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University Microfilms International 300 North Zeeb Road Ann Arbor, Michigan 48106 USA St. John's Road, Tyler’s Green High Wycombe, Bucks, England HP10 8HR I I 78-10,137 MU, M1ng-Wu, 1934SUPPLY AND DEMAND ANALYSIS FOR TART CHERRIES IN MICHIGAN WITH PROJECTIONS TO 1990. Michigan State University, Ph.D., 1977 Economics, agricultural University Microfilms International, AnnArbor, Michigan48ioe SUPPLY AND DEMAND ANALYSIS FOR TART CHERRIES IN MICHIGAN WITH PROJECTIONS TO 1990 By Ming-Wu Wu A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Economics 1977 ABSTRACT SUPPLY AND DEMAND ANALYSIS FOR TART CHERRIES IN MICHIGAN WITH PROJECTIONS TO 1990 By Ming-Wu Wu This dissertation develops econometric models of the tart cherry industry in Michigan, (1) The main objectives are: to investigate present and past trends of the Michigan tart cherry industry with particular emphasis on the insti­ tutional framework used to counteract the unstable market conditions, (2 ) to theoretically formulate and statistically estimate the supply response model of tart cherries to profit and non-profit incentives, (3) to construct a demand model for tart cherries at the grower level, and (4) to predict future trends in tart cherry supply and demand. The process involves the construction of acreage response models, demand models and projection of the exogenous variables contained in the models. The empirical results were evaluated and comparison made between selected models, and relationships analyzed between market variables in the industry, with specific emphasis upon identifying Ming-Wu Wu the separable effects of the independent variables. Projections of future supply and demand for tart cherries in Michigan were made to 1990. The analytical procedures and tools applied to develop the econometric models have been carefully chosen and stem from economic theory and characteristics of the industry. The selected models for empirical analysis included the geometric distributed lag models and the polynomial lag models. The models were estimated by using the Ordinary Least Squares method. The Cochrane-Orcutt iterative technique was used in instances where serial correlation errors were present. The variables used to estimate the supply response model were adj'usted by applying six-year moving averages to eliminate the drastic cyclical fluctuations due to the weather. This will also reflect the impact of the time span required for the growers to make decision covering planting and removal since tart cherry production involves a long term investment. In view of the six year span needed for the trees to bear fruit, the independent variables in the model were then lagged six years. In constructing supply and demand models for tart cherries, a series of regression equations were formulated. Statistical tests and evaluations of each estimated equation Ming-Wu Wu are conducted to measure the performance of the model, especially in coping with the statistical problems induced by the application of a distributed lag formulation. The constructed demand model was incorporated into the supply model together with two identity equations to facilitate future predictions. Before making the prediction, equations which resemble the future trends of each of the exogenous variables were estimated. Four alternative projections for future tart cherry acreages and price levels were made depending upon selected combinations of conditions. The predicted market outlook for Michigan tart cherries indicates that a gradual expan­ sion in tart cherry bearing acreage up to a total of around 44,600 acres can be anticipated by 1990, This increase, of nearly 20 percent over the current acreage level would mean an increase of 35 percent in the total production as indicated by the empirical analysis. The acreage adjustment, in response to changes in profitability is projected to be a continuous process. Attention must be given to the required capital, processing and storage capacity and other associated resources vital to achieve this successful adjustment. The study revealed that any policy towards an improvement in a yield higher than the projected rate of Ming-Wu Wu increase would require careful forethought in order to avoid a drastic upward shift in supply. Thus it would prevent a drastic drop in grower price and income, unless the industry seeks to stimulate the consumption of tart cherries and to develop overseas markets for cherries. The theoretical and the empirical analysis contained in this dissertation may be used as an important guideline towards successful production and marketing plans concering the more distant future. ACKNOWLEDGMENTS I wish to express my appreciation to those persons who have contributed to my education and to this thesis. I am immeasurably indebted to the Chairman of my Guidance Committee, Dr. Warren Vincent, for his judicious advice and Counsel in this and many other facets of my graduate program. Special appreciation is extended to Dr. John Ferris, serving as the Chairman of my Thesis Commettee, for his tireless assistance in the development and completion of this thesis. Moreover thanks are due to Dr. Donald Ricks for his helpful suggestions in the formation and preparation of the thesis; and to Dr. Stanley Thompson for his many valued suggestions. Special thanks are due to my wife, Chin Shang, for her constant encouragement and typing of the manuscript, and to my children whose understanding and companionship provided the inspiration necessary to the completion of this endeavor. TABLE OF CONTENTS Page A C K N O W L E D G M E N T S ............................. ii LIST OF T A B L E S ............................ vi LIST OF F I G U R E S ............................ viii LIST OF A P P E N D I C E S ......................... xi CHAPTER I. I N T R O D U C T I O N ...................... Need of the Study • • • • • • Objective of the Study • • • • Outline of the Study • • • • • II. TART CHERRY PRODUCTION IN THE UNITED STATES 1 2 3 4 6 Introduction • • • • • • • 6 Production and Utilization of Tart Cherriesl3 Tart Cherry Supply Control Through the Marketing Order .............. 20 Tart Cherry Crop Forecasting . . 25 III. SUPPLY RESPONSE MODELS FOR TART CHERRIES Analytical Models • • • . • • Geometric Lag Models . . . . Adaptive Expectation Model . Partial Adjustment Model . . Polynomial Lag Model . . . . Simple Model... .................. Testing of theSupply Response Model IV. EMPIRICAL RESULTS OF SUPPLY RESPONSE MODEL Geometric Distributed Lag Model • Coefficient of Adjustment . . Elasticities .................. iii 31 36 36 37 39 41 43 44 48 53 56 57 Page Polynomial Distributed Lag Model • • Summary • • • • • • • • • . V. DEMAND MODEL FOR TART CHERRIES . . . 64 82 86 Specification of Model ............. 86 Empirical Result and Analysis of the Model 88 ................... 100 Summary VI. PROJECTION OF THE EXOGENOUS VARIABLES . 101 Gross Margins of Growing Tart Cherries 101 Consumer Price Index ............. 112 Yield of Tart Cherries . . . . 105 Cost of Growing Tart Cherries . . 108 Gross Margins of Growing Apples . . 110 Yield of A p p l e s ....................... Ill Price of Apples Received by Growers . 115 Cost of Growing Apples . . . . 116 Gross Margin of Growing Sweet Cherries 121 Yield of Sweet Cherries . . . . 122 Price of Sweet Cherries • • • • 122 Cost of Growing Sweet Cherries . . 127 Population . 128 Carryover Stock of Tart Cherries . . 130 Per Capita Consumption of Frozen Apples 131 Per Capita Disposable Income . . . 131 Summary of the Model .................134 VII. FUTURE PREDICTIONS OF TART CHERRY SUPPLY AND DEMAND TO 1990 Price Predictions . Tart Cherry Gross Margin Predictions Acreage Predictions . Production Predictions ............. Impacts of a Higher Tart Cherry Yield on Production and Price Levels . . Stability and Supply Response . • VIII. 140 146 152 152 159 162 166 SUMMARY AND C O N C L U S I O N .................... 172 Summary of Study Implications • • • « • • • • • • • • iv • • • • 172 178 Page BIBLIOGRAPHY ......................... APPENDIX A - Geometric Model • • • 182 • APPENDIX B - D a t a ................ APPENDIX C - StatisticalResults APPENDIX D - Computational Methods v . 187 190 . , 198 • • 201 LIST OF TABLES Table 2.1 2.2 2.3 2.4 4.1 4.2 4.3 4.4 4.5 . 4.6 Page Number of Bearing and Non-bearing Tart Cherry Trees in the United States and Michigan, 1938-1974 ............................... 8 Commercial Tart Cherry Farms in Michigan and the United States, 1938-1974 . . . . . 10 Tart Cherry Production, Michigan and United States, 1938-1976 14 Percent Distribution of U.S. Disposition of Tart Cherries, 1938-1976 I8 Geometric Lag Models for Michigan Tart Cherry Acreage Response from 1938-1976 . . . . 54 Estimate of Short and Long-run Elasticities of Tart Cherry Acreage Response . . . . 59 Comparison of Observed and Predicted Acreage of Michigan Tart Cherries, 1949-1976 • . 62 Tart Cherry Gross Margin Distributed Struc­ tural Coefficients for Second Degree Polynomial • • • • • • 87 Tart Cherry Gross Margin Distributed Weights in Association with Other Selected Variables 74 Polynomial Distributed Lag Model for Tart Cherry Acreage Using Tart Cherry and Competing Fruit Gross Margins ............. 78 Table 5.1 5.2 6.1 7.1 7.2 7.3 7.4 7.5 7.6 Page Comparison of Estimated Demand Models for Michigan Tart Cherries • • • • • • • 9l Comparison of Observed and Predicted Tart Cherry Grower Prices in Michigan, 1955-1976 98 Alternative Projections <£ United States Population to 1990 • • • • • • • • 129 Future Price Predictions for Michigan Tart Cherries, 1977-1990 • • • • • • • • 147 Alternative Projections for Future Tart Cherry Gross Margins, Michigan, 1977-1990 . 153 Future Bearing Acreage, projections for Michigan Tart Cherries 1977-1990 . . 155 Future Production Predictions for Michigan Tart Cherries, 1977-1990 160 Comparison of Future Predictions Between Alternatives No. 3 and the Higher Yield Level for Michigan Tart Cherries, 1977-1990 163 Distributed Weights for Different Lag Periods vii 167 LIST OF FIGURES Figure 2.1 2.2 2.3 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 Page Index of Tart Cherry Production, Michigan and United States, 1938-1976 • • • • • 15 Relationship between Tart Cherry Production and Price, Michigan, 1945-1976 • • • • 17 Disposition of Tart Cherry Crop in the United States, 1938-1976 19 Adjustment Time Path for Tart Cherry Acreage in Michigan • • • • • • • 58 Actual Versus Predicted Tart Cherry Bearing Acreage Using Partial Adjustment Model . 63 Tart Cherry Gross Margin Distributed Weights . . • • • • • • • • 68 • Actual Versus Predicted Tart Cherry Bearing Acreage Using Tart Cherry Gross Margins Estimated From a Polynomial Lag Model • . 72 Tart Cherry Gross Margin Distributed Weights in Association with Other Selected Variables 73 Actual Versus Predicticted Tart Cherry Bearing Acreage Using Tart Cherry Gross Margins and Other Selected Variables Estimated from a Polynomial Lag Model • • • • • • • 77 Distributed Cpefficients for Tart Cherry Gross Margins and the Competing Fruit Gross Margins . . . . . . . . . . . 79 Actual Versus Predicted Tart Cherry Bearing Acreage Using Tart Cherry and Competing Fruit Gross Magins Estimated from a Polinomial Lag Model • • • • • • • • • . . si viii Figure 5*1 6.1 6*2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10 6.11 6.12 6.13 6.14 Page Actual and Predicted Tart Cherry Grower Price in Michigan, 1955-1976 • • • • • 99 Consumer Price Index Projected to 1990, United States • . . . • • ■ • • • 104 Yield of Tart Cherries in Michigan Projected to 1985 107 Cost per Acre of Tart Cherries in Michigan Projected to 1985 .......... ... 109 Gross Margins of Growing Apples, Michigan, 1950-1976 112 Yield of Apples per Acre in Michigan and Projected to 1985 114 Price of Apples per Pound Received by Growers in Michigan Projected to 1985 , . H 7 Cost of Growing Apples in Michigan Projected to 1985 119 Gross Margins of Growing Apples in Michigan Projected to 1985 . . 120 Yield of Sweet Cherries in Michigan and Projected to 1985 123 Price of Sweet Cherries in Michigan Projected to 1985 124 Cost of Growing Sweet Cherries Projected to 19 85 125 Grower Gross Margins of Sweet Cherries and Six-year Moving AverageProjected to 1985 • 126 Per Capita Consumption of Frozen Apples in the United States and Projected to 1985 132 Per Capita Disposable Income in the United States and Projected to 1990. . . . . 133 Figure 7.1 Page Average Farm Prices of Michigan Tart Cherries, Projected to 1990 « • « • • • • • 148 7.2 Alternative Projections for Future Tart Cherry Gross Margins, Michigan, 1977-1990 . , • 154 7.3 Future Bearing Acreage Prediction for Michigan 156 Tart Cherries, 1977-1990..... .............. 7.4 Future Prodiction Predictions for Michigan Tart Cherries, 1977-1990 .............. jf 161 LIST OF APPENDICES Page A.l Nerlove Expectation M o d e l ................... 187 A.2 Partial Adjustment Model 188 B.l Tart Cherry Statistics, Michigan, 1938-1976 B.2 Apple Statistics, Michigan, 1938-1976 • 193 B.3 Sweet Cherry Statistics, Michigan, 1938-1976 • 194 B.4 Population, Disposable income and Consumer Price Index, United States, 1938-1976 • • • • • 195 B„5 Tart Cherry Cost Items 197 C.l Second Degree Polynomial Lag Model of Michigan Tart Cherry Bearing Acreage Response . . . 198 (Figure) Distribution of Correlation Coefficients with Different Degree of Polynomial • • • 199 Simple Correlation Metrix for Variables in the Supply M o d e l ................ • • • • 200 Col C»2 C.3 D.l D.2 D 03 D.4 • • • • • • • • • • • • • • . • • • • 190 Simple Correlation Metrix for Variables in the Demand Model • • • • • 200 Calculations for Projection of Apple Grower Gross Margins, Michigan, 1977-1990 . • • • • • 201 Calculations for Projection of Sweet Cherry Gross Margins, Michigan, 1977-1990 • • • 202 • Calculations for Projection of Tart Cherry Gross Margins, Alternative No. 3, Michigan, 1977-1990 203 Calculations of the Long Run Dynamic Equilibrium Gross Margins • • • • • • • • • . . 204 xi CHAPTER I INTRODUCTION The total production of tart cherries in the United States was valued at about 36.2 million dollars in 1976, and 25,4 million dollars in 1975. Michigan is by far the leading tart cherry producing state, representing over two thirds of all tart cherries grown in the United States, followed by New York with about 10 percent and Wisconsin with 4 percent. From regional distribution, the Great Lakes states (Michigan, New York, Wisconsin, Pennsylvania and Ohio) accounted for over 90 percent of the nation's produc­ tion and the Western States (Colorado, Utah, Oregon, Washington, Idaho and Montana) accounted for the remaining 10 percent .1 Tart cherries are grown in strips of favorable climate, soil and topography. They do not tolerate exces­ sively low temperatures or high humididty during the growing season. In Michigan, tart cherries are grown in the western counties of the lower penninsula along Lake Michigan. ‘'‘USDA, "Fruit - Noncitrus: Production, Use and Value," Statistical Reporting Service (various issues). 2 Need of the Study Tart cherry production in Michigan and the United States is characterized by rather large year to year varia­ tions. These variations are very drastic as compared to those of apples, peaches or other fruit crops. year period In the 39 from 1938 to 1976, there were 7 years in which the national crop was either less than one-half as large or more than twice as large as the preceding year. only 12 There were years in which the crop varied between 80 percent and 125 percent of the preceding year.^ The greatest single factor causing variation of production is weather conditions.3 A widely fluctuating supply of cherries causes the price to fluctuate in the opposite direction, i.e., higher production, lower prices and vice versa. Such fluctuation also severely hampers the development of a stable market as well as expansion of the long term demand for tart cherries .4 Little can be done in the short-run to improve the situation of the annual variability of the size of tart 2 USDA, op. cit. (various issues). 3 Marshall, Roy E. Cherries and Cherry Products, Interscience Publishers, Inc., New York, 1954, p. 60. 4 Ricks,Donald J., "Fluctuating Cherry Supplies and Some Alternative Remedial Actions," Department of Agricul­ tural Economics, Report No. 144, Michigan State University, June 1969. 3 cherry crop due to the dominant impact of weather. However, reliable long term projections of supply response and demand upon uncertain market situations has assumed increasing importance in recent years in decision making. This allows growers and processors to adjust or change for planning production and marketing to meet the expected situations in years to come. Knowledge of tart cherry supply and demand is necessary for a better understanding of the economic problems in order to formulate and implement effective marketing and production policies, A greater knowledge of supply response can also help extension specialists provide improved infor­ mation to aid the farmer's decision. Therefore, it is of great importance to growers, processors and users of tart cherries to have good infor­ mation on the prospective position of the industry. This study will be focused on an analysis of factors affecting the tart cherry industry's position in respect to long term demand and supply. Objective of the Study The main objective of this study is to quantitatively investigate the relationships among market variables in the 4 tart cherry industry. Specific objectives are: (1 ) to describe the present and past trends of the Michigan tart cherry industry with particular emphasis on the institutional framework used to counteract the unstable market conditions, (2 ) to theoretically formulate and statistically estimate the supply response model of tart cherries to profit and non-profit incentives, (3) to construct a demand model for tart cherries at the grower level, (4) to predict future trends in tart cherry supply and demand. Outline of the Study Chapter II provides a basis from which to view the overall industry situation as well as a descriptive analysis of the current institutional measures used in counteracting the unstable tart cherry market conditions. Chapter III discusses a theoretical framework consisting of the selected econometric models as a basic tool for the analysis of supply response, and the empirical results of the analysis are presented in Chapter IV. Comparisons of the results estimated from alternative models are discussed in detail 5 along with an interpretation of the quantified economic relationships among variables in an attempt to provide a better understanding of their forces affecting future tart cherry demand and supply. Chapter V deals with the procedures utilized in formulating the demand model for tart cherries. cal results are also carefully evaluated. study of the exogenous variables. The empiri­ Chapter VI is a The historical trend of each variable is examined, and projections are made based on the historical indications as well as future prospectives, For variables with a large extent of future flexibilities, alternative functional relationships are constructed to facilitate future predictions of tart cherry demand and supply. Chapter VII presents projections of the tart cherry prices, acreage and production levels for 1990, Several alternative projections are made to delineate the upper and lower boundaries. An assumed higher rate of growth in tart cherry yield is also incorporated in the projection analysis so as to evaluate consequences of this possibility. Chapter VIII, the last chapter, presents the summary and conclusions. CHAPTER II TART CHERRY PRODUCTION IN THE UNITED STATES INTRODUCTION According to the Agricultural Census, cherry produc­ tion in the United States started in the late 1800's. Historical data for cherry production, particularly on number of trees and acreage information are not as complete as would be desired. Prior to 1938 the census did not dis­ tinguish between tart cherries and sweet cherries. Tart cherry growing is a very specialized business and production is concentrated in a few favorable areas determined by special climatic and topographic features. Cherries are sensitve to weather conditions. The spring temperature should remain cool to retard fruit bud develop­ ment in order to minimize danger of damage due to spring freezes. During the pollination-fertilization period of bloom, temperatures should exceed 8 °C in daytime for bee activity and should not drop below - 2 ° C to -l^C for any period of time to previent freeze damage. The desirable site would be one with fairly uniform slope and well-drained 6 7 water and air flowage ways.