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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., University of 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 i n 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 thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA November, 1977 (c)Roger Charles McNeill, 1977 In presenting th i s thes is in pa r t i a l fu l f i lment of the requirements for an advanced degree at the Un ivers i ty of B r i t i s h Columbia, I agree that the L ibrary shal l make it f ree ly ava i l ab le for reference and study. I further agree that permission for extensive copying of th is thesis for scho lar ly purposes may be granted by the Head of my Department or by his representat ives. It is understood that copying or pub l i ca t ion of th is thesis fo r f inanc ia l gain sha l l not be allowed without my writ ten permission. Department of Agricultural Economics The Univers i ty of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date April 26, 1978 ABSTRACT The basic objective of t h i s thesis was to estimate disaggregated production functions for apple orchard systems i n the Okanagan area of B r i t i s h Columbia. Because of the complexity of the production process and r e l a t i v e l y recent technological developments, i t was considered that production function estimation would be useful i n aiding resource a l l o c a t i o n . In order to be useful at the farm l e v e l i t was necessary that the model incorporate factors of major importance i n managerial decisions. P a r t i c u l a r emphasis was placed on orchard establishment a l t e r n a t i v e s r e l a t i n g to the planting concept which included density, tree design and rootstock. Weather variables and i n t e r a c t i o n s were also of major i n t e r e s t . The conceptual model was therefore highly disaggregated and included a large number of v a r i a b l e s . Measurement of these v a r i a b l e s was based on data obtained from an orchard survey plus records of experimental blocks at the Summerland Research Station. Problems i n estimation arose due to the large number of explan-atory v a r i a b l e s . Two basic methods were used i n dealing with these problems. The f i r s t involved a sequential t e s t i n g procedure whereby groups of explanatory variables were entered separately into multiple regressions with y i e l d per acre as the dependent v a r i a b l e . Subsets of each group were retained i n the f i n a l model. The second method involved the estimation of separate functions for each t r e e - s i z e category, thereby eliminating rootstock and re l a t e d i n t e r a c t i o n s as explanatory v a r i a b l e s . In both cases weather v a r i a b l e s were pre-selected based on the r e s u l t s of a separately estimated regional model which used only weather influences as explanatory v a r i a b l e s . i i i The s t a t i s t i c a l r e s u l t s showed that the production function could best be represented by separate functions for each t r e e - s i z e category. Interactions proved to be s i g n i f i c a n t and added considerable explan-atory power to the model. Weather variables were also s i g n i f i c a n t , e s p e c i a l l y at the regional l e v e l where a large amount of v a r i a t i o n i n average y i e l d s could be explained by blossom time influences. The estimated production functions were used to predict y i e l d streams over a 20 year period. I t was shown under c e r t a i n conditions that the p o t e n t i a l e x i s t s for much higher y i e l d s and p r o f i t s from high density systems than from low density systems. The functions also showed the higher v a r i a b i l i t y of y i e l d s from high density systems and greater responsiveness to v a r i a b l e inputs and exogenous f a c t o r s , implying that a greater management e f f o r t i s required i n t h e i r operation. Other applications of the production functions were discussed including 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 harvest volume from observed blossom time weather v a r i a b l e s , evaluation of weather re l a t e d technology, and d i r e c t i o n s of future s c i e n t i f i c and economic research. i v TABLE OF CONTENTS Chapter I INTRODUCTION 1 1.1 Background Information 2 1.1.1 The Okanagan Region 2 1.1.2 History of F r u i t Growing i n the Region . 2 1.1.3 Economic Importance 4 1.1.4 External and C u l t u r a l Benefits 4 1.2 The Problem Setting 5 1.3 Attempts to Aid Resource A l l o c a t i o n 6 1.3.1 Role of S c i e n t i f i c Research 6 1.3.2 Role of Economic Research 7 1.3.3 The Production Function Approach . . . . 8 1.4 S p e c i f i c Objectives of the Thesis 9 1.5 Research Procedure 10 1.6 Guide to Thesis 13 II THE ECONOMIC MODEL 14 2.1 The Production Function 14 2.1.1 Parameters 15 2.1.2 Stages of Production 15 2.1.3 Other C h a r a c t e r i s t i c s 16 2.2 Functional Forms 17 2.2.1 Homogeneous Functions 18 2.2.2 Non-homogeneous Functions 20 2.3 Producer Behaviour 23 2.3.1 P r o f i t Maximization 24 2.3.2 Constrained Output Maximization . . . . 25 2.3.3 Constrained Cost Minimization 26 2.4 Implications f o r Estimation 27 2.4.1 V a r i a t i o n i n Input Levels 27 2.4.2 M u l t i c o l l i n e a r i t y of Inputs 28 2.4.3 Simultaneous Equation Bias 29 2.4.4 Left-out Variables 31 2.4.5 Summary of Implications for Estimation . . . 32 I I I THE CONCEPTUAL MODEL AND MEASUREMENT OF VARIABLES . . . . 34 3.1 Management 35 3.2 Physical Features and Fixed Inputs 37 3.2.1 S o i l 37 3.2.2 Frost S u s c e p t i b i l i t y 38 3.2.3 Frost Prevention System 39 3.2.4 P o l l i n a t i o n Method 39 3.2.5 Rootstock 40 3.2.6 Density 41 3.2.7 Spur-type 42 3.2.8 Tree Design 42 3.2.9 Variety 43 3.2.10 Age of Trees 43 3.2.11 Machinery Inputs 44 3.2.12 I r r i g a t i o n System 46 3.3 Variable Inputs 46 3.3.1 F e r t i l i z e r 46 3.3.2 Pesticides 48 3.3.3 I r r i g a t i o n 49 3.3.4 Labour 50 3.4 Weather Variables 53 3.4.1 Blossom Influences 53 3.4.2 Spring Frost 54 3.4.3 Temperature 56 3.4.4 Sunlight 56 3.4.5 Wind 57 3.4.6 Rain 58 3.4.7 Growing Season Influences 58 3.4.8 Cold Winter Temperatures 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 PRODUCTION FUNCTION 67 4.1 Estimation Strategy 67 4.2 Results for the Weather Model 72 4.2.1 Estimations Excluding Sunlight 75 4.2.2 Estimations Including Sunlight 77 4.2.3 E f f e c t of Weather on D i f f e r e n t Grades of Apples 79 4.2.4 Conclusions Regarding the Weather Model . . 81 4.3 The Complete Orchard Level Model . . 82 4.3.1 Robustness of the Estimates 85 4.3.2 M u l t i c o l l i n e a r i t y Problems . 88 4.3.3 E f f e c t s of Disaggregation 91 4.4 Tree-size and Variety Functions 92 4.4.1 Results for the Tree-size Functions . . . . 93 4.4.2 Robustness of Tree-size Category Estimates . . . . . 103 4.4.3 Variety Functions 103 4.5 Conclusions Regarding Methodology 104 4.6 Importance of Weather Variables 107 4.7 Importance of Interactions 109 V APPLICATION OF THE ESTIMATED PRODUCTION FUNCTIONS . . . 112 5.1 Adjustments i n Orchard Establishment and Operation 112 5.1.1 Relative P r o d u c t i v i t y of Orchard Systems 114 5.1.2 Relative P r o f i t a b i l i t y of Orchard Systems 116 5.1.3 Other Factors Influencing the Choice Between Systems 119 5.2 Evaluation of Technological Innovations 121 5.3 P r e d i c t i n g Y i e l d s 122 v i i VI SUMMARY, CONCLUSIONS AND IMPLICATIONS FOR FUTURE RESEARCH . . . . . . 123 6.1 Summary 123 6.2 Conclusions and Implications for Further Research 128 6.2.1 For the Orchardist 128 6.2.2 For the Government 130 6.2.3 For the Marketing Agency 131 6.2.4 For the S c i e n t i s t 131 6.2.5 For the Economist 133 BIBLIOGRAPHY . . 138 APPENDIX A . . . . . 142 APPENDIX B . . . 149 v i i i LIST OF TABLES 3.1 Index of S o i l Type Based on Farmer's Estimate of Texture . . 38 3.2 Tree Size Index Based on Rootstock Type 41 3.3 Indexed Age of Trees Based on Rootstock C l a s s i f i c a t i o n . . . 45 3.4 Temperatures Below Which Damage Occurs During Blossom Period 54 3.5 Al t e r n a t i v e Measures of Frost During Bloom 55 3.6 Al t e r n a t i v e Measures of Temperature During Bloom 56 3.7 Al t e r n a t i v e Measures of Sunlight During Bloom 57 3.8 A l t e r n a t i v e Measures of R a i n f a l l During Bloom . 58 4.1 Estimated Functions for Weather Model—Excluding Sunlight 76 4.2 Estimated Functions for Weather Model—Including Sunlight 78 4.3 Estimated Functions for Weather M o d e l — D i f f e r e n t Grade Categories 80 4.4 C o l l i n e a r i t y with an Interaction 83 4.5 Estimated Functions f o r Complete Orchard Level Model . . . . 86 4.6 Estimated Functions for Dwarf and Semi-dwarf Categories . . 95 4.7 Estimated Functions f o r Standard and Semi-standard Categories 98 5.1 Present Value of Production from Major Apple Production Systems for 20 years 115 5.2 Present Values of Costs and Returns for Apple Systems . . . 118 5.3 Level and V a r i a b i l i t y of Apple Yi e l d s from Four A l t e r n a t i v e Systems over a 20 year Period 119 6.1 Summary of S t a t i s t i c a l Results 127 A . l Dwarf Production 145 A. 2 Semi-Dwarf P r o d u c t i o n — l b s per acre 146 A. 3 Semi-Standard P r o d u c t i o n — l b s per acre . . . 147 A. 4 Standard P r o d u c t i o n — l b s per acre 148 B. l Per Acre Costs and Returns—Dwarf 150 B.2 Per Acre Costs and Returns—Semi-dwarf 151 B.3 Per Acre Costs and Returns—Semi-standard 152 B.5 Per Acre Costs and Returns—Standard 153 i x LIST OF FIGURES 3.1 Factors i n Apple Production 36 3.2 Comparison of concepts, required measure and actual measures 63 4.1 Overview of the Estimation Procedure 70 X ACKNOWLEDGEMENTS I wish to express my sincere appreciation to Dr. John Graham, my thesis advisor, for h i s guidance i n the undertaking of t h i s research. The organization and presentation of the f i n a l manuscript has been greatly improved by his suggestions.. Acknowledgements must be made to other members of the thesis committee including Dr. G. Kennedy for h i s o r i g i n a l conceptualization of the 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 for h i s valuable comments on methodology, and Dr. R. A l l e n f or h i s review on short notice. Mr. Maurice Welsh, h o r t i c u l t u r i s t with the B.C. Mi n i s t r y of Ag r i c u l t u r e provided information on te c h n i c a l aspects of apple production, p a r t i c u l a r l y i n the area of weather v a r i -ables, which greatly f a c i l i t a t e d t h i s research. Thanks are extended to Ag r i c u l t u r e Canada for p r o v i s i o n of fi n a n -c i a l and research support. I am indebted to Mr. A. Andison of that organization for 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 of the data. The continuing support and encouragement of many past and present members of the Department of A g r i c u l t u r a l Economics at U.B.C. has been deeply appreciated. CHAPTER I INTRODUCTION The Okanagan t r e e - f r u i t industry has been the subject of consider-able economic research i n the l a s t three decades. Some major studies have been ca r r i e d out concerning the structure and performance of the industry by Hudson (1973) and MacPhee (1958) from which recommendations have been made on how to improve the incomes of the growers. The most recent major study by Hudson recommends, among other things, that growers receive d i r e c t personal assistance to improve technological and managerial weaknesses. In order for government o f f i c i a l s and industry f i e l d s t a f f to e f f e c t i v e l y carry out t h i s recommendation i t i s necessary for them to have information on the r e l a t i v e p r o d u c t i v i t y of orchard systems, the e f f e c t s of input v a r i a t i o n , and the importance of geographical f a c t o r s . Recently economic research by Dorling (1975), Lee (1972) , and Campbell (1976) has aimed at improving t h i s knowledge through orchard surveys and s t a t i s t i c a l a n a l y s i s . In 1975, the Economics Branch of A g r i c u l t u r e Canada began construction of a d e t a i l e d data base containing information on many of the variables i n f r u i t production and corresponding y i e l d s . This data base i s undergoing continual updating each season. The information has been c o l l a t e d and presented i n a form that enables growers and exten-sion personnel 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 various h o r t i c u l t u r a l practices and input l e v e l s (Kennedy, Andison and Graham, forthcoming). This thesis has taken the objective somewhat further by 1 2 using regression analysis to estimate production functions for apples, using the same body of data. The impact of each recorded v a r i a b l e on apple production can be estimated, hence providing better information for management practices as well as providing some d i r e c t i o n for further economic and s c i e n t i f i c research. 1.1 Background Information 1.1.1 The Okanagan Region i In t h i s thesis the Okanagan region r e f e r s to the Canadian portion of the Okanagan Valley and the adjacent Similkameen Valley. This region i s located i n the south c e n t r a l i n t e r i o r of B r i t i s h Columbia, beginning at Osoyoos on the American border from where i t branches out north, following the Okanagan system of lakes and r i v e r s and north-east through the Similkameen Valley. The producing area of the Okanagan Valley runs about 100 miles north to Vernon, while the producing area of the Simil-" kameen Valley i s confined to a short b e l t between Keremeos and Cawston. 1.1.2 History of F r u i t Growing i n the Region The industry 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 for a number of reasons. The f i r s t plantings i n the region were associated with h i s t o r i c a l pioneer-ing settlements such as the Oblate Mission i n Kelowna i n 1862 and the E l l i s Ranch i n Penticton i n 1869. The f i r s t plantings i n the S i m i l -kameen were i n 1867, while other parts of the Okanagan region opened up i n the 1890's and early 1900's except for the southern area around O l i v e r which was planted i n the 1920's. S i g n i f i c a n t commercial production began around 1900. The e f f o r t s of early f r u i t growers i n the region to obtain an orderly 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 . The Okanagan 3 United Growers Co-op was formed i n 1914 with the object of developing an orderly market strategy and was successful i n obtaining governmental support for a compulsory marketing a s s o c i a t i o n . The B.C. Produce Marketing Act passed i n 1927, superceded i n 1934 by Federal L e g i s l a t i o n and by the B.C. Natural Products Marketing Act of 1937 was to a large extent due to the consistent e f f o r t s and lobbying of the growers' assoc-i a t i o n . This o r i g i n a l act and subsequent l e g i s l a t i o n have since played 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 industry's i n t e r a c t i o n with the Federal Research Station i n Summerland has resulted i n important technological advances which have been adopted l o c a l l y , n a t i o n a l l y and i n t e r n a t i o n a l l y . The s t a t i o n set-up i n 1914 under the federal experimental farm system has devoted a great deal of i t s research e f f o r t s to pomology. Much of the study has dealt with productive and marketing problems of the l o c a l apple growing industry. Work has been ca r r i e d out i n developing new v a r i e t i e s adapted to the area and having good market acceptance. The most notable new v a r i e t y developed was the Spartan v a r i e t y , now a major commercial v a r i e t y of the region. The station's research into storage systems, spray equipment, i r r i g a t i o n systems and f r o s t prevention has resulted i n several applications f or the l o c a l industry. The trends towards dwarfing root-stocks, higher density plantings and spur-type trees was influenced by the station's research. In the area of tree n u t r i t i o n , research concern-ing boran and nitrogen i s credited with r e v i t a l i z i n g the industry i n the 1930's. More recent research i n food processing has resulted i n a better q u a l i t y of j u i c e , new j u i c e blends, a v a r i e t y of processed apple products and new processing equipment. The research 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 to orchardists through free p u b l i c a t i o n s , b u l l e t i n s and a l i b r a r y s ervice. 1.1.3 Economic Importance About 33,000 acres were planted with f r u i t trees according to the 1973 tree census (Hudson, 1973). About 73 percent of t h i s t o t a l (25,000 acres) i s planted with apple trees. On the basis of the 1972-1973 crop year Hudson has calculated that the t r e e - f r u i t industry pro-vides a base for an annual contribution of over 50 m i l l i o n d o l l a r s to the region's economy, calculated by adding 17 m i l l i o n d o l l a r s net returns to 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 roadside sales, 14 m i l l i o n d o l l a r s for payment i n administration, s e l l i n g and packing, 12 m i l l i o n d o l l a r s worth of processed f r u i t products and 6 m i l l i o n d o l l a r s worth of transportation of the produce. About 64% of t h i s value was a t t r i b u t a b l e to apples and apple products. The v a r i e t i e s of apples produced i n order of importance are the Red Delicious s t r a i n s , Mcintosh, Spartan, Golden D e l i c i o u s , Winesap, Newton, and Tydeman Early. The annual production p o t e n t i a l for the area planted has been estimated at 9 to 10 m i l l i o n bushels (Swales, 1971). 1.1.4 External and C u l t u r a l Benefits The t r e e - f r u i t industry has a value to the region that cannot be measured i n market terms alone. External benefits from the industry occur because of the orchard s e t t i n g and i t s e f f e c t on the landscape of the region. The t o u r i s t industry i s a major be n e f i c i a r y and the orchard 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 . The same e x t e r n a l i t i e s which benefit tourism also benefit the permanent residents of the area. The industry i s also of some c u l t u r a l importance i n the region. 5 Because of the long 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 several annual community f e s t i v i t i e s . The industry i s also of importance as a way of l i f e to orchardists and t h e i r f a m i l i e s . The psychic income which i s derived from t h i s way of l i f e i s an important s o c i a l benefit from the industry not measurable i n market terms. 1.2 The Problem Setting A basic problem i n the industry i s low farm incomes. This problem has been discussed by Hudson (1973), Dorling (1975), and Smith (1976) and has been recognized by the B.C. F r u i t Growers Association for several years. Low farm incomes may r e s u l t from a number of causes. Smith states changes i n market demands for v a r i e t i e s and geographic i s o l a t i o n from markets as being basic causes. Hudson outlines further reasons incl u d i n g increased supplies on the world market and increasing costs of inputs. Dorling's work i n t h i s area has shown that low incomes can often be traced to low or negative returns to management a f t e r allowing f a i r l y conservative returns to other f a c t o r s . He discusses a phenomenon i n the industry: Many f r u i t growers would tend to discount t h e i r own and family labour as well 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 standpoint they often have no choice i f they wish to stay i n f r u i t growing. (Dorling, 1975, p. 21) Poor management returns may not be due so much to the shortcomings of the grower but rather to the complexity of the production process. The orchard manager must f i r s t decide what long-run planting concept he w i l l use i n h i s orchard, i . e . , density, rootstock, hedgerow, t r e l l i s , or freestanding. This decision must be based on the geographical factors of h i s orchard which include f r o s t incidence, aspect, s o i l and f r o s t r i s k c 6 as well 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 . Each year he must decide what short-term inputs to use and to what l e v e l . His a l l o c a t i o n of both short and long term inputs depends on h i s assessment of the r e l a t i v e marginal products of these inputs. This assessment i s compli-cated and d i f f i c u l t as there are many inputs, many of which were recently developed. The advantages and disadvantages of new innovations have not always been adequately evaluated and the knowledge thereof disseminated. It i s d i f f i c u l t to s i n g l e out the e f f e c t of any one of these a l t e r n a t i v e s upon production. Furthermore, there i s reason to believe that several int e r a c t i o n s occur, 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 marginal product of another. Because of the time l a g between the a p p l i c a t i o n of several inputs and the resultant impact upon production, i t i s d i f f i c u l t to a r r i v e at optimal l e v e l s of inputs by t r i a l and error-. The orchard renewal and tree replacement problem i s also complex, as the e f f e c t s of age upon production and replacement costs must be considered. Thus a basic problem i n the industry i s how to e f f e c t i v e l y manage a complex business i n a technologically dynamic s e t t i n g . The next section d i s -cusses attempts to overcome some of these management problems and to improve growers 1 incomes. 1.3 Attempts to Aid 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 research at the Summerland Research Station continues to study technology aimed at s p e c i f i c problems i n the l o c a l industry. Much of t h e i r e f f o r t i s i n "pure research" which i s aimed at increasing the general understanding and f i l l i n g i n gaps i n knowledge i n the f i e l d of pomology. However, general areas of research have usually been 7 cl o s e l y r e l a t e d to the problem areas of the industry. For example the st a t i o n has tackled the problem of marketing a large, seasonal geograph-i c a l l y i s o l a t e d crop by research into storage systems. They have helped a l l e v i a t e the winter i n j u r y problem by t h e i r research into cover crops and winter-hardy v a r i e t i e s , and t h e i r continuing research into new va r i e t y development i s i n l i n e with s a t i s f y i n g the changing demands of consumers. 1.3.2 Role of Economic Research A major area of research by economists has been i n the general area of production economics. This area of study o f f e r s four p o t e n t i a l areas for increasing growers' incomes, p a r t i c u l a r l y i f economists can co-ordinate t h e i r work with that of s c i e n t i s t s and extension personnel. These areas include the f e a s i b i l i t y and the adoption of new technology, the re l a t e d problem of orchard renewal, 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 the a l l o c a t i o n of resources towards further technological research. When considering the f e a s i b i l i t y and adoption of new tech-nology, several:.of ..the r e l a t i v e l y new and recent inputs such as dwarfing rootstocks, high density plantings, 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 prevention systems and new v a r i e t i e s should be considered. Some i n i t i a l work by Dorling (1975) has been c a r r i e d out on the compar-ison of y i e l d s and p r o f i t a b i l i t y between high density and standard systems, but he found that differences were not easy to i d e n t i f y , using the sampling coverage afforded by his study. Regarding the second area, orchard replacement, research has been c a r r i e d out i n developing a l i n e a r programming model giving optimal replacement strategies (Marshall, 1975). This work has been hindered by a lack of knowledge as to marginal products of several inputs and v a r i a b l e s . Research into the 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 existence of d i s e q u i l i b r i u m i n input l e v e l s among growers and at the factors which r e s u l t i n growers being better able to a l l o c a t e e f f i c i e n t l y . Some work by Campbell (1976) has shown that estimates of the marginal value prod-ucts of p e s t i c i d e s and 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 higher than the prices of these inputs. The fourth area, a l l o c a t i o n of resources for technological research concerning the l o c a l industry has not been explored by economists. Research can be c a r r i e d out into t e c h n i c a l production problems of the l o c a l area, to study the impact upon produc-t i o n i f constraints are removed. Weather and s o i l v a r i a b l e s would be the main production constraints i n t h i s category. By determining the impact of these v a r i a b l e s on production the p o t e n t i a l benefit of tech-nology concerning these variables i s measured. These benefits can be weighed against the costs of the technological research and the p r o b a b i l -i t i e s of i t s success i n overcoming the constraining f a c t o r s . 1.3.3 The Production Function Approach Production function studies may be of value i n a l l four of the areas mentioned above. New technology has been incorporated as inputs i n experimental blocks and i n some commercial orchards. Through the estimation of a production function the marginal products of these new inputs can be measured and compared with the p r i c e of incorporating them. In the area of orchard renewal, production function estimation can give the marginal product of a l l the new inputs and the e f f e c t of age on y i e l d which i s e s p e c i a l l y important i n the tree replacement d e c i s i o n . In the area of a l l o c a t i v e e f f i c i e n c y , the estimated production functions w i l l i n d i c a t e i f growers are using inputs to p r o f i t maximizing l e v e l s and i f any input adjustment i n the industry can improve incomes. In 9 the area of measuring p o t e n t i a l technological research b e n e f i t s , the main use of an estimated production function i s the measure i t gives of the impact of s o i l and weather variables upon production. A production function which i s u s e f u l to areas mentioned above, should be based on data where inputs have been disaggregated into basic components. For example, the c a p i t a l input must be broken down into planting concept, i r r i g a t i o n system, density and s i z e of trees. Land should be c l a s s i f i e d into s o i l type, aspect and f r o s t r i s k . The data c o l l e c t e d by A g r i c u l t u r e Canada supplemented with regional weather data i s more disaggregated and includes more va r i a b l e s than data used i n previous studies. This thesis attempts to estimate such a production function using t h i s data and apply i t i n comparisons of the a v a i l a b l e technological a l t e r n a t i v e s i n apple production. The study w i l l also examine possible input adjustment within the industry, the i n t e r a c t i o n between inputs and the impact of weather and s o i l v a r i a b l e s . 1.4 S p e c i f i c Objectives of the Thesis The basic objective of t h i s thesis i s : 1. To estimate production functions for the main v a r i e t i e s of apples produced i n the Okanagan area of B r i t i s h Columbia. The following sub-objectives follow from the basic objective: 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 which.affect apple produc-t i o n i n the area. 3. To i d e n t i f y and measure the in t e r a c t i o n s between factors i n apple production. 4. To i n t e r p r e t the estimated production functions i n the follow-ing terms: 10 (a) the choice among a v a i l a b l e technologies or orchard systems (b) to assess the r e l a t i v e p r o d u c t i v i t y of various orchard systems being used for apple production i n the area (c) possible input adjustment i n the industry (d) d i r e c t i o n of research to develop new technology. 1.5 Research Procedure There are two basic areas of research which are undertaken i n t h i s t h e s i s . The f i r s t area i s the s t a t i s t i c a l portion of the research which deals with the f i r s t objective; the estimation of production functions for i n d i v i d u a l v a r i e t i e s of apples. The estimations are confined to the f i v e most important v a r i e t i e s : Mcintosh, Spartan, Newton, Winesap and the Delicious s t r a i n s . S t a t i s t i c a l 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 i n t e r -actions between factors of production. The second area of research i s i n the i n t e r p r e t a t i o n of the e s t i -mated functions and i t deals with s a t i s f y i n g the fourth objective. Of the two areas of research, more emphasis i s put on the s t a t i s t i c a l portion. The inte r p r e t a t i o n s of the functions as outlined i n objective four are secondary i n t h i s thesis and are subject to the success of and confidence that can be placed i n the s t a t i s t i c a l research. The procedure for meeting objective one has three steps. The f i r s t step i s an examination of the economic theory relevant to produc-t i o n functions. This theory i s reviewed for implications concerning the f e a s i b i l i t y of econometric estimation and the desirable properties of the mathematical form of the production function. Secondly, a conceptual model of apple production which outlines the factors i n apple 11 production and t h e i r influence upon output i s presented. P a r t i c u l a r emphasis i s placed on c l i m a t i c variables and i n t e r a c t i o n s . T h i r d l y , a s t a t i s t i c a l representation of the conceptual model i s developed and estimated by regression analysis. Ordinary and r e s t r i c t e d l e a s t squares regression i s applied to data previously c o l l a t e d by A g r i c u l t u r e Canada, supplemented by regional weather data. The major obstacle i n estimation of the s t a t i s t i c a l model i s the problem of handling an extremely large number of factors considered important on a p r i o r i grounds i n the conceptual model. Two str a t e g i e s are used i n dealing with t h i s problem. The f i r s t strategy i s to reduce the model on a p r i o r i or s t a t i s t i c a l grounds by leaving out v a r i a b l e s of minor importance. This paring down i s c a r r i e d out for two classes of fac t o r s , weather variables and i n t e r a c t i o n s . A separate model using regional averages of production and only weather factors as explanatory v a r i a b l e s i s estimated and used to select, a subset of weather factors to be included i n the s t a t i s t i c a l model. Important int e r a c t i o n s are chosen through a step-wise process i n estimation. Some other v a r i a b l e s are dropped from the model as they prove i n s i g n i f i c a n t through a number of runs. Although the paring down strategy i s a reasonable econometric procedure i t s use i s l i m i t e d i n the case of t h i s research, as i t leads to some c o n f l i c t with the objectives of the t h e s i s . The objectives aimed at incl u d i n g a large number of factors i n order that the estimated functions be useful on an i n d i v i d u a l orchard basis, and i n paring down the model information i s l o s t about factors which are of s p e c i a l i n t e r e s t . Thus a second strategy f o r obtaining a manageable s t a t i s t i c a l model i s used. This strategy i s to sub-group the data into t r e e - s i z e categories and estimate models f o r each category. In so doing the 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 eliminated from each equation. Further p a r t i t i o n i n g of the data by s o i l type and geographical l o c a t i o n i s also considered but i s not c a r r i e d out due to data l i m i t a t i o n s . The second and t h i r d objectives concern the i d e n t i f i c a t i o n and measurement of 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 factors 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 of c o e f f i c i -ents and the consistency with a p r i o r i expectations i s discussed. The fourth objective concerns i n t e r p r e t a t i o n s of the estimated functions. The f i r s t 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 of various orchard systems based on rootstock: dwarf, semi-dwarf, semi-standard and standard. Optional management and phys i c a l features within each of these categories are considered i n terms of r e l a t i v e p r o d u c t i v i t y . As equations are estimated for each of these four cate-gories, inter-equation comparisons become the basis f o r assessing the r e l a t i v e p r o d u c t i v i t y of each system. In these comparisons, inputs are generally set at mean l e v e l s , although age of trees i s allowed to vary i n order to show r e l a t i v e p r o d u c t i v i t i e s of the systems at various ages. The second i n t e r p r e t a t i o n deals with the choice between the four s p e c i f i c tree s i z e systems. In t h i s i n t e r p r e t a t i o n , p rices are placed on the inputs and outputs, and a rough comparison of t o t a l revenue and t o t a l cost f o r each system i s given. The t h i r d i n t e r p r e t a t i o n which concerns possible input adjustment i n the industry concerns annual v a r i a b l e inputs. Within each equation the r a t i o of the marginal product of each v a r i a b l e input to i t s p r i c e i s calc u l a t e d . When t h i s r a t i o i s s i g n i f i c a n t l y d i f f e r e n t from unity an analysis i s made whether the r e s u l t i s due to di s e q u i l i b r i u m or biases i n estimation. The fourth i n t e r p r e t a t i o n which considers d i r e c t i o n of research to develop 13 new technology, assesses p o t e n t i a l gains from removing weather and s o i l constraints and discusses new inputs which could be developed. 