Giannini V Foundation I of Agritulturol Economics An Analysis of Economic Relationships and Projected Adjustments in the U.S. Processing Tomato Industry Giannini Foundation Research Report No. 331 Division of Agricultural Sciences UNIVERSITY OF CALIFORNIA PRINTED DECEMBER 1981 A CKNOWLEDGMENTS The authors benefited substantially from comments by Gordon A. King, Samuel H. Logan, and an unidentified reviewer on an earlier draft of the report and, also, from conversations with Arthur M. Havenner concerning model solution procedures. We are most appreciative of the timely computational and programming assistance provided by William Wagner and Cristi Bengard of the Agricultural Economics Data Services Unit, University of California, Davis. We also acknowledge the typing assistance and preparation for publication provided by the Agricul- tural Economics Word Processing Unit, University of California, Davis, under the direction of Janice Aboytes, and by Gertrude Halpern of the Giannini Foundation Typesetting Unit, University of California, Berkeley, under the direction of Ikuko Takeshita. FOREWORD This is the second report of a two-part study of the economics of the processing tomato industry. The first report, primarily descriptive in nature, dealt with the structural characteristics and economic performance of the industry over the past 25 years. This report formulates an econometric model of the processing tomato economy. The study differs from another recently published econometric analysis of the tomato industry by Chern and Just (1978) in that it includes estimates of demand relationships for processed products and is broader in its area of coverage. It also develops an alternative formulation of the grower supply and processor demand structure for the raw product component. The model is used as a framework for projecting future levels of industry production and prices and for further evaluation of the economic impact of mechanical harvesting and other technological developments. Both reports in this series are extensions of research results reported in Brandt's doctoral dissertation (1977). Most of the work was supported by a research agreement between the California Agricultural Experiment Station and the Economics and Statistics Service, U. S. Department of Agriculture. TABLE OF CONTENTS Page SUMMARY i^iii Estimation Results Applications of the Model ix 1. INTRODUCTION i 2. STRUCTURE OF THE INDUSTRY 2 3. THEORETICAL FRAMEWORK OF THE MODEL 5 Outline of the Model Structure 5 Processed Product Demand and Market Allocation 11 California Grower Supply and Processor Raw Product Demand 13 The C hern-Just Model 13 Modifications of the Supply Relationship 16 Modifications of the Processor Demand Relationship 18 Production and Grower Prices in the Midwest and the East 20 4. DATA AND VARIABLE MEASUREMENT 21 Farm Prices, Production, and Acreage 21 Pack and Inventory Data 22 Processed Product Prices 23 Exogenous Variables 23 5. ESTIMATES OF MODEL PARAMETERS 23 Processed Product Demand and Inventory Allocation 24 Individual Commodity Interpretations 25 -Hi- Page California Grower Supply and Processor Raw Product Demand 29 Supply 30 Demand 31 Equation Selection 35 Elasticities 35 January 1 Stock Prediction 37 Other Region Production and Acreage 37 6. THE COMPLETE MODEL 37 Model Components 42 Solution Procedures 42 Appraisal of the Model 44 Validity of the Behavioral Equations 44 Goodness of Fit 44 Prediction Beyond the Observation Period 49 Stability Properties 49 Structural Properties 50 7. IMPACT OF MECHANIZED HARVESTING ON OUTPUT, EMPLOYMENT, AND PRICES 51 Supply Response with Continued Hand Harvest 51 Impacts on Output and Prices 53 Impacts on Employment 56 8. LONG-RUN MULTIPLIERS AND ECONOMIC PROJECTIONS 61 Multiplier Analysis 62 Economic Projections 71 Technological Change 71 Shifts in demand 74 Total Change Projections 76 -iv- Page 9. MODEL EVALUATION 78 APPENDIX A 80 APPENDIX B 98 APPENDIX C 101 APPENDIX D 105 LITERATURE CITED 108 LIST OF TABLES Table 1 Structure of the Industry Model 6 2 Three-Stage Least Squares Estimates of Processed Tomato Product Demand and Market Allocation Relationships, Linear Equations, and Five 2-Equation Systems, 1954-1977 26 3 Three-Stage Least Squares Estimates of Processed Tomato Product Demand and Market Allocation Relationships, Log Formulation, and Five 2-Equation Systems, 1954-1977 27 4 Estimates of Grower Supply and Processor Raw Product Demand Relationships for California Processing Tomatoes, 1954-1977 32 5 Grower Supply and Processor Raw Product Demand Elasticities Before and After Harvest Mechanization for Selected Years, 1960, 1970, 1975, and 1977 36 6 Ordinary Least-Squares Estimates of Acreage and Grower Price Relationships for the Midwest and East, 1954-1977 38 7 U. S. Processing Tomato Industry Structural Equations 39 8 Goodness-of-Fit Measures, Processing Tomato Industry Model, One- Period-Change Predictions, 1955-1977, and 1978-79 and 1979-80 Prediction Errors 46 9 Goodness-of-Fit Measures, Processing Tomato Industry Model Sequential Predictions, 1955-1977 48 -V- Table Page 10 Model Predictions of Changes in California Acreage, Production, and Prices if Mechanical Harvesting Had Not Been Developed, 1964-1977 54 1 1 Comparison of Model Predictions of California Processing Tomato Industry Employment With and Without Mechanical Harvesting Development, 1960-1977 57 12 Model Predictions of Changes in California Tomato Industry Employment If Mechanical Harvesting Had Not Been Adopted, 1964-1977 58 13 Base Conditions for Economic Projections 64 14 Long-Run Multipliers for the Processing Tomato Industry Model ... 67 15 Approximations of Long-Run Population Multipliers for the Processing Tomato Industry 75 16 Summary of "Optimistic" Tomato Industry Growth Projections for California Acreage, Production, and Price Variables, 1980 to 1990 77 Appendix table A.l Processing Tomato Production Statistics for California, 1954-1980 81 A.2 Processing Tomato Production Statistics for the East, 1954-1980 ... 82 A-3 Processing Tomato Production Statistics for the Midwest, 1954-1980 ; 83 A.4 Processing Tomato Production Statistics for the United States, 1954-1980 84 A.5 Canned Tomatoes: Supply and Disposition Statistics, 1954-1979 .... 85 A.6 Tomato Juice: Supply and Disposition Statistics, 1954-1979 86 A.7 Tomato Catsup and Chili Sauce: California Supply and Disposition Statistics, U. S. Exports, 1954-1979 87 A.8 Tomato Puree: Supply and Disposition Statistics, 1954-1979 88 A.9 Tomato Paste: California Supply and Disposition Statistics, U. S. Imports and Exports, 1954-1979 89 -vi- Appendix table Page A.IO U. S. Per Capita Disappearance and Aggregate California Pack and Stocks of Processed Tomato Products, 1954-1979 90 A.l 1 Season Average F.O.B. Processor Prices of Tomato Products, 1954-1979 91 A.12 Season Average Prices of Tomatoes and Tomato Products Deflated by the Consumer Price Index, 1954-1979 92 A. 13 Processed Tomato Product Prices Per Unit of Raw Product and Average Processoi^Grower Margin Indicators, 1954-1979 93 A.14 Values of Selected Exogenous Variables Affecting Demand and Supply of Tomatoes and Tomato Products, 1954-1979 94 A.15 Processed Tomato Product and Minor Region Allocation Ratios, 1954-1979 95 A.16 Conversion Factors for Containers to No. 303 Cans and to Cases of 24 No. 303 Can Equivalent 96 A. 17 Conversion Factors for Processing Tomato Products, Cases, and Prices 97 B. l Trend Values of California Processing Tomato Production Costs, 1953-1979 100 C. l Labor Conversion Coefficients for the Processing Tomato Industry, 1960-1979 103 D. l Matrix Representation of the U. S. Processing Tomato Industry Model, Bj Yt = B2 Yt-i + B3 Zt 106 Figure 1 Structure of the Processing Tomato Industry 4 -vii- SUMMARY This study formulates a dynamic econometric model of the U. S. processing tomato industry. The behavioral elements of the model consist of processed product demand equations facing processors, processor market allocation equations, raw product demand equations facing growers, and grower supply equations. The primary focus is on California but included are grower price and acreage equations for the Midwest and East. The processed product demand and market allocation equations involve a block of five sets of simultaneously determined equations — one set for each of the five major commodity forms. The California processor raw product demand and grower supply equations form another block of simultaneous equations. The Midwest and East grower price and acreage equations are sequentially linked to California adjustments through a price relationship. The estimates of supply and demand equations, which are the basis for the model, are all consistent with theoretical expectations; and the estimates of equation coefficients are generally within acceptable bounds of statistical significance. Altogether, the model consists of 56 endogenous and 14 exogenous variables. Estimation Results The most significant of the estimation results of the model can be summarized as follows: 1. The demands for the more concentrated tomato products (catsup and paste) at the f.o.b. processor level are inflexible with respect to quantity.^ (Puree demand price flexibility was not estimated.) The demands for canned tomatoes and tomato juice are flexible with respect to quantity. 2. Processors' supply allocations to the domestic market for the five processed products are all inelastic with respect to price. 3. Processor demand for the raw product is inelastic when estimated with quantity as the dependent variable. Lagged composite processed product price, deflated income, inventories, and the influence of the growers' bargaining association were all found to be important variables in explaining processor derived demand. 4. Grower short-run supply was estimated to be inelastic with respect to price. Explanation of grower behavior was improved through the incorporation of a partial adjustment model. The adjustment coefficient was estimated to range from .30 to .40, indicating a slow-to-moderate grower adjustment process. Long-run supply elasticity was substantially greater than in the short run. Price flexibility is the percentage change in price associated with a given percentage change in quantity. Demand is said to be flexible when the absolute value of the price flexibility is greater than 1.0 and inflexible for values less than 1.0. -viii- Applications of the Model The industry model provides a tool that may be used to aid in a short-run prediction, to analyze economic performance, and to evaluate potential impacts of changes in exogenous variables on industry development and growth. Because of the considerable amount of residual variation which remains unexplained by the behavioral equations, the model does not predict year-to-year variation in prices and outputs with great precision. Nevertheless, the estimates of processed product demand slopes, inventory effects, market allocation relationships, and processor demand and grower supply relationships provide a framework within which short-term forecasts may be evaluated. The unexplained disturbances which affect the accuracy of the short-run forecasts are of less concern with respect to evaluating longer term adjustments since they tend to average out. An interesting behavioral characteristic of the industry, also revealed by the study, is the tendency for both inventories and average processor margins to vary cyclically. An economic performance issue of great public interest and controversy has been the economic and social consequences of the adoption of mechanical harvesting of processing tomatoes. The industry model provides a more rigorous and detailed method of evaluating these consequences than has been available heretofore. The model is used to make comparative estimates of output, employment, and prices with and without the development of mechanized harvesting. Since supply conditions were altered by the termination of the Bracero Program about the time mechanized harvesting began, the effects of several alternative labor cost scenarios are examined. The model shows that total industry employment was greater after the full adoption of mechanized harvesting than before mechanization. This, however, reflects a response to greatly expanded demand as well as mechanization. When the effects of mechanization are isolated, the model predictions indicate that, even under the most restrictive (high cost) labor scenario considered, total harvest season labor employment would have been greater with a continuation of hand-harvest methods. This has been offset to a considerable degree by growth in cannery and assembly labor employment as a result of greater output induced by mechanization, but total employment is shown to be less under mechanization for all the scenarios considered. Balanced against the labor displacement under mechanization is a reduction in consumer prices compared to hand harvest of from 5 to 15 percent and a shift in the distribution of employment toward higher paying and less physically demanding jobs. Another application of the model was as a tool for economic projection. The procedure was first to solve the model to obtain long-run multipliers. These are coefficients which predict how a one-unit change in an exogenous variable, with other exogenous variables constant, affects the final values of endogenous variables after the system has stabilized. Since the endogenous variables tend to converge quickly to values near their stationary equilibrium values, the long-run values predicted by the multipliers are not far from interim period values. The long-run multipliers then provide a means of evaluating and separating the effects of conditionally considered changes in exogenous variables. The first application of the multiplier analysis was to evaluate the impact of the addition of electronic sorting to the mechanical harvester. Using data from a recent study of harvesting cost, the model indicates that the effect of electronic sorting on grower price is modest, and the effect on industry output is surprisingly low. However, it has a substantial -ix- impact on employment. Labor displacement with full adoption of electronic sorting is projected at between roughly 4,400,000 and 5,400,000 hours of labor per year (8,800 to 10,800, 10-week jobs). This is not as large as the estimated displacement of seasonal labor due to the initial adoption of the mechanical harvester. The latter is estimated at near 20,000,000 labor hours by 1977. However, seasonal labor displacement from the initial harvester adoption was offset by the creation of new cannery and assembly jobs to a much greater extent than will be the case for the electronic sorter. An evaluation of other plausible gains in production and processing efficiency indicates that their potential impacts on industry output and prices are likely to be small relative to potential expansion in response to population growth and, possibly, continued growth in per capita demand. Summing these potential effects, the model suggests that California's average acreage could expand by up to 60,000 acres in the next decade, but a figure about half that may be more likely. The projected adjustments to changes in technology suggest that most, but not all, efficiency gains would be passed on to consumers in the form of reduced prices. However, the price-lowering effects of efficiency gains likely would be offset by price-increasing effects of expanded population and market demand, leaving the real (deflated) prices not greatly changed. -X- AN ANALYSIS OF ECONOMIC RELATIONSHIPS AND PROJECTED ADJUSTMENTS IN THE U. S. PROCESSING TOMATO INDUSTRY by Jon A. Brandt^ and Ben C. French' 1. INTRODUCTION Tomatoes are the most important vegetable grown for processing in the United States (excluding potatoes), and California is the most important producing state. In the period since the early 1950s, the output of this industry increased from an annual average of 3.4 million tons valued at $98.1 million (1950-1953) to nearly 7 million tons valued at $467 million during 1976-1979.*^ This growth has been associated with major changes in the location of production, in production and processing technology, in the employment of labor, in the demand for various processed tomato products, and in the industry structure. The likelihood of continued change in factors affecting demand and supply make future planning and decision making especially difficult for both producers and processors. This report describes the formulation and estimation of an econometric model of the tomato industry and its use as a tool for planning and for evaluating the impacts of some of the technological and structural developments which have occurred and still are occurring. The model is a mathematical representation of the processes by which producer and processor prices and quantities are determined. It consists of three types of equations: (1) supply and allocation equations which relate quantities produced or made available for sale to prices and to supply-shifting variables such as costs and inventories; (2) demand equations which relate quantities purchased by consumers, processors, and marketing groups to prices and to demand-shifting variables such as income and population; and (3) identities or technical relationships which tie the equations together to form a complete system. No econometric model can fully represent all of the adjustment detail and all of the horizontal, vertical, spatial, and temporal dimensions of an industry. The objective here is to provide a framework for estimating how the major endogenous price and quantity variables are related and how they are influenced by changes in the values of key exogenous factors which affect levels of demand and supply. Economic influences which cannot be captured by the behavioral equations or as technical restrictions are reflected as random errors or disturbances. Thus, the predictions of the model are in the form of expected values of variables from some probability distribution of actual values. ^Assistant Professor, Department of Agricultural Economics, Purdue University, West Lafayette, Indiana. ^Professor of Agricultural Economics and Agricultural Economist in the Experiment Station and on the Giannini Foundation, University of California, Davis. ^Farm value, measured at the processing plant door; for data sources, see Appendix tables, infra, p. 80. The model development proceeds in two stages. The first step is to formulate hypotheses about the kinds of economic relationships required to model the system and the variables to be included. Most such relationships are obtained from generally accepted theories of economic behavior. However, several aspects, such as the formation of price expectations and lags in adjustment processes, may plausibly assume a number of different forms. The modeler must choose among the alternative formulations in accordance with c priori theoretical considerations and statistical criteria. The second step in the analysis involves empirical estimation of the parameters of the equations hypothesized to exist and testing and comparing the results obtained with alternative behavioral hypotheses. At this stage, the model development was further constrained by a lack of data pertaining to some of the variables believed to be important. It also turned out that some variables move so closely over time that it is difficult to separate their individual influences. Existence of these conditions has required additional simplification or aggregation of some components in the model. Section 2 briefly describes some key characteristics of the structure and organization of the processing tomato industry. Section 3 develops the theoretical framework for the econometric model and suggests behavioral hypotheses to be tested. Section 4 describes the data used in the analysis. Section 5 reports the results of empirical estimation and testing of alternative model formulations. Section 6 summarizes the other complete model. Section 7 applies the model in a simulation framework to evaluate the impacts of mechanical harvesting developments on output and employment. Section 8 uses the model as a base to evaluate the further impacts of the electronic sorter and to explore potential future impacts of changes in exogenous variables such as population, income, and further technological progress. Section 9 provides a general evaluation of the analysis. 2. STRUCTURE OF THE INDUSTR Y Tomatoes for processing are grown primarily in three regions of the United States. California is the dominant producer with over 83 percent of U. S. production for the years 1976-1979. The midwestern states of Indiana, Ohio, and Michigan have accounted for another 10 percent, while the eastern states of Delaware, Maryland, Pennsylvania, Virginia, and New York have produced a little over 4 percent. The remaining production has been scattered among states in several other areas. The shares noted above may be contrasted with 1950-1952 shares of 48 percent for California, 19 percent for the Midwest, and 27 percent for the East.^ In the years prior to the mid-1960s, all tomatoes were hand picked and transported to canneries in lug boxes. Today all processing tomatoes in California are harvested mechanically and transported in bulk to the processing plants. Some mechanical harvesting of tomatoes is performed in the Midwest and East, but hand harvesting is still the most common form. At the canneries, tomatoes are converted into six major forms: ^The characteristics of the tomato industry and its evolution during the past 30 years have been described at some length in King, Jesse, and French (1973); Brandt, French, and Jesse (1978); and Chern and Just (1978). Readers interested in the descriptive details are advised to refer to these reports. More recent extensions of production, acreage, and price data may be found in the Appendix tables at the end of this report. -2- (1) canned tomatoes 1 (2) juice, (3) catsup and chili sauce, (4) puree, (5) paste, and (6) sauce and other products.-^ Since the harvest season is relatively short (extending mainly from late July to early October), processors accumulate large inventories of processed products which are then reduced by sales during the interval to the next harvest season. The exchange structure in California has been altered somewhat in recent years by two developments. The first has been an increase in the share of tomatoes processed by associations of farmer cooperatives, currently estimated by industry sources to be near 40 percent. The second development has been the efforts of the Cahfornia Tomato Growers Association (CTGA), beginning in 1974, to bargain with processors over prices and other terms of trade for its members. In 1979, roughly 70 percent of California tomato growers were members of the CTGA. These structural changes are examined further in the later analysis. The flow of tomatoes and tomato products from producers to consumers and the interactions among the various stages in the system are illustrated in Figure 1 .3 The total commodity system may be divided into four major components: the grower subsystem, the processor subsystem, the marketing group subsystem, and the consumer group subsystem. In addition, several secondary groups are influenced by the behavior of the main groups. These include, but are not limited to, (1) suppliers of agricultural and nonagricultural inputs such as machinery, fertilizer, seed, and chemical companies as well as banks and credit institutions; (2) cannery and farm labor; (3) communities where tomatoes are produced or processed; and (4) governmental institutions. The influences of federal, state, and local governments on the system are reflected in various laws and policies among which are those regulating (1) pollution levels, (2) pesticide and herbicide use, (3) labor practices and minimum wage rates, (4) product grades and standards, and (5) import/export standards. The solid rectangles in Figure 1 show the product flow, and the broken rectangles indicate the influence of major exogenous or predetermined variables on the product output and movement. The circles show the interaction and feedback effects of the price variables. The division between year t and year t - 1 illustrates the delayed effects of changes in the values of some of the variables affecting output decisions. Beginning with the grower subsystem at the bottom of Figure 1, the levels of planted and harvested acreage are affected by the contract price, costs of production, weather conditions, and acreage planted in previous years. The expected profitability levels of alternative crops may also influence the production of tomatoes. The price received by growers is shown to be jointly determined (by the dual directional arrows) with processors' demand for raw tomato production. Through the feedback process, prices at higher levels of the market channel (e.g., f.o.b.) send signals to the grower level. Processors receive and pack the raw tomatoes into the various product forms illustrated in the center of the diagram. This allocation process is based on expected sales and price levels for the next market period and is also affected by plant operating costs and capacity. Canners distribute their finished products either to domestic sales, export sales. Includes whole-round, pear-shaped, and specialty packs such as wedges, sliced, diced, and crushed. 2 Includes specialized pack items such as tomato aspic, fish sauce, cocktail sauce, pizza sauce, spaghetti sauce, and tomato soup. 3 To simplify the presentation, regional components have been excluded from the diagram and are discussed in later sections of the model development. -3- I Population I 1 I I I I I I Consumer Tastes and Income "1 . _i I I Substitutes ] II and I 1 I Complements i Processed* Product Sales Market GrouD" Carryin Stocks Imports [- Market Group* Carryout Stocks Market* Group Supply I Market Group I Costs I L Canner* Carryin Stocks Canner* Carryout Stocks Processing Costs J I 1 ' Grower !_ I Costs I I I Planted Acreage Year t-1 Plant Capacity Canner Pack* I Production of Raw Tomatoes I I Yield I 'I Harvested Acreage i I Weather i I I *Product Forms: Canned Juice Catsup Puree Paste Sauce Other I Market System Costs Planted Acreage Year t FIGURE 1. Structure of the Processing Tomato Industry -4- or inventory carry-over. This allocation decision is influenced by current domestic f.o.b. prices, export prices, expected f.o.b. prices in future market periods, and inventory costs. The marketing group distributes the processed products from the three major production regions to retail outlets and institutional and remanufacturing establishments located throughout the United States. Consumer demand is reflected directly through purchases of the products in their final form (e.g., juice, catsup, and sauce) and indirectly through purchases of prepared food items using tomato products as ingredients. Factors affecting demand include consumer tastes and preferences and disposable income, population, and the prices of competing and complementary products. 