^ The trends of tree population in Michigan as well as in all other states are shown in Table 2.1. The number of tart cherry trees increased rapidly in the early 1940's. Information on annual new plantings has never been estimated. The total number of trees in the United States increased from 4.9 million trees in 1940 to a record of 7.4 million trees in 1959, with a decline to 5.7 million trees in 1969. In Michigan, the total number of trees increased from 2.3 million trees in 1940 to a peak with 4,2 million trees in 1964, then they declined to about 3.7 million trees in 1974. The ratio of bearing trees as percent of all trees increased steadily since the 1950's. The ratio was about 86 percent in 1969 and currently it is about 80 percent, reflecting a higher new plantings in recent years. The number of tart cherry growers in the United States declined from the record high of 158 thousand growers in 1940 to 5,401 growers in 1969. In Michigan, the number of growers declined rapidly from about 29 thousand growers in 1940 to around 1,900 in 1974. However, the size of operation per farm has increased from less than one acre in e USDA, "Red Tart Cherry Site Inventory for Grand Traverse County, Michigan," Soil Conservation Service, 1971, p. 2 . 8 Table 2,1, Number of Bearing and Non-bearing Tart Cherry Trees in the United States and Michigan, 1938-74 United States Census Michigan Year Non-bearing Bearing Total Non-bearing Bearing Total 1,000 trees 4,874 2,267 NA NA a a 1945 NA NA NA 1950 1,690 3,977 5,667 907 2,176 3,083 1954 1,802 5,108 6,910 1,177 2,570 3,743 1959 1,428 5,951 7,379 723 3,357 4, 130 1964 1,086 5,644 6,730 700 3,748 4,178 1969 857 4,812 5,669 550 3,249 3,799 1974 a a a 755 2,970 3,725 Sources: a U.S. Census of Agriculture, Commerce, Census Bureau. Not yet published. 290 1,977 1940 NA U.S. Department of 9 1940 to an average of 20 acres in 1974 (Table 2,2). Like in many other highly competitive businesses, small cherry growers unable to take advantage of economics of scale, and efficiently compete with larger growers, have been forced out of business or absorbed into larger units of operation* Due to the change in the definition of commercial farms, the census data shown in Table 2,2 should be compared with care. The definition of a commercial tart cherry farm prior to 1954, was one with 80 or more trees. But for 1960, the definition was changed to a farm that had sales of products with at least $2,500 per year. Some decline in the number of tart cherry farms from 1954 to 1974 resulted from the change in census definition. According to the 1973 Michigan Fruit Tree Survey,^ there was a total of 2,252 growers operating 41,223 acres of tart cherry trees. Of the total acreage, about 42 percent was located in the northwest district of the State; 30 percent in the west central district and 26 percent in the southwest district. The remaining acreage of tart cherries, approximately 2 percent, was located in other districts. Unchanged from the 1969 census total, growers in 1973 reported 6 Wu, Ming W., "Michigan Fruit Tree Survey, 1973," Crop Reporting Service, Michigan and U.S. Department of Agriculture, August 1974. 10 Table 2.2, Commercial Tart Cherry Farms in Michigan and the United States, 1938 - 74 Number Farms of reporting tart cherry trees trees 1,000 Michiga n: 2,267 28,944 1940 Census Year NA Number of trees per farm Bearing trees as a percent of all trees Acres per farm (Bearing ag< Percent 78 NA 87.2 .87 NA NA 1945 NA 1950 20,091 3,083 153 70.6 1.50 1954 8,395 3,743 446 68.7 4.15 1959 6,348 4,130 651 81.3 6 .66 1964 4,797 4,178 871 83.2 8.46 1969 2,397 3,799 1,585 85.5 16.69 1974 1,942 3,725 1,918 79.8 19.52 United States: 157,564 1940 4,874 31 NA NA NA NA 1945 NA 1950 114,259 5,667 50 70.2 NA 1954 36,299 6,910 190 73.9 NA 1959 27,880 7,379 265 80.6 NA 1964 18,607 6,730 362 83.9 NA 1969 5,401 5,669 1,050 84.9 NA 1974 a Source: a NA a NA a a a U.S. Department of Commerce, U.S. Census of Agriculture, Washington, D.C., U.S. Government Printing Office, Various issues. Not yet published. 11 about 3.7 million trees of all ages, of which, about 17 percent were not of bearing age (less than six years of a g e ) . The density of tart cherry trees planted in Michigan averaged 92 trees per acre, with younger orchards having higher densities per acre. Of the total 2,252 tart cherry growers, over onefourth, or 627 growers operated less than 5 acres of tart cherries. This size group, from 1 to 4 acres, contained the largest number of growers, but accounted for only 3.4 percent of the total tart cherry acreage. operating 100 acres or more. There were 53 growers This size group contained only 2.4 percent of the growers, but accounted for over 20 per­ cent of total acreage. The average size of operation was 18.3 acres of tart cherries per grower. However, approximately 70 percent of the growers operated less than this amount. The survey also revealed that nearly all (99 percent) of the total trees were of the Nontmorency variety. The harvest of cherries was historically done by hand picking which induced higher labor costs. The adoption of mechanical harvesters during the 1960's rapidly replaced hand picking, and now nearly all commercial tart cherries in Michigan are harvested by mechanical harvesters. 7Project 80 & 5, Michigan State University, 1973. 12 As cherries mature and ripen on the tree they become progressively softer. Scald damage in cherries can become severe because of greater bruising during harvest plus compaction in the container. This is most critical on hot days as hot cherries accelerate scald which results from increase in temperature through respiration. Scald damage in cherries is the major cause of losses in harvesting cherries .8 Mechanical harvest reduces harvest costs and permits harvesting the crop in a given period of time at optimum maturity of processing. The use of the mechanical harvester can aggravate the scald problem, but with its associated innovations in cooling, handling, sorting, and processing methods through the use of water-filled pallet tanks and hydrohandling of the cherries, the scald problem has been held to a minimum. 8 Bolen, J. S., and B. F. Cargill, "Mechanized Harvest Systems for Red Cherries," Extension Bulletin E-660, Farm Science Series, Cooperative Extension Service, Michigan State University, June 1970. 13 Production and Utilization of Tart Cherries Tart cherry production in the United States averaged 111,589 tons per year during the ten years from 1967 to 1976, varying from a low of about 72 thousand tons in 1976 to a high of 152 thousand tons in 1969. The record high crop since 1938, the year that the tart cherry production infor­ mation was first separated from sweet cherries, was in 1964. That year the crop reached 226 thousand tons, while the record low was only 40 thousand tons experienced in 1943 (Table 2.3). Michigan's tart cherry production averaged 82,200 tons per year during the 1967-1976 period, and accounted for about 70 percent of the total U.S. crop. The production during this period varied from a low of 44 thousand tons in 1967 to a high of 107 thousand tons in 1972. The record high crop since 1938 was 150 thousand tons in 1964 and the record low was less than 11 thousand tons observed in 1943. Comparing the U.S. crop with the Michigan crop, it is easy to see that Michigan dominates the U.S. tart cherry crop (Figure 2.1). 14 Table 2.3 Tart Cherry Production, Michigan and United States. 1938 - 1976 United States Michigan Production Index Production Index of value 1960=100 of value 1960=100 Tons Tons 23.8 1938 63,000 19,000 54.4 48.0 38,400 65,960 1939 82.8 57.0 103,480 1940 45,600 89.3 34.6 1941 27,700 79,700 68.8 58.1 1942 104,040 46,500 89.8 13.5 1943 10,800 40,280 34.8 62.5 1944 50,000 112,200 96.9 17.5 1945 14,000 45,650 39.4 75.6 1946 60,500 116,010 100.1 61.9 1947 49,500 90,380 78.0 86.3 1948 69,000 131,790 113.8 75.6 1949 60,500 108,290 93.5 121.3 97,000 1950 155,240 134.0 93.8 1951 75,000 148,060 127.8 74.4 1952 59,500 109,650 94.7 95.0 1953 76,000 131,490 113.5 60.0 1954 48,000 106,320 91.8 88.8 1955 71,000 149,070 128.7 68.8 1956 55,000 99,040 85 .5 111.3 1957 89,000 146,670 126.6 61.9 1958 49,500 103,410 89.3 107.5 1959 86,000 137,958 119.1 100.0 1960 80,000 115,840 100.0 111.9 1961 89,500 164,670 142.2 138.4 1962 110,700 166,655 143.9 46.3 1963 37,000 69.7 80,790 187.5 1964 150,000 225,923 195.0 133.8 1965 107,000 161,414 139.3 68.1 1966 54,500 89,496 77.3 55.0 1967 44,000 88,990 76.8 125.0 1968 100,000 137,654 118.8 132.5 1969 106,000 152,230 131.4 98.8 1970 79,000 118,990 102.7 111.3 1971 89,000 139,260 120.2 133.8 1972 107,000 134,180 115.8 72.5 1973 58,000 87,020 75.1 128.6 1974 103,000 114.2 132,300 113.8 1975 91,000 123,070 106.2 56.3 1976 45.000 72,200 62.3 _ •« mj _ ^ * Source: Fruit-Noncitrus, Production, Price and Utilization, Statistical Reporting Service, U.S. Department of Agriculture, various issues. Year 15 Index 160 140 United States 120 100 Michigan 80 60 40 20 1940 45 Figure 2.1 Source: 50 55 60 65 70 75 (Four-Year Moving Average Based Upon 1960=100) 80 Index of Tart Cherry Production, Michigan and United States, 1938-1976. Fruits-Nonsitrus. Production, Price and Utilization. Statistical Reporting Service, U.S. Department of Agri­ culture, various issues. The long-run pattern of tart cherry production and market supplies has been that of a large crop followed by a small crop in alternate years. The more recent production, however, tends to have a four-year cyclical 16 variation of low production in two years followed by high production the next two years as shown in Figure 2.2. This cyclical nature of production is believed to be influenced by the weather conditions. With extremely favorable weather condition the production potential is great, but the hazards are usually equally as great with unfavorable weather condition. As demonstrated in Figure 2.2, the tremendous variability in production form year to year would naturally be expected to be a contributor to year to year price instability. The relationship between these two factors would be inverse, i.e., large crops generally brought lower prices, while small crops sold for higher prices. As shown in Table 2.4 and Figure 2.3 there has been a substantial change in the proportions of the tart cherry utilization. Canned cherries accounted for about 55 percent in late 1930's but declined rapidly to the present level of 32 percent with some interruptions during the war years. Tart cherries for fresh consumption also declined steadily from 22 percent to only 3 percent during the same period. However, frozen cherries have increased their share very rapidly, from 20 percent in late 1930's to the current level of about 64 percent. Cherries for other uses such as juices or wines, have declined from 3 to 1 percent during the same 17 Production 1,000 tons Price $/ton 700 ISO Production 125 600 100 500 75 400 50 300 25 Price 200 100 1945 50 Figure 2,2 55 60 65 70 Relationship between Tart Cherry Production and Price, Michigan, 1945-76 18 Table 2.4 Year Percent Distribution of U.S. Disposition of Tart Cherries, 1938-76 Fresh Canned Frozen 53.4 1938 28.6 14.5 21.8 57,4 17.7 1939 19.5 57.3 18.9 1940 1941 20.9 28.0 47.5 20.8 1942 58.0 19.1 34.8 31.4 32.6 1943 1944 48.6 17.3 31.5 55.5 19.8 1945 23.0 38.1 1946 12.6 48.2 14.2 44.8 39.3 1947 1948 10.6 51.4 35.3 54.1 11.7 32.9 1949 34.1 56.6 8.5 1950 33.8 1951 8.5 56.9 1952 9.3 61.3 28.9 46.6 1953 7.9 44.9 1954 9.2 49.3 40.7 39.4 53.2 1955 6.3 8.0 1956 44.7 45.9 48.4 1957 5.9 45.1 1958 7.7 46.5 45.1 5.4 51.6 1959 42.3 38.2 5.5 55.4 1960 1961 4.7 38.0 57.0 4.2 1962 50.6 44.2 1963 6.0 38.2 54.9 3.7 1964 51.6 44.7 1965 4.0 52.7 43.3 1966 7.4 41.0 51.6 1967 5.2 34.1 60.7 1968 4.2 35.2 60.6 3.7 1969 41.6 54.6 1970 36.4 5.1 58.5 1971 4.0 29.6 66.3 1972 35.8 2.3 61.9 1973 3.0 66.1 30.9 1974 1.7 61.4 36.9 1975 2.9 33.1 60 .6 1976 4.2 25.7 68.0 Dashes indicate insignificant quantity Sources : USDA, op. cit. (various issues) Other 3.5 3.1 4.3 3.6 2.1 1.2 2.6 1.7 1.1 1.7 2.7 1.3 0.8 0.8 0.5 0.6 0.8 1.1 1.4 0.6 0.7 0.7 0.9 0.3 1.0 0.9 — — a* — — 3.3 2.2 19 period. These changes have partially resulted from the continuous advancements and innovations in the technologies of processing and handling cherries. Other reasons for the change include changes in taste and preference of the con­ sumers, Factors such as the increase in the consumption of pies and convenience foods, have contributed to the decline of fresh and canned uses and increase in the frozen forms. Percent 70 60 Canned SO 40 Frozen 30 20 Fresh 10 Other 0 1940 Figure 2.3 45 50 55 60 65 70 75 Disposition of Tart Cherry Crop in the United States, 1938-1976 20 Tart Cherry Supply Control Through the Marketing Order The Tart Cherry Marketing Order was established and is based on the Agricultural Adjustment Act of 1933. This Act was amended by the Agricultural Marketing Agreement Act of 1937. The segment of the Agricultural Act of 1933 that is concerned with the Marketing Order are the laws covering the regulation of marketing through voluntary agreement from processors, associations of producers and other handlers of agricultural commodities or products, and the surplus disposal programs, The regulations that were enacted through the Agricultural Marketing Agreement Act of 1937 with respect to products have to do with the control of their quantity and quality. Also they deal with their rate of shipment to market in order to maintain the price of the products and hence the income of the growers at a reasonable level. The Tart Cherry Marketing Order was voted and passed by both the growers and processors of tart cherries in January, 1971. This Marketing Order allows the growers and processors of tart cherries in Michigan, New York, Wisconsin, Pennsylvania, Ohio, Virginia, West Virginia and Maryland to withhold part of the cherries from the market at any time, have it processed in acceptable saleable forms, and to store 21 and release it back to the market at expedient times.^ The growers in the western states, sharing about 10 percent of the nation's total of cherries, are not included in the order as of this time, because the cost of admini­ strating the order in that area may not be justified. Also, tart cherries sold by growers direct to retail customers or for fresh consumption are not included. The tart cherry marketing order is run by a twelve member Board, called the Cherry Administrative Board. Six member of the Board are growers and six are processors. In addition to these twelve members, there is a non-voting chairman. The grower members are voted upon by the growers in their district, and the processor members are elected in the same manner. Since this is a federal order, the persons voted upon are presented to the Secretary of Agri­ culture, who then appoints them to be the members of the Administrative Board. Each member serves for a three year term, but is not eligible for more than two consecutive three year terms. The Chairman is recommended by the Board and appointed by the Secretary of Agriculture to serve for an indefinite period of time. The primary objective of the marketing order is to 9 Owen, Prank, "Red Tart Cherry Marketing Order," Fruit Grower News, November 1971. 22 xegulate the supply of cherries through the use of set aside^-0 provisions decided upon by the Marketing Board. The amount of cherries under the set aside program in a particular year can be handled in two distinct ways .*-1 One is to divert the cherries, to leave the cherries un­ harvested on the tree, and the other is to harvest the cherries and to store them in the reserve pool for sale at later time. The main control mechanism, use of a storage reserve pool, is designed to play an important role in stabilizing long-run supplies and thus prices of tart cherries. A fundamental idea is to remove some cherries from the market in years of excessively large crops to the storage reserve pool and release these pooled cherries when cherries are scarce, price are higher, and more cherries are needed to maintain supplies in the market place. As a result, it is intended that growers will get a higher return in the large crop years than without the Order and they will have more cherries to sell in short-supply, high-price periods. Set aside means to withhold cherries from the market for a certain period of time, or to leave a certain volume of cherries unharvested in order to strengthen price to the grower. “^Ricks, Donald J., "Economic of Storage and Partial Non-harvest Programs for the Tart Cherry Industry," Agricul­ tural Economic Report No. 150, Michigan State University, November 1970. 23 Through the application of this provision, supplies and prices will be stabilized from year to year. This greater stability is desirable from the view point of consumers, institutional buyers and food manufacturing firms who use cherries in their final consumer products. 12 A minor control mechanism which is included is to dispose of the excess option. cherries by means of the non-harvest This is the same as destroying the amount of cherries that are over-produced and is useful when the crop exceeds the processing capacity, or perhaps when the carryover stocks plus a previous reserve pool are very large. The decision to participate in the reserve pool is up to each individual grower. Some growers may not be able to afford to pay for the processing and storage cost. Some may envision the possibility of the future supply being large enough for the market so they may not see any advan­ tage to putting the cherries in the pool. The cost of carrying out the order is spread between growers and processors but not equally. The processors pay for the general administration of the Order in proportion to the volume of cherries each has handled. The growers pay for the reserve pool and all costs involved in diversion. TO Ricks, Donald J., "An Evaluation of the Tart Cherry Marketing Order," Dept, of Agricultural Economics, Michigan State University, 1974. 24 All costs are determined by the Board and are charged relative to the amount of participation. The benefits resulting from the administration of the Order have to date surpassed the cost. The tart cherry Marketing Order alone cannot solve all the problems of the industry. Many decisions which are made outside the scope of the Marketing Order may have a great impact on the marketing order and the industry. One of these is the forecasting of the anticipated size of crop. The official tart cherry forecasting programs have been carried out by the Crop Reporting Service of the USDA for many decades. The next section is designated for the presentation of the general procedures used by the United States Department of Agriculture in arriving at the forecasts. 