c l u d e t h i s  because i t p r o v i d e d important v a r i a t i o n i n i n p u t l e v e l s  data  thereby  r e d u c i n g the degree of m u l t i c o l l i n e a r i t y o f the complete body o f d a t a . The a c t u a l measure o f y i e l d  i s pounds per a c r e , e x c l u d i n g c u l l s .  61 3.6  Summary There a r e a number of p r e c o n c e i v e d v a r i a b l e s f o r which t h e r e i s no  measure i n the s t a t i s t i c a l model.  These a r e management, l a b o u r ,  machinery i n p u t s , i r r i g a t i o n l e v e l s , growing and wind d u r i n g bloom. ery w i l l inputs.  accumulation,  The e x c l u s i o n o f management, l a b o u r and machin-  l i k e l y impart a s y s t e m a t i c b i a s i n t h e e s t i m a t e s o f s e v e r a l Because of the p o s i t i v e i n t e r a c t i o n of management w i t h v a r i -  a b l e i n p u t s i t i s expected w i l l be b i a s e d upwards. effect,  season heat  t h a t the f e r t i l i z e r  and p e s t i c i d e  coefficients  The e x c l u s i o n o f l a b o u r should have a s i m i l a r  i m p a r t i n g a g e n e r a l upward b i a s .  Because t h e r e i s some a p r i o r i  knowledge o f the c o r r e l a t i o n between l a b o u r and some f i x e d i n p u t s , the b i a s imparted  t o these c o e f f i c i e n t s can be accounted  i n g the r e s u l t s .  f o r , when i n t e r p r e t -  I t i s not c l e a r what t h e g e n e r a l e f f e c t w i l l be o f  l e a v i n g out the machinery i n p u t s , a l t h o u g h i t i s known t h a t they have a p o s i t i v e i n t e r a c t i o n w i t h p e s t i c i d e s , so a f u r t h e r upward b i a s w i l l be imparted  to i t s c o e f f i c i e n t .  Although  t h e r e i s no d a t a on t h e amount  of i r r i g a t i o n a p p l i e d , t h e r e i s a v a r i a b l e r e p r e s e n t i n g the i r r i g a t i o n system which should c a p t u r e some of t h e e f f e c t s of the l e v e l o f i r r i g a tion.  The overhead  i r r i g a t i o n systems a r e l a b o u r s a v i n g and i t i s  r e a s o n a b l e t o assume t h a t more water w i l l be a p p l i e d t o o r c h a r d s to orchards w i t h p o r t a b l e systems.  Important  i n c l u d e d a r e heat u n i t s and wind.  than  weather v a r i a b l e s n o t  I t i s known t h a t t h e s o u t h e r n  areas  w i t h h i g h e r heat u n i t a c c u m u l a t i o n a l s o have a g r e a t e r i n c i d e n c e o f f r o s t and s u n l i g h t d u r i n g blossom b i a s imparted  p e r i o d s so t h e r e w i l l l i k e l y be some  t o these c o e f f i c i e n t s .  There  i s no known c o r r e l a t i o n  between wind and o t h e r v a r i a b l e s so any b i a s imparted ents w i l l be due o n l y t o random c o r r e l a t i o n w i t h wind.  to o t h e r  coeffici-  62 F i g u r e 3.2 f o l l o w i n g shows t h e d e t a i l e d c o n c e p t u a l model and t h e r e l a t i o n s h i p between t h e concept, measure.  the r e q u i r e d measure and t h e a c t u a l  I t can be seen from t h i s f i g u r e t h a t t h e number o f v a r i a b l e s  i s extremely  l a r g e , w i t h s e v e r a l dummy v a r i a b l e s and i n t e r a c t i o n s .  O v e r a l l most o f t h e r e q u i r e d measures, o r r e a s o n a b l e p r o x i e s t h e r e o f are a v a i l a b l e f o r e s t i m a t i o n . For s e v e r a l p r e c o n c e i v e d v a r i a b l e s t h e r e a r e o n l y proxy ments a v a i l a b l e .  There i s no reason t o expect  measure-  any s y s t e m a t i c b i a s i n  these v a r i a b l e s a l t h o u g h a c e r t a i n amount o f i m p r e c i s i o n i s expected. Proxy v a r i a b l e s based  on farmers' e s t i m a t e s i n c l u d e s o i l q u a l i t y ,  r i s k , f e r t i l i z e r and p e s t i c i d e s .  I t i s expected  that o r c h a r d i s t s are  w e l l a c q u a i n t e d w i t h these a s p e c t s o f p r o d u c t i o n so t h a t t h e i r w i l l be r e a s o n a b l y a c c u r a t e .  estimates  P e s t i c i d e s tend towards a c o n s t a n t v a l u e  so some of i t s a c t u a l v a r i a t i o n i s not measured. i n c l u d e a l l weather v a r i a b l e s . used  frost  Other proxy  variables  Data from r e g i o n a l weather s t a t i o n s i s  i n p l a c e o f a c t u a l o b s e r v a t i o n s from t h e o r c h a r d s .  This data  s h o u l d c a p t u r e much of the v a r i a t i o n and t h e r e i s no reason t o b e l i e v e t h a t any b i a s w i l l  occur i n e s t i m a t i o n .  The remaining v a r i a b l e s , a l l  i n t h e p h y s i c a l f e a t u r e c a t e g o r y a r e a c c u r a t e l y measured, a l t h o u g h t h e preponderance o f dummy v a r i a b l e s i s a problem f o r s t a t i s t i c a l e s t i m a t i o n . The dependent v a r i a b l e i s a proxy as pounds o f f r u i t r a t h e r than v a l u e of t h e f r u i t  i s used,  and a l l e s t i m a t e d m a r g i n a l p r o d u c t s  e f f e c t on t h e q u a n t i t y r a t h e r than the v a l u e of t h e f r u i t .  represent  Thus t h e  m a r g i n a l products a r e o n l y i n t e r p r e t e d as g u i d e l i n e s o r i n d i c a t o r s o f the m a r g i n a l v a l u e p r o d u c t s .  63 Concept  Required measure  A c t u a l measure  Yield  v a l u e of y i e l d per  Management  t o t a l management a b i l i t y grower  Physical features & f i x e d inputs s o i l quality frost risk p o l l i n a t i o n method rootstock density tree  design  variety age machinery i r r i g a t i o n system Variable inputs fertilizer pesticides irrigation labour  acre  lbs.  depth, t e x t u r e , ph, n u t r i e n t s a s p e c t , a l t i t u d e , pockets number and p r o x i m i t y of h i v e s , number of p o l l i n a t o r t r e e s e f f e c t on t r e e s i z e number of t r e e s per a c r e d i s t i n g u i s h between hedgerow and f r e e s t a n d i n g d i s t i n g u i s h between v a r i e t i e s s t a g e of development k i n d , amount of time d i s t i n g u i s h between systems amount of each type amount and frequency amount and frequency amount of p r u n i n g , t h i n n i n g and i n p u t a s s o c i a t e d l a b o u r frequency and v e l o c i t y amount and frequency amount above c r i t i c a l l e v e l s for insect a c t i v i t y  sun  t o t a l amount  f r o s t d u r i n g bloom  amount below c r i t i c a l  growing season heat winter k i l l  heat u n i t s not r e q u i r e d  Interactions rootstock-fertilizer rootstock-pesticides rootstock-age rootstock-frost age-fertilizer age-pesticide age-frost soil-irrigation soil-fertilizer soil-rootstock l a b o u r - w i t h most inputs F i g u r e 3.2.  acre  of  Weather i n f l u e n c e s wind d u r i n g bloom r a i n d u r i n g bloom temperature d u r i n g bloom d u r i n g bloom  per  levels  e s t i m a t e of t e x t u r e e s t i m a t e of r i s k number of h i v e s per acre index of t r e e s i z e number of t r e e s per acre dummies f o r each design dummies f o r v a r i e t i e s indexed age dummy f o r each system t o t a l amount i n l b s . t o t a l value  r e g i o n a l t o t a l s 1/100" r e g i o n a l accumulated degrees above c r i t i c a l levels r e g i o n a l t o t a l amount i n 1/10 hours r e g i o n a l amount below c r i t i c a l levels  f o r sample  tree-size x f e r t i l i z e r tree-size x pesticides t r e e - s i z e x age tree-size x frost age x f e r t i l i z e r age x p e s t i c i d e s age x f r o s t s o i l quality x i r r i g a t i o n s o i l quality x f e r t i l i z e r s o i l quality x tree-size  Comparison of c o n c e p t s , r e q u i r e d  tree-size x f e r t i l i z e r tree-size x pesticides t r e e - s i z e x age tree-size x frost age x f e r t i l i z e r age x p e s t i c i d e s age x f r o s t soil soil  measure and  quality quality  actual  fertilizer tree-size  measures  64 3.7  Data Sources Most o f t h e measures d i s c u s s e d i n p r e v i o u s s e c t i o n s a r e based on  data o b t a i n e d from a survey  conducted  T h i s survey was not designed  by A g r i c u l t u r e Canada i n 1975.  e x c l u s i v e l y f o r production f u n c t i o n estima-  t i o n but a l s o aimed a t p r o v i d i n g data f o r mathematical program modeling and  f o r comparative  (Kennedy, Andison  t a b l e s of y i e l d s and i n p u t s of d i f f e r e n t  and Graham, f o r t h c o m i n g ) .  data from as many orchards take l i t t l e  In o r d e r to o b t a i n d e t a i l e d  as p o s s i b l e , q u e s t i o n n a i r e s were designed to  of the growers' time.  The l a c k of d e t a i l e d r e c o r d s kept by  many o r e h a r d i s t s was r e c o g n i z e d and q u e s t i o n s were asked of  such r e c o r d s was not r e q u i r e d .  no d a t a were gathered.  o n l y where use  Hence, f o r a few i n p u t s such as l a b o u r  D e s p i t e t h e s e shortcomings,  t h e d a t a were f a r  b e t t e r s u i t e d to the purposes of t h i s study than any o t h e r d a t a , as i t was h i g h l y d i s a g g r e g a t e d The 1.  survey u t i l i z e d  systems  available  and i n c l u d e d most major i n p u t s .  t h r e e sources of i n f o r m a t i o n .  O r e h a r d i s t s i n the a r e a who were i n t e r v i e w e d and f i l l e d  out ques-  t i o n n a i r e s on i n p u t s and p h y s i c a l f e a t u r e s of s p e c i f i c b l o c k s of fruit.  I n f o r m a t i o n was gathered  on 15 i n p u t s and p h y s i c a l f e a t u r e s  i n c l u d i n g v a r i e t y , d e n s i t y of p l a n t i n g r o o t s t o c k , spur o r non-spur, soil  texture, frost  bees are used), ing, of  r i s k , p o l l i n a t i o n method, a c r e s per h i v e ( i f  i r r i g a t i o n method, p l a n t i n g concept,  year o f p l a n t -  p e s t i c i d e use per a c r e , and f e r t i l i z e r use per a c r e .  The v a l u e s  t h e s e i n p u t s a r e e s t i m a t e s by the growers of the average amount  used i n the l a s t few y e a r s . 2.  I n f o r m a t i o n on y i e l d s from t h e s e b l o c k s came from packout r e c o r d s o f the p a c k i n g houses where the growers had s o l d t h e i r a p p l e s .  The  packout r e c o r d s show the t o t a l weight i n pounds and the p r i c e p a i d  65 each year  c a t e g o r i z e d by v a r i e t y , grade and s i z e .  Some d i f f i c u l t y  was encountered i n r e l a t i n g i n p u t t o y i e l d d a t a . have more than one b l o c k of t r e e s producing apple.  I n these  cases  the t o t a l p r o d u c t i o n  Most o r e h a r d i s t s  a c e r t a i n v a r i e t y of  i t cannot be determined what p r o p o r t i o n o f  accrues  growers have kept s e p a r a t e  t o each b l o c k of f r u i t , u n l e s s t h e  records.  Attempts were made t o s e l e c t  growers who had o n l y one homogeneous system o f p r o d u c t i o n  of a  p a r t i c u l a r v a r i e t y , so t h e y i e l d on t h e packout r e c o r d c o u l d be d i r e c t l y r e l a t e d to the producing 3.  An a d d i t i o n a l source  block.  o f i n f o r m a t i o n was r e c o r d s o f  o r c h a r d p l o t s a t t h e Summerland Research S t a t i o n .  experimental The r e c o r d s  c o n t a i n i n f o r m a t i o n on i n p u t s , p h y s i c a l f e a t u r e s and y i e l d s , although.;the  y i e l d s a r e not c a t e g o r i z e d by grade or s i z e .  Approximately 40 o r e h a r d i s t s were surveyed blocks of f r u i t .  Data on 90 a d d i t i o n a l b l o c k s were o b t a i n e d  records of the research s t a t i o n ' s experimental t h e r e were f o u r y e a r s  plantings.  from On average  of o b s e r v a t i o n on y i e l d s from t h e o r c h a r d s and  seven t o e i g h t from t h e e x p e r i m e n t a l Information  r e p r e s e n t i n g about 120  plots.  on weather v a r i a b l e s was c o l l e c t e d from f e d e r a l meteor-  o l o g i c a l r e c o r d s and kept f o r s e v e r a l p o i n t s throughout t h e v a l l e y . Data was compiled  f o r O l i v e r , Summerland and Kelowna.  Daily  observa-  t i o n s o f maximum and minimum temperatures, hours of s u n l i g h t , r a i n f a l l and  snowfall are a v a i l a b l e . Records o f f u l l - b l o o m dates  f o r several centers  kept by t h e Summerland Research S t a t i o n .  i n the area are  The date may v a r y  a b l y w i t h i n each r e g i o n , depending on t h e a l t i t u d e , aspect to t h e l a k e of t h e t r e e s .  consider-  and p r o x i m i t y  T h i s v a r i a t i o n was accounted f o r i n t h e  Summerland r e c o r d s , and f o r the o t h e r areas o n l y the e a r l i e s t f u l l - b l o o m date i s g i v e n . Input and  data were s u b j e c t to q u a l i t y c o n t r o l procedures.  Visual  computer checks were r u n f o r extreme v a l u e s which were v e r i f i e d o r  r e c t i f i e d where n e c e s s a r y . also mailed  The c o l l a t e d  i n p u t and output  data were  to each grower f o r r e - c h e c k i n g .  T h i s chapter has p r e s e n t e d a d i s a g g r e g a t e d a p p l e p r o d u c t i o n a t the o r c h a r d l e v e l .  c o n c e p t u a l model of  D e t a i l s of the r e q u i r e d mea-  s u r e s and the a v a i l a b l e data were d i s c u s s e d .  The g e n e r a l c o n c l u s i o n  i s t h a t the dataware complete enough to j u s t i f y e s t i m a t i o n o f a d i s aggregated p r o d u c t i o n f u n c t i o n which i n c l u d e s the major i n p u t s of the c o n c e p t u a l model.  The next  chapter d i s c u s s e s the s t a t i s t i c a l method-  o l o g y and p r e s e n t s r e s u l t s of the e s t i m a t i o n s .  CHAPTER IV ESTIMATION OF THE PRODUCTION FUNCTION T h i s c h a p t e r d e a l s w i t h t h e e s t i m a t i o n of t h e c o n c e p t u a l model as summarized i n f i g u r e 3.2.  A number o f problems i n e s t i m a t i n g t h i s model  a r e apparent and a g e n e r a l e s t i m a t i o n s t r a t e g y i s f i r s t f o r m u l a t e d t o d e a l w i t h t h e s e problems.  P r i o r t o t h e e s t i m a t i o n o f t h e complete  s t a t i s t i c a l model a r e g i o n a l weather model, u t i l i z i n g o n l y weather f a c t o r s as e x p l a n a t o r y v a r i a b l e s i s e s t i m a t e d .  The r e s u l t s a r e used t o  s e l e c t a subset o f weather v a r i a b l e s t o be i n c l u d e d i n t h e complete model.  The complete o r c h a r d l e v e l model i s then p r e s e n t e d  and expected  problems w i t h m u l t i c o l l i n e a r i t y and i n t e r a c t i o n s a r e examined.  A  procedure i s developed f o r s e l e c t i n g s p e c i f i c i n t e r a c t i o n s t o be i n c l u d e d i n t h e e s t i m a t e d model. some r e g a r d s  The r e s u l t s of t h e model a r e poor i n  and p o s s i b l e e x p l a n a t i o n s a r e d i s c u s s e d .  A second approach t o e s t i m a t i o n i s c a r r i e d out where t h e d a t a a r e p a r t i t i o n e d i n t o a number o f s u b s e t s .  W i t h i n each subset  t i o n s have a common r o o t s t o c k o r v a r i e t y . c a r r i e d out f o r each subset o f d a t a .  the observa-  Separate r e g r e s s i o n s are  T h i s approach proves t o be some-  what more s u c c e s s f u l and more emphasis i s put on i t s r e s u l t s i n t h e ensuing d i s c u s s i o n s .  4.1  Estimation  Strategy  G i v e n t h e a v a i l a b l e d a t a , t h e e s t i m a t i o n s t r a t e g y aims a t o b t a i n i n g 67  68 information  about as many o f t h e c o n c e p t u a l v a r i a b l e s as p o s s i b l e .  i s i m p r a c t i c a l , however, to p l a c e  a l l the v a r i a b l e s o f the c o n c e p t u a l  model i n t o a s i n g l e e q u a t i o n f o r e s t i m a t i o n . variables  There a r e a t o t a l o f 29  i n c l u d i n g i n t e r a c t i o n s and dummy v a r i a b l e s  available.  It  f o r which d a t a a r e  The l a r g e number of v a r i a b l e s p a r t i c u l a r l y the dummies and  i n t e r a c t i o n s l e a d s t o s e v e r e m u l t i c o l l i n e a r i t y problems (see s e c t i o n 4.3).  A further d i f f i c u l t y  i s that  f o r the c l a s s o f weather v a r i a b l e s  t h e r e a r e a number o f measures a v a i l a b l e f o r each concept. cumbersome complete model i t i s d i f f i c u l t each v a r i a b l e .  information  d i v i d i n g the e x p l a n a t o r y v a r i a b l e s of v a r i a b l e s  2.  from w i t h i n  Under the f i r s t groups:  constant w i t h i n  reduction  variables.  i n the reduction  i n t o groups and s e l e c t i n g s u b s e t s  s e t s each s e t c o n t a i n i n g  procedure the v a r i a b l e s a r e d i v i d e d  including physical features  of the orchards.  management  three  No attempt i s made t o although the  i n t h e e s t i m a t i o n s i s l e s s than i n the c o n c e p t u a l  model because o f d a t a l i m i t a t i o n s .  There a r e numerous weather v a r i a b l e s  they p r e s e n t some scope f o r a s e p a r a t e a n a l y s i s .  considering  into  variables  s e l e c t a p r i o r i a subset o f important management v a r i a b l e s  and  one o r  the s e t .  weather v a r i a b l e s , i n t e r a c t i o n s ' a n d  a c t u a l number i n c l u d e d  process:  each group.  p a r t i t i o n i n g the d a t a i n t o s m a l l e r more v a r i a b l e s  t h e e s t i m a t e d models, without  about any o f t h e important  Two g e n e r a l procedures a r e f o l l o w e d 1.  t o choose the b e s t measure of  Because o f these problems attempts a r e made t o reduce  the number of e x p l a n a t o r y v a r i a b l e s w i t h i n foregoing  W i t h i n the  weather f a c t o r s i n a s e p a r a t e a n a l y s i s  One advantage o f  i s that  observations  may be grouped to maximize between-group v a r i a t i o n i n weather w h i l e m i n i m i z i n g between-group v a r i a t i o n i n other i n p u t s .  variables  This  69 procedure  i s c a r r i e d out by grouping t h e d a t a i n t o t h r e e s e p a r a t e r e g i o n s  over the time p e r i o d regions i s s t i l l  of t h e sample.  The v a r i a t i o n i n weather between  r e t a i n e d w h i l e the v a r i a t i o n between average  l e v e l s of management v a r i a b l e s  i s g r e a t l y reduced.  regional  Regressions are  then c a r r i e d u s i n g o n l y t h e weather f a c t o r s as e x p l a n a t o r y v a r i a b l e s and the more important v a r i a b l e s  and t h e i r a p p r o p r i a t e measures a r e r e t a i n e d  f o r i n c l u s i o n i n a complete o r c h a r d l e v e l model (see s e c t i o n 4.2). Interactions  between v a r i a b l e s a r e d i f f i c u l t  to d e a l w i t h as a  s e p a r a t e group.  I t i s d e s i r a b l e t o reduce  g r e a t l y compound  the m u l t i c o l l i n e a r i t y problem (see s e c t i o n 4.3).  s e p a r a t e group a n a l y s i s highly  can be performed  c o r r e l a t e d with the basic  t h e i r number as they can  w i t h them because they a r e  inputs.  A procedure  i s developed  whereby a subset o f i n t e r a c t i o n s i s entered i n t o the e s t i m a t e d a l o n g w i t h managerial  equations  i n p u t s and the s e l e c t e d weather f a c t o r s .  i n t e r a c t i o n s are retained added and the procedure  from the s u b s e t , b e f o r e the next  repeated.  No  Specific  subset i s  The d i v i s i o n of i n t e r a c t i o n s  into  subsets and t h e s e l e c t i o n c r i t e r i a f o r s p e c i f i c i n t e r a c t i o n s a r e d e s c r i b e d i n s e c t i o n 4.3. An overview  of t h e r e d u c t i o n procedure  f o r a r r i v i n g a t a complete  o r c h a r d l e v e l model i n c l u d i n g t h e s e l e c t i o n o f weather v a r i a b l e and i n t e r actions  i s shown i n F i g u r e 4.1.  procedure  used  l e v e l model. point  T h i s f i g u r e i l l u s t r a t e s the stepwise  to a r r i v e a t a f i n a l subset o f v a r i a b l e s I t can be seen t h a t  f o r the o r c h a r d  every v a r i a b l e i s entered a t some  i n t h e e s t i m a t i o n s , which i s an advantage over an a p r i o r i  t i o n procedure.  As mentioned, v a r i a b l e s which have been entered  i n the p r o c e s s may tend to be s e l e c t e d stages.  reducearly  over those entered i n the l a t t e r  In o r d e r t o a s s e s s t h e degree o f s e l e c t i o n b i a s , t h e r o b u s t n e s s  1.  Estimate regional weather model  2.  S e l e c t subset of weather v a r i a b l e s  3.  Estimate l i n e a r orchard l e v e l model i n c l u d i n g weather v a r i a b l e s  4.  C l a s s i f y and rank i n t e r a c t i o n s a c c o r d i n g to a p r i o r i importance  average y i e l d per  5. Re-estimate e q u a t i o n including rootstock interactions 6.  y i e l d per acre  region  = f(weather  s e l e c t e d subset of weather v a r i a b l e s 4inputs, weather f physical + variable features subset rootstock interactions 4-  y i e l d per acre  f  weather inputs, physical + variable features subset  8.  S e l e c t subset of interactions  9.  Re-estimate i n c l u d i n g s o i l i n t e r a c t i o n s , keeping selected rootstock & age i n t e r a c t i o n s S e l e c t subset of s o i l interactions  11.  Re-estimate e q u a t i o n w i t h subsets of a l l three i n t e r a c t i o n categories F i g u r e 4.1.  y i e l d per acre  age  10'.  age interactions  soil interactions  rootstock  + interactions subset of r o o t stock i n t e r a c t i o n s  S e l e c t subset of r o o t stock i n t e r a c t i o n s  7. Re-estimate e q u a t i o n i n c l u d i n g age i n t e r a c t i o n s and s e l e c t e d rootstock interactions  variables)  y i e l d per acre  y i e l d per acre  weather subset of inputs, + age physical + variable + rootstock interactions interactions features subset 4subset of age interactions 4weather subset of •inputs, subset of rootstock + f physical + variable + age subset interactions features interactions f  f  inputs, weather physical + variable subset features  Overview of the E s t i m a t i o n Procedure  soil interactions  4subset of s o i l interactions 4subset of subset of subset of + soil rootstock + age interactions interactions interactions  o  71 of t h e f i n a l r e s u l t s a r e a l s o t e s t e d are  by changing t h e o r d e r i n which groups  entered i n t o t h e e s t i m a t i o n . Under t h e second r e d u c t i o n  illustrated  i n f i g u r e 4.1 i s c a r r i e d out w i t h one major  Instead of estimating functions  procedure t h e same stepwise procedure  functions  difference.  over t h e complete s e t o f d a t a ,  separate  a r e estimated f o r each t r e e s i z e c a t e g o r y and v a r i e t y .  In  o t h e r words each subset of data e x h i b i t s o b s e r v a t i o n s of a common s i z e or common v a r i e t y .  