1.6 Guide to Thesis The next chapter discusses an economic model of the production function including the parameters and f u n c t i o n a l form s p e c i f i c a t i o n s . Models of producer behaviour and t h e o r e t i c a l issues are presented. In chapter three a s p e c i f i c conceptual model i s developed where on the basis of t e c h n i c a l data important inputs and i n t e r a c t i o n s are chosen. The correspondence between the i d e a l measures and the a v a i l a b l e data i s discussed. In chapter four r e s u l t s are presented for a regional weather model based on grouped data and for three categories of farm l e v e l production functions. Chapter f i v e deals with the i n t e r p r e t a t i o n of the estimated model. The marginal value products of inputs are compared with t h e i r marginal costs to see i f there i s any i n d i c a t i o n of d i s e q u i l -ibrium. Possible biases i n the estimated c o e f f i c i e n t s are outlined. 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 orchard systems i s compared. The f i n a l chapter presents a summary of the study, conclusions and implications for further research. CHAPTER II THE ECONOMIC MODEL The purpose of t h i s chapter i s to review economic theory i n order to examine the general nature of the production process, mathematical representations of t h i s process and implications that a r i s e for estima-t i o n of production functions. The f i r s t section of t h i s chapter examines the c l a s s i c a l theory of the production function. Mathematical c h a r a c t e r i s t i c s of production functions and t h e i r relevance i n terms of t h i s research are outlined. D i f f e r e n t f u n c t i o n a l forms are reviewed and considered as to t h e i r a b i l i t y to incorporate the required para-meters and an appropriate form i s chosen for use i n s t a t i s t i c a l estima-t i o n . The second section of t h i s chapter deals with aspects of pro-ducer behaviour which have implications for estimating the production function. P r o f i t maximization, output maximization and cost minimiza-t i o n models are presented and problems i n estimation, which may a r i s e as a r e s u l t of optimizing behaviour are discussed. 2.1 The Production Function The economic d e f i n i t i o n of a production function i s "a schedule (or table or mathematical equation) showing the maximum amount of output from any s p e c i f i e d set of inputs" (Ferguson, 1969, p. 116). In the estimation of a mathematical production function i t i s assumed that such a function e x i s t s , that i t i s continuous and twice d i f f e r e n t i a b l e and that the inputs are continuously v a r i a b l e and substitutable. 14 15 2.1.1 Parameters In mathematical formulations of production functions four general economic parameters can be considered (Arrow et a l . , 1961). These are: (1) e f f i c i e n c y of technology ( s h i f t parameters), (2) te c h n i c a l economies of scale, (3) degree of factor i n t e n s i t y , and (4) factor s u b s t i t u t a b i l -i t y . These parameters might not e x p l i c i t l y appear i n the equation as they may have a value of zero or one i n d i f f e r e n t f u n c t i o n a l forms. The e f f i c i e n c y of technology parameter s h i f t s the whole production function without a f f e c t i n g the 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 of the change i n technology where a greater output can be achieved using the same l e v e l of inputs. The economy of scale parameter r e f l e c t s the e f f e c t s of increasing a l l inputs by an equal proportion. The degree of fa c t o r i n t e n s i t y i s a parameter showing the impact of an input r e l a t i v e to other inputs while the s u b s t i t u t a b i l i t y parameter indicates the degree of s u b s t i t u t a b i l i t y between inputs. The parameter of primary concern i n t h i s study i s the degree of factor i n t e n s i t y . By measuring the impact of an input r e l a t i v e to other inputs some inference as to the a l l o c a t i o n of resources can be made. 2.1.2 Stages of Production The theory of the c l a s s i c a l three stages of production has been well expounded (Brennan, 1970; Ferguson, 1969; Henderson & Quandt, 1971). The main im p l i c a t i o n from t h i s theory i s that producers should be i n the second stage where both the average and marginal products of a l l inputs are decreasing, and the marginal product i s p o s i t i v e . There may be some cases where the producer i s not i n the second stage. A production 16 function not having constant returns to scale and with c e r t a i n input constraints may r e s u l t i n the producer being i n stage one or three. Given l i m i t a t i o n s to the a v a i l a b i l i t y of resources or i n d i v i s i b i l i t i e s i n resources the producer might not be able to move into the second stage f o r a l l inputs. I f there i s an upper l i m i t on a c e r t a i n resource, i t may prevent the operator from using enough to move into the area of diminishing returns. He might be able to compensate by reducing l e v e l s of other inputs, but i f these are fixed (buildings or land) he w i l l be unable to move from the uneconomic region of the production function. This r e s u l t could also occur because of an i n d i v i s i b l e input, such as a trac t o r which i s too large and crushes some of the crop. The producer cannot move from the t h i r d stage of negative returns to the second stage of p o s i t i v e and diminishing returns because the t r a c t o r i s not d i v i s i b l e into smaller u n i t s . The conclusion from the stages of production theory i s that produc-ers w i l l generally be i n the second stage although the p o s s i b i l i t y e x i s t s that they may be i n either of the other stages under c e r t a i n conditions. 2.1.3 Other C h a r a c t e r i s t i c s There are a number of fun 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. These include homogeneity, returns to scale, output e l a s t i c i t y , 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 rate of t e c h n i c a l s u b s t i t u t i o n , shape of isoquants, convexity or concavity of the function and i n t e r a c t i o n s . In regards to the objectives of t h i s thesis there are no s p e c i f i c requirements for any of these c h a r a c t e r i s t i c s except that i n t e r a c t i o n s be represented as e x p l i c i t terms and that there be no r e s t r i c t i o n s on the signs of these terms. 17 2.2 Functional Forms The basic requirements of the f u n c t i o n a l form of the production function for t h i s study i s that i t be able to incorporate a large number of explanatory v a r i a b l e s and allow i n t e r a c t i o n s between these to be e x p l i c i t l y i d e n t i f i e d and measured. It i s desirable that i t have isoquants which are convex towards the o r i g i n thus allowing for l e a s t cost combinations of inputs to be calculated. I t i s preferable but not e s s e n t i a l that i t has decreasing marginal products for inputs. Other mathematical c h a r a c t e r i s t i c s such as homogeneity and e l a s t i c i t y of s u b s t i t u t i o n are not of d i r e c t concern and 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. It was d i f f i c u l t to f i n d a f u n c t i o n a l form which was both p r a c t i c a l to estimate and had a l l of the desirable mathematical properties. The form eventually chosen can handle large numbers of inputs, allows s p e c i f i c 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 tested, has convex isoquants between some pair s of inputs but does not exhibit decreasing marginal products. Functional forms may be c l a s s i f i e d according to a number of char-a c t e r i s t i c s but a convenient c l a s s i f i c a t i o n i s that of Christenson, Jorgenson and Lau (1973). Two classes are considered: (1) homogeneous functions with 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 (2) generalized functions which are not always homogeneous and do not always have 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 . Functions i n the f i r s t group often prove to be s p e c i a l cases of functions i n the second group i f c e r t a i n parameters are r e s t r i c t e d . 18 2.2.1 Homogeneous Functions  Linear Form. The l i n e a r form considering two inputs x^ and X 2 with output Q may be presented as: Q = axj + bx 2. (2.1) S t r i c t l y speaking t h i s function does not have a constant e l a s t i c i t y of s u b s t i t u t i o n although under equilibrium conditions where p r i c e r a t i o s of inputs are equal 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 e l a s t i c i t y of s u b s t i t u t i o n would be i n f i n i t e . It i s possible for 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 other conditions. There are some t h e o r e t i c a l drawbacks to t h i s form. It has con-stant marginal products for both inputs although over a short range of input v a r i a t i o n t h i s feature might not be unreasonable. This type of function has negatively sloped st r a i g h t l i n e isoquants, thus the second order s u f f i c i e n t conditions for cost minimization and output maximiza-t i o n are not met as they require the isoquants to be convex towards the o r i g i n . The l i n e a r form also excludes any i n t e r a c t i o n between inputs implying that the marginal product of any input i s not dependent on the l e v e l s of other inputs. Because of these drawbacks, e s p e c i a l l y the lack of in t e r a c t i o n s t h i s form was not used i n t h i s study except i n some instances as a comparison to i n t e r a c t i v e forms. Cobb-Douglas. Since i t s development i n 1928 (Cobb and Douglas, 1928) the Cobb-Douglas has been a popular form for empirical estimations of production functions. The basic form i s : Q = k X l a x 2 b . (2.2) 19 The function i s homogeneous of degree a + b, exhibits decreasing marginal products when a and b are l e s s than one and has an e l a s t i c i t y of s u b s t i t u t i o n always equal to one. I t s isoquants are convex towards the o r i g i n so the second order conditions s u f f i c i e n t for cost minimiza-t i o n or output maximization are s a t i s f i e d . The function i s e a s i l y estimated i n log form: log Q = log k + a(log X l ) + b(log x 2 ) . (2.3) The major drawback of t h i s form for use i n t h i s study again con-cerns i n t e r a c t i o n s . The marginal physical product (M.P.P.) of x^ i s : f l = akx^ a ^"x2^. (2.4) The higher the l e v e l of x 2 the higher the M.P.P. of xj 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 inputs. This r e s t r i c t i o n on the sign of the i n t e r a c t i o n s i s not desirable i n t h i s study as there i s reason to believe that several i n t e r a c t i o n s w i l l be negative. The Cobb-Douglas function also 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 inputs. For t h i s research i t i s more desirable to have a form which presents i n t e r -actions as d i s t i n c t terms i n the equation which can be included or l e f t out according 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 E l a s t i c i t y of Substitution (CES). The CES function developed by Arrow, Chenery, Minhas and Solow (1961) retains a constant 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 i t to being equal to one. It has the following form: Q = g [ a X l " C + (1 - a ) x 2 " C ] " v / c . (2.5) 20 The function gives an e x p l i c i t representation of the parameters mentioned e a r l i e r . 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 factor 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 scale parameter. This function i s homogeneous of degree v, has diminishing returns for each input and has isoquants convex towards the o r i g i n . The main drawback of the CES for t h i s study i s the d i f f i c u l t y i n extending i t to include more than two inputs. The function does not 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 an approximation must be used when estimating i t . Because of these d i f f i c u l t i e s i t was not con-sidered a p r a c t i c a l form for use i n t h i s work. 2.2.2 Non-homogeneous functions Transcendental. A transcendental function i s e i t h e r an exponential function where independent v a r i a b l e s appear i n the exponent or a l o g a r i t h -mic function where a log value of an independent v a r i a b l e i s i n the equa-t i o n . Halter, Carter and Hocking (1957) discuss such a function that has a l l three of the c l a s s i c a l stages of production. It takes the form: Q = c X l a i e b l X l x 2 3 2 e b 2 X 2 . (2.6) where e i s the natural number and a^, a 2 , b j , b 2 , and c are estimated parameters. This function i s e a s i l y estimated i n log form: log Q = log c + a^log x i + b^xj + a 2 l o g x 2 + b 2 x 2 . (2.7) This f u n c t i o n a l form can e a s i l y handle a large number of inputs. Non-homogeneity i s not a conceptual problem i n the study nor i s the v a r i a b l e e l a s t i c i t y of s u b s t i t u t i o n . However, i t lacks e x p l i c i t i n t e r a c t i o n terms and therefore was not used i n t h i s study. Generalized Power Function (GPF). A power function represents the dependent v a r i a b l e as a function of the independent v a r i a b l e ( s ) taken to a c e r t a i n power. A generalized power function discussed by DeJanvry (1972) includes as s p e c i a l cases the Cobb-Douglas and the t r a n -scendental functions: k f (x) g v(x) Q = A n x ^ K e K . (2.8) k=l k where f ^ ( x ) a n d S^( x) a r e polynomials of any degree i n the arguments of the input vector x and which has k elements. In log form t h i s equation i s s i m i l a r to equation (2.7) but i n t e r a c t i o n s and squared terms of the x.'s and log x.'s are included. The choice of the degree and kind of i n t e r a c t i o n s i s l e f t open. This form warrants consideration for use i n t h i s study as i t allows for e x p l i c i t i n t e r a c t i o n terms i n the equation. It does not give any r e s t r i c t i o n s or impose any 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 -t i o n s , but leaves the choice to the researcher. In order to u t i l i z e the form c e r t a i n a p r i o r i expectations are needed to specify the poly-nomials f ^ ( x ) a n d g^(x). The form i s so general that i t i s l i k e l y that any 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 i n fact be a s p e c i a l case of the generalized power function. Before deciding on a s p e c i f i c form for t h i s work, two other i n t e r a c t i v e forms, both s p e c i a l cases of the GPF are discussed. Transcendental Logarithmic (Trans-log). This f u n c t i o n a l form was developed from a Taylor expansion of the CES and under c e r t a i n r e s t r i c -tions w i l l give an approximation of the CES l i n e a r i n i t s parameters. It was f i r s t used by G r i l i c h e s and Ringstad (1971) i n an analysis of 22 Norwegian manufacturing. With two inputs xi and x 2 i t takes the form: log Q = a i l o g X ! + a 2 l o g x 2 + a 3 l o g x 2 l o g x 3 + ai+Clog x x ) 2 + a 5 ( l o g x 2 ) 2 . (2.9) This function i s a polynomial form of the logs of the input v a r i -ables. It i s a s p e c i a l case of the GPF where the polynomial g, (x) = 0, and i s s i m i l a r to the quadratic form which follows. Quadratic. This function i s a polynomial form of the inputs-X]^ and x 2: Q = a i x i + a 2 x 2 + a 3 x i x 2 + ai^x^ 2 + a s x 2 2 . (2.10) When there are more than two inputs there w i l l be an i n t e r a c t i o n between every pair of inputs and a squared term f o r each input. This form i s capable of representing a l l three c l a s s i c a l stages of production as i t has increasing, decreasing, and negative marginal products depending on the input l e v e l s . The major drawback of t h i s form i s the large number of parameters that have to be estimated when more than two inputs are considered. Every time a v a r i a b l e i s added to the function the number of terms, including square and cross terms increases by two plus the present number of v a r i a b l e s . In the conceptual model outlined i n the next chapter there are 16 inputs so a f u l l quadratic equation would have 168 terms. The same problem a r i s e s with the trans-log when used i n i t s complete form. The two forms closest to meeting the requirements for t h i s 23 research are the trans-log and the quadratic. The main problem with both these forms i s the large number of parameters that must be estimated. To p a r t l y overcome t h i s problem the forms can be modified by eliminating some of the parameters. Most of the terms of the polynomial are i n t e r -actions and eliminating some of them would be useful i n reducing the function to a form that can be estimated. Both the quadratic and the trans-log forms allow for an i n t e r a c t i o n between every p a i r of inputs but through an examination of the t e c h n i c a l process a subset of c e r t a i n important i n t e r a c t i o n s can be chosen a p r i o r i , the others being el i m i n -ated. The group of squared terms can also be eliminated, although i n the quadratic form t h i s elimination r e s u l t s i n marginal phy s i c a l products becoming constant rather than decreasing or increasing. It' i s not clear exactly what the e f f e c t s w i l l be i f the squared terms are removed from the trans-log function, although decreasing marginal products could s t i l l occur without them. In several t r i a l estimations the quadratic form without the squared terms and with only a few selected i n t e r a c t i o n s provided a better f i t than a s i m i l a r l y modified trans-log function. On t h i s basis the modified quadratic form was chosen as the functional form for the estimated production functions. 2.3 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 surface. When producer behaviour i s considered the portion of the surface which represents economic e f f i c i e n c y as well 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 . It i s usually assumed that producers attempt to operate at such areas on the surface where the outputs are produced with the least cost combination of inputs. Under equilibrium conditions t h i s area may only be a sin g l e point or locus of points. The tendency for actual observations of inputs and corresponding outputs to be on or near these economically e f f i c i e n t areas has important implications f o r estimation of the production function. Three models of producer behaviour where producers operate at economically e f f i c i e n t points have been w e l l developed i n the l i t e r a t u r e and are b r i e f l y discussed below. 2.3.1 P r o f i t Maximization In t h i s model where input and output prices are constant, producers w i l l operate at a s i n g l e point on the p r o f i t function where p r o f i t i s maximized, input costs are minimized f or the p a r t i c u l a r l e v e l of output, and output i s maximized for the p a r t i c u l a r l e v e l of cost. The p r o f i t function ir can be stated as: where f ( x l 5 x 2 ) i s the production function, P i s the p r i c e of the output, r j and r 2 are input prices and B i s the fixed cost. The f i r s t order conditions for p r o f i t maximization require that Pf^ = r 1 and P f 2 =• r 2 where f j and f 2 are the marginal products of x^ and x 2. The second order conditions require that IT = P f ( x i , x 2 ) - r i x i - r 2 x 2 - B. (2.11) "2 p f n < 0, d x 2 2 p f 2 2 < 0, (2.12) 25 These conditions state that the marginal value products of both inputs be decreasing and that the production function be s t r i c t l y concave i n the neighbourhood of the p r o f i t maximizing point. The second order condi-tions preclude p r o f i t maximization i f the production function i s of any homogeneous form of degree greater than or equal to one. The modified quadratic form chosen f o r t h i s research does not s a t i s f y the second order conditions, as marginal ph y s i c a l products are not decreasing, given that the squared terms are zero. However, t h i s form was chosen mainly because of i t s a b i l i t y to represent a complex short run s i t u a t i o n . It i s s t i l l quite possible that orchardists are attempting to maximize p r o f i t s over the long run and any r e s u l t i n g implications for estimation s t i l l hold. 2.3.2 Constrained Output Maximization This model i s relevant where producers have a given cost outlay to use i n production. With prices f i x e d they are assumed to maximize out-put subject to t h i s cost constraint. maximize Q = f ( f i , f 2 ) (2.13) subject to C = r ^ x i + r 2 x 2 + B. The f i r s t order conditions for output to be maximized are that f l / f 2 = r i / r 2 or = £zlr2' These conditions state that the rate of 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 slope to the isoquant must be equal to the p r i c e r a t i o at the maximization point. The second order conditions require that the relevant bordered Hessian determinant be p o s i t i v e . This condition requires that the rate of change of the slope of an isoquant must be p o s i t i v e which means that the isoquants must be convex towards the o r i g i n i n the neighbourhood of 26 the output maximization point. 2.3.3 Constrained Cost Minimization If a producer has a prescribed l e v e l of output such as an order or quota he may attempt to minimize the cost of producing i t . His problem then becomes one of constrained minimization. minimize C = r i x i + r 2 x 2 + B (2.14) subject to Q = f ( x i , x 2 ) , where C i s the cost function, Q i s the prescribed l e v e l of output and f(xi,x 2.) i s the production function. In t h i s model the f i r s t and second order conditions for minimization are the same as the output maximization problem. The rate of t e c h n i c a l 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 the isoquants must be convex towards the o r i g i n . This model i s not e s p e c i a l l y relevant to the Okanagan t r e e - f r u i t industry as there i s no quota or contract system. There may be some cases where orchardists themselves set a c e r t a i n l e v e l of production as a goal. For example i f an orchardist operates a roadside stand and f e e l s that a s p e c i f i c quantity of f r u i t w i l l maximize revenue, he may aim to produce t h i s amount i n his own orchard. The cost minimization model i s of t h e o r e t i c a l importance because i t i s the dual problem of output maximization. The s o l u t i o n to either problem represents an economically e f f i c i e n t point on the production function. In summary, t h e o r e t i c a l models suggest that producers w i l l attempt to operate at economically e f f i c i e n t points on the production function. As output increases, with prices constant, the locus of e f f i c i e n t points 27 w i l l form the expansion path. The tendency for producers to be on the expansion path can hinder the s t a t i s t i c a l estimation of the production functions. S p e c i f i c problems which may a r i s e i n estimation are d i s -cussed i n the next section. 2.4 Implications for Estimation If i t i s expected that producers are attempting to operate at economically e f f i c i e n t points on the production function then a number of problems i n estimation may a r i s e . The behaviour of producers may introduce biases into the estimated parameters or present problems i n obtaining precise estimates of these parameters. A lack of v a r i a t i o n i n input l e v e l s , high m u l t i c o l l i n e a r i t y between inputs, simultaneous equation bias and l e f t out v a r i a b l e bias may occur because producers are attempting to operate at economically e f f i c i e n t points. These problems are analyzed i n the following sections. 2.4.1 V a r i a t i o n i n Input Levels It has been noted by G r i l i c h e s (1971) and others that s t a t i s t i c a l estimation of production functions could be impossible i f a l l producers possess unlimited c a p i t a l and are p r o f i t maximizing. As each input would be used to i t s optimum l e v e l , there would be no v a r i a t i o n i n input l e v e l s and hence no s t a t i s t i c a l estimation would be possible. The only causes of input v a r i a t i o n under equilibrium conditions would be p r i c e v a r i a t i o n of output and inputs between regions and over time. There w i l l l i k e l y be v a r i a t i o n i n the p r i c e growers assign to t h e i r own labour, and t h i s could cause v a r i a t i o n i n other input l e v e l s i f there are i n t e r a c t i o n s with labour. In addition there may be some differences i n the p r i c e expectations of growers. Because of a considerable lag between a p p l i c a t i o n of many inputs and the marketing of the output, growers use an expected output p r i c e , when considering a l l o c a t i o n decisions. Those growers who have high p r i c e expectations w i l l tend to use higher input l e v e l s than those with low p r i c e expectations. Orchardists may not be using inputs at p r o f i t maximizing l e v e l s because of a lack of knowledge of t h e i r marginal p r o d u c t i v i t y . This lack of knowledge may occur because of the substantial time lag between use of inputs and the r e s u l t i n g returns. Inputs i n t h i s category include rootstock, density and planting system. The grower would have to wait several years between the planting date and the f i r s t season of commercial production to assess the e f f e c t s of changing these inputs. Because the concept of high density production i s r e l a t i v e l y recent i n the area, i t would also be d i f f i c u l t for growers to assess surrounding orchards i n terms of marginal returns to these inputs. Complicating hi s assessment of these inputs are the large number of other v a r i a b l e s in f l u e n c i n g production. For older and established inputs, such as f e r t i l i z e r and p e s t i -cides, i t i s more l i k e l y that orchardists have adjusted to equilibrium l e v e l s , and a smaller variance in' t h e i r sample l e v e l s i s expected. In summary, because of the r e a l world differences i n p r i c e s , p r i c e expectations and lack of knowledge, i t i s expected that 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 although there should be some tendency for a lack of v a r i a t i o n i n c e r t a i n inputs, p a r t i c u l a r l y for older and established inputs. 2.4.2 M u l t i c o l l i n e a r i t y of Inputs If producers are p r o f i t maximizing, cost minimizing or output maximizing they w i l l be operating on t h e i r expansion path. For a func-t i o n with an i n t e r a c t i o n between inputs the equation of the expansion path i s r 2 ( a + cx 2) - r i ( b + cx 2) = 0. (2.15) This equation i s derived from an i n t e r a c t i v e production function given as: Q = axi + bx 2 + c x i x 2 . (2.16) Equation (2.15) can be rearranged to solve f or x 2: x2 = ( r i / r 2 ) x ! + ( r ! / r 2 ) c - ac. (2.17) As the parameters a and c and prices r^ and r 2 are constant, equation (2.17) indicates that x\ i s a l i n e a r function of x 2 meaning that the two inputs are p e r f e c t l y correlated. Equation (2.17) does not imply that the input r a t i o x^/x 2 i s constant, but rather as output increases the input r a t i o converges on a constant equal to r 2 / r ^ . I t i s expected that the problems of c o l l i n e a r i t y w i l l be a l l e v i -ated somewhat by the points mentioned e a r l i e r , namely, input 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 expectations, differences i n expected marginal products and differences i n values assigned to operators' own labour. 2.4.3 Simultaneous Equation Bias It has been shown by Hoch (1962) and others that under p r o f i t maximizing behaviour, with or without output and cost constraints, simultaneous equation bias may occur, i n the estimation of Cobb-Douglas production functions. Using a s i m i l a r d e r i v a t i o n i t can be 30 shown that estimation of the i n t e r a c t i v e form used i n t h i s thesis may also be subject to such bias. The production function as i n equation (2.16) can be expressed as a s t a t i s t i c a l model by adding a random disturbance term U: Q = ax]. + bx 2 + cx!xc 2 + U. (2.18) A f i r s t order condition f o r p r o f i t maximization P = r i can q d X l 1 be expressed as: P q ( a + cx 2) = r x . (2.19) Solving for a from equation (2.16) and s u b s t i t u t i n g into equation (2.19) r e s u l t s i n P [ ( Q - b X 2 - C X 1 X 2 ) + cx 2] = r i . (2.20) q x i 1 Solving for x i and s i m p l i f y i n g r e s u l t s i n : xi = P q(Q - b x 2 ) / r i . (2.21) If the value for Q from equation (2.18) i s substituted into equation (2.21) then x i becomes p a r t i a l l y dependent on U and i s thus correlated with the disturbance term. This c o r r e l a t i o n v i o l a t e s one of the assumptions of using l e a s t squares estimation and a biased estimate of the parameters w i l l occur. This simultaneity w i l l not occur i f farmers base t h e i r production decisions on expected value of output rather than actual values, providing that the expected value i s not exactly equal to actual value. This i s l i k e l y to be true i n apple production because of the lag between the a p p l i c a t i o n of inputs and the r e s u l t i n g output and p r i c e s . 31 DeJanvry (1972) has shown that i f producers use expected prices and out-puts i n decision making then the G.P.F. can be estimated by ordinary l e a s t squares without simultaneous equation bias. As the i n t e r a c t i v e function used i n t h i s thesis i s a s p e c i a l case of the G.P.F. the proof also holds for i t . 