3. THEORETICAL FRAMEWORK OF THE MODEL A completely general model of the system illustrated in Figure 1 would include demand functions facing retailers for each processed commodity in each consuming region, distribution cost functions between all producing and consuming regions, and grower supply functions and processor allocation and demand functions for each producing region. Since the data required to estimate such a multimarket, multilevel, multiproduct model are not available, it is necessary to restrict the scope of the model to include only a more limited and more aggregated set of relationships. The model focuses only on the processor and grower subsystems. This does not preclude the formulation of a complete model since the f.o.b. demand functions facing processors are derived from consumer and distributor demands and contain as variables the major factors thought to influence consumer and distributor demand. The model predicts how changes in exogenous variables, such as population and input prices, affect endogenous variables such as total California and U. S. production, consumption of the various processed commodities, and processed product and grower prices. However, it is not formulated to predict interregional commodity flows or retail prices. Outline of the Model Structure The structure of the industry model is outlined in Table 1. The symbols used to identify the variables are defined at the end of the table, and the data series for all variables are given in the Appendix tables. In each of the behavioral equations, the variables listed to the right of the colon are treated as exogenous in this study, i.e., their values are determined primarily by forces outside the tomato economy. Exogenous variables which appear in identities are placed within parentheses. Variables on the left of the colons are endogenous, i.e., their values are determined as outcomes of the system for given values of the exogenous variables. For ease of later reference, all of the behavioral relationships are expressed with one of the endogenous variables as the dependent (normalized) variable. As noted below, however, the values of some of the current endogenous variables appearing in each equation are jointly determined. The variable on the left is the variable chosen for normalization in the simultaneous estimation procedure as described later. The complete model consists of 16 behavioral equations and about 40 identities and technical relationships which are necessary to complete the system. For analytical and estimation purposes, the behavioral equations are grouped into three blocks. Block I contains processed product demand equations facing processors for each of the five major commodity types [Table 1, equations (1), (6), (10), (14), and (18)] and processor market allocation equations for the same commodities [Table 1, equations (2), -5- TABLE 1 Structure of the Industry Model Type of relationship Variable structure I. Processed Product Demand and Market Allocation Canned tomatoes (W) 1. Demand 2. Market allocation 3. Consumption identity 4. Inventory identity 5. California stock prediction Tomato juice (J) 6. Demand 7. Market allocation 8. Inventory identity 9. California stock prediction Catsup and chili sauce (C) 10. Demand 11. Market allocation 12. California sales prediction 13. Inventory identity Tomato puree (U) 14. Demand 15. Market allocation 16. Inventory identity 17. California stock prediction Tomato paste (P) 18. Demand 19. Market allocation 20. Consumption identity 21. California sales prediction 22. Inventory identity PWt = £w (DWt: DOVt, Yj. Nj, CPIt, u^) AWt = [(QWt + SW^), PWj, PWt_i: N^, CPIt, DWj = AWj + (IWj) SWj+i = SWj + QWj - AWj - (EWj) SWq = [QWCt_i/QWt_i] SWj PJt = fj (DJt: Nt, CPIt, VJf T, Ujt) DJt = hj ((QJt + SJt),PJt, PJt-r Nf CPIt, vjtl SJt+1 = + QJf - DJt - (EJt) SJCt = [QJCt_i/QJt-i] SJt PCt = fe (DCf SCCj: Yt, Nt, CPIt, u^) DCt = \ [(QCCt + SCCt), PCf PCt_i: Nj, CPIt, Vct! DCCj = (KCCt • DCt) SCCj+i = SCCt + QCCt " DCCt PUt = fu (DUf SUt: Yf Nt, CPIt, "ut) DUt = h„ [(QUt + SUt), PUt_i: Nt, CPIj, v„tl SUt+i = SUt + QUt - DUt SUCt = [QUCt_i/QUt_i] SUt PPt = fp (DPt, SPICt: Yt, Nt. CPIt, V APt = hp [(QPICt + SPICt), PPf PPt-i: Nt, CPIt, DPt = APt + (IPt) DPICt = (KPCt) [APt + (EPt)] SPIC^^-i = SPICt + QPICt - DPICt (Continued on next page.) -6- TABLE 1— continued. Type of relationship Variable structure II. California Grower Supply and Processor Raw Product Demand 23. California acreage supply 24. California quantity supply 25. Processor raw product demand 26. Observed processor purchases 27. Processor demand for acreage 28. January 1 stock prediction 29. Stock aggregation 30. Allocation to product pack (a) Canned tomatoes (b) Juice (c) Catsup (institutional) and chili sauce (d) Puree (e) Paste (institutional) (f) Total reported pack A(f^ = f^^ (PGC^, ACt_i: YMACj. GCRt_i, CPI^, TC, v^^) QCT^ = (YLDCPj) • AC| QCTOj = (PGCt. PRWt_i, SlTj: Y^, CPIt, M^, u^^) QC-I^ = QCTDj + (e^) AdJ = QCTDj -H (YMAC^) SlTt = f, (QCTRt_i, SCTt_i: Ugj) SCTj = SWCjAh^) + SJCj/Chj) + SUCt/(hu) + SCCt/(h^) + SPICt/( (hp) QJCt = (gj^t) • (hj) • QCTt QCCt = (gcct) • (he) • QCTt QUCt = (guet) • (hu) • QCTt QPICt = (gp,t) • (hp) • QCTt QCTRj = QWCt + QJCj + QCCj + QVC^ + QPIC^ in. Other Region Production and Acreage 31. Midwest grower price 32. Midwest acreage 33. Midwest production 34. Eastern grower price 35. Eastern acreage 36. Eastern production 37. Minor production 38. Minor acreage 39. Other region production 40. Total U. S. production 41. Allocation of other region pack (a) Canned tomatoes (b) Jmce (c) Puree 42. U. S. product pack (a) Canned tomatoes (b) Juice (c) Puree PGMt = (PGMt_i, PGCt, QMTt_i: T, CPIj, u^^) AMt = fam (PCMj, PMS^.j: T, CPIt, u^^) QMTj = (YLDMPf) • AMj PGEt = fpe (PGEt_i, PGCt, QETt.j: T, CPIj, AEt = fae (^^^t ^ T, CPIt, u,t) QETt = (YLDEPf) • AEj QRTt = (RRt) • (QCTt + QMTj + QETj) ARt = (RAt) • (ACt + AMt + AEt) QOTt = QMTt + QETt + '^'^'^t QTt = QCTj + QOTt QWOt = (g„ot) • (hw) • QOTt QJOt = (gjot) ■ (hj) • QOTt QUOt = (g„ot) • (hu) • QOTt QWj = QWCt + QWOt QJt = QJCt + QJOt QUt = QUCt + QUOt (Continued on next page.) -7- TABLE 1— continued. Variable identification'^ Endogenous variables PK = average California f.o.b. price for product K (dollars per case) K = W (canned) 24/303 cans, standard J (juice) 12/46 oz. cans fancy C (catsup) 24/14 oz. glass bottles, fancy U (puree) 6/10 cans, 1.06 sp. gr. P (paste) 6/10 cans, 26 percent solid DK = U.S. disappearance of processed tomato products (1,000 24/303 case equivalent) K = W (canned), J (juice), C (catsup and chili sauce), U (puree), and P (paste) DKC = California disappearance of institutional-size tomato products (1,000 24/303 cases) K = C (catsup and chili sauce) and PI (institutional paste) AK = U. S. processed product allocation to domestic sales (1,000 24/303 cases) K = W (canned) and P (paste) SK = U. S. carry-over stocks of tomato products, July 1 (1,000 24/303 cases) K = W (canned), J Ouice), and U (puree) SKC = California carry-over stocks of tomato products, July 1 (1,000 24/303 cases) K = W (canned), J (juice), U (puree), and CI (institutional catsup plus chili sauce) and PI (institutional paste) QK = U. S. pack of tomato products (1,000 24/303 cases) K = W (canned), J (juice), and U (puree) QKC = California pack of tomato products (1,000 24/303 cases) K = W (canned), J (juice), U (puree), CI (institutional catsup and chili sauce), and PI (institutional paste) QKO = other regional pack of tomato products, excluding CaHfomia (1,000 24/303 cases) K = W (canned), J (juice), and U (puree) (Continued on next page.) S- TABLE 1— continued. , Variable identification^ ! Endogenous variables (continued) PGK = raw tomato contract price (dollars per ton) K = C (California), M (Midwest), and E (East) QKT = raw tomato deliveries to processors (1,(XX) tons) K = C (California), E (East), M (Midwest), R (Minor), and O (East plus Midwest plus Minor) QCTR = aggregate California processed tomato pack reported (1,(XK) tons, farm weight) AK = planted tomato acreage (1,000 acres) K = C (California), M (Midwest), E (East), and R (Residual) SIT = stocks of California tomato products, January 1 (1,000 tons, farm weight) SCT = carry-in inventory of California processed tomato products reported, July 1 (1,000 tons, farm weight) j Exogenous variables DOV = U. S. consumption of processed and frozen vegetables other than canned tomatoes (pounds) Y = total disposable income (1,(XK) dollars), calendar year T = time trend (1954 = 1 ) VJ = diuimiy variable which accounts for difference in reporting tomato juice pack (1952-1967 = 1; 1968-1977 = 0) IK = U. S. tomato product imports (1,000 24/303 cases) K = W (canned) and P (paste) EK = U. S. tomato product exports (1,000 24/303 cases) K = W (canned), J (juice), and P (paste) CPI = consumer price index (1967 = 100), calendar year . (Continued on next page.) -9- TABLE 1— continued. Variable identification** Exogenous variables (continued) N = population as of January 1 of market year (thousands) YLDKP = average yield of raw tomatoes (tons per planted acre) K = C (California), M (Midwest), and E (East) YMAC = three-year lagged moving average of California yield (tons per harvested acre) GCR = representative grower cost of producing tomatoes in Cahfomia (dollars per acre) TC = adoption rate of mechanical tomato harvester (percent of California crop harvested mechamcally) as reported m Appendix Table A.14 QRT = residual raw tomato dehveries excluding California, the Midwest, and the East (1,000 tons) PMS = seasonal average price of soybeans deflated by CPI, Ohio (dollars per bushel) PRW = weighted average processed product price (farm-weight equivalent)'' M = dummy variable: M = 1, 1974-1977; M = 0 all years preceding 1974 hi^ = farm weight to canned weight conversion factor for tomatoes (tons to 24/303 cases) i = w (canned), j (juice), c (catsup) u (puree), and p (paste) KiC = California's institutional share of U. S. sales i = C (catsup and chili sauce) and P (paste) raw tonnage to product pack allocation rate (three-year centered moving average) i = w (carmed), j (juice), c (catsup and chiU sauce), u (puree) and p (paste) k = c (California) and o (Other Regions: Midwest plus East plus Residuals) RR = three-year centered moving average of QRT (QCT + QMT + QET) RA = three-year centered moving average of AR ^ (AC + AM + AC) u, V, and e = terms to account for unexplained disturbances I ° A more complete description of the data including sources is contained in section 4 and Appendix A. *For further definition, see Table 7, infra, p. 39. ^Values of gj^ • hj are defined as RKC and RKO in Table 7, infra, p. 39. -10- (7), (11), (15), and (19)]. 1 For each commodity, the product price and quantity allocated to current sales are simultaneously determined within each sales period. Because of data limitations, it was not possible to estimate demand and supply equations for imports and exports. These variables are treated as exogenous in the analysis. This simplified specification is reasonable in view of the very small percentages of production exported and imported and the dominance of exogenous factors on international markets. Block II contains the California grower supply and processor raw product demand functions. These equations form another interdependent system with grower price, acreage, and production simultaneously determined. The processor demand for the raw product is also influenced by the final product demand through inventory levels and lagged values of product prices. Efforts to estimate functions which would allocate the raw product to processed product forms by economic criteria were unsuccessful. Equation set 30, therefore, allocates California production in accordance with historical shares. Other region raw product is allocated in a similar manner [equation (41)]. Block III contains acreage and grower price equations for the Midwest and East [Table 1, equations (31), (32), (34), and (35)]. These equations are formulated as a recursive system in which grower prices of the Midwest and East are sequentially related to California grower prices and other variables. The small quantities of tomatoes produced outside the three major regions are treated as exogenous variables for purposes of determining total industry output. The remainder of this section explains the reasoning behind the specification of the particular sets of variables for each of the behavioral equations in Table 1. Processed Product Demand and Market Allocation The demand functions facing California processors for each of the five product types are derived firom the consumer and marketing group demands and thus include all the major variables thought to influence the levels of consumer and marketing-group demand.2 The inventory allocation equations explain how available quantities (pack plus carry-in stocks) are allocated between current sales and inventories to be carried into the next season. The demand function relates product price to quantities sold, quantities of competing products, income, population, price level, time trend (where appropriate), and a residual disturbance term. For catsup, puree, and paste, a stock variable is introduced into the demand function as a proxy variable to account for effects of inventory accumulations by manufacturing purchasers, as explained more fully with the presentation of econometric results. In the case of tomato juice, a trend variable was Data for tomato sauce and other specialty products are not of adequate quality to permit meaningful statistical estimation of economic relationships. The basic formulation of consumer demand theory can be found in numerous publications such as Henderson and Quandt (1971), Malinvaud (1972), and Phlips (1974). The problems of multiple- product choices, aggregation over individuals, and other related issues are largely ignored in this report. Phlips discusses several of these issues and suggests specifying per capita demand relations; for further development of these topics, see Brandt (1977, pp. 119-124). -11- introduced to account for a general downward shift in per capita demand, and a shift variable, VJ, was included to account for a change in the method of reporting juice packs and movement (Appendix Table A«6, footnote a). In the empirical analysis the effects of population are imposed by expressing quantity variables and income on a per capita basis, and the effects of price level changes are incorporated by expressing prices and income as deflated values [i.e., divided by the Consumer Price Index (CPI)]. Omitted from the demand equations facing processors is a variable which specifically accounts for changes in marketing-group costs such as transportation, warehousing, and retail and distributor margins. It was not possible to find a time series measure of such costs. However, it seems likely that the general movement of marketing costs has been highly correlated with movements of the CPI. To the extent that this has been the case, expressing prices in deflated terms would remove the marketing-cost influence as a variable, leaving it a part of the constant term of each equation. Changes in marketing costs not associated with changes in the CPI may be reflected as trend influences and as elements of the disturbance term. Since income changes have been highly correlated with time, it is likely that, if any other residual influence of changes in marketing costs exists, it may be absorbed by the income variable. Market-allocation equations are required because available supplies (SK + QK) can be distributed either to current U. S. markets, to export sales, or carried forward as stocks to be sold in the next period. Equations (2), (7), (1 1), (15) and (19) model the allocation decision. The dominant factor determining current sales is the available supply. If processors could anticipate production and demand conditions with complete certainty, there would be no carry-over stocks except as might be required to maintain flows through marketing channels. Quantities marketed would be very closely tied to available supplies. In practice, however, processors experience substantial difficulties in coordinating production with demand. Short-term equality of supply and demand may be achieved either by permitting product prices to fall below or rise above expectations, by allowing inventories carried forward to fluctuate, or both. The allocation equations are based on the hypothesis that, as the current price increases relative to the price expected in the next period, processors increase allocations to current sales and, therefore, reduce carry-out stocks. The expected future price seems likely to be closely related to price experience in the most recent period (Pt-i), particularly when expressed in deflated terms (i.e., divided by CPI). In a more constrained formulation, P^ and Pt-i are formed into a single variable, P^ - Pi-i . A positive change in price relative to the previous period may encourage processors to allocate more product to current sales; a decrease in price causes resistance and discourages current sales. The allocation decision might be expected to be further influenced by unit costs of carrying inventories to the next period, primarily by interest rates. However, the interest rate proved nonsignificant as a variable in the empirical analysis and so is excluded in Table 1. The inclusion of population in the allocation equations permits quantities to be expressed in per capita terms as in the demand equations. Population is a measure of market size, so it is also a factor influencing inventory levels needed to serve the market. Since prices and current sales are determined simultaneously, either variable might be selected as the dependent variable in the estimation process. The choice of normalized variable is of some importance with two-stage least squares (2SLS) and three-stage least squares (3SLS) estimating methods because the estimation results may differ. The normalized variable choices in Table 1 reflect the authors' view as to primary directions of causation and recursiveness. In particular, the total supply, SK + QK, which is predetermined with respect to product sales, is the dominant variable influencing these -12- sales. With sales DK thus quasi predetermined, it seems appropriate to treat price as the normalized variable in the demand equations. California Grower Supply and Processor Raw Product Demand The equation system in this component of the model (Block II of Table 1) determines the California acreage and quantity of tomatoes produced by growers and purchased by processors and the price paid to growers. It rests on the same basic theoretical foundations as an earlier study by Chern and Just. However, the variable structure and the final forms in which the equations are expressed are a bit different. The remainder of the section describes the essential conceptual features of the Chern-Just model and the modifications introduced here. The Chern-Ju8t Model The Chem-Just study, published in 1978, is an econometric analysis of supply response and demand for processing tomatoes applied to a 10-county region of California which accounts for 85 percent of the state production. The objectives were to investigate economic trends of key variables in the California tomato industry, to assess the effect of contracting on acreage and price determination in the raw tomato market, and to estimate the impact of the tomato harvester on structural parameters of acreage response and demand for processing tomatoes. Their model consists of an acreage supply response equation, a processor demand for raw product equation, and a demand for acreage equation. Supply of Acreage. — To develop the acreage supply function, Chern and Just (1978, pp. 30-34) start with the concept of a production function which relates output of raw tomatoes to acreage and other inputs such as labor, fertilizer, and capital. The profit- maximizing calculations generate a grower supply function which relates expected production to the price received by the grower and to prices of the various inputs. Aggregation of quantity over growers then defines an industry supply function which involves the same set of price variables. An acreage supply function is obtained by (1) using the identity which equates expected production to acreage multiplied by expected yield; (2) substituting the output supply equation in the identity; and (3) solving for acreage to obtain an equation which expresses acreage supplied as a function of the grower price, prices of other inputs, and the expected yield. Chern and Just note that, while their model could have been derived from a multiproduct production function, such treatment would substantially complicate the theoretical model without adding substantively to it. It is pointed out that the results of the multiproduct model are similar to the single-product model except that the prices of competing crops would be introduced into the acreage-response function. The influence of the competing crop prices is explored in their later empirical analysis. Since growers may be concerned with the riskiness of an enterprise, Chern and Just initially included the standard deviation of past yields as a risk measure in the supply- response function. The variable did not turn out to be statistically significant in their analysis nor did it in this one. Therefore, it has been omitted in all further discussion. ^ For a discussion of tomato yield variation in California, see Brandt, French, and Jesse (p. 79). -13- A major factor affecting supply response during the period of the study was the development of the mechanical harvester. Chern and Just approached the problem of incorporating this change into the analysis in two ways. They first estimated supply response as an aggregate function for the 10 major tomato-producing counties, with a shift variable included to allow for a change in the slope of the (logarithmic) equation. This took the form of a variable N • In PGC, where PGC is the grower price and N is the percentage adoption rate of the harvester. This variable turned out to have a different sign than expected. Moreover, when more years of observation were added to the original data set, the model results were changed considerably and the standard errors increased substantially.! The second approach was to estimate separate supply-response functions for periods before and after the adoption of the mechanical harvester, with observations during the transition period excluded. To increase the number of observations and to incorporate the possible benefits of county-level detail, they estimated the second model using pooled county and time series data. These results turned out to be more consistent with the authors' behavioral hypotheses. Derived Demand for AcreagCi-ln formulating the demand component of their model, Chern and Just argued that, since there are few processors in the industry, it is plausible to consider that processors procure their raw product in an oligopsonistic market. While equilibrium conditions for oligopsony are generally difficult to derive, a previous study and informal interviews suggest that tomato processors may engage in a form of oligopsony that is more tractable for analytical purposes — that of price leadership. Under price leadership, one firm may take the initiative in making price changes. These changes are followed by other processors who, in effect, act as price takers. The model thus is developed in two stages: it first considers the behavior of the price-taking processor and then considers the effect of the price leader on the industry. To derive the product demand function for the price-taking processor, Chern and Just start by assuming the existence of a cost-minimizing processing cost function for each product (net of raw product cost) which expresses cost as a function of volume of the processed product. This function may be expressed in relation to the volume of raw product by imposing constant conversion factors (Chern and Just, pp. 34-36). The profit- maximizing calculations yield a set of demand functions for tomatoes used to produce the processed products. Each demand function expresses the quantity of tomatoes desired for a particular processed product as a function of the price paid to growers for tomatoes, the expected price of the processed product, and the raw-to-processed-product conversion ratio. Chern and Just note that prices of inputs used in processing could have been included as variables, but they did not do so. Summing over all the individual commodity raw product demand functions gives a total demand for raw tomatoes. This equation expresses total quantity demanded as a function of the grower price, the expected prices for each processed product, and the conversion ratios — the latter being fixed parameters. Expected price for each processed product is assumed to be a function of the processed product price at the time of contracting, inventory of the product at the time of ^The variable N • In PGC had a positive sign. It is possible that, if N and N • In PGC had both been included in the same equation thus allowing for a change in the intercept as well as slope, the coefficient of N • In PGC might have been negative. Even with this adjustment, however, problems of high intercorrelation might have precluded obtaining meaningful estimates. -14- contracting, and projected U. S. income. To simplify the analysis, the several product pnces are consolidated into a single quantity-weighted average price; and inventories of an individual commodities are summed into a single inventory variable. Thus the final processor demand function expresses quantity of raw tomatoes demanded as a function of grower price, average price for processed products at contracting time, consumer income and aggregate inventories of processed products of contracting time. Chem and Just used the average f.o.b. price for January-March and inventories were measured as of April 1. A A ™ost processor-grower contracts have been specified in terms of acres 1 A deniand function for acreage may be defined by noting that acreage demanded is equal to quantity demanded divided by expected yield. Using this identity, Chern and Just express the^demand for acreage more generally as a function of quantity of tomatoes and expected Market Equilibrium.— In an industry in which all processors behaved as price takers, the equilibrium grower price, acreage, and quantity processed would be determined by solving the three-equation system described above. That is, the grower price would be determined by the intersection of the grower supply and processor-derived demand curves. In a market characterized by monopsony (a single buyer of the raw product), a monopsonist would determine its profit-maximizing rate of purchase by equating marginal input cost of the raw tomatoes with its marginal revenue product. The raw product price to growers would be set at the corresponding output on the grower supply curve which lies below the marginal input cost curve. Thus, the grower price for any output would be less than in the case of purely competitive purchases. Under price leadership oligopsony, the observed price would lie somewhere between the monopsony and purely competitive price. Chern and Just point out that, under oligopsony or monopsony, time series observations of market price and quantity do not provide a basis for estimating the marginal revenue product curve as is the case under pure competition. If the marginal revenue product and supply curves are linear and if the supply curve shifts over time in a parallel fashion (no change in slope), the market observations will trace out what Chern and Just call a "perceived demand" curve. This curve will be steeper than and lie below the marginal revenue product curve. If the slope of the supply curve should change in the linear model described above, it would result in a change in the slope of the perceived demand curve.2 This suggests that. III recent years, contracts increasingly have been specified in terms of quantities to be delivered, based on an average yield multiplied by a given acreage. If actual yields exceed the average valued processors may not accept all the production fi-om a given acreage. ^his may be illustrated by the following simple model: Marginal revenue product: MRP = - a^ Q Supply function: P = bg + bj^ Q Marginal input cost: MIC = bg + 2bj Q. Profit-maximizing Q is obtained where MRP = MIC which yields Q = (sq - bo)/(ai + 2bi) and ^0 = ~ (ai + 2bi) Q. Substituting for bg in the supply function gives the perceived demand function P = - (a^ + b^) Q. If bj (the slope of the supply curve) remains constant, the slope of the PD curve remains constant. Changes in b^ alter the slope of the PD curve. For a further illustration as applied to the dominant firm oligopsony model (rather than pure monopsony) see Just and Chem (1980, pp. 589-593). under these conditions, changes in the structure of supply must be carefully considered in determining what sort of demand relation is being measured by time series of price and quantity observations. It is possible, of course, that a price leader may behave more as a pure competitor than a pure monopsonist. That is, the leader may determine output and raw product price by equating marginal revenue product with supply price rather than with marginal input cost. It is also possible that a leader firm may act as an oligopsonist during some periods and behave more as a pure competitor at other times. There may also be variations in the extent to which other firms follow a particular leader. Under these circumstances, the perceived demand function that is derived by econometric estimation may be subject to more bias and may be less reliable than the associated supply component of the model. Modifications of the Supply Relationship Using the acreage and price symbols of Table 1, the Chern-Just acreage response function may be expressed as ACt = \,iPGC^, Wot, Wit, W2t, Wgt, yJ) (i) where the W's refer to the price of land, labor, fertilizer, and capital, and is expected yield. A multiple-product model would add prices of competing crops to the set of price variables. Chern and Just used a three-year average of past yields as a proxy for expected yield, and that procedure is followed here. The variable is defined as YMACt and replaces n A problem with the Chern-Just specification is that it may be difficult to obtain statistically significant estimates of the coefficients of the W's. For example, Chern and Just did not obtain significant coefficients for prices of land (Wq) and capital (W3). Another limitation is that, with relatively small numbers of observations, only a small number of input variables can be included in the model. An alternative formulation is to replace the input price variables with a cost series derived from sample cost-of-production studies. This reduces the number of variables and, at the same time, takes account of the effects of changes in prices of the complete set of input variables. It also may incorporate the effects of parameter change associated with changes in production techniques.^ With these modifications, the basic supply model takes the general form -^^t = ha^(PGCt, YMACt, CGt*, CPIt, IPGt, vt) (2) The computation of the production cost series is described in section 4 and Appendix B, supra, p. 21 and p. 98, respectively. -16- where and PGC+ = 1 yflllfn'TTllfi GTY'rWJU'O'f" Titni^Q YMACt = three-year average yield CG*t = measure of expected grower cost per acre CPI = consumer price index IPG = index of grower prices for competing crops vt = unexplained disturbance. Since current year costs are not known fully at the time of contracting, CGt is expressed as the observed cost measure in t- 1 (i.e., as CG^_j). Note that CG is a function of the input prices, Wq, W^, Wg, and W3, which are included in the Chern-Just equation, plus other inputs not included in the Chern-Just formulation. The use of the CPI as a price-level indicator rather than an alternative indicator, such as the Index of Prices Paid by Farmers, maintains consistency with the demand estimates. This simplifies margin calculations and the later application of the model for projection purposes. The movement of the CPI has been highly correlated with movements of other price-level indicators. The effects of changes in the CPI are incorporated as in the demand formulation by expressing price and cost variables in deflated terms. Chern and Just made no distinction between long-run and short-run response in their model formulation. It is hypothesized here that, while short-run response rates may change with the substitution of fixed for variable input costs, long-run response rates may not be greatly affected. This may be approached by considering the year-to-year changes as a partial adjustment process of the form ACt = ACt_i + a(AC; - ACt_i) (3) where AC| is the long-run desired level of acreage in year t, and a is an adjustment coefficient (0 < a <1). If a = 1.0, the adjustment is complete each year, and AC^ = ACJ. Values of a < 1.0 may be associated with factors such as long-term rental commitments, reluctance to change long-standing production operations or buyer relationships, and the existence of sunk investments in specialized machinery. If equation (2) is assumed to represent the long-run desired acreage for given values of price, cost, and yield expectation, then the short-run supply response becomes ACx = a Ac! + (1 - a) AC., or = "^^^(PGCt, YMACt, CGt_i, CPIt, IPGt, v^) + (1 - a) AC^.i. -17- One way to test whether or not the value of a may have declined with the shift to mechanization would be to estimate supply functions for periods before and after mechanization. However, the small number of time ^^"f^ «^!f^^*^°^l "^f *3 difficult. A disaggregated pooled county model, such as used by Chem and Just was not considered appropriate here because of the broader objectives whichrequire functions that encompass the total state industry and because of differences in the basic supply-model formulation. While selected production cost estimates are available for a number ot counties, the continuous time series of production cost could be developed only as a general statewide indicator. Thus, the cost-oriented supply model would not be feasible on a county level. In the more aggregative statewide supply model estimated here, a test for changing a may be formulated by specifying that a is a function of TC, the proportion of acreage harvested mechanically (which is equivalent to Chem and Just s N). In ahnear model, this requires adding cross-product terms for each variable with TC and may also be used to evaluate a possible upward shift in the level of supply response as a result of the altered labor environment with mechanization. As in the Chern-Just study, efforts to measure the influence of a variable (or variables) to account for the profitability of alternative crops [IPG in equation (2)] were generally not very successful. One reason for this is the existence of several alternatives (which may vary among areas) so that no single crop clearly reveals its impact. Consequently, the influence of such variables is reflected as part of the disturbance term. The final supply equation thus includes the general variable specification given in Table 1, equation (23). Modifications of the Processor Demand Relationship Chem and Just specified the processor demand for the raw product as a function of grower price, average processed price at contract time, total income, and total stocks at contract time. Using the notation adopted here, the equation may be expressed as QCTt = fqc(PGCt, PRW^. Yt, SlT^). (5) This study modifies or extends the Chem-Just formulation in several ways. The first modification was to try to account for changes in the processing cost as a factor affecting processor demand. This was approached in two ways. First, price and income variables were deflated by the CPI . Since much of the change in processmg cost has been associated with change in the CPI, deflation by this index removes (or accounts for) much of the cost influence. Second, to consider the possible impact of cost variation not associated with the CPI, an Index of Processing Cost (also deflated) was introduced as an additional variable.! However, the addition of this variable did not give plausible results, possibly because it is not a good indicator of changes in tomato-processing costs and, also, because of its high correlation with other variables. It is omitted in the further discussion. A second modification involved a change in the specification concerning the manner in which processors form their expectations of prices received for processed products. lNotethat,ifproce88ingco8tisPC = b • CPI, then deflation of all dollar variab^^^^ PC/CPI = b, a constant. If PC = b • IPC, deflation by CPI gives PC/CPI = b (IPC)/CPI. -18- Chern and Just assumed that the expected price may be expressed as a function of the current price at contract time, inventory level, and projected income, the latter assumed to be based on current income. We include the further assumption that processors may recognize that price may also be affected by the quantity of production. Thus, quantity of pack becomes an additional variable in the price expectation function. This does not result in any change in the variables included in the final processor demand function, but it is of some importance in the later interpretation of model results. Chern and Just used a single weighted average f.o.b. price (PRW9 in the notation of this study) to represent processor price expectations for all processed products. That simplification is retained here. However, in order to maintain continuity within the general model, it is necessary to relate the average price at contract time to the season average prices predicted by the general model. The production and marketing year is defined as July 1 to June 30, so contracting for year t occurs during year t - 1 (i.e., from January to April). The average processed product price during contracting thus overlaps and is closely associated with the average price experienced for year t - 1. Therefore, PRW9 may be regarded as a function of PRWt-i. The latter variable then replaces PRW9 in the demand function. Since the general model predicts inventory levels on July 1, it is also necessary to specify a relationship between observed stocks at contract time, SIT, and carry-over stocks on July 1.1 A possible procedure would have been simply to replace SIT with SCT^-i (the J uly 1 inventory figure). However, a better predictor is obtained by retaining SIT as a variable in the demand equation and specifying an additional technical equation to predict SIT as indicated in Table 1, equation (28). The initiation of price bargaining by the CTGA in 1974 transformed the industry into a possible bilateral oligopoly-oligopsony structure for which price and output equilibrium conditions may be determined only within some range, with the outcome depending on relative bargaining strength and strategies. This adds to the uncertainty as to the nature of the perceived (or realized) demand-side, price-quantity relationship and possibly may also influence the supply relationship. One approach to allowing for this change in structure is to introduce a shift variable, M, into the demand and supply equations. This variable has a value of zero for all years prior to 1974 and of one for the periods when the CTGA actively bargained (1974-1977 in the empirical data set used for estimation). If successful, the CTGA bargaining efforts would have the effect of shifting the realized processor demand function upward, i.e., processors would pay more for a given quantity of raw tomatoes than before bargaining. It is possible that the CTGA bargaining procedures would also alter the effective supply curve such that a given quantity would be supplied only at a higher price (or a lesser quantity supplied at any given previous price). However, the CTGA bargaining efforts focus mainly on price issues with restrictions of supply more a threat than an active control variable.2 Under such conditions, supply would tend to continue to respond to the negotiated price, with little alteration of the basic supply equation itself. The latter hypothesis is supported by the later empirical results in which the shift variable, M, turned Chern and Just measured the stock level during contracting as of April 1. In this study the inventory level at time of contracting SIT is specified as the level on January 1. April 1 stock levels are not known during the early part of the contracting period. Stocks on the two dates are closely correlated. 