The t r e e s i z e v a r i a b l e s  t i o n s o r t h e v a r i e t y dummies a r e thus e l i m i n a t e d procedure a l s o tions  for  from each e q u a t i o n .  The  4.5) and a l l e v i a t e s m u l t i c o l l i n e a r i t y problems t o some  The procedure f o r choosing weather v a r i a b l e s  the p a r t i t i o n e d  over t h e f u l l  interac-  imposes l e s s r e s t r i c t i o n s on t h e b e h a v i o u r o f t h e i n t e r a c -  (see s e c t i o n  extent.  and r e l a t e d  tree-  functions  and i n t e r a c t i o n s  i s t h e same as f o r t h e f u n c t i o n  estimated  data s e t .  Other problems i n e s t i m a t i o n a r e r e l a t e d t o t h e d i s a g g r e g a t e d n a t u r e o f t h e d a t a , t h e s m a l l s i z e o f i n d i v i d u a l o b s e r v a t i o n s and d a t a partitioning. but  F o r most o f these problems t h e r e i s no immediate  solution  t h e i r e f f e c t s a r e d i s c u s s e d as they become apparent i n t h e e s t i m a t i o n s . The  sections. explaining  statistical  procedures and r e s u l t s a r e d i s c u s s e d i n f o l l o w i n g  Three b a s i c models a r e p r e s e n t e d :  (1) a weather model  r e g i o n a l v a r i a t i o n i n y i e l d s , (2) a f u l l model  explaining  v a r i a t i o n between o r c h a r d s , and (3) p a r t i t i o n e d models where i n d i v i d u a l functions  a r e e s t i m a t e d f o r each t r e e - s i z e c a t e g o r y and v a r i e t y .  The  e s t i m a t e d parameters of t h e weather model prove t o be s t a t i s t i c a l l y s i g n i f i c a n t and a subset o f weather v a r i a b l e s use.  i s selected  f o r further  The r e s u l t s from t h e complete o r c h a r d l e v e l model a r e poor by  some s t a n d a r d s , and p o s s i b l e  reasons f o r t h i s a r e d i s c u s s e d .  The  r e s u l t s from t h e p a r t i t i o n e d models a r e c o n s i d e r e d a c c e p t a b l e f o r the t r e e - s i z e c a t e g o r y f u n c t i o n s but a r e poor f o r t h e v a r i e t y c a t e g o r y tions.  I t i s concluded  func-  t h a t t h e main t h r u s t o f f u t u r e s t a t i s t i c a l  r e s e a r c h should c o n c e n t r a t e on f u n c t i o n s f o r t r e e s i z e c a t e g o r i e s and these r e s u l t s a r e d i s c u s s e d i n more d e t a i l than t h e o t h e r  4.2  estimates.  R e s u l t s f o r the Weather Model The purpose o f t h i s s e c t i o n i s t o e s t i m a t e a model o f apple produc-  t i o n f o r which v a r i a t i o n i n y i e l d  i s e x p l a i n e d s o l e l y by weather  The model i s used t o a s s e s s the impact  factors.  o f weather v a r i a b l e s and determine  the s t a t i s t i c a l s i g n i f i c a n c e o f v a r i o u s r e c o r d e d measure o f weather f a c t o r s which a r e a v a i l a b l e .  A subset o f weather v a r i a b l e s and t h e i r  a p p r o p r i a t e measures a r e s e l e c t e d f o r use i n e s t i m a t i n g t h e complete orchard l e v e l production f u n c t i o n . Y i e l d data f o r each o r c h a r d b l o c k was aggregated r e g i o n t o g i v e an annual area.  by year and by  average y i e l d p e r a c r e f o r t h r e e r e g i o n s i n t h e  Hence v a r i a t i o n i n t h e non-weather v a r i a b l e s i s reduced,  because  average v a l u e s o f these i n p u t s per r e g i o n a r e o b t a i n e d r a t h e r than i n d i v i d u a l v a l u e s f o r each b l o c k .  I n comparison, t h e v a r i a t i o n o f  weather v a r i a b l e s w i l l be l a r g e , because the d i f f e r e n c e s between y e a r s and r e g i o n s a r e not l o s t  i n aggregation.  T h i s procedure  may not com-  p l e t e l y i s o l a t e the e f f e c t s o f weather as t h e r e w i l l s t i l l be some v a r i a t i o n i n the average v a l u e s o f the o t h e r i n p u t s .  Because t h e r e may be  some c o r r e l a t i o n between weather v a r i a b l e s and l e f t - o u t v a r i a b l e s t h e r e w i l l be some b i a s i n the estimated  coefficients.  The dependent v a r i a b l e i s average p r o d u c t i o n p e r a c r e f o r each r e g i o n and year from 1967 t o 1974 i n c l u s i v e .  The r e g i o n s a r e Kelowna,  73 Summerland and O l i v e r .  The  p r o d u c t i o n from each o r c h a r d has been added  to the r e g i o n t h a t most c l o s e l y approximates i t s l o c a t i o n . To o b t a i n o b s e r v a t i o n s of the dependent v a r i a b l e from the sample i t was  necessary  to have both t o t a l sample y i e l d  sample p r o d u c i n g  acreage.  The  t o t a l y i e l d was  sample i n t o the t h r e e r e g i o n s and The  c a l c u l a t i o n of t o t a l acreage  f o r each r e g i o n and  total  o b t a i n e d by s o r t i n g  the  adding up p r o d u c t i o n f o r each y e a r . under p r o d u c t i o n i n each r e g i o n was  more  d i f f i c u l t because the l a g between the p l a n t i n g dates of the t r e e s and f i r s t year of commercial p r o d u c t i o n had y e a r s f o r standard f o r dwarfs and  t r e e s , f i v e y e a r s f o r semi-standards,  semi-dwarfs were used.  t r e e s p l a n t e d i n 1960 u n t i l 1966.  to be c o n s i d e r e d .  four years  would not be i n c l u d e d i n t o t a l p r o d u c i n g  standard acreage  i n the sample were not  was  available.  the n o n - d e f i n i t e b l o c k type, where t r e e s were h i g h l y  i n t e r m i x e d o r s c a t t e r e d throughout  the o r c h a r d .  Acreage of t h i s  f o r about 50% of the t o t a l sample acreage  O l i v e r and  and  A second problem i n the c a l c u l a t i o n of t o t a l acreage  T h i s acreage was  accounted  Lags of s i x  For example a b l o c k of  t h a t p l a n t i n g dates f o r c e r t a i n acreages  f o r about 20%  i n Kelowna.  I t was  type  i n Summerland  assumed t h a t t h i s  and  acreage  came i n t o p r o d u c t i o n i n the same p r o p o r t i o n s as the s p e c i f i c b l o c k of acreage.  the  For example i f p r o d u c i n g  i n c r e a s e d 20% between 1967  and 1968  acreage  i t was  of s p e c i f i c b l o c k  assumed t h a t p r o d u c i n g  from n o n - s p e c i f i c b l o c k s a l s o i n c r e a s e d by 20%.  The  calculated  of n o n - s p e c i f i c b l o c k s c o u l d be added to the known acreage  types  type acreage acreage  to g i v e a  t o t a l f o r each y e a r . The model shows t h a t a l l f o u r c a t e g o r i e s of blossom i n f l u e n c e s t e s t e d a r e important. and  f r o s t , a combination  The most a p p r o p r i a t e of these would be s u n l i g h t which has  the b e s t e x p l a n a t o r y power.  However,  due  to m i s s i n g r e c o r d s f o r s u n l i g h t i t w i l l be necessary  t u r e i n i t s p l a c e i n some e s t i m a t i o n s . f u r t h e r use  to use  tempera-  The v a r i a b l e s r e t a i n e d f o r  are:  1.  t e m p e r a t u r e — a c c u m u l a t e d degrees above 65 F. f o r a 10 day p e r i o d  2.  rainfall—in  3.  s u n l i g h t i n 1/10  4.  frost—accumulated and  31 F.,  1/100  i n c h e s f o r a f i v e day p e r i o d  hours f o r a 10 day p e r i o d degrees below c r i t i c a l l e v e l s of 27 F., 30  from the green t i p to green  fruit  F.,  stage.  In the f o l l o w i n g s e c t i o n s the s e l e c t e d weather v a r i a b l e s a r e i n c o r p o r a t e d i n t o an o r c h a r d l e v e l model where d i s a g g r e g a t e d f u n c t i o n s , i n c l u d i n g a l l i n p u t s , are  estimated.  Weather v a r i a b l e s t e s t e d i n t h i s model f a l l under f o u r c a t e g o r i e s : blossom s u n l i g h t , blossom temperatures, fall.  There a r e other i n f l u e n c e s t h a t should be c o n s i d e r e d  growing season heat a c c u m u l a t i o n , kill  rain-  especially  but data were not a v a i l a b l e .  Winter-  i n f l u e n c e s were not c o n s i d e r e d because t h e r e were no c r i t i c a l  s p e l l s d u r i n g the time covered the weather concepts The  blossom f r o s t and blossom  by the sample.  and measurements was  c o n c e p t u a l model can be summarized  cold  A d e t a i l e d d i s c u s s i o n of  g i v e n i n the p r e v i o u s  chapter.  as:  average r e g i o n a l _ f ( b l o s s o m s u n l i g h t , blossom temperatures, p r o d u c t i o n per a c r e blossom f r o s t , blossom r a i n f a l l ) In the r e s u l t s presented Mcintosh  a l l v a r i e t i e s w i t h the e x c e p t i o n of  and Newton a r e aggregated.  Thus the model does not t e s t f o r  d i f f e r e n c e s i n the manner t h a t s p e c i e s a r e a f f e c t e d by these weather variables.  Mcintosh  and Newton g e n e r a l l y bloom a t d i f f e r e n t times  the o t h e r s p e c i e s (which u s u a l l y bloom on the same date) and s e t s of weather v a r i a b l e s were compiled  f o r them.  than  different  However, no  separate  75 t  estimate  c o u l d be made f o r t h e Newton a p p l e v a r i e t y because of a l a c k of  observations. likely  Some t e s t s were made on M c i n t o s h  because of a s m a l l sample problem.  and proved u n s u c c e s s f u l ,  F o r most y e a r s and r e g i o n s  t h e r e were o n l y v e r y s m a l l acreages under Mcintosh  so t h e a v e r a g i n g  procedure was not v e r y e f f e c t i v e i n r e d u c i n g v a r i a t i o n i n non-weather inputs. A major problem apparent a f t e r a few e s t i m a t i o n s was t h e m u l t i c o l l i n e a r i t y between s u n l i g h t and temperature and between s u n l i g h t and rainfall.  Thus two b a s i c c a t e g o r i e s o f e s t i m a t i o n s were made:  (1)  e s t i m a t i o n s i n c l u d i n g s u n l i g h t but e x c l u d i n g temperature and r a i n f a l l , and  (2) e s t i m a t i o n s i n c l u d i n g temperature and r a i n f a l l  but e x c l u d i n g sun-  light . 4.2.1  Estimations Excluding Sunlight  As t h e r e were t h r e e d i f f e r e n t l e n g t h s o f blossom p e r i o d for  temperature and r a i n f a l l ,  s e v e r a l runs were undertaken i n o r d e r t o  f i n d t h e most a p p r o p r i a t e l e n g t h f o r each v a r i a b l e .  A consistent  r e s u l t was t h a t t h e l o n g e s t p e r i o d of 10 days was t h e most for  considered  significant  temperature and t h a t t h e s h o r t e s t l e n g t h of f i v e days was t h e most  significant  for r a i n f a l l .  T a b l e 4.1 shows t h e estimated  parameters f o r  these v a r i a b l e s . In t h e f i r s t e q u a t i o n  the f r o s t c a l c u l a t i o n with the higher  i c a l temperatures was used as i t w a s c o n s i s t e n t l y more s i g n i f i c a n t the f r o s t v a r i a b l e w i t h t h e lower c r i t i c a l temperatures. equation  shows f r o s t r e p r e s e n t e d  critthan  The second  by t h e t o t a l number o f days on which  temperatures o c c u r r e d below t h e c r i t i c a l l e v e l s , a measurement which gives s l i g h t l y  less significant  results.  S e v e r a l runs were made experimenting  with logarithmic values f o r  76 T a b l e 4.1.  Dependent V a r i a b l e  E s t i m a t e d F u n c t i o n s f o r Weather M o d e l — excluding sunlight  Production per acre  Independent V a r i a b l e  1  ( r e g i o n a l average) Coefficient 2 3  Constant  10462 (4.24)*  93936.4 (3.85)  10588 (4.30)  Accumulated degrees above 65°F--10 day period  807.18 (2.94)  889.96 (3.16)  814.31 (3.00)  Accumulated f r o s t below c r i t i c a l l e v e l of 27°F, 30°F and 31°F  -332.82 (-2.45)  11434.55 (3.26)  -343.1 (2.37)  -91.59 (-2.07)  T o t a l days on which f r o s t o c c u r r e d below c r i t i c a l levels  -1842.55 (-2.51)  Log of accumulated f r o s t below c r i t i c a l l e v e l R a i n over 5 day p e r i o d  4  -75.14 (-2.16)  -64.62 (-1.83)  -70.41 (-2.07)  -75.14 (-2.10)  Accumulated degrees a l o n e 6 5 ° F — f i r s t 5 days o f bloom  757.57 (2.46)  Accumulated degrees a l o n e 6 5 ° F — l a s t 5 days of bloom  758.87 (2.48)  R  2  .67  .64  *T s t a t i s t i c s a r e i n parentheses under estimated  .67  coefficients  .67  temperature,  r a i n f a l l and f r o s t .  F o r temperature and r a i n f a l l the  l o g a r i t h m i c forms g e n e r a l l y r e s u l t e d fit.  i n l e s s e r s i g n i f i c a n c e and poorer  The l o g form of f r o s t gave s l i g h t l y more s i g n i f i c a n t r e s u l t s  the l i n e a r form, as shown i n the t h i r d  than  equation.  Some e s t i m a t i o n s were c a r r i e d out d i v i d i n g the blossom p e r i o d i n t o two f i v e - d a y p e r i o d s and e n t e r i n g the compiled  v a r i a b l e s f o r each p e r i o d  in  the same e q u a t i o n .  in  s i g n i f i c a n c e between the e a r l i e r and l a t t e r p a r t of the f u l l blossom  period. for  The o b j e c t was to see i f t h e r e was any d i f f e r e n c e  The f o u r t h e q u a t i o n was estimated u s i n g temperature v a r i a b l e s  the f i r s t  appear almost  f i v e days and f o r the l a s t  f i v e days.  The two p e r i o d s  e q u a l i n t h e i r s i g n i f i c a n c e w i t h regards  to  temperature.  A s i m i l a r r u n was c a r r i e d out d i v i d i n g t h e blossom p e r i o d i n t o two for  rainfall.  most s i g n i f i c a n t  The r e s u l t s confirmed  t h a t the f i r s t  stages  f i v e days were t h e  f o r r a i n f a l l , and showed v e r y l i t t l e s i g n i f i c a n c e f o r  the l a t t e r f i v e days. 4.2.2  Estimations Including Sunlight  For some y e a r s and a r e a s , s u n l i g h t v a r i a b l e s c o u l d not be as r e c o r d s were m i s s i n g from the m e t e o r o l o g i c a l d a t a .  compiled  As a r e s u l t  only  12 o b s e r v a t i o n s were a v a i l a b l e f o r s u n l i g h t , l e a v i n g o n l y n i n e degrees of  freedom f o r most e s t i m a t i o n s . I t was found  through  s e v e r a l runs t h a t the l o n g e s t p e r i o d o f 10  days was the most a p p r o p r i a t e f o r s u n l i g h t , as i t was f o r temperature. The  first  c a l c u l a t i o n w i t h the h i g h e r c r i t i c a l temperatures  also  more a p p r o p r i a t e as was the case i n the p r e v i o u s e s t i m a t i o n s . r e s u l t s a r e shown i n the f i r s t t h i r d equations  e q u a t i o n i n t a b l e 4.2.  of t h i s t a b l e show the e f f e c t s of a  proved The  The second and  sunlight-temperature  index and of d i v i d i n g the s u n l i g h t v a r i a b l e i n t o two p e r i o d s .  Dependent  T a b l e 4.2.  E s t i m a t e d F u n c t i o n s f o r Weather including sunlight  Variable  P r o d u c t i o n per a c r e  Independent V a r i a b l e  ( r e g i o n a l average)  1  Constant  -10.250 (-2.40)*  Accumulated b r i g h t sunl i g h t d u r i n g 10 day p e r i o d 1/10 hours  26.96 (6.20)  Accumulated f r o s t below c r i t i c a l l e v e l s o f 27°F, 30°F and 31°F  -255.98 (-2.40)  Sunlight  temperature i n d e x * *  Model—  2  -10.013 (-2.38)  -10.129 (-2.17)  -226.64 (-1.94)  -235.18 (-1.61)  26.53 (6.26)  Accumulated b r i g h t s u n l i g h t d u r i n g f r o s t 5 day p e r i o d of bloom 1/10 hours  25.98 (2.86)  Accumulated b r i g h t s u n l i g h t d u r i n g l a t t e r 5 day p e r i o d of bloom 1/10 hour  27.50 (4.31)  R  2  Number o f o b s e r v a t i o n s  *T s t a t i s t i c s a r e i n p a r e n t h e s i s **Index = Temperature •5  Sunlight 2  .86  .87  .86  12  12  12  Because s u n l i g h t and temperature c o u l d be used i n the same equat i o n due to the c o l l i n e a r i t y between them, an attempt was made to comb i n e the two v a r i a b l e s i n t o a s i m p l e s u n l i g h t temperature i n d e x . Accumulated  degrees above 65 F. were m u l t i p l i e d by 10 t o b r i n g i t i n t o  the same o r d e r of magnitude  as s u n l i g h t and then was  s u n l i g h t , the t o t a l b e i n g d i v i d e d by two. of magnitude  added  Thus the index had an o r d e r  c l o s e to the o r i g i n a l s u n l i g h t v a r i a b l e .  seen i n the second e q u a t i o n i n t a b l e 4.2  The r e s u l t s as  show a m a r g i n a l l y  s i g n i f i c a n c e than the pure s u n l i g h t v a r i a b l e and a s l i g h t i n the  to hours of  better improvement  R. 2  As w i t h the temperature and r a i n v a r i a b l e s , t o t a l s u n l i g h t divided  i n t o two f i v e - d a y p e r i o d s .  same e q u a t i o n to t e s t  was  Both p e r i o d s were e n t e r e d i n the  f o r d i f f e r e n c e s i n importance between the e a r l i e r  and l a t t e r p a r t s of the blossom p e r i o d .  The r e s u l t s a r e shown i n the  t h i r d e q u a t i o n i n t a b l e 4.2 where i t can be seen t h a t the c o e f f i c i e n t s f o r each p e r i o d a r e v e r y c l o s e t o b e i n g e q u a l . 4.2.3  E f f e c t of Weather on D i f f e r e n t Grades of Apples  Some r e g r e s s i o n s to t e s t blossom i n f l u e n c e s on the amount of f e r e n t grades of a p p l e s were attempted.  P r o d u c t i o n was  divided  t o t a l e x t r a - f a n c y and t o t a l o f o t h e r grades e x c l u d i n g c u l l s . 4.3  shows t h e r e s u l t s f o r t h e s e e s t i m a t i o n s .  into  Table  I t can be seen t h a t t h e  model has l e s s s u c c e s s i n e x p l a i n i n g the v a r i a t i o n f o r i n d i v i d u a l c a t e g o r i e s than i t does f o r the t o t a l q u a n t i t y .  dif-  grade  I t has much h i g h e r  e x p l a n a t o r y power f o r the e x t r a - f a n c y c a t e g o r y than i t does f o r t h e r e m a i n i n g grades.  This fact  i s somewhat unexpected as t h e r e was  r e a s o n to expect t h a t blossom weather  influences f r u i t  quality.  no  80 T a b l e 4.3.  Estimated F u n c t i o n s f o r Weather M o d e l — D i f f e r e n t Grade C a t e g o r i e s  Dependent V a r i a b l e  l b s per a c r e XFLY Grade Independent V a r i a b l e  1  2  l b s per a c r e a l l o t h e r grades 1  2  Constant  3925.85 (3.22)  -5274 (-1.85)  6535 (3.15)  8303 (.57)  Accumulated f r o s t below c r i t i c a l levels  -114.33 (-1.76)  -60.01 (-.76)  -208.45 (-1.88)  -565.1 (-1.4)  Accumulated b r i g h t sunl i g h t 10 day p e r i o d 1/10 hour  11.56 (3.98)  1.27 (.08)  Accumulated degrees about 65°?'. 10 day period  412.69 (3.05)  394.50 (1.71)  Accumulated r a i n f a l l d u r i n g 5 day p e r i o d  -27.58 -1.61  -47.56 (-1.63)  R  2  Number o f o b s e r v a t i o n s  .62  .70  .47  .21  19  12  19  12  4.2.4 All yields. 1.  Conclusions  Regarding the Weather Model  f o u r v a r i a b l e c a t e g o r i e s have s i g n i f i c a n t  impacts upon t o t a l  A b r i e f d i s c u s s i o n of each of the c a t e g o r i e s f o l l o w s .  Temperature as measured by accumulated degrees above 65 F. p l a y s a s t r o n g r o l e i n p o l l i n i z a t i o n and t i o n s show a per a c r e .  'marginal  product'  A full  t e n day  Most  estima-  of temperature of at l e a s t 800  That i s an i n c r e a s e of one  blossom p e r i o d w i l l r e s u l t acre.  resulting yields.  lbs.  degree over 65°F. d u r i n g  i n an i n c r e a s e d y i e l d of 800  p e r i o d best r e p r e s e n t e d  l b s . per  temperature  influ-  ence, i n d i c a t i n g r . t h a t s i g n i f i c a n t p o l l i n a t i o n takes p l a c e i n the l a t t e r h a l f of the f u l l bloom p e r i o d .  This conclusion i s r e i n -  f o r c e d i n e s t i m a t i o n s where the p e r i o d i s d i v i d e d which show t h a t the f i r s t  and  second h a l v e s of the bloom p e r i o d are e q u a l l y  ant w i t h regards 2.  to the temperature v a r i a b l e .  T o t a l p r e c i p i t a t i o n d u r i n g the f i r s t has  import-  a s i g n i f i c a n t negative  h a l f of the f u l l bloom  impact upon y i e l d s .  Every  one  stage hundredth  of an i n c h which f a l l s d u r i n g t h i s time r e s u l t s i n a d e c r e a s e i n yield  of about 75 l b s . per a c r e .  The  f i n d i n g t h a t o n l y the  h a l f of the blossom p e r i o d i s s i g n i f i c a n t w i t h r e s p e c t t o seems to i n d i c a t e t h a t the blossoms and  than i n the l a t t e r p a r t — a  rainfall  p o l l e n are much more sus-  c e p t i b l e to damage by r a i n i n the e a r l i e r p a r t of the f u l l stage  first  bloom  f i n d i n g f o r which t h e r e does not  seem to be much s c i e n t i f i c b a s i s . 3.  S u n l i g h t has  the g r e a t e s t e x p l a n a t o r y  the v a r i a b l e s t e s t e d .  power and  s i g n i f i c a n c e of a l l  As a v a r i a b l e i t c o n t a i n s t h r e e  i n f l u e n c e s on p o l l i n i z a t i o n :  i t s own  c o r r e l a t i o n w i t h temperature, and  separate  influence, i t s positive  i t s negative  correlation  with  82 rainfall. day  I t was  period.  most s i g n i f i c a n t when c o n s i d e r e d over the f u l l  10  For every t e n t h of an hour of b r i g h t s u n l i g h t d u r i n g  the blossom p e r i o d p r o d u c t i o n per a c r e should i n c r e a s e by over  26  lbs. 4.  F r o s t has  a c o n s i s t e n t l y s i g n i f i c a n t e f f e c t on y i e l d s .  degree of f r o s t  from d a i l y minimum temperatures  would be expected The v a r i a b l e was  Every  below c r i t i c a l  to decrease y i e l d by a t l e a s t  225  levels  l b s . per a c r e .  more s i g n i f i c a n t when c r i t i c a l temperatures  were  put at s l i g h t l y h i g h e r l e v e l s than those e s t a b l i s h e d under t e s t  con-  ditions. In summary, w i t h R  2  v a l u e s r a n g i n g from .67  t h a t blossom and p o l l i n a t i o n  to  .87  i t i s evident  i n f l u e n c e s p l a y a major r o l e i n d e t e r m i n i n  average r e g i o n a l y i e l d per a c r e .  I t i s l i k e l y t h a t the R  2  v a l u e would b  Improved i f t h e r e were some a p p r o p r i a t e measure of wind d u r i n g blossom time.  Given more a c c u r a t e data on blossom dates and  v a l u e s would l i k e l y be s t i l l  4.3  The  Complete Orchard  acreages,  the  R  2  higher.  L e v e l Model  T h i s model i s of p r o d u c t i o n at the i n d i v i d u a l o r c h a r d or b l o c k l e v e l , and  each o b s e r v a t i o n i s of an i n d i v i d u a l b l o c k ' s p r o d u c t i o n r a t h e r  than a r e g i o n a l average. v a r i a b l e s , i n t e r a c t i o n s and f i g u r e 3.2  i n the p r e v i o u s  The next to  c o n c e p t u a l model i n c l u d i n g a l l measured  s e l e c t e d weather v a r i a b l e s was  summarized i n  chapter.  