2.4.4 Left-out Variables If the production function i s considered as part of a simultaneous system which also includes the f i r s t order p r o f i t maximizing condition that the marginal value product be equal to the marginal cost f o r each input, then probable bias w i l l be imparted to the estimated c o e f f i c i e n t s of the production function i f va r i a b l e s are l e f t out of the estimation. For example, management bias i s l i k e l y to occur, i f i t i s supposed that there 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 inputs. In t h i s case better managers w i l l obtain higher marginal products from inputs 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 order p r o f i t maximizing conditions. The r e s u l t i s a p o s i t i v e c o r r e l a t i o n between management l e v e l s and l e v e l s of other inputs imparting an upward bias to the input c o e f f i c i e n t s i f management i s l e f t out of the estima-t i o n . S i m i l a r l y i f other inputs, such as labour, have i n t e r a c t i o n s with other inputs, leaving them out of the estimation 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 labour 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 with many inputs, leaving i t out of the estimation w i l l probably cause further upward bias i n the c o e f f i c i e n t s . If management and labour do not have in t e r a c t i o n s with other i n -puts, then t h i s bias w i l l not occur, aside 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 the included v a r i a b l e s . In t h i s case management and labour could be considered as s h i f t v a r i -32 ables, s h i f t i n g the l e v e l s of output by an amount independent of the l e v e l s of other inputs. 2.4.5 Summary of Implications for Estimation The most serious implicat i o n for estimation i s the p r o b a b i l i t y of l e f t - o u t v a r i a b l e bias. Because measurements of management and labour inputs are not a v a i l a b l e (chapter three), the estimated c o e f f i c i e n t s for other inputs w i l l l i k e l y be biased. As there i s probably some p o s i t i v e 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 inputs a general upward bias i n the estimated parameters i s expected to occur. Any 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 to t h i s b i a s . However, an allowance can be made for the magnitude of the bias due to the influence of labour. Because estimations are based on short run data, representing a period of four to f i v e years, assuming f i x e d pro-portions between labour and other inputs i s not unreasonable. Hence the estimated c o e f f i c i e n t for an input represents the influence of both the input and a s p e c i f i e d amount of labour required for i t s a p p l i c a t i o n . The influence of labour can then be removed from the c o e f f i c i e n t , where necessary. The tendency of variables to be correlated or have low v a r i a t i o n was not f e l t to be so serious. There are adequate reasons for expecting a s i g n i f i c a n t amount of input v a r i a t i o n and differences i n input r a t i o s , although some tendency of variables to move together w i l l s t i l l e x i s t . Thus m u l t i c o l l i n e a r i t y may a f f e c t the p r e c i s i o n of the estimates to a c e r t a i n extent. Because i t i s reasonable to assume that decisions are made on expected p r i c e s , the production function does not have to be considered as part of a simultaneous system. Thus ordinary l e a s t squares estimation 33 can be used without the p r o b a b i l i t y of simultaneous equations b i a s . Some of the problems suggested by the theory can be overcome through care i n data c o l l e c t i o n . E f f o r t s were made to obtain data on a l l important inputs and with 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 , i n order to reduce biases and f a c i l i t a t e estimation. D e t a i l s of the data used and the concepts represented are presented i n the next chapter. CHAPTER III THE CONCEPTUAL MODEL AND MEASUREMENT OF VARIABLES The purpose of t h i s chapter i s to i d e n t i f y the important variables i n apple production and to discuss the measures of these v a r i a b l e s which are used i n the estimated model. Because a primary objective of t h i s research i s to d i s t i n g u i s h between the e f f e c t s of orchard systems and inputs which are of importance to an orchard manager, the conceptual model i s quite d e t a i l e d i n comparison to e a r l i e r studies (Lee, 1972; Campbell, 1976). In p a r t i c u l a r the c a p i t a l input i s broken down into many components including features of the land, density, rootstock, v a r i -ety, planting concept, age of trees, machinery and i r r i g a t i o n system. Other factors which influence the choice of system including weather influences and i n t e r a c t i o n s are also presented i n d e t a i l as are the annual v a r i a b l e inputs. The conceptual model i s thus highly disaggre-gated and i s relevant to a small homogeneous unit or orchard block. The conceptual model considers the major production decisions i n est a b l i s h i n g and operating an apple orchard. It i s l a r g e l y based on extension l i t e r a t u r e , p a r t i c u l a r l y Swales (1971), who presents p r i n -c i p l e s of commercial apple growing for new and experienced orchardists. A more or le s s d e t a i l e d conceptual model could be u t i l i z e d depending on the objectives of the research. For example, i n s c i e n t i f i c research one would l i k e l y conceive of a more d e t a i l e d model with higher emphasis on the b i o l o g i c a l f a c t o r s , while i n economic research for p o l i c y purposes, 34 35 the researcher might only consider major aggregated inputs such as land, labour and c a p i t a l . It i s considered that the d e t a i l of the conceptual model i n t h i s research i s consistent with the objectives which aim at supplying quantitative information on s p e c i f i c inputs to orchardists and extension workers. The variables can be c l a s s i f i e d into four groups which are (1) management, (2) fi x e d inputs and physical features, (3) annual v a r i -able inputs, and (4) weather influences. These factors and in t e r a c t i o n s between them are shown i n f i g u r e 3.1. This figure i l l u s t r a t e s the complexity of the conceptual model and the r e l a t i o n s h i p between inputs. It also i d e n t i f i e s major sources 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 rootstock, age and s o i l . Management, which i n t e r a c t s with a l l other inputs, i s shown as a separate category as i t t i e s together the production process. Each cl a s s of variables as shown i n fig u r e 3.1 i s discussed separately i n the following sections. The actual measures of these v a r i a b l e s versus the i d e a l or required measures are outlined and a d e t a i l e d tabula-t i o n of the variables used f o r estimation i s given l a t e r i n the chapter. 3.1 Management Two general aspects of management i n apple production may be considered. The f i r s t 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 using optimal l e v e l s of inputs. A good manager could obtain a higher output using the same value of inputs as a poor manager by a l l o c a t i n g h i s funds to obtain the best combination of inputs. The second aspect of management i s the a b i l i t y to increase the effectiveness of p h y s i c a l inputs. For example a good manager obtains a better q u a l i t y of f r u i t because h i s pruning techniques are more e f f e c t i v e than 36 j Management « ^ Weather Physical Features Variable Influences and Fixed Inputs Inputs blossom time influences wind r a i n temperature sunlight f r o s t growing season heat accumulation winter k i l l severe cold t ^j s o i l q u a l i t y f r o s t r i s k p o l l i n a t i o n method rootstock density spur-type jplanting concept v a r i e t y age machinery inputs pruning thinning harvesting input assoc-iated i r r i g a t i o n system y i e l d -«-»- shows an i n t e r a c t i o n between inputs Figure 3.1. Factors i n Apple Production the poor manager's, although both may spend the same amount of time pruning. This aspect of management includes a number of factors which are not e a s i l y measurable as phys i c a l u n i t s . The effectiveness of p e s t i c i d e a p p l i c a t i o n , thinning, f e r t i l i z e r a p p l i c a t i o n , i r r i g a t i o n , f r o s t prevention and labour supervision a l l come i n t h i s category. Because management a b i l i t y i s affected by a number of intangibles and q u a l i t a t i v e v a r i a b l e s i t i s d i f f i c u l t to conceive of an i d e a l measure. Such variables as education and experience might prove to be adequate proxy v a r i a b l e s . No data was c o l l e c t e d on these aspects and no e x p l i c i t representation i s included i n the estimated models. 3.2 Physical Features and Fixed Inputs These inputs are expected to remain constant for a number of years. They include geographical factors 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 planting such as density, tree design and rootstock and fi x e d inputs such as i r r i g a t i o n system and machinery. 3.2.1 S o i l The q u a l i t y of the s o i l for apple production i s determined by a number of factors including depth, texture, a c i d i t y , a l k a l i n i t y and drainage (Swales, 1971). Deep s o i l s are expected to increase produc-t i o n as correct moisture l e v e l s can be more e a s i l y maintained and there i s a greater supply of nutrien t s . S o i l s with l i g h t e r texture should r e s u l t i n h e a l t h i e r more productive trees because they have better drainage than heavier s o i l s . S o i l s with high PH l e v e l s have adverse e f f e c t s on the a v a i l a b i l i t y of s o i l nutrients and y i e l d i s expected to be lower. There i s a complicated i n t e r a c t i o n between these s o i l features 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 with rootstock and 38 an i n t e r a c t i o n with i r r i g a t i o n . These are discussed under the relevant input category. An i d e a l measurement would consider s o i l depth, texture, PH l e v e l and nutrient content. The actual measure recorded i s only of s o i l texture based on the farmer's estimate. S o i l i s c l a s s i f i e d as either sandy, clay or rocky. An index based on texture was constructed. This i s a reasonable proxy f o r s o i l q u a l i t y , as other influences on qu a l i t y are often associated with texture. The e f f e c t s of s o i l texture Table 3.1. Index of s o i l type based on farmer's estimate of texture Index Texture 1 sandy 2 clay 3 rocky are also measured using dummy variables which allow the e f f e c t s of each type of s o i l to be measured as a s h i f t v a r i a b l e unrestrained by the nature of the index. In some cases the index i s used instead of the dummies because of m u l t i c o l l i n e a r i t y problems. The expected sign of the c o e f f i c i e n t i s negative as clay and rocky s o i l s are considered to be le s s productive than sandy s o i l s . 3.2.2 Frost S u s c e p t i b i l i t y Orchards highly susceptible to f r o s t are expected to have les s production, a l l other things being equal, than le s s susceptible orchards. This v a r i a b l e i s expected to in t e r a c t with the winter hardiness of the 39 rootstock and tree s i z e . The smaller the tree s i z e , the greater t h i s i n t e r a c t i o n i s expected to be, as a higher concentration of the blossoms w i l l be close to ground l e v e l and more subject to spring f r o s t s . This f r o s t 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 the kind and amount of f r o s t protection used. When e f f e c t i v e f r o s t prevention i s used, i t w i l l obviously lessen the influence of f r o s t pockets and channels. Ideal l y a measure which takes into account f r o s t pockets, the drainage, the exposure and the aspects of the i n d i v i d u a l blocks should be included. Actual measurement i s based on a farmer's estimates as f o l -lows: 1—low, 2—moderate, 3 — h i g h . The expected sign i s negative. 3.2.3 Frost Prevention System The use of f r o s t prevention systems i s expected to increase y i e l d s by lowering the incidence of f r o s t damage to buds, blossoms and green f r u i t . Smudge pots which heat the a i r near the ground's surface and wind machines which break up natural temperature inversions are both used by growers. Davies (1974) has shown the effectiveness of wind machines i n increasing temperatures at t r e e - l e v e l . Dummy var i a b l e s are used to represent these systems and are expected to have p o s i t i v e signs. 3.2.4 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 for f r u i t - s e t i n s e l f - u n f r u i t f u l v a r i e t i e s and should improve f r u i t - s e t i n other v a r i e t i e s (Swales, 1971). The incidence of p o l l i n a t o r trees and the amount of insect a c t i v i t y are both expected to increase production. Ideal l y there should be a measure incorporating the number of p o l l i n a t o r trees per acre, the number of bee-hives per acre and the proximity of neighbouring hives. The actual measure considers the p o l l i n a t i o n method, either bees or p o l l i n a t o r trees. Where bees are used the number of hives per acre i s given. The v a r i a b l e entered i n the model i s the number of hives per acre (which i s zero i f only p o l l i n a t o r trees are used). The measure does not account for orchards which have both p o l l i n a t o r trees and beehives. The expected sign i s p o s i t i v e . 3.2.5 Rootstock The e f f e c t of rootstock i s control of tree s i z e . An estimate of the r e l a t i v e tree s i z e produced by the Mailing and Malling-Merton root-stocks which are the most common rootstock i n the area i s given by Swales (1971). It i s expected that the e f f e c t s of y i e l d of varying the rootstock to get a larger tree s i z e w i l l be p o s i t i v e . Rootstock can i n t e r a c t with s o i l factors i n i t s e f f e c t s on y i e l d . The dwarfing rootstocks, MIX and M 26 both stunt badly on l i g h t shallow s o i l s . The semi-dwarf M VII has the same problem, and i t i s expected that y i e l d s from these three rootstocks w i l l be lower on l i g h t shallow s o i l s than on heavier s o i l . There w i l l l i k e l y be several i n t e r a c t i o n s with v a r i a b l e inputs although the sign and magnitude of these i n t e r a c -tions are uncertain. Pesticides may 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 reach a l l parts of a small tree easier than a larger tree. F e r t i l i z e r , pruning and thinning require-ments may also d i f f e r between small and large trees. The e f f e c t of age i s also d i f f e r e n t for dwarf and semi-dwarf trees than for standard s i z e trees, as much e a r l i e r bearing takes place i n the smaller trees. Interactions with blossom f r o s t and severe winter cold w i l l occur. Smaller trees are more susceptible to blossom f r o s t because t h e i r b l o s -soms are concentrated close to ground l e v e l . Their roots are more 41 susceptible 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) estimates has been constructed as i n table 3.2. Table 3.2. Tree Size Index Based on Rootstock 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 The expected sign of the index c o e f f i c i e n t i s p o s i t i v e , but there may be some range over which the marginal ph 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 in t e r a c t i o n s with s o i l texture, blossom f r o s t and winter-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 with age and pe s t i c i d e s are expected. Interactions with f e r t i l i z e r , density and labour are also possible although t h e i r signs are not known. 3.2.6 Density It i s expected that up to a point, increasing the number of trees per acre w i l l increase y i e l d per acre but beyond that point y i e l d w i l l decrease. At t h i s c r i t i c a l point the trees become too crowded and sunlight, sprays and applications of f o l i a r nutrients cannot reach the 42 inner and crowded portions of the trees. This crowding e f f e c t i s caused by tree s i z e as well as d e n s i t y — a n orchard can be very crowded with large trees i n a planting of only moderate density. This i n t e r a c t i o n between density and rootstock i s again hard to specify i n terms of sign and magnitude. If the density of a planting i s low, then the addition of a large tree to a standard planting would l i k e l y increase output more than the addition of a small tree to a dwarf planting. However, i n crowded conditions increasing density i n a standard planting could have a more negative e f f e c t on output than increasing density i n a dwarf plant-ing so the i n t e r a c t i o n may be p o s i t i v e or negative depending on the actual l e v e l of crowding. The number of trees per acre (the required measure) has been accurately recorded for each block. The expected sign i s p o s i t i v e but l i k e t r e e - s i z e there may be some range over which the M.P.P. i s negative. 3.2.7 Spur-type Generally, spur-type are about 60% of the si z e of non spur trees. The dwarfing e f f e c t may r e s u l t i n a lower y i e l d per tree, but the improved p o s i t i o n of the f r u i t bearing may compensate for t h i s . Thus 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 . A dummy v a r i a b l e has been used to represent the e f f e c t s of spur-type trees i n the e s t i -mated models. 3.2.8 Tree Design The basic designs are either hedgerow or i n d i v i d u a l trees i n rows. Hedgerows can eith e r be t r e l l i s e d or free-standing. Hedgerow designs, p a r t i c u l a r l y t r e l l i s e d hedgerows provide greater bearing surface per acre and are expected to r e s u l t i n higher y i e l d s . A dummy v a r i a b l e has been used for hedgerow planting to allow for 43 a diffe r e n c e from the i n d i v i d u a l tree concept. Aside from m u l t i -c o l l i n e a r i t y problems t h i s i s probably the best method of measuring the influence of the hedgerow planting concept. The expected sign i s po s i t i v e for the hedgerow dummy. 3.2.9 Variety The e f f e c t s of 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 well known. However, Golden D e l i c i o u s , Spartan and Winesap are considered highly productive. Dummy variables are used to represent the major v a r i e t i e s which are Red De l i c i o u s , Golden D e l i c i o u s , Spartan, Newton, Winesap and Tydeman Red. Individual functions are also estimated for some v a r i -e t i e s . 3.2.10 Age of Trees Y i e l d i s expected to increase as trees become older, l e v e l o f f a f t e r a c e r t a i n age and eventually s t a r t d e c l i n i n g . (The age where y i e l d s t a r t s to decline i s uncertain although i t i s quite old and i t i s doubtful i f the sample contains many trees of t h i s age.) The age var i a b l e i n t e r a c t s with the types of rootstock. Standard trees on seedling rootstock usually are commercially non-bearing u n t i l t h e i r s i x t h year as indicated by Van Roechoudt's r e s u l t s (1962). Semi-standard trees reach commercial l e v e l s of production about a year e a r l i e r , while dwarf and semi-dwarf trees come into production i n t h e i r t h i r d year. F u l l production from standard trees w i l l not be reached u n t i l about t h e i r twelfth year, for semi-standard trees i t w i l l be reached around the tenth year and for dwarf and semi-dwarf i t w i l l be reached i n about s i x years (Van Roechoudt, 1962). An a d d i t i o n a l factor to be considered under age i s biannual bearing where some trees tend to produce a l t e r n a t i v e l y l i g h t and heavy 44 crops. Golden Delicious and Newton have strong tendencies towards biannual bearing, as well as Tydeman to a lesser extent. Alternate bearing may occur to some degree i n other v a r i e t i e s (Carlson et a l . , 1974) . When trees are i n t h e i r formative (non-bearing) stage they produce l i t t l e or no f r u i t . It follows that the y i e l d from very young trees should not be affected to a large degree by f e r t i l i z e r , p e s t i c i d e , i r r i g a t i o n and labour. As the trees become older and reach t h e i r beartr ing stage i t i s l i k e l y that the influence of the v a r i a b l e inputs w i l l be much greater. However, there w i l l : l i k e l y be a lagged e f f e c t of these v a r i a b l e s , as maintenance of the tree health i n the formative years w i l l improve y i e l d s i n the bearing years. A measure which accounts for the formative, bearing and post-bearing stages of the trees should be considered. The actual age, entered as an independent v a r i a b l e would r e s t r i c t the regression to estimating an average c o e f f i c i e n t f o r each year, when i t i s known that an a d d i t i o n a l year during the formative stage has much less impact than an a d d i t i o n a l year during the bearing stage. It i s also not conceptu-a l l y correct to r e s t r i c t the age of d i f f e r e n t categories of tree sizes to have the same c o e f f i c i e n t . The following index (table 3.3) from Van Roechoudt's r e s u l t s (1962) i s used. 3.2.11 Machinery Inputs Machinery inputs are expected to increase y i e l d s i n several ways. Weed spraying and mowing w i l l improve l i g h t penetration at lower l e v e l s and aid i n the e f f i c i e n c y of pruning, thinning and p e s t i c i d e a p p l i c a t i o n . Mechanical aids such as g i r e t t e s should improve the effectiveness of time spent i n thinning and pruning. Higher powered trac t o r s and 45 Table 3.3. Indexed Age of Trees Based on Rootstock C l a s s i f i c a t i o n Actual Age (years) Standard Indexed 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 ' 15 8. 5 6 6 16 9 6 6 higher air-volume-velocity sprayers w i l l improve the effectiveness of p e s t i c i d e s . I d e a l l y a measure of the time and effectiveness of machinery use i s required. Proxy variables such as sprayer c a p a b i l i t y or t r a c t o r horsepower would l i k e l y capture some of the e f f e c t s of machinery. However, no data was obtained for these v a r i a b l e s so they have not been included i n the s t a t i s t i c a l model. There i s no evidence to suggest that machinery inputs are correlated with other inputs, so no bias i s expected to occur because of the exclusion of t h i s v a r i a b l e . 46 3-.-2.12 I r r i g a t i o n System There are three major systems being used i n the area which are overhead, portable s p r i n k l e r and t r i c k l e systems. The r e l a t i v e e f f e c t s of these systems are not w e l l known. Dummy var i a b l e s have been used to represent overhead and t r i c k l e systems versus the more common portable s p r i n k l e r s . If there were more information on the e f f e c t s of the systems i t would also be desirable to construct an i r r i g a t i o n index which could be used i f the dummies cause m u l t i c o l l i n e a r i t y problems. In summary, fixed inputs are well represented by the a v a i l a b l e data. Through the use of dummy var i a b l e s and indices a l l f i x e d inputs with the exception of machinery can be represented i n the e s t i -mated models. Although machinery i s an important input no systematic bias i n estimation i s expected to occur as a r e s u l t of i t s exclusion. 3.3 Variable Inputs Variable inputs are those where an annual decision i s made con-cerning l e v e l s of use. Whereas fi x e d inputs would usually be expected to remain constant over a number of years, 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 of v a r i a b l e inputs. They include 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 labour. 3.3.1 F e r t i l i z e r The e f f e c t s of plant food elements on y i e l d s and f r u i t q u a l i t y vary depending on l o c a l s o i l conditions. However, a l l orchard s o i l s i n B r i t i s h Columbia should benefit from a p p l i c a t i o n on nitrogen and boron (Swales, 1971). The timeliness and the quantity of nitrogen supplied are both considered important. If nitrogen i s applied too la t e i t can cause poor f r u i t colour (although f r u i t s i z e should be good) , as w e l l as making the trees more susceptible to winter i n j u r y . If too l i t t l e nitrogen i s applied y i e l d s w i l l l i k e l y be l i g h t with highly coloured small f r u i t . Too l i t t l e boron w i l l r e s u l t i n l i g h t misshapen y i e l d s . A p p l i c a t i o n of other elements including z i n c , magnesium i r o n and 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 quantity depend-ing on l o c a l s o i l d e f i c i e n c i e s . Previous regression analysis on the e f f e c t s of f e r t i l i z e r have pointed out the p o s i t i v e influence of f e r t i l i z e r on y i e l d s . Campbell (1976) found that the amount of f e r t i l i z e r applied had a p o s i t i v e influence on the t o t a l value of the f r u i t , i n d i c a t i n g a p o s i t i v e e f f e c 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 . Lee (1972) had a s i m i l a r r e s u l t using quantity rather than value 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 nutrient elements that are required for tree growth and plant production. F r u i t production 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 les s to f e r t i l i z e r than would production from poor s o i l s . Y i e l d on s o i l s with a PH 7.5 or higher would be expected to have a greater response to f e r t i l i z a t i o n than y i e l d on lower. PH s o i l s because the correct f e r t i l i z e r reduces a l k a l i n i t y as well as supplying nutrient elements. The 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 nitrogen a p p l i c a t i o n i s complicated and i t s e f f e c t s on output w i l l vary. Certain boron d e f i c i e n t and poorly drained s o i l s may respond poorly to nitrogen a p p l i c a t i o n because the nitrogen w i l l not be u t i l i z e d by the trees. The response to nitrogen w i l l probably be better from s l i g h t l y better s o i l s , but from very good s o i l s the response w i l l also be poor, because the nutrient elements are already contained i n the s o i l . Thus the 48 i n t e r a c t i o n between nitrogen and s o i l f e r t i l i t y can be either p o s i t i v e or negative, depending on the range of s o i l f e r t i l i t y . I d e a l l y , a measure of each nutrient added including nitrogen, boron, zinc, i r o n magnesium, manganese and potassium i s required. The measure used i n t h i s study i s the farmer's estimate of t o t a l pounds of f e r t i l i z e r per acre. This measure does not account for the r e l a t i v e concentrations of the applied f e r t i l i z e r s . It i s assumed that most orchardists are using the common ammonium n i t r a t e f e r t i l i z e r which i s 34% nitrogen. 3.3.2 Pesticides The effectiveness of the various p e s t i c i d e s depends on l o c a l c l i m a t i c conditions. Higher r a i n f a l l areas have higher occurrences of apple scab while i n the dryer areas mites and codling moths require more attention. However, a l l areas are under some threat from these pests as well as others including l e a f r o l l e r , aphids, bud moth, le a f hopper, th r i p s and powdery mildew (B.C.M.A., 1975). European f r u i t scale and San Jose scale can occur i n some d i s t r i c t s . The most e f f i c i e n t way to deal with these pests i s to spray several times during the season at varying i n t e r v a l s depending on the stage of the buds and f r u i t (B.C.M.A., 1975). Thus the orchardist can vary the number of applications as well as the concentration of each a p p l i c a t i o n . It i s expected that increases i n either the frequency or concentration of applications w i l l lead to an increase i n y i e l d , by reducing the quantity of c u l l s and by maintaining the health of the tree. The studies by Campbell (1976) and Lee (1972) have both confirmed t h i s expectation as they showed a p o s i t i v e influence of p e s t i c i d e s on value and quantity of y i e l d r e s p e c t i v e l y . An important v a r i a b l e r e l a t i n g to the effectiveness of p e s t i c i d e s 49 i s the machinery used i n spraying. Sprayers capable of a high a i r volume output as well as high a i r v e l o c i t i e s are thought to be more e f f e c t i v e for control of c e r t a i n pests, p a r t i c u l a r l y San Jose scale. These features are necessary i n order to completely coat the f o l i a g e i n the upper and inner areas of the tree with p e s t i c i d e . A higher powered tr a c t o r w i l l r e s u l t i n higher a i r volume and v e l o c i t y from the sprayer, thus r e s u l t i n g i n better pest c o n t r o l . Ideally a measure accounting for the amount and number of a p p l i c a -tions of each of the major chemicals should be included. The actual measure used was the orchardist's estimate of the t o t a l value of p e s t i -cides applied per acre. In cases where t h i s was not a v a i l a b l e , growers were asked whether they followed the recommendations set out i n the B.C.M.A. spray calendar (B.C.M.A., 1975), or sprayed more or le s s often than the guidelines suggested. If the recommendations were f o l -lowed, the cost per acre was set at the average cost of following these guidelines. Cases where farmers did not follow the guidelines and could not make an estimate of the value per acre were rare and these observations were excluded. Many growers tended to say they followed the recommendations when they were only using them as a l b a s i c guide. The r e s u l t i s that $65 per acre became the predominant value for p e s t i -cide i n the data with l i t t l e v a r i a t i o n occurring. Over large sub-sets of the data p e s t i c i d e i s often constant or near constant. 3.3.3 I r r i g a t i o n The importance of i r r i g a t i o n i s i n the maintenance of s o i l mois-ture. Up to a c e r t a i n point s o i l moisture can be expected to have a p o s i t i v e influence on flower i n i t i a t i o n , tree s i z e and f r u i t s i z e (Childers, 1954) and thus on y i e l d s and q u a l i t y . 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 moisture i t i s expected that i t w i l l also i n f l u -ence y i e l d s and q u a l i t y . However, the influence which i r r i g a t i o n has upon s o i l moisture varies according to l o c a l s o i l and c l i m a t i c condi-tion s . Swales (1971) estimates that the rate of i r r i g a t i o n to maintain optimum s o i l moisture v a r i e s from once every four or f i v e days during hot, dry weather on l i g h t shallow s o i l s , to once a month i n the cooler d i s t r i c t s on heavy s o i l s . I r r i g a t i o n i s most desirable during the growing season of the tree and f r u i t , and l e a s t desirable during early f a l l when i t can increase s u s c e p t i b i l i t y to winter cold. The i d e a l measurement should account for both the timeliness and the amount of water applied. No measure was a v a i l a b l e so the v a r i a b l e was not included i n the s t a t i s t i c a l models. 3.3.4 Labour The amount of labour i s associated with previously mentioned v a r i -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 and i r r i g a t i o n and so would be expected to have some p o s i t i v e influence on y i e l d s and q u a l i t y . The remaining labour used could mostly be accounted for i n pruning, thinning and harvesting. The reasons for pruning are to l e t the sunlight and spray reach the inner branches of the trees, to f a c i l i t a t e harvesting by l i m i t i n g tree s i z e and to eliminate unproductive wood. For these reasons i t i s expected that the amount of pruning labour (up to c e r t a i n l e v e l s ) w i l l p o s i t i v e l y influence both quantity and q u a l i t y of f r u i t . The quantity w i l l increase because there w i l l be le s s c u l l s as a r e s u l t of l i g h t and spray penetration, but a f t e r a c e r t a i n point w i l l decrease, simply because the bearing area of the tree decreases with pruning. The e f f e c t s of pruning on f r u i t q u a l i t y would be expected to continue to be 51 p o s i t i v e to a higher point than for quantity. 