25 Tart Cherry Crop Forecasting The Statistical Reporting Service (SRS) of the U.S. Department of Agriculture has the responsibility of collec­ ting and distributing the annual and current agricultural statistics. The two distinct functions of SRS are (1) forecasting of crop production from current crop conditions during the growing season, and (2 ) annual estimates of actual crop production. The term "forecast'' refers to expectations of what is likely to be accomplished at some time in the future, while the term "estimate" indicates a measure of accomplished fact, e.g., crop yields, and pro­ duction after tbe crop is harvested. It should be clearly understood that a forecast is made on the basis of known facts on a given date, assuming weather and other conditions during the remainder of the growing season to be similar to those experienced in past seasons. For tart cherries, the SRS issues a forcast of the size of a crop several months before harvest time. One of the most important price-determining factors is the estimates for mid-June, generally released on June 23rd. This fore­ cast is based on actual fruit conditions, while the mid-May 26 forecast is based on bloom conditions. In the past, the SRS based its tart cherry forecasts on reports from individual growers who evaluated their crops according to their normal and previous year's output. Frequently, the producers and others have differed signifi­ cantly with the official forecasts. The Marketing Order Administrative Board and many others make major marketing decisions based on the official forecasts. Thus, the mid-June forecast becomes a matter of dollars and cents as far as the tart cherry industry is concerned. An objective yield survey, designed to improve forecasting accuracy and thereby ease some of the grower's apprehensions, has been adopted for the forecasting of Michigan's tart cherry crop since 1972. Both the tart cherry industry and the Statistical Reporting Service had long sought the improved forecasting techniques which the objective yield survey provides. The objective yield survey involves a more direct and scientific approach then the conventional grower report­ ing method .*3 The survey is patterned after a special pilot study on tart cherry objective yield project conducted by 13 From the author's experience in participating in the crop forecasting programs with the SRS from 1972 to 1975. 27 the Statistical Reporting Service over a five-year period from 1958 to 1962* The first step of the objective yield survey is the selection of sample blocks and trees. More than 3,2 million tart cherry trees hug the long stretch of Lake Michigan shoreline from Benton Harbor to Grand Traverse Bay, However, only 300 blocks and three trees per block or a total of 900 trees are needed for the survey. In fact, only a small fraction of each of the 900 sample trees is used for survey purposes. Blocks of trees are sampled with probabilities proportional to the number of trees, which results in a self-weighted sample. According to the distribution of tart cherry trees in Michigan; about 41 percent of the sample blocks should be from the northwest district; 32 percent from the west central district; 25 percent from the southwest district, and 2 percent from other districts Under this method it is conceivable that growers with large orchards could be selected more than once. Enumerators were trained to make field observations during mid-April, Individual growers were contacted during late April and the enumerators again made observations in ^ W u , Ming W., 0£. cit, 4 28 early May. The first of four surveys takes place in mid-May before the peak of bloom. Bloom counts and careful observations on the stages of fruit bud development are made on a small section of 100 preselected trees. The primary purpose of the bloom survey is to obtain as precisely as possible the data during full bloom, as most of cherry droppage1^ occurs during the first 20 days after full bloom. The second phase of the survey occurs about midJune and is the most important one. on all 900 trees in the sample. A fruit count is made Field enumerators are divided into teams of two and are allocated only a single week to complete the counts. Limbs used in the bloom survey will be re-examined and counts made on the green cherries. help to provide data on fruit droppage. These counts will In addition, cherries on a small section of the preseleceted 100 trees will be stripped, counted and sent to special field laboratories for weighing and other testing. The number of cherries plus expansion factors and projected weight per cherry will determine yield per tree. 15 Such things as droppage and Natual droppage of unmatured small cherries. 29 harvesting losses are included in the calculation of the expansion factor. An indication of the prediction for the production of the State can be established by extrapolation by the number of bearing trees. It is at this time that SRS issues its official tart cherry forecast, based on the midJune phases of the objective yield survey. The third phase of the survey takes place shortly before harvest. A return visit will be made to 100 of the sample blocks and fruit counts will once again be taken. A few cherries will be picked for laboratory purposes. This phase of the survey is primarily to evaluate the fore­ casting performance, but is also to measure any further cherry drop. The fourth phase of the survey is completed not more than 5 days after harvest. Sixty blocks are used for counts of fruits left on the tree and also on a measured area of ground under the tree. The objective yield survey approach has improved significantly the accuracy of prediction in terms of short term crop forecast. The forecast for tart cherries is generally released approximately one week prior to the beginning of harvest, or some time around June 23rd each year. This improved forecasting method provides the industry with very important information for price 30 determination and the basis f o x that year's Marketing Order• CHAPTER III SUPPLY RESPONSE MODELS FOR TART CHERRIES With a perennial crop such as tart cherries, supplies available in a current period are influenced in part by p r o ­ duction decisions made six years ago. The study of supply response here is to start from identifying the variables or factors expected to influence the number of bearing acres of trees and the size of the crop. These variables then are to be incorporated into the empirical models. The list may not exhaust the totality of the variables, but the important variables expected to play a part in an explanatory role will be carefully examined. Tart cherry production does not start immediately after the trees are planted since the trees usually take at least six years to reach bearing age. Accordingly, the g r o ­ wer's production response to prices of tart cherries is d e ­ layed by the lag in production. This lag is indicated by the time span between the decision to produce and actual produc­ tion. The trees will need another ten years or so to attain their full production potential and the life expectation of 31 32 the trees may last as much as 30 years depending on the c u l ­ tural practices applied. The expected returns from tart cherries are spread over a long time span; hence, the r e l a ­ tionship of supply response in tart cherries differs from that of annual crops such as corn, wheat or other field crops To construct supply and demand models for tart cher­ ries, a series of regression equations were formulated. The empirical results were evaluated and compared among s e ­ lected models. In this study, "supply" is defined as gr o w e r Ts in­ tended output of tart cherries rather than the actual q u a n ­ tity marketed. Hence the tart cherry supply is indicated by the product of the total number of acres that are of bearing age acre. (six years or older) and the average yield per The functional relationship can be expressed in three equations. The first equation is: Q t = A t x Yt (3.1) where, Q-j. represents output of tart cherries, at time t; A t is total number of bearing acres at time t; Yt is yield of tart cherries per acre at time t. This equation is a non-linear identity defining the annual tart cherry output. The second equation i s : 33 Y* = f(T) (3.2) This function indicates that the yield of tart cherries (Y"*") is a function of a trend variable (T). The third equation is a behavioral equation expla­ ining the determination of the total number of bearing acres. Due to the gap between farmers' response in tree plantings and the actual production, various distributed lag models are specified in the attempt to explain the b e a ­ ring acreage response. 11 kt - * $ The equation can be shown as: t 1 IX G «M 4t__. i , i| 1=6 i =6 variables, 11 £ < A t-1, I. other 1=6 i =6 ......et ) (3 .3 ) where, A t = Bearing acreage of tart cherries at time tj 11 1 11 t £ GMt-l 6 •? “ Sisc"y®ar moving average of gross margins i =6 per acre for tart cherries lagged six years from time (t-6 ) to (t-1 1 ); 11 1_ “ — c 2. GM t_^ = Six-year moving average of gross margins i —6 per acre for alternative competitive fruit crop, i.e., apples, lagged six years from time (t-6 ) to (t-ll)j A t-1 = Bearing acreage of tart cherries at time (t-1); a lagged dependent variable; 34 T = Trend variable* et = Error terms. Gross margins in this study receipts less total costs excluding are defined as total the payment to the manager on his money capital and for his managerial talents. If such payment to the manager is not realized the owner's resources and his managerial talents may be withdrawn and reallocated to some alternative line of production or enterprise. Total costs in this study are itemed in Appendix Table B. 5. Export of tart cherries as a proxy for market poten­ tial was not included in the models because the quantity of cherries exported averaged only about 3 percent of the total production each year and in most years were zero. Stock of tart cherries was also excluded because it seemed to be unimportant in affecting grower's tree planting decisions. The major competitive fruits for the acreage or site of orchards in the major tart cherry production states are sweet cherries, apples, plums, pears, peaches, asparagus, etc. The competition has been the profitability of growing tart cherries relative to other fruit crops, which is mainly determined by gross margins of each of the fruits per acre. The price variables were not directly used because 35 tart cherry production is characterized by long periods of gestation such that production does not directly respond to price changes. The typical response to rising prices is to plant more but when prices are falling, the supply falls as acreage is reduced, but only by small amounts as the growers expect the price to rise again in the future. For a perennial crop like tart cherries it is necessary to take into account the cost of production. The annual drastic change in tart cherry price is directly associated with the size of crops. Higher price do not necessarily mean higher gross margins to farmers as the increased return per unit resulting from higher prices is usually more than offset by the loss of smaller production per acre. Their gross margins depend on the price the growers receive, size of crop and cost of production. In this study gross margins are selected rather than prices as independent variables under the assumption that growers' decisions on tree plantings are made based on the gross margins. Another important reason to use the gross margins in the analysis is that cost is an integral part of the theory of production and hence supply theory, particularly in studying the long-run relationships. Emphasis is therefore placed on the gross margins which include cost considerations. It has generally been observed that for perennial 36 crops, growers' planting and removal decisions are based on observations covering a time span longer than one year. Therefore, six-year moving averages of gross margins are applied in an attempt to cover the decision period as well as to reduce cyclical variation. It should be noted here that using the bearing acreage as the dependent variable in the supply equation gives alternatives for testing various levels of yield for the production because supply or production is composed of acreage and yield factors as shown in Equation (3.1). Fur­ ther discussion on this will be presented in the projection chapter. Analytical Models Alternative formulations of regression models selected for tart cherry supply response are as follows: Geometric Lag Models Geometric lag distribution is the most popular form of distributed lag Models. Of the geometric lag models there are many submodels, namely: model, (a) adaptive expectation (b) partial adjustment model, (c) compound geometric model, and (d) two expected variable model, etc. In this study, the first two models are chosen because of their 37 simplicity of estimation since only one lagged dependent variable is involved, and both the long-run and short-run relationships can be estimated. Another reason for choosing these two models is that the results obtained from both models are essentially the same; they differ only in the assumption of the error terms, (1) Adaptive expection model: This model is characterized as: A^ = a + + et (3.4) * where, A^ is the bearing acreage at time t and Pt represents the expected price at the same period, and et is an error term. The following relationship is postulated by Nerlove ?-6 Pt - P?-l B (1 “ A ) (pt-l - P?_i) (3.5) Neither planned output nor expected price can be observed. Planned output is represented by the proxy vari­ able of planted acreage which is of bearing age. price is eliminated from the estimating equation. Expected The ex­ pected price is represented by the previous year's price and the expected price in the same year. This indicates 16 Nerlove, M., "The Dynamics ofSupply Estimation of Famer's Response to Price," The John Hopkins Press, Baltimore, 1958, pp. 236-242. 38 that the change in the expected pxice or gross margin is determined by some fraction of the forecasting error of the previous year's prices or gross margins. From equations (3,4) and (3.5), the following f u n ­ ctional relationship is derived: A t = Kq + + A A t _! + E t (3.6) where, Kq = a (1 - A ) % = b (1 - A) Et = et - Ae-t-1* and (1 - A) = the coefficient of expectation adjustment. The condition 0 < (1 - A) < 1» holds when growers make "in­ complete" adjustments for their mistakes, due mainly to their having incurred fixed costs. Koyck uses a different assumption for the expected price. His assumption is based on the concept that current expectations are derived by modifying previous observations or experience P * = (1 - A)(Pt .! + AP-t-2 + A 2P t _3 + — Manipulating equations ) (3 .7 ) (3,4) and (3.7), the following eq u ­ ation is derived: A t = a(l - A) + b(l - A)Pt-i + A A t-1 + e t - A©t-1 17 See computation in Appendix A.I. 39 Substituting Kg for a (1 - A) , for b(l - A) » and Et = (et " Aet-1) A t = *0 + V t - l + * A t-l + E t This result is essentially the same as Nerlove's 18 expectation models The coefficients a and b of Equation (3.4), and the long-run elasticities can be derived from the relationships among Kg, (2) and A. Partial adjustment model: Partial adjustment or habit persistence model assumes that it is only partially feasible to bring the actual level of acreage ring any one period. to the desired level of acreage A * d u ­ This "partial adjustment" results from technological constraints, institutional rigidities and growers' persistence of habits. This model can be denoted a s : (3.8) A t “ A t -1 = r (A t ' At-l) (3.9) 18 See the demonstration by Kraenta, J. in his Elements of Econometrics, the Macmillan Company, New York, 1971, pp. 474-476. 40 where, * is desired level of acreage at time t P-t-i represents previous year's price A t is actual level of acreage at time t A t -1 Previous year's actual level of acreage r is the supply adjustment coefficient, and 0 r 1, The value or r lies between 0 and 1 and means that * the adjustment of A^ to A-t is incomplete in any one period. If r equals 1, the adjustment is completed in one period, whereas if r equals 0 , there is no adjustment toward the desired level. From equations (3 .8 ) and (3.9) we obtain a new equation as:*^ A t - ra + rbPt_i + ret substituting = ar K 1 = br K3 = (1 - r) E t = ret Thus A t = Kq + KiPt,! + KgAt + Et (3.10) Comparing the price or gross margin expectation model and the partial adjustment model we may notice that in determining the expected levels of the explanatory vari­ 19The manipulation is presented in appendix A.2. 41 able the former model incorporates the past experience, while the latter takes into account the technological and institutional constraints and farmer's persistence of habit. Polynomial Lag Model The polynomial lag or so-called Almon lag technique is used to estimate the nature of the distributed lag struc­ ture that follows a polynomial of a given degree. The g e ­ neral functional relationship can be expressed as: A t = a + b(w1Pt_1 + w2Pt_2 + --- wnPt_n ) + other variables + Et (3.11) where, w^'s are the weights of the lagged variables and constrained by w0 = °; wn+1 = 0 Assume the parameters of w^ are rQ, r^, ---- rk such that w i = rQ + rji + r2i2 + r3i3 + ---- + rk iR where, i - 0, 1 , polynomial. n; K < n , and K isthedegree of the By transforming Equation (3.11) and using gross margin notations At = a + b ((r0 + r x + r2 + ---+ rk )GMt _1 42 + (r0 + 2rx + 22r2 + ----+ 2krk )GMt_2 + — + (rQ + nrjL + n2r2 + ----+ nkrk )GMt _n ) + other variables + E^. The hypothesised model for the polynomial lag can be simplified as: T At - K + b(iJ6WjLGMt_i) + other varialbes + E t (3,12) where, A t = bearing acreage of tart cherries K = constant - lagged variables (prices) from time (t-6) to (t-T), where T is the length of lag structure. E^. = error terms In this analysis the variable, gross margins per acre, is used to replace the price variables in the equation. The first lag variable start from (t-6) because six years are required for the trees to reach the bearing age. To formulate the model, there must be a prior spe­ cification of the degree of the polynomial. In addition, the lag structure can be vestricted to either start and/or end at zero. To select the degree of polynomial, one should try several degrees of polynomial and then compare the distri­ bution of the estimated coefficients. The distribution 43 of the estimated coefficients should be compatible with the behavior of the forces which the study seeks to measure. If the shapes of the coefficient distribution among different degrees of polynomial appear to be similar, the lower degree polynomial should be considered because the higher degree of the polynomial gives fewer degree of freedom, In general, selection among second, third, and fourth-degree polynomial seems to be quite appropriate. Four alternative restrictions can be imposed on the estimated lag structure, namely; (1) both the beginning and the last periods constrained to zero; period constrained to zero; (2) only the last (3) only the first period con­ strained to zero, and (4) unconstrained. Selection of this limit depends on the behavior to be measured. To determine the length of the polynomial lag(i.e.,n) it is advisable to try a range of different lengths and then consider the most appropriate lag length depending upon a priori expectations, the values of R2 , t statistics, and Durbin Watson tests. In this study the functional relation­ ship represented by Equation (3.12) will be estimated. Simple Model A simple lagged model is different from the distri- 44 buted lag models in such a way that no restrictions are placed on the coefficients of the explanatory variables. Generally, a time variable is used in place of the lagged dependent variable such as At = bQ + * 1 * 1 ^ + b2P?-l + b3T + ---- + et (3.13) One advantage of this type of model over the distributed lag model is its simplicity in estimation and interpretation. Estimating procedures of the above discussed models will include: (1) the ordinary least squares methods, and (2) Cochrane-Qrcutt iterative techniques. Cochrane-Orcutt techniques are useful in the estimation of the first order serial coefficient of the disturbances. These techniques can be used to correct for serially correlated residuals when the polynomial distributed lag model is estimated. Testing of the Supply Response Model The purpose of testing the model is to find out how accurately the model can explain observed behavior. By feeding the past values of the exogenous variables in the system and comparing the output of the model with those actually observed, an indication of model performance can be provided. 