s t e p i n e s t i m a t i o n as shown p r e v i o u s l y i n f i g u r e 4.1  e s t i m a t e a l i n e a r form without  interactions. of  The  i n t e r a c t i o n s and  then'tes.t subsets  is of  T h i s i s c o n s i d e r e d n e c e s s a r y because of the l a r g e number  i n t e r a c t i o n s and  t h e i r tendency to cause m u l t i c o l l i n e a r i t y problems.  83 Interaction  terms are o f t e n c o r r e l a t e d w i t h one  between which the  i n t e r a c t i o n s are  when one of the v a r i a b l e s value.  This  occurring.  occurrence i s i l l u s t r a t e d  i n the  C o l l i n e a r i t y w i t h an  w i t h low  X!X  1  2  4  1  4  6  1  6  8  1  8  6  1  6  4  0  0  2  1  2  example shown i n t a b l e  Because t h e r e are many dummy v a r i a b l e s and felt  that entering  developed whereby the  model i n groups r a t h e r Interactions  a l l the For  other  variables  interactions in  the  t h i s reason a pro-  i n t e r a c t i o n s were entered i n t o  the  than a l l a t once.  were c l a s s i f i e d  i n t o t h r e e groups which were r o o t -  s t o c k or t r e e - s i z e i n t e r a c t i o n s , age  i n t e r a c t i o n s and  A linear regression  was  actions  A s i n g l e c l a s s o f i n t e r a c t i o n s was  included.  4.4.  c o r r e l a t e d w i t h the i n t e r -  model would l e a d to severe m u l t i c o l l i n e a r i t y . cedure was  a predominant  2  2  v a r i a t i o n i t was  true  Interaction  seen t h a t the v a r i a b l e x i i s h i g h l y 2  is especially  2  *1  a c t i o n x^x .  variables  i n t e r a c t i o n between xx and x  variables  can be  This  e x h i b i t s l i t t l e v a r i a t i o n or has  T a b l e 4.4.  It  or b o t h of the  then c a r r i e d out  a group i n t o the model and  any  specific  on the b a s i c  soil  interactions.  i n p u t s , no  inter-  then e n t e r e d  i n t e r a c t i o n s that  as  significantly  84 improved the r e g r e s s i o n was  then entered and  improved the  were r e t a i n e d .  any  next c l a s s of  f u r t h e r i n t e r a c t i o n s which  r e s u l t s were r e t a i n e d .  the procedure r e p e a t e d . were the  The  Two  The  significantly  f i n a l c l a s s was  important c o n s i d e r a t i o n s  i n t e r a c t i o n s from w i t h i n impact on the R ,  i n t h i s process  a priori  e x p e c t a t i o n s and  efficients.  for selecting  (adjusted  2  R ), 2  signs  or R  2  c u l t y i n using  2  and  using  i n f l u e n c e on  (U.C.L.A., 1977).  I t was  d e c i d e d not  co-  an diffi-  them to s e l e c t a subset from o n l y a p o r t i o n of the  these procedures i s the need to c o n s i d e r the s i g n s and  most important and  generally I f an  tude or the  s i g n i f i c a n c e of an  a  variable's  input  i t was I f an  Because the R felt  that  retained  i t was  groups are  s i g n , the magni-  regardless  accounts f o r the  2  a better 2  of how R  it  2  loss i n  c r i t e r i a to judge  statistic.  entered may  the  of  i n t e r a c t i o n improved the  i n t e r a c t i o n or group of i n t e r a c t i o n s than the R o r d e r i n which the  at l e a s t one  i n t e r a c t i o n improved the  the o t h e r c r i t e r i a .  degrees of freedom i t was  A second r e a s o n  c r i t e r i a were c o n s i d e r e d  i f a variable satisfied  retained.  usually retained.  vari-  magnitudes of o t h e r c o e f f i c i e n t s .  them i t was  fared against  to use  f o r s e l e c t i o n of i n t e r a c t i o n s because of the  In s e l e c t i n g s p e c i f i c i n t e r a c t i o n s two  The  of o t h e r  s e l e c t a subset of a s p e c i f i e d s i z e w i t h  a b l e s , meanwhile r e t a i n i n g a l l of the other v a r i a b l e s .  i t was  sign with  Some s t a t i s t i c a l procedures are a v a i l a b l e which w i l l  e x i s t i n g algorithm  not  specific  accordance of the  e f f e c t s on magnitudes and  s e a r c h a group of v a r i a b l e s the b e s t R  the o r d e r i n  each group i n c l u d i n g s t a t i s t i c a l s i g n i f i c a n c e ,  impact on R  2  and  regression.  There are a number of p o s s i b l e c r i t e r i a  for  entered  c r i t e r i a f o r r e t a i n i n g s p e c i f i c i n t e r a c t i o n s and  which the groups were entered i n the  interactions  i n f l u e n c e which  an  i n t e r a c t i o n s are e v e n t u a l l y r e t a i n e d , as the s i g n i f i c a n c e of an a c t i o n may I f two  inter-  depend to a great extent upon v a r i a b l e s a l r e a d y i n the model.  i n t e r a c t i o n s a r e h i g h l y c o r r e l a t e d the one  that i s entered  i n the r e g r e s s i o n w i l l u s u a l l y be the one r e t a i n e d i n the procedure  o u t l i n e d above.  the second  may  I f the f i r s t  first  selection  i n t e r a c t i o n improves the R ,  not because much of i t s i n f l u e n c e w i l l have a l r e a d y been  captured by the f i r s t An a p r i o r i  i n t e r a c t i o n due  t o the c o r r e l a t i o n between the  r a n k i n g of the importance  the groups were t e s t e d i n t h i s o r d e r . ranked most important,  of each group was  Rootstock  f o l l o w e d by age and  two.  made and  i n t e r a c t i o n s were  then by s o i l  interactions.  E n t e r i n g the groups i n t h i s o r d e r would tend to cause the r e t e n t i o n of i n t e r a c t i o n s of h i g h e r a p r i o r i earity.  The  importance  i n the event  extent of t h i s s e l e c t i o n b i a s was  o r d e r of e n t r y of v a r i a b l e s and  examining  of m u l t i c o l l i n -  examined by a l t e r i n g  the r o b u s t n e s s of the  the  final  results. The  e s t i m a t e d c o e f f i c i e n t s f o r the model u s i n g the complete s e t of  d a t a are shown i n t a b l e 4.5.  Two  l i n e a r e q u a t i o n s are shown a l o n g w i t h  an i n t e r a c t i v e form showing the f i n a l first  interactions selected.  l i n e a r form shows some evidence of a near  a second 4.3.1  e q u a t i o n i s e s t i m a t e d without Robustness of the  The  s i n g u l a r data matrix,  some of the troublesome  so  variables.  Estimates  The r o b u s t n e s s of the f i n a l r e s u l t s were t e s t e d by changing o r d e r t h a t groups of v a r i a b l e s were entered i n t o the stepwise Two  a l t e r n a t i v e o r d e r i n g s were t r i e d :  1.  the weather v a r i a b l e s were entered l a s t  2.  the order of e n t r y of i n t e r a c t i o n subsets was  ( i n s t e a d of  same order f o r a l l o t h e r groups of v a r i a b l e s .  the  procedure.  first),  r e v e r s e d keeping  the  86 T a b l e 4.5.  Estimated F u n c t i o n s f o r Complete Orchard  L e v e l Model  Dependent V a r i a b l e — l b s . p e r a c r e e x c l u d i n g c u l l s Independent Variable  U n i t of Measurement  Linear (1)  .54 x 1 0 (.01)*  Constant *  (2)  9  With Interactions  -9,983 (-4.90)  -24,568.C (-3.72)  Age  Indexed Age  10,597 (11.2)  10,496.1 (11.44)  -8,363 (-2.62)  Density  Trees p e r A c r e  53.9 (1.82)  54.7 (1.86)  -186.7 (-1.50)  Fertilizer  lbs.  174.4 (9.11)  176.4 (9.11)  718 (8.0)  Pesticides  Value p e r a c r e  192.9 (.98)  196.3 (.98)  526 (2.69)  Soil-type  Texture  -10,840.1 (-3.43)  42.131 (1.63)  Red  dummy  224.6 (.06)  -215.5 (.05)  -3510.0 (-1.09)  Mcintosh  dummy  -6451.2 (-1.39)  -7431.8 (-1.62)  -17296.6 (-4.44)  Newton  dummy  .10 x 1 0 (.01)  Spartan  dummy  15127.1 (2.39)  13650.2 (2.19)  -18540.1 (-2.96)  Winesap  dummy  12358 (.39)  10738.5 (.34)  4807.0 (.18)  Tydeman  dummy  14797.1 (2.20)  13319.8 (2.01)  12111.2 (2.01)  Spur-type  dummy  -9867.2 (-2.55)  -9746.7 (-2.53)  10529.9 (2.78)  Tree-size  dummy  1031.8 (2.00)  767.6 (1.58)  3945.8 (1.82)  Hedgerow planting  dummy  3869.3 (.88)  2429.1 (.60)  10810.8 (2.55)  Overhead irrigation  dummy  10860.9 (1.26)  8876.1 (1.03)  -2871.1 (-.38)  Trickle irrigation  dummy  -46545.5 (-5.6)  -48701.5 (-6.00)  -71763.5 (-8.82)  Delicious  per a c r e  index  -11,557.1 .(-3.37)  9  87 T a b l e 4.5.  (continued)  Unit of Measurement  Independent Variable  Frost  risk  Temperature bloom  during  Frost during  bloom  Rain during  bloom  Linear (1)  (2)  With Interactions  index  .54 x 1 0 (.01)  accumulated degrees F. above 65  239.5  239.1  252.9  accumulated degrees F. below c r i t i c a l levels  295.0 (.43)  315.1 (.46)  11947.4 (3.50)  1/100  312.4 (.06)  309.7 (.06)  -609.0 (-.15)  inches  8  Tree-size-fertilizer Interaction  -21.14 (-4.63)  Tree-size-density Interaction  15.0 (2.63)  Tree-size-frost Interaction  -299.3 (-2.90)  Tree-size-soil Interaction  557.0 (.69)  Age-fertilizer Interaction  57.9 (6.37)  Soil-fertilizer Interaction  -114.1 (-2.31)  Soil-density Interaction  -52.1 (-2.78)  R  2  .40  .40  .57  R  2  .38  .38  .55  503  503  503  Number o f Observations  *T-statistics  shown i n parentheses  Golden D e l i c i o u s  i s the base v a r i e t y  (with no dummy v a r i a b l e )  88 When t h e f i r s t change was c a r r i e d selected  occurred, i n d i c a t i n g  robust.  out no d i f f e r e n c e  t h a t t h e weather v a r i a b l e s  tree-size-soil interaction,  subset  are quite  However, when t h e o r d e r o f e n t e r i n g t h e i n t e r a c t i o n s  changed, some change i n t h e f i n a l v a r i a b l e s The  i n the f i n a l  and c o e f f i c i e n t s  was occurred.  which was o f low s i g n i f i c a n c e  i n the  o r i g i n a l e s t i m a t i o n , was e l i m i n a t e d and r e p l a c e d by an a g e - s o i l action.  An a g e - f r o s t i n t e r a c t i o n was a l s o  inter-  found t o have v i r t u a l l y t h e  same e f f e c t on t h e a d j u s t e d R , as d i d t h e t r e e - s i z e - f r o s t There were o n l y s l i g h t changes i n c o e f f i c i e n t s  interaction.  of o t h e r v a r i a b l e s , t h e  most n o t a b l e b e i n g t h a t of s o i l which dropped by about 10%, w i t h a s m a l l decrease i n t h e s i g n i f i c a n c e .  Overall  r e s u l t s were q u i t e r o b u s t , e s p e c i a l l y  when c o n s i d e r i n g t h e h i g h degree  of m u l t i c o l l i n e a r i t y  i t was f e l t t h a t t h e  i n the model.  4.3.2. M u l t i c o l l i n e a r i t y  Problems  Three o f t h e c o e f f i c i e n t s  i n t h e f i r s t l i n e a r e q u a t i o n have such  extreme v a l u e s t h a t i t i s expected t h e X'X m a t r i x i s s i n g u l a r singular, constant the  w i t h o n l y rounding e r r o r s  enabling i t s inversion.  (.54 x 1 0 ) , t h e dummy c o e f f i c i e n t 9  frost risk coefficient  (-.54 x 1 0  t h a t s i n g u l a r i t y must be expected. multicollinearity offsetting  including  coefficients.  1 0  t h e c o n s t a n t term.  The  f o r Newton (.10 x 1 0  ) exhibit  They a l s o  ) , and  such extreme v a l u e s  extremely l a r g e s t a n d a r d e r r o r s  and u n s t a b l e  I t was expected t h a t dummy v a r i a b l e s  were  because of t h e e f f e c t  Estimates of other c o e f f i c i e n t s  seem r e a s o n a b l e i n comparison t o t h e problem  1 0  show w e l l known s i g n s of  perhaps t h e g r e a t e s t source o f m u l t i c o l l i n e a r i t y on  or near-  i n the equation  variables.  There was n o t much t h a t c o u l d be done t o overcome t h i s problem except t o exclude some o f t h e troublesome v a r i a b l e s  from t h e r e g r e s s i o n .  89 The  exclusion  of f r o s t r i s k was a t l e a s t p a r t i a l l y j u s t i f i e d by t h e o f f -  s e t t i n g e f f e c t of t h e f r o s t p r e v e n t i o n system w i t h which i t i s h i g h l y correlated.  The Newton dummy was a l s o excluded and the model r e -  e s t i m a t e d as i n the  second e q u a t i o n .  dummy and f r o s t r i s k c o u l d  The low T - v a l u e s o f t h e Newton  not be taken as j u s t i f i c a t i o n f o r d r o p p i n g  these v a r i a b l e s because they c o u l d w e l l be due t o m u l t i c o l l i n e a r i t y rather  than i n s i g n i f i c a n c e of the v a r i a b l e s .  However, the o t h e r  f i c i e n t s estimated i n t h e second e q u a t i o n do not show a great from those i n the f i r s t The was  e q u a t i o n except f o r t h e c o n s t a n t  i n t e r a c t i o n t e s t i n g procedure as d e s c r i b e d  c a r r i e d out and s e v e r a l  actions signs  difference  term.  i n s e c t i o n 4.2  i n t e r a c t i o n s were r e t a i n e d .  p r e s e n t e d i n t h e t h i r d e q u a t i o n on t a b l e 4.5.  The r e s u l t i s  The i n c l u s i o n o f i n t e r -  s u b s t a n t i a l l y improves the model a l t h o u g h t h e r e a r e s t i l l  of m u l t i c o l l i n e a r i t y .  t e s t e d because they r e s u l t e d  coef-  some  No i n t e r a c t i o n s w i t h p e s t i c i d e s c o u l d be i n a singular or near-singular  data matrix.  There are both a l a r g e number o f v a r i a b l e s and s i g n i f i c a n t c o r r e l a t i o n s between s e v e r a l coefficient  inputs.  F e r t i l i z e r and p e s t i c i d e have a c o r r e l a t i o n  o f .71, d e n s i t y  tree size i s negatively  and t r e e - s i z e have a c o r r e l a t i o n o f -.75,  c o r r e l a t e d w i t h p l a n t i n g concept w i t h a c o e f f i c -  i e n t of .61 and s o i l i s n e g a t i v e l y c o e f f i c i e n t o f -.6.  correlated with t r e e - s i z e with a  As f r o s t r i s k and f r o s t p r e v e n t i o n were almost  p e r f e c t l y c o l l i n e a r only  one of them was i n c l u d e d  a t one time.  There a r e t h r e e o p t i o n s i n d e a l i n g w i t h m u l t i c o l l i n e a r i t y . (1) Ignore i t and accept t h e e s t i m a t e d c o e f f i c i e n t s , (2) t r y t o o b t a i n d a t a w i t h l e s s c o r r e l a t i o n between v a r i a b l e s , o r (3) l e a v e out some o r all  of t h e o f f e n d i n g  v a r i a b l e s , perhaps making some allowance f o r t h e i r  i n f l u e n c e on t h e dependent v a r i a b l e . .  The f i r s t  option  i s not n e c e s s a r i l y  90 undesirable  as some s t u d i e s have o b t a i n e d r e a s o n a b l y p r e c i s e  c o e f f i c i e n t s despite ables  h i g h c o r r e l a t i o n s between p a i r s o f independent  (Johnston, 1972).  is unfeasible  The second o p t i o n  f o r t h i s research  i n a l o n g e r term p r o j e c t .  specification bias.  first  a l t h o u g h i t would warrant  i s followed,  consideration  of l e a v i n g out some o r  some atonement must be made  There a r e s e v e r a l suggested p r o c e d u r e s .  i s t o t r e a t t h e e s t i m a t e d c o e f f i c i e n t s as r e p r e s e n t i n g  e f f e c t s of the i n c l u d e d  v a r i a b l e s and t h e c o r r e l a t e d  T h i s approach i s u n d e s i r a b l e required.  vari-  of t r y i n g t o o b t a i n more d a t a  I f the t h i r d option  a l l of the troublesome v a r i a b l e s for  estimates of  The  the combined  left-out variables.  i f the s p e c i f i c e f f e c t o f each v a r i a b l e i s  The c o n d i t i o n a l or r e s t r i c t e d l e a s t squares method has o f t e n  been used i n d e a l i n g w i t h m u l t i c o l l i n e a r i t y (Kmenta, 1971).  I f the  c o e f f i c i e n t s o f some o f t h e v a r i a b l e s a r e known or can be e s t i m a t e d i n advance, the e f f e c t s of the v a r i a b l e s v a r i a b l e and a r e g r e s s i o n  can be removed from t h e dependent  c a r r i e d out on the remaining v a r i a b l e s .  t e c h n i q u e i s used f o r a few s p e c i f i c i n s t a n c e s t i o n 4.4. nique.  i n t h i s research  This  i n sec-  Another p o s s i b l e method i s t o use a stepwise r e g r e s s i o n  The troublesome v a r i a b l e s may be l e f t  out and a  regression  c a r r i e d out on the remaining v a r i a b l e s .  The r e s i d u a l s from t h i s  s i o n a r e then r e g r e s s e d on t h e p r e v i o u s l y  left-out variables.  e s t i m a t e of the i n f l u e n c e  of t h e f i r s t  tech-  regres-  An  set of l e f t - o u t v a r i a b l e s  on t h e  o r i g i n a l dependent v a r i a b l e can be made from t h e i r i n f l u e n c e on t h e r e s i d u a l s a l t h o u g h the c o e f f i c i e n t s cannot u s u a l l y be e x a c t l y The  determined.  procedure used i n t h i s t h e s i s i s t o use a subset o f d a t a over  which one or more v a r i a b l e s the r e g r e s s i o n .  a r e c o n s t a n t so they can then be l e f t  out of  Unbiased c o e f f i c i e n t s can then be o b t a i n e d f o r t h e  remaining v a r i a b l e s a l t h o u g h they a r e c o n d i t i o n a l on the l e v e l o f t h e  91 constant v a r i a b l e s i f i n t e r a c t i o n s between the constant and variables exist.  T h i s approach of p a r t i t i o n i n g the d a t a has  advantages b e s i d e s a l l e v i a t i n g m u l t i c o l l i n e a r i t y and detail i n section 4.3.3  non-constant other  i s pursued  i n more  4.5.  E f f e c t s of D i s a g g r e g a t i o n  A reason f o r the low R n a t u r e of the d a t a .  2  i n the model may  be the  disaggregated  The v a r i a b l e s a r e d i s a g g r e g a t e d  and  the s i z e of  i n d i v i d u a l o b s e r v a t i o n s are s m a l l as they a r e of s p e c i f i c b l o c k s o f t e n under an a c r e i n s i z e . i n econometric  D i s a g g r e g a t i o n i s o f t e n thought  s t u d i e s (Johnston,  1972)  and  of as d e s i r a b l e  i s r e q u i r e d i n t h i s work i n  o r d e r to o b t a i n u s e f u l i n f o r m a t i o n about o r c h a r d systems. some d i s a d v a n t a g e s ,  however.  There a r e  By d i s a g g r e g a t i n g v a r i a b l e s the  o b s e r v a t i o n s tend t o become much s m a l l e r i n terms of acreage r e l a t i v e e f f e c t s of s t o c h a s t i c i n f l u e n c e s become g r e a t e r . have the e f f e c t  of i n c r e a s i n g the standard e r r o r s and  c i s i o n of the e s t i m a t e s . s t o c h a s t i c element tends  individual  and  the  This  may  l o w e r i n g the p r e -  I f o b s e r v a t i o n s a r e grouped the e f f e c t of to average out f o r each group.  group of o b s e r v a t i o n s , the more a v e r a g i n g w i l l  The  larger  1976;  Lee,  1972)  c e r t a i n extent.  have used grouped data and Observations  the  take p l a c e and w i t h v e r y  l a r g e groups the s t o c h a s t i c e f f e c t s w i l l be v e r y s m a l l (Johnston, Previous production f u n c t i o n estimates  the  f o r Okanagan a p p l e s aggregated  1972). (Campbell,  i n p u t s to a  were grouped i n t h a t each o r c h a r d  counted  as a s i n g l e o b s e r v a t i o n d e s p i t e having d i f f e r e n t v a r i e t i e s , r o o t s t o c k s and  p l a n t i n g systems.  Aggregation  v a l u e or c a p i t a l index was estimated may  c a r r i e d out to a c e r t a i n e x t e n t .  f u n c t i o n s had h i g h e r R  be accounted  of v a r i o u s s p e c i f i c i n p u t s i n t o a  2  v a l u e s i n the  f o r by the a g g r e g a t i o n and  .65 to  grouping.  Their  .80 range which  92 4.4  T r e e - s i z e and V a r i e t y F u n c t i o n s The  to  second major method of e s t i m a t i n g the p r o d u c t i o n f u n c t i o n s i s  group the d a t a by t r e e - s i z e or v a r i e t y and  t i o n f o r each group.  estimate a separate  func-  The main reason f o r doing t h i s i s to reduce  number of v a r i a b l e s w i t h i n each e q u a t i o n .  By e s t i m a t i n g t r e e - s i z e  f u n c t i o n s a l a r g e number of i n t e r a c t i o n s c o n c e r n i n g r o o t s t o c k can e l i m i n a t e d as e x p l a n a t o r y v a r i a b l e s . r o o t s t o c k was  the  Tree s i z e , as determined  c o n s i d e r e d the major source of i n t e r a c t i o n s , and  be  by by  d i v i d i n g the d a t a i n t o t r e e - s i z e c a t e g o r i e s , the i n t e r a c t i o n s can  be  seen by comparing c o e f f i c i e n t s of the f o u r s e p a r a t e e q u a t i o n s , r a t h e r than h a v i n g them as s e p a r a t e terms i n the r e g r e s s i o n .  T h i s i s an  advantage as i n t e r a c t i o n s when entered as s e p a r a t e terms tend t o compound the m u l t i c o l l i n e a r i t y problem.  There may  w i t h i n each of the dwarf, semi-dwarf and  be some v a r i a t i o n i n r o o t s t o c k  semi-standard  i t s r e l a t i v e e f f e c t on t r e e - s i z e i s s m a l l .  c a t e g o r i e s , but  When the equations  are  e s t i m a t e d f o r each v a r i e t y the s i x v a r i e t y dummies can be e l i m i n a t e d which i s advantageous as dummy v a r i a b l e s were l e a d i n g t o n e a r - s i n g u l a r i t y i n the e s t i m a t i o n of a f u n c t i o n over the complete d a t a s e t . Another advantage of grouping the d a t a f o r s e p a r a t e r e g r e s s i o n s i s r e l a t e d to i n t e r a c t i o n s .  While  an i n t e r a c t i o n may  be r e p r e s e n t e d as a  s i n g l e term i n an e q u a t i o n t h i s assumes t h a t the i n t e r a c t i o n has c o n s t a n t c o e f f i c i e n t , and  the i n t e r a c t i v e e f f e c t of the two  a  inputs  depends o n l y on the s i z e of the i n t e r a c t i o n term and not on the magnitude of e i t h e r of the i n p u t s .  By e s t i m a t i n g s e p a r a t e equations f o r  each t r e e - s i z e c a t e g o r y , t h i s assumption interactions. and  tree size.  i s r e l a x e d f o r the  For example c o n s i d e r an i n t e r a c t i o n between I t i s p o s s i b l e that f e r t i l i z e r  tree-size fertilizer  has a h i g h m a r g i n a l  93 p h y s i c a l product on dwarf, semi-dwarf and m a r g i n a l p h y s i c a l product  s t a n d a r d v a r i e t i e s , and  f o r semi-standards.  A tree-size  a  low  fertilizer  i n t e r a c t i o n i n a s i n g l e e q u a t i o n c o u l d not c a p t u r e t h i s e f f e c t , whereas s e p a r a t e e q u a t i o n s f o r each t r e e - s i z e c a t e g o r y c o u l d . An a d d i t i o n a l advantage of e s t i m a t i n g t r e e - s i z e f u n c t i o n s i s t h a t the m u l t i c o l l i n e a r i t y between d e n s i t y and  t r e e - s i z e over the whole sample  i s no l o n g e r a problem as t r e e s i z e i s n e a r l y c o n s t a n t w i t h i n each equation. 4.4.1  R e s u l t s f o r the T r e e - s i z e F u n c t i o n s  Most of the s t a t i s t i c a l of  e a r l y encouraging  four categories: estimated.  emphasis i s on t r e e - s i z e f u n c t i o n s because  r e s u l t s w i t h t h i s form.  Production functions for  dwarf, semi-dwarf, semi-standard  It i s s t i l l  p o s s i b l e to observe  and  standard  some v a r i a t i o n i n t r e e s i z e  w i t h i n these c a t e g o r i e s a l t h o u g h i n the sample o n l y the  semi-standard  c a t e g o r y has more than one r o o t s t o c k on which the s t a t i s t i c a l based.  