" .vvlw: ECONOMETRIC ANALYSiS OF THE FEEDCRAIN LIVESTOCK ECONOMY Thesis for the beam of Ph. D. MCHIGAN STATE UNEVERSITY Michel Jean Pafif 196:4 THEQS L 113 K AR Y Michigan State ‘ University This is to certify that the thesis entitled ECONOMETRIC ANALYSIS OF THE FEED GRAIN LIVESTOCK ECONOMY presented by Michel Jean Petit has been accepted towards fulfillment of the requirements for _Eh.-.D_n_ degree ' in_Ag1:i.cnltural j Economics 1 v / . MajW‘fessor New 0-169 I I -' W -~~"u ‘ J eff-Fm“- k: I r: [jar-a ? 3 1“» I J rr-tflfl‘???” ’ U “Ali-'19 8 r4» - -' ‘9 1-. 3.!” L I B R A R Y Michigan State . - Univemi “2 t7 fie: ABSTRACT ECONOMETRIC ANALYSIS OF THE FEED GRAIN LIVESTOCK ECONOMY by Michel Jean Petit As part of a regional, broad research effort to esthmate the supply of feed grains, pork and beef, this thesis presents three econometric models of the feed-grain and livestock sectors of the U.S. economy, built on the basis of national, annual data for the 1929-1962 period. Each one of the independent models for feed grain, pork and beef production includes a production function and equations used to "predict" the amount of inputs used for a given product. For feed grains the three inputs taken into account are land, labor and fertilizer, it was found impossible to include machinery because of the lack of adequate data. For both hog and beef, the inputs taken into account are feed grains, high protein feeds and labor. Besides, several equations predict the numbers of various types of livestock kept in farms at the end of the year. The independent variables of the models are various expected prices, the industrial ‘wage rate, some input prices, and time. The quantity of feed grains available is considered as an exogenous variable in the livestock models . The expected prices used in this work were derived on the basis of information available at the time farmers make their decisions. Michel Jean Petit This work was performed by a fellow student as part of this doctoral thesis. The results of the study throw some light on the dynamics of supply of the three products as the recursiveness of the models reflects the chronological order of decisions. The mechanismus of resourse fixation in agriculture are crucial for the explanation of variations in the volume of supply in later years. In the model a shock to the system, e.g. an increase in expected prices for a product, results in a variation of the quantity produced during the same year and also of the quantity of durables resources, ‘mainly the breeding and feeding stocks kept in farms at the end of the year, which in turn leads to a new variation of the volume of supply in later years. Generally held ideas concerning the low elasticity of supply in the short run and the irreversibility of supply functions are confirmed. These phenomena may occur independently of the lag in the adjustment of expected prices to new market conditions since expected prices are taken as given in this study. ECONOMETRIC ANALYSIS OF THE FEED-GRAIN LIVESTOCK ECONOMY by Mithel Jean Petit A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Economics 1964 331 ACKNOWLEDGMENTS Among the many peOple who helped make this thesis possible, the author wishes to express particular gratitude to: Dr. Glenn L. Johnson, his major professor, whose guidance and inspiration were greatly appreciated throughout the author's doctorate studies, Dr. Robert Gustafson, who gave generously of his time for consul- tation and advice and who served as alternative major professor in Dr. Johnson's absences from the U.S.A. At various stages of the research program, the constructive criticisms and suggestions of Drs. D.E. Hathaway, C.F. Lard, J.N. Ferris, C. Hildreth, B. Pesek and of Mr. W. Ruble were greatly appre- ciated. Special thanks are due to persons who made the author's stay in the U.S. possible: MM. Bustaret and Bergmann of I.N.R.A. (France) and Dr. L. Boger, Chairman, Department of Agricultural Economics who provided financial assistance. The author thanks the clerical staff, and particularly Miss Marguerite Miller, for competent and diligent help in the computa- tional‘work. The author's thanks to his wife will be best expressed privately. Needless to say, the author assumes full responsibility for any errors in this dissertation. ii TABLE OF CONTENTS ACKNOWIEchfENTS O O O I O O O O O O O O O O O O O 0 LIST OF TABI-ES O O O O O O O O O O O O O O O O O 0 LIST OF ILLUSTRATIONS . . . . . . . . . . . . . . . Chapter I INIIIIRODI-ICI| ION O O O O O O O O O O O O O O 0 Place of Feed-Grain, Hog and Beef Production in American Agriculture . . . . . . . . . . . . Problems Facing the Feed-Grain-Livestock Sector . Need to Study Supply Response: The NC-54 Project Objectives of this Thesis . . . . . . . . . . . . Outline Of the Work 0 o o o o o o o 0 II METHODOLOGY . . . . . . . . . . . . . . . Features and Limitations of a Study Based on Time Series Data . . . . . . . . . . Changes in the Feed-Grain-Livestock Economy Since 1929 o o o o o o 0 Problems Raised by the Aggregation in This Study . . . . . . . . The MOdel o o o o o o e o o o o o 0 General Shape of the Model . . . . Price EXpectations . . . . . . Sources of Data - Problems Raised . . . Justification of the Time Period . . . Estimation Procedure . . . . . . . . . Recursiveness . . . . . . . . . Serial Correlation . . . . . . . . III FEED GRAIN PRODUCTION . . . . . . . . . . Economic Analysis . . . . . . . . . . Statistical Problems . . . . . . . . . Problems Due to the Data . . . . . Estimation Problems . . . . . . iii Implied Page ii vi vii \DNO‘tWN 10 11 12 15 20 20 22 25 27 28 29 33 35 35 37 37 40 Chapter Page RESUlts a o o o e e o e o o o o o o o o o o o o 46 Individual Equations . . . . . . . . . . . . 46 The Model as a Whole . . . . . . . . . . . . 58 Appraisal of the Model . . . . . . . . . . . . 63 COUClUSions o o o o o o o e o o o o o o o o o e 70 IV HOG PRODUCTION . . . . . e . . . . . . . . . . o . 78 Economic Analysis . . . . . . . . . . . . . . . . 78 Statistical Treatment . . . . . . . . . . . . . . 83 Problems Due to the Data . . . . . . . . . . 83 Estimation Problems . . . . . . . . . . . . 85 RESUItS o o o o e o o o o o o o o o o o o o o 92 Individual Equations . . . . . . . . . . . . 93 The MOdel as a WhOIE o o o o o o o o o o o 108 Appraisal Of the Madel o e o e e o o o o o o o o 117 PradiCtion Of 1963 RESU1t8 o e o c o o o o o 118 1948-1962 "Predictions" . . . . . . . . . 120 Residuals of Some Individual Equations . . . 126 Summary Remarks . . . . . . . . . . . . . . 128 Gone luSions C O O O O O O O O O O O O O I O O O 129 V BEEF PRODUCTION o o 0‘. o o o o o o o o o o o o o o 135 Economic Analysis . . . . . . . . . . . . . . . . 135 Statistical Problems . . . . . . . . . . . . . . 139 Problems Due to the Data . . . . . . . . . . 139 Estimation Problems . . . . . . . . . . . . 142 Results 0 o o o o e o e e o o e o o e o o o o o 149 Individual Equations 0 e o o o o o o e o o o 149 The “Odel as a WhOIC o o e o o o o o o o o o 174 Appraisal Of the MOdel o e o o o o o o o o o o 183 Prediction Of 1963 RESUIC; o o o o o o o o o 184 1949- 1962 "Predictions" . . . . . . . . 186 Residuals of Individual Equations . . . . . 189 Summary Remarks . . . . . . . . . . . . . . 197 Conclusions . . . . . . . . . . . . . . . . . . 197 VI SUMMARY AND CONCLUSIONS . . . . . . . . . . . . . . . 201 Appraisal of the Results . . . . . . . . . . . . 201 Commitment of Resources . . . . . . . . . . 201 Volume of Sopply . . . . . . . . . . . . . 207 iv Chapter Page VI (Contd.) Appraisal of the Research Method . . . . . . . . 213 Features of the Research Method Used . . . 214 Main Shortcomings of the Models . . . . . 215 Future Research . . . . . . . . . . . . . 216 APPENDIX C O O O O O O O O O O O O O O O O O O O O O O O 218/19 B IBLIOGRAPHY O O C O O O O O O O O O O O O O O O O O O O O O 220 I Ill-I'll (\l‘tlll‘l‘ll‘t 1' (ll 10. 11. 12. 14. LIST OF TABLES Variables Of the FCCd-Grain MOdel o o o e o o o o o 0 Equations of the Feed-Grain Model . . . . . . . . . . Feed-Grain Model. Alternative Estimates of the Coefficients . . . . . . . . . . . . . . . . Variables Of the Hog Medel o o o o o o o o o o o e 0 Equations of the Hog Model . . . . . . . . . . . . . Hog Model. Ordinary Least Square Estimate of the Linear Form C O O O O O O O O O O O O O O O O O Hog Model. Ordinary Least Square Estimate of the Logarithmic Form 0 O O O O I I O O O O O O O 0 Compared Input Elasticities of Output. Hog Model ... Percentage Increases of Several Variables Relative to their Level in Year t-l, Following a 1% Increase in Expected Prices of Hogs at the Beginning of year t O O O O O O O O O O O O O O O O O O O O O O 0 Absolute and Percentage Increases in Various Variables Following an Increase of 1 Million Tons in the Quantity of Feed Grains Available in year t. Hog MOde 1 o C O o O O O O O O o e O O I O O O O O O O 0 Variables of the Beef Model . . . . . . . .. . . . . Equations of the Beef Model . . . . . . . . . . . . . Alternative Estimates of the Coefficients. Beef MOdel O O O O O O O O O O O O O O O O O O O O O 0 Comparison of the Predicted and Actual Values of the Various Numbers of Beef Cattle. 1963 . . . . vi Page 43 44 45 88 89 9O 91 105 110 116 145 146 147/148 185 6. 10. 11. LIST OF ILLUSTRATIONS Page Residuals of the Ordinary Least Square Linear Equations for Land Used in Feed-Grain Production . . 62 Residuals of the Ordinary Least Square Equation for Fertilizer Used in Feed Grain Production . . . . . . 65 Residuals of the Feed-Grain Linear Production Function and Expected Price for Corn Deflated by the Index of Prices Paid by Farmers . . . . . . . . . . . . . 67 Expected Price for Corn Deflated by the Index of Prices Paid by Farmers and Manufacturers' Shipments of Grain Combines, Corn and Cotton Planters, and Corn Pickers. U.S. 1950-1962 . . . . . . . . . . . 74 Actual and "1948-1962 Predicted" Values of the Numbers of Saws Farrowing in the Spring, of Sows Farrowing in the Fall and of Sows at the End of the Year . . . 122 Actual and "1948-1962 Predicted" Values of the Number of Male Hogs over 6 Months 01d at the End of the Year and of the Annual Volume of Hog Production . . 123 Residuals of the Linear Equation Giving the Number of Saws at the End of the Year . . . . . . . . . . . 125 Residuals of the Linear Equation Giving the Quantities of Feed Grains, High-Protein Feeds and Labor Used in Hog Production . . . . . . . . . . . . . . . . . 127 Actual and "1949-1962 Predicted" Values of the Numbers of Calves Born, of Calves Slaughtered, of Calves Raised and of Calves on Farms at the End of the Year 0 O O O O O O O O O O O O O O O O O O O O O O O 187 Actual and "1949-1962 Predicted" Values of the Volume of Beef Production and of the Number of Cows, of Steers and of Heifers on Farms at the End of the Year 0 O O O O O O O O O O .0 O O O O O O O O O O O O 188 Residuals of the Linear Equations Giving the Numbers of Calves Born, of Calves Raised and of Calves Slaughtered O O O O O O O O O O O O O O O O O O O O 190 vii Figure Page 12 Residuals of the Linear Equations Giving the Number of Heifers on Farms at the End of the Year and the Change in the Number of Steers . . . . . . . . . 193 13. Residuals of the Equation Giving the Change in the Number of Cows on Farms at the End of the Year . . . 195 14. Residuals of the Linear Beef Production Function .. . 196 viii CHAPTER I TNTRODVCTION Since prehistoric times, meat and meat animals have played a r? he major role in human civilization. There are plentiful remains of Neolithic age proving early domestication of cattle; even a superficin reading of the Bible indicates this importance in the remote post. At the present time, the role of red most in the diet hardly needs to he emphasised. In rich countries, it is on important source of proteins. The consumption of meat products per capita vorics v.ry much between countries. An increase of meat production in many countries could be a factor of deve10pment, the lack of sufficient proteins certainly being one of the serious problems facing the so-cnlled underdeveloped countries where two thirds of mankind live and often suffer from hunger. This is not the place to analyze the numerous obstacles to an expansion and a better distribution of meat production in the world. More modestly, it is hOped that this study, as well as any study of the economics of livestock production, will contribute to a better understanding of the economic forces and limitations underlying the production of meat. Such an understanding seems much needed since, obviously, it is not possible to remedy a situation considered unsatis- factorv unless it is understood. This thesis deals with only hog and beef production, the two major sources of red meat in the U.S. At the same time, it has been deemed necessary to include the production of feed grains in this study because, in the U.S. as well as in most industrialized countries, meat .(I'l‘ .[ ‘ ..V.[|‘l|||l\'l\ production is hichly dependent on feed grains. Pl"C€ 0f popa_crgip non npd Rho? prodncrjnfi_ _-— -.n- - - --..-- __ .—-~ - -.- _._.__. ————~——-__.—. in American Aerinulenrp Sales of beef and pork provided about ?0 percent of cash receipts h" U.9. farmers in 1967. This is the larcest sin"le sector . . \c V in American acriculture. Many termers are encased in at least one of these livestock enterprises and very otten in both. Besides these, the numerous farmers specialising in Feed—prcin production should not be forgotten when one tries to appraise the importance 0? this sector. Thus, it seems safe to assert that feed-crain-liyestock production is the most important sector o? American agriculture. Over the last three decades, the relotive importance 0? hops and beef cattle has increased from around 25 percent to 30 percent of all sales by farmers. The most sijni‘icant increase has taken place in the production of beef cattle vhich represented hetveen lq and 15 percent of all cash receipts in the mid thirties and has represented around 21 percent 0‘ cash receipts for the lest Few years. The share of hefs increased until the early lofin's hut has been declining since then. Most authors, such as ".P. Preimver 1 believe that this relen 2 tive evolution of hee‘f end pork is due to shitts in the demand pattern for meat. This e"olution ‘or heeF would appear more dramatic yet it the value of dairy cows slaughtered had been subtracted from these figures since there is strong indication that their numbers have lqu. Rrpimwor, Dnmnfid epd Pripn F0? "055, WOQ.U.A. wncpnicql Rulletin No. 175?, 1961, Annrnoqnd or, or fight, romoipnfl onnqropto TO: nknula hp 010“? T‘fiYJ flea“. f-‘~-v'_n aha-“ny- (‘5 nrr‘rJHr-gh-inrs {(3 important heceuse o? the volume o‘ sales it ir"ol"“", “‘4 also honnvon v V .. . . -. . . . . _. - ..- . . ‘ ... gnat“ra n: b—L-{q oppO-r‘v 1.0 {kn “”1“ ’15 q oqcnI-‘v Vvfl1wvn CA? (\"flOOQ r.vvj-:-q v production durin" the last decades end mottl" sirce the end ot the p second "orld "at. The production o‘ meat, perticulerl" oF hee‘, hes ineressed tremendousl" over the last q0 years. The relatively high elasticities of demand for meat, with respect to income and to price, have permi— tted this large increase in production vithout drastic price declines. Many crops have been tuhmitted to various control programs; as a result ...... devoted to feed—grain and livestock production. Some observers ouestion the ahilitu of this sector to continue ahsorhine this eycess k.) capaCity.' Problems Facing the Feed—"rein~li"estoch Qector - _ --..._-.V.—a-_..-—._~.—_—_- -...-_. - .-.--.-.- .—_. ..— -—_._.__..——--__ __--_... - - - - J.“ (l) The existence 0‘ larte Feed—"rein surpluses tends to indicate some degree of unsatisfactory pertormepce in the feedngrain— livestock sector of the economy. Some of the resources committed to 2More rigorously, by relatively high elastiCIties, we mean that the demand for meat is less inelastic than that for most other agricultural products. Yet it is smaller than 1. 3See J.P. Gavin, "The Present Feed-Livestock Qituation" in 8) Proceedings of the Iowa State Collece Food Livestock morkshop, Am Feh. 1959 or O.B. Jesness, "Agricultural Adiustment in the Past 2 Years", J32, A0, pp. 255—64, May 1953. p 5 5 these orooucts could hove heen use” more orocuctively elsewhere. Since the mic—thirties , the stochs at the end of the cron year have heen increasing and, in recent years have reecheri very hi h levels. : C In 1961, the stock at the hoginnirg of the year was sore than 50 per cent of the annual yrocuction of feed grains. These surpluses have accumulated heceuso the oroouction o? meat, even though it is free from production control progrars, has not increased as rapidly as the production of Feed grains. This discrepancy in rates of growth is partly due to the existence of price sunnorts on ‘oed grains. This may not he a had thing for livestock producers since lower prices of feed would lead farmers to use more of it and thus to increase the live— stock output in such a manner that lower yrices of meat would resu t. Whether this would lower their net income would he prohlematicol. (2) Another important orohlem of the livestock sector is its instahility. There are good reasons to helieve that the cyclicel fluctuations ohserved in the amount of meat proeuced and/or consunefl each year do not corresyond to parallel shifts in apman, since it appears reasonahle to helieve that large changes in cewonfl occur in a progressive and more or less continuous wanner, cue recount being taken of income cycles. Thus, it is not surprisine that the earliest explanations of the so—called cattle and hog cycles were already based on conditions of supply. The usually accepted crplenntion of these cycles is hased on the cohweh model more or less motified to relax the heroic assumption that ferwers exoect current prices to remain constant even though they vary constantly. Though in some reSpects this eXplanation may appear fairly satisfactory, it has the A, shortcoming of not suggesting an effective way to dampen these cycles. Most agricultural economists would agree that a clear under— standing of the forces which produce cattle and hog cycles requires a better knowledge of how farmers formulate price evpectations and adjust to these expectations. It is hoped that this thesis will help clarify our ideas slightly on the latter point. (1) Changes in beef and pork production are not all of a cyclical nature. A trend can be seen in changes in technology and Specialization for livestock. This may have several effects: (a) A shift in the regional pattern of production may take place as it did in the case of hroiler production hecause of increased specialization mode possihle hv the availahility of new technologies. (h) A concen- tration of production units has taken place and will prohahly continue. (c) The substitution of capital For lahor has heen important; however, there is very little evidence permitting us to predict how far this substitution will 30. (d) At the present time, more than 50 percent of the feed grains produced are fed to livestock on the farms where produced. Forces pushing to enterprise Specialization may be such that two categories of producers will develop: one highly Specialized in feed—grain production, the other in livestock. Here again, very little evidence is availahle to help predict the future of this trend. (e) As production techniques hecame more standardized, vertical inte— gration develOped quickly and extensively in hroiler production. Other hYet explanations of this type appeared as early as the 1920's. See for instance: S. Wright, Eflfpniflf_flflfl_£9333lfEISCEJ U.S.A. Bulletin 1300, 60 pp., 1925. or C.C. Haas and Mordecai Ezekiel, Factorsmflfifcting_the_ Price of Hogs, U.S.D.A. Bulletin IAAO, 68 pp., 1976. ...? il‘ l .l ‘7‘ A ‘sctors were also innortsnt in this develonrent. Th“°, there are 90mm numerinfc on *0 Lqra T“"(‘“ wvnrr‘inn'l w'r‘ro'rrpr‘ior‘ own now pv-nnnr __- ,n.i_i _r .. . _ _ .H . it, _ i. .g .u - H, i . L in 1‘” “0"" productian C(37- 4gckqwnp ‘ir‘ Plan «A‘rf- {Torn ~~nnrn. ..--.. i 4_ . _ ... . _‘ .... i . ’ v g- . I- ., u - RYnnf] kn CFC-r1" C"T‘T‘1" pfifif‘nwfin: Tiar‘ \‘P :/J Dvn:nn‘— -....._— -._~-_ ...-- --. - .----- ..-. ....n.- __ ._’-_._. ..----_- -.- - _. -.- - .- -.-__-.~-_. .- - E‘s-hm “Ln-n1 $.51“; vn---;nv~ (-‘C FLA “ynl-lamc Cnnfl'w" Flap. cf‘fiA _r~vn4~\ liwvnornplr onnhr‘v AC O-kn nfinwnm“ 4*- nknvar‘ Rn fififi"1"fi*‘" nnvw tho“ 6 . . ._' ..‘_.~ ‘r ‘ ‘ ._ .. ~ V V , .. . ..— . . . . . . i. ' _- . nlpdvpr vyrrlnv‘nfi-nwrlw'wr» 0C fins-Aha vwvernv-Il'wi-n'r F‘"*‘fi1" «'rfi rbnrqfirq. T“_'Jp¢3f‘, - \—r in the U.9., the evolution "rd le"ol c? donatd for went prod"cts seem I‘Q"mf11 f‘fir'? pflrlfnf‘ffe“ n‘ofiwrolln o-V-rs vpnnnrnLI'v' ntcinionk; “Isnvntnrn, 4‘- I; v .A‘ ._i at. ‘4. ‘.~.J---.4.«-:-._ u; a - A- — -~._. seems logical to helieve that most malad‘ustment prohlens stew iron U the production side ot the warhet. Accordingly a regiorol research project has heen developed ir the North Central states ertitled "Qupply Deepense and Adjustment for "o: and Rec? Cattle Production." (Hereafter referred to as NC—SA). r"he relevance of this project in the North Central region is clear from the following figures:5 in 196? the North Central states produced 14.6 hillion lhs. of beef (i.e., A87 of the U.9. production) 16.5 Lilllfif lhs 3 81% of the U.S. production), and 107.7 million tons of feed grain (i. 8., 75% of the U.S. production). These livestock enterprises hrought 45% of the cash receipts hy farmers in this region. This thesis is a small part of the Michigan contrihutior to this regional proiect. NC—SA involves several approaches to the studv 5Computed from U.S.D.A. Statistical Bulletins No. 333 (July 1963) and No. 159, Supplement For 1962 (July 1963). of supply response one of which is time series anal"sis which is employed herein. The main core of the work heing done in NC-54 is \l.\.- .I linear progremmetion analysis of typical ferns. In Michigan, the data collected to set up the linear pronremmine prohlem hove also heen used to mehe a cross section functional analysis. Depresenting another approach, this thesis is an attempt to answer some of the questions developed earlier, from information availehle in time series data. It must he considered as one part of a team effort. Though H. some valid conclns ons can he drawn directly from it, it will only take its full significance when the various approaches can he compared and when each approach can contribute its share to the final evalua— tion and the formulation of comprehensive "factual judgements" concer— ning the whole prohlem dealt with in this re ioral project. Ohiectivcs of this Thesis The NC—Sh project statement mentions the following ohjectives:6 (3) Estimate farm resource use and supply response of hogs and beef. (h) Estimate total production of hogs and heef and patterns Of resource use for the nation.7 More precisely, the main ohje-t2ve of this thesis is to study 6Regional Research Project Statement NC—Sfl (Revised Angust 18, 1961) (Mimeo), p. 10. 7The third ohjective (to determine the Optimal production methods and location) cannot he fulfilled with this approach. 1‘ the structural relitionships underl"ing the production of hogs and heef. Tn most Ltudies puhlished to date, the economic forces underlying pro— .- -A duction are summarized in a supply function. The disadvantage of this o s '3 recedure is to p"t too much emphasis on price as a strategic veriehle. In this work, we nfitomnt to push the analysis further and to appraise the influence of different veriehles and the way these veriehles play their role. wollor'irg recommendations made hf several authors, and parti— cularly G.L. .Tohnsop,8 we have attempted to estimate the influence of the amount of resources flowing into agriculture, or remaining in agriculture, on the output of feed grains heef and pork. At the 3 same time, one of the ohiectives of this thesis is to determine the factors erplaining the amount of resources used in the production of feed grains and livestock and to estimate the influence of these factors. As the second ohjective indicates, it is hoped that the 'results of this thesis can he used to predict the amoun- of heef ‘find pork produced. However, the main ohjective of the model used is not predictive; we have been more interested in trying to under- stand the influences of economic forces underlying production. This is why we have not huilt a complete model of the meat markets; in View of the present knowledge, it has heen deemed more profitable to devote our limited resources to a deeper study of production 8G.L. Johnson, "The State of Agricultural Supply Analysis", JFE, Vol. 42, No. 2, May 1960, p. 457. phenomena rather than to huild a complete, hut more superficial, model involving consumption as well as the production of meat products. Outline oF the Work —.——. -..— Atter this introductory chapter, the nevt chapter is devoted to a discussion of the research methods used and ot the major prohlems raised hy these methods. Chapters ITI, IV and V present econometric models for the production of Feed erains, hoes end heet respectively. In each of these, the economic analysis underlying the model is first discussed. Then the statistical prohlems are reviewed. Finally, empirical results are presented and appraised. The lest chapter is devoted to a summary of the results and to the conclusions which can he drawn from this thesis regardine: (l) the feed—grain livestock economy, and (2) the research methods. CHAPTFR II MFTHOUOLOCY As indicated in the previous chapter, this thesis deals with the production problems of the feed—train livestock sector of the North Central States aericultural economy. We want to use the most appropriate methods of investieation hut we are not interested in the methods as such. In Pipou's terms; we are tool users and not tool makers.1 For most prohlems the researcher or, often, a research team must resort to an arrav of complementary tools. The hrief presenta— tion of the regional project “0-54 made in our introduction illustra- ted the diversitv of methods often reouired to solve an important problem. As was mentioned earlier, linear programming, function ana Ml: Hi and time series will he called upon to identify, measure and predict the consequences of chaneinc economic forces underlying feed—grain, beef and hoe production. Quch utilization of various methods in a research project permits division of lahor and a Specialization amone the various parti c.pants. More importantly, it permits researches to examine results from different methods with their different inevitahle shortcomings before reaching overall 1A.C. Pi7ou, "The Function of Economic Analvsi.s, " Sidfipv Ball Lecture, 1979, reprinted in Fconomic Fssazs and Addres°e°, p. 3 as quoted by J. Robinson, The Fconom10° of Imperfect (*"Porit‘on, McMillan, 1951 edit., p. V. 10 ll Pnntnrno "73 Timihnhinnc O: n thflv '-->----—-‘-‘-- ..---. u s—- - . r —-.-- .-- - v - - 0,. RfiflflA nfi Timn Qnrino nntn ._-._ ._ _._—...-_.....-_-’-.-.-_-----.-_.__- --- Who ”Fifi Hividinp lino {onlotimo nur puhmrninot from other swhprndootc of NP-§A ic one of roonoroh mothnfl. To "in" 0F rhp onmmlo_ mnptpritr hnfhnon rocporeh tnnle "hinh "no momtinmofl shown is 3t justifiahle to attempt to answer so many important questions through a study hosed entirely on time serinq Hero? The pvicrppoe of this thesis indicates a conviction that this approach, along with other ones, can contrihute siorifieantly to a hotter understandino of the Twrnlolnmg mofhinfaord “Raina. (Ni- non-rota, ran r10 fen“ Fnlinvn f‘t‘fi‘f Plait: approach will provide complete solution". However, a study hased on time series data car he pursued without eallin: formally upon other ”P?*°“F“°9 at” there is no douht that some irfo*”"“"“, “ale"art to the prohlems at hand, is contained in the annual data which rearlt ,crom kkp ban knhovinr n? Fpoflmproim, ha? end hoof h*03"finfc. TF9 results of this worh should he helpful in derivinf the final esti~ mates, and they should contrihute to the formulation of the conclu— sions of the whole project. It is in that final sta:e of the research worh that the complementarity hetwoen the various methods will he most ohvious. As was said earlier, the approach used in this worh is hpsumr; on time series date. whouah lora discussioa 0‘ *ha 94?9?f“”“° ”fi" .. - tr .H._U i_ .i _. . t. V _ ‘\ disadvantases of time series nnalvsis is done hetter h" econometrfii cians, some discussion of the method is necessary to help appraise; results and to compare them with those ohtaiped hv other methods- One of the basic assumptions of an" time series studv is J I“ I‘D ‘ L , ‘ Q t, 1‘. .. r ‘ . . 7 J . » . . ~ « I " ' ‘ ‘ v - ‘ . A . . , ..- O u ’ V .. - - . é . ’ -‘ ‘ * ' ' A .. , . . .4. . . 21'. ,‘ u ‘ a — J-A . .A ‘. ‘50- c . . ‘ ~ . ~ , . . V ‘ . 7 > .. - ... V . A . ‘ -_ 0 v —« x \ that significant relationships anon: rariahles have not charged over the period of analysis and that, thereiore, time series data can he used as observations in the statistical estimation of the parameters of those relationshins. When apparent chances in relationships among variables are due to chances in still other variahles, the situation can he tandled by the ernlicit introduction o? the other variahles into the system. povever, it as ditticult to formulate models comnlete enough to handle all factors involved in these relationships. This is clear when one considers the drastic changes undergone hy the feed— grain-liverstock economy over the last '20 years. A rapid review of these charges may be useful here: Cheeses in the Feed—Crain—livestoch Economy Qince 1979 One of th (1’ - W08 1 ohvious changes which took place in the production of feed—grains and meat products is the large increase in the productivity of labor. Between 1999 and 1°62 the .J J ’1. o ‘ < 0 re farm production nor nan-hour (Base 100 in 1957—59), increased from 73 to 114 for meat animals and from 19 to 158 for feed-grains." This increase in the nroductivity of lahor was due to a large nunber of factors.3 One of the most important among these was an extensive 2Chanees in Farm Production and FftiCiencv, USDA Stat. “—-~.. Bulletin No. 233, revised Septemher 1962 and July 1963. _ ..--....... —-—- —-—-o- 3 . . . . See for instance: R.A. Loomis and C.T. Barton, Produc53v1ty ofi_5;riculture - United States, 1870—1958, U.S. Dept. of Agri. Tech. —-—.- —...—- Bul. No. 1238, 1961, p. 6?. 1'2 suhstitM ion of capital for lahor. A priori, such a chanee should not lead the researcher usine time series data to worry too such. According to the economic theory of production, a suhstitution hetween inputs can he due to A chance in relative prices oi these inputs and does not necessarily indicate a shift in the production function. But there are other indieotions that the cause oF this suhsti- tution involves chances in other variahles correlated with time. The or hlen bPCOW“° 0““ OF measurine the influence oi these other vario— bles.A In general the prohlem is not easy. In their pion M wort Hildreth and Jerrett write: "The use oF tine as a variahle in the production relation nay pronerly cause sone uneasiness. At host, time is a vague representation of various influences whose net effect during the period of ohservation has heen a fairly steady increase in the efficiency with which feed is converted into livestock products."5 In the form discussed in these sentences, their production function included only the numher of animals on hand, feed and tire es indepen— dent variahles. This is why thev speak spec ific all_ of an increase in feeding efficiency. Purely, all the results of chances which have occurred cannot he neasured as increases in feeding efticiency; clearly this does not do for changes in the production of feed-frainS. Even for the production of livestock one vmy choose other criteria AGlenn L. Johnson, "A Note on Non-conventional Inputs and Conventional Production Functions," Aeri_culture in Fcopom4c Develop- menL, Eds. C.K. Eicher and TH”. Witt, McPraw—"ill Inc., New York, ..--.. 196A pp. 120 f. SC .H. Hildreth and F .G. Tarrett, A Statistical Study of Livestock Production and Varhetine, Cowles Commission Monograph No. 15, -~—.~~ ...__. - ...___—'..._ John Wiley and Sons, New York, 195h, p. 11. 1A (e.g., lahor efticiency as in the preceding nose). Nevertheless, the quoted parajraph hv Pildreth and Jarrett indicates clearlv the problems raised hv the use of time to take these chances into account. 1 As some authors have pointed out "time' is another "name for ionoran- " Various methods have heen devised to alleviate these nrohlems. ce. This is not the place to discuss these methods systematically. In several instances we have used "dummy variahles" to take into account sudden changes such as the introduction of antihiotics. Such a treat— ment is not wholly satistactorv hecause the effect of the introduction of antibiotics has been prosressive over several veers. However, in view of the limited availahility ot data, this procedure is otten superior to omission. Other shifters ot the production function are reflected in Our equations throush the time variahle. They include improvement in feedine practices, hreed improvements, better sanitary conditions, change in the relative importance of various hreeds (e.n., introduc— tion of Rrahman blood in the south to increase the resistance to diseases), improvement in manofement, regional specialization, etc. From conversation with beef cattle specialists, it is also our impression that important chances in the techniques of handling cattle in the ranch area have taken place. These changes not only intluence production Functions hut also the other relations in the heet and hog economies. These relations involve decisions taken in the conduct of the livestock enterprises about the use of inputs. A simple example can illustrate this point: v.’ 1!..I‘ ‘ I I .‘lll‘r.lslnlln\l|||lll.l¢l[ .l O 1? the cmovnt of hiehnnrotein teed ted to heef cattle for siren expected prices depends on the "en“r°l °wnrenees hv farmers of the protitnhiw litv of foedine such teeds and also on the respnsiveness o‘ nettle dsins to these teedin“". There is no deuht that these two Factors s.— are important, however, we have handled them throueh the use o‘ t4mn «l-I‘n nmn'qnf-q nC {nhvshfl synfirJ I‘n-vn 0L44FO-nrl sywr‘nv‘ Fish {nc1svrsfinn n: pianos] fif‘f‘l i? tinn “‘V‘aniifj+";nfi cw‘Y-«(jk'gnao (\c fimhn*;nqw “rnflyva-fl fivwr‘ 0“: #kn {fin'1O-q f’kf‘mfihl‘."‘<‘ From this section, it should he elesr that we are tullv gunro of chnpeos not fiAOFHptpl” tobnm into onnonnt hv our novticnlnr V . '1 . i. - _. . . -_ , .-. t V . Thor‘pl. T159 gituiflfinn’ isnYflnVVpr, ;" 7:04- hc Far: 6p nnnqiklvr imn1inr1 .00 A J a for t'or it will prove possihle to predict and understend important V 0 however, other ct““”“", "hich have not heen mentioned in this Cgpk-{nn kavv'iv-‘rv J—n An 7.14 0-1‘ flan *nfinvnhkw'n fi““"nrh (‘4‘: nrnAvch-{nn’ o-lsn —. I. - s ...-v ... g. . l.. t . V E L .-V .i‘ K ‘ --‘V .V . ~‘ ‘1‘ K A. ‘nroduction of leaner hoe? or the diminution in the seasonalit" of v “raggspk-‘f‘fi nyr‘ c4nP4FJnAV-b '57"; (gnafiO-44-‘qJ-A 5“,.»1-(‘7- 1qmqhnbn‘nwfl nc t-‘sr‘ L . . .- .- s- - A - ..U. ......4 . _. A. s... - i..,. . -._ . g. . .7 . 7., ‘hroeedure used. These st'recetion nrohlems ere discussed in the \‘J .4 following section Prohlems Raised h" the Ae~reeeting TmnTioH .1 "~./ t_' "‘ ‘ "" in This Qtud" An" model as a simpli‘ied representation 0‘ reel phenomena, {mnliqq gomn Hnnvnn 05 nonvnnohin«.6 Tn ppnnnmntvino, tho chnvhoon 0‘ . " u” “ vu' « H“” " "h“ '“”' “ ‘ “‘ ‘ - “ 5 . . Rwy nflfivnflflFflOV“ v.70 mnlnfi Lynn-n f-‘ap hwypvnn-snrv «kn pan ~101~n1 . J . ”V .L ...—— L. \ -- L' a»- 5L 1-x .- -- ... \ ..b,.. V ~ - . . Q" .- relation of a large nvmhcr of relations vhich are not reall" identical. 1+" Hfif? “"d +kC lee“ Dc Pnn?nfirifi*fi 0*“tifltin61 antimo*4nw nvnnnflurnq ' 4o- o—L «C 'k A r» 3 ‘ r» r 4-' 'n ‘ 11W_US -se Hess: le e ree o, dice T*° “iron. In interpretirf V \— results, the aseresation simplifications should not he overloohed. Va ._ T's «9th o chm/1v “ten one-vnooh-in“ tnlvnr: “I‘r‘hn in rope-inne- .... A.-. .. ' I ’ .. ' - 4“ - . s H .- --- 'v». \ .. .‘ v- -4 w dimensions: tin“, 9n“C°, C’fi°"°*" 0; “Ina"Pnrqa Cfitpénrinq 0F livestotb, Ptc. A short discussion oc these "c“re"etiots will he the suhiect of the last pernorephs of this section 1. Ahfivonpfinfi {fi ofinnn _. .HJIL. _._.---—...__. -—... -... -.-—"A..- .. __ The production of fecdmcreirs, hoes and heef is for from hein" homoecneousl" distrihuted over the entire area of the continen- tal U.S. end theheoerephicsl pattern of production has chanced sicni~ ficantlr over the last 90 veers.7 however, our model dealing with U.S. totals (A8 states) does not tehe this geographical redistrihu— tion into account. Specification mistakes may he introduced since s0me ohserved variation in one of the variehles studied may he associated with a change in the geographical pattern of production which also influences our dependent veriahles. Aggregation in Space further limits us in that it does not permit analysis of some of the very significant prohlems mentioned in our introduction, mainly those concerned with shifts in the geogra— phical pattern of production (area specialization, development of production in the Covth, etc.). It has hecn necessary to limit the ...; 7See for instance, 9.9. Fowler, The Marketin; of livestock and Meat, Danville, Illinois, Interstate Printers and Puhlishers, Inc., 1957, p. 33. scope of our research; nevertheless, it shovld he remomhered that time series enalvsis does rot permit us to dccl eesilv with problems of inter-recional competition such as those stvdied tv Fox,8 Judee and Wallace9 or ueedy and Fehert}0 2 Aeereeetion in time . _ar..-..'_.'..h-_ ...... .' ___.. H .44.... The ohservstions need to estimate the veriovs coefficients are on an annual basis. Thus, the deta used do not pernit acconnt to he taten of seasonal phenonecc. Our resvlts covld he hissed because variations in dependent voriehles dve to chances in the seasonal pattern of production might be attributed to some other factors. de Graft has pointed out thet the seasonelity of produc— tion has chanced durinc the past three decades.11 The flow of products is much more even over the nonths even though the produc— tion of hogs, for instance, still shows wide seasonal fluctuations. As was nentioned in the preceding section, the estimction of a relationship tased on time series data implies the csswmption that this relationship has not changed over the time span covered by the observations. One may consider this assumption as equivalent to an aggregction of the relationships in time. Yet there are 8K. FOX, "A Qpfltif’l EQHilil‘riHm Model Of the Livestock—Feed Economy," Feeneeetticn, 21:547—66, 1053. O . o o o ’C.”. findge end T.n. L1"llama, "Qpatial Price Eovilihrinm Analvses: of the livestock Fcononv." Oklahoma Stete University Tech. Bnl. TB—7R, June 1959. 10 . . . F.O. Ready and A.C. thert, "Programmine Regional Adjust- ' ' \J ments in Grain Production to Eliminate Snrplvses," JFK 41:718-33,105°. 11“ .x. de Greff, "Fconomic Inpact of Identified Reef in the Market Place" in Pee? for Tomorrov. Conference, Purdue, 1959, Washington National Academy of Sciences, National Research Council, 1960. 18 reasons to doubt thet such relationships have not chenfed.1o Concen- tnslly such charges cen he viewed as resultihfi from 1 chsnfe in some veriehle not included in the model. Onerstionelly such a View may not permit ore to improve the model heceuse snFFicient inFormetion is rot avnilshle on all the "crinhles havin" attected the relation- ship studied. It is helieved that essnmins a fived relstionshin way he a nsetnl First aphrovimstion. Actnslly, snch is the justiti— cation for e11 the simnlitications present in this tfne oF vorh. 3. Ansresatin“ h" cateenrv nF nrodnenrs _..¢ — ...—......— ..‘__.._ ...- 4—- ..g.. - i- -.4.--_._.-... -.- - --.» Time series anelysis oftW"“‘dete does not tahe into ecconnt the changing relative importance 0? the individual nrodncers. Tmoli- citly, it is assumed that this does not chsnje or that if such chanes take place they do not sieni‘icsntly inFlnence orodnction and derived demsnd for ianfQ. Vet, as has heen clearly hoirted out hy sevorsl 11 anthorsl , specialivetion find the concentration ot nrodncers has heen importent. At the ssme time there censot he es? do"ht th°t thess changes have attected the relstionshins inclnded in onr model (nr0”"s— tion Functions end utilisstion o‘ inputs). Another chsr:e nointed on“ hv Kramer is the develonment 0? verticsl intesrstin“. TheQO “h°“"es are not tahen into ecconnt in this stHAV. uere aésin, these m- ~— ----.. .—-.—.-o—.-—- .- ,--.- ___.—.—._.——-_—._.-—__— M.‘ -‘77-—. 9 . O O 1'9ee For instance the resnlts o? the emnirical stud" oresented h" 0.”. Dean and F.O. Weed", "Phenees in annlv Pesnonse sod Plasticitv for uneq," IV? Vol. A“, no. Rog-60, NO", 1958. “...- 1qwor instance see: F.p. Q”““°on, "Cunnl" Pesnonee end the Feed—Livestock Vcoromy" in ”.0. Wendy et 91. (“4.) A"rie"1tvrsl °“““1" F"“htiot", A“°°, Tore Qtate Universit" Press (1051), n. 97h ov 9.0. Krnmnr, "V°?o~omnrt Qvetnmq end Prodnc‘ion pgcieinfé" i? Pee? Cattle" in use? tor Tomorrow . on. cit. J._.3 . “.-....” ...— .. — .. - - -- ....-. - .. -. A-.—._-_- ....- 10 ]_'i_pwj."flf‘i‘nf"q pknvvlri hrs rannhv‘innei ah nx'ov..