2 Recall that the CTGA membership has included no more than 70 percent of growers and probably less of production. -19- out to be statistically nonsignificant in the supply equation but highly significant in the demand equation. It is possible, of course, that, in spite of the apparent oUgopoly- oligopsony structure, actual behavior may not depart greatly from the competitive model. Under such conditions, other interpretations of the shift variable, M, are possible. This is discussed with the presentation of empirical results. As a further modification of the Chern-Just raw product demand model, a partial adjustment hypothesis for processors was explored. The formulation was similar to that specified for the supply relationship. The coefficient of the lagged quantity variable, QCT^_j^, was statistically significant in an early model which did not include lagged processed product price, PRW^-i , as a variable (Brandt, 1977, pp. 188-193). However, with the addition of PRWx^j and the shift variable, M, the coefficient for QCTt_i became statistically nonsignificant. This apparently occurred because the lagged process product price introduced an offsetting lagged adjustment process, and the shift variable, M, is positively correlated with QCT, the latter being much higher in the 1974-1977 period than earlier years. The formulation with PRW^_]^ and M provided better overall estimation results, so the partial adjustment formulation was dropped. It might also be expected that the levels of production in other regions would be an important variable influencing California processor demand for the raw product. Chem and Just noted that total other region production had not fluctuated much during the period of their analysis and argued that treating California demand as independent of production in other regions was, therefore, econometrically feasible. Explorations which included other region production in the demand function of the present analysis did not yield statistically significant results. Therefore, the Chern-Just specification pertaining to that aspect is retained. Changes in other region production influence California production through the impact on the prices of processed products. With the modifications noted above, the equation for quantity of raw tomatoes demanded by processors takes the form of equation (25), Table 1. Note that the quantity demanded, QCTD, is not necessarily observable. The actual quantity purchased, QCT, may differ from the quantity demanded by a random element due mainly to yield variations as indicated by equation (26), Table 1. In the empirical analysis, equation (25) is substituted into (26). For equilibrium, it is required that the quantity bought equals the quantity suppUed (QCTb = QCT^). Equations (23), (24), and (26), with (25) inserted, thus form a three-equation simultaneous system. Production and Grower Prices in the Midwest and the East In both the Midwest and East, tomatoes commonly are produced as a supplementary crop rather than the major farm commodity as is usually the case in California operations. Much of the relative decline in production in these two regions may be attributed to (1) urban sprawl (particularly in the East), which reduces available farmland, (2) grower inability to adopt cost-saving technological improvements (e.g., mechanical harvester), and (3) declining processing capacity causing further grower uncertainty. The effects of changes of this sort are difficult to separate from the influence of other price and cost variables. Consequently, efforts to estimate growei^supply and processor-demand systems having the same form as the California model provided generally unsatisfactory results. Because one of the objectives of this study was to formulate a model which would account for total U.S. production and consumption of tomatoes, it was important to be able to develop equations which would predict production in the Midwest and East and account -20- for its interaction with California. This was accompUshed by formulating equations which are as much descriptive as structural but which still incorporate the influence of price and quantity variables. Since California contracting begins earlier and since California is the dominant producing region, grower prices in the Midwest and East are influenced by what happens first in Cahfornia. Other variables used to predict prices of the Midwest and East are the price and quantity of the previous year and a trend factor. Acreage is related to the current season grower price, price of competing crops, and a trend variable. The price and acreage equations for the Midwest and East are represented by equations (31)-(36), Table 1. These equations form a recursive system in which grower price IS regarded as predetermined. Although the endogenous variable, PGC, appears in the Midwest and East grower price equations, it is assumed that the causation is unidirectional; that is, the California grower price affects the prices of the Midwest and East, but the latter have little direct effect on the California price.l 4. DATA AND VARIABLE MEASUREMENT The quality of the econometric estimates of the parameters of the model, conceptualized in the previous section, is substantially influenced by the available data.' As noted in the introductory discussion, the model formulated is constrained in its scope because some data series either are not available or are not suitable for statistical analysis. This section discusses the characteristics of the data used to estimate the model. The time series observations are given in the Appendix tables. F arm Prices, Production, and A creage Farm prices, production, and acreage data used in the analysis were compiled from reports of the U. S. Statistical Reporting Service, Crop Reporting Board (1954-1980). For California, grower prices are measured at the first delivery point which usually is a receiving station near the area of production (California Crop and Livestock Reporting Service, 1954-1980). For other regions, the prices are measured at the first delivery point until 1964 and at the processing plant door thereafter. Data series were not available to continue the first delivery point series in these regions or to adjust the earlier year values to a processing plant door level. The bias introduced into the price series by the change in reporting point is believed to be small.2 The acreage contracted at these grower prices is not identical to acreage planted because small quantities have been produced each year without contracts. The latter is referred to as "open market acreage." Acreage planted is assumed to reflect the amount of acres growers are willing to supply at the reported contract prices. The output in other regions has an indirect (lagged) influence on California grower price through the effect on the processed product price which influences California processor demand for the raw product. ■^he difference in price at the first delivery point and price at the processing plant door is large due to transportation costs. In the Midwest and East, this cost tends to be much smaller than in California due to shorter hauling distances. Thus, there was only a relatively small change in the levels of reported prices in regions other than California. -21- Since yields are not known at the time of contracting, observed total tonnage produced by growers and purchased by processors is not necessarily identical with tonnage demanded by processors at the given contract price.l However, Chern and Just argue that the total quantity produced (sum of quantity from contracted and open-market acreage) may be taken as an approximation of processor demand at the time of contractmg. They reason that open-market purchases may be used by the processor to fill a g^ between desired quantity and the actual quantity produced from contracted acreage. Thus, total observed purchases approximate the desired quantity. An alternative specification is that the observed total harvested production differs from the unobservable desired production only by a random error term due mainly to yield variations.^ With this specification, the unobservable desired quantity in the processor demand function may be replaced by the actual observed quantity, noting that this adds conceptually to the error variance of the equation. In practice, both the Chern-Just assumptions and the specification here yield identical variable structures, but the interpretation differs slightly. Paxsk and Inventory Data Data pertaining to quantities of various processed products packed and held as inventories were obtained from publications of the Canners League of California and the National Canners Association (Appendix Tables A.5 to A. 10). In order to sum the quantities in various can and bottle sizes, all pack figures were converted to cases of 24/303 can equivalents, using standard conversion factors (Appendix Table A.16). The scope of the processed product demand analysis is limited by the fact that the industry does not report fully the quantities of all items packed. In 1960, processors discontinued reporting paste pack in retail-size containers and all tomato sauce pack; and the pack of tomato catsup in retail-size containers has not been reported since 1968. The data series used here also omit miscellaneous processed items such as tomato aspic, fish sauce, spaghetti sauce, and soups for which associated price data are generally not available. In the analysis of demand for catsup and paste products, the reported pack figures were supplemented by confidential market survey data on retail-size purchases. This provided a basis for generating more complete estimates of total catsup and paste disappearance. Although the accuracy of the data series is not known, the statistical results obtained were more plausible than obtained using only the reported institutional pack data. Import and export data were computed from pubhcations of the U. S. Economic Research Service (see Appendix Tables A.5 to A.IO). Because of differences in reporting units and reporting year, the final quantities of equivalent 24/303 cases, as calculated for use in this analysis, are approximate. However, imports and exports are small relative to production; and any errors in estimation seem unlikely to have much effect on the analysis. ^Quantities purchased by processors are not actually identical to reported harvested production since small percentages are rejected at inspection stations or discarded in processor inspections. ^Recent increases in the use of contracts based on volume rather than acreage could modify the error structure. This would not be an important factor for the period for which the model parameters were estimated. -22- Processed Product Prices There are two possible sources of data on wholesale prices for processed tomato products: (1) prices compiled by the U. S. Bureau of Labor Statistics (BLS) used to compute the Wholesale Price Indexes (now called Producer Price Indexes) and (2) reports in trade publications. The BLS price series currently covers canned tomatoes, tomato juice, and catsup. However, the series generally does not extend back far enough to provide a continuous series appropriate to the period covered in this analysis. Moreover, the sampling base appears very limited, and there is no regional breakdown of the prices. Finally, the BLS data do not include any prices for paste and puree. F.o.b. processor prices for all the major processed products are published in trade publications such as The Canning Trade; Pacific Fruit News; and the American Institute of Food Distribution's /ieport on Food Markets. Summary computations are also found in The Almanac of the Canning, Freezing, Preserving Industries. These prices are primarily list prices and may not fully reflect discounts and other trade adjustments which determine the final average transaction price. However, they are believed to be generally indicative of price movements from year to year. The prices used in this analysis are the reported prices for the dominant container type for each product. Annual average values were computed as simple averages of quarterly or monthly reported values. The price series are given in Appendix Table A.U, along with more specific source notes. Exogenous Variables Data pertaining to population, income, CPI, and per capita consumption of other processed vegetables were compiled from government publications as indicated in the Appendix tables. Disposable income and the CPI are reported on a calendar year basis, whereas all production and price data used in the analysis are tabulated on a market year basis (July 1 to June 30). Thus, production and prices for, say, July 1 , 1971 , to June 30, 1972, would be associated with income and the CPI computed for January 1 , 1971 , to December 31 , 1971. This slight lag does not appear to introduce any serious bias for purposes of this analysis, given the continuous nature of changes in the CPI and income series. Population is measured on January 1 of the crop year (e.g., January 1, 1972, for 1971-72). Cost data were compiled from studies of the Cooperative Extension Service as described in King, Jesse, and French (1973). A description of the updated cost series is given in Appendix B. It differs slightly from the series reported in Brandt, French, and Jesse (1978) in that it fits a slightly different predicting equation to the data observations and uses three-year averages of yields, rather than actual yields, in order to compute expected costs. 5. ESTIMATES OF MODEL PARAMETERS This section presents the econometric estimates of the behavioral and technical equations outlined in Table 1 . The data series for each variable are given in the Appendix tables. All equations were estimated using data for the marketing years, 1954-55 to -23- 1977-78. This period was selected in accordance with data availabiUty and with the objective of providing enough observations to achieve statistical reliability while at the same time keeping the period short enough to avoid major structural changes not accounted for by the variables in the model. Observations for some variables used in the model were not available prior to 1954. Because of the lags in reporting for some of the data series used, more recent 1978-79 and 1979-80 observations were not available at the time the statistical estimation was undertaken. The model's ability to predict prices and quantities for these later years, given reported values of exogenous and lagged endogenous variables, will provide one test of the reliability of the model. Processed Product Demand and Inventory Allocation The processed product demand and market allocation block of the model consists of equations (1) to (22) in Table 1. Equations (1), (6), (10), (14), and (18) are demand equations for the five product groups. Equations (2), (7), (11), (15), and (19) allocate supplies of each product between current sales and inventories to be carried to the next period, the latter determined residually by the inventory identity equations. The remaining equations are identities or technical allocation relationships [(3), (5), (9), (12), (17), (20), and (21)] required to complete the model. Two alternative specifications of the simultaneity of the equation sets were explored. In the first, the equation sets for each of the five commodities were viewed as five separate interdependent systems, with the parameters of the two behavioral equations in each set estimated by 3SLS. A second formulation viewed the equations for each commodity as part of a single simultaneous system, with the 10 behavioral equations estimated simul- taneously by 3SLS.1 Both estimation procedures yielded results that appeared acceptable by statistical and theoretical criteria. However, while the 10-equation formulation has an advantage in accounting more fully for possible interdependencies in the disturbance elements among commodity demand equations, it has a disadvantage in that specification errors in one set of equations may strongly affect the estimates of demand and allocation equations for other processed products. In view of the data problems encountered with the measurement of quantities of catsup and paste products, specification error may be a possible consideration in these equations. Therefore, separate 3SLS estimates for each commodity system were chosen for use in the final model rather than the single 10-behavioral equation estimates. ^ The influence of price level changes is incorporated by expressing prices and income as deflated values (divided by the CPI), and the influence of population changes is imposed by expressing quantities on a per capita basis.3 Formulations linear in the variables and linear in logarithms of the variables were estimated. third specification which treated concentrated products (catsup, puree, and paste) as an interrelated group was also explored. The results were similar to those obtained with the full 10-equation system. ^Each of the individual commodity demand and allocation sets was also estimated by 2SLS. In these cases, the results were generally similar to the three-stage estimators. ^Previously defined aggregate data variables are denoted as per capita variables with the addition of an N to the variable notation; for deflated values, add a D (see Table 2, footnote c, infra, p. 2&>. -24 The 3SLS estimation results for the five separate equation systems are given in Tables 2 and 3. Table 2 presents the linear estimates; and Table 3, the estimates obtained with the variables expressed in logs. The coefficient estimates in both tables all have signs in agreement with theoretical expectations, and most coefficients are large relative to their standard errors. The log formulation has an advantage that the price-quantity coefficients provide direct estimates of price flexibilities which show the percentage effects on price of a 1 percent change in quantity. However, the linear formulation is easier to incorporate into solutions of the model. Since there is little difference in the statistical significance of the two formulations, the linear estimates are used in the later model analysis. The log results are reported to facilitate interpretation in percentage terms. In either case, the particular equation form should be viewed as an approximation that is valid only over the general range of past data observations. Individual Commodity Interpretations Canned Tomatoes. — The demand function for canned tomatoes suggests that, with other variables held constant, an increase of .01 cases in per capita disappearance has been associated with a decline of 16.9 cents per case. In terms of price flexibilities, as measured in Table 3, a 1 percent increase in per capita disappearance has been associated with slightly over a 1 percent decrease in price. Changes in the sales of competing vegetables, DOVN, also appear to have significantly influenced the price of canned tomatoes. In terms of price flexibilities, a 1 percent increase in DOVN has been associated with about a 1.9 percent decrease in price. Per capita income shows a strong positive relationship with price. The income variable probably is closely correlated with other unmeasurable factors which have shifted demand. The income coefficient thus should be interpreted as a general indicator of demand shifts rather than a true measure of the income effect alone. The allocation equation for canned tomatoes [equation (2)] indicates that the available supply (pack plus carry-in stocks) is the dominant factor affecting allocations to current sales and, therefore, levels of carry-out stocks. ^ However, this allocation is also significantly influenced by changes in price compared to the previous period. U. S. per capita disappearance, DWN, is obtained by adding per capita imports, IWN, to AWN. Tomato Juice. — Estimation of the demand for tomato juice presented special problems because of a change in the method of reporting pack and movement beginning in 1968 (Appendix Table A.6) and because of a downward shift in the level of demand for tomato juice. The reporting problem was handled by introducing the dummy shift variable, VJ, which has a value of one for all years through 1967 and a value of zero thereafter. Efforts to account for changes in demand for tomato juice by changes in consumption of frozen orange juice did not provide statistically significant results. The shift thus is accounted for by the trend variable, T, with income omitted as a separate variable. Holding the trend shifter constant, an increase of .01 cases in per capita disappearance has been associated, on the average, with a decrease in price of 20.6 cents per case. The price flexibility coefficient (Table 3) suggests that, in percentage terms, a 1 percent increase in quantities marketed has been associated with about a 1.18 percent decrease in price. The allocation equation (7) is interpreted similarly to that for canned tomatoes. Catsup and Chili Sauce. ^ — It was noted in the discussion of data problems (section 4) that thereporting of pack of catsup in retail-size containers was discontinued in 1968. Because For the inventory identity which completes the system, see Table 1, supra, p. 6. Quantities of catsup and chili sauce were combined in the analysis because of the general similarity of the products and the difficulty of obtaining separate demand estimates. Chili sauce is a minor product compared to catsup. -25- TABLE 2 Three-Stage Least Squares Estimates of Processed Tomato Product Demand and Market Allocation Relationships, Linear Equations'* and Five 2-Equation Systems,^ 1954-1977 (1) PWDt - 7.0763 (1.1680)C - 16.9024 (4.8638) DWN^ - .0957 (.0425) DOVNj + .0018 (.0006) YNDt (6) PJDt = 7.1758 (1.3731) - 20.6285 (5.4838) DJNt + .6041 (.2032) VJt - .0503 (.0205) T (10) PCDt - 5.3873 (.9956) - 22.5035 (10.3423) DCNt - 11.6775 (15.4600) SCCNt + .0009 (.0004) YNDt (14) PUDt 2.6699 (.7955) - 30.1158 (16.0254) SQUN^ + .0013 (.0004) YNDt (18) PPDt - 2.5398 (3.0184) - 24.1768 (23.7942) DPNt - 147.8438 (42.5181) SPICN^ + .0033 (.0020) YNDt (2) AWN^ .0442 (.0207) + .6354 (.0192) SQWNj + .0242 (.0097) APWDt (7) DJNt .0270 (.0118) + .6877 (.0469) SQJN^ + .0344 (.0115) APJD^ (11) DCNt .1025 (.0158) + 1.2924 (.3290) SQCN^ + .0452 (.0193) APCD^ (15) DUNt -.0008 (.0061) .7896 (.1227) SQUNt + .0106 (.0026) APUDt (19) APNt .0173 (.0026) + .9812 (.0331) SQPIN^ + .0037 (.0010) APPD^ ° Variable combinations are defined as follows (Table 1, supra, p. 6). Deflated price: PKD (PK/CPI) • 100; (K = W, J, C, U, and P) APKD^ PKDt - FKD^_^ Per capita consumption: DKN DK/N Per capita income: YND (Y • 100) (N • CPI) Stocks: SCCN SCC/N; SPICN = SPIC/N SQKN (SK + QK)/N; (K = W, J, C, U, and PI) U. S. per capita sales: AWN DWN - IWN; APN = DPN - IPN Time: T 1 in 1954 VJ 1 for t = 1954-1967; 0 for t = 196S-1977. 'The five equation systems are formed by equations (1) and (2), (6) and (7), (10) and (11), (14) and (15), and (18) and (19), plus identities (Table 1, supra, p. 6). Numbers in parentheses are standard errors. -26- TABLE 3 Three-Stage Least Squares Estimates of Processed Tomato Product Demand and Market Allocation Relationships, Log Formulation''' and Five 2-Equation Systems, 1954-1977 (IL) LPWD^* = -6.0336 - 1.0594 LDWN^ - 1.8929 LDOVN^. + 1.6528 LYND^ (1.5104)'^ (.2944) (.7000) (.4848) (6L) LPJD^ (lOL) LPCD^ -.5447 (.4850) 1.1762 LDJN^ + .1905 VJ^ (.3409) (.0723) = -5.2146 - .8316 LDCN^ (2.4931) (.3659) (.0266) (18L) LPPD^ = -10.1169 - .4131 LDPN^ (5.9446) (.2958) (.0260) (2L) LAWN^ = (7L) LDJN^ (IIL) LDCN. = (15L) LDUN^ - . 0149 T (.0073) .0461 LSCCN^ + .6145 LYND^ (.2439) (14L) LPUD^ = -7.4480 - .7237 LSQUN^ + .6685 LYND^ (1.2140) (.0895) (.1264) .1420 LSPICN^ + 1.3243 LYND^ (.6621) -.5492 + .7541 LSQWN^ + .3506 ALPWD^ (.1553) (.1037) (.1508) -.3801 + .8892 LSQJN^ + .5236 ALFJD^ (.0846) (.0591) (.1812) -.6676 + .3718 LSQCN^ + .7876 ALPCD^ (.2108) (.0673) (.3101) -.2727 + .9899 LSQUN^ + 1.2647 ALPUD^ (.4216) (.1387) (.2917) (19L) LAPN. = -.2920 + .8051 LSQPINj+ .4330 ALPPD^ (.0911) (.0328) (.1086) "For further variable definitions, see Table 2, footnote c, supra, p. 26. ^The L preceding a variable indicates logged value. '^Numbers in parentheses are standard errors. -27- this omitted a major portion of sales, an effort was made to improve the series by adding estimates of catsup consumption in retail-size containers obtained from confidential market survey data. The confidential series were available for 1968-1973. Extrapolations for 1974-1977 were made to complete the series.