45 Each equation will be evaluated by the coefficient of multiple determination, consistency of signs, significance of coefficients, presence of autocorrelation, and Theil's inequality coefficient. One important step in estimating these regression models is to examine the feature of the regression distur­ bances, known as autocorrelation or as some econometricians 20 refer to it, the serial correlation. It implies that the correlation of the disturbance occurring at one point of observation is related to any other disturbance. This problem should be examined carefully in the case of equa­ tions estimated from time series data. The problem becomes more critical when dealing with the shorter interval of observations because the carryover effects of the distur­ bances become more severe. For instance, the effect of an irrigation to a crop at a point of time may last for several weeks until it finally dries out. But the shorter the time between each irrigation, the greater is the possibility of having carryover effects from one irrigation to the next. A problem in estimating the model is the presence of serial correlation. Serial correlation may arise because of an improper specification of the model or may be induced by the distributed lag formulation. 20Kmenta, o p . cit.. p. 269. If the error term 46 follows the standard assumptions, Ordinary Least Squares procedures may have consistent and asymptotically efficient coefficients. The Durbin-Watson statistics is generally considered to be an invalid indication of serial correlation when the lagged dependent variable is included as an independent variables.21 The problem with the application of the adaptive expectation model is the new disturbance, E^, may be cor­ related with the lagged dependent variable. In this case, the ordinary least squares estimates of the regression parameters will be biased, because the assumption that E^ is not correlated with any of the independent variables is being violated. Since the Durbin Watson test is not appropriate, other alternative estimating methods to correct the possible serial corelation should be explored. They include the Cochrane-Orcutt iterative (CORC) techniques, Hildreth-Lu (HILU) technique, First Difference Regression, or Maximum Likelihood method, etc. In this study the Cochrane-Orcutt iterative technique is chosen. 21Durbin, J., "Testing for Serial Correlation in Least Squares Regression when Some of the Regressions Are Lagged Dependent Variables," Econometrica, Vol. 38, No. 3, May 1970, pp. 410-421. 47 T h e i l ^ inequality coefficients 22 are also used to evaluate the forecasting ability of the estimated models. Theil's inequality coefficient, U, shows the relationship between the individual predictions (P^) and the actual values (A^) U (3.14) where, N represents number of observations. The coefficient U varies between 0 and 1. In general a lower value of U indicates a more preferable than a higher value. When U = 0, the model forecasts perfectly, or P. = A j , and when U = 1.0, the worst possible forecast JL * is obtained. 22Theil, H., Economic Forecasts and policy. NorthHolland Publishing Company, Amsterdam, Holland, 1965. CHAPTER IV EMPIRICAL RESULTS OF SUPPLY RESPONSE MODEL The model was constructed using annual data from 1938, the earlist available data relating tart cherries, to 1976; a total of 39 observations. The data series used in this study are listed in Appendix B. In the attempt to formulate the tart cherry supply response model, various functional relationships and estimation techniques have been applied. One of the major tasks in con­ structing the desired model is to cope with the statistical problems induced by the application of a distributed lag estimation. Statistical tests and evaluations of each estimated equation are then conducted. The results of the statistical test and evaluation suggest that the agreement of economic rationality and simplest is best. To measure the impact of growers' response to changing profit levels on tart cherry production, gross margin vari­ ables were used instead of the prices of tart cherries and other competing fruits in the supply equation. A response to a change in gross margins essentially will not take place 48 49 once and for all within a single year but is usually dis­ tributed over several years due to growers' habit persis­ tence, adjustment lags, uncertainty, resource constraints and or other factors. One means to take into account such response was to apply a moving average of the relevant in­ dependent variables. Another means to measure such effects was to use the lagged dependent variable as an independent variable, and , of course, the third method would be to apply both approaches simultaneously. The data on the cost of production were from the Annual Cost Account Reports of New York, published by the Department of Agricultural Economics, Cornell University. This is the only available data with respect to the cost of production since 1938. However, the report was used only as an indication because it is not applicable to average farms and has only a few cherry growers participating in the project each year. The New York cost account farmers have a large capital investment,, grow more crops, hire more labor and are more progressive than the average farmer. The averages, therefore, probably reflect the relative costs of moderately sized good farms only. This indicated the 23Carroll, Thomas F., "Background Information and Statistics for Fruit Marketing-Cherries", Department of Ag­ ricultural Economics, Cornell University A.E. 662, Ithaca, New York, March 1948, p.43. 50 cost fox average faxms to be lower than that of the cost account farms. Cost of growing tart cherries in the New York Cost Account Reports were divided into three groups: costs, costs. (1) growing (2) harvesting costs, and (3) storing and selling The items included in each of these groups are shown in Appendix B Table B .5• Wright and Johnston2^ made a study relating to cherry production costs for 69 orchards in Michigan in 1943. The study revealed that the average cost was $146.00 per acre as compared to $193.00 per acre for the New York cost account farms in the particular year. This indicated that the cost of tart cherry production in Michigan was about 76 percent of the cost of New York cost account farmers. The ratio might change over time; however, for the purpose of this study it was assumed that the cost for average Michigan farms is about 80 percent of the New York cost account farms. Nonetheless in this study the "trend" of a factor was assumed to be more important than its absolute values. The average gross margins per acre were then computed based on this cost information. 24Wright, K. T., and Stanley Johnston, "Peach and Cherry Costs in Michigan," Department of Agricultural Eco­ nomics, Agricultural Experiment Station, Circular Bulletin No. 201, June 1946. 51 The gross margins per acre for tart cherries and for the competing crops used as independent variables were thus expressed as six-year moving averages in an attempt to capture the above impacts and to reduce the fluctuations in prices resulting from annual variations in production. If the annual cyclical effect due to the impact of weather is not removed, the variation in yields tends to obscure the nature of the supply response. Application of six-year moving average reduces ob­ servations by five. In addition, the use of independent variables which are lagged by six years further reduces the observations by six. As a result, the total number of ob­ servation is reduced from 39 to 28 for this study. However, for a time series analysis using the annual data, this is considered to be sufficient with respect to the number of observations. It would be desirable to estimate one function that respresents tree removals and another function that specifies tree plantings. Unfortunately, both the removal and plan­ ting data are not available at any level. However, in this analysis only the annual total bearing acreage is concerned. In other words, if the new plantings made six years ago (t-6) were greater than the removals made in the current year (t), then there will be an increase in the bearing 52 acreage in the current year (t), and vice versa for a de­ crease in the bearing acreage. Another factor that is also extremely complex to take into account is the age distri­ bution among trees. Yield varies with age of trees as well as locality, cultural practices and weather conditions, etc. To disentangle these effects is extremely difficult. None­ theless, it may be logical to assume that these yield factors remain a linear trend throughout the entire period. The first two sections of this chapter are to present the selected geometric models. The distinction between the adaptive expectation model and the partial adjustment model must be made clear. The adaptive expectation model is to reflect the importance of past experience in determining the expected values of the price or gross margin variable. The partial adjustment model reflects technological and institutional constraints which allows only a fraction of the intended acreage response or production response to be realized during a period. In the study both the Ordinary Least Squares and the Cochrane-Qrcutt iterative methods have been used for estimation purposes. Following are the discussion and examination of the results of the alternative schemes. 53 Geometric Distributed Lag Model According to Nerlove's model, planned output (repre­ sented by planted acreage) is a function of the price which growers expect to receive for their crop. In this study, the expected price is replaced by the gross margin of tart cherries per acre because the gross margin is used as a measure of profitability of tart cherry production. The growers' incentive in planting tart cherries is assumed to be motivated by the gross margins rather than by the prices the growers receive as discussed earlier. The production decision is made on the basis of a past price or profit performance. In other words, the growers' planting response can be expressed in the previous year's gross margins and the previous year's acreage. Accor­ dingly, those trees that reach bearing age the current year (t) were the result of the planting response made six years ago (t-6). These behavioral relations make it possible to estimate the relationship. The estimated results from the partial adjustment model, Equation (3.10), are as shown in Table 4.1. The results of Equations (4.1) and (4.2) are estimated by using the Ordinary Least Squares and the Cochrane-Orcutt iterative techniques, respectively. All signs of the regression Table 4.1 Equ­ Esti­ ation mation tech­ No. nique (4. ) OLS Geometric Lag C Models for Michigan Tart Cherry Acreage Response from 1938 to 19761 1 11 t l 11 =, A(t—1) T.Z (CJMt.i) i Z (GM?_i; • °x=6 i=t> 2.9886 .92953a (.0236) .00362a (.0008) 3.70482 .90954* .00306* (4. ) C0RC (.0316) (.0011) 11 sw Ms*'5"*-11 R2 -.00201b -,00358b (.0012) (.0021) -,00259b -,00304b (.0016) (.0022) R2 d.w. U h .993 .9922 1.43 .00773 1.59 .993 .9921 1.96 .00895 - ^The dependent variable is tart cherry bearing acreage at time t (At) in 1,000 acres. Figures in parenthesis are standard errors. Where, C = Constant terms; 11 — 6 X g m 3 . = Six year moving average of the gross margins of jth fruit per acre i=6 lagged six years from time t in dollars, expressed in real terms. (where, j=t, a, and sw for tart cherries, apples, and sweet cherries, respectively); A^ 1 = Previous yearb tart cherry bearing acreage; R2 = Correlation of multiple determination; R2 = Corrected coefficient of determination; d.w. - Durbin Watson statistics (not for precise indicator of autocorrelation as the lagged variable is on the right hand side of the equation); U = Theil's inequality coefficient; h — Statistic testing for the presence of serial correlation, evaluated as a t statistic; a = Statistically significant at the one percent probability level; b = Statistically significant at the 20 percent probability level. 55 coefficients are in agreement with economic rational„ The coefficient of tart cherry gross margins and the previous years' acreage in each of the equations are significant at one percent probability level, while the gross margins for the competing fruits, apples and sweet cherries, are significant at the 20 percent probability level. Equations (4.1) and (4.2) have similar R2 values at •992 and the Theil's inequality coefficients from .008 to •009. But the h statistic of Equation (4.1) indicates the presence of serial correlation at the 20 percent probability level. Equation (4.2) with serial correlation absent is preferred to Equation (4.1) to represent the partial adjust­ ment model for tart cherry acreage response in Michigan. Equation (4.2) indicates a one dollar per acre of tart cherry gross margin increase expressed in real terms resulting in a 3.1 acre increase in the tart cherry bearing acreage, ceteris paribus. Applying the current average yield of cherries per acre, at 4,700 pounds, a one dollar per acre increase in tart cherry gross margins will result in an increase of 14,570 pounds of cherries in the total tart cherry supplies. A one dollar per acre change in apple gross margins will generate an inverse change in the tart cherry acreage by 2.6 acres or 12,220 pounds of cherries per acre. A one dollar increase in the gross margins of 56 sweet cherries results in a 3.0 acre decrease in tart cherry acreage. The function also indicates that a one acre change in the previous year's tart cherry acreage change current acreage positively by .90 acres. The correlation of multiple determination .99 means that this function explains about 99 percent of the variation in tart cherry acreage. Coefficient of Adjustment The geometric model postulates that actual acreage 'ft (A-t) adjusts over time to the desired level (A^), and that such an attempt is only partially successful during any one year period. The possible explanation of this includes technological constraints, biological constraints, institu­ tional rigidities, uncertainty of long run profits and per­ sistence of habits, etc. It is interesting to see how many years are required for the growers to adjust their acreage to the long run equilibrium level and what is the shape or locus of the adjustment time path. According to Nerlove and Addision's adjustment formula25 (1 - r)ts .1 25Nerlove, M , , and W, Addision, "Statistical Esti­ mation of Long Run Elasticities of Supply and Demand," Journal of Farm Economics, Vol. 40, No. 1-4, 1958, pp. 861880. 57 where, r is the coefficient of adjustment and t is the number of periods required for adjustment and .1 indicates the adjustment made within ten percent of the desired level. The estimated coefficient of adjustment (r) from the selected partial adjustment model equals ,09041 indica­ ting that the growers require about 24 years to adjust to within ten percent of the long run equilibrium acreage.^6 The adjustment time path is shown in Figure 4,1, The verti­ cal axis shows the acreage difference between time t and (t-1) while the horizontal axis represents the time period. Elasticities As shown in Table 4,2, all gross margin elasticities are estimated at the respective means over the sample period. The elasticity of tart cherry acreage with respect to its gross margins derived from the two models presented above ranges from ,009 to ,010 in the short run and from .082 to ,108 in the long run. The estimated cross elasticities of tart cherries with respect to the apple gross margins ranges from -.003 26 Computation of t: + (1 - ,09041) x £ ,1 (.90959) % £ .1 t £ log(.l) / log(.90959) t £ 24.30 58 1.0 0 5 Figure 4.1, 10 15 YEARS REQUIRED 20 25 Adjustment Time Path for Tart Cherry Acreage in Michigan 30 Table 4.2, Estimate of Short and Long-run Elasticities of Tart Cherry Acreage Response* Equation Estimation Elasticities with respect to GM^t-6) Number Technique Short-run Long-run Short-run Long-run Short-run Long-run A (t-1) (4.1) OLS .01037 .10818 -.00306 -.03194 -.01340 -.13977 .91337 (4.2) CORC .00876 .08235 -.00394 -.03704 -.01137 -.10688 .90154 ^Estimated at means for the sample period, = Gross margins of jth fruit per acre lagged six years from time t in real dollars, (j=t, a, and sw for tart cherries, apples, and sweet cherries, respectively); + A t-1 = Previous year's tart cherry bearing acreage. 60 to -.004 in the short run and from -.032 to -.037 in the long run. The cross elasticity of sweet cherry gross margins is from -.0114 to -.0134 in the short run and from -.1069 to -.1398 in the long run. The estimated elasticity for each of the gross margins is very inelastic. This means the growers have a relatively insensitive response on tart cherry acreage with respect to the variation of gross margins. However, the long run elasticities, as is the case, appear to be slightly higher than the short run elasticities because some economic, institutional, behavioral and technical con­ straints which hindered the acreage adjustment in the short run are eased in the longer run. The inelastic response in the tart cherry acreage with respect to its gross margins may also be explained by the fact that growers are very careful in making their long term production commitments. For instance, when the gross margin is low the growers will not immediately reduce their acreage, rather, they tend to keep the variable costs at a minimum, and hope the profit will rise again in the future. The reverse is true when the profit is rising; the growers tend to wait and not to take immediate actions to expand the size of operation, because they suspect the profit may drop in the future. To visualize how accurately the selected model 61 (Equation 4.2), in an overall perspective, can reproduce the observed past, the observed values and the predicted values using Equation (4.2) are shown in Table 4.3 and in Figure 4.2. For the estimated acreage, each dot represents a six-year average centered on the years specified. By feeding the past values of the variables into the system and upon comparing the output of the model with those actually observed, a judgement can be made. Although the estimated supply model does not explain much of the year to year change in acreages, it does explain most of the long run variation in average levels of acreage that are of bearing age. For the estimated model, it can be concluded safely that the tracking ability and the reliability of Equation (4.2) are highly satisfactory. 62 Table 4.3 Comparison of Observed and Predicted Acreage of Michigan Tart Cherries, 1949 - 1976 Year_______ Observed Acreage_______ Predicted acreage 1949 1950 29,300 30,100 29,119 30,234 1951 1952 1953 1954 1955 31,300 32,200 33,500 34,800 36,300 31,083 32,568 33,572 34,846 36,295 1956 1957 1958 1959 1960 37,700 39,800 41,300 42,300 42,100 37,870 39,157 40,669 41,881 42,566 1961 1962 1963 1964 1965 41,900 41,700 41,000 40,600 40,100 42,377 41,863 41,424 40,874 40,558 1966 1967 1968 1969 1970 40,100 40.500 40,100 40,000 39,500 40,070 39,739 40,036 39,727 39,552 1971 1972 1973 1974 1975 1976 39,100 39,100 38,500 37,900 37,400 37,500 38,897 38,587 38,594 38,233 37,803 37,324 63 Acres 42,500r 40,000 37,500 35,000 32,500 Actual Bstimated 30,000 50 Figure 4,2, 55 60 65 70 75 Actual Versus Predicted Tart Cherry Bearing Acreage Using Partial Adjustment Model 64 Polynomial Distributed Lag Model In applying the polynomial distributed lag model, an a priori specification of the degree of polynomial with the constraints of the weight distribution must be selected. In order to select an appropriate degree of the polynomial, a second, third, and fourth-degree polynomial models were estimated. The results indicate that the distri­ butions of the estimated coefficients for the third and fourth-degree are nearly identical; both have skewed distri­ butions with near zero and small negative coefficients in the first three lagged periods. The lag coefficients for the second-degree polynomial appear to have negative and small coefficients in the first two lagged periods but are more symmetrically distributed over the entire lagged periods than other degrees of polynomial. A plot of the coefficients representative of the second, third and fourth-degree polyno­ mial is shown in Appendix C Figure C,l. In this study a second-degree polynomial was selected because: (1) the structure of the coefficient distribution was conceptually similar to other degrees of polynomial, (2) it has more degrees of freedom than the higher order polynomials, and (3) the distribution of 65 the coefficients seemed to be more compatible with the pattern of the cherry growers tree planting decisions. The selected constraint for the lag distribution is such that it forces the weights at the last period of the lag to be zero. This constraint is selected to reflect the growers1 behavioral characteristics which suggests that profits in some distant past period cease to influence their planting decisions in the present. The third specification is the length of the distributed lag. Since the length of the lag is not known in advance, several experiments with a range of lag length have been conducted. Some important criteria used for the selection of the length of lag are: how well the lag shape fits with economic theory, the associated R2 values, and the t-statistic of each lagged coefficient. When ordinary least squares methods were employed, the results appeared to have serial correlation errors and the R2 values were quite small. Appendex C.J. These results are shown in The equations were corrected for serial correlation, using a technique which combines the ordinary least squares and the Cochrane-Qrcutt iterative methods.27 27 Bronuyn H. Hall, "Time Series Processor," Version 2, Harvard Institute of Economic Research, Technical Paper Series, Combridge, Massachusetts, Dec. 1976. 