-$";mn1j'£1'h,fif'infie 'it‘kCSV‘cfit‘i" 9'0 f‘hif‘. *‘VT‘V‘ 0F 0““4" “n kn Dan‘- in min/4 ‘3“ inhnrnrnt-i-«rv vnnnTO-o. A Ahflvnfifitinn h" no+o~nrw n5 fiYfiAHfi“ o L 7 1 _.,H.hl...._ a. .._......._... - a ...... v. . _. I... .- __.......- -- - - - ...- T‘fin "imfilfi ofnmnrnO-j'n'j n5 Oil-n ‘-ih1_p (‘5 “kn \TC__§/J nvndnnkz tonfl_~vri“c, Ln“ QWA Fans :6 n 14nh 0c +krpo n~flrn~nhn finnn¥4&{nc 5-4 ~_; x For infifohnn canflworoinc innlnflo flfi'“, n°t°, knr1fi" fl“4 “*fii“ °fi*— . y __ . _ i' V. .. "it"“m. unr‘p"p*‘, (“hurl"‘ir‘r‘ *hnon to"? canr‘_~r«1’v~c 'i“f1';vr1'r11141]~~ {nqhnafl \—“ u ~ . - .,.' I _ K.’ .. . _. . ,- .-. of feed—"rains es a whole would o“l“ reduce, not elininste, hesreee~ a w . I . 1 9 clear thst any economic st"dy implies some degree ot egfreestion with respect to noods. An nvemnle of dififin"lties reised hf such aggregation may he pointed out. In our model evnlcinin: the produc- tion of heet, ennuel heet outnut per year in nillion pounds is one of the dependent veriehles. This implies one or hoth of the two following assumptions: that one pound of heet coming From a steer is the same thing es one pound of heet coming From on old cow or that the relative inportsnce ot, shy, steers end cows in the produc- tion of heef hes not chnneed over the last three decades. Neither of these two conditions is Fulfilled. Quch chanfes hsue atfected the production function which we have used and theretore the derived demend for inputs. Though these effects are not taken into cccount, 1/ definition of an economic food. See for instqnce: 4.P. Lerner, I ”We do not want to enter here into a discussion 05 the "The Concept of MonOpoly and Measurement of Monopoly Power.' Review ot pconfinics Studies, Vol. 1, no. 157—175 (1014), especially p. 148 .-—-———-_. .._—- ~. .._._—_—_- ff. The currently held intuitive ides of a good will he sufticient for our purpose. ")f\ the" should he horse in T“ind. in interpretino results es the" are likel" to he serious. 15 AS 3.9. Ives has pointed out,‘ the lack of precise defini- tions forces us to use livestock categories “hioh are verv heteroge— neous and which have chanced much from 1999 to 196?. The evamnle of H- calves is snff cient to carry this point. Calves include hoth young vealers of strictly dairy hreedino and 600 lh. feeder steers. Though es in the composition of this category are important, the lack of precise data prevents us fron taking them into account. As was mentioned in the previous paragraphs, the aggregation iwplipd in the model way affine: the results and hiss the coefficients through Specification mistakes. Tn addition to these very annoying shortcomings, such aggreoations preclude answering some important questions raised earlier concerniny the refional pattern of produc— tion and the possihle concentration and so901”1i79t10“ “F PVOdUOPrQ- These shortcomings, however, do not precl"de answers to other impor— tant nuestions. Tho Modal ---_—.——-.-..- ... .— Cereral Shape of the Model Fssentiellv our model is made of three suhmodols for feed- Grains, hogs and heef. n all three models it is assnned that resources aro comrvitena -l- to a given production on the hasis of some price expectations CC“1CHPr_ \_¥ ‘\ H, 15J.9. Ives, "An Vvalus ion of Availahle Data for Fstinww+_s -».ino Market Supplies and Prices of Cattle," JV“, Vol. 39, Dec. 1957, ‘ h 1411-1419. ‘ 3“ nine products. Tn menu cases, once resources have been committed to a r‘iven production, the cost of shi‘tins to another production is very high. As a result the output of a given product is determined, 2* in part, h" the amount of resources previouslu committed to ts pro- duction. This .4. "plies that farmers make decisions concerning the amount of factor to use and that output is determined by the quan- tities of inputs employed and, o? course, such uncontrolled factors as Weather. S“ch a model is in accordance with assHmptions usually made in agricultural product demand analysis, wherehy the supply is 16 assumed to he pnakrermined in any one year." The main ohfiect of this tHPSiS ‘9 *0 ‘ind out what "predetermines" sunply. Pollovipg C.L. 17/18 Johnson's so—cclled theory of fired assets and its consequences to explain the seemingly low elasticity of supply in the contraction phase, it is believed that resources are committed to a particular enterprise on the hasis of some price evnectations. This contorms with the generally accepted theory 0? derived demand with the expected price of the product explicitly taken as exnlanatory variahle. Leaving the discussion of price espectations for the next section, it seems 1gSee for instance K.A. For, "The Analysis 0? Demand For Farm Products," USWA Tech. Bull. 1081, 195?. 17 . . . G.L. Johnson, "Supply Funct1on—-Some Facts and Notions" 1n F.O. Heady et a1. (edit.) Anriculturol Prohlems in a Growing Economy, -_-_-_..—_— Iowa State Collene Press, 1958, p. 78 ft. and "The State of Africul- tural Supply Analysis," JV?) 0p. cit. hathaway, D. E., Government and Aoriculrure-—Vconom1e Policv . a. -__._._--.—.—._. --. -.\——.—o —- - ..- _-_.— .. ----- —. .._‘_ in a Democrctic Society, McMillan, New York, 1963, particularlv Chapter IV. 99 useful at this stage to descrihe the types of equations included in Our model. Each suhmodel includes (1) some equations explainire the - ) utilization of various resources hv the enterprise and (2) one 3 aggregate production ‘unction equation. In the case of hoes and of heef, equations eXplaininn the sive and composition of livestock inventories are included. These latter equations are necessary because the live animals play a double role as input and as product. As was mentioned earlier, the data are annual for the contirentel U.S. When data are availehle, the coefficients have heen estimated on the basis of the series from 1979 to 196?. Price eypectations play a strategic role in our model. The prohlems raised by using such veriehles and the method used to esti- mate them, are discussed in the nest section. Price FXpectations As Nerlove has so well said, "The chiet diFficulty in empiri— cal work in economics is that theory rarely deals with variahles which can he observed. The prohlem to he solved is to relate the unohserved variables of a theory to variahles which can actuallf he ohserved."19 One of the main prohlems he tackled in his book was that of price eupectetions. He continued: "Previous workers have too readily iden— tified price lafged one year with the price which formers tahe into ’70 account in planning their acreage."' -..—...--—‘—---—..a—--.— -- 19 Response to Price," Baltimore, The Fohns Hopkins Press, 1958, n. ”4. M. Nerlove, "The Dvr“mics o9 Suppl": Fstimation o? Parmere' o . :)FL Nerlove, on. cit. -—‘-*.—.-.- . 5 17- 9" "PF-{o ‘3": ant 0-1‘9 n‘lopo tn n-rvnr-vn if“ n Innntl‘wtv riitynnng-inn (vs For: f'n manenrp pricp Qanpfnfinno. To mokp n dphqi]pfl roviom n? *kp wpys variong anthnrq have havdlpfl tkiq nrohlom vnnjd glen ho kpynfifl tho FEOhO n; thio *‘knhip. T“ mfiv‘nIY “varyinncf 73“]."9‘Oq, it ‘27“9 {999‘1mpfl f-tyn‘F- {av-Mn??? O‘th‘ff*' fin varniv’o tho nrnw‘inno :vnnv'q nv-irfn nae ammo t'vo'iol‘f'ofl fnprozn n? o fnmhov n? nrnnofiin: fpnvo' “*490". T5 mnrn Cnbklbflffi- fnri P“'?1:'.°‘3°, onnt‘ of: Novlnvp'p’ tho vvn-i_nl~f-g~ for hank T’nfl‘.‘ Pox-n hopvf dotormifiofl h" pnmn mothnwotiool hrnnnflwro Aorivpfl cram pimnln flFPVan an *Ln wroxr in v7‘r4fi1“ raw-nuns." cnvm “Ln-iv- «nr'irun nvnnp“fi*1.n"n TLA O .‘ ‘-. . .. . . '. r,.‘.. 9'4”" mnw'n ql-Aq-“nnm'iwho ac Pkbon finnvnor-Lno Lew-us Ran-n uninhafi (“1%- 1‘Vv (7 1". ‘ .— .1 n— \ . . s . V .. _. . 71 09 TnLnQO": Wmfifl'r'ipnl Y’nvlr 4""01“ flf‘ tL" T”"""f“'."“" “‘q7-h:°r;nj C1‘?‘vp:' hove indiceted that tormers use nrioo ovnectctior models much more Pnfikl9fififlffia *kfif the siwmln ptotiotinol mndolg pnfigidnrnfl in brevious enclyses. Much Forvord~loohinc in‘ormctior cvoilehle to fermers at "n? noint in time is rot re‘loctod in date on nest nrices k“? 59 relcvort. C‘“oe the 1070'? cormerc horn pvmorionpod thg Freer “enroccion, a world vcr inclction e‘ter rolcvetion o‘ nrico controls, the Voroon "or, husirees cycles, institutional changes and charging involvment of the government in the price making nrocess. A fellow graduate student, Milhrrn Ierohl, produced the espec— tation dots used herein. Tn develonirg his series, he took into _ —.————.._.H-....——_. *_.—— __ fl... .-._- —-———o-—-—.- ”...-.7, .- 0 . ° ‘10.?” Iohnson, Dev1ew of Marc Nerlove "The “"nnmics o? annlv: Vatimetion of Formers' Desnonse to Pri.ce" on _cit., in .-J-— .- A—Zrip111t'11rpl pf‘fi".fim'ir‘9 Dnohpan-ll, Vol. YTT’ N0. 1 (Tammany-«r 10.60), See “or inc. tar ce V T. Portenheimer and P.“. Roll, "Mara— U 0 a1 pchavior o‘ Vermers in Formulating Fvnectstiots of Future EVET‘LtS" in 0.7.. 1'0an 90?} P." 91.. (“Al". ). A 0""A" 0: M“"‘“""T""-_"1 __..._.--._._..--..... - _._...._-—..__—h{._- - .4”. prnooecpq (sf Miflmypgfprq 17"?“1710‘5'1‘, 'T“l p T0770 Cent-{3 IT“3VVr\Y‘¢"1§'VV Dav-(133, ——.—._—-—.—- 1o 61 pn 8?:th , 9/. account more in‘ormetion eveilchlo to formers at the time they take their decisions than has hcen done hf earlier researchers. Fundamene tally, the firicp pynectatiors he develoned are hased on the various reports nuhlished and availahle to Well intermed farmers at the date for which the price eyoectotion ves es‘imctod. The estimates renresert nrices which it would have heen reasonahle for well—intormod Farmers to hold at the time they tohe crucial decisions. For instance, the series of one year exnected prices for corn represent prices which it would have heen reasonahle ‘or vell-intormod Farmers to hold in the Spring (Aoril, Merl he‘ore nlertin: tor corn to he harvested in the fall. r"he actual value was determined, according to Terohl's hest judgment, on the hasis of previous nrices of the ounlitative state— .I ’ ments contained in the various situation renorts and of cerorcl iréoru 3 nation availahle at the time of decision. Tt is outside the scone of this thesis to attemnt to annrsise Ierohl's procedure in detail. Tn accorderce with the advantages 0‘ 9? the division of lehor, that task is lth to him. The most imnortant point for this thesis is that we helieve that these esnected prices are closer to PYDPC*9tiOfiS actually held hy Farmers than series which have heen previously used. However, one imnortert shortcoming 0? our method should he mentioned here: if in the case of feed crair nroduc~ tion, it can he assumed that decisions regarding how much to nroduce 7? " It must he noted that Mr. Lerohl die is research irdenecdent 1‘ P. of work on this thesis. This r derivation of his esti~ mates has not been iniluenced bv su_sequent d Fticulties encourtered in using them for this purpos réb 0s are taken once a year, essentially at planting time, the some is not true in the case of livestock production. Tn the United States deci— sions concerning the volume of meet production are taken in a more or less continuous manner throughout the year. Vet the price expectations series which were developed are nnnvnl in case of heef and semiannual in case of hogs, (tro series V'ere developed: one relevant For spring ferrowinss, the other for i:all Ferrowinfs). This is, of course, an instance of the time 9::regnti02 nrohlem previously discussed on pege 17 of this chapter which should he horne in mind when the results are interpreted. Conrces of tha - Trnhlems Poised Lack of appropriate Ants has heen a major obstacle to overcome. Availahle dnta never represent an erect measure at a theoretical varia— hle appearing in the economic model. One ohvious example of such a shortcoming is the lack of data concerning expectntions actually held hy farmers. As was evolained earlier, our method is somewhat original. As a result, we were forced to use unpublished meterial resulting From the work done hy a colleague. This is ohviouslv dangerous because Lerons work has not yet been appraised as pert of his Ph. D. program nor has it benefited from critical appraisal Following its puhlication. Another important question to he raised concerning these series of prices involves inflation. To put it in very simple terms: there is no douht that a price of 80 cents per bushel for corn in 1935 would have meant semething quite different than what such a price would heve meant in 1963. As a result, price evoectatiors were deflated hv the index of prices paid hy farmers. Puch a procedure involves several 96 problems whatever the de€1ator chosen. Quch prohlems are discussed where appropriate in the course ot the Following chapters dealinn with each commoditv. The lack ot detailed data on livestock mortality is another illustration of the limitations resulting From lack oF data. Vearly flows of various tvnes of animals were desired to permit a Finer hrenkdown than is availahle From nuhlished data. UnFortunatelr, this attempt has heen Fruitless because of the ahsence of data on mortality and even on total sleuohter hv type 0‘ animals (cows, heifers, steers...l. The data which have heen used in this thesis are mainly annual data nuhlished hr U.Q. federal departments, the major portion coming from F99 (Vconomic Pesearch Qervice) and its Forerunners AMQ (Agricul— tural Marketing Cervice) and, earlier, the RAF (Rureau 0F Agricultural pconomics). Most data come From periodic or occasional puhlicetions of the "Q“A. Livestock runhers and production iiigures were taken i’rom the U.S.“.A. Statistical Bulletin No, 11?, "Meet and Tivpstock Statistics," (196?) and also the previous issue of this nuhlication: Qtatistical Fulletin No. 770 (1097). Feed—crain production and acreage tigures were taken from ".Q.“.A. Qtetistical Pulletin No. 190, "Grain and weed Statistics Through 1061," (Perised edition, Tune 1957). V095 COPSOmD" tion figures by each class of livestock (heat, hoes) were taken From Jennings' UQNA Production Peport No. 71, "Ponsumntion 0F Feed—Crains hy Livestock," hroufht up to date intormallv For us hr UQDA sts‘t workers. Uses of lahor in the various enterprises were tehen From U¢“A Statistical Bulletin No. ??9, "Phanges in farm production and 97 efficienc" - A S"mmorv vpfinre 1og0)" (An~u¢r 10Aq)_ vacticinorino nc tl-n 'T'imo Darind ._-. -.-. -..—.... .—- —_._-._ --—-——_—-—-~——.__—.- ..-.-— AR Was mentioned earlier: the nornmotorc n? the models are estimated on the hasie o? annral date from 10°C to 106°. The choice at this time neriod is a comnromise hetveen con‘lictin: reauirements. TT‘ Vipr: ()5 the. .fl‘vfiil,fihi1‘l’t:’ oi: 8"“, V’9 phnpp 9- 1f) 1“”er 94 ohservation neriod. Thoujh a larfe numher o‘ ohservations (hence, a long time neriodl is necessarr in order to jet a good "statistical fit", other considerations demanded a shorter time neriod. Tn order to ohtain a meanitjtul estimate o‘ structural coefficients, the struc— ture must have remained constant: hence, the time period must he short. The time period settled on had to he such that sutticiently reliahle data VOTE availshle t'or enough years under stahlc enough conditions to permit estimation ot most o‘ the narameters ot the models. Nineteen twentynnine was chosen as the hecinnin: of the neriod studied. Thus the narameters are estimated on the hasis oF data which result from a variety of general economic conditions: denrension, World War TT, the Korean T”v'ar and various husiness crcles. Come ques- tiors can he raised renarding this nrocednre, The time snan covered includes so many different conditions that one mar nronerly wonder whether or not it is legitimate first to assume that the same Structuu ral relationships were in eftect from 1099 to 106? and second, to 7ATncidcntally, it should be noted here thst as adjustmert had to he made hccause most livestock data are nuhlished on a calendar vear hasis whereas data on feed consumntion are on a cron near hasis. (Fee following chapters for adiustments made in various cases). as attempt to estimate the structural coccticicrt using data which are the results of so menu "accidents." Accordinglj', in a rumher ot econometric studies hosed on time series data covering a period originating prior to world. "ar TT, the authors have lc‘t out some war years There is no conclusive argument For deciding whether or not to include the war years. On the one hand, war conditions are such that one mar suspect the structural relationships to he altered, which is a strong argument for ercluding the war fears. Another argument would he that the functional relationship which is assumed may he a Fair approrimatioh For small variations hut not for larger ones such as those experienced during war years. On. the other hand, from these larger variations it man he possihle to infer which varia— bles had a significant influence. They can he included in the models in such a way that the structure remained almost the same during the war years. In conclusion, the choice hetween including and excluding war years is a matter oh judgment hy the researcher. They are inclu- ded because the arguments sunnorting such procedure have seemed stronger. Fetimotino Procedure As was descrihed shove, the nature of the models used can he summarized as follows: some equations predict the commitment of various inputs to production of a given product on the hasis of seve— ral predetermined variahles, including expected prices. Other equa— tions then estimate output produced from the amounts of the various resources committed to production. Presented in such a manner, our 90 models appear recursive. Recursiveness There is not complete agreement on the preperties which are required to make a system recursive. In a first step one may accept o the original characteristic properties given hv Wold: (1) The systems are recursive in a twofold sense: (a) it the develOpment of the variahles is known up to time t—l, the system gives us the variahles at time t, (h) the variahles at time t are ohtained one by one. (7) Fach equation 0? the system expresses a unilateral causal dependence. me do not wish to enter the controversy which has deve- IOped concerning the di‘Ferences in causal interpretation 0? coetti— cients of recursive and inter-dependent sustems.?6 Our interest in recursive svstems arises from our desire to find the "hest" estimation procedure For our model. As Wold has shown, if a sustem of equations is really recursive, the coefficients of these equations can he estimated hu ordinary least equares anplied to each equation. Tn mathematical terms, the conditions for recursi— veness can he eXpressed as tolloms: If the system 0‘ structural equations is written 9% O O U C O ‘ H. ”old in assoc1at1on With L. Jureen, "“emand Analysis, A 9tudy in Fconometrics," John Wilev and Cons, New Vork, 10:1, p. 14. 76 . For a recent reference on this matter see Resmann, P.1w, "The Causal Interpretation of Non Triangular Cystems of Fconomic Relations," Pconometrica, Vol. d1, July 106?, pp. ARC—A9, the reply to this article hy R.H. Strotz and H.O.A. mold and the Rejoipder hp Basmann in the same issue of Eggpgmetrjca. ...—-...— '10 An 4— R" + (‘2 = H ' Q where.A, R avfl C are matrices of coeffic4ents v is tkp vacfnr 0F efifln~pfinuq wavinRTGS . t. g " o ‘9 *“P vov*nr of nr939*nrminofl pvfln~osons vnrinklos . *— \_— 7 is *“e vnvfor n‘ pvnsesons variakle '- " is “he "Psfnr 0‘ 9*ochnsfic flis*nr%nscos. t' The svs*9m is said *0 5? rocnrsive i5, p‘fsr pronor OVderinfi of the PQHinO"9, H. D J J. H 1) fhp WQfT'i" A is frinnnu]pr ‘ i n ‘0? 5 > .3 —1 For i = i .J. ".4 ll 7) the cnvsrifihva matriv 0‘ cOfimenornnpnns disfnrknscps V(vru'r) is diagonal. P.H. 9*rnfz co“siflers fhnt 9 svsfom is rocnrsive i‘ and 97 orly if the Firs? cnhflis€nn is s~*5sF4nH.‘ Wovavar, ‘nr purpnsa n? this fhnsis, it spams “offs? fin bash in mind Roth rnvflifinvs sires thsy are npcossarv for +59 Aasirnk1p nronerfiips of loss? snnprn esfimn*ors to hold, Tt can easily he soon Pkpf *ko mnflols 0? this tbpsis snf*sFy tFe first ronfli*ion 0F rpcursfvefiass (*risvsularifv 0F mfi*riy A). The crucial qnostinn is *0 flecifle whprkor fkp Histnrhnnnps 0? *%e differehf ennnfinhs afin Fe assumefl inflenerflpfif (flinfofi21i*v 0‘ *%0 covariafice wafrix). ”018 has prgnofl tknf snn“ n rahwrsivs anOI, representing a stepwise chain of csusafion, is 0? :efisrfll abplicpki— 98 11*“ to evnlnis ¢¢0fiomic notivi*ios. A annr95°“si"0'tr°"*mo"f .......-—.— -...._-_._—_.....-- - ‘ ..--.. - .- - _.__._. ~fl__. _ _. -—..—.__--_- 97P.N. Cfrnfz, "TrfordonorAervo 99 a CfiOh‘fin~f*ns Vrrnr," ppnhm0*r{pfl’ ‘701. pg, 1060, 11. /anfi. “—.~._ _ ’—--. -_ h 99 W,A. WnIH pad I. Turpor, on, P**., n. 7“. ‘~_._-.—.._._. 11 of fFis cwpsfinn has “so“ f4vnv by Ror*7el nrfl Wansen.°° Tkey h°v9 flrfvpfl tknt a roovrsivp 9*rwcfnr9 is nf*0n Phnrnhrintp For a moflsl made "sva‘sio“*lf 30*0i193 finfl anhrnnris*n7y snnn4‘in9, 9r“ i‘ tFO 1n beriods firs sv‘550*0hf?f sForf." Tknv hn‘"* n"* *kfif rnnnvsivn m0391s ave host Fi**nfl Fnr Avvnmic nfljwssmns*s of the *ynn pnsfwln— fed By the "Aiconwi14kr%nm" mo+hna of rho C*ncv*o1m Q(”m-"~13 F”? inferflenpfiflovc" s**shs vkon *Fs mafia] rpnrosnfifs a sfs*5c Pavili— Frivm. Tfifnrflnnnrgnncy sr‘sos ”790 ‘rnw nfjvsgfitinfi nvnv rFs prpvin? 1_11_~.1'*'g ”31“ "kp ncnfinm" ““3 0"9‘7 511° ZOOHR, "WA {7’01“ "Si-’3‘: *ime norioAs 10“"or fkns fks h1fisnind n°*infl 0‘ fko various Pcovnmis whifs. Acnon*{“7 tF4s 9n41fisis, fHo wnAals of Drnflncfinn bngofl on nrics evner*1fi‘nss soom more dynfim4r *“fin sfsfiC. TFern is rn rnsm friction imslr‘sfi “v fifljns*mnst of svnfiTf ”b3 Afimhfifl. “0“°"0*, BQCT‘IQP of? ~~9r4nnq h:»:rh:«f‘~1'_nno vaenrtnfl kg, nq pvnln-‘finA flkn‘rn’ 2rd of Using PfihHfil 86*s, if is 4i5fisvlf to know, n “r4n*i, 65““ the covtsmhorfisoons 8‘s“"*Fshsoc nrn 4“Anno“4n“f. "a“sfidwnfi*1" *RO v POO‘Ficiorfs OF tFn moan] rvn ss*im~*nA L" kof“ 0*‘4?“*v loss? 8""?“0Q 11 mothnd asfl fHe mnfko‘ *“cnmmn*403 R" Von“o. T“s*n°4 n? “nfi1"is" nvgissr" 10"s* sfivsros f0 ohnv*‘““ ‘, ““0 nksovvn‘ v~1vns 0‘ *Lo Assn» \ “hfnuf; V70v4n‘F-‘ng V7;({ < i) urn 3-91-3190an 1“, #Ln{« fink-{mnbgfi ~vn1q1oq ‘7. L . ..\ .- V d,“ . J . ‘ .. - V . __' m—go‘—_—_—.. -..--.—._ -...- A- __.- - __—.- .- _. - -_. - -—-_.——— -.. "c. -_.-~_- ..-- — _. --—.———- 00 D. Rnr*7nl v?“ R. Passe“, "0n Rsnursivsfiess and Tsfsrgnpnr— Annoy 4? Whosnmic Mnflels," ]RQH1GR, (Iqas_ss). Pew-inter nF F‘pnhnm4n Qf‘wr41'noa an. 79) 1‘“. I “~-—_-..__._—_.._._ - — - - ..--..— - -..- _. — -.— qn , P Rhfif701 9?3 P. u°?°“7: nn, 04“., “‘ 1A0. -—.— ---.- ....— Q19 T 'F‘nn‘n "Ahn1v‘fw'na1 'T‘nn10 5n». C+nfiw4nn Unm"7‘A '5“A 13*"fn ~' ' - a *~ . - _, _ Cf-vuo‘twran " IT Q h A Afivw'r‘n10'wva1 UnerLnr-flr ”a. TAR) Awnncfl’ 105.93 '~—-'~- - -‘ D O Q . o s \ n 6/1. C O COTp"th ‘rofi eowntions i, startin“ with rte ‘irgt pnuotion (Contnihinw only one endoeenons "arinhlel For wtic“ ordinar" least sonnres can on annlied. This is done beenwse iF Hi and n; are correlated, Vi and v} are correlated whereas ;? and 5? are not. This second motkod is very close to the "snal two stete least se"ares “ethod. Provided that tkere are no sneciFieation ristahos, simnle intuition indicates tkat t‘nis mother! is firebaoly better ton: the vsnnl two stnse least squares since it incornoretes tte extri in‘ornation ttat sooe variatly Vi does not desend on sore exofien0ns variahlq annenrin~ in another nonstion. ”owover, this swneriority over two stone is oF out little contort since very little is ”sown ‘ Crucinl on tee small sennle nronerties of two staee least sowaros. qnestion is reached Fore w‘sic11 is not Fully answered as very little can be said concerninfi tte snail samnle nrooerties of the estimators used. However, in View of the tools which are available, these estimators seen to he too best, even thonfih it would even be difFicnlt to rigorously define the word "best". 7ellner and Theil have shown that the three staoe least sonare method which they have pronosedq? is more efficient than two stage least squares. The feasibility 0? adding a third stafie to our estimation method was considered; this appeared conceptually easy but the lac? of a comnuter proeram at the time we needed it prevented us from mahinq this improverent. Full 32A. Zellner and F. Theil, "Three Stowe Least Squares: Simul- taneous Estimation of Simultaneous Eqnations," EEQESEEEIEEE’ Vol. 30, ’3’2 intorfintion wovirrm likelihood was not oorsidered “or the some resto“°. 'T‘quq) 6Q ve-vne pk’nhnfl nknwvo 1‘0““ (fir/:4fifir17 1Dfi09‘_qfl'fllfjffiq ”war; | u t ‘ . . , ' .. -4 ‘ ~ A . . -_ 4. the "recursive" “*“”°A”’” r°tnmmerded h" Wooto were "sod. As will he spay“ {a king cn‘llnyflw'nn ,TLnfiQ-nvn O—Ln .1fl“i‘flv‘ hrnbnAHr‘n A:A r‘n" “4"0 yv‘r‘s-wv satis‘ootorr results. Q0riol Forrolotion Tn several eonetions, osrtiorlorl" From the teed—"roirs ard I O 0 q . O heef svhmodels, the nonlication o? the “nrhin—Wntson test 1 indicated that the h"nothosis of seriol indenendence of the residuals could not he accented. The nrohlor o‘ soriOl correlation has loro heen reooori— O zed in econowetrics. Tt is si ni‘icor‘ heoanso it loads to errors 2rd 3, even hisses (when tho evoeoted valne of the distvrhanoe is not zero) in the estimation of the coeFticieots. Tn oll cases the nsval tests do not apply. There is no completely satisfactory technique to take care of this condition. Very often researchers have used first differen— ces of ohserved verinhles to estimate the coeF‘icients. several econometricions have recommended to he cautions with resnect to this procedure. Tn this study we hove nonlied the procedure nronosed hy '16 Pildreth and In. ' Their method is hased on the esswmotion that the disturhonoes are yenerated h" a simole Verve“? nrocess. .-.~.._ _-——- '— .....-“ 13 J. Drrhin and C.¢. Votson, "Testino for Periol Correlation if? 11‘qu Canarpg Pnfirnqqinr T" pifimhrrilrfi, Q7, fin [Inc—.09 (10Rn) . - n _ . «l.- s “K..“ L-- .. Q , --O \ - I “nrhin, T , "Tootiro i'rw' Corio] Forrelntino ie Taper Cownros “oorossiOn . _ .— ' -_ . ._ . ._ ""g,‘ .:_ _, _ , . . .u A _ - _. . _ ____ _, .‘ ‘_ i, l. __ v‘ x. I- - -- . . IT". pififiptribfi, 79, or. qu—7R (1951). 3hFildreth C. and J.Y. In, "Pemaod Relations with Antocorrela- -.—, ..r. ted Disturhances," Station Tech. RHl. 776, p. 76 (1060). Michienn Qtsro Univnrsitt, ““ricwirvra1 Froorirent _.,. .v .. - . _\ _, . . \ J..- V,-,.. ~ ..- _ _. i . ._ . . '1 A. "f = )0 "“-l + Vt Then the environ liholihood estimators o? the ooo‘Fioient are those ohtoinod hf generalised least sqnares with f taking the value minimi— zirg the son of sonarod residuals ohtained hy snhtrsctio observed valve of the deoordent voriohle its estiwnted value. The mothersticol nrohler o‘ finding the value of/fawhich winimizes this sum 0? sq"ares is very diftioult. Hildreth ard T" propose a "crvde" method which is to comouto the rosidnsls for voriors values of If . This is the procedure which we hove followed, 1° taking all values from -.8 to 1.0, .9 avert (-.8, -.6, —.4....l.0). The major limitation of this procedure at this stage is that very little is known concerning th, small 99mple properties of the estiootors so derived. Consistency has been demonstrated anflkr“vntotic normality coniectured but the usual tests concerning the ooetfioieots ore not valid. Yet it has been felt advisohle, in View 0? the ewoirioel results ohteined hy Hildroth and In, to use this procedvre and to present the results along with those of ordinary least sonares (which assnme ever the nrohlem o? serial correlation). ”. ...—.m—H_. gguildreth, n. ard T.V. in, no. cit., on. 11 hod,l?. ._-"--r CHAPTER III FEED-GRAIN PRODUCTION Economic Analysis As stated earlier, the economic analysis underlying the construction of our models implies that the output of feed grains is determined (1) by the amount of resources which are committed to their production, (2) by the degree of technological advance, (3) by the weather and (4) by some other nonstudied non-controlled elements. In view of the existence of these uncontrolled factors, it is obvious that the amount of most inputs devoted to the produc-‘ tion of feed grains is determined before the output is known. Thus, it seems logical to consider the quantities of various inputs commi- tted to the production of feed grains as a function of the economic information available and of the economic incentives influencing the entrepreneurs. The amount of feed grains produced is then viewed as a function of the quantities of inputs committed to that produc- tion. Use of Inputs What are the main factors determining the amounts of inputs which are committed to feed-grain production? As G.L. Johnson1 has pointed out, a resource will be profitably committed to a given produc_. tion process if the sum of its expected, discounted, marginal value 1 Op. Cit. G.L. Johnson "Supply Functions - Some Facts and Notions" 35 36 products is higher than its acquisition price; a resource already committed to a given production will be shifted to some other use if the sum of its expected discounted marginal value products is lower than its salvage value. It is clear that the expected marginal value product (MVP) plays a strategic role. Given technical "knowhow", the MVP depends on the price of the output. Thus, it can be antici- pated that the expected price of the product will be one of the fac- tors determining the amount of input committed to the production of a given product. Another relevant variable in the decision concerning the amount to use is the acquisition price. For inputs which are used up during the production period, such as fertilizer, the acquisition price is the market price. For inputs already committed to the agri- cultural sector of the economy such as land and, to a large extent, labor, the acquisition price is internal to the agricultural economy and is determined by the Opportunity cost principle. Market prices are not very relevant. In a model describing short-run adjustments, it cannot be anticipated that prices will be the exclusive determinants of the variations in quantities of inputs used. A limiting factor which may be of major importance in this respect is the quantity of resources available. At the same time, once land has been planted to feed grains, the marginal cost of producing feed grains on that piece of land is very low, thus, in any one year (i.e. for a given techni- que of production), the amount of very variable resources, such as fertilizer used in this production depends heavily on the number of acres planted. 37 The Production Function The economic analysis underlying this part of the model hardly needs to be emphasized. It is simple common sense which indicates that the production of feed grains depends on the amount of resources used in their production and on various uncontrolled factors among which weather plays an important role. The real problems are statistical in measuring the relevant variables and the relationship. Statistical Problems Problems Due to the Data As mentioned before, oneo/fthe main difficulties of any econome- tric research is to find apprOpriate data reflecting sufficiently closely changes in the variables used in economic theory. The objects of this section are (l) to point out the major difficulties of this type encountered in the estimation of our feed-grain models, (2) to explain how we have attempted to solve these difficulties, and (3) to justify the procedure used. Output Though most difficulties stem from the lack of adequate data, important problems arise from a lack of rigor in the definition of variables in economic theory. In this respect, quantitative studies are more demanding than qualitative ones. Thus, it is quite sufficient to speak of feed grains in many qualitative macro economic analyses but in an econometric model it is necessary to be more specific. In parti— cular, an explicit decision must be taken regarding the method of 38 aggregation. The feed grains included in our model are corn for grain, barley, oats and sorghum for grain. Since the quantities of feed grains consumed by livestock are aggregated according to the weight of these feed—grains, the same procedure was chosen to insure coordination of the three models. This method of aggregation has the disadvantage of overlooking differences in feeding efficiency among these feed grains as well as their differences in requirements of inputs (i.e. there is no reason to believe that it takes the same amounts of resources to produce one ton of corn as one ton of oats). Yet it was deemed prefe- rable to ignore these differences as not warranting the efforts necess- ary to build a model for each feed-grain. Lack of data for such more detailed models also supported the aggregation decision. Inputs It has often been noted that data on the amounts of inputs used in producing specific products are not available. As a result it has not been possible to take into account a very important input in the production of feed grains, the use of machinery. In addition to the lack of data on machine services rendered for specific crops, changes in mechanical technology have been such that one tractor in 1962 or one combine in 1962 is quite different from a tractor in 1930 or a combine in 1940 respectively. Attempts to take into account these changes in quality by converting to constant dollar value have led to meaningless results because changes in relative prices reflect changes in the efficiency of the production of these machines as well as changes in the quality of the services which they perform. A similar problem'was faced in the case of fertilizer. There are very few data on the use of fertilizer by various crops and no such 3? th ve 8114 CH 110: "a MiSI Bul 39 time series. In this case we resorted to the amount of fertiliser, measured in tons of principal nutrients sold in the North Central region.2 Roughly 75 percent of the total U.S. output of feed grains is produced in this area and there are strong reasons to believe that the bulk of the fertilizer purchased in this region is applied to feed grains and that no major discrepancy is introduced by other craps as would be the case for tobacco or cotton in other areas. There is a question as to the best way to aggregate the various components of chemical fertilizer. Because of the availability of data, we have used tons of the three main plant nutrients (nitrogen, potash and phosphoric oxide). These components are not substitute and applications of fertilizer were probably better balanced in the 50's than in the 30's. This shortcoming is recognized but not felt to be very limiting. In the case of labor, the available data published by the U.S.D.A.3 are used. A word of warning may be useful here. As can be imagined, it is very difficult to measure the amount of labor devoted to specific enterprises. The U.S.D.A. estimates are based on educated guesses of the amount of labor required to produce one acre of a given crop and then to harvest it, these guesses are derived from micro eco- nomic studies and through discussion with a number of experts from 2Following U.S.D.A. classification this region includes 12 states: Ohio, Indiana, Illinois, Michigan, Wisconsin, Minnesota, Iowa, Missouri, North Dakota, South Dakota, Nebraska, Kansas. 3"Changes in Farm Production and Efficiency," U.S.D.A., Stat. Bul. No. 233, o . cit., p. 35. 40 various areas in the 0.8. Once the estimates per acre have been obtained, the estimate of total labor used is derived by multiplying these estimates by the number of acres planted and harvested respec- tively. Such a series cannot be very reliable; however, it is the best available and some information can be gained from using it provided care is taken in interpreting the results. In the beginning of this chapter the concept of technologi- cal advance was mentioned. This is obviously not the place to enter the controversy relative to this hazy concept. It is sufficient to say that there is far from a complete agreement on how it should be defined. Yet it is sure that the variations in the quantities of inputs as measured and present in our model (land, labor, fertilizer) cannot explain all the variations in output (even after the effect of weather has been taken into account). After an unsuccessful attempt to measure "technological advance" by the prOportion of hybrid seed in corn, the somewhat questionable device of using time as an explana- tory variable in the production function was adapted. Estimation Problems Choice of the Functional forms The usual recommendation in econometrics is that the algebraic form of the functions should be determined to the extent possible from economical and technical considerations. The law of decreasing margi- nal returns is one of the corner stones of economic theory. Yet very little is known about aggregate production function such as that of our model. We have fitted one production function purely linear and 41 another one linear in logarithms (Cobb-Douglas). It is not rigorous to call an equation which includes time, the number of acres planted but not harvested for grains and the weather index among its explanatory variables a "production function." Clearly these are not inputs. Yet it is legitimate to assume that the volume of output depends on the quantities of inputs used and on these varia- bles. The law of decreasing marginal returns should not be expected to apply to these other variables. Several attempts have been made to include these variables in different functional forms. For exam- ple, the number of unharvested acres was subtracted from.the number of acres planted but the result was not satisfactory or surprising because the acres which are not harvested were those with the lowest yield. Aha, instead of entering weather as an independent variable, \ we attempted to eliminate its effects by dividing the volume of feed grains produced by the weather index and by taking the ratio as the dependent variable. The results were erratic (negative regression coefficients for several inputs). Thus, all the explanatory variables in this equation are not inputs but,‘with these qualifications in mind it is called a produc- tion function for the sake of efficiency. The uncertainty concerning the functional form is at least as great in the case of the equations explaining the use of inputs. Again both types linear and logarithmic are fitted. Recursiveness of the model As can be seen in Table 2, p. 44, the acreage of land planted to feed grains is one of the explanatory variables of the variations 42 in labor and fertilizer used for feed-grain production. Moreover, the acreage planted to feed grains and the quantities of labor and fertilizer used are included in the production function. The presence of more than one endogenous variable in some equations raises the problem of simultaneity. It is clear that the first condition men- tioned by Wold for the recursiveness of the system (triangularity of the coefficient matrix of the endogenous variables) is satisfied. Can it be said that the second condition (diagonality of the cova- riance matrix of the disturbances) is also satisfied? It is practically impossible to answer this question solely on the basis of a priori considerations. Why should the disturbances of the equation explaining the acreage of land planted to feed grains be related to the disturbances of the fertilizer equation? If one could think of some incentive pushing farmers to produce more feed grains but not taken into account in the model, the correlation between the two disturbances would be positive. On the other hand, the long claimed substitution of fertilizer for land in response to acreage control programs indicates apposite signs for the two distur- bances. Therefore, it is not easy to decide whether one should expect a positive or a negative linear correlation, if any. is '1 [J 43 Table 1. Variables of the feed grain model Symbol Definition Units F.G. Feed grain production in the U.S. million tons L Land planted to feed grains million acres Lab. Labor used in feed grain production million man hours F Fertilizer used in the North Central region 1,000 tons of princ. nut. U Unharvested acres of feed grains million acres Uw Unharvested acres of winter wheat million acres W Weather index (Stalling's) T Time l929=l year IWR/CPI Industrial Wage Rate deflated by the consumer l947-49= cts/hr price index EP Expected price for corn cts/bushel IPP Index of prices paid by farmers (1910-14=100) Liv. Index number of livestock on farms, January 1 (l947-49)=100 Index of fertilizer price (1910-14=100) 44 Table 2. Equations of the feed grain model Equations Use of Input Production Variables Land Labor Fertilizer function L E E E E Lab E E F E E FG E U X W X T X X EP/IPP x x x U', X Liv X Pf/IPP X IWR/CPI X E: Endogenous variables X: Exogenous variables q v “I. w. '55 'u‘n -e N,‘ |g. I'M Table 3. Feed grain model. 45 Alternative estimates of the coefficients (Standard errors between brackets) Estimation technique and functional form £2 Equations 0.L.s. linear .61 L=114.57 - 1.151 + .60 Liv + .53 UV - .21 EP/IPP (.17) (.27) (.39) (1.41) log .39 L=4.691 - .067T + .200 Liv + .043 HW + .032 EP/IPP (.015) (.225) (.021) (.054) Autoregressive linear f’=.6 L=cste - 1.427T + .354 Liv +..33 Uw - 1.363 EP/IPP log /’ =.6 =cste - .14lT + .139 Liv +,.017 U.w - .013 EP/IPP 0.L.s. linear .88 Lab=l351.5 + 18.7 L - 191.1 IWR/CPI + 17.6 EP/IPP (13.4) (40.8) (53.8) log .85 Lab=9.996 + 2.717 L - 1.138 IWR/CPI + .496 EP/IPP (1.493 (.344) (.182) Autoregressive 11near_f’=.6 Lab=cste + 15.6 L - 193.1 IWR/CPI +-35.8 EP/IPP log }’ =.8 Lab=cste + 1.507L - 1.522 IWR/CPI + .221 EP/IPP 0.L.s. special .97 log F=2.053 - .0009 Pf/EP + .0492 T (.0003) (.0020) special .97 log F=-.316 + .173 log(L) + .639 log(EP/IPP)+ .417 10g (.702) (257) (.827) (Pf/IPP) + .056 T (.007) OOLQS. linear .94 FG=-18.78 +-.220 L + .0161 Lab + .0162 F - .664 u + (25.9) (.153) (.0070) (.0031) (.177) 1.772 T+ .287 w (.570) (.100) log .92 FG=-l.615 + 1.081 L - .281 Lab + .035 F - .482 U + (1.405) (.359) (.110) (.053) (.107) .018 T + .474 W (.033) (.112) For definition of variables see Table 1 0.L.S.: Ordinary least squares Autoregressive: Indicates Hildreth and Lu's autoregressive procedure as defined in Chapter 2. 