0 AN EXPERIMENT IN. DESIGN-MG AN EconoMEtRIc MQDEL TO ' ' EXPLAIN SHORT TERM? -- E. DEMAND, FLUCTUATIONS :EoR APPLES, I Thesis for the Dam-oi M. s. MICHIGAN STATE COLLEGE William A. *Cr'gma‘r'ty 195-3 — “-‘1—‘1 ' "'W " ' I—_l" ' ' ‘V—_I—.‘—-"—.—_-—r"1 “——"T—‘—'— This is to certify that the thesis entitled AN EXPERIMENT IN DESIGNING AN BCONOMETRIC MODEL TO EXPLAIN SHORT TERM DEMAND FLUCTUATIONS FOR APPLES presented by William A. Cromarty has been accepted towards fulfillment of the requirements for Master ”magma innginnlmral Economics 0-169 \ .'4 ' L. . - " "Il . (r. .. ", ' (, 1"" A , . . vs:- I . . '_. '.,1 Wwathwm' .2 $‘W‘F' Mw£~mwm’wu‘lnsfi dW.§m¢“”‘ “CD. I. I ‘flln ’Mflflw II- , ufikul/ng 5 (VFW, bimftduiu .‘t In: . J (.0 1" u .l- I \ N ulk .. an). , tynrflréw, .‘isv I9? ”Hudlvtw3fl4... DII .1" .UOIHeruroJrulfi .2, 1.]. ‘31,, ‘81.... .r,.n )p.htv. .. Arr/.1 .1 .dt .Keyfivv h.’.:.’ 0.5“}. Jv-uraiza . . . , . .. I . \ . t ‘ V . . ’ 1 . . u 1 u a I . . \ . . . , . ,.. .suvww .. ...\I..C :n -.J\ Era. . . .5 .0v. .0 . . . 4 he E . .n .. , a v , v . . . a L , nt .U A. .. . ,« fl“ , ‘ .I. I.’ A“ \ ‘Otf . .J n. .V. 3 ... I‘ w . . p 0“..\ £11K IQ‘I. .IIV .\.u '4‘. “AW ‘ Llo'_.l‘§...ol“. .9 u 1:3! I .. . . o ‘v, 4 A.t..., .I.. . .. .l . . . I ‘ I . , \ .. . . \i J . .. . us . . a . A . v o D 1 .. I I \ r ,. E .15. 0‘ ‘ AN EXPERIMENT IN DESIGNING AN ECONOMETRIC MODEL TO EXPLAIN SHORT TERM DEMAND FLUCTUATIONS FOR APPLES By William A. Cromarty A THESIS Submitted to the School of Graduate Studies of Michigan State College of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Agricultural Economics 1953 ACKNOWLEDGMENTS The author wishes to eXpress his gratitude to all those who contributed to the organization of this study and in the preparation of the manuscript. The assistance of Dr. L. L. Boger in planning and supervising the study was invaluable. His critical review of the material and his encouragements were appreciated at all times. Of major importance was the guidance and advice given by Dr. Clifford Hildreth of the Cowles Commission, University of Chicago. His discussions on analytical procedure and his contributions toward the develOpment of a preliminary model were of great benefit to the author. Thanks also are due to Dr. Glenn Johnson for his advice and interest in the project. Numerous improvements and corrections were suggested by him prior to the final preparation of the manuscript. The author is also indebted to other faculty members and to fellow graduate students for suggestions and contributions. Finally, thanks are given to the Agricultural Economics department for the opportunity and assistance provided the author as a graduate student. Errors which may appear in the manuscript are the sole reaponsibility of the author. "0-8575 TABLE OF CONTENTS Page LIST OF FIGURES . . . . . . . . . . . . . . . . . . . 11 LIST OF TABLES . C O O O O O O C O O O O O O O O O O . iii Chapter I INTRODUCTION . . . . . . . . . . . . . . . . . . ObJQCtiveS O O O O O O O 0 O O O O O O 0 O 0 0 Major Hypothesis . . . . . . . . . . . . . . . .4 03 cn :4 Basic Assumptions and Beliefs . . . . . . . . NUltiple Equations as a Tool in Demand Analysis . . . . . . . . . . . . . . . . . . 8 II REVIEW OF LITERATURE . . . . . . . . . . . . . . 14 III ECONOMIC BEHAVIOR OF THE APPLE ECONOMY . . . . . 18 IV RETAIL DEMAND FUNCTION . .‘. . . . . . . . . . . 27 V STORAGE DEMAND FUNCTION . . . . . . . . . . . . 55 VI PROCESSING DEMAND FUNCTION . . . . . . . . . . . 45 VII EXPORT DEMAND FUNCTION . . . . . . . . . . . . . so VIII SUMMARY AND CONCLUSIONS . . . . . . . . . . . . 60 BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . 67 APPENDIX - DATA FOR STRUCTURAL EQUATIONS . . . . . . . 71 ...... ...... Figure I LIST OF FIGURES Period of Investment in Storing Apples . . ii 0 LIST OF TABLES Table Page 1 United States EXports of Fresh and Dried Apples to Four Important Countries, Average, 1934-58 0 o o o o o o o o o o o o o 53 2 Apples: Production by Periods, Commercial Areas of United States, 1929-51 . . . . . . . 72 5 Apples, Fresh: Storage Stocks at End of Period, United States, 1929-51 . . . . . . . 73 4 Apples, Fresh: Quantity Available for Consumption, by Periods, United States, 1929-51 0 o o o o o o o o o o o o o o o o o o 74 5 Apples, Processed: Storage Stocks Beginning Season, and Quantity Processed in Period II, United States, 1929-51 0 O O O O O O O O O O 75 6 Apples: Total Quantity of Net Exports from the United States in Terms of Fresh Apples, by Periods, 1929-51 . . . . . . . . . . . . 76 7 Apples, Fresh: Average Price Received by Farmers, by Periods, United States, 1929-51 . 77 8 Personal Diaposable Income: Seasonally Adjusted at Annual Rates, by Periods, United States, 1929-51 0 o o o o o o o o o o 78 9 Price Index for Six Fresh Fruits at Farm Level,by Periods, United States, 1929-51 . . 79 10 Apples, Fresh: Retail Sales, Average of Three Preceding Years, by Periods, United States, 1929—51 . . . . . . . . . . . . . . . 80 11 Apples, Fresh: Storage Stocks, Average of Three Preceding Years, by Ending Periods, United States, 1929-51 . . . . . . . . . . . 81 12 Apples, Fresh: Percent That Average Price Per Bushel Received by Farmers for the Months of March, April, and May Was of the Average Price Received During the Preceding Months of September, October, and November, United States, 1929-51 . . . . . . . . . . . . 82 iii LIST OF TABLES (Continued) Table 15 Apples, Fresh: Storage Costs Per Bushel, by Periods, United States, 1929-51 . . . . . . l4 Apples: Index of Processing Costs, United States, 1929-51 0 O 0 O O O O O O O O O O O 0 O 15 Price Index for Fruits Competitive with Canned Apples, for Period II, United States, 1929-51 . 16 Cherries, Red Sour: Average Price Per Ton Received by Farmers, United States, 1929-51 . . l7 Apples, Fresh: Exports by Canada and Production for United Kingdom, France, Germany, and Belgillm, 1929-51 0 O O O O O O O O O O O .1 O O 18 Wholesale Prices: Index for France, Belgium, United Kingdom, and Germany, Weighted by Average Annual Imports of Apples 1954-58, for the Years 1929-51 . . . . . . . . . . . . . 19 Apples, Fresh: Average Price Per Bushel for Apples Exported from the United States, by PeriOdS, 1929-5]. 0 o o o o o o o o o o o o o o 20 Conversion Factors and Weights and measures for Apples . . . . . . . . . . . . . . . . . . iv CHAPTER I INTRODUCTION The development of basic research and the application of new methodology to particular fields remain as major problems facing research workers in economics at this date. The area of statistical demand analysis, which deals with the measurement of mass reaponse in a given market, has undergone continuous eXperimentation and improvement, as workers have tried to develop and use price forecasting formulae as guides to marketing policies. The following study is another in this area with emphasis on a particular commodity -- apples. The main problem which has arisen in this area centers around seasonal fluctuations in demand. Justification.for selecting apples as the commodity to be studied is found in, (l) the importance of apples as a major fruit crop in the United States . . . . farm value of 192 million dollars for the commercial apple crop in 1950,1 (2) the inadequate conclusions which can be derived from previous attempts to explain short term demand fluctu- ations coupled with the importance of having sufficient and lAnonymous, Agricultural Statistics, United States Department of Agriculture, Washington.25, D. C., p. 188, 952. 