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 pruning and f r u i t s i z e , but q u a l i t y w i l l f a l l i n the very large f r u i t s as the f l e s h w i l l become soft and the colouring poor. The e f f e c t s of thinning are s i m i l a r to pruning. If no thinning i s done, quantity w i l l be low because there w i l l be a large number of small f r u i t c u l l s . As thinning increases, these c u l l s w i l l decrease and quantity w i l l increase. After a c e r t a i n point quantity w i l l decrease as the thinning w i l l be removing p o t e n t i a l l y commercial f r u i t . The amount of thinning w i l l be p o s i t i v e l y r e l a t e d to f r u i t s i z e , but when c a r r i e d to excess w i l l r e s u l t i n overly large soft f r u i t of poor q u a l i t y . Within a c e r t a i n range an increase i n harvesting labour w i l l increase production. Obviously once the f r u i t has a l l been 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 occurring. In fact one would usually observe the exact amount of harvesting labour necessary to harvest the crop although i n a few instances there might not be enough seasonal labour a v a i l a b l e and some of the crop w i l l remain unharvested. When there i s a shortage of seasonal labour c e r t a i n orchardists who have better con-tacts i n the industry or more e a s i l y harvested orchards would l i k e l y obtain more and a better q u a l i t y of labour than others. The i d e a l measure of pruning and thinning labour should include both the time spent and the effectiveness of these a c t i v i t i e s . No accurate measure was possible without s i g n i f i c a n t l y added research e f f o r t , so t h i s v a r i a b l e i s not included i n estimations. This input may be somewhat associated with the planting system and can be accounted 52 for by assuming a fixed amount of labour i s required for each system. The exclusion of t h i s v a r i a b l e , i s a recognized weakness of the model. Ideally there should be some measure of the q u a l i t y of the harvest-ing labour rather than the actual value paid for harvesting. Because pickers are paid by the pound or bin, usually at common rate for the area, there w i l l be a high c o r r e l a t i o n between the amount paid for harvesting and y i e l d s . Harvesting labour measured by value paid would l i k e l y be a dominant v a r i a b l e i n the regressions, thus impairing the estimation of other c o e f f i c i e n t s . No measure of the amount or q u a l i t y of harvesting labour i s included i n the estimations. The e f f e c t s of t h i s v a r i a b l e can be removed a f t e r the estimations have taken place, by subtracting the harvesting costs from the predicted value of the y i e l d s . Because input associated labour i s dependent on the amount of inputs applied, i t i s best not to measure i t on a per-acre basis as are other inputs. A measure could be made on a per unit basis such as the time taken to apply a hundred gallons of spray material or the time taken to apply 100 lbs of f e r t i l i z e r . No measure was recorded and consequently t h i s v a r i a b l e i s not included i n the estimations. It i s f e l t that a fixed amount of labour per unit of input i s not an unreasonable assump-t i o n over the short run, so the analysis w i l l not be hindered by the exclusion of t h i s v a r i a b l e . In summary, the v a r i a b l e inputs are not as strongly represented i n the data as fixed inputs. Labour i s accounted for by assuming fixed proportions which i s reasonable over the short run although i t may lower the p r e c i s i o n of the estimates. Because of measurement problems the p e s t i c i d e data i s imprecise which might also a f f e c t estimation. In general no systematic bias i s expected to occur because of data problems 53 with v a r i a b l e inputs, unless the assumption of fixed proportions of labour 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 show an upward bias. 3.4 Weather Variables Weather variables present a d i f f e r e n t type of problem i n measure-ment than the inputs already discussed. Although i t i s known which weather factors are important i n tree f r u i t production the most approp-r i a t e measures of these factors are not always obvious. For example, i t i s known that below freezing temperatures during the blossom period have adverse e f f e c t s on the buds and blossoms and therefore w i l l reduce the ensuing crop, but i t i s not known what the best measure of the influence of f r o s t i s . It could be measured by the duration of cold temperatures, the incidence of temperatures below a c e r t a i n l e v e l , or a combination of duration and incidence. Similar problems i n determining the i d e a l measurements of most of the other weather variables are also encountered. A separate weather model, section 4.2, i s estimated with the object of s e l e c t i n g a set of appropriate measures of weather i n f l u -ences and assessing t h e i r impact at a regional l e v e l . The following variables were considered i n the model. 3.4.1 Blossom Influences A number of factors during the green t i p to green f r u i t stage w i l l influence p o l l i n a t i o n and f r u i t set with a r e s u l t i n g e f f e c t on y i e l d . These factors are f r o s t , temperature, sunlight, wind and r a i n . The period during which the blossoms can be p o l l i n a t e d i s approx-imately four to ten days long. There i s a natural compensation e f f e c t at work during t h i s period, i n that the weather factors which cause p o l l i n a t i o n to be poor, also lengthen p o l l i n a t i o n period. However, i t 54 i s f e l t that a short blossom period, with 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 i s preferable to a longer blossom period with le s s s u i t a b l e weather. P o l l i n a t i o n depends for the most part on honey bees, wild s o l i t a r y bees and bumble bees, with honey bees generally doing most of the p o l -l i n a t i o n . The weather variables which a f f e c t the a c t i v i t i e s of these insects w i l l thus influence the amount of p o l l i n a t i o n and the f r u i t y i e l d . The periods preceding and following the blossom stage are also important because cold 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 constitutes a major hazard during the blossom period of the f r u i t . The major damage during t h i s time occurs on the p i s t i l of the blossom, which i f injured before p o l l i n a t i o n , cannot be f e r t i l -ized (Karmo et a l . , 1956). After p o l l i n a t i o n the p i s t i l becomes s l i g h t l y more hardy, but s t i l l can be injured 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 susceptible to i n j u r y during the f u l l bloom period. The following temperatures are the minimum temperatures that apple blossoms can stand for 30 minutes, at various stages of development (Davis, 1974). Table 3.4. Temperatures below which damage occurs during blossom period showing colour f u l l bloom green f r u i t 25 F. 28 F. 29 F. duration 3 to 4 weeks 4 to 10 days 10 days to 2 weeks 55 Thus there i s a period of about 35 to 50 days where a spring f r o s t can cause blossom damage and a possible reduction i n y i e l d . The factors of influence can be summarized as the frequency of cold below the c r i t -i c a l temperatures, the i n t e n s i t y of t h i s cold and the stage of blossom development. Ideall y a measure including both length and i n t e n s i t y of f r o s t i n each orchard below c r i t i c a l l e v e l s at each stage of blossom development should be included. The actual measurements are as follows. The f i r s t stage, green t i p , was taken from 25 days before the recorded data of f u l l bloom to one day before. The second stage, f u l l bloom was from one day before the recorded date to 6 days a f t e r and the t h i r d stage, green f r u i t , was taken as the next 12 days. The variables compiled are as follows. Table 3.5. A l t e r n a t i v e measures of f r o s t during bloom Variable Explanation Expected sign Frost 1 Accumulated degrees from minimum temperatures below 27 F. 30 F. and 31 F. for the green t i p , f u l l bloom and green f r u i t stages re s p e c t i v e l y . Frost 2 As i n Frost 1, but with c r i t i c a l temperatures of 25 F. 28 F. and 29 F. Frost 3 The number of days during the whole period on which any f r o s t occurred. Temperatures were recorded at regional weather s t a t i o n s . 56 3.4.3 Temperature Honey bees are unable to f l y at temperatures below 55 F. and are .. not capable of carrying 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 the tempera-ture reaches at le a s t 65 F. (Karmo, 1956). Bumble bees are able to p o l l i n i z e at s l i g h t l y lower temperatures while wild bees need a s l i g h t l y warmer temperature. It i s expected that the frequency and the duration of 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 influence on y i e l d . I d e a l l y a measure f or each orchard of the duration and i n t e n s i t y of temperatures conducive to insect p o l l i n a t i o n a c t i v i t y during the f u l l bloom period should be used. Unfortunately, the exact length of the f u l l bloom period f o r each year i s not known, so measures of t h i s influence are compiled over d i f f e r e n t lengths s t a r t i n g at the recorded data of f u l l bloom of the closest recording s t a t i o n . The measures below are recorded for each region, namely (1) Kelowna Westbank, (2) Penticton-Summerland-Naramata, and (3) Oliver-Osoyoos. Table 3.6. A l t e r n a t i v e measures of temperature during bloom Accumulated degrees (from d a i l y maximums) Temp 1 Temp 2 Temp 3 Temp 4 over 65 F. 5 day period 7 day period 10 day period i t II II 5 day period from 6th day to 10th day 3.4.4 Sunlight It has been observed that bees prefer bright sunny days to over-cast days for a c t i v i t y (even i f there i s no difference i n temperature) (Karmo, et a l . , 1956). I t i s therefore expected that the amount of bright sunlight occurring during f u l l bloom period w i l l p o s i t i v e l y influence y i e l d . Again, i t would be i d e a l to consider measure of t h i s v a r i a b l e for each orchard over the f u l l bloom period. The measures a c t u a l l y recorded are s i m i l a r to those already discussed, as they are on a regional l e v e l and over d i f f e r e n t lengths s t a r t i n g on the f i r s t recorded day of f u l l bloom. Table 3.7. A l t e r n a t i v e Measures of Sunlight during Bloom sun 1 hours of bright sunlight - 5 day period sun 2 7 day period sun 3 " 10 day period s u n 4 " 5 day period from 6th to 10th day 3.4.5 Wind Wind i s thought to be one of the greatest influences on bee a c t i v i t y (Karmo, et a l . , 1956). Honey bees cannot work i n winds of over 15 mph., while bumble bees can work i n s l i g h t l y stronger winds and wild bees must stop at a l e s s e r wind speed. It i s expected that the frequency and duration of winds over 15 mph. w i l l have a negative influence on y i e l d . A measure of both the i n t e n s i t y and duration of wind i n each orchard during the blossom period would be i d e a l . No d a i l y data on winds was 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 included i n estimations. 58 3.4.6 Rain Heavy r a i n w i l l cause a l l types of bees to cease working (Karmo, et a l . , 1956). Often bees w i l l not resume work immediately a f t e r a r a i n -f a l l , but w i l l wait u n t i l the next day. Rain can also a f f e c t p o l l i n -a tion by ruining the plooen on the anthers of p o l l i n a t i n g v a r i e t i e s . New pollen w i l l then be produced by the blossom but i n the period required for production, any insect a c t i v i t y w i l l have no e f f e c t . I t i s hypothesized that the frequency and i n t e n s i t y of r a i n f a l l during the f u l l bloom period w i l l negatively influence y i e l d s . I t i s also expected that the e a r l i e r a r a i n f a l l occurs during t h i s period, the greater w i l l be i t s e f f e c t s on y i e l d . I d e a l l y a measure of the t o t a l r a i n f a l l occurring i n each orchard during the f u l l bloom period should be included. Because the exact length of the f u l l bloom period i s not known, these variables are also compiled over d i f f e r e n t time periods. The t o t a l s shown are recorded for the three regions mentioned above. Table 3.8. A l t e r n a t i v e measures of r a i n f a l l during bloom Tot a l p r e c i p i t a t i o n i n hundredths of an inch Rain 1 II 5 day period Rain 2 II 7 day period Rain 3 10 day period Rain 4 5 day period from 6th day to 10th day Rain 5 number of days where p r e c i p i t a t i o n occurred i n 10 day period 3.4.7 Growing Season Influences Temperature i s a primary factor c o n t r o l l i n g the growth of plants 59 and heat unit accumulation has been demonstrated as an accurate predictor of f r u i t maturity (Ag. Canada, 1959). While i t i s expected that heat accumulation during the growing season w i l l influence y i e l d , there i s some compensation for a lack of heat i n that the f r u i t can be l e f t longer on the tree i n order to size-up and mature. A measure of the t o t a l heat accumulated from the green-fruit to the harvesting stage would be i d e a l . A good approximation of t h i s measure can be made by c a l c u l a t i n g heat units f o r each region and year. However, heat units were not calculated i n t h i s research, as tempera-tures for nearly 4,000 days would have to be compiled. 3.4.8 Cold Winter Temperatures When winter temperatures are abnormally cold i n the Okanagan area, several forms of injury to f r u i t trees can occur. Apples are the most hardy f r u i t and a temperature at le a s t as cold as -25°F. i s necessary for s i g n i f i c a n t damage and a subsequent drop i n production to occur (Mann, et a l . , 1952). Cold 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 small limb and twig i n j u r y r e s u l t s more often, cut 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 bearing area. Large limb and trunk i n j u r y i s often caused by sunscald on the southwest side of trees where the alternate warming during the day and severe freezing at night causes damage i n the bark, cambium and wood conducting t i s s u e s . The r e s u l t of the sunscalding can be a weakened or dying condition of the upper portion of that side of the tree. Crown i n j u r y can be severe enough to k i l l the tree with the damage near ground l e v e l and associated with the bud union of the tree. Root injury can occur i n several degrees, ranging from damage to only the small feeding roots to k i l l i n g of a l l the roots. In the former case the trees recover with only some delayed f o l i a g e development while i n the l a t t e r case the trees usually die with the coming of spring. It i s expected that the f r e -quency and i n t e n s i t y of cold below -25°F. w i l l thus negatively influence y i e l d s i n the following season. During the period covered by the sample there was no serious amount of winter k i l l i n the area, so no measure of t h i s v a r i a b l e was recorded or used i n estimations. Generally the weather variables are adequately represented i n the data. Measures are a v a i l a b l e f or most of the important blossom time influences while no measure was required for w i n t e r - k i l l v a r i a b l e s i n recent years. The only area with a lack of data i s growing season influences where the required measurement i s not presently a v a i l a b l e . Because weather variables were recorded at regional weather s t a t i o n s , rather than on the actual orchard s i t e s , some imprecision i n the e s t i -mated c o e f f i c i e n t s for orchard l e v e l functions may r e s u l t . 3.5 Y i e l d Per Acre The i d e a l measurement accounts for both q u a l i t y and quantity of f r u i t per acre. Value paid to the farmer with some adjustment made for yearly p r i c e f l u c t u a t i o n s would be an appropriate measure. How-ever, for the data from experimental plots there i s no q u a l i t y grading and values cannot be assigned. It was e s s e n t i a l to include t h i s data because i t provided important v a r i a t i o n i n input l e v e l s thereby reducing the degree of m u l t i c o l l i n e a r i t y of the complete body of data. The actual measure of y i e l d i s pounds per acre, excluding c u l l s . 61 3.6 Summary There are a number of preconceived variables f or which there i s no measure i n the s t a t i s t i c a l model. These are management, labour, machinery inputs, i r r i g a t i o n l e v e l s , growing season heat accumulation, and wind during bloom. The exclusion of management, labour and machin-ery w i l l l i k e l y impart a systematic bias i n the estimates of several inputs. Because of the p o s i t i v e i n t e r a c t i o n of management with v a r i -able inputs i t i s expected that the f e r t i l i z e r and p e s t i c i d e c o e f f i c i e n t s w i l l be biased upwards. The exclusion of labour should have a s i m i l a r e f f e c t , imparting a general upward bias. Because there i s some a p r i o r i knowledge of the c o r r e l a t i o n between labour and some fi x e d inputs, the bias imparted to these c o e f f i c i e n t s can be accounted f o r , when i n t e r p r e t -ing the r e s u l t s . It i s not cl e a r what the general e f f e c t w i l l be of leaving out the machinery inputs, although i t i s known that they have a p o s i t i v e i n t e r a c t i o n with p e s t i c i d e s , so a further upward bias w i l l be imparted to i t s c o e f f i c i e n t . Although there i s no data on the amount of i r r i g a t i o n applied, there i s a va r i a b l e representing the i r r i g a t i o n system which should capture some of the e f f e c t s of the l e v e l of i r r i g a -t i o n . The overhead i r r i g a t i o n systems are labour saving and i t i s reasonable to assume that more water w i l l be applied to orchards than to orchards with portable systems. Important weather va r i a b l e s not included are heat units and wind. It i s known that the southern areas with higher heat unit accumulation also have a greater incidence of f r o s t and sunlight during blossom periods so there w i l l l i k e l y be some bias imparted to 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 other variables so any bias imparted to other c o e f f i c i -ents w i l l be due only to random c o r r e l a t i o n with wind. 62 Figure 3.2 following shows the de t a i l e d conceptual model and the rel a t i o n s h i p between the concept, the required measure and the actual measure. It can be seen from t h i s f i g u r e that the number of var i a b l e s i s extremely large, with several dummy var i a b l e s and i n t e r a c t i o n s . Overall most of the required measures, or reasonable proxies thereof are a v a i l a b l e f or estimation. For several preconceived v a r i a b l e s there are only proxy measure-ments a v a i l a b l e . There i s no reason to expect any systematic bias i n these v a r i a b l e s although a c e r t a i n amount of imprecision i s expected. Proxy variables based on farmers' estimates include s o i l q u a l i t y , f r o s t 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 . It i s expected that orchardists are well acquainted with these aspects of production so that t h e i r estimates w i l l be reasonably accurate. Pesticides tend towards a constant value so some of i t s actual v a r i a t i o n i s not measured. Other proxy variables include a l l weather v a r i a b l e s . Data from regional weather stations i s used i n place of actual observations from the orchards. This data should capture much of the v a r i a t i o n and there i s no reason to believe that any bias w i l l occur i n estimation. The remaining v a r i a b l e s , a l l i n the ph y s i c a l feature category are accurately measured, although the preponderance of dummy variables i s a problem for s t a t i s t i c a l estimation. The dependent v a r i a b l e i s a proxy as pounds of f r u i t rather than value of the f r u i t i s used, and a l l estimated marginal products represent e f f e c t on the quantity rather than the value of the f r u i t . Thus the marginal products are only interpreted as guidelines or ind i c a t o r s of the marginal value products. 63 Concept Required measure Actual measure Y i e l d Management Physical features  & fixed inputs s o i l q u a l i t y f r o s t r i s k p o l l i n a t i o n method rootstock density tree design v a r i e t y age machinery i r r i g a t i o n system Variable inputs f e r t i l i z e r p e s t i c i d e s i r r i g a t i o n labour Weather influences wind during bloom r a i n during bloom temperature during bloom sun during bloom f r o s t during bloom growing season heat winter k i l l Interactions r o o t s t o c k - f e r t i l i z e r rootstock-pesticides rootstock-age rootstock-frost a g e - f e r t i l i z e r age-pesticide age-frost s o i l - i r r i g a t i o n s o i l - f e r t i l i z e r s o i l - r o o t s t o c k labour-with most inputs value of y i e l d per acre t o t a l management a b i l i t y of grower depth, texture, ph, nutrients aspect, a l t i t u d e , pockets number and proximity of hives, number of p o l l i n a t o r trees e f f e c t on tree s i z e number of trees per acre d i s t i n g u i s h between hedgerow and free standing d i s t i n g u i s h between v a r i e t i e s stage of development kind, 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 pruning, thinning and input associated labour 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 t o t a l amount amount below c r i t i c a l l e v e l s heat units not required for sample t r e e - s i z e x f e r t i l i z e r t r e e - s i z e x p e s t i c i d e s t r e e - s i z e x age t r e e - s i z e x f r o s t 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 q u a l i t y x i r r i g a t i o n s o i l q u a l i t y x f e r t i l i z e r s o i l q u a l i t y x t r e e - s i z e l b s . per acre estimate of texture estimate of r i s k number of hives per acre index of tree s i z e number of trees per acre dummies for each design dummies for v a r i e t i e s indexed age dummy fo r each system t o t a l amount i n l b s . t o t a l value regional t o t a l s 1/100" regional accumulated degrees above c r i t i c a l l e v e l s regional t o t a l amount i n 1/10 hours regional amount below c r i t i c a l l e v e l s t r e e - s i z e x f e r t i l i z e r t r e e - s i z e x p e s t i c i d e s t r e e - s i z e x age t r e e - s i z e x f r o s t 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 q u a l i t y s o i l q u a l i t y f e r t i l i z e r t r e e - s i z e Figure 3.2. Comparison of concepts, required measure and actual measures 64 3.7 Data Sources Most of the measures discussed i n previous sections are based on data obtained from a survey conducted by A g r i c u l t u r e Canada i n 1975. This survey was not designed e x c l u s i v e l y for production function estima-t i o n but also aimed at providing data for mathematical program modeling and for comparative tables of y i e l d s and inputs of d i f f e r e n t systems (Kennedy, Andison and Graham, forthcoming). In order to obtain d e t a i l e d data from as many orchards as possi b l e , questionnaires were designed to take l i t t l e of the growers' time. The lack of detai l e d records kept by many orehardists was recognized and questions were asked only where use of such records was not required. Hence, for a few inputs such as labour no data were gathered. Despite these shortcomings, the data were f a r better suited to the purposes of t h i s study than any other a v a i l a b l e data, as i t was highly disaggregated and included most major inputs. The survey u t i l i z e d three sources of information. 1. Orehardists i n the area who were interviewed and f i l l e d out ques-tionnaires on inputs and phy s i c a l features of s p e c i f i c blocks of f r u i t . Information was gathered on 15 inputs and phy s i c a l features including v a r i e t y , density of planting rootstock, spur or non-spur, s o i l texture, f r o s t r i s k , p o l l i n a t i o n method, acres per hive ( i f bees are used), i r r i g a t i o n method, planting concept, year of plant-ing, p e s t i c i d e use per acre, and f e r t i l i z e r use per acre. The values of these inputs are estimates by the growers of the average amount used i n the l a s t few years. 2. Information on y i e l d s from these blocks came from packout records of the packing houses where the growers had sold t h e i r apples. The packout records show the t o t a l weight i n pounds and the p r i c e paid 65 each year categorized 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 input to y i e l d data. Most orehardists have more than one block of trees producing a c e r t a i n v a r i e t y of apple. In these cases i t cannot be determined what proportion of the t o t a l production accrues to each block of f r u i t , unless the growers have kept separate records. Attempts were made to sele c t growers who had only one homogeneous system of production of a p a r t i c u l a r v a r i e t y , so the y i e l d on the packout record could be d i r e c t l y r e l a t e d to the producing block. 3. An a d d i t i o n a l source of information was records of experimental orchard p l o t s at the Summerland Research Station. The records contain information on inputs, p h y s i c a l features and y i e l d s , although.;the y i e l d s are not categorized by grade or s i z e . Approximately 40 orehardists were surveyed representing about 120 blocks of f r u i t . Data on 90 a d d i t i o n a l blocks were obtained from records of the research station's experimental plantings. On average there were four years of observation on y i e l d s from the orchards and seven to eight from the experimental p l o t s . Information on weather variables 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 records and kept f or several points throughout the v a l l e y . Data was compiled f o r O l i v e r , Summerland and Kelowna. Daily observa-tions of maximum and minimum temperatures, hours of sunlight, r a i n f a l l and snowfall are a v a i l a b l e . Records of full-bloom dates f o r several centers i n the area are kept by the Summerland Research Station. The date may vary consider-ably within each region, depending on the a l t i t u d e , aspect and proximity to the lake of the trees. This v a r i a t i o n was accounted for i n the Summerland records, and for the other areas only the e a r l i e s t full-bloom date i s given. Input data were subject to q u a l i t y control procedures. V i s u a l and computer checks were run for extreme values which were v e r i f i e d or r e c t i f i e d where necessary. The c o l l a t e d input and output data were also mailed to each grower for re-checking. This chapter has presented a disaggregated conceptual model of apple production at the orchard l e v e l . D e t a i l s of the required mea-sures and the a v a i l a b l e data were discussed. The general conclusion i s that the dataware complete enough to j u s t i f y estimation of a d i s -aggregated production function which includes the major inputs of the conceptual model. The next chapter discusses the s t a t i s t i c a l method-ology and presents r e s u l t s of the estimations. CHAPTER IV ESTIMATION OF THE PRODUCTION FUNCTION This chapter deals w i t h the e s t i m a t i o n of the conceptual model as summarized i n f i g u r e 3.2. A number of problems i n e s t i m a t i n g t h i s model are apparent and a general 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 formulated to deal w i t h these problems. P r i o r to the e s t i m a t i o n of the 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 only weather f a c t o r s as explanatory v a r i a b l e s i s estimated. The r e s u l t s are used to s e l e c t a subset of weather v a r i a b l e s to be included i n the complete model. The complete orchard l e v e l model i s then presented 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 are 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 to be included i n the estimated model. The r e s u l t s of the model are poor i n some regards and p o s s i b l e explanations are discussed. A second approach to es t i m a t i o n i s c a r r i e d out where the data are p a r t i t i o n e d i n t o a number of subsets. Within each subset the observa-t i o n s have a common ro o t s t o c k or v a r i e t y . Separate regressions are c a r r i e d out f o r each subset of data. This approach proves to 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 the ensuing d i s c u s s i o n s . 4.1 E s t i m a t i o n Strategy Given the a v a i l a b l e data, the e s t i m a t i o n s t r a t e g y aims at o b t a i n i n g 67 68 information about as many of the conceptual v a r i a b l e s as possible. It i s i m p r a c t i c a l , however, to place a l l the va r i a b l e s of the conceptual model into a s i n g l e equation f o r estimation. There are a t o t a l of 29 variables including i n t e r a c t i o n s and dummy variables f o r which data are av a i l a b l e . The large number of va r i a b l e s p a r t i c u l a r l y the dummies and inter a c t i o n s leads to severe m u l t i c o l l i n e a r i t y problems (see section 4.3). A further d i f f i c u l t y i s that for the class of weather va r i a b l e s there are a number of measures a v a i l a b l e f o r each concept. Within the cumbersome complete model i t i s d i f f i c u l t to choose the best measure of each v a r i a b l e . Because of these problems attempts are made to reduce the number of explanatory v a r i a b l e s within the estimated models, without foregoing information about any of the important v a r i a b l e s . Two general procedures are followed i n the reduction process: 1. d i v i d i n g the explanatory variables into groups and s e l e c t i n g subsets of v a r i a b l e s from within each group. 