46 In view of this uncertainty it was thought better to use both the ordinary least square and Foote's "recursive" methods as explai- ned above in Chapter 11., The results of the recursive method are disappointing3£many regression coefficients do not differ significantly from zero and some of them have the "wrong" sign.) The statistical interpretation of this result is fairly easy. It appears that repla- cing some explanatory variables by their estimated values from another equation, introduces a higher degree of intercorrelation among the explanatory variables and decreases the reliability of the estimates. For this reason, only the results of the ordinary least-square estima- tion method are presented in the next section. Serial correlation As noted in the previous chapter, serial correlation was found, on the basis of the DurbinAWatson test, in several equations. Hildreth and Lu's procedure was then used as described above and the results presented in the next section. Results Estimates for the feed-grain model are summarized in Table 3, page 45. As previously noted, all equations were estimated in two func- tional forms: linear and logarithmic. These results are discussed equation by equation before considering the feed-grain model as a whole. Individual Equations Land planted to feed grains The variable most closely associated with variations in land planted to feed grains is time as shown by beta and partial correlation 47 coefficients: respectively -.90 and -.78 in the linear form; -.70 and -.64 in the logarithmic form. Using time explains very little. Factors other than those taken into account in this equation (number of livestock on farms at the beginning of the year, acreage of winter wheat not harvested for grain and expected price of corn) have pushed the acreage planted downwards. A priori, two factors stand out as probably important in this shrinkage: the government conservation programs and the technical progress which has permitted higher yields per acre. As a result of these higher yields, the land area required to produce even increasing quantities of feed grains has decreased. Unfortunately, it has not been possible to introduce these factors 'more explicitly into this model. The main difficulty here is, of course, to find a way to measure them. .An attempt to use a dummy variable taking the values 0 in the absence of government program and 1 when they were in effect failed. Such an "all or nothing" variable does not measure the variations in the pressure put on farmers to reduce their acreage. To measure technical progress for such an equation would have been.more difficult yet and was considered beyond the scape of this thesis. Although much less important than time, some of the other variables have also been associated with land use. The index number of livestock on farms January 1 (base 1947-49=100) appears as the second most closely associated variable on the basis of the beta and partial regression coefficients of the linear form (respective- ly .29 and .38). The magnitude of the regression coefficient (601.5) indicates that an increase of one point in the index of 48 livestock on hand, ceteris paribus, has been associated with an increase of 601 thousand acres of land planted to feed grains. This corresponds to a relative coefficient (elasticity) of .25 as compa- red to .20 obtained in the logarithmic form.. In the logarithmic form, the acreage of winter wheat not harvested is the second most hmportant variable on the basis of the beta and partial correlation coefficients (respectively .29 and .35 as compared with .15 and .25 in the linear form). The regression coefficients in both functional forms indicate a small influence of this variable on the acreage of land planted to feed grain. The constant elasticity computed in the logarithmic form is .04 as compared to .02 for the elasticity at the mean computed from the linear form. The magnitude of the regression coefficient (.53) indicates that, other things being equal, 53% of the acreage of wheat seeded but not harvested is planted into feed grains. Some reservations should be made concerning these estimates. ‘The DurbinAWatson test indicates serial correlation of the residuals. frherefore, we have applied Hildreth and Lu's estimation procedure which will henceforth be called the "autoregressive model." It turns out that the sum of squared residuals is minimum for f = .6 1J1 both functional forms. Time appears as the most important expla- untory variable. The regression coefficients for the number of livestock on farms and the acreage of winter wheat harvested are ‘hmualler than in ordinary least squares but of the same order of “fig-nitude (354 in lieu of 601 for the number of livestock and .33 inlatead of .53 for winter wheat in linear form). Though these 49 results indicate that the regression coefficients may have been overestimated by ordinary least squares, it is difficult to decide whether this is actually so. The deflated expected price of corn appears to play a very minor role in explaining the acreage of feed grains planted. In the linear form, its regression coefficient is even negative though far from being significantly different from zero. In the logarithmic form, the coefficient is positive, not statistically different from zero and very small (.03). This very minor role of price agrees with results from the autoregressive model. Labor used in feed—grain production The quantity of labor used in feed-grain production appears as a function of the acreage of land planted to feed grains, the industrial wage rate deflated by the consumer price index and the expected price of corn deflated by the index of prices paid by farmers. The most important explanatory variable is the industrial wage rate (beta and partial regression coefficients respectively '-.74 and -.65 in the linear form and -.61 and -.52 in the logarith- llic form). The average industrial wage rate was deflated by the consumer price index to reflect the financial incentive in real terms pushing farmers to move out of farming. More technically 1t was considered that feed-grain production had really to compete "hlth.industrial enterprises for labor. The magnitude of the regre- 8Bion coefficient in the linear form corresponds to an elasticity fit the mean of -l.23; this result is confirmed by the logarithmic 50 esttmate (-l.l4). Some warning may be necessary at this point. The influence of this variable may be overestimated as it may actually represent the various influences which have led to a higher producti- vity of labor and the substitution of capital for labor. In the other sets of explanatory variables tried for this equation were time and the size of the agricultural labor force. Both were drapped because of their high correlation with the industrial wage rate. Thus, it is very likely that the estimated coefficient of the industrial wage rate measures the influence of a complex set of factors including but not limited to the industrial wage rate. According to the estimates for the linear form, the acreage of land planted to feed grains is associated with labor use even- though its partial correlation coefficient is small (.24) and its regression coefficient is not significantly different from zero at the 51 level of significance. The estimated magnitude of this coefficient indicates that an increase of 1,000 acres in land plan- ted to feed grains has, ceteris paribus, been associated with an increase of 18,000 man-hours of labor used in the production of :feed grains over the 1929 to 1960 period. This coefficient appears reasonable for this period. The results of the logarithmic form indicate a similar {illfluence of the acreage of land planted to feed grains. The partial Correlation coefficient is slightly larger thani/rthe linear form (.32 tillatead of .24). In this case, the regression coefficient is signi- flesntly different from zero at the 5 percent level of significance. Its magnitude (2.71) corresponds to a linear coefficient at the mean 51 of .034 (i.e. 34,000 man-hours of labor for an increase of 1,000 acres of feed grains planted). The discrepancy between the two functional forms is more drastic yet in the case of the expected price of corn. We have chosen the expected price of corn to represent the expected price of feed grains because other prices are linked to corn and because the deri- vation of an average expected price for feed grains would have been very difficult. In the linear form, the regression coefficient is not significantly different from zero (t=.33) and corresponds to an elasticity at the mean of .045. In the logarithmic form, the elasti- city was estimated at .50 and was found to be significantly different from zero. In completing this discussion of the influence of the expec- ted price of corn, it is useful to examine the estimates provided by the autoregressive model. This model was used because the Durbin- Watson statistic calculated on the residuals of both functional forms indicated presence of serial correlation. The sum of squared resi- duals is minimum for f - .6 in the linear form and f = .3 in the logarithmic form. In the linear form the estimated coefficient of the expected price corresponds to an elasticity at the mean of .10 ‘whereas the logarithmic forms give an elasticity of .22. These ‘values are close together. 0n the basis of the standard deviations computed for the ordinary least-squares estimates, an elasticity of ‘about .2 is consistent with all estimates. Clearly, no confidence interval can'be given for this "guesstimate." The estimate of the coefficient for land planted to feed grain is .015 in the linear 52 autoregressive model and .019 in the logarithmic autoregressive ‘model. These results tend to increase confidence in the value .018 found in the linear form by ordinary least squares, as presented above. Fertilizer used for feedegrain production To predict variations in quantity of fertilizer sold in the North Central Region (assumedly representing the amount of fertilizer used in the production of feed grains), a different functional form than either the linear or the logarithmic was used. Numerous sets of explanatory variables and several functional forms were tried. Consistent results were obtained only when the dependent variable was the logarithm.of the quantity of fertilizer and when time was included among the explanatory variables. The simple correlation coefficient between these two variables is .98. Using time as an "explanatory” variable, however, does not explain much. Erratic estimates were obtained when time was deleted and such economic variables as the acreage of land planted to feed grains, the price of fertilizer, or the expected price of corn were included. This result is not entirely negative; it indicates instead that factors other than those mentioned above and very heavily linked with time have been crucial. The growing awareness by farmers of the profita- bility of using fertilizer on their feed grains has probably been important among these factors. Unfortunately, it was difficult to introduce this variable in the model because of the difficulty of measuring it . Even though the role of prices has been minor, it should not be neglected. In a first trial, it was assumed that the logarithm b. 53 of the quantity of fertilizer used was a function of time and of the price of fertilizer divided by the expected price of corn. The elas- ticity at the mean derived from the correSponding regression coeffi- Cient was found equal to -.32, the partial regression coefficient (-.47) indicates that this variable is associated with the amount of fertilizer used. These results can be compared with results of another regre- ssion in which the same dependent variable was assumed to be a linear function of the logarithms of three variables (acreage of land planted to feed grains, expected price of corn deflated by the index of prices paid and the price of fertilizer deflated by the same index) and of time. The regression coefficient for the eXpected price of corn indicates an estimated constant elasticity of .64 (standard deviation .26). Thus, this elasticity is not inconsistent with the value .32 found above. The regression coefficient for the price of fertilizer is positive, not significantly different from zero (t = .5) and, of course, not in accord with the economic model. In any event, this Variable is not closely associated with the quantity of fertilizer Ilsed (the partial regression coefficient is .09). In summary, the nusdels predicting use of fertilizer do not permit a definite conclu— Eiion about the influence of prices. Yet it appears that the expected Irrice of corn has a significant effect whereas the influence of chan- gas in price of fertilizer seems to have been very small. The influence of the acreage of feed grains seems very weak (IDeta coefficient .01) and the regression coefficient is far from being significantly different from zero (t = .24). Its magnitude 54 corresponds to an increase of 1.2 tons of fertilizer (in principal nutrients) per acre at the mean; this may be overestimated even though the total quantity of fertilizer used in the North Central region is probably larger than the quantity of fertilizer used in the U.S. on feed grains only. Production function In the production function,the annual output of feed grains appears as a function of: - the acreage of land planted to feed grains - the amount of labor used in feed-grain production - the quantity of fertilizer used in the North Central region - the acreage of feed grains planted but unharvested - time - Stalling's weather index4 As noted in the discussion of functional forms, this equation is not strictly a production function because the number of acres ‘unharvested, time and the weather index are not inputs. Conceptually it would be possible to estimate a strict production function if sufficient information were available on all inputs used, including those contributing to what we call weather. Practically sufficient information is not available and these variables can be considered as representing shifters of the subproduction function relating output 4J.I.. Stallings, "Weather Indexes," ggg, Vol. 42, p. 180 (Feb. 1960). His index was brought up-to-date by Mr. William Kost 9f this department. 55 to land, labor and fertilizers. The results of both the linear and the logarithmic estimations are given in Table 3, page 45. The degree of intercorrelation is ra- ther high and decreases the reliability of our estimates. This is particularly true for the logarithmic form, it-was found that the ma- trix of sum of squares and cross products "approached" singularity when the fourth explanatory variable was added. According to the size of the beta and partial regression coefficients, fertilizer and time appear to be the most important explanatory variables of the variations in the volume of feed grains produced. The linear regression coefficient for fertilizer indicates that an increase of 1,000 tons of principal nutrients used in the North Central region corresponds with an increase of 16,200 tons in the production of feed grains, other things being equal. The order of magnitude appears reasonable. The regression coefficient in the logarithmic form (.035) appears underestimated because it corres- ponds, at the mean, to only 10% of the coefficient computed in the linear forms We believe that the exponent of fertilizer in a Cobb- Douglas function should be more than .035. This point is discussed again in the next subsection‘which appraises the whole model. The relative importance of time is not surprising. It indi- cates the increase in productivity associated with machinery and the improvement in the efficiency of conventional inputs due to the utilization of better varieties, better weed control and to the other factors generally associated with technical progress. Land and labor are the two other inputs included in the 56 production function. In the linear form, the partial correlation coefficient for land is .27 and the regression coefficient indicates that to an increase of 1,000 acres of land planted to feed grains will correspond an increase in production of 220 tons (i.e. 440 pounds per acre, the equivalent of 7.5 bushels of corn or of 10 bushels of barley). This corresponds to an "elasticity" at the mean of .31 which appears reasonable. The constant elasticity estimated in the logarithmic form for land is 1.08. This appears overestimated since it is believed that the law of diminishing returns applies. From the results of the linear form, labor appears to play a significant role in the explanation of the variations in the volume of feed-grain production as is illustrated by the partial correlation coefficient (.40). The magnitude of the regression coefficient indicates that an increase of 16,200 tons of feed grains produced is associated with an increase of one million man-hours of labor in the use of labor. It is very difficult to appraise this figure. It corresponds to an "elasticity" at the mean of .30 which seems reasonable. The estimated regression coe- fficient of labor in the logarithmic foam is negative in contradic- tion with the economic model. Statistically this sign.may be inter- preted as the result of the substitution of capital for labor. For our practical purpose, we believe that this estimate is economically meaningless and can be ignored. The number of acres unharvested plays an important role as indicated by the magnitude of its partial correlation coefficient 57 (-.59 in the linear fonm, -.65 in the logarithmic form). The ma- gnitude of the linear regression coefficient indicates that, ceteris paribus, when the number of acres unharvested increases by 1,000 acres the volume of production declines by 664 tons (i.e. 1328 pounds/ acre, the equivalent of 22 bushels of corn or 29.5 bushels of barley). This appears quite reasonable. The last explanatory variable included in our production function is the weather index, it plays a nonnegligible role (t= 2.9 in the linear form, t=4.2 in the logarithmic form, with 27 degrees of freedom). The partial regression coefficient is .48 in the linear 5 these indicate that weather form, .63 in the logarithmic form; accounts for some of the variance in the feed-grain output, which is, of course, what one would expect. The magnitude of the regre- ssion coefficient is difficult to appraise since the independent variable is measured with an index; in such a case the beta coeffi- cient appears more meaningful. In the linear form it is equal to .18 which indicates that a variation of .18 standard deviation in the output of feed grains (i.e. 4.48 million tons) will correspond to a variation in the weather index of one standard deviation. The 51f the weather index was a perfect measure of the effect of weather, one would expect this logarithmic coefficient to be 1 and the dependent variable could be chosen to be the quantity of feed grains produced "deflated" by the weather index. As noted above (page 41), results were erratic with this functional form. We believe that this estimate of the elasticity of output with res- pect to weather (.63) reflects the fact that the weather index is not a perfect measure of the influence of weather. This result is in accordance with Gustafson's thorough discussion of Stalling's .index in D.G. Johnson and R.L. Gustafson, Grain Yields and the American Food Supply, University of Chicago Press, 1962. See particularly page 51f. 58 presence of the variable "unharvested acres" in the production func- tion may have led to this underestimation of the weather coefficient. The Model As a Whole After the above presentation of the results equation by equation, the feed-grain model as a whole remains to be appraised. In this subsection, the effects of the expected price of corn and of the number of livestock on farms at the beginning of the year on the annual output of feed grains will be discussed first. Then the effects of other factors will be briefly reviewed. Effects ofthe expectedgprice of corn In order to derive a price elasticity of supply, estimates of the price elasticities for the use of inputs mentioned above are multiplied by the estimated input elasticities of output. It should be clear from the presentation of the results equation by equation that considerable judgment is involved in choosing among the various earn-ates of the same parameter. The "Guesstimates" of the price elasticities of the use of labor and of fertilizer are respectively .2 and .3.6 In view of the erratic results of the logarithmic form of the production function, probably due to the high degree of inter- correlation, we have preferred to use the estimated coefficients 6See the previous subsection, "Individual equations" for a discussion of these estimates. 59 from the linear form. From these regression coefficients, we have then derived "input elasticities" at the mean of .31 for land, .30 for labor and .17 for fertilizer. The sum of these coefficients (.78) seems reasonable since all the inputs were not included. However, as land, labor and fertilizer are major inputs, the sum of these coefficients should not be too far from one. Following this method, we have computed a price elasticity of supply. The result is .11, which is small. This result may be explained by two considerations. 0n the one hand, the model probably underestimates this elasticity while, on the other hand, the actual elasticity is probably small. Some of the inputs which do not appear in the production function probably respond to changes in expected prices. Another cause of underestimation is that the expected price of corn deflated by the index of prices paid does not reflect rela- tive profitability of growing feed grains rather than other craps. Actually, the possibilities of substitution, account being taken of the economic conditions which have prevailed since 1929, have not been very great. The effect of price may have been domina- ted by the effect of changes in such variables as time and the indus- trial wage rate. It seems very likely that the numerous and important changes which have taken place since 1929 have been more important than prices in determining the production of feed grains. Finally, the probability of inputs becoming easily fixed (such as specialized machinery) probably reduces the average short run elasticity. As will be seen later, there is fairly strong evidence that such has been the case particularly since the early 50's. 60 Effects of the number of livestock on farms, January 1 The procedure for estimating the influence of expected prices was also used to estimate the effects of the number of livestock on feed-grain production. The number of livestock on farms influences the acreage of land planted to feed grains; in turn this acreage influences the use of the other inputs, labor and fertilizer. Accor- ding to the estimates mentioned above, the computed elasticity of feed-grain production to changes in livestock numbers is .19. The two influences of price and livestock numbers are not independent as the expected price depends on the predicted demand for feed grains which is itself a function of the livestock inventory at the beginn- ing of the year. Incidentally, this relationship may explain.why no significant influence of price on the acreage of feed grains planted was found. It is difficult, if not impossible, to isolate the direct influence of livestock number from the influence of expected prices. Yet it remains that the production of feed-grains is associated with changes in livestock numbers as is to be expected on a priori grounds. Other factors As should be clear now, many factors inadequately handled by this model have been important in determining feed grain production. Heather plays, of course, a role as reflected by the importance of the weather index in the production function and also by that of the variable "unharvested acres" which depends heavily on weather. The major role played by time in the various equations of our model indicates that we have not been able to measure several important 61 factors which determine the annual feed-grain supply. Among the most important of these factors are probably government programs, the use of machinery, the growing awareness of the profitability of using fertilizer and the numerous technical improvements ranging from the use of better varieties (hybrid corn) to better weed and disease controls. 62 .Craw.wL_.TCL.p r..~F.MLIIL¢.J 1w 16.0.; 7L»... LC.. OwnCm .farrsuw LLQ...HP Q.¢fi...r...u. -..LWQH . trawlwtiwpv wt“. LC cmfirdwewmbww .... H time.» Q . I’l. .IW. IIIQ!‘.9,.II.O.II-OI.I> I,’ f!aii-‘.Pl.llflll+lif[$.1.l+i+ 4 IV -H m T. who at. on“; m... T 0% mm. ..H .m \AW I w J 4 / deems / . . . M Hex} o J 4.“: x: . m . e .... I a , ”00¢! , e . x ’ ... I . ah I/ — a. \ Io- 1‘ ‘ . l . y - . . . . . I. , ... I]..- .lll.)ov ,. -.‘i .01.)- .II - Iii . . rl ... (olivhsllvlf «Illll‘u‘vlli \ {I i new \. sk ' a m. t at? Anette tc_~.eit fimLDC£.CnE cofipm_f. 63 Appraisal of the Model The model yields some information concerning the economic forces underlying feed-grain production. This section is devoted (1) to an appraisal of the validity of the results obtained so far, (2) to an attempt to make qualitative statements concerning the influences of some factors which our model failed to measure. Analysis of the Residuals A study of the evolution, over time, of the residuals of the various equations, can well serve this double purpose. It will point out some insufficiencies and suggest how some factors, not included in the model, have affected feed-grain production. Lend The residualsof tha equations for land are plotted over time in Figure 1, page 62. The pattern of residuals for the land equation indicates that two factors not taken into account in the model have an influence on the number of acres planted to feed grains: government programs and the acreage of wheat planted. Thus the overestimation of 1937 is probably due to the effect of the Soil and Conservation Act and also to the increase in the acreage of wheat planted. Similarly the overestimation for 1961 and 1962 is very likely due to the govern- ‘lcnt feed-graih programs; the acreage planted declined from.148 in 1960 to 129 million acres in 1961. The pattern of residuals from 1951 t0 1959 can be explained by variations in the acreage of wheat planted. It was higher than "normal" in 1951-53 and lower afterwards. Thus our lDdal fails to recognize the fact that land is a fixed resource for 64 the agricultural sector and it does not take sufficiently into account the factors which determine the allocation of land among the various agricultural enterprises. Thus, it is very likely that the price elas- ticities of the use of land and consequently of supply have been under- estimated. Since 1955 the expected real price of corn has declined, yet the residuals are positive. The acreage of land planted to feed grains did not decline as fast as the model indicates. We feel that the-fixed asset theory provides the explanation of this divergence. The fixed assets which prevented this decline are land itself and probably the specialized machines such as corn pickers and combines bought when prices were high. The average number of corn pickers bought per year from 1950 to 1953 was 70,500; it dropped to 36,000 for the period 1954-1958.7 are: The residuals of the labor equation are plotted on the same Figure 1, page 62. It appears that the variations in these residuals can best be linked with the prOportion of acres planted to feed grains and not harvested for grain. Accordingly, the overestimations for 1934 and 1936 correspond to a high percentage of acres unharvested (212 and 20% respectively). The underestimation of the quantity of labor used from 1938 to 1946 corresponds to a lower percentage of unharvested acres (171 on the average) and, also, to an underesti- 7U.S.D.A., "Number of Selected Machines and Equipment on Farms with Related Data," Statistical Bulletin No. 258, (Feb. 1960). 65 .ITI. . Illllilllll' .LcweL21CLR Cmeku town i“ Tom: Lcumfifiehmu.L0w CCwiezru mLaLCU tuncg >thprC cit wc mHmSTwmcm I m .seu he he he, no. we 3 .5. or: T..:+Il:+il.+:lrf: I.it|.1nls...-il+.l.:+;i+i+at+.i17!lri¢ l. L.| q 4 4r 4? ii i 4.! t V v o w w 9 l -..—pm ’4. I i i | Y . 3‘ ..\ 4 . i it. in? .. i A ? 1n ‘9 ufviifi..rlu LL“ i mi: 95. C LCKw—mlicu «C— 66 mation of the influence of higher expected price for corn (and other feed grains). This influence of expected prices is clear because the year-to-year variations in the residuals follow those of the percentage of acres nonharvested but their average value is too high as compared with the following period (1947 to 1955) during which the year-to-year variations still follow those of the percentage of acres nonharvested but for which this percentage has an average value of 16%. It seems that higher expected real prices before 1947 led to a larger use of land than predicted by the model and vice versa afterwards (expected real prices during the Korean.War were lower than from 1943 to 1946). Fertilizer The residuals for the fertilizer equation are plotted against time in Figure 2, page 65. The dependent variable of this equation is the logarithm of the quantity of fertilizer used. In this equation the acreage of land planted to feed grain is not included among the explanatory variables. Therefore one would expect that the residuals of this equation reflect the influence of variations in the acreage of land planted to feed grains. This factor seems to explain the negative residuals of 1960 and 1961 and the high positive residuals of 1953 and 1954. But prior to 1954, it is difficult to point out a definite relationship between the acreage of land planted and the residuals of the fertilizer equations. The time variable has great importance in this equation. The residuals could be reduced if the functional form was changed as making logarithm of the quantity of fertilizer a linear function of time is not very satisfactory. In summary, it is concluded that the analysis does not tell 67 .ULQrCLKh» :4 Twrw; MCLwL; hr. XCT£~ Q4. .rL Tewkfipbflic CtrC.-. hcw UUWHQ ItitQCX: tfn LcwitLI; LCth27CLL Lcwc_~ twmbtliwc: axe uC mafiZiwwc; 1 .mL r. «e 3 M10 on ma 3 cm 2...: ‘1. § ... a. IXI‘O.QI1.I. 9021‘é‘3‘l‘fli‘. ..-.ll‘t-.‘4 1 144| 41 l1. 1 1 1 1 I) *I 1" .1 ‘ 3“... . 1.9.1111] 1,!!‘1‘1 > “xx N ¢ \ 1 t I l II. 1 ' ...-u. DrU_ \ Amnou GOHHHHEV :iCL LO» cbwkfi Tertoi>© ti.m~eci _eciut;,h.t pi.” e E... ”...—o” —. ...-a ‘40-..4 \ k stenprsag 68 much regarding variations in the use of fertilizer except that short- run economic considerations do not seem to be of an overwhelming importance . Production function The residuals of the production function are plotted over time in Figure 3, page 67. Generally speaking their year-to-year variations are difficult to interpret. Until 1948 these residuals follow a general trend parallel to that of the expected real price which is plotted on the same diagram. After 1948 the parallelism disappears. Several observations stand out as exceptions to the general statement made above. In 1947 the residual is negative and large even though the expected real price is high. Here the adverse effect of weather has probably been underestimated by the equation, even though the weather index is small (82.7), as the percentage of acres unharvested was small (15%). Similarly adverse effects were not underestimated in 1934 and 1936 because, for these years, the percentage of unharvested acres was large (41% and 34% respectively). The roughly parallel pattern of the residuals of the production function and of the expected real price for corn until 1948 indicates that the influence of expected prices on production has been under- estimated for that period at least. A possible explanation of the change in the pattern of residuals around 1948 can be given. Until that date, specialized inputs were not of a paramount importance; thus the factors not taken into account in the production function and reflected in the residuals are inputs whose use varied with the expected real price of feed grains. The evolution is clearly in 69 the opposite direction from 1954 to 1960, the residuals increased while the expected real price decreased. This evolution.may reflect the use of specialized farm machinery (corn pickers, combines, corn planters, etc.) bought during and after the Korean.War. From 1954 to 1960, the variations in use of these machinery inputs are not as well reflected in the other inputs as they were before. Between 1948 and 1954, the residuals decreased in spite of relatively high expected prices. Apparently the increase in the use of all inputs (including machinery) was reflected in the variables present in the equation, particularly fertilizer and time. The decrease in the residuals probably indicates an underestimation of the effect of weather. From 1948 to 1953, the weather index decreased continuously from 121.1 to 79.2. During the same period, the percen- tage of acres unharvested was not especially large (16% on the average from 1949 to 1954). Implications of This Analysis The previous analysis of the residuals of the various equations of the model indicates that our model does not take into account some significant factors determining the use of resources and the amount of feed grains produced. The amount of land planted to feed grains depends not only on the acreage of winter wheat not harvested but also on the total acreage of wheat planted and the stock of specialized machinery on hand before planting. Thus it appears that a weakness of this model ) is its failure to recognize the influence of relative prices of farm. I products and of government programs in shifting the use of land to and away from feed-grain production. 70 It seems as if the major factors explaining the use of labor are included in the equation. The residuals seem to be due to varia- tions in the acreage unharvested and to an underestimation of the effects of feed-grain prices. The shortcomings of the production function are the absence of a variable representing variations in the use of machinery and the underestimation of the effect of bad weather. The influence of machinery seems to have been the most significant after 1954. Conclusions One important limitation of this feed-grain.mode1 is that it is not complete. Without independent price forcasts, it is impossible to predict how many resources will be committed to the production of feed grains and what volume of production will result. But such price forcasts were not included as objectives of the study. As was stated above, research resources were concentrated on the production sector which is poorly known. It is now time to appraise achievements in that sector. Commitment of Resources Land Land is one of the resources taken into account in our model. The results of the statistical estimation indicate that factors which can be linked even roughly to a trend variable such as government program.and the increase in yield have been important in reducing the acreage of land planted to feed grains. The influence of govern- 'ment programs is confirmed by the analysis of the residuals of the 71 equation. Another important factor determining variations in the acreage of land used for feed-grain production is the set of alternative Oppor- tunities for profitable use of land. Land is fixed within agriculture. Accordingly the model indicates the importance of the acreage of winter wheat planted but not harvested. Also, study of the unexplained resi- duals shows that some of their variations are linked with variations in the total acreage of wheat planted. Therefore, it is very likely that the influence of prices on the use of land for feed grains has been underestimated because the allocation of land between various agricultural enterprises has probably been strongly influenced by relative prices for craps (particularly feed grains, wheat and also soybeans) and changes in their relative cost of production. Finally the model indicates a nonnegligible influence of the number of livestock on farms at the beginning of the year on the year-to-year variations in the acreage of land planted to feed grains. Labs; Labor is another nonspecialized input which is fairly fixed within agriculture, even though the massive migration out of farming is a clear indication that this fixity is not absolute. Because of the high degree of complementarity between land and labor,8 it is not surprising to find that the acreage of land planted to feed grains is an important explanatory variable of the variations in the quantity 8Of course, this does not deny the possibilities of substitu- tion between these two inputs; it only indicates that complementarity has been.more important. 72 of labor used in feed-grain production. The analysis of the residuals has shown that this variable was not sufficient; when the pr0portion of land planted but not harvested increases, the use of labor per planted acre decreases, other things being equal. The model does not necessarily show a high degree of fixity of labor within agriculture. This result cannot be considered as evidence indicating that labor is not fixed. As labor is mobile from one agricultural enterprise to the other and feed-grain produc- tion does not use up the bulk of farmers' working time, labor is quite variable for the feed-grain enterprise. Finally, the effects of the lack of mobility, if any, are hidden by the large decrease in labor requirement due to the substitution of capital for labor. This last influence is reflected in the high coefficient of the "industrial wage rate" variable. The analysis of the residuals of the "linear" equation estima- ted by ordinary least squares has shown that the influence of the expected price of corn is underestimated. This confirms the results of the other functional forms as presented above. Thus it can safely be asserted that the expected price of corn has a definite influence on the amount of labor used in feed-grain production. To give an idea of the order of magnitude of this influence, an average elasticity of .2 is tentatively mentioned. Fertilizer Fertilizer is a nonfanm produced expendable input. Variations in its use have not been successfully related to clearly identified economic factors. Yet this is not complete failure. This result may 73 indicate the importance of the degree of awareness by farmers of available "technology." This factor may have been so strong that variations in the real price of fertilizer have not been a major determinant of consumption and that farmers did not use fertilizer ; up to the economic Optimum on the average between 1929 and 1962. Other inputs As mentioned several times, the lack of adequate data preven- ted us from including other inputs in our econometric model. However, the crucial role played by specialized durable inputs, such as machi- nery, in the determination of the volume of supply leads to a few comments on this important question. The measure of demand for machinery raises many questions9 not to be discussed here. Suffice it to say that manufacturers ship- ments have been taken as an indicator of the number of various machi- nes bought each year. In Figure 4, page 74, the pattern from 1950 to 1962 of the annual shipments of corn pickers, corn and cotton planters and grain combines are plotted against time. On the same diagram.a fourth curve gives the corresponding pattern in the expected price for corn deflated by the index of prices paid. These variables have been chosen because of the availability of data.10 For the same reason 9For a discussion of these problems see: W.A. Cromarty, "The Demand for Farm Machinery and Tractors," Tech. Bul. 275 (Michigan State University, Agr. Expt. Sta., East Lansing, Michigan, 1959) and E.A. Reiling, "Demand Analysis for Combines, Pick-Up Balers and Forage Harvesters," (unpublished MS thesis, Dept. of Agr. Econ., Michigan State University, East Lansing, 1962). 10The sources of these data are "Numbers of Selected Machines and Equipment on Farms with Related Data," U.S.D.A. Stat. Bul. No. 258 (Feb. 1960) and the ”Farm.Machine and Equipment" section of the periodic Current Industrial Reports (Series M35A-09), Bureau of Census, U.S. Department of Commerce. 74 M (thousand units) 80 ” Corn pickers t 1 QC 4 30 1 (thousand units) lOé/T ! I Corn and cotton planters lfo i wo-lr 52', A (thousand units) loo V Grain combines 30 b 60 + including imports \ v,- 40 J- ‘r’ ‘x \x\ excluding imports :;;‘;Erfii*rf,f 5'560 6?. Fi‘ G — Vxnsc‘ed “r‘re ’o“ For? Deflated b' *Fe Tndny of I'Ir:cp(. T‘qu’ 1-“y Fgrpxprc ”V‘A ""‘IY‘HFGI‘LY'Y‘OI‘Q' -’ L‘:Y\'-‘Qwv~O-C or r‘rn‘:vfi (‘0.1.‘ ...-rJQ‘ Carr and Cotton Platterr, and Corn Pickers. ”.