Hence t r e e - s i z e as an independent  semi-standard In  are  v a r i a b l e appears  index i s  o n l y i n the  category.  g e n e r a l , p a r t i t i o n i n g the d a t a by t r e e - s i z e causes  problems than p a r t i t i o n i n g by v a r i e t y .  For the dwarf and  less serious semi-dwarf  c a t e g o r i e s t h e r e i s no problem w i t h m u l t i c o l l i n e a r i t y , t h e r e i s adequate v a r i a t i o n i n most i n p u t l e v e l s  (although some i n p u t s a r e c o n s t a n t ) , and  t h e r e i s a l a r g e number of o b s e r v a t i o n s . s t a n d a r d c a t e g o r i e s t h e r e i s troublesome important  inputs:  For the standard and  c o r r e l a t i o n s between t h r e e  f e r t i l i z e r , p e s t i c i d e and d e n s i t y .  A fourth v a r i -  a b l e , s o i l - t y p e a l s o causes problems, showing some degree of with these three v a r i a b l e s . of  semi-  For semi-standard  correlation  t h e r e are a l a r g e number  o b s e r v a t i o n s , but f o r the standard c a t e g o r y t h e r e are o n l y twenty.  94 As s e v e r a l i n p u t s a r e c o n s t a n t f o r s t a n d a r d they cannot the r e g r e s s i o n , so the degrees Dwarf and  of freedom problem i s not too s e r i o u s .  Semi-Dwarf C a t e g o r i e s .  the weather model are e n t e r e d , and procedure  as was  be entered i n  S e l e c t e d weather v a r i a b l e s  i n t e r a c t i o n s are t e s t e d i n a  stepwise  done i n the f u n c t i o n f o r the complete d a t a s e t .  r e s u l t s f o r the dwarf and  from  The  semi-dwarf c a t e g o r i e s are shown i n t a b l e  4.6.  For the dwarf e q u a t i o n s p e s t i c i d e c o s t i s c o n s t a n t a t $65 per a c r e , a l l r o o t s t o c k s are M.M.  26,  frost  p l a n t e d i n hedgerow d e s i g n .  i s zero and a l l observed  b l o c k s were  For the semi-dwarf c a t e g o r y  a r e a g a i n c o n s t a n t a t $65 per a c r e , a l l r o o t s t o c k s are M.M. s o i l i s r a t e d as two  ( c l a y ) on the t e x t u r e i n d e x .  pesticides 7 and a l l  A l l equations  are  e s t i m a t e d w i t h O.L.S. For both c a t e g o r i e s l i n e a r and o n l y i n t e r a c t i o n term found  i n t e r a c t i o n forms are g i v e n .  to be s i g n i f i c a n t was  The  a g e - f e r t i l i z e r which  -2 s u b s t a n t i a l l y improves the R  f o r both c a t e g o r i e s .  Signs of a l l co-  e f f i c i e n t s are c o n s i s t e n t w i t h a p r i o r i e x p e c t a t i o n s w i t h the p o s s i b l e e x c e p t i o n of f e r t i l i z e r  i n the i n t e r a c t i v e form f o r semi-dwarf and  i n t h e ' i n t e r a c t i v e forms f o r b o t h c a t e g o r i e s .  However, when the  a c t i v e terms a r e c o n s i d e r e d the m a r g i n a l p r o d u c t s of both age fertilizer  age inter-  and  a r e p o s i t i v e over most of the range of these v a r i a b l e s .  a g e - f e r t i l i z e r i n t e r a c t i o n indicates that f e r t i l i z e r  has a lower  The  marginal  product when t r e e s are i n t h e i r f o r m a t i v e y e a r s than f o r t r e e s i n the bearing  stage.  Most of the e s t i m a t e d c o e f f i c i e n t s d i s p l a y h i g h degrees icance. variables.  E x c e p t i o n s a r e the v a r i e t y dummies and The  the f r o s t and  o n l y v a r i e t y dummy s i g n i f i c a n t a t the  Tydeman i n the dwarf e q u a t i o n s .  The  s o i l and  of  signif-  soil  .01 l e v e l  was  f r o s t v a r i a b l e s , w h i l e not  95 T a b l e 4.6.  E s t i m a t e d F u n c t i o n s f o r Dwarf and Semi-dwarf  Dependent V a r i a b l e — l b s . p e r a c r e e x c l u d i n g  Independent Variable  Unit of Measure  Constant  Age  indexed age  Density  trees per acre  Fertilizer  l b s . per a c r e  Soil-type  texture  Red  index  D e l i c i o u s dummy  Categories  culls  Dwarf Category With I n t e r Linear action  Semi-dwarf Category With InterLinear action  -193,563.0 (-4.20)*  -66,443. 6 (1.53)  -187,092.0 (-4.32)  -76,043.0 (1,87)  14,319.3 (11.87)  -21,702. 8 (-4.37)  10,984.4 (10.54)  -18,984.9 (-4.23)  21.3 (.34)  21. 3 (.40)  310.3 (3.03)  388.0 (4.36)  3. 21 (.05)  86.7 (1.24)  -318.8 (-3.77)  372.1 (9.18) -14,289.8 (-.93)  -7,547 (-.57)  9,085.0 (1.58)  9,084. 4 (1.83)  -1,227,4 (-.25)  -1,227.4 (-.29)  Mcintosh  dummy  252.0 (.04)  252. 0 (.04)  -9,086.1 (-1.43)  -9,097.3 (-1.66)  Spartan  dummy  -9,978.9 (-1.16)  -9,979. 0 (-1.35)  -8,219.0 (-.92)  -8,219.3 (1.07)  Tydeman Red  dummy  21,830.6 (2.54)  21,830. 5 (2.95)  2,699.0 (.30)  2,699.7 (.35)  Spur Type  dummy  4,307.8 (.67)  4,307. 9 (.77)  3,580.3 (.70)  3,580.2 (.80)  Overhead Irrigation  dummy  27,513 (2.14)  Trickle Irrigation  dummy  -24,313.9 (-1.83)  -27,076.0 (-2.37)  Hedgerow Planting  dummy  27,583.9 (2.20)  35,450.4 (3.27)  Frost Bloom  Accumulated Degrees F.  -1,737 (-.25)  during  34,502.0 (3.12)  -524.8 (-.09)  96 T a b l e 4.6  (continued)  Independent Variable  Unit of Measure  Sunlight 1/10 hours d u r i n g Bloom  Dwarf Category With I n t e r Linear action  50.1 (5.53)  Age-fertilizer Indexed age Interaction X lbs./acre R  2  R  2  Number o f Observations  50.6 (6.40)  Semi-dwarf Category With I n t e r Linear action  46.5 (5.85)  99.3 (7.42) .69  170  .77  170  87.7 (6.82) .74  144  * T - s t a t i s t i c s shown i n parentheses Golden D e l i c i o u s i s the base v a r i e t y  46.7 (6.83)  (with no dummy v a r i a b l e )  .81  144  s i g n i f i c a n t are c o n s i s t e n t i n both equations and were thus r e t a i n e d . The poor s i g n i f i c a n c e of these v a r i a b l e s may  be due  to the f a c t t h a t both  are proxy measures. G e n e r a l l y the dwarf and  semi-dwarf f u n c t i o n s a r e more s a t i s f a c t o r y  than the f u n c t i o n f o r the f u l l data s e t . power, s i g n i f i c a n c e of c o e f f i c i e n t s and a l l higher.  T h i s i s p r o b a b l y due  The degree of e x p l a n a t o r y consistency with expectations are  to some of the advantages  e a r l i e r i n c l u d i n g l e s s m u l t i c o l l i n e a r i t y and f i c i e n t s and  listed  l e s s r e s t r i c t i o n s on c o e f -  interactions.  Semi-standard  and  Standard.  a c t i v e forms f o r the semi-standard s t a n d a r d c a t e g o r y e q u a t i o n and  T a b l e 4.7 and  standard c a t e g o r i e s .  interFor  the  f o r the s o u t h e r n r e g i o n e q u a t i o n f o r semi-  s t a n d a r d , c o n d i t i o n a l l e a s t squares  e s t i m a t e s , where an adjustment  been made f o r p e s t i c i d e s , have been used. dure are d i s c u s s e d below.  shows l i n e a r and  The  reasons  for this  has proce-  O r d i n a r y l e a s t squares have been used  f o r the  remaining e s t i m a t i o n s . The  first  l i n e a r e q u a t i o n f o r semi-standard  several regards.  The  i s unsatisfactory i n  s i g n s of two v a r i a b l e s , f e r t i l i z e r  and  frost,  are  wrong on a p r i o r i grounds, l e v e l s of s i g n i f i c a n c e a r e low f o r most v a r i a b l e s and  the R  2  i s l e s s than h a l f of what i t i s f o r the dwarf and  dwarf c a t e g o r i e s .  The poor r e s u l t s may  be p a r t i a l l y due  to m u l t i -  c o l l i n e a r i t y , p a r t i c u l a r l y the wrong s i g n on f e r t i l i z e r which has f a i r l y high c o r r e l a t i o n may  be l e f t  (.80)  out v a r i a b l e s and  with p e s t i c i d e s . interactions.  i n c l u d e d , however, the e q u a t i o n s t i l l for  fertilizer  semi-  a  Other p o s s i b l e causes When the i n t e r a c t i o n s  shows a n e g a t i v e m a r g i n a l  are  product  although i n o t h e r a s p e c t s the e q u a t i o n i s improved.  Another p o s s i b l e reason f o r the poor r e s u l t s i s t h a t w i t h i n the  T a b l e 4.7.  Dependent  Estimated F u n c t i o n s f o r Standard and S emi—Standard C a t e g o r i e s  V a r i a b l e — l b s . per a c r e e x c l u d i n g  Independent Variable  Unit of Measure  Constant  culls  Semi-Standard With Southern InterRegion Linear actions Linear  -59381.1 35098.1 (-.06)* (.33)  125141.3 (2.80)  -10794.5 (1.01)  11252.2 (.46)  2415.2 (.95)  965.0 (2.95)  -785.2 (-.62)  7.67 -56.0 (.19) (-1.10)  133.8 (1.06)  133.9 (1.07)  .70 (.08)  40.9 (.91)  35.1 (2.60)  -3.02 (-1.95)  -4858.8 (-1.56)  Age  indexed age  Density  trees per acre  Fertilizer  l b s . per acre  -11.8 (-2.56)  Pesticides  $ value per a c r e  6.7 (.26)  -320.8 (-1.78)  Soil-type  texture index  -2746.0 (-2.32)  -2086.1 (-1.80)  -4837.1 (-.35)  Red D e l i c i o u s  dummy  673.1 (.89)  811.0 (1.05)  20481.3 (2.94)  Mcintosh  dummy  373.3 (.30)  872.3 (.79)  302.8 (.04)  Newton  dummy  637.4 (.03)  -2215.7 (-.12)  Spartan  dummy  -930.4 (.09)  -3854.4 (-.36)  Winesap  dummy  3670.8 (.35)  12228.0 (1.08)  Tydeman Red  dummy  790.0 (.15)  6184.5 (.39)  Spur-type  dummy  138.4 (.15)  683.2 (.81)  Hedgerow Planting  dummy  3017*0 (.90)  12468.8 (2.55)  746.6 (3.54) 10.0 (.26)  Standard With InterLinear actions  -1970.6 (-1.01)  -3930.0 (-1.74)  19084.2 (1.10)  -4860.0 (-1.56)  99 T a b l e 4.7 (continued)  Independent Variable  Unit of Measure  Linear  Semi-Standard With Southern InterRegion actions Linear  -566.4 (-.18)  Standard With InterLinear actions  -3930.0 (-2.60)  Tree-size  s i z e index  Temperature  accumulated degrees above 65°F.  -.05 (-.05)  -.6 (-.47)  39.8 (.59)  29.8 (.55)  Frost  accumulated 305.3 degrees below (3.23) critical level  -4715.8 (-2.66)  438.2 (2.01)  -127.3 (-1.78)  Rain  1/100 i n c h e s --1060.0 (-.87)  -1327.2 (-1.02)  -2129.3 (-.28)  -2135.3 (-.28)  Age P e s t i c i d e Interaction  59.8 (1.80)  Age F e r t i l i z e r Interaction  .37 (1.54)  8.7 (3.10)  Age-Frost Interaction  277.0 (2.55)  3.2 (2.29)  R  2  .26  •54  .64  .54  .69  R  2  .19  .44  .43  .25  .38  194  194  30  19  19  Number of Observations  * T - s t a t i s t i c s shown i n parentheses Golden D e l i c i o u s  i s t h e base v a r i e t y  (with no dummy v a r i a b l e ) -  100 semi-standard  category there i s s t i l l  substantial variation i n tree size.  U n l i k e the dwarf, semi-dwarf and standard samples which each c o n t a i n o n l y r o o t s t o c k , t h e r e a r e t h r e e r o o t s t o c k s i n the semi-standard  sample.  In  o r d e r t o see i f t h i s v a r i a t i o n was the cause o f the poor r e s u l t s t h e data were d i v i d e d i n t o t h r e e groups where t h e r o o t s t o c k was constant w i t h i n each group.  Separate  r e g r e s s i o n s were then c a r r i e d out f o r each  of these s u b d i v i s i o n s o f semi-standard.  These e s t i m a t i o n s were o n l y  m a r g i n a l l y b e t t e r than t h e e s t i m a t i o n f o r the whole of  semi-standard  samples. Another p o s s i b l e cause o f the poor r e s u l t s was the m i x t u r e of experimental Semi-standard  data from t h e r e s e a r c h s t a t i o n w i t h the o r c h a r d survey was d i f f e r e n t  data.  from dwarf and semi-dwarf i n t h a t a much  h i g h e r p r o p o r t i o n o f t h e t o t a l o b s e r v a t i o n s was from t h e o r c h a r d About 40% o f the semi-standard  o b s e r v a t i o n s were from the o r c h a r d  survey. survey  w h i l e o n l y about 15% of the dwarf and semi-dwarf o b s e r v a t i o n s were from the o r c h a r d survey.  The e x p e r i m e n t a l  data f o r semi-standards  also  c o n s i s t e d o f v e r y s m a l l p l o t s , about 1/10 of an a c r e i n s i z e , and t h i s r e l a t i v e smallness might have r e s u l t e d  i n higher s t o c h a s t i c i n f l u e n c e s .  There might a l s o be d i f f e r e n c e s i n the l e f t - o u t v a r i a b l e s , management and  l a b o u r , between the e x p e r i m e n t a l  p l o t s and the commercial  which would l e a d t o d i f f e r e n c e s i n the estimated inputs.  orchards  c o e f f i c i e n t s of other  When t h e two types of data a r e combined the r e s u l t s would be  some average c o e f f i c i e n t s of lower p r e c i s i o n . experimental  To see i f i t was the  data t h a t was c a u s i n g the poor r e s u l t s i t was d e c i d e d t o  e s t i m a t e a f u n c t i o n u s i n g o n l y the o r c h a r d survey data from the southern region.  The reason  f o r u s i n g o n l y t h i s r e g i o n (which  50% o f t h e survey data f o r semi-standards)  contained  about  was t o t r y t o a v o i d some o f  101 problems t h a t might a r i s e by l e a v i n g the heat u n i t s v a r i a b l e out o f t h e estimation.  As t h e r e i s g e n e r a l l y a h i g h e r l e v e l of both f r o s t and  h e a t - u n i t s i n t h e southern r e g i o n t h e r e would l i k e l y be a p o s i t i v e c o r r e l a t i o n between these two v a r i a b l e s .  T h i s would r e s u l t  e s t i m a t e of the f r o s t c o e f f i c i e n t and may be t h e reason  i n a biased  f o r i t s wrong  sign i n previous estimations. U n f o r t u n a t e l y when r e g r e s s i o n s were attempted on t h i s s m a l l e r body of  d a t a , m u l t i c o l l i n e a r i t y proved  t o be a problem.  a b l e e f f e c t s of m u l t i c o l l i n e a r i t y o c c u r r e d — w r o n g  Most o f the p r e d i c t s i g n s , extremely  and u n s t a b l e c o e f f i c i e n t s , and h i g h standard e r r o r s . problem l a y w i t h t h r e e v a r i a b l e s , s o i l type, f e r t i l i z e r P e s t i c i d e was h i g h l y c o r r e l a t e d w i t h s o i l type (.83).  of  Most o f t h e and p e s t i c i d e .  (.78) and f e r t i l i z e r  There was a l s o some degree o f c o r r e l a t i o n between f e r t i l i z e r and  s o i l type and  high  (.61).  I t was decided  to r e s o r t to c o n d i t i o n a l l e a s t  squares  l e a v e out p e s t i c i d e , which was the most troublesome v a r i a b l e i n terms collinearity. The  e f f e c t s o f p e s t i c i d e on p r o d u c t i o n were removed as f o l l o w s .  I t was assumed t h a t the m a r g i n a l v a l u e product i t s marginal  cost.  o f p e s t i c i d e was e q u a l t o  S i n c e t h e v a r i a b l e was g i v e n i n terms o f c o s t p e r  a c r e , each a d d i t i o n a l d o l l a r ' s worth o f a p p l e s o r about 19 l b s . u s i n g t h e 1975  average net p r i c e of 5.3c.  Thus the dependent v a r i a b l e , pounds  per a c r e was a d j u s t e d by s u b t r a c t i n g 19 m u l t i p l e d by the v a l u e of t h e pesticide.  The r e s u l t of t h i s e s t i m a t i o n a r e shown i n the southern  r e g i o n e q u a t i o n i n t a b l e 4.7. T h i s e s t i m a t i o n i s an improvement over the model f o r t h e f u l l standard  semi-  sample, a l t h o u g h t h e n e g a t i v e s i g n s f o r t r e e - s i z e and d e n s i t y  were unexpected.  I t was noted  i n the c o n c e p t u a l model t h a t some  102 o r c h a r d s may  have too h i g h a d e n s i t y f o r the s i z e of t h e i r t r e e s ,  production i s adversely affected.  and  A preponderance of such o r c h a r d s i n  the sample c o u l d cause d e n s i t y and  t r e e - s i z e t o have n e g a t i v e  coeffici-  ents . I t was mation.  found  Two  caused near  t h a t no i n t e r a c t i o n s s i g n i f i c a n t l y improved the  i n t e r a c t i o n s , age  singularity  f e r t i l i z e r and  tree-size-fertilizer  i n the d a t a m a t r i x and  c o u l d not be t e s t e d ,  s u g g e s t i n g t h a t t h e r e was the d a t a .  s t i l l a l a r g e degree of m u l t i c o l l i n e a r i t y i n  M u l t i c o l l i n e a r i t y was  a l s o suggested  c o e f f i c i e n t s f o r hedgerow p l a n t i n g and Red The  by -the u n u s u a l l y h i g h  Delicious.  standard c a t e g o r y had much fewer o b s e r v a t i o n s than the o t h e r s  and a l l observed  b l o c k s were from the o r c h a r d survey.  s t a n d a r d c a t e g o r y , m u l t i c o l l i n e a r i t y a g a i n proved P e s t i c i d e a g a i n proved  As w i t h the  (-91)  and  semi-  to be a problem.  to be a major source of t r o u b l e as i t was  correlated with f e r t i l i z e r density  esti-  somewhat w i t h s o i l  (.45)  highly  and  (.44).  Conditional least P e s t i c i d e was were accounted  left  squares was  a l s o used  out of the r e g r e s s i o n and  f o r the s t a n d a r d  i t s e f f e c t s upon p r o d u c t i o n  f o r as they were i n the semi-standard  V a r i e t y , p l a n t i n g concept  and  category.  estimation.  i r r i g a t i o n method were c o n s t a n t , w i t h a l l  t r e e s b e i n g f r e e - s t a n d i n g , Golden D e l i c i o u s w i t h p o r t a b l e s p r i n k l e r irrigation.  The  l i n e a r e q u a t i o n f o r the s t a n d a r d c a t e g o r y ,  upon the a s s i g n e d c o e f f i c i e n t While and R  f o r p e s t i c i d e s i s shown i n t a b l e  the s i g n s of t h i s e s t i m a t i o n are mostly 2  are lower  c o r r e c t the  than i n the o t h e r c a t e g o r i e s .  are on r a i n f a l l and  frost.  case of semi-standards  may  conditional  The  The wrong s i g n on f r o s t be due  4.7.  t-statistics  o n l y wrong s i g n s as suspected  t o i t s c o r r e l a t i o n w i t h the  i n the  left-out  103 v a r i a b l e heat u n i t s .  I n c l u s i o n of an a g e - f e r t i l i z e r i n t e r a c t i o n does  p a r t i a l l y c o r r e c t the problem as w e l l as s i g n i f i c a n t l y of the e q u a t i o n .  No  improving  o t h e r i n t e r a c t i o n s t e s t e d were found  to be  i c a n t a s i d e from a g e - f r o s t as shown i n the i n t e r a c t i v e e q u a t i o n standard  category  4.4.2  standard  and  standard  The  that a s o i l - f e r t i l i z e r fertilizer  signiff o r the  f o r the  complete  c a r r i e d out f o r the dwarf, semi-dwarf, semi-  categories.  In g e n e r a l , r e - a r r a n g i n g the o r d e r no  e n t r y of groups i n t o the e s t i m a t i o n caused s e l e c t e d subset.  2  Estimates  t e s t s i m i l a r to the one u t i l i z e d  l e v e l model was  R  4.7.  Robustness of T r e e - s i z e Category  A robustness orchard  i n table  the  semi-standard  change i n the  c a t e g o r y was  of  final  s l i g h t l y unstable i n  i n t e r a c t i o n would have been s e l e c t e d and  i n t e r a c t i o n d e l e t e d when i n t e r a c t i o n s were entered  the  age-  i n reverse  order. 4.4.3  V a r i e t y Functions  T h i s method of e s t i m a t i o n was mates when i t was  not pursued beyond a few  abandoned i n f a v o u r of other methods.  i n g by v a r i e t y takes p l a c e the subsets problems.  trial  When p a r t i t i o n -  of data have some c h a r a c t e r i s t i c  C e r t a i n groups of i n p u t s tend to be a s s o c i a t e d and  c o l l i n e a r i t y o c c u r s between them.  P e s t i c i d e , d e n s i t y and  move t o g e t h e r s t r o n g l y , p l a n t i n g concept c o r r e l a t e d and d e n s i t y and  and  high  fertilizer  i r r i g a t i o n are o f t e n h i g h l y  t r e e s i z e are n e g a t i v e l y c o r r e l a t e d .  a l s o tends to be low v a r i a t i o n i n some i n p u t s . t h e r e are a low number of  esti-  There  For some v a r i e t i e s  observations.  Poor s t a t i s t i c a l e s t i m a t i o n s r e s u l t  from t h i s method, n o t a b l y  wrong s i g n s on v a r i a b l e s , low t - s t a t i s t i c s , h i g h o r d e r s of magnitude and  low R  values.  c o e f f i c i e n t s of  unusually  104 4.5  C o n c l u s i o n s Regarding  Methodology  A dominant theme i n t h i s r e s e a r c h has been the i n c l u s i o n of a l a r g e number of e x p l a n a t o r y v a r i a b l e s i n the e s t i m a t i o n of the p r o d u c t i o n function.  The  f e a s i b i l i t y and  l a r g e number of v a r i a b l e s and  success of the attempt to i n c l u d e a  the v a r i o u s methods used to undertake  mation are d i s c u s s e d i n the next  sections.  esti-  Four s e p a r a t e c a t e g o r i e s of  e s t i m a t i o n which are r e g i o n a l average p r o d u c t i o n , o r c h a r d l e v e l  production  f o r a l l c a t e g o r i e s and v a r i e t i e s , t r e e - s i z e f u n c t i o n s , and v a r i e t y f u n c t i o n a r e d i s c u s s e d i n the context of t h e i r purpose and  success  i n meeting  the  o b j e c t i v e s of the r e s e a r c h . The  r e g i o n a l model used o n l y weather v a r i a b l e s as e x p l a n a t o r y  a b l e s and proved  to be adequate i n a s s e s s i n g t h e i r importance and  s e l e c t i n g a subset I t was  felt  of weather v a r i a b l e s f o r use  vari-  pre-  i n orchard l e v e l f u n c t i o n s .  t h a t a r e g i o n a l model would not be adequate i n a s s e s s i n g the  l a r g e number of o t h e r v a r i a b l e s i n the f u n c t i o n which were more e a s i l y observed The  a t the o r c h a r d  level.  o r c h a r d l e v e l f u n c t i o n s u s i n g a l l d a t a had  discussed e a r l i e r .  The  s e v e r a l problems as  e x p l a n a t o r y power of the model was  low  consider-  i n g t h e r e were as many as 28 e x p l a n a t o r y v a r i a b l e s i n some r e g r e s s i o n s . I t was  apparent  t h a t m u l t i c o l l i n e a r i t y was  of the data m a t r i x h i n d e r e d model d i d show s t a t i s t i c a l l y  the n e a r - s i n g u l a r i t y  estimations.  D e s p i t e these problems the  significant  c o e f f i c i e n t s consistent with  e x p e c t a t i o n s f o r many important had been extended to i t s l i m i t Any  severe and  variables.  I t was  felt  t h a t t h i s model  i n i n c o r p o r a t i n g explanatory  variables.  f u r t h e r i n c l u s i o n would cause near o r complete s i n g u l a r i t y of  d a t a m a t r i x , h i n d e r i n g e s t i m a t e s of a l l c o e f f i c i e n t s . t h a t f u r t h e r i n f o r m a t i o n was  needed and  a different  I t was  concept  the  decided  of e s t i m a t i o n  105 was r e q u i r e d i n o r d e r t o more c o m p l e t e l y research.  s a t i s f y the o b j e c t i v e s o f the  The t h r u s t o f the e s t i m a t i o n was thus turned towards  esti-  mating s e p a r a t e f u n c t i o n s f o r each t r e e - s i z e c a t e g o r y and v a r i e t y . F u n c t i o n s e s t i m a t e d f o r i n d i v i d u a l t r e e - s i z e c a t e g o r i e s had g r e a t e r e x p l a n a t o r y power than t h e s i n g l e e q u a t i o n model. tended  Their coefficients  to be more s i g n i f i c a n t and more c o n s i s t e n t w i t h e x p e c t a t i o n s .  There a r e s e v e r a l p o s s i b l e reasons why t h e c a t e g o r y f u n c t i o n s proved successful.  