)V153I_J RETURNING MATERIALS: PIace in book drop to LIBRARJES remove this checkout from 4—3—1... your record. FINES wiII be charged if book is returned after the date stamped beIow. DYNAMICS OF THE HOG MARKET WITH EMPHASIS ON DISTRIBUTED LAGS IN SUPPLY RESPONSE BY John Nelson Fe rris A THESIS Submitted to the School for Advanced Graduate Studies of Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Economics 1960 ACKNOWLEDGMENTS ’The author wishes to exPress his sincere appreciation to all those who assisted him in the preparation of this thesis. The author is capecially indebted to Dr. Clifford Hildreth who served as the major professor and supervised the research, and to Dr. Robert Gustafson who gave freely of his time for consultation and assistance. Gratitude is also expressed to the other members of the guidance committee, Dr. Lawrence Boger, Dr. Lawrence Witt, ‘ Dr. Victor Smith, and Dr. James Hannan, for their comments. in reviewing the manuscript. The author also wishes to recognize 'Dr. Harold Riley, Lester Manderschied, and Dr. William Cromarty for their helpful suggestions. The clerical staff under the supervision of Mrs. Arlene King handled the large amount of computational work involved in this study. Their cooperation was appreciated very much. Thanks are also due Mrs. Phyllis Quinn for her help in the preparation of the copy. The author is indebted to Dr. Lawrence Boger for providing the financial assistance which enabled the author to complete his graduate program. *********** ii DYNAMICS OF THE HOG MARKET WITH EMPHASIS ON DISTRIBUTED LACS IN SUPPLY RESPONSE BY John Nelson Ferris AN ABSTRACT Submitted to the School for Advanced Graduate Studies of Michigan State University of Agriculture and ‘Applied Science in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Economics 1960 Approved (1/ 5%§/,/)/6é Lei/2, " , I f/ ABSTRACT Instability has been a trademark of the hog industry. The instability has tended to be cyclical, a phenomenon explained most simply by Ezekiel's Cobweb Theorem. The hog market, for the most part, fulfills the conditions Specified as necessary for the Cobweb Theorem to apply. Ezekiel presumes in his Cobweb Theorem that producers expect present prices to continue through the production period. However, it seems unrealistic to believe that farmers naively expect present prices to continue in a market characterized by widely fluctuating prices. The Cobweb Theorem was modified in this study by applying a more general assumption that expected price is some positive function of past prices. The effort was directed toward testing two hypotheses: (l) The response of hog production to actual prices is a distributed lag extend- ing over more than one year with the reaponse in the first year greater than that in the second, the response in the second greater than that in the third, etc. ,- and (2) The hog market has cyclical tendencies and is convergent. Two techniques were used to estimate distributed lags in supply response. One was the traditional regression approach of F. L. Alt , and the other was the method pr0posed by Marc Nerlove. Estimates were obtained for three periods, 1908 to 1924, 1925 to 1941, and 1947 to 1958. The price of hogs and the price of corn in the previous fall and early winter periods were the main independent variables iv and spring farrowings (1924-41 and 1947-1958) and hog slaughter (1908-1924) were the dependent variables. Least squares estimates obtained by both Alt's and Nerlove's procedures gave substantial support to the first hypothesis. There was difficulty in obtaining reasonable estimates on the parameters of the Nerlove model, however. A retail demand equation was estimated using quarterly data on the retail price of pork as the dependent variable and diSposable income, supply of pork, supply of competing meats, time, p0pulation and dummy variables representing the seasons as independent variables. An esti- mating technique was used to mitigate the effect of autocorrelation in the residuals. Price flexibilities of the retail demand for pork at the means were found to be -. 80, -. 77, -. 84, and -. 73 for quarters one through four, resPectively. Equations representing the marketing margin for pork were estimated for each quarter. Combining these equations with the retail demand equation, the price flexibilities of the demand for hogs were estimated to be -2.09, -1. 12, -l. 33, and -l. 56 for the four quarters, reapectively. By combining three equations, (1) the fourth quarter demand for hogs equation,» (2) an equation relating spring farrowings to the fall supply of pork, and (3) a supply equation, a complete model of the hog market was constructed. By setting the exogenous variables at their means, a second order difference equation was constructed. Four such models were constructed using four alternative supply equations. From the solution of the difference equations, it was determined that all four models were cyclical and convergent, substantiating the second hypothesis. A cycle of five to six years was indicated. V TABLE OF CONTENTS CHAPTER Page I. INTRODUCTION The Problem ............... . . . . 1 Producers.... ....... 1 Market Agencies, Meat Packers, Con- , sumers . . . . .............. 4 Purpose of Study ......... . . . . . . . . 5 Some Previous EXplanations .......... . 5 II. STRUCTURE OF THE INDUSTRY AND THEORETI- CAL BASIS The Characteristics of Hog Production and Marketing . . ..... . .......... 12 Producer Level ............... 12 Markets . . . . . . ....... . ..... 14 Packer Level ................ 16 Wholesale Level . . . . ..... . . . . . 17 RetailLevel................. 18 Relative Importance of Marketing Functions 19 The Competitive Structure . . . . . . . . . . . 19 Producer Supply of Hogs . . . . . . . . . . 19 Livestock Markets . . . . . . . . . . . . . 21 The Meat Packing Industry. . . . . . . . . 21 RetailMargins............... 23 The Competitive Structure in Summary . 23 III. EXPECTATIONS AND LAGS IN SUPPLY RESPONSE Time SeriesApproach. . . . . . . . . . . . . . 25 Alt'sApproach...............30 Fisher's Approach. . . . . . . . . . . . . . 3O Koyck's'Approach. . . . . . . . . . . . . . 31 Nerlove‘s Approach. . . . . . . . . . . . . 34 Other Time Series Models . . . . . . . . . 39 Sur'veyApproach.................41 Theoretical Approach. . . .. . . . . . . . . . . 45 Katona....................45 Shackle................... 47 Information Theory. . . . . . . . . . . . . 48 Continued TABLE OF CONTENTS - Continued CHAPTER Page IV. HYPOTHESES Statement . ...... . . . . . . . . . . . . 50 Hypothesisl . . . . . . . . . . . . . . . 50 Hypothesis II . . . . . . . . . . . . . . . 52 Methodology. . . . . . . . . . . . . . . . . . 54 Statistical Procedure . . . . . . . . . . . . . 55 V. SUPPLY RESPONSE Background . . . ....... . . . . . . . . 57 Time Periods . . . . . . . . . . . . . . 57 Variables ..... . . . . . . . . . . . 58 Selection of Variables ........ . . 60 Form of Variables. . . . . . ..... . 62 Alt's Procedure ...... . . . . . . . . . . 65 1908-1984 . . . . . . . . 66 Dependent Variable in First Differ- ences . . . . . . . . . . . . . . . 66 Dependent Variable in Absolute Values . . . . . . . . . . . . . . 68 1925-1941. . . . . . . . . . . 72 Dependent Variable in First Differ- ences. . . . . . . . . . . . . . 72 Dependent Variable in Absolute Values .. . . . . . . . . . . . . . 75 1947- 1958. . . . . . 77 Dependent Variable in First Differ- ences . . . . . ..... . . . 77 Dependent Variable in Absolute Values . . . ..... . 80 1925— 1941 Compared with 1947-1958. . 82 Nerlove' 5 Method . . . . . . . . . . . . . . 84 1908-1924 . . . . . . . . . . . . . . . . 90 1925-1941 . . . . . . . . ....... . 93 1947-1958 . . . . . . . . . . . . . . . . 97 Summary and Conclusions . . . . . . 100 Regression Estimates for Fall Pig Cr0p. . . 102 Continued TABLE OF CONTENTS -. Continued CHAPTER VI. V’. 1-4 1-4 VIII. THE DEMAND FUNCTION Consumer Demand . ....... . . . . . . . . Model I . . . .. ...... . ........ Model II. . . . ............... Model III ................. Model IV ............... Demand for Hogs ............... “Complete” Demand Function for Hogs. . . . SUPPLY~-DEMAND MODELS Farrowingstupply of Pork Relations--ip. . . . . Farrowings-Commercial Hog Slaughter Rea lationslcip. . . . . .............. Farrowing~Price of Hogs Relationship ...... Difference Equation Models. . . . . Conclusions. and Implications . . ......... SUMMARY AND CONCLUSIONS ..... . . . . . . BIBLIOGRAPHY........... ..... APPENDICES..... ..... ..... viii Page 107 110 113 115 120 123 129 138 1359 1‘39 141 145 TABLE 10 LIST OF TABLES Page Pr0portion of total pigs saved in the United States byregions,1930t01958............... 13 Hogs and pigs sold by farmers through different market outlets, United States, 1955 ..... . . . . 15 Distribution of the total marketing margin for pork and all meat in 1925-34 and for all meat in 1947 . . 19 Regressions of alternative hog supply equations, with the dependent variable in first difference of hog slaughter, hog and corn prices as a ratio; 1908-1924. . . . . . . ................ 6‘7 Regressions of alternative hog supply equations with the dependent variable in first differences of hog slaughter, hog and corn prices separate; 1908-1924. . ............. . . . . . . . . 69 Regressions of alternative hog supply equations with dependent variable in absolute numbers of hogs slaughtered; 1908-1924. . ........ . . . . . . 70 Regressions of alternative hog supply equations, with the dependent variable in first differences of sows farrowing, hog and corn prices as a ratio; 1925-1941....................... 73 Regressions of alternative hog supply equations with the dependent variable in first differences of sows “farrowing, hog and corn prices separate; 1925-1941. 0 o o o o o o o o o o o a o o o o o o o o o 74 Regressions of alternative hog supply equations with the dependent variable in absolute numbers of sows farrowing; 1925-1941. . . . . . . . . . . . ..—. 76 Regressions of alternative hog supply equations, with the dependent variable in first differences of sows farrowing, hog and corn prices as a ratio; 1947-1958. . . . . . ..... . ...... . . . . . 78 5.}: LIST OF TABLES - Continued TABLE 11 12 13 14 15 16 17 18 19 20 Page Regressions of alternative hog supply equations, with the dependent variable in first differences of sows farrowing, hog and cornprices separate; ' 1947-1958. c o oooooooo o o o o o o o o o o o o 79 Regressions of alternative hog supply equations, . with the dependent variable in absolute numbers of sows farrowing; 1947-1958. . . . . . . . . . . . . . 81 Significance of differences between coefficients of variables in 1925-1941 and coefficients of corres- ponding variables in 1947-1958, in reference to Equation(5.22).................... 83 Regressions of hog slaughter re3ponse equations using Nerlove's method, under alternative assump- tions; 1908-1924. 0 o o o o o o o o ...... o o o ' 91 Estimates of the parameters and elasticities of hog slaughter response using Nerlove's method; 1908- 1924. O O I O O O O O O O O O O O O O O O O O O O O O 92 Regressions of farrowing response equations using Nerlove's method, under alternative assumptions; 1925' 194 1 o o o o o o o o o o o o o o e o o o o o o o 94 Estimates of the parameters and elasticities of farrowing response using Nerlove's method; 1925-194100000000oooooooooooooo 96 Regressions of farrowing response equations using Nerlove's method, under alternative assumptions; 1947-1958000000000.000.00.000... 98 Estimates of the parameters and elasticities of farrowing response using Nerlove's method; '1947-19580000000.000000000000000loo ‘Regressions estimating hogs slaughtered from fall farrowings (1908-1924) and sows farrowing in the fall; 1925—1941 and 1947-1958. . . . . . . . . . . . 104 LIST OF TABLES - Continued TABLE 21 22 23 24 25 26 Quarterly retail price of pork deflated by the Consumers‘ Price Index; estimated by Equation (6. 18) as compared with the actual; 1948-1958. . . Regression equations representing the demand for hogs by quarters, 1947-1958. . . . . . . . . . . . Quarterly price of 200-220-pound barrows and gilts at Chicago deflated by the Wholesale Price Index; estimated by Equations (6. 19), (6. 20), (6. 21), and (6. 22) as compared with the actual; 1947-1958. . . Quarterly price of 200-220-pound barrows and gilts at Chicago; estimated by Equations (6. 23), (6. 24), (6. 25), and (6. 26) as compared with the actual; 1948-1958 ...................... Complete demand function for hogs by quarters, derived by substituting (6. 18) into (6.19). (6. 20), (6.21), and (6.22). O O O O O O O O O I O O O O O O 0 Prices of 200-220—pound barrows and gilts in the fourth quarter; estimated by Equation (7. 7) as compared with the actual; 1948—1958. . . . . . . . xi Page 124 128 130 133 136 140 - FIGURE LIST OF FIGURES Page Total United States hog slaughter and the average annual price of medium weight barrows and gilts at Chicago, 1907-1958 ......... , ....... 2 Case I of Ezekiel's Cobweb Theorem: Continuous fluctuation with a two-year lag. . . . . . . . . . .. . 9 Case II of Ezekiel's Cobweb Theorem: Convergent fluctuation with a one year lag ............ 9 Case III of Ezekiel's Cobweb Theorem: Divergent fluctuation with a one year lag. . . . . . . . . . . . 9 Continuous time path of production response (Y) to a change in price (P) ................ 29 Discrete changes in the rate of production reSponse (AY) to a change in price (P) in FIGURE 5 . . . . . 