‘. ‘950-1‘62 75 two curves are shown for combines (one including imports, the other excluding them) which overlap from 1952 to 1959 but complement each other outside of this time span. It appears immediately that these curves are very much parallel ‘with a general declining trend from 1950 to 1962. Though this declining trend is partly due to the shift to larger machines, a breakdown by size indicates that the number of machines of each size category decli- nes in most instances. Cromarty's results indicate that farmers ! income is a key variable in the explanation of machinery purchase by farmers. Prices make one dimension of income, thus it is not surprising that machinery purchases respond to changes in feed-grain prices as indicated by the curves on Figure 4. These are very general remarks, they throw a little more light on the influence of price on feed-grain production through the commit- ‘ment of specialized machinery. A detailed study of the demand for machinery is clearly out of the scape of this thesis. Feed-Grain Production As was stated above, most empirical results of research in production can be summarized in a supply function. Such a procedure is dangerous because it often implies that the price of the product is the major economic factor of variation of the volume of production. Our results indicate that this has not been true for feed grains. ) They confirm that the price elasticity of supply is probably small, \ and that other factors influence the volume of feed-grain production. : However, the failure of the econometric model to take into 4 account the effect of inputs which become easily fixed in feed-grain 76 production (such as specialized machinery) has prevented a comprehen- sive picture of the influence of prices. However, our analysis of the results and of the residuals of the various equations permits us to ‘make some qualitative statements. It appears that, at least since the early 50's, the response of feed-grain production to variations in the expected prices of grain (particularly decreases) was hampered. The evidence provided by the analysis of the residuals is consistent 'with the hypothesis that fixed assets have hampered the adjustment. Thus, the value of the price elasticity given above is only indicative of the order of magnitude of the average influence of prices on year- to-year variations in the volume of supply for the period 1929-1962. When fixed assets play a significant role, one "price elasticity? is not sufficient to characterize the short run influence of prices on output since past purchases of durables push the supply up. As the analysis of the residuals indicated, this study lends support to the thesis of greater price elasticities for expansion than for contrac- tion.,. / The scanty evidence given above, relative to the influence of prices on purchase of machinery, indicates that the influence of pri- ces on the volume of production is probably significantly greater in the long run than in the short run. This result is in agreement with the usual economic theory. Unfortunately the limitations of the econo- metric model prevented "measurement" of long run price elasticities. The factor other than price which was clearly isolated is size of livestock inventory in farms at the beginning of the year. Yet the great importance of time in many equations shows that other 77 factors have had a significant influence on the volume of production. Unfortunately, the analysis can only indicate some of these factors which may loosely be grouped under the heading "technical improvements." Though their importance has not been measured, the analysis indicates that their aggregate influence has been strong. 1The low price elasticity of supply is a factor favoring year~ to-year instability of prices. Of course, the price support programs have partially eliminated this potential source of price instability. This low elasticity indicates that the volume of feed-grain production does not respond very much to changes in prices but it does not mean that the supply of feed grains is constant. Actually the standard deviation computed over 34 years represent 25% of the mean value. Thus prices are a poor means of adjusting production to demand. The low elasticity of the volume of production with respect to the number of livestock on farms at the beginning of the year is another indication that adjustment of the supply of and of the demand for feed grains is far from good in any one year. CHAPTER IV HOG PRODUCTION This chapter presents the main results relative to hog production. The same plan has been followed as in Chapter III for feed grains: (1) an explanation of the economic analysis underlying the hog model is given, (2) the statistical treatment is presented along with a discussion of the statistical difficulties Specific to this submodel, (3) the main statistical results are summarized and, finally, (4) a section is devoted to an appraisal of the model and to the conclusions which can be drawn from this part of the study. Economic Analysis Introduction Basically, the structure of the hog model is similar to that for feed grains. It is assumed that resources are committed to the hog enterprise on the basis of various factors, including price expec- tations. Output is then determined by the amount of resources used and by some uncontrolled factors. Since the model is based on annual data, it is implicitly assumed that decisions concerning the amounts of inputs to use are taken once a year, at the beginning of the year. One may prOperly wonder whether or not we have thereby ignored an important aspect of the adjustment of supply to market conditions through changes in fall farrowing and changes in marketing weight. Though this reservation should be kept in mind, it does not destroy the validity of the work. First, it would have been very difficult, 78 79 if not impossible, to do otherwise because of the impossibility of estimating all the relevant price expectations and because current prices which could not be considered as predetermined variables ‘were omitted.1 Besides, as Harlow has pointed out: "Most analysts have found that farmers make their basic decisions as to the number of sows to farrow on a yearly basis, with some adjusoment of fall "2 Since our model farrowing in response to changed conditions. incorporates an equation for sows farrowing in the spring and another one for fall and since farrowings are estimated on the basis of two series of price expectations, it is haped that adequate care has been taken of these adjustments. Yet it remains true that the model does not permit full account to be taken of intra-year adjustments in the amount of feed fed to hogs and of labor used in that production. The presence of the expected price for hogs farrowed in the fall among the explanatory variables, permits partial account to be taken of such adjustments since this eXpected price is formed during the year in question. LThe treatment of current prices as endogenous variables would have required the allocation of considerable research resources to the study of demand. As was said earlier, we have felt that it would be much more profitable to devote the resources available to us to the study of the production sector. 2A.A. Harlow, "Factors Affecting the Price and Supply of Hogs," U.S.D.A. Tech. Bul. No. 1274 (December 1962), p. 27. The studies referred to are: G.E. Brandow, "Factors Associated With Number of Sows Farrowing in the Spring and Fall Seasons," Pennsylvania Agricultural Experiment Station, A.E. and R.S. Bulletin 7. (1955). G.W. Dean, and E.O. Heady, "Changes in Supply Functions and Supply Elasticities in Hog Production," Iowa Agriculture and Home Economics Experiment Station Research Bulletin 471 (1959). R.L. Kohls and D. Paarlberg, "The Short Time Response of Agricultural Production to Price and Other Factors," Purdue University Agricultural Experiment Station Bulletin 555 (1950). 80 Changes in Inventory It is clear that hog production should not be confused with hog slaughter. Changes in hog inventories at the beginning of the year are too important to be disregarded and final demand is in terms of pork. The model, as described so far (i.e. made up of a production function and of some equations explaining the amounts of inputs used) is not sufficient to explain the supply of pork. Thus, it is necessa- ry to disaggregate the annual hog output into at least two components: pork production and changes in hog inventories. When there are decreases in inventories, the supply of pork during that year is increased accordingly. As a result, the model is extended by adding equations reflecting the behavior of hog farmers regarding the number of animals they keep on hand at the end of the year. It must, indeed, be recognized that hogs on farms are not a homogenous commodity. Sows to be bred and hogs to be fed play quite different roles and their numbers are determined by two distinct sets of decisions. More detai- led categories could be distinguished but, for obvious reasons of simplicity and availability of data, only two categories are used: sows and other hogs. In the model, changes in inventory are essentially dependent on the amount of feed available and on the expected profitability of hog production. The existence of cycles in price, production and numbers of hogs has long been recognized.3 An abundant literature 3The earliest reference which we found was: S. Benner, "Benner's Prophecies of Future Ups and.Ibwns in Prices," Cincinnati: R. Clerks Co., 131 p. (1876). 81 exists on this subject both at the theoretical and empirical levels. The theoretical model used most often to explain this cycle is the cobweb theorem as presented by Ezekiel“ or as modified by Akerman5 or others such as Harlow.6 The essential feature of most of these explanations of the hog cycle is a lag in the adjustment of supply to price.7 Our model, being concentrated on supply and taking expected prices as predetermined variables, cannot eXplain these cycles. However, the model is consistent with cycles since the estimated values of the output in the production function and of the numbers of sows and hogs in the corresponding equations, follow cycles. A complete explanation of this cycle requires a better statement of and understanding of the way hog producers form price expectations. Production Function - Use of Inputs Output, the dependent variable of the production function, has been defined above. It is assumed that this output depends on the 4M; Ezekiel, "The Cobweb Theorem, " Quarterly Journal of Economics, 52:255-280 (February 1938). 5G. Akerman, "The Cobweb Theorem; A Reconsideration," Quarterly Journal of Economics, 71:151-160 (February 1957). 6A.A. Harlow, ”The Hog Cycle and the Cobweb Theorem”, JFE 42, 4 pp. 842-854 (November 1960). 7See for instance: W.R. Maki, "Decomposition of the Beef and Pork Cycles," g§§_44, pp. 731-43 (August 1962). 82 amounts of various inputs used, on technology and on some uncontrolled factors. In the case of hog production, technical progress is taken into account through two variables: the annual average number of pig- lets saved per litter and time. Both are considered as exogenous variables. The other eXplanatory variables in the production function can be considered as inputs. They include the number of sows farrowing in the spring, the number of sows farrowing in the fall,8 the amount of feed grains consumed by hogs, the amount of high protein feed consumed by hogs and the amount of labor used in the hog enterprise. The economic analysis of the use of inputs in hog production is very similar to that set forth in the case of feed grains. It is assumed that the amounts of feed grains and high-protein feeds consu- med by hogs, as well as the amount of labor used in hog production, are essentially a function of the amount of available input and of the expected price of hogs. In the case of high-protein feed and labor, the prices of these inputs are included. Sows to farrow appear as a special type of input, yet the explanatory variables used in the equation predicting the number of sows farrowing are very similar to those used for the other inputs. We have assumed that the number of sows to farrow in a given season is a function of the number of sows available, the expected price of hogs which will be farrowed and the amount of feed available. A aAccording to USDA data, spring farrowings extend from December 1 to May 31 and fall farrowings from.June l to November 30. 83 (distinction has been made between fall and spring farrowings. As stated earlier, according to previous studies, the number of sows to farrow is determined on a yearly basis at the beginning of the year with some adjustments for fall farrowings. .As a result, the number of sows on hand January 1 has been used as an explanatory variable for spring farrowings whereas, in the case of fall farrowings, the corresponding explanatory variable is the predetermined number of sows farrowing in the previous spring. Statistical Treatment Two types of problems are dealt with in this section: (1) those due specifically to data, (2) those involving estimation. Problems Due to the Data As stated above, the dependent variable of the production function is the amount of hogs (in liveweight equivalent) produced in a given year, i.e. the amount of pork slaughtered in any one year plus the increase or minus the decrease in hog inventory. Such data are now provided directly in a series published by the-USDA9 which involves some errors of measurement not believed to be drastic or to raise major problems. The situation is probably different in the case of inputs such as feed-grains and high-protein feed consumed by hogs and labor used in the production of hogs. As remarks made in the case of feed grains 9U.S. Dept. of Agriculture, Livestock and Meat Statistics, 1962, Stat. Bul. No. 333, July 1963. 84 for the labor input apply here, too, it is not necessary to repeat them. Data on feed-grain and high-protein feed consumed by hogs are provided by a statistical series of the USDA.10 They are not published on a calendar year basis but for years beginning October 1. In spite of the seasonality of hog production, it was found best to correct these estimates and adjust them to a calendar year basis by weighing them 3/4-1/4. Though this procedure calls for some reservations, a better method was not available in view of the research resources at hand. These data are not likely to raise major problems. The amount of feed grains available appears as an explanatory variable in several equations. In order to take government storage of feed grain into account, the amount of feed grains available in any one crap year is defined as production plus the stocks held in commercial storage at the beginning of the year. This procedure raises some problems as, first, the stocks in government storage probably put a certain amount of pressure on prices and induce some hog production and, second, pro- duction in any one year is not marketed entirely through commercial channels and some feed-grain producers intend to market through the CCC when they decide to plant. Feed-grain production by such produ- cers should not be placed on the same level as that of farmers who produce corn to feed to their own hogs. Yet it was impossible to distinguish between these various types of feed-grain producers. 10Ralph D. Jennings, Consumption of Feed by Livestock, 1909- 1956, USDA Production Research Report No. 21, November 1958. The figures were brought up-to-date by USDA staff workers. 85 The method outlined above is probably adequate in the case of this model. Remarks in the previous chapter, concerning eXpected prices and the problems of the deflator, apply here, too. Estimation Problems Recursiveness As stated in Chapter II, it is clear that Wold's first condi- tion for recursiveness (triangularity of the coefficient matrix of endogenous variables) is satisfied by the hog model (see Table 5, page 89). The usual prOperties of the ordinary least-squares estima- tors hold if the disturbances of the equations for sows farrowing in the fall (SE) and for hogs over 6 months old on farms at the end of the year (at) are not correlated with the disturbances of the equa- tion explaining the number of sows farrowing in the spring S3, since f s; appears as one of the explanatory variables of both Sf and Ht° The f only other equation for which there may remain a question as to the effects of simultaneity on the preperties of the ordinary least-squares estimators is the production function where five of the explanatory variables are endogenous. If farmers really make their decisions on the number of sows to farrow on a yearly basis with adjustments in fall farrowings accor- ding to changing conditions, there is no strong indication that the disturbances of the equations for fall and spring farrowings are correlated; these equations describe decisions taken six.months apart. However, the "recursive" procedure has been followed along with ordi- nary least-squares and the results of the former have been rather 86 disappointing. In the linear form, the coefficient of multiple de- termination, corrected for the number of degrees of freedom, is .47 as against .81 by ordinary least-squares. The regression coefficient for sows farrowing in the spring has a negative sign but is not significantly different from 0. A positive sign was expected and was obtained by ordinary least-squares. Since there are no apparent reasons to believe that the dis- turbances of the equations for SE and Ht are correlated, the ordinary least-squares method alone was used. The magnitude of the correlation coefficient between the residuals of the two equations (-.10) justifies this procedure. It is far from being significantly different from 0, even at the .50 level of significance. In the case of the production function, the results of the "recursive" method are disappointing also. Using the estimated rather than the actual values of the explanatory variables may remove some correlation between them and the disturbances but it introduces more intercorrelation between explanatory variables. As a result, the regression coefficient estimates are much less reliable (larger stan- dard deviations) but they remain consistent with the estimates obtai- ned by ordinary least-squares. A priori, the reasons which would lead us to expect correlation between the production function distur- bances and the disturbances of the equations predicting the use of inputs seem weak. The disturbances of the production function reflect the influence of neglected inputs and there are no apparent reasons to expect a strong correlation between these and the disturbances ,5 of the equations predicting the use of input since most of the 87 important economic variables appear already among the explanatory variables. Accordingly, the correlation coefficients computed bet- ween the residuals of the production function and those of each input equation are not significantly different from O at the 5 percent level of significance for all equations. Choice of the functional form In.most cases, economic analysis is not sufficient to deter- mine the functional form of the various equations representing econo- mic relationships. In the case of the equations explaining the use of inputs, economic analysis indicates which variables can be expec- ted to influence the dependent variable and in what direction but little more. Thus, it is very difficult to make a choice. For the sake of simplicity, a linear equation seems to be the best. 88 TABLE 4 Variables of the Hog Model Symbol Definitions Units SE No. of sows farrowing in the fall 1,000 heads 82 No. of sows farrowing in the spring idem p Average no. of pigs saved per litter head FG Feed-grains consumed by hogs 1,000 tons HP High-protein feeds consumed by hogs idem Lab. Labor used in hog production 1,000,000 man hours T Time years t=l in 1929 F. av. Feed—grains available (Production and commercial stocks) 1,000,000 tons EP Expected price of hogs (average for the year) Cts/th IPP Index of prices paid by farmers, l9lO-l4=100 EPf Expected price for hogs farrowed in the fall Cts/th EP. Expected price for hogs farrowed in the spring Cts/th EPc Expected price for corn Cts/lO bushels St_1 Number of sows at the end of year t-l 1,000 heads Ht-l Number of hogs other than sows, 6 months and older at the end of year t-l 1,000 heads TH Total number of hogs at the beginning of the year 1,000 heads IWR/CPI Industrial wage rate deflated by the Output consumer price index Hog production (liveweight equivalent) 1947-49 cts/hr 1,000,000 lbs. 89 TABLE 5 Equations of the Hog Model Equations (indicated by the dependent variable) 3 f Variables Sf Sf I FG HP Lab St Ht Output s; E E E E f Sf E FG E E HP E E Lab E E st_1 x x EP3/IPP x EPf/IPP x x EP/IPP x x x x Fav. x x x x EPc/IPP x x IWR/CPI x r x x x TH x x x f Sf (t-l) x E: Endogenous variables X: Exogenous variables For definition of variables see Table 4. 90 TABLE 6 Hog Model. Ordinary Least Square Estimates of the Linear Form (Standard Errors in Brackets) R2 Equations .90 $2 = -330.4 + 3.87 Fav + 127.1 EPs/IPP - 135.6 EPC/IPP + .853 _1 (2.7) (60.3) (88.9) (.055 .81 s§ = -713.9 + 23.7 Fav + 103.2 EPf/IPP - 229.5 EPC/IPP +.44zs§ (2.8) (67.7) (109.7) (.06) .90 FG = -12098.3 + 191.2 Fav +,771.9 EP/IPP + .427 TH (18.1) (287.4) (.052) .95 H.P. = -733.6 + 178.6 Time - 2.10 EP/IPP + .034 TH (7.3) (35.9) (.009) .63 Lab = 71.958 + .006 TH + 20.5 EP/IPP - 4.1 IWR/CPI (.001) (5.9) (2.4) .99 Output = -l7478.6 +u033sf + .85638 + 2794p + .113 F6 + .29 HP + 9.14 Lab (.126)ft-1 (.427)f (427) (.021) (.10) (1.93) .88 at = -181.1 + 2.4788 - 276.8 Time + 351.7 EPf/IPP (.24) (28.7) (195.5) .64 st = 249.3 - 119.1 Time + 43.98 Fav +-394.1 EP/IPP + .337 st_1 (29.1) (11.17) (102.2) (.113) 91 TABLE 7 Hog model. Ordinary least-square estimates of the logarithmic form (Standard errors in brackets) R2 Equations .91 s; - .029 + .946 st-1 +.050 Fav + .115 EPs/IPP - .095 EPC/IPP (.206) (.055) (.034) (.039) (.047) .81 s; = .271 + .611 s; + .536 Fav + .088 EPf/IPP - .176 EPc/IPP (.391) (.097) (.060) (.091) (.104) .92 PC = .206 + .604 TH + .585 Fav + .111 EP/IPP (.318) (.071) (.048) (.042) .78 HP = -.088 + .4997 T + .656 TH - .0089 EP/IPP (1.314) (.0481) (.277) (.1563) .61 Lab - -.879 + .734 TH + .250 EP/IPP - .097 IWR/CPI (.537) (.114) (.077) (.061) .58 st . 1.539 + .410 st_1 - .088 r + .322 Fav + .277 EP/IPP (.472) (.119) (.029) (.102) (.079) .71 at = -.045 + 1.096 s; + .229 EPf/IPP - .180 r (.726) (.187) (.124) (.033) .99 Output a -.495 +-.006 sg + .449 s; + 1.169 + .294 FG +-.0428 HP + (.137) (.0371) t-1 (.059) (.1483 (.049) (.0187) .1998 Lab (.0623) 92 Another very strong motive leading us to consider linear equations is that some accounting identities are linear (e.g. the hog output is composed of changes in inventories plus pork production). When all terms but one are estimated in such identities, it is possible to estimate the last one by deduction and know something about its statistical pr0perties (unbiasness for instance). But many econometricians do not like to use linear relation- ships11 in such empirical studies. Feeling that to assume a constant effect of one variable over a large range of production is an over- simplification they often prefer relationships that are linear in logarithms. In the case of a production function, this gives the classical Cobb-Douglas. For these reasons, we have estimated.most of our equations both as linear in the variables and as linear in the logarithmo of the variables. It is interesting to note that the economic interpretation of the resulting elasticities at the mean is not much changed by shifting from.one functional form to the other. Serial correlation In the hog model, serial correlation has not been a major statistical difficulty. In most cases the DurbinAWatson test led to acceptance of the hypothesis of serial independence at the 5% level of significance in which cases the problem was ignored. Results The estimates for the hog model are presented in Tables 6 and 7, pages 90 and 91. As was mentioned earlier, all equations have 11Among those, very prominent ones can be found such as H. Theil. 93 been estimated under two functional forms (linear in the variables and linear in their logarithms). Accordingly, account is taken of both estimates in this discussion. The equations are first presented individually. This is followed by an appraisal of the whole model. Individual Equations For all equations, several sets of explanatory variables were tried. Only the most significant results are presented and the results of alternative formulations of the equations are brought to bear on the analysis when deemed useful. Saws farrowing_in the spring The explanatory variable having the largest beta coefficient is the number of sows on hand January 1. The importance of this variable can also be seen from the magnitude of the partial correla- tion coefficient (.95). It is not surprising that the number of sows on hand January 1 is so important in explaining the number of sows farrowing in the spring (that is from December 1 to May 31). The magnitude of the regression coefficient (.85) in the linear form seems reasonable. The second most important explanatory variable is the defla- ted eXpected price for hogs farrowed in the spring. Yet, its impor- tance is much less than that of the inventory variable (partial correlation coefficient .36 in the linear form, .47 in the logarithm form). The value of the regression coefficient in the linear form determines a price elasticity of .l at the mean point (.12 in the logarithmic form). This is probably an.underestimation because the 94 most important explanatory variable (St-l) also depends on the expected price of hogs. (See page 80). The other explanatory varia- bles (feed grains available and the deflated expected price for corn)12 do not seem to play major roles. The signs of the regression coeffi- cients are as expected but the t-values indicate that these coeffi- clients are probably not significantly different from 0 at the 5% level of significance in the linear form, whereas the coefficient for the eXpected price of corn appears significantly negative in the logarithmic form. Intercorrelation between the quantity of feed grain available and the real expected price for corn cannot be blamed for this lack of significance of the coefficients since the simple corre- lation coefficient between these variables is only -.05. In conclusion, these results appear quite reasonable as an explanation of the number of sows farrowing in the spring, given the number of sows on farms January 1. As will be seen later, the amount of feed grains available and the expected price of hogs have some influence on this explanatory variable. As a result, their influences s on Sf are not measured completely by their regression coefficients in this equation. Saws farrowing in the fall The results obtained in the explanatory of the variations in fall farrowings confirm the conclusions of previous studies mentioned 13 above. They strongly indicate that plans for farrowings are made on 12The expected price for corn reflects the cost of the input feed grains as forecast by farmers when they take the decisions rela- tive to the number of sows to farrow. Obviously, using such "proxy" is not completely satisfactory; it has been done for want of better data. 13See footnote 2, page 79. 95 a yearly basis, with minor adjustments in fall farrowings in response to changing conditions. Accordingly, as the magnitudes of the beta and partial correlation coefficients indicate, the two most important explanatory variables are the number of sows farrowing in the spring and the quantity of feed grains available, that is the production of feed grains during the year plus commercial stocks before harvest. Though the amount of feed grains available is not known at the time fall farrowing decisions are taken (between February and August) it can be fairly well predicted by farmers; it is this expectation which seems to be the relevant variable since hogs farrowed in the fall consume these feed grains. The regression coefficients for the expected price of hogs farrowed in the fall and for the expected price of corn have the "right" signs although the former is not significantly different from 0 at the 51 level of significance in either the logarithmic or the linear form. Its estimated value in the linear form corresponds to a price elasti- city at the mean of .14; the standard deviation of this regression coefficient corresponds to a variation in this elasticity of .10. In the logarithmic form, the estimated elasticity is .09 with a standard deviation of .09. The presence of the number of sows farrowing in the spring, among the explanatory variables, could raise the problem of simulta— 14 this equation was neous determination. As was explained above, also estimated by the "recursive" method; the meaningless results obtained and the lack of positive reason to expect a correlation 14See page 85. 96 between the disturbances of the two equations for spring and fall farrowings led to the assumption of recursiveness in Wold's sense.15 Thus, ordinary least-squares seem a legitimate estimation method to use here. Among the alternative formulations attempted for this equation, the most interesting ones are those in which the number of sows farro- wing in the spring was replaced by the number of sows on farms January 1. This lowered the coefficient of multiple determination and made the regression coefficients less reliable. Feed grains consumed by hogs The two most important explanatory variables for the amount of feed grains consumed by hogs are the quantity of feed grains available and the number of sows and hogs on hand at the beginning of the year for both the linear and logarithmic forms. Here the quantity of feed grain available during the calendar year t is defined as 3/4 of the quantity available from the previous crap year (production + commercial stocks) plus 1/4 of the quantity available after the crap year finishing during year t. The magnitude of the regression coefficient, in the linear form, indicates that, other things being equal, 19% of a given change in the quantity of feed grains available will be reflected in a corresponding variation in the amount consumed by hogs. Such a figure 15However, the correlation coefficient between these two distur- bances (r=.44) is significantly different from zero at the 5% level of significance. The meaningless results obtained when S? is replaced by its estimated value led to ignoring the problem of recursiveness. This procedure seems legitimate because of the small, even though not null, correlation observed. 97 appears reasonable in view of the fact that, on the average, hogs have consumed around one-third of the feed grains available. There is little doubt that the number of sows and hogs on January 1 (included in the "ceteris paribus" category) is also influenced by the previous harvest of feed grains. The magnitude of the regression coefficient for this number of sows and hogs on January 1 appears reasonable, too; the linear form indicates that to an increase of 1000 head in the number of hogs will correspond a 427.5 ton increase in the quan- tity of feed grains consumed by hogs, that is 8.5 cwt.per head on farms January 1. It should be remembered that the inventory at the beginning of the year includes sows whose pigs, farrowed during the year, will consume these feed grains. Here again we find that eXpected prices do not play a major role. Yet the regression coefficient for the expected price of hogslfi is significantly different from 0 at the 1% level. Its magnitude in the linear form corresponds to a price elasticity at the mean of .13, as compared with a constant elasticity of .11 in the logarithmic form. The expected price of corn reflecting the price of feed grains does not appear in this equation. An attempt was made, of course, to incorporate it into the regression equation. This attempt failed as a positive regression coefficient is economically meaningless. The statistical explanation of this sign seems very simple. Expected 16We used here the simple average of expected prices for spring and fall farrowings. 98 prices of corn and hogs are intercorrelated and, since their influ- ence is minor, it is not possible to differentiate between them. As a result, the influence of the eXpected price of hogs has probably been underestimated. We have a measure of its influence as dampened by correlated variations in the price of feed grains. High-protein feed consumed by hogs In both functional forms, the major independent variable of this equation is time, which is to say that the equations fail to give an economic explanation of the variations in the quantity of high-protein feed consumed. This is not surprising. It is believed that this indicates the importance of the growing awareness by farmers of the profitability of using high-protein feeds. The number of hogs on farms January 1 plays a minor role as an explanatory variable, yet its regression coefficient is significant- ly different from zero at a high level of significance. Its magnitude seems underestimated. In the linear form, it indicates that a varia- tion of 33.9 tons in the amount of high-protein feed consumed by hogs corresponds to a variation of 1000 head in the beginning inventory, that is, 68 lbs./head. The corresponding figure computed at the mean from the logarithmic form is 96 lbs./head. This appears too small as compared to 855 lbs. (linear form) or 843 lbs. (logarithmic form) of feed-grains per head. The expected price of hogs has a very small negative coefficient (it would correspond to an elasticity of -.004 (linear form), of -.009 (logarithmic form) which is obviously meaningless. The DurbinAWatson test applied to this equation indicates serial correlation of the 99 residuals. Such a condition reduces the confidence in the estimated regression coefficients. Nevertheless, time is by far the most impor- tant "explanatory" variable in the equation. The price of high-protein feeds was included among the expla- natory variables in several of the alternative formulations of this equation which were attempted. This price was not kept in the final equation because its influence was never found to be significantly different from zero (-1 (lt (LO). Intercorrelation cannot be blamed for this lack of significance since the simple correlation between this price and time is only -.16 and between this price and the total number of hogs .36. This result is interpreted as indicating that the main factor of increase in the consumption of high-protein feeds has been a growing awareness by farmers of the profitability of using them. Labor used in hoguproduction The most important eXplanatory variable for predicting labor used in hog production, as indicated by the magnitudes of the beta and partial correlation coefficients, is the number of hogs and sows on farms January 1. The regression coefficient is significantly different from 0 at a high level. Its magnitude in the linear form indicates a variation of 6228 man-hours of labor per 1000 head variation in beginning inventory. This figure appears reasonable. One may wonder whether or not such a regression is very meaningful when one is aware that the estimation of the quantity of labor used is obtained by first estimating the labor requi- rement per head and then multiplying by the number of hogs. Yet the approach is justified in the sense that the labor requirement per head has 100 changed over the years with progress in labor efficiency but also with patterns of behavior which are under the influence of economic incentives. Thus, it is not surprising to find that the two other ‘explanatory variables were not negligible. The beta coefficient for the expected price of hogs is .37 in both functional forms as compared to .66 (linear form) and .70 (logarithmic form) for the inventory variable. The regression coefficient is significantly different from zero. Its magnitude corresponds to a price elasti- city of .28 at the mean and .25 in the logarithmic estimation. This ‘may be too high as compared to the elasticity for feed-grains and high-protein feeds. The negative sign of the regression coefficient for the indus- rial wage rate, deflated by the consumer price index, is as expected; its estimated magnitude corresponds to an elasticity of labor use with respect to the deflated industrial wage rate equal to -.l at the mean. This is small in absolute value, yet it may have been overestimated because the industrial wage rate is highly correlated with time (positively) and with the agricultural labor force (negati- vely). In this regression, the wage rate may have "picked up" the influences of the higher productivity of labor and of the quantity of labor available. Several alternative sets of explanatory variables were tried for this equation yet it has not been possible to improve the results presented above. The introduction of the agricultural labor force and of time, in lieu of the industrial wage rate, does not increase the coefficient of multiple determination.much; the regression coefficient 101 for time and the labor force are respectively positive and negative, that is, exactly the apposite of what one would expect. The introduction of the rate of unemployment among the explana- tory variables does not improve the results; the sign of its regression coefficient is negative which is the apposite of what one would expect since the higher the rate of unemployment the less is the incentive to leave farming therefore, ceteris paribus, the larger the use of labor in farm production, including that of hogs. Thus, the equation as presented in Table 5, page 89, is used. It implies the reservations made above concerning the industrial wage rate variable. Number of saws on farm January 1 Several variables appear important in explaining variations in the number of saws on farms at the end of the year. The quantity of feed grains available (production during that year plus commercial stocks before harvest) is the most important variable among those which have a positive regression coefficient. Time, with a negative regression coefficient, also appears to be important. The influence of feed grains which is as one would eXpect does not call for any special comments. But how can one interpret the negative sign for the time variable? It probably reflects the change in number of pigs saved per litter, which means that fewer sows are necessary now than in the 30's to produce the same output. It also reflects the shorter feeding period for finishing hogs. Saws, which are sold for meat leave the farms earlier now than in the 30's. The average expected price for hogs farrowed in the spring 102 and in the fall has some influence on the dependent variable as seen from the magnitudes of the beta and partial correlation coefficients (.48 and .58 respectively in the linear form, .42 and .55 in the logarithmic form). There might be a specification difficulty in the case of this variable. One could think that the expected price of hogs farrowed in the fall and in the following, rather than the previous, spring would be more approPriate. Yet, this hypothesis is not borne out by the statistical results which appear very similar to those presented here but slightly less meaningful. In addition, when one wants to predict the number of sows at the end of year t, one usually does not know what the relevant expected price for spring farrowings in year t+l will be. The magnitude of the price variable coefficient corresponds to an elasticity of .30 at the mean in the linear form and .28 in the logarithmic form with a standard deviation of .08. The number of sows on farms at the beginning of the year does not have a major influence on the number of sows at the end of the year. This is another illustration of the instability of hog produc- tion. Number of hogs over 6 months old other than sows and gilts on farm, January 1 The group "male hogs over 6 months old" is made of two catego- ries of animals, those which are kept for breeding purposes and unfinished feeders which will be sold when finished. The former category is not very important as a source of meat. The size of the latter category has been declining with the progressive shift 103 to leaner hog production and to fast-growing breeds. Thus, it may even be surprising to find that there were still over 10 million such hogs on January 1, 1963 which is more than the number of sows and gilts over 6 months old. The main explanatory variable is the number of sows farrowing in the previous spring. Time, with a negative regression coefficient, appears important too; this is not surprising in view of the shift to shorter feeding periods. The expected price for hogs farrowed in the fall has some influence (the partial correlation coe- fficient is .31 in both functional forms). This variable was chosen as an indicator of the profitability of feeding hogs farrowed in the spring to heavier weights. The elasticity with respect to this price has been estimated at .23 (standard deviation .12) in the logarithmic form and at .14 (standard deviation .08) at the mean in the linear form. It was anticipated that the feed variables (the amount of feed grains available or the expected price of feed grains) would have a definite influence on the number of hogs on farms at the end of the year. Yet, this has not been borne out by statistical results for the numerous alternative formulations which have been tried for this equation.17 In most cases, the regression coefficients for these two variables have the wrong sign.18 In a few other cases, the 17.As seen above (p. 94 of this chapter) intercorrelation between the quantity of feed grains available and the expected price of corn cannot be blamed for this apparent lack of a significant influence of these variables. 