more  Because t r e e - s i z e and i t s i n t e r a c t i o n s d i d not need t o be  i n c l u d e d i n any o f t h e i n d i v i d u a l c a t e g o r y f u n c t i o n s , t h e number o f e x p l a n a t o r y v a r i a b l e s was reduced which p a r t i a l l y a l l e v i a t e d  the m u l t i -  c o l l i n e a r i t y problem, p a r t i c u l a r l y f o r t h e dwarf and semi-dwarf c a t e g o r ies.  The c o l l i n e a r i t y between t r e e - s i z e and d e n s i t y which was t r o u b l e -  some over t h e whole sample was e l i m i n a t e d i n t h e t r e e - s i z e functions.  A second  category  reason f o r t h e g r e a t e r success i n e s t i m a t i n g  c a t e g o r y f u n c t i o n s may be t h a t they impose l e s s r e s t r i c t i o n s on i n t e r a c tions.  Over t h e complete s e t o f d a t a , a s p e c i f i c i n t e r a c t i o n term  measures the average  e f f e c t of the i n t e r a c t i o n i n the sample.  only  However,  the n a t u r e or magnitude o f t h e i n t e r a c t i v e e f f e c t may v a r y depending upon the range o f the v a r i a b l e s .  F o r example, t h e r e i s no reason t o  b e l i e v e t h a t t h e i n t e r a c t i o n between age and f e r t i l i z e r , all  rootstocks.  Separate r e g r e s s i o n s f o r each r o o t s t o c k a l l o w t h e d i f -  f e r e n c e s t o be estimated r a t h e r than averaged Another important t h a t t h e ranges  i s the same f o r  into a single  coefficient.  factor i n estimating i n d i v i d u a l tree-size functions i s  o f other i n p u t s a r e r e s t r i c t e d  over t h e subsets of d a t a .  For example, the s t a n d a r d c a t e g o r y f u n c t i o n i s e s t i m a t e d f o r a sample where the d e n s i t y i s always l e s s than 100 t r e e s per a c r e whereas i n the dwarf c a t e g o r y d e n s i t y i s i n the 300 t o 400 t r e e s p e r a c r e range.  It i s likely  106 t h a t the m a r g i n a l p h y s i c a l product of d e n s i t y i s not c o n s t a n t over whole range of the v a r i a b l e i n the complete d a t a s e t .  E s t i m a t e s of the  m a r g i n a l product over a r e s t r i c t e d range f o r each c a t e g o r y w i l l s e r i e s of l i n e a r approximations  of the average  give a  of the c o e f f i c i e n t of d e n s i t y w h i l e a  s i n g l e e q u a t i o n e s t i m a t e over the whole sample w i l l approximation  the  e f f e c t of d e n s i t y .  give a  linear  A g r e a t e r amount of  v a r i a t i o n i n y i e l d would be e x p l a i n e d by the s e r i e s of e s t i m a t e d f i c i e n t s r a t h e r than by the s i n g l e c o e f f i c i e n t  coef-  f o r the whole sample.  Other v a r i a b l e s i n c l u d i n g f e r t i l i z e r and p e s t i c i d e a l s o showed some a s s o c i a t i o n w i t h t r e e - s i z e c a t e g o r i e s , so the same argument c o n c e r n i n g a changing  m a r g i n a l product  should h o l d f o r them.  C o n s i d e r i n g the nature of the problem, e s t i m a t i n g i n d i v i d u a l t i o n s f o r each t r e e - s i z e c a t e g o r y was  a reasonable strategy.  func-  I t would  have been d e s i r a b l e to c o n t r o l l e v e l s of o t h e r v a r i a b l e s as w e l l as type or g e o g r a p h i c a l l o c a t i o n .  For example a f u n c t i o n c o u l d be  mated f o r an i n d i v i d u a l t r e e - s i z e c a t e g o r y on a p a r t i c u l a r s o i l T h i s would e l i m i n a t e both s o i l type and g i v e f u r t h e r freedom to the behaviour dure of d a t a p a r t i t i o n i n g was  soil  estitype.  t r e e - s i z e from the equations  of i n t e r a c t i o n s .  If this  and  proce-  c a r r i e d to the extreme i t would be a n a l -  agous t o the type of s c i e n t i f i c  experiment  where the l e v e l of o n l y  v a r i a b l e i s v a r i e d and a l l other f a c t o r s a r e h e l d c o n s t a n t . n a t u r a l to move i n t h i s d i r e c t i o n c o n t r o l l i n g the v a r i a t i o n of  one  I t seemed factors,  because the c o n c e p t u a l model i s c o n s i d e r i n g a number of t e c h n i c a l  factors  on a d i s a g g r e g a t e d b a s i s , such as might be c o n s i d e r e d i n a p h y s i c a l or b i o l o g i c a l model. E s t i m a t i o n of i n d i v i d u a l t r e e - s i z e f u n c t i o n s i s a l s o convenient i n t e r p r e t i n g the r e s u l t s .  Each f u n c t i o n r e p r e s e n t s a b a s i c k i n d of  in  107 system, w i t h o p t i o n a l management f e a t u r e s , and yield  stream f o r the purposes of comparing p r o d u c t i v i t y . Estimations  due  can be used to p r e d i c t a  of f u n c t i o n s  to h i g h m u l t i c o l l i n e a r i t y ,  instances  a low  f o r each v a r i e t y proved to be i n f e a s i b l e ' low v a r i a t i o n i n i n p u t s  number of o b s e r v a t i o n s .  The  these d i s a d v a n t a g e s .  v i d u a l v a r i e t y f u n c t i o n s was the o b j e c t i v e s  4.6  c o u l d be met  Importance of Weather A general  are sary  conclusion  I t was  not by  felt  an e s s e n t i a l to the r e s e a r c h  estimating  out-  of  indi-  and  that  Variables from t h i s r e s e a r c h  i s t h a t weather v a r i a b l e s  the weather v a r i a b l e s used show g r e a t e r  i n g v a r i a t i o n i n average r e g i o n a l p r o d u c t i o n  l a r g e l y due  are t h e r e f o r e  between o r c h a r d s .  neces-  function.  In  significance i n explain-  than i n e x p l a i n i n g v a r i a t i o n  I t i s expected t h a t t h i s o c c u r r e n c e i s  to the measurements used f o r these v a r i a b l e s which were  r e c o r d e d at s e l e c t e d weather s t a t i o n s i n the v a l l e y .  There i s a c e r t a i n  amount of v a r i a t i o n i n these v a r i a b l e s between o r c h a r d s which was c a p t u r e d by  during  Because i t was  not  t e s t e d i n the r e g i o n a l weather model f o r the dwarf and  r e c o r d e d f o r c e r t a i n areas and  i n other estimations.  any  bloom was  the o r c h a r d l e v e l f u n c t i o n s  r e g i o n a l and  not  the r e g i o n a l measures.  Sunlight and  to  the other type of models.  f o r the complete s p e c i f i c a t i o n of the p r o d u c t i o n  i n production  having  e q u a t i o n s was  that estimation  important f a c t o r s i n f l u e n c i n g apple y i e l d s and  general  i n some  advantages of not  i n c l u d e a s e t of dummy v a r i a b l e s f o r v a r i e t y i n the weighed by  and  I t proved to be h i g h l y  o r c h a r d l e v e l and  semi-dwarf y e a r s i t was  categories. not  s i g n i f i c a n t at both  used the  added to the e x p l a n a t o r y power more than  of the other weather v a r i a b l e s .  I t s m a r g i n a l e f f e c t on  production  108 ranged lbs.  from 27 l b s . per l / 1 0 t h hour i n the r e g i o n a l models t o about  per l / 1 0 t h hour f o r the dwarf and  semi-dwarf c a t e g o r i e s .  s i g n i f i c a n c e of t h i s v a r i a b l e can be a t t r i b u t e d to a number of I t was  expected  i t was  a s t i m u l o u s to bee a c t i v i t y .  it  50  The  strong  factors.  on a p r i o r i grounds to p o s i t i v e l y a f f e c t p o l l i n a t i o n I t was  a l s o had h i g h c o r r e l a t i o n w i t h temperature  as  found d u r i n g e s t i m a t i o n t h a t and  some n e g a t i v e  correla-  t i o n w i t h r a i n so i t s e f f e c t s encompass the i n f l u e n c e of t h e s e v a r i a b l e s . The measures as r e c o r d e d as weather s t a t i o n s a r e r e a s o n a b l e proxy  vari-  a b l e s f o r the r e q u i r e d i n d i v i d u a l o r c h a r d measures, because s u n l i g h t i s r e l a t i v e l y c o n s t a n t over a s m a l l a r e a . F r o s t c o e f f i c i e n t s were somewhat i n c o n s i s t e n t between the v a r i o u s e s t i m a t e d e q u a t i o n s , but s u b j e c t t o the measures used i t was to  concluded  t h a t i t had  be s t a t i s t i c a l l y  significant  impacts  to r e p r e s e n t  upon y i e l d s .  s i g n i f i c a n t a t the r e g i o n a l l e v e l and  a c t i v e form f o r the semi-standard entered i n the e s t i m a t e s , i t was  category.  I t proved  f o r the  inter-  In other forms, when  c l o s e to b e i n g s i g n i f i c a n t  the semi-dwarf c a t e g o r y where i t had  frost,  low s i g n i f i c a n c e .  except f o r  I t was  not  entered i n the dwarf c a t e g o r y because i t had a v a l u e of zero f o r t h i s subset of the d a t a .  In l i n e a r e s t i m a t e s i t o f t e n had  the wrong s i g n  a l t h o u g h i n i n t e r a c t i v e forms i t u s u a l l y e x h i b i t e d n e g a t i v e m a r g i n a l e f f e c t s on y i e l d s .  I t was  felt  the e s t i m a t i o n of a c o e f f i c i e n t the a c t u a l measure used was v a r i a t i o n between o r c h a r d s .  t h a t t h e r e were two for this variable.  factors hindering The  f i r s t was  that  o n l y a proxy and d i d not c a p t u r e a l l the The  second was  growing season heat accumulation which was  the l i k e l y c o r r e l a t i o n w i t h  left  out of the r e g r e s s i o n s .  A c o r r e l a t i o n between these v a r i a b l e s i s expected be h i g h e r i n the s o u t h e r n r e g i o n s of the v a l l e y .  as they both tend to The  e f f e c t s of the  109 c o r r e l a t i o n and i m p r e c i s i o n i n measurement w i l l be t o b i a s the c o e f f i c i e n t towards b e i n g p o s i t i v e and t o i n c r e a s e t h e s t a n d a r d e r r o r s o f the c o e f f i c ients.  I n s p i t e of these f a c t o r s , t h e v a r i a b l e s t i l l  c o n s i s t e n c y and s i g n i f i c a n c e t o be regarded  showed enough  as h a v i n g an important  effect  upon y i e l d s . Temperature d u r i n g bloom was h i g h l y s i g n i f i c a n t a t t h e r e g i o n a l l e v e l and i n t h e o r c h a r d l e v e l s model e s t i m a t e d over t h e f u l l  set of data.  I t showed low s i g n i f i c a n c e i n the standard c a t e g o r y e s t i m a t i o n and was not used  i n the other category f u n c t i o n s .  t i o n with sunlight  i t was d i f f i c u l t  each v a r i a b l e upon y i e l d s . 250  correla-  t o s e p a r a t e out the i n f l u e n c e s of  The impact  upon y i e l d p e r a c r e ranged  l b s . to_'over 700 l b s . f o r each degree above 65 F.  that the v a r i a b l e i s a s i g n i f i c a n t its  Because of i t s h i g h  I t was  from  concluded  f a c t o r i n apple production although  i n f l u e n c e can mostly be captured by the s u n l i g h t  variable.  R a i n f a l l d u r i n g bloom had l e s s s i g n i f i c a n c e than the o t h e r weather v a r i a b l e s t e s t e d , a l t h o u g h i t s s i g n was q u i t e c o n s i s t e n t w i t h a p r i o r i expectations.  I t s lower  s i g n i f i c a n c e may be due t o the f a c t t h a t i t  was r e p r e s e n t e d by a proxy v a r i a b l e which does n o t c o m p l e t e l y between o r c h a r d v a r i a t i o n i n p r e c i p i t a t i o n . v a r i a b l e does have some impact  capture the  I t was concluded  that the  on y i e l d s , a l t h o u g h i t s i n f l u e n c e i s l e s s  p r e d i c t a b l e than t h e e f f e c t s o f o t h e r weather v a r i a b l e s .  4.7  Importance o f I n t e r a c t i o n s The  evidence c o n c e r n i n g i n t e r a c t i o n s i s b o t h d i r e c t and i n d i r e c t .  The d i r e c t evidence i s t h a t s e v e r a l s p e c i f i c i n t e r a c t i o n s prove  t o be  s i g n i f i c a n t and add c o n s i d e r a b l e e x p l a n a t o r y power i n t h e e s t i m a t e d functions.  The i n d i r e c t  evidence i s t h a t t h e r e a r e d i f f e r e n c e s i n some  110 c o e f f i c i e n t s between t h e t r e e - s i z e c a t e g o r y f u n c t i o n s  i n d i c a t i n g some  i n t e r a c t i o n between these c o e f f i c i e n t s and t r e e - s i z e .  The g e n e r a l  conclusion  i s that  on y i e l d s .  i n t e r a c t i o n s have an important and measurable e f f e c t  Conclusions regarding s p e c i f i c i n t e r a c t i o n s are discussed  below. I t was expected on a p r i o r i grounds that  rootstock or tree  size  i n t e r a c t i o n s were t h e most important c l a s s o f t h e i n t e r a c t i o n s . statistical actions  r e s u l t s seem t o c o n f i r m t h i s e x p e c t a t i o n .  of t r e e - s i z e and f e r t i l i z e r , d e n s i t y ,  s i g n i f i c a n t i n the f u n c t i o n the  actions frost  can be seen.  t r e e - s i z e decreases. the  trees  increases,  and f r o s t prove t o be When  a r e examined some t r e n d s i n the i n t e r -  Larger trees  than s m a l l e r t r e e s .  Specific inter-  estimated over the f u l l d a t a s e t .  t r e e - s i z e category functions  The  are less influenced  by f e r t i l i z e r and  Age has a much g r e a t e r e f f e c t on y i e l d s as  D e n s i t y has l a r g e r c o e f f i c i e n t s as the s i z e of i n d i c a t i n g the a d d i t i o n  of a l a r g e r t r e e  increases  y i e l d more than the a d d i t i o n o f a s m a l l e r t r e e under the observed tions.  The behaviour of t h e d e n s i t y  f a c t that trees. and If  the l e v e l o f t h i s v a r i a b l e The average d e n s i t y  the average d e n s i t y  i n t e r a c t i o n may a l s o be due t o t h e i s lower f o r the l a r g e r  density  f o r t h e dwarf c a t e g o r y i s 366 t r e e s p e r a c r e .  Thus the d i f f e r e n c e s  t o t a l l y due t o a d e n s i t y  tree-size  i n t h e c o e f f i c i e n t s may n o t be  interaction.  group o f age i n t e r a c t i o n s was c o n s i d e r e d important i n t h e  c o n c e p t u a l model p r i m a r i l y because young t r e e s are  then i t f o l -  t h e standard c a t e g o r y should have a h i g h e r c o e f f i c i e n t as  i s lower.  The  sized  o f the standard c a t e g o r y i s 61 t r e e s per a c r e  a d e c r e a s i n g m a r g i n a l product i s expected f o r d e n s i t y ,  lows t h a t  condi-  i n t h e i r f o r m a t i v e stages  expected t o respond l e s s to the l e v e l o f v a r i a b l e  inputs.  The o n l y  such i n t e r a c t i o n which proved interaction. d a t a s e t and  to be s i g n i f i c a n t was  T h i s term proved  the  age-fertilizer  to be h i g h l y s i g n i f i c a n t over the  the i n d i v i d u a l t r e e - s i z e c a t e g o r i e s .  full  I t s i n c l u s i o n adds  c o n s i d e r a b l e e x p l a n a t o r y power t o the t r e e - s i z e c a t e g o r y f u n c t i o n s . Other  i n t e r a c t i o n s w i t h age  t e s t a b l e due  i n c l u d i n g p e s t i c i d e s and  t o d a t a problems.  Age  l a b o u r were not  a l s o showed a s i g n i f i c a n t  interac-  t i o n w i t h r o o t s t o c k or t r e e - s i z e c o n f i r m i n g the e x p e c t a t i o n t h a t the smaller trees' y i e l d than the l a r g e r  i n c r e a s e d f a s t e r d u r i n g the e a r l y b e a r i n g  trees.  The group of s o i l i n t e r a c t i o n s were not g e n e r a l l y as as the r o o t s t o c k and age significant  interactions.  The  data set s o i l  and d e n s i t y a l t h o u g h  t o be  equations.  summary the r e s u l t s of s t a t i s t i c a l e s t i m a t i o n s p r e s e n t e d i n R e s u l t s were  p r e s e n t e d f o r a r e g i o n a l weather model, f o r a complete o r c h a r d f o r t r e e - s i z e c a t e g o r y models.  whole suggests  The  level  e m p i r i c a l evidence as a  t h a t most i n p u t s i n c l u d i n g weather v a r i a b l e s and  a c t i o n s have s i g n i f i c a n t level.  func-  s i g n i f i c a n t .'in any  t h i s chapter have confirmed most a p r i o r i e x p e c t a t i o n s .  model and  had  these  i n the t r e e - s i z e c a t e g o r y  i n the c o n c e p t u a l model d i d not prove  the estimated In  significant  significant  i n t e r a c t i o n between s o i l type and r o o t s t o c k , expected  q u i t e important of  Over the f u l l  i n t e r a c t i o n s with f e r t i l i z e r  i n t e r a c t i o n s d i d not prove tions.  stages  inter-  e f f e c t s upon y i e l d s a t the i n d i v i d u a l o r c h a r d  A g e n e r a l c o n c l u s i o n i s t h a t e s t i m a t i o n of a d i s a g g r e g a t e d  orchard l e v e l production f u n c t i o n i s f e a s i b l e , p a r t i c u l a r l y i f functions a r e estimated f o r i n d i v i d u a l t r e e - s i z e c a t e g o r i e s . utilizes  The next  the e s t i m a t e d models t o examine p o s s i b l e v a r i a b l e and  input adjustment  i n the i n d u s t r y .  chapter fixed  CHAPTER V APPLICATIONS OF THE ESTIMATED PRODUCTION  FUNCTIONS  The e s t i m a t e d p r o d u c t i o n f u n c t i o n s have a number o f a p p l i c a t i o n s f o r i m p r o v i n g r e s o u r c e a l l o c a t i o n and f o r a i d i n g f u t u r e r e s e a r c h and development.  In t h i s chapter d i r e c t a p p l i c a t i o n s of the f u n c t i o n s  c o n c e r n i n g i n p u t adjustment, t i o n are discussed.  e v a l u a t i o n of t e c h n o l o g y and y i e l d p r e d i c -  The e s t i m a t e d p r o d u c t i o n f u n c t i o n s a r e f i r s t used  to p r e d i c t y i e l d streams over a twenty y e a r p e r i o d and a c o r r e s p o n d i n g stream of c o s t s i s c o m p i l e d from o t h e r s o u r c e s .  The n e t p r e s e n t  value  and v a r i a b i l i t y o f p r o d u c t i o n from each system a r e d i s c u s s e d i n t h e c o n t e x t o f t h e c h o i c e between systems.  T e c h n o l o g i c a l e v a l u a t i o n and  y i e l d p r e d i c t i o n a r e based on t h e impact o f weather v a r i a b l e s as e s t i mated i n t h e r e g i o n a l and o r c h a r d l e v e l f u n c t i o n s .  These a p p l i c a t i o n s  are discussed l a t e r i n the chapter.  5.1  Adjustments i n Orchard E s t a b l i s h m e n t and O p e r a t i o n By u s i n g t h e f u n c t i o n s t o p r e d i c t y i e l d s f o r v a r i o u s systems and  management o p t i o n s t h e r e l a t i v e a l t e r n a t i v e s can be determined.  p r o d u c t i v i t y and p r o f i t a b i l i t y o f these Where i t i s obvious t h a t c e r t a i n  systems a r e more p r o f i t a b l e i t i s expected  t h a t adjustment w i l l  p l a c e towards i n c o r p o r a t i n g t h e s e a l t e r n a t i v e s .  take  The f u n c t i o n s prove  t o be much more u s e f u l i n a s s e s s i n g t h e impact  of f i x e d i n p u t s  f e a t u r e s ) than i n a s s e s s i n g v a r i a b l e i n p u t s .  I n f a c t o n l y two v a r i a b l e  112  (physical  113 inputs, f e r t i l i z e r  and  p e s t i c i d e , were i n c l u d e d  i n the e s t i m a t i o n s .  It  was , f e l t t h a t the upward b i a s imparted to these c o e f f i c i e n t s because of the l e f t - o u t v a r i a b l e s management and invalid  for assessing  labour,  the impacts of p e s t i c i d e and  over, the a c t u a l measure f o r p e s t i c i d e was i n f u r t h e r b i a s to the  coefficient.  pounds r a t h e r than v a l u e an i n a c c u r a t e  rendered the  of f r u i t ,  functions  fertilizer.  a proxy and  may  have r e s u l t e d  Because the dependent v a r i a b l e i s the f e r t i l i z e r  e s t i m a t e of the m a r g i n a l v a l u e  c o e f f i c i e n t may  of f r u i t  mated c o e f f i c i e n t may pounds of f r u i t , a constant  but w i l l  decrease i t s q u a l i t y .  g i v e an a c c u r a t e  p r i c e i s assumed.  worth from $1.82  c o s t s of 5.2c  i n 1975  The  Thus the  esti-  i d e a of the m a r g i n a l product  on  estimated c o e f f i c i e n t s i n d i c a t e t h a t c o s t i n g about 7c r e s u l t s i n a d d i t i o n a l  I t was  felt  harvesting  t h a t the extremely  high  product to m a r g i n a l c o s t were l a r g e l y due  to  the  mentioned. There may  inputs  increase  to $19.34 i f the average p r i c e net  i s used.  r a t i o s of m a r g i n a l v a l u e biases  It  w h i l e o v e r s t a t i n g the m a r g i n a l product on v a l u e , i f  an a d d i t i o n a l pound of f e r t i l i z e r production  give  product of f e r t i l i z e r .  i s known t h a t w i t h i n a c e r t a i n range a d d i t i o n a l n i t r o g e n w i l l the q u a n t i t y  More-  and  a l s o be some b i a s imparted to the c o e f f i c i e n t s of f i x e d  p h y s i c a l f e a t u r e s by  t h a t the b i a s was  not  In the case of l a b o u r ,  when a s s e s s i n g  may  be  i t was  so s e r i o u s as i n the case of the v a r i a b l e t h e r e i s consensus d a t a r e l a t i n g labour  ments to orchards systems, and for  the l e f t - o u t v a r i a b l e s , but  the i n f l u e n c e of labour  the r e l a t i v e p r o f i t a b i l i t y  can be  of the systems.  felt  inputs. require-  accounted There  some management b i a s i n the c o e f f i c i e n t s f o r c e r t a i n p h y s i c a l  features.  T h i s would occur i f b e t t e r managers tended to u t i l i z e  systems, an o c c u r r e n c e which might be  expected i f they had  better  certain access  114 to knowledge c o n c e r n i n g the estimated due  the p r o d u c t i v i t y of these a l t e r n a t i v e s .  c o e f f i c i e n t s for highly productive  to the e f f e c t of the systems but may  management a s s o c i a t e d w i t h subject  them.  The  systems may  a l s o be due  r e s u l t s and  not  to the  i n t e r p r e t a t i o n s are  R e l a t i v e P r o d u c t i v i t y of Orchard Systems  rootstock,  i r r i g a t i o n system and  categorized  p l a n t i n g concept.  b a s i c systems  optional features including  a)  f r e e standing  b)  overhead, p o r t a b l e , or t r i c k l e  or hedgerow irrigation  2.  h i g h d e n s i t y semi-dwarf r o o t s t o c k w i t h  3.  medium d e n s i t y semi-standard w i t h  4.  low d e n s i t y standard As  The  density,  as:  h i g h d e n s i t y dwarf r o o t s t o c k w i t h  a yield  be  better  Orchard systems are r e l a t e d to the f i x e d i n p u t s such as  1.  only  to t h i s p o s s i b l e b i a s .  5.1.1  can be  Thus  the same o p t i o n a l  features  the same o p t i o n a l f e a t u r e s  r o o t s t o c k w i t h p o r t a b l e or t r i c k l e  f u n c t i o n s have been estimated  f o r each of the b a s i c  stream can be p r e d i c t e d f o r each system.  purposes a time h o r i z o n of 20 y e a r s was  irrigation.  For  categories  comparative  taken f o r the y i e l d  streams.  Where the e f f e c t s of t r e e d e s i g n and  i r r i g a t i o n system was  identifiable,  comparative y i e l d s f o r these o p t i o n s  are a l s o p r e s e n t e d .  Where pos-  s i b l e y i e l d s from d i f f e r e n t years'  production  s o i l s are shown.  