2. p a r t i t i o n i n g the data into smaller sets each set containing one or more variables constant within the set. Under the f i r s t reduction procedure the variables are divided into three groups: weather v a r i a b l e s , interactions'and management va r i a b l e s including p h y s i c a l features of the orchards. No attempt i s made to select a p r i o r i a subset of important management variables although the actual number included i n the estimations i s les s than i n the conceptual model because of data l i m i t a t i o n s . There are numerous weather va r i a b l e s and they present some scope for a separate a n a l y s i s . One advantage of considering weather factors i n a separate analysis i s that observations may be grouped to maximize between-group v a r i a t i o n i n weather variables while minimizing between-group v a r i a t i o n i n other inputs. This 69 procedure i s ca r r i e d out by grouping the data into three separate regions over the time period of the sample. The v a r i a t i o n i n weather between regions i s s t i l l retained while the v a r i a t i o n between average regional l e v e l s of management variables i s greatly reduced. Regressions are then c a r r i e d using only the weather factors as explanatory v a r i a b l e s and the more important variables and t h e i r appropriate measures are retained for i n c l u s i o n i n a complete orchard l e v e l model (see section 4.2). Interactions between variables are d i f f i c u l t to deal with as a separate group. It i s desirable to reduce t h e i r number as they can greatly compound the m u l t i c o l l i n e a r i t y problem (see section 4.3). No separate group analysis can be performed with them because they are highly correlated with the basic inputs. A procedure i s developed whereby a subset of inte r a c t i o n s i s entered into the estimated equations along with managerial inputs and the selected weather f a c t o r s . S p e c i f i c i n t e r a c t i o n s are retained from the subset, before the next subset i s added and the procedure repeated. The d i v i s i o n of in t e r a c t i o n s into subsets and the s e l e c t i o n c r i t e r i a for s p e c i f i c i n t e r a c t i o n s are described i n section 4.3. An overview of the reduction procedure f o r a r r i v i n g at a complete orchard l e v e l model including the s e l e c t i o n of weather v a r i a b l e and i n t e r -actions i s shown i n Figure 4.1. This fi g u r e i l l u s t r a t e s the stepwise procedure used to a r r i v e at a f i n a l subset of variables f o r the orchard l e v e l model. It can be seen that every v a r i a b l e i s entered at some point i n the estimations, which i s an advantage over an a p r i o r i reduc-t i o n procedure. As mentioned, va r i a b l e s which have been entered early i n the process may tend to be selected over those entered i n the l a t t e r stages. In order to assess the degree of s e l e c t i o n bias, the robustness 1. Estimate regional weather model 2. Select subset of weather variables 3. Estimate l i n e a r orchard l e v e l model including weather variables 4. C l a s s i f y and rank i n t e r -actions according to a p r i o r i importance 5. Re-estimate equation including rootstock i n t e r a c t i o n s 6. Select subset of root-stock in t e r a c t i o n s 7. Re-estimate equation including age i n t e r -actions and selected rootstock in t e r a c t i o n s 8. Select subset of age i n t e r a c t i o n s 9. Re-estimate including s o i l i n t e r a c t i o n s , keep-ing selected rootstock & age i n t e r a c t i o n s 10'. Select subset of s o i l i n t e r a c t i o n s 11. Re-estimate equation with subsets of a l l three i n t e r a c t i o n categories average y i e l d per region = f(weather variables) selected subset of weather variables 4-inputs, weather f physical + variable features subset y i e l d per acre y i e l d per acre y i e l d per acre y i e l d per acre y i e l d per acre inputs, f physical features inputs, f physical features weather + variable subset weather + variable subset + rootstock interactions 4-rootstock interactions age interactions s o i l i n t e r a c t i o n s subset of root-stock interactions subset of + rootstock interactions •inputs, f physical features weather + v a r i a b l e subset subset of + rootstock interactions + age interactions 4-subset of age interactions 4-subset of + age interactions inputs, f physical features weather + variable subset subset of rootstock interactions subset of + age interactions s o i l i n t e r a c t i o n s 4-subset of s o i l i n t e r a c t i o n s 4-subset of + s o i l i n t e r a c t i o n s Figure 4.1. Overview of the Estimation Procedure o 71 of the f i n a l r e s u l t s are also tested by changing the order i n which groups are entered i n t o the estimation. Under the second reduction procedure the same stepwise procedure i l l u s t r a t e d i n figu r e 4.1 i s ca r r i e d out with one major d i f f e r e n c e . Instead of estimating functions over the complete set of data, separate functions are estimated f o r each tree s i z e category and v a r i e t y . In other words each subset of data exhibits observations of a common tree-s i z e or common v a r i e t y . The tree s i z e v a r i a b l e s and rela t e d i n t e r a c -tions or the v a r i e t y dummies are thus eliminated from each equation. The procedure also imposes les s r e s t r i c t i o n s on the behaviour of the i n t e r a c -tions (see section 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 to some extent. The procedure for choosing weather va r i a b l e s and int e r a c t i o n s for the pa r t i t i o n e d functions i s the same as for the function estimated over the f u l l data set. Other problems i n estimation are rela t e d to the disaggregated nature of the data, the small s i z e of i n d i v i d u a l observations and data p a r t i t i o n i n g . For most of these problems there i s no immediate s o l u t i o n but t h e i r e f f e c t s are discussed as they become apparent i n the estimations. The s t a t i s t i c a l procedures and r e s u l t s are discussed i n following sections. Three basic models are presented: (1) a weather model explaining regional 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 orchards, 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 are estimated f o r each t r e e - s i z e category and v a r i e t y . The estimated parameters of the weather model prove to 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 of weather va r i a b l e s i s selected for further use. The r e s u l t s from the complete orchard l e v e l model are poor by some standards, and possible reasons for t h i s are discussed. The r e s u l t s from the p a r t i t i o n e d models are considered acceptable for the tr e e - s i z e category functions but are poor f o r the v a r i e t y category func-tio n s . I t i s concluded that the main thrust of future s t a t i s t i c a l research should concentrate on functions for tree s i z e categories and these r e s u l t s are discussed i n more d e t a i l than the other estimates. 4.2 Results for the Weather Model The purpose of t h i s section i s to estimate a model of apple produc-t i o n for which v a r i a t i o n i n y i e l d i s explained s o l e l y by weather f a c t o r s . The model i s used to assess the impact of weather variables 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 of various recorded measure of weather factors which are a v a i l a b l e . A subset of weather variables and t h e i r appropriate measures are selected f o r use i n estimating the complete orchard l e v e l production function. Y i e l d data for each orchard block was aggregated by year and by region to give an annual average y i e l d per acre for three regions i n the area. Hence v a r i a t i o n i n the non-weather v a r i a b l e s i s reduced, because average values of these inputs per region are obtained rather than i n d i v i d u a l values for each block. In comparison, the v a r i a t i o n of weather variables w i l l be large, because the differences between years and regions are not l o s t i n aggregation. This 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 of weather as there w i l l s t i l l be some v a r i -a t i o n i n the average values of the other inputs. Because there may be some c o r r e l a t i o n between weather variables and l e f t - o u t v a r i a b l e s there w i l l be some bias i n the estimated c o e f f i c i e n t s . The dependent v a r i a b l e i s average production per acre f o r each region and year from 1967 to 1974 i n c l u s i v e . The regions are Kelowna, 73 Summerland and O l i v e r . The production from each orchard has been added to the region that most c l o s e l y approximates i t s l o c a t i o n . To obtain observations 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 f o r each region and t o t a l sample producing acreage. The t o t a l y i e l d was obtained by sorting the sample into the three regions and adding up production for each year. The c a l c u l a t i o n of t o t a l acreage under production i n each region was more d i f f i c u l t because the lag between the planting dates of the trees and the f i r s t year of commercial production had to be considered. Lags of s i x years for standard trees, f i v e years for semi-standards, and four years f o r dwarfs and semi-dwarfs were used. For example a block of standard trees planted i n 1960 would not be included i n t o t a l producing acreage u n t i l 1966. A second problem i n the c a l c u l a t i o n of t o t a l acreage was that planting dates for c e r t a i n acreages i n the sample were not a v a i l a b l e . This acreage was the non-definite block type, where trees were highly intermixed or scattered throughout the orchard. Acreage of t h i s type accounted for about 50% of the t o t a l sample acreage i n Summerland and Ol i v e r and for about 20% i n Kelowna. It was assumed that t h i s acreage came into production i n the same proportions as the s p e c i f i c block types of acreage. For example i f producing acreage of s p e c i f i c block type increased 20% between 1967 and 1968 i t was assumed that producing acreage from non-specific blocks also increased by 20%. The calculated acreage of non-specific blocks could be added to the known acreage to give a t o t a l f o r each year. The model shows that a l l four categories of blossom influences tested are important. The most appropriate of these would be sunlight and f r o s t , a combination which has the best explanatory power. However, due to missing records for sunlight i t w i l l be necessary to use tempera-ture i n i t s place i n some estimations. The variables retained for further use are: 1. temperature—accumulated degrees above 65 F. for a 10 day period 2. r a i n f a l l — i n 1/100 inches for a f i v e day period 3. sunlight i n 1/10 hours for a 10 day period 4. frost—accumulated degrees below c r i t i c a l l e v e l s of 27 F., 30 F., and 31 F., from the green t i p to green f r u i t stage. In the following sections the selected weather variables are incorporated into an orchard l e v e l model where disaggregated functions, including a l l inputs, are estimated. Weather variables tested i n t h i s model f a l l under four categories: blossom sunlight, blossom temperatures, blossom f r o s t and blossom r a i n -f a l l . There are other influences that should be considered e s p e c i a l l y growing season heat accumulation, but data were not a v a i l a b l e . Winter-k i l l influences were not considered because there were no c r i t i c a l cold s p e l l s during the time covered by the sample. A d e t a i l e d discussion of the weather concepts and measurements was given i n the previous chapter. The conceptual model can be summarized as: average regional _ f(blossom sunlight, blossom temperatures, production per acre 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 a l l v a r i e t i e s with the exception of Mcintosh and Newton are aggregated. Thus the model does not t e s t f or differences i n the manner that species are affected by these weather v a r i a b l e s . Mcintosh and Newton generally bloom at d i f f e r e n t times than the other species (which usually bloom on the same date) and d i f f e r e n t sets of weather v a r i a b l e s were compiled for them. However, no separate 75 t estimate could be made for the Newton apple v a r i e t y because of a lack of observations. Some tes t s were made on Mcintosh and proved unsuccessful, l i k e l y because of a small sample problem. For most years and regions there were only very small acreages under Mcintosh so the averaging procedure was not very e f f e c t i v e i n reducing 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 estimations was the m u l t i c o l -l i n e a r i t y between sunlight and temperature and between sunlight and r a i n f a l l . Thus two basic categories of estimations were made: (1) estimations including sunlight but excluding temperature and r a i n f a l l , and (2) estimations i n c l u d i n g temperature and r a i n f a l l but excluding sun-l i g h t . 4.2.1 Estimations Excluding Sunlight As there were three d i f f e r e n t lengths of blossom period considered for temperature and r a i n f a l l , several runs were undertaken i n order to fi n d the most appropriate length for each v a r i a b l e . A consistent r e s u l t was that the longest period of 10 days was the most s i g n i f i c a n t for temperature and that the shortest length of f i v e days was the most s i g n i f i c a n t f or r a i n f a l l . Table 4.1 shows the estimated parameters for these v a r i a b l e s . In the f i r s t equation the f r o s t c a l c u l a t i o n with the higher c r i t -i c a l temperatures was used as i t wasconsistently more s i g n i f i c a n t than the f r o s t v a r i a b l e with the lower c r i t i c a l temperatures. The second equation shows f r o s t represented by the t o t a l number of days on which temperatures occurred below the 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 l e s s s i g n i f i c a n t r e s u l t s . Several runs were made experimenting with logarithmic values for 76 Table 4.1. Estimated Functions f o r Weather Model— excluding sunlight Dependent Variable Production per acre (regional average) C o e f f i c i e n t Independent Variable 1 2 3 4 Constant 10462 (4.24)* 93936.4 (3.85) 10588 (4.30) 11434.55 (3.26) 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) -343.1 (2.37) T o t a l days on which f r o s t occurred below c r i t i c a l l e v e l s -91.59 (-2.07) Log of accumulated f r o s t below c r i t i c a l l e v e l -1842.55 (-2.51) Rain over 5 day period -75.14 (-2.16) -64.62 (-1.83) -70.41 (-2.07) -75.14 (-2.10) Accumulated degrees alone 65°F—first 5 days of bloom 757.57 (2.46) Accumulated degrees alone 65°F—last 5 days of bloom 758.87 (2.48) R 2 .67 .64 .67 .67 *T s t a t i s t i c s are i n parentheses under estimated c o e f f i c i e n t s temperature, r a i n f a l l and f r o s t . For temperature and r a i n f a l l the logarithmic forms generally resulted i n le s s e r s i g n i f i c a n c e and poorer f i t . The log 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 than the l i n e a r form, as shown i n the t h i r d equation. Some estimations were ca r r i e d out d i v i d i n g the blossom period into two five-day periods and entering the compiled variables for each period i n the same equation. The object was to see i f there was any di f f e r e n c e i n 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 part of the f u l l blossom period. The fourth equation was estimated using temperature v a r i a b l e s for the f i r s t f i v e days and for the l a s t f i v e days. The two periods appear almost equal i n t h e i r s i g n i f i c a n c e with regards to temperature. A s i m i l a r run was c a r r i e d out d i v i d i n g the blossom period into two stages fo r r a i n f a l l . The r e s u l t s confirmed that the f i r s t f i v e days were the most s i g n i f i c a n t f o r r a i n f a l l , and showed very 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 years and areas, sunlight v a r i a b l e s could not be compiled as records were missing from the meteorological data. As a r e s u l t only 12 observations were a v a i l a b l e f o r sunlight, leaving only nine degrees of freedom f or most estimations. It was found through several runs that the longest period of 10 days was the most appropriate f o r sunlight, as i t was for temperature. The f i r s t c a l c u l a t i o n with the higher c r i t i c a l temperatures also proved more appropriate as was the case i n the previous estimations. The r e s u l t s are shown i n the f i r s t equation i n table 4.2. The second and t h i r d equations of t h i s table show the e f f e c t s of a sunlight-temperature index and of d i v i d i n g the sunlight v a r i a b l e into two periods. Table 4.2. Estimated Functions f o r Weather Model— including sunlight Dependent Variable Production per acre (regional average) Independent Variable 1 2 Constant -10.250 -10.013 -10.129 (-2.40)* (-2.38) (-2.17) Accumulated bright sun- 26.96 l i g h t during 10 day (6.20) period 1/10 hours Accumulated f r o s t below -255.98 -226.64 -235.18 c r i t i c a l l e v e l s of 27°F, (-2.40) (-1.94) (-1.61) 30°F and 31°F Sunlight temperature index** 26.53 (6.26) Accumulated bright sunlight 25.98 during f r o s t 5 day period (2.86) of bloom 1/10 hours Accumulated bright sunlight 27.50 during l a t t e r 5 day period (4.31) of bloom 1/10 hour R 2 .86 .87 .86 Number of observations 12 12 12 *T s t a t i s t i c s are i n parenthesis **Index = Temperature Sunlight •5 2 Because sunlight and temperature could be used i n the same equa-t 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 com-bine the two v a r i a b l e s i n t o a simple sunlight temperature index. Accumulated degrees above 65 F. were m u l t i p l i e d by 10 to bring i t into the same order of magnitude as sunlight and then was added to hours of sunlight, the t o t a l being divided by two. Thus the index had an order of magnitude close to the o r i g i n a l sunlight v a r i a b l e . The r e s u l t s as seen i n the second equation i n table 4.2 show a marginally better s i g n i f i c a n c e than the pure sunlight v a r i a b l e and a s l i g h t improvement i n the R 2. As with the temperature and r a i n v a r i a b l e s , t o t a l sunlight was divided into two five-day periods. Both periods were entered i n the same equation to test for differences i n importance between the e a r l i e r and l a t t e r parts of the blossom period. The r e s u l t s are shown i n the t h i r d equation i n table 4.2 where i t can be seen that the c o e f f i c i e n t s for each period are very close to being equal. 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 regressions to test blossom influences on the amount of d i f -ferent grades of apples were attempted. Production was divided into t o t a l extra-fancy and t o t a l of other grades excluding c u l l s . Table 4.3 shows the r e s u l t s f o r these estimations. It can be seen that the model has les s success i n explaining the v a r i a t i o n for i n d i v i d u a l grade categories than i t does for the t o t a l quantity. It has much higher explanatory power f o r the extra-fancy category than i t does for the remaining grades. This fact i s somewhat unexpected as there was no reason to expect that blossom weather influences f r u i t q u a l i t y . 80 Table 4.3. Estimated Functions for Weather Model— D i f f e r e n t Grade Categories Dependent Variable lbs per acre a l l other lbs per acre XFLY Grade grades Independent Variable 1 2 1 2 Constant 3925.85 -5274 6535 8303 (3.22) (-1.85) (3.15) (.57) Accumulated f r o s t below -114.33 -60.01 -208.45 -565.1 c r i t i c a l l e v e l s (-1.76) (-.76) (-1.88) (-1.4) Accumulated bright sun- 11.56 1.27 l i g h t 10 day period (3.98) (.08) 1/10 hour Accumulated degrees 412.69 394.50 about 65°?'. 10 day (3.05) (1.71) period Accumulated r a i n f a l l -27.58 -47.56 during 5 day period -1.61 (-1.63) R 2 .62 .70 .47 .21 Number of observations 19 12 19 12 4.2.4 Conclusions Regarding the Weather Model A l l four v a r i a b l e categories have s i g n i f i c a n t impacts upon t o t a l y i e l d s . A b r i e f discussion of each of the categories follows. 1. Temperature as measured by accumulated degrees above 65 F. plays a strong r o l e i n p o l l i n i z a t i o n and r e s u l t i n g y i e l d s . Most estima-tions show a 'marginal product' of temperature of at least 800 l b s . per acre. That i s an increase of one degree over 65°F. during blossom period w i l l r e s u l t i n an increased y i e l d of 800 l b s . per acre. A f u l l ten day period best represented temperature i n f l u -ence, indicatingr.that s i g n i f i c a n t p o l l i n a t i o n takes place i n the l a t t e r h a l f of the f u l l bloom period. This conclusion i s r e i n -forced i n estimations where the period i s divided which show that the f i r s t and second halves of the bloom period are equally import-ant with regards to the temperature v a r i a b l e . 2. T o t a l p r e c i p i t a t i o n during the f i r s t h a l f of the f u l l bloom stage has a s i g n i f i c a n t negative impact upon y i e l d s . Every one hundredth of an inch which f a l l s during t h i s time r e s u l t s i n a decrease i n y i e l d of about 75 l b s . per acre. The f i n d i n g that only the f i r s t h a l f of the blossom period i s s i g n i f i c a n t with respect to r a i n f a l l seems to indicate that the blossoms and 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 part of the f u l l bloom stage than i n the l a t t e r p a r t — a f i n d i n g f or which there does not seem to be much s c i e n t i f i c b a s i s . 3. Sunlight has the greatest explanatory power and s i g n i f i c a n c e of a l l the v a r i a b l e s tested. As a v a r i a b l e i t contains three separate influences on p o l l i n i z a t i o n : i t s own influence, i t s p o s i t i v e c o r r e l a t i o n with temperature, and i t s negative c o r r e l a t i o n with 82 r a i n f a l l . It was most s i g n i f i c a n t when considered over the f u l l 10 day period. For every tenth of an hour of bright sunlight during the blossom period production per acre should increase by over 26 l b s . 4. Frost 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 . Every degree of f r o s t from d a i l y minimum temperatures below c r i t i c a l l e v e l s would be expected to decrease y i e l d by at least 225 l b s . per acre. The v a r i a b l e was 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 higher l e v e l s than those established under test con-d i t i o n s . In summary, with R 2 values ranging from .67 to .87 i t i s evident that blossom and p o l l i n a t i o n influences play a major r o l e i n determinin average regional y i e l d per acre. I t i s l i k e l y that the R 2 value would b Improved i f there were some appropriate measure of wind during blossom time. Given more accurate data on blossom dates and acreages, the R 2 values would l i k e l y be s t i l l higher. 4.3 The Complete Orchard Level Model This model i s of production at the i n d i v i d u a l orchard or block l e v e l , and each observation i s of an i n d i v i d u a l block's production rather than a regional average. The conceptual model including a l l measured v a r i a b l e s , i n t e r a c t i o n s and selected weather v a r i a b l e s was summarized i n figure 3.2 i n the previous chapter. The next step i n estimation as shown previously i n fi g u r e 4.1 i s to estimate a l i n e a r form without i n t e r a c t i o n s and then'tes.t subsets of i n t e r a c t i o n s . This i s considered necessary because of the large number of 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 often correlated with one or both of the variables between which the i n t e r a c t i o n s are occurring. This i s e s p e c i a l l y true when one of the v a r i a b l e s exhibits l i t t l e v a r i a t i o n or has a predominant value. This occurrence i s i l l u s t r a t e d i n the example shown i n table 4.4. Table 4.4. C o l l i n e a r i t y with an Interaction v a r i a b l e s i n t e r a c t i o n between xx and x 2 *1 X ! X 2 2 1 2 4 1 4 6 1 6 8 1 8 6 1 6 4 0 0 2 1 2 It can be seen that the v a r i a b l e xi i s highly correlated with the i n t e r -a c t i o n x^x 2. Because there are many dummy var i a b l e s and other v a r i a b l e s with low v a r i a t i o n i t was f e l t that entering a l l the i n t e r a c t i o n s i n the model would lead to severe m u l t i c o l l i n e a r i t y . For t h i s reason a pro-cedure was developed whereby the i n t e r a c t i o n s were entered into the model i n groups rather than a l l at once. Interactions were c l a s s i f i e d into three groups which were root-stock 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 s o i l i n t e r a c t i o n s . A l i n e a r regression was then c a r r i e d out on the basic inputs, no i n t e r -actions included. A s i n g l e c l a s s of i n t e r a c t i o n s was then entered as a group into the model and any s p e c i f i c i n t e r a c t i o n s that s i g n i f i c a n t l y 84 improved the regression were retained. The next class of i n t e r a c t i o n s was then entered and any further i n t e r a c t i o n s which s i g n i f i c a n t l y improved the r e s u l t s were retained. The f i n a l c l a s s was entered and the procedure repeated. Two important considerations i n t h i s process were the 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 the order i n which the groups were entered i n the regression. There are a number of possible c r i t e r i a for 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 from within each group including 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 the R 2, impact on R 2 (adjusted R 2 ) , accordance of the sign with a p r i o r i expectations and e f f e c t s on magnitudes and signs of other co-e f f i c i e n t s . 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 search a group of variables and s e l e c t a subset of a s p e c i f i e d s i z e with the best R 2 or R 2 (U.C.L.A., 1977). It was decided not to use an e x i s t i n g algorithm for 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 d i f f i -c u l t y i n using them to s e l e c t a subset from only a portion of the v a r i -ables, 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 . A second reason for not using these procedures i s the need to consider a v a r i a b l e ' s influence on the signs and magnitudes of other c o e f f i c i e n t s . 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 c r i t e r i a were considered the most important and generally i f a v a r i a b l e s a t i s f i e d at l e a s t one of them i t was retained. If an i n t e r a c t i o n improved the sign, the magni-tude or the s i g n i f i c a n c e of an input i t was retained regardless of how i t fared against the other c r i t e r i a . If an i n t e r a c t i o n improved the R 2 i t was usually retained. Because the R 2 accounts for the loss i n degrees of freedom i t was f e l t that i t was a better c r i t e r i a to judge an 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 2 s t a t i s t i c . The order i n which the groups are entered may influence which i n t e r a c t i o n s are eventually retained, as the s i g n i f i c a n c e of an i n t e r -a ction may depend to a great extent upon variables already i n the model. If two i n t e r a c t i o n s are highly correlated the one that i s entered f i r s t i n the regression w i l l usually be the one retained i n the s e l e c t i o n procedure outlined above. If the f i r s t i n t e r a c t i o n improves the R , the second may not because much of i t s influence w i l l have already been captured by the f i r s t i n t e r a c t i o n due to the c o r r e l a t i o n between the two. An a p r i o r i ranking of the importance of each group was made and the groups were tested i n t h i s order. Rootstock in t e r a c t i o n s were ranked most important, followed by age and then by s o i l i n t e r a c t i o n s . Entering the groups i n t h i s order 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 higher a p r i o r i importance i n the event of m u l t i c o l l i n -e a r i t y . The extent of t h i s s e l e c t i o n bias was examined by a l t e r i n g the order of entry of v a r i a b l e s and examining the robustness of the f i n a l r e s u l t s . The estimated c o e f f i c i e n t s f o r the model using the complete set of data are shown i n table 4.5. Two l i n e a r equations are shown along with an i n t e r a c t i v e form showing the f i n a l i n t e r a c t i o n s selected. The f i r s t l i n e a r form shows some evidence of a near singular data matrix, so a second equation i s estimated without some of the troublesome v a r i a b l e s . 4.3.1 Robustness of the Estimates The robustness of the f i n a l r e s u l t s were tested by changing the order that groups of v a r i a b l e s were entered into the stepwise procedure. Two a l t e r n a t i v e orderings were t r i e d : 1. the weather v a r i a b l e s were entered l a s t (instead of f i r s t ) , 2. the order of entry of i n t e r a c t i o n subsets was reversed keeping the same order for a l l other groups of v a r i a b l e s . 86 Table 4.5. Estimated Functions for Complete Orchard Level Model Dependent V a r i a b l e — l b s . per acre excluding c u l l s Independent Unit of Linear With Variable Measurement (1) (2) Interactions Constant .54 x 10 9 -9,983 -24,568.C * (.01)* (-4.90) (-3.72) Age Indexed Age 10,597 10,496.1 -8,363 (11.2) (11.44) (-2.62) Density Trees per Acre 53.9 54.7 -186.7 (1.82) (1.86) (-1.50) F e r t i l i z e r l b s . per acre 174.4 176.4 718 (9.11) (9.11) (8.0) Pe s t i c i d e s Value per acre 192.9 196.3 526 (.98) (.98) (2.69) Soil-type Texture index -11,557.1 -10,840.1 42.131 .(-3.37) (-3.43) (1.63) Red Delicious dummy 224.6 -215.5 -3510.0 (.06) (.05) (-1.09) Mcintosh dummy -6451.2 -7431.8 -17296.6 (-1.39) (-1.62) (-4.44) Newton dummy .10 x 10 9 (.01) Spartan dummy 15127.1 13650.2 -18540.1 (2.39) (2.19) (-2.96) Winesap dummy 12358 10738.5 4807.0 (.39) (.34) (.18) Tydeman dummy 14797.1 13319.8 12111.2 (2.20) (2.01) (2.01) Spur-type dummy -9867.2 -9746.7 10529.9 (-2.55) (-2.53) (2.78) Tree-size dummy 1031.8 767.6 3945.8 (2.00) (1.58) (1.82) Hedgerow dummy 3869.3 2429.1 10810.8 planting (.88) (.60) (2.55) Overhead dummy 10860.9 8876.1 -2871.1 i r r i g a t i o n (1.26) (1.03) (-.38) T r i c k l e dummy -46545.5 -48701.5 -71763.5 i r r i g a t i o n (-5.6) (-6.00) (-8.82) 87 Table 4.5. (continued) Independent Variable Unit of Measurement Linear (1) (2) With Interactions Frost r i s k Temperature during bloom Frost during bloom index accumulated degrees F. above 65 accumulated degrees F. below c r i t i c a l l e v e l s Rain during bloom 1/100 inches T r e e - s i z e - f e r t i l i z e r Interaction Tree-size-density Interaction T r e e - s i z e - f r o s t Interaction T r e e - s i z e - s o i l Interaction A g e - f e r t i l i z e r Interaction S o i l - f e r t i l i z e r I nteraction S o i l - d e n s i t y Interaction R 2 R 2 Number of Observations .54 x 10 8 (.01) 239.5 295.0 (.43) 312.4 (.06) .40 .38 503 239.1 315.1 (.46) 309.7 (.06) .40 .38 503 252.9 11947.4 (3.50) -609.0 (-.15) -21.14 (-4.63) 15.0 (2.63) -299.3 (-2.90) 557.0 (.69) 57.9 (6.37) -114.1 (-2.31) -52.1 (-2.78) .57 .55 503 * T - s t a t i s t i c s shown i n parentheses Golden Delicious i s the base v a r i e t y (with no dummy va r i a b l e ) 88 When the f i r s t change was car r i e d out no difference i n the f i n a l subset selected occurred, i n d i c a t i n g that the weather variables are quite robust. However, when the order of entering the int e r a c t i o n s was changed, some change i n the f i n a l v a r i a b l e s and c o e f f i c i e n t s occurred. The t r e e - s i z e - s o i l i n t e r a c t i o n , which was of low s i g n i f i c a n c e i n the o r i g i n a l estimation, was eliminated and replaced by an age- s o i l i n t e r -action. An age-frost i n t e r a c t i o n was also found to have v i r t u a l l y the same e f f e c t on the adjusted R , as did the t r e e - s i z e - f r o s t i n t e r a c t i o n . There were only s l i g h t changes i n c o e f f i c i e n t s of other v a r i a b l e s , the most notable being that of s o i l which dropped by about 10%, with a small decrease i n the s i g n i f i c a n c e . Overall i t was f e l t that the re s u l t s were quite robust, e s p e c i a l l y when considering the high degree of m u l t i c o l l i n e a r i t y 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 of the c o e f f i c i e n t s i n the f i r s t l i n e a r equation have such extreme values that i t i s expected the X'X matrix i s singular or near-singular, with only rounding errors enabling i t s inversion. The constant (.54 x 10 9), the dummy c o e f f i c i e n t f o r Newton (.10 x 1 0 1 0 ) , and the f r o s t r i s k c o e f f i c i e n t (-.54 x 10 1 0) exhibit such extreme values that s i n g u l a r i t y must be expected. They also show well known signs of m u l t i c o l l i n e a r i t y including extremely large standard errors and unstable o f f s e t t i n g c o e f f i c i e n t s . It was expected that dummy variables were perhaps the greatest source of m u l t i c o l l i n e a r i t y because of the e f f e c t on the constant term. Estimates of other c o e f f i c i e n t s i n the equation seem reasonable i n comparison to the problem v a r i a b l e s . There was not much that could be done to overcome t h i s problem except to exclude some of the troublesome va r i a b l e s from the regression. 