1alt is clear that one would eXpect a positive sign for the amount of feed grains available and a negative sign for price of feed grains. 104 introduction of these variables lead to wrong signs for some of the other explanatory variables. In view of the inaccurate specification of the price variable, it is not surprising that it has been difficult to isolate a clear influence of this price of feed. The lack of evidence concerning the influence of the quantity of feed grains available may also preper- 1y reflect the weakness of this influence on an aggregate level. Production function In the production function, the annual hog output appears as a function of: - the number of sows farrowing in the spring: 3; - the number of saws farrowing in the fall: 3: - the average number of piglets saved per litter: p - the amounts of feed grains consumed by hogs: F.G. - the amount of high-protein feed: H.P. - the quantity of labor used in hog production: Lab. All these explanatory variables, except the average number of piglets saved per litter, are considered as predetermined endogenous variables. This raises the problem of the "recursiveness" of the model. As was discussed above, recursiveness in.Wold's sense is assumed and therefore ordinary least-squares estimating techniques are used. Ongithe main difficulties encountered here in measuring the effect of each input on output is the high degree of intercorrelation among the various inputs which reduces the reliability of the estima- ted regression coefficients. Yet the statistical analysis holds even 105 in case of high intercorrelation between explanatory variables. As a result, the computed standard deviations of the regression coeffi- cients give an indication of the reliability of these coefficients.19 With these reservations in mind, the two regressions in linear and logarithmic variables give surprisingly similar results, as can be seen on the following table No. 8 which gives, for each explanatory variable, the logarithmic regression coefficients and the elasticity at the mean computed from the linear coefficients. Table 8: Compared input elasticities of output, Hog Model. f 8 5f sf p FG H.P. Lab. Logarithmic regression coefficients .006 .45 1.17 .29 .04 .20 Elasticity at the mean computed from the linear coefficients .01 .38 1.0 .25 .07 .26 From the magnitudes of the beta and partial correlation coe- fficients, it appears that several variables are important in the explanation of the variations in the volume of hog production; the most important ones being the average number of pigs saved per litter 19As R. Frish has pointed out, intercorrelation between explanatory variables coupled with errors of measurement in these variables will jeepardize the validity of the usual t- and F- tests. (See R. Frish, "Statistical Confluence Analysis by Means of Complete Regression Systems," University Economics Institute, Oslo, 1934, as quoted in J. Johnston, Econometrics Methods, McGraw-Hill, New York, 1963). It is believed that the degree of intercorrelation is not so high here as to make errors of measurement the dominant part in the relative variations of the explanatory variables. 106 and the number of sows farrowing in the spring. In this model, we have considered the average number of piglets saved per litter to be exogenous. It depends on the fertility of the breeds and also on the progress in sanitary practices. Actually, the series of data for this average is highly correlated with time which is not included among the explanatory variables; therefore, one should be aware that this variable probably "carries" the effect of various technical improvements in bag production and of the use of more equipment from 1929 to 1962. The importance of the number of saws farrowing in the spring is not surprising since pigs farrowed during that period have time to be fed and sold for meat or are mature animals that appear in farm inventories at the end of the year. Yet, the very small coefficient obtained for the number of saws farrowing in the fall raises a question as to whether or not the immportance of spring farrowings has been overestimated at the expense of fall farrowings. This may be true in spite of a low simple correlation coefficient (.49) between these two explanatory variables but this does not matter much from the standpoint of the predictive capacity of the whole annual model. The amount of feed grains consumed by hogs is the next most important explanatory variable. In both regressions, the coefficient differs from 0 at a very ligh level of significance. Its magnitude (.113 in the linear model) indicates that the production of pork increases on the average by 113,000 pounds, that is 57 tons, as the consumption of feed grains increased by 1000 tons. This would 107 indicate a very low conversion rate (17/1) but this coefficient cannot be interpreted as an average conversion rate since it indi- cates the importance of the input "feed grain" only, other inputs being assumed constant. Labor is another important input in hog production; in both linear and logarithmic forms, its regression coefficient is highly significantly different from 0 (t=4.7 and 3.2 respectively). The magnitude of this coefficient (9.14 in the linear form) seems reaso- nable; it indicates that a change of 1 million man-hours in the use of labor will lead to a change in the same direction of 9.14 million pounds in hog production (or 914 pounds per 100 man-hours). High-protein feeds do not appear to be very important but cannot be neglected; the regression coefficient is significantly different from 0 at a high level in both the linear and logarithmic regressions (t=2.9 and 2.28 reapectively). Its magnitude (.29 in the linear form) indicates that an increase in high-protein feed consumption of 1000 tons has, on the average, assuming the other inputs as fixed, led to an increase of 145 tons in hog production. It will be noted that several inputs have been ignored; the lack of data on equipment prevented inclusion of this variable in the production function. As was stated above, some of its effect has probably been "picked up" by the average number of pigs saved per litter and also by the other inputs. At the beginning of this study, it was believed that the introduction of antibiotics in hog feeds shifted the production function. To test this hypothesis we introduced a tummy variable taking the value 0 until 1948 and l afterwards among the explanatory 108 variables. The estimated regression coefficient turned out to be very small and far from being significantly different from 0. The Model as a Whole The previous presentation of the results does not tell the whole story. The main interest of the model is to trace through the effects of variations in predetermined variables on the annual hog output and on the size and structure of hog inventories at the end of the year. The predetermined variables considered can be grouped in three categories: 1. Expected prices. 2. Amounts of feed grains available. 3. Technical progress. This last, ill-defined category includes such variables as the number of pigs saved per litter, time and, perhaps, the industrial wage rate. For the sake of clarity, the effects of these three groups of variables will be presented one after the other. Actually, as there is some interaction between them, they will be treated toge- ther with emphasis on the group concerned in each subsection. Effects of expected prices At the onset, it should be recalled once again that expected prices are treated as predetermined variables in the model. In order to illustrate the effects of a change in expected prices, the effects were computed of an increase of 12 in the expected price of hogs for spring and fall farrowings. The model indicates clearly a lag in 109 production adjustment since the increases in numbers of hogs and saws on farms at the end of the year will induce further increases in farrowings and in consumption of feed grains, of high-protein feeds, and of labor, and in output the following year. In turn, the increase in farrowings will induce further increases in inven- tory numbers at the end of the second year. Since the use of elasticities is familiar and convenient, we have used the estimates of the logarithmic form of our model (given in Table 7, page 91) to compute the elasticities of produc- tion with respect to price after 1, 2, 3 and 4 years.20 These elasticities measure the change in output from some equilibrium level, following a once-and-for-all shift in the expected prices of hogs, assuming that the other predetermined variables (including the production of feed grains) remain constant. Following an increa- se of 11 in eXpected prices of hogs at the beginning of year t, output in year t will increase by .14,21 the number of saws (St) at the end «of the year will increase by .271 and the number of hogs, other than sows and gilts older than 6 months (Ht)' will increase by .402. The corresponding increase in park production‘will be lower than .141 since the output, which increases by .141, is made up of the two quhe derivations of elasticities after the first year required to weigh the relative importance of saws and hogs in order to compute the relative change in the total number of hogs on farms at the beginning of the year. These weights were derived at the mean. 21For the computation of this figure, we have used the esti- mated regression coefficients of the logarithmic form, but assumed that the quantity of high-protein feed consumed was not affected (rather than decreased). 110 components: increase in inventory and pork production.) Such price elasticity of output (.14) is indeed quite low and is probably under- estimated here because the model, based on annual data, forces recogni- tion of lags of no less than one year which is probably too long. The corresponding results for subsequent years are given in the following table: Table 9: Percentage increases of several variables relative to their level in year t-l, following a 11 increase in eXpected prices of hogs at the beginning of year t. Number of sows ~ Number of hogs Year Output Dec. 31 Dec. 31 t .14 .27 .40 t+1 .32 .39 .60 t+2 .43 .44 .72 t+3 .48 .46 .76 Though t+3 is not the last year of adjustment according to the model, it is clear that the various changes are tapering off. Being based as they are on the "ceteris paribus" assumption they became economically quite meaningless. The evolution of the hog output confirms previous ideas on the elasticity of supply. We find it to be very low in the short run and then progressively increasing but not reaching a very high level (around .5). Such a set of elasticities for various years is far from sufficient to summarize the influence of expected prices on hog pro- duction and slaughter. The previous figures were derived under the assumption that the price change occurred after equilibrium had been 111 reached. Of course, the lag in adjustment of supply, as seen above, would be sufficient to indicate that hog production has never been in a state d5 static equilibrium. The next logical step is to ana- lyze the effects of various expected prices on hog supply and inven- tories starting from a given situation. This was done with inventory numbers at their January 1, 1963 levels, assuming that all predeter- mined variables take on the same values as in 1962 but with all expected hog prices 10% higher, and then 10% lower than the expected price for hogs farrowed in the fall of 1962. In both cases hog production increased. According to the linear estimates of the model (given in Table 6, page 90) it rose from 20.3 billion tons in 1962 to 20.8 billion tons in 1963 under the hypothesis of higher prices and to 20.6 with lower prices. In both cases the total number of ‘hogs on farms at the end of the year decreased but more with lower prices than with higher prices. As a result, hog slaughter (pork meat production) was a1m0st the same under both price hypotheses (21.2 versus 21.1 billion pounds liveweight equivalent). Assuming that the same conditions prevail during the following year, the difference in production under the two price hypotheses increases (20.6 versus 20;1 billion pounds for production, 20.6 versus 20.3 billion pounds for slaughter). These results point out, first, a small immediate influence of expected prices (a 20% difference in prices leads to a 1% diffe- rence in production the first year). They also illustrate the importance of initial conditions. The number of sows on farms declined even with rising price expectations. This decline is due to the 112 negative coefficient for time which cannot be assumed to be constant. Incidentally, the inclusion of time in the model precludes the existence of any static equilibrium. In order to measure the influence of prices only, one may think of making computations by assuming that the trend variable remains constant, i.e., that the factors, which are responsi- ble for the trend, remain constant. It is then possible to compute only changes from a hypothetical static equilibrium situation, abstrac- ting from the absolute level of variables at the beginning of period t. The evolution of the system after changes in price expectation (first shock) is interesting to study. The influence of subsequent shocks can also be appraised. This has been done taking the estimated coefficients of the linear form of the model given in Table 6, page 90. The results confirm very strongly that one should expect a higher elasticity of supply with reSpect to price at expansion than at contraction. If we start with an increase in price, assuming everything else constant, all variables, but H.P., increase a little during year t, as indicated by the positive coefficient of expected price in all equations (see previous sub- section). If expected prices do not change afterwards, resources used in hog production, output and livestock numbers will increase during year t+1 because of the increase in beginning hog inventory. Similarly, all variables increase in year t+2. If at any time during this process, the expected price decreases by the same amount as it increased in year t, production will decrease but the decrease will be smaller than the previous increase. Mathematically, this pattern can be expressed in terms of production lags with the lagged effect of the first shock attenuating the effect of the second shock. A likely economic interpretation of 113 such lags can be given as follows: breeding sows are a very specialized asset. They cannot be used to produce anything else but hogs. Once they have been raised, they will increase prodUction. In case of a rise in price the number of sows raised increases and it will take a larger price decrease to bring production back to its previous level. In this model, the influence of a price variation is the same whether one starts with a price decrease or with a price increase, the effect of the second shock is attenuated by the lagged effect of the first one. However, the ceteris paribus assumption is not realistic. Increase in feed-grain production and technical progress push produc- tion up. As a result, their lagged effects attenuate the effect of a price decrease, even if they are kept constant during the period considered. Therefore, it is not surprising that the elasticity of supply appears higher at expansion than at contraction. It should be clear from these results that a single figure (or even two) labeled price elasticity of supply, would be quite inadequate to summarize supply conditions. The result of a change in price depends too much on the previous evolution of the herd. Our model has some dynamic features and thus it is not surprising that static supply parameters (e.g., price elasticities) are not sufficient to characterize the system. As A.B. Larson wrote: "In a dynamic analysis, one cannot reduce all forces acting on a body to static counterparts, because some of the forces are generated by the momentum of the moving body."22 22 A.B. Larson, "The Hog Cycle as Harmonic Motion,” JFE, Vol. 46, No. 2, p. 383 (May 1964). 114 Effects of variations in the amount of feed grains available Although the previous chapter has dealt with a model explai- ning the production of feed grains, feed-grain production is considered predetermined in the "hog model". Justification for this procedure is fairly simple as treating the expected price of earn as an exogenous variable in the feed grain model led to recursiveness in Wold's sense. A more complete treatment, which recognizes that the expected price of corn depends on conditions in the hog market, would have required a thorough inquiry into the way price expectations are formed. As was mentioned earlier several times, this task has been avoided. Remarks made above on the insufficiencies of static parameters to characterize the influence of changes in expected prices apply to the influence of feed grains. In the model, a change in the amount of feed grains available in year t can be seen as a shock affecting the system. The change in volume of production during year t is the result of both this shock and the lagged effect of previous shocks, assuming that other variables remain constant during year t. However, in order to appraise the order of magnitude of the effects of a change in feed grains available, it is assumed that the change occurs when the system is in static equilibrium. The lagged effects of previous shocks are assumed away. We have then traced through the changes in production and in hog inventories during a few years following this shock. As can be seen in Table 6, page 90, an increase in the produc- tion of feed grains in year t induces an increase in fall farrowings, a small increase in feed grains consumed and, therefore, some increase 115 in the hog output of year t. But, as can be expected, the effects are more important in year t+1 when spring farrowings are influenced and the consumption of feed grains in year t+1 increases more than in year t. In estimating these changes, the linear form of the model (given in table 6) has been used because the production of feed grains in year t enters in a linear fonm in the explanatory variable: "feed grain available" of the equation explaining feed-grain consumption by hogs.23 The results are summarized in Table 10, page 116. The number of saws farrowed and the amount of feed grains consumed respond to an increase in the quantity of feed grains availa- ble. It was obviously impossible to take full account of the comple- mentarity of inputs; however, this was partly done through the inclusion of the number of hogs on farms at the beginning of the year in the equations explaining the use of feed grains, high-protein feeds and labor. 23Let us recall that this "feed grain available" is a weighted average (weights 3/4, 1/4) of production plus commercial stocks at the beginning of the harvesting period in year t-l and t. 116 Table 10: Absolute and percentage increases in various variables following an increase of 1 million tons in the quantity of feed grains available in year t, Hog Model Variable Units t t+1 Saws farrowing in the spring 1000 heads 0 41.25 % O .5% Saws farrowing in the fall 1000 heads 23.7 18.23 % .42% .35% Feed-grains consumed by hogs 1000 tons 47.8 153.16 % .l3% .4% Output 1,000,000 lbs. 6.18 54.7 1 .0470 o 370 Number of sows at the end 1000 heads 43.98 14.82 of the year % .5% .16% NOTE: It is assumed that commercial stocks have not changed; while the production of feed grains in year t is larger by one mi- llion tons, than in year t-l, its t-l level is resumed in year t+1. The figures in the table indicate absolute changes relative to t-l levels; the percentage changes have been computed relative to the mean value of the variables in the sample period. Here again, the lag in adjustment is probably overestimated because annual data were used in the model. With these reservations in mind, the model indicates clearly a response of hog production to an increase in the availability of feed grains, as illustrated by the estimated 54.7 million pound increase in hog output in year t+1. Such a response corresponds to an elastici- ty, at the mean, of hog production with respect to availability of feed grains of .35. Such an elasticity is of the same order of magni- tude as that relative to expected prices. It confirms the assumption 117 that one of the reasons for the instability of hog supply is the large variability in the amount of feed grains produced. Effects of several variables related to technical progress Several variables included in the model are more or less related to changes which took place but which were not fully identified. Some of these changes were genuine improvements in production techniques while others were of various natures and difficult to isolate. The variables considered here are: the average number of pigs saved per litter, time, and the industrial wage rate. The influence of these exogenous variables has been reviewed in the presentation of the results equation by equation. They are summarized here in their global effect as it is felt that it would not be economically meaning- ful to attach significance to the estimates of their individual effects. During the sample period, with technical progress (i.e., essen- tially as time went by), the consumption of high-protein feed increa- sed, the efficiency of hog production increased (more output per unit of the inputs considered here), the quantity of labor per hog declined and the numbers of hogs and sows on farms at the end of the year followed a declining time trend, as less of these "inputs" were required to produce the same output. Appraisal of the Model As was seen above the model provides plausible results. Before accepting it as an explanation of hog production, it seems necessary to test it further. The first test performed is the prediction of 118 1963 results on the basis of actual values taken by the predetermined variables. Another test, which may be more interesting, has been performed afterwards: starting from the situation on January 1, 1948 and given the values of exogenous variables until 1962, the values of endogenous variables were predicted for each year from 1948 to 1962. For each year, the lagged endogenous variables were replaced by their predicted rather than their actual values. It was felt that such a procedure would permit one to test the dynamic features of the model. In this section the results of these tests are presented and an attempt is made at an overall appraisal of the model in view of these results and of the residuals for the individual equations. Prediction of 1963 Results . The model predicted 1963 results fairly well on the basis of values taken by exogenous variables (expected prices were derived for 1963 in the same manner as those for previous years). The predicted volume of production was 20,241 million pounds (liveweight equivalent). The predicted pork meat production on a liveweight basis was 20,526 million pounds. The difference, due to decrease in hog inventories, was computed assuming an average liveweight of 150 pounds per head on farms, January 1. 24 To date, the only published data for 1963 are estimates of pork production from commercial slaughter (11,868 million pounds) 24This number was derived from the comparison of marketing, production and inventory figures for previous years. 119 and average dressed weight per 100 pounds of liveweight (60 lbs.). Farm slaughter must be added to commercial production. 0n the basis of previous years, this has been estimated to be 5% of commercial production. Under these plausible assumptions, the actual production for 1963 is estimated at 20,768 million pounds liveweight. Thus the model underestimated production by about 1%. The estimated change from 1962 to 1963 is of the same sign as the actual change (positive) but smaller (65% of the actual variation). The total number of hogs at the end of the year was predicted to be 56.80 million head25 as compared to the actual number of 55.95 (i.e. an overestimation of about 1.5%). Such an estimate corresponds to a variation from 1962 to 1963 of the same sign as the actual variation but smaller (70%). Incidentally, this error of estimation is responsible for a part of the underestimation of meat production since the decrease in inventory has been larger than predicted. Unfortunately, the breakdown of the January 1, 1964 hog inventory @mong sows, males over six months and young hogs) has not been published to date. According to our model, the number of sows on farms declined from 8,027 million head to 7.805 head. 0n the 25The predicted total number of hogs is the sum of the predicted numbers of saws, male hogs over six months old and young hogs. The number of young hogs is predicted as the predicted number of sows farrowing in the fall multiplied by the average number of pigs saved per litter multiplied by an adjustment coefficient (.886). This coefficient was derived as the ratio of the average number of young hogs at the end of the year over the annual average of fall pigs saved for the last 10 years. 120 basis of data published by the USDA regarding the number of sows predicted to farrow in the Spring of 1964, this decline seems to have been underestimated. In 1962, the predicted number of sows to farrow in the spring was 7.268 million and there were 8.056 million sows on farms at the beginning of the Spring. In 1963 the corresponding figures were 7.225 and 8.027 million. The predicted number of sows to farrow in 1964 is 6.594 million. Assuming prOpor- tionality of these figures, the number of sows on farms at the end of 1963 would have been 7.32 million. This is probably an under- estimation but it indicates that the number predicted by the model (7.805 million) is probably an overestimation. Two other key variables, for which comparison with actual data can be made, were predicted by the model: the numbers of sows farrowing in the spring and in the fall. The predictions were 7.304 million and 6.065 respectively as compared with the corres- ponding actual numbers: 7.022 and 5.906. Thus the model overesti- mated these numbers by about 4% and 2.5% reSpectively. In this case, actual variations from 1962 to 1963 have not been very V811 estimated. The number of sows farrowing in the Spring was practi- cally unchanged whereas the model predicted a .3 million head increase. 0n the whole, it appears that the model slightly underesti- mated the decline in hog production and inventory at the end of the year but it is felt that it performed satisfactorily in this test. 1948—1962 "Predictions" The second test of the model was to compare actual values 121 of the endogenous variables to their "predicted" values from 1948 to 1962; here the "predicted" values were obtained by "plugging in" the actual values of the exogenous variables over the whole period and of the lagged endogenous variables in 1948 but replacing, for subsequent years, the actual values of the lagged endogenous variables by their predicted values from the previous period or a previous equation during the same year. This procedure is possible since the system is recursive. The argument for performing this test (even though the model was estimated on the basis of observations covering the same time span) was to check whether the errors of prediction will cumulate or offset each other in some manner. A priori, it is conceivable that the model can diverge progressively from the actual values or even "explode." The year 1948 was chosen so as to have a long enough testing period (15 years) while avoiding the disturbances caused by the war and lifting of price controls immediately following World War II. A diagrammatic presentation of the results of this test was felt to be efficient. Figures 5 and 6, pages 122 and 123, show the patterns from 1948 to 1962 of the actual and predicted series of the most relevant variables: the numbers of sows farrowing in the spring (3:) and in the fall (SE), the number of saws at the end of the year (St)! the number of male hogs older than six months on farms at the end of the year (Ht)’ and the volume of production. These curves indicate very clearly that the model does not diverge progressively. Though the general trend seems to be respected l'lll‘lI-‘l. 7500 J {1,flflu hnpflq} {500 0 5000. 5000. QOOOl (1,000 heads} $5001r szC>T N”mhnrs F2511 qv‘d \ Of ~c -.. .‘Hfl. . 5b (’(‘nyn C n'-'q 122 Cows Farrowfnn 4? 4L tq'hs_f?[ll / \ x / / / \ \ D - ~ - \ \ ~ ~ / Sons farroV‘n~ in the gvr€r~ \ \, ’tr-—-— -r..--_.+._......+.a- -- +— ....-A. ..-...+-.-.___.§....., .4..........+.——_.—+—~———.—+—-—-——-Q ‘ .. I! , "(7 ”3] -..rl; 1“.“ L‘nrvnv-;-1- {71 ".(*- (‘5‘ “!§ "'~,' 'fix .. 1"(‘9 “Prinx l-V‘p.¢("(\’ “’1" t"- C ,0 ‘Ynfir' ‘ I '3. fian v.1 «c ‘qu‘V'0"' (or 123 [ \ ,. 1. _- (m g .“'r. v' .1" gfi‘r","- ' 1‘ q f‘ 1:3 H‘ CL] 0 (7300‘ Kano» H0001 (M‘llion pounds) «I has prod rtwcn ~-..--~- - ~ -- --- .....- Qficcol I c 4 *00 O Lissa --¢ ”..-..- -~-me-»- we - --4 ... ---e - -+- ~» -&~ A - t | t- «1 1743; So {3,- 60 (963, ”1.“ {x A .P.|"\1 v3 ‘71 ”1(n'.:“1t./~rl) }>‘v-nrllfl9(.(”' V'fl1v1'eQ 3"“- ‘-‘hp vuribpr of leu #039 ownr h ‘owfhg F13 1f fLW'TVW?r\‘ ‘We You" ”,4 of ~~n Antval ”Ul'ne 0‘ pm- rroannefow lllll‘ll‘ll 124 (as is clear in the case of Mt) for the five series, the model very clearly misses some important year-to-year variations. The model anticipates the large increases of 1950-51. However, the general decline in 1953, the peak of 1955 and the decline of 1960 are not reflected, or not sufficiently, by the model. It can be noticed that the same variations occurred one year earlier for the number of saws on farms at the end of the year. Thus it is suspected that the failure of the model to follow these variations in the number of saws at the end of the year is responsible for at least part of these divergences between the other actual and predicted series. The number of sows at the end of the year is one of the explanatory variables of the number of sows farrowing the following spring which, in turn, is an important eXplanatory variable of both the number of saws farrowing in the fall and the number of hogs at the end of the following year. It remains to explain why the model failed to predict these important changes in the inventory number of sows. The explanation may lie in the use of the expected price series. From 1951 to 1952, the average price received per 100 pounds for hogs declined from $20.00 to $17.80, whereas the expected price series indicates a decline from $20.50 to $19.00. In 1954 the actual price was $21.60 while the "expected" price was only $17.00. In several instances, it seems as if Lerohl's expected prices are too forward-looking. But, in general, the model appears to have underestimated the importance of variations in prices; this is confirmed by the analysis of the resi- duals, as described below. llllll‘l ‘Illll. 125 t is. ....C 1.. 1 (.4. v0. $53... to \rQ...L:, CL. ... ~.~L 0.th.... ...{nw erestH 9.4,. WC m—fi..—mu.~CCE I B .tmh at (m 11 :1. t v e u a (-.., T: r b 1i>|fl v i d 1. IL, I14»: I40 r 0 U 4 1 .0: (7’ L 1 > L i It i > F !( b . Li “Y. I". 30,... # .09» n m k . / t \ ’ » v4\.Qq I a H x u at T? a . P b t rV p A 1 n g e a ..l. 8 4|. 41 M - \~ ~‘ ‘.-‘~'- :..,JM 1 r\ .8-.. ._ 50.0. m ,, Vaupua‘rw 139.“. H» 126 Residuals of Some Individual Equations The previous remarks are confirmed by the analysis of the residuals of the equation for Stlehich are plotted against time in Figure 7, page 125. These residuals follow the same cycle as 8:. This indicates that the equation does not fully take into account the factors responsible for the cycle. A casual examination of the diagram indicates that the variations in the residuals are related to variations in the current price of hogs. Such a result is not surprising, since the average expected price does not reflect actual price conditions in the latter part of the year, which are certainly relevant to farmers' decisions regarding the number of saws kept on their farms. This points out one of the limitations of the model resulting from the choice of annual data. As can be seen on Figure 8, page 127, the residuals of the equation predicting the use of variable inputs (feed grains, high- protein feed and labor) follow roughly parallel patterns. This general pattern is that of the cycle followed by the total number of hogs. The explanation of this result is fairly simple. The number of hogs at the beginning of the year is an important explana- tory variable in the three equations. It is clear that this number does not reflect variations in hog numbers during the year which, of course, influence the use of these inputs. This is another weakness of the model. Special conditions, which could not be taken into account in such a model, are responsible for the exceptions to the general pattern described above. The decline in high protein feeds used from 1929 to 1932 is probably due to the depression, when 127 ‘I Il‘ [EH wrwrx—w—v Lc_.t:rca; _c; L» tee: to.ag (in «Teen inc.C;i.n m; .LumnatzTCOQ ac ¢C.i SJ» :wam; LCuanSUw pair»; QL. dc aanTaudo I a . Mk 1 . 3 7x .. ,. A l ..o.\ O ..vh .. war 0% MN 3m ad: 11:}? L r . r a 39:1}? Ifgili {Iii ll . . 4| .4 4 . 4 J1 I41 .1!) 4 v 1 i v . i In . . a- - , x. . _ . i . e . . x r a Mir \ . ./. MW. .6 \,M f . . a 7 A ./ . a. A, . _. . O areas twoyontuiaha muse: sea uoHHHwa . A A . . . . A / .lllilllwli-‘ , . A v t i t _v\ i a A \ . . i . my _. . /, . e a or /, . m N i . _ _ _ / as ,eeem- . . . u.. _ a /.1 ._ /. M .. oo¢+§~- \ _\..___ stsnprseg I MLMmLLItctb CC... . w 128 farmers reduced their cash expenses. Between 1946 and 1949, the regular pattern of the residuals is somewhat disturbed. The residuals for high-protein feeds and those for feed grains vary in apposite directions. One possible explanation of this phenomenon is that some substitution of feed grains for the high-protein feeds occurred in 1946 when the deflated price of high- protein feeds was high. Then it declined and the substitution took place in the other direction. This hypothesis is confirmed by the following figures. The percentage of high-protein feeds in the total high-protein feeds plus feed-grains declined from 8.7% in 1943 to 7.7% in 1946 and then increased to 10.9% in 1949. This suggested that the model underestimates the influence of changes in the prices of high- protein feeds and that "growing awareness of the importance of using high-protein feeds" may be less important than implied above. Summary Remarks From the results of the tests mentioned above and the analysis of the residuals, it appears that the model reflects fairly satisfact- orily the general pattern of hog production and inventory numbers. The 1963 values were predicted reasonably well and the "predictions" from 1948 to 1962 followed the same general trend as the actual values. However, the model does not take full account of all the factors res- ponsible for the hog cycle even though the predicted values in the ‘warious equations do follow the "hog cycle." In most instances, it ‘1s believed that failures to follow the cycle is due to the use of jprice expectations; in some cases, particularly for St’ current prices ‘would be more relevant, in other cases the expected price series seem 129 too sensitive (e.g. 1949). Various other particular circumstances are responsible for the divergence between the values derived from the model and the actual series; some of these have been mentioned. While a model cannot take all the causal factors into account, it is haped that the most relevant ones are in our model. Conclusions A major limitation of this work is that the model is not complete because price expectations are treated as predetermined variables, even though price expectations are influenced by current supply plans. Yet, it is felt that the procedure is valid for the study of hog production as the chronological order of the chain of causa- tion has been respected. Of course, this model would be insufficient, in and of itself, to predict the future pattern of hog prices and production. Such prediction would also require incorporation of .demand functions and some knowledge of the way in which price expec- tations are formed. Since this study concentrates research resources on the study of supply, it is now time to appraise what the model contributes to knowledge concerning hog supply. The two main objectives of this chapter were (1) to study the factors influencing the quantities of resources used in hog production and (2) to appraise the influence of these factors and possibly others on hog supply. Commitment of Resources Our model takes into account four main resources used in hog 130 production: feed grains, high-protein feeds, labor and the feeding and breeding stock. It should be clear now that the key factor of produc- tion is the last one; the number of hogs on farms at the beginning of the year is an important explanatory variable in the three equations predicting the use of the other inputs. Since this stock of animals at the beginning of year t, is part of the output of period t-l, the factors determining its commitment to hog production in period t are partly those which determined hog production in year t-l. The main factors influencing these numbers are the expected price for hogs and the amount of feed grains available. Mathematically, the effect of a variation in one of these variables can be expressed in terms of lags. As stated earlier, a likely economic interpretation of such lags is as follows: the feeding and breeding stock is a specia- lized, farm-produced resource which becomes easily fixed in the hog enterprise since, as hog prices decrease, the sum of its discounted marginal value product decreases as well as well as that of other resources, but its salvage value decreases at the same time. In addition to the availability of feed grains and the expec- ted price for hogs, time appears as one of the explanatory variables in both equations for the numbers of saws and of male hogs older than (six months on farms at the end of the year. As stated in the previous ‘section, the negative coefficient is interpreted as follows: (1) for the former category, it reflects the influence of improved efficiency: ILess breeding sows are necessary to produce the same hog output, and (2) for the latter category the negative coefficient reflects the Shift to shorter feeding periods. Obviously these are important fac- tors influencing the use of this resource. 