2 accurate data for this purpose and (5) the relatively better time series data for the apple market as compared with many other agricultural products. This latter reason is important because of the statistical analysis which will be used. In the past a strong interest has centered around what can.be termed the “single equation, least squares” approach and in many cases this has proven to be a very useful tool in economic analysis. Refinements in this particular tech- nique are constantly being made but there are severe limitations to its general application.2 The usual accepted procedure is to more or less arbitrarily assume one variable as being dependent upon all others with none of the independent variables being significantly influenced by the dependent variable. A line of regression is then.fitted by minimizing the sum of the squared deviations of the observations from it. This method further assumes that any errors present in the model are associated with the dependent variable only. A.further limitation ascribed to aggregation arises when the product involved is assumed to have only one major use 2For a discussion on "least-squares” bias see Bennion, E. G. The Cowles Commission Simultaneous Equation Approach: A Simplified Explanation. Review of Economics and Statistics, Vol. 34, pp. 49-56, 1952, or Bronfenbrenner, J., Chapter IX, Sources and Size of Least-Squares Bias In a Two-Equation Model. Hood, W. C. and KOOpmans, T. 0., Editors. W Method. John Wiley and Sons, New York, 1953. 3 and therefore only one market outlet. When the apple market is studied it is apparent that there are several uses and outlets with different characteristics, thus consideration for a method of analysis is needed which permits a study of the short run market fluctuations for the several demands. EconomiSts in conjunction with statisticians and mathematicians, or econometricians as a separate group have, and are, developing statistical tools which can be applied to data not readily or completely adaptable to the ”single equation, least squares“ approach. The greatest contribution which has been made in this area has been the development and consideration of complete econometric models.3 The primary 3This work has been developed along two lines, (a) the theoretical and intuitive concepts which form a formal and logical background for the construction of econometric models and (b) experimentation and application of such theory using empirical data. Some of the major contributions to the first part have been, (a) Anderson, T. w. and Rubin, H. Estimation of the Parameters of a Single Equation in a Complete System of Stochastic Equations. Annals of Mathematical Statistigg, Vol. 20, pp. 46-63, March, 1949. (b) Anderson, T. W. and Rubin, H. The A symtotic PrOperties of Estimates of the Parameters in a Complete System of Stochastic Equations. Annals of Mathematical Statistiga, Vol. 21, pp. 570-582, December, 1950. (c) Rubin, H. Systems of Linear Stochastic Equations. Unpublished Ph. D. Thesis, University of Chicago, 1948, 50 pp. (d) Cowles Commission for Research in Economics. Statistical Inference In Dynamic Economic Models, edited by Koopmans, T. C. John Wiley and Sons, New York, 1950. (e) Haavelmo, T. The Probability Approach In Econometrics. Econometric , Vol. 12 (supp.), July, 1944. Some of the major contributions in the field of application are, 4 step in this method of analysis is to Specify the variables which are relevant to the study and what form the relation- ships between the variables will take. These relationships between variables result in structural equations, and enough equations must be constructed to explain every variable which is not determined outside of the system being studied. This eliminates the need for assigning one variable as dependent and all others as independent. The structural equations which form the model may be solved simultaneously allowing for the interaction of all included variables. It is realized that this newer approach also has definite limitations and no claim is made that it can completely replace the older, single equation regression technique which is a special case of the new approach. The brief is held that each is useful in.known limited areas of demand analysis (a) Girshick, M. A. and Haavelmo, T. Statistical Ana§ysis of the Demand for Food. Econom trica, Vol. 15: 7 f. (b) Klein, L. Pitfalls in the Determination of the Investment Schedule. E onometric , Vol. 11, pp. 246-258, July-October, 1943. (c) Allen, S. G. Inventory Fluctuations in Flaxseed and Linseed Oil, 1926-1939. Cowles Commission Discussion Paper: Economics 276, unpublished paper. Cowles Commission for Research in Economics, University of Chicago, Chicago 57, (d) Hildreth, C. and Jarrett, F. Cowles Commission Discussion Paper: Economics 2055, unpublished paper. Cowles Commission for Research in Economics, University of Chicago, Chicago 57, Illinois, November, 1952. while in a third, and possibly the largest area, the appropriate techniques have not been determined. In general, statistical difficulties arise and should be dealt with regardless of the technique used. These difficulties concern the availability and accuracy of economic data or what are termed “errors“ in the model, the problem of identifying relationships as being demand or supply functions or other behavior or technical relations,4 and the technical problems of serial correlation and multi- collinearity. As far as possible these problems shall be dealt with in this study in a practical manner. Objectiyes The primary objective of this study is to construct an econometric model which will be useful in analyzing seasonal or short-term demand fluctuations in the apple market. The successful attainment of this objective will be reached when the structural equations have been developed to explain the variables which are determined by forces within the apple market. A second and concurrent Objective will be to determine the appropriate data or evidence needed for fitting the IKoopmans, T. C. Identification Problems in Economic Model Construction. Econometrics, Vol. 17, No. 2, pp. 125-144, April, 1949. 6 structural equations and assigning values to the parameters. This evidence must be relevant to the problem and be assembled and classified in such a manner that it is adapted to a solution of the model. It is not within the scope or purpose of this study to test the reliability of this model by actually fitting the structural equations for the Specified periods, but it is most important that the model be in a form that such a fitting may be undertaken with a minimum amount of revision. major Hypothesis The major hypothesis of this study is that by using theory as a framework, and statistical analysis to achieve numerical results, it is possible to isolate and study short- run demand relationships for apples. Economic theory will be used in forming the structural equations which make up the model. The determination of which variables are relevant is based upon observation of economic behavior, introspection, and consideration of economic relationships on which theorists have reached some agreement and which logically apply to the apple market. Thus the model will be a system of structural equations formed from the relevant economic variables and will enable one to state and employ all Efpriori information concerning the problem. 7 After these equations have been.formulated a statistical process of fitting can be adopted. This will permit the replacement of unknown parameters in the equations by numerical values representing average relationships for each period to which the model applies. Future values of unknown variables can then be predicted on the basis of the constructed model. Basic Assumptions and Beliefs (a) An assumption is made for simplicity that all equations are linear in known functions (such as logarithms or powers) of the observed variables. This is equivalent to sayingithat the algebraic forms finally used will be linear in the unknown parameters. (b) Certain variables are predetermined. That is, certain variables can be regarded as being determined outside of the system under study. Such an assumption is based upon the use of valid economic theory or observed economic behavior. (c) An assumption is made that all numerical coefficients in the fitted equations represent average relationships and that these relationships have not been abnormal during the time period investigated. A suggestion is made that the ”war" years be omitted from an alternate statistical fitting process to see if the parameters vary greatly from those 8 where the “war" years were included. Abnormalities do result inasmuch as the export demand for apples was disrupted and government purchases were significant during this period. Yet it is felt that a more satisfactory model can be developed by first fitting the equations for a period which includes the war years. ‘ (d) It is believed that, where the most desirable data cannot be found, compromises can be made which will not invalidate the conclusions. Assumptions made regarding time lags, linearity in the model, normal distribution of reSiduals, etc. are sufficient to prevent the actual description of reality within the model. Yet the hope and belief is held that the choice of the model used approximates reality to a degree sufficient for the purposes of the study undertaken. The complexities involved in dealing with a fully complete model are too great for the human mind to understand. Thus recognition is taken of our limitations and a simpler model is constructed which balances needs against human ability.5 ti 1e ation as a Too in Dema An 5 Prior to 1954 demand analyses were undertaken with single equation, multiple regression techniques being the 5See final chapter for a discussion of adjustments necessary to get a "true” model. 9 main statistical tool used. As previously stated, certain assumptions must be made with the single equation, least squares approach which are in many cases unrealistic and which can be eliminated if a multiple equation, simultaneously determined system is used. With a system of multiple equations including all important relevant variables it becomes unnecessary to designate one variable as being dependent and all others in the predicting equation as independent. Instead, enough equations are constructed so that it is possible to solve the system for each variable which is to be explained. Such variables are termed endogenous. These endogenous variables depend upon, or are influenced by, other variables (both exogenous and endogenous)6 within the system and a system is not complete until there are an adequate number of equations to explain each endogenous variable. Exogenous variables are those which are explained by factors not entering into the relationships being studied. Lagged endogenous variables are in a similar category. Both exogenous and lagged endogenous are termed "predetermined variables". It is necessary to determine Which variables 5K00pmans, T. C. Identification Problems in Economic Model Construction. Econometric , Vol. 17, No. 2, p. 135, April, 1949. 10 are relevant and to classify these variables as endogenous or predetermined on the basis of theory or observed economic behavior of consumers and firms. When a complete model has been developed the "single equation, regression technique" assumption of independence between the predicting variables can be discarded and interdependent relationships are accepted. Two problems are met when a complete system is to be developed. The first concerns errors in the model and the second is the problem of identification in model construction. Two types of errors may arise. The first is termed "errors of observation". These arise if the data used are subject to large errors of observation giving inaccurate estimates of the true data. In this study the methods develOped by the Cowles Commission at the University of Chicago will be followed in which errors of observation in the exogenous variables are assumed to be small relative to disturbances in equations. Errors of measurement in the endogenous variables are permitted if the disturbances are randomly and normally distributed about the true values of the variables, thus yielding unbiased estimates of the parameters in question. The second type of error occurs if certain important relevant variables have been omitted from the equations. This source of error occurs if data representing relevant 11 variables cannot be gathered or if the investigator is unable to correctly determine and include all relevant variables. This model is constructed realizing that such errors may be present. But this study assumes that any disturbances caused by errors of omission are randomly distributed and that the mean.value of these disturbances is equal to zero. If this assumption holds true, the resultant estimates of the structural coefficients will be unbiased. Explicit account is taken of the identification problem when a multiple equation model is constructed. Identification, simply stated, means that each structural equation in the model is unique, it being impossible to construct an equation of like form.by taking linear combinations of any or all structural equations. Such a test is necessary to accurately determine true demand functions and supply functions. It is not within the purpose of this paper to explain how a mathematical solution to the problem of identification is reached but the criteria necessary for identifying each equation will be stated according to the following method outlined by Koopmans:7 ”A necessary condition for the identifiability of a structural equation within a given linear model is that the number of variables (counting lagged variables as separate 7Ibid., p. 155. 12 variables) excluded from that equation be at least equal to the number (G, say) of structural equations less one. This is known as the ppg§;_condition of identifiability. A necessary and sufficient condition for the identifiability of a structural equation within a linear model, restricted only by the exclusion of certain variables from certain equations, is that we can form at least one non-vanishing determinant of order G-l out of those coefficients prOperly arranged, with which the variables excluded from that structural equation appear in the pgpk condition of identifiability.” When all structural equations with appropriate variables have been decided upon the identification problem is dealt with. The model can then be classified as over-identified, just-identified, or not-identified.8 If the model cannot be identified then it is impossible to estimate the co- efficients within this system. In applying the multiple equation method to demand analysis in the apple market the above problems of identi- fication, interdependency and random disturbances are dealt with. For this reason it is felt that less bias will be All 3For a more complete analysis of these identification problems see Tintner, G. Econometpics, John Wiley and Sons, New York, pp. 154-184, 1952. 13 present than if separate independent equations were to be fitted according to "least squares". The next step shall be to determine the economic relationships that apply to the production, marketing and consumption of apples and to separate the useful endogenous and exogenous variables. The procedure will then be to specify the relations that determine the current endogenous variables for given values Of the other variables to get a complete and practical model. CHAPTER II REVIEW OF LITERATURE Investigations into the marketing of apples have been undertaken on both a descriptive and analytical basis. One of the earlier and more complete studies which provided an insight into the production and marketing of apples was undertaken by Pailthorp and Park.1 Production, harvesting, storing, utilization, and marketing are all discussed as integral parts of the apple economy. Reference is also made to trends in the industry concerning production, foreign trade, and prices. This study implies that apples, pears, citrus fruits, prunes for drying, and banana imports are competitive in nature although no statistics are used in verification. Factors listed as influencing apple prices are volume of supply, general price level, variety, grade and condition, size of apples, time of year when sales are made, kind of container, origin of Supply, market where sold, method of sale and export conditions. Considerable emphasis is placed on the competitive market which exists between lPailthorp, R. R. and Park, J. w., Marketing Apples, United States Department of Agriculture, Bureau of Agricultural Economics, Washington, D. 0., Bulletin 474, 1935. 15 different varieties of apples as judged by the volume of each variety appearing on selected city markets. Lloyd and Ekstromg undertook a study in the State of Illinois which is typical of the work done in many apple- growing states. They gave some special emphasis to the marketing problems in years of heavy crop. Competition between apples and other fresh fruits was assumed although no coefficients of cross-elasticity were computed or quoted. w. E. B1 ackz’ in a study of consumer demand for apples noted that factors other than income had little effect on the per-capita amount Spent for apples. In each of the three income ranges which his survey covered the same proportion of the food dollar was spent on apples. High income groups had a higher expenditure for apples not . because of increases in the quantity bought, but because higher prices were paid. He found that variations in the demand for apples as measured by quantity, price, or expenditure were not related to variations in the quantity, price, or expenditure of oranges. Statistical techniques in this 2Lloyd, J. W. and Ekstrom, V. A. Marketing the Illinois Apple CrOp, University of Illinois Agricultural Experiment Station, Urbana, Illinois, Bulletin 497, August, 1943. 3Black, W. E. Consumer Demand for Apples and Oranges. Cornell University Agricultural Experiment Station, Ithaca, New York, Bulletin 800, 1943. 16 study were based on variations between classes or groups and no apparent attempt was made to fit a regression of price on consumption or vice verse by using the ”least squares” method. M. D. Woodin4 discussed yearly and seasonal changes in apple prices in New York State. Yearly price changes were associated with the price level of all commodities and the size of the apple crOp. He concluded that citrus prices and apple exports had little effect on domestic apple prices. Seasonal price changes were associated with changes in the general price level with a price variation being present between varieties. Woodin used a formal statistical technique in his analysis based on the single equation, least squares approach. X1, wholesale apple prices (dependent), was explained in terms of X2, commercial apple production in New York State, X3, index of wholesale prices of farm products in the United States, and.X4, production of oranges within the United States. Fox5 investigated the relationship between X1, the farm price of apples (dependent), and X2, production changes. 4Woodin, M. D. Changes in the Price of Apples and Other Fruits. Cornell University Agricultural Experiment Station. Ithaca, New York, Bulletin 773, December, 1941. 5Fox,K,A. Factors Affecting Farm Income, Farm Prices, and Food Consumption. Agpigpltural Economigngesearch, Vol. 3, No. 3, pp. 65-82, July, 1951. 17 The price elasticity here was approximately .80. The regression of farm price on consumer disposable income was also made and an income elasticity of 1.04 was computed. Analysis was again done by fitting single equations by the method of least squares. Fox also succeeded in establishing similar coefficients for other fresh fruits which are possible competitors with apples, i.e. peaches, oranges, lemons. This is perhaps the most complete study on demand elasticities at the present time.4 CHAPTER III ECONOMIC BEHAVIOR OF THE APPLE ECONOMY The determination of relevant variables can best be accomplished by describing the operation of the apple market. Such a description must be realistic and include the economic behavior of the peOple as well as the climatic and physical factors which guide producers, processors and consumers. After a preliminary examination of the data, the years 1929-51 inclusive were selected for study. The production of apples is seasonal in nature. Depending upon the variety, geographical area, and weather conditions, harvesting begins in July of each year and is continued until early November. Varieties are commonly classified as "summer”, "fall”, and “winter". The harvesting of summer varieties begins in July and is actively carried on until the end of August.1 These apples are stored for a very short period to permit cooling and distribution to truckers and then move directly into retail markets from packing sheds. The harvest period for fall and winter varieties follows the harvesting lPalmer, C. D. and Schlotzhauer, E. O. Apples, Uspa; Time of Bloom and Haryest. United States Department of Agriculture, Bureau of Agricultural Economics, Washington, D. 0., November, 1950. 19 of summer varieties and extends from late August to early November.2 These apples may move directly into retail channels from packing sheds as fresh apples or they may serve to meet the demands of processors and eXporters. Commercial storage is carried on and reaches a peak by the time the harvest season is completed.3 The Opening and closing dates for processing of apples are August 1 and December 31 respectively,4 with the most important period being September 1 to December 31. Utilization of apples by processors varies, with drying, canning, freezing, and crushing for vinegar, cider and juice all being important. Apples are exported from a given year's crop from July through June of the following year. The bUlk of those exported are shipped from September through March during the crop year.5 The volume of exports varies from year to year with from 1 to 17 percent of total United States' production having been exported during the period 1929-51. 2Pailthorp, R. R. and Park, J. W. Marketing Apples. United States Department of Agriculture, Bureau of Agricultural , Economics, Washington, D. 0., Bulletin 474, 1935. 3Ibid., p. 31. 4Anonymous, The Cannipg Trade Almgpac-195 , p. 22. The Canning Trade, Baltimore 2, Maryland, 1952. 5Anonymous, Monthly Spmmary of Foreign Commerce of the United Stapep. United States Department of Commerce, Bureau of Foreign and Domestic Commerce, Washington, D. 0., monthly 1929-1951. 20 Imports of apples into the United States have been small in total volume, never having reached 3 percent of total United States' production during the period 1929-51. A When harvesting has-been completed and storage is at a maximum the supply of apples correSponds to the movement from storage and is governed by the keeping quality of the apples as well as current and expected prices. The greatest movement from storage occurs from November through April. By the end of June storage stocks are at a minimum and are considered insignificant for all practical purposes. From the above description several phenomena are apparent. The data can be aggregated according to definite time periods. This procedure is useful since short-run fluctuations are to' be studied. The first period could satisfactorily include the months of July and August. Harvesting begins during this period, fresh apples are available for the retail market and a few may even be exported. Storage stocks at the beginning of this period are at a minimum and storage is Inot important during these two months. Processing operations likewise are small enough to be considered insignificant. Again, using considerations based on time of harvesting, marketing and storing, the second time period can.be dis- tinguished as including the months of September, October and November. In this period (Period II) the bulk of the crop 21 is harvested -- the fall and winter varieties -- and the harvest is completed by the end of November. Large quantities of apples move into retail markets for consumption in a fresh form and exports of apples rapidly increase in volume. Large quantities of apples also enter the processing plants. Storage is important in this period reaching a peak sometime before the end of November. The third period includes the months of December, January, February and March. Apples continue to move into retail markets in fresh form and in smaller quantities to export markets and to processors. Harvesting is not carried on within the United States but apples move out of cold storage warehouses to meet demand. A.fourth and final period includes the months of April, May and June. Activity is reduced during this period. Apples continue to move from storage into retail channels and export markets. Processing is insignificant. Storage stocks reach a minimum before the next crop harvest begins in July. An aggregation by months as indicated above means that data must be similarly aggregated. It is apparent that the economic relationships of periods III and IV are identical. Since the purpose of this study is to explain short-term demand fluctuations there is considerable justification for not combining the two periods. Consequently the data have been aggregated to give separate periods. Iii!!- .‘ I 'l l d ‘ I! t l is I I l 1 I I l I III II J! I] 22 Examination of economic relationships between the variables discussed above indicates that four possible demand relationships for apples can be separated. These are l) demand by retailers for apples in a fresh form, 2) demand for apples to be processed, 3) an export demand for fresh apples, and 4) a demand for apples to be kept in storage. I The physical supply which is available in each period is equal to the beginning amount of apples in storage plus the quantity harvested during that period. Using an inventory relation and the first three of the above demand relationships a supply function can be written as, (1) S(m-l)t * th ' Smt + rmt + amt * emt In the notation used capital letters indicate stocks, while small letters indicate flows. The subscripts p_and 1 indicate reSpectively the period and year being considered. CrOp years beginning Ju1y 1 are dealt with rather than calendar years. Thus Period I which includes the first two months (July and August) of the crop year represents the beginning of a new year for analytical purposes. The above identity states that the physical supply on hand at the beginning of any period, s(m-l)t' plus the quantity harvested during that period, qmti constitute the total physical supply available during any one period. As 'ii ‘1' I ll“ I‘llllu'llllllll‘llll.‘ i l .l I 23 shown in equation (1) this supply is equal to the physical stocks on hand at the end Of‘a period, Smt’ plus the amounts used for retailing, rmt, processing, amt, and exporting, emt° This identity holds for all periods although some of the parameters within it will equal zero during certain periods. In the demand for storage relation to be develOped later (2) Smt 3 S(m-l)t - Smt to giVe a flow during the mth period rather than beginning or ending stocks. Smt may be negative depending upon the period being considered. The amount of fresh apples available for consumption during each crOp year will be equal to the amount harvested, since no carry-over is present. The quantity of apples harvested can be classified as an exogenous variable. This classification is made since current price has little to do with what is produced. The volume ready at harvest time is affected only by initial investment and production techniques or practices during the growing stage which have little relation to the price received when picking is actually carried on. Irrigation, fertilization, thinning, spraying and pruning may all be carried on and influence the yield, but the degree to which these practices are undertaken is not directly related to the price to be received by farmers. There is the possibility that harvesting will be curtailed ‘).-l_-\ .t i | 'l 11‘] l I l .1 .‘II I II .."I II I ll .1: Illllllll III II I II. | l lull l l! | | '24 if price is exceptionally low in the fall when harvesting is in progress. In all cases it should pay the producer to harvest his crOp if the variable costs of harvesting (i.e. picking, packing, tranSporting) are being met. Within a limited range the producer can postpone picking or can spot-pick but he is limited in such a practice and this may increase harvesting costs if the usual policy is to remove all apples from the trees at one piCking.6 ' Q There 13‘s high degree of competition in the production of apples as individual producers or small groups of producers ' have little effect upon the quantity harvested. In this study the supply at time of harvest will be termed exogenous and the rate of harvesting is assumed to be unaffected by current price. Production figures are based on the quantity of apples which are actually sold. This is equal to total production7 6Pailthorp, R. R. and Park, J. W. Op. cpp., p. 22. 7Source 1954-1951: Agricultpral Statistics. United States Department of Agriculture, Washington, D. C., Annual 1936-52. Data was adjusted prior to 1934 to get the quantity sold from the commercial areas of 35 states. This correSponds with the method of reporting after 1934. Source 1929-1933: Fruits non-citrus Prod ct o Disposition and Utilization pfpSales. United States Department of Agriculture, Bureau of Agricultural Economics, Washington, .D. C., 08-27, may, 1948. II ‘ ’ I. I ‘ III. III’ I 25 less the amount not harvested because of economic or climatic conditions and less the amount used in farm households.8 The data on quantity of summer apples harvested were supplied by the International Apple Association (IAA)9.for the years 1929-31 and 1942-51. For the years 1932-41 extrapolation was made on the basis of IAA data representing the years 1925-31, and 1942-51. This was done by plotting production of summer varieties against total production and fitting a regression line for each of the periods 1925-31 and 1942-51. Extrapolation was then made, assuming that there was a constant change in the production of summer varieties relative to total production during the period 8Because a portion of the apple crOp may not be harvested due to economic conditions, production is not completely exogenous. An additional structural equation could be included showing quantity harvested qmt as an endogenous variable being dependent upon the price at—EIme of harvest and the variable costs of harvesting. The omission of this additional structural equation will cause errors in the estimated regression coefficients of the demand equations. If the residuals in the regression equations are normally distributed and independent the estimates of the coefficients will be unbiased but the standard errors of estimate will be increased. If they are not normally distributed and independent the regression coefficients will also be biased. The decision was made to omit this equation and gain simplicity. The sacrifice of doing so is the loss in efficiency in estimating structural parameters. However the percent of apples not harvested due to economic conditions has never reached 10% of total production and therefore the loss of efficiency should not be large. 9From private correSpondence with the Secretary of the International Apple Association (1AA). September, 1952. 26 1932-41. Though inaccuracies result from this type of estimation, it appears to be the best approximation to reality at this time. Prior to 1944 the IAA collected production data for all varieties on only that portion of the crop which was consumed fresh. But for all practical purposes this equals the total quantity of summer varieties produced since processing and exporting at this time are unimportant. Data on the production of fall and winter varieties (Period II) are based upon published material in Agricultural 10 Statistics, and a United States Department of Agriculture publication.ll lOAgricultural Stapistipp, United States Department of Agriculture, washington, D. C., Annual 1935-1951. llAnonymous. Fruits non-citrus Prod ction Farm Disposition ang Utilization of Sales.. United States Department of Agriculture, Bureau of Agricultural Economics, Washington, D. C., 08-27, May, 1948. CHAPTER IV RETAIL DEMAND FUNCTION It was noted that four demand relationships are involved in the apple market, and each of the respective quantities demanded (i.e. for retail, processing, export, storage) is considered as a current endogenous variable. That is each is a function of other variables and cannot be considered as being predetermined, but must be explained in terms of other endogenous and exogenous variables. The first demand function to be determined and for which a structural equation is given is the quantity of apples demanded at the retail level. This demand function is present in each of the four periods. The equation takes the form of (3) dumt' Pmt‘ ymt' r*mta I'(m-l)t’ cmt) = O pmp = average price of apples at the farm for the period m and the year t. ymt consumer disposable income for a like period, rmt quantity of apples available for consumption during this period, r(m-1)t - consumption of apples during the immediately ' preceding period, ert = average consumption of apples during the same period but for several of the preceding years, Cmt - the price of competing fruits. 28 Hildrethl points out that there is much to be said for writing the equations in an implicit form as above, dis- tinguishing between the endogenous and predetermined variables by, e.g. use of a semicolon. This manner of writing the equation implies that either of the endogenous variables could be considered dependent, or it could be thought of as two endogenous variables appearing in a relationship with several predetermined variables. The average price of apples per bushel received by farmers is used as the price indicator.2 This choice was made because of the availability and completeness of these data as compared to those for retail prices and also because of the advantage of having it in this form for prediction purposes.3 lHildreth, C. and Jarrett, F. Cowles Commission Discussion Paper: Economics No. 2055, unpublished paper. Cowles Commission for Research in Economics, University of Chicago, Chicago 37, Illinois, November, 1952. 2This price series was compiled and supplied by United States Department of Agriculture, Bureau of Agricultural Economics, Washington, D. C., 1953. 5Where marketing margins are constant farm prices may be used and a simple correlation set up to relate them to retail prices. Where marketing margins are abnormal and data are available it would be more desirable to use retail prices when dealing with consumer demand to get true coefficients of price elasticity. Farm value as a percent of retail value is shown as follows: 29 The monthly prices have been averaged arithmetically to give an average price for each of the four periods. An average weighted by monthly marketings would be more accurate but data giving apple marketings by months were not available for the years considered. However, when the period is as short as those being used unweighted averages will not differ greatly from weighted averages. Pmt is considered an endogenous variable, and it must be possible to explain it in terms of other variables. Prices affect the quantity taken according to the Marshallian concept which states that the quantity demanded varies inversely with the price. The change in real income caused by price changes can be explained in terms of an income and a substitution affect as outlined by J. R. Hicks.4 Apples are not considered to be an inferior commodity and therefore consumer reaction to a fall (rise) in apple prices Farm Value as a Percent of Retail Apple Prices 1934-1943 Yea; 1934 1935 1936 1937i1938 1939 1940 1941 1942 1943 Percent 40 4O 42 46 38 4O 41 45 48 51 Source: Been, R. 0. Price Spreads Between Farmers and Consumers for Food Products 1913-44. United States Department of Agriculture, Bureau of Agricultural Economics, Washington, D. C., Misc. Pub. 576, p. 219, September, 1945. 4Hicks, J. R. lalue and Capitgl. Second Edition, Oxford University Press, Chapter III, London, 1948. 30 will always be to increase (decrease) the quantity bought. This represents the substitUtion effect. The “income" effect is unimportant in such a case since apples are a small portion of the total expenditure for food and therefore any price decrease in apples causes only a minute increase in real income. The relatively important effect is the substitution effect which reacts according to the Marshallian concept stated above. Consumer personal dISposable income is included as an exogenous variable affecting retail demand for apples . since it is determined outside of that system which explains the apple market. There is little reason for considering it as an endogenous variable because of any interdependent effects from producer‘s income or that of marketing agencies. 5 are given Published data on personal disposable income by quarters only. These quarters do not coincide with the four periods as outlined previously and an adjustment was made by using personal income which is reported monthly. Quarterly values of personal diSposable income were plotted against personal income and a regression line fitted freehand 5Anonymous. National Income. United States Department of Commerce, Bureau of Foreign and Domestic Commerce, washington, D. C., 1951 ed. Also Anonymous. Survey of Cprrent Bpsinesp. United States Department of Commerce, Office of Business Economics, 'Washington, D. C., July, 1952 and March, 1953. 31 for two periods. The first was from January 1929 to January 1943 and the second was from July 1943 to December 1952. Personal income was then aggregated according to the periods used in this study and the correSponding values of personal disposable income were read Off the plotted chart. For the period January 1943 to July 1943 observations did not fall on either of the two fitted lines and interpolations were made for these months. Two additional variables affecting retail demand which can also be classified as predetermined are 1) consumption during the immediately preceding period and 2) average consumption during the same period for several of the preceding years. It is difficult to hypothesize as to the manner in which consumption during the preceding period affects present consumption. Yet, intuitively it is possible to say that cumulated consumption will affect present con- sumption according to the law of diminishing marginal utility. The consumer's desire for apples will have been partially satisfied if purchases during the preceding period were abnormally large. It is also possible that storage facilities 'within the household have been partially filled by previous purchases. The variable r*mt is included on the grounds that <3onsumers buy according to some previously established habit. 32 Dusenberry6 presents a psychological foundation for this argument stating that families will not reduce consumption proportionally with income decreases. Their tendency is to buy according to a past period when satisfactions were maximized. This then assumes that apples are bought not only in reaction to price changes but that an established buying pattern is formed based on knowledge of varieties, quality, product uses, etc. The time lag is arbitrary, but a 3 year moving average is suggested, with the possibility of revisions being made. Thus r*mt = rm(t-1) * rm(t-2) * rm(t-§) a . Data for these two variables are formed by solving for rmt in the “storage stocks" identity previously given. rmt = Sm-l t + qmt ' smt ‘ amt ' emt The final variables affecting consumer demand for apples are the prices of competing fruits. If none of these are considered as being inferior goods a rise (fall) in the price of substitute fruits will result in a rise (fall) in the quantity Of apples demanded.'7 Income effects are again considered to be relatively unimportant. 6Dusenberry, J. S. Income. Employment and Public Policy. JEssays in honor of Alvin H. Hansen, W. W. Norton and Company, New York, p. 54, 1948. 7Hicks, J. R. Value and Capital. Op. cit., Chapter III, car Prest, A. R. Some Experiments in Demand Analysis, Rev. IEconomics and Statistics, Vol. 31, pp. 33-49, 1949. 33 Prices of competing fruits are determined by economic forces outside of the apple market and a function should be included which explains them if a complete model is to be constructed. Since a model would be extremely complex if the price of each competing fruit was taken as a separate variable an index of prices is used. This index is weighted by the quantity of each fruit marketed by periods for the years 1941-51. If elasticities of demand for each of the competing fruits were known the index could be more accurately computed by weighting those fruits which have a strongly elastic demand more heavily. Monthly marketings of oranges, lemons and grapefruit were supplied through correSpondence8 with the Bureau of Agricultural Economics, as were the prices of all fruits. Monthly marketings of pears, peaches and grapes9 were obtained from the Market NewsService Branch, Production and Marketing Administration of the United States Department of Agriculture. The decision made on whether a fruit is a competitor or not is quite arbitrary. Research workers10 have obtained 8From correspondence with United States Department of Agriculture, Bureau of Agricultural Economics. Op. cip. 9Monthly marketings of grapes include only those used in a fresh form and excludes use for production of wine or raisins. loWoodin, M. D. Changespgn the Prices of Apples and Othgp Fruits. Cornell University Agricultural Experiment Station Bulletin 773, December, 1941. 34 results which would indicate that fresh fruits do not compete closely with each other. In other instances considerable degrees of substitution are shown.ll While these studies are not necessarily conflicting it does show that considerable uncertainty exists as to the relations between fresh fruits. Intuitively it appears that other fresh.fruits do compete with apples for the consumer's money if both are available during the same period. Rather than discard cmt as a variable there is justification for including it unless further studies indicate more clearly a lack of substitutability. 11Boos, 8. An Investigation on Complementarity Relations Between Fresh Fruits. Journal of Farm Economics, Vol. 23, p. 4210 CHAPTER V STORAGE DEMAND FUNCTION Once apples are placed in storage, supply is considered to be an endogenous variable. Supply will be equal to the rate of movement from storage and will be governed by current and expected prices along with other relevant variables. In period I, there will be no demand for storage. In period 11, a positive demand will be present while in periods III and IV there will be a negative demand for storing apples, which indicates a movement from storage warehouses to the market. Storage stocks on June 30 are assumed to be zero. The storage function is considered as, (“31‘va Pm; S(m-l)t' Sins: cmt' km.» g-(t-l) ' 0 Where Pmt and cmt have the same meaning as outlined in the retail demand equation, (5) amt ' Smt - 3(m-1)t S(m-l)t is the quantity of apples on hand at the beginning of the period, S*mt is the average quantity of apples on hand at the end of similar periods during several of the preceding years, kmt is an index of the costs of storing apples and, g(t-1) is an index of the seasonal price increase for the previous year. 36 Current price may have an ambiguous effect upon the demand for storage depending upon expectations. Apples will remain in storage as long as the expected price at some future date is greater than the current price plus storage costs (which inelude losses from spoilage and a value judgment as to the risk involved). The following simple diagram indicates this process. The price of apples is plotted against time in monthly periods. Figure I Period of Investment in Storing Apples XP - schedule of expected prices with the shaded area indicating a range of uncertainty. schedule of storage costs. current price of apples. I I I I l I I OX'- current price plus T O . handling charge to place time (months) apples in storage. At time OT SXpected price per bushel is TR and cost per bushel is TS. Empected profit is than equal to RS and the owner of the apples Operating at time 0 would make the decision to store. 37 The inclusion of 5(t-l) is made on the grounds that the decision to store apples is in part based on the seasonal movement of apple prices during the preceding year. The index, 8(t-1) is constructed by taking the ratio of p2,t-1 and the average price of apples during the months March, April, and May of the t-l year. This gives a lagged endogenous variable. A large index indicates that a con- siderable increase in the seasonal price took place during the preceding storage period. Storage Operators will react by increasing the present demand for storage with the expectation that conditions will repeat themselves. This variable will be included in Period II only. A refinement in Period III would be possible by considering month to month storage decisions. A variable such as 3(t-l) could be constructed using the ratio of last year's price for the present month and last year's average price in March, April and May. Carry-over stocks1 of apples S(m-1)t affect present storage demand since it represents a portion of current demand which has been satisfied. (Current demand includes demand by retailers for fresh apples and also the demand for exports and for processing.) In physical terms carry-over lSoleau, B. S. United States Department of Agriculture, Production and Marketing Administration, Washington, D. C. Written communication, July 27, 1951. 38 represents that portion of storage facilities which is not available. Average storage holdings for the same period during several of the preceding years Swmt is an arbitrary guide to present storage demand based upon past habits and experience. It may also reflect commitments which storage owners have made legally or through trade experience over a long period of time. Again as in rfmt a 3 year moving average is used to give 5*mt - SpSt-l) + Sg(t-_2) + PM The price of competing fruits will partially determine what the current storage demand for apples shall be. If more accurate data were readily available on current and expected supplies of competing fruits, it would be more suitable to use it as an indicator. However, more complete data can be supplied on monthly prices than on monthly supplies. Since price is a function of quantity the substitution of price for quantity is made directly. It is felt that greater inaccuracy might be incurred through observations of the data if supplies were used than is incurred by errors in the variable (shock errors)2 when price is included as the variable. If the current 28ee discussion on types of errors, Chapter I. 39 price of competing fruits is low relative to its normal seasonal value there will be a tendency for current apple prices to be lower and storage operations will be intensified. If however the storage owners have the expectation that future prices of competing fruits will continue to be low the current storage demand for apples will be decreased. Storage costs influence decisions to store by influencing expected profits. A large percentage of storage costs are fixed and thus increase the demand to store apples, i.e. taxes, buildings, crates, grading machinery, refrigeration equipment. But the variable costs are also very important and decrease the desire to store apples. Labor is important in this category, not only its price but also its availability during the time when apples must be moved from storage ware- houses. Extra crates, operational costs for refrigeration units, or rental costs if storage facilities are not owned all serve to decrease the demand for storage. The decision to store is influenced by storage costs in two ways. The first is the level of the initial cost and the second is the storage rate per month once apples have been placed in storage. If the initial cost is high, fewer apples will go into storage. From the storage costs and November 30 stocks dates 3SoIeau, B. S. Op. cit. 40 a scatter diagram was constructed. There was no indication from this that the initial cost, which includes a handling charge plus a storage charge for the first month, had any effect upon the volume of apples moving into storage. From this the conclusion is drawn that initial charges have not been high enough to deter storage. Once apples have been placed in storage the initial charge will have an influence on the length of the storage period. Since initial cost is a fixed cost a longer storage period will reduce the average storage cost per bushel. The storage period will be shortened because of the variable cost of month to month storage charges. Storage stocks of February 28 were plotted against initial storage charges plus a three month storage rate per bushel and there is an indication from inSpection of the scatter diagram that the amount of apples held in storage is larger when costs of storage were low. An interpretation of this is difficult since price of apples may have had an overshadowing effect, but at least it does not disprove the thesis that the quantity stored varies inversely with storage costs. This latter scatter diagram would indicate that monthly rates per bushel are a more important consideration in the decision to store apples than is the initial storage charge. If the initial charge lengthens the storage period then where storage rates 41 (handling and storing) were highest the quantity of apples in storage should have been greatest. (Inspection of the data reveals that storage rates per bushel have been constant while handling charges have gradually increased from 1929-51). Thus, average total cost and not average fixed cost is the more decisive criteria in storing decisions. In some cases seasonal storage rates are quoted which offer a discount for long storage periods. These will also induce producers to store for longer periods. In any case one should remember that deterioration in the quality of the apples and the market price will be the important factors in moving apples into or out of storage. Some varieties cannot be stored for long periods while others retain their quality until period IV.4 For period II the index of storage costs will include handling charges plus storage costs for one month. This assumes one month of storage in period II. For periods III and IV only a storage rate per month will be used since handling charges have been paid for. The index of storage costs has been constructed for boxes stored in quantities great enough to get the regular 4Smock, R. M. Controlled - Atmosphere Storage of Apples. Cornell University Agricultural Experiment Station, Ithaca, New York, Bulletin 759, pp. 18-19, February, 1949. 42 or discounted rate. Data for the index were gathered through correSpondence with storage and warehouse Operators in the nine most important apple producing states.5 Their information was supplemented with storage cost data from several bulletins. From the two sources storage cost figures were derived for 12 of the 22 years studied (1929-51). For the remaining 10 years interpolations were made. ”The general tone of the correspondence carried on with the warehouse operators was that monthly storage rates had not varied a great deal since 1929. This is possible because of increased storage capacity reducing average fixed costs, constancy in costs of refriger- ation equipment needed per bushel stored, and also because of increased efficiency and technology in storing apples. Gradual increases in the handling charges were noted the range being from 3 cents per bushel in 1929 to 9 cents per bushel in 1951. Because of the great stability in year-to-year storage rates and the gradual increase in handling charges interpolation should introduce little error into the variable. 5 Washington, New York, Pennsylvania, Michigan, California, Virginia, Ohio, Idaho, and Oregon. CHAPTER VI PROCESSING DEMAND FUNCTION The third demand relationship used in building this model is that for processing. Processing of apples refers to drying, freezing, canning (both whole apples and apple sauce) and other uses which include cider, vinegar and juice. All of these processes were of importance throughout the period studied except for the freezing process which began in the early 1940's. The trend has been for the drying process to decline somewhat in importance relative to the others. Vinegar, cider, and juice have varied in importance during the years, leading one to believe that they are residual or marginal products in processing. The most important processing period is period II.l Period III is of lesser importance while in periods I and IV lProcessing periods for apples havebeen prepared by the American Can Company as follows: Opening and Closing Canning Dates for Apples New State Wash. York Penn. Mich. Va. Ohio W.1p. Ore. Opening Sept.15 Sept.15 Aug.15 Aug. 1 Aug. 1 Sept.15 Aug.15 Sept.15 Date , Closing Dec.3l Dec.3l Dec.3l Nov.30 Dec.3l Dec. 31 Nov.30 Dec.3l Date Source: The Canning Trade, Baltimore 2, Maryland, Part 2, V01. 75, p. 222. 1952. processing is almost non-existent. For the early years studied, data were not available on processing by months. Thus, it was necessary to specify processing operations as being undertaken in period II only. In the future a refine- ment in these data will be possible. The following variables are included as part of the processing relationship. (5) Y