‘- ‘h‘mflul‘ numM‘u‘nA-ulll — LATE SUMMER ONION SUPPLY RESPONSE IN THE UNITED STATES Thesis for the Degree of M. S. MICHIGAN STATE UNIVERSITY Lee F. Schrader 1958 I II IIIII II III IIII III III II IIIIII IIII II IIIIII III I PLACE IN RETURN BOX to rcmavc thIs checkout from your record. TO AVOID FINES return on or More data due. DATE DUE DATE DUE DATE DUE FEB I 7199? MSU Is An Affirmative Action/Equal Opponunity Institution LATE SUMMER ONION SUPPLY RESPONSE IN THE UNITED STATES by LEE F. SCHRADER AN ABSTRACT Submitted to the College of Agriculture of Nflchigan State University of Agriculture and Applied Science in.partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Agricultural Economics 1958 Approved6EZZ2Zi2aZ%Z1123232122224Z;z&fiZé/7 ABSTRACT The objectives of this study were first to determine a useful model for prediction of late onion supplies under specified conditions and second, to test the applicability to the late onion crOp of some proposed hypotheses regard- ing supply response. Four prediction models were constructed for harvested acreage of late onions using information available prior to planting. The primary differences between the models in— volve the assumptions regarding expected prices. The methods are termed 1) conventional, 2) Hicksian, 3) dis- tributed lags, and 4) a special model constructed for the late onion crOp. Yield, unharvested production and pro- duction are analyzed using methods in the latter category. Estimates of expected prices, expected costs, techno- logy and, in some cases, fixed asset position are considered in the supply models. The percent of variance explained is fairly high, that is, from 45 percent for unharvested production to 90 percent for production. Performance of several models depends on the inclusion of a time variable which is not a cause in itself. Usefulness for prediction is limited to estimates prior to planting. Once planting has been completed sub- jective modifications are necessary to allow for the effects of weather. Estimates of price elasticity of supply are low (+.O28 to +.27l). The high degree of uncertainty involved in onion prices and production brings about the low elas- ticity and contributes to the difficulty in ascertaining a measure of expectations. Each of the methods applied proved to be useful in establishing the particular relationships it measures with the exception of the Hicksian model which proved inappro- priate in this study. All models were fitted using least squares regression on data within the years 1921 to 1957, excluding the World War II years. The parameter estimates are subjected to statistical tests of significance. The criteria for judg- ments concerning the models presented are statistical signi- ficance, prediction performance, and reasonableness of the estimates. LATE SUMMER ONION SUPPLY RESPONSE IN THE UNITED STATES by LEE F. SCHRADER A THESIS Submitted to the College of Agriculture of Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Agricultural Economics 1958 ACKNOWLEDGEMENTS The author wishes to express his gratitude to the many people who assisted in the preparation of this thesis. Special thanks are due Hr. Lester V. Manderscheid for his help, encouragement, and criticisms during its develOp- ment and completion. It was an honor and a pleasure to be his first graduate student. The financial assistance provided by the Department of Agricultural Economics, Dr. L. L. Boger, Head, made the author's study and this thesis possible. Thanks are expressed to the secretarial staff of the Department of Agricultural Economics, Krs. Joann Premier- gast and Mrs. Mona Mischi, for typing the first draft and to the statistical pool where the computations were com- pleted in spite of the "mystic." The author is also indebted to many other staff mem- bers and fellow graduate students who took time to discuss, make suggestions, and criticize the work throughout its development. TABLE OF CONTENTS Chapter I Introduction . . . . . . . . The Setting . . . . . . . The Objective . . . . . . II Review of Literature . . . . III The Analysis . . . . . . . . The Data . . . . . . . . The Method . . . . . . . Harvested Acreage . . . . Yield . . . . . . . . . . Unharvested Production . Production . . . . . . . IV Some Concluding Remarks . . General Problems . . . . General Conclusion . . . Application . . . . . . . Suggested Further Study . Appendix 0 O O O O O O O O O O O I O 0 Bibliography 0 0 O O O O O O O O O O O Page 18 21 22 25 42 48 55 58 60 62 62 65 71 Table 1.1 1.2 1.5 4.1 LIST OF TABLES Onions for Fresh Market and Processing (1949-55 average) 0 c o c c c o o c o o o Variability of Corn and Late Onion Acreage, Yield, Price, and Income Expressed as Coef— ficients of Variability . . . . . . . . . . Within Season Price Variability for Speci- fied Commodities . . . . . . . . . . . . . Variance Explained by and Elasticity Esti- mates from Several Late Onion Supply Models 56 LIST OF FIGURES Figure Page 1 Actual and Calculated Late Onion Acreage from the Conventional Model (5.5) . . . . 29 2 Actual and Calculated Late Onion Acreage Using the Hicksian Model (5.17) . . . . . 