131 The other resources: feed grains, high-protein feeds and labor, are more variable within agriculture than feeding and breeding stock. Feed grains are farm produced. The previous chapter dealt with the main factors determining the quantity produced. Once they have been produced, they are fixed within agriculture to a high degree. If government storage is treated as exogenous, the model indicates that the quantity of feed grains fed to hogs depends heavily on the amount available and on the number of hogs on farms at the beginning of the year. The importance of the latter is due to the high degree of complementarity between feed and animals fed. Labor is probably relatively fixed in the agricultural sector but variable between enterprises. In the model, the factors which determine the quantity of agricultural labor available are summarized in the industrial wage rate variable. Reservations are called for by the use of this variable. Yet its negative regression coefficient "carries" the various influences which have led to the substitution of capital for labor in hog production and to more efficient use of labor. Unfortunately, the lack of adequate data on equipment preven- ted further pursuit of the analysis of this important question. Two (other factors were important in determining the quantity of labor ‘used in bag production: the number of hogs on farms and the expected ‘price for hogs. The former reflects the high degree of complementarity between the two inputs. The quantity of high-protein feeds used depends also on the xlumber of hogs on farms. This influence reflects again input comple- Imentarity. As said earlier, the great importance of time in the 132 determination of the amount of this input used should not, in our Opinion, be considered as a failure of the model. It reflects the influence of factors which indeed have not been measured adequately including, perhaps, price and a growing awareness by farmers of the profitability of using these feeds. Hog Supply Traditionally, supply conditions are summarized in a supply function which shows the influence of price on the volume of supply. Another difficulty arises from the fact that the supply of hogs by farmers is made up of (l) outright hog production plus (2) depletion of inventories. Even though these two categories are quite different from the point of view of the producer, they are very similar from the point of view of the buyer. The model, being a production model, distinguishes clearly between these two categories and permits one to explain the evolution of both. Discussion of the influence of varia- tions in the expected price for hogs has shown that the dynamic nature of our model implies more than one short-run supply function. Thus, it seems impossible to summarize supply conditions in a single curve. The results of our study lend very strong support to the thesis of diverging elasticities of supply at contraction and expan- sion.26 As stated above several times, two price elasticities are not sufficient to characterize supply conditions. But, according 26For the importance of this thesis see: G.L. Johnson, "The State of Agricultural Supply Analysis," JFE, Vol. 42 (1960), pp. 435f, in particular his review of past work. 133 to our model, it is likely that an increase in price will be followed by a larger variation in production than a decrease in price of the same magnitude. This discrepancy is due to the lagged effects of previous shocks. It has been seen that most of the production lags can be interpreted as resulting from technical lags and from the high degree of fixity of the breeding stock and, to a lesser extent, of the feed stocks. With these qualifications in mind, the computation of same average elasticities with respect to the main variables influencing supply may be useful in indicating the magnitude of these influences. The model indicates an important influence of expected prices for hogs on the hog output. An elasticity of .4, even after several years, is important. The minor importance of the price of feed grains may appear somewhat surprising in view of the fact that the hog-corn ratio has long been recognized as one strategic variable in the explanation of 27 The estimations of this model may be due to inappro- hog production. priate specification of our price variable, but the presence of the quantity of feed grains available provides, we believe, a better interpretation of this seemingly surprising result. The major part of feed grains fed to hogs do not go through commercial channels; thus in many cases, the market price for corn or other feed grains is not relevant to the decision of how much grain to feed. If 27A.A. Harlow, Tech. Bul. 1274, 02. cit., p. 19 134 Specialization wouldvaeIOp to a large extent, differentiating feed- grain producers from hog feeders, the importance of the price of feed grains may increase. The results imply that supply conditions are largely reSpon- sible for the instability of hog production. Large variations in feed-grain production contribute to large variations in hog produc- tion. Also the lags in production and the high degree of fixity of the breeding stock render adjustments of supply to price changes difficult, and time consuming; besides once the adjustment is started it often "overshoots the mark." CHAPTER V BEEF PRODUCTION This chapter presents the main results relative to beef production. As in the previous chapters, it is divided into four sections presenting (1) the economic analysis underlying the model, (2) the statistical problems which were encountered, (3) the results, and (4) an appraisal of the model and the conclusions which can be drawn regarding beef production. Economic Analysis Introduction "Research workers have probably had more difficulty deriving meaningful and realistic supply price elasticities for beef than for any of the other commodities."1 The main difficulty seems to be the dual role played by livestock inventories as part of the output of year t-l and as a major input in year t production. In order to take this dual role into account, beef production from slaughter plus changes in inventories are included in the output, as in the case of hogs. Furthermore, these changes in inventory have been disaggregated into various livestock categories, namely: (1) cows and heifers older than two years, (2) heifers between one and 1Knight, D.A., "Estimation of Time Series as Data for Estimating Supply Parameters" in E.0. Heady et a1. "Agricultural Supply Functions," Iowa State University Press, Ames, 1961, p. 81. 135 136 two years old, (3) steers one year and older and (4) calves (i.e. animals less than one year old). These categories exclude dairy cattle. The statistical problems raised by this exclusion will be tackled later. As a result, the beef model is slightly more compli- cated than the hog model even though it looks very similar. It is made up of three types of equations: (1) equations to predict the use of input, (2) the production function, and (3) several equations for predicting livestock numbers. The economic analysis underlying the first two types of equations (prediction of the use of input and the production function) is very similar to that presented for hogs in Chapter iV; thus, it is not necessary to discuss them further here since the results will be presented later, equation by equation. However, as the prediction of livestock numbers deserves some atten-- tion, a model which was tried but found impossible to fit because of lack of data will be presented first followed by presentation of the model which was fitted. First Model of Cattle Farmers' Behavior Regarding the Conduct of Their Beef Enterprise As was stated earlier, the main problem with beef studies is achieving sufficient disaggregation. As in most time series studies, this first model considered the beef sector as one big enterprise. Changes in inventory were considered not the result of one set of decisions only but of several. For instance, the change in the num- ber of cows is equal to the number of heifers which are raised to become cows during that year minus the number of cows which are slaughtered, if mortality is neglected. Similarly, the change in 137 number of heifers during the year is equal to the number of female calves which are raised minus the number of heifers which are slaugh- tered minus the number of heifers which are raised to become cows. The decisions regarding the number of heifers raised are not the same as those regarding the number of cows slaughtered. In this first attempt, an equation was desired for each one of these variables: heifers raised, cows slaughtered, heifers slaughtered, steers slaugh- tered, etc. The set of decisions determining these numbers was consi- dered relatively homogenous and it seemed legitimate to represent them by one equation. Thus, estimates of the following variables were required: numbers of calves born, calves slaughtered, female calves raised, Isle calves raised, steers slaughtered, heifers slaughtered, heifers raised, and cows slaughtered. All these data were not available. However, there existed some identities which permitted derivation of some of them. One such identity is based on the sure I knowledge that heifers between one and two years old in year t will } not be heifers in year t+1. Either they will have been slaughtered or they will have been raised to become cows. Our attempts to use 1 these identities failed because it was found impossible to take into account mortality (which was required to achieve reasonable accuracy) as data on mortality are not sufficiently complete. There are no A estimates of the numbers of heifers, steers, etc. which die during a given year. Another inadequacy in the data was found on the break- down of cattle slaughtered. For later years, there exists a breakdown for cattle slaughtered under federal inspection. However, the applica- tion of percentages derived from federal inspection data to total 138 slaughter was not satisfactory and led to inconsistencies. It appears as if the number of cows slaughtered in slaughter-houses which are not under federal inspection was relatively higher than those slaughtered in slaughter-houses under federal inspection; it was not known by how much. The Model Fitted As a result, work was started at a higher level of aggregation. Single equations were used for dependent variables such as the change in the number of cows on farms or the change in the number of steers on farms. For heifers a single equation was used in which the depen- dent variable was the number of heifers on farms at the end of the year. For calves three variables were used: number of calves born, number of calves slaughtered and number of calves raised to become either heifers or steers. Thus, the model had six equations of the third type to predict the size of the cattle herd. As can be seen in Table 12 (p. 146), the explanatory variables for these equations are various numbers of live- stock on hand at the beginning of the year, various expected prices, amount of feed-grain available and, in some instances, time. It seems apprOpriate to discuss these explanatory variables in connection with each equation and this is the object of the section on results. Since the model is a beef production model, dairy cattle are eliminated on the grounds that their contribution to meat production results from quite specific sets of decisions, obviously influenced by conditions on milk and milk product markets. Accordingly, culled 139 / cows are excluded from data on output and the females from the dairy herd are completely excluded from our various numbers. This is legi- timate because the influence of culled cows on the price of meat and, thus, on the production of beef by beef cattle is reflected or carried through price expectations for beef products which are considered as predetermined variables in our model. However, male animals (calves and steers) from the dairy breeds were not eliminated since, when they are raised, it is essentially to produce meat. Bulls were excluded altogether from our considerations. Statistical Problems Problems Due to the Data As is clear from Chapter II and from the previous section of this chapter, lack of sufficient data is a major limitation to the study of beef production. To avoid repeating what has already been stated, this section . wh ch will be devoted merely to a presentation of how the estimates are used in the model actually fitted were derived. Livestock numbers Most data on livestock numbers used in the model are readily available from U.S. Department of Agriculture series. Others were derived from them. This section indicates the assumptions implied by the computations made to derive these estimates. To reiterate, the meat production coming from culled dairy cows was subtracted from our output series. For this purpose, the number of dairy cows slaughtered (CS) was estimated as the number of 140 dairy heifers on farms at the beginning of the year (Hg_1) minus the algebraic increase in dairy cows (ACd) during that year d= d d Cs Ht-l -AC This neglects the death losses on dairy heifers and cows present on farms at the beginning of the year which cannot be estima- ted since the only breakdown available on death losses is between all calves and all other cattle (dairy and beef). In order to take some account of these death losses, the number of cows slaughtered was mul- tiplied by an underestimated average weight of 900 lbs. This figure was chosen more or less arbitrarily in view of the average weight of cows slaughtered. The other livestock numbers derived from U.S.D.A. series are those concerning calves: Calves born (Vb) Calves born are reported by the U.S.D.A. by number and as a percentage of the number of cows and heifers two years and older on farms January 1. The problem was to eliminate the female calves born vdf from dairy cows (vgf). To compute b and Vb we have assumed that dairy cows had the same percentage of calves as the other cows and that half of these calves were female. Calves slaughtered (Vs) Calves slaughtered are reported by the U.S.D.A. Here again df) the problem was to eliminate female dairy calves slaughtered (V8 which was estimated as follows. A female calf present on farm at the beginning of the year either becomes a heifer by the end of the year, has been slaughtered or has died. A female calf born during 141 the year will be among the female dairy calves (less than one year old) at the end of the year, will have been slaughtered or will have died. These two classes are mutually exclusive. They include all female dairy calves slaughtered and all death losses. Thus: V? + Dv‘if -- V351 - m‘tlf + V? - vgf where DVdf : death losses of female dairy calves vgf : dairy female calves on farms at the end of year t H: : dairy heifers on farms at the end of year t The numbers of female dairy calves and heifers on farms January 1 are reported by the U.S.D.A. vgf was estimated as indicated above. DVdf was estimated from the total number of calves lost by mortality assuming the same prOportion of losses among dairy and other calves. Calves raised (Vt) This number was estimated on the basis of the following identity: the change in number of calves (AC) is equal to the number of calves born minus the number of calves slaughltered minus the number of calves raised minus the number of calves lost by mortality. Ac=vb-v8 -Vr-(DV-DVdf) In this identity, Vr is the only unknown. Output and inputs The U.S.D.A. publishes estimates of beef production (in pounds of meat) which take changes in inventory into account. From this number, for each year the contribution of culled dairy cows was subtracted in the manner explained at the beginning of the 142 previous subsection. Though some error is attached to the output estimates used, such errors are thought not to raise major problems. Reservations made about data on labor used in the production of hogs, feed-grains, and high-protein feeds fed to hogs, feed-grains available, and expected prices and their deflator also apply to beef production. It would be redundant to repeat them here. Estimation Problems Here again, only problems specific to the beef model will be discussed and references will be made to previous discussions whenever possible. Recursiveness As can be seen in Table 12, page 146, giving the variables included in the equations of the beef model, the first condition mentioned by Wold for recursiveness (triangularity of the coefficient matrix of endogenous variables) is satisfied by the beef model. Whether or not the second condition (diagonality of the covariance matrix) is fulfilled is Open to discussion. The only equations concerned are (l) the production function where three explanatory variables (labor, feed-grains, and high-protein feeds consumed by beef cattle) are endogenous and (2) the equation explaining the numbers of calves slaughtered, which includes the number of calves born among the explanatory variables. For the production function, the "a priori" reasons are weak for expecting correlation of the disturbances. True, some factors such as equipment and capital input are not taken into account in 143 this model. They lead to a positive disturbance of the production function, and also to a positive disturbance of, for instance, the feed-grain equation. But these factors are fixed in the short run (one year). For longer run adjustments, it may be argued that the number of cattle at the beginning of the year reflects changes in feeding capacity. However, the production function has been fitted by both the ordinary least square method and the "recursive" method recommended by Foote as explained earlier. As the results of Foote's "recursive" method are disappointing, only results from ordinary least-squares are presented. This is justified by the matrix of covariance of the residuals. The correlation coefficients between the residuals of the production function and those of the three equations for feed-grains, high-protein feeds and labor are respec- tively -.20, .04 and -.OO6, all far from significantly different from zero. For the equations concerning the number of calves slaugh- tered, Vs, there were no readily apparent reasons for expecting the disturbances to be related to the disturbances of the equation for Vb. Though a positive disturbance in the equation for Vb will increase Vb, its effect on V8 will be reflected through Vb without an apparent a priori effect on the disturbance of V8. This was confirmed by the matrix of covariance of the residuals of the equa- tions estimated in the model which revealed a correlation coefficient (-.32) not significantly different from zero at the 5 percent level of significance. 144 Choice of the functional form The problem of choosing functional forms for the equations of the beef model was similar to that for hogs and the discussion will not be repeated. All equations were estimated as linear in the variables. Also most equations were estimated as linear in the logarithms of the variables. The logarithmic form was not used for the equations eXplaining changes in number of cows and in number of steers since the dependent variable takes on negative values for several years. In cases where both functional forms were used, both results are presented. Serial correlation As indicated in Chapter II, serial correlation was found, on the basis of the DurbinAWatson test, in several equations. Hildreth and Lu's procedure was then applied, as described above, to the pro- duction functions and the three equations for feed-grains, high- protein feeds and labor used in beef production. 145 Table 11. Variables of the beef model. Symbol Definition Unit FG Feed grains consumed by beef cattle 1,000 tons HP High-protein feeds consumed by beef cattle idem. Lab Labor used in beef production 1,000,000 man hours Output Beef production (liveweight equivalent) 1,000,000 pounds Vb Number of calves born in year t 1,000 heads Vr Number of calves raised to become heifers and steers idem. Vs Number of calves slaughtered idem. Ht Number of heifers at the end of year t ---- St Number of steers at the end of year t ---- Ct Number of meat cows at the end of year t ---- TC Total number of cattle at the beginning of year t ---- Fav Feed grains available 1,000,000 tons EPB 1 year expected price for beef (at beginning of year t) Cts/th EP5 5 year expected price for beef (at beginning of year t) ---- EP1(t+1) 1 year expected price of beef for year (t+1) during year t) ---- EPc Expected price for corn Cts/lO bushels IPP Index of prices paid by farmers (l9lO-l4=lOO) IWR/CPI Industrial wage rate deflated by consumer price index 1947-49 cts/hr PHP ‘ Index of high-protein feed prices (l957-59=lOO) Range Index of range condition Cd(t-l) Number of dairy cows at the end of year t-l 1,000 heads CP comm Current price of beef (commercial grade at Chicago) Cts/th Vt Number of calves (including males from dairy breeds) at end of year t 1,000 heads Tab 18 12 0 Equations of the beef model. 146 Variables Equations (indicated by the dependent variable) PC HP Lab Output Vb Vr Vs Ht ‘AS ‘56 A S=St-St_1 A C=Ct-Ct-1 TC T Fav EPB/IPP EPS/IPP EP1(t+1)/IPP EPc/IPP IWR/CPI Pup/IPP Range Cd(t-1) Ct-l CPC 0mm St-l at-1 Vt-l '><><><>< FINN?! X: Exogenous variable E: Endogenous variable Table 13. Alternative Estimates of the Coefficients. 147 Beef Model. (standard deviations in brackets) Estimation technique _ and functional form R O.L.S. (a) linear Autoregressive linear log O.L.S. log (b linear log {Autoregressive O.L.S. log linear 10g Autoregressive O.L.S. log linear log Autoregressive O.L.s. linear‘f log linear log ) f linear}? f linear )9 f 2" 2 .91 .96 3.8 3.6 .94 .97 2.8 .6 .84 .88 1.0 3.8 .96 .96 .8 23.8 .98 .98 Equation FG=10,046.5 + .196TC - 32.1w + 61.7 Fav + 252.1 EPB/EPC (.056) (86.6) (22.2) (88.5) FG=-l.9464+ .6292TC +-.0233T + 1.2512 Fav. + .2885 (.1425) (.0508) (.1743) (.0933) EPB/EPC FG=cst + .163TC + 141.9T + 56.0 Fav. + 147.0 EPB/EPC FG=cst + .7438TC - .O626T + 1.318 Fav. + .3002 EPB/EPC HP=-l,627.5 +-.076TC + 42.41 +.122,9 EPB/IPP - 191.2 (.020) (30.2) (76.8) (131.6) PEP/IPP HP=-4.2102 + 1.4871Tc + .1406T + .6324EP3/IPP - .0453 (.1314) (.0571) (.1080) (.1520) Pup/IPP HP=cst + .O47TC +-131.0T + 81.4 EPB/IPP + 94.2 Pup/IPP HP=cst + .931Tc + .6OOT + .232 EPB/IPP + .144 Pup/IPP Lab=269.4 +-.0076Tc + 25.65 EPB/IPP - .213 IWR/CPI (.0023) (9.04) (1.038) Lab=3.5937 + .4572TC + .1732 EPB/IPP + .0085 IWR/CPI (.2748) (.1068) (.0664) (.1311) Lab=cst +-.0078TC - .649 EPB/IPP - .881 IWR/CPI Lab=cst + .542TC + .047 EPB/IPP - .195 IWR/CPI 0utput=269.4 + .250 F.G. + .713HP +-10.9 Lab +-.163 TC (.167) (.697) (3.4) (.063) 0utput=—.1145 + .263F.G. + .072HP + .4138 Lab + .3942TC (.5474) (.067) (.086) (.2169) (.1682) Output=cst + .262 F.G. + .850HP +.20,9 Lab +-.064 TC Output=cst + .147 F.G. + .242HP + 1.128 Lab - .102TC Vb=361.8 + 115.rr + .77(ct_1 + 1/2Cdt_1) - 5.5 Range (40.5) (.07) (32.6) Vb=-.3524 + .0386T + 1.019 (Ct_1+1/2Cd(t_1)) + .0747Range (.0127) (.056) (.1069) Table 13 (continued. 148 Estimation technique and functional form E Equation linear .97 Vr=-3633.3 + 1.07vt_1 + 457 BPS/IPP + 2.73 Fav + 29.8 (.07) (173) (12.5) (155.4) EPC/IPP log .97 Vr=-.2370 + .9994v _1+ .0386 Fav + .2059 EPS/IPP + (.0499) (.0799) (.074) .0239 EPc/IPP (.0426) linear .65 Vs=2567.8 + .95vb - 1.05vt_1 - 695 BPS/IPP - 10.5 Fav (.18) (.27) (240) (14.8) + 282 EPC/IPP (230) log .61 Vs=-1.5285 +-3.6639Vb - 2.3258Vt_1- .3369 Fav - .6750 (.8468) (.8174) (.6399) (.2676) (.2763) BPS/IPP + .2203 EPc/IPP (.1734) linear .96 Ht=-14l9.8 +-l6.8T + 5.9 Fav + .27vt_1+ 231.9 EP5/IPP (20.7) (4.6) (.05) (71.0) log .96 Ht=-.3465 + .0297T + .1409 Fav + .8254v _1+ .3480 (.3057) (.0257) (.1026) (.0938) (.0968) BPS/IPP linear .54 As=.2973.7 - 113.11: + 381.5 EPB/IPP + .468Vt_1 - (38.6) (85.6) (.099) 5733 - 194 EP /IPP + 201 2 EP /IPP ' -1 C ' 1 t+1 (.1305 (80.6) (95.9) ( ) linear .47 Ac=-8138.7 + 535.2 BPS/IPP - .2520t_1 + 1.20411“1 (156.7) (.119) (.520) - 86.2 EP /IPP - 90.5 C? /IPP (181.8) 1 (169.3) c°mm (a) O.L.S.: Equation estimated by ordinary least squares (b) Autoregressive: Equation estimated by Hildreth and Lu's autoregressive technique as described in Chapter II. 149 Results The estimates for the beef model are presented in Table 13, page 147. As for feed-grains and hogs, these estimates are discussed equation by equation and followed by an appraisal of the model as a whole. Individual Equations Consumption of feed-grains by beef cattle The number of nondairy cattle on farms at the beginning of the year and the quantity of feed-grains available2 appear as the most impor- tant explanatory variables of the amount of feed-grains fed to beef cattle. Their partial correlation coefficients are respectively .55 and .46 in the linear form and .64 and .80 in the logarithmic form. The regression coefficient for the number of beef cattle on farms at the beginning of the year indicates that an increase of 196 tons of feed-grain consumed by beef cattle is associated with an increase of 1,000 head in the number of cattle. This number is difficult to interpret because feed-grains are consumed in various quantities by the various types of cattle present on farms at the beginning of the year (some will be slaughtered soon, others later while still others are cows or young heifers which do not consume much feed-grains, 2Here feed-grain available for year t is defined as in the hog model, i.e., 3/4 of production plus commercial stocks before harvest in year t-l plus 1/4 of production plus commercial stocks before harvest in year t. 150 etc.). It can only be stated that the order of magnitude seems reasonable. The regression coefficient of the logarithmic form corresponds, at the mean, to a marginal consumption of 122 tons of feed-grains per 1,000 head increase in cattle inventory. Since the DurbinAWatson test indicates that the residuals are serially correlated, it is important to examine the results of the "autoregressive model" in order to appraise the value of these estimates. For the linear form the sum of squared residuals is minimum for /9= .8, in the logarithmic form the minimum occurs for Jf’I .6. The regression coefficients for the number of cattle give closer results than those computed by ordinary least squares for both functional forms. In the linear form, the coefficient is .163 as compared to .196; in the logarithmic form .74 instead of .63, (.74 corresponds to a marginal consumption of 143 tons per 1,000 head of cattle). These results tend to indicate that the coefficient is overestimated by ordinary least squares in the linear form. The "true" value is believed to be around 150 tons of feed-grains per 1,000 head of cattle. The two estimation methods give closer results concerning the influence of the quantity of feed-grains available. In the linear form, the magnitude of the regression coefficient indicates that 6.2% of an increase in feed-grain available will be consumed by beef cattle according to ordinary least square results; whereas the autoregressive model yields an estimate of 5.6%. The results computed from the loga- rithmic form are slightly different according to both estimation techniques. The regression coefficients correspond to comparable oath-ates at the mean of 9.3% and 9.6% respectively. Intuitively, 151 the linear form seems more appr0priate here as, other things being equal, the consumption of feed-grain by beef cattle should be somewhat pr0portional to the quantity of feed-grain available because consumption of feed-grain by beef cattle is an important outlet of feed-grain pro- duction. Therefore more confidence is felt in the linear estimate (around 6%) than in the logarithmic one. Another variable explaining some of the variations in the amount of feed-grain consumed by beef cattle is the ratio of the expected price of beef to the expected price of corn. These prices are used as a ratio in order to save degrees of freedom. This procedure has both advantages and disadvantages and the scrupulous reader is granted that some arbitra- riness is involved here. All estimation techniques used give similar results. By ordinary least squares, the partial correlation coefficient.is estimated to be .47 in the linear form and .50 in the logarithmic form. The magnitude of the regression coefficient in the linear form corresponds to a price elasticity at the mean of .39 as compared to a constant elasticity of .29 estimated from the logarithmic form while the autoregressive model indicates elasticities of .22 and .30 in the linear and logarithmic forum, respectively. In this case, an educated guess is around .30; this is consistent with the ordinary least square estimates, taking the estimated standard deviations into account. Time was included among the explanatory variables to reflect changes in feeding efficiency and habits. According to these results, the trend effect is weak. 152 Consumption of high-protein feeds by beef cattle The high-protein feeds included here are made up mostly of commercial by-products rich in protein (oilseed meals, tankage and meat scrap, fishmeal, etc.). The number of beef cattle at the beginning of the year is again the most important explanatory variable of changes in consump- tion of these feeds by beef cattle (partial correlation coefficients: .59 in the linear form, .91 in the logarithmic form). The linear regression coefficient indicates that an increase of 76 tons in the consumption of high-protein feeds was associated with an increase of 1,000 head of cattle at the beginning of the year. This appears to be overestimated as compared to the 150 tons of feed-grains per 1,000 head of cattle mentioned in the previous subsection. Yet the regression coefficient of the logarithmic form corresponds, at the mean, to a marginal consumption of 84 tons of high-protein feeds per 1,000 head increase in cattle inventory. Overestimation may be due to the intercorrelation between cattle number and time (simple correlation coefficient: .95). This suspicion is supported by the results of the autoregressive model. The sum of squared residuals was found to be minimum for f = .8 for the linear form, and f= .6 for the logarithmic form. It turns out that this procedure reduces the intercorrelation between cattle numbers and time. The estimated regression coefficients are lower for cattle number and higher for time than the corresponding coefficients estimated through ordinary least squares. In the linear form, the regression coefficient indicates a marginal consumption of 47 tons per 1,000 head of 153 cattle while the logarithmic coefficient corresponds, at the mean, to a marginal consumption of 53 tons per 1,000 head of cattle. An estimate of around 50 tons is indicated by our results. Such a figure is consistent with ordinary least-square results, taking the estimated standard deviations into account. Therefore, the influence of the trend is underestimated by ordinary least square and must be measured from the autoregressive model. The linear regression coefficient indicates that, other things being equal, the consumption of high-protein feeds by beef cattle increased each year by 131,000 tons. This figure indicates the impor- tance of the trend variable since over 34 years this corresponds to an increase of 4.454 million tons due to time out of a total increase of 5.57 million tons. Here, as in the case of hogs, we believe that this importance may reflect a growing awareness by farmers of feeding these high-protein feeds. The deflated expected price of beef is also a factor eXplai- ning variations in high-protein feed consumption. Its partial corre- lation coefficient is .29 in the linear form and .74 in the logarithmic form. The regression coefficient estimated in the linear form corres-’ ponds to a price elasticity at the mean of .32. In the logarithmic form the constant elasticity is estimated to be .63. This last figure seems to overestimate the parameter. This belief is confirmed by the results of the autoregressive model which indicates beef price elas- ticities of .23 in the logarithmic form and .21 at the mean in the linear form. The standard deviations given by the ordinary least- square estimation are fairly large, which indicates that these 154 estimates are not reliable. However, the results show a definite influence of the expected price of beef on the amount of high-protein feeds consumed. Though there is not much basis for choosing a point estimate of the beef price elasticity, .25 has been chosen for later use of this equation in the whole model.3 The influence of the price of high-protein feeds4 on the amount of these feeds consumed by beef cattle seems to be weak. In the estimation by ordinary least squares, the regression coefficient in both functional forms is negative, as expected, but not significantly different from zero. The autoregre- ssive model yields a positive estimate which is economically meaning- less. Either this variable has had very little influence on high- protein feed consumption, or the model underestimates its influence. Intercorrelation cannot be blamed for the small regression coefficient as the simple correlation coefficient between this price and time is only .14, and between this price and cattle number .05. The small influence of price lends some support to the previous hypothesis: farmers have not used these feeds up to the economic Optimum and the quantities fed have not responded to variations in prices but to what may be called, for want of a finer analysis, a growing awareness of the profitability of using high-protein feeds. 3It should be noted that choosing .2 or .4 will not affect the derived elasticity of supply very much because of the small weight of high-protein feeds in the production function. 4Here prices are used separately, in the feed-grain equation they were used as a ratio. There is no indication that one form is superior to the other. 155 Use of labor in beef production The number of cattle on farms at the beginning of the year is the most important explanatory variable of the variations in use of labor for beef production. The beta and partial correlation coefficient are respectively .82 and .52 in the linear form versus .79 and .62 in the logarithmic form. The linear regression coefficient indicates that the use of labor will increase by 7,600 man-hours following an increase of 1,000 head in the number of nondairy cattle on farms at the beginning of the year, assuming that other variables remain constant. This seems fairly reasonable as compared to an average utilization of 16.7 man- hours of labor per head of cattle on farms at the beginning of the year. The logarithmic regression coefficient corresponds to a very similar value. At the mean, it corresponds to 7.63 man-hours per head increase in cattle inventory. The presence of serial correlation in the residuals, as indica- ted by the Durbin4Watson test, may raise some doubt about the validity of this estimate. The application of the "autoregressive model" gives a minimum sum of squared residuals for I'= 1.0 (i.e., first difference of variable). The results of this method applied to the logarithmic form would indicate a slightly stronger influence of cattle number, the regression coefficient then being .51 instead of .46; however, the same method applied to the linear form gives the same estimate as ordinary least squares. Thus there is reason to be fairly confident of this estimate. The two other explanatory variables included in this equation are tl'e expected price of beef and the industrial wage rate deflated 156 by the consumer price index. The rationale for including these variables is the same as for feed-grains and hogs. The results of the two estimation methods on both functional forms are somewhat inconsistent. According to ordinary least square results, the influence of the industrial wage rate is minor, the regression coefficient being not significantly different from O (t = .06 in the logarithmic form, -.04 in the linear form). The estimates from the autoregressive model are larger and in both functional forms the coefficient is negative as expected. In the linear form, the magnitude of the regression coefficient corresponds to an elasticity at the mean of -.15 while the constant elasticity estimated in the logarithmic form is -.27. There is little basis for choice between these estimates. It is very likely that this variable has a negative influence. An elasticity of -.l or -.15 is consistent with the ordinary least squares estimates if account is taken of the estimated standard deviations. For these reasons, -.15 is chosen as the "estimate" of this elasticity to use when integrating this equation into the whole model. The results concerning the effects of the expected price of beef are still less clear. According to ordinary least square results, this variable has a significant influence (beta coefficients: .28 and .23, partial regression coefficients: .47 and .44 in the linear and logarithmic forms respectively). The regression coeffi- cients are significantly different from zero in both functional forms, (t I 2.8 and 2.6). The regression coefficient in the linear 157 form indicates an elasticity at the mean of .22 as compared to .17 estimated for the logarithmic form. However, the results of the autoregressive model contradict this estimate. In the linear form, the regression coefficient is negative, which is economically meaningless. In the logarithmic form, the coefficient is positive but very small (.005). This creates a difficult problem of choosing an estimate of the beef price elasti- city. This elasticity is probably positive and small. Labor use responds to changes in expected price essentially through changes in cattle number, labor and cattle being quite complementary at each stage in technology. Thus, .1 is chosen as the estimate of this elasticity in later use of this equation in the whole model. Production function In this model, beef output (meat production plus changes in inventory) appears as a function of: the quantity of feed-grains fed to beef cattle the quantity of high-protein feeds9¥6 beef cattle the quantity of labor used in beef production the number of nondairy cattle on farms at the beginning of the year. All these explanatory variables can be considered as measures of flows of various inputs. As will be seen later, other explanatory variables introduced to reflect changes in technology and in the use of other inputs did not improve this model. 158 Statistical considerations The statistical problems encountered for the estimation of this equation have been such that the reliability of the estimates has been affected. First there are very high intercorrelation among these inputs, particularly in the logarithmic form. Second, the quantities of feed-grains, high-protein feeds and labor used in 5 one may pr0perly wonder whether beef production being endogenous, or not the second Woldian condition for recursiveness of the system (diagonality of the covariance matrix) is satisfied. As explained above (see page 142), a priori reasoning and the lack of significant correlation between the residuals of the equations involved have led to the assumption that the disturbances were independent. Another source of difficulty has been the presence of serial correlation among the residuals of the ordinary least-square estima- tion. Thus, Hildreth and Lu's regressive model has been used as explained above. The sum of squared residuals was found to reach a minimum for I = .8 in both the linear and logarithmic forms. The coefficients estimated by this method are presented along with the ordinary least square estimates in the following paragraphs. Influence of inputs The linear regression coefficient for feed-grains (.25) 5The amounts of feed-grains, high-protein feeds and labor committed to beef production cannot be, a priori, considered pre- determined since farmers take decisions regarding their use during the year. 159 indicates that a 250,000 pound increase in the production of beef is associated with an increase of 1,000 tons in the amount of feed grains consumed (i.e. 125 tons of beef per 1,000 tons of feed-grains or a conversion ratio of 8 to 1). This figure appears plausible. The logarithmic regression coefficient (.24) corresponds to a marginal productivity of feed-grains at the mean equal to .22 pounds of beef per pound of feed-grains. This seems to be an overestimation which is confirmed by the results of the autoregressive model. The linear regression coefficient corresponds to a marginal productivity of .13 lbs. of beef per pound of feed-grains, the logarithmic coefficient to .14 lbs. of beef per pound of feed-grains at the mean.6 The linear regression coefficient for the quantity of high- protein feeds fed to beef cattle (.71) indicates that a 710,000 pound increase in beef production is associated with an increase of 1,000 tons in the quantity of high-protein feeds consumed (i.e. a marginal producti- vity of .355 lbs. of beef/lb. of high-protein feeds). This figure seems plausible as compared to .125 for feed-grains. The results of the linear autoregressive model confirm this order of magnitude since the regression coefficient (.85) corresponds to a marginal productivity of .425 lbs. of beef per pound of high-protein feeds. Both estimates 6This figure can be compared with results of feeding experiments done in the early 1940's. See A.G. Nelson Relation of Feed Consumed to Food Products Produced by Fattening_Cattle, U.S.D.A. Technical Bulletin No. 900, 1945. It was found that an increase of 100 lbs. of Total Digestible Nutrients (TDN) led to a 16.5 lb. liveweight average increase for calves, 15.1 lbs. for yearling steers, 15.2 lbs. for 2 yr. steers when these animals were at slaughter grade "Good." It can be consi- dered that 130 lbs. of feed-grains contain on the average 100 lbs. of TDN. Therefore, these results correspond to 7.9, 8.6 and 8.5 lbs. of grains per lb. of liveweight gain. 160 in the logarithmic form are further apart. The estimates of the regression coefficients (.07 by ordinary least squares, .24 in the autoregressive model) have probably been affected by the presence of intercorrelation. Taking into account the standard deviation of the ordinary least square estimation, an "input elasticity" (Cobb- Douglas coefficient) of .15 seems fairly consistent with all estimates. The linear coefficient corresponds to elasticities at the mean of .12 in ordinary least squares and .14 in the autoregressive model. The linear regression coefficient for labor used in beef pro - duction (10.9) indicates that a 10.9 million pound increase in beef production is associated with an increase of one million man-hours in the use of labor. Such a figure is difficult to appraise; it can be compared to the average productivity of labor: 20.6 lbs. of beef per man-hour of labor. One expects that the marginal productivity should be smaller than the average. At the mean, this coefficient corres- ponds to an "input elasticity" of .44 which can be compared to the logarithmic estimate of .41. Thus, the magnitude of this coefficient seems reasonable. This result is not confirmed by the autoregressive model; however, the linear coefficient of this latter model (20.9) seems overestimated since it indicates a marginal productivity of labor larger than the average productivity. The logarithmic coeffi- cient (1.13) seems still more overestimated as increasing returns to scale are questionable. A statistical explanation of the results of the autoregressive model would be very difficult to give but it seems obvious that the influence of the number of cattle has been under- estimated and that of labor overestimated. The regression coefficient for cattle number is negative in the logarithmic form of this model. 