89 The exclusion of f r o s t r i s k was at le a s t p a r t i a l l y j u s t i f i e d by the o f f -s e t t i n g e f f e c t of the f r o s t prevention system with which i t i s highly correlated. The Newton dummy was also excluded and the model re -estimated as i n the second equation. The low T-values of the Newton dummy and f r o s t r i s k could not be taken as j u s t i f i c a t i o n for dropping these variables because they could well be due to 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 other coef-f i c i e n t s estimated i n the second equation do not show a great d i f f e r e n c e from those i n the f i r s t equation except for the constant term. The i n t e r a c t i o n t e s t i n g procedure as described i n section 4.2 was c a r r i e d out and several i n t e r a c t i o n s were retained. The r e s u l t i s presented i n the t h i r d equation on table 4.5. The i n c l u s i o n of i n t e r -actions s u b s t a n t i a l l y improves the model although there are s t i l l some signs of m u l t i c o l l i n e a r i t y . No int e r a c t i o n s with p e s t i c i d e s could be tested because they resulted i n a singular or near-singular data matrix. There are both a large number of va 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 several 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 c o e f f i c i e n t of .71, density and t r e e - s i z e have a c o r r e l a t i o n of -.75, tree s i z e i s negatively correlated with planting concept with a c o e f f i c -ient of .61 and s o i l i s negatively correlated with t r e e - s i z e with a c o e f f i c i e n t of -.6. As f r o s t r i s k and f r o s t prevention 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 included at one time. There are three options i n dealing with m u l t i c o l l i n e a r i t y . (1) Ignore i t and accept the estimated c o e f f i c i e n t s , (2) try to obtain data with le s s c o r r e l a t i o n between v a r i a b l e s , or (3) leave out some or a l l of the offending v a r i a b l e s , perhaps making some allowance for t h e i r influence on the dependent variable.. The f i r s t option i s not nec e s s a r i l y 90 undesirable as some studies have obtained reasonably precise estimates of c o e f f i c i e n t s despite high c o r r e l a t i o n s between pai r s of independent v a r i -ables (Johnston, 1972). The second option of t r y i n g to obtain more data i s unfeasible f o r t h i s research although i t would warrant consideration i n a longer term project. If the t h i r d option of leaving out some or a l l of the troublesome variables i s followed, some atonement must be made for s p e c i f i c a t i o n bias. There are several suggested procedures. The f i r s t i s to treat the estimated c o e f f i c i e n t s as representing the combined e f f e c t s of the included variabl e s and the correlated l e f t - o u t v a r i a b l e s . This approach i s undesirable i f the s p e c i f i c e f f e c t of each v a r i a b l e i s required. The con 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 often been used i n dealing with m u l t i c o l l i n e a r i t y (Kmenta, 1971). If the c o e f f i c i e n t s of some of the var i a b l e s are known or can be estimated i n advance, the e f f e c t s of the var i a b l e s can be removed from the dependent v a r i a b l e and a regression c a r r i e d out on the remaining v a r i a b l e s . This technique i s used for a few s p e c i f i c instances i n t h i s research i n sec-t i o n 4.4. Another possible method i s to use a stepwise regression tech-nique. 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 residuals from t h i s regres-sion are then regressed on the previously l e f t - o u t v a r i a b l e s . An estimate of the influence of the f i r s t set of l e f t - o u t v a r i a b l e s on the 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 influence on the residu a l s although the c o e f f i c i e n t s cannot usually be exactly determined. The procedure used i n t h i s thesis i s to use a subset of data over which one or more variables are constant so they can then be l e f t out of the regression. Unbiased c o e f f i c i e n t s can then be obtained f o r the remaining v a r i a b l e s although they are co n d i t i o n a l on the l e v e l of the 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 non-constant variables e x i s t . This approach of p a r t i t i o n i n g the data has other advantages besides 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 i s pursued i n more d e t a i l i n section 4.5. 4.3.3 E f f e c t s of Disaggregation A reason for the low R 2 i n the model may be the disaggregated nature of the data. The v a r i a b l e s are disaggregated and the s i z e of i n d i v i d u a l observations are small as they are of s p e c i f i c blocks often under an acre i n s i z e . Disaggregation i s often thought of as desirable i n econometric studies (Johnston, 1972) and i s required i n t h i s work i n order to obtain useful information about orchard systems. There are some disadvantages, however. By disaggregating v a r i a b l e s the i n d i v i d u a l observations tend to become much smaller i n terms of acreage and the r e l a t i v e e f f e c t s of stochastic influences become greater. This may have the e f f e c t of increasing the standard errors and lowering the pre-c i s i o n of the estimates. If observations are grouped the e f f e c t of the stochastic element tends to average out for each group. The larger the group of observations, the more averaging w i l l take place and with very large groups the stochastic e f f e c t s w i l l be very small (Johnston, 1972). Previous production function estimates for Okanagan apples (Campbell, 1976; Lee, 1972) have used grouped data and aggregated inputs to a c e r t a i n extent. Observations were grouped i n that each orchard counted as a si n g l e observation despite having d i f f e r e n t v a r i e t i e s , rootstocks and planting systems. Aggregation of various s p e c i f i c inputs into a value or c a p i t a l index was c a r r i e d out to a c e r t a i n extent. Their estimated functions had higher R 2 values i n the .65 to .80 range which may be accounted for by the aggregation and grouping. 92 4.4 Tree-size and Variety Functions The second major method of estimating the production functions i s to group the data by t r e e - s i z e or v a r i e t y and estimate a separate func-t i o n for each group. The main reason for doing t h i s i s to reduce the number of variables within each equation. By estimating t r e e - s i z e functions a large number of in t e r a c t i o n s concerning rootstock can be eliminated as explanatory v a r i a b l e s . Tree s i z e , as determined by rootstock was considered the major source of i n t e r a c t i o n s , and by d i v i d i n g the data into t r e e - s i z e categories, 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 four separate equations, rather than having them as separate terms i n the regression. This i s an advantage as i n t e r a c t i o n s when entered as separate terms tend to compound the m u l t i c o l l i n e a r i t y problem. There may be some v a r i a t i o n i n rootstock within each of the dwarf, semi-dwarf and semi-standard categories, but 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 small. When the equations are estimated for each v a r i e t y the s i x v a r i e t y dummies can be eliminated which i s advantageous as dummy variables were leading to n e a r - s i n g u l a r i t y i n the estimation of a function over the complete data set. Another advantage of grouping the data for separate regressions i s rel 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 represented as a s i n g l e term i n an equation t h i s assumes that the i n t e r a c t i o n has a constant 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 inputs depends only on the s i z e of the i n t e r a c t i o n term and not on the magni-tude of either of the inputs. By estimating separate equations for each t r e e - s i z e category, t h i s assumption i s relaxed for the t r e e - s i z e i n t e r a c t i o n s . For example consider an i n t e r a c t i o n between f e r t i l i z e r and tree s i z e . I t i s possible that f e r t i l i z e r has a high marginal 93 phy s i c a l product on dwarf, semi-dwarf and standard v a r i e t i e s , and a low marginal physical product for semi-standards. A t r e e - s i z e f e r t i l i z e r i n t e r a c t i o n i n a s i n g l e equation could not capture t h i s e f f e c t , whereas separate equations for each t r e e - s i z e category could. An a d d i t i o n a l advantage of estimating t r e e - s i z e functions i s that the m u l t i c o l l i n e a r i t y between density and t r e e - s i z e over the whole sample i s no longer a problem as tree si z e i s nearly constant within each equation. 4.4.1 Results for the Tree-size Functions Most of the s t a t i s t i c a l emphasis i s on t r e e - s i z e functions because of early encouraging r e s u l t s with t h i s form. Production functions for four categories: dwarf, semi-dwarf, semi-standard and standard are estimated. It i s s t i l l possible to observe some v a r i a t i o n i n tree s i z e within these categories although i n the sample only the semi-standard category has more than one rootstock on which the s t a t i s t i c a l index i s based. Hence t r e e - s i z e as an independent v a r i a b l e appears only i n the semi-standard category. In general, p a r t i t i o n i n g the data by t r e e - s i z e causes le s s serious 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 semi-dwarf categories there i s no problem with m u l t i c o l l i n e a r i t y , there i s adequate v a r i a t i o n i n most input l e v e l s (although some inputs are constant), and there i s a large number of observations. For the standard and semi-standard categories there i s troublesome c o r r e l a t i o n s between three important inputs: f e r t i l i z e r , p e s t i c i d e and density. A fourth v a r i -able, s o i l - t y p e also causes problems, showing some degree of c o r r e l a t i o n with these three v a r i a b l e s . For semi-standard there are a large number of observations, but for the standard category there are only twenty. 94 As several inputs are constant for standard they cannot be entered i n the regression, so the degrees of freedom problem i s not too serious. Dwarf and Semi-Dwarf Categories. Selected weather variables from the weather model are entered, and in t e r a c t i o n s are tested i n a stepwise procedure as was done i n the function for the complete data set. The r e s u l t s for the dwarf and semi-dwarf categories are shown i n table 4.6. For the dwarf equations p e s t i c i d e cost i s constant at $65 per acre, a l l rootstocks are M.M. 26, f r o s t i s zero and a l l observed blocks were planted i n hedgerow design. For the semi-dwarf category p e s t i c i d e s are again constant at $65 per acre, a l l rootstocks are M.M. 7 and a l l s o i l i s rated as two (clay) on the texture index. A l l equations are estimated with O.L.S. For both categories l i n e a r and i n t e r a c t i o n forms are given. The only i n t e r a c t i o n term found to be s i g n i f i c a n t was 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 for both categories. Signs of a l l co-e f f i c i e n t s are consistent with a p r i o r i expectations with the possible exception 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 for semi-dwarf and age i n t h e ' i n t e r a c t i v e forms for both categories. However, when the i n t e r -a c t i v e terms are considered the marginal products of both age and f e r t i l i z e r are p o s i t i v e over most of the range of these v a r i a b l e s . The 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 marginal product when trees are i n t h e i r formative years than for trees i n the bearing stage. Most of the estimated c o e f f i c i e n t s display high degrees of s i g n i f -icance. Exceptions are the v a r i e t y dummies and the f r o s t and s o i l v a r i a b l e s . The only v a r i e t y dummy s i g n i f i c a n t at the .01 l e v e l was Tydeman i n the dwarf equations. The s o i l and f r o s t v a r i a b l e s , while not 95 Table 4.6. Estimated Functions for Dwarf and Semi-dwarf Categories Dependent V a r i a b l e — l b s . per acre excluding c u l l s Dwarf Category Semi-dwarf Category Independent Unit of With Inter- With Inter-Variable Measure Linear action Linear action Constant -193,563.0 (-4.20)* -66,443. (1.53) 6 -187,092.0 (-4.32) -76,043.0 (1,87) Age indexed age 14,319.3 (11.87) -21,702. (-4.37) 8 10,984.4 (10.54) -18,984.9 (-4.23) Density trees per acre 21.3 (.34) 21. (.40) 3 310.3 (3.03) 388.0 (4.36) F e r t i l i z e r l b s . per acre 372.1 (9.18) 3. (.05) 21 86.7 (1.24) -318.8 (-3.77) Soil-type texture index -14,289.8 (-.93) -7,547 (-.57) Red Delicious dummy 9,085.0 (1.58) 9,084. (1.83) 4 -1,227,4 (-.25) -1,227.4 (-.29) Mcintosh dummy 252.0 (.04) 252. (.04) 0 -9,086.1 (-1.43) -9,097.3 (-1.66) Spartan dummy -9,978.9 (-1.16) -9,979. (-1.35) 0 -8,219.0 (-.92) -8,219.3 (1.07) Tydeman Red dummy 21,830.6 (2.54) 21,830. (2.95) 5 2,699.0 (.30) 2,699.7 (.35) Spur Type dummy 4,307.8 (.67) 4,307. (.77) 9 3,580.3 (.70) 3,580.2 (.80) Overhead I r r i g a t i o n dummy 27,513 (2.14) 34,502.0 (3.12) T r i c k l e I r r i g a t i o n 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 during Bloom Accumulated Degrees F. -1,737 (-.25) -524.8 (-.09) 96 Table 4.6 (continued) Dwarf Category Semi-dwarf Category Independent Unit of With Inter- With Inter-Variable Measure Linear action Linear action Sunlight 1/10 hours 50.1 50.6 46.5 46.7 during Bloom (5.53) (6.40) (5.85) (6.83) A g e - f e r t i l i z e r Indexed age 99.3 87.7 Interaction X lbs./acre (7.42) (6.82) R 2 .69 .77 .74 .81 R 2 Number of Observations 170 170 144 144 * T - s t a t i s t i c s shown i n parentheses Golden Delicious i s the base v a r i e t y (with no dummy variable) s i g n i f i c a n t are consistent i n both equations and were thus retained. The poor s i g n i f i c a n c e of these variables may be due to the fa c t that both are proxy measures. Generally the dwarf and semi-dwarf functions are more s a t i s f a c t o r y than the function for the f u l l data set. The degree of explanatory 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 consistency with expectations are a l l higher. This i s probably due to some of the advantages l i s t e d e a r l i e r including l e s s m u l t i c o l l i n e a r i t y and le s s r e s t r i c t i o n s on coef-f i c i e n t s and i n t e r a c t i o n s . Semi-standard and Standard. Table 4.7 shows l i n e a r and i n t e r -a ctive forms for the semi-standard and standard categories. For the standard category equation and for the southern region equation for semi-standard, c o n d i t i o n a l l e a s t squares estimates, where an adjustment has been made for p e s t i c i d e s , have been used. The reasons for t h i s proce-dure are discussed below. Ordinary l e a s t squares have been used for the remaining estimations. The f i r s t l i n e a r equation for semi-standard i s unsatisfactory i n several regards. The signs of two v a r i a b l e s , f e r t i l i z e r and f r o s t , 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 are low for most v a r i -ables and the R 2 i s less than h a l f of what i t i s for the dwarf and semi-dwarf categories. 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 sign on f e r t i l i z e r which has a f a i r l y high c o r r e l a t i o n (.80) with p e s t i c i d e s . Other possible causes may be l e f t out v a r i a b l e s and i n t e r a c t i o n s . When the in t e r a c t i o n s are included, however, the equation s t i l l shows a negative marginal product for f e r t i l i z e r although i n other aspects the equation i s improved. Another possible reason for the poor r e s u l t s i s that within the Table 4.7. Estimated Functions f o r Standard and S emi—Standard Categories Dependent V a r i a b l e — l b s . per acre excluding c u l l s Semi-Standard Standard With Southern With Independent Unit of Inter- Region Inter-Variable Measure Linear actions Linear Linear actions Constant -59381.1 (-.06)* 35098.1 (.33) 125141.3 (2.80) -10794.5 (1.01) 11252.2 (.46) Age indexed age 746.6 (3.54) -1970.6 (-1.01) 2415.2 (.95) 965.0 (2.95) -785.2 (-.62) Density trees per acre 10.0 (.26) 7.67 (.19) -56.0 (-1.10) 133.8 (1.06) 133.9 (1.07) F e r t i l i z e r l b s . per acre -11.8 (-2.56) .70 (.08) 40.9 (.91) 35.1 (2.60) -3.02 (-1.95) Pesticides $ value per acre 6.7 (.26) -320.8 (-1.78) Soil-type texture index -2746.0 (-2.32) -2086.1 (-1.80) -4837.1 (-.35) -4858.8 (-1.56) -4860.0 (-1.56) Red Delicious 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) -3930.0 (-1.74) Spur-type dummy 138.4 (.15) 683.2 (.81) Hedgerow Planting dummy 3017*0 (.90) 12468.8 (2.55) 19084.2 (1.10) 99 Table 4.7 (continued) Semi-Standard Standard With Southern With Independent Unit of Inter- Region Inter-Variable Measure Linear actions Linear Linear actions Tree-size s i z e index -566.4 (-.18) -3930.0 (-2.60) Temperature accumulated degrees above 65°F. -.05 (-.05) -.6 (-.47) 39.8 (.59) 29.8 (.55) Frost accumulated degrees below c r i t i c a l l e v e l 305.3 (3.23) -4715.8 (-2.66) 438.2 (2.01) -127.3 (-1.78) Rain 1/100 inches --1060.0 (-.87) -1327.2 (-1.02) -2129.3 (-.28) -2135.3 (-.28) Age Pe 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 Number of 194 194 30 19 19 Observations * T - s t a t i s t i c s shown i n parentheses Golden Delicious i s the 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 s u b s t a n t i a l v a r i a t i o n i n tree s i z e . Unlike the dwarf, semi-dwarf and standard samples which each contain only rootstock, there are three rootstocks i n the semi-standard sample. In order to see i f t h i s v a r i a t i o n was the cause of the poor r e s u l t s the data were divided into three groups where the rootstock was constant within each group. Separate regressions were then c a r r i e d out for each of these subdivisions of semi-standard. These estimations were only marginally better than the estimation for the whole of semi-standard samples. Another possible cause of the poor r e s u l t s was the mixture of experimental data from the research s t a t i o n with the orchard survey data. Semi-standard was d i f f e r e n t from dwarf and semi-dwarf i n that a much higher proportion of the t o t a l observations was from the orchard survey. About 40% of the semi-standard observations were from the orchard survey while only about 15% of the dwarf and semi-dwarf observations were from the orchard survey. The experimental data for semi-standards also consisted of very small p l o t s , about 1/10 of an acre i n s i z e , and t h i s r e l a t i v e smallness might have resulted i n higher stochastic influences. There might also be differences i n the l e f t - o u t v a r i a b l e s , management and labour, between the experimental plots and the commercial orchards which would lead to differences i n the estimated c o e f f i c i e n t s of other inputs. When the two types of data are 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 . To see i f i t was the experimental data that was causing the poor r e s u l t s i t was decided to estimate a function using only the orchard survey data from the southern region. The reason for using only t h i s region (which contained about 50% of the survey data for semi-standards) was to t r y to avoid some of 101 problems that might a r i s e by leaving the heat units v a r i a b l e out of the estimation. As there i s generally a higher l e v e l of both f r o s t and heat-units i n the southern region there 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 . This would r e s u l t i n a biased estimate of the f r o s t c o e f f i c i e n t and may be the reason for i t s wrong sign i n previous estimations. Unfortunately when regressions were attempted on t h i s smaller body of data, m u l t i c o l l i n e a r i t y proved to be a problem. Most of the p r e d i c t -able 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 occurred—wrong signs, extremely high and unstable c o e f f i c i e n t s , and high standard e r r o r s . Most of the problem lay with three v a r i a b l e s , s o i l type, f e r t i l i z e r and p e s t i c i d e . P e s t i c i d e was highly correlated with s o i l type (.78) and f e r t i l i z e r (.83). There was also some degree of 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 (.61). It was decided to resort to condit i o n a l l e a s t squares and leave 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 of c o l l i n e a r i t y . The e f f e c t s of p e s t i c i d e on production were removed as follows. It was assumed that the marginal value product of p e s t i c i d e was equal to i t s marginal cost. Since the v a r i a b l e was given i n terms of cost per acre, each a d d i t i o n a l d o l l a r ' s worth of apples or about 19 l b s . using the 1975 average net p r i c e of 5.3c. Thus the dependent v a r i a b l e , pounds per acre was adjusted by subtracting 19 multipled by the value of the p e s t i c i d e . The r e s u l t of t h i s estimation are shown i n the southern region equation i n table 4.7. This estimation i s an improvement over the model for the f u l l semi-standard sample, although the negative signs for t r e e - s i z e and density were unexpected. It was noted i n the conceptual model that some 102 orchards may have too high a density for the s i z e of t h e i r trees, and production i s adversely a f f e c t e d . A preponderance of such orchards i n the sample could cause density and t r e e - s i z e to have negative c o e f f i c i -ents . It was found that 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 e s t i -mation. Two i n t e r a c t i o n s , age f e r t i l i z e r and t r e e - s i z e - f e r t i l i z e r caused near s i n g u l a r i t y i n the data matrix and could not be tested, suggesting that there was s t i l l a large degree of m u l t i c o l l i n e a r i t y i n the data. M u l t i c o l l i n e a r i t y was also suggested by -the unusually high c o e f f i c i e n t s f o r hedgerow planting and Red D e l i c i o u s . The standard category had much fewer observations than the others and a l l observed blocks were from the orchard survey. As with the semi-standard category, m u l t i c o l l i n e a r i t y again proved to be a problem. P e s t i c i d e again proved to be a major source of trouble as i t was highly correlated with f e r t i l i z e r (-91) and somewhat with s o i l (.45) and density (.44). Conditional least squares was also used for the standard category. P e s t i c i d e was l e f t out of the regression and i t s e f f e c t s upon production were accounted for as they were i n the semi-standard estimation. Variety, planting concept and i r r i g a t i o n method were constant, with a l l trees being free-standing, Golden Delicious with portable s p r i n k l e r i r r i g a t i o n . The l i n e a r equation for the standard category, c o n d i t i o n a l upon the assigned c o e f f i c i e n t f o r p e s t i c i d e s i s shown i n table 4.7. While the signs of t h i s estimation are mostly correct the t - s t a t i s t i c s and R 2 are lower than i n the other categories. The only wrong signs are on r a i n f a l l and f r o s t . The wrong sign on f r o s t as suspected i n the case of semi-standards may be due to i t s c o r r e l a t i o n with the l e f t - o u t 103 v a r i a b l e heat u n i t s . Inclusion 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 correct the problem as well as s i g n i f i c a n t l y improving the R 2 of the equation. No other i n t e r a c t i o n s tested were found to be s i g n i f -icant aside from age-frost as shown i n the i n t e r a c t i v e equation for the standard category i n table 4.7. 4.4.2 Robustness of Tree-size Category Estimates A robustness test s i m i l a r to the one u t i l i z e d for the complete orchard l e v e l model was c a r r i e d out for the dwarf, semi-dwarf, semi-standard and standard categories. In general, re-arranging the order of entry of groups into the estimation caused no change i n the f i n a l selected subset. The semi-standard category was s l i g h t l y unstable i n that a s o i l - f e r t i l i z e r i n t e r a c t i o n would have been selected and the age-f e r t i l i z e r i n t e r a c t i o n deleted when in t e r a c t i o n s were entered i n reverse order. 4.4.3 Variety Functions This method of estimation was not pursued beyond a few t r i a l e s t i -mates when i t was abandoned i n favour of other methods. When p a r t i t i o n -ing by v a r i e t y takes place the subsets of data have some c h a r a c t e r i s t i c problems. Certain groups of inputs tend to be associated and high c o l l i n e a r i t y occurs between them. P e s t i c i d e , density and f e r t i l i z e r move together strongly, planting concept and i r r i g a t i o n are often highly correlated and density and tree s i z e are negatively correlated. There also tends to be low v a r i a t i o n i n some inputs. For some v a r i e t i e s there are a low number of observations. Poor s t a t i s t i c a l estimations r e s u l t from t h i s method, notably wrong signs on v a r i a b l e s , low t - s t a t i s t i c s , c o e f f i c i e n t s of unusually high orders of magnitude and low R values. 104 4.5 Conclusions Regarding Methodology A dominant theme i n t h i s research has been the i n c l u s i o n of a large number of explanatory v a r i a b l e s i n the estimation of the production function. The f e a s i b i l i t y and success of the attempt to include a large number of v a r i a b l e s and the various methods used to undertake e s t i -mation are discussed i n the next sections. Four separate categories of estimation which are regional average production, orchard l e v e l production for a l l categories and v a r i e t i e s , t r e e - s i z e functions, and v a r i e t y function are discussed i n the context of t h e i r purpose and success i n meeting the objectives of the research. The regional model used only weather variables as explanatory v a r i -ables and proved to be adequate i n assessing t h e i r importance and pre-s e l e c t i n g a subset of weather v a r i a b l e s for use i n orchard l e v e l functions. It was f e l t that a regional model would not be adequate i n assessing the large number of other v a r i a b l e s i n the function which were more e a s i l y observed at the orchard l e v e l . The orchard l e v e l functions using a l l data had several problems as discussed e a r l i e r . The explanatory power of the model was low consider-ing there were as many as 28 explanatory variables i n some regressions. It was apparent that m u l t i c o l l i n e a r i t y was severe and the n e a r - s i n g u l a r i t y of the data matrix hindered estimations. Despite these problems the model did show s t a t i s t i c a l l y s i g n i f i c a n t c o e f f i c i e n t s consistent with expectations f o r many important v a r i a b l e s . It was f e l t that t h i s model had been extended to i t s l i m i t i n incorporating explanatory v a r i a b l e s . Any further i n c l u s i o n would cause near or complete s i n g u l a r i t y of the data matrix, hindering estimates of a l l c o e f f i c i e n t s . It was decided that further information was needed and a d i f f e r e n t concept of estimation 105 was required i n order to more completely s a t i s f y the objectives of the research. The thrust of the estimation was thus turned towards e s t i -mating separate functions f o r each t r e e - s i z e category and v a r i e t y . Functions estimated for i n d i v i d u a l t r e e - s i z e categories had greater explanatory power than the single equation model. Their c o e f f i c i e n t s tended to be more s i g n i f i c a n t and more consistent with expectations. There are several possible reasons why the category functions proved more successful. 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 did not need to be included i n any of the i n d i v i d u a l category functions, the number of explanatory 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 mu 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 the dwarf and semi-dwarf categor-i e s . The c o l l i n e a r i t y between t r e e - s i z e and density which was trouble-some over the whole sample was eliminated i n the t r e e - s i z e category functions. A second reason for the greater success i n estimating category functions may be that they impose les s r e s t r i c t i o n s on i n t e r a c -t i o n s . Over the complete set of data, a s p e c i f i c i n t e r a c t i o n term only 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. However, the nature or magnitude of the i n t e r a c t i v e e f f e c t may vary depending upon the range of the v a r i a b l e s . For example, there i s no reason to believe that the i n t e r a c t i o n between age and f e r t i l i z e r , i s the same for a l l rootstocks. Separate regressions for each rootstock allow the d i f -ferences to be estimated rather than averaged into a sin g l e c o e f f i c i e n t . Another important factor i n estimating i n d i v i d u a l t r e e - s i z e functions i s that the ranges of other inputs are r e s t r i c t e d over the subsets of data. For example, the standard category function i s estimated f o r a sample where the density i s always l e s s than 100 trees per acre whereas i n the dwarf category density i s i n the 300 to 400 trees per acre range. It i s l i k e l y 106 that the marginal physical product of density i s not constant over the whole range of the v a r i a b l e i n the complete data set. Estimates of the marginal product over a r e s t r i c t e d range for each category w i l l give a seri e s of l i n e a r approximations of the c o e f f i c i e n t of density while a s i n g l e equation estimate over the whole sample w i l l give a l i n e a r approximation of the average e f f e c t of density. A greater amount of v a r i a t i o n i n y i e l d would be explained by the ser i e s of estimated coef-f i c i e n t s rather than by the s i n g l e c o e f f i c i e n t for the whole sample. Other v a r i a b l e s including f e r t i l i z e r and p e s t i c i d e also showed some assoc i a t i o n with t r e e - s i z e categories, so the same argument concerning a changing marginal product should hold for them. Considering the nature of the problem, estimating i n d i v i d u a l func-tions for each t r e e - s i z e category was a reasonable strategy. It would have been desirable to control l e v e l s of other v a r i a b l e s as well as s o i l type or geographical l o c a t i o n . For example a function could be e s t i -mated for an i n d i v i d u a l t r e e - s i z e category on a p a r t i c u l a r s o i l type. This would eliminate both s o i l type and t r e e - s i z e from the equations and give further freedom to the behaviour of i n t e r a c t i o n s . If t h i s proce-dure of data p a r t i t i o n i n g was c a r r i e d to the extreme i t would be anal-agous to the type of s c i e n t i f i c experiment where the l e v e l of only one v a r i a b l e i s varied and a l l other factors are held constant. I t seemed natural 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 f a c t o r s , because the conceptual model i s considering a number of t e c h n i c a l factors on a disaggregated basis, such as might be considered i n a p h y s i c a l or b i o l o g i c a l model. Estimation of i n d i v i d u a l t r e e - s i z e functions i s also convenient i n i n t e r p r e t i n g the r e s u l t s . Each function represents a basic kind of 107 system, with optional management features, and can be used to predict a y i e l d stream for the purposes of comparing p r o d u c t i v i t y . Estimations of functions for each v a r i e t y proved to be infeasible' due to high m u l t i c o l l i n e a r i t y , low v a r i a t i o n i n inputs and i n some instances a low number of observations. The advantages of not having to include a set of dummy var i a b l e s for v a r i e t y i n the equations was out-weighed by these disadvantages. It was f e l t that estimation of i n d i -v i d u a l v a r i e t y functions was not an e s s e n t i a l to the research and that the objectives could be met by estimating the other type of models. 