66 The results were encouraging. From among the ten different lengths of lags estimated for Michigan tart cherry acreage response, the shorter distributions frequently have kinks with larger negative weights at the beginning period. For the longer distri­ butions this characteristic diminishes and a smooth and more symmetric curve is formed. As shown in Table 4.4, the R2 value of each estimate increases with the lag lengths, contributing more explanatory power to the variables. The R2 value reaches maximum at the lag length of 12 periods then declines as more periods are added. Of these estimates, the ones with 11, 12, 13 and 14 lag lengths appear to be equally good. There is not much difference among their R2 values; all exceed .99 and the structures of the lag shape conform with a priori expecta­ tions. The shape for lag lengths of 9 (from t-6 to t-14) through 14 (from t-6 to t-19) years are shown in Figure 4.3. The Durbin-Watson statistics for all estimates indi­ cate that the error terms may be autocorrelated except for those with lag lengths of 12 and 13 periods. The Durbin- Watson test indicates that the hypothesis of no serial cor­ relation for these two estimates should not be rejected at the .05 percent level of significance (d^=1.05, and du=1.33)• 67 Table 4.4, Vari­ able Tart Cherry Gross Margin Distributed Structual Coefficients for Second Degree Polynomial Length of Distributed Lag 9 10 11 12 13 14 15 C 39.5175 39.2804 38.9704 38.6388 38.3796 38.2022 38.0466 t-6 -18 -.00068 - .00063 -.00067 -.00057 -.00046 -.00026 -.00006 (1.S3) .00036 .00047 .00045 .00044 .00043 .00051 .00059 (1.43) .00116 .00113 .00132 .00133 .00126 .00116 .00115 (4.30) .00163 .00191 .00198 .00189 .00173 .00168 .00161 (6.10) .00196 .00185 .00224 ,00240 .00233 .00215 .00208 (7.01) .00258 .00180 .00231 .00222 .00257 .00242 .00235 (7.43) .00147 .00212 .00253 .00262 .00254 .00249 .00237 (7.64) .00087 .00167 .00225 .00248 .00250 .00251 .00243 (7.74) .00096 .00238 .00173 .00215 .00231 .00240 (7.80) .00098 .00163 .00196 .00217 .00224 (7.82) .00146 .00091 .00182 .00199 (7.83) Figures in parenthesis .00081 .00134 .00164 are t statistics .00073 .00120 -19 .00065 -7 -8 -9 -10 -11 -12 -13 -14 -15 -16 -17 R2 .9818 .9864 .9901 d.w. ,6771 .9891 1.2277 1.3617 1.4070 R2 .9804 .9854 Average2.3237 3,5742 t value .9893 .9918 .9912 .9909 .9902 4.8926 5.7797 5.499 .9907 .9893 1.1513 1.0848 .9900 .9885 5.5843 5.1665 6q c, Cjt«ilit ‘ °°2 S r •9< ,9*64 -*a ,9®aa\ -a "io °ose 'is '*4 n *90etf 4 Ocf T*tt Oh ***» C,°SS % *9iti *>i St*ihU*©cf Stflts 69 In view of the slight difference among their R2 values and close similarity of the lag shapes, selection among them becomes very difficult„ However, the one with the lag length of 12 seems to be the best by using the R2 criterion even though its value is only slightly larger than the other. The values of the t statistics for the lagged tart cherry gross margins range from 1.43 to 7.83 and average at S.7797, indicating the distributed lag coefficients for this function are quite significant, and the average t statistics indicate they are significantly different from zero at the one percent probability level. The lag coefficients of the selected 12 period (from t-6 to t-17) distribution is roughtly symmetric c e n ­ tered around the 12th lagged period, or six years prior to planting. The maximum degree of growers' response occurs within 10 to 13 lagged years. In all cases the grower's response started with negative, increasing steadily to a maximum and declining toward zero response at the end of the period. A plausible interpretation for the negative coeffi­ cient in the beginning period might be that growers tend to respond in a cautious manner. High gross margins stimulated plantings but high gross margins in the current period may 70 serve to warn growers of possible impending increases in production when the new trees reach the bearing age and result in low prices. The empirical evidence indicates that the growers tend to emphasize the gross margins 3 years to 6 years prior to planting seasons. They may be conservative in making plan­ ting decisions immediately after the change of gross margins. However, a discussion with the knowledgeable industry leaders in Michigan indicates that this might not seem to agree with the real situation. They feel that the weight distri­ bution should start with some positive value for the most recent year. The hypothesis is that growers tend to place heavier weight on responding immediately to the gross margins during the first 4 to 6 years and then decline rapidly toward the end of the period around 10 to 12 years. This would conform more to the geometric lag model than the estimated polynomial lag model. The estimated regression coefficients for the selected polynomial distributed lag model are represented by the following equation: A+ = 38.6388 - .OOOS7GMJ * + .00044Gm J - + .00126GM* 0 (1,531) (1.433)15"7 (4,298) + .00189GM* g + .00233GM* (6.104) (7,005) + ,00257GM^ (7.432)t‘11 71 + .00262GM+ 10 + .00248GM+ ,o + .00215GM+.14 (7.640) (7.744) " (7.797) + .00163GMj_15 + .00091GM^_16 (7.822) " (7.833) (4.3) R2 = .9918 d.w. = 1.3617 u = .0578 Figures in parenthesis are t statistics of the coefficients. GMt-i represent the gross margins of tart cherries per acre in time (t-i) in dollars per acre. The predicted and the actual acreage are depicted in Figure 4.4. As shown in this figure, the forecasting ability of Equation (4.3) is quite poor eventhough its R value exceeds .99. 2 Essentially this is due to high auto­ correlation resulting from specification errors. Equation (4.3) was expanded to include two other variables, one is the previous years acreage (At _^) and the other is the average gross margins of the competing fruits per acre (GM^!^). and sweet cherries. Competing fruits include apples The preliminary results of this esti­ mate are shown in Table 4.5 and are graphically demonstrated in Figure 4.5. Inclusion of the previous year's acreage and the average gross margins of the competing fruits reduce 72 Acres 42,500 40,000 37,500 35,000 32,500 Actual — Estimated 30,000 0 50 Figure 4,4, 55 60 65 70 75 Actual Versus Predicted Tart Cherry Bearing Acreage Using Tart Cherry Gross Margins Estimated From a Polinoraial Lag Model 73 Lag Coefficient 00200 00150 9932 00100 !2=.9934 \ 00050 14 -16 Figure 4,5, Tart Cherry Gross Margin Distributed Weights in Association with other Selected Variables 18 74 Table 4.5, Vari­ able C Tart Cherry Gross Margin Distributed Coefficients in Association with other Selected Variables Length of Distributed Lag 10 11 12 7.60927 19.5715 22.2498 .79333 .48569 -.00006 -.00020 -.00043 -.00072 t- 7 .00011 .00005 - 8 ,00053 .00066 - 9 .00082 .00112 -10 .00100 .00142 -11 .00105 .00157 -12 .00097 .00156 -13 .00077 .00140 -14 .00045 .00109 A t-1 <3M?-6 -15 .00062 -16 -17 .41447 (3.38) -.00017 ( .67) -.00063 (1.77) .00007 ( .27) .00065 (2.44) .00109 (3.55) .00141 (3.97) .00160 (4.14) .00166 (4.22) .00158 (4.25) .00138 (4.27) .00105 (4.28) .00059 (4.28) Figures in parenthesis are t statistics 13 22.1718 d.w. 32 21.4160 .41472 .43208 -.00018 -.00010 -.00051 -.00031 .00008 .00017 .00057 .00057 .00095 .00090 .00125 .00116 .00144 .00133 .00153 .00143 .00152 .00146 .00142 .00140 .00121 ,00128 .00091 .00107 .00050 .00079 -18 R2 14 .00043 .9934 2.45 .9926 Average 3.39 t value .9941 2.63 .9934 3.08 .9944 2.37 .9938 3.08 .9932 2. 20 .9924 2.47 .9930 1.91 .9922 2.43 75 possible autocorrelation errors as compared to Bquation (4.3), The selected equation is A t » 22.2498 + .41447At -1 - .00017GM? - .00063GM* (3.380) 1 (.669) t 6 (1,771) 6 + .00007GM* - + ,00065GM^-a + ,00109GM^_9 (.2708) (2.440) (3.545) + .00141GM5ln + .00160GMJ n (3,970) (4.140) + .00158GMI (4.250) + + .00166GM$_i2 (4.215) + .00138GMJ 1A + ,00105Gm J lq (4.267) (4.276)t“X5 .00059GM^16 (4.279) (4 4) R2 = .9944 d.w. = 2.3717 U = .0279 Figures in parenthesis are t statistics of the regression coefficients. where, = previous years bearing acreage of tart cherries, GM^_£ = average gross margins of competing fruits (apples and sweet cherries) in time (t-6) in dollars per acre. GM^_£ = gross margins of tart cherries in time (t-i) on dollars per acre. The value of the t statistics for the gross margins of tart cherries averages at 3.4, indicating the distributed 76 lag weights for Equation (4.4) are significantly different from zero at the 5 percent probability level. The forecasting ability of Equation (4.4), as graphically shown in Figure 4.6, also shows an improvement over Equation (4.3) and is more satisfactory. It is interesting to explore the growers1 response to the gross margins of competing fruit along with the gross margins of tart cherries over the distributed lag periods, 12 years. Again, this equation is estimated by means of the Cochrane-Orcutt iterative techiniques to avoid possible serial correlation errors induced by the lagged dependent variable. The results are shown in Table 4.6, The distri­ buted coefficients associated with the competing fruits are all negative, except for the one for thefirst period. The coefficient for the first period, as indicated by its tstatistic, is not significantly different from zero. The largest coefficient for tart cherry gross margins appears in the 12th lagged period which is the same period in which the competing fruit coefficient is at the low point. The distributions are also roughly symmetic over the entire distributed lag periods, higher coefficients for tart cherry gross margins are associated with lower coefficients far competing fruits as seen in Figure 4.7. 77 Acres 40,000 37,500 35,000 32,500 Actual - Estimated 30,000 50 55 Figure 4.6, 60 65 70 75 Actual Versus Predicted Tart Cherry Bearin Acreage Using Tart Cherry Gross Margin and Other Selected Variables Estimated from a Polynomial Lag Model 78 Table 4.6* Polynomial Distributed Lag Model for Tart Cherry Acreage using Tart Cherry and Competing Fruit Gross Margins (Equation 4.5) Regression Coefficients and t-values for: Time Period st» ^ t * P0Pt> CPIt» Qt» V T* et) For estimation purposes, price is considered here as a dependent variable. This is with the assumption that other variables affect the price of tart cherries, but they are not influenced by the tart cherry prices in return during the same period. It means that the farm price of tart cherries in a given period (Pt) is functionally related to 86 87 the total production of tart cherries sold in the United States during the same period (Q^), disposable income of consumers (PDIt), United States population (POP^.)y the consumer price index (CPIt), consumption of the competing product - frozen apples (Q^), carryover stocks of processed tart cherries from the previous year's crop (S^) as surplus cherries reflect the level of stocks which are to be added to the following year's total supply, tart cherry exports (Xt ), and time variable (T). Tart cherries are mostly canned or frozen for pies and other bakery products. The amount of tart cherries for fresh use, according to the Crop Reporting Board, USDA, accounted for just over 1 percent of the total production. Therefore, in this analysis, all tart cherries are con­ sidered for processing use. The coefficients of the demand model will be derived from annual data for the 22-year period from 1955, through 1976. The main reason for using the data covering this period is due to the fact that the utilization of tart cherries have formed more distinct patterns within this time period. As can be seen in Figure 2.3, a pattern of tart cherry disposition following a steady set of trends among all uses was formed in mid 1950's. The steady increase in the ratio of frozen cherries reflects the growing demand 88 for convenience food such as cherry pies. If a shorter period for data is used, the estimated model due to lower degrees of freedom may not adequately embrace some forces that prevail into the future and thus make the long term projections inaccurate* While if a substantially longer period is used some factors that were important in the past but are no longer important currently, will materially alter the results obtained. Empirical Results and Analysis of the Model The demand function for tart cherries has been estimated with measurements in natural logarithmic forms* The Cochrane-Orcutt iterative techniques are applied to estimate the coefficients to minimize possible serial correlation errors* The variable, United States population (POPt ), is not entered in the equation as a separate variable since all related explanatory variables are expressed in "per capita" (1,000 people) terms* The time variable (T) represents the taste and preference of consumers and the steady changes of other excluded factors over time, is being dropped because the variable of the consumer price index (CPI) carries strong trend impacts. The quantity of 89 tart cherries exported (Xt ) is also dropped from the equa­ tion because the historical data showed very insignificant quantities of tart cherry exports. The correlation matrix for the Michigan farm prices of cherries is shown in Appendix C, Table C.3. The simple correlation between the consumer price index (CPI) and the per capita disposable income (PDI) was •98, Inclusion of these two variables as separate measure­ ments will induce multicollinearity problems. However, multicollinearity problems in this study would not seem to produce serious damaging results because the major objective of this study is to construct a model for future projections. The simple correlations among other variables appear to be fairly low and should be of little concern to multicol­ linearity. It should be noted that the main emphasis in this analysis is first in forecasting future cherry price and production levels, and secondly, in analyzing the separable effects of the independent variables. An entry or deletion of a new variable should be determined to be based on theoretical grounds as well as empirical observations. If the empirical results contradict with the economic theory, the decision will be geared by the objectives of the study. The price, per capita disposable income, and the 90 value of the competing fruit (frozen apples) consumed per person are in current dollars. Production figures are defined as the total U.S. of crop having value which is the quantity sold or utilized. This is estimated by subtracting the quantities not harvested for economic reasons and excess cullage of harvested fruit from the total production, and using only net production as having value per capita (1,000 people) as the production variable. The empirical results of the estimated demand model, using Cochrane-Orcutt iterative techniques, are shown in Table 5,1, To evaluate the performance of the model, similar criteria as are used in evaluating the supply res­ ponse models will be applied. estimated r 2, These critiria are: (1) the (2) the statistical significance of the coefficients of each of the variables, (3) the conformity to economic theory by the signs or the directions of influ­ ences of each explanatory variable upon the dependent vari­ able, (4) the presence of serial correlation, and (5) Theil's inequelity coefficient. Of the six demand equations presented in Table 5,1 the first three equations are estimated with nondeflated values, and the second three equations with deflated values in an attempt to take into account inflationary changes in the economy. Table5.1, Comparison of Estimated Demand Models for Michigan Tart Cherries Equation Constant No. A . Nondeflat ed (5.1) Qt bt <4 CPI. t Pt-1 -1.91053 -1.22164a -.61837a -.02542h -,76869e .70083° (.7921) (.4946) (.1310) (.0926) (.2233) (5.2) 1.0770 -1.20663 (.1280) -.615483 .06251h*-.17527d (.1894) (.1738) (.0914) (5.3) -1.1848 -1.21783 (.1441) -.6300® (.1346) B. PDIt .1686f* -.6165® (.7644) (.2696) .3208 .6182° -.3417h* (.4756) (.1431) 2 R R2 d.w. U .963 .955 2.18 .0121 .961 .954 2.17 .0123 .928 .904 2.02 .0125 Deflated (5.4) 8.534 -1.076953 -,56883a (.1456) (.1120) ,29294d*-.61708b* (.3204) (.3673) .893 .874 1.91 .0159 (5.5) -7.199 -1.175833 -.600463 (.1263) (.0981) -,22374e 1.3421 (.27910) .750 .706 2.45 .0412 (5.6) 8.8008 -1.060253 - .605143 .28541e* (.1313) (.3386) (.1530) bv -.61375 -.0674g* .891 .864 1.89 .0160 (.39356) (.13031) The dependent variable is the grower prices of tart cherries (P^), in dollars per ton. where P.(._i = the grower price of tart cherries in Michigan in year t-1 in dollars per ton, the lagged dependent variable. t = tart cherry production of value (Total production less economic abandoment) in the U.S., in year t, in tons per 1,000 people. S* = Tart cherry carryover stocks on April 1, in the U.S., in year t in tons per 1,000 people (expressed in raw product equivalent). Qj. ~ Consumption of frozen apples in the U.S., in the year t, in pounds per 1,000 people (expressed in raw product equivalent). CPIt = Consumer Price index, in year t PDLf. = U.S. per capita disposable income in year t, in dollars. The figuxes in parentheses are standard errors of the regression coefficients Significant level of each coefficient: a = 1 percent; b - 10 percent; c = 20 percent d = 30 percent; e= 40 percent; f = 50 percent; g = 60 percent; and h = over 80 percent. x indicates the sign expectations. of the estimated coeffiecient is opposite to conceptual 93 The estimation procedure for Equations (5,2) and (5.5) must be explained here. The coefficients for the per capita personal disposable income in each of these two equations are adapted from previous studies made by Thompson and Butler,30 and Ricks,3* respectively. In this study, both equations are estimated in such a way that the pre-estimated variable with its coeffi­ cient is placed on the left hand side of the equation along with the dependent variable to compute the regression coefficients for other variables, such as: P* - K (PDI) = f(Qt, S|, Q»„ CPI, e ) where, K is the pre-estimated coefficient for the personal disposable income, After such a functional relationship has been estimated, the pre-estimated variable is then moved to the right hand side of the equation, such that Pt = St> C P I > + K