29 Sum of squares of residuals (V'V) and estimates of regression coefficients for Model 111 at values of the autocorrelation coefficients ranging from 0 to 1 119 Sum of squares of residuals (V'V) and estimates of the regression coefficients for Model IV at values of the autocorrelation coefficient ranging from 0to.9 ............... .........122 CHAPTER I INTRODUCTION The Problem Instability has long been a trademark of the hog industry. The "invisible hand" which guides hog producers has been something less than satisfactory in achieving a stable supply of pork. With some degree of regularity, periods of relatively low production and attendant high prices have been followed within two or three years by periods of high production and low prices. This has triggered contractions which have proceeded for two or three years, completing the cycle. FIGURE 1 attests to this characteristic of the hog industry. To say that instability is a problem is not to say that absence of change is desirable. New technology which modifies the cost structure in production, increasing population, changing consumer tastes and similar trends do require changes in hog production. It is believed, however, that the endogenous mechanism of the hog industry has certain oscillatory tendencies which represent a problem. This problem ex- tends from the producer, through the markets and meat packers and to the consumer. Producers The instability of hog prices contributes to the uncertainty of selling prices. Optimum allocation of resources is difficult to achieve under conditions of uncertainty. This is because (1) farmers must Price of ba: IS Der cwt 25 ‘ rows 81 gilts gilts at Chicago, 1907 to 1958. FIGURE 1. Total United States hog slaughter and the average annual price of medium weight barrows and rtainty and incorrect. nticipation cope with it aversion ___________ used to take >dities and allows assumption .ing time is .ge of favor- ing purchases 1nfavorab1e rotors" refers .abor than farmer can .ced with loss Slaughte r Lemselves in .oning. : to them. ‘_ . 11ers all the \ .oning enables . ’18 Opportuni- ZChicago: The I the Cycle, " — htera' n hea 100 90Tu 80 70 I— Slau (Milli Total U. s. Hog s O use certain informal insurance schemes to cope with uncertainty and (2) expected prices used in allocating resources are often incorrect. D. Gale Johnson, drawing from Hart's analysis of anticipation and business planning, lists four methods farmers use to cope with uncertainty--diversification, flexibility, liquidity and "risk aversion and combination of factors. "I In brief, diversification is used to take advantage of offsetting price variations in different commodities and thereby reduce the variation in gross income. Flexibility allows adjustments to changing price relationships, based on the assumption that price can be predicted with more certainty as the selling time is approached. Liquidity permits the farmer to take advantage of favor~ able situations which require readjustment of plans involving purchases or to reduce the possibilities of loss of assets should an unfavorable circumstance arise. "Risk aversion and combination of factors" refers to the tendency to place a greater emphasis on the use of labor than other resources which may require fixed payments. The farmer can absorb a certain reduction in labor income but would be faced with loss of part of his total assets should a contingency deve10p. To obtain liquidity, farmers place restrictions on themselves in borrowing money, a practice known as internal credit rationing. That is, they do not borrow all the money that is available to them. For similar reasons, credit agencies do not extend to farmers all the credit available to the agencies. This external credit rationing enables the lending agency to take advantage of unexpected favorable opportuni— ties or adjust to contingencies. .ID. Gale Johnson, Forward Prices for Agriculture (Chicago: The University of Chicago Press, 1947), pp. 44-46. A. G. Hart, "Anticipations, Business Flaming and the Cycle, " Quarterly Journal of Economics, Vol. 51, (1937). Survival is an important objective of a farming Operation. A particular enterprise may offer higher long run profit than any other. But if the selling price is so unstable as to jeopardize the solvency of the farm in the short run, the long run profits would never be realized. Therefore, the farmer may select an enterprise which promises more stable profits than another enterprise though. lower profits in the long run. - Uncertainty then results in certain inefficiencies in the selection of enterprises and allocation of resources. Heady states "Precautions which are taken to meet uncertainty almost always necessitate a sacrifice; they either result in a less-than-maximum product from given resources, or, conversely, do not allow a minimum cost for a given output. "2 . Although the informal insurance schemes mitigate the undesirable consequences of uncertainty, there are still the inefficiencies resulting from. inaccurate expectations. Consider a farmer who could alternatively feed hogs or cattle. In any year he would select the enterprise which promised the greatest net profit. If the prices are highly uncertain, he would frequently make the wrong choice. His allocation of resources would be less than Optimum in those years. Market Agencies, Meat Packers,- Consumers Marketing agencies and meat packers in particular have fixed costs of land, plant, equipment and, to a certain extent, labor. They are interested in obtaining a steady flow of livestock to cover these costs. Yet, as can be observed in FIGURE 1, annual supplies of hogs have fluctuated over relatively wide ranges in past years. zEarl O. Heady; Economics of Agricultural Production and Resource Use, (New York: Prentice-«Hall, Inc.,.tli952), p. 530. There is reason to believe that consumers would prefer more steady supplies of pork from year to year in comparison with the pre- vailing situation. ‘ Consumer tastes do change, but changes are usually gradual and monotonic, not cyclical. Problems arise in re- building demand for pork when consumers have previously been forced to substitute other meat and poultry for scarce pork supplies. Purpose of Study The task of this study is to investigate the endogenous mechanism of the hog industry, employing some of the commonly held theories which have been used to exPlain the "hog cycle" and employing some new approaches as well. Previous explanations and tools of analysis are considered and used as a starting point. Some Previous EXplanations Previous studies of factors causing cyclical tendencies in hog production have attributed this phenomenon to some combination of corn and hog prices in an earlier period. One of the first and most comprehensive studies of hog prices was by Haas and‘ Ezekiel.3 They supported the theory of hog production cycles and pointed out that the main reason had been the failure of farmers to look ahead. They contended that farmers tended to exPect present prices of hogs and corn to continue at present levels. In adjust- ing to this expectation, their collective efforts resulted in "over- production" following periods of a favorable relationship between hog '3G.~ C.‘ Haas and Mordecai Ezekiel,= Factors Affecting the Price of Hogs, U.~ S.- Department of Agriculture, Bulletin No. 1440, (Washington: U.~ S. Government Printing Office, 1926). and corn prices. - The over-production and concomitant low or negative profit in feeding hogs then would cause farmers to cut back hog production unduly, since they would eXpect the low hog prices to continue. This tendency was termed the "self perpetuating mechanism" in the hog cycle. In explaining this tendency, Haas and Ezekiel pointed out that hog production lagged hog and corn prices by about a year and a half. Using data from the 1903- 1915 period they successively correlated monthly hog prices adjusted for seasonal variation with the "corn—hog differential" lagged 10 months, 12 months, 14 months, etc. on up to 22 months.“r The correlation coefficient for an 18 month lag was -. 504. The corre- lation coefficients for shorter lags were successively smaller negative numbers declining to —. 131 for a 10 month lag. The correlation co- efficients were also smaller negative numbers for longer lags declining to -.474 for a 22 month lag. Elliott was the first to experiment with the re8ponse of farmers to the hog-corn ratio lagged by more than one time period in the same equation}, In analyzing the 1898 to 1916 period, he included the December hog-corn ratio, the previous June to November hog-corn ratio and the following January to March hog—corn ratio in explaining the receipts of hogs at Chicago in the following September to April period. In addition, other independent variables were "index of climate at farrowing time, " "time, " December steer-hog ratio, change in percentage of non- merchantable corn in Illinois and Iowa from the previous year, disease loss and estimated number of breeding sows on farms. The December ‘Ibid. , p. 47, The "corn-hog differential" was computed by multiply- ing the price of corn by 11.42 (an average corn-hog ratio) and subtracting the result from the price of hogs. .5F.~ F. Elliott, Adjustinng-Ioég Production to Market Demand, University of Illinois Agricultural Experiment Station, Bulletin No. 293, (Urbana: June, 1927). and the previous June to November hog-corn ratios were by far the most important in explaining changes in receipts. Wells considered lags which extended over a longer period than the time lags investigated by either Haas and Ezekiel or Elliott.6 . By graphical analysis for the 1919 to 1930 period, Wells observed that percent changes in federally-insPected hog slaughter were appar- ently related to the hog-corn ratio lagged one and two years. Mordecai Ezekiel published his classic article on "The Cobweb Theorem" in 1938.7 He assumed that hog production re5ponded to prices two years before; that is, that farmers eXpect to receive-the same price-for their hogs as they did two years before.' Ezekiel ex- plained the hog cycle by means of the supply-demand chart shown in FIGURE 2. He'assumed the industry to be initially out of adjustment at (Ql, P1), withprices below equilibrium and production above. He also assumed that production was technically restricted to Q; in year 2, - so. that farmers could only partly adjust production in response to P1 , within‘a year's time. In year 3, farmers would continue to expect P1 andwould decrease production from Q; to Q3. But Q3 would bring a price of P3. In year 4,. production would increase to Q, as given by the technical restriction, and then to Q5 in year 5 as the response to ‘P3 is completed. But Q5 only bringsrprice P5 and the next cycle begins. ‘ In this model, the slopes of the supply and demand. curves are equal except for sign-and account for the constant amplitude of variation ,6Oris V. Wells,- Farmers' Response to Price in HogProduction and'Marketing, U.- S. Department of Agriculture, Technical Bulletin 'No.. 359,- (Washington: U.- S. Government Printing Office, April, 1933). .7Mordecai Ezekiel, "The Cobweb Theorem, " Quarterly Journal of Economics, Volume 51, (February, 1938),. pp. 255-280. inproduction and price and the continuous fluctuations through time. - Ezekiel explained two other theoretical cases. For simplification, these are illustrated with time lags of one year. One was a situation in which the slope of the supply curve is greater than the sloPe of the demand curve (FIGURE 3). This leads to convergency over time to the equilibrium price and quantity. The other case is divergent and would theoretically exist if the sloPe of the supply curve was less than the sloPe of the demand curve (FIGURE 4). The three cases of the Cobweb Theorem were delineated by the comparison of the slopes of the supply and demand curves. The same delineation can be made by comparing the elasticities of supply and demand at the intersection of the two curves. Linear demand and and supply equations were assumed in these illustrations. The Cobweb Theorem also applies to non-linear func- tions. But since the slopes of non-linear functions are not constant throughout, such models may not be easily classified into one of the three above cases. One case may apply to one section of the supply and demand curves, and another case may apply to a different section. ~ Ezekiel set forth the following conditions which must be fulfilled for the Cobweb Theorem to apply: (1) Production is completely determined by the producers' response to price, under conditions of perfect competition (where the producer bases plans for future production on the assumption that present prices will continue, and that his own production plans will not affect the market). (2) The time needed for production requires at least one full period before production can be changed, once the plans are made. (3) The price is set by the supply available.8 éMordezai Ezekiel, 22. cit., pp. 437-438. , FIGURE 2. ‘ Case‘I of Ezekiel's Cobweb Theorem: Continuous fluctuation with‘ra two year lag. Price - Quantity FIGURE 3. Case 11 of Ezekiel's Cobweb‘Theorem: Convergent fluctuation with a one year lag. ' Price FIGURE 4. ' Case III‘of Ezekiel's Cobweb Theorem: : Divergent fluctuation with a one year lag. Price 10 Kohls and'Paarlberg explained changes in Spring farrowings by September to November hog prices and September to November corn prices, these prices being considered separately.9 These variables were deflated by the index of prices received by farmers. The appli- cation. of the hog-corn ratio as a single variable involves the assump- tion that the effect of hog prices is equivalent to the effect of corn prices in. causing farmers to react. A There is no a priori reason to believe this is true. To avoid this difficulty, Kohls and Paarlberg separated hog and corn prices in their analysis. - Prominent among recent attempts to quantify the supply response 10 Brandow used for hogs is a study by G. E. Brandow at Pennsylvania. the hog-corn ratio in'October to December to explain the number of sows farrowing in‘ December to May. He also included a variable to account for changes inproduction of minor feed grains and a variable to account for differences between 1926-1941 to 1947-1956. He obtainedan‘Ré of . 83 in this equation, and found all estimates of the coefficients signifi- cant at the 5 percent level. Gerald Dean, in his Ph. D. dissertation at Iowa, used an approach similar to Brandow but added a variable to account for the relative profitability of feeding beef cattle.11 Dean analyzed two periods, 1924- 1937 and 1938-4956, omitting 1942-1944. - Hestudied the supply response in the North‘ Central region in addition to the United States as a whole. .9R. L. Kohls. and'Don‘Paarlberg, Short Time Response of Agri- cultural Production to Price and Other Factors, Purdue University Agricultural Experiment Station Bulletin 555, (Wast Lafayette: 1950). mG.’ E. Brandow, Factors Associated with Numbers of Sows Farrowing in the Spring and Fall Seasons, Pennsylvania State'University Agricultural Experiment Station, A. E. and R.‘ S. #7, (University Park: . August 1956). 3 ”Gerald Wallace Dean, "Supply Function for Hogs, " Unpublished Ph.‘ D. dissertation, Iowa State College, ,(Ames: 1957). 11 ‘ Dean obtained highly significant regression coefficients on the hog-corn ratio in October to December and change in production of minor feed grains, using the first difference of sows farrowing in the following Spring as the dependent variable. His equations also included a variable to measure cattle feeding profits. ' In one equation, he tried the price margin between feeder cattle and slaughter cattle in the fall of the previous year. The Sign on this variable was negative as expected for the 1938-56 period but positive in 1924-37. He tried another variable in its place, the price ratio between feeder cattle prices and hog prices in the fall of the year prior to farrowings. The Sign on this variable was positive in the 1938-56 period and contrary to the expected Sign. ' Dean also considered distributed lags in the supply re3ponse of farrowings to the hog-corn ratio, using an approach suggested by Marc Nerlove. 12' Dean concluded that the production reaponse was almost entirely to the hog-corn ratio in the fall prior to farrowings; that the hog-corn ratio in earlier years had no significant effect. - mNerlove's technique will be discussed in Chapter III. - CHAPTER II STRUCTURE OF THE INDUSTRY AND THEORETICAL BASIS The Characteristics of Hog; Production and Marketing « This section is devoted to a presentation of some facts about hog production and marketing. These facts are relevant to the discussion of the competitive structure of the hog industry in the second section of this chapter and the deveIOpment of the supply and demand equations in subsequent chapte r s . Producer Level The 1954 Census of Agriculture reported hogs were being produced on 2, 365, 708 farms in the United States, a large number although con- siderably less than the 3, 011, 807 farms with hogs in- 1950. 1 In 1920, 4, 805, 807 farms were reported raising hogs. ' During this same period, the total number of farms in the United States declined from 6, 448, 343 in 1920 to4, 782, 416 in 1954. The decline in the number of farms with hogs has been even more striking than the downward trend in the total number of farms. The shift to fewer farms raising hogs has involved an increase in the number of hogs per farm. The average number sold per farm in 1954 was 40 as compared to 32 in 1944.3 ~1U.‘S.' Department of Commerce, Bureau of the Census, Census of Agriculture: 1954 (Washington: U.' S. Government Printing Office), Vol; II,- General Report, p. 434. ,zlbid. ,. p. 509. 12 13 Half of the farms producing hogs sold fewer than 20 hogs in 1954. Only 11 percent sold more than 100 hogs.3 . Hog production is concentrated in the Corn Belt. The North Central states have accounted for nearly three-fourths of the pigs saved. (See TABLE 1) Most of the corn produced has been fed out on the same farm where it was grown. Typically, hogs are produced in combination with other livestock, principally beef or dairy cattle. TABLE 1. PrOportion of total pigs saved in the United States by regions, 1930 to 1958. Perc ent Of Total Region North North South South Total Time Period Atlantic ‘Central Atlantic Central West U. S. 1930-34 1.7 75.6 6.5 - 12.3 3.9 100.0 1935-39 2.4 67.8 8.9 16.4 4.5 100.0 1940-44 2.1 70.9 7.8 14.7 4.5 100.0 1945-49 2.2 72.4 8.4 13.8 3.2 100.0 1950-54 2.0 76.2 8.2 11.2 .2.4 100.0 1955-58 1.7 76.7 8.4 11.0 2.1 100. 0 a Calculated from: U.‘ S. Department of Agriculture, Agricultural Marketing Service, Pi ~Cr0ps by States, 1930-54 (Statistical Bulletin _No.- 187, July, 1956) and EigCrOp Reports of December 1956, 1957 and 1958‘ (Washington: U.‘ S. Government Printing Office) Average fixed costs in hog production have been low relative to average total costs. - Feed has been, by far, the most important cost, typically representing 70 to 80 percent Of the total cost in commercial hog Operations. * A study Of Central Illinois farms in1924- 1926 indicated ,3Ibid. ,. p. 505. ‘ 14 that feed and pasture comprised 84 percent Of the cost of producing 100 pounds of marketable pork.4 : A study by Haver in 1950 Showed feed costs on a. 20-sow herd Operation to represent 71 percent Of the . total cost in production. 5 ; He found labor costs were about 8 percent Of the total, and fixed costs only 7 percent Of the total. Informationis scarce on the role played by "inners and outers" in hog production though they are believed important in changes. Wells reported on a survey in 1926 which indicated that 80 percent Of the increase in farrowings intended for the spring Of 1927 was from farmers who had" no sows in the previous Spring.6 The organization Of the hog enterprise on Corn Belt farms has been predominantly based on the one or the two litter systems. A trend is evident toward more two litter systems. In 1924, 21 percent of the farrowings was in the fall season. In 1958, 44percent of the total farrowings wasin the fall.7 Markets Several different market Outlets have taken a sizeable share of total hog marketings during the period of this study (1907 to 1958). ' Early in this period, the terminal market was predominant. In 1923, 77 percent of the hogs slaughtered under federal inspection were purchased from. terminal markets.8 By 1956, this percentage had ,‘R. H.‘ Wilcox, W. E.- Carroll, and T. G. Hornungy Some Important FactorS‘AffectirigCosts. in Hog-Production, University Of Illinois Agri- cultural Experiment Station Bulletin 390,- ‘(Urbana: June 1933), p. 11. 5Cecil B. Haver, Economic A3pects of HogProduction in North _D_____akota, North Dakota Agricultural Experiment Station Bulletin NO. 391, (Fargo: June 1954), p. 15. GOris V. Wells, 22. £113., p. 34. .7Calculated from the source noted in TABLE 1. 8U. S. Department Of Agriculture, Market Outlets for Livestock _Producers, Marketing Research Report NO. 216, (Washington, D. C.: .U. S. Government Printing Office, March 1958), p. 5. ’ 15 declined to about 37 percent. The percentage'purchased from terminal markets by non-federally inSpected slaughtering. plants has been. some- what less than by federally inSpected plants. The proportion of all hogs-sold through the major channels in 1955 is shown in TABLE 2. TABLE 2. Hogs and pigs sold by farmers through different market outlets, United States, 1955.3“ Outlet Percentage Terminal public markets 30. 8 Auctions 16. 5 Country sales ; Direct to packers 21. 4 Local dealers 25. 3 Farmers , 4. 9 Total country sales 51.6 'All others 1. 1 Total 100. 0 .aMarket Outlets for Livestock Producers, _qp. £11., p. 11. Auction markets have increased rapidly in number over the last 30 years. ' An estimated: 200 were in Operation in 1930, l, 345 in 1937, . 2, 500 in 1952 and about 2, 322 in 1955.9 I . "Country selling" hasrbecome relatively important. Included in this category is direct selling to packers which has become the dominant method of marketing. hogs‘in many parts of the Corn Belt. Since 1921, the Packers and Stockyards Branch of the Agricultural Marketing-Service has had jurisdiction over the 64 terminal markets, nearly 500 other "posted" markets, 1300 livestock commission firms .9Ibid. ,. p. 8. 16 and about 200 livestock dealers, with the re5ponsibility of preventing unfair trade practices. 1° - Packe r Level The meat packing industry is characterized by a few large firms along with many small independent firms.. The number of meatpacking establishments increased from 1221 to 1909 to 1478 in 1939 to 2367 in 11954. 11 A sizeable portion of the total hog slaughter has been handled by 4 companies. These 4 companies processed 51 percent of the total commercial hog slaughter in 1916. Since 1921, they have handled remarkably close to 40 percent Of the total commercial hog slaughter each year. The recent rapid expansion in the number of packing plants has been mainly in non-federally inspected plants slaughtering over two million pounds of livestock per year. The number of these plants increased by a third in 1950 to 1955.12 These were owned almost exclusively by independent Operators. ' In this same period, the number of plants owned by dominant firms have remained the same or declined. At the same time, there has been a trend toward geographic decentrali- > zation of the meat packing industry. Meat packers Obtain about 71 pounds of edible pork products from 100 pounds Of liveweight of hogs. About 47 pounds of the edible products are major fresh and cured cuts sold in the wholesale trade to retailers. . 10United States Senate, Subcommittee on Antitrust and Monopoly of the Committee on the Judiciary, Unfair Trade Practices in the Meat Industry, (85th Congress, First Sess., 1957), p. 71. 11United States House of Representatives, Subcommittees of the Committee on the Judiciary and Committee on Interstate and Foreign Commerce, Hearings, Meatpackers, (85th Congress, First Sess. , 1957), p. 141. ”Willard F. Williams, "Structural Changes in the Meat Whole- saling Industry, " Journal of Farm Economics, XL. (May 1958), p. 317. l7 Hams, loins, bacon, picnic, butts and Spareribs are included in these cuts. About 9 pounds are minor edible products, which are mostly processed into sausage in the same plant where the hogsare slaughtered. Packers render about 15 pounds Of lard from 100 pounds of live hog. 13 , Some wholesale cuts (loins, Spareribs, butts, neckbone) are sold immediately to the retail trade. Some pork is cured or frozen (bellies, jowls, hams, picnics) and stored from fall and winter into the spring and summer. The amount stored from season to season has been relatively small. In 1948 to 1958, the additions to cold storage stocks of pork during October to December amounted to an average of 7 percent of total commercial production in those months. ‘ Additions in January to March represented 4 percent of commercial productionin ' those months. The labor cost represents about one-half of the gross margin of packers. TranSportation costs have been about 10 percent Of the gross margin. Wholesale Level _Early in the 1907 to 1958 period covered in this study, a large proportion of the red meat moved from slaughter plants to retailers through packer branch houses. Most of these branch houses were owned by national packers. By 1929, about one-half of the total meat sales was handled by packer branches. 1‘ , Since 1929, the Operations Of the packer branch houses have de- clined and the importance of independent (non slaughtering) meat whole- salers has increased. Between 1929 and 1954, the number Of packing 1.31.1. S. Department of Agriculture, Pork MarketingMarJgins and 5122, Miscellaneous Publication 711,- (Washington: U.- 5.; Government Printing Office, April 1956),. pp.- 29-30. “Willard‘F. Williams, 23. 513., pp.. 322-323. 18 house branches declined from 1157 to 664 as the number of wholesalers increased from 2225 to 4357. 15. Sales Of wholesalers (deflated by price level) have doubled in this period and, in 1954, were about equal to the sales Of packing house branches. ' Direct sales have increased Since the pre World War 11 period along with the expansion in the retail food chains. ' Some reversal of this trend is evident in recent years, but direct selling has remained an important marketing channel. 16 Retail Level In 1958, there were 175, 500 independents (one to ten stores), 16, 300 chains (eleven or more units) and 22, 500 Specialty stores (chains and independent) retailing meat. 17 In a recent year, the chains accounted for 38 percent Of total sales. Of the super markets belonging to the Super Market Institute, 29 percent owned their central warehouse, 34 percent belonged to a COOperative, 18 percent belonged to a voluntary and 23 percent had no central warehouse or affiliation. 18 Labor has been the most important cost item in retailing pork. A study by Farstad and Brensike Showed that 65 percent of the total Operating. costs in retailing meat was labor. 19 None Of the other items of expense amounted to more than 8 percent Of the total. ".slbid” p. 323. -- I‘lbid” p. 324. ”Facts in Grocery Distribution (Progressive Grocer; 1958). p. F-3. lpaThe Supermarket Industry Speaks--1958 (Super Market Institute; Chicago: 1958), p- 16. 19E; Farstad and U.» Brensike,~ Costs of Retailing Meats in Relation to Volume,- Marketing Research Report No. 24, U.- 8. Depart- ment of Agriculture (Washington: U.~ S. Government Printing Office, August, 1952). 19 Relative Importance of Marketing Functions The marketing margin on pork averaged 51 percent of the retail price in 1925 tO 1941 and 39 percent in 1947 to 1958. TABLE 3 presents the relative importance of the various marketing functions to the total marketing margin. TABLE 3. Distribution Of the total marketing rm rgin for pork and all meat in 1925-34 and for all meat in 1947.5L 1925-34 1947 Marketing Function Pork All Meat All Meat (percent) (percent) (percent) Retailing 38. 2 50. 2 44. 9 Wholesaling 10.4 9. 7 11. 6 Meat Packing 42.4 31. 7 37.1 Marketing Of Livestock 9. 0 8. 4 y 6. 4 Total Margin 100.0 100.0 100. 0 aKathryn‘Parr, Farm-to-Retail Maigins for Livestock and Meat, (Washington,- D.- C.: U.- S. Department Of Agriculture, B.A.E. , June 1949), p. 4 and 29. The Competitive St ructure Producer Supply of Hogg The characteristics of hog production outlined in the previous section suggest that the perfect competition model would be appropriate for analysis. The short run supply curve in the perfect competition model of static economic theory traces the relationship between price and the production which price brings forth. The supply curve is derived by aggregating the marginal cost curves of individual firms in the industry with allowance for possible economies or diseconomies of scale. 