l e s s harvest  The  present  c o s t s i s shown i n t a b l e  value  of  5.1.  In terms of the b a s i c systems i t i s apparent t h a t p r o d u c t i o n a c r e i n c r e a s e s as t r e e - s i z e d e c r e a s e s and average p r e s e n t $7,630 s t a n d a r d ,  value  l e s s harvest  density increases.  per  The  c o s t s f o r a 20 year p e r i o d i s  $7,398 f o r semi-standard, $16,171 f o r semi-dwarf  $25,821 f o r dwarf.  20  When the semi-standard and  semi-dwarf-systems  and are  115 T a b l e 5.1.  Average  P r e s e n t Value of P r o d u c t i o n from Major Apple P r o d u c t i o n Systems over 20 y e a r s  Dwarf  SemiDwarf  SemiStandard  Standard  $ 25,821  16,171  7,398  7,630  Sandy  25,962  7,133  9,780  Clay  22,072  7,133  9,780  5,122  5,817  Rocky Hedgerow  29,710  12,945  Non-hedgerow  19,469  6,806  Spur  27,410  17,631  Non-spur  25,201  15,974  Overhead Irrigation  34,088  Non-overhead Irrigation  19,504  p l a n t e d as hedgerows, p r o d u c t i o n i n c r e a s e s s i g n i f i c a n t l y .  The p r e s e n t  v a l u e of p r o d u c t i o n i s $12,945 f o r a hedgerow semi-standard  system, and  $29,710 f o r a hedgerow semi-dwarf system. hedgerow p l a n t i n g was h i g h l y s i g n i f i c a n t semi-standard  The dummy v a r i a b l e f o r i n both the semi-dwarf and  c a t e g o r i e s w i t h T - s t a t i s t i c s of 3.27 and 2.55 r e s p e c t i v e l y .  I t was concluded  t h a t hedgerow p l a n t i n g has a s i g n i f i c a n t p o s i t i v e  impact  on y i e l d s . Other  components o f p l a n t i n g system i n c l u d i n g s o i l type,  irrigation  system, and spur o r non-spur r e s u l t e d i n n o t a b l e d i f f e r e n c e s i n product i o n a l t h o u g h t h e e f f e c t s of these v a r i a b l e s were not as s t a t i s t i c a l l y s i g n i f i c a n t o r as c o n s i s t e n t as the e f f e c t s o f t r e e - s i z e , d e n s i t y and tree design.  I n p r e s e n t v a l u e terms sandy s o i l s r e s u l t  i n about  $2000  ^"A p r i c e o f 5.20 per pound and a 5 p e r c e n t i n t e r e s t r a t e a r e used. F u l l p r o d u c t i o n streams p r e d i c t e d from t a b l e s 4-6 and 4-7 a r e shown i n Appendix A.  116 to $3000 i n c r e a s e i n y i e l d s over what o c c u r s on c l a y or rocky The t e x t u r e index of s o i l i s not s i g n i f i c a n t although i t s s i g n i s c o n s i s t e n t . i s q u i t e s i g n i f i c a n t , and economic s i g n i f i c a n c e .  i t was  i n the  soils.  tree-size functions  Over the whole data s e t , the v a r i a b l e thus f e l t  t h a t s o i l t e x t u r e was  The i r r i g a t i o n system was  semi-dwarf c a t e g o r y , where i t proved  of  o n l y t e s t a b l e i n the  to be h i g h l y s i g n i f i c a n t and  added  a p r e s e n t v a l u e of about $14,000 to y i e l d s over a 20 y e a r p e r i o d . was  felt  been due  t h a t t h i s i n c r e a s e i n p r o d u c t i o n was  r a t h e r h i g h and may  to some b i a s i n the e s t i m a t e d c o e f f i c i e n t .  l a b o u r i s r e q u i r e d w i t h a f i x e d overhead would l i k e l y  get a h i g h e r l e v e l of i r r i g a t i o n , and  Spur-type  trees result  have  Because l e s s  i r r i g a t i o n system these  on y i e l d s would be captured by the c o e f f i c i e n t  It  orchards  the r e s u l t i n g  effect  f o r the overhead  system.  i n an i n c r e a s e i n p r e s e n t v a l u e of about $2000 i n  production.  However, the c o e f f i c i e n t  statistically  significant  i n any  s i s t e n t l y positive signs.  f o r spur-type d i d not  prove  of the e s t i m a t i o n s a l t h o u g h i t had  Hence the r e s u l t s were taken o n l y to  con-  suggest  r a t h e r than prove at h i g h l e v e l s of c o n f i d e n c e t h a t spur type t r e e s are b e t t e r producers 5.1.2  than non-spur type  Relative P r o f i t a b i l i t y  trees. of Orchard  Systems  I t has been e s t i m a t e d t h a t annual maintenance c o s t s f o r a dwarf system w i l l be about 20% g r e a t e r than maintenance c o s t s f o r s t a n d a r d systems  (Kennedy, 1976).  ence i n the investment 1975).  Other  r e s e a r c h has o u t l i n e d a s i m i l a r  c o s t of h i g h v e r s u s low d e n s i t y systems  Since a t h r e e - f o l d  (Dorling,  i n c r e a s e i n the p r e s e n t v a l u e of y i e l d s  be achieved through a r e l a t i v e l y  can  small increase i n costs, high density  systems appear t o be s u p e r i o r investments tems at c u r r e n t p r i c e s .  differ-  compared to low d e n s i t y s y s -  An annual stream o f c o s t s f o r each system has been estimated v a r i o u s sources  and these a r e compared t o the v a l u e o f t h e y i e l d  from  streams.  A case i s o u t l i n e d where producers a r e c o n s t r a i n e d t o 10 a c r e s of l a n d , faced w i t h e s t a b l i s h i n g and m a i n t a i n i n g year  time p e r i o d .  an o r c h a r d  system over a twenty  Some c o s t s i n c l u d i n g taxes and u t i l i t i e s have not  been i n c l u d e d and t h e p r i c e of the undeveloped land i s s e t a r b i t r a r i l y at  $5,000 per a c r e .  The c o s t s a r e not intended  purposes, but should  for accurate  budgeting  g i v e a s a t i s f a c t o r y i n d i c a t i o n o f the r e l a t i v e  p r o f i t a b i l i t y of systems.  Both c o s t s and b e n e f i t s a r e i n constant  d o l l a r s w i t h the r e a l i n t e r e s t r a t e taken as f i v e  percent.  L e v e l s of a l l i n p u t s a r e s e t a t averages, and the average y i e l d for  each system i s used t o determine the y e a r l y r e t u r n s .  p r i c e less harvest standard  c o s t s i s 5.2c per pound f o r standard  and 5.1c f o r dwarf and semi-dwarf.  The average and semi-  These p r i c e s a r e based on  the 1974 average p r i c e s r e c e i v e d by o r e h a r d i s t s i n t h e survey. Machinery i n c l u d e s a t r a c t o r i n the 40-horsepower range, a s p r a y e r adequate f o r t h e t r e e - s i z e , a weed s p r a y e r , an o r c h a r d mower, b u i l d i n g s used t o house equipment, and m i s c e l l a n e o u s pruning  a i d s and h a r v e s t i n g equipment.  equipment such as l a d d e r s ,  I t i s assumed t h a t the major  machinery items a r e r e p l a c e d a f t e r 10 y e a r s . cides, f e r t i l i z e r ,  t r a c e elements, and i r r i g a t i o n equipment.  $5 per hour i s charged f o r a l l l a b o u r . was  obtained Table  system.  Materials include p e s t i -  Information  A r a t e of  on machinery c o s t s  from t h e B.C. M i n i s t r y o f A g r i c u l t u r e i n Vernon, B.C. 5.2 g i v e s t h e present  v a l u e o f c o s t s and r e t u r n s f o r each  A year-by-year break-down of c o s t s and r e t u r n s f o r each o f the  systems i s g i v e n i n appendix B.  118 T a b l e 5.2.  P r e s e n t Values of Costs and Returns f o r Apple Systems 1  Costs  Dwarf  Semidwarf  Semistandard  Standard  $ 17,732  16,048  16,906  13,359  25,821  16,171  7,398  7,630  8,449  87  -9,508  -5,729  Returns Net p r e s e n t value  I t can be seen from the t a b l e t h a t dwarf and are s u p e r i o r investments The  compared to standard and  semi-dwarf systems semi-standard  r a n k i n g i n terms of net p r e s e n t v a l u e puts dwarf f i r s t ,  second, s t a n d a r d t h i r d , and  semi-standard  last.  semi-dwarf  I f some of the o p t i o n a l  management f e a t u r e s were i n c o r p o r a t e d f o r semi-dwarf and systems, p a r t i c u l a r l y  semi-standard  hedgerow p l a n t i n g , the p r o d u c t i v i t y of these  tems would i n c r e a s e g r e a t l y at a s m a l l c o s t , so the net p r e s e n t would improve. dwarf and  sys-  value  However, a t the p r e s e n t average l e v e l of i n p u t s o n l y  semi-dwarf systems have net p r e s e n t v a l u e s g r e a t e r than  r e p r e s e n t i n g economic The  systems.  investment  investments. d e c i s i o n o u t l i n e d i n the t a b l e s may  r e l e v a n t problem i n the a r e a . o r c h a r d replacement  zero,  What may  not be the most  be of more concern  i s the  d e c i s i o n where o r c h a r d i s t s a r e c o n s i d e r i n g r e p l a c i n g  a low d e n s i t y system w i t h a h i g h d e n s i t y system.  While t h e r e are many  f a c t o r s i n v o l v e d i n t h i s d e c i s i o n most of the b a s i c i n f o r m a t i o n needed i s g i v e n i n the p r e c e d i n g as a r e s u l t  tables.  of removing a standard  I t can be seen t h a t the p r o f i t of semi-standard  "'"Returns a r e c a l c u l a t e d as i n t a b l e 5.1. g i v e n i n Appendix B.  lost  system i s s m a l l even  A c o s t breakdown i s  119 if  t h e t r e e s have reached  t h e i r f u l l b e a r i n g p o t e n t i a l , w h i l e the  p o t e n t i a l annual p r o f i t s from t h e h i g h d e n s i t y systems a r e much h i g h e r . 5.1.3  Other F a c t o r s I n f l u e n c i n g the Choice Between Systems  Although  the e s t i m a t e d p r o d u c t i o n f u n c t i o n s i n d i c a t e t h a t h i g h  d e n s i t y systems a r e more p r o f i t a b l e than low d e n s i t y systems over a medium term, t h e r e a r e o t h e r f a c t o r s which may i n f l u e n c e the c h o i c e between systems.  There i s evidence  systems have h i g h e r v a r i a b i l i t y  s u g g e s t i n g t h a t the h i g h d e n s i t y  of y i e l d s , r e q u i r e more management  e f f o r t and a r e a f f e c t e d t o a g r e a t e r degree by i n f l u e n c e s not completely under the growers' c o n t r o l .  These f a c t o r s may tend t o counter t h e  inducement of h i g h e r p o t e n t i a l p r o f i t s when t h e c h o i c e between systems i s considered.  T a b l e 5.3 shows the means and standard d e v i a t i o n s o f  y i e l d s from t h e f o u r systems and i l l u s t r a t e s the g r e a t e r v a r i a b i l i t y of y i e l d s from h i g h d e n s i t y systems.  T a b l e 5.3.  L e v e l and V a r i a b i l i t y o f Apple • Y i e l d s from Four A l t e r n a t i v e Systems over a 20 year P e r i o d  Average y i e l d per acre  System  Standard Deviation  Dwarf  36,786  43,138  Semi-dwarf  26,336  35,088  Semi-standard  15,424  30,183  2,807  4,535  Standard  The h i g h e r v a r i a b i l i t y  of t h e dwarf and semi-dwarf systems i s  i n d i c a t e d by t h e i r h i g h e r standard d e v i a t i o n s . cause d i f f i c u l t i e s  i n y e a r l y budgeting  might n e c e s s i t a t e g r e a t e r e f f o r t  This v a r i a b i l i t y  may  and cash flow a l l o c a t i o n and  or a b i l i t y  i n the f i n a n c i a l  120 management o f h i g h d e n s i t y v e r s u s r a t i o of the standard d e n s i t y systems.  low d e n s i t y systems.  d e v i a t i o n to the mean y i e l d  However, the  i s s m a l l e r f o r the h i g h  T h i s i n d i c a t e s t h a t the p r o b a b i l i t y of an o r c h a r d i s t  i n the sample f a l l i n g below a s e t p r o d u c t i o n l e v e l i s lower f o r h i g h d e n s i t y systems than f o r low d e n s i t y systems. primary  I f an o r c h a r d i s t ' s  o b j e c t i v e i s not t o f a l l below a c e r t a i n p r o d u c t i o n l e v e l the  evidence  i n d i c a t e s t h a t h i g h d e n s i t y i s p r e f e r a b l e t o low d e n s i t y .  Over the observed  ranges of i n p u t s the h i g h d e n s i t y systems a r e  more r e s p o n s i v e t o the l e v e l s of f e r t i l i z e r . t h a t dwarf systems a r e more r e s p o n s i v e  I f i t can be g e n e r a l i z e d  to a l l v a r i a b l e inputs i n c l u d i n g  l a b o u r and p e s t i c i d e s , then t h e l e v e l s of these i n p u t s would have t o be c l o s e l y monitored, r e q u i r i n g more management e f f o r t and a b i l i t y . I t a l s o appears t h a t h i g h d e n s i t y systems a r e more s e n s i t i v e t o f a c t o r s which a r e not completely o r c h a r d has been e s t a b l i s h e d .  under t h e grower's c o n t r o l , once t h e Frost, i n particular,  shows a s t r o n g  i n f l u e n c e on h i g h d e n s i t y systems w i t h a n e g a t i v e c o e f f i c i e n t 1,700 l b s per degree below c r i t i c a l standard  l e v e l s , whereas the c o e f f i c i e n t f o r  systems i s about 100 l b s per degree of f r o s t .  f o r one or two n i g h t s would almost completely dwarf system w h i l e c a u s i n g a c o m p a r a t i v e l y from a standard  system.  of about  A severe  frost  d e s t r o y p r o d u c t i o n from a  small reduction i n y i e l d s  High d e n s i t y systems a l s o show a h i g h e r  s e n s i t i v i t y t o s u n l i g h t and temperature d u r i n g bloom.  In g e n e r a l i t  appears t h a t blossom i n f l u e n c e s have a g r e a t e r i n f l u e n c e on h i g h d e n s i t y dwarf systems than they do on low d e n s i t y standard geographical factor with a s i m i l a r e f f e c t s o i l type. evidenced  systems.  t o the weather v a r i a b l e s i s  Dwarf systems were more s e n s i t i v e t o poorer by t h e n e g a t i v e  coefficient  Another  s o i l s as  f o r the s o i l index of -7547 l b s  121 v e r s u s -4860 l b s f o r semi-standards,  and -4837 l b s f o r s t a n d a r d s .  Thus  c a r e must be taken i n matching r o o t s t o c k to s o i l type or low y i e l d s  can  result. Some c o n s t r a i n t s as noted I n f e a s i b l e to p l a n t dwarf and t r e e s s t u n t b a d l y on l i g h t standard  trees.  i n the c o n c e p t u a l model may  semi-dwarf t r e e s i n c e r t a i n a r e a s .  s h a l l o w s o i l s which may  F r o s t pockets  or channels  u n s u i t a b l e f o r dwarf t r e e s a l t h o u g h fruit  make i t Dwarf  be s u i t a b l e f o r  l e a v e c e r t a i n areas  standard t r e e s may  still  completely  produce some  i n these areas because of the h i g h e r e l e v a t i o n of the b e a r i n g  limbs.  Because h i g h d e n s i t y systems do not appear i n these l o c a t i o n s , the sample and  e s t i m a t i o n s do not c o m p l e t e l y  c a p t u r e the e f f e c t of some of  these  c o n s t r a i n i n g v a r i a b l e s on p r o d u c t i o n .  5.2  E v a l u a t i o n of T e c h n o l o g i c a l The  Innovations  c o e f f i c i e n t s of the e s t i m a t e d p r o d u c t i o n f u n c t i o n s can be used  to a s s e s s the p o t e n t i a l b e n e f i t s of some important  innovations.  a p p l i c a t i o n i s of importance to both o r e h a r d i s t s who p o r a t e these i n n o v a t i o n s and impact  r e s e a r c h e r s who  may  wish to  This incor-  are e v a l u a t i n g t e c h n o l o g i c a l  and a l l o c a t i n g r e s o u r c e s to f u t u r e r e s e a r c h  (see c h a p t e r V I ) .  For example, i f the degree of p r o t e c t i o n from a f r o s t p r e v e n t i o n system i s known, the t o t a l e x t r a y i e l d r e s u l t i n g from t h i s system can be c u l a t e d from the e s t i m a t e d  coefficient  for frost.  t h e assessment of t h e b e n e f i t s of hand or mechanical g a i n from these a r t i f i c i a l  cal-  Another example i s pollination.  The  forms of p o l l i n a t i o n c o u l d be c a l c u l a t e d  from  the l e v e l s of v a r i a b l e s known to a d v e r s e l y a f f e c t n a t u r a l p o l l i n a t i o n i n c l u d i n g f r o s t , r a i n and  c o o l daytime temperatures,  and  from the  esti-  mated c o e f f i c i e n t s of t h e s e v a r i a b l e s i n the p r o d u c t i o n f u n c t i o n .  Any  122 new  development which can be r e l a t e d to c o e f f i c i e n t s i n the  f u n c t i o n can be s i m i l a r l y  5.3  production  evaluated.  Predicting Yields The  r e g i o n a l weather model developed  i n chapter  IV has  the c a p a b i l -  i t y of e x p l a i n i n g a l a r g e amount of the v a r i a t i o n i n y i e l d s over  time  and  between r e g i o n s on the b a s i s of weather v a r i a b l e s d u r i n g the blossom period.  As the blossom p e r i o d precedes the h a r v e s t by f o u r or  five  months, the weather model c o u l d be used f o r p r e d i c t i n g y i e l d s g i v i n g the marketing agency and  governments advance knowledge of t o t a l  production.  T h i s knowledge would be p a r t i c u l a r l y u s e f u l i n the f o r m u l a t i o n of marketing  strategies. The  p r e d i c t i v e power of t-he model estimated  i n t h i s research could  be t e s t e d by u s i n g i t to p r e d i c t the average y i e l d used i n e s t i m a t i o n .  The  f o r recent years  not  data r e q u i r e d would be the 1975-76 blossom  f o r each r e g i o n , and o b s e r v a t i o n s on d a i l y sun, r a i n , temperature f r o s t d u r i n g the blossom p e r i o d .  The  estimated  dates  and  c o e f f i c i e n t s would  be  a p p l i e d to the l e v e l s of these v a r i a b l e s to g i v e a p r e d i c t e d average y i e l d which would then be compared w i t h the observed sibilities  f o r improving  i n 1975-76.  Pos-  the present model to g i v e more a c c u r a t e p r e d i c -  t i o n s a r e d i s c u s s e d i n the next T h i s chapter has  yield  chapter.  g i v e n some d i r e c t a p p l i c a t i o n s of the  estimated  p r o d u c t i o n f u n c t i o n s r e l a t i n g to the c h o i c e between systems, e v a l u a t i o n of i n n o v a t i o n s and  p r e d i c t i o n of y i e l d s .  Other i m p l i c a t i o n s can  drawn from the p r o d u c t i o n f u n c t i o n s p a r t i c u l a r l y mining d i r e c t i o n s of f u t u r e r e s e a r c h . summary of the r e s e a r c h and chapter.  be  i n the a r e a of d e t e r -  These i m p l i c a t i o n s a l o n g w i t h  the c o n c l u s i o n s a r e p r e s e n t e d  i n the  final  a  CHAPTER VI  SUMMARY, CONCLUSIONS AND IMPLICATIONS FOR FUTURE RESEARCH  T h i s chapter b r i e f l y summarizes the content  o f t h e r e s e a r c h and o u t -  l i n e s t h e c o n c l u s i o n s t h a t have been drawn from the e m p i r i c a l r e s u l t s . The  c o n c l u s i o n s and i m p l i c a t i o n s f o r f u r t h e r r e s e a r c h a r e c a t e g o r i z e d  a c c o r d i n g t o t h e i r r e l e v a n c e t o v a r i o u s groups i n v o l v e d i n t h e t r e e - f r u i t i n d u s t r y through p r o d u c t i o n , e x t e n s i o n , m a r k e t i n g , p o l i c y and r e s e a r c h .  6.1  Summary The  opening chapter  t a k i n g the r e s e a r c h .  of t h i s t h e s i s d i s c u s s e d the r a t i o n a l e f o r under-  The argument was developed  i n d u s t r y have been c l e a r l y r e c o g n i z e d  t h a t low incomes i n t h e  and t h a t some government attempt  should be made t o improve r e t u r n s i n the i n d u s t r y .  The l a r g e c o n t r i b u t i o n  to the economic base o f t h e area as w e l l as c u l t u r a l and e x t e r n a l b e n e f i t s were c i t e d as reasons  f o r d i r e c t i n g s c i e n t i f i c and economic r e s e a r c h  towards s o l v i n g t h e low income problem through attempting resource  t o improve  allocation.  Because o f t h e complex n a t u r e  of the p r o d u c t i o n p r o c e s s  i n v o l v e s many r e c e n t i n n o v a t i o n s i t was f e l t  which  t h a t e s t i m a t i o n of p r o d u c t i o n  f u n c t i o n s f o r t h e major apple v a r i e t i e s would s e r v e t o c l a r i f y and quantify  the e f f e c t s o f many i n p u t s .  Knowledge o f t h e e f f e c t s o f these  i n p u t s c o u l d then be used t o a i d i n r e s o u r c e a l l o c a t i o n d e c i s i o n s . be u s e f u l i n a l l o c a t i o n d e c i s i o n s a p r o d u c t i o n f u n c t i o n should be  123  To  124 s u f f i c i e n t l y d i s a g g r e g a t e d and  d e t a i l e d to show the  systems, weather v a r i a b l e s and  interactions.  t h i s research  was  The  to e s t i m a t e such a f u n c t i o n .  were to i d e n t i f y s p e c i f i c weather v a r i a b l e s and interpret  the e s t i m a t e d f u n c t i o n s  i n f l u e n c e of  primary o b j e c t i v e  Secondary  i n t e r a c t i o n s , and  i n o r d e r to a s s e s s the  The  i n t e r p r e t a t i o n s were a l s o aimed at o u t l i n i n g p o s s i b l e i n p u t implications  to  productivity  p r o f i t a b i l i t y of o r c h a r d systems and  i n d u s t r y and  of  objectives  and  ment i n the  orchard  optional physical  features.  f o r f u r t h e r economic and  adjustscientific  research. The  first  step  i n the r e s e a r c h  models of the p r o d u c t i o n an a p p r o p r i a t e tion.  An  f u n c t i o n and  f u n c t i o n a l form and  f u n c t i o n be  important i m p l i c a t i o n s  to review the w e l l known economic  producer behaviour i n o r d e r to  implications  i n t e r a c t i v e (quadratic)  ment t h a t the  was  form was  a b l e to e x p l i c i t l y  for estimation  require-  identify interactions.  were due  The  to the tendency f o r on the p r o d u c t i o n  function.  cause e i t h e r a complete l a c k of i n p u t v a r i a t i o n ,  p e r f e c t c o l l i n e a r i t y between i n p u t s tion.  f o r econometric e s t i m a -  chosen because of the  producers to seek e c o n o m i c a l l y e f f i c i e n t p o i n t s In theory t h i s c o u l d  find  However, i t was  felt  and  simultaneous problems i n e s t i m a -  t h a t i n p r a c t i c e growers are f a c i n g  varying  p r i c e l e v e l s , a l a c k of knowledge of m a r g i n a l p r o d u c t s and d i f f e r e n t valuations  of t h e i r own  v a r i a t i o n i n input  labour,  l e v e l s and  p o s s i b i l i t y of s i m u l t a n e i t y  The  increase  decrease c o r r e l a t i o n between i n p u t s .  was  producers based t h e i r d e c i s i o n s actual prices.  a l l of which would tend to  The  d i s c o u n t e d because of the knowledge t h a t on expected p r i c e s of output r a t h e r  most s e r i o u s  i m p l i c a t i o n was  than  left-out variable bias.  P r o f i t maximizing behaviour would tend to r e s u l t i n a c o r r e l a t i o n between the  l e v e l s of s e v e r a l i n p u t s  and  the l e v e l s of management  and  125 l a b o u r n e i t h e r of which were a v a i l a b l e f o r i n c l u s i o n .  The  estimated  c o e f f i c i e n t s of the v a r i a b l e s would then be upward b i a s e d . concluded t i o n was  It  was  t h a t on t h e o r e t i c a l grounds e s t i m a t i o n of the p r o d u c t i o n f e a s i b l e a l t h o u g h some problems w i t h m u l t i c o l l i n e a r i t y  r e s u l t and  some estimated  func-  could  c o e f f i c i e n t s would have to be taken as upward  biased. A c o n c e p t u a l model of a p p l e p r o d u c t i o n o u t l i n i n g the concepts  and  i d e a l measures of these concepts was  important  developed  s t a t i s t i c a l model g i v i n g the a c t u a l measures a v a i l a b l e .  