' CPrt-6 and Q\ = (A* . Y*) / POPt <7'1) (7.2) where, is the yield of tart cherries in year (t-6); ^t-6 variat>le cost per acre of growing tart cherries. Other variables in the equations are as defined in the preceding section. Equation (7.1) indicates the relation­ ship between the gross margins in the supply model and prices of tart cherries in the demand model. Equation (7.2) shows the relationship between the per capita consumption of tart cherries in the demand model and the bearing 142 acreage of tart cherries in the supply model. Tart cherry prices estimated from the demand model will then be used to eatimate the gross margins of the supply response model through Equation (7.1) . While the bearing acreage estimated from the supply model will be translated into quantities of tart cherries and hence per capita consumption of tart cherries through Equation (7.2). These equations are thus formed to recursively generate future predictions of price and production levels of tart cherries• An outstanding feature of the formulated model is the use of six-year lags in the exogenous variables which provides self generated predictions up to six years into the future. This corresponds to the reality of the cherry industry relative to plantings and future production levels. Another feature of the model is the capability of construc­ ting the time path of the independent variables projected from year to year. For example, the prediction of the tart cherry bearing acreage for 1977 relies upon the acreage in 1976 and the six-year average of the observed gross margins of tart cherries, and that of apples and sweet cherries from 1966 to 1971. The 1978 acreage can be generated from the predicted 1977 acreage and the observed six-year average of the gross margins for each fruit from 1967 to 1972. This process can be continued to predict 143 the acreage up to 1982 without having separate projections for the exogenous variables. However, as the recursive process continues, the possible errors involved in the projection may become cumulative and magnify into the more distant future as a result of the inclusion of the lagged dependent variable. As described previously, the selected model provides a fairly reliable description of the historical structure and variation of the tart cherry demand and supply. They do not consequently lend themselves to reliable future projections. To reflect the models' reliability for future projections, certain assumption underlying future possible outcomes must be made. There are numerous ways in which the projections can be made. The process can be greatly complicated with respect to the possible alternatives, and the results may be greatly diverse. Here only those alternatives will be selected that are most likely to occur under certain assum­ ptions. It is especially important with respect to the assumptions. Following are some of them that need to be emphasized: 1. No significant change in the present government economic policies would take place, 2. No maj'or deviation in the economic conditions, 144 such as wax ox depression would o c c u x , and 3. The future change in the economic magnitudes xelated to the pxoduction and consumption of taxt chexxies will xesult from presently operating causes. It should be noted here that the predicted price and acreage levels represent such levels that would be expected for normal or average crop years with normal weather conditions. The projected levels thus represent long term trends rather than actual levels observed in particular years. Actual price and acreage levels may differ from the projected long term trends due to fluctuations in weather and other uncontrollable random biological factors. Nevertheless, the projection of the prices and acreage of tart cherries considers a range of possibilities based on several selected alternatives. Variables that appear to be more certain as to their future trend, as discussed in the preceding chapter, have only one level of prediction. But those with special future uncertainties have alternative projections for their expected trends. The selected combination of these alternatives are as follows: Alternative 1 145 Disposable income: High projection, see Figure 6,13 Gross margins of apples: Remain at the current average of $51,928 per acre Population: Series C, see Table 6,1 Alternative 2 Disposable income: High projection, see Figure 6,13 Gross margins of apples: Trend downward, see Figure 6.7 Population: Series D, see Table 6,1 Alternative 3 Disposable income: Low proj'ection, see Figure 6,13 Gross margins of apples: Remain at the current average of $51,928 per acre Population: Series C, see Table 6,1 Alternative 4 Disposable income: Low projection, see Figure 6,13 Gross margins of apples: Trend downward, see Figure 6.7 Population: Series D, see Table 6,1 146 The mechanics of calculating the price and acreage predictions involve many steps: (1) Estimate the six year moving average of gross margins for tart cherries, apples and sweet cherries* (2) Plug the average gross margins es­ timated in (1) and the previous year's acreage into the supply model* (3) Compute the per capita (1,000 people) consumption of tart cherries from the predicted acreage along with the projected yield and population* (4) Insert the value obtained from (3) along with the projected values of carryover stock, consumption of frozen apples, consumer price index, and disposable income in the demand model to obtain tart cherry prices for each year* (5) Generate gross margins of tart cherries from the price obtained from (4) along with yield of tart cherries, cost of production and consumer price index, and repeat from step (1) for further predictions. Price Predictions As anticipated, a higher level of disposable income will bring about a relatively higher prediction in the price series* The predicted prices for each of the alternatives described above are presented in Table 7,1 and are shown graphically in Figure 7*1* 147 Table 7.1, Future Price Predictions for Michigan Tart Cherries, 1977 - 1990 Alternative 1977 No. 1______ No. 2________ No.3_______ No. 4 Dollars per ton 587.98 593.14 592.93 588.19 1978 496.39 488.57 495.78 487.98 1979 501.18 489.50 497.20 487.54 1980 505.29 493.54 500.94 489.29 1981 514.21 500.18 506.51 492.69 1982 525.26 508.73 513.13 496.98 1983 534.01 515.18 516.43 498.22 1984 540.23 519.01 516.26 495.98 1985 546.04 521.19 515.09 491.26 1986 551.81 522.34 512.16 484.74 1987 555.95 522.27 507.62 476.43 1988 559.08 521.75 500.60 467.04 1989 565.24 524.08 495.64 459.39 1990 574.94 529.73 493.41 454.45 Dollars Per Ton 600 Alternative No. 1 , 500 No. 4 400 300 200 100 1960i Figure 7.1, 65 70 75 80 85 Average farm prices of Michigan tart cherries, projected to 1990 1990 149 Note that the prices discussed here refer to current dollars. In all cases, the predicted prices for the first year (1977) all fall at or near $590.00 per ton. This is essentially approximately on the level being observed currently. However, the actual average price for the year will not be available until the end of the crop season. According to the model, this year's price is due mainly to the low carryover stocks from last year, because the 1976 crop was the record low during the past ten years. As shown in Figure 7.1, when the carryover stocks and other variables return to the projected "normal” levels, the price for 1978 drops about $90.00 dollars per ton to near $500.00 per ton. Alternative No. 1 includes both high disposable income and high population (Series C) together with the constant gross margins of apples. This alternative is a very "optimistic" view which provides the highest series of price predictions of all selected alternatives. It might be somewhat overly optimistic because of the inclusion of both optimistic projections for disposable income and population. The results show that the price increases steadily from $496,39 per ton in 1978 to $574.94 per ton in 1990. This projection delineates the upper boundary to the projection of future tart cherry prices. 150 Altexnative No. 2 involves the combination of high disposable income, low population (Series D) and a downward trend in the gross margins of apples. This alternative gives an intermediate level of projection. The predicted prices rise slowly from 1978 and taper off in 1988 then up slowly again and reach $528.00 per ton in 1990. The combination of lower population and capita disposable income appears to higher per result in a fairly stable level of prices. Alternative No. 3 differs from Alternative No. 1 in the level of personal disposable income, which is lower than that being used in Alternative No. 1. The result indicates the net effects of the change in income levels. As shown in Figure 7.1, the predicted prices rise moderately from 1978, reach a peak with $516.43 per ton in 1983 followed by steadily decreasing price levels toward 1990. In 19.90 the predicted price is $493.41 per ton, situated at slightly lower than the mean of all predicted price series. Comparing the results of Alternatives No. 1 and No. 3, the net impact on price levels form the change in disposable income is considerably large; from $574.94 per ton for high income level down to $493.41 per ton for low income level. A net decrease of $81.53 per ton can be realized resulting from using the lower income level. 151 Alternative No. 4 includes both low income and low population (Series D) and downward gross margins for apples. This is rather a "pessimistic" view in terms of the expected future situations. The projected prices make only a very small increase from 1978 toward a peak in 1983 with $498.22 per ton and decline relatively rapidly to $454.45 per ton in 1990. As it has been expected, Alternative No. 4 delineates a lower boundary to the projection of tart cherry prices as shown in Figure 7.1. Differences in predicted prices for the upper and lower boundaries amount to about $5.15 per ton in 1977, and slowly increase to about $120.50 per ton by 1990. The analysis suggests that the most likely predic­ tion appears to be either Alternative No. 2 or Alternative No. 3, or around the central part of the projected range. As mentioned previously, Yield is the major factor that causes the upswings and downswings in the production as well as prices. This situation is unavoidable in view of the fact that tart cherries are sensitive to uncontroll­ able weather conditions. Prices of tart cherries are deter­ mined by many factors but among them the quantity produced is one. 152 Tart Cherry Gross Margin Predictions As has been discussed in the preceding chapter, Tart cherry gross margins can be generated from one of the identity equations (Equation 7.1). The calculation procedure, using Alternative No. 3 as an example, is shown in Appendix O, Table D.3. The results generated from each of the Alter­ natives are presented in Table 7.2 and Figure 7.2. The projected levels of the real gross margin have almost the same trending pattern as the projected tart cherry prices; Alternatives No. 1 and 4 delineate the upper and lower boundaries,respectively. The projections show around $500.00 per acre in 1977 and drop substantially to $350.00 to $360.00 range in 1978. By 1990, the projected levels range from $330.00 to $356.00 per acre, with an average of about $343.00 per acre. Acreage Predictions The projections of tart cherry bearing acreage calculated from the model for each of the four alternatives described in the preceding section are shown in Table 7.3 and graphically presented in Figure 7.3. 153 Table 7.2, Alternative Projections for Future Tart Cherry Gross Margins, Michigan, 1977 - 1990 Alternative No. Year1 1 2 3 4 Dollars per acre 1977 503.50 497.18 503.24 496.92 1978 360.91 351.35 360.17 350.63 1979 348.74 334.95 344.05 332.66 1980 341.42 327.91 336.42 323.03 1981 341.61 325.80 332.93 317.35 1982 345.47 327.11 332.00 314.07 1983 347.66 327.01 328.39 308.42 1984 347.88 324.84 321.85 299.83 1985 348.27 321.51 314.94 289.28 1986 349.14 317.62 306.73 277.41 1987 348.71 312.90 297,32 264.16 1988 347.61 308.10 285.71 250.19 1989 350.01 306.61 276.63 238.41 1990 356.43 308.91 270.73 229.77 1 Data for 1972- 1976 are observed values. Dollars Per Acre 500 400 Alternative N o l _1_ No. 2 300 "' - - No . 3 200 100 1971 Figure 7.2, 75 80 85 Alternative Projections for Future Tart Cherry Gross Margins, Michigan, 1977-1990 1990 154 No. 4 " 155 Table 7.3, Year Future Bearing Acreage Projections for Michigan Tart Cherries, 1977 - 1990 Alternative ____________________________________________ No. 1 No. 2 No. 3 No. 4 Acres 1977 37,607 37,607 37,607 37,607 1978 37,767 37,767 37,767 37,767 1979 38,059 38,059 38,059 38,059 1980 38,360 38,360 38,360 38,360 1981 38,572 38,572 38,572 38,572 1982 38,860 38,860 38,860 38,860 1983 39,363 39,352 39,363 39,352 1984 39,981 39,972 39,980 39,972 1985 40,635 40 ,700 40,632 40,698 1986 41,354 41,510 41,352 41,504 1987 42,201 42,421 42,184 42,406 1988 43,097 43,378 43,064 43,350 1989 43,849 44,188 43,792 44,182 1990 44,541 44,936 44,450 44,854 Tousand Acres 50 45 40 > 156 35 30 1960 65 Figure 7.3, 70 75 80 85 1990 Future Bearing Acreage Prediction for Michigan Tart Cherries, 1977-1990 157 The predicted acreage for the first six years from 1977 to 1982 are generated from the observed data so that they all appeared to be the same for all alternatives, because the explanatory variables in the supply model are lagged six years. During the first six-year period the acreage rises fairly slowly, averaging about 250 acres per year, from 37,607 acres in 1977 to 38,860 acres in 1982, Beginning from 1983 the rate of increase accelerates to and maintains at about 750 acres per year. By 1990 all predicted acreage climbs to near 45,000 acres. All predictions appear to be very consistant with each other with very small deviations. The predicted levels for 1990 range from 44,450 acres from Alternative No, 3 to 44,936 acres from Alternative No. 2, each of which delineates the lower and upper boundaries, respectively. Alternatives No, 1 and No, 4 lie within the boundaries with Alternatives No, 4 slightly higher than Alternative No. 1, Alternatives No, 2 and No, 4 result in a higher series of acreage predictions, it would seem they are significantly attributable to the downward trend of the gross margins of apples, as these two alternatives contain downward trend of apple gross margins, and the tart cherry acreage is negatively correlated with this variable. 158 The result of this projection is somewhat higher than the one projected by Ricks,38 The exact difference between these two projections is hard to measure because Ricks projects the number of bearing trees based on the Agricultural Census data, while this study projects the bearing acreage based on the data published by the Michigan Crop Reporting Service, Ricks' projection reflects expected tree removals during the next few years because of (a) a high proportion of old trees, and (b) the damage that has occured to old trees from mechanical harvesting - particularly with the earlier machines. Thus, the major difference appears in the upturn point in the projected trends. The upturn point in Ricks' projection appears in 1980, four years later than that projected in this study but its rate of increase after the upturn point is faster and hence both projections may be expected to merge sometime around 1990, 38 Ricks, Donald J., "U.S. Cherry Plantings and Production Trends," Staff paper No, 77-55, Department of Agricultural Economics, Michigan State University, June 1977. 159 Production Predictions Tart cherry production can be generated from the predicted acreages by applying the relationship with annual tart cherry output, such as where, Q* is the annual output of tart cherries, A* is the predicted bearing acreage and tart cherries per acre. is the predicted yield of The calculated tart cherry output is shown in Table 7.4 and Figure 7.4. The output trend for each of the alternatives is exactly the same as the acreage trend because of the same yield pattern. The estimated output levels for 1990 range from a low of 120,265 tons from Alternative No. 3 to a high of 121,580 tons from Alternative No. 2, a total difference of only 1,315 tons. It should be emphasized that the pro­ jected output represents the level that would be expected for a normal or average crop year with nomal weather con­ ditions. 160 Table 7.4, Future production Predictions for Michigan Tart Cherries, 1977 - 1990 Year Alternative No. 1 1977 93,257 No. 2 No. 3 No. 4 Tons 93,257 93,257 93,257 1978 94,311 94,311 94,311 94,311 1979 95,700 95,700 95,700 95,700 1980 97,124 97,124 97,124 97,124 1981 98,330 98,330 98,330 98,330 1982 99,741 99,741 99,741 99,741 1983 101,715 101,686 101,714 101,686 1984 104,006 103,984 104,005 103,982 1985 106,414 106,584 106,405 106,577 1986 109,014 109,427 108,991 109,410 1987 111,981 112,563 111,934 112,525 1988 115,107 115,857 115,019 115,782 1989 117,876 118,788 117,724 118,654 1990 120,509 121,580 120,265 121,357 Production 1,000 tons 125 Alternative No. No. No. No. 100 2 4 1 3 161 25 1971 Figure 7.4, 75 80 85 Future Production Predictions for Michiaan Tart cherries* 1990 162 Impacts of a Higher Tart Cherry Yield on Production and Price Levels A n interesting phenomenon which appears to be quite important to observe is the response and impact upon prices and production due to yield changes. To demonstrate this, the yield of tart cherries is assumed to increase at a relatively higher rate than the predicted one as specified in Equation (6,3). The equation assumes that the yield will increase from the current average of about 2,5 tons per acre to 3,0 tons per acre in 1990 rather than 2,71 tons per acre as projected by estimated Equation (6,2), For the purpose of comparison, an additional alternative in the future price predictions is made in contrast to Alternative No, 3, This relatively higher rate of increase in yield of tart cherries is to replace the lower yield rate while all other variables are held at the same level as in Alternative No, 3, The results show that the projected prices of tart cherries are substantially lower. The predicted prices in 1990 drop from $493,41 per ton for predicted yield level to $406,65 per ton for higher yield level, a total decline of about $87,00 per ton. projected prices along with the projected acreage and production are shown in Table 7,5, The 163 Table 7,5, Comparison of Future Predictions Between Altervatives No. 3 and the Higher Yield Level for Michigan Tart Cherries, 1977-1990 Price Year No. 3 Higher Yield $ per ton Acreage No. 3 Higher Yield Production No. 3 Higher Yield Tons Acres 1977 592.93 586.86 37,607 37,607 93,257 94,047 1978 495.78 485.03 37,767 37,767 94,311 95,899 1979 497.20 477.74 38,059 38,059 95,700 98,100 1980 500.94 472.30 38,360 38,360 97,124 100,350 1981 506.51 470.25 38,572 38,572 98,330 102,384 1982 513.13 469.23 38,860 38,860 99,741 104,643 1983 516.43 465.15 39,363 39,372 101,714-*107,533 1984 516.26 458.23- 39,980 39,986 104,005 110,745 1985 515.09 450.56 40.632 40,629 106,405 114,087 1986 512.16 442.35 41,352 41,328 108,991 117,635 1987 507.62 432.52 42,184 42,143 111,934 121,573 1988 500.60 421.77 43,064 42,990 115,019 125,668 1989 495.64 412.88 43,792 43,673 117,724 129,343 1990 493.41 406.65 44,450 44,277 120,265 132,831 164 The associated impact of adopting a higher yield rate is a lower level of acreage response, projected at 44,277 acres in 1990 or 173 acres lower than that using the predicted yield level. The derived total output in Michigan for 1990 is 132,831 tons, a total of 12,566 tons higher than the predicted level of 120,265 tons. This indicates that the rate of decline in acreage resulting from higher yield will not be fast enough to offset the rate of increase in the total production. This is the major factor contributing to the substantially lower prices. Will the growers be better off from a higher rate of increase in yield? Assuming the costs per acre for the higher yield are exactly the same as those for the projected (lower) yield, the gross revenue generated from the predicted yield is $1,233.15 per acre in the year 1990. This compares favorably with the revenue generated from the higher yield at $1,219.94 per acre or a decline of $13.21 per acre. Evidently, the efforts to increase yield should be carefully evaluated. Clearly, the revenue would be even lower if the adoption of new techniques or methods for a higher yield would be concomitant with higher production and handling costs, which they will be, particulary for harvesting, storing and selling costs. The above analysis is just an indication, and might 165 not be the case if the incxease in yield would accompany favorable changes in othex factors