52 5 Actual and Calculated Late Onion Acreage Using the Distributed Lags Model (5.255 . 37 4 Actual and Calculated Late Onion Acreage Using the Special Model (5.27) . . . . . 41 5 Actual and Calculated Late Onion Yield Per Acre Using Model (5.51) . . . . . . . 45 6 Actual and Calculated Unharvested Late Onion Production Using Model (5.55) . . . 49 7 Actual and Calculated Late Onion Produc— tion Using Model (5.57) . . . . . . . . . 51 8 Actual and Calculated Late Onion Produc- tion Using Model (5.59) 55 9 Planted Acreage as an Indicator of Har- vested Acreage . . . . . . . . . . . . . 61 10 March 1 Intentions to Plant as an Indi- cator of Planted Acreage . . . . . . . . 61 CHAPTER I Introduction Supply response in agriculture has long been a subject of controversy both in and outside agricultural economics. Not only are there differences of Opinion as to the magni- tude of supply response to price but also disagreement as to the direction of the response. The greatest controversy exists regarding the total agricultural supply; however, there is less than full agreement even at the single com- modity level. Ample evidence of disagreement at both levels may be found in papers submitted to the Joint Economic Com- mittee of Congress in November 1957.1 Congressional Hear- 2 reveal ings on the bill to ban future trading in onions rather extreme impressions regarding onion supply response. Studies involving empirical verification of supply response hypotheses, several of which are discussed in Chapter II, are subject to less divergence than the writings referred to above. 1Poligy for Commercial Agriculture: Its Relation pg Growth and Stability, Joint Economic CSmmittee, Government Printing Office, Washington, D. C., November 22, 1952, Sec. VI. 2Hearings Before the Subcommittee on Domestic Market- ing of the Committee on Agriculture House of Representa- tives, on H. R. 576, 1955-1955, 541s, May 12 and 15, U. 8. Government Printing Office, Washington, D. C., 1957. The Setting5 Table 1.1 below is an indication of the size and value of the total onion crop and the late summer onion crOp (here- after referred to as Iate onions). Late onion yields have increased from a level of 550 sacks in 1920-50 to approxi- mately 600 sacks per acre in the past five years. Acreage Table 1.1 Onions for Fresh Market and Processing (1949-55 average)* L Unit Michigan United States Acreage: Total acres 9,500 119,850 Late crOp 9,500 61,600 Production: Total thousands of 2,266 45,284 Late crop 50# sacks 2,266 55,004 Value: Total thousands of 6,514 55,021 Late crop dollars 6,514 59,512 *Ve etables - Fresh Market, 1957 Annual Summary, Dec. 17, 195 , USDA, AMS, p. 4 . 3Information about the crOp was obtained in informal interviews with Dr. Lucas, Soils Department, Michigan State University and Dr. Carew, Horticulture Department, Michigan State University. Further information is available in: D. Milton Shuffett, The Demand on Price Structure for Selected Ve etables, Tech. Bul. 1105, USDA, December, I954. J. W. Park, Marketing Onions, Tech. Bul. 555, USDA April, 1957. Commodity Yearbook, 1956, Commodity Research Bureau Inc., New YOrk, 1956. increased from about 45,000 in the early twenties to the 70,000 area in 1950 and has since declined to the 60,000 acre level. Late onions are produced commercially in 19 states with the bulk of production in New York, Michigan, Colorado, Oregon, and California. The crOp is harvested during August, September, and October. A substantial portion of the late crop is stored each year to provide for trade needs until the spring crOp is moving in volume (usually March). Approximately half to two-thirds of the crop is placed into storage, mostly on farms. There is no carryover from one year to the next. Prior to 1950 it could be said that the late crop marketing season extended through the month of March. The early spring crOp harvest has shifted to the point that Texas onions are competing with late onions in March. The 1950-54 average carlot and boat ship- ments of early onions was 27 cars during March. The cor- responding 1954-56 average was 1750 cars. Much of the price uncertainty associated with late onions arises from the variability in size and harvest date of the early crop. Production within the late summer states is concentrated into areas where soil type and climate are favorable. The tendency has been toward large (100 or more acres) special- ized farms. Fixed costs involved in production and storage are high, but labor costs are the largest item in onion production amounting to 40-55% of the total costs. Harmer and Lucas]+ estimated that 450 labor hours/acre are required to produce onions on 100 acres yielding 800 bags per acre , using primarily hand methods. In addition, about 20 equip- ment hours and 55 tractor and truck hours per acre are re- quired for production and movement into storage. Costs of bags, seed, fertilizer, fuel, etc. would amount to approxi- mately 3200 per acre. Costs would be somewhat less per acre at lower yields. Labor costs would be lower in the western states where mechanical harvesting is more common, however, the irrigation costs are likely to offset this factor. Alternative use of the land is limited. The land in- volved is too expensive for grain production and a switch to another vegetable crop is likely to require additional specialized equipment, knowledge, and market potential. Growers in the western area would seem to be less limited as to alternative use and suitable land available. Coeffi- cients of variability (standard deviation divided by the mean) computed for harvested acreage by area are Eastern .125, Central .175, and Western .152. Weather effect on harvested acreage may be less in the western area, however, the differ- ence is not large enough to justify a supposition that acreage in the western area is adjusted more readily. 