4.6 Importance of Weather Variables A general conclusion from t h i s research i s that weather va r i a b l e s are important factors i n f l u e n c i n g apple y i e l d s and are therefore neces-sary for the complete s p e c i f i c a t i o n of the production function. In general the weather va r i a b l e s used show greater s i g n i f i c a n c e i n explain-ing v a r i a t i o n i n average regional production than i n explaining v a r i a t i o n i n production between orchards. I t i s expected that t h i s occurrence i s l a r g e l y due to the measurements used for these variables which were recorded at selected weather stations 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 variables between orchards which was not captured by the regional measures. Sunlight during bloom was tested i n the regional weather model and the orchard l e v e l functions for the dwarf and semi-dwarf categories. Because i t was not recorded for c e r t a i n areas and years i t was not used i n other estimations. It proved to be highly s i g n i f i c a n t at both the regional and orchard l e v e l and added to the explanatory power more than any of the other weather v a r i a b l e s . Its marginal e f f e c t on production 108 ranged from 27 l b s . per l/10th hour i n the regional models to about 50 l b s . per l/10th hour for the dwarf and semi-dwarf categories. The strong 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 f a c t o r s . It was expected 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 as i t was a stimulous to bee a c t i v i t y . It was found during estimation that i t also had high c o r r e l a t i o n with temperature and some negative c o r r e l a -t i o n with r a i n so i t s e f f e c t s encompass the influence of these v a r i a b l e s . The measures as recorded as weather stations are reasonable proxy v a r i -ables for the required i n d i v i d u a l orchard measures, because sunlight i s r e l a t i v e l y constant over a small area. Frost c o e f f i c i e n t s were somewhat inconsistent between the various estimated equations, but subject to the measures used to represent f r o s t , i t was concluded that i t had s i g n i f i c a n t impacts upon y i e l d s . It proved to 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 at the regional l e v e l and for the i n t e r -a ctive form for the semi-standard category. In other forms, when entered i n the estimates, i t was close to being s i g n i f i c a n t except for the semi-dwarf category where i t had low s i g n i f i c a n c e . It was not entered i n the dwarf category because i t had a value of zero for t h i s subset of the data. In l i n e a r estimates i t often had the wrong sign although i n i n t e r a c t i v e forms i t usually exhibited negative marginal e f f e c t s on y i e l d s . It was f e l t that there were two factors hindering the estimation of a c o e f f i c i e n t for t h i s v a r i a b l e . The f i r s t was that the actual measure used was only a proxy and did not capture a l l the v a r i a t i o n between orchards. The second was the l i k e l y c o r r e l a t i o n with growing season heat accumulation which was l e f t out of the regressions. 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 as they both tend to be higher i n the southern regions of the v a l l e y . The e f f e c t s of the 109 c o r r e l a t i o n and imprecision i n measurement w i l l be to bias the c o e f f i c i e n t towards being p o s i t i v e and to increase the standard errors of the c o e f f i c -i e n t s . In sp i t e of these f a c t o r s , the v a r i a b l e s t i l l showed enough consistency and s i g n i f i c a n c e to be regarded as having an important e f f e c t upon y i e l d s . Temperature during bloom was highly s i g n i f i c a n t at the regional l e v e l and i n the orchard l e v e l s model estimated over the f u l l set of data. It showed low s i g n i f i c a n c e i n the standard category estimation and was not used i n the other category functions. Because of i t s high c o r r e l a -t i o n with sunlight i t was d i f f i c u l t to separate out the influences of each v a r i a b l e upon y i e l d s . The impact upon y i e l d per acre ranged from 250 l b s . to_'over 700 l b s . for each degree above 65 F. It was concluded that the v a r i a b l e i s a s i g n i f i c a n t factor i n apple production although i t s influence can mostly be captured by the sunlight v a r i a b l e . R a i n f a l l during bloom had less s i g n i f i c a n c e than the other weather variables tested, although i t s sign was quite consistent with a p r i o r i expectations. Its lower s i g n i f i c a n c e may be due to the fact that i t was represented by a proxy v a r i a b l e which does not completely capture the between orchard v a r i a t i o n i n p r e c i p i t a t i o n . It was concluded that the va r i a b l e does have some impact on y i e l d s , although i t s influence i s l e s s predictable than the e f f e c t s of other weather v a r i a b l e s . 4.7 Importance of Interactions The evidence concerning i n t e r a c t i o n s i s both 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 that several s p e c i f i c i n t e r a c t i o n s prove to be s i g n i f i c a n t and add considerable explanatory power i n the estimated functions. The i n d i r e c t evidence i s that there are differences i n some 110 c o e f f i c i e n t s between the t r e e - s i z e category functions 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 general conclusion i s that i n t e r a c t i o n s have an important and measurable e f f e c t on y i e l d s . 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. It was expected on a p r i o r i grounds that rootstock or tree s i z e i n t e r a c t i o n s were the most important cl a s s of the i n t e r a c t i o n s . The s t a t i s t i c a l r e s u l t s seem to confirm t h i s expectation. S p e c i f i c i n t e r -actions of t r e e - s i z e and f e r t i l i z e r , density, and f r o s t prove to be s i g n i f i c a n t i n the function estimated over the f u l l data set. When the t r e e - s i z e category functions are examined some trends i n the i n t e r -actions can be seen. Larger trees are less influenced by f e r t i l i z e r and f r o s t than smaller trees. Age has a much greater e f f e c t on y i e l d s as tr e e - s i z e decreases. Density has larger c o e f f i c i e n t s as the s i z e of the trees increases, i n d i c a t i n g the addition of a larger tree increases y i e l d more than the addition of a smaller tree under the observed condi-t i o n s . The behaviour of the density i n t e r a c t i o n may also be due to the fact that the l e v e l of t h i s v a r i a b l e i s lower f o r the larger sized trees. The average density of the standard category i s 61 trees per acre and the average density for the dwarf category i s 366 trees per acre. If a decreasing marginal product i s expected for density, then i t f o l -lows that the standard category should have a higher c o e f f i c i e n t as density i s lower. Thus the differences i n the c o e f f i c i e n t s may not be t o t a l l y due to a density t r e e - s i z e i n t e r a c t i o n . The group of age in t e r a c t i o n s was considered important i n the conceptual model pr i m a r i l y because young trees i n t h e i r formative stages are expected to respond le s s to the l e v e l of v a r i a b l e inputs. The only such i n t e r a c t i o n which proved 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 i n t e r a c t i o n . This term proved to be highly s i g n i f i c a n t over the f u l l data set and the i n d i v i d u a l t r e e - s i z e categories. I t s i n c l u s i o n adds considerable explanatory power to the t r e e - s i z e category functions. Other i n t e r a c t i o n s with age including p e s t i c i d e s and labour were not testable due to data problems. Age also showed a s i g n i f i c a n t i n t e r a c -t i o n with rootstock or t r e e - s i z e confirming the expectation that the smaller trees' y i e l d increased f a s t e r during the early bearing stages than the larger trees. The group of s o i l i n t e r a c t i o n s were not generally as s i g n i f i c a n t as the rootstock and age i n t e r a c t i o n s . Over the f u l l data set s o i l had s i g n i f i c a n t i n t e r a c t i o n s with f e r t i l i z e r and density although these i n t e r a c t i o n s did not prove s i g n i f i c a n t i n the t r e e - s i z e category func-t i o n s . The i n t e r a c t i o n between s o i l type and rootstock, expected to be quite important i n the conceptual model did not prove s i g n i f i c a n t .'in any of the estimated equations. In summary the r e s u l t s of s t a t i s t i c a l estimations presented i n t h i s chapter have confirmed most a p r i o r i expectations. Results were presented for a regional weather model, for a complete orchard l e v e l model and for t r e e - s i z e category models. The empirical evidence as a whole suggests that most inputs including weather va r i a b l e s and i n t e r -actions have s i g n i f i c a n t e f f e c t s upon y i e l d s at the i n d i v i d u a l orchard l e v e l . A general conclusion i s that estimation of a disaggregated orchard l e v e l production function 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 are estimated for i n d i v i d u a l t r e e - s i z e categories. The next chapter u t i l i z e s the estimated models to examine possible v a r i a b l e and f i x e d input adjustment i n the industry. CHAPTER V APPLICATIONS OF THE ESTIMATED PRODUCTION FUNCTIONS The estimated production f u n c t i o n s have a number of a p p l i c a t i o n s f o r improving resource 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 research 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 concerning input adjustment, e v a l u a t i o n of technology and y i e l d p r e d i c -t i o n are discussed. The estimated production f u n c t i o n s are f i r s t used to p r e d i c t y i e l d streams over a twenty year period and a corresponding stream of costs i s compiled from other sources. The net present value and v a r i a b i l i t y of production from each system are discussed i n the context of the choice 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 are based on the impact of weather v a r i a b l e s as e s t i -mated i n the r e g i o n a l and orchard 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 Establishment and Operation By using the f u n c t i o n s to 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 options the r e l a t i v e 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 these a l t e r n a t i v e s can be determined. Where i t i s obvious that c e r t a i n systems are more p r o f i t a b l e i t i s expected that adjustment w i l l take place towards i n c o r p o r a t i n g these a l t e r n a t i v e s . The f u n c t i o n s prove to be much more u s e f u l i n assessing the impact of f i x e d inputs ( p h y s i c a l f e atures) than i n assessing v a r i a b l e i n p u t s . In f a c t only two v a r i a b l e 112 113 inputs, f e r t i l i z e r and p e s t i c i d e , were included i n the estimations. I t was , f e l t that the upward bias 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 labour, rendered the functions i n v a l i d for assessing the impacts of p e s t i c i d e and f e r t i l i z e r . More-over, the actual measure for p e s t i c i d e was a proxy and may have resulted i n further bias to the c o e f f i c i e n t . Because the dependent v a r i a b l e i s pounds rather than value of f r u i t , the f e r t i l i z e r c o e f f i c i e n t may give an inaccurate estimate of the marginal value product of f e r t i l i z e r . It i s known that within a c e r t a i n range a d d i t i o n a l nitrogen w i l l increase the quantity of f r u i t but w i l l decrease i t s q u a l i t y . Thus the e s t i -mated c o e f f i c i e n t may give an accurate idea of the marginal product on pounds of f r u i t , while overstating the marginal product on value, i f a constant p r i c e i s assumed. The estimated c o e f f i c i e n t s i n d i c a t e that an a d d i t i o n a l pound of f e r t i l i z e r costing about 7c r e s u l t s i n a d d i t i o n a l production worth from $1.82 to $19.34 i f the average p r i c e net harvesting costs of 5.2c i n 1975 i s used. It was f e l t that the extremely high r a t i o s of marginal value product to marginal cost were l a r g e l y due to the biases mentioned. There may also be some bias imparted to the c o e f f i c i e n t s of f i x e d inputs and p h y s i c a l features by the l e f t - o u t v a r i a b l e s , but i t was f e l t that the bias was not so serious as i n the case of the v a r i a b l e inputs. In the case of labour, there i s consensus data r e l a t i n g labour require-ments to orchards systems, and the influence of labour can be accounted for when assessing the r e l a t i v e p r o f i t a b i l i t y of the systems. There may be some management bias i n the c o e f f i c i e n t s for c e r t a i n p h y s i c a l features. This would occur i f better managers tended to u t i l i z e c e r t a i n systems, an occurrence which might be expected i f they had better access 114 to knowledge concerning 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 . Thus the estimated c o e f f i c i e n t s for highly productive systems may not only be due to the e f f e c t of the systems but may also be due to the better management associated with them. The r e s u l t s and i n t e r p r e t a t i o n s are subject to t h i s possible bias. 5.1.1 Relative P r o d u c t i v i t y of Orchard Systems Orchard systems are related to the f i x e d inputs such as density, rootstock, i r r i g a t i o n system and planting concept. The basic systems can be categorized as: 1. high density dwarf rootstock with optional features including a) free standing or hedgerow b) overhead, portable, or t r i c k l e i r r i g a t i o n 2. high density semi-dwarf rootstock with the same optional features 3. medium density semi-standard with the same optional features 4. low density standard rootstock with portable or t r i c k l e i r r i g a t i o n . As functions have been estimated for each of the basic categories a y i e l d stream can be predicted for each system. For comparative purposes a time horizon of 20 years was taken for the y i e l d streams. Where the e f f e c t s of tree design and i r r i g a t i o n system was i d e n t i f i a b l e , comparative y i e l d s f o r these options are also presented. Where pos-s i b l e y i e l d s from d i f f e r e n t s o i l s are shown. The present value of 20 years' production less harvest costs i s shown i n table 5.1. In terms of the basic systems i t i s apparent that production per acre increases as t r e e - s i z e decreases and density increases. The average present value less harvest costs for a 20 year period i s $7,630 standard, $7,398 for semi-standard, $16,171 for semi-dwarf and $25,821 for dwarf. When the semi-standard and semi-dwarf-systems are 115 Table 5.1. Present Value of Production from Major Apple Production Systems over 20 years Dwarf Semi-Dwarf Semi-Standard Standard Average $ 25,821 16,171 7,398 7,630 Sandy 25,962 7,133 9,780 Clay 22,072 7,133 9,780 Rocky 5,122 5,817 Hedgerow 29,710 12,945 Non-hedgerow 19,469 6,806 Spur 27,410 17,631 Non-spur 25,201 15,974 Overhead I r r i g a t i o n 34,088 Non-overhead I r r i g a t i o n 19,504 planted as hedgerows, production increases s i g n i f i c a n t l y . The present value of production i s $12,945 for a hedgerow semi-standard system, and $29,710 for a hedgerow semi-dwarf system. The dummy va r i a b l e f o r hedgerow planting was highly s i g n i f i c a n t i n both the semi-dwarf and semi-standard categories with 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 . It was concluded that hedgerow planting 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 of planting system including s o i l type, i r r i g a t i o n system, and spur or non-spur resulted i n notable differences i n produc-t i o n although the 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 or as consistent as the e f f e c t s of t r e e - s i z e , density and tree design. In present value terms sandy s o i l s r e s u l t i n about $2000 "^A p r i c e of 5.20 per pound and a 5 percent i n t e r e s t rate are used. F u l l production streams predicted from tables 4-6 and 4-7 are shown i n Appendix A. 116 to $3000 increase i n y i e l d s over what occurs on clay or rocky s o i l s . The texture index of s o i l i s not s i g n i f i c a n t i n the tr e e - s i z e functions although i t s sign i s consistent. Over the whole data set, the v a r i a b l e i s quite s i g n i f i c a n t , and i t was thus f e l t that s o i l texture was of economic s i g n i f i c a n c e . The i r r i g a t i o n system was only testable i n the semi-dwarf category, where i t proved to be highly s i g n i f i c a n t and added a present value of about $14,000 to y i e l d s over a 20 year period. It was f e l t that t h i s increase i n production was rather high and may have been due to some bias i n the estimated c o e f f i c i e n t . Because les s labour i s required with a f i x e d overhead i r r i g a t i o n system these orchards would l i k e l y get a higher l e v e l of i r r i g a t i o n , and the r e s u l t i n g e f f e c t on y i e l d s would be captured by the c o e f f i c i e n t f o r the overhead system. Spur-type trees r e s u l t i n an increase i n present value of about $2000 i n production. However, the c o e f f i c i e n t for spur-type did not prove s t a t i s t i c a l l y s i g n i f i c a n t i n any of the estimations although i t had con-s i s t e n t l y p o s i t i v e signs. Hence the r e s u l t s were taken only to suggest rather than prove at high l e v e l s of confidence that spur type trees are better producers than non-spur type trees. 5.1.2 Relative P r o f i t a b i l i t y of Orchard Systems It has been estimated that annual maintenance costs for a dwarf system w i l l be about 20% greater than maintenance costs for standard systems (Kennedy, 1976). Other research has outlined a s i m i l a r d i f f e r -ence i n the investment cost of high versus low density systems (Dorling, 1975). Since a three-fold increase i n the present value of y i e l d s can be achieved through a r e l a t i v e l y small increase i n costs, high density systems appear to be superior investments compared to low density sys-tems at current p r i c e s . An annual stream of costs for each system has been estimated from various sources and these are compared to the value of the y i e l d streams. A case i s outlined where producers are constrained to 10 acres of land, faced with e s t a b l i s h i n g and maintaining an orchard system over a twenty year time period. Some costs including taxes and u t i l i t i e s have not been included and the p r i c e of the undeveloped land i s set a r b i t r a r i l y at $5,000 per acre. The costs are not intended for accurate budgeting purposes, but should give a s a t i s f a c t o r y i n d i c a t i o n of 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 costs and benefits are i n constant d o l l a r s with the r e a l i n t e r e s t rate taken as f i v e percent. Levels of a l l inputs are set at averages, and the average y i e l d for each system i s used to determine the yearly returns. The average p r i c e less harvest costs i s 5.2c per pound for standard and semi-standard and 5.1c for dwarf and semi-dwarf. These prices are based on the 1974 average prices received by orehardists i n the survey. Machinery includes a t r a c t o r i n the 40-horsepower range, a sprayer adequate for the t r e e - s i z e , a weed sprayer, an orchard mower, buildings used to house equipment, and miscellaneous equipment such as ladders, pruning aids and harvesting equipment. It i s assumed that the major machinery items are replaced a f t e r 10 years. Materials include p e s t i -cides, f e r t i l i z e r , trace elements, and i r r i g a t i o n equipment. A rate of $5 per hour i s charged for a l l labour. Information on machinery costs was obtained from the B.C. Minis t r y of Ag r i c u l t u r e i n Vernon, B.C. Table 5.2 gives the present value of costs and returns for each system. A year-by-year break-down of costs and returns for each of the systems i s given i n appendix B. 118 Table 5.2. Present Values of Costs and Returns for Apple Systems 1 Semi- Semi-Dwarf dwarf standard Standard Costs $ 17,732 16,048 16,906 13,359 Returns 25,821 16,171 7,398 7,630 Net present value 8,449 87 -9,508 -5,729 It can be seen from the table that dwarf and semi-dwarf systems are superior investments compared to standard and semi-standard systems. The ranking i n terms of net present value puts dwarf f i r s t , semi-dwarf second, standard t h i r d , and semi-standard l a s t . If some of the optional management features were incorporated for semi-dwarf and semi-standard systems, p a r t i c u l a r l y hedgerow planting, the p r o d u c t i v i t y of these sys-tems would increase greatly at a small cost, so the net present value would improve. However, at the present average l e v e l of inputs only dwarf and semi-dwarf systems have net present values greater than zero, representing economic investments. The investment decision outlined i n the tables may not be the most relevant problem i n the area. What may be of more concern i s the orchard replacement decision where orchardists are considering replacing a low density system with a high density system. While there are many factors involved i n t h i s decision most of the basic information needed i s given i n the preceding tables. It can be seen that the p r o f i t l o s t as a r e s u l t of removing a standard of semi-standard system i s small even "'"Returns are c a l c u l a t e d as i n table 5.1. A cost breakdown i s given i n Appendix B. 119 i f the trees have reached t h e i r f u l l bearing p o t e n t i a l , while the p o t e n t i a l annual p r o f i t s from the high density systems are much higher. 5.1.3 Other Factors Influencing the Choice Between Systems Although the estimated production functions ind i c a t e that high density systems are more p r o f i t a b l e than low density systems over a medium term, there are other factors which may influence the choice between systems. There i s evidence suggesting that the high density systems have higher v a r i a b i l i t y of y i e l d s , require more management e f f o r t and are affected to a greater degree by influences not completely under the growers' c o n t r o l . These factors may tend to counter the inducement of higher p o t e n t i a l p r o f i t s when the choice between systems i s considered. Table 5.3 shows the means and standard deviations of y i e l d s from the four systems and i l l u s t r a t e s the greater v a r i a b i l i t y of y i e l d s from high density systems. Table 5.3. Level 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 year Period Average y i e l d Standard System per acre Deviation Dwarf 36,786 43,138 Semi-dwarf 26,336 35,088 Semi-standard 15,424 30,183 Standard 2,807 4,535 The higher v a r i a b i l i t y of the dwarf and semi-dwarf systems i s indicated by t h e i r higher standard deviations. This v a r i a b i l i t y may cause d i f f i c u l t i e s i n yearly budgeting and cash flow a l l o c a t i o n and might necessitate greater e f f o r t or a b i l i t y i n the f i n a n c i a l 120 management of high density versus low density systems. However, the r a t i o of the standard deviation to the mean y i e l d i s smaller for the high density systems. This indicates that the p r o b a b i l i t y of an orchardist i n the sample f a l l i n g below a set production l e v e l i s lower for high density systems than for low density systems. I f an orchardist's primary objective i s not to f a l l below a c e r t a i n production l e v e l the evidence indicates that high density i s preferable to low density. Over the observed ranges of inputs the high density systems are more responsive to the l e v e l s of f e r t i l i z e r . If i t can be generalized that dwarf systems are more responsive to a l l v a r i a b l e inputs including labour and p e s t i c i d e s , then the l e v e l s of these inputs would have to 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 . It also appears that high density systems are more s e n s i t i v e to factors which are not completely under the grower's co n t r o l , once the orchard has been established. Frost, i n p a r t i c u l a r , shows a strong influence on high density systems with a negative c o e f f i c i e n t of about 1,700 lbs per degree below c r i t i c a l l e v e l s , whereas the c o e f f i c i e n t f o r standard systems i s about 100 lbs per degree of f r o s t . A severe f r o s t for one or two nights would almost completely destroy production from a dwarf system while causing a comparatively small reduction i n y i e l d s from a standard system. High density systems also show a higher s e n s i t i v i t y to sunlight and temperature during bloom. In general i t appears that blossom influences have a greater influence on high density dwarf systems than they do on low density standard systems. Another geographical factor with a s i m i l a r e f f e c t to the weather v a r i a b l e s i s s o i l type. Dwarf systems were more s e n s i t i v e to poorer s o i l s as evidenced by the negative c o e f f i c i e n t f o r the s o i l index of -7547 lbs 121 versus -4860 lbs for semi-standards, and -4837 lbs f o r standards. Thus care must be taken i n matching rootstock to s o i l type or low y i e l d s can r e s u l t . Some constraints as noted i n the conceptual model may make i t I n f e a s i b l e to plant dwarf and semi-dwarf trees i n c e r t a i n areas. Dwarf trees stunt badly on l i g h t shallow s o i l s which may be s u i t a b l e for standard trees. Frost pockets or channels leave c e r t a i n areas completely unsuitable f o r dwarf trees although standard trees may s t i l l produce some f r u i t i n these areas because of the higher elevation of the bearing limbs. Because high density systems do not appear i n these l o c a t i o n s , the sample and estimations do not completely capture the e f f e c t of some of these constraining v a r i a b l e s on production. 5.2 Evaluation of Technological Innovations The c o e f f i c i e n t s of the estimated production functions can be used to assess the p o t e n t i a l benefits of some important innovations. This a p p l i c a t i o n i s of importance to both orehardists who may wish to i n c o r -porate these innovations and researchers who are evaluating technological impact and a l l o c a t i n g resources to future research (see chapter VI). For example, i f the degree of protection from a f r o s t prevention system i s known, the t o t a l extra y i e l d r e s u l t i n g from t h i s system can be c a l -culated from the estimated c o e f f i c i e n t for f r o s t . Another example i s the assessment of the benefits of hand or mechanical p o l l i n a t i o n . The gain from these a r t i f i c i a l forms of p o l l i n a t i o n could be calculated from the l e v e l s of v a r i a b l e s known to adversely a f f e c t natural p o l l i n a t i o n including f r o s t , r a i n and cool daytime temperatures, and from the e s t i -mated c o e f f i c i e n t s of these v a r i a b l e s i n the production function. 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 production function can be s i m i l a r l y evaluated. 5.3 P r e d i c t i n g Y i e l d s The regional weather model developed i n chapter IV has the c a p a b i l -i t y of explaining a large amount of the v a r i a t i o n i n y i e l d s over time and between regions on the basis of weather variables during the blossom period. As the blossom period precedes the harvest by four or f i v e months, the weather model could be used for p r e d i c t i n g y i e l d s giving the marketing agency and governments advance knowledge of t o t a l production. This knowledge would be p a r t i c u l a r l y u s eful i n the formulation of market-ing s t r a t e g i e s . 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 tested by using i t to predict the average y i e l d for recent years not used i n estimation. The data required would be the 1975-76 blossom dates for each region, and observations on d a i l y sun, r a i n , temperature and f r o s t during the blossom period. The estimated c o e f f i c i e n t s would be applied to the l e v e l s of these v a r i a b l e s to give a predicted average y i e l d which would then be compared with the observed y i e l d i n 1975-76. Pos-s i b i l i t i e s f o r improving the present model to give more accurate predic-tions are discussed i n the next chapter. This chapter has given some d i r e c t a p p lications of the estimated production functions r e l a t i n g to the choice between systems, evaluation of innovations and p r e d i c t i o n of y i e l d s . Other implications can be drawn from the production functions p a r t i c u l a r l y i n the area of deter-mining d i r e c t i o n s of future research. These implications along with a summary of the research and the conclusions are presented i n the f i n a l chapter. CHAPTER VI SUMMARY, CONCLUSIONS AND IMPLICATIONS FOR FUTURE RESEARCH This chapter b r i e f l y summarizes the content of the research and out-l i n e s the conclusions that have been drawn from the empirical r e s u l t s . The conclusions and implications for further research are categorized according to t h e i r relevance to various groups involved i n the t r e e - f r u i t industry through production, extension, marketing, p o l i c y and research. 6.1 Summary The opening chapter of t h i s thesis discussed the r a t i o n a l e for under-taking the research. The argument was developed that low incomes i n the industry have been c l e a r l y recognized and that some government attempt should be made to improve returns i n the industry. The large c o n t r i b u t i o n to the economic base of the area as well as c u l t u r a l and external benefits were c i t e d as reasons for d i r e c t i n g s c i e n t i f i c and economic research towards solving the low income problem through attempting to improve resource a l l o c a t i o n . Because of the complex nature of the production process which involves many recent innovations i t was f e l t that estimation of production functions f o r the major apple v a r i e t i e s would serve to c l a r i f y and quan-t i f y the e f f e c t s of many inputs. Knowledge of the e f f e c t s of these inputs could then be used to aid i n resource a l l o c a t i o n decisions. To be useful i n a l l o c a t i o n decisions a production function should be 123 124 s u f f i c i e n t l y disaggregated and d e t a i l e d to show the influence of orchard systems, weather va r i a b l e s and i n t e r a c t i o n s . The primary objective of t h i s research was to estimate such a function. Secondary objectives were to i d e n t i f y s p e c i f i c weather va r i a b l e s and i n t e r a c t i o n s , and to i n t e r p r e t the estimated functions i n order to assess the 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 orchard systems and optional p h y s i c a l features. The i n t e r p r e t a t i o n s were also aimed at o u t l i n i n g possible input adjust-ment i n the industry and implications for further economic and s c i e n t i f i c research. The f i r s t step i n the research was to review the well known economic models of the production function and producer behaviour i n order to f i n d an appropriate f u n c t i o n a l form and implications for econometric estima-t i o n . An i n t e r a c t i v e (quadratic) form was chosen because of the require-ment that the function be able to e x p l i c i t l y i d e n t i f y i n t e r a c t i o n s . The important implications for estimation were due to the tendency for producers to seek economically e f f i c i e n t points on the production function. In theory t h i s could cause either a complete lack of input v a r i a t i o n , perfect c o l l i n e a r i t y between inputs and simultaneous problems i n estima-t i o n . However, i t was f e l t that i n p r a c t i c e growers are facing varying p r i c e l e v e l s , a lack of knowledge of marginal products and d i f f e r e n t valuations of t h e i r own labour, a l l of which would tend to increase v a r i a t i o n i n input l e v e l s and decrease c o r r e l a t i o n between inputs. The p o s s i b i l i t y of simultaneity was discounted because of the knowledge that producers based t h e i r decisions on expected prices of output rather than actual p r i c e s . The most serious i m p l i c a t i o n was l e f t - o u t v a r i a b l e b i a s . 