The  model was  aimed a t r e f l e c t i n g the major d e c i s i o n s of concern  producer,  w i t h p a r t i c u l a r emphasis on systems and  features.  The  s t r e s s e d i n the c o n c e p t u a l model. model adequately although  i t was  inputs.  represented  I t was  felt  conceptual to a  orchard  interactions  t h a t the  the p h y s i c a l f e a t u r e s and  was  statistical  fixed  inputs .  somewhat weaker i n i t s r e p r e s e n t a t i o n of the v a r i a b l e  I t c o n t a i n e d most of the major weather i n f l u e n c e s .  w i t h the s t a t i s t i c a l model was  t h a t i t had  A problem  the t o t a l q u a n t i t y r a t h e r than  v a l u e of the f r u i t as the dependent v a r i a b l e . difficulty  long-term  importance of weather v a r i a b l e s and  along with a  T h i s problem caused  some  i n the i n t e r p r e t a t i o n of the estimated models l a t e r i n the  thesis. Because the s t a t i s t i c a l p a r t i c u l a r l y dummies and estimate. of  model had  a l a r g e number of v a r i a b l e s ,  i n t e r a c t i o n s , i t was  A g e n e r a l e s t i m a t i o n s t r a t e g y was  extremely  cumbersome to  f o r m u l a t e d w i t h the o b j e c t  r e d u c i n g the number of v a r i a b l e s w h i l e at the same time o b t a i n i n g as  much i n f o r m a t i o n as p o s s i b l e from the d a t a .  A problem a r o s e because  the i n p u t c l a s s e s which were of p a r t i c u l a r i n t e r e s t  i n the r e s e a r c h were  a l s o c o n t r i b u t i n g t o . t h e problem of a l a r g e number:of v a r i a b l e s .  A  126 stepwise r e g r e s s i o n procedure of  g r e a t e r importance  first  was used which tended  on a p r i o r i  grounds.  to s e l e c t  variables  A r e g i o n a l weather model was  e s t i m a t e d i n o r d e r t o s e l e c t the more important weather  influences.  These weather v a r i a b l e s were then i n c l u d e d a l o n g w i t h a l l i n p u t s i n a l i n e a r form.  Subsets  o r d e r of a p r i o r i  of i n t e r a c t i o n s were then added to the model i n  importance.  The f i n a l  e s t i m a t e was poor i n some  r e g a r d s and showed s i g n s of m u l t i c o l l i n e a r i t y . slightly  u n s t a b l e i n t h a t changing  r e g r e s s i o n caused  The f i n a l r e s u l t s were  the order o f e n t r y i n the stepwise  a few d i f f e r e n t v a r i a b l e s to be r e t a i n e d .  In g e n e r a l ,  the c o e f f i c i e n t s of v a r i a b l e s which were c o n c e p t u a l l y important to  be s i g n i f i c a n t  proved  and c o n s i s t e n t w i t h e x p e c t a t i o n s a l t h o u g h the e x p l a n -  a t o r y power of the model was not g r e a t . A second  approach to e s t i m a t i o n was c a r r i e d out where the o b s e r v a -  t i o n s were grouped a c c o r d i n g t o t r e e - s i z e c a t e g o r y and a f u n c t i o n e s t i mated f o r each c a t e g o r y .  The purpose of t h i s procedure was t o reduce  the number of i n t e r a c t i o n s and g i v e l e s s r e s t r i c t i o n s on the e s t i m a t e d coefficients.  The stepwise procedure was a g a i n c a r r i e d out e n t e r i n g the  weather v a r i a b l e s and i n p u t s f i r s t tions.  and then e n t e r i n g groups of i n t e r a c -  The r e s u l t s of the t r e e - s i z e category f u n c t i o n s were more  f a c t o r y than the s i n g l e e q u a t i o n model i n s e v e r a l r e g a r d s  satis-  including  2 statistical  significance, R  r o b u s t n e s s , and c o n s i s t e n c y of c o e f f i c i e n t s .  T a b l e 6.1 g i v e s a summary of the impact  of the major v a r i a b l e s i n the  v a r i o u s models. A number of c o n c l u s i o n s based methodology were drawn.  on the s t a t i s t i c a l  r e s u l t s and  V a r i o u s i n t e r p r e t a t i o n s were made u s i n g the  e s t i m a t e d models to p r e d i c t a stream of p r o d u c t i o n . annual o p e r a t i n g c o s t s were c o l l e c t e d  E s t a b l i s h m e n t and  from other s o u r c e s , and were  127 T a b l e 6.1.  Independent Variable  Summary of S t a t i s t i c a l  Results  Statistical Significance R e g i o n a l Complete I n d i c a t i o n from Model Model By System Coefficient  medium  sandy s o i l s superior  high  high  dwarf and semidwarf g i v e higher y i e l d s  medium  low to high  higher density increases y i e l d s except f o r semistandard  low  s l i g h t l y higher y i e l d f o r spur  high  much h i g h e r yield for hedgerow  Soil  high  Rootstock (tree-size) Density  Spur-type  1  high  Tree-design  Qualification  associated with high d e n s i t y systems  coefficient be b i a s e d upwards  may  may  Variety  high  low t o high  inconsistent  Age  high  high  e a r l i e r product i o n from h i g h density  high  overhead i r r i g a t i o n has higher y i e l d s  coefficient be b i a s e d upwards  l e s s than o p t i mum p r e s e n t l y b e i n g used  management and labour bias suspected  Irrigation system Fertilizer  high high  Pesticide  medium to h i g h medium to h i g h  Temperature at blossom  high  medium  S u n l i g h t of blossom  high  medium  high  major impact on y i e l d s  Rain at blossom  high  low  medium  reduces y i e l d s  Frost at blossom  high  medium  medium  reduces y i e l d s substantially  h i g h i n d i c a t e s s i g n i f i c a n c e a t the .05 l e v e l ; T - r a t i o o f g r e a t e r than u n i t y  higher density systems a r e more s e n s i t i v e to weather variables  medium i n d i c a t e s a  128 compared.with the p r e d i c t e d y i e l d streams i n o r d e r to a s s e s s the a b i l i t y and v a r i a b i l i t y  6.2  C o n c l u s i o n s and  profit-  of the f o u r major systems.  I m p l i c a t i o n s f o r F u r t h e r Research  A number of c o n c l u s i o n s r e g a r d i n g methodology, weather v a r i a b l e s , i n t e r a c t i o n s , p r o d u c t i v i t y of v a r i o u s systems and made i n the p r e v i o u s c h a p t e r s .  p r o f i t a b i l i t y have been  T h i s s e c t i o n b r i e f l y summarizes  the  c o n c l u s i o n s as they r e l a t e to v a r i o u s groups i n v o l v e d i n the i n d u s t r y . I m p l i c a t i o n s f o r f u r t h e r r e s e a r c h by s c i e n t i s t s and c o u l d prove b e n e f i c i a l to the i n d u s t r y are a l s o 6.2.1  economists which  presented.  For the O r c h a r d i s t  A number of c o n c l u s i o n s r e l e v a n t t o e x i s t i n g and i s t s can be drawn from the r e s e a r c h . systems, replacement  of p r e s e n t  and p o s s i b l e a d o p t i o n of new An important  These concern  potential  the c h o i c e between  systems, importance of weather v a r i a b l e s  technology.  c o n c l u s i o n f o r both e x i s t i n g and  future orehardists  i s t h a t h i g h d e n s i t y systems have the p o t e n t i a l to generate and  higher  income over a medium term (20 y e a r ) range, than do standard  standard result  systems.  orehard-  The h i g h e r d e n s i t y dwarf and  i n a p r e s e n t v a l u e of p r o d u c t i o n two  i f a l l i n p u t s a r e taken a t p r e s e n t l e v e l s . i n both e a r l i e r and h i g h e r y i e l d s .  and  semi-  semi-dwarf systems  to t h r e e times g r e a t e r  the p r e s e n t v a l u e of p r o d u c t i o n from standard and  profits  semi-standard  than  systems  High d e n s i t y systems r e s u l t  F e a t u r e s which i n c r e a s e b e a r i n g  s u r f a c e per a c r e , such as d e n s i t y and hedgerow p l a n t i n g have l a r g e s i g nificant  impacts  upon y i e l d s .  In terms of net p r e s e n t v a l u e , dwarf and both p r o f i t a b l e investments  semi-dwarf systems are  c o n s i d e r i n g a r e a l i n t e r e s t r a t e of  five  129 percent. but  Dwarf has  the h i g h e s t net p r e s e n t v a l u e f o r a 20 year p e r i o d ,  semi-dwarf can be e q u a l l y as p r o f i t a b l e when p l a n t e d i n the hedgerow  concept.  Standard  and semi-standard  systems are poor investments  r e s u l t i n g i n net l o s s e s over 20 y e a r s . of  orchards  Growers who  should c o n s i d e r a replacement  ability  these  However, t h e r e i s a l s o  t h a t h i g h d e n s i t y systems r e q u i r e g r e a t e r management e f f o r t than do low d e n s i t y systems.  y i e l d s , h i g h e r response  to i n p u t s , and  the f i n a n c i a l and d e n s i t y standard  and  The h i g h e r annual v a r i a t i o n i n g r e a t e r s u s c e p t i b i l i t y to geo-  g r a p h i c a l i n f l u e n c e s of the h i g h d e n s i t y systems are l i k e l y  to  render  r e s o u r c e management more d i f f i c u l t than f o r a  low  system.  Another c o n c l u s i o n of r e l e v a n c e to the o r c h a r d i s t i s the of weather v a r i a b l e s .  on y i e l d s .  importance  In g e n e r a l the weather v a r i a b l e s t e s t e d i n c l u d i n g  f r o s t , s u n l i g h t , maximum temperature and impacts  types  scheme towards h i g h e r d e n s i t y  p l a n t i n g s where s p e c i f i c c o n d i t i o n s p e r m i t . evidence  operate  both  The  impact  r a i n prove to have  significant  of weather v a r i a b l e s on y i e l d s  emphasizes  the need f o r o r e h a r d i s t s to c o n s i d e r the use of weather management t e c h niques. for  In p a r t i c u l a r ,  f r o s t p r e v e n t i o n systems would o f f e r  h i g h i n c r e a s e s i n y i e l d s i n many c a s e s .  The  potential  estimated f u n c t i o n s  i n d i c a t e t h a t a s i n g l e degree o f f r o s t below c r i t i c a l l e v e l s can i n a l o s s of up to 1700  pounds per a c r e i n y i e l d .  result  I f b l o c k s are geo-  g r a p h i c a l l y p l a c e d such that, the o r c h a r d i s t expects  a s i g n i f i c a n t amount  of  i n an  f r o s t d u r i n g the blossom p e r i o d , then investment  f r o s t p r e v e n t i o n system should be c o n s i d e r e d .  effective  At p r e s e n t , t h e r e a r e  d i r e c t means of c o n t r o l l i n g other weather i n f l u e n c e s b e s i d e s However, d u r i n g the e s t a b l i s h m e n t  no  frost.  phase of the o r c h a r d the grower should  choose a s i t e which gets maximum exposure to s u n l i g h t w i t h no  frost  130 pockets or channels. result  from proper  A s i g n i f i c a n t pay-off  s e l e c t i o n of the o r c h a r d  of weather ( f r o s t and light  and 6.2.2  i n increased y i e l d s  site,  r a i n ) are reduced, and  i f the n e g a t i v e  the p o s i t i v e a s p e c t s  (sun-  For the Government  governments i n s o l v i n g the low governments can a i d and  from t h i s r e s e a r c h which c o u l d  Increased  1  from government a i d i n the a d o p t i o n and  If  encourage the adjustment from low d e n s i t y to  i n farm incomes c o u l d be a c h i e v e d .  technology  help  income problem i n Okanagan o r c h a r d s .  h i g h d e n s i t y systems where f e a s i b l e , a s i g n i f i c a n t  related  aspects  temperature) are maximized.  There are some c o n c l u s i o n s  result  could  and  i r r i g a t i o n systems.  a i d the o r c h a r d i s t i n r e s o u r c e  a l l o c a t i o n by  and  l o n g term i n c r e a s e  incomes s h o u l d  also  s e l e c t i o n of weather  In g e n e r a l , governments  can  (1) improving  and  dissemin-  a t i n g i n f o r m a t i o n on the best management p r a c t i c e s , and by  (2)  improving  c a p i t a l markets a l l o w i n g c a p i t a l to be a l l o c a t e d f o r r e n o v a t i o n establishment  of e f f i c i e n t o r c h a r d  and  systems.  I n s t i t u t i o n s a l r e a d y e x i s t which c o u l d r e a d i l y be u t i l i z e d seminating  i n f o r m a t i o n and  i n providing capital.  Extension  Branch of the B.C.  in dis-  For example, the  M i n i s t r y of A g r i c u l t u r e and  the Farm  and  R u r a l Development D i v i s i o n of A g r i c u l t u r e Canada have s e v e r a l  personnel  involved i n extension  concrete  i n the o r c h a r d  industry.  I f they have  i n f o r m a t i o n on the p o t e n t i a l r e t u r n s of a l t e r n a t i v e systems and combinations, the management and  f i n a n c i a l requirements,  of r i s k i n v o l v e d f o r v a r i o u s t r e e - f r u i t  and  e n t e r p r i s e s then they  input  the degree can be  "'"The i n d u s t r y competes on a world market and f a c e s an e l a s t i c demand f u n c t i o n . Thus an i n c r e a s e i n p r o d u c t i o n should have l i t t l e e f f e c t on p r i c e .  of  131 s i g n i f i c a n t h e l p i n improving f o r the area of improving  resource a l l o c a t i o n i n the i n d u s t r y .  As  c a p i t a l markets, the Farm C r e d i t C o r p o r a t i o n  a l r e a d y a d m i n i s t e r s s e v e r a l programs aimed at f i n a n c i n g investments  which  w i l l improve a g r i c u l t u r a l e f f i c i e n c y .  these  I t seems f e a s i b l e to expand  programs to o f f e r f u r t h e r i n c e n t i v e s f o r o r c h a r d r e n o v a t i o n and  estab-  l i s h m e n t aimed at u t i l i z i n g h i g h d e n s i t y systems and weather r e l a t e d technology. 6.2.3  For the Marketing  Agency  A c o n c l u s i o n from t h i s r e s e a r c h i s t h a t weather v a r i a t i o n d u r i n g t h e blossom p e r i o d can e x p l a i n a l a r g e amount of t h e v a r i a t i o n i n average y i e l d s between y e a r s and r e g i o n s . f o u r c o u l d be improved or u t i l i z e d  The weather model developed as a f i r s t  i n chapter  s t e p i n p r e d i c t i n g the t o t a l  h a r v e s t of the a r e a on the b a s i s of o b s e r v a b l e weather i n f l u e n c e s d u r i n g the blossom p e r i o d .  Advance knowledge of q u a n t i t i e s would be u s e f u l i n  f o r m u l a t i n g market s t r a t e g i e s c o n c e r n i n g p r i c e , s t o r a g e and d i s t r i b u t i o n . A model which p r e d i c t s t o t a l y i e l d f o r the whole r e g i o n ( r a t h e r than y i e l d per a c r e f o r a sample) would be of g r e a t e r b e n e f i t to the agency.  By u t i l i z i n g  t h e i r own r e c o r d s on the aggregate  marketing  p r o d u c t i o n of  a p p l e s i n the r e g i o n and f o l l o w i n g the b a s i c s t r u c t u r e of the model mated i n t h i s r e s e a r c h a s u i t a b l e p r e d i c t i v e model c o u l d be  esti-  developed.  There would l i k e l y be s u f f i c i e n t data t o be a b l e to e s t i m a t e a model f o r each of the major v a r i e t i e s of apples produced i n the a r e a . the marketing  The c o s t to  agency of d e v e l o p i n g the p r e d i c t i v e model would l i k e l y  be  s m a l l , depending upon the a v a i l a b i l i t y of the d a t a . 6.2.4.  For the S c i e n t i s t  A major t h r u s t of s c i e n t i f i c r e s e a r c h a t the Summerland Research S t a t i o n has been aimed a t improving  the t e c h n i c a l e f f i c i e n c y and v i a b i l i t y  132 of  the t r e e - f r u i t i n d u s t r y i n the Okanagan.  i t a t e d by  information concerning  T h i s work would be  facil-  the s p e c i f i c areas where t e c h n o l o g i c a l  development would have the g r e a t e s t p a y - o f f i n improvement of the industry.  The  p r o d u c t i o n f u n c t i o n s estimated  i n the p r e s e n t  local  research  s e r v e to show some of these s p e c i f i c problem areas where t e c h n o l o g i c a l development should be Although  beneficial.  t h i s r e s e a r c h has  illustrated  the g r e a t e r p r o d u c t i v i t y and  p r o f i t a b i l i t y of h i g h d e n s i t y systems over the l o n g run, i t has the h i g h v a r i a b i l i t y difficult  of y i e l d s from these systems which makes them more  to manage on a y e a r - t o - y e a r  basis.  i s caused by a h i g h response to weather and tific of  r e s e a r c h can develop  technology  these f a c t o r s , then a s i g n i f i c a n t  Much of t h i s  variability  soil variation.  If scien-  which reduces the n e g a t i v e  Some developments a l o n g  t h i s l i n e have a l r e a d y taken p l a c e — e s p e c i a l l y i n the a r e a of  artificial  Other suggested  areas  p o l l i n a t i o n techniques,  a f f e c t e d by c o o l temperatures,  impacts  impediment to a widespread adop-^  t i o n of h i g h d e n s i t y systems c o u l d be removed.  prevention.  a l s o shown  frost  f o r r e s e a r c h a r e the development of new  breeds of p o l l i n a t i n g i n s e c t s l e s s  and v a r i e t i e s of a p p l e s where t h e r e i s  f a s t e r g e n e r a t i o n of p o l l e n , making p o l l i n a t i o n l e s s s u s c e p t i b l e to fall.  Developing  rain-  dwarf v a r i e t i e s which are b e t t e r adapted to l i g h t  and  rocky s o i l s c o u l d remove a f u r t h e r impediment to p l a n t i n g h i g h d e n s i t y dwarf systems. A f e a t u r e which stands e f f e c t s on y i e l d  i s b e a r i n g s u r f a c e per a c r e , as evidenced  tance of d e n s i t y and f e a t u r e s had of  out i n the f u n c t i o n s as having  tree design.  Given the dramatic  i n the f u n c t i o n s i t would be r e a s o n a b l e  f u r t h e r i n c r e a s i n g b e a r i n g s u r f a c e per  acre.  important by the  e f f e c t that  imporboth  to examine methods  133 Research s c i e n t i s t s c o u l d a l s o a i d i n improving f u r t h e r of p r o d u c t i o n  functions.  ety of systems now  Many experimental  exist  f o r pruning  c o n f r o n t i n g the p r e s e n t function  b l o c k s which i n c l u d e a v a r i -  f o r the purposes of s c i e n t i f i c r e s e a r c h .  adding more d e t a i l to the i n p u t r e c o r d s man-hours u t i l i z e d  estimation  and  research  By  f o r these b l o c k s , e s p e c i a l l y on  t h i n n i n g a c t i v i t i e s , the d a t a  c o u l d be a l l e v i a t e d  i n future  problems  production  estimation.  6.2.5  For the Economist  Several conclusions concerned w i t h  from t h i s r e s e a r c h  the Okanagan t r e e - f r u i t  industry.  f u n c t i o n a l c h a r a c t e r i s t i c s of the p r o d u c t i o n estimating  are of i n t e r e s t to economists These i n c l u d e  f u n c t i o n and  i t , methods f o r improving the p r e s e n t  estimates  the  methods of and  evaluation  of t e c h n o l o g i c a l developments. 6.2.5.1.  P r o p e r t i e s of the F u n c t i o n .  f u n c t i o n estimated  i n t h i s r e s e a r c h has  two  In summary the basic  (I) i t i s h i g h l y i n t e r a c t i v e w i t h r o o t s t o c k b e i n g i n t e r a c t i o n f o l l o w e d by age  and  by  s o i l , and  extremely l a r g e number of s i g n i f i c a n t orchard  level.  characteristics: the major source of  (2) i t i s composed of  i n p u t s and  separate  I t i s p a r t i c u l a r l y s e n s i t i v e to weather v a r i a b l e s  6.2.5.2 d e t a i l e d and production  one  the  and  density.  f u n c t i o n can be more e a s i l y expressed and w r i t t e n as  equations,  an  exogenous f a c t o r s at  f i x e d i n p u t s r e l a t e d to p l a n t i n g concept, t r e e d e s i g n and production  production  The  four  f o r each of the major systems.  Methodology of E s t i m a t i o n . disaggregated  production  E s t i m a t i o n of a h i g h l y  f u n c t i o n which r e f l e c t s  d e c i s i o n s of the o r c h a r d i s t i s d i f f i c u l t but  important  feasible.  The  l a r g e number of v a r i a b l e s l e a d s to severe problems w i t h m u l t i c o l l i n e a r i t y , h i n d e r i n g e s t i m a t i o n or making i t i m p o s s i b l e  i n some i n s t a n c e s .  134 The  stepwise r e g r e s s i o n procedure  used makes e s t i m a t i o n p o s s i b l e ,  a l t h o u g h i n t h e complete f u n c t i o n t h e f i n a l v a r i a b l e s s e l e c t e d depend somewhat on the o r d e r i n which groups o f v a r i a b l e s a r e e n t e r e d i n t o the model.  I t was f e l t  t h a t r e p r e s e n t i n g the complete p r o d u c t i o n p r o c e s s  i n a s i n g l e model taxed t h e r e g r e s s i o n technique t o t h e l i m i t usefulness.  When the stepwise procedure  i s combined w i t h  of i t s  partitioning  the d a t a by t r e e - s i z e c a t e g o r y , the e s t i m a t i o n i s f a c i l i t a t e d . C a t e g o r i z i n g o b s e r v a t i o n s by t r e e - s i z e and e s t i m a t i n g s e p a r a t e t i o n s f o r each c a t e g o r y improves e s t i m a t i o n without The  func-  a l o s s of information.  improvement i s due t o a. r e d u c t i o n i n t h e number o f v a r i a b l e s ,  restric-  t i o n on the range of i n p u t s and l e s s r e s t r i c t i o n s on the behaviour of interactions.  The e s t i m a t e s f o r the t r e e - s i z e c a t e g o r y f u n c t i o n s a r e  more s t a b l e , s i g n i f i c a n t and c o n s i s t e n t than those f o r t h e s i n g l e model.  I n d i v i d u a l v a r i e t y f u n c t i o n s were not s u c c e s s f u l l y On a r e g i o n a l b a s i s , v a r i a t i o n i n average  p a r t be e x p l a i n e d s o l e l y by weather f a c t o r s .  equation  estimated.  p r o d u c t i o n can f o r a l a r g e The model e s t i m a t e d on t h i s  b a s i s i s a u s e f u l t o o l f o r a s s e s s i n g the r e l a t i v e aggregate  e f f e c t of the  v a r i o u s weather f a c t o r s . 6.2.5.3  Improving  the P r e s e n t E s t i m a t e s o f t h e P r o d u c t i o n F u n c t i o n .  A primary a r e a f o r f u r t h e r r e s e a r c h would be i n improving estimates o f the f u n c t i o n s .  on t h e p r e s e n t  The e s t i m a t e s i n t h i s r e s e a r c h were  h i n d e r e d by two f a c t o r s which were (1) some i m p o r t a n t ! l e f t - o u t v a r i a b l e s , and  (2) extremely  l a r g e number of dependent v a r i a b l e s .  Both o f t h e s e  problems c o u l d be l a r g e l y remedied by u p d a t i n g and expanding d a t a base.  The important  the present  l e f t - o u t v a r i a b l e s were growing season  a c c u m u l a t i o n , machinery i n p u t s , l a b o u r and management.  Of t h e s e ,  heat  135 machinery i n p u t s would be the e a s i e s t f o r which to gather d a t a .  Some of  the measures mentioned p r e v i o u s l y such as t r a c t o r horsepower and c a p a b i l i t y would be adequate. and  i t i s simply a matter  form.  