^ Another factor which appeared to be influencing the demand facing processors for concentrated products was the accumulation of stocks in the hands of buyers. Continuous data series pertaining to such stocks are not available. However, it seems reasonable to assume that such stock levels might be strongly correlated with levels of carry-in stocks in the hands of canners. Canner carry-in stocks thus were introduced as a proxy shift variable. With these modifications, the demand estimates for catsup and chili sauce turned out to be similar to those for canned tomatoes and juice but with somewhat lower price and income flexibilities. The influence of the stock variable on price was much smaller than for paste and puree, and the coefficient was less significant as measured by the t ratio. This is not surprising since paste purchases tend to be used more for further manufacturing. In the allocation equation for catsup and chili sauce, the coefficient for the available supply variable, SQCN, is greater than 1 .0. This would not be possible if the stock and pack data accounted for all of the product. However, SQCN refers only to California institutional pack while DCN, as noted previously, has been augmented by additional retail sales data. Thus, the allocation based on SQCN is greater than 1.0. Puree. — It may be noted that the demand equation for puree departs slightly from the specification in Table 1. Initial estimates with DUN and SUN as separate variables provided coefficients of the correct sign, but the coefficient of DUN was peculiarly large and was not statistically significant. Utilization of this equation in the later applications of the total model injected an element of instability which seemed unwarranted. Consequently, the equation was respecified to express the price of puree as a function of available supply (pack plus carry-in stocks) and income. It may be regarded as a partial reduced-form equation rather than a demand equation. The equation indicates that an increase in the initial supply of puree of .01 cases per capita has been associated with a decrease in price of about 30 cents per case. The income coefficients and the allocation equations are interpreted as described for canned tomatoes, juice, and catsup. Paste. — As in the case of catsup, recent data on paste pack and stocks exclude retail-size containers. Reporting of these sizes was discontinued in 1960. As in the case of catsup, the data on sales in institutional-size containers were augmented by confidential survey data. Although institutional sales represent a much larger proportion of sales for paste than for catsup, the additional data nevertheless improved the statistical results obtained. It was noted in the discussion of the estimates for catsup and puree that it appeared that the demand facing processors of concentrated products might be strongly influenced by accumulations of stocks in the hands of institutional-size buyers. This seemed especially important in the case of paste where much of it is purchased for remanufacturing For a further discussion, see Brandt (1977). -28- or other food uses. Complete and continuous data pertaining to such stocks were not available, but it was hypothesized that such stocks would be highly correlated with levels of canner carry-in stocks. This hypothesis seems well supported by the demand estimation results for paste where the stock variable is highly significant. For the linear equation, the data suggest that an increase in California institutional carry-in stocks, SPICN, of .01 cases per capita has been associated with a decrease in price of $1.47 per case. The coefficients for per capita disappearance, while not statistically different than zero at a high level of significance, is of the correct sign and is of the same general magnitude as the coefficients for the other products. However, the price flexibility is lower. The per capita disappearance of paste has tripled over the period of investigation. Its rise in popularity seems to be associated, in part, with the expansion of fast-food outlets, especially pizza establishments, and its wide use as an ingredient in many convenience foods purchased in food stores. Because of this rapid rise in the demand for paste and its importance as the largest volume product packed, extensive efforts were made to identify the factors causing these shifts in demand. Data indicating the expansion of the four largest pizza chains, as well as data reflecting the increase in the volume of business in the firanchise food chain industry, were collected and included as explanatory variables. However, these and other shift variables failed to explain the variation in the dependent price variable. These shift variables were highly correlated with paste disappearance and with per capita disposable income and led to problems of multicoUinearity in the price- dependent relation. The paste price appears to be highly flexible with respect to income. As in the previous cases, however, income is actually a proxy for a number of factors which have shifted demand upward. Changes in consumer life-styles reflected by more away-from- home eating and purchases of convenience foods associated with higher incomes are undoubtedly contributing factors to the recent rise in use of tomato paste and probably account for the magnitude of the income coefficient. Calif omia Grower Supply and Processor Raw Product Demand The California raw product supply and processor demand block of the model consists of equations (23) through (30) of Table 1. For estimation purposes, equation (25) is substituted in equation (26) to eliminate the unobservable ex ante quantity demanded by processors (as distinguished firom actual purchases) at a given price. This equation, along with equations (23) and (24), form a three-equation simultaneous system in which (24) is an identity.! Equations (27) through (30) are identities and technical relationships used in the complete model. Equation (28) predicts January 1 stocks as a function of previous pack and July 1 stocks and is estimated independently by ordinary least squares (OLS). It may be noted that the simultaneous equation specification here differs slightly from that of Chern and Just in that they assumed observed purchases were equivalent to quantity demanded. Their three-equation system then consisted of an acreage-supply equation; a quantity-demand equation; and, from equation (27), an acreage-demand equation which is expressed as a linear approximation in terms of quantity demanded and and expected yield. Applying this specification to the present model would not affect the 2SLS estimates of the acreage-supply and quantity-demand equations since the third ^There is actually a fourth equation; the identity which equates quantity purchased to quantity supplied (footnote o, Table 4, infra, p. 34). -29- equation is not taken into account in the estimation process. However, it would affect the parameter estimates under 3SLS, because the statistical specification of the third equation — an identity in this model and a linear approximation in the Chern-Just model — is incorporated into the estimation procedure. Table 4 presents the estimation results for several hypotheses concerning the specific form of the growei^supply and processoi^demand equations. In each case, the equations are expressed in linear form with all price and income variables in deflated terms (1967 dollars). Estimates in log form and nondeflated form were also explored. The log formulation provided parameter estimates that were consistent in sign with the linear model and which were about the same or slightly lower in statistical reliability. The linear formulation was selected primarily because of its greater convenience in the later model analysis. The model using undeflated values did not perform well. In Table 4, equations (23.1a) and (26.1a) reflect the basic behavioral hypothesis discussed in section 3. Equation (26.1b) explores the effect of normalizing the processor demand equation on price rather than quantity. Equation set (23.2) and (26.2) is an attempt to evaluate the possibility of changes in short-run supply response as a result of the introduction of the mechanical harvester. Equation set (23.3) and (26.3) explores the possibility of a change in perceived processor demand slope after the adoption of mechanical harvesting. 1 Supply Equation (23.1) indicates that plantings of tomato acreage have responded significantly to changes in expected profit per acre as measured by PRAR^ = PGCD^ • YMACt - GCRDt_i. The coefficient ofthePRAR variable measures short-run response. Referring to the 3SLS estimate, the coefficient .2551 indicates that, with all other variables constant, each dollar increase in return per acre or decrease in cost per acre has been associated with an average increase of 255 acres in that year. The long-run response, obtained by setting AC^.j = AC^ and solving for AC, is .6343. This indicates that, with all other factors constant, the final effect of each dollEir increase in return per acre would be to increase acreage by about 634 acres. The variable, TC (percent of acreage harvested mechanically), was introduced to account for a possible change in response level due to the different labor environment and perceptions of uncertainty with the shift to mechanized harvest. It was not strongly significant as indicated by the relatively low t ratio. However, it is of the expected sign, and retention of the variable improves the overall estimation results. Chern and Just have argued that the increased fixed cost relative to variable cost associated with the change to mechanized harvesting would be expected to reduce the elasticity of supply. Moreover, their pooled county supply model generated results which supported that hypothesis. In the present analysis, this kind of change is expressed as a hypothesis that the partial adjustment coefficient may have declined with increased mechanization. This would reduce the short-run supply response while leaving long— run supply response unchanged. For reasons noted in the discussion of results, this equation set does not provide a precise specification for purposes of testing the Chern-Just hypotheses as to the effects of changes in supply response on processor perceived demand. -30- To test this hypothesis, cross-product terms with TC were introduced to allow the value of the partial adjustment coefficient and, therefore, all other coefficients to change with the shift to mechanization [Table 4, equation (23.2)]. The estimation results with this formulation turned out to be statistically nonsignificant, primarily for two reasons. First, the cross-product specification necessary to allow supply slopes to change with harvest mechanization introduced substantial intercorrelation among the explanatory variables. Second, an examination of the acreage and price variation during the sample period (1954-1977) shows that relatively larger variations occurred during the period after the introduction of harvest mechanization. The statistical estimates, therefore, tend to be dominated by adjustment rates after mechanization so that possible response differences prior to mechanization are not revealed by the analysis of this data set. Thus, the analysis was not able to verify further or reject the Chern-Just hypothesis. Demand The basic demand equation is (26.1a) in Table 4 which was estimated jointly with equation (23.1a). All coefficients are of the expected sign, and most coefficients are reasonably large relative to their standard errors. The equation indicates that the quantity of tomatoes purchased by processors decreases with increases in grower price, PGCD; increases with increases in the average price of processed products in the previous year, PRDWt_i; decreases with increases in levels of carry-in stocks, SlT^; and shifted upward during the period 1974 to 1977 when growers began active group bargaining with processors over prices. The bargaining association influence is suggested by the positive coefficient for the dummy variable, M, which by using the 3SLS result for the 1974 to 1977 period indicates that processors desired to purchase about 1.6 million tons more per year at the same real grower price than in earlier periods. Alternatively, as suggested by (26.1b) in Table 4, processors were willing to pay a higher price for a given quantity. Whether this reflects a change in processor attitudes as a consequence of activities of the grower bargaining association or was a result of changes in other factors, such as physical characteristics of the raw tomato, is not verifiable from the data. Possibly, it reflects some combination of these influences. In any case it seems evident that the processor demand function did shift upward during this period. The lagged average processed product price variable, PRDW^-^, introduced through the price expectation submodel (section 3), suggests a two-stage processor adjustment to changes in grower prices. First, if grower price were reduced by $1.00 per ton (say, as a result of a cost reduction), the expected initial increase in processor purchases would be 51,318 tons. If all other things remained constant, the added 51,318 tons, when processed and offered for sale, would reduce the average processed product price. This would reduce the processor demand level in the next period so that the final effect of the change in grower price would be something less than 51,318 tons. Conceptually, processors could take immediate account of the effect of raw product changes on processed product prices, thus eliminating PRDW^-j as a variable. However, explorations with alternative models suggest that the present format provides a better predictor of behavior. The dynamics of the adjustment process are explored further in a later section. In Table 4, equation (26.1b) formulates the processor demand equation with grower price as the normalized variable. The statistical results are generally acceptable, but normalization on QCT [equation (26.1a)] gives parameter estimates with lower relative standard errors and is more consistent with the original behavioral hypothesis. -31- Table 4 Estimates of Grower Supply and Processor Raw Product Demand Relationships for California Processing Tomatoes, 1954-1977" 1. Grower Supply Right-side v£uriable 23.1a AC'' Equation number and normalized variable 23.1b 23.2 AC* AC* 23.3 AC* Two-stage least squares Constant term 49.5412 (20.6133)'^ Same as (23.1a) 78.9362 (64.2766) Same as (23.2) .2382 (.0689) .0393 (.2595) fff .1542 (.1796) n - .0322 (.6689) .6574 (.1478) .4200 (.5010) » TC/(100) • PRARj .2330 (.2915) TC/(100) ■ ACt_i .1800 (.4968) Three-stage least squares Constant terms 56.6968 (20.2973) 43.1118 (20.3325) 74.9137 (62.9033) 77.8701 (64.2484) .2551 (.0681) .2250 (.0685) .1377 (.2545) .0543 (.2594) .1982 (.1767) .0926 (.1767) .0243 (.6562) - .0231 (.6686) .5978 (.1445) .7171 (.1449) 1 .4525 (.4900) .4289 (.5008) TC/(100) • PRARj .1268 (.2870) .2165 (.2914) TC/(100) • ACt_i .1416 (.4858) .1720 (.4965) (Continued on next page.) -32- 2. Processor Raw Product Demand Right-side variable 26.1a QCT^ Equation number and normalized variable 26.1b 26.2 PGCD^ QCT^ 9fi ^ qct/ Two-stage least squares Constant term - 1957.6260 10.6476 - 1891.6870 - ^74Q R7'i9 O / ***7.0 ( Oil (1319.8526) (12.7998) (1315.9478) (1946.7863) PGCD/ t - 51.4228 - 54.6720 CO CC\A A - 0^.5944 (33.3757) (32.7309) (33.3821) PRDWx 1^ " t-1 91 Vi7R .1264 21.5822 28.0869 (9.1105) (.0925) (9.1234) (10.5265) YDt' 10.5590 .0459 10.6055 13.4678 (1.2812) (.0264) (1.2809) (2.5359) sit/ - 1.4156 - .0116 - 1.4431 - 1.5220 (.4803) (.0043) (.4780) (.4906) 1570.9260 8.9914 1586.2711 1498.0530 (372.9761) (4.5090) (372.5683) (385.4264) TC/(100) • PGCDj - 26.8199 (20.3746) qct/ - .0032 (.0024) Three-stage least squares Constant term - 1625.8034 10.5464 - 1597.5149 (1246.5239) (12.2223) (1291.6239) (1945.8478) PGCDj'^ Oi.oioO - 52.7460 - 52.2284 (31.3825) (31.8801) (33.3643) PRDW, i'" 19.1082 .1262 19.0791 97 9/1 nfi Z / .Z4Uo (8.5379) (.0876) (8.9785) (10.5223) yd/ 10.3040 .0406 10.3950 13.2621 (1.2474) (.0254) (1.2681) (2.5341) SIT/ - 1.3431 - .0120 - 1.3782 - 1.5055 (.4651) (.0043) (.4722) (.4904) 1604.9538 7.1676 1621.6507 1509.6829 (356.6679) (4.3405) (368.0976) (385.3249) TC/dOO) • PGCDj - 25.2263 (20.3633) qct/ - .0022 (.0023) (Continued on next page.) -33- TABLE 4— continued. ^Estimated as a foui-equation system involving endogenous variables QCT'', QCT^, AC^, and PGCD. Equation numbers refer to Table 1. Equation (26) is obtained by substituting (25) in (26) in Table 1. (26) Demand: QCT^ = (PGCDt, PRDWt_i. YDt, SlTt, Mt) (23) Acreage supply: AC? = fg (PGCDt, YNACt, GRDt_i, T^, ACt_i) (24) Tomato supply: QCT^ = YLDCPj • AC^ Equilibrium identity: ''California acreage (1,(XX) acres). ^Figures in parentheses are standard errors. '^PRAR = deflated return per acre (price times expected yield less cost per acre) = PGCDj • YMACj - GCRDt_i. Proportion of acreage harvested mechanically. ^California production (1,000 tons). ^Deflated California grower price. ''Weighted average f.o.b. processed product price expressed per ton of raw product equivalent. 'Deflated total income. ■'California January 1 stocks of tomato products, farm weight equivalent. *Zero for all years before 1974; one thereafter. -34- Chern and Just have noted that, under conditions of oUgopsony in the purchase of the raw product, the slope of the perceived raw product demand curve would be affected by changes in the slope of the supply curve (section 3). Their statistical findings seem consistent with such a hypothesis. Since the present analysis was unable to measure shifts in short-run supply response after harvest mechanization, a test of the associated change in demand slope may not be very meaningful. However, it may be of some interest to explore possible changes in demand slope regardless of reason. Moreover, it is still possible that the short-run supply coefficient may have decreased, although it was not verified in the analysis. In Table 4, equation set (26.3) and (23.3) provides a formulation which allows for this kind of change in demand slope. ^ The negative coefficient for the cross-product term, TC/(100) • PGCD in equa- tion (26.3), suggests that the slope of the demand curve may have become a bit more negative after the adoption of the mechanical harvester. However, adding this variable tends to increase the coefficients and standard errors of the income and lagged price variables, and the standard error of its own coefficient is relatively large. Equation Selection Evaluations of the several alternative supply and demand formulations suggest that equations (26.1a) and (23.1a) provide the best estimates of raw product demand and supply relationships in the context of this study. With the focus on aggregate aspects of industry behavior, the analysis was unable to discriminate between alternative market structure hypotheses. Hence, equations (26.1a) and (23.1a) could be reflective of either competitive or oligopsonistic behavior. Elasticities Supply and demand elasticity values for selected years before and after harvest mechanization, using the 3SLS results, are given in Table 5. The values obtained are generally within the range of aftei^mechanization elasticity estimates obtained by Chern and Just (1978, pp. 78 and 80). With higher quantities and prices in recent periods, the linear equations suggest some decline in supply elasticity after mechanization, but the magnitude of the decline is less than that found by Chern and Just. Again, however, it should be noted that the results of the present study tend to be dominated by after- mechanization behavior.2 Equation (26.3) is incompletely specified for purposes of evaluating the possible effects of a change in supply slope on perceived demand. Just and Chern (1980) showed that the slope coefficients of all variables in the perceived demand equation would be affected by a change in the slope of the supply curve. To allow for this effect, cross-product terms with TC would be required for all explanatory demand variables rather than just with PGCD as in (26.3). However, this would create difficult intercorrelation and degrees-of-freedom problems that preclude the obtaining of meaningful results. ^Chem and Just also included three more years (1951, 1952, and 1953) in their premechanization data set. -35- TABLE 5 Grower Supply and Processor Raw Product Demand Elasticities Before and After Harvest Mechanization for Selected Years, 1960, 1970, 1975, and 1977 Values 1960 1970 1975 1977 Elasticities Short-run supply" jBas .785 .681 .654 Long-run supply* 2.072 1.952 1.694 1.627 Demand*^ .602 .331 - .243 .238 Data YMACf^ 16.100 20.070 23.670 23.130 PGCDt« 26.380 21.670 34.490 30.910 AC/ 130.000 141.300 305.600 278.800 QCTt* 2249.000 3363.000 7271.000 6670.000 "Short-run supply elasticity = 2551 ■ YMAC • (PGCD)/AC. ''Long-run supply elasticity = 6343 • YMAC • (PGCD)/AC. ''Short-run elasticity of demand for raw product = -51.3183 • (PGCD)/QCT. ''Three-year average California yield per acre. ^Deflated California grower price. f California acreage (1,000 acres). ^California production (1,000 tons). Source: Computed from equations (26.1a) and (23.1a), three-stage least squares. Table 4, supro, p. 32. -36- The short-run supply elasticities show the immediate percentage change in acreage associated with a given percentage change in grower price. In 1970, for example, a 1 percent increase in grower price was associated with .785 percent increase in acreage. The long-run elasticities reveal the final percentage response of acreage to a given percentage change in grower price, with all other factors constant. The long-run elasticity is substantially greater than the corresponding short-run elasticity. The processor raw product demand appears rather inelastic and also has declined, although the decline would be less if equation (26.3) in Table 4 were used. The values are in the same general range as obtained by Chem and Just (1978, p. 80) for the 1967-1975 period. The concept of a long-run elasticity is less clear in the case of the demand equation. When expressed within the framework of the complete system, the lagged average processed product price and the January 1 inventories are affected by lagged quantity. These dynamic effects are calculated in the later analysis of the complete system. January 1 Stock Prediction Since the industry model is formulated in terms of annual observations beginning July 1 , it is necessary to have an equation to predict January 1 stocks, SIT, which appears as a variable in the California processor demand equation. The OLS estimate of this equation in Table 1 is (28) SIT^ = 21.9220 + .8464 SCT^.j + .3772 QCTR.,, r2 = .863. (85.8650) (.1491) (.0382) The values in parentheses are standard errors. The Other Region Production and Acreage block consists of equations (31) through (42) in Table 1. Estimates of the four behavioral equations are given in Table 6. The equations are estimated by OLS since the explanatory variables are all regarded as predetermined in each equation. Grower price is determined by lagged values of price and quantity, by a trend factor, and by California grower prices which are usually established earlier in each year. The regional grower price then enters as a predetermined variable in the regional acreage equation. As was indicated in section 3, these equations are partially descriptive but provide acceptable estimates of acreage adjustment processes in these regions. The signs of all coefficients are consistent with theoretical expectations, the standard errors are mostly low relative to the coefficient values, and the equations explain reasonably large proportions of variations in the endogenous variables. Alternative formulations, which were explored but gave less satisfactory results, are not reported. The empirically estimated counterpart of the model outlined in Table 1 is presented in Table 7. For ease of computer calculations, the equations are numbered consecutively rather than grouped as in Table 1 . Equation (25) in Table 1 is eliminated by substitution, as Other Region Production and Acreage 6. THE COMPLETE MODEL -37- TABLE 6 Ordinary Least-Squares Estimates of Acreage and Grower Price Relationships for the Midwest and East, 1954-1977 Midwest East Equation number (Table 1) and de- pendent variable Equation number (Table 1) and de- pendent variable Right-side variable (31) (32) PGMDt" AM^^ Right-side variable (34) PGEDt'' (35) AEt"^ Constant tenn 18.5951 47.6922 (5.8829)^ (10.5384) Constant tenn 19.2293 (8.0545) 51.6847 (11.4147) PGMDj" 1.4612 (.4349) PGEDt*^ 1.0228 (.2981) .2948 (.1200) PGEDt_i'' .3724 (.1630) QMTt_/ - .0080 ( 0026) QETt_i* - .0066 (.0046) PMSDj.j'' - 8.8346 (2.3088) PGCDj' .2707 (.0853) PGCDj' .3754 (.1253) .2071 - 1.2518 (.0665) (.1568) t'' - .1306 (.1068) - 2.9111 (.1565) .769 J29 r2* .510 D.W.' 2.21 1.90 D.W.^ 1.75 1^ "Deflated grower price of tomatoes (Midwest). ^Planted tomato acreage (Midwest; 1,000 acres). "^Deflated grower price of tomatoes (East). ''planted tomato acreage (East; 1,000 acres). figures in parentheses are standard errors. ^Tomato production (Midwest; 1,000 tons). *Tomato production (East; 1,000 tons). ''Deflated farm price of soybeans (Ohio; dollars per bushel). 'Deflated grower price of tomatoes (California). h in 1954. ^Coefficient of determination. 'Durbin-Watson statistic. (For further details of variable definitions, see Table 1, supra, p. 6.) -38- TABLE 7 U. S. Processing Tomato Industry Structural Equations (1) SlTj 21.9220 + .8464 SCT^.^ + .3772 QCTRt_i (2) QCTt -1625.8034 - 51.3183 PGCDt + 19.1082 PRDWt_i + 10.3040 YDt - 1.3431 SIT (3) ACj 56.6968 + .2551 YMAC • PGCDt " -2551 GCRDt_i + .1982 TC + .5978 ACt_i (4) QCTt YLDCPt ■ ACt (5) POMDj 18.5951 + .2948 PGMDt_i + .2071 T - .0080 QMTt_i + .2707 PGCDj (6) AMt 47.6970 + 1.4612 POMDj - 8.8346 PMSDj.^ - 1.2518 T /IS in QMTj (8) PGEDj 19.2293 + .3724 rUcJU^_^ - .1306 1 - .006o yt.lt_j + .3754 rlK^U^ (9) AE^ 51.6850 + 1.0228 PGEDj - 2.9111 T (10) QETj YLDEPt • AEj (11)** QRTt RRt (QCTj + QMTt + QETj) (12) QOTt QMTt + QETj + QRTt (13)* ARt RAt (ACj + AMt AEt) (14) At ACt + AMt + AEj + ARj (15) QTt - QCTj + QOTt (16)'' QWCt RWCj • QCT (17)'^ QJCt RJCt • QCT (18)C QCCt RCCt • QCT (19)"^ QUCt RUCt • QCT (20)'^ QPICt RPCt • QCT (21) QCTRt .014 QWCt + Q-'Ct + QCCt + QUCt + QPICj {22Y^ QWt QWCj + RWOt • QOTt (Continued on next page.) -39- TABLE 7— continued. Q TP 4- P in . dfYT QII GW 4_ OW AW VMI ~t Q.T -1- O T Ti T IT T y£t 1 J Qpp -1- opp r\pp \£tO) CTT _L OTT niT QPTP -i- OPTP r\DTP TP T \ O T (yj — t_i ) sjj <'V)\ \oo) ni jl GWP _1_ f\^ A C TO J_ AOA Crf^O I rtoer otto i r^r^Ty^ .U14 awu^ -t- .U14 oJL/^ + .(WO otA^t + .035 SUC^ + .066 SPICj pwn /.U/Do lo.i^Z4 UWiNj - .0307 iXJVWj + .0018 YND^ AWN .U44Z -r .D004 IvoW -T WWyXMJj + .Oz4z rWU^ - .0242 FWDj_j^ nwN AWM 4- TWM PTn 7 1 7CQ Ort CODE TV TXT _1_ Cn J 1 \TT f\e/\n rn i.LiOo - zO.ozoo I-'uMf + .6041 VJj — .0503 T n.TM .UiS/o + .0877 [(oJ + yj)/NJj + .0344 rJDj - .0344 PJDj_]^ \ovf ppn o.doli - Zl.a035 UCNj - 11.6775 [(SCC)/NJt + .0009 YND^ (40) DCNj = .1025 + 1.2924 [(SCC + QCC)/N]t + .0452 PCDj - .0452 PCDt_i (41) PUDj 2.6699 - 30.1158 [(SU + QU)/N]t + .0013 YNDj (42) DUNt -.0008 + .7896 [(SU + QU)/N]^ + .0106 PUDj - .0106 PXJD^_^ (43) PPDt 2.5398 - 24.1768 DPNj - 147.8438 [(SPIO/Nlj + .0033 YNDj (44) APNt .0173 + .9812 [(SPIC + QPIC)/N]j + .0037 PPDj - .0037 PPDj.j (Continued on next page.) -40- TABLE 7— continued. (45) DPNt = APNj + IPNt (46) AWj = (AWNj) (47) DWt (DWNj) (48) DJt = Nj (DJNj) (49) DCt = Nj (DCNj) (50) DUt = (DUNj) (51) = (APNj) (52) DPt = Nj (DPNj) (OH) (54/ DPICt KPCj. (APj + EPj) (55)8 PRDWt 9.9968 PWDj + 4.2901 PJD^ + 10.2211 PCDj + 1.3042 PUDj + 4.2411 PPD^ (56) MRDWt PRDWt " PGCDj °RR = three-year centered moving average of QRTj -r (QCTt + QNITf + QETj). ^RA^ = three-year centered moving average of ARj -r (ACj + AMj + ACj). '^Cj = three-year centered moving average of QKCj ^ QCTj; K = W, J, C, U, and P. '^RKOj = three-year centered moving average of QKOj + QOT^; K = W, J, and U. ^CCj = three-year centered moving average of DCCj 4- DCj. ^KPC, = three-year centered moving average of DPICj H- (APj + EPj). ^Computed from the following: PWRD = 71 PWDj; PJRD = 46.43 PJD; PCRD = 43.42 PCD; PURD = 17.89 PUD; PPRD = 9.25 PPD (Appendix Table A.17 for coefficient values); and PRDW = .1408 PWRD + .0924 PJRD + .2354 PCRD + .0729 PURD + .4585 PPRD where the weights are 1973-1977 average proportions of reported processed product sales in each product form, measured in farm-weight equivalents. -41- explained previously. The model consists of 56 behavioral equations, technical relationships, and identities — one equation for each endogenous variable in the system. It provides a means of predicting expected annual values of the endogenous price and quantity variables, given the values of the exogenous income, cost, population, yield, import, export, trend, and shift variables. Model Components In Table 7, equations (1) through (4) involve processor demand and grower supply relationships in California. Equations (5) through (10) pertain to grower price and production in the Midwest and East. The small amounts of production and acreage in regions other than CaUfomia, the Midwest, and the East are calculated by equations (11) to (13). Equations (14) and (15) accumulate regional values into U. S. totals. As noted in section 3, attempts to predict allocations of the raw product to processed forms according to economic criteria were unsuccessful. The raw product, therefore, was allocated according to historical moving average ratios of the reported processed product in each of the major forms to the quantity of the raw product produced. This is accomplished by equations (16) to (24). As was noted previously, because of data limitations the reported pack values do not account for all of the tomatoes delivered to canners. In California, the reported pack is about 55 percent of the equivalent raw product deliveries (compare QCTR and QCT). Equations (25) to (29) compute carry-in stocks from previous year values of carry-in stocks, pack, sales, imports, and exports. Equations (30) to (32) predict California carry-in stocks of canned tomatoes, juice, and puree, using U. S. stocks and the lagged ratio of California pack to U. S. pack. Equation (33) aggregates the California stocks in terms of raw product equivalents. Equations (34) to (45) are the f.o.b. processor demand functions and the processor market allocation equations for the five major processed product forms. Equations (46) to (52) compute total disappearance values by multiplying per capita quantities by population. Equations (53) and (54) provide estimates of California shipments of catsup and chili sauce and paste using historical moving average ratios to U. S. values. Equation (55) calculates a weighted average processed product price in the raw product weight, and (56) computes the residually determined processed product margin indicator. Solution Procedures If the values of the exogenous and lagged endogenous variables of the model are given, the equation set in Table 7 can be solved to obtain predicted values of all of the endogenous variables. Two solution approaches were used: (1) a modified Gauss-Seidel procedure for historical predictions and (2) an analytical solution (with nonlinear equations converted to linear approximations) which provides a basis for evaluating dynamic properties and calculating long-run multipliers. The Gauss-Seidel solution is an iterative procedure that is particularly useful with nonlinear systems. The equations are ordered in a sequence, such as in Table 7, but with the equations structured so that every endogenous variable appears once on the left-hand side. To start the solution, initial values of the first endogenous variable in each jointly related -42- set of equations are read in. For example, the initial values may be the values of the previous year. The predicted value of the left-hand endogenous variable in the first equation is computed, and that value is used to obtain the prediction for the next equation, and so on. After a complete iteration, the new predicted value of the first endogenous variable is applied to the first equation, and the process is repeated. A final solution is obtained when the changes in values of the endogenous variables from one iteration to the next are all less than some predetermined value such as, say, .1 percent. Since the California growei^supply and processor demand submodel was estimated with quantity (acreage or production) as the normalized variable in both the supply and demand equations, it was necessary to transform the demand equation so as to make grower price the dependent variable. This caused a convergence problem. 1 The problem was solved by replacing equation (2) with the partial reduced-form solution for PGCD obtained from equations (2) and (3) and the identity, QCTD = AC • YMAC. The latter identity is appropriate at this point since, with the disturbance term set at zero, equation (2) predicts QCTD (quantity demanded) as well as quantity purchased, QCT. The efficiency of the solution procedure was further increased by replacing the structural equations of the processed product demand and market-allocation block [equations (34) through (45)] with partial reduced-form equations for each commodity subset. With these adjustments, a solution is obtained with a single pass for the values of the endogenous variables which satisfy the equation system, given the values of all exogenous variables and lagged endogenous variables. In the solution for year, t + 1, the solution values of endogenous variables for year t become the lagged endogenous variables in t + 1. If the values of yields, population, and the technical coefficients of the model are specified, all the equations of the system are linear except for (30), (31), and (32). Linear approximations of these equations may be obtained by Taylor Series expansion around the mean values of the stock and pack variables. 2 With this modification, the complete model may be expressed in matrix form as Bj Yt = B2 Yt_i + Eg Zt (6) where Yt = 56 X 1 element vector of current endogenous variables Yt_i = 56 X 1 element vector of lagged endogenous variables Zt = 15 X 1 element vector of exogenous variables (including the constant term) Bi and B2 = 56 X 56 element matrices of coefficients of current and lagged endogenous variables and 63= 56 X 15 element matrix of coefficients of the exoge- nous variables (Appendix Table D.l). ■'^For a discussion of such convergence problems with the Gauss-Seidel procedure, see Helen, Matthews, and Womack (1973). When equation (2), Table 7, supra, p. 39, was replaced by the processor demand equation estimated with PGCD as the dependent variable, the solution converged readily. ^he linear approximations are given in Appendix Table D.l, footnote a, infra, p. 106. -43- or (7) A difficulty with this procedure is that a new inverse must be computed whenever values of yields, population, or the technical coefficients change (Appendix Table D.l). Thus, the modified Gauss — Seidel solution is more efficient for computing historical predictions of the model. On the other hand, the analytical solution provides a more convenient means of evaluating dynamic properties and computing long-run multipliers for use in projection analysis.