20 The aggregation includes the rising portion Of the individual marginal cost curves above the intersection Of the marginal cost curve and the average variable cost curve for producing firms and above the average total cost curve for potential producing firms. ~ A farmer would not rationally go into the hog business unless the price he expected was above his average total costs. On the other hand, if he were in, he would continue to produce as long as he covered average variable costs, even though hog prices may drOp below average total costs. He would lose more by not producing hogs than by staying in and paying off at least part of his fixed costs. This suggests that, within the lower ranges, there may be two aggregate supply curves, one when hog prices are increasing and another to the right Of the first when hog prices are declining. However, this difference would be exPected to be small, since the fixed costs in producing hogs are only a small part of the total. The classical supply function involves the assumption that all other product prices are unchanged. To isolate the supply function for hogs, prices Of other farm products must be taken into account. ' Firms producing more than one commodity will adjust production in such a way that the ratio between the marginal cost in producing one commodity and its price is equal to this ratio for all other commodities. The adjustment will proceed to the point where the marginal cost Of producing each commodity is equal to the price of that commodity. In the perfect competition model, each firm attempts to allocate its inputs among several alternative enterprises in such a way that the -marginal physical product Of inputs times the price of the product Of one enterprise is equal to the marginal physical product of these inputs times the price of the product of each Of the other enterprises. This is a necessary though not sufficient condition for maximizing profits. 21 The sufficient condition is attained when the marginal physical product of the inputs times the price of the product is equal to the marginal factor cost of the inputs for each enterprise. If no firm is large enough .to employ more than a small fraction Of the total supply Of inputs avail- able, then each firm deals with a perfectly elastic supply curve for inputs. The marginal factor cost then equals the price of the inputs. Live stock Markets This segment of the marketing chain has features of a competitive market. In the major hog producing areas, farmers have several altern- ative market outlets. Entry into and exit from the livestock marketing trade is not difficult. These characteristics would tend to prevent live- stock dealers, commission firms and stockyards from receiving large abnormal profits over an extended period. In any case, imperfections in competition would have only a small effect on the average price of hogs. The cost Of livestock marketing has represented less than 10 percent of the total marketing margin. The Meat Packing Industry The assumptions of the perfect competition model do not fit the meat packing industry. This industry is characterized by a few dominant firms and many small relatively competitive (firms. ' According to Nicholle, evidence has been strong that the dominant meat packers have been price leaders but have not resorted to aggressive pricing policies among themselves or against the small packers." Rather, they have followed market sharing practices with buying prices approaching the collusive-Oligopsony level. ' At this level, the market share of each dominant firm has adjusted in such a way that any further 20William H. Nicholls, . Imperfect competition Within Agricultural Industries, (Ames, Iowa: The Iowa State College Press, 1941), pp. 114- 131. 22 change would have reduced the profits of at least one of the firms. 'Abnormal profits have likely persisted but have been limited by the threat Of entry of new firms and anti-trust action, according to Nicholls. Williams, in his evaluation of the meat wholesaling industry (packers and distributors), claims that the competitive structure Of the industry has changed since Nicholls made his study; that it has taken on more Of the attributes Of the perfect market.21 He cites that the in- creased use Of uniform grade standards and market news hasmore equalized knowledge throughout the industry, tending to eliminate quality as a variable factor in bargaining. These developments along with decentralization and reduced concentration have resulted in more price competition, according to Williams. ’ To account for changing margins at the packer level, the analyses Of Nicholls and Williams suggest an investigation Of major cost items of meat packing firms. It will be assumed that abnormal profits have not been persistently large in the meat packing business and can be neglected in studying margins at the packer level. As packers face falling, then rising ayerage cost curves with increasing supplies, the volume of slaughter would also affect the margins taken by packers. Margins at the packer level, then, are considered to depend mainly on the marginal costs of the most efficient firm or firms. - Rising costs Of operation, both fixed and variable, would adjust the total average cost curve Of each firm upward and increase the minimum margin which firms would accept over any extended period Of time. For short periods, the minimum could drop below the average total cost but not below the average variable cost. Increasing supplies of hogs at levels in excess of the minimum Of the average total cost curves would tend to widen margins as marginal costs would be increasing in this range. On the “Willard-F. Williams. 313. 313.12. 328- 23 other hand, margins would tend to be inversely related to supplies at supply levels below the minimum Of the average cost curve. ' Retail Margins The-pricing of meat at retail has been based primarily on whole- sale prices though modified by local competition. ' According to a'U.~ S. ‘ Department Of Agriculture publication on pork marketing margins, "The combined effect of price leadership by some retailers and the actual changes in wholesale prices themselves tend to bring about a general change in the level of retail pork prices. "22 . A North Central Regional study Of principal methods of pricing retail cuts of meat found that 70 percent of the retailers were using "cents per pound markup, " "percentage markup over cost, " or "percentage of selling price (for margin). "23 About 15 percent used meat pricing charts or guides and 15 percent used competitors prices only. Most used some combination of these methods. These studies indicate that the focal point in pricing pork-is at the packer level rather than at the retail level. This is also supported by the lag Of retail prices behind changes in wholesale prices. . This lag has generally been about one to two weeks.“ The Competitive Structure in Summary The competitive structure of the hog market generally fulfills the conditions set forth by Ezekiel for the applicability of the Cobweb ”U; S. Department of Agriculture, Pork Marketing Margins and Costs, 9p- iii. , pp.- 20-21. ”North Central Regional Livestock Marketing» Research Committee, Retailing Meat in the North Central States, North Central Regional Publi- cationNO. 55; Purdue University, Station Bulletin 622,- (Lafayette: March 1955), pp. 23-24. “Hershel W. Little and Albert L. Meyers, Estimated Lag: Between Farm, Wholesale and Retail Prices for Selected'FOOds, (U.~ S. Department Of Agriculture Mimeograph), (Washington: June 1943),. p. 5. 24 Theorem. The characteristics of hog production are compatible with the perfect competition model. Certain imperfections in competition in the marketing of hogs, particularly at the packer level, are recognized. However, the previous studies cited in this chapter suggest that the error would not be serious in regarding hog prices as set by the supply available in the short run. At least, supply could be considered the predominant factor. CHAPTER III . EXPECTATIONS AND LAGS‘IN SUPPLY RESPONSE The supply curve described on page 19,. as applied to hog pro- duction, is a construction composed of the supply response curves of the individual hog producers and potential hog producers. This curve relates total production Of hogs to prices expected for hogs. The individual supply curves are constructs involving production functions, expected prices of inputs, expected prices of alternative outputs in each farm situation, and a Specified length of time. A change in any of these variables would change the industry supply curve. A problem to be investigated is how to identify these expected prices, which are paramount to the determination Of a supply curve (or curves), and supply elasticities. Time Series Approach In most studies of supply reSponse in hogs, the assumption has been made that the expected price is equivalent to the actual price‘at the time or immediately preceding the time when the sows are bred and the production decision is made. Most of the attention has been directed toward predicting year to year changes in supply. - Consequently the supply response has been measured in terms of the adjustments in one production period, usually within a year. ~ Ezekiel, in applying his Cobweb’Theorem to hogs, considered that the production period could extend over two or more years. -25 26 ‘Using a two year lag as an example, he assumed a given adjustment in production during the first year. The change in production during the second year completed the adjustment to the actual price of two years before, which Ezekiel assumed to be the expected price. There are economic, technical and subjective reasons for lags in adjustment which extend over more than one production period. ' Some of the inputs in hog production are fixed for the enterprise in the span of one productionperiod. This would include such items as hog houses, feeder equipment and breeding stock. For certain marginal hog pro- ducers, a drOp in hog prices (or, more preperly, expected hog priceS) may encourage a. shift to a business or enterprise which-promises greater long run returns. However, they may delay the shift until the worth of their fixed assets in hog production has declined to a certainpoint. This point would theoretically be the level where the scrap value was equal to or greater than the discounted expected return from the asset during the remainder of its life, i. e. , Ei (1 + r) n VS> E i: i 1 where Vs is the scrap value, i is the year, n is number of remaining years of the lifetime Of the asset, Ei is the expected return in year i and r is the rate of return avail- able to the farmer in an alternative investrnent of compar— able risk. Certain technical factors may limit expansion within one production period. ‘ A farmer expanding his hog enterprise or going into hogs for the first time may first decide to build a central farrowing house. Constructing a central farrowing house requires a certain amount of time. Because Of this, his adjustment to expected price would not necessarily be registered within one productionperiod. 27 In addition to the economic and technical restrictions, there are certain subjective reasons why the adjustment to price isn't immediate in one production period. Farmers are Often reluctant to shift from one enterprise to another or adjust levels Of production because Of resistance to change or personal preferences, even when they know the profit alternatives. Another reason which could be classified as subjective is the element Of uncertainty and its effect on exPectations. A given price change in a market characterized by frequent and extreme changes in price would likely involve a lagged response, even if, in fact, the price did remain stable at the new level for a long period Of time. ' It would take some time before entrepreneurs would become confident that the new price level would be maintained. Hicks was concerned with this problem and introduced the concept of elasticity of expectations. This he defined as the ratio of the prepor- tional rise in expected future prices of a commodity to the prOportional rise in its current price. 1 The elasticity would be one if the change in price expectation were equal to the change in price at the time the pro- duction decision was made. The price change would be expected to be permanent. The elasticity would be less than one if part of the price changewas considered to be transitory and not likely to persist. TO summarize, the lag between supply and price involves two separate lags, (1) between a change in actual price and expected price and (2) between expected price and the adjustment to this expected price. The reSponse to an actual price change, then, involves an expecta- tion lag and an adjustment lag, and may be considered as a function 1J. R. Hicks, Value and Capital (Second Edition, Oxford: Oxford University Press, 1953),. p.- 205. 28 of time. - This function may be assumed to be of various forms. A realistic example is given by Koyck as shown in FIGURE 5.2 In-period t = 0, actual price (P) is allowed to rise instantaneously from a to b. The response in production (Y) is very small at first. The dYt dt period (t = l) and then tapers Off. ' Production approaches the new rate Of reSponse( ) reaches a maximum at the end Of the first equilibrium level ( Y: k) asymptotically as t increases. dYt dt and production response Y over the 8 time periods shown in FIGURE 5. The function gives the distribution of the lag between price'P If price P lagged only one year were used? to explain supply reSponse Y, it is evident that only part of the adjustmdnt would be explained. A drop in Pt would generate a downward reaction in production. ‘ If the parameters of the production response function to a price decrease are the negative of the response function to an increase, the function would be considered symmetrical. It is not necessary to assume this and in many cases it is more realistic to assume an asymmetrical relationship as pointed out in Chapter 11. However, because of the - relatively low fixed costs in hog production, asymmetry is likely to be negligible. 1 FIGURE 6 is a representation of the éaytl‘ Of FIGURE 5 in discrete changes. ‘ Statistical analysis Of economic relations Often involves discrete variables as a representation of continuous variables. The (11 represent the distributed lags, i. e. , the change in Y in each production period in reSponse to a change in price. Multiple regression methods have been used to estimate the 0.1, using Yt as the dependent variable and the Pt _ i as the explanatory variable 8 . .zL. M. Koyck, Distributed Lagp and Investment Analysis (Amsterdam: North Holland Publishing Company, 1954), pp- 9—10. 