4Paul M. Harmer and Robert E. Lucas, Muck Soil Manage- ment for Onion Production, Extension Bulletin 125, Michigan StateICollege COOperative Extension Service, East Lansing, Second Revision, February, 1955, p. 46. Late onions are traded on organized cash and futures exchanges. Dealers, brokers, and association publications keep the trade, including growers, well informed. The crop is relatively free from government regulation, being in- volved in neither acreage controls nor price support pro- grams. Imports of late onions are of minor importance, in most years amounting to only about 1% of the total U. S. onion cr0p. _The U. S. import duty applicable to countries exporting onions to the U. S. of 87% cents per 50 pound bag5 precludes imports except at prices considerably higher than this figure. The onion grower's situation is commonly characterized as highly uncertain. Table 1.2 below provides an indication Table 1.2 Variability of Corn and Late Onion Acreage, Yield, Price, and Income Expressed as Coefficients of Variability‘ W Harvested Acreage Yield/A. Price Gross Income/A. Late onions .094 .092 .518 .478 Corn (all) .044 .160 .461 .565 *Standard deviation divided by the mean, computed using data for 1921-41 and 1946-56, see Appendix for onion data, corn data from agricultural statistics, trend removed from acreage, yield, and income. 5United States Import Duties, 1952, United States Tariff Commission, U. S. Government Printing Office, Washington, D. C., 1952. of the relative variability of late onions and corn. Much of the uncertainty attributed to the late onion crOp is be- cause of the price variation within the crOp year. The yearly high-low range of mid-month farm prices as a percent- age of the average monthly farm prices is a measure of this variation. Averages of the yearly percentages for five com- modities in the 26 year period, 1929 through 1955 are shown in Table 1.5. Table 1.5 Within Season Price Variability for Specified Commodities* Price range as a percentage Commodity of average price Onions 111.5 Potatoes 58.8 Eggs 49.9 Corn 50-5 Wheat 20.4 *Futures Trading 1g Onions, Commodity Exchange Author- ity, USDA, Washington, 25, D. C., Dec. 1956, p. 12. This within year variation relates to the early spring crop size and timing and to the difficulty of obtaining ac- curate production estimates early in the marketing season. Since such a large portion of the crOp is stored on farms the within year variation is very important. Th2 Objective The objective of this study is twofold. The first is to determine a useful model for prediction of late onion supplies under specified conditions. The second is to test the applicability to the late onion crOp of some prOposed hypotheses regarding supply response. CHAPTER II Review of Literature Important work has been done at both the total agricul- tural supply level and at the single commodity level. While this study falls into the latter category some of the lit- erature at both levels will be discussed. At the aggregate level recent contributions have been made by D. Gale Johnson,l Glenn L. Johnson,2 3 Heady, Cochrane,4 and Hathaway.5 D. Gale Johnson develOps a theory of aggregate production response which he believes is appli- cable to both depression and full employment conditions. His 1D. Gale Johnson, "The Nature of the Supply Function for Agricultural Products," American Economic Review, Vol.40, N00 43381313., 1950, p. 559° 2Glenn L. Johnson, "Supply Function - Some Facts and No- tions," Agricultural Adjustment Problems in g Growing Economy, Earl O. Heady, Howard G. Diesslin, Harold_ R. Jensen, and Glenn L. Johnson, ed., North Central Farm Management Committee, Iowa State College Press, Ames, Iowa, 1958. 3Earl 0. Heady, "The Supply of Farm Products Under Con- ditions of Full Employment," American Economic Review, Vol. 45, No. 2, May, 1955, p. 228. 4Willard W. Cochrane, "Conceptualizing the Supply Rela- tion in Agriculture," Journal 2; Farm Economics, Vol. 57, No. 5, Dec., 1955, p. 1161. 