The  sprayer  Data on growing season heat are a v a i l a b l e  of man-hours t o c o l l a t e the d a t a i n t o  useable  s i t u a t i o n r e g a r d i n g l a b o u r and management i s more d i f f i c u l t .  To o b t a i n a c c u r a t e i n f o r m a t i o n on l a b o u r i t would be n e c e s s a r y t o have each o r c h a r d i s t keep r e c o r d s of time spent on t h e s p e c i f i c b l o c k s under observation.  T h i s would i n v o l v e s i g n i f i c a n t l y added r e s e a r c h e f f o r t ,  and might not be f e a s i b l e on a l a r g e s c a l e . worthwhile  to ask the o r c h a r d i s t to make an  However, i t would e s t i m a t e of how  spends on a p a r t i c u l a r b l o c k p e r f o r m i n g the important ities,  p a r t i c u l a r l y p r u n i n g and  e s t i m a t e but i t may labour.  The  thinning.  be s u f f i c i e n t  p r e s e n t r e s e a r c h has  inputs give both s i g n i f i c a n t Measuring  and  much time  labour-using a c t i v -  T h i s would o n l y be a rough  to c a p t u r e much of the i n f l u e n c e of shown t h a t farmers' e s t i m a t e s of o t h e r consistent coefficients.  the same h o l d s t r u e f o r apple p r o d u c t i o n  C e r t a i n proxy v a r i a b l e s may  d a t a on t h e s e c o u l d be gathered w i t h o u t  c a p t u r e some of the i n f l u e n c e and great a d d i t i o n a l e f f o r t .  These  i n c l u d e f a c t o r s such as y e a r s of s c h o o l i n g , type of s c h o o l i n g , y e a r s of e x p e r i e n c e and  contact with extension personnel.  Another a r e a f o r which b e t t e r d a t a can be o b t a i n e d concerns i n c i d e n c e and  he  the i n f l u e n c e of management has been a problem i n most  p r o d u c t i o n f u n c t i o n e s t i m a t e s and functions.  be  frost risk.  f r o s t v a r i a b l e used was  In the p r e s e n t o r c h a r d l e v e l e s t i m a t e s  a proxy  i n t h a t i t was  frost the  taken from the r e g i o n a l  weather s t a t i o n n e a r e s t to the observed  orchard.  proved  significance in regional'level  to be of g r e a t e r c o n s i s t e n c y and  f u n c t i o n s than i n o r c h a r d l e v e l f u n c t i o n s .  As a r e s u l t  frost  A b e t t e r e s t i m a t e of the  136 f r o s t o c c u r r i n g on each o r c h a r d c o u l d perhaps be developed o r c h a r d l o c a t i o n to zones on f r o s t maps. b e i n g c a r r i e d out by Kennedy, Andison  by r e l a t i n g  the  T h i s approach i s p r e s e n t l y  and Graham  (forthcoming).  I t i s recommended t h a t f u r t h e r s t u d i e s c o n t i n u e the approach of p a r t i t i o n i n g the data i n t o s e p a r a t e t r e e - s i z e c a t e g o r i e s . gested  I t i s sug-  t h a t c o n t r o l l i n g the l e v e l of other v a r i a b l e s by f u r t h e r p a r t i -  t i o n i n g of the data should a l s o be attempted and  t h a t data should  gathered w i t h the o b j e c t of making t h i s procedure 6.2.5.4  yzed u t i l i z i n g  The  Two  i n n o v a t i o n s which c o u l d be a n a l -  the f u n c t i o n s are f r o s t p r e v e n t i o n systems and  pollination.  present  i n e v a l u a t i n g the b e n e f i t s of c e r t a i n weather  related technological innovations.  mechanical  feasible.  E v a l u a t i o n of T e c h n o l o g i c a l Developments.  f u n c t i o n s c o u l d be u t i l i z e d  be  The  estimated  hand-  f u n c t i o n s s t a t e the e f f e c t of an  i n d i v i d u a l degree of f r o s t on p r o d u c t i o n and  i f this effect  is utilized  a l o n g w i t h i n f o r m a t i o n about the f r o s t p r e v e n t i o n c a p a b i l i t i e s  an  assessment can be made of the t o t a l b e n e f i t s t h a t w i l l a c c r u e by use the system g i v e n the expected average expected and  weather p a t t e r n .  f r o s t below c r i t i c a l  each degree r e s u l t s i n about 250  For example, i f the  l e v e l s i s f o u r accumulated degrees l b s per a c r e l e s s p r o d u c t i o n , then a  system which i s capable of p r e v e n t i n g the t o t a l amount of f r o s t result  i n a g a i n of 1,000  would be the i n s u r a n c e and Hand or mechanical  of  l b s of f r u i t per a c r e .  will  A further benefit  s t a b i l i z i n g e f f e c t p r o v i d e d by the system.  p o l l i n a t i o n c o u l d be s i m i l a r l y e v a l u a t e d i f i t i s  assumed t h a t the b e n e f i t s from t h i s a c t i v i t y a r e e q u a l to the l o s s i n p r o d u c t i o n t h a t would r e s u l t a t i o n such as r a i n and  from n e g a t i v e i n f l u e n c e s on n a t u r a l p o l l i n -  c o o l day  time temperatures.  Any  f u r t h e r inven-  t i o n which can combat n e g a t i v e weather i n f l u e n c e s or can be r e l a t e d  to  137 c o e f f i c i e n t s i n the p r o d u c t i o n  f u n c t i o n c o u l d be e v a l u a t e d  i n a similar  manner. 6.2.5.5  F u r t h e r Economic A n a l y s i s .  could u t i l i z e  Further  some of the f i n d i n g s o f t h i s r e s e a r c h  a n a l y s i s of t h e a p p l e i n d u s t r y , p a r t i c u l a r l y impact o f weather v a r i a b l e s i n t h e p r o d u c t i o n they should  economic  be i n c o r p o r a t e d  knowledge of t h e v a r i a n c e  studies  i n a more aggregate  i n supply  estimation.  The  f u n c t i o n suggests t h a t  i n an i n d u s t r y supply  function.  The  of weather v a r i a b l e s c o u l d g i v e an expected  supply v a r i a t i o n over f u t u r e y e a r s , which would be u s e f u l f o r s t a b i l i z a t i o n p o l i c y o r aggregate i n d u s t r y l e v e l models.  The p r o d u c t i o n  f u n c t i o n a l s o i d e n t i f i e s the important i n p u t s of which the c o s t s a r e a v a r i a b l e i n t h e supply  equation.  Any t r e n d s  i n the c o s t s of these  i n p u t s , which can be i d e n t i f i e d , would g i v e an i n d i c a t i o n o f f u t u r e supply  and r e t u r n s i n the i n d u s t r y . An a r e a f o r f u t u r e r e s e a r c h  i s the assessment of the t o t a l  where r e p l a n t i n g w i t h h i g h d e n s i t y systems i s f e a s i b l e . would be u s e f u l i n e s t i m a t i n g  the p o t e n t i a l s h i f t  f o r a s s o c i a t e d f i x e d i n p u t s and f o r a s s e s s i n g the i n d u s t r y o f a major s h i f t  This  acreage  knowledge  i n the d e r i v e d demand  the p o t e n t i a l impact on  t o h i g h d e n s i t y systems.  138 BIBLIOGRAPHY Arrow, K. J . , Chenery, H. B., Minhas, B. S., and Solow, R. M. 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"The P l a c e of Honey Bees i n Orchard Pollination." Nova S c o t i a Department of A g r i c u l t u r e and M a r k e t i n g , Mimeographed C i r c u l a r S e r v i c e — N o . 67 (1956). Kennedy, G. Some Economic C o n s i d e r a t i o n s Relevant t o Apple Orchard Replacement i n the Okanagan V a l l e y . Economics Branch, A g r i c u l t u r e Canada, Vancouver, B.C. (1976). Kennedy, G., Andison, A., and Graham, J . H i s t o r i c a l P r o d u c t i o n Data f o r S p e c i f i c Apple B l o c k s i n t h e Okanagan V a l l e y . Economics Branch, A g r i c u l t u r e Canada, Vancouver ( f o r t h c o m i n g ) . Kennedy, G., A n d i s o n , A., and Graham, J . H i s t o r i c a l P r o d u c t i o n Data f o r Tree F r u i t s i n the Okanagan V a l l e y . Economics Branch, A g r i c u l t u r e Canada, Vancouver ( f o r t h c o m i n g ) .  140  Kmenta, J . Elements (1971).  of E c o n o m e t r i c s .  The M a c m i l l a n Company, New  York  Lee, E. "A Study of Apple Y i e l d R e l a t i o n s h i p s i n 1969 i n the Okanagan Area of B r i t i s h Columbia." M.Sc. T h e s i s i n A g r i c u l t u r a l Economi c s , U n i v e r s i t y o f B r i t i s h Columbia, Vancouver (1972). Mackenzie, W. M., and Poetschka, L. E. The Development of Producer M a r k e t i n g Boards i n Canadian A g r i c u l t u r e . Department of P o l i t i c a l Economy, U n i v e r s i t y of A l b e r t a , Edmonton (1956). MacPhee, D. F. R o y a l Commission on the Tree F r u i t I n d u s t r y of B r i t i s h Columbia. B r i t i s h Columbia Department of A g r i c u l t u r e , V i c t o r i a (1958). Mann, A. J . , Keane, W. L., and L a p i n s , K. "Winter I n j u r y of T r e e F r u i t s i n B r i t i s h Columbia." S c i e n t i f i c A g r i c u l t u r e , A p r i l (1952), V o l . 32, p. 173. Marschak, J . , and Andrews, W. Theory of P r o d u c t i o n . " no. 3, p. 143.  "Random Simultaneous E q u a t i o n s and the Econometrica, J u l y - O c t o b e r (1944), V o l . 12,  M a r s h a l l , A. "A M u l t i p e r i o d Management A n a l y s i s of an Orchard i n the Okanagan V a l l e y . " B.Sc. T h e s i s i n A g r i c u l t u r a l Economics, U n i v e r s i t y of B r i t i s h Columbia, Vancouver (1974). M e t e o r o l o g i c a l Records, Dept. of T r a n s p o r t , M e t e o r o l o g i c a l Branch 1974) , Government of Canada.  (1967-  Mundlak, Y. " E m p i r i c a l P r o d u c t i o n F u n c t i o n F r e e o f Management B i a s . " , J o u r n a l of Farm Economics, February (1961), V o l . 43, no. 1, p. 44. Rao,  P., and M i l l e r , R. A p p l i e d E c o n o m e t r i c s . Wadsworth P u b l i s h i n g Company, I n c . , Belmont, C a l i f o r n i a (1971).  Smith, J . A. "Development of F r u i t Growing i n the American S t a t e s and Canadian P r o v i n c e s — B r i t i s h Columbia," i n H i s t o r y of F r u i t Growing and H a n d l i n g i n U.S.A. and Canada 1860-1972, W. H. U p s h a l l ( e d . ) . Regatta C i t y P r e s s , Kelowna, B.C. (1976). " S o i l Management P r a c t i c e s f o r Reducing Winter I n j u r y . " Okanagan A g r i c u l t u r a l C l u b , Mimeographed, B r i t i s h Columbia Department o f A g r i c u l t u r e , Summerland, B.C. (1956). Swales, J . E. Commercial Apple Growing i n B r i t i s h Columbia. British Columbia Dept. o f A g r i c u l t u r e , H o r t i c u l t u r a l Branch, Queen's P r i n t e r , V i c t o r i a (1971). T h e i l , H. P r i n c i p l e s of E c o n o m e t r i c s . York (1971).  John W i l e y and Sons, I n c . ,  New  141 T r e e F r u i t P r o d u c t i o n Guide f o r I n t e r i o r D i s t r i c t s . B r i t i s h Columbia M i n i s t r y of A g r i c u l t u r e , Queen's P r i n t e r , V i c t o r i a , B.C. (1975). Van Roechoudt, L. L. "Dwarf Apple Trees i n Okanagan Commercial O r c h a r d s . " M.Sc. T h e s i s i n H o r t i c u l t u r e , U n i v e r s i t y of B r i t i s h Columbia, Vancouver (1962).  142  APPENDIX A P r o d u c t i v i t y of Orchard Systems  143 Dwarf P r o d u c t i o n T a b l e A - l shows t h e p r e d i c t e d y i e l d streams f o r the dwarf sample which was 42% Red D e l i c i o u s , 21% M c i n t o s h , 21% Golden D e l i c i o u s , 8% Spartan, and 8% Tydeman. The b l o c k s were mainly hedgerow p l a n t i n g (96%) w i t h t h e r e s t f r e e s t a n d i n g . About f o u r p e r c e n t o f the sample had f i x e d overhead i r r i g a t i o n w i t h the r e s t h a v i n g p o r t a b l e s p r i n k l e r systems. Most of t h e b l o c k s were on sandy s o i l (94%) w i t h t h e remainder on c l a y s o i l . Spur-type b l o c k s r e p r e s e n t e d 29% o f the o b s e r v a t i o n s . A l l i n p u t s and weather v a r i a b l e s were s e t a t mean l e v e l s f o r t h e sample. P e s t i c i d e i s $65 per a c r e , f e r t i l i z e r i s 361 l b s p e r acre, d e n s i t y i s 362 t r e e s per a c r e , and s u n l i g h t i s 85.8 hours and f r o s t below c r i t i c a l levels i s n i l . P r e d i c t e d y i e l d streams a r e shown f o r spur v s . non-spur, and sandy, c l a y v s . rocky s o i l s . No d i f f e r e n t i a t i o n w i t h r e s p e c t t o t r e e d e s i g n o r i r r i g a t i o n method were made as t h e s e v a r i a b l e s were n o t i n c l u d e d i n t h e f u n c t i o n s because of m u l t i c o l l i n e a r i t y problems. F o r each y i e l d stream a l l o t h e r v a r i a b l e s a r e taken a t average l e v e l s . The y i e l d s a r e p r e d i c t e d from t a b l e 4.7 i n chapter f o u r .  Semi-dwarf P r o d u c t i o n The semi-dwarf y i e l d streams were p r e d i c t e d from t a b l e 4.6 i n chapter f o u r . The sample o b s e r v a t i o n s a r e composed o f 39% Red D e l i c i o u s , 28% Golden D e l i c i o u s , 23% M c i n t o s h , 5% Spartan, and 5% Tydeman. Approximately 90% of t h e b l o c k s were i n sandy s o i l w i t h the remainder on clay s o i l . However, no d i f f e r e n t i a t i o n o f y i e l d s between s o i l types was p o s s i b l e because o f m u l t i c o l l i n e a r i t y problems. Most o f the sample was f r e e s t a n d i n g (74%) w i t h the r e s t p l a n t e d i n hedgerow f a s h i o n . About f i v e p e r c e n t o f the b l o c k s had overhead i r r i g a t i o n , and 11% had trickle irrigation; t h e remainder h a v i n g t h e p o r t a b l e s p r i n k l e r system. Spur type p l a n t i n g s accounted f o r 34% of t h e o b s e r v a t i o n s . The average d e n s i t y o f each b l o c k was 306, t r e e s per a c r e and t h e average f e r t i l i z e r was 355 l b s p e r a c r e . There was an average of 86.0 hours o f b r i g h t sunl i g h t d u r i n g bloom p e r i o d and .03 degrees of f r o s t below c r i t i c a l l e v e l s . P e s t i c i d e a p p l i c a t i o n was constant a t $65 per a c r e .  Semi-standard  Production  The y i e l d s a r e p r e d i c t e d from t h e i n t e r a c t i v e e q u a t i o n f o r semistandard i n t a b l e 4.7. The sample o b s e r v a t i o n s a r e composed o f a number of v a r i e t i e s i n c l u d i n g 29% Golden D e l i c i o u s , 27% Red D e l i c i o u s , 14% Mclntoch, 7% Newton, 7% Spartan, 8% Winesap, and 8% Tydeman. About 87% o f the b l o c k s were f r e e s t a n d i n g w i t h the r e s t p l a n t e d i n hedgerow f a s h i o n , w h i l e 46% were spur type and 54% non-spur. They were p l a n t e d on a l l t h r e e s o i l t y p e s , 54% on sandy s o i l , 26% on c l a y s o i l , and 20% on rocky s o i l . The average p e s t i c i d e a p p l i c a t i o n was $79 p e r a c r e , the average f e r t i l i z e r was 343 l b s per a c r e , and average d e n s i t y was 205 t r e e s per a c r e . During blossom p e r i o d s t h e r e was an average of 52.4  144 hours of b r i g h t s u n l i g h t , .15 i n c h e s of r a i n , 61 accumulated degrees above 65 F. and .89 degrees of f r o s t : below c r i t i c a l l e v e l s .  Standard P r o d u c t i o n A l l of the observed b l o c k s were f r e e s t a n d i n g w i t h p o r t a b l e s p r i n k l e r i r r i g a t i o n systems. The s o i l s ranged from sandy ( 5 % ) , c l a y (75%) and rocky (20%). The average d e n s i t y was 61 t r e e s per a c r e , the average f e r t i l i z e r a p p l i c a t i o n was 217 l b s per a c r e , and the a v e r age p e s t i c i d e c o s t was $42 per a c r e . The t r e e s were 92% Golden D e l i c i ous w i t h the remainder Red D e l i c i o u s . D u r i n g blossom p e r i o d s t h e r e was an average of .10 i n c h e s of r a i n , 3.74 accumulated degrees of f r o s t below c r i t i c a l l e v e l s and 67.6 accumulated degrees above 65 F.  145 Table A . l .  Average  Year  Dwarf P r o d u c t i o n  Non-spur  Spur  Sandy  Soil  Clay  Soil  1  0  0  0  0  0  2  0  0  0  0  0  3  0  1573  0  0  0  4  12658  15717  11409  12941  5111  5  26802  29861  25553  27085  19255.  6  40946  44005  39697  41229  33399  7  48018  51077  46769  48301  40471  8  55090  58149  53841  55373  47543  9  62162  65221  60913  62445  54615  10  62162  65221  60913  62445  11  62162  65221  60913  62445  54615  12  62162  65221  60913  62445  54615  13  62162  65221  60913  62445  54615  62162  65221  60913  62445  54615  15  62162  65221  60913  62445  54615  16  62162  65221  60913  62445  54615  17  62162  65221  60913  62445  54615  18  62162  65221  60913  62445  54615  19  62162  65221  60913  62445  54615  20  62162  65221  60913  62445  54615  25821  27410  25201  25962  22072  14  .  Present Value $ Less Harvest Costs  '  54615  146 T a b l e A.2.  Year  Average  Overhead Irrigation  Semi-Dwarf P r o d u c t i o n — l b s per a c r e  NonOverhead Irrigation  Hedgerow  NonHedgerow  Spur  NonSpur  1  0  0  0  0  0  0  0  2  0  0  0  0  0  0  0  3  0  20848  0  12751  0  0  0  4  0  32998  5485  24901  5414  1031  0  5  10810  45148  17635  37051  17564  13181  9701  6  22960  57298  29785  49201  29714  25331  21851  7  29035  63373  35860  55276  35789  31406  27926  8  35110  69448  41935  61351  41864  37481  34001  9  41185  75523  48010  67426  47939  43556  40076  10  41185  75523  48010  67426  47939  43556  40076.  11  41185  75523  48010  67426  47939  43556  40076  12  41185  75523  48010  67426  47939  43556  40076  13  41185  75523  48010  67426  47939  43556  40076  14  41185  75523  48010  67426  47939  43556  40076  15  41185  75523  48010  67426  47939  43556  40076  16  41185  75523  48010  67426  47939  43556  40076  17  41185  75523  48010  67426  47939  43556  40076  18  41185  75523  48010  67426  47939  43556  40076  19  41185  75523  48010  67426  47939  43556  40076  20  41185  75523  48010  67426  47939  43556  40076  16171  34088  19504  29710  19469  17631  15974  Present Value $ Less Harvest Costs  147 Semi -Standard P r o d u c t i o n — •lbs per a c r e  T a b l e A.3.  Year  Average  Hedgerow  NonHedgerow  Sandy  Soil  Clay  Soil  Rocky  Soil  1  0  0  0  0  0  0  2  0  0  0  0  0  0  3  0  0  0  0  0  0  4  0  11169  0  0  0  0  5  3842  15011  2542  3260  0  0  6  6442  17611  5142  5860  1174  1088  7  9042  20211  7742  8460  3774  3688  8  11642  22811  10342  11060  6374  6288  9  14242  25411  12942  13660  8974  8888  10  16842  28011  15542  16260  11574  11488  11  18142  29311  16842  17560  12874  12788  12  19442  30611  18142  18860  14174  14088  13  20742  31911  19442  20160  15474  15388  14  22042  33211  20742  21460  16774  16688  15  23342  34511  22042  22760  18074  17988  16  23342  34511  22042  22760  18074  17988  17  23342  34511  22042  22760  18074  17988  18  23342  34511  22042  22760  18074  17988  19  23342  34511  22042  22760  18074  17988  20  23342  34511  22042  22760  18074  17988  Present Value $ 7398 12945 Less Harvest Costs  6806  7133  5059  5122  T a b l e A.4.  Year  Average  Standard P r o d u c t i o n — l b s per a c r e  Sandy S o i l  Clay S o i l  Rocky  Soil  1  0  0  0  0  2  0  0  0  0  3  0  0  0  0  4  0  0.  0  0  5  10460  15189  11331  6473  6  11575  16304  12446  7588  7  12690  17419  13561  8703  8  13805  18534  14676  9818  9  14920  19649  15791  10933  10  16035  20764  16906  12048  11  17150  21879  18021  13163  12  18265  22994  19136  14278  13  18380  23109  19251  14393  14  19495  24224  20366  15508  15  20610  25339  21481  16623  16  21725  26454  22596  17738  17  21725  26454  22586  17738  18  21725  26454  22587  17738  19  21725  26454  22587  17738  20  21725  s26454  22587  17738  7630  9780  8026  5817  Present Value $ Less Harvest Costs  149  APPENDIX B Annual Costs and Returns of V a r i o u s Systems  150 Table B . l .  Per Acre Costs and R e t u r n s — D w a r f  Costs  Year  Materials $  Machinery  Returns i Value o f Crop Less Harvest Costs  TT  Labour  Land  $  $  $  Total $  c  $  1  2007  484  545  250  3286  0  2  147  177  183  250  757  0  3  117  166  594  250  1127  0  4  124  176  669  250  1219  646  5  124  170  745  250  1289  1367  6  124  164  745 '  250  1283  2088  7  124  158  745  250  1277  2449  8  124  152  745  250  1271  2810  9  124  148  745  250  1267  3170  10  124  142  745  250  1261  3170  11  124  438  745  250  1557  3170  12  124  189  745  250  1308  3170  13  124  183  745  250  1302  3170  14  124  176  745  250  1295  3170  15  124  170  745  250  1289  3170  16  124  164  745  250  1283  3170  17  124  158  745  250  1277  3170  18  124  152  745  250  1271  3170  19  124  148  745  250  1267  3170  20  124  142  745  250  1261  3170  17372  25821  Present Value Net Present Value  $8449  151 T a b l e B.2.  Per Acre Costs and Returns- -Semi-Dwarf  Total  Returns Value of Crop Less Harvest Costs  $  $  Costs  Year  M a t e r i a l s Machinery  Labour  Land  $  $  $  $  1  1800  478  500  250  3028  0  2  141  175  168  250  734  0  3  111  166  520  250  1047  0  4  121  172  585  250  1128  0  5  121  165  650  250  1186  551  6  121  159  650  250  1180  1171  7  121  153  650  250  1174  1481  8  121  148  650  250  1169  1791  9  121  142  650  250  1163  2100  10  121  138  650  250  1159  2100  11  121  437  650  250  1458  2100  12  121  186  650  250  1207  2100  13  121  179  650  250  1200  2100  14  121  172  650  250  1193  2100  15  121  165  650  250  1186  2100  16  121  159  650  250  1180  2100  17  121  153  650  250  1174  2100  18  121  148  650  250  1169  2100  19  121  142  650  250  1163  2100  20  121  138  650  250  1159  2100  16048  16171  Present Value  Net Present Value  $123  152 T a b l e B.3.  Per A c r e Costs and R e t u r n s — S e m i - S t a n d a r d  Costs  Year  Returns Value of Crop L e s s Harvest  Materials  Machinery  $  $  $  $  $  1  1580  489  420  250  2739  0  2  99  182  140  250  671  0  3  99  176  585  250  1110  0  4  146  182  625  250  1203  0  5  146  175  665  250  1236  200  6  146  169  705  250  1270  335  7  146  163  745  250  1304  470  8  146  158  745  250  1299  605  9  146  152  745  250  1293  741  10  146  147  745  250  1288  876  11  146  459  745  250  1600  943  12  146  198  745  250  1339  1011  13  146  190  745  250  1331  1079  14  146  182  745  250  1323  1146  15  146  175  745  250  1316  1214  16  146  169  745  250  1310  1214  17  146  163  745  250  1304  1214  18  146  158  745'  250  1299  1214  19  146  152  745  250  1293  11214  20  146  147  745  250  1288  1214  16906  7534  Present Value  Net P r e s e n t Value -$9363  Labour  Land  Total  Cost  $  153 T a b l e B.4.  Per Acre Costs and  Returns—Standard  Costs  ' Year  Materials  Machinery  Labour  Land  $  $  $  $  Total  Returns Value o f Crop Less Harvest Cost  $  $  1  1243  481  315  250  2289  0  2  115  186  160  250  711  0  3  70  178  378  250  876  0  4  108  186  390  250  934  0  5  108  179  403  250  940  544  6  108  174  415  250  947  602  7  108  168  428  250  954  660  8  108  162  440  250 •  960  718  9  108  158  453  250  969  776  10  108  152  465  250  975  834  11  108  459  478  250  1295  892  12  108  200  490  250  1048  950  13  108  193  490  250  1041  956  14  108  186  490  . 250  1034  1014  15  108  179  490  250  1027  1072  16  108  174  490  250  1022  1130  17  108  168  490  250  1016  1130  18  108  162  490  250  1010  1130  19  108  158  490  250  1006  1130  20  108  152  490  250  1000  1130  13359  7780  Present Value  Net P r e s e n t V a l u e  -$5,579  

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