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 several inputs and the l e v e l s of management and 125 labour neither of which were a v a i l a b l e for 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 ables would then be upward biased. It was concluded that on t h e o r e t i c a l grounds estimation of the production func-t i o n was f e a s i b l e although some problems with m u l t i c o l l i n e a r i t y could r e s u l t and some estimated c o e f f i c i e n t s would have to be taken as upward biased. A conceptual model of apple production o u t l i n i n g the important concepts and i d e a l measures of these concepts was developed along with a s t a t i s t i c a l model giving the actual measures a v a i l a b l e . The conceptual model was aimed at r e f l e c t i n g the major decisions of concern to a producer, with p a r t i c u l a r emphasis on systems and long-term orchard features. The importance of weather variables and i n t e r a c t i o n s was stressed i n the conceptual model. I t was f e l t that the s t a t i s t i c a l model adequately represented the physical features and fixed inputs . although i t was somewhat weaker i n i t s representation of the v a r i a b l e inputs. It contained most of the major weather influences. A problem with the s t a t i s t i c a l model was that i t had the t o t a l quantity rather than value of the f r u i t as the dependent v a r i a b l e . This problem caused some d i f f i c u l t y 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 t h e s i s . Because the s t a t i s t i c a l model had a large number of v a r i a b l e s , p a r t i c u l a r l y dummies and i n t e r a c t i o n s , i t was extremely cumbersome to estimate. A general estimation strategy was formulated with the object of reducing the number of v a r i a b l e s while at the same time obtaining as much information as possible from the data. A problem arose because the input classes which were of p a r t i c u l a r i n t e r e s t i n the research were also contributing to.the problem of a large number:of v a r i a b l e s . A 126 stepwise regression procedure was used which tended to s e l e c t v a r i a b l e s of greater importance on a p r i o r i grounds. A regional weather model was f i r s t estimated i n order to sel e c t the more important weather influences. These weather variables were then included along with a l l inputs i n a l i n e a r form. Subsets of in t e r a c t i o n s were then added to the model i n order of a p r i o r i importance. The f i n a l estimate was poor i n some regards and showed signs of m u l t i c o l l i n e a r i t y . The f i n a l r e s u l t s were s l i g h t l y unstable i n that changing the order of entry i n the stepwise regression caused a few d i f f e r e n t variables to be retained. In general, the c o e f f i c i e n t s of variables which were conceptually important proved to be s i g n i f i c a n t and consistent with expectations although the explan-atory power of the model was not great. A second approach to estimation was c a r r i e d out where the observa-tions were grouped according to t r e e - s i z e category and a function e s t i -mated for each category. The purpose of t h i s procedure was to reduce the number of inte r a c t i o n s and give less r e s t r i c t i o n s on the estimated c o e f f i c i e n t s . The stepwise procedure was again c a r r i e d out entering the weather variables and inputs f i r s t and then entering groups of i n t e r a c -t i o n s . The r e s u l t s of the t r e e - s i z e category functions were more s a t i s -factory than the single equation model i n several regards including 2 s t a t i s t i c a l s i g n i f i c a n c e , R robustness, and consistency of c o e f f i c i e n t s . Table 6.1 gives a summary of the impact of the major variables i n the various models. A number of conclusions based on the s t a t i s t i c a l r e s u l t s and methodology were drawn. Various i n t e r p r e t a t i o n s were made using the estimated models to predict a stream of production. Establishment and annual operating costs were c o l l e c t e d from other sources, and were 127 Table 6.1. Summary of S t a t i s t i c a l Results S t a t i s t i c a l S ignificance Independent Regional Complete Indication from Variable Model Model By System C o e f f i c i e n t Q u a l i f i c a t i o n S o i l Rootstock (tree-size) Density Spur-type Tree-design Variety Age I r r i g a t i o n system F e r t i l i z e r P e s t i c i d e Temperature at blossom Sunlight of blossom Rain at blossom Frost at blossom high high high high h i g h 1 high medium high high high high high medium medium low medium medium high low to high low high low to high high high medium to high medium to high high sandy s o i l s superior dwarf and semi-dwarf give higher y i e l d s higher density increases y i e l d s except f o r semi-standard s l i g h t l y higher y i e l d for spur much higher y i e l d f o r hedgerow inconsistent e a r l i e r produc-t i o n from high density overhead i r r i -gation has higher y i e l d s less than opti-mum presently being used associated with high density systems major impact on y i e l d s medium reduces y i e l d s medium reduces y i e l d s s u b s t a n t i a l l y c o e f f i c i e n t may be biased upwards c o e f f i c i e n t may be biased upwards management and labour bias suspected higher density systems are more s e n s i t i v e to weather var i a b l e s high indicates s i g n i f i c a n c e at the .05 l e v e l ; medium indicates a T-ra t i o of greater than unity 128 compared.with the predicted y i e l d streams i n order to assess the p r o f i t -a b i l i t y and v a r i a b i l i t y of the four major systems. 6.2 Conclusions and Implications for Further Research A number of conclusions regarding 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 various systems and p r o f i t a b i l i t y have been made i n the previous chapters. This section b r i e f l y summarizes the conclusions as they r e l a t e to various groups involved i n the industry. Implications for further research by s c i e n t i s t s and economists which could prove b e n e f i c i a l to the industry are also presented. 6.2.1 For the Orchardist A number of conclusions relevant to e x i s t i n g and p o t e n t i a l orehard-i s t s can be drawn from the research. These concern the choice between systems, replacement of present systems, importance of weather v a r i a b l e s and possible adoption of new technology. An important conclusion for both e x i s t i n g and future orehardists i s that high density systems have the p o t e n t i a l to generate higher p r o f i t s and income over a medium term (20 year) range, than do standard and semi-standard systems. The higher density dwarf and semi-dwarf systems r e s u l t i n a present value of production two to three times greater than the present value of production from standard and semi-standard systems i f a l l inputs are taken at present l e v e l s . High density systems r e s u l t i n both e a r l i e r and higher y i e l d s . Features which increase bearing surface per acre, such as density and hedgerow planting have large s i g -n i f i c a n t impacts upon y i e l d s . In terms of net present value, dwarf and semi-dwarf systems are both p r o f i t a b l e investments considering a r e a l i n t e r e s t rate of f i v e 129 percent. Dwarf has the highest net present value for a 20 year period, but semi-dwarf can be equally as p r o f i t a b l e when planted i n the hedgerow concept. Standard and semi-standard systems are poor investments both r e s u l t i n g i n net losses over 20 years. Growers who operate these types of orchards should consider a replacement scheme towards higher density plantings where s p e c i f i c conditions permit. However, there i s also evidence that high density systems require greater management e f f o r t and a b i l i t y than do low density systems. The higher annual v a r i a t i o n i n y i e l d s , higher response to inputs, and greater s u s c e p t i b i l i t y to geo-graphical influences of the high density systems are l i k e l y to render the f i n a n c i a l and resource management more d i f f i c u l t than for a low density standard system. Another conclusion of relevance to the orchardist i s the importance of weather v a r i a b l e s . In general the weather v a r i a b l e s tested in c l u d i n g f r o s t , sunlight, maximum temperature and r a i n prove to have s i g n i f i c a n t impacts on y i e l d s . The impact of weather v a r i a b l e s on y i e l d s emphasizes the need for orehardists to consider the use of weather management tech-niques. In p a r t i c u l a r , f r o s t prevention systems would o f f e r p o t e n t i a l for high increases i n y i e l d s i n many cases. The estimated functions i n d i c a t e that a s i n g l e degree of f r o s t below c r i t i c a l l e v e l s can r e s u l t i n a loss of up to 1700 pounds per acre i n y i e l d . If blocks are geo-gra p h i c a l l y placed such that, the orchardist expects a s i g n i f i c a n t amount of f r o s t during the blossom period, then investment i n an e f f e c t i v e f r o s t prevention system should be considered. At present, there are no d i r e c t means of c o n t r o l l i n g other weather influences besides f r o s t . However, during the establishment phase of the orchard the grower should choose a s i t e which gets maximum exposure to sunlight with no f r o s t 130 pockets or channels. A s i g n i f i c a n t pay-off i n increased y i e l d s could r e s u l t from proper s e l e c t i o n of the orchard s i t e , i f the negative aspects of weather ( f r o s t and rain) are reduced, and the p o s i t i v e aspects (sun-l i g h t and temperature) are maximized. 6.2.2 For the Government There are some conclusions from t h i s research which could help governments i n solving the low income problem i n Okanagan orchards. If governments can a i d and encourage the adjustment from low density to high density systems where f e a s i b l e , a s i g n i f i c a n t and long term increase i n farm incomes could be achieved. 1 Increased incomes should also r e s u l t from government aid i n the adoption and s e l e c t i o n of weather rela t e d technology and i r r i g a t i o n systems. In general, governments can aid the orchardist i n resource a l l o c a t i o n by (1) improving and dissemin-ating information 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 allowing c a p i t a l to be allocated for renovation and establishment of e f f i c i e n t orchard systems. I n s t i t u t i o n s already e x i s t which could r e a d i l y be u t i l i z e d i n d i s -seminating information and i n providing c a p i t a l . For example, the Extension Branch of the B.C. M i n i s t r y of A g r i c u l t u r e and the Farm and Rural Development D i v i s i o n of A g r i c u l t u r e Canada have several personnel involved i n extension i n the orchard industry. If they have concrete information on the p o t e n t i a l returns of a l t e r n a t i v e systems and input combinations, the management and f i n a n c i a l requirements, and the degree of r i s k involved for various t r e e - f r u i t enterprises then they can be of "'"The industry competes on a world market and faces an e l a s t i c demand function. Thus an increase i n production should have l i t t l e e f f e c t on p r i c e . 131 s i g n i f i c a n t help i n improving resource a l l o c a t i o n i n the industry. As for the area of improving c a p i t a l markets, the Farm Credit Corporation already administers several programs aimed at financing 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 . It seems f e a s i b l e to expand these programs to o f f e r further incentives f or orchard renovation and estab-lishment aimed at u t i l i z i n g high density systems and weather rel a t e d technology. 6.2.3 For the Marketing Agency A conclusion from t h i s research i s that weather v a r i a t i o n during the blossom period can explain a large amount of the v a r i a t i o n i n average y i e l d s between years and regions. The weather model developed i n chapter four could be improved or u t i l i z e d as a f i r s t step i n p r e d i c t i n g the t o t a l harvest of the area on the basis of observable weather influences during the blossom period. Advance knowledge of quantities would be u s e f u l i n formulating market strategies concerning p r i c e , storage and d i s t r i b u t i o n . A model which predicts t o t a l y i e l d f o r the whole region (rather than y i e l d per acre for a sample) would be of greater benefit to the marketing agency. By u t i l i z i n g t h e i r own records on the aggregate production of apples i n the region and following the basic structure of the model e s t i -mated i n t h i s research a s u i t a b l e p r e d i c t i v e model could be developed. There would l i k e l y be s u f f i c i e n t data to be able to estimate a model for each of the major v a r i e t i e s of apples produced i n the area. The cost to the marketing agency of developing the p r e d i c t i v e model would l i k e l y be small, depending upon the a v a i l a b i l i t y of the data. 6.2.4. For the S c i e n t i s t A major thrust of s c i e n t i f i c research at the Summerland Research Station has been aimed at 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 industry i n the Okanagan. This work would be f a c i l -i t a t e d by information concerning the s p e c i f i c areas where technological development would have the greatest pay-off i n improvement of the l o c a l industry. The production functions estimated i n the present research serve to show some of these s p e c i f i c problem areas where technological development should be b e n e f i c i a l . Although t h i s research has i l l u s t r a t e d the greater 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 high density systems over the long run, i t has also shown the high v a r i a b i l i t y of y i e l d s from these systems which makes them more d i f f i c u l t to manage on a year-to-year b a s i s . Much of t h i s v a r i a b i l i t y i s caused by a high response to weather and s o i l v a r i a t i o n . I f s c i e n -t i f i c research can develop technology which reduces the negative impacts of these f a c t o r s , then a s i g n i f i c a n t impediment to a widespread adop-^ t i o n of high density systems could be removed. Some developments along t h i s l i n e have already taken p l a c e — e s p e c i a l l y i n the area of f r o s t prevention. Other suggested areas for research are the development of a r t i f i c i a l p o l l i n a t i o n techniques, new breeds of p o l l i n a t i n g insects l e s s affected by cool temperatures, and v a r i e t i e s of apples where there i s f a s t e r generation of p o l l e n , making p o l l i n a t i o n l e s s susceptible to r a i n -f a l l . Developing dwarf v a r i e t i e s which are better adapted to l i g h t and rocky s o i l s could remove a further impediment to planting high density dwarf systems. A feature which stands out i n the functions as having important e f f e c t s on y i e l d i s bearing surface per acre, as evidenced by the impor-tance of density and tree design. Given the dramatic e f f e c t that both features had i n the functions i t would be reasonable to examine methods of further increasing bearing surface per acre. 133 Research s c i e n t i s t s could also aid i n improving further estimation of production functions. Many experimental blocks which include a v a r i -ety of systems now exist for the purposes of s c i e n t i f i c research. By adding more d e t a i l to the input records for these blocks, e s p e c i a l l y on man-hours u t i l i z e d for pruning and thinning a c t i v i t i e s , the data problems confronting the present research could be a l l e v i a t e d i n future production function estimation. 6.2.5 For the Economist Several conclusions from t h i s research are of i n t e r e s t to economists concerned with the Okanagan t r e e - f r u i t industry. These include the 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 production function and methods of estimating i t , methods for improving the present estimates and evaluation of technological developments. 6.2.5.1. Properties of the Function. In summary the production function estimated i n t h i s research has two basic c h a r a c t e r i s t i c s : (I) i t i s highly i n t e r a c t i v e with rootstock being the major source of i n t e r a c t i o n followed by age and by s o i l , and (2) i t i s composed of an extremely large number of s i g n i f i c a n t inputs and exogenous factors at the orchard l e v e l . It 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 and f i x e d inputs r e l a t e d to planting concept, tree design and density. The production function can be more e a s i l y expressed and written as four separate equations, one for each of the major systems. 6.2.5.2 Methodology of Estimation. Estimation of a highly d e t a i l e d and disaggregated production function which r e f l e c t s important production decisions of the orchardist i s d i f f i c u l t but f e a s i b l e . The large number of variables leads to severe problems with m u l t i c o l l i n e a r -i t y , hindering estimation or making i t impossible i n some instances. 134 The stepwise regression procedure used makes estimation possible, although i n the complete function the f i n a l v a r i a b l e s selected depend somewhat on the order i n which groups of va r i a b l e s are entered into the model. It was f e l t that representing the complete production process i n a s i n g l e model taxed the regression technique to the l i m i t of i t s usefulness. When the stepwise procedure i s combined with p a r t i t i o n i n g the data by t r e e - s i z e category, the estimation i s f a c i l i t a t e d . Categorizing observations by t r e e - s i z e and estimating separate func-tions for each category improves estimation without a loss of information. The improvement i s due to a. reduction i n the number of v a r i a b l e s , r e s t r i c -t i o n on the range of inputs and less r e s t r i c t i o n s on the behaviour of in t e r a c t i o n s . The estimates for the t r e e - s i z e category functions are more stable, s i g n i f i c a n t and consistent than those f o r the sing l e equation model. Individual v a r i e t y functions were not su c c e s s f u l l y estimated. On a regional basis, v a r i a t i o n i n average production can for a large part be explained s o l e l y by weather f a c t o r s . The model estimated on t h i s basis i s a useful t o o l for assessing the r e l a t i v e aggregate e f f e c t of the various weather f a c t o r s . 6.2.5.3 Improving the Present Estimates of the Production Function. A primary area for further research would be i n improving on the present estimates of the functions. The estimates i n t h i s research were hindered by two factors which were (1) some important!left-out v a r i a b l e s , and (2) extremely large number of dependent v a r i a b l e s . Both of these problems could be l a r g e l y remedied by updating and expanding the present data base. The important l e f t - o u t v a r i a b l e s were growing season heat accumulation, machinery inputs, labour and management. Of these, 135 machinery inputs would be the easiest for which to gather data. Some of the measures mentioned previously such as t r a c t o r horsepower and sprayer c a p a b i l i t y would be adequate. Data on growing season heat are a v a i l a b l e and i t i s simply a matter of man-hours to c o l l a t e the data into useable form. The s i t u a t i o n regarding labour and management i s more d i f f i c u l t . To obtain accurate information on labour i t would be necessary to have each orchardist keep records of time spent on the s p e c i f i c blocks under observation. This would involve s i g n i f i c a n t l y added research e f f o r t , and might not be f e a s i b l e on a large scale. However, i t would be worthwhile to ask the orchardist to make an estimate of how much time he spends on a p a r t i c u l a r block performing the important labour-using a c t i v -i t i e s , p a r t i c u l a r l y pruning and thinning. This would only be a rough estimate but i t may be s u f f i c i e n t to capture much of the influence of labour. The present research has shown that farmers' estimates of other inputs give both s i g n i f i c a n t and consistent c o e f f i c i e n t s . Measuring the influence of management has been a problem i n most production function estimates and the same holds true for apple production functions. Certain proxy variables may capture some of the influence and data on these could be gathered without great a d d i t i o n a l e f f o r t . These include factors such as years of schooling, type of schooling, years of experience and contact with extension personnel. Another area for which better data can be obtained concerns f r o s t incidence and f r o s t r i s k . In the present orchard l e v e l estimates the f r o s t v a r i a b l e used was a proxy i n that i t was taken from the regional weather s t a t i o n nearest to the observed orchard. As a r e s u l t f r o s t proved to be of greater consistency and s i g n i f i c a n c e i n r e g i o n a l ' l e v e l functions than i n orchard l e v e l functions. A better estimate of the 136 f r o s t occurring on each orchard could perhaps be developed by r e l a t i n g the orchard l o c a t i o n to zones on f r o s t maps. This approach i s presently being c a r r i e d out by Kennedy, Andison and Graham (forthcoming). It i s recommended that further studies continue the approach of p a r t i t i o n i n g the data into separate t r e e - s i z e categories. It i s sug-gested that c o n t r o l l i n g the l e v e l of other v a r i ables by further p a r t i -t i o n i n g of the data should also be attempted and that data should be gathered with the object of making t h i s procedure f e a s i b l e . 6.2.5.4 Evaluation of Technological Developments. The present functions could be u t i l i z e d i n evaluating the benefits of c e r t a i n weather rela t e d technological innovations. Two innovations which could be anal-yzed u t i l i z i n g the functions are f r o s t prevention systems and hand-mechanical p o l l i n a t i o n . The estimated functions state 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 production and i f t h i s e f f e c t i s u t i l i z e d along with information about the f r o s t prevention c a p a b i l i t i e s an assessment can be made of the t o t a l benefits that w i l l accrue by use of the system given the expected weather pattern. For example, i f the average expected f r o s t below c r i t i c a l l e v e l s i s four accumulated degrees and each degree r e s u l t s i n about 250 lbs per acre le s s production, then a system which i s capable of preventing the t o t a l amount of f r o s t w i l l r e s u l t i n a gain of 1,000 lbs of f r u i t per acre. A further benefit would be the insurance and s t a b i l i z i n g e f f e c t provided by the system. Hand or mechanical p o l l i n a t i o n could be s i m i l a r l y evaluated i f i t i s assumed that the benefits from t h i s a c t i v i t y are equal to the loss i n production that would r e s u l t from negative influences on natural p o l l i n -a t i o n such as r a i n and cool day time temperatures. Any further inven-t i o n which can combat negative weather influences or can be re l a t e d to 137 c o e f f i c i e n t s i n the production function could be evaluated i n a s i m i l a r manner. 6.2.5.5 Further Economic Analysis. Further economic studies could u t i l i z e some of the findings of t h i s research i n a more aggregate analysis of the apple industry, p a r t i c u l a r l y i n supply estimation. The impact of weather variables i n the production function suggests that they should be incorporated i n an industry supply function. The knowledge of the variance of weather variables could give an expected supply v a r i a t i o n over future years, which would be useful for s t a b i l -i z a t i o n p o l i c y or aggregate industry l e v e l models. The production function also i d e n t i f i e s the important inputs of which the costs are a va r i a b l e i n the supply equation. Any trends i n the costs of these inputs, which can be i d e n t i f i e d , would give an i n d i c a t i o n of future supply and returns i n the industry. An area for future research i s the assessment of the t o t a l acreage where replanting with high density systems i s f e a s i b l e . This knowledge would be useful i n estimating the p o t e n t i a l s h i f t i n the derived demand for associated f i x e d inputs and for assessing the p o t e n t i a l impact on the industry of a major s h i f t to high density systems. 138 BIBLIOGRAPHY Arrow, K. J . , Chenery, H. B., Minhas, B. S., and Solow, R. M. 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Marshall, A. "A Multiperiod Management Analysis of an Orchard i n the Okanagan V a l l e y . " B.Sc. Thesis i n A g r i c u l t u r a l Economics, University of B r i t i s h Columbia, Vancouver (1974). Meteorological Records, Dept. of Transport, Meteorological Branch (1967-1974) , Government of Canada. Mundlak, Y. "Empirical Production Function Free of Management Bias." , Journal of Farm Economics, February (1961), Vol. 43, no. 1, p. 44. Rao, P., and M i l l e r , R. Applied Econometrics. Wadsworth Publishing Company, Inc., 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 States and Canadian P r o v i n c e s — B r i t i s h Columbia," i n History of F r u i t Growing  and Handling i n U.S.A. and Canada 1860-1972, W. H. Upshall (ed.). Regatta Ci t y Press, Kelowna, B.C. (1976). " S o i l Management Practices f or Reducing Winter Injury." Okanagan A g r i -c u l t u r a l Club, Mimeographed, B r i t i s h Columbia Department of A g r i -culture, Summerland, B.C. (1956). Swales, J . E. Commercial Apple Growing i n B r i t i s h Columbia. B r i t i s h Columbia Dept. of 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 Econometrics. John Wiley and Sons, Inc., New York (1971). 141 -Tree F r u i t Production Guide for 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 Minis 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 Orchards." M.Sc. Thesis 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 Production Table A - l shows the predicted y i e l d streams for the dwarf sample which was 42% Red De l i c i o u s , 21% Mcintosh, 21% Golden D e l i c i o u s , 8% Spartan, and 8% Tydeman. The blocks were mainly hedgerow planting (96%) with the rest free standing. About four percent of the sample had fixed overhead i r r i g a t i o n with the rest having portable s p r i n k l e r systems. Most of the blocks were on sandy s o i l (94%) with the remainder on clay s o i l . Spur-type blocks represented 29% of the observations. A l l inputs and weather variables were set at mean l e v e l s for the sample. Pe s t i c i d e i s $65 per acre, f e r t i l i z e r i s 361 lbs per acre, density i s 362 trees per acre, and sunlight i s 85.8 hours and f r o s t below c r i t i c a l l e v e l s i s n i l . Predicted y i e l d streams are shown for spur vs. non-spur, and sandy, clay vs. rocky s o i l s . No d i f f e r e n t i a t i o n with respect to tree design or i r r i g a t i o n method were made as these variables were not included i n the functions because of m u l t i c o l l i n e a r i t y problems. For each y i e l d stream a l l other v a r i a b l e s are taken at average l e v e l s . The y i e l d s are pre-dicted from table 4.7 i n chapter four. Semi-dwarf Production The semi-dwarf y i e l d streams were predicted from table 4.6 i n chapter four. The sample observations are composed of 39% Red D e l i c i o u s , 28% Golden D e l i c i o u s , 23% Mcintosh, 5% Spartan, and 5% Tydeman. Approximately 90% of the blocks were i n sandy s o i l with 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 of y i e l d s between s o i l types was possible because of m u l t i c o l l i n e a r i t y problems. Most of the sample was free standing (74%) with the rest planted i n hedgerow fashion. About f i v e percent of the blocks had overhead i r r i g a t i o n , and 11% had t r i c k l e i r r i g a t i o n ; the remainder having the portable s p r i n k l e r system. Spur type plantings accounted for 34% of the observations. The average density of each block was 306, trees per acre and the average f e r t i l i z e r was 355 lbs per acre. There was an average of 86.0 hours of bright sun-l i g h t during bloom period 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 at $65 per acre. Semi-standard Production The y i e l d s are predicted from the i n t e r a c t i v e equation for semi-standard i n table 4.7. The sample observations are composed of a number of v a r i e t i e s including 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% of the blocks were free standing with the rest planted i n hedgerow fashion, while 46% were spur type and 54% non-spur. They were planted on a l l three s o i l types, 54% on sandy s o i l , 26% on clay 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 per acre, the average f e r t i l i z e r was 343 lbs per acre, and average density was 205 trees per acre. During blossom periods there was an average of 52.4 144 hours of bright sunlight, .15 inches of r a i n , 61 accumulated degrees above 65 F. and .89 degrees of frost: below c r i t i c a l l e v e l s . Standard Production A l l of the observed blocks were free standing with portable 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 % ) , clay (75%) and rocky (20%). The average density was 61 trees per acre, 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 lbs per acre, and the aver-age p e s t i c i d e cost was $42 per acre. The trees were 92% Golden D e l i c i -ous with the remainder Red D e l i c i o u s . During blossom periods there was an average of .10 inches 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 . Dwarf Production Year Average Spur Non-spur Sandy S o i l Clay S o i l 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 ' 54615 11 62162 65221 60913 62445 54615 12 62162 65221 60913 62445 54615 13 62162 65221 60913 62445 54615 14 . 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 Present Value $ Less 25821 27410 25201 25962 22072 Harvest Costs 146 Table A.2. Semi-Dwarf P r o d u c t i o n — l b s per acre Non-Year Average Overhead I r r i g a t i o n Overhead I r r i g a t i o n Hedgerow Non-Hedgerow Spur Non-Spur 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 Present Value 16171 34088 19504 29710 19469 17631 15974 $ Less Harvest Costs 147 Table A.3. Semi -Standard Prod u c t i o n — •lbs per acre Year Average Hedgerow Non-Hedgerow Sandy S o i l Clay S o i l Rocky S o i l 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 Table A.4. Standard P r o d u c t i o n — l b s per acre Year Average Sandy S o i l Clay S o i l Rocky S o i l 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 Present Value 7630 $ Less Harvest Costs 9780 8026 5817 149 APPENDIX B Annual Costs and Returns of Various Systems 150 Table B . l . Per Acre Costs and Returns—Dwarf Returns Costs T T i c Value of Crop Less Harvest Year Materials Machinery Labour Land T o t a l Costs $ $ $ $ $ $ 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 Present Value 17372 25821 Net Present Value $8449 151 Table B.2. Per Acre Costs and Returns- -Semi-Dwarf Year Materials Costs Machinery Labour Land Tot a l Returns Value of Crop Less Harvest Costs $ $ $ $ $ $ 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 Present Value 16048 16171 Net Present Value $123 152 Table B.3. Per Acre Costs and Returns—Semi-Standard Costs Returns Value of Crop Less Harvest Year Materials Machinery Labour Land T o t a l Cost $ $ $ $ $ $ 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 Present Value 16906 7534 Net Present Value -$9363 153 Table B.4. Per Acre Costs and Returns—Standard Costs Returns Value of Crop Less Harvest ' Year Materials Machinery Labour Land To t a l 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 Present Value 13359 7780 Net Present Value -$5,579 

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