5Dale E. Hathaway "Agriculture and the Business Cycle," 9 . Policy for Commercial Agriculture: Its Rgigpigg to Economic Erowth and StabiIity, U. S. Government Printing Office, 1957, p. 51. theory rests on the assumptions 1) farmers are profit maxi- mizing entrepreneurs, and 2) the following characteristics of factor supply to agriculture: a) labor supply shifts with business activity, b) land supply is inelastic, and 0) capital supply has a low elasticity for downward move- ment and higher for expansion. He defends the idea that agriculture is price responsive. He introduced the notion that fixed assets and resource availability are more impor- tant in the explanation of output than fixed costs which had been advanced as the explanation of agriculture's failure to reduce output in depressions.6 Johnson notes that a response may take place as failure to maintain pre- sent assets which has no immediate effect on output. Glenn Johnson emphasizes that supply is affected by many factors and that attempts to explain agricultural supply with any one factor are not likely to succeed. In addition to price-cost relationships and levels of business activity, he suggests consideration of 1) technology, 2) re- source movements between regions, firms, and enterprises, 5) changes in risk, 4) changes in asset holdings. He for- malizes the fixed asset approach to the analysis of supply 6Fixed assets refer to factors of production fixed to the farm and fixed costs refer to costs which the farm incurs regardless of production such as taxes, interest and sup- port of family labor (which may be a fixed asset . 10 response to price.» Johnson defines an asset as fixed if its marginal value productivity in its present use neither jus- tifies acquisition of more of it nor its disposition. Use of this fixed asset theory indicates that the aggregate supply function is only partly reversible. Heady sees agriculture as a price responsive industry. He attributes the low elasticity of supply in the short run to 1) low reservation price for labor, 2) capital limita— tions, 5) risk discount, and 4) fixed short run production function. He also calls attention to the "identification problem." That is to say, conventional regression analysis may indicate an erroneous relationship if the data repre- sents different supply curves rather than successive obser- vations along the same supply curve. Cochrane believes productivity advances are due pri- marily to technological advances and concludes that the sup- ply relation is not reversible. While the aggregate supply is inelastic to price decreases, the substitution of re- sources between enterprises does allow for considerable re- sponse to relative price. Hathaway shows that inputs are varied in response to price levels and presents empirical evidence that aggregate production is responsive to price. ll 7 Cromarty presents a combination approach to supply analysis. His aggregate estimates are built from separate commodity analysis. He attempts to include 1) price expec- tation (lagged product prices), 2) prices of alternative crOps, 5) costs of production, 4) weather and 5) techn010gy as measured by physical units of equipment or changing cul- tural practices in the case of crOps. Some elasticity estimates made by Cromarty using data for 1929-1955 are: Wheat .129 Feed grains .564 Dairy .212 Fresh vegetables .516 The various single commodity supply estimates include a wide variety of expectation models and measures of response. Halvorson8 attempted to measure supply elasticity for milk using feeding rates related to milk-feed ratio, pasture condition, and cow numbers. His correlation and regression coefficients did not appear significant. He concludes that the short run elasticity of milk production is less than .25 in winter and less than .10 in summer. He also found some 7William A. Cromarty, Economic Structure in American Agriculture, Ph.D. thesis, Michigan State University, 1957. 8Harlow W. Halvorson, "The Supply Elasticity for Milk in the Short Run," Journal 9; Farm Economics, Vol. 57, No. 5, Dec., 1955, p. 1186. l2 slight evidence that feeding rates are more responsive to price increases than to price decreases. Walsh9 found a significant relationship between acreage and the price of cotton with no improvement in fit when cot- tonseed prices were included. He found an increase in both the level and s10pe of the acreage response function after 1924 as cotton growers gained confidence in their ability to control the boll weevil. For prediction he used absolute first differences in acreage and price adjusted for an index of prices paid. A relatively good fit (correlation coeffi- cient of .90) was obtained for 1911-55 data. He concluded that, yields being price inelastic but more variable than acreage, production is quite inelastic to changes in price. Bowlenlo using lagged first differences of price and acreage, found a discontinuous and perfectly inelastic sup— ply function for wheat in the specialized areas of Kansas in the short run. The favorable relative price of wheat in the specialized areas accounts for this situation. An elasticity of .515 was determined for the less specialized eastern Kansas area. Correlation coefficients were rela— tively low, e.g., .05 to .62. He points out the problem of 9Robert M. Walsh, "Response to Price in Production of Cotton and Cottonseed," Journal 9f Farm Economics, Vol. 26, No. 2, May, 1944, p. 559. 10B. J. Bowlen, "The Wheat Supply Function," Journal 93 Farm Economics, Vol. 57, No. 5, Dec., 1955, p. 1177. 15 estimating the lag in the employment of additional resources when prices increase or the withdrawal of resources when prices decline. 11 found evidence that farmers as a Kohls and Paarlberg group do respond to changing deflated crop prices from year to year by changing acreage planted. They attempted to explain changes in acreage using lagged deflated price. They found 55 percent of the acreage variability in onions was associated with deflated price one and two years pre- ceding. Nerlovel2 emphasizes the fact that the farmers react not to last year's price, but rather to the price they ex- pect, and this expected price depends only to a limited ex- tent on last year's price. He hypothesizes that the expected price is a weighted average of past prices with the most recent weighted heaviest and that this expecta- tion is revised in prOportion to the error made in predict- ing current price. He sees agricultural production as more 11R. L. Kohls and Don Paarlberg, The Short Time Response 9: Agricultural Production 29 Price and Other Factors, Sta- tion u et1n 555, Purdue University, Agricultural Experi- ment Station, Lafayette, Indiana, Oct., 1950. 12Marc Nerlove, "Estimates of the Elasticities of Sup- ply of Selected Agricultural Commodities," Journal gf Farm Economics, Vol. 58, No. 2, May, 1956, p. 496. l4 responsive to price than is revealed in less general hypo- theses applied in the past. His "more general" method pro- vided elasticity estimates as follows: Commodity Estimated elasticity of supply Cotton 0.67 Wheat 0.95 Corn 0.18 Nerlove's hypothesis will be explored further in Chapter III. Brennan15 estimated cotton acreage on an area basis using "expected prices" of cotton and four competing crops plus a trend variable. His "expected prices" are computed from Hicks' "elasticity of price expectation." Coefficients of determination are .75, .79, and .84 for the areas studied. The expectation model will be considered later. Suits and Koizumil4 constructed a three equation model of the United States onion market. Their supply schedule was fitted using first differences of logs. Lagged price, cost index and trend were used to predict production. Their method will be discussed at greater length below. 13Michael J. Brennan, Progress Report on Cotton Produc- tion Response, FERD, ARS, USDA, Apr., 1958.— 14D. B. Suits and s. Koizumi, "The Dynamics of the Onion Market," Journal 9f Farm Economics, Vol. 58, No. 2, May, 1956. p- ZF75. 15 Johnson,15 Gray, Sorenson, and Cochrane,l6 and Hathawayl7 in their separate analyses of the effects of government pro- grams on burley tobacco, potato and dry bean industries pro- vide information on farmer's response to reduced price un- certainty. All three studies reveal a willingness on.the part of farmers to supply more product at the same average price after the reduction in uncertainty. Johnson used lagged price deflated by costs of produc- tion, acreage allotment minus previous 6—year average acre- age, and overplanting penalty to estimate underplantings of burley tobacco. His yield model included lagged price (in logs), prices paid, trend, acreage allotment minus 5-year average acreage harvested and a weather index (computed from test plot yields). In the dry bean study, Hathaway calculated planted acre- age as a function of percentage of previous year's acreage 15Glenn L. Johnson, Burley Tobacco Control Programs, Bul. 580, Kentucky Agricultural Experiment Station, University of Kentucky, Lexington, Feb., 1952. 16Roger W. Gray, Vernon L. Sorenson, and Willard W. Cochrane, An Economic Analysis of the Impact of Government Pro rams on the Potato Industry” of the United States, Tech. Bul. 211, University of Minnesota —Agricultural Experiment Station, June, 1954. PrOgram 3n the Dry Bean Industry in Michigan, Michigan State ege, Agricultural Experiment Station, April, 1955. l6 abandoned before harvest, index of expected income from corn and wheat, cost of production and log of price received the previous year. In his yield model he considered weather (test plot yields), log of price received the previous year and current acreage. Coefficients of determination obtained were .805 and .872 for the acreage and yield models. Gray, 23 gl. estimated changes in acreage using price received for potatoes divided by an index of prices re- ceived for all farm products lagged one and two years. This method yielded a coefficient of determination of .74 for the years 1925-41. In addition to the change in re- sponse, there was a shift in production area. Acreage in the specialist states increased and maintained one-third higher acreage than that which existed prior to price sup- port action. Growers in the lake states, after a one-year increase, continued a downward trend in acreage. The above studies represent the more usual approach 18 advance a to supply analysis. Knudtson and Cochrane linear programming approach to the determination of a supply function for flax. They observe that a supply function.may be constructed in this way when historical data are not 18A. C. Knudtson and W. W. Cochrane, "A Supply Function for Flax at the Firm Level," Journal 2f Farm Economics, Vol. 40, No. 1, Feb., 1958, p. 117. 1‘7 available. Separate estimates would be required for each homogeneous production area to establish an "average" re- sponse for prediction purposes. An extreme view is represented in a paper prepared for the 1952 International Wheat Council by the Food and Agri- culture Organization of the United Nations19 the hypothesis was advanced that the world supply schedule for wheat is backward sloping above a certain price level. This situation is attributed to the "income effect" of a price change. No empirical evidence is presented in support of the hypothesis. It involves much of the same reasoning which appears in the "high fixed cost" explanations of output maintenance during the great depression. The above review is by no means exhaustive but presents a variety of Opinions and methods. The empirical studies cited generally support the notion that agriculture does respond to price. In different ways they reveal the diffi- culty of obtaining an accurate estimate of expected price and measures of relevant variables other than price. 19A Reconsideration of the Economics of the Interna- tional Wheat Agreement, Food and Agriculture Organization of the United Nations Commodity Policy Studies, No. 1, Sept., 1952, pp. 17-22. CHAPTER III The Analysis This is a study in economic dynamics. Economic dyna- mics is defined by Hicks as that part of economic study in which every quantity must be dated.1 A comparative static analysis similar to that proposed by Hicks in conjunction with the above definition is applied. Time must be considered for two reasons. Most important is the fact that the current supply of a commodity depends not so much on current price as upon what farmers expected the price to be when production plans were made. Secondly, adjustments toward an Optimum require time and, in many cases, are not made in the span of a single production period. A modified partial equilibrium analysis involving an aggregation of firms is utilized in this study. The farmer is a price taker in both the factor and product markets. Assume profit maximization as the motive for production. Then factors of production (x . . . 2) will be applied to enterprises (f . . . h) to the extent and in combinations such that: 1J. R. Hicks, Value and Capital, Clarendon Press, Oxford, Second edition, 1946, p. 115. 19 ’5: EL ’53 2 a: N = 2 = o o o o o o o o = P P P x y z X = = o o o o o o o o = Z P P § x y z MVPhX = MVPh = = LWPE P P P x y z where MVPi = expected marginal value product of factor x used in enterprise f. PX = expected price of factor x. Thus, given farmers expectations as to price, techno- logy, weather, institutional factors, etc., plus an estimate of asset fixity2 the adjustment to be made may be estimated. It cannot be assumed, however, that adjustment is from a state of equilibrium. Rather the firm is in a position which would have approached an optimum organization in the unlikely event that expectations held in the previous period had been fully realized. The empirical studies discussed in Chapter II attest to the acceptability and usefulness of the assumption of profit 2Fixed asset defined as one for which salvage value is less than expected MVP which is less than cost of ac- quiring an additional unit. 2O motivated production and indicate that resource allocation in agriculture is price responsive. A major portion of the problem at hand is that of ob- taining values for the farmers expectations. The relative certainty with which an expectation is held is very impor- tant at the single firm level; however, since this study involves "average" expectations the problem is of lesser importance. The method of analysis employed in this study dictates that the expectations considered be single valued. The only allowance for uncertainty is a risk discount (posi- tive or negative) implicit in the supply response equation which does not appear as such.5 By this method the risk discount becomes a constant which may well be unrealistic. Economic theory has little to offer as to hypotheses on the nature and formation of expectations which may be 5On the existence of risk discount, Hicks,gp,gip.,p. 155, observes "we shall find as we go on that there are reasons for suspecting that the economic system loses more by mistrust than by overconfidence." Conversely, Keynes states "it is probable that the actual average results of investments, even during periods of progress and prosperity, have disappointed the hOpes which prompted them. Business- men play a mixed game of skill and chance, the average re- sults of which to the players are not known by those who take a hand. If human nature felt no temptation to take a chance, . . . there might not be much investment merely as a result of cold calculation." J. M. Keynes, The General Theory 9f Employment Interest and Money, Harcourt, Brace, and Company, New York, 1955, p. 150. 21 applied to a study such as this. Specific hypotheses will be presented as the various supply models are considered. The Data The harvested acreage, yield, production, unharvested production and price data utilized in this study consist of series published by the United States Department of Agri- culture. Data for the periods 1918 to 1941 were obtained from USDA general publications for commercial vegetables (provided by the Statistical and Historical Research Branch of the Agricultural Marketing Service) for 1959-1949 from Commercial Vegetables for Fresh Market, Revised Estimates, Statistical Bulletin 126, USDA, 1955; for 1949-1955, Ve e- tables for Fresh Market, Revised Estimates, Statistical Bul- letin 212, USDA, 1957, and data for the 1956 and 1957 crOps from Vegetables for Fresh Market, Annual Summary, 1957. The series are presented in the Appendix. The data for 1959 forward includes a change in the definition of "commercial." Production for sale on local markets is included after 1959. Previous estimates related to production in well recognized commercial areas mainly producing for shipment to distant markets. Comparable estimates are not available for the years prior to 1959. There is an overlap of three years, however, the differences vary to the extent that a correction factor cannot be applied with any degree of confidence. No 22 correction procedure is prOposed in the basic publication. The discrepency amounts to approximately +2000 acres and -5 sacks per acre in yield. While the 1957 publications listed above do not include the word commercial in the title, the estimates are comparable to the 1959 to 1949 data. The observations for the years 1942-45 are excluded to avoid the distortion caused by wartime controls. Data for planted acreage are not available prior to 1946, therefore, the harvested acreage series is used in the analysis. No estimates of unharvested production are avail- able prior to 1928. Further comments as to data limitations are made as the various models are considered. The Method Models for harvested acreage, yield, unharvested produc- tion and quantity available for harvest are constructed for the late onion crop. Single equation methods are applied in all models pre- sented. The line of causation between the variables con- sidered is clear. Late onion production, as is the case in nearly all crOps, is influenced not by current prices but by price expectations which have existed in the past. Lag- ged values of variables determined within the system are con- sidered as "independent." There is but one "dependent" 23 variable in each model. On the surface it would appear that unharvested production does not satisfy these conditions, however, under the conditions to be outlined in the discus- sion of that model as single equation estimate is justified. The equations are fitted using the method of least squares. Preliminary graphic inspection of the relationships provided insufficient evidence to reject the assumption of approximate linearity. Thirty-three observations are used in fitting the equa- tions in all cases except for production which includes thirty-two and unharvested production for which only 25 ob- servations are available. Thus, it was possible to consider a relatively complete model without suffering a lack of re- liability due to insufficient degrees of freedom. To facilitate evaluation and comparison certain statisti— cal tests of significance are applied. The t test is applied to test the hypothesis that the regression coefficient (b) tested does not differ significantly from zero against the alternative hypothesis that it is significantly different from zero. If the ratio of the parameter to its standard error is greater than Uga, the hypothesis that the b is equal to zero is rejected. The t value is obtained from the "Stu- dents'" distribution with n—k—l degrees of freedom where k is the number of independent variables in the model and ac is the probability of rejecting the hypothesis that b is zero 24 when in fact it is true. Standard errors of the b's are included in all cases. One of the assumptions made in the estimation process is that of serial independence of the re- siduals. The Durbin-Watson test4 is applied to determine the degree of independence. Results of the test are re- ported only as indeterminate, acceptance or rejection at the .05 level of significance of the hypothesis of serial independence. Results of the test applied to a model con— taining a lagged variable determined within the system are only approximate. This must be considered since most of the models presented do include lagged price as an explanatory variable. The tests of significance are designed for use with 5 (l) the population must data having these characteristics: be homogeneous, (2) the variables must be normally distri- buted, (5) observations must be independent, and (4) the 'sample must be selected at random. Since the data used in the study do not have these characteristics except only ap- proximately it follows that while the results are expressed 4For computational method and tables used see J. Fried- man and R. J. Foote, Computational Methods for Handling_Sys- tems g; Simultaneous Equations, Agriculture Handbook No. 94, USDA, AMS, Nov., 1955. 5G. 8. Shepherd, Agricultural Price Analysis, Fourth edition, The Iowa State College Press, Ames, 1957, p. 188. 25 to the fourth decimal they must be evaluated as to reason- ableness and correspondence with experience. Unless other- wise stated, all equations are fitted using data for the 55 years, 1921-41 and 1946-57. Harvested acreage is considered first and used to test four expectation hypotheses. The four include a conventional, Hicksian, distributed lags (Nerlove) and a model constructed specifically for the late onion crop. One model is pre- sented for unharvested production and two for quantity avail- able for harvest. Consideration of the latter two models includes an evaluation of the methods advanced by Suits and' Koizumi mentioned in Chapter II. Harvested Acreagg The conventional analysis of supply response to price involves an attempt to associate changes in acreage to lag- ged adjusted price. The work of Kohls and Paarlberg dis- cussed in Chapter II is an example. The assumptionsin- volved are 1) price expectations are equal to prices re- ceived in the immediate past, 2) expectations as to state of the arts are constant or follow a uniform trend, 5) the level of all prices has no effect on resource allocation, and 4) the farmer is a profit maximizing entrepreneur. Four variations of the conventional method are considered. 26 (5.1) Y1 = a1 + lel + 111 X + b X 1 22*‘12 (5.2) Y1 a2 + bl.l (5.5) Y1 = a5 + b5X5 + u5 (5.4) Y1 = a4 + b5.lX5 + b4X4 + u4 Y1 a late onion acreage in year t expressed as percent of year t—l. season average price received by farmers for late onions year t-l in cents per bag divided by an in— dex of prices paid for items used in onion pro- duction in year t-l multiplied by 100. X - season average price received by farmers for late onions in year t-2 in cents per bag divided by an index of prices paid for items used in onion pro- duction in year t—2 times 100. X3 = prices received by farmers for late onions in year t—l in cents per bag divided by USDA index of prices received by farmers for all crOps in year t~1 times 100. X = prices received by farmers for late onions in year t-2 in cents per bag divided by USDA index of prices received by farmers for all crOps in year t-2 times 100. and the u's are different randomly distributed residuals. The X's above measure only expected price. Deflation ‘by the cost index provides a very rough net price measure in constant dollars. The use of prices received index removes :price level effects and a very rough measure of onion price 6Computed using USDA index of prices paid by farmers for items used in productiOn weighted according to estimated use for onion production. 27 relative to price of all crops. The deflated prices lagged two years are included to allow for the possibility of measurable adjustment lags and that expectations may be based on more than the previous year's experience. The fitted equations are as follows (standard errors of the b's in parentheses): (3.5) '? = 88.23 + .2765*X r2 = .41 s = 6.66 l (.0599)1 y . W (5.6) f = 84.55 + .2923*x '+ .O64OX 32 = .39 s. =Eh66 1 (.0617)1 (.0618? Y - y (3.7) T, e 89.71 + .1859*X r2 = .32 s. = 7.16 (.0486)5 y Y _ .~ ~ 2 _ = (5.8) $1 - 87.28 + Eigg§8§5 + E?g§2éfl Ry - .28 s? :A25 * Significant at the .01 level. The Durbin—Watson statistic computed for equation 5.5 is 2.22 and provides insufficient evidence to reject the hypothesis of serial independence of residuals at the .05 level. Price adjusted for production costs appears to be a 'better indicator of changes in acreage than price adjusted .for the price of other crops. The regression coefficients are not significant at the .10 level for either deflated :price lagged two years. Model 5.5 is considered as repre- sentative of the conventional method. To compare the per- formance of this model with those to follow Wi from 5.5 is converted to an acreage estimate. The correlation coefficient 28 between the estimated and actual acreage is 0.89 and the coefficient of determination is 0.79. The price elasticity of supply indicated by equation 5.5 is .125. A comparison of actual and estimated acreage is presented in Figure 1. Because of the limited amount of information considered and the sweeping nature of the assumptions involved, this method alone does not provide a satisfactory estimate of the basic relationships involved. A desire to allow the relation between past and expected prices to be determined by a means other than entirely by assumption leads to a consideration of Hicks" elasticity of expectation. Hicks defines elasticity of expectation of_ commodity X as the ratio of the prOportional rise in ex- pected future prices of X to the prOportional rise in its current price.7 The method used to derive expected price (P*) in ac- cord with the above definition is as follows.8 Assume the :price in period t-l is an exponential function of price in ,period t—2. Then: DC (3'9) P(t—l) = k P(t-2) ‘where k and 0< are constants. Expressed in logarithmetic form 5.9 becomes 7Hicks, 92. cit., p. 205. 8Brennan, gp. cit., p. 29. 70.. .—— actual --- calculated 29 Figure 1 Actual and Calculated Late Onion Acreage from the Conventional Model (5.5) m g 60.. 2 .655- .5. s 50" o 5.5,. 40.. l 1 I 111 .1 l 20 25 50 55 40 46 50 55 Time Actual as a Percent of Calculated 110L- 4.: 81 AM A \ a 00 v .- 90b 20 2? 310 3‘5 46 1416 50 55 Time 50 (5.10) log P(t-l) = ex 10g P(t-2) + log k differentiating 5.10 with respect to P