29 FIGURE 5. Continuous time path Of production response (Y) to a change in price (P). b I Pt a I xv ' / : k» :I I . I J 7 ' - I I / I ' l dYt I dt : 0 I - I ' l I I I I I J I - 1 0 1 Z 3 4 5 6 7 8 Time (t) FIGURE 6. ‘ Discrete changes in the rate of production reSponse (AY) to a change in price (P) in-FIGURE 5. I l I I ‘11 l 10.1 93 04 ‘15 06 <17 <18 0 1 -— e I J l I l I l I -1 o 1 2 3 4 ‘ 5 6 7 8 “$.77" — 30 Alt' 8 Approach Alt develOped a method for estimating distributed lags with regres- sion methods.3 His approach was to successively compute the regression coefficients for Yt = f (Pt), Yt = f (Pt, Pt-1): Yt = f (Pt, Pt_1, Pt-2), Yt = f (Pt. Pt-lt Pt-Z" Pt-3) etc. until the coefficients ceased to make sense. Another criterion he used was the standard errors of the regression coefficients. Pt-i would be included as long as the oi were significantly different from 0. I In Alt's approach, no assumption is necessary about the form of the distributed lag. His technique is an attempt to determine-what that form is. This may be viewed as a weakness of this method since no theory Of distributed lags is being tested other than establishing whether or not a distributed lag relationship exists. ‘ A statistical problem in using the regressiOn approach to estimate distributed lags is that time series, such as the Pt-i’ are Often serially correlated, hence there is Often correlation between independent vari- ables. ' Although correlation between independent variables does not invalidate an equation for prediction purposes, it does present difficulty in Obtaining accurate estimates of the parameters. F-isher' 8 Approach Irving Fisher recognized the distributed lag concept and placed some restrictions on the form that such a distribution would have.‘ The form he postulated as the most common was a type of probability curve skewed toward the right, i. e. the rate Of reSponse eventually 33F. L.'A1t, "Distributed Lags," Econometrica, Vol. 10,1 (1942). pp. 113-128. ‘Irving Fisher, "Note on a‘Short Cut Method for Calculating 'Distributed Lags, " Bulletin de L'Institut International de Statistique, Vol. 29, (La Haye: 1937). 31 tapers off with time after rising to an early peak. He suggested that a logarithmically normal distribution curve would therefore be appropriate. Because of computational difficulties, he developed a short cut in which it was assumed that the greatest reSponse to price was in the following time period. The re Sponse declines linearly in- succeeding time periods. - The procedure is illustrated by the following example. ‘Using the regression technique, the following equations are considered consecutively. l (3. 1) Yt = (3 Pt + 2-Pt_1+ Pt-Z) Yt = (4‘Pt + 3 Pt-l + 2 Pt-Z + Pt-3) Yt = (5 Pt + 4 Pt..1+ 3 Pt-2 +12 Pt-3 + Pt-4) The trial which produces the highest correlation coefficient is chosen. - Koyck' 5 Approach Fisher's method assumed a linear decrease Of lagged influences. - Koyck developed a technique which assumed that there was a proportional decrease Of lagged influences. Both approaches mitigated the problem Of correlation between independent variables present in the standard regression approach. Koyck's technique and assumptions are as follows. 5 , Let “i be a. series of coefficients 1 = 0, 1, 2 . . . in the supply on reSponse equation‘Yt = ,3 0 (11 ' Pt-i- ' Assume that the a1 fromi > k 1 = "‘ can be' approximated by a converging geometric series. (3H2) 9k+m=x°k+m-1 »whereim_>_ 0 and '0 _<_ x<1 . Then sLoMoKOYCk, 220 9—1.2. ,~ PO‘ 200 32 (3. (3. (3. (3. (3. .(3 (3. (3. (3. .9) Yter e. 1J1: + ak'Pt-k + QkXPt—k-l + a k )‘Z‘Pt-k-2+°" - For Simplicity, assume Pt rises from a constant level, Pt.=0fort < 0, toanewlevelPt= lfort>0. 'k-1_ Letting 2‘. oi: 8 i=0 n-l 4)Yk+n=B +akk2+. . . + ck). “k 9k n 5’ 2 ‘3 + 1‘7). " l-x I The new equilibrium value of Y is then ok :1-900 The change in Yk+n per unit Of time is 7) A Yk+n = ok I“ If we consider a simpler case where the entire adjustment path of Y can be approximated by an exponential curve, i.e. k: 0, then ” 8) Yt = .Z .91 Pt-i becomes . < t-j 0 «v x < 1 Then A Y can be Obtained by the following method. 10)Yt+1=0.o Pt+1+ 0.0th +00X2Pt_1+... 11) XYt= ooth+dokth_1+... 12) Yt+1-KYt=GoPt+l Adding x Yt to and subtracting Yt from both sides Of (3. 12) —-.--fi 33 (3.13) Yt+1-Yt= aoPt 1-(l-X)Yt + Then (3.14) AYt= 90Pt+1' YYt where 7:: l-x In this form only two coefficients ( a. o and 7 ) need to be estimated rather than the many that may be involved using t raditional technique 8 . At equilibrium A Yt = 0 and -— o. (3.15) Yt = 72- Pt The coefficient for the long run reaction 0. is a 3. 16 o. = —-9-- ( I 7 It can be shown that the speed Of the adjustment to the new equilibrium is indicated by 'Y . By substitution (3.17) AYt= 7 (Yt+1-Yt), 0 < 'y :1. An increase in the value of ‘Y (up to 1) means that the rate of adjustment of Yt to the equilibrium increases. ' A 7 equal to 1 would mean that the entire adjustment would be made in 1 period. Koyck's technique, then, was essentially to estimate the first few coefficients (up to k) Of the increasing phase of the distributed lag function by traditional regression methods. He assumed the declining phase to be a converging geometric progression. With this restriction, the estimation Of the coefficients k + m can be simplified. At this point, the reader may have sensed the empirical problem which is developing. Essentially, two problems are involved. One is " to Obtain estimates of expected prices and the other is to Obtain esti- mates Of the distributed lags of adjustment in the reSponse to expected 34 prices. In models using time series, there is a difficult, if not impossible, task in isolating lags in adjustment from a measurement of expectations . Ne rlove' 3 Approach Marc Nerlove, drawing upon the concepts Of Hicks and Koyck, has given considerable attention to these problems. Nerlove's approach as developed in his book, The Dynamics Of Supply: Estimation of 6 Farmer's ReSponse to Price, is as follows: "The price which farmers exPect at any time period can be considered as equivalent to the prices they expected in the period before but adjusted for the difference between the actual price and the price expected in the period before. That is (3.18) P*t=P*t-1+fi[Pt..1'P*t-1] O 0 Under usual circumstances, the equilibrium output would be a direct function of expected price. The problem then is to determine the adjustment path of production over time to a change in the equilibrium level of output which is sought. Nerlove, as did Koyck, assumed this adjustment path to approximate a geometric or exponential curve over time.8 Nerlove advanced as plausible the proposition that output in each period is adjusted in pro- portion to the difference between the output desired in long run equilibrium and actual output. That is, 81bid., pp. 62-63. 36 (3.23) ”art-3%1 = ‘y[Y*t-Yt_1]. o<7§ 1 where Yt is actual output in t, Y*t is the long run equilibrium output desired in t and 7 is the constant representing the rate of adjustment. This rate is presumably related to the time necessary for firms to acquire or depreciate inputs fixed in the short run but variable as time increases. The 7 represents the elasticity or coefficient of adjustment depending on whether the output is expressed in logarithmic or absolute terms. The form is similar to the price expectation relationship and the solution to the first order difference equation can be similarly derived to give: 1: t X (3.24) Yt = z 'y (1 — 7) Y: with output expressed at time t as a deviation from output at t = 0. Output is assumed to be at equilibrium at t i 0. - Since neither expected price nor long run equilibrium output is observable, the equation involving these variables must be transformed to equations with only observed variables. Then the problem of identifi- cation deve10ps, that is, the solution of the separate effects of expectation and distributed lags in adjustment. - Substituting equation (3. 23) into equation (3. 24) (3.25) Yt“; 7 (1:1)t-x u = 0 P* cl1: Substituting the right hand side of equation (3. 21) for P*t above. t t _ u u (3.26) Yt: 23 (1-7) u = 0 x 2: (1- mu“? 0 X-l .l‘ 37 = wig-1+[(1-a)+<1-mp,_2+ [(1-$)z.+(1-£3)(1-7)+(1-7')2.]Pt__3+ [(l-BPHI-MW1-7)+(1-fi)(1-7)Z.+ (1-7)3] + ...} The fact that (3 and 7 enter symmetrically into (3.26) makes identification of these terms impossible. - Both (3 and 7 can be found by , a set of simultaneous equations using estimates of the coefficients of the regression but there is no way to determine which of B and 7 is the elasticity of expectations and which is the adjustment coefficient. Inability to distinguish the two is a serious restriction in analyzing situ- ations where one or the other of these parameters would change. Nerlove suggests) a way for extracting additional information about these coefficients. If the equation (3. 22) is lagged one year and sub- stituted into (3. 19) the result is Yt -1 (3.27) P*t= p Pt_1 + (1 43) Substituting (3. 27) into (3. 22) (3.28) Y3 =aBPt_1 + (1 - (3) “5,4 - Substituting (3. 28) into (3. 23) (3.29) Yt-Yt_1 = 'y[o.[3Pt_1 +(1-(3)Yt*.1 -Yt,_1] Lagging (3. 23) by one year (3.30) Yt-l " Yt-z =7Yt-1* ..‘YYt-Z (3.31) 'y Yt_1* = Yt_1- (1- 7) Yt-z Substituting (3. 31) into (3. 29) (3.32) Yt=Yt_1+ ‘ya. (a pt_1+(1 - B)Yt-1-‘(1 - (3) (1 w) Yt-.-2 - 7 Yt_1 (3.33) Yt= afl'yPt-1+(Z-B-Y) Yt-1- (1-5) (1-7) Yt-Z 38 Again 7 and 6 enter the regression coefficients symmetrically and cannot be identified. If, however, we can determine whether the co- efficient of Yt-Z is 0, then we can distinguish between two cases; (I) neither (3 nor 7 is one (the coefficient of Yt-2 is nOt 6) and (2) either (3 or 7 or both, is one (the coefficient of Yt-Z is 0). - In other words, this imparts information about whether there are lags in both expected price to actual price and current output to long run equilibrium output or whether one or the other, but not both, occur. In any case, a can be determined, and this enables the computation of the long run supply elasticity. . ' Another situation Nerl'ove considered was the case where more than one price with different elasticities of eXpectations entered the supply relationship. The adjustment coefficient was assumed tobe equal to one.9 Two methods were presented. One was by a single equation technique developed by Theil using Nerlove's approach. 1° From aproduction reSponse equation a): at (3.34) Yt = 0.0 + 0.1 P11: + 0.; P21; Whe re 1: t- (3.35) Pit’“ = 2: pi (l-pi) x p i = 1,2 i=0 3’1 (3.36) Yt = 303133 + a,(3,Pl,t_1 + azpzpz,t-1 - a,(3,(1-sz)P1,t_z - «1.3.0 43.) P2,t-2 + [1 - (5. + 1 - 13.] Y._1 - (1 - 3..)(1- a.) Y,_2 The expectation, coefficient [31 and (32 can be estimated although more than one estimate is possible. .9Ibid. ,. pp. 193- 196. . 10H. Theil, Forecasts and Economic Policy, unpublished manuscript, (April 1956). 39 Nerlove proposed another method whereby expectations co- efficients were determined jointly utilizing additional information. This additional information involves production reSponse of other commodities whose prices are included in the equation of interest. Other Time Series Models The evidence has been strong that hog farmers have responsed to past prices which further indicates that past prices are important in formulating expectations. The problem becomes one of discovering the functional relationship between past prices and expectations, or between past prices and production adjustment. Several alternative functions were investigated by Darcovich 1 These were listed as (1) average, (2) normal, (3) random, and Heady. 1 (4) current year (5) 5 year moving average, (6) weighted 5 year moving average, (7) trend, (8) reverse trend, (9) outlook and (10) parallel price models. In (1), the mean of the entire price series was projected forward as the predicted value for every period in the future. This model was used as a standard to evaluate the other models. In (2), expectation was based on some period of a just or fair price such as 1910-1914. In model (3), a value'was selected at random from past prices. In (4) the current year's price was projected forward one year. The expected price in model (5) was the moving average price of the previous 5 years. Model (6) is similar to (5) except that the most recent year was given the weight of 4 and earlier years each the weight of l. The lineartrend of the price between two consecutive years was added to the price in the second year in (7) and subtracted in (8). Annual farm outlook reports from federal and state agencies were used in (9). In model (10), the expected price was based on a price which nWilliam Darcovich and Earl O. Heady, AJJplication of Expecta- tion Models to Livestock and CrOp Prices and Practices, Research Bulletin 438, Agricultural EXperiment Station, Iowa State College, Arnes, Iowa, (February 1956). 40 existed in a parallel period. An example is the price decline expected after World War 11 based on the parallel period of the early 1920's. These models were evaluated in two hypothetical situations; one in which a price series was assumed to have an autocorrelation co- efficient of one and the second in which a random price series was assumed. A limitation of this evaluation was that the inbetween cases of autocorrelation, most likely in hog and corn prices, were not examined. An empirical evaluation was made on all the models using actual prices on several major farm products during 1917 to 1950. Three criteria were used, "absolute mean erros, " "percentage of extreme error" and "coefficients of the range. " 3 The outlook, current year, parallel and weighted moving average models generally gave the best results on both hogs and corn. The performance of the weighted moving average model, a particular case of distributed lags in expectations, is of particular interest. In every test, it was a better predictor than the unweighted average, which is another Special case of distributed lags (rectangular distribution). Compared with the current price model, the weighted average was a better predictor of hog prices under the range criterion but somewhat less satisfactory by the other criteria. By each measure on corn, however, the weighted average was superior to current price. The evaluation of these 10 expectation models says nothing about which one(s) farmers actually use the most. They were selected to be reasonable approximations of models farmers are believed to use or to be logical mechanical models that farmers could easily adept. 41 Survey Approach The time series approach alone is limited in yielding much-pre- cise information about farmers' expectations. Questions may be raised as to whether farmers actually do have expectations, and if so, what the nature of these expectations is. To test hypotheses about expectations and to obtain new insights into farmers' decision making process, numerous surveys have been made. Elliott” and 13211113 interviewed hog farmers in Iowa during 1946 to 1949. They found that farmers did have eXpectations which could be considered as probability distributions. Ball found farmers quite willing to quote the lowest, the highest and the most likely price they eXpected for both hogs and corn. Observing that the most likely price on hogs was near the midpoint of the lowest and highest prices expected, he concluded that the distribution of a farmer's expectation on hogs approximates a normal curve or at least is not inconsistent with a hypothesized normal distribution. As the lowest expected price on corn was nearer the most likely price than was the highest expected price, he concluded that the distribution of expected prices on corn was skewed to the right. This is logically due to the lower limit guaranteed by the support program. The results of the studies by Elliott and Ball also revealed that expected prices on hogs and corn were often considerably different from the-prices prevailing during the season the expectation was reported. 12Robert T. Elliott, "Adjustments to Risk and Uncertainty in Hog Production, " unpublished Masters thesis, Iowa State College, (1947). 13A.C}ordon Ball, "Expectations in the Agricultural Firm, " unpublished Masters thesis, Iowa State College, (1950). 42 Brownlee and Gainer interviewed Iowa farmers in March of 1947 about their expectations for corn and soybean prices in the following December. M All the farmers interviewed stated a "most probable anticipated price. " They were also asked to state the probability that the price would be as much as 25 cents above or below the most probable price. Brownlee and Gainer were not able to ascertain from the answers whether a very high percentage of the farmers formulated their antici- pations in terms, of probabilities. They also asked farmers to state whether they thought a price above the most probable price was more or less likely than a price below; then whether a price 25 cents above the most probable price was more likely than a price 25 cents below. There was no strong evidence of asymmetry in the distribution of expectations on corn prices, although a few more farmers thought a price 25 cents above the most probable price more likely than 25 cents below. D. B. Williams, who surveyed Illinois farmers in December 1949, gained a strong impression that they based their expectation of the price of corn for the following December mainly on the present price. 15 He observed that weighted averages of past prices which involved heavy weighting of prices in the immediate past did give close approximation to the farmers' exPected price on corn. He also found that the standard deviation in expectations of hog prices was relatively small in the sample. Drawing from the Interstate Managerial Survey of the North Central Farm Management Research Committee, Partenheimer studied the price 14O. H. Brownlee and Walter Gainer, "Farmers' Price Antici- pations and the Role of Uncertainty in Farm Planning, " Journal of Farm Economics, Vol. 31 (May 1949), pp. 266-275. ”D. B. Williams, "Price Expectations of Illinois Farmers, " Journal of Farm Economics, Vol. 33, No. l (1951). 43 exPectation models used by farmers. 16 He concluded that a high proportion of farmers use so-called supply, supply—demand, and government action models in contrast to the highly mechanistic models such as advanced by Darcovich and Heady. 17 However, the interviews were made at a time when the forthcoming supply of hogs, for instance, was fairly well-known. At least, the farrowing intention reports had been released. The government support program on corn was also known at that time. Partenheimer noted that for expectations covering more than one production period, the less sophisticated, mechanistic models may be more important. The criticism leveled against the mechanistic models of Ezekiel, Alt, Nerlove, Darcovich and Heady, and others is that farmers form their exPectations by a far more complex process than by using some function of past prices. Farmers are conscious of many of the important factors affecting price such as production, consumer incomes, prices of competing products and the government support program. The particular expectation model used would depend on the commodity in question. If the government support program had been instrumental in establishing prices, then farmers would be attentive to the prOSpective government program. Farmers receive outlook information which no doubt influences their exPectations. The selection of an appr0priate expectation model involves implicit assumptions about the level of knowledge and understanding by farmers of economic relationships. A high level of knowledge and understanding can not be adequately handled in a mechanistic type “Earl J. Partenheimer, "Some Expectation Models Used by Selected Groups of Midwestern Farmers, " unpublished Ph. D. dissertation, Michigan State University, (1959). 17William Darcovich and Earl O. Heady, op: cit. 44 model which presumes that expected prices are a function of past prices alone. Nor would such a model properly account for changes in the level of knowledge and understanding over time. This is a valid criticism of the mechanistic approach and should be given serious consideration in expectation studies. Even here, questions would have to be raised on how farmers form expectations of future production, consume r incomes, prices of competing products, a support price before it has been announced and other relevant vari- ables. Can they adequately appraise each of these factors in forming a price expectation? There is the question, too, on how much farmers are inclined to form their eXpectations from outlook material. In hog production, it has been observed that a change in price usually has to be realized before a response in production is forthcoming. From a survey of commercial hog farmers in Illinois, Ross concluded that most of them were "amazingly uninformed about economic factors which affect their hog business. "18 The study was made in September of 1958, a time for caution and careful planning by swine growers. Yet the study indicated that they paid little attention to outlook information in planning their future swine enterprise. Even if farmers ac.u.ally do recognize the important factors that determine the price of their products they may not apply these in formulating expectations, however. When asked, they may state that prices will depend on several very relevant factors. But in formulating expectations, they may not go through the complex process of attempt— ing to forecast these variables and assess their relative importance in establishing price. This is a difficult task even for experienced economists. The enormity of this undertaking may force even the best informed farmers to rely on some simpler, mechanistic expectation models. m 18James E. Ross, "Where do Illinois Swine Growers Get Their Outlook Information?" Journal of Farm Economics, XLI (November 1959). pp. 830. 45 Evidence that such may be the case is observed in the close concurrent relationship between the prices on feeder livestock and slaughter prices. Feeder pig prices tend to parallel the slaughter hog market. ~ Prices on feeders cattle have depended on the current slaughter market, recent profit experiences of cattle feeders and the prosPective supply of range forage and feed grain. Theoretical Approach There is a great void in most studies of expectations in economic behavior. ' An underlying theoretical structure has not been developed. Although considerable work has been done in survey procedures, that is, in asking people what their expectations are, attempts to con- struct behaviorial models have been feeble. The Survey Research Center of the University of Michigan has drawn from some theoretical concepts in psychology in their surveys of businessmen's and consumers' expectations. Empirical verification of the theories is only in the early stages, however. Katona _A leading proponent of the psychological approach) has been ‘George'Katona. Katona has criticized the great body of economic theory which draws only upon "mechanistic psychology"--the assumption that under given external conditions, human actions are entirely determined by those conditions. 19 Because human behavior is pliable and modifiable, and because human beings are capable of using past experiences, he is skeptical about broad generalizations tlat assume invariable inte r relationship 8 . 1"George Katona, Psychological Analysis of Economic Behavior, (First Edition, New York: McGraw-‘Hill Book Company, Inc. , 1951), pp. 6‘7. 46 Katona points out that economic behavior is sometimes habitual and does not involve expectations. In some cases, exPectations are so weak that entrepreneurs (or consumers) do not reSpond and, in other cases, little doubt enters the expectation and appropriate response is noted. But in the majority of instances of uncertainty, Katona noted that expectations influenced action, especially if that action was in line with the hopes and desires of those concerned.20 About eXpectations, Katona states: "The study of expectations forms a part of the psychology of learning since expectations are not innate or instructive forms of behavior but rather the result of experience. Therefore, expectations are explained by the same two principles by which all learning is explained, that is, by repetition or understanding (or both). The theory of expectations based on repetition alone is: "I expect those things to happen that have happened before, and the frequency of my past experience (the number of rein- forcements) determines the strength of my expectations. "21 But Katona points out that the strongest and most influential expectations originate in understanding. New understanding results from a restructuring of the psychological field, the whole situation which involves a change in the perception of the environment. What people perceive depends on the organization of their perceptions, which differs from person to person and in the same person from time to time. ‘ Changes in the organization of perceptions are conditioned by motives, past experience, attitudes and emotions. Reaction to stimuli depends upon the particular structure of the perceptions. 20George Katona, "Expectations and Decisions in Economic Behavior, " The Policy Sciences: Recent Developments in Sc0pe and Method, (Ed. Daniel Lerner and Harold Lasswell, Stanford: Stanford University Press, 1951), pp.- 230-231. 21Ibid., p. 53. 47 Changes in the structuring of the psychological whole and con- sequently of understanding are infrequent. Katona reasons that if under standing is the source of strongest ex- pectations, changes in the expectations of businessmen are not constantly being revised.“ But when there is a revision, the change is likely to be substantial. In addition, many individual businessmen are likely to revise their eXpectations at the same time and in the same direction. ‘ Shackle G. L.‘ S. Shackle has been concerned with problems of uncertainty in situations involving choices between "non-divisible, non-seriable" experiments.23 Here expectations cannot be based on frequency ratio probabilities since the conditions under which action is to be taken are unique. To the extent that conditions attendant to the hog industry change over time and that each year is somewhat unique, some attention should be given to this phase of the problem of specifying farmers' expectations. Shackle reasons that entrepreneurs have some idea of the gain that would accrue to them in each of a set of mutually exclusive hypotheses if the given hypothesis were true. This he defines as the "face value" of the hypotheses and is an independent variable in his expectation model. The set of hypotheses involved could be discrete or continuous. For example, a hog farmer would have some idea of his gains under several mutually exclusive hypotheses concerning the price of hogs at the future date when he was ready to sell. “lbid” p. 54-55. ”G. L.’ S.‘ Shackle, Uncertainty in‘ Economics and Other Reflections (Cambridge: University Press, 1955),- Chapters 1, II, III and IV. 48 A second "independent" variable in Shackle's model is called "potential surprise. " This represents the decision-maker's degree of belief in or distrust of a hypothesis. This registers the feeling of the individual, should the particular hypothesis be true. A third variable is a function of the two independent variables and measures the "degree of stimulus" from a combination of the "face value" of a hypothesis and the potential surprise associated with the hypothesis. Shackle's approach probably has only limited application with reSpect to farmers' hog production decisions. First of all, for many farmers the decision of whether to raise hogs or how many to raise is not completely unique but is based on personal experience or the experience of others whom they have observed. The situation is not entirely unique although some conditions (new technology in raising hogs, attractiveness of other enterprises, business outlook, etc.) involved in the decision may be new within the experiences of the entrepreneurs. Information Theory If a probability model of eXpectations using past prices is appro- priate for hog production, is there any theoretical basis for postulating what the parameters of the model should be? Alt, Fisher, Koyck, Nerlove and others using this model have made certain reasonable assumptions about the values of these parameters. Noteworthy, also in this regard, are some recent explorations of expectations based on certain concepts of communication or information theory.“ Using the terminology of this field, prices may be thought to 2“Listed below are some selected references on this subject: C. E. Shannon, "A Mathematical Theory of Communication, " Bell Sjstem Technical Journal, (1948). Norbert Wiener, Cybernetics (New York: John Wiley and Sons, Inc. 1948), pp. 74-112. 49 serve as signals which impart certain information to producers. In formulating expectations, the signals must first be received (actual prices must be known) and decoded. The signal is composed of information and noise. The problem of the receiver is .to separate out the information from the noise. Noise is considered a random element and an interference in the transmission of the signal. ' A change in price may not be'a message to change long-range'production plans if the change originated from- a random and temporary disturbance. Production and price are much more unstable on certain farm products than others. Year to year fluctuation in onion production and prices is much greater than on milk. Onion prices are more dependent on weather, a random element. This wOuld suggest that a given per- centage change in onion prices would likely impart less information about a basic long run (more than one year) adjustment in the level of onion. prices than the same percentage change in milk prices would about adjustments in the level of milk prices. If hog prices were completely random, we wouldexpect farmers to pay little attention to price in their production decisions. But annual hog prices are serially correlated. Cyclical patterns persist. Certain trends are in evidence. . Using information theory we would expect farmers to extract certain information from past hog prices but discount prices in any individual year because (of the "noise" component. (Continuation of footnote 24) David A. Grant, "Information Theory and'Discrimination of Sequences in stimulus Events, " Current Trends in Information Theory (Pittsburgh: University of Pittsburgh Press, 1953). CHAPTER IV HYPOTHESES Statement The task of this dissertation is concentrated on testing two hypotheses. The first hypothesis is that the response of hog production to price is in the form of distributed lags. The second hypothesisis that the endogenous mechanism of the hog market is cyclic and con- vergent. Hypothesis I Hog farmers, in the aggregate, base their price expectations mainly on prices at the time they make their production decision and take action. However, their expectations are conditioned by prices in previous years, with the most recent years being mo re dominant than earlier years. In other words, the prices farmers expect to receive for their hogs and pay for corn‘(or receive for corn) are functions of actual prices in the present and previous seasons. The prices in the present season are more important than those in the season before. The prices in the season before are more important than prices two years ago, etc. Mathematically, ' * I 0 O 0 where t is the year, Pt 18 the eXpected price in year t, Pt-i 18 the actual price in year t-i,‘ Ei is the weight given to year t-i, n is 50 51 the number of years influencing expectations, n .2 “Ei = 1, Bi > Ei+1 1 = o It is recognized that present and past prices arenot the only influences on farmers' expectations. The) general business climate is believed to effect price expectations, for example. The support program on cornrprobably narrowed the range of price expectation on corn in the late 1950's. It is argued in this dissertation, however, that present and past prices have been predominant factors in hog farmers' expectations during peacetime. Inaddition, it is believed that there is alag in the adjustment of production to expected prices which extends over more than one-year. Because fixed costs in hog production represent a relatively small preportion of the total costs, the-hog enterprise isflexible; entry into and exit from the hog industry is comparatively easy. The adjust- ment of production to a change in the expected price is assumed to be greater in the first year than in any succeeding year. Adjustments continue in succeeding years but at a declining rate. The distributed lag function for adjustment would be similar to that for expectations. That is, m * Qt-l-l = K + .2 Ai Pt‘i 1 = o where Qt+l is the supply in year t+l (assuming a technical lag of 1 year), - Pf-i is therprice expected in the long run in year t-i, k is a constant, Al is the coefficient of P:-i,' m is the number of years necessary to complete an adjustment, and A1 > A1+1 52 ' As explained in Chapter 111, if lags in expectation and adjustment both involve more than one year, neither the expectation function nor the adjustment function can be identified from time series data. The observed distributed lag of production reSponse to actual prices would be a combination of the expectation function and the adjustment function. This total reSponse function would be m n m,n Qt+1 = K + .2 A1 .2 (El Pt-i = K + 2 W1 Pt-i 1 : o 1 = l i = o where Qt+l is the supply in year t+l, Pt-i is the actual price in year t-i, W1 is the weight given to year t-i, n is the number of years influencing expectations, and m is the number of years influencing adjustments (one may involve more years than the other). The summation is over n or m years, whichever is the larger. It is also assumed that “'1 > W1+1 The hypothesis is, then, that the response of hog production to actual prices extends over more than one year and is distributed among the relevant years as is shown in the function above. Hypothesis II _The hog market has been used as a classic example of the Cobweb Theorem of Ezekiel's.l One assumption underlying this theorem is that farmers' production decisions are based on the eXpectation that the present hog price would continue through the following production period (which Ezekiel considered as two years). 1Mordecai Ezekiel, 2p. git. 53 This assumption would seem to be a Special case of a more general assumption. This general assumption is that the expected price is a positive function of present and past prices. This would include the case where the expected price was based on the present price only and, in addition, the case of distributed lags in Hypothesis 1. This generalization seems particularly important in explaining *Ezekiel's Case 111, the exploding model. ' Sucha case would occur, according to Ezekiel's assumption, in a market where the supply curve was more elastic than the demand curve. It seems quite probable that the supply reSponse curve for hogs based on expected prices could be elastic over, say, a two-year planning and production period. An inelastic demand curve for hogs at the farm is also quiteprobable as shown by previous studies. 7‘ Yet the possibility that the hog market is an "exploding" case seems quite remote. The difficulty lies in the assumption that farmers naively expect present prices to continue in an industry characterized by highly fluctuating prices. If farmers are reluctant to change their expectations to the same extent that actual prices change, the model could be con- vergent even though the supply curve for the production period may be more elastic than the demand curve. Nerlove demonstrates that as the coefficient of expectations decreases from 1 to 0, the probability of a diverging or exploding market declines.’ That is, a wider range in the ratio between the supply and the demand elasticities is admissible under the convergent model as B —> 0. Ezekiel assumes that, B = l. zKarl A. Fox, The Analysis of Demand for Farm Products, U.’ S.‘ Department of Agriculture Technical Bulletin No. 1081, (1953), . p- 46. 3Marc Nerlove, _op. gi_t_., pp. 55-59. 54 Ezekiel also assumed that adjustment of production to an initial price continues over a two-year period regardless of any change in price during the first year. At the end of two years, the adjustment is complete and the market re-evaluated in making production plans for the next two years. Under Hypothesis 1, the assumption was made that considerable adjustment could be made within a year in reSponse to an expected price. Adjustment to the initial expected price would not necessarily continue in the second year regardless of any change in expectations in the meantime, however. The second hypothesis is that the hog market has cyclical tendencies but would eventually converge to an equilibrium in the ' absence of external disturbances. This is based on the Cobweb Theorem as modified above. Methodology Two methods of estimating distributed lags were tried in testing Hypothesis 1. One was the traditional regression approach as used by Alt in which hog and corn prices were lagged one, two, and three years in successive equations. Hog production was used as the dependent variable. The signs on the coefficients and statistical properties of the equations were used as criteria in judging the validity of the distributed lag hypothesis. The second technique was the one prOposed by Nerlove. The estimates of the parameters in these equations along with the statistical preperties of the equations were comparediwith those of Alt's procedure. To test Hypothesis II and to ferret out the characteristics of the endogenous mechanism of the hog industry, "complete"imodels of the hog market were developed for the 1947-1958 period. Each model 55 included, in addition to a supply equation, a consumer demand equation, a marketing Ira rgin equation used to obtain the farm price of hogs, and equations linking sows farrowing in the Spring to pork production in the fall. Four of these "complete" models were constructed using four alternative supply equations. Each model was "reduced" to a difference equation by holding the exogenous variables constant. The solution of the difference equation yielded certain information about the dynamics of the hog market, including whether or not it was cyclic and whether or not it was convergent. Statistical Procedure Estimates of the parameters of the relationships investigated were obtained by the single equation least squares regression technique. Under certain assumptions, this procedure is formally equivalent to the maximum likelihood estimating procedure. The random disturbance is assumed to be normally distributed with mean O and a finite variance, and independent of the "independent" variables of the equation. This involves the assumption that there are no errors in the measurement of the independent variables nor simultaneous relationships among the endogenous variables. Maximum likelihood estimates have certain desirable properties 1 such as being "efficient" under certain Specified conditions, "consistent" in a wide variety of problems, "sufficient" if a "sufficient" estimator exists and "invariant. "‘ Least squares estimates in themselves require only that the disturbances are independently distributed in order to obtain the best, unbiased linear estimates of the parameters. “Lecture notes taken in a course given by Dr. Clifford Hildreth on "Estimating Economic Relationships in Agriculture, " Agricultural EconomicsDepartment, Michigan State University, East Lansing, Michigan, Spring 1957. 56 Several tests were conducted on the estimates, including the "t" test on the regression coefficients and the computation of the R values, the coefficients of correlation, to test the explanatory power of the equations. The Durbin—Watson and Von Neumann-Hart ratio tests were applied to the residuals to test for serial correlation. An-F test was conducted on the R2 values of successive equations under Alt's procedure to determine whether the addition of variables in the second equation explained significantly more of the variation in the dependent variable than did the first equation. The standard error of the estimate was also computed for each equation. CHAPTER V SUPPLY RESPONSE Background Time Periods The data used in this study extended over a 51-year period from 1908 to 1958. This period was punctuated by two major wars and a government control program on hogs. The 1908 to 1958 period was divided into three separate periods, 1908 to 1924, 1925 to 1941 and 1947 to 1958. The World War I (1918 and 1919) and World War II (1942 to 1946) periods were omitted because the structure of farmers' eXpectations was thought to have changed during wartime. The 1933-34 crop year was omitted because of the government's program to reduce hog numbers in that year. Before 1925, hog slaughter was used to indicate supply response. Since 1924, the United States Department of Agriculture has estimated the number of sows farrowing in the Spring and in the fall. The number of sows farrowing is a more accurate indication of year to year supply response than hog slaughter which is modified by weather and short term influences. For this reason, the number of sows farrowing was used since 1924. The pre-World War II and post-World War II periods were separated because the general economic climate changed and because the structure of the hog industry, both in production and marketing, underwent a transition not easily explained by a trend factor. The 1925-1941 period was an era of a declining general price level 57 58 and depression. The 1947-1958 period, on the otherhand, was characterized by inflation and rising per capita incomes. Adeption of new technology in agriculture was of revolutionary proportions. during World War II and in the succeeding years. Dissemination of outlook information has increased and the government's support program on feed grains has become more important since the pre-World'War 11 period. These changes would likely affect farmers' expectations and production response to these expectations. Variables Thevariables included in the supply re Sponse equations are defined and coded as follows: Spring Pig Crop F, t Sows farrowing in the Spring: Sows farrowing in the United“ States between December, t-l, and May, t; in thousands. ' Sh, t ‘ Slaughter of hogs from Spring pig crop: Total slaughter of hogs in the United States between October, t, and April t+1; in thousands. 1 Ph, t Price of hogs at breeding time for Springpig crop: . Average pricerper hundred weight of 200-220 pound barrows and gilts at Chicago between October, t, and January, t+1; in dollars. Pc, t Price of corn: Average price‘perbushel of No. 3 yellow corn at Chicago between October, t, and January, t+ 1; in dollars. Sg, t Free supply of feed grain other than corn: (a) 1908-1924: ‘lFor derivation, see APPENDIX C. -“ 59 Production of oats and barley, t, (b) 1925-1958: Stocks of oats and barley on July 1, t, (and sorghum grain stocks on October 1, t, between 1947 and 1957) not owned by the C. C. C.; plus production of oats, barley and sorghum grain in t; in thousands of tons. H:C, t = Ph,t-:- PC, t Hog: Corn' Ratio ‘Fd,t = F,t - F,t-l 'Shd,t = Sh,t - Sh,t~l Sgd,t = Sg,t - Sg,t-l ' Fall Pig Cr0p Ff, t 'Shf,t H:Cf, t .Ich, t ‘ Sows farrowing in the fall: Sows farrowing in the ‘United States between June, t, andNovembe r, t; in thousands. ‘ Slaughtervof hogs from fall pig cr0p: Total slaughter of hogs in the United States between May, t+1, and September, t+ 1; in thousands. Hog: corn ratio (modified) at breeding time for fall pig cr0p: (Average price per hundred weight of 200-220- pound barrows and gilts at Chicago between April, t, and June, t) -I-- (Average price per bushel of No. 3 yellow corn at Chicago between October, t-l, and January, t). Indicated free supply of corn and other feed grain: (a) 1908—1924: (Indicated production of corn in the United States, as of July 1, t, + actual production of oats and barley, t) -‘ (Actual production of corn, oats and barley, t-l); in thousands of tons. . (b) 1925-1958: ("Free" stocks of corn, oats, barley and sorghum grain at beginning of crop years, t, + indicated production 60 of corn, oats and barley on July 1, t, sorghum grain on August 1, t.) - ("Free" stocks of corn, oats, barley and sorghum grainz at beginning of crOp years, t-l, + Actual production, t-l). T Time in years: (a) 1908-1924: 1907 = l (b) 1925-1958: 1924 = 1 Selection of Variables United States total farrowings, slaughter data, and grain production data were employed. Corn and hog prices were based on Chicago quotations. Chicago prices of hogs and corn were used because Chicago is centrally located in the great surplus corn and hog area. The Chicago grain and livestock markets have historically been recognized as lead- ing markets and price quotations there have been widely publicized. The 200 to 220-pound weight bracket was selected because it is a price series representative of all butcher hogs and would be less affected by changing average weights of hogs slaughtered from year to year than an “average" hog price. Number 3 yellow corn was selected rather than an average farm price which is affected more by the changing quality of the cr0p from year to year. In the Spring pig crop equations, the hog and corn price variables were October to January averages. This particular period was selected for three main reasons. (1) The bulk of the previous Spring pig crop has been sold during these months. Therefore, the price of barrows and gilts during this period is representative of the returns on the 2Sorghum grain stocks available only for 1947 to 1958. 61 previous Spring pig crop. Hog farmers would presumably be particularly conscious of hog prices at that time. (2) During October to January, sows are bred to farrow in the following February to May, the important farrowing season. As late as January, the sows bred earlier in the fall and not yet "piggy" could be shipped to market without substantial discounts, if price expectations had dropped in the meantime. In other words, October to January is a critical period in which farmers would be conscious of the prices received for the previous Spring pig crop and also in which production decisions for the following Spring are made and carried through. (3) The October to January average corn price is representative of the fall corn crop and with normal seasonal adjustments would be a good indicator of prices of corn during the remainder of the crop year. With- in that cr0p year the Spring pig crop would be at least partly fed out. The finishing period would also include much of the following October to January period for pigs farrowed in March to May. For this reason, farms rs must anticipate corn production and/or corn prices in the October to January period of the following crop year. Although hog and corn prices were postulated as the predominant variables in guiding hog production, other variables are recognized as components of the hog supply model. However, the limited number of observations precluded the inclusion of all of these variables. These variables were tried in different combinations with hog and corn prices to determine their effect on supply of hogs. Only the supply of feed grains other than corn was selected as an additional variable in the supply equations for the spring pig crop. Theoretically, the prices on all variables which are substitutes for hogs in production or are inputs along with corn and other feed 62 grains determine the supply curve. Fat cattle are one such substitute. Cattle feeding operations are important in the Corn Belt states, the major hog feeding area. Cattle suitable for fattening on grain compete with hogs for the feed grain supply. - Profit in feeding cattle was there- fore introduced into the supply equation. The coefficients on this variable were not significant and the Sign in one of the periods investi- gated was inconsistent with theory. To account for costs other than corn in producing hogs, the index of prices paid by farmers for production items was tried but was not found to be significant nor to add to the explanation of the dependent variable. Because most of the corn fed to hogs is raised on the same farm as the hogs, corn supply was considered in addition to and in place of corn prices. This formulation did not improve on the use of corn prices alone, based on the coefficient of determination. As expectations of farmers would be affected by the general business climate, an attempt was made to account for this influence. A change in stock (corporation) prices during the previous year was tried to represent this element. Inconsistent signs on the coefficients of this variable were obtained in the two periods investigated. The co- efficients were alsoinsignificant under the null hypothesis. Several of the equations in which these variables were tried are presented in APPENDIX A. Form of the Variables The variables were all in arithmetic form. There was no a priori reason for putting the variables in the form of logarithms. ' Although such a form would Simplify computation of elasticities, this was not considered a major advantage in this study. 63 The hogzcorn price ratio has been commonly used in-predicting hog supplies, This does involve the rather restrictive assumption that ‘hog and “corn prices are of equal importance to farmers in their production decisions. Because hog prices would be thought to be somewhat more important than corn prices, hog prices and corn prices were used separately as well as in ratio form to test this possible difference. The variables F, t, Sh, t and Sg, t were used in the form of first differences and actual values as well. The first difference'(or, similarly, percentage change) of hog production from. year to year in response to price has been widely used in studying supply reSponseon hogS. An objection to putting the dependent variable in the first dif- ference form is that the coefficient of the dependent variable in the previous year (t-l) is assumed to be 1, possibly an unjustified restriction. ' Consider the equation, F,t = a0 + alF,t-1 + azH;C,t-1 ‘Assume an equilibrium at t = 0 with-F, t = F, t-l. If a1 = l, thenany increase in H:C,t-1 would generate a linear increaseinF, t which would continue without bound with the passage of time. F, t would decrease similarly if H:c, t-l was reduced. ' If 0 < a; < 1, any increase in H:C,t-1W0uld generate an increase in F, t but at a decreasing rate. F, t would approach an upper limit. Similarly, F,’t would decline at a decreasing rate to a lower'limit, if for some reason-H:C, t-l were to be reduced. Theoretically, the assumption that 0 < a, < l is more realistic. The management factor, feed supplies, availability‘of land, etc. would tend to put an upper limit on hog production by increasing marginal costs. The lower limit is zero—production. 64 Because the hog—corn ratio does not remain favorable or unfavor- able long enough for the extremes in production to be approached, the error in assuming a1 = 1, that is, using first differences, would not necessarily be a serious one. The primary purpose of this chapter is to test Hypothesis 1, that hog farmers reSpond not only to prices during the breeding season but also to prices in previous years, though to a lesser extent. Two methods were used, the traditional method as demonstrated by Alt and the technique suggested by Nerlove.3 Alt's procedure was tried in each of the three time periods using lagged values of the hog:corn ratio as independent variables and first differences of hog slaughter from the Spring pig crop (1908-1924) or first differences of sows farrowing in the Spring (1925-1941 and 1947- 1958) as the dependent variable. To check the possible error in assuming that hog and corn prices were of equal importance, as -iS the case when they are used in ratio form, hog and corn prices were also tried separately. Also, a check was made on the use of first differences by reformulating certain equations; putting the dependent variable in absolute values and using the dependent variable lagged one year as an independent variable. _ ‘ Elasticities of production to observed prices were calculated from the estimates of the regression coefficients. Three alternative Nerlove type models were then estimated for each of the three time periods. In the) first model, the hog:corn ratio was used and no restrictions were placed on the values of the coefficient of expectation and the coefficient of adjustment. Hog, and corn prices were tried separately in the second model, with the restriction that 3Refer to page 30 for Alt's method and to pages 34-39 for Nerlove's approach. 65 the coefficient of eXpectation on hog prices was equal to the co- efficient of expectation on corn prices. In the third model, hog and corn prices were also separate, but the expectation coefficients were not restricted to be equal. However, to estimate the separate expectation coefficients, the adjustment coefficient was restricted to equal one. The parameters and elasticities of the Nerlove model were calcu- lated from the regression equations. The equations for both the Alt and Nerlove models were estimated by the traditional least squares, single equation regression technique. In addition to the "t" tests on the coefficients and the computation of the coefficient of determination (and adjusted coefficient of determination) and the standard error of the estimate, the Durbin—Watson statistic was calculated from the residuals of each equation. The results of all the Durbin-Watson tests either indicated no serial correlation at the 5 percent level of confidence, or the test was inconclusive. The Von Neumann-Hart ratio test was also applied to these residuals and, in all cases no serial correlation was indicated at the 5 percent level. To simplify the discussion of the statistical results in the remainder of this chapter, references to the Durbin-Watson statistic presented in the tables will be omitted. Alt's Procedure As presented in CHAPTER III, the procedure which Alt suggested in accounting for distributed lags in supply reSponse was to fit successively equations with the price variable lagged one year; one and two years; one, two and three years; etc. until the coefficients ceased to make sense. The values of the coefficients over the relevant time period would indicate the distribution of the lagged response over time. 66 1908- 1924 Dependent Variable in First Differences With the dependent variable in first differences, the three equa- tions in TABLE 4 demonstrate Alt's procedure for 1908-1924. In Equation-(5. 1), the hog:corn ratio at breeding time was a highly signifi- cant indicator of year to year changes in hog slaughter from the spring pig crop. The Sign on the coefficient of Sgd, t-l was negative, contrary to the presumed relationship. However, the value of the coefficient was not significantly different from zero. - Equation (5. 2) is identical to Equation (5. 1) except that H:C, t—Z was added. The coefficients of H:C, t-l and H:C, t-2 were both signifi- cant, at the 1 and 5 percent levels reSpectively. ' As in (5. 1), the coefficient of Sgd, t-l was negative but insignificant. ‘ Equation‘(5. 2) eXplains a significant pr0portion of the unexplained variation in the dependent variable of Equation (5. 1) as indicated by F(T-kz- 1’ kz'kfl- The F statistic determines the significance of the difference between the R values of the two equations. The F statistic is described in APPENDIX B. The coefficient of H:C, t-l in‘Equation (5. 2) was larger and more significant than the coefficient of H:C, t-2, conforming to Hypothesis I. The inclusion of H:C, t-3 in'Equation (5. 3) added very little to the exPlanation of Shd, t over Equation (5. 2). In fact, R1 was actually less and S greater in (5. 3). The significance of the coefficient of H:C,t-l in (5. 3) was greater than in either (5. 1) or (5. 2). However, the coefficient of H:C, t-2 which was significant in (5. 2) became insignificant in (5.3). AS in (5.1) and in (5.2) the coefficient of Sgd, t-l was negative and insignificant. By inspection of the three equations in TABLE 4, there is reason to consider lags distributed over a two-year period as sufficient in 67 TABLE 4. Regressions of alternative hog supply equations, with dependent variable in first differences of hog slaughter, hog and corn prices as a ratio; 1908-1924. Item Equation ““ (5.1) (5.2) (5.3) IDependent Variable Shd,t Shd,t - Shd,t Constant -13984 -24018 -25430 Independent Variables Coefficients with t values in parenthesis PhCLt-l 1217.0 1155.1 .1766.7 (3.34)** (3.66)** (4.51)** PkCLt~s 862.8 20.0 (2. 26)* (. 05) H:C, t—3 369. 0 (.80) Sgd,t-1 —.2793 -.0246 -.4574 (1.43) (.12) u.56) R2 .49 .65 .65 E? .41 .56 .51 s 3713 3206 3363 1.75 1.75 1.82 5.09* 0 F0 (5.24) H:C*,t = {3 H:C,t-l + (1-8)H:C*,t-l O