161 More confidence is felt in the ordinary least square esti- mate of the influence of cattle numbers. The linear regression coefficient indicates that, when the number of cattle on farms at the beginning of the year increases by 1,000 head, beef output increases by 170,000 pounds (i.e., 170 pounds/head). This seems plausible when it is remembered that this marginal productivity assumes that other inputs are held constant. This coefficient correSponds to an "input elasticity" at the mean of .45 as compared to .39 in the logarithmic form. The sum of the input elasticities mentioned in the previous paragraphs as most reasonable estimates is .12 + .15 + .45 + .40 = 1.12. Such a figure is too large. The sum should be smaller than one since some inputs have been left out of the model. The explana- tion of this result seems fairly simple: - The effect of other inputs has been picked up, to a large extent, by the inputs included here, particularly cattle number, because of intercorrelation. - The difference between 1.12 and 1.0 is probably not statis- tically significant. These considerations will have to be borne in mind for the appraisal of the whole model and of the overall effect of various exogenous variables. Number of calves born during the year As should be clear from what was stated above, female dairy calves are excluded from consideration here whereas male dairy calves are included. This was the reason for choosing as one of the indepen- dent variables for this equation, half the number of dairy cows plus 162 the number of nondairy cows on farms at the beginning of the year. This variable plays an important role in explaining variations in the number of calves born as evidenced by its beta coefficient (.79 in linear form, .87 in legarithmic form). The magnitude of its regression coefficient is reasonable in both functional forms. The linear coefficient indicates that, ceteris paribus, 77% of a given variation in the number of cows will be reflected in a corresponding variation in the number of calves born. The logarithmic coefficient, very close to 1, indicates a pr0portional relationship between number of cows and number of calves born which is what is expected, a priori. Time is the other important "explanatory" variable in this regression as indicated by the magnitude of its beta coefficient (.21 in linear form, .14 in logarithmic form). Its coefficient is interpreted to indicate progress in animal health control and the progressive shift to more fertile breeds (or the improved fertility of existing breeds) so that more calves now than in the past are born from the same number of cows. The various coefficients which indicate the importance of an explanatory variable do not reflect an influence of range conditions during year t on the number of calves born during the same year. Number of calves raised Vr As was defined above, calves raised are animals which were calves at the beginning of the year and have reached at leasqage one year during year t. At the end of year t, they are either among the steers and heifers or they died but after they had turned one year old. Thus, this category is relatively homogeneous although it would have 163 been better to break it down according to whether the calves have been raised to become feeder cattle or to be incorporated in the breeding herd. Unfortunately such a breakdown is not available. The most important explanatory variable is the number of calves on farms at the beginning of the year (Vt-l)’ Obviously this is what one would eXpect since all calves raised during year t were on farms at the beginning of year t (calves born during year t are less than one year old at the end of year t). The logarithmic regression coefficient (1.0) indicates that V1. is preportional to Vt-l' Varia- tions in Vt_1 explain most of the variations in Vr (simple correla- tion coefficient: .98). Yet the five year expected price of beef7 plays a nonnegligible role as its partial correlation coefficients indicate (.44 in the linear form, .46 in the logarithmic form). The magnitude of the linear coefficient correSponds to a price elasticity at the mean of .21; this is the same value as that given by the logarithmic regression coefficient. The five year expected price was chosen to reflect the anticipated future profitability of produ- cing beef. The five year horizon is fairly arbitrary. Such arbitra- riness cannot be avoided since what expected prices would be relevant for decisions regarding V1. is unknown and there is no satisfactory 7This five year expected price was obtained by Mr. Lerohl on the basis of a distributed lag model with previous prices. -(Pt+Pt+1 + ... + Pt+4) 1/5 was made a function of Pt-l’ Pt-2"° Pt-i (i being chosen so as to maximize R2). The five year expected price was then chosen to be the estimated value modified in view of forward looking information of the type used to derive the one year expected price as explained above. 164 way of measuring them. We feel that our procedure may be a useful first approximation, since Vr includes animals which will be slaugh- tered within the next two or three years and animals which will be bred and whose products will not reach the market before four or five years. The influence of the other explanatory variables: feed-grains available and price of corn, seems to be very small. Their regression coefficients are far from being significantly different from zero and one (that of the price of corn) has the wrong sign. Number of calves slaughtered V8 Calves slaughtered during year t were either born during year t or present on farms at the beginning of the year. Thus, it is not surprising that Vb and Vt_1 are the two most important explanatory variables of the variations in Vs° The regression coefficient of Vb is positive, which is what one would expect. The regression coefficient of Vt_1 is negative and very significantly different from zero (t = -3.6 in the logarithmic form and -3.9 in the linear form, with 28 degrees of freedom). This negative sign indicates that when the number of calves on farms at the beginning of the year is large, the number of calves slaughtered will be small as farmers are attempting to build up their herds. This indicates a cumulative action in response to a change in farmers' eXpectations (e.g. as they become more Optimistic). The five year eXpected price of beef has some influence on V8 (partial correlation coefficients: -.48 in the linear form, -.42 in the logarithmic form). The negative sign is as expected as 165 farmers are expected to build up their inventories and not slaughter their calves when they eXpect good prices for beef. The magnitude of elasticities with respect to price is fairly high in absolute value. The logarithmic form gives a constant elasticity of -.67 while the elasticity at the mean computed from the linear form is -.74. The cost of feed, represented here by the price of corn as expected at the beginning of the year, seems to influence slightly the number of calves slaughtered (partial correlation coefficient: .23). The regression coefficient is positive as exPected and signifi- cantly different from zero at the 10% level. The logarithmic estimate gives an elasticity with respect to that price equal to .22 while the linear estimate corresponds to an elasticity of .23 at the mean. The influence of feed-grains available during year t seems to be very small as would be expected. (The regression coefficient is far from significantly different from zero in both functional forms). Number of heifers at the end of the year Ht Since heifers at the end of year t do not include animals which were in the same category at the end of year t-l, the number of heifers present on farms at the end of the year has been used,rather than changes in this number, as the dependent variable in this equation. Thus, the set of decisions represented by this equation is fairly homogeneous since the category itself is homogeneous. 0n the basis of the beta and partial correlation coefficients, the number of calves on farms at the beginning of the year (Vt-1) is the most important "explanatory" variable. These coefficients are respectively .71 and .74 in the linear form and .73 and .85 in the 166 logarithmic form. The magnitude of the regression coefficient in the linear form indicates that 27% of an increase in the number of calves at the beginning of the year will be reflected in an increase of the number of heifers at the end of the year. The logarithmic coefficient (.82) indicates that at may be less than pr0portional to Vt-l’ This figure corresponds to a linear coefficient at the mean of .30 (as compared to .27 mentioned above from the linear form). The second most important explanatory variable is the five year expected price of beef deflated by the index of prices paid (Partial correlation coefficients: .52 in the linear form, .55 in the logarithmic form). The regression coefficient in the logarithmic form gives a constant elasticity relative to this five year expected price equal to .35. The standard deviation estimated for this elasticity is .10. The linear regression coefficient corresponds to an elasticity at the mean of .32. The regression coefficients of the two other explanatory variables are not significantly different from zero at the 5% level of significance. Yet it seems as if the amount of feed-grains avai- lable has a positive effect on the number of heifers at the end of the year. The regression coefficient in the linear form indicates that an increase of 5,930 heifers at the end of the year will correspond to an increase of one million tons in the amount of feed-grains. This indicates an elasticity at the mean equal to .14. The logarithmic coefficient has the same value, .14. Time was introduced among the explanatory variables to take into account the growing importance of feeder heifers. Our results 167 indicate that the important factors are already taken into account by the other variables, or at least that, if there are other important factors, they are not well approximated by a trend. In alternative formulations of this equation, the expected price of corn was introduced among the explanatory variables to reflect feed cost. In all cases, the regression coefficient was positive but not very significantly different from zero. The positive sign contradicts what one would expect a priori. According to these results, the price of feed-grains plays a minor role in the determination of Ht. Changes in number of steers In the case of steers, which are defined as males over one year, some animals present on farms at the beginning of year t are still there at the end of year t. Thus, it was felt that it would be better to choose the change in the number of steers as a dependent variable. Since this variable is negative for several observations, it was not possible to take its logarithm and the most meaningful functional form here is probably linear. Linearity is also indicated as the number of calves and steers at the beginning of the year are included among the "explanatory" variables. 0n the basis of the partial correlation coefficients, the number of calves on farms, January 1, the number of steers on farms January 1 and the deflated expected price of beef are the most important explana- tory variables (the partial correlation coefficients-for these variables are respectively: .67, -.65, .65).8 The regression coefficient for the 8The beta coefficients give closely similar results. ‘ 'II lill‘ il‘ 1‘ .03 31130 3 (7| HIJ 168 number of calves (.47) indicates that 47% of an increase in the number of calves on hand at the beginning of the year will become steers at the end of the same year, other variables remaining constant. Of course the "ceteris paribus" assumption takes much meaning out of this interpretation because at least time (which is included among the eXplanatory variables) does not stay constant. As a result this figure 47% appears reasonable because there are more male than female calves (only dairy females have been excluded) and time, with its negative coefficient, decreases this number. The regression coefficient for the number of steers on hand, January 1 (-.57) must be interpreted in a similar fashion. If we ignored time, it would indicate that 57% of the steers present on farms January 1 are slaughtered or die during the year. This is probably slightly underestimated with the coefficient for time bringing about the required correction. Two expected prices for beef are included among the eXplana- tory variables for this equation: Both are for the one-year horizon but they refer to years t and t+1. The expected price for the current year was included as a "proxy" for current price in order to indicate the relative profitability of either slaughtered beef during year t or to keep them longer and slaughter them in year t+1. We used expected rather than current price in order to keep the recursiveness of our model. Current prices are endogeneous. To have built a complete model would have required the addition of several demand equations while, as stated many times already, available research resources were to be concentrated on the study of production. Besides in!" I .III In I‘ll-III I..|I I'll lunllu.I I. ..l ‘1 169 the use of expected price instead of current price may have made predictions easier. As it turned out, the results did not confirm our analysis. Both expected prices have a positive regression coefficient. It seems fairly easy to interpret this result. Data on price expectations are only rough approximations and, other factors, more important than prices, may have caused the shortening of the feeding time for steers since 1929. Such factors have been the change in demand toward leaner beef meat and probably the use of faster growing animals now than in the past. These factors are partly reflected in the time variable as will be discussed below. It is to be eXpected that the regression coefficients for both expected prices would be positive and significantly different from zero. This result may indicate that the increase in number of steers at the end of the year results from decisions taken at the beginning as well as the end of the year. The expected price for the current year is relevant for decisions taken early during the year. The other one for later decisions. These eXpected prices being related (simple corre- lation coefficient between them: .72), the only meaningful economic coefficient may be their sum which roughly measures the effect, on steer inventories, of more optimistic eXpectations by farmers concer- ning the price of beef. These regression coefficients indicate a price elasticity of the number of steers equal to .53 at the mean.9 9This elasticity was computed from the sum of the regression coefficients for EPB and EP1 1). Thus it assumes that both expected prices increase by the same amount. l‘! I'v‘lllll‘ I’ll. Its-I'll I. . (ll. 1 U 170 As stated above, time has been included among the "explanatory variables". Its coefficient is negative and significantly different from O (t = -2.9, 27 degrees of freedom). The interpretation of this coefficient seems fairly easy. It reflects the younger age at which steers are slaughtered because of changes in demands of consumers and the use of faster growing animals. The expected price of corn has also some influence on changes in number of steers. It indicates the cost of a relatively important input. The regression coefficient is negative, as expected, and significantly different from zero. Its magnitude indicates an elas- ticity of the number of steers with respect to this price of feed of -.13. In judging the amount of information gained from this equation, the coefficient of multiple determination corrected for the number of degrees of freedom (R2) is a fairly good criterion. It is equal to .53, which is useful if it is remembered that the dependent variable is change in the number of steers and not the number of steers itself.10 Changes in numbers of cows The change in number of cows is equal to the number of heifers 10It can be shown that a small R2 for an equation whose dependent vaEiable is a first difference, A1Y=Yt-Yt_1, is equivalent to a large R for an equation with the same explanatory variables (including Yt-l)’ but with Yt as the dependent variable, if the simple correlation coefficient between Yt and Yt-l is high. There is no doubt that the condition is fulfilled in the case of steers. 171 which have been raised and have become cows (i.e., in our definition, females over two years old) minus cows slaughtered minus death losses for cows. The greatest difference is found in this case between the model fitted and the model originally designed (see the first section of this chapter). The set of decisions regarding the slaughter of cows is different from the set of decisions underlying the number of heifers raised. Another way to express these considerations is to recognize that cows do not constitute a homogeneous category of livestock essentially because of age. In terms of the fixed asset theory, cows in the herd can be considered as a fixed asset when their value in the herd falls between salvage value (price of a culled cow) and acquisi- tion cost (value of a feeder-heifer). Given the forementioned lack of apprOpriate data to build a finer model, considering cows as possible fixed assets may provide a satisfactory way of explaining variations in their number. Accordingly, three prices are included among the explanatory variables. These prices reflect the expected (marginal) value of a cow kept in the herd, her acquisition cost and her salvage value. The expected price of beef over the next five years is certainly an important factor detenmi- ning the sum of discounted expected future MVP's of a cow kept in the herd. For this reason it is included in the equation. The acquisition cost of the cow during year t which is equal to the price of a feeder-heifer (Opportunity cost principle) is repre- sented by the expected price of beef for year t+1. The rationale for this procedure is that the heifer which one starts to feed in year t will be sold for beef during year t+1. Actually, the expected price mm ‘3. a a 3.11,. 172 series was developed by Mr. Lerohl11 on the basis of information available during the later part of year t. Yet it was felt that this series of prices would come closest to the appr0priate measure among the available series of data. For the salvage value of cows, the current price of beef (average, grade "commercial" at Chicago) has been used. Obviously this variable is not completely exogenous. The importance of culled dairy cows is assumed to permit neglect of the "feed-back" influence of the number of meat cows slaughtered on the price of this grade. The estimates appear fairly satisfactory. The coefficient of multiple determination corrected for the number of degrees of freedqs R2 is acceptable (.44) since the dependent variable is change in num- ber of cows and there is serial correlation in the number of cows. 0n the basis of the partial correlation coefficient, the most important explanatory variable is the five year expected price for beef. Its regression coefficient is positive and significantly different from zero (t=3.4). The magnitude of this coefficient indicates an elasticity of the number of cows with respect to this price of .23 at the mean. The next most important explanatory variables are the numbers of cows and heifers at the beginning of the year. The regression coefficient for the number of cows is negative as expected and significantly different from zero at the 5% level. Its magnitude (-.25) indicates that, "ceteris paribus," 25% of an increase in the 118cc above, page 24. 173 number Of cows on farms at the beginning of the year will disappear during the year (i.e., other things equal, cows are kept four years on the average). The regression coefficient for the number of heifers on farms January 1 is positive as expected and significantly different from zero at the 5% level. It is clearly overestimated because its magnitude (1.20) indicates that more heifers are raised than are present on farms at the beginning of the year. The estimated standard deviation Of this coefficient (.55) permits the model to remain consistent. A likely explanation of this overestimation is that when more heifers are kept on farms at the beginning of the year, the factors which have led to this increase (farmers' Optimism) also influence cow slaughter. Another explanatory variable included in this equation is the index Of range condition. This variable was included on the assump- tion that availability Of feed in the range area is a positive factor in the increase in the size of the beef cattle herd. This hypothesis seems to be confirmed since the regression coefficient is significantly different from zero at the 5% level. Though the beta coefficient (.28) indicates a nonnegligible influence, it is difficult to interpret the regression coefficient since range condition is not a measurable magni- tude. The regression coefficients for the other explanatory variables are not significantly different from zero but have the "right" signs. The coefficients of both the expected price of beef for year t+1 and the current price of grade commercial cows are negative. They indicate correSponding price elasticities at the mean of the number of cows 174 both equal to -.03. It is very likely that the absolute values of these elasticities have been underestimated. The Model as a Whole After this long presentation of the results equation by equa- tion, it is necessary to examine the model as a whole and to study the effects of changes in various exogenous variables on beef output and on the size and structure of cattle inventories. The exogenous varia- bles whose effects will be analyzed can be grouped in two categories. 1. Expected beef prices. 2. Conditions relating to feed grains (quantity available and price). Effects of exPected prices of beef Several variables have been labeled expected price of beef. They differ by their length of horizon and the period to which they refer. However, only the effects Of an "over-the—board" increase in all expected prices of beef have been studied in detail in this model. Of course, there is no reason to believe that expected prices for all horizons will increase by the same percentage. As a result, this procedure only gives a rough approximation of the influence of beef prices. It was not practical to attempt a finer analysis because very little is known concerning the behavior of expected prices relative to each other. Incidentally, if we know more on this matter, such a knowledge would first have to be incorporated in the specifications of the price variables in the model. In order to appraise the changes in the various variables 175 of the model resulting from an increase of 1% in all expected prices for beef, it is assumed that this increase takes place at the beginning of year t (the system being in equilibrium otherwise). Cattle numbers at the end of year t-l are given. During year t, the three inputs present in the production function--feed-grains, high-protein feeds and labor- change under the effect of the expected price of beef only. On the basis of the results presented in the previous subsectiodg feed-grains change by .3%, high-protein feeds by .25% and labor by .l%. Entering these changes into the production function gives an increase in output from year t-l to year t equal to .12%. Our price elasticity of beef production in the short run (1 year) is therefore .12. The elasti- city of meat production is lower than .12 because changes in inven- tories, included in beef production, are positive as described below. During year t, the expected prices of beef are the only expla- natory variables of the cattle number equations (Vb, Vr, V8, Ht (SS, rA,C) which vary. Thus, the derivation of the changes in cattle number is straightforward. The relative change in the number of cattle of one category is the algebraic sum of expected beef price elasticities of this number of cattle. Thus cows increase by .20%, heifers by .35%, steers by .53% from the beginning to the end of year t. The number of calves born does not change (or at least not as a result of the increase in expected prices), the number of calves raised increases by .21% 12The simplified form of the equations used for the following computation is given in the Appendix. 176 and the number of calves slaughtered decreases by .70%. The change in number of calves on farms at the end of year t must then be derived from these changes. Recalling the identity of page 141 regarding change in calf inventory: V + Vb = Vr +-V8 +-DV +Vt (where DV is the number of t-l mortality losses on calves) hence: V = V t +Vb-Vr-Vs-DV t-l V1. and V8 have changed, Vt_1,Vb and DV have remained constant}3 At this stage, the relative changes inVr and V. must be converted to absolute changes. Since relative changes at the mean have been used to derive the price elasticities, conversions will continue to be made from relative to absolute changes at the mean. Thus .21% of V1. minus .70% of Va represent (at the mean) a 12.5 thousand increase in the number of calves at the end of the year (i.e., a .09% increase). It is also necessary to weight these changes in livestock categories in order to derive the change in the total number of livestock. Since the relevant variable in the production function is the number of cattle on farms, variations in one category, for instance cows, is weighted by the average prOportion of cows in the total number of beef cattle. The resulting change in cattle inventory is then .24%. 13More rigorously, the number of calves dead (DV) varies probably with the number of calves slaughtered; we neglect this effect considered small. 177 In year t+1, the use of inputs will be affected by this change in cattle inventory. The relative variations over the t-l levels are therefore: .48% for feed-grains, .49% for high- protein feeds, .21% for labor. As these increases result in a .32% increase in output in year t+1, i.e., the second year price elasticity is .32. During year t+1, the number of calves born (Vb) is higher than during year t because the number of meat cows at the beginn- ing of the year is higher. According to our results, Vb is higher by .ll%. To compute changes in numbers of cows and steers from the beginning to the end of year t+1, relative variations are again converted to absolute changes since the relevant equations are and S linear in terms of Ct-l’ Ht-l’ V Following the method t-l‘ described above for year t, it is found that the relative varia— t-l tions in numbers of livestock at the end of year t+1, as compared to t-l level are .26% for cows, .42% for heifers, .28% for steers and .203 for calves. The total number of livestock at the end of year t+1 is then .26% higher than at the beginning of year t. The resulting output during year t+1 is .34% higher than during year t-l, and the third year price elasticity is .34. As in the case of hogs, this set of elasticities is not sufficient to summarize the influence of expected prices on beef production. To repeat, the changes indicated by the previous computations will take place if the shock (e.g. increase in expected price) occurs when the system is in static equilibrium. As it would not be realistic to assume that such a condition is 178 usually fulfilled, it is necessary to appraise the influence of variations in expected prices when the system is not in static equilibrium. As in the case of hogs, variations in the endogenous variables are estimated (1) from a price increase, (2) from a price decrease starting with January 1, 1963 conditions. The exogenous variables other than expected beef prices were given the same values as in 1962. In both cases (the five-year horizon and one-year horizon), expected prices for 1963 and 1964 were assumed to be equal. In the first case this common value was 10% higher than the one-year eXpected price for 1962; in the second case, it was 10% lower than the same price. According to the least square estimates of the linear form of the model, the number of cattle on farms increased from 74.9 million head on January 1, 1963 to 79.5 million head, at the end of the first year and 84.8 million head at the end of the second year following the 10% increase in price. With the decrease in price, the same number increased from 74.9 million head to 77.4 million head at the end of the first year and to 81.1 million head at the end of the second year. The volume Of production is 27.6 billion pounds during the first year and increases to 29.2 billion pounds during the second year if expected prices increase. It is 26.8 billion pounds the first year and it increases to 27.7 during the second year if eXpected prices decrease. The increase in production and in cattle inventory numbers when expected prices decline indicates very dramatically the influence of starting conditions, or, more precisely, |‘.l1.l_|l. 1") bIIllv 1 A II. 179 of the past evolution of the system. At the end of 1962, the system was not in equilibrium; instead, it was in a herd build-up phase . Resources committed to beef production in 1962 were not diSposed of the following year in spite of price declines and thus causing an increase in production. One can compute price elasticities of production on the basis of these results since all variables but prices are assumed to remain constant. Under the hypothesis of rising prices, output increases by 2.2 billion pounds the first year and 3.8 billion pounds the second year (i.e., relative increases of 8.3% and 13.9%). Prices having risen roughly 10%, the elasticity of output appears quite large, .83 the first year, 1.39 the second year. Under the hypothesis of decreasing prices, negative elasti- cities are obtained of -.53 and -.86 the first and second year. These results illustrate very clearly that such elasticities require a careful interpretation. Because of lagged effects of previous shocks to the system, it cannot be said that the decrease in price causes an increase in production; rather, it causes a decline in the rate of increase of the output. A more meaningful comparison can be made between the computed outputs under the two price hypo- theses. The differences are .8 and 1.5 billion pounds for the first and second year respectively. These correSpond to relative diffe- rences of 3% and 5.6% in response to a 20% difference in expected prices (i.e., average elasticities of .15 and .28). Yet these average elasticities are not very meaningful, as they depend so heavily on the lagged influences of shocks which occurred prior to 1963. 180 In order to measure more fully the impact of changes in expected prices, as implied by the model, it is necessary to assume a static equilibrium at the starting situation and then submit the system to the shock Of a change in prices and study the effects through several time periods. The impact of subsequent shocks can also be studied. In a first step of the analysis, the trend variable is assumed constant in order to isolate fully the effect of prices. The results are similar to those obtained for hogs. Following a change in price of A P1 (measured in 1910-14 cts/ cwt)14, the number of cattle on farms increases, according to ordinary least square linear estimates, by 1411 x £1P1 thousand head during the first year, by 1219 x.¢LP1 thousand head over the previous level during the second year, by 1049 x llPl thousand head during the third year. This is a rate of increase slowly tapering off. If a second change in price APZ (measured in 1910-14 cts/cwt)1A occurs after the first year (e.g. the second year) the number of meat cattle on farms changes by 1219 x 4P1 + 1411 Ale thousand head during the second year. Thus, if the second change in price is of Opposite sign but of the same magni- tude as the first one, the number of cattle will not resume its previous level. As in the case of hogs, the results of this model indicate very strongly why the supply elasticity has been found larger at laThe changes in price AP1 and APZ may be positive (price increase) or negative (price decrease). ‘1 I I II . ‘ 181 eXpansion than at contraction. Beef cattle production has been increasing under the influence of various factors. In any one year, the lagged effects of previous shocks has tended to push production up; thus, even if the influence of a change in price is isolated from the influence of other variables during that year, the response is larger at expansion than at contraction. Our model indicates that the influence of a given change in expected prices depends heavily on the previous evolution of beef production and cannot be adequately summarized by a small number of elasticities. In particular, the turning points in the cow number cycles cannot be predicted on the basis of prices only. The model clearly indicates that the change in the number of cows depends heavily on the previous evolution of the beef herd. The economic interpretation of this behavior is the same as for‘hogs. Cattle on farms are a very specialized input. Once they have been acquired (through breeding) they put a very strong upward pressure on production because they cannot be diaposed of advanta- geously when prices are low. Effects Of changes in feed-grain availability Two variables related to feed-grains, expected price of corn and quantity Of feed-grains available, have been included in this beef model. In reality they are not independent and their effects should be aggregated, but since one cannot say that a given change in the quantity of feed-grains available will always be accompanied by the same change in expected price for corn, their effects will be considered separately, assuming the other variables to remain constant. 182 Remarks made above on the insufficiencies of static elasti— city parameters to characterize the influence of a shock to the system apply to shocks such as changes in the availability of feed- grains. The results from the models will be presented assuming an initial static equilibrium. This is an unrealistic assumption but, as already stated, it is useful in appraising the influence of changes in feed-grain availability per se. Changes in expected price of corn Assuming a 1% increase in the eXpected price of corn at the beginning of year t, the quantity of feed-grains consumed will de- crease by .30%. As a result the beef output will decrease by .O4%. Such an elasticity of output relative to the expected price of corn (-.04) seems very small. It is probably underestimated here because, as stated, the amount of feed grains available was assumed to remain constant and the effect on the number of livestock is assumed to have a lag of one year, which is probably overestimated. The number of calves slaughtered increases by .22%. As a result the number of calves on farms at the end of year t decreases by .1% while the number of steers on farms at the end of year t decreases by .13%. According to the model, there is no effect on Ct and Ht' The effect of the decrease in the total number of cattle at the end of year t (.057%) is an output, during year t+1, which is .09% lower than during year t-l (i.e., a second year elasticity of -.09 with reapect to the expected price of corn). Changes in the quantity of feed-grains available A 1% increase in the quantity of feed-grains available at 183 the beginning of year t, will result in a .80% increase in the quantity of feed-grains fed to livestock. This will, other things constant, give a .1% increase in beef output during year t. In the model, the only effect on livestock numbers at the end of year t is on heifers. Their number will increase by .l4%. The result of this small increase in the number of livestock at the end of year t is to produce an output during year t+1, .11% higher than during year t-l. Of course, in order to analyze the complete effect of this change in feed-grains available, it would be necessary to extend the computa- tions over several years as the number of cows would increase in year t+1, the number of calves born increase during year t+2 and all numbers increase later as a result of the increased number of calves. Yet as can be seen without actually doing the computations, this increase would be small probably because so many of the feeders are raised so far from the feed-grain producing areas. Thus the increase in beef production resulting from an increase in feed-grains available is not large. But it must be said once again that this increase in output is probably underestimated because prices are assumed to remain constant. However, the combined effect of both feed-grain variables appears small. Appraisal of the Model lFrom the previous section, it appears that the results obtained from the model are plausible and that some interesting conclusions can be drawn regarding the economic forces underlying beef production. In order to get an idea on how reliable these results are, the model has been submitted to the same tests as the hog model: (1) prediction of 184 1963 results on the basis of actual values taken by the predetermined variables, (2) prediction of the evolution of production and cattle herds from 1949 to 1962 on the basis of the recursively predicted values of lagged endogenous variables. The performance of the model under these tests is analyzed in this section; an overall appraisal of the model is then given on the basis of results and of examination of the unexplained residuals for the most crucial individual equations. Prediction of 1963 Results As in the case of hogs, actual values taken by prednnrmined variables were "plugged" into the model. The expected prices used were derived by Mr. Lerohl in the same manner in which he had derived them for previous years. The results of the computations are presented in table 14, page 185, along with the actual data as they have been published to date.15 The other variables predicted by the model, notably the volume of production, do not appear in this table because actual data are not yet available for 1963. The table indicates that the model has predic- ted the various cattle numbers fairly well. However, the last column, showing the percentage of actual variation from 1962 to 1963 predicted by the model, indicates that the variation predicted for heifers, even though small, was in the wrong direction. The increase in the number 1"USDA, Livestock and Meat Situation, LMS-l36, March 1964. 185 mo Human: one wcauowuoum .nmamr coo.Oe ammo he OHuumo mo unease HeuOu one :o uouuo.onu someones“ ooao> Nome mum an maasn .Hovoa moo OH anodes uoa on songs means nonnaoxo Heuou mesa Amy onoHuumo new Ne. . emm.ee ooe.ee Hea.ma mane ooo.a more no .02 .— muons an - am . amm.m eem.e amm.a mama ooo.H or New am.N- ame.am mme.om cea.am meme ooo.~ no amen mm. + oma.~a emn.Na NNH.NH mama ooo.a be game em.~+ Nem.em mao.mu mma.m~ mane ooo.~ 0> wouoaooum. uouum N oon> OOHO> Amoma 4H .OOhv mugs: oanmwum> eoaamanap Heaboa mean emauuamanme mean aaaa> «can . Hummus «6 a moma .oauumo moon no woman: mooHuo> may no mosam> ensues use cohoaooue one mo cOmaumdaoo "OH manna 186 of calves has been overestimated and that in the number of cows underestimated. 1949-1962 Predictions The year 1949, rather than 1948 as in the case of hogs, was chosen as the starting point of this test because the residuals of the calf equations were large in 1948. Apparently this precaution was not sufficient. The predicted, and actual series diverge fairly rapidly. The results are presented on diagrams showing the evolution over time of the actual and predic- ted values of several endogenous variables (see fig. 9 and lO,‘p.lB7, 138). 0n the diagrams, it appears that the first important divergence occurs in 1952 for V8 (calves slaughtered). The predicted value is more than 20 percent below the actual value. Accordingly, the number of calves on farms at the end of the year is overestimated. Yet for 1952 the predicted value of V8 is an overestimation when the actual values of the lagged endogenous variables are used for prediction. Thus, the cause of the present underestimation lies with the values of the lagged endogenous variables which were used; Vb is slightly underestimated in 1952 while Vt is overestimated in 1951. These have caused the divergence for V3. For later years, errors cumulate, Vs being underestimated and Vt overestimated which causes Vs to be more underestimated the following year. The overestimation of Vt causes overestimation of Ht, St and Ct in the later years. Accor- dingly, the predicted values of Ct which were lower than the actual values became larger in 1956. The divergence occurs in 1955 for Ht, and around 1953 or 1954 for St' In turn, the overestimation of Ct ' 1 1 ‘r (a 1. (g I - l ‘u ' " 1 C . t“; ' {r .. a a ‘4‘ . 5; -¢' '1 J ’ ,1 1 I ! \ .‘ t _ JJ ,_ Y0 of 13¢}: (‘r‘ Ivns l Anu&. 'Cfis rho ) T';III":‘OPY'S‘ (NF Ififllvng "NWT!“ 187 . / \ .1. ,2 \ ./ \ .‘ \ \/ \ ”Lha] \ \ \ \ \ \ \ \ \ \ \ {)1‘0..‘1.C"ed ‘ \ ~ Fred " (tted. / "21119 at par? / (fir par- .— "(7“.‘5‘1 / III/ I" 1“.”(zicf ()(1 ,/ (1211'pg I 7’ (3:32) / I J 1‘ \C’I‘I'J} ', . I / /’ I ’fl/ r-‘ a’ / / 1""(‘1(‘? 0H I . / Pslvne ‘nrn , ) - - - ’ "' ,1'.