^ The usefulness of the tomato industry model in further analysis is determined by the extent to which it is a valid representation of the system under study. This may be judged in accordance with (1) the logic of the basic behavioral equations, (2) the statistical tests applied to the estimates of equation parameters, (3) the ability of the model to track historical movements of key variables in the system, (4) the ability to predict values of variables in recent years beyond the observation period, (5) the stability properties of the model, and (6) the structural properties when viewed as a complete system. Validity of the Behavioral Equations The logical structure and the statistical properties of individual equations were discussed in sections 3 and 5. All of the equation specifications appear consistent with generally accepted theoretical concepts of firm and market behavior, and the coefficients of all equations have the theoretically expected sign. The standard errors are generally smaller than the values of their coefficients, and most coefficients are significantly different fi-om zero at the 5 percent level of significance. Goodness of Fit The closeness with which the model is able to track or predict historical movements of the endogenous price and quantity variables may be evaluated in terms of (1) its ability Note that stationary equilibrium values for given values of exogenous variables may be readily computed by either method. In the modified Gauss-Seidel solution, this is done by fixing the exogenous variables and technical coefficients and letting the model run for 20 or so periods into the future. The analytical solution computes the stationary equilibrium values by Y* = (I - Hj)~l Ho Z* as explained more fully with the later presentation of long-run multipliers. The two estimates of stationary equilibrium values do not coincide precisely because of the linear approximations used in the analytical solution; however, they are very close. This provides an important means of checking for possible errors which may creep in as a result of accidentally entering wrong coefficient values in the computer model. Appraisal of the Model -44- to predict one-period changes for given values of exogenous variables and lagged endogenous variables and (2) its ability to predict movements of endogenous variables over time, given some initial set of values of endogenous variables and the values of all exogenous variables. The sequential model (2) uses the past predicted values of lagged endogenous variables rather than actual values in generating current year predictions. Table 8 presents several measures of the model's performance in predicting changes in the major endogenous variables one period ahead. Column 2 gives the average difference between the actual and predicted values of each variable. For unbiasedness, it would be desirable for these mean differences to be zero. While only one average difference is zero, most are very small relative to the mean values of the variables. Thus, the model does not appear to predict significantly too high or too low. The mean absolute errors and the root mean square errors (RMSE) provide measures of how closely the model predictions associate with the actual values. 1 The RMSE may be used to obtain a rough indication of the distribution of the unexplained differences. If the differences are approximately normally distributed, about two-thirds of the predictions may be expected to fall within one RMSE of the actual values and about 95 percent between two RMSE. For most variables, the average percentage error is between about 5 and 8 percent. The higher average errors for the puree variables (DUN and PUD) reflect the previously noted difficulty in obtaining a good estimate of the demand for this commodity. Another measure of forecast accuracy is given by Theil's U statistic or inequality coefficient (Theil, 1966). It is computed by dividing the RMSE (in relative terms) by the mean of the squared actual relative changes.^ The denominator is the RMSE assuming zero forecasted change. If forecasts are perfect, U is zero. A value of U = 1 would indicate a status quo forecast. Values of U greater than unity suggest a forecast that is worse than simply projecting the status quo. The values of U given in Table 8 suggest that the model forecasts, while generally better than simply projecting the previous-year value, do not provide highly accurate forecasts of yeai^to-year changes. However, the total set of goodness-of-fit measures suggest that the model is a reasonable representation of the industry structure in longer run terms, although a considerable amount of year-to-year variation remains unexplained. Table 9 presents measures of historical accuracy of predictions in which only the values of exogenous variables and the initial (1954) values of lagged endogenous The RMSE is the square root of the mean of the squared differences between predicted and actual values. Let A be the actual value of a variable in period t and the predicted value of the variable. Define at = (At - At_i)/At_i andpt = (Pt - Pt-i)/Pt-i. Then, MSE = ^ 2 (pt - at)2 and Vmse -45- TABLE m Goodness-of-Fit Measures, Processing Tomato Industry Model, One-Period- Variable Mean^value, Mean of differences, Mean absolute error Actual units Percent 100 AC PGCD QCT AM PGMD QMT AE PGED QET DWN PWD DJN PJD DCN PCD DUN PUD DPN PPD PGDW MRDW 177.3 29.11 3,618.6 56.2 34.10 814.3 52.3 37.63 586.2 .211 3.20 .195 2.84 .164 3.92 .038 4.74 .099 7.90 123.9 94.8 .26 - .45 4.61 2.15 1.28 25.03 - 1.21 - 1.12 -18.8 - .005 - .130 .000 .019 - .001 .085 m. .128 .002 .071 .090 .536 14.06 3.04 290.99 4.27 1.61 61.07 4.30 2.55 48.62 .011 .158 .008 .136 .010 .266 .005 .446 .005 .925 8.14 7.10 .083 .113 .085 .078 .047 .081 .075 .071 .081 .051 .048 .043 .050 .060 .063 .147 .095 .057 .117 .065 .073 '^Actual values of DCN and DPN were computed by supplementation from confidential survey data. These Source: Calculated. -46- 8 Change Predictions, 1955-1977, and 1978-79 and 1979-80 Prediction Errors Actual units Root mean square error Percent 100 Theil's U statistic 1978 1978 and 1979 prediction errors (Xa - Xp) 1979 17.44 3.78 372.09 .101 .138 .105 .527 .748 .403 - 14.84 - 3.98 -331.3 5.03 - 8.63 124.63 4.97 2.45 70.72 .095 .073 .097 •940 .796 .411 10.02 ■ 3.01 199.8 4.27 6.42 71.68 5.51 3.47 62.20 .092 .096 .103 .828 .970 .365 1.93 - 5.32 23.79 2.35 8.56 31.04 .014 .213 .064 .065 .810 .816 .018 .114 .015 .659 .009 .181 .052 .065 .817 .770 .001 .149 .006 .254 .011 .372 .069 .093 1.174 .894 a .202 a - .282 .007 .593 .185 .119 2.259 .937 .013 1.082 - .013 - 1.784 .008 1.247 .075 .144 .598 .799 a 1.332 a - 1.151 10.17 8.68 .083 .090 .773 .784 5.78 9.76 - 19.12 - 10.50 data were not computed for 1978. -47- TABLE 9 Goodness-of-Fit Measures, Processing Tomato Industry Model Sequential Predictions, 1955-1977 Variable Mean value, Xa Mean of Mean absolute error Root mean square error differences, ^a ~ Xp Actual units Percent 100 Actual units Percent 100 AC 177.3 1.31 17.70 .105 22.80 .132 PGCD 29.11 - .38 3.45 .125 4.20 .150 QCT 3,618.6 2736 366.03 .110 492.94 .141 AM 562 2.50 4.92 .091 5.82 .110 PGMD 34.1 1.52 1.97 .058 2.68 .080 QMT 814.3 30.69 71.65 .096 85.54 .117 AE 52.3 - 1.45 5.05 .088 6.42 .107 PCED 37.63 - 1.35 3.18 .089 3.90 .109 QET 586.2 -21.86 57.54 .095 73.22 .117 DWN .211 - .002 .011 .053 .013 .064 pwn 1 VY LJ _ 1 SIA .197 .060 .256 .078 DJN .195 - .002 .010 .050 .011 .059 O OA .Udo .207 .077 .256 .094 DCN .164 - .004 .012 .072 .014 .084 PCD 3.92 .167 .416 .103 .476 .119 DUN .038 - .000 .003 .071 .003 .086 PUD 4.74 .081 .530 .114 .679 .139 DPN .099 .001 .005 .049 .007 .063 PPD 7^ .158 1.052 .131 1.286 .156 PRDW 123.9 .901 8.98 .071 11.02 .088 MRDW 94.8 1.29 7.36 .075 9.067 .093 Source: Calculated. -48- vEiriables are given. The predictions following the first year use predicted values of lagged endogenous variables in further calculations rather than actual values. As would be expected, the overall fit is less close than for the one-period-change model, but the absolute percentage error still remains reasonably small. The U statistic was not calculated in this case since it appears to have limited applicability in the context of the sequential calculations. Prediction Beyond the Observation Period It may be recalled that the parameters of the behavioral equations of the model were estimated from data which extended through the 1977-78 crop year. As more recent data became available, the model's applicability to 1978-79 and 1979-80 conditions was tested by comparing model predictions with actual values for these later years. The differences between actual and predicted values of the key endogenous variables of the system are given in the last two columns of Table 8. All of the predictions fall within three standard deviations (RMSE) of the actual values, with one exception; and most are within two standard deviations. This suggests that the model has continued to generate predictions within the general probability range of the observed data. The exception noted above is for the estimate of the puree price (PUD) where the predicted value for 1979-80 exceeded the actual value by slightly more than three times the RMSE. This larger than expected deviation is associated with a reduction in the reported (undeflated) 1979-80 price which, when deflated, yields a price below any observed during the previous 25 years. At this point, it is difficult to tell whether this reflects some difference in data reporting, a temporary aberration, or a more fundamental change in the structure of demand. In any case, it should be noted that puree accounts for only about 7 percent of the reported pack of tomato products, so the impact on the overall model predictions is not great. Stability Properties A dynamic model should have the property that, when all exogenous variables are held constant, the endogenous variables eventually converge to stationary equilibrium values or oscillate around stationary values rather than continually increasing or decreasing. To test for convergence using the modified Gauss— Seidel solution procedure, all exogenous variables are held constant at some specified level and the model allowed to generate values of the endogenous variables for a number of periods in the future. When this was done with the exogenous variables held at 1979-80 values, all endogenous variables appeared to be closely converging to stationary equilibrium values within a few years. A more rigorous test for stability may be obtained from the analytical solution of the linearized model. For convergence, it is required that the absolute value of the largest characteristic root (or modulus) of Hj [equation (7)] be less than one. As expected, this proved to be the case. The dominant root of Hi is complex with modulus equal to .75, -49- indicating a dampening cycle in the movement of the system. Inspection of the printout of time paths of the endogenous variables revealed the amplitude of the cycles to be very small, with each variable closely approaching the stationary equilibrium value within a few years. Structural Properties Sometimes when an apparently well-formulated dynamic model of a complete system is used to project beyond the range of observed values of the data set or when the model is manipulated to evaluate the impact of some policy or technical change, it may generate values for some variables that appear inconsistent with expected behavior. This may occur because the linear or other specific algebraic equation forms used can only approximate the substantially more complex actual relationships and because the model, of necessity, relegates the influence of some variables to a component of the unexplained residuals. When such problems are encountered, it may be necessary to reformulate the model or, if that does not appear feasible, to impose restrictions designed to keep any errant variable within acceptable bounds. The restrictions should, of course, be examined carefully to insure that they do not introduce other significant distortions into the model. The model of the tomato industry appears generally well behaved in most applications. In a computer experiment to evaluate what might have happened without mechanical harvesting, it was found that processor margins, if left unconstrained, would change to levels which appear questionable as a permanent outcome. The source of the difficulty is in the manner in which margins are determined. The average processor margin (MRDW in the model) is determined residually as the difference between the realized average processed product price and grower price. These margins have varied considerably over time (Appendix Table A.13), and the model simulates the historical variation reasonably well. Since the average processed product price-quantity demand slope is less than the estimated raw product price-quantity demand slope, increases in quantity processed (with all other variables constant) are associated with increases in the margin. Historically, variations in income, production inventories, population, and unexplained disturbances have been such that the margin has fluctuated around an overall average level even though output has increased. The positive association of margins and production could be considered to reflect an imperfectly competitive structure of demand and/or increasing marginal costs of processing. Note, however, that, if equation (26.1b) were used in place of (26.1a)— raw product demand normalized on grower price— the margin-production relationship would be reversed. That is, the price-quantity demand slope at the grower level would be less than at the f.o.b. processor level, and the margin would be a decreasing function of production. These inconsistencies are reflective of the problems associated with defining and estimating a true processor demand function for the raw product as noted in sections 3 and 5. If demand slopes were the same at both the f.o.b. processor and grower level (as would be expected if competition were perfect and marginal costs constant), margins would not change with output. While the possibility of margin variation with output cannot be rejected on either logical or empirical grounds, such variation seems likely to be associated with variation -50- r around general trend levels of output. It seems unlikely that the average level of margins would change significantly with more permanent shifts in output levels. ^ However, the margin-predicting equation of the model is not able to distinguish between long- and short-run output variation. Thus, in a simulation experiment in which other margin- affecting variables remain constant and in which only the changes in general output level are examined, it seems reasonable to impose a restriction to allow the processor to shift the raw product demand curve so as to maintain whatever predetermined margin level is deemed appropriate. Results with and without the restriction and with possible alternative parameter values may be explored to define plausible ranges within which the expected output and price effects might be contained. This is discussed more specifically in the next two sections which utilize the model for issue analysis and projection. 7. IMPACT OF MECHANIZED HARVESTING ON OUTPUT, EMPLO YMENT, AND PRICES The development of mechanical harvesting of processing tomatoes has generated substantial discussion and controversy concerning its impact on employment and prices of tomato products. Social welfare and sociological effects have been evaluated by Schmitz and Seckler (1970); Hightower (1972); Friedland and Barton (1975); Thompson and Scheuring (1978); and de Janvry, LeVeen, and Runsten (1980). Further calculations of effects on supply response and labor displacement are found in Chern (1976); Brandt, French, and Jesse (1978); and Chern and Just (1978). A limitation of all of these studies, with the partial exception of the Chern-Just study, is that the estimates of acreage change and labor displacement focus only on the growing side, without taking full account of the interaction of shifting supply functions with processor demand functions. This may result in an overestimation of supply impacts and underestimation or overlooking of important price influences. To evaluate the impact of mechanical harvesting, we need to be able to estimate and compare expected differences in output, employment, and prices with and without this development. The industry model estimated in this study provides a framework for making such comparisons. Supply Response with Continued Hand Harvest It may be instructive first to note how the supply response function [equation (23.1a)] may be altered to reflect a continuation of hand-harvest conditions. The general function is: Whether the marginal cost of processing is constant, increases or decreases with industry output is an empirical question which cannot be answered fully with the data at hand. However, in view of the modular nature of processing plant organization and the ability to vary output by length of run (number of shifts and number of days), it seems likely that marginal costs would not change much with variations in short-run industry output. Over longer periods, the modular structure noted above plus ability to vary plant numbers and locations may be such that long-run unit processing costs also are not greatly influenced by industry output levels. -51- ACt = 56.70 + .2551 YMACt (PGCD^.) - .2551 GCRDt_i (23.1a) + .1982TCt + .5978ACt_i where GCRD estimates the general trend of actual average cost per acre over time for whatever harvest method or combination of methods was in use each year. The equation for long-run response may be obtained by setting AC^-i = AC^ to obtain ACt = 140.97 + .6343 YMAC^ (PGCDt) - .6343 GCRDt_i (23.1a') + .4928 TC^. The supply equation assuming continued hand harvest is obtained by setting TC = 0 and replacing GCRD with GCRHD. The GCRHD series is identical to GCRD up to 1961. From 1961 to 1969, it is based on reported costs in hand harvest studies (Appendix B). Estimates from 1970 on were obtained by multiplying machine harvest costs by 1.21, the ratio of hand harvest to machine harvest in 1969.^ To illustrate the interpretation of the equations, consider the situation in 1970 in which hand harvest costs per acre were estimated at $110 above mechanical harvest cost. With grower price constant, growers would have been willing to plant 47.88 thousand acres less under hand harvest in the short run (.2551 x 110 + 19.82) and 119.05 thousand acres less in the long run (.6343 x 110 + 49.28). It is clear, however, that grower price would not remain constant. As growers reduced acreage, this would increase price, so the final reduction in acreage would be considerably less than indicated above. To obtain the predicted differences in the equilibrium values of acreage, with and without mechanical harvest, it is necessary to solve the complete model. The procedure followed is first to generate predictions of historical variation in output and prices using the sequential model whose performance was evaluated in Table 9. The supply component of this model is then modified by using the production cost series based on the higher hand harvest costs and by setting the TC variable in the supply equation at zero and then generating sequential predictions of output and prices under these conditions. Differences in associated employment levels then are estimated, using estimates of labor requirements per acre or per ton as described in Appendix C. With the termination of the Bracero Program in 1964, it seems very doubtful that the labor needed to hand harvest the volume of production required to satisfy increased demands for tomato products could have been obtained without substantial wage The average ratio for 1967 to 1969 was also 1.21. inducements. The uncertainties of the hand labor supply also made tomatoes so much less attractive to many growers that there was considerable speculation that much production might be shifted to Mexico. While there is no way to know what actually would have happened, the industry model provides a framework for evaluating the effects under alternative labor cost scenarios, thus suggesting some quantitative dimensions to the issue. Each scenario varies the assumed wage cost where the wage cost reflects the combined effects of wage rates, labor acquisition cost, and uncertainty cost. Impacts on Output and Prices Model predictions of changes in California acreage, production, and prices (if mechanical harvesting had not been developed) are presented in Table 10 for the period 1964 (when mechanized harvesting started gaining a significant portion of total harvest) until 1977. The latter date might be regarded as roughly the end of the first wave of mechanization and the start of the second wave involving electronic sorting. The impact of electronic sorting is considered in the next section. The acreage and price values were obtained by starting the model operating with actual values of the lagged endogenous variables for 1954 and then generating sequential predictions to 1977, the last year for which data were available when the model was estimated. The values of the exogenous variables are the same in each simulation run. Only the production cost series and the TC variable change. ^ In the hand-harvest simulation, the processor margin, MRDW, is constrained to be within ± 50 cents per ton of the margin predicted under mechanical- harvest development as explained in the previous section. It should be stressed that what is being compared are predictions of the model, with and without harvest mechanization, rather than actual values. The objective is to isolate the effects of the harvest method. If the simulated hand-harvest results were compared with actual historical values of acreage and prices rather than with model predictions, an influence would be included in one series which is not included in the other. The figures in Table 10 indicate that, without the development of the mechanical harvester, acreage and production would have been lower and grower and processed product prices higher. How much lower and higher depends on the assumptions made with regard to the labor market.^ Model 1 assumes that labor would have continued to be fully available, with wage increases no greater than experienced under mechanical harvesting. Under these conditions, the model predicts that without mechanical harvesting there would have been 11,000-18,000 fewer acres in the early years, with the reduction reaching Note that the production cost series used to simulate the historical development under mechanical harvesting, GCRD, is a TC weighted average of hand-harvest and mechanical-harvest costs from 1961 to 1970 when the harvester was fully adopted (Appendix B, infra, p. 98). The GCRD series does not include costs with electronic sorting. It is possible that higher processed product prices would have encouraged increased imports. If that happened, some U. S. production would have been displaced, so acreage declines with hand harvest would have been greater than indicated in Table 10. It is believed that this effect would have been minor within the range of projected price increases. -53- TABLE 10 Model Predictions of Changes in California Acreage, Production and Prices if Mechanical Harvesting Had Not Been Developed 1964-1977 Year Model 1« Model 2* Model 3«^ Model 4« Predicted decrease in acreage (AC, 1,000 acres) 1964 0.3 OJ 0.3 0.3 1965 1.3 1.3 1.3 1.3 1966 10.6 24.0 37.4 57.3 1967 18.3 30.7 42.1 56.8 1968 17.6 25.1 32.9 50.3 1969 14.2 20.3 27.6 42.4 1970 12.8 ^ 19.7 27.5 39.8 1971 12.1 18.6 27.7 38.8 1972 12.2 20.5 29.2 41.2 1973 14.9 23.5 31.8 44.5 1974 20.0 32.3 45.3 63.2 1975 21.0 33.9 47.5 65.5 1976 23.5 36.9 50.4 68.2 1977 29.5 46.1 62.8 85.1 Predicted decrease in production (QCT, 1,000 tons) 1964 8 8 8 8 1965 27 27 27 27 1966 204 723 1,103 1967 313 524 720 971 1968 372 m 696 1,066 1969 311 m 582 829 1970 306 m 655 947 1971 286 440 657 919 1972 302 506 722 1,017 1973 323 606 689 964 1974 462 im 1,049 1,463 1975 499 807 1,131 1,558 1976 450 705 963 1,303 1977 705 1,104 1,503 2,035 (Continued on next page.) -54- TABLE 10— continued. Year Model 1° Model 2* Model 3<^ Mn/lal Ad Predicted increase in grower price (PGCD) 1964 .35 .35 .35 .36 1965 .80 .80 .80 .80 1966 2.02 4.15 6.27 8.75 1967 4.94 8.89 13.03 18.87 1968 7.45 12.62 17.65 22.78 1969 8.71 13.50 18.25 23.94 1970 8.40 12.57 16.60 22.47 1971 7.66 11.53 15.02 20.08 1972 7.28 10.66 14.22 18.81 1973 6.56 9.92 13.38 17.75 1974 6.49 9.65 12.70 16.82 1975 7.22 11.00 14.73 19.79 1976 7.21 11.21 15.26 20.67 1977 6.84 10.64 14.45 19.51 Predicted increase in average processed product price (PRDW) 1964 .31 e 1965 .39 1966 1.89 1967 4.57 1968 7.21 1969 8.49 1970 8.30 1971 7.69 1972 7.38 1973 6.50 1974 6.49 1975 7.15 1976 7.14 1977 6.74 "Assumes labor fully available at wage rates experienced with mechanical harvest development. ''Increases effective wage cost by 30 percent over Model 1. '^Increases effective wage cost by 60 percent over Model 1. ''increases effective wage cost by 100 percent over Model 1. ^Blanks indicate that, with the marketing margin (MRDW) constrained to be approximately the same for both the mechanical harvesting and hand-harvest simulations, the average processed product price difference is approximately the same as the grower price difference. -55- about 30,000 by 1977. The reason for the widening gap is the continued growth in total demand and the fact that the difference between the hand-harvest and mechanical- harvest cost series continues to widen in an absolute sense, although not in percentage terms (compare series GCRD and GCRHD, Appendix B). With the continued gain in mechanical-harvesting efficiency, even without electronic sorting, it is possible that the estimated hand-harvest production cost series actually may be a bit too low relative to the mechanical-harvest costs. If so, the reductions in acreage and production with continued hand harvest would be calculated to be a bit larger. Associated with the reduced production is a higher price to growers required to cover the higher production costs that would have been experienced with continued hand harvest. Under Model 1, the prices increase by around $7.00 per ton or roughly 20-25 percent at the grower level and 5-7 percent at the f.o.b. processor level. Model 2 assumes that, starting in 1965, wage costs would have increased by 30 percent. With labor accounting for about half of the total costs for hand harvest, the production cost per acre is increased by about 15 percent (series GCRHDl in Appendix B). Model 3 increases labor cost by 60 percent starting in 1965 (total production cost per acre increases by an additional 30 percent compared to GCRHD), and Model 4 doubles labor cost (series GCRHD2 and GCRHD3, respectively, in Appendix B). As would be expected, the scenarios involving greater labor cost with continued hand harvest lead to greater reductions in acreage and production and larger increases in prices. In the most extreme scenario depicted (Model 4), acreage declines and price increases are about three times greater than for Model 1 which maintains the status quo with respect to the labor market. If the estimates of hand-harvest production and prices had been made without imposing restrictions to maintain margins at the computed level under mechanical- harvest adoption, the predicted reduction in acreage and production would have been about half as great as indicated in Table 10. Grower prices would have increased slightly more, and final product price increases would have been about half as much as in Table 10, with the difference reflected in a reduced processing margin. Had processor demand equation (26.1b) been used (equation estimated with price as the normalized variable), the estimates of acreage reduction under hand harvest would have been a little larger and the grower price increase not quite as great as shown in Table 10. The average processed product price increase under hand harvest would have been predicted to be slightly larger than in Table 10, and the average processing margin would have been predicted to increase. Although the present study was unable either to confirm or reject the Chern-Just conclusions concerning competitive behavior, the aggregate results presented in Table 10 are broadly consistent with the empirical findings of their eight-county study. Both studies conclude that grower prices were reduced as a result of the adoption of mechanical harvesting. On the supply side, Chern and Just concluded that, after allowing for the effects of other demand-shifting factors, production could be affected either positively or negatively. Their study suggested that in some counties the net impact of mechanical- harvest adoption on output was negative. In this study, mechanical harvesting is estimated to have had an overall positive net effect on output. Impaxsta on Employment Tables 11 and 12 present the results that were obtained by using the estimates of acreage and production change to predict changes in employment in the tomato industry -56- TABLE 11 Comparison of Model Predictions of California Processing Tomato Industry Employment With and Without Mechanical Harvesting Development, 1960-1977 Year harvest adoption Hand harvest only Model 1 Model 2 Model 3 iVlUUcl million hours Preharvest production labor 1960 5.77 5.77 5.77 5.77 5.77 1965 5.75 5.70 5.70 5.70 5.70 1970 6.39 6.96 5.71 5.43 5.00 1975 8.15 7.48 7.07 6.63 6.06 1977 8.32 7.41 6.89 6.37 5.68 Harvest season labor^ 1960 18.97 18.97 18.97 18.97 18.97 1965 16.88 21.69 21.69 21.69 21.69 1970 10.00 28.30 27.15 23.81 1975 10.61 38.93 36.78 34.51 31.52 1977 11.55 40.00 37.21 34.41 30.69 Assembly labor 1960 jao 30 .30 .30 .30 1965 JS3 .53 .53 .63 1970 .96 .89 .85 .81 .75 1975 1.64 1.60 1.42 1.33 1.22 1977 1.73 1.54 1.44 1.33 1.18 Seasonal cannery labor 1960 9.61 9.61 9.61 9.61 9.61 1965 12.03 11.93 11.93 11.93 11.93 1970 16.74 15.57 14.93 14.22 13.09 lulu *o.oo 21.41 20.23 18.98 1 T OA 17.34 1977 24.71 22.00 20.46 18.93 16.88 Off-season cannery labor 1960 4.19 4.19 4.19 4.19 4.19 1965 5.20 5.20 5.20 R on 1970 730 6.79 6.52 6.20 5.71 1975 10.18 9.34 8.83 8.28 7.57 1977 10.78 9.60 8.93 8.26 7.37 Total tomato industry labor 1960 38.85 38.85 38.85 38.85 38.86 1965 40M 45.05 45.05 45.05 45.06 1970 41.39 57.50 55.16 52.51 48.36 1975 63.91 78.66 74.33 69.73 63.71 1977 57.09 80.55 74.93 69.30 61.80 "From 1965 on, hand-harvest labor estimates are based on the 1960-1963 average of 7.0 labor hours per ton. (For a further explanation, see Appendix C, infra, p. 101.) Source; Calculated from data in Table 10, supra, p. 54, and Appendix Table C.l, infra, p. 103. -57- TABLE 12 Model Predictions of Changes in California Tomato Industry Employment If Mechanical Harvesting Had Not Been Adopted, 1964-1977 Year Model 1 Model 2 Model 3 Model 4 million labor hours'^ Decrease in preharvest production labor 1964 .01 .01 JOl .01 1965 .05 .05 .05 .05 1966 .38 .86 135 2.06 1967 .66 1.11 1.52 2.04 1968 .62 .88 1.15 1.7b 1969 .50 .71 .97 1.49 1970 .44 .68 •96 1.39 1971 .41 .63 .94 1972 .41 .70 .99 1 An 1.4U 1973 .49 .78 1.05 1 AH 1.4/ 1974 .66 1.07 1.49 2.08 1975 .67 1.08 lJi2 2.09 1976 .75 1.18 1£1 2.18 1977 .91 1.43 1.9S 2.64 Increase in harvest season labor 1964 2.15 2.15 2.15 2.15 1965 4.81 4.81 4.81 4.81 1966 6.18 4.36 2M 0.12 1967 7.16 5.68 4.31 2.56 1968 13.64 12.52 11.37 8.78 1969 15.58 14.66 13^ 11.26 1970 18.30 17.15 15.86 13.81 1971 17.53 16.45 14.94 13.10 1972 19.15 17.72 18.21 14.14 1973 18.04 16.74 15.47 13.55 1974 25.44 23.42 21.32 18.42 1975 28.32 26.17 23.90 20.91 1976 21.25 19.47 17.66 15.28 1977 28.45 25.66 22.86 19.14 Decrease in off-season cannery labor 1964 .01 m .01 .01 1965 .05 .06 .05 .05 1966 .34 .78 1.21 1.85 1967 .53 1.21 1.63 1968 .62 M 1.17 1.79 1969 .52 .74 .98 1.39 1970 .51 M 1.10 1.59 1971 .48 .74 1.10 1.54 1972 .51 JS IM 1.71 1973 .54 .85 1.16 1.62 1974 .78 1.26 .76 2.46 1975 .84 1.35 1.90 2.61 1976 .76 1.18 iM 2.19 1977 1.18 1.85 3.41 (Continued on next page.) -58- TABLE 12-continued. Year Model 1 Model 2 Model 3 Model 4 million labor hours" Decrease in assembly labor 1964 6 1965 1966 .04 .08 .13 .20 1967 .06 .10 .14 .18 1968 .07 .11 .14 .21 10RB ffj .09 .12 .17 1970 xn .11 .15 .21 1971 Sfl .10 .15 .22 1972 .0/7 .12 .17 3A 1973 M .13 .17 .24 1974 .12 .19 .27 38 1975 .14 .22 .31 .42 1976 .12 .19 .26 .36 1977 .19 .29 .40 .56 Decrease in seasonal cannery labor 1964 .03 .03 .03 .03 1966 .10 .10 .10 .10 1966 .79 1.79 2.78 4.26 1967 1.21 2.02 2.77 3.74 1968 1.43 2.06 2.68 4.10 1969 1.20 1.71 2.24 3.19 1970 1.17 1.81 2.52 3.66 1971 1.10 1.68 2.53 am 1972 1.16 1.95 2.78 3.92 1973 1.24 1.96 2.65 3.71 1974 1.78 2JBS 4.04 6.63 1975 1.92 3.10 4.35 aSn 1976 1.73 2.71 3.71 e /us 0AJ2 1977 2.71 4.25 5.78 7.83 Change in total tomato industry labor 1964 2.10 2.10 2.10 2.10 1965 4.61 4.61 4.61 4.61 1966 4.63 0.86 - 2.93 - 8.48 1967 4.70 157 - 1.33 - 5.03 1968 10.90 8.59 6.23 1969 13.29 11.41 9.38 5.02 1970 16.11 13.77 11.12 &97 1971 15.47 13.29 10.22 6.48 1972 17.00 14.10 11.06 6.87 1973 15.69 13.02 10.44 6.51 1974 22.10 18.02 13.76 7.87 1975 24.75 20.42 15.82 9.80 1976 17.88 14.21 10.46 5.54 1977 23.46 17.84 12.21 4.71 "Models 1 to 4 vary the effective level of labor wage rates under hand harvest compared to wage rates experienced with mechanical harvest (Table 10, supra, p. 54, and text). 'Blanks indicate less than .005. -59- under hand harvest compared to mechanical harvest. Table 11 gives predictions of preharvest, harvest, assembly, and cannery employment levels for selected years in order to provide benchmarks for comparative purposes. Table 12 gives the estimated changes in labor requirements if mechanical harvesting had not been developed, i.e., if hand harvest had continued. The estimates of labor requirements per ton or per acre used to calculate the total employment values in each labor category are described in Appendix C. Tables 11 and 12 refer only to employment in the tomato industry and do not take into account the effects on other employment as land is shifted from producing tomatoes to other crops, or vice versa. If cultural labor requirements per acre for crops alternative to tomatoes were similar to tomatoes, reduced acreage of tomatoes under hand harvest would have little effect on total employment in activities such as land tillage and irrigation. In that case the predicted differences in preharvest labor, which are small in any case, could be ignored. Similarly, the model does not take into account the additional labor that might have been used to harvest alternative crops grown on land not used for tomatoes under the higher cost, hand-harvest scenarios. For the major alternatives, such as corn, wheat, sugar beets, and alfalfa hay, the amount would be very small relative to tomato hand- harvest labor requirements. Table 11 indicates that, with the adoption of mechanical harvesting, estimated harvest season labor declined sharply and then increased somewhat with industry growth but still remained well below hand-harvest levels. At the same time, industry employment in all other labor categories increased with the higher industry output resulting from higher demand and lower costs. The net impact was that, following a small initial decline, total industry employment increased substantially above premechanization levels. While these figures provide impressive evidence of an expanded total industry employment opportunity after the adoption of mechanical harvesting, the model results suggest that, if hand harvest had continued, total industry employment would have been still greater under all scenarios. However, the job distribution would have been quite different from that under mechanization. For example, in 1977 harvest season labor was estimated to have accounted for about 20 percent of the tomato industry employment under mechanization but would have been about 50 percent with continued hand harvest. Turning to Table 12, the various scenarios suggest that continued hand harvest would have provided between 23,450,000 and 4,690,000 more total hours of labor in 1977. Since the conditions of Model 1 seem very unlikely, a more plausible range would be 17,820,000 to 4,690,000, or possibly even the narrower range defined by Models 3 and 4. Many discussions of the effects of mechanized harvesting have been in terms of lost jobs. However, a job is not a precisely defined unit of measure. It may consist of a worker employed one day, one week, or one month or, more precisely, some specified number of hours. Since the primary harvest season for tomatoes in the major areas extends from late July to early October, it seems reasonable to define a job as about 10 weeks of work at 50 hours per week, or 500 hours. In these terms the 12,180,000 hours of labor displaced under Model 3 in 1977, for example, would account for 24,360 jobs. If 12 weeks were used to define a job, the job displacement would be 20,300. Schmitz and Seckler estimated total harvest season labor displacement for 1973 at about 19,477,100 hours which exceeds the estimated values in Table 12 for that year. The difference is due to the fact that the present study draws on additional information in estimating labor requirements; takes more explicit account of supply and demand functions and the price effects of output change; and, through the several scenarios, considers possible shifts in the labor supply curve. -60- While the estimates of seasonal labor displacement developed in this study are less than indicated by Schmitz and Seckler, it is clear that, even under scenarios which substantially increase hand-harvest labor costs, the increased nonharvest labor employment after mechanization has not been sufficient to offset fully the displaced harvest labor. However, balanced against the reduced total employment is an estimated increase in f.o.b. processor prices of from 5 to 15 percent (roughly $7.00 to $20 per raw product ton in Table 10) under hand harvest and a change in the distribution of labor activity under mechanization toward work of higher skill and pay rates. The welfare aspects of these trade-offs have been discussed by Schmitz and Seckler; Brandt, French, and Jesse; and Thompson and Scheuring and need not be repeated here. While the findings of the present analysis would not greatly alter the general conclusions of these earlier studies, the model provides a stronger and more rigorously developed empirical base. Further estimates of the impact of the adoption of electronic sorting on production, prices, and employment are presented in the next section. 8. LONG-RUN MULTIPLIERS AND ECONOMIC PROJECTIONS In section 6 it was explained how the industry model may be solved to obtain yeai^to-year predictions of each endogenous price and quantity variable for given values of exogenous variables and the lagged endogenous variables. This section applies the model in order to explore the effects of possible future changes in exogenous factors such as population, technology, and income on longer term average values of acreage, prices, and production. The accuracy of the future projections depends on (1) the accuracy of estimates of the model parameters, (2) the stability of the model's structural relationships in future periods, (3) the flexibility of the model in measuring substitution and allocation adjustments, and (4) the accuracy with which the exogenous variables can be predicted. The stochastic properties of the estimated parameters of the model are indicated by the standard error terms given with the estimation results. In making projections it is assumed that the equations estimated for the historical period will hold at least approximately in the future. However, it is possible that conditions affecting slopes and levels of the equations may change. For example, a change in the competitive environment might affect the slope and level of the processor raw product demand equation, and unmeasured changes in consumer tastes might affect the relationship between per capita income and per capita consumption. It may be recalled that the model allocates total output among product forms in accordance with historical ratios. This can distort some aspects of the projections. Such distortions do not appear serious in this model, but they require explanation and special interpretation. Regardless of how well a model represents the behavior of a system, projections of future levels of price and quantity variables can be no more accurate than the projections of the exogenous variables. Changes in some exogenous variables, such as population, can be projected for a decade or so with a reasonable degree of accuracy. Others, such as changes in technology, are much more speculative. From the previous discussion, it is evident that the probability distributions of the projected values of acreage, prices, and production are complex functions of the error distribution associated with the estimates of equation parameters, the possible changes in -61- structure, the possible specification errors, and the probabiUty distributions of projections of the future values of the exogenous variables. This compound distribution is unknown. Hence, it is not possible to compute meaningful confidence intervals for the acreage, price, and production projections. The projections should be viewed, therefore, as conditional solutions of the model rather than specific forecasts. While the difficulties noted above are present in almost any type of economic projection, they are particularly apparent when a model is used to project specific levels of price and quantity variables. The accuracy in such cases is influenced by the levels of all exogenous variables, including such things as trend relationships which are representative of past adjustments but which may not hold in future periods. The procedure here will be first to compute the changes in final long-run equilibrium values of the endogenous variables for a one-unit change in each exogenous variable, holding other exogenous variables constant. Coefficients which measure these relationships are called long-run multipliers. The multipliers then may be used to calculate likely total changes in production and prices for possible alternative projections of total change in exogenous factors over some future period. Multiplier Analysis Estimates of long-run impacts may be obtained by extending either (or both) the modified Gauss-Seidel solution procedure or the analytical solution of the linearized model. With the modified Gauss-Seidel procedure, future values of the exogenous variables are projected over some chosen time interval and the model solved sequentially to generate future predictions of the endogenous variables for the same period. By varying the exogenous variables one at a time, it is possible to compute approximations of the long-run multipliers. When the model is specified completely in linear terms, a more direct and general alternative is to compute the long-run multipliers by further manipulation of the reduced- form matrix solution [equation (7)]. This may be accomplished by solving the reduced-form system to obtain the final form. The final form then may be used to obtain both interim- period and long-term multipliers.^ However, if only the long-term multipliers are of interest, they may be obtained more simply by setting Y^; = Y^-i since, in long-run equilibrium, there are no changes in the endogenous variables. Equation 7 thus may be written as Yt = HiYt + HgZt. (8) Solving for Y^ gives: Yt = (I - Hi)-! H2Zt - MZt. (9) The elements ofthe matrix (I - Hj) ^ H2 = Mare the long-run multipliers. The values of the endogenous variables (vector Yt) obtained by solving (9) for given values ofthe vector Discussions of dynamic model analysis may be found in most econometric texts as well as in other publications [see, for example, Intriligator (1978), pp. 490-507]. -62- of exogenous variables, Z, are called long-run stationary equilibrium values. In the tomato industry model, the endogenous variables tend to converge quickly to values near the final equilibrium values, so the interim period multipliers and interim values of endogenous variables tend to be near the long-run values. ^ While the emphasis in this analysis is on change relationships rather than levels, it may be instructive first to note the recent values of the major endogenous variables of the system and to examine the relation of these values to their final stationary equilibrium values. The first column of Table 13 gives reported values for 1979. The next two columns give the 1979 predictions of the linearized version of the model summarized in Table 7 (see Appendix D) for two sets of grower cost conditions. Condition I sets grower cost at the 1978 level (GCRD^-i) and pertains only to harvest cost with hand sorting. Condition II reduces growing cost by $94 per acre to take account of recent gains in general harvest efficiency (1979 cost value, Appendix Table B.l) and the lowered costs with electronic sorting. These cost adjustments are explained more fully in the later section which evaluates effects of technological change. The remaining columns under Model I give the final equilibrium values predicted by the model after all dynamic adjustments have run their course, i.e., if the exogenous variables remain at the 1979 level. They are not forecasts of the future. An evident feature of the model predictions for 1979 is that they generally overestimate prices. This is modified a bit under the more likely cost levels of Condition II, but the price predictions still remain too high. A factor accounting for part of the differences is the higher than average yields experienced in 1979 which produced greater output from about the same total acreage as predicted by the model. Note also that the reported (deflated) prices for 1979 are well below values experienced in more recent years (Appendix Tables A.12 and A.13). At the grower level, this may reflect some shift in the processor derived demand due to escalating interest rates and the higher costs of holding inventories. The reduced prices for processed products are more difficult to explain, especially for puree and paste. This could indicate some change in demand structure or possibly some change in price reporting. However, the differences between predicted and actual values for 1979 are generally within the range of maximum historical prediction error. Further observation would be required to ascertain whether or not structural changes have occurred. It may be recalled that estimation of the processor raw product demand equation with price rather than quantity as the normalized variable resulted in a substantial change in the estimated price elasticity (Table 4). The model presented in Table 7 (referred to as Model I) uses equation (26.1a) which was estimated with quantity as the normalized variable. While this result is regarded as superior, the alternative price-dependent formulation (equation 26.1b) cannot be rejected entirely. Model II replaces equations (2) and (3) in Table 7 with the simultaneously estimated equation set (23.1b) and (26.1b) in Table 4.2 Since this formulation leads to some differences in long-run multipliers for grower cost, GCRD, and per capita income, YND, it is appropriate to evaluate the effects of using the alternative Model II equation system. Interim period values are cumulative effects obtained after the elapse of some specified period shorter than required to achieve approximate stationary equilibrium. 2 With the price-dependent formulation, the 2SLS estimates seemed subjectively superior to the 3SLS estimates and so were used. However, the modeling results would not differ significantly if the 3SLS estimates had been used. -63- TABLE 13 Base Conditions for Economic Projections Endogenous variable" 1979 reported value Model I 1979 model prediction 1979 long-run equilibrium Condition T 1 Condition TT 11 Condition T 1 Condition II PGCD 26.08 33.97 31.08 33.42 29.75 AC 256.0 253.5 260.0 269.8 274.3 QCT 6,350 5,778 5,926 6,147 6,249 PGMD 31.77 37.99 37.21 38.51 37.42 AM 36.1 40.2 39.1 40.9 39.3 QMT 607 719 699 733 704 PGED 31.09 39.27 38.22 42.25 40.35 AE ia9 16.2 15.1 19.2 17.8 QET 250 225 210 267 240 A 321.4 321.8 326.2 342.5 343.0 QT 7331 6,853 6,968 7,287 . 7,335 PWD 2.78 3.46 3.43 3.43 3.41 DWN .240* .247 .249 .249 .250 PJD 2.69 2.97 2.97 2.95 2.95 DJN .145* .141 .141 .142 .142 PCD 3.50 3.99 3.97 4.50 4.42 DCN .165^ .189 .189 .172 .175 PUD 3.58 5.45 5.42 5.37 5.35 DUN .044* .066 .055 .044 .045 PPD 6.60 8.06 7.99 7.63 7.47 DPN .170*^ .162 .165 .170 .173 PRDW 106.5 129.4 128.6 132.28 130.68 MRDW 80.4 95.5 97.6 98.86 100.93 (Continued on next page.) -64- TABLE 13— continued. Endogenous vanaole Model II 1979 model prediction 1979 long-run equilibrium Condition I Condition II Condition 1 Condition II PGCD 30.06 28.93 30.81 27.80 AC 243.75 259.3 269.8 282.2 QCT 5,555 5,909 6,150 6,433 PGMD 36.93 36.62 37.7 36.8 AM 38.7 38.3 39.8 38.5 OMT 692 684 71 Q PGED 37.82 37.40 40.9 39.3 ATT 14.7 14.3 in Q 1 I.O ICO Ib.Z QET 204 198 248 226 A A 308 323 OCA QT 6,577 6,924 7,249 7,490 3.53 3.44 O.40 o oo DWN .243 ^48 .248 .256 PJD 3.02 2.99 2.99 2.96 DJN .138 .140 .139 .140 PCD 4.02 3.98 4.49 4.27 DCN .188 .190 .172 .180 PUD 5.50 5.43 5.38 5.34 DUN .054 .055 .044 .046 PPD 8.16 8.00 7.62 7.18 DPN .158 .165 .170 .162 PROW 131.09 128.9 132.7 127.0 MRDW 101.03 99.94 101.8 99.2 "PGCD, PGMD, and PGED are deflated grower prices for California, the Midwest, and the East; AC, AM, and AE are acreage (1,000 &cr68) for C8lifomi&, the Midwest, and the East; QCT, QMT, and QET are total production for California, the Midwest, and the East (1,000 tons); A and QT are U. S. acreage and production; PWD, PJD, PCD, PUD, and PPD are deflated California f.o.b. processed product prices for principal canned, juice, catsup and chili sauce, puree, and paste forms; DWN, DJN, DCN, DUN, and DPN are per capita consumption of the processed products in cases; PRDW is the weighted average processed product price (in farm weight); and MRDW = PGCD - PRDW. ^1978 value (later value not available when table was prepared). '^1977 value (later value not available). -65- The Model II predictions given in the last four columns of Table 13 are similar overall to the results obtained with Model I. Model II gives slightly lower price predictions: acreage predictions are lower for the short run and above the Model I predictions in the long run, especially for the lower cost Condition II. The magnitudes of deviations between actual and predicted values are of the same general order for both models, suggesting that the general results are at least consistent. Some differences in estimated long-run multipliers between the two models and their effects on economic projections are noted in the later discussion. The long-run multipliers for the major endogenous and exogenous variables of the tomato model, obtained as in (9), are given in Table 14. They are based on the linearized version of the model presented in Table 7, as given in Appendix D. The values apply strictly to a situation in which population and the allocation coefficients are held at 1979 values, and yields are 1975-1979 averages.! However, moderate variation in population and yield levels would not have much effect on the coefficient values. In computing the coefficients, account was taken of the fact that population, total income, and per capita income are not independent; that is, it is not possible to hold both total income and population constant and vary per capita income. The long-run multiplier for YND thus incorporates an associated variation in total income, YD.2 The effect of a change in population is not shown in Table 14. It is evaluated later by obtaining solutions over future time periods with population held at different levels. The YND column shows how a change in per capita income would affect each of the endogenous variables, assuming a continuation of past relationships between income and demand levels. It shows, for example, that a $10{)-pei^year increase in average deflated income per person would increase California acreage by 6,310 acres and increase the Allocation coefficients are given in Appendix Table A.15, infra, p. 95. ^Both YD and YND appear as separate variables in the exogenous set. Express endogenous variable yi as yi = f (YD, YND). Then, dyi = ^ dYD + ^ dYND and dy^ ^ Jyi dYD 3y^ dYND aYD ■ dYND aYND • Since YD = Thus, dYND " N(YND) dYD = N 1,000,000' dYND 1,000,000 N ay^ dy^ 1,000,000 aYD aYND- -66- TABLE 14 Long-Run Multipliers for the Processing Tomato Industry Model" Endogenous variable^ Per capita income, YND Production cost per acre, GCRD Exports canned, EW Exports juice, EJ Exports paste, EP PGCD AC QCT PGMD AM QMT PGED AE QET A QT PWD DWN PJD DJN PCD DCN PUD DUN PPD DPN PROW MRDW .004204 .063097 1.437935 .001245 .001819 .032555 .002170 .002219 .030894 .069709 1.530744 .000952 .000050 .000500 .000024 .000237 .000040 .000930 .000010 .001085 .000038 .010767 .006563 .039084 - .047743 -1.088065 .011570 .016906 .302616 .020171 .020631 .287185 .010598 .508008 .000264 .000016 .000404 .000020 .000860 .000031 .000203 .000005 .001676 .000029 .017070 .022014 .000Q48 .00727 016571 .000014 .000021 .000375 .000025 .000026 .000356 .000803 .017641 .000066 -.000004 -.000006 .0000003 -.000013 .0000005 -.000004 .0000001 -.000026 .0000004 .000392 .000344 .000028 .000425 .009681 .000008 .000012 .000219 .000015 .000015 .000208 .000469 -.010305 -000006 .0000003 .000090 -.000004 -.000008 .0000003 -.000002 .0000001 -.000015 .0000003 .000183 .000155 .000190 .002854 .065036 .000056 .000082 .001472 .000098 .000100 .001397 .003153 .069233 -.000038 .000002 -.000023 .000001 -.000051 .000002 -.000017 .0000004 .000689 -.000003 .001892 .001702 (Continued on next page.) -67- TABLE 14-continued. Endogenous variable^ Imports canned, IW Imports paste, IP Competing vegetables, DOVN Shift variable,*^ M -.000020 -.000012 - .024763 2.1741 -.000296 -.000180 - .371611 32.6256 QCT -.006747 -.004094 -8.46902 743.5373 -.000006 -.000004 - .007331 .6436 AM -.000009 -.000005 .010711 .9404 -.000153 -.000093 - .191734 16.8333 PGED -.000010 -.000006 - .01278 1.1220 A I? -.000010 -.000006 - .013072 1.1476 QET -.000145 -.000088 - .181957 15.9749 A -.000327 -.000198 - .410564 36.0454 QT -.007182 -.004358 -9.015632 791.5274 PWD -.000072 .000002 - .090704 - .4387 DWN .000004 -.0000001 - .000296 .0260 PJD .000002 .000001 .002943 - .2584 DJN -.0000001 -.0000001 - .000143 .0125 PCD .000005 .000003 .006694 - .5877 DCN -.0000002 -.0000001 - .000238 .0209 PUD .000002 .000001 .002177 - .1911 DUN -.0000001 -.00000003 - .000057 .0050 PPD .000010 -.000103 .013045 - 1.1452 DPN -.0000002 .000004 - .000227 .0199 PRDW -.000611 -.000371 - .767535 - 16.6072 MRDW -.000592 -.000359 - .742771 - 18.7813 "Coefficients indicate the final effect on the indicated endogenous variable of a one-unit change in each exogenous variable. Computed for the following conditions: Population held at 1979 level of 221,700 (l.OOO's); all allocation coefficiente held at 1979 (1977-1979 average) levels (Appendix Table A.15); yields specified at 1975-1979 average values (YMAC = 23.66, YLDPC = 22.79, YLDMP = 17.90, and YLDEP = 13.92; and trend set at 1979 value (T = 26). ''For a short definition of the endogenous variables, see Table 13, footnote a, supra, p. 64; for a more complete definition, see Table 1, supra, p. 6. = 0 for years before 1974; 1 thereafter. -68- grower price by about $0.42 per ton in 1967 dollars. It would also increase the average processed product price by $1 .08 per farm weight ton and lead to a margin increase of $0.66 per ton. The negative YND coefficients for PJD and PCD (deflated juice and catsup prices) would not ordinarily be expected. They are largely a consequence of the fixed allocation coefficients for quantities distributed to each product form.^ When total output increases as a result of an increase in income, increased quantities are allocated to juice and catsup. Since income does not appear directly as a variable in the juice demand equation, there is no compensating shift in demand level and the juice price falls. In the case of catsup, the income coefficient in the demand equation is small so that the increase in demand level is insufficient to offset the price-decreasing effect of greater quantities of catsup processed. In practice, shares allocated to each product form would not necessarily remain constant. Increased quantities likely would be allocated to the forms showing greater price increases and less to the juice and catsup forms. Thus, the long-run income multipliers for commodities other than catsup and juice tend to overstate the effect on price and understate the effects on quantity, while the catsup and juice coefficients allocate too much pack to those commodities. The coefficients in the GCRD column indicate how changes in farm production costs affect each endogenous variable. A cost increase of $100 per acre in 1967 dollars, for example, would lead to a 4,774-acre reduction in California acreage and to a $3.91 per ton increase in the California grower price. This price increase would approximately reflect the added cost per ton. Reverse conclusions would be reached for a $100 reduction in cost per acre. As would be expected, increases in California cost (with cost in other regions constant) would lead to some increase in other regions' acreage and production. The net effect is a decline in U.S. acreage (A) of 1,060 acres for each $100 increase in California production costs. Concurrent with the reduced production, all processed product per capita quantities would be reduced (except for juice) and the price increased. The seemingly perverse behavior of the juice component may be explained by the fact that reduced California production and associated increases in other regions' production might actually lead to an increase in juice output since the other regions allocate higher proportions of output to juice. Whether the shares in other regions would remain at historical levels might be questioned, but the model tends to capture the basic influence. The economic effects of varying levels of exports are shown by the multipliers in the EW, EJ and EP columns.^ The figures indicate, for example, that a 1,000,000-case in- crease in canned tomato exports would lead to increases of about $.07 in the per case price of canned tomatoes, PWD; about $.39 per ton in the average processed product price, PRDW; about $.34 per ton in the processor margin, MRDW; and about $.05 per ton in the deflated California grower price, PGCD. Correspondingly, California production, QCT, would increase by 16,571 tons. The multiplier coefficients for juice and paste exports are interpreted in a similar manner. Because of the constant product form allocation ratios, the export multipliers for the processed products require careful interpretation. In the case of canned exports, EW, ^Recall that in the earlier discussion it was noted that efforts to relate the allocations of product forms to price and cost variables were unsuccessful. The small quantities of catsup and chili sauce exported were not included in the model calculation. -69- for example, the canned tomato price increases with increases in exports as might be expected. However, the prices of other processed products are shown to decUne shghtly. The reason is that, when total production increases in response to the increased exports, the model allocates constant shares to each product, thus slightly increasing the pack of commodities other than canned tomatoes. The U. S. per capita disappearance of canned tomatoes is reduced by the increased exports. In practice, it would be expected that the share of production allocated to canned tomatoes would increase. Thus, the positive effect on PWD and the negative effects on other prices would be less than indicated. In any case, the canned tomato export multiplier coefficients for the other commodities would remain very small. Although holding allocation shares constant slightly distorts the multiplier effects, the model nevertheless appears to capture the major influence of exports on the commodity exported and on the farm price and production. A similar interpretation applies to the multiplier coefficients for juice, EJ, and paste, EP. Changes in paste exports have a somewhat greater effect on prices and output than the other commodities, reflecting the more concentrated nature of the product. Overall, if exports of canned, juice, and paste products were expanded to twice their recent (1978) values (EW78 = 1211, EJ73 = 1170, and EPyg = 1325), the multipliers suggest that the California grower price would increase by about $.34 per ton (more than double that in 1979 dollars), and California production would increase by about 118,000 tons. Thus, rather large relative increases in export levels would be required to have much impact on grower returns, although it clearly would provide a market for more tomatoes. The long-run effects of changed imports are given in the IW and IP columns of Table 14. Increasing imports of canned tomatoes by 1 ,000,000 cases, for example, would be expected to decrease the average price of canned tomatoes by about $.07 per case. This is similar in effect to a 1,000,000-case increase in U. S. production if sold in the U. S. market [Table 2, equation (1)].^ Much of the decrease in price is absorbed by a reduction in the average processing margin, PRDW, so the net effect on California grower price, PGCD, is only about $.02 per ton. The constant share allocation again results in some distortion of the multipliers for the processed product prices and pack. An increase in IW increases DWN and, as would be expected, decreases PWD. However, with shares of all processed forms remaining constant, the reduced total production slightly reduces quantities for all commodities except canned tomatoes, so the model predicts a slight price increase for those commodities. Actually, lesser quantities likely would be allocated to canned tomatoes and more to the other commodities, thus preventing a price increase for other commodities. These cross- effects are very small in any case, so the main effects of increased IW on PWD and DWN and the overall effects on acreage and production seem likely to be reasonably close approximations, given the other properties of the model. The DOVN column of Table 14 gives the effects of changes in per capita consumption of competing vegetables. This variable appears only in the demand equation for canned tomatoes and has not varied widely in recent years. Its effect is more to capture a historical trend influence rather than to serve as a basis for further projection. The coefficients £ire interpreted similarly to those in the other columns. ^ Supra, p. 26. Dividing the coefficient for DWN (16.9024) by the 1979 U. S. population (221 ,700,000) gives .000076. -70- The final column shows the effect of the shift variable, M, which was introduced in the processor raw product demand equation in association with the initiation of price bargaining by the California Tomato Growers in 1974. As noted earlier, the positive coefficient for M indicates that processor demand apparently shifted upward during that period, although it is not clear whether it was a result of the influence of the CTGA or other factors, or some combination of both. The coefficients in the M column of Table 14 provide estimates of the effects if processor demand conditions were to revert to pre-1974 levels with respect to this particular shift influence. The coefficients suggest, for example, that grower price would be reduced by $2.17 per ton (in 1967 dollars), California acreage would decrease by 32,626 acres, and the average processed product price, PRDW, would increase by $16.61 per raw product ton. If industry Model II is used (processor demand estimated with price as the normalized variable), the estimates of long-run multipliers for income and grower cost are somewhat altered. The multipliers for GCRD become .0320 for PGCD, -.1320 for AC .0602 for PRDW, and .0282 for MRDW. For YND, the values would become .0029 for PGCd' .0506 for AC, .0172 for PRDW, and .0143 for MRDW.l Economic Projections Among the exogenous factors likely to impact heavily on the processing tomato industry during the next decade are (1) further technological developments which affect costs and input requirements, (2) population growth which expands market size, and (3) possible further shifts in consumer incomes, tastes, and other factors affecting the derived demands facing processors and growers. The long-run multipliers and the simulation model provide a framework for evaluating likely effects of these probable developments on output, employment, and prices in the tomato industry. Technological Change During the past 15 years, the processing tomato industry has drastically changed its harvest and assembly technology and has introduced changes in processing methods such as aseptic bulk storage. Other developments have included improvements in cultural efficiency and better yielding varieties. Many of these developments are likely to continue during the next decade. The recent change of greatest significance, at least insofar as it affects employment, has been the development of electronic sorting as a further innovation in mechanical harvesting. This section presents an evaluation of the impact that electronic sorting has had and will have on output and employment in the industry. It also presents some conditional projections of possible impacts of other less spectacular changes. Impact of the Electronic Sorter. — All of the cost figures and analysis presented to this point have been based on mechanical harvest with hand sorting only. A study by Zobel (1979) shows a reduction in cost with electronic sorting of $2.94 per ton or $73.50 per acre (25-ton yield). Dividing by the CPI value for 1978 of 1 .954 gives a deflated cost saving of The effects of these variations are considered in the development of economic projections in the next section. -71- $1.50 per ton or $37.62 per acre.l Multiplying the cost saving by the long-run grower price and acreage multipliers for GCRD in Table 14 (.0391 and -.0477) gives a decrease in price of $1.47 per ton and an increase of 1,794 acres. If the long-run multipliers based on Model II are used (.0320 and -.1320), the price decrease is $1.20, and the acreage increase is 4,966.^ The magnitude of the cost saving clearly is not large enough in either case to have a great impact on final output. However, the reduction in labor requirements suggests a much greater impact on employment. The Zobel study estimated harvest labor at approximately 35.7 labor hours per acre with manual sorting and 19 labor hours per acre with electronic sorting — a reduction of 16.7 hours per acre. The total reduction in labor hours depends on the magnitude of industry output. Using the 1979 stationary equilibrium value of California acreage given in Table 13 for Condition I and the Model I projection, the reduction in harvest labor is calculated as: 35.7(269.8) - 19(269.8 + 1.794) = 4,471.574 or a reduction of 4,471,574 harvest labor hours. The estimates based on Model II are only slightly smaller: 35.7(269.8) - 19(269.8 + 4.960) = 4,411.420. The figures would be expanded a bit more with further projected increases in acreage due to expansion of population and demand. These aspects are explored subsequently. While this is a substantial reduction in labor requirements, it is considerably less than the estimated reduction due to the initial adoption of mechanical harvesting (Table 12). Other Efficiency Gains. — Continued research on improved tomato varieties and further experience with mechanical harvesting techniques may result in further cost reductions when measured in constant dollars, although such gains may be offset to some extent by increased energy costs. Unfortunately, there are no studies which provide a basis for projecting the potential net magnitude of such efficiency gains. A figure of 10 percent over the next 10 years does not seem unreasonable. A gain of this magnitude would amount to about $60 per acre (in 1967 dollars) which, when multiplied by the Table 14 GCRD multiplier, suggests a potential farm price reduction of $2.35 and a further increase in California production of 2,865 acres. If Model II is used, the values are $1.92 and The 1978 CPI value was used since the Zobel study was published early in 1979 and, thus, seems likely to reflect the 1978 average price experience more than later 1979 values. ^The supply response equation [Table 3, equation (7)] includes a variable TC which increased the level of supply in association with the transition from hand harvest to mechanical harvest. This adjustment, which was in addition to the cost effect, is interpreted as mainly a response to changed perceptions of labor uncertainty. It seems unlikely that further substitutions of capital for labor, such as the electronic sorter, would have the psychological impact of the original transition from hand harvest. Therefore, no attempt was made to include any alteration in future response not accounted for by cost changes. -72- 7,920 acres. A 10 percent cost increase would, of course, have opposite price and production effects. These figures are speculative, but the calculations illustrate how the long-run multipUers may be used to make conditional projections based on the user's subjective estimates of technological potential. 1 In formulating the processing tomato industry model, it was assumed implicitly that most of the change in processing cost had been closely associated with changes in the movement of the general price level as measured by the CPI. Unfortunately, there are no cost studies available which would confirm or reject that assumption. In recent years the introduction of new technology, such as aseptic bulk storage and handling and some consolidation of plants, may have had and may continue to have some impact on average processing cost. While there are no studies which might suggest the magnitude of potential gains in processing efficiency, some useful insights may be gained by utilizing the tomato industry model to delineate likely production and price effects of plausible assumptions concerning efficiency improvement. To evaluate the effects of a change in the unit cost of processing, it is assumed that processors would regard such a cost increase or decrease as equivalent to an increase or decrease in grower price, PGCD. Therefore, PGCD in the processor demand equation [(Table 7, equation (2)] is replaced by PGCD + C, where C is a change in processing cost per unit of the raw product from the initial equilibrium solution such as in Table 13, column 1. The variable, C, is added to the set of exogenous variables, and the system is solved as before. When C = 0, the solutions are identical to those in columns 2 to 8 in Table 13. However, this process yields long-run multipliers for C. Using Model I, processing cost multiplier values for California grower price, acreage, average processed price, and average margin are APGCD/AC = -.070, AAC/AC = -1.043, AQCT/AC = -23.77, APRDW/AC = .531, and AMRDW/AC = .601, respectively. Comparable values based on Model II are -.184, -3.244, -73.94, 1.646, and 1.830, respectively. To illustrate the use of these multipliers, assume that gains in processing efficiency result in a $10-per-ton (farm weight) reduction in processing cost. This would be approximately a 10 percent reduction. The Model I multipliers suggest that California acreage would increase by 1,043 acres, the grower price would increase by $.70 per ton, the average processed product price would decrease by $5.31, and the average margin would decrease by $6.01 per ton. Thus, $3.99 of the $10 gain would be retained by processors, $5.31 passed on to consumers (wholesale buyers), and $.70 to farmers. Model II yields the somewhat implausible result that the average processor margin, MRDW, would decrease by $18.30 which is considerably more than the cost reduction. This would involve a reduction in PRDW of $16.46 due to an increase in QCT of 73,940 tons and a $1.84 per ton increase in the grower price. It is possible, of course, that bargaining by the Tomato Growers Association would permit growers to obtain some of the $3.99 retained by processors under the Model I calculations. However, without supply control, increased grower shares of the processing- cost reduction would lead to increased production which, in turn, would reduce the average processed product price, thus shifting an even greater portion to consumers. In an alternative Model I formulation in which none of the gains in processing efficiency were These calculations are based on constant average yields set here at the 1975-1979 average level. If efficiency gains involve further increases in yields, this would slightly reduce the GCRD long-run multiplier for acreage. Hence, acreage increases would be slightly less than suggested above. retained by processors, the $10-per-ton cost saving was allocated — $8.43 to consumers (wholesale buyers) and $1.56 to growers— with AC increasing by 2,270 acres rather than the 1,043 in the solution above. In either case, the model results suggest that gains in processing-cost efficiency up to about 10 percent would not lead to large increases in production and that, while all participants would gain to some extent, consumers would be the primary benefactors. Shifts in Demand The most predictable exogenous variable affecting the processing tomato industry is growth of population. Since population appears as a variable affecting matrix coefficients rather than as a linearly related exogenous variable (Appendix D), its effect could not be computed in the same way as were the long-run multipliers for the other variables. The procedure followed was first to compute stationary equilibrium values for all endogenous variables as in Table 13, column 2. Then population was increased, with all other factors except total income held constant. With per capita income constant, total income necessarily increases proportional to population. The change in the stationary equilibrium value of each variable then was divided by the change in population to obtain approximate long-run multipliers. Estimates of long-run population multipliers for the major production and price variables are given in Table 15 for Model I. The figures indicate, for example, that an increase in U. S. population of 1,000,000 (1,000 units of N) is associated with an expected increase in the California acreage of 1,059 acres and an expected increase in average grower price of $.07 per ton. U.S. Census projections indicate that population will increase by about 10 percent from 1980 to 1990, from 221,651 to 243,004, and to 259,869 by the year 2000.1 Applying these estimated increases to the population multipliers suggests that, with other factors constant, the growth in U. S. population would lead to increases of 22,613 acres in California by 1990 and 40,473 acres by 2000. This would, of course, involve reductions of the same amount in the total acreage of other alternative crops. During the past 15 years, the total demand for processed tomato products has increased more rapidly than population. This is reflected in the significance of the per capita income coefficients, with deflated per capita income increasing from about $2,000 in 1954-55 to $2,500 in 1964-65 and to $3,400 by 1978. Whether real per capita income will continue that growth rate and whether the rate of growth in demand for tomato products will be sustained during the next decade is by no means clear. If the growth pattern of the 1970s is maintained through the 1980s, per capita income in 1990 will be increased by roughly $500 in 1967 dollars.^ If the past association between per capita income and demand for tomato products were to continue, the per capita income multipliers in Table 14 (YND coliunn) suggest that California production would expand by 31 ,549 acres (.063097 • 500) in 1990 to meet that demand. Associated would be an increase of 3,306 acres in other regions, an increase in California grower price of $2.10 per ton and an increase in the average processed product price, PRDW, of $5.38 per farm weight ton, all in 1967 dollars as measured by the CPI. If Model II multipliers for YND are used, the estimated California ^U. S. Department of Commerce (1979). ^The amount would be roughly doubled in 1978-1979 dollars (see Appendix Table A.14, infra, p. 94, for CPI values). -74- TABLE 15 Approximations of Long-Run Population Multipliers for the Processing Tomato Industry Endogenous variable^ Population multiplier Endogenous variable" Population multiplier PGCD .000070 PWD .0000034 AC .001059 DWN -.0000002 QCT .024037 PJD .0000044 PGMD .000021 DJN -.0000002 AM .000030 PCD .0000027 QMT .000544 DCN -.0000001 PGED .000036 PUD .0000012 AE .000037 DUN -.0000003 QET .000516 PPD .0000009 A .001165 DPN -.0000001 QT .025589 PRDW .0000849 MRDW .0000146 "PGCD, PGMD, and PGED are deflated grower prices for California, the Midwest, and the East; AC, AM, AE and QCT, QMT, QET are corresponding acreage and production; A and QT are U.S. acreage and production; PWD, PJD, PCD, PUD, and PPD are deflated f.o.b. California prices for the five product forms; DWN, DJN, DCN, DUN, and DPN are corresponding U.S. per capita disappearance values; PRDW is the weighted average processed product price (farm weight); and MRDW = PRDW - PGCD. (For further details, see Table 1, supra, p. 6.) Source: Calculated. -75- acreage increase by 1990 would be 25,300, and the grower price increase would be $1.45. In view of present uncertainties about the continued growth rate in real per capita income and the likehhood of some tapering off of the rate of growth of demand for tomato products in excess of population growth, it seems reasonable at this time to view the projections above as optimistic from an industry perspective. The realized growth may be somewhat less.l Total Change Projections Table 16 summarizes the several types of industry-growth projections developed above. The projections are optimistic in the sense of evaluating the effects of changes that would be favorable for growers and processors. The figures reflect possible values rather than forecasts. This is especially applicable to the evaluation of the impact of further per capita income growth and the associated continued upward shift in demand. The changes due to this influence could easily be very small. However, even with these words of caution, the table provides some interesting figures. Perhaps the most striking thing is the indication that the industry expansion may be influenced substantially more by increases in population and other demand shifts than by improvements in efficiency. The calculated influence of the electronic sorter on output is surprisingly low. While the other possible efficiency gains are based on hypothetical and speculative assumptions, the magnitudes of the resulting output calculations are such that the impact seems clearly to be small relative to possible demand shifts, even if only population growth is considered. Also of interest is the fact that the price effects of efficiency gains and demand increases tend to be offsetting. Thus, it would be possible to achieve gains in efficiency which, along with population growth and demand shifts, would substantially expand output, with relatively little net change in prices. Presumably, producers and processors would at the same time be better off. If the labor reduction per acre with the electronic sorter is now applied to the acreage projections, the estimated labor displacement is substantially increased. If output increased in accordance with the most extreme projections of Table 16, the 1990 long-run equilibrium acreage would be 269.8 + 59.9 = 329.7. The labor displacement due to the adoption of the electronic sorter then would be 35.7(329.7 - 1.79) - 19(329.7) = 5,442,087 or 5,442,087 harvest season labor hours. Thus, the potential displacement by 1990 should be between a value based on 269,800 acres and the 329,700 acres, or roughly between Recall that in all these projections, yields are held constant at 1977-1979 average levels (for values, see Table 14, footnote a, supra, p. 67). It is likely that average yields will show further increases in the future. This would have both positive and negative influences on the acreage projections. Higher yields increase grower returns per acre which is an output-expanding influence. Increased yields would also reduce the acreage required to achieve given levels of output. The net result, compared to the constant yield results presented, would be a slight increase in acreage, a small increase in production, and small decreases in prices. -76- TABLE 16 Summary of "Optimistic" Tomato Industry Growth Projections for California Acreage, Production, and Price Variables 1980 to 1990" Change in: Influencing factor California acreage, AAC California production, AQCT California grower price, APGCD Average processed product price, APRDW 1 000 acres 1 000 tnnR J.jW/V/ \AJHO /I ^ 1 1 o fa uuiiciro Cost decreas- ing factors Adoption of elec- tronic sorter* 1.794 40.9 -1.47 -0.64 Other production efficiencies 2.865 65.3 -2.35 -1.02 Processing efficiency 1.043 23.8 0.70 -5.31 Demand increas- • ing factors Population increase 22.613 513.0 1.50 1.81 Per capita income growth^ 31.549 719.0 2.10 5.38 Optimistic total 59.864 1,362.0 0.48 0.22 ''Based on long-run multiplier coefficients of Model I. ''Reflects difference between all band sorting and all electronic sorting. '^Assumes continuation of bistorical trend in demand growtb. -77- 4,472,000 and 5,442,000 hours. This reduction would be offset to some extent by the addition of up to 237,000 hours of cannery and tomato assembly labor. ^ 9. MODEL EVALUATION While the model formulated in this study appears to be a reasonable representation of industry behavior, it potentially could have been improved had better and more complete data been available. A major limitation is the fact that published industry pack statistics do not account for all of the raw product delivered to canners. Particularly notable is the lack of data series on pack of catsup and paste in retail-size containers. The use of market survey data as a supplement to calculate per capita disappearance of these products improved the estimates, but it is not a fully satisfactory procedure. Since a data series pertaining to canning costs was not available, it was necessary to reflect the influence of that variable by assuming a close correlation with movements of the general price level as measured by the CPI. However, if a representative cost series could be obtained, it might be possible to include the average processed product margin as something other than a residually determined variable. Such cost data might also aid in estimating equations which would allocate the raw product to various product forms. Prices of processed products are represented in the model by reported prices for the dominant container size. These reported prices may not always reflect actual transaction prices, although they probably reflect general movements over time. Some further study of the relationships among prices in various container types could be fruitful. Regardless of the quality of data, it is likely that efforts to estimate processor raw product demand slopes will continue to be difficult. The difficulty is inherent in the imperfectly competitive structure of the industry. Chern and Just have noted that, under conditions of monopsony or oligopsony, the observed market-price and quantity values may define some relationship other than that of an industry marginal revenue product curve (industry demand curve). If demand and supply curve slopes remain stable and the supply curve shifts systematically, the market observations may define what Chern and Just call a perceived demand curve. In practice, however, the structure of competition may well have varied over time and may continue to vary with changes in the degree of imperfection and the variable influence of bargaining activities such as by the CTGA. Thus, it may not always be clear as to exactly what is being measured by a statistically estimated processor raw product demand function. If the actual departures from pure competition are small, the estimated function may be reasonably stable. Where they are large, this adds to the uncertainty of the estimate. In the present study the estimated demand coefficient in the processor raw product demand equation is of the expected sign and, while the ratio of the coefficient to its standard error is not large, it is at least greater than one. However, the fact that the demand slope estimate is greatly affected by the choice of normalized variables in the 2SLS and 3SLS estimation process makes it difficult to reach firm conclusions concerning the magnitudes of processor price elasticity or flexibility values. Where the value of the If the calculations had been based on Model II results, the projected acreage increases due to the electronic sorter development would have been a bit larger and the effects of population and income changes a little lower. -78- i elasticity estimates may significantly influence the outcome in further applications of the model, it is important, as was done here, to consider the effects of using the alternative estimators. An earlier study of supply response by Chern and Just concluded that supply elasticity was greatly reduced after adoption of the mechanical harvester. The results of this study neither confirm nor reject the Chern-Just conclusions. This may be due in substantial part to the fact that the largest price and acreage variations during the sample period used here occurred after mechanization, so the estimates are dominated by, and tend to reflect, behavior after mechanization. The supply model estimated here also differs from the Chern-Just model in that it applies a partial adjustment hypothesis, uses a representative grower cost series, and, for results presented, uses linear rather than logarithmic functions. Furthermore, Chern and Just estimated their model for an eight- county region, using pooled cross-section data rather than an aggregate model as was done here. If the grower cost series used in this study could be partitioned into fixed and variable components, it would be possible to explore more directly the possible influence of changed proportions of fixed costs on short-run and long-run responses. A weakness of the supply function estimated here is that it does not take into account the effects of returns to alternative crops as a factor influencing supply. While this aspect needs more future study, it should be noted that Chern and Just were only marginally successful in this regard and that estimation of the effects of returns to alternative crops has been difficult in nearly all supply response models. In other respects the supply model developed here shows relatively good statistical significance and appears reasonable in the uses made of it in this analysis. Recent changes in the bargaining status of the California Tomato Growers Association, continued growth in the share of tomatoes processed by farmer cooperatives, high inventory costs, and some indication of a slackening of processed product prices relative to previous actual and predicted values are all suggestive of some possible further changes in the structure of the industry. Continued high inflation rates may present another forecasting problem. While the CPI provided a satisfactory price deflator for the sample period of the study, it is possible that the association of tomato product prices and the CPI may vary in future periods. Thus, alternative deflators might be considered. As additional years of data become available and, hopefully, as the data base is improved, it will be interesting to reexamine the model and explore further possible extensions of the model formulation. -79- APPENDIX A -80- APPENDIX TABLE A.l Processing Tomato Production Statistics for California, 1954-1980 Acreage Yield Produc t ion t; rower n 1 3/ Prlce- Pl.inteil Harvested Proct'Rsor Planted Harvested acres acres Field door Year AC ACH YLDCP YLDC QCT PGC PGPC 1000 acres tons per acre 1000 tons dollars per ton 1954 79.5 79.50 16. VO 16.90 1343.55 20.40 20.40 1955 116.3 116.30 17.10 17.10 1900.73 22.00 22.00 1956 151.5 151.50 10.30 10.30 2772.45 22. 70 22. 70 1957 129.6 128.70 15.59 15.70 2020.59 21 .90 21 .90 1950 152.9 152.90 17.20 17.20 2629.00 22 . 70 22 . 70 1959 129.7 129.70 15.40 15.40 1997.30 21 . 00 21 . 00 1960 130.0 130.00 17.30 17.30 2249.00 23.40 23 .40 1961 146.0 146.00 15.00 15,00 2319.44 30. 10 30.10 1962 177.2 177.20 10.20 10.20 3225.04 27.60 27.60 1963 129.0 129.00 19.10 19.10 2463.90 25.40 25.40 1964 143.0 143.00 21 .00 21 .00 3003.00 25.30 31.30 1965 122.0 122.00 20. 10 20. 10 2460.28 35.40 41.60 1966 162.5 162.50 19.30 19.30 3136.25 30.00 36.10 1967 106.7 106.70 17.10 17.10 3192.57 30.70 44.90 1960 231.3 231.30 21.20 21.20 4903.56 35.20 41 .40 1969 154.0 154.00 2. .90 21 .90 T7 /A J J / J . 6 U 27.20 33.50 1970 141.3 141.30 23.00 23.00 3362.94 25.20 31.60 1971 163.7 163.70 23.70 23.70 3879.69 20.00 34.00 1972 10J.4 170.90 24.60 25.30 4526. 15 20.00 34.00 1973 224.4 210.00 21.66 22.30 4061 .40 35.00 41.10 1974 252.4 249.90 23.17 23.40 5047.65 56.00 63.00 1975 305.6 299.20 23.79 24.30 7270.55 55.60 62.50 1976 265.0 233.00 19.12 21.70 5066.45 47.40 56.20 1977 270.0 276.40 23.92 24.10 6669.60 56.10 63.90 1970 237.0 231.90 22.32 22.00 5209.65 53.00 63.70 1979 256.0 250.00 24.00 25.40 6350.00 56.70 67.50 1980 211.2 20S. j() 26.23 20.t,O S54(). 78 47.70 S9.(in a/ Prior to 1964, prices were reported only at the first receivinj? point (field price). In 1964 the USDA began reporting prices only as delivered at the prot i ;sor door. However, the California Crop Reporting Service has continued to report both a field and processor door price. The field price is used in the analysis to preserve continuity. Sources: U. S. Statistical Reporting Service, Crop Reporting Board (1954-1980) and the Cali- fornia Crop and Livestock Reporting Service, 1954-1979. APPENDIX TABLE A. 2 Processing Tomato Production Statistics for the East, 1954-1980^' Acr eage Yield Prnduc t Ion Planted Harvested r •) \A ^ rxr o c f" or! acres acres price Year AE AEH YLDEP YLDE OFT PCE 1000 tons per acre 1000 tnnc; $ / ton 1954 09 . 9 07 . 7 O . U i3 7.00 413.84 31.15 1 955 94 • 2 93 . 5 A AO 4.02 451 . 04 31.97 1954 92 . 9 90 . 7 n n 1 U . U 1 9.02 010.19 34.08 1957 74 . 4 74 . 0 0 . UO 7.01 524 . 15 34 .92 1950 78.0 76 . 5 o oo 10.08 770 . 75 32. 14 1959 44 . 0 63 . 9 n /. Q 8.01 542.65 30.87 1940 50.7 57.4 1 Art 12.22 704 . 1 1 31.04 1941 61.0 40 . 4 1 J . U J 13.14 796 . 23 32. 13 1942 40 . 9 60 . 4 14.24 14.36 867 . 47 31 .50 1943 40.3 40.5 1 ^ . 1 z 12.19 591 . 23 31 . 75 1 964 51.5 51.1 12.17 12.26 424 . 72 O 1 . f £. 1965 54.6 54. 1 14.25 14.38 777.90 33.56 1964 59.3 50.4 10.29 10.45 410.34 37.94 1967 56.4 55.4 12.71 12.94 714.74 42.35 1960 53.7 52.5 14.24 14.57 744.72 38.77 1969 42.0 40.9 12.44 12.93 530.87 39.00 1970 37.2 34.5 15.87 14.17 590.21 40.55 1971 35.2 34.4 13.27 13.50 447. 11 41.41 1972 33.9 31.3 10.51 11.41 354.56 43.73 1973 31.3 30.3 12.44 13.04 395.71 48.36 1974 33.9 33.1 13.66 13.99 462.96 72.39 1975 29.5 20.4 13.21 13.42 309.55 70.46 1976 23.0 23.3 16.64 17.00 396.10 63.19 1977 21.9 21 .4 14. 16 14.50 310.45 63.54 1970 20.5 10.0 12.34 13.45 252,90 45.39 1979 10.9 17.8 13.23 14.05 250.11 47,59 1980 14.5 14.3 10. 15 10 . 30 147.24 a/ East Includes New Jersey, Pennsylvania, Maryland, Virginia, New York (prior to 1976), and Delaware (prior to 1975). b/ Field price prior to 1964; processor door price from 1964 on. c/ Data not available when the table was prepared. Source: U. S. Statistical Reporting Service, Crop Reporting Board, 1954-1980. APPENDIX TABLE A. 3 Processing Tomato Production Statistics for the Midwest, 1954-1980— Acreage Yield Production Crowe r— Planted Harvested Planted Harvested acres acres price Year AM AMH YLDMP YLDM PGM 1000 acres tons per acres J UUl) tons $ / ton l-JS^ 50.0 56.9 9.57 9.76 555 . 1 A T7 nA ^/ • Ofl 1755 62.6 61.3 9.26 9.46 579.03 Z / . J** 1?56 70.6 69.3 11.12 11.33 /o J » ^ / 1957 69.2 64.9 8.06 8.5? ^ ^ 7 A A "in 17 1958 75.5 69,3 0.07 9.66 i /. O A f JO 1959 66.6 65.3 11.41 11 .64 / J / » 7 7 26.93 1960 64.9 64.0 13.60 13.07 b U / • 7 <: on £0 * »jJ 1961 65.3 64. 1 13.62 13.07 o y / » ^ 7 1962 63.5 62.9 16.47 16.63 I U** 0 » 1 J 20 .07 1963 40.6 40. 1 16.92 17.09 I) / <. • ^ z 27.53 1964 52.5 51.4 14.12 14.42 741 .22 <:o . vu 1965 59.0 50.0 10.33 10.64 1 Uu 1 . Z 1 m A 1 J u . O 1 1966 58.1 56. 1 12 . 36 12.00 "7 10 1 O / 1 U • 1 7 7 T IT o J . 1 ^ 1967 61 .0 60.1 17.05 17.31 1040. 15 38.00 1968 63.7 62.0 17.10 17.40 1092.94 36.77 1969 56.7 54.2 14.79 15.47 B30.45 37. 19 1970 50.0 47.3 19.36 19.63 967.09 30.12 1971 48.1 47.8 21 .05 21 .79 1051.00 30.26 1972 46.6 45.2 17.64 10.19 022.22 30.13 1973 39.4 37.9 15.03 15.6? 592.37 44.51 1974 46.6 45.5 12.90 13.21 601.00 66.55 1975 45.3 44.3 15.36 15.70 695.60 66.10 1976 41.0 39.0 20.21 21 .25 820.80 65.79 1977 30.3 37.0 17.22 17.44 659.35 66.17 1978 34. 1 33.7 19.93 20. 17 679.60 67.95 1979 36.2 34.6 16.7S 17.55 607.39 69.06 1980 3A.9 34.1 12.39 12.68 432.24 ... a/ Midwest includes Ohio, Indiana, Michigan, and Illinois (prior to 1974). b/ Field price prior to 1964; processor door price from 1964 on. c/ Data not available when the table was prepared. Source: U. S. Statistical Reporting Service, Crop Reporting Board, 1954-1980. APPENDIX TABLE A. A tlon Statist 1954-19803:/ Processing Tomato Production Statistics for the United States a/ Year Ac r eage Yield Product Ion Grower priced' PG Planted A Harvested AH YLD QT 1000 acres tons/har- vested acre 1000 tons $/ton 1954 270.40 262.95 10.30 2700.39 24.30 1955 335.60 330.50 9.90 3271 .95 24.90 1956 359.00 354.48 13.10 4643.69 25.70 1957 312.67 304.32 10.90 3317.09 25.20 1958 357.50 343.65 12.50 4295.63 25.40 1959 300.33 296.93 11 .90 3533.47 24.46 1960 202.90 279.95 14.50 4059.20 26.12 1961 307.45 304.55 14.00 4263.70 29.65 1962 330. 10 327.90 16.40 5377.56 20.42 1963 252.57 250.46 16.40 4107.54 26.74 1964 276. 11 273.35 16.80 4592.28 30.72 1 965 260 . 99 1 1 1 / . jU 4503 . 00 37.16 1964 306.05 300. 13 15.50 4652.02 35.69 1967 333.43 327.56 15.00 5175.45 42.00 1960 373.76 370.15 10.80 6950.02 40.20 1969 272.35 266.94 10,35 4090.35 34. 70 1970 240.60 245.0? 20.64 5050.95 34.00 1971 256.86 254.73 21 .65 5515.55 35.50 1972 276.31 265.02 21.90 5003.70 35.20 1973 305.94 295.10 20.11 5934.55 42.00 1974 343.69 337.70 20.79 7019.05 64.50 1975 393.93 384.25 22.13 0503.44 63.20 1976 346.82 30G.96 20.95 6471.75 50.00 1977 352.31 346.66 22.44 7779. 15 64.10 1970 304.06 295.56 21 .54 6366.40 64.20 1979 321.40 311.73 23.52 7331 .40 67.60 _198(L._ 267.38 263.03 23.61 6210.60 60.40 J a/ Includes California, the East, the Midwest (QT = QCT + QET + QMT + ()RT) . b/ Field price prior to 1964; processor door Source: U. S. Statistical Reporting Service, 1954-1980. and Other Regions price from 1964 on. Crop Reporting Board, APPENDIX TABLE A. 5 Canned Tomatoes: Supply and Disposition Statistics, 1954-1979 a/ Imports— a/ Export s— Sales , Stocks Pack U.S. cong^ sumpt ion in U.S.- U.S. California U.S. Ca I i f ornia Other July 1 Til 1 IT 1 J u i.y L Jan 1 EW DW AW Year SW SIW QW QWC QWO IW 1000 case equiva lent , 24 No. 303 cans 1954 5834 3412 26629 10100 16529 3334 404 32140 28814 1955 3245 997 Do 30167 13050 17109 3558 350 33623 30065 1956 2909 1 Jim O U / V 36457 15996 20461 4060 1014 35512 31444 1957 6900 3680 1 UU / I 26446 13340 13106 3048 279 33699 29051 1950 3304 1 .500 tf / 7 O 37152 10307 18765 5104 352 37202 32178 1959 7924 1 1 *\1A 1 1 J JO 29422 14116 15306 4123 474 37013 32090 1960 3904 OQ/\/. y yuo 30991 15141 15050 5419 299 34805 29306 1961 5290 / U H J 34034 14028 19206 6357 174 39005 33448 1962 5702 7ns9 9562 35541 17511 10030 5303 141 39707 34324 1963 6773 4uyo 33041 17308 15733 3447 345 36160 32721 1964 6753 4^D0 36431 20149 16202 3557 790 40799 37242 1965 5144 3430 13450 36015 19070 16137 4400 500 30799 34391 1966 6260 4397 13007 32662 20703 11959 4700 461 39561 34773 1967 3696 2231 12422 39127 23442 15605 6702 204 41702 34920 1960 7619 4310 14120 40422 34921 13501 5029 434 47030 42009 1969 13598 10771 22068 32036 23038 0993 4792 765 41291 36497 1970 8370 6520 20300 39017 29300 9637 6144 700 44105 37961 1971 0638 7017 21279 30027 29024 9003 5928 730 46178 40250 1972 5677 4770 19097 43301 34921 8300 5420 974 47704 42364 1973 5640 4246 10024 45347 30302 7045 3107 1090 49906 46799 1974 3090 2405 20200 43774 30170 5604 2780 907 43367 40507 1975 5310 4033 10805 53510 46603 6907 3205 1472 40575 45290 1976 12066 10240 20727 4 2805 3504 ! 7762 3190 1009 47350 44160 1977 9431 7000 24763 54124 46406 7630 3256 1136 48013 45557 1978 16043 14493 33630 49241 40924 0317 3183 1211 52630 49455 1979 14610 12626 33306 52896 44781 8115 d/ d/ d/ d/ a/ Imports and exports converted from pounds to cases at 23.3 pounds per case, b/ DW^ = SW^ + QW^ + IW^ - EW^ - SW^^^. c/ AW^ = DW^ - IW^. d/ Data not available when table was prepared. Sources- U. S. stocks: U. S. Economic Research Service (1954b-1979b) . California stocks: Canners League of California ( 1954a-1979a) and (1954e-1979e) . Pack: National Canners Association (1954-1979); Canners League of California (19541-19791). Imports and exports: U. S. Economic Research Service (1954a-1979a) . APPENDIX TABLE A. 6 Tomato Juice: Supply and Disposition Statistics, 1954-1979 Vila r- I ear Stocks Pack Exports U.S. con- sumpt Ion DJ U.S. July 1 SJ California July 1 Jnn 1 SJC SI J U.S. Californln QJ QJC-^ Other QJO EJ 1000 case equ ival ent s , 24 Ni). 303 cans 195< 1 3975 4300 11472 32701 1 1737 21044 1563 37917 1955 7474 2012 9485 32044 15313 1 7526 1730 35750 1 956 2630 1690 7562 53133 21760 31365 2484 40861 1757 12426 5773 15462 37760 10524 21236 2217 30529 1 950 1 1440 6700 14972 45710 18657 27053 1530 42533 195? 1 3079 6440 15256 37762 14462 23500 1 160 3921 1 1 960 1 0670 4103 12336 40202 15094 25180 1107 39439 1 961 10326 3731 10758 30545 14068 24477 1119 40754 1 962 6970 2071 7708 48793 21283 27710 1113 42230 1963 12640 6013 15725 42114 15617 26497 1339 43467 1964 7756 5351 14071 43067 17853 25214 1209 41749 1965 9985 5703 14584 40047 13573 26474 084 40792 1966 0356 3448 10762 30907 18539 20360 807 39560 1967 6096 3212 11859 42015 16510 26305 726 40446 1968 8539 2696 11251 40167 19030 20339 572 37457 1969 1067? 5919 15665 33653 16295 17358 494 36212 1970 7626 4265 14016 35752 16261 19691 610 36146 1971 6014 3447 12200 30411 10483 19928 454 36748 1772 8023 3942 12403 31074 17301 13773 770 35600 1973 2647 1330 10656 37736 19967 17969 900 34017 1974 4066 2210 11708 36133 20083 16050 985 34300 1975 5706 2615 10534 35358 21371 13907 1600 32727 1976 6535 3200 12235 32154 18152 14002 2038 27856 1977 0775 3462 11069 27044 10263 7501 1577 29516 1770 5544 325C 12227 33920 17206 16642 1170 31903 197? 5779 2381 9922 31517 17119 14398 hi hi a/ For 1967 and prior years, the California pack lnclude, c t" 1 I X W C o 1_ Cal if ornia Eas t Midwest California Midwest Cal Ifornin — California — Year PWE PWM PWC PJE PJM PJC PCM PCC PUC PPC dol lars per case 1954 £. * D £. £ * r J 2 .60 2 . 42 2.37 2 . 37 3.52 3 . 39 3.15 5 . 00 1 955 •5 o y, Z • Uo 2,57 2 .60 2. 59 2.54 3 . 75 3 . 75 3.61 7. 32 1956 S 7 ^ * o / 2 . 40 2 . 64 2 . 46 2 .38 3.53 3.55 3.41 6 . 99 1957 J » J ) £^ 2.76 2.69 2.66 2. 48 3 . 42 3.32 3.17 5.74 1958 1 A A T /, (7 i: * OU 2 .54 2.51 2.42 2.36 3.36 3.16 3.27 5.05 1959 0 A A O 79 2.63 2 . 45 2.47 2.38 3.42 3.20 3.56 5.53 1960 1 /. Q ^ * UO 2 . 72 2.59 2.46 2.51 3.55 3.34 4.00 6.63 1961 Z * *T O 9 7T 2. 95 2 . 57 2 .42 2.56 3.62 3.44 4.49 7.75 1 962 9 An 2.54 2 . 30 2.33 2.24 3.27 2.98 3.06 6.00 i /OJ 2.31 2.79 2 . 36 2 .53 2.51 2 . 39 3 . 23 3.13 3 .93 6.11 1 9Ai 1 fli^ 2.66 2.Q4 2 . 06 2 . 59 2 .56 2.51 3.36 3.36 4.10 6.53 1965 2.99 3.14 3.12 2. 75 2.66 2.03 3.60 3.75 5.34 8.75 1966 3.48 3.66 3 .39 2 . 96 2.94 2.94 4.04 3.86 5.70 9.63 1967 3.59 3.68 3.51 2.93 2.78 2.97 3.97 4.14 6.29 10.88 1968 3.10 3.22 3 . 06 2 . 56 2 .55 2 . 65 3.99 3.90 4.99 8.31 1969 3.78 3.55 3.42 2.33 2.93 2.75 4.11 4.09 4.50 6.68 1970 3.77 3.91 3.64 3.15 3.04 3.05 4.30 4.30 4.93 7.53 1971 3.86 4.04 3.00 3.15 3.10 3.13 4.34 4.39 5.39 8.49 1972 4.40 4.43 3.96 3.49 3.64 3.47 4.78 4.60 5.79 8.59 1973 5. 14 4.96 4.23 4.26 4.26 3.06 5.28 4.67 6.75 10.99 1974 5.88 5.94 5.43 5.60 5.59 5.15 7.04 7.00 9.31 16.98 1975 b.63 5.75 5.29 5.36 5.41 4.03 7.05 7.39 0.25 13.63 1976 5.78 6.00 6.13 5.36 5.53 5. 40 7.95 8.05 8.75 14.17 1977 5.73 6.20 5.78 5.56 5.59 5.07 7.50 6.74 7.00 13.03 197G 6.35 6.12 6.11 6.37 6.47 5.09 7.56 7.50 8.27 14.02 1779 6.07 6.12 6.04 6.30 6.46 5,05 7.36 7.60 7.78 14.34 a/ Prices are simple averages of monthly or quarterly reported values. Sources: Jud^e (1954-1979) and Pacific Fruit News (various Issues). APPENDIX TABLE A. 12 Season Average Prices of Tomatoes and Tomato Products Deflated by the Consumer Price Index, 1954-1979 Deflated Regiona 1 Tomato Grower I'rice Deflated Season Average F.o.b. Price Per Case In California Canned Tomato Catsup Puree Paste tomatoes juice (24/14 (6/10 (6/10 (24/303 (12/46 oz.. o z . , cans , cans , cans, cans , glass , 1.06 26 California Udwest East standard) fancy) fancy) sp. gr.) percent) Year PCCD PGMD PGED PWD PJD PCD PUD PPD dollars per ton dollars per case 1954 25.34 33.59 38.70 3.23 2.94 4.21 3.91 7.20 1955 20.43 34.34 39.06 3.20 3.17 4.68 4.50 9.13 1956 27.09 34.25 41 .07 3.05 2.92 4.36 4.19 0.59 1957 25.90 33.42 41.42 3.27 2.94 3.94 3.7B 6.01 1958 26.21 32.75 37. 14 2.93 2.73 3.65 3.70 5.03 1959 24.97 30.65 35.36 3.07 2.73 3.67 4.08 6.33 1960 26.30 31.96 35.92 ^ A"7 2.03 3.77 4 . 60 7.47 1961 33.59 30.76 35.86 3.29 2.06 3.84 5.01 8.65 1962 30.46 31.87 34.06 2.00 2.47 3.29 4.26 6.62 1963 27,70 30.02 34.62 3.12 2.61 3.41 4.29 6.66 1964 27.23 31.19 33.02 3.00 2.70 3.62 4.50 7.03 1965 37.46 32.39 35.51 3.30 2.99 3.97 5.65 9.26 1966 30.36 34.07 39.03 3.49 3.02 3.97 5.36 9.91 1967 30.70 30.00 42.35 3.51 2.99 4.14 6.29 10.80 1963 33.73 35.29 37.21 2.94 2.54 3.02 4.79 7.98 1969 24.77 33.07 35.52 3.11 2.50 3.72 4.10 6.00 1970 21 .67 32.70 34.07 3.13 2.62 3.70 4.24 6.47 1971 23.00 31.54 34.14 3.13 2.50 3.62 4.44 7.00 1972 22.35 30.43 34.90 3.16 2.77 3.67 4.62 6.06 1973 26.30 33.44 36.33 3.22 2.90 3.52 5.07 0.26 1974 30.46 45.06 49.01 3.60 3.49 4.74 6.30 11 .50 1975 34.49 41.00 4J.71 3.20 ,i.00 4.58 5.12 0.46 1976 27.00 30.59 37.06 3.60 3.21 4.72 5.13 0.32 1977 30.91 36.46 35.01 3.18 2.00 3.71 4.34 7.62 1970 27.53 34.77 33.46 3.34 3.01 3.04 4.23 7.50 ' 1979 26.08 31.77 31.09 2.73 2.69 3.50 3.58 6.60 Source: Calculated from data in Appendix Tables A.l, A. 2, A. 3, A. 11 and A. 14. APPENDIX TABLE A. 13 Processed Tomato Product Prices Per Unit of Raw Product and Average Processor-Grower Margin Indicators, 1954-1979^' Processed Product Prices"' Weighted Marg In Canned Juice Ca t sup Puree Paste c/ average— md Icator Year r Wr\Ll p ion PCRD PURD PPRD PRDW MRDW dollars per ton of raw produc t 1754 1 Jo * ^ 1 OT OA 1 o z . u u 6 " » Y 5 66 . 60 123 . 59 1 . — 90 . 25 1955 997 9ft 14/ OA 1^0* /U Zv J * Z 1 OA CI oU * J 1 04*45 130.03 107.60 1 956 216*55 ITS 7 1 1 nc 71 1 U 7 * J 1 71 OX . TO "7 0 A X /y * 46 127 . 50 101.61 1957 232 • 1 7 17/. OA 1 JO * ^ t 171 ft7 1 / 1 . u / 0 / . oZ 0 z . y T 117.41 93. 43 1950 9fto 07 X ^ O . D 1 ISO in 1 JO * 0/ * oZ 53*93 107. 70 81 . 77 1959 217.97 126*51 1 S9 1*; 1 J / * J J 71 00 / t, *7 J CO KK JU • J J 112.10 07.13 1960 217 . 97 131*14 1x7 /. 0 1 01J . 0 / 0 t Z A X 0 1 A oV . 1 U 117.07 92.69 1961 233 . 59 132*53 1 /./. 77 1 00 * / J no y. 7 u / . 0 J flft A 1 Uw » U 1 1 Z / . 6 J 74 . 06 1962 198 . 00 114*46 142*05 76.21 A 1 11 01*^^ 1963 221*52 1 9A . 1 m ft < 1 ^ 0 . y 0 7/1 7"; / 0 * / J 0 1 * 0 1 1 1 1 . 1 u 1 OAA z 1 U * ou 1 Z D * 1 Z 157 . 10 80 * 51 65 . 03 1 15 . 00 87. 05 1 7 O J 911 "Xft 1 7fi 1 JU * JO 1 /Z . JO 1 A 1 AO I V 1 * Uo 05 . 66 133.06 95 . 60 i / oo 917 79 1 7*3 0=; 1 J / . 7 J 1 / Z . JO 1 04 . 04 91.67 130.12 107. 26 1 Q/. 7 Z ^ / » Z 1 1 JU * JO If" t 7 Q 112.53 100 . 64 144 .60 105.90 1 969 208 . 74 117 7ft 1 0 J . 00 0^ X 0 0 J . 0 V / J . oZ 117.44 05 . 66 1969 220*01 115.05 161*52 73.35 56.24 110.77 06.22 1970 222 » 23 121*41 160*65 7S . / J . D J J / . 0 J 1 1 7 71 01 i 7 71*0/ 1971 222*23 119.56 157*13 79*43 64.75 114.36 91 .78 1972 224*36 120*36 159.35 02*65 63.46 116.13 93.70 1973 220*62 134*39 152.04 90.70 76.41 122.27 95.97 1974 261.20 161.73 205.01 112.71 106.30 157,22 118.76 1975 232.03 139.02 190*06 91.60 70.26 135.05 100.56 1976 255.60 140*75 204*94 91.70 76.76 140.00 112.12 1977 225*78 129.75 161.09 77.64 70.47 117.72 00.01 1978 237.14 139.40 166.73 75.67 70. 12 123.24 95.71 1979 197.38 124.65 151.97 64.05 61 .05 106.46 80.38 a/ Values deflated by CPI. hi Processed product prices In Appendix Table A. 12 converted to raw product basis using the follow- ing conversion factors (see Appendix Table A. 17): PWRD = 71PW11. P.IRD = 46.34P.ID, PCRD = 43.42PCD, PURD = 17.89PUD, PPRD = 9.25PPD. c/ Weighted average of PWRD, PJRD, PCRD. PURD, PPRD. Weights are proportions of sales (farm weight) in each of the measured processed product categories during 1973-1977. Weights are: W = .141, J = .092, C = .235, U = .073, P = .459. d/ MRDW = PRDW - PGCD. Source: Calculated as Indicated In footnotes. APPENDIX TABLE A. 14 Values of Selected Exogenous Variables Affecting Demand and Supply of Tomatoes and Tomato PraductH, l9V*-i97^ r a/ ulat ion- U.S. Deflated 1 Price of U.S. Pop Disposable Income Cmisumer Grower '' July 1 Jan 1 t+1 Total Per Capita i ndex c/ soyl^eans , „ . d / Ohio el YMAC- cost r/ indica tor g/ TC^ 1 Year NM N YD YND CPl PMSD &CRD billion 1967 = do] lars tons dollars thousands dollars dollars 100 pounds per bushel per acre per acre percent 1954 1 /. T A n n 1 /.An AO 320 1969 DO. 5 41.91 3.07 16.00 301 .70 0.00 1955 1 /. A n A A 1 ooUvv 343 2077 00.2 43.56 2.84 16.67 416.60 0.00 1956 1 ouzuv 360 2141 01.4 44.14 2.70 17.00 443.00 0.00 1957 1 7 1 7rt A I / I JVV 366 2136 04.3 44.54 2.49 17.43 459.30 0.00 1950 1 7 J 1 An 1 /fl 1 U U 1 7^ 7 A A 360 2114 06.6 45.50 2.33 17.03 477.00 0.00 1959 177100 179400 306 2102 87.3 45.01 2.26 17.07 504.60 0.00 1960 1 nn7An 1 Vv /vv 1 091 AA 395 2104 00.7 45.75 2.46 16,10 526.60 0.00 1961 103700 105300 407 2214 09.6 45.60 2.51 16.63 550.30 0.50 1962 106500 100000 425 2200 90.6 40.02 2.57 16.17 572.70 1 .30 1963 109200 190600 441 2332 91.7 40.65 2.77 17.10 594.90 1 .30 1964 191900 193200 472 2457 92.9 48.00 2.06 17.70 613.20 3.50 1965 194300 195500 501 2577 94.5 50.55 2.74 19.43 610.70 20.00 1966 196600 197700 527 2679 97.2 51 .70 2.84 20.07 560.50 70.00 1967 190700 199000 546 2749 100.0 53.33 2.52 20. 13 550.00 80.00 1960 200700 201000 567 2026 104,2 55. 13 2.30 10.33 547.20 92.00 1969 202700 203000 570 2C50 109.0 55.76 2.15 19.20 536.00 98.00 1970 204900 206100 595 2903 116.3 55.91 2.44 20.07 526.00 100.00 1971 207000 200100 615 2973 121 .3 55.90 2.54 22.30 525.30 100.00 1972 200000 209700 640 3067 125.3 57.03 3,45 23.13 520.90 100.00 1973 210400 211200 679 3227 133. 1 59.13 4.29 24.27 571 .00 100.00 1974 211900 212000 663 3130 147.7 50.64 4.56 23.77 612.70 100.00 1975 213600 214500 671 3139 161.2 56.01 3.10 23.67 635.90 100.00 1976 215100 216000 493 3222 170.5 50.65 4. 10 23.33 671.60 100.00 1977 216000 217700 721 3327 101.5 59.24 3.11 23.13 702.50 100.00 1970 210500 219700 746 3416 195.4 57,77 3.45 23.37 665.30 100.00 1979 220600 221700 747 3304 217.4 h/ h/ 22.07 609,50 100.00 a/ Total Including armed forces overseas. hi All commodities. c/ Total per capita disappearance of frozen and canned vegetables excluding potatoes, sweet potatoes, and canned tomatoes . d/ Deflated price received by growers. e/ Three-year average of California yield per harvested acre ending in year t - 1 (Appendix Tab^o A.l data). f^l Deflated cost per acre. (For an explanation, see Appendix B, infra, p. 98.) g/ Percent of California tomato acreage harvested meclianlcally [Brandt, French, and Jesse (1978)]. h/ Data not available when the table was prepared. Sources: Population, income, consumer price index, and DOVN: U. S. Economic Research Service (1968-1979). Soyb^ and processed vegetables: idem (1954d-1979d) . APPENDIX TABLE A. 15 Processed Tomato Product and Minor Region Allocation Ratios, 1954-1979—' Year 1954 1955 1956 1957 1950 1959 1960 1961 1962 1963 1964 1965 1966 1967 1960 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 Allocation of California production RWC RJC RCC RUC RPC 7.040 6.610 6.313 6.454 6.C07 6.930 6.731 6.185 6.202 6.330 7.263 7.121 7.332 7.022 7.098 7.563 7.683 7.978 7.692 7.374 6.939 6.617 6.764 7.207 7.246 7.246 8.068 0.146 G.241 0.038 7.034 7.015 6.672 6.457 6.334 6.294 927 705 527 042 4.602 4.570 4.010 4.474 4.231 3,788 3.494 3.319 3.087 3.196 2.901 2.901 2.019 2.122 2.159 2.091 2.056 2.176 2. 144 2.193 2.036 2.072 2.115 2.510 2.711 2.726 2.411 2.214 2.088 2.035 2.063 1.995 2.086 1 .871 1.048 1 .791 1 .786 1.706 1 .540 1 .667 1 .779 1 .660 1 .577 1.554 1.050 1 .905 1 .931 1.701 1 .791 1.906 2.119 2.207 2.111 1.055 1.621 1.701 1.031 1 .007 1 .751 1 .627 1 .54? 1.439 1 .450 1 .450 3.224 3.042 3. 157 3.149 2.785 2.882 2.999 3.205 3.309 3.333 3.161 3.120 3. 108 3.253 3.306 3.347 3.429 3.543 3.011 4.060 4.312 4.311 4.470 4.434 4,716 4.716 Allocation of other regi on production— RWO R.IO RUO 11.591 12. 126 11 .459 10.769 10.446 995 ',7.7, 9 9 9.003 9.276 9.390 9.240 0.607 7.909 7.456 6.792 6.050 5.694 5.915 6.209 5.960 5.649 5. 102 6.003 6.710 7.626 7.62fi 15.425 15.27? 15.600 16.461 15.973 15.151 13.934 13.126 13.061 14.953 14.997 14.103 13,236 12.200 11.513 10.961 11.723 11.524 13.236 13.739 13.927 11 .667 9.901 11 .352 12.921 12.921 1 , .379 ,308 256 .065 .065 .030 0.059 0.091 0.046 0.716 0.601 0.719 0.059 0.091 0.016 0.737 0.693 0.768 .738 .739 ,672 .655 ,620 .601 .601 a/ Each number is a three-year centered moving average of the following ratios: RWC- RIC- 9^ RCC- RUC- ^ RPC- RWO- 'i"-"- RJQ- ^ QCT ' QCT ' QCT ' QCT ' QCT ' QOT ' QOT Cal If ornla catsup chili sauce, and pas te sa le KCC KPCE ' 0.177 0. 189 0.202 0.204 0.210 0.199 0. 103 0.170 0.168 0.179 0. 183 0.216 0.218 0.240 0.233 0.248 0.245 0,245 0.263 0,279 0.306 0.292 0.287 b/ b/ hi 0. 583 0.617 0. 6 20 0 . 609 0. 557 0. 587 0. 602 0. 64 5 0. h58 0. 679 0. 623 0.662 0. 645 0. 669 0' 679 0.693 0. 0, 0, • 696 • 707 ■ 732 0. 760 0. 786 0. 789 0. 794 b/ b/ b7 Allocation of minor region pr od uct ion ~ RR RA 0.081 0.074 0.071 0.062 0.063 0.059 0.062 0.056 0,057 0,052 0.050 0.044 0.043 0.039 0.036 0,030 0.028 0.022 0.018 0.016 0,016 0,021 0.022 0.023 0.020 0.020 0.199 0.183 0.165 0.148 0.151 0.144 0. 131 0, 112 0.112 0.109 0.112 0. 105 0.090 0.087 0.082 0.079 0.069 0.058 0.041 0,039 0,035 0.040 0.042 0.045 0.030 0.032 RUO; QUO QOT KCC: DCC DC KPC; DPIC AP + EP RR: QRT : (QCT + QMT + QET) , RA: AR 4 (AC + AM + AE) . Note that QCT is in tons farm weight and QKC is cases. The coefficients are used to allocate raw production to processed product pack forms. b/ Not calculated for years after 1976 because data to compute DC and DP were not available. Latest year average values were used in all further projections of model values. Source: Calculated as indicated In footnote a/. APPENDIX TABLE A. 16 Conversion Factors for Containers to No. 303 Cans and to Cases of 24/303 Can Equivalent 1 Container Case conversion 1 1 1 conversion Number of factor to containers Factor to Container designation No. 303 per case 24/303 ^ ! Tin containers j 6 oz. .360 /•Q T o r\ . 720 ! 8 oz. short .470 HO . 940 ' 8 oz. tall (buffet) .514 La 1 r\ o o i . O/O No. 1 flat .527 to X . zyo ' No. 1 picnic .648 to 1 . /yo ; No. 211 cylinder .803 OA . oUJ No. 2 vacuum (12 oz. vacuum) .871 Q 7 1 .8/1 i No. 300 .902 9A . yuz i No. 1 tall .989 9A ; No. 303 1.000 1 . UUU i No. 300 cylinder 1.149 24 1.149 No. 2 1 1.217 ZH 1 . Zl / No. 303 cylinder 1.295 No. 3 vacuum 1.416 24 1.416 ; Jumbo 1.531 , No. 2 cylinder 1.564 1 KC/, \ I No. 2-1/2 1.765 1 .765 29 oz. 1.925 12 .962 ! 32 oz. (quart) 2.103 12 1.052 i No. 3 cylinder (46 oz.) 3.063 12 1.532 1 No. 5 squat 4.034 6 1.008 I No. 10 , 6.483 6 1.621 No. 12 (gallon)— 8.207 . 6 2.052 5 gallon 41.035 1 1.710 ; Glass containers 12 oz. bottles .680 24 .680 14 oz. bottles .906 24 .906 18/20/24 oz. bottles .515 12 1.130 a/ No. 12 gallon = 6.744 No. 2 can equivalent; No . 2 can = 1. 217; and No. 303 can equivalent (6.744 • 1.217 = 8.207) Sources: Judge (1976) and King, Jesse, and French (1973). -96- APPENDIX TABLE A. 17 Conversion Factors for Processing Tomato Products, Cases, and Prices Product Canned Tomato tomatoes juice Catsup and chili sauce Puree Paste Pounds farm weight per case of United States Calif ornia^/ 36.36 28 36.36 28 66.67 60 80.00 70 b/ 142.86 132^/ li^l^/Q^ cases per ton farm weight United States Cal 1 f ornla 55 71 55 71 30 33 25 29 14 15 F.o.b. product price per ton farm weight Case unit d/ Conversion factoid 24/303 can, standard 71.00 12/46 oz. can, fancy 46.34 24/14 oz. glass, fancy 43.42 6/10 17.89^/ 6.10 9 . 25i/ a/ Estimates based on industry data and Hoos (1956) . W 11 percent solids. c^l 33 percent solids. d/ Conversion factors calculated using column 4 and appropriate conversions from Appendix Table A. 16. &I 1.06 sp. gr. f^/ 26 percent solids. Sources : For farm weight. United States: U. S. Economic Research Service (1972). For farm weight, California: Hoos (1956) and King, Jesse, and French (1973). APPENDIX B -98- Appendix B Appendix Table B.l contains trend values of California processing tomato produc- tion costs per acre used in the supply response analysis and the assumed production-cost values for the alternative hand-harvest scenarios. The trend values were derived from sample cost of production studies compiled by the California Agricultural Extension Service in a number of counties during the period 1956 to 1979. The values of GCRH and GCRM were obtained as predictions of equation (8) in King, Jesse, and French (1973) for the period 1954 to 1972, assuming one-half of the land rented and one-half owned. After 1973, reported costs began increasing at a much more rapid rate than had been maintained during the previous two decades. Thus, the trend equation used in earlier periods was no longer appropriate. Trend values from 1973 to 1979 were obtained by a free-hand fit to available sample cost of production studies.l The OCR series is aTC/100 weighted average of the hand- and machine-harvest trend series. The GCRD series divides the OCR series by the CPI (CPI/100). The GCRHD series attempts to approximate production costs with hand harvest as it was and as it would have been had it continued past 1969. The series is simply GCRH CPI/100 up to 1970. In 1969 the hand-harvest costs were estimated to be 1.21 times the machine-harvest cost. This figure was used to extend the hand-harvest cost through later years. The ratio rather than a constant difference was chosen to reflect proportionate increases in hand-harvest costs as costs increased generally and to allow in an absolute sense for some further improvement in relative efficiency of mechanical harvest with added experience. The GCRHD series assumes that hand-harvest wage rates would have increased no more than wage rates under mechanical harvest. The GCRHDl, GCRHD2, and GCRHD3 series provides three alternative scenarios with respect to possible increases in labor costs required to obtain the added hand-harvest labor. GCRHDl increases wage costs by 30 percent. Since labor accounts for about half of total cost with hand harvest, this increases per acre total cost by 15 percent. GCRHD2 increases wage costs by 60 percent, and GCRHD3 doubles wage costs. ^Observed values of cost studies for the period 1956-1973 are given in King, Jesse, and French (1973, pp. 70 and 71). Cost study values obtained for the period 1974 to 1979 are as follows (dollars per acre): For 1974, San Joaquin, Contra Costa, and Stanislaus Counties, $1,084; Sacramento County, $990; and Merced County, $913. For 1975, San Joaquin County, $941. For 1976, San Joaquin, Contra Costa, and Stanislaus Counties, $1,164; and Yolo County, $1,194. For 1977, Yolo County, $1,285. For 1979, Yolo County, $1,339. These figures are for machine harvest with manual sort. -99- APPFNIMX TARI,r; R.l Trend Values of California Processing Tomato Production Costs, 1953-1979 Proportion Current dollar value s Deflated va 1 ues of acres (dollars per acre) (dollars per acre) harvested Hand Mach ine Weighted We igh ted Year fflechanically harvest harvest average Average Alternative hand harvest Scenarios TC/ 100 GCRH GCRM OCR GCRI) GCRHD GCRHD 1 GCRHD2 GCRHD3 1953 0 280.8 280 .8 350.6 350 .6 b/ b/ hi 1954 0 307.3 307 .3 381.7 38] . 7 1955 0 334.1 334 .1 416.6 416 .6 1956 0 360.6 360 .6 443.0 443.0 1957 0 387.2 387 .2 459.3 459 .3 1958 0 413.8 413 .8 477.8 477 .8 1959 0 440.5 440 5 504.6 504 .6 1960 0 467.1 467 .1 526.6 • 526 .6 1961 .005 493.7 382.0 493.1 550.3 551 0 1962 .013 530.4 407.5 528 .8 583.6 585 .4 1963 .013 547.0 433.0 545 5 594.9 596 .5 1964 .035 573. 7 458.6 569 7 613.2 617 5 1965 .200 600.3 484.1 577 1- 610.7 635 2 730 .5 825 8 952.8 1966 . 700 626.9 509.6 544 8 560.5 644 6 741 .3 838 0 966.9 1967 .800 653.6 535. 1 558 8 558.8 653 6 751 .6 849 7 980.4 1968 .920 680.2 560 6 570 2 652 8 750 7 848 6 979 . 2 1969 .980 706.9 586.1 588 5 536.0 643 8 740 4 836 9 965.7 1970 1.00 S.I 611. 7 611 7 526 .0 636 5 7 32 0 82 7 5 954.8 1971 1.00 637.2 637 2 525.3 635 6 730 9 826 3 953.4 19 72 1.00 662.7 662 7 528.9 640 .0 736 0 832 0 960.0 1973 1.00 760.0 760 0 571.0 690 9 794 5 898 2 10 36.4 19 74 1.00 905.0 905 0 612.7 741 4 852 6 963 8 11J2.1 1975 1.00 1025.0 1025.0 635.9 769 4 884 8 1000 2 1154. 1 19 76 1.00 1145.0 1145,0 671.6 812 6 934 5 1056 4 1218. 9 1977 1.00 1275 .0 12 75. 0 702.5 850 . 0 978 2 1105. 0 1275.0 1978 1.00 1300.0 1300.0 665 .3 a/ a/ a/ a/ 19 79 1.00 1325.0 1325.0 609.5 a/ Blanks Indicate series not computed for that period, b/ Prior to 1965, the series is identical to GCRHD. Source: For an explanation, see Appendix B, sup-pa, p. 98. -101- Appendix C Estimates of Conversion Ratios Between Output and Employment in the California Processing Tomato Industry The estimates of total employment in the processing tomato industry presented in section 6 were computed from the estimates of labor requirements per acre or per ton in Appendix Table C . 1 . They were obtained as follows. Preharvest Production Labor Estimates of preharvest production labor requirements per acre were constructed from inputs specified in 28 Cooperative Extension sample cost-of-product studies in 14 different California counties covering the period 1958 to 1979. While varying somewhat the studies revealed a general downward trend in cultural labor requirements The numbers given in Appendix Table C.l are representative of the values in the various studies and reflect the downtrend. The numbers do not necessarily represent actual average values. Harvest Season Labor Estimates of harvest season labor per ton were computed from data reported in Brandt, French, and J esse (1978, p. 33) assuming a 50-hour work week. The values for later years compare well with reported hours per ton in Cooperative Extension studies of mechanical harvesting. The earlier Extension studies did not report labor hour requirements for hand harvest since the workers were paid by the box. The work week totals during the period of hand harvest (early 1960s) are consistent with fresh tomato harvest studies which would suggest picking rates of about five to six 50-pound lugs per hour. The declining average labor hour values reflect the shift from strictly hand harvest to strictly mechanical harvest and then a small further decline as mechanical harvest efficiency improved with experience. The estimates exclude mechanical harvesting with electronic sorting. Assembly Estimates of labor required to transport tomatoes from fields to processing plants were computed from values suggested in Brandt, French, and Jesse (1979 p 53) They estimated assembly labor at .12 hours per ton in 1960 and .27 hours per ton in 1975, the higher figure attributed to increased hauling distances. The values in Appendix Table C 1 for the years between were obtained by interpolation. Cannery Labor Emerson (1976) reported that 7.7 seasonal workers and 2.1 other season workers were required per 1,000 tons canned. Unfortunately, there is no specification as to how many days or hours each worker worked. While California canneries may operate for up to lb weeks, it seems doubtful that many would operate with full crews for that length of time 1" or the purposes of this study, it was assumed that the average seasonal job was 500 hours 1 his yields an average value of 3.85 seasonal workers per ton (7.7 X 500 H- 1 000) -102- APPENDIX TABLE C.l Labor Conversion Coefficients for the Processing Tomato Industry, 1960-1979^' Year Preharvest production labor Harvest season labor Assembly labor labor hours per acre labor hours per ton 1960 40 7.60 .12 1961 40 7.90 .13 1962 38 6.25 .14 1963 38 6.25 .15 1964 37 6.30 ,16 1965 37 5.40 .17 1966 36 4.60 .18 1967 36 3.90 .19 1968 35 3.00 .20 1969 35 2.70 .21 1970 35 2.30 .22 1971 34 2.35 .23 1972 34 2 30 1973 33 2.15 .25 1974 33 2.10 .26 1975 32 1.75 .27 1976 32 1.95 .27 1977 31 1.80 .27 1978 31 1.80 .27 1979 30 1.80 .27 a/ Estimates of cannery labor coefficients are 3.85 hours per ton for canning season labor and 1.68 hours per ton for off-season labor. Source: For an explanation, see Appendix C, supra, p. 101. -103- The hours of off-season work are even more difficult to estimate. It is assumed here that, while some workers are retained year-round, the average off-season job consisted of twenty 40-hour weeks. The average off-season labor requirement per ton is 2.1 X 500 1,000 = 1.68, and total cannery labor is estimated at 5.53 hours per ton. While these are very crude values, substantial variations above or below would not greatly alter the estimates of comparative employment under conditions of mechanical harvest adoption and continued hand harvest. -104- APPENDIX D -105- APPENDIX TABLE 0.1 Matrix Representation of the U.S. Processing Tomato Industry Modeli.^ Bi Yt = B2 Yt-i + Bj Zt BI Matrix (56 x 56) Column vector of Row Values of Row Values of Row Values of endogenous column non-zero column non-zero column non-zero variables (Y) i^j elements i^j elements i^j elements 1 S1TT 1, 1 1 20, 20 1 39, 40 22.5035 2 PGCD 1, 1 1.3431 21, 16 -.014 40, 18 -1.2924/N 3 AC 2, 2 51.3183 21, 17 -.014 40, 27 -1.2924/N 4 QCT 2, 4 1 21, 18 -.030 40, 39 -.0452 5 PGMO 3, 2 -.2551 YMAC 21, 19 -.035 40, 40 1 6 AM 3, 3 1 21, 20 -.066 41, 24 30.1158/N 7 QMT 4, 3 -YLDCP 21, 21 1 41, 28 30.1158/N 8 PGED 4, 4 1 22, 12 -RWO 41, 41 1 9 AE 5, 2 -.2707 22, 16 42, 24 -.7896/N 10 QET 5, 5 1 22, 22 1 42, 28 -.7896/N 1 1 QRT 6, 5 -1.4612 23, 12 -RJO 42, 41 -.0106 1 2 QOT 6, 6 1 23, 17 42, 42 1 13 AR 7, 6 -YLDMP 23, 23 1 43, 29 147.8438/N 14 A 7, 7 1 24, 12 -RUO 43, 43 1 1 5 QT 8, 2 -.3724 24, 19 43, 45 24.1768 16 awe 8, 8 1 24, 24 1 44, 20 -.9812/N 17 QJC 9, 8 -1.0228 25, 25 ■J 44, 29 -.9812/N 18 QCC 9, 9 1 26, 26 l 44, 43 -.0037 19 QUL 10, 9 -YLDEP 27, 27 •] 44, 44 1 20 QPIC 10, 10 1 28, 28 1 45, 44 -1 21 QCTR 11, 4 -RR 29, 29 1 45, 45 1 22 QW 11, 7 -RR 30, 25 -.8466 46, 35 -N 23 9J 11, 10 -RR 30, 30 1 46, 46 1 24 QU 11, 11 1 31, 26 -.5733 47, 36 -N 25 SW 12, 7 -1 31, 31 47, 47 1 26 SJ 12, 10 -1 32, 28 -.9236 48, 38 -N 27 sec 12, 11 -1 32, 32 48, 48 1 28 SU 12, 12 1 33, 27 -.030 49, 40 -N 29 SPIC 13, 3 -RA 33, 29 -.066 49, 49 1 30 swc 13, 6 -RA 33, 30 -.014 50, 42 -N 31 SJC 13, 9 -RA 33, 31 -.014 50, 50 1 32 sue 13, 13 1 33, 32 -.035 51, 44 -N 33 SCTT H, 3 -1 33, 33 1 51, 51 1 34 PWD 14, 6 -1 34, 34 1 52, 45 -N 35 AWN u. 9 -1 34, 36 16.9024 52, 52 1 36 OWN H, 13 -1 35, 22 -.6354/N 53, 49 -KCC 37 PJD 14 1 35, 25 -.6354/N 53, 53 1 38 DJN 15, 4 -1 35, 34 -.0242 54, 51 -KPCE 39 PCD 15, 12 -1 35, 35 1 54, 54 1 40 PCN 15, 15 1 36, 35 -1 55, 34 -9.9968 41 PUD 16, 4 -RWC 36, 36 1 55, 37 -4.2901 42 DUN 16, 16 1 37, 37 1 55, 39 -10.2211 43 PPD 17, 4 -Rje 37, 38 20.6285 55, 41 -1.3042 44 APN 17, 17 1 38, 23 -.6877/N 55, 43 -4.2411 45 DPN 18, 4 -RCC 38, 26 -.6877/N 55, 55 1 46 AW 18, 18 1 38, 37 -.0344 56, 2 1 47 DW 19, 4 -RUC 38, 38 1 56, 55 -1 48 DJ 19, 19 1 39, 27 11.6775/N 56, 56 1 49 DC 20, 4 -RPC 39, 39 1 50 DU 51 AP 52 DP 53 DCC 54 DPIC 55 PROW 56 MRDW (Cont inued) -106- Appendix TABLE D.I (Continued) B2 Matrix (56 X 56) B3 Matrix (56 X 15) Co L ufnn Column vGctor of Row Values of vector of Row Values of pnHnnPnniJ5 column non-zero exogenous column non-zero u a r T Ah 1 P<; t Y ^ vol lOL/LCa VI/ i/ e lement s variables (Z) i i J elements 1 «;1TT in PCN 1 o 1 1 1 H u r u 1^ 1/ 21 .3772 1 . 1 n 1 1 \ 21.9220 ? PGCD 41 PUD 1/ 55 .8464 c. T U ^, -1625.8034 2, 55 19.1082 1 J. n 2 10.3040 U OCT 43 PPD 3/ 3 .5978 / H. 7 C, T 1604.9538 5 P6MD 44 APN r 5, r D .2948 c :> . Tr J, 56.6968 A AM 4S DPN •J f -.0080 0. T 1 J, -.2551 7 OMT 46 AU 8/ o fS .3724 7 1 . ■» •J, 5 .1982 O r u 1 1/ "T 1 WW 8, 1 U -.0066 o o . J, 1 1 18.5951 QIC 48 D 1 25, o C 1 « A O .2071 in QET 49 DC 25, £5 1 n 1 u. UU VN A o. 47.6970 11 QRT 50 DU 25, 46 1 1 1 1 • A °, -1.2518 12 90T 51 AP 26, c3 1 c. TUN inn A o. 7 -8.8346 1 AR 52 DP 26, CO 1 J. V J 8 1 19.2293 14 A 53 DCC 26, / Q 48 1 L 1 r ri B °, g -.1306 1 5 QT 54 DPIC 27, i Q 1 O 1 3. q ■) 51.6850 16 owe 55 PROW 27, C I g 5 -2.9111 17 QJC 56 MRDW 27, <-3, g -1 1 8 QCC 28, 9 -1 1 9 QUL •DO 28, O 0 CO ■^4 1 7.0763 20 QPIC ■50 28, c n !>U ■^4 1 0 -.0957 21 QCTR ?9 20 34, 11 .0018 22 QW 29, 29 35, 1 .0442 23 QJ 29, 54 36, 12 1 24 QU 30, 16 .2258 37, 1 7.1758 25 SW 30, 22 -.1927 37, 6 -.0503 26 SJ 31, 17 .2026 37, 13 .6041 27 sec 31, 23 -.1162 38, 1 .0270 28 SU 32, 19 .3270 39, 1 5,3873 29 SPIC 32, 24 -.3020 39, 11 .0009 30 SWC 35, 34 -.0242 40, 1 .1025 31 SJC 38, 37 -.0344 41, 1 2.6699 32 sue 40, 39 -.0452 41, 11 .0013 33 SCTT 42, 41 -.0106 42, 1 -.0008 34 PWD 44, 43 -.0037 43, 1 2.5398 35 AWN 43, 11 .0033 36 DWN 44, 1 .0173 37 PJD 54, 14 1 38 DJN 54, 15 KPCE 39 PCD a/ Equations 30, 31 and 32 in Table 7 were converted to Linear approximations by ~ Taylor series expansion around the 1975-79 average values of pack and stocks to obtain 30. SWCt = .8466 SWt + .2258 QWCt-1 - .1927 Q«t-1 31. SJCt = .5733 SJt + .2026 QJCt-1 - .1162 QJt-1 32. SUCt = .9236 SUt + .3270 SUCt-1 - .3020 QUt-1 -107- LITERATURE CITED Brandt, J on A. "An Economic Analysis of the Processing Tomato Industry." Unpublished Ph.D. dissertation, Department of Agricultural Economics, University of California, Davis, 1977. Brandt, Jon A., Ben C. French, and Edward V. Jesse. Economic Performance in the Processing Tomato Industry. University of California, Giannini Foundation Information Series 78-1. Davis, 1978. California Crop and Livestock Reporting Service. "Processing Tomatoes, Annual Report," Vegetables — Processing. Sacramento, 1954-1979. Canners League of California. "Canner Stocks and Movement, January 1: Canned Tomatoes (Including Other Styles)." Sacramento, 1954a-1979a. . "Canner Stocks and Movement, January 1: Canned Tomato Catsup and Chili Sauce." Sacramento, 1954b-1979b. . "Canner Stocks and Movement, January 1: Canned Tomato Juice." 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