such as lower production and handling costs, and or market expansions, etc. Those growers who are early adopters will probably gain from the adoption of the improved techniques or varieties for higher yields because they will likely be able to capture some profits before the price starts to fall. Other growers will likely suffer from lower prices than they use to receive after supplies increase. From the consumer's point of view, the lower market prices resulting from the increased supply may benefit them by enabling retail prices to be less for the cherries they consume. An increase in production may benefit cherry processors and marketers if such an increase in efficiency enables the industry to become more competitive in foreign markets. In summary, we can ask - what rate of increase in yield will be the most appropriate? This is not an easy question to answer since the answer will depend heavily on the costs of production, particularly those related to the new technologies, and the interrelationship among variables and market situations. However, a possible answer may hinge on further analysis on the level of the growers' gross margins. The analysis in the following section may serve 166 as an ovexall quideliene for answers to these questions. Stability and Supply Response Static economic theory suggests that in a competitive market an equilibrium is reached when the cost of production including depreciation and interest on investment is equal to the market price. At this point, the size of operations will remain unchanged over time. Further evaluation in the growers1 gross.margins in tart cherries should be of interest in exploring the empirical evidence in the current operation. This approach is essentially another way to examine the growers response to the changing profitability of growing tart cherries. In doing so, a polynomial distributed lag model will be constructed using the annual net change of bearing acreages as the dependent variable and the gross margins as the independent variables. Again the data are fitted to the polynomial distri­ buted lag model as specified previously. The results are shown in Table 7,6. The distributed lag length used ranges from six to twelve year periods. Of these alternative periods, the one with nine periods has highest R2 values, with .79. The estimated student t values of each period in this equation 167 Table 7*6, Distributed Weights for Different Lag PeriodsVariable Length of Distributed Lag a 9 10 £ 7 c -.01914 -.13703 -.13220 -.29663 -.17937 -.09658 .02367 t-6 -.00050 -.00049 -.00038 -.00031 -.00022 -7 .00027 .00031 .00021 -.00001 -.00004 -8 .00070 .00083 .00061 -9 . .00080 •00105 .00085 .00057 .00099 .00090 .00064 .00078 -.00046 -.00035 (1.16) .00006 .00016 (.51) .00062 .00038 (1.89) .00061 .00091 (2.54) .00074 .00105 (2.81) .00103 .00078 (2.94) .00085 .00072 (3.01) .00058 .00050 (3.05) .00034 -10 -11 -12 .00048 -13 -14 -IS 11 .00023 . .00011 .00040 .00022 .00052 .00030 .00058 .00036 .00059 .00038 .00053 .00036 .00041 .00032 .00023 .00024 -16 R2 d.w. 12 .00014 .7537 2.338 .7834 2.279 Tf2 .7446 .7754 Average t value .99266 1.73805 .7667 2.482 .7892 2.371 .7552 2.337 .7373 2.182 .7581 .7814 .7461 .7276 1.57534 1.94805 1.37943 1.02168 .7221 2.120 .7118 .64783 t t The dependent variable = (At - A ); degree of polynomial - second, and zero restriction = last period. 168 ranged from .51 to 3.05 and averaged 1.95, indicating that the estimated coefficients are significantly different from zero at a 10 percent probability level. The highest weight for the selected equation is observed in the (t-10) period, or five years prior to planting The functional relationship of the selected equation can be denoted as: AA| = -.296626 - .000457 GM*_6 + .00016 GM^_7 + .000618 GM^_8 + .000915 GM|_g + .001052 GM^_1Q + .001029 G m J + .00085 G m J ,0 t-ll + .000503 G M ^ -13 (7.1) where, AA^ means the net change of tart cherry bearing acreage in year t, which is the difference of bearing acreage between t and (t-1). The current y e a r ’s bearing acreage (A^) is deter­ mined by (1) the previous y e a r ’s bearing acreage (A^ ^), (2) new bearing acreage that was planted six years ago (At_^), and (3) current y e a r ’s removal of bearing acreage The relationship i s : A t s A t-1 + A t-6 “ Rt or, A t - A t-1 = A t_6 - R t In years when there is no change in acreage, then A t “ A t-1 “ 0 (Rt) . 169 So that = Rt From Equation (7.1), we can derive the long term equilibrium or the condition in which the tart cherry industry achieves its long term stability* One important condition to be maintained for that stability is when there is no expansion or contraction in the bearing acreage over the years while the growers' gross margins in each year are all equal. No expansion in the bearing acreage implies that the annual increase in the demand for tart cherries is equal to the annual increase in the yield of tart cherries. By inserting this condition into Equation (7.1), the calculated equilibrium gross margin is $63.52 per acre in real terms. In other words, the empirical results generated from Equation (7.1) show that a static equilibrium real gross margin of $63.52 per acre over an indefinite period would be required to stablize the industry. When this equilibrium point is maintained the new bearing acreage equals the amount of acreage removed in that year, such that t-6 t Gross margins must cover all costs with any remainder being the profit. When the long run equilibrium is reached the amount of profit is equal to the level required to keep the resources employed. Note that in this discussion gross margins are referred to in real terras and are defined as the 170 gross income less total costs, excluding the payment to the manager on his money capital and for his managerial talents. To equalize the projected gross margins generated from different yield levels to the one at the equilibrium level one could approximate when the industry would reach the long run static equilibrium. The projected gross margins generated from the two different yield levels are both considerably higher than the equilibrium level. This indicates that, ceteris paribus, the Michigan tart chery industry would not seem to reach the long run equilibrium in the foreseeable future. To derive the tart cherry industry's long run dynamic equilibrium, a few assumption with respect to the annual growth rate of related variables must be made. are: (1) the price of tart cherries, S percent, They (2) per capita disposable income, 8 percent, and (3) the United States population, ,8 percent. The remaining variables are assumed to be constant over time. Using the above assumptions together with the elasticities of each variable derived from the demand model, the annual increase in the tart cherry acreage ( A At) can be calculated. D.4. The calculation is shown in Appendix D Table The results show the annual change in tart cherry bearing acreage ( a A t) are 87.23 acres per year for the 171 projected yield level, and 37,88 acres per year for the higher yield level. Substituting the annual growth rates of acreage into Equation (7,1), the level of gross margins that is required to maintain the long run dynamic equilibrium can be derived. The results indicate that $82,20 of tart cherry gross mar­ gins per acre for the projected yield level, or $71,63 per acre for the higher yield level is required to achieve the long run dynamic equilibrium. From this empirical analysis, it could be concluded that the projected yield (lower) level would seem to require a higher gross margins ($82.20 per acre) to secure the long run dynamic equilibrium than for the assumed higher yield level ($71.63 per acre). CHAPTER VIII SUMMARY AND CONCLUSION This chapter is presented in two main sections. The first section describes the approaches used and the signi­ ficant aspects of the results. The second section presents the implications drawn from the findings. Summary of Study The main objectives of this study were to theore­ tically formulate and statistically estimate the supply response and demand for Michigan tart cherries with respect to price or profit, and non-price variables. This study identifies the cause and consequence of tart cherry growers' supply response during the period from 1938 to 1976. The process involves the construction of acreage response models, demand models and projection of the exogenous variables contained in the models. Projections of future demand and supply of tart cherries in Michigan were made to 1990. The analytical procedures and tools applied to develop the econometric models have been carefully chosen and are based on economic theory and the characteristics 172 173 of the industry. The selected models for empirical analysis include the geometric distributed lag models and the poly­ nomial lag models. For the geometric distributed lag models the adaptive price expectation and partial adjustment models formulated by Koyck and Nerlove were chosen for their simpli­ city and ease of comprehension. The variables used in the estimation of the supply response model were adjusted by applying six year moving averages to eliminate the cyclical fluctuations due to the weather. This will also reflect the impact of the time span required for the growers to make the adjustment. In view of the biological process for a tart cherry tree to reach the bearing age, the gross margins in the model were then lagged six years. The Ordinary Least Squares method and the CochraneQrcutt iterative techniques were applied. The Cochrane- Orcutt iterative technique is used in instances where presence of serial correlation errors. It is difficult to evaluate the performance of the model, and no single criterion can adequately provide that evaluation. However, there are several commonly used measures and their combined results may give a reasonably reliable indication of the model's performance. measures are: These (1) size of the calculated R2 , (2) conformity 174 to economic theory, (3) significance of coefficients, (4) Theil's inequality coefficient, and (5) the Dubin-Watson statistics* However, the Durbin-Watson test is not appro­ priate in instances where the lagged variable as an independent variable is used. Many important quantified relationships were derived from the results of the estimated models. The selected supply response model, as discussed in Chapter IV, indicates that the level of tart cherry bearing acreage in Michigan is a function of the gross margins of tart cherries; apples and sweet cherries, and last year's tart cherry bearing acreage. The estimated function explains over 99 percent of the variation in the growers expectations of eventual tart cherry output. The estimated coefficient of adjustment of tart cherry acreage indicates that the growers require about 24 years to adjust their acreage to within ten percent of the long run equilibrium level. For the polynomial lag models alternative length of lags were tried to examine the magnitude bution over the lagged periods. was found to be 12 periods. of weight distri­ The optimum length of lag The distribution of the weights was centered around six years prior to tree plantings. The model was expanded to include the grower gross margins of the major competing fruits. The results indicate 175 a roughly symmetrical distribution of weights over the selected 12-year period for both tart cherry gross margins and these of the competing fruits. These empirical results provide some information about the growers decisions between competing fruit growing enterprises. The estimated demand model indicates that the grower price of tart cherries is dependent on its own consumption, and consumption of the major competitve fruit-frozen apples, carryover stocks, disposable income and consumer price index. These independent variables explain about 96 percent of the variation in tart cherry prices. The demand model was incorporated into the supply model together with two identity equations to facilitate future predictions. Before making the prediction it was necessary to estimate equations which resemble the future trends of each of the exogenous variables. Projection of exogenous variables requires under­ standing of the past trends as well as special knowkedge about the future perspectives regarding each of the variables. Projections of some variables have been disaggregated into coraponenets in order to measure the various impacts under different conditions. For instance, the growers' gross margins were projected by using estimates of the functional relationship between the yield, price and cost of production 176 as a endogenous variable. If a variable appears to have a stable historical trend and a lower level of future uncertainty, course was represented by one equation. its future In contrast, alternative equations were estimated for those variables that are characterized as highly uncertain. Four alternative projections for future tart cherry acreages and price levels were made depending upon selected combinations of conditions. The predicted acreage levels for 1990 range from 43,782 acres to 44,936 acres, whereas, the predicted prices range from $454.45 per ton to $574.94 per ton. The generated total Michigan tart cherry production ranges from 120,265 tons to 121,580 tons by 1990. This compares to the current annual average production of about 90,000 tons, a total increase of about 35 percent from the current level. The projected tart cherry production and prices represent the levels that would be expected for a normal, or average condition and will not reflect the year to year fluctuations in response to weather variations. Since tart cherry production involves a long term investment, it will generally be the normal or average trend levels that will be the most important for decision making. In order to perceive the consequences of alternative 177 yield rate, an assumed higher rate of yield increase in tart cherries is tested in the future prediction. The assumed higher yield trend is to increase from the current average of 2.46 tons per acre to 3.0 tons per acre by 1990 in contrast to 2.71 tons per acre projected for 1990. The results reveal that, other things being equal, the efforts for bringing about a yield trend higher than the projected level will result in,as would be expected, lower grower prices and, hence, lower farm income (Chapter VII) . The principal aim of the discussions throughout this study is to present evidence that will give the leaders of the industry and policy makers enough confidence in the model actually to forecast with it. Another purpose is to facilitate the intelligent use and further application of the methodology for similar studies in other fruit crops in Michigan as well as in the United States as a whole. As discussed previously, Michigan has been the most important of the tart cherry producing states. As a result, production and price of tart cherries in the United States is heavily weighted by the production and price of those grown in Michigan. There are great similarities between the supply and demand patterns of Michigan and the U.S.; but the difference is in magnitude. It is realistic 178 to assume that the formulation of structual relationships that are based on Michigan data can be applied to the United States as a whole. Implications The market outlook for Michigan tart cherries indicates that a gradual expansion in tart cherry bearing acreage up to a total of around 44,600 acres can be anti­ cipated by 1990. This increase, which is nearly 20 percent over the current level of 37,500 acres would mean an increase of 35 percent in the total production as indicated by the empirical analysis. The acreage adjustment, in response to the changing profitability is projected to be a continuous process. Attention must be given to the required capital, processing and storage capacity and other associated resources vital to achieve this successful adjustment. The expansion of acreage may probably be made possible by an extension of the margin. An extension of the margin means to bring in new lands that are less suitable than that already under cultivation. Since the tart cherry crop is highly sensitive to weather conditions, a further expan­ sion of the margin of such land will increase its vulnerability 179 to uncontrollable factors unless the growers and the scientists counteract these influences. This would be done by means of improving technologies and by development of freeze resistant varieties. However, it appears that part of the additional land for tart cherries could come from the area currently occupied by competitive crops, possibly from sweet cherries since this crop has shown a sign of declining acreage due to high competition with the western states. It should be noted that an important factor that gears the rate of acreage adjustment is the availability of nursery stock. Nursery stock is usually planted one or two years prior to its sale. In addition, the trees will require an additional six years to reach the bearing age. The nurserymen would need to keep close estimates of the anticipated rate of growth in numbers of trees at least seven years in advance. A sudden expansion of orchards may be tempered by the availability of nursery stock. It is quite difficult for nurserymen to decide how many trees are needed without knowing the future prospects of the cherry industry. Following are basic guidelines that would assist the nur­ sery suppliers in making this decision. First, the nurserymen must figure out the annual 180 tree replacement rate required for the next year, or the one following based upon the life expectancy of tart cherry trees, i.e., the annual replanting rate will be 3.33 percent of the total trees if the life expectancy of these trees is 30 years.39 maintain This will enable the state's producers to approximately 16.67 percent non-bearing trees, if the life expectancy of trees is 25 years, i.e., a shorter life expectancy resulting from the application of mechanical shakers (harvesters). The annual replacement rate will be 4 percent of the total trees. In this case the ratio of nonbearing trees to the total will be 20 percent. Secondly, it is necessary to estimate the anticipated increase in the number of trees that will begin bearing 7 to 8 years from now, and to plant nursery stock accordingly along with those trees computed above. The annual Objective yield Survey program carried out by Crop Reporting Service, and the Market Order admini­ stered by the Cherry Administrative Board has improved the tart cherry pricing and supply control mechanism on a short term basis. However, the industry leaders and decision makers need also to be aware of market conditions, production prospects for tart cherries, and to have some concept of 39 1 Rate of annual replacement = ---- ■ Years of life expectancy x 100 181 the future demand for tart cherries in order to make satisfactory plans in relation to the more distant future. It is suggested that the cherry industry should emphasize the longer-term development of continuing markets for tart cherries based on the results of this study. The study revealed that any policy towards an improvement in a yield substantially higher than the projected rate of increase would require careful forethought in order to avoid a drastic upward shift in supply. This might result in declines in grower price and income, unless the industry seeks to stimulate the consumption of tart cherries and to develop overseas markets for cherries. There may be different views in the policy decisions in regard to the allocation of research funds, i 0e., a higher priority to for yield improvement, or market develop­ ment; or equal priority to both. Another implication drawn from the findings of this study is that the need for interdisciplinary studies covering subjects of economics, marketing, horticulture, engineering, etc., is needed. These studies would ultimately reduce the uncertainty confronting the tart cherry industry through improved comprehension of forces that will shape the market in the distant future. BIBLIOGRAPHY BIBLIOGRAPHY Almon, S., "The Distributed Lag Between Capital Appro­ priations and Expenditures," Econometrics, Vol. 33, No. 1, 1965. Boger, Lawrence, L., "An Economic Analysis of the Red Cherry Industry in Michigan with Special Emphasis upon Pricing," unpublished Ph. D. thesis, Department of Agricultural Economics, Michigan State University, 1950. Bolen, J. S. and B. F. Cargill, "Mechanizing Harvest Systems for Red Tart Cherries," Extension Bui. E-660, Farm Science Series, Cooperative Extension Service, Michigan State University, June 1970. Carroll, Thomas F., "Background Information and Statistics for Fruit Marketing-Cherries," Department of Agri­ cultural Economics, Cornell University, A.E. 662, Ithaca, New York, March 1948. Cornell University, "Farm Cost Account Reports," Department of Agricultural Economics, Ithaca, New York, (various issues) . Crop Reporting Service, "Michigan Agricultural Statistics," Michigan and U.S. Department of Agricluture (various issues) . Durbin, J«, "Testing for Serial Correlation in Least Squares Regression When Some of the Regressions Are Lagged Dependent Variables," Econometrica, Vol. 38, No. 3, May 1970. Ferris, John, and K. T. Wright, "The Status of Michigan Agriculture, 1976," Agricultural Economics Report No. 299, Michigan State University, 1976. Griliches, Zvi, "Distributed Lags: A Survey," Econometrica, Vol. 35, No. 1, January 1967. , "A note on Serial Correlation Bias in Estimates of Distributed Lags," Econometrica,29: 65-73, 1961. 183 184 Hall, Bronuyn H., "Time Series Processor," Version 2, Harvard Institute of Economic Research, Technical Paper Series, Cambridge, Massachusetts, December 1967. Kmenta, Jan, Elements of Econometrics. The Macmillan Company, New York, 1971. Johnston, J., Econometric Methods, Second Ed., MeCraw-Hill Book Co. Inc., New York, 1972. Marshall, Roy E., Cherries and Cherry Products. Interscience Publishers, Inc., New York, 1954. Michigan State University, "Project 80 & 5," Agricultural Experiment Station and Cooperative Extension Service, E. Lansing, Michigan, 1973. Nerlove, Marc., "Distributed Lags and Demand Analysis for Agricultural and Other Commodities," U.S. Department of Agriculture, Handbook 141, 1958. ________ , "The Dynamics of Supply Estimation of Parmer's Response to Price," The John Hopkins Press Baltimore, 1958. ________ , and W. Addision, "Statistical Estimation of Long Run Elasticities of Supply and Demand," Journal of Farm Economics, Vol. $0, No. 1-4, 1958. Owen, Frank, "Red Tart Cherry Marketing Order," The Great Lakes Fruit Growers News, November 1971. Ricks, Donald J., "An Evaluation of the Tart Cherry Marketing Order," Department of Agricultural Economics, Michi­ gan State University, 1974. ________ , "Economic of Storage and Partial Non-harvest Programs for the Tart Cherry Industry, " Agricultural Economics Report No. 150, Michigan State University, November 1970• ________ , "Fluctuating Cherry Supplies and Some Alternative Remedial Actions," Department of Agricultural Econo­ mics, Report No. 144, Michigan State University, 1969. ________ , "U.S. Cherry Plantings and Production Trends," Staff paper No. 77-55, Department of Agricultural Economics, Michigan State University, June 1977. 185 , and David Amon, "Tart Cherry Market Information and Price Analysis," Agricultural Economics Report No. 291," Michigan State University. Theil, Henri, Principles of Econometrics, Center for Mathe­ matical Studies in Business and Economics, The University of Chicago, John Wiley & Sons, Inc. 1971, , Economic Forecasts and Policy, North-Holland Publiching Company, Amsterdam, Holland, 1965. Thompson, Stanly R. and L. J. Butler, "Price Relationships for Apples and Tart Cherries," Staff Paper No. 77-41, Department of Agricultural Economics, Michigan State University, 1977. U.S. Department of Agriculture, "Agricultural Statistics," U.S. Government Printing Office, Washington, D.C., (various issues). ________ , 'Cold Storage Report," Statistical Reporting Service (various issues). . "Fruit-Noncitrus: Production, Use and Value,11 Statis­ tical Reporting Service, (various issues). . "Red Tart Cherry Site Inventory for Grand Traverse County, Michigan," Soil Conservation Service, 1971. U.S. Department of Commerce, "U.S. Census of Agriculture," Washington, D.C., U.S. Government Printing Office, (various issues). Wright, K, T. and Stanley Johnston, "Peach and Cherry Costs in Michigan," Department of Agricultural Economics, Agricultural Experiment Station, Circular Bulletin No. 201, June 1946. Wu, Ming W., "Michigan Fruit Tree Survey, 1973 Crop," Crop Reporting Service, Michigan and U.S. Department of Agriculture, August 1974. APPENDICES 186 187 Appendix A.l, Nerlove expectation model At = a + bp£ + et (a) pt - K-i = (i - » ) (c)to (a) = a + b(Pt_i -APt-1 = Since At-i Rearrange (b), thus + A p J.j a + b(l- A )Pt-i + A b F ^ + et + et (d) = a + bP*_x + bpt-l = A t-1 “ a “ et-l (e ) Substituting (e) to (d) A t = a + b(l - A )Pt-x + A A t_i -A a - A et _x + e t or, A t = a (1 - A ) + b (1 - A )Pt_x + A A t_x + et - A et _- Therefore, At = kg + k 1Pt _ 1 + a A t_1 + E t 188 where kg = a (1 - A ) kx = b(l - a ) Et = et - A e t _1 and (1 - A ) = price expectation adjustment coefficient. Appendix A.2, Partial adjustment model aJ = a + bP^^ + A t " A t-1 = r (A* - A t-1) (b) where 0 S r £ 1 From (b) we derive A t = rA* + At-l(l - r) (c) Substituting (a) to (c) A t = r(a + bPt-1 + et) + A-t^fl - r) - ra + rbPt _! + A t - 1 (l - r)+ ret Therefore, A t " k o + k lpt-l + ^ t - l where kg = ra ki = rb k2 = (1 - r) Et ” + Et (d ) 189 and r = the supply adjustment coefficient* Equation (a) can be expanded to include other explanatory variables such as the price of competitive £ crops (P ), stocks (S^) etc. A t = Kq + K1P t_1 + The result becomes + KgP^ + K4 St .1 + Bt 190 Table B.l, Tart Cherry Statistics, Michigan _____________________1938-1976_____________________ Bearing Total value Total Price received Year of by 1 acreage production cost growers 1,000 1938 25 .0 1939 24.8 1940 25 .1 $1,000 1,273 1,613 2,645 $/acre 88 .80 98.40 72.00 $/ton 67.00 42.00 58.00 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 25 .4 25 .2 25 .9 26.1 26.5 26.9 27.5 28.1 29.3 30.1 2,548 4,650 1,858 7,800 4,116 18,029 9,504 12,489 11,011 12,610 71.20 160.80 154.40 124.00 158.40 222.40 144.00 158.40 110.40 260.80 92.00 100.00 172.00 156.00 294.00 298.00 192.00 181.00 182.00 130.00 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 31.3 32.2 33.5 34.8 36.3 37.7 39.8 41.3 42.3 42.1 10,350 7,080 13,376 10,560 8,591 8,195 11,748 8,068 10,750 12,320 291.20 192.80 188.00 199.60 211 .02 162.38 203.82 226.12 249.07 236.89 138.00 119.00 176.00 220.00 121.00 149.00 132.00 163.00 125.00 154.00 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 41.9 41.7 41.0 40.6 40.1 40.1 40.5 40.1 40.0 39.5 14,857 10,516 7,215 15,150 10,593 15,260 15,840 30,000 16,112 11,297 377.21 287.54 291.71 333.56 310.15 213.77 462.12 427.86 398.66 394.40 166.00 95.00 195.00 101.00 99.00 280 .00 360.00 300.00 152.00 143.00 1971 1972 1973 1974 1975 1976 39.1 39.1 38.5 37.9 37.4 37.5 17,622 17,227 22,620 37,801 18,473 22,815 512.80 346.40 400.00 432,80 416.00 545.84 198.00 161.00 390.00 367.00 203.00 507.00 Sources and footnotes, see p. 196, 191 Table B.l, Tart Cherry Statistics, United States, 1955-1976 (Continued) Carryover stocks Total production Year of (April 1) value Tons 1955 1956 1957 1958 1959 1960 149,070 99,040 146,670 103,410 137,958 115,840 26,400 35,400 22,050 31,100 29,100 31,700 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 164,670 166,655 80,790 225,923 161,414 89,496 88,990 137,654 152,230 118,990 20,500 49,100 58,750 22,050 69,200 52,450 20,650 19,500 39,050 41,250 1971 1972 1973 1974 1975 1976 139,260 134,180 87,020 132,300 123,070 72,200 33,350 44,950 35,100 18,550 38,250 32,950 Source: USDA, "Fruit - Noncitrus: Production, Use, Value," and 'Cold Storage", Statistical Reporting Service (various issues)• 192 Table B.l, Tart Cherry Statistics, United States, 1938-1976 (Continued) 18,252 20,879 19,593 Disposition Canned Fr oz en Tons 9,290 34,117 17,025 55,047 59,254 20,150 2,241 3,009 4,483 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 16,632 19,860 14,020 19,410 10,550 14,620 12,840 14,000 12,650 13,160 37,822 60,328 12,649 54,530 25,320 55,930 40,470 67,690 58,625 87,310 22,301 21,616 13,136 35,330 9,025 44,160 35,530 46,570 35,575 52,920 2,945 2,236 474 2,930 755 1,300 1,540 3,530 1,440 1,350 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 12,659 10,190 10,385 9,790 9,350 7,963 8,624 7,968 7,413 6,365 84,256 67,285 61,330 52,455 79,363 45,423 66,104 48,089 71,225 44,307 49,895 31,675 59,035 43,255 58,689 44,254 71,042 46,588 58,320 64,168 1,250 500 740 820 1,668 1,400 900 765 1,000 1,000 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 7,677 7,016 4,880 8,258 6,495 6,592 4,662 5,734 5,691 6,012 62,563 84,293 30,845 101,031 69,918 36,738 30,374 48,411 63,357 43,358 93,870 73,676 44,350 116,634 85,001 46,166 53,954 83,509 83,182 69,620 560 1,670 715 0 0 0 0 0 0 0 Year Fresh 1938 1939 1940 1971 1972 1973 1974 1975 1976 Other 5,620 41,280 92,360 0 3,080 47,990 83,110 0 2,630 26,900 57,490 0 2,210 48,800 81,290 0 3,600 40,770 74,640 4,060 3,000 18,580 49,120 1,500 Source: USDA, "Fruit - Noncitrus: Production, Use,Value," Statistical Reporting Service(various issues). 193 Table B.2, Apple Statistics, Michigan, 1938 - 1976 Bearing acreage Total value of production 1938 1939 1940 1,000 76.6 76.7 76.8 $1,000 4,600 4,802 5,245 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 77.1 77.5 77.1 76.3 75 .4 74.4 72.3 69.4 65.9 62.2 6,322 9,406 13,719 11,798 3,625 12,474 8,296 10,626 8,168 10,541 84.00 130.40 132.00 169.60 91,20 240.80 258.40 246.40 272.80 309.60 1.98 2.83 5.58 5.10 8.05 5.00 3.21 5.24 2.50 3.33 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 58.1 55.4 54.1 53.2 65.4 65 .4 65.9 61.6 60.0 59.5 10,400 14,012 19,504 15,794 13,778 22,440 17,600 19,558 20.115 22,713 372 .00 284.80 360.80 378.69 468.33 400 .66 385.82 506.90 362.58 349.78 3.33 5.12 5.05 4.98 3.95 4.45 4.19 3.67 3.52 4.79 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 59.5 60.5 63.0 63.2 54.5 55.1 55.0 55.5 56.0 56.0 23,360 24,050 22,560 24,948 24,116 25,350 28,083 29,082 24,503 25,703 349.31 325.94 358.14 342.87 366.26 349.34 382.84 402.26 439.82 487.20 3.48 4.40 4.48 3.67 3.63 3.77 5.06 5.24 3.74 3.79 1971 1972 1973 1974 1975 1976 55.5 54.5 54.0 53.5 53.5 53.5 26,061 31,390 43,710 41.540 34,680 40,500 474.40 483.20 560.00 662.40 696.00 708.00 3.57 4.30 9.30 6.20 5.10 8.10 Year Total ^ cost $/acre 105.60 106 .40 84.00 Sources and footnotes, see p. 196 Price received bygrowers d/lb 2.05 1.26 2.07 Table B.3, Sweet Cherry Statistics, Michigan, Bearing Year 1938 1939 1940 acreage 1,000 2.5 2.5 2.6 Total value of production $1,000 302 234 364 Total „ cost‘d $/acre 88.80 98.40 72.00 1938 - 1976 Price received by growers $/ton 108 90 104 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 2.8 3.0 3.2 3.4 3.7 3.8 3.8 3.9 4.1 4.2 433 452 352 1,113 190 1,274 1,159 1,297 972 1,212 71.20 160.80 154.40 124 00 158.40 247.20 144.00 158.40 110.40 289.60 114 116 220 220 380 275 235 260 135 146 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 4.3 4.5 4.6 4.7 4.9 5.1 5.5 5.7 5 .9 6.2 1,306 1,320 2,052 2,420 1,485 2,100 4,076 3,172 2,618 3,570 323.60 192.80 188.00 200.00 346.56 101.72 362.34 523.87 448.71 334.77 192 145 228 275 198 270 263 235 187 255 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 6 .6 7.3 7.6 8.1 8.8 9.3 9.9 10.4 11.3 11.4 3,472 4,389 2,387 4,070 4,464 4,590 5,198 7,480 4,580 4,242 332.96 336.40 327.55 457.23 281.22 291.10 425.35 464.22 528.10 340.00 248 231 327 185 186 240 297 340 213 202 1971 1972 1973 1974 1975 1976 11.6 11.7 11.5 11.5 11.5 11.5 4,489 5,460 4,480 9,180 6,426 3,948 470.40 442.40 422.40 380.80 430.30 481.94 191 195 280 360 238 376 Source and footnotes, see p. 196. 195 Table B.4, Population, Disposable Income and Consumer Price Index, United States, 1938-1976 Total Year Population 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 Sources: 129.8 130.9 132.1 131.8 131.5 128.9 128.6 129.1 138.4 142.6 145 .2 147.6 150.2 151.0 153.3 156.0 159.1 162.3 165.4 168.4 171.5 174.5 178.1 181.1 183.6 186.4 189.1 191.5 193.3 195.2 197.0 199.1 201.6 204.2 206.5 208.1 209.7 211.4 213.0 see p. 196, Capita disposable income Dollars 504 537 573 695 867 976 1,057 1,074 1,132 1,178 1,290 1,264 1,364 1,469 1,518 1,583 1,585 1,666 1,743 1,801 1,831 1,898 1,934 1,976 2,058 2,128 2,278 2,430 2,597 2,740 2,930 3,110 3,348 3,588 3,837 4,285 4,639 5,060 5,138 Consumer price index(1976=100) 42.2 41.3 42.0 44.1 48.8 51.8 52.7 53.9 58.5 66.9 72.1 71.4 72.1 77.8 79.5 80.1 80.5 80.2 81.4 84.3 86.6 87.3 88.7 89.6 90.6 91.7 92.9 94.5 97.2 100.0 104.2 109.8 116.3 121.3 125.3 133.1 147.7 161.2 178.8 196 Sources and Footnotes for Tables B.l, B.2 and B a3 All Michigan statistics except for costs - Crop Reporting Service, '•Michigan Agricultural Statistics,11 Michigan and U.S. Department of Agriculture (various issues) Total costs - Derived from "Farm Cost Accounts Reports," Department of Agricultural Economics, Cornell University, Ithaca, New York (various issues). 1See total cost items in Table B.5. Sources for Table B.4 Population - USDA, "Agricultural Statistics, 1976," Economic Research Service, p. 557. Beginning 1960, includes Alaska and Hawaii. Data for 1938-1958 in 1972 issue Table 805. Disposable income - Ibid. p. 466. Data for 19381958 in 1972 issue Table 685. Consumer price index - Ibid. p. 567. 1938-1958 in 1972 issue Table 816. Data for 197 Table B.5, Tart Cherry Cost Items (1) Growing costs: Labor Tractor Truck, equipment, custom work, equipment rent Orchard overhead Fertilizer Spray, dust material Interest Other (2) Harvesting costs: Labor Tractor, truck Equipment Custom work, equipment rent Other (3) Storing and selling costs: Labor Tractor, truck, equipment Building use Direct selling cost Other Soruce: Darwin P. Snyder, "Farm Cost Accounts", Department of Agricultural Economics, Cornell University, Ithaca, New York, 1974, p. 17. 198 Table C.l, Second Degree Polinotnial Lag Model of Michigan Tart Cherry Bearing Acreage Response Distributed Lag Variable 8 9 10 11 12 13 14 C 36.6737 36.3607 36.0289 35.6424 35.2387 34.9147 34.4433 t-6 -.00749 -.00250 -.00565 -.00450 -.00344 -,00275 -.00182 -7 .00301 -.00286 -.00255 -.00201 -.00143 - .00105 - .00044 -8 .00046 .00013 -.00001 .00007 .00028 .00040 .00076 -9 .00292 .00236 .00196 .00174 .00167 .00161 .00176 -10 .00436 .00385 .00337 .00298 .00274 .00256 .00256 -11 .00479 .00458 .00422 .00381 .00350 .00327 .00318 -12 .00421 •00456 .00450 .00422 .00395 .00373 .00360 -13 .00261 .00379 .00422 .00421 .00408 .00394 .00382 .00227 .00338 .00378 .00389 .00391 .00356 .00197 .00294 .00339 .00362 .00370 .00168 .00258 .00309 .00335 .00145 .00231 .00280 .00128 .00206 -14 -IS -16 -17 -18 -19 .00113 .4042 .4590 .5012 .5131 .5239 .5506 .5637 d.w. .2379 •2030 .1580 .1246 .0953 .0854 .0712 .3601 .4189 .4643 .4770 .4886 .5173 .5314 » to R2 199 Coefficients 003C ■ Third-degree Second-degree 002C Fourth-degree 001C -8 -10 -12 -14 -16 000 Figure C.l, Distribution of Correlation Coefficients With Different Degree of Polynomial 200 Table C«2, Simple Correlation Metrix for Variables in the Supply Model A* GMt GM® GMSW A* 1,000 GMt -.441 1.000 GM3 .520 .112 1.000 -.001 .455 .116 1.000 .657 -.084 .698 -.204 GMSW T Table C.3, P* T Simple Correlation Metrix for Variables in the Demand Model Q* S11 Q3 CPI PDI pt 1.000 Q* -.798 -1.000 St -.392 -.142 1.000 Q3 .289 -.278 .034 1.000 CPI .652 -.518 -.177 .258 1.000 PDI .651 -.501 -.164 .353 .978 1.000 T .625 -.481 -.124 .447 .942 .983 201 Table D.l, Year Calculations for Projection of Apple Grower Gross Margins, Michigan, 1977-1990 Yield Lb/acre Price d/lb Total Cost $/acre Gross1 margin $/acre CPI Def latec gross margin 1967—100 $/acre 1977 12835 5.0822 620.02 32,291 194.13 16.634 1978 12961 5.0638 632.72 23.597 205.00 11.511 1979 13087 5.0454 645.42 14.856 213.43 6.961 1980 13213 5.0270 658.12 6.071 220.32 2,755 1981 13338 5.0086 670.82 -2.762 226.15 -1.221 1982 13464 4.9902 683.52 -11.641 231.19 -5.035 1983 13590 4.9718 696.22 -20.566 235.64 -8.728 1984 ’ 13715 4.9534 708.92 -29.538 239.62 -12.327 1985 13841 4.9350 721.62 -38.555 243.23 -15.851 1986 13967 4.9166 734.32 -47.619 246.51 -19.317 1987 14093 4.8982 747.02 -56.729 249.54 -22.733 1988 14219 4.8798 759.72 -65.886 252.34 -26.110 1989 14344 4.8614 772.42 -75.089 254.95 -29.452 1990 14470 4.8430 785.12 -84.337 257.39 -32.766 Gross margin = (Yield * Price) - Total Cost 202 Table D* 2, Year Calculations for Projection of Sweet Cherry Gross Margins, Michigan, 1977-1990 Yield Ton/acre Price Total Cost Gross1 margin $/ton $/acre $/acre CPI 1967=100 Def late< gross margin $/acr< 1977 2.2272 230.45 485.77 27.495 194.13 14.163 1978 2.2336 229.70 496.35 16.713 205.00 8.153 1979 2.2400 228.95 506.93 5.922 213.43 2.775 1980 2.2465 228.20 517.50 -4.856 220.32 -2.204 1981 2.2529 227.45 528.08 -15.667 226.15 -6.928 1982 2.2593 226.69 538.66 -26.487 231.19 -11.457 1983 2.2657 225.94 549.23 -37.317 235.64 -15.836 1984 2.2721 225.19 559.81 -48.157 239.62 -20.097 1985 2.2786 224.44 570.39 -58.984 243.23 -24.250 1986 2.2850 223.69 580.97 -69.842 246.51 -28.33 1987 2.2914 222.93 591.54 -80.711 249.54 -32.34 1988 2.2978 222.18 602.12 -91.590 252.34 -36.30 1989 2.3042 221.43 612.70 -102.477 254.95 -40.19 1990 2.3107 220.68 623.27 -113.352 257.39 -44.04 ■ksross margin = (Yield x Price) - Total Cost 203 Table D. 3, Year Calculations for Projection of Tart Cherry Gross Margins, Alternative No. 3, Michigan, 1977-1990 Yield Ton/acre Price'1, $/ton Cost2 $/acre 3 Gross margin Deflated gross margin CPI 1967=100 $/acre $/acre 1977 2.4798 592.93 493.42 976.93 194.13 503.235 1978 2.5072 495.78 504.68 738.35 205.00 360.169 1979 2.5145 497.20 515.92 734.30 213.43 344.045 1980 2.5319 500.94 527.13 741.20 220.32 336.423 1981 2.5493 506.51 538.32 752.92 226.15 332.931 1982 2.5667 513.13 549.49 767.56 231.19 332.004 1983 2.5840 516.43 560.64 773.81 235.64 328.386 1984 2.6014 516.26 571.77 771.22 239.62 321.853 1985 2.6188 515.09 582.88 766.02 243.23 314.938 1986 2.6361 512.16 593.97 756.12 246.51 306.731 1987 2.6535 507.62 605.04 741.93 249.54 297.318 1988 2.6709 500.60 616,09 720.95 252.34 285.707 1989 2.6882 495.64 627.12 705 .26 254.95 276.629 1990 2.7056 493.41 638.13 696.83 257,39 270.728 1 Projected from the demand model. 2 Total costs. 3 Gross margin = (Yield x Price) - Total Cost 204 Appendix D. 4, Calculations of the Long Run Dynamic Equilibrium Gross Margins The Carryover stocks of tart cherries, the per capita consumption of frozen apples, and the consumer price index are assumed to remain unchanged over time, while the annual growth rates of the price of tart cherries(P^), and the per capita disposable income(PDI) are assumed to be 5 percent, and 8 percent, respectively. The effect of the consumer price index is assumed to be negligible because the estimated coefficient is insignificant. The annual growth rate of the consumption of tart cherries, as calculated in the following table, is .5 percent. PDI Elasticity Growth factor o• m Pt Growth rate w -.819 -.041 00 • o Variable .574 .046 Quantity of tart cherries (Q ) - .005 In addition, the annual growth rate for the United States population(POP) is assumed to be .8 percent. The growth rates for the yield of tart cherries are 1.737 percent per year for the projected yield level and 4.0 percent per 205 Year for the assumed higher yield level. Substituting the above growth rates to the identity equation Qt = (A* X Yt) / POP, or A* = (Q* * POP) / Y t The annual increase in the tart cherry acreage based on the projected yield level is A t = (.005 X .008) / .01737 = .0023, or .23 percent and the annual increase in the acreage ( aA't) is .0023 x 37.88(average acreage)= .08723 (in 1,000 acres Substituting the A1* value to Equation (7.1) and solve for the level of the gross margin, thus GM* =(.08723 + .296626) / .00467 = 82.20 (dollars) Therefore, the long run dynamic equilibrium gross margin for the projected yield level is $82.20 per acre. Using the same procedure, the level of the gross margin required to maintain the long run dynamic equilibrium for the assumed higher yield level is $71.63 per acre.