(“1}'1] /~2 I v ' f I -’ / I \’ I"/. ’y/ ’5/ ”1156"“ " 5 ‘ “"80“"192; 1‘1.» (. _ 1‘2?an 1 a, (I 1|](1.L;‘-1()““r) I’r13f11C1 0(1'Q \,.T‘. l'Ifiq 1“ if 0‘ Calvnq C14n~hrprp4. n; Calves ("159A 9“” nt Calves 0“ Vnrws at (he find of the Your. 188 1’, :11;,—\. (5...,1v - . .. ‘ . -. . / 3 rc-(f1c'0’1 1’ / -, I 3 , / 1 fl ‘ m; 1 . " ‘ ‘ C val o I / 4" / / ”/ ..Af: ’ / / \- K ' ’ Q 4’ I g1. , v \ l/ a? II/ I if '-"*"‘_J‘ L/ 1‘ red is red C. ow s (1.001 bonds) ‘. 5705:” Acre"). i ! i a - c a 511%" I I I". / I ’ I, I (r, ' 1. J - J ‘V.‘ ‘ ' D ' t- . (1.000 yppdgg Stonyg .r’ .redlc (d lie-co: I / / /4 CW , I / I ./ ACE”)? 1 [0,-0ch '____,"/\// IL/N I / .'.M/ 606941 R / yr961C'Pd r“ '\ ' ' .- ’ (1,100 leads) un1‘ers ’ ' fl- ‘ ---- _ / ?Juk I I r‘xckL'ql ‘7,“C - our; & L A A L .4 L A. A— A 1 f - W NW 50 55 60 61 Fifi. 10 - Ac'rnl 8*"1 “1‘.“-1“n° Predicted” Values of the Volume of Reef Production and CF the Tuwber of Cows, 0F T‘teers and of Heifers on Farms at 1be 1nd of the Year. 189 causes the overestimation of Vb and thus of Vt the following year. Thus, it seems that the eventual upward divergence of all predicted series has been triggered by cumulating errors in the calf variables. Other less important divergences must also be mentioned. The buildup in cow inventory in 1952 and 1953 has been underestimated. Accordingly, the increase in the number of calves born is underestimated in 1953 and 1954. The volume of production has been fairly well predicted until 1955 but the large increase in 1953 has been underestimated. What then are the implications of this failure of the model to predict the evolution of beef production and cattle inventories from 1949 to 1962? Without denying that such a performance weakens confidence in the model, it is believed that this test involves only one of the criteria which should be used in evaluating such a model. All models yield predictions subject to errors. It is unfortunate that here the errors cumulate for the calf equations, and hence put the whole model on the wrong sequential track. Residuals of Individual Equations In order to complete the appraisal of the model's ability to reflect year-to-year variations in the various endogenous variables, attention is now turned to an analysis of the residuals of the indi- vidual equations. The residuals of the calf equations are plotted over time on fig. 11, page 190. The "smoothness" of the curve representing the evolution of the residuals of the equation giving Vb (the number of calves born) suggests that the model has failed to recognize the influence of 190 .UOLOaLtSndm m¢>~mo MC cum Temwcm mozamz no .tec; an>ecc do who;E;a sci eca>wc mooaemzta unsung one no mfimstmed 1 ~H can - I . r ,- . . me u. no . On < 1}) Willi. "sll'vllll ’.‘. 1.1.6,le11 +1+|11Nl+t§il ) em: .1 Amewgn . 0.0.m ’ _- —-l v" u.xu_ . eeeeei ecc.ee . ©dh...7..._-h:c.flm .. . . . (2. / . Wave/H T; re. / CLCI, VQCH C L. sIenprssu 191 some economic variable. Comparing these residuals with the 5-year expected price for beef, it appears that they vary together except for the period 1945-48 for which no important decreases in price correspond to the large negative residuals. However, the large R2 of the equation for Vb (.98) suggests that such an influence of prices, if it exists, is probably small (the expected price for beef is not highly correlated with any of the explanatory variables). The same figure shows that the residuals for Vr and V8 vary in Opposite directions. This is not surprising since calves present on farms at the beginning of the year are either slaughtered or raised during the year (neglecting mortality). Of course, this dichotomy is not exhaustive. Many calves slaughtered during the year were born during the same year. If they had not been slaughtered, they would be calves at the end of the year and would not have entered the Vr category. Thus, these variations in Opposite directions imply that probably the influence of the same factors has been neglected or under- estimated by both equations for Vr and Vs. As is clear on the same figure, the residuals of the equation giving Vr follow a pattern very much parallel to that of the residuals of the Vb equation. Yet the calves raised to become steers or heifers during year t were not born during year t; Vb and VI. represent mutually exclusive classes. As the variations in the residuals for Vb may be linked to expected prices for beef, it appears that the influence of expected prices on Vr and V3 may have been underestimated. This result could be due to an impr0per specification of the price variable and/or to errors in its measurement. In both cases, a limitation of the procedure 192 followed is found and it seems difficult to improve the model in the present state of the arts. In the preceding subsection, it was indicated that the calf equations, and particularly that for V5, were probably responsible for the divergences between the 1949- 1962 predicted and actual series. This analysis of the residuals confirm this suspicion. The R2 for the V8 equation is not very large (.65) even though the number of calves slaughtered varies from.4.3 to 9.1 million during the 1929-1962 period. Accordingly, several residuals are large (up to 25% of the actual values). The pattern of residuals for the equations for Ht and AS (number of heifers and change in number of steers) shown on figu-‘ re 12, page 193, seems to indicate that the influence of prices has not been completely taken into account by the econometric model. The variations in the residuals for Ht are somewhat parallel to those for Vr. Such a result is not surprising since all the heifers on farms at the end of the year were raised and became heifers du- ring that year. The 5-year horizon expected price is the only price variable included in the Ht equation. Yet the residuals follow a cycle roughly parallel to that of Ht itself; they seem to respond to variations in eXpected prices. It is very likely that a single price variable representing the average expected price for beef over the next five years is not sufficient to explain variationsin the number of heifers. This number includes both feeders and animals kept for breeding purposes. The residuals Of the equation for A S follow a less "smooth",although somewhat parallel, pattern. There- fore, it can be concluded that the neglected variables are less 193 .mhcoum mo LOJESZ axe Cw wzzaip eat can amd> to use OLE mince at needed: at poxasz can utw>wc atomic:cm Latte; one at m~u2rwmdm ..r. 1 2 ...: we um , .\ nww - 1 ..0M 1 . r ,MW4,1zr , on p - . ) mm . . r r mmwwz a 2 a. _ . . . dbeml . . . _ LVQQV) — . ~ - ‘ . x \ . a .. —.. \. . . m aoow \ . a m . _ . as . . \w m \ i mitten; no no;&:7 _ 100% Amanda CCC._. waters to Leifitz cw e.chu stunprsau 194 important than in the case of Ht. This is not surprising since two one-year expected prices were used for beef (those for years t and t+1) and longer horizon expected prices seem irrelevant. The residuals of the equation for AC (change in number of cows) follow the same general evolution as those for Ht. They are plotted against time in figure 13, page 195. Thus, it is very likely that the influence of eXpected prices has been underestimated by the model. However, these residuals are fairly small. They rarely represent more than 5% of the number of cows on farms at the beginn- ing of the year. Therefore, it seems safe to assert that this under- estimation has not been very large. The residuals of the production functions plotted against time in figure 14, page 196, form a relatively smooth curve, which indicates that some significant variable has probably been left out of the model. The figure next to each Observation on the diagram is the number of calves born during that year as a percentage of the number of cows on farms at the beginning of the year. It seems fairly clear that most year-to-year variations in the residuals can be linked to parallel changes in this percentage. This result is not surprising: beef production depends on the number of cattle at the beginning of the year, it depends also on the number of calves born during the year. . As the influence of variations in capital equipment is not reflected in the residuals,14 it was probably "carried" by the 14Although we have no data on capital equipment, it seems very likely that it is highly correlated with a trend variable; from the diagram it appears that the residuals of the production function are not highly correlated with time. 195 mSCC we aan:x .... --o-.— . .. .. 1T1.Il11111.):.!ln mLa Cw .QLCWF—“V .hwoew QLa 9.0 15...“ mL. em ”LUZ“; no rewgmrcu eLa mo unw:t_mcm I 8H .omh Lq .3 L de N If 11.9. E '7‘! 1 Q | stunprseu _ mmemwa.e inure. A a 196 see; are wo ccvtcfieor err rm u3tt we norEze ext flwc QTRaLCLlCC G Vfl LLOL EU>HWC WC LCJE3C Qfiu Vawfitwki CHV anewuocom camcoomoam moom umociq osu we maeovmmom 1 :H .nae WMT$.QX e .. ..4 LWM111+§111¢1m% ?!1 L. $.WW., r pltrQHu. 9.1 >.Mm..r) Llirwwmx E 4 a. s a ... b a Q .... a. a 13 Mm .631 .4%. me $ $014 w% a. x u .w% .XUQAV_ ma. .% $0033 e 009.12.12.78 197 number of cattle at the beginning of the year. Summary Remarks From the results of the two tests, it appears that the beef model is not as good as the hog model. The 1963 values are fairly well predicted but the 1949-1962 predictions diverge from the actual values. It has been shown that cumulating errors in the calf equa- tions are probably reSponsible for this divergence. The analysis of the residuals has indicated that the most likely causes of these errors were probably mis-Specification of expected price variables, and/or errors of measurement of these variables. The analysis of the residuals also indicated that the major factors of determination have been taken into account by the econometric model but that the influence of expected prices has probably been underestimated in most equations. Conclusions It seems hardly necessary to repeat here that the model, as well as those for hogs and feed-grains, is incomplete. Thus it cannot fully predict beef cycles. The purpose was to study the economic forces underlying beef supply within the following Objec- tives: (1) to identify the factors determining the use of resources in beef production and to attempt to measure their influence, (2) to measure the influence of the factors determining supply. Since the beef model is very similar to the hog model presented in the previous chapter, the conclusions which can be drawn are very simi- lar in both cases. When the analysis is the same it is not fully repeated but rather recalled briefly. Emphasis is placed on the 198 differences between the two productions in an attempt to clarify understanding of the economic forces underlying both. Commitment of Resources Here the key factor of production is also breeding and feeding stock, because they become easily fixed in production and because they play a dual role as an input and as part of the output. Because of the longer lags in beef production than in hog production, the system is more complex. Accordingly, six equations plus one identity have been used to describe the evolution of the herd (equa- tions for Vb, Vr, Vs, Ht’ AS and AC and the accounting identity relative to calves). The three equations for calves are not suffi- cient to describe satisfactorily the determination of the number of calves at the end of the year. Yet our analysis has shown that this number depends mainly on the number of calves born, on expected prices for beef (increasing with the degree of Optimismgand on the availability of feed. In the treatment of heifers, it has not been possible to separate heifers on feed from heifers kept for breeding purposes. Accordingly, the model does not reflect all variations in the number of heifers on farms at the end of the year. As seen above, the introduction of a single horizon expected price (5 year) may be an oversimplification which explains most of the residuals. Yet the analysis indicates that the most important factors of variations in the number of heifers, given the number of calves at the beginning of the year, are factors related to the degree of farmers' Optimism concerning the future profitability of beef production. The change in number of cows on farms is a variable more 199 heterogeneous than the other livestock numbers. Considering them as a durable input which can easily become fixed in beef production gave some satisfactory results in this model. At such a level of aggregation, the precise specification of price variables represen- ting acquisition cost, salvage value and MVP in production is difficult. However the results are consistent with the theoretical model. In summary, variations in the breeding and feeding stock appears to be function of expected prices for beef, of the quantity of feed-grains available and on the past evolution of the herd. This last factor reflects the high degree of fixity of this input in the short run. Herd size may even increase, in the face of declining expected prices, as a result of previous commitments to its production. The other inputs (feed—grains, high-protein feeds and labor) are expendable for this enterprise. Their use responds immediately to price incentives but the high degree of complementarity between these inputs and livestock makes their use highly dependent on the use of the feeding and breeding stock. Thus it is not surprising that the amounts of these inputs used in a year can even increase' in spite of falling expected prices for beef. Beef Supply As in the case of hogs, the supply of meat animals to slaugh- terhouses can be divided into two components: (1) Outright beef pro- duction and (2) depletion of inventories. The model permits distinc- tion to be made between the two. It is also clear that a single supply function is not sufficien: 200 to characterize the annual adjustment of the volume of production to changes in price. The results lend very strong support to the thesis of diverging elasticities of supply at contraction and expansion because the evolution of output is influenced by changes in price during the same year but also by the lagged effects of previous shocks. Historically, beef production has been expanding, thus it is normal to expect that the lagged effects of previous shocks will generally be factors of expansion. These conclusions are very similar to those reached for hogs. But they appear to be more true, so to speak, in the case of beef. The technical lags in production are longer than in the case of hogs. The difference between acquisition cost and salvage value for animals of the breeding stock is wider. The salvage value of a cow is the price of a culled cow which is quite lower than the price of a feeder heifer (acquisition cost). For sows the salvage value is the value of a sow for slaughter. This value is not much lower than that of a gilt (acquisition cost) because of the increase in weight. In Spite of the serious qualifications called for when using elasticities, it is felt that such elasticities are useful to charac- terize the order of magnitude of the influence of some variables on the volume of production. Changes in expected prices for beef are an important factor determining variations in the volume of produc- tion. A price elasticity Of .32 for the two year adjustment is not (at all negligible. By the same procedure it has been seen that changes in the availability of feed-grains have a smaller effect on beef production than on hogs. This is in accordance with genera- 11y held ideas on the feed-grain livestock economy. .l‘l'v 5141.1]. 1111' llllallllllllll 5"] CHAPTER VI SUMMARY AND CONCLUSIONS The objectives of this study were to analyze the major economic forces affecting feed-grain, hog and beef production and to estimate the influence of various factors. This study, being only a part of a larger project, used only one research approach. An econometric model was built at a rather high level of aggrega- tion. It is Obvious that other approaches, especially at the microeconomic level, must also be used and their results be brought to bear on the conclusions regarding the economic forces studied. This latter task is beyond the sc0pe of this thesis, but we can summarize and appraise the results obtained here and compare them with results obtained by previous workers. In view of this compa- rison, it will be possible to appraise the research methods used and, lastly, to suggest areas for further research. A. APPRAISAL OF THE RESULTS This study provides some information on the factors affecting the commitment of resources to the production of feed-grains, pork and beef and, in turn, determining the volumes of production. Conclu- sions on these points are summarized on the following pages. (1) Commitment of resources First, the nonstructural nature of most equations predicting the use of various inputs must be emphasized. These equations are inainly predictive. They can be interpreted as demand equations only 201 202 under very restrictive assumptions concerning the supply of these inputs. Yet information on the relationship between some variables and the quantity of an input actually used is useful, pg£_§g, Esti- mates based on such relationships are precisely what is needed to derive the final influence of these variables on the volume of pro- duction. Such considerations justify the procedure. It is not denied that there has been some arbitrariness in deciding which variables would be treated as exogenous as all useful models must abstract from reality in some respects and, therefore, involve some degree of arbitrariness. Using an earlier classification,1 the inputs considered in this study can be grouped into six categories: - Nonfarm produced durables (machinery, equipment) - Specialized farm produced durables (breeding stock) - NonsPecialized farm produced expendables (feed grains) - Nonfarm produced expendables (fertilizer, high-protein feeds) - Labor - Land Because of the lack of data, very little has been done about the first category (nonfarm produced durables). The scanty evidence available from this study indicates that purchases of specialized Inachinery respond to changes in eXpected prices for corn but the 1G.L. Johnson, "Supply Function - Some Facts and Notions" in Agricultural Adjustment Problems in a Growing Economy, E.0. Heady et a1. editors, Iowa State College Press, Ames, Iowa (1958). 203 influence of these prices has not been measured. The breeding (and feeling) stocks of hogs and beef cattle are specialized farm produced durable inputs. This model throws some light on the factors determining the use of these inputs. Because of various production lags, previous stocks of these dura- bles have very strong influences. The most important causes of changes in such stocks are changes in expected prices and in availability of feeds (feed-grains and roughage as measured by the index of range conditions). Thus, the long-term influence of prices on production and herd size is rather large even though it can be hidden, from year to year, by the lagged effect of previous changes in herd size. In several equations dealing with livestock inventories, the trend variable appears with a regression coefficient estimated to be significantly different from zero. This reflects the impact of various changes. Some can be called technological improvements (increased fecundity and rates of growth). Others are in response to changes in the tastes of consumer. Such information is transmitted to producers through price and cost differentials not taken into account by our model. The fact that these resources can easily become fixed in livestock production is reflected in our model by the one year lag which is assumed and by the importance of the size of the beginning inventory of livestock in both models. Feed-grain is a nonspecialized, farm-produced, expendable input used in meat production. Concern in this subsection is with 204 the use of this input,once produced. For both hog and beef produc- tion, it has been found that the quantity of feed grains available was a major factor associated with variations in the quantity of feed grains consumed. Another important factor is the number of lirestock on farms at the beginning of the year which reflects the high degree of complementarity between these inputs. The expected price of the product plays a role but it is not so important as the two previous variables, in the short run. The equations predicting the use of feed grains can hardly be considered demand equations even though supply can be considered predetermined. Most feed grains do not move through the market; instead, they are fed directly on the farm where produced. As a result, the price of feed grains appears to influence the consumption of feed grains only slightly.2 Fertilizer and high-protein feeds are the two nonfarm produ- ced expendable inputs considered in this model. For these two inputs, time is the most important explanatory variable. We have interpreted this result to reflect the growing awareness by farmers of the advan— tages of using these inputs. There is far from complete agreement on this issue in the economic literature. Using a distributed lag model 3 Zvi Griliches concluded that the use of fertilizer in U.S. agricul- 2As noted above, the lack of statistical significance of the price of feed-grains cannot be blamed on a high correlation between this variable and the quantity of feed grains available. 3Z. Griliches, "Distributed Lags, Disaggregation and Regional Demand Functions for Fertilizer", JFE, Vol. 41, p. 90 e . an same aut or, e eman or Fert zer: n cono- (Fb 1959), d h "Th D df 111 A E mic Interpretation of a Technical Change", JFE, Vol. 40, p. 591 205 ture could be eXplained largely by the decline in the real price of fertilizer. However, Heady and Tweeten have written "Numerous alter- native models can be used in specifying demand structure for fertili- zer and individual nutrients; on a purely statistical basis all are about equally acceptable, and it appears that any equation containing two variables relating to time and price, over a large span of the period studied, explains a major portion of variance in fertilizer consumption."4 Griliches' model falls into this category since he uses the previous year's consumption of fertilizer as one eXplanato- ry variable. As the real price of fertilizer has decreased over time, it is difficult to separate the influence of price frOm that of other variables linked with time. The evidence is not altogether convincing that the fall in real price of fertilizer is the cause of the increase in consumption. Griliches' justification for incorpora- ting a distributed lag is precisely that the lack of sufficient knowledge about the use of fertilizer prevents the Optimum adjustment to lower prices to take place immediately. Our results suggest that the Optimum adjustment has seldom, if ever, been achieved in the case of fertilization of feed grains. They are in accord with Ibach and Lindberg's conclusion that "the present level of use on many crOps in many areas is below the level that would be most profitable for most farmers".5 4E.O. Heady and L.G. Tweeten, Resource Demand and Structure of the Agricultural Industry, p. 193, Iowa State University Press, Ames, Iowa (1963). 5D.B. Ibach and R.C. Lindberg, The Economic Position of Fertilizer Use in the United States, p. 3, USDA Stat. Bull. NO. 202 (Nov. 1958). 206 A very similar argument could be made for price and the use of high-protein feeds. In addition to time, the number of livestock on farms at the beginning of the year is an important determinant of year-tO-year variation in the quantity of high-protein feeds consumed by both hogs and livestock. This illustrates the high degree of complementarity between these inputs. Lgbgg_is a resource used for all three products considered in this model. Generally Speaking, it can be viewed as variable between agricultural enterprises but much less mobile between the agricultural sector and other sectors of the economy. Obviously, it is out of the scOpe of this thesis to study the factors influen- cing labor mobility. In this econometric model, their effect is only reflected through the deflated industrial wage rate variable. Therefore, it is clear that our equations for labor are not struc- tural. They should be expected to be only moderately effective for predictions. For hog and beef production, the number of animals on farms at the beginning of the year is the most important explanatory variable in our equations. This reflects the complementarity between these inputs, given existing equipment, buildings and methods of pro- duction. Industrial wage rates are most important in the case of feed grains. They are also very important for hogs. However, their influen- ce is not strong in the case of the beef equation. As stated above, this variable "carries" the influence of a complex set of factors which have led to the reduction of labor use in agriculture and the substitution of capital for labor. Apparently these influences have been much less powerful or harder to estimate in the case of beef 207 than in the case of hogs and in the case of hogs than in the case of feed grains. The results of the model indicate that the use of labor does respond to changes in the expected price of the product even though the influence of the latter is weaker than that of the other factors mentioned. lggg_is the last resource included in the analysis. It is an input in the production of feed grains. Land is variable between agricultural enterprises but relatively fixed in the agricultural sector.6 Accordingly, the acreage of wheat planted influences the use of land for feed-grain production. Government programs are another important factor influencing the use of land. The expected price for corn plays only a minor role according to our raw estima- tes but analysis of the residuals has shown that its influence has probably been underestimated. The influence of the number of live- stock on farms is not negligible. This reflects the fact that, on many farms, feed grains are an intermediate good whose value is not well reflected by the market price, a fortiori and, especially, when the latter is influenced by government price support programs. (2) Volume of supply The econometric model predicts first the volume of production. 6It would be a mistake to think that crOpland is completely fixed in agriculture. Cropland planted varies with agricultural prices and government programs. It has decreased by 20% from 1929 to 1962. 208 In the case Of feed grains, no attempt is made to differentiate production from the volume of supply because feed-grain inventories do not technically affect the production of feed grains. In the case of pork and beef, the difference is important because of changes in livestock inventories resulting from the dual role of output and input played by hogs and beef cattle. Since the model explains both the volume of production and changes in inventories, the volume of supply at the farms can be derived from it. Through the use of price eXpectations and period analysis incorporating fixed assets, the model acquires certain limited dynamic features. These permit partial estimation of the irreversibility in supply responses. The results of the model indicate that supply conditions are favorable to instability in the meat industry. The lack of knowledge of the way price expectations are formed, however, limits the model's ability to explain cycles for pork and beef. What are then the main factors of variations in supply? (1) In the short run, it is clear that durable resources committed to the particular production during previous production periods are often fixed and thus influence output. This is true for feed grains, particularly after 1952 or 1953 because of the heavy purchases of machinery at that time. Though this study does not demonstrate this point directly, analysis of the residuals of the production function strongly suggests it. In the case of hogs and beef, the impact of changes in livestock inventories are very clear. Their size and structure at the beginning of the year play a major role in determining the volume of output and, in turn, the size and 209 structure of inventories at the end of the year. This reflects the high degree of fixity of these animals in the production of the corresponding product. It reflects also the high degree of complemen- tarity between these and other inputs (feed and labor). Though the ratio between animals and feed or labor used changed between 1929 and 1962, in any one year this ratio is much more predetermined. C. Lard's linear programming results7 indicate that fixed resources play a major role in determining the organization of enter- prises on the farm. Thus, the volume of output of a particular product depends on the fixed resource base, the availability of credit, the availability of nonfarm employment, etc. Under some conditions the most profitable adjustment even called for the sale of land in order to purchase beef facilities including equipment. This result illustrates the importance of equipment inputs omitted by our model. However, the year-tO-year variations in the quanti- ties of these inputs used are reflected by changes in livestock inventories at the beginning of the year. Therefore, the influence of livestock beginning inventories as measured for the model actually reflects also that of fixed factors not taken into account. The very important role played by fixed resources is to carry the effects on production of variations in price, in feeds available, in technology, from one time period to another. (2) EXpected prices certainly play an important role in inducing changes in the volume of supply. As explained in Chapter II, the price expectations series used in this study were derived by a fellow graduate student. Each value represents the average price 7C.F. Lard, Op. cit. 210 well-infonmed farmers could have reasonably expected at the date for which the price expectation holds, on the basis of information current- ly available at that date. The results of this study confirm generally held ideas about the low price elasticity of supply in the relatively short run (one year). Two important reservations must be made at this point, before comparing our results with those of previous authors. First our elasticities apply to our particular set of price expectations; therefore, the price elasticities computed from the model do not ' necessarily measure the elasticity with respect to either current or "the correct" price eXpectation. The second reservation refers to the meaning of a limited number of values, labeled price elasti- cities, to characterize the influence of prices when resources, which can become easily fixed, are being considered. With these qualifications in mind, it is legitimate to give price elasticities of supply as indicators of the order of magnitude of the influence of eXpected prices. For feed grains we found an average one-year elasticity equal to .11. This is fairly close to Nerlove's estimates (.09 and .18) for corn.8 For hogs the one-year elasticity given by our model (.14) is very close to that found by Cromarty9 (.13). It is in disagreement with the estimated elasticity of Spring farrowings found by Dean 8Marc Nerlove, "Distributed Lags and the Estimation of Long Run Supply and Demand Elasticities," JFE, 40: p. 301-11, 1958. 9W. Cromarty, "Economic Structure in American Agriculture," unpublished Ph.D. thesis, Michigan State University, 1957. 211 and Heady10 (.46 to .73, we found .1 for spring farrowings). But these divergences can be explained to some extent. In our equation for spring farrowings, the number of sows at the beginning of the year is considered to be predetermined. More generally the one-year elasticity computed in our model is a measure of the influence of expected prices, given the hog and sow inventories at the beginning of the year. Thus it refers to a shorter run than Dean and Heady's. Accordingly the two-year elasticity computed from the model (.32) is larger and the four-year elasticity (.48) indicates a significant influence of price on hog production. For beef our model gives a one-year price elasticity of .12 which is larger than the results of Cromarty (.037) and Wallace and Judge (.043).11 Quite normally, elasticity increases with the length of run. We found .32 for the two-year elasticity and .34 for the three-year elasticity. In summary, the elasticities given above are only rough measures of the influence of price on the volume of production. They confirm the generally held ideas that for feed-grain, pork and beef production the price elasticity is small in the short run 10G.W. Dean and E.O. Heady, "Changes in Supply Response and Elasticity for Hogs," JFE, 40, P. 845-60, 1958. The elasticity was computed with respect to the hog-corn ratio during the previous October, November and December. 11T.D. Wallace and G.G. Judge, "Econometric Analysis of the Beef and Pork Sectors of the Economy," Oklahoma Agr. Expt. Sta., Tech. Bull. 75, 1958. 212 tho.2for one year). The use of expected rather than current prices indicates that factors other than the lag of adjustment of expected prices can be responsible for these low elasticities. In this reapect, our analysis has underscored the important role played by durable resources becoming easily fixed in the production of a particular product. Besides explaining the low short-run elastici- ties, these durable resources are also an important cause of the divergence between the expansion and contraction elasticities claimed by some to result from asset fixities arising out of diver- gencies between acquisition andsalvage values. This model does not provide an estimate of the ultimate long-run price elasticity of production. But the major influence of eXpected prices on the quantities of durable resources committed to a particular production strongly indicates that prices are a major factor explaining variations in the volume of production in the long 12 run, i.e., the long-run supply function is relatively elastic. This confirms the following results of Lard's study and should dispel some reservations he made concerning them. He found that in "phase 2" (i.e., a linear program with most resources variable at acquisition costs higher than salvage values) the adjustment to changes in price was substantial; however, he raised questions concerning the problems of aggregation. This phase 2 corresponds to "long run" 12Using a different approach, J. Ferris has found a long-run elasticity of supply for hogs between 2.0 and 3.2. See J. Ferris "Dynamics of the Hog Market with Emphasis on Distributed Legs in Supply Reaponse." Unpublished Ph.D. thesis, Michigan State University, 1960. 213 We see that both approaches lead to a effects of changes in price. The substantial influence of prices on the volume of production. fact that our model is based on annual national aggregate data and gives the same general orientation as Lard's microeconomic model increases the reliability of the common conclusion. (3) Other variables are also associated with changes in the volume of production. For feed grains, the number of livestock on farms at the beginning of the year plays a significant role as indi- cated by the computed elasticity (.19) of feed-grain production with respect to the index number of livestock on farms at the beginning Numerous other variables significantly influence the 0f the year. It is sufficient to mention weather, production of feed grains. the acreage of wheat planted, the acreage of wheat not harvested and an ill-defined set of variables more or less related to tech- nical progress (These enter the model through the trend variable and to some extent through the industrial wage rate). The availability of feed grains is a key factor in the hog production. Its influence has been less important although quite significant for beef production. Other variables more or less related to technical progress These have also played an important role in hog and beef production. enter the model through time, the industrial wage rate, the price of Such high-protein feeds, the average number of pigs saved per litter. variables proved to be important in several equations. APPRAISAL OF THE RESEARCH METHOD B. In Chapter II on methodology, the limitations of the procedure 214 chosen were outlined. The limitations appeared of such an importance that some questions could be raised concerning the value of the study. It is now time to appraise the research method used in view of the results and of their limitations. This is not the place to discuss fully the advantages and shortcomings of econometrics as applied to annual data on feed grains and livestock in the U.S. A review of the main features of the method used will be more apprOpriate here. (1) Features of the research method used The main originality of this thesis lies in the use of Lerohl's price expectation series and in the structure of the model. Taking Lerohl's price expectations as given, this thesis does not examine However, it can be viewed the process of forming price expectations. Gene- as a practical test of the hypotheses underlying Lerohl's work. rally speaking, it appears that these price expectations give reasonable results. However, either they or the models are subject to the limita- tions indicated by the analysis of the residuals of several equations. In the case of hogs and particularly in the eXplanation of the number of sows at the end of the year, current prices might have predicted better. For farrowings, we have not shown that these price expectations were superior to current prices for hogs at the time decisions to farrow are taken. However, the reverse is not true either as these price expectations have never proven inferior to any other price variable used and, in many instances, give fairly good results. The performance of the "5-year" expected price for beef is surprisingly good. Therefore our In many equations, it appears as the key explanatory variable. However, results are encouraging for the new method employed by Lerohl. "-r_ 215 more evidence is needed to give a complete appraisal on his method. The structure of the various models emphasizes the process through which resources are committed to a production of a particular product. In spite of the lack of adequate data and of the shortco- mings of those which are available, the results clearly indicate that this approach is fruitful. In the case of hogs and beef, for which the livestock input can be well measured, this study has shown the great importance for the dynamics of supply of eXplaining resource fixation. The present lack of adequate data on the use of inputs by the various agricultural enterprises indicates that the profession should take steps to improve such data. Shortco- ming for the feed-grain model indicates the need for improved data. (2) Main shortcomings of the models (1) It is intuitively obvious that feeder cattle play a strategic role in beef production. Yet they are not even mentioned in our model. This indicates the degree of aggregation of the model. Because of data limitation, it was not thought advisable to incorporate them in the model for separate treatment; thus, they have been viewed as an intermediate product within the aggre- gate beef cattle enterprise which is treated as a unit in this study. (2) No real link exists between the feed-grain model and the livestock models. At first it was intended to integrate them. However, the analysis does indicate something about the relationships between them. The number of livestock on farms at the beginning of the year is associated with the acreage of feed grains planted while Its—4- a. l I? 216 feed-grain supplies play important roles in the hog and the beef models. To link these models together would have required exten- sive study of the way price expectations are formed for corn or to drop this variable altogether. The first alternative was beyond the scape of this thesis while the second alternative promised to worsen the already inadequate explanation of feed-grain production. (3) Future research As one of our professors humorously said: "All researchers find at least one thing: the need for further research." This study does not escape the general rule and suggests areas for which further research seems necessary. (1) Our results will have to be analyzed and qualified in the light of the results of other approaches followed in NC-54, particularly, the aggregation of the programming results. Considerable research is needed to orient the collection (2) of data relevant to studies of resource use and agricultural commo- dity supply. Indeed, there is a lack of adequate data on this matter Furthermore, there is a lack of knowledge on at the present time. In some cases the what data are needed and how to collect them. cost of obtaining the data required by theory may be prohibitive. Theoretical efforts are then needed to build a more Operative analy- tical framework. (3 ) The importance of the process through which resources are committed to production of a particular product suggests that studies in this area are crucial for a better knowledge of supply phenomena. 217 (4) Last, but not least, a better knowledge of the way price exPec- tations are formed and, more generally, of the way farmers receive information concerning demand appears essential for a better coordi- nation of supply and demand studies. , Qu- rug-g 92mm ,bal m “'- vo' a .Juoi ace 3" .33 1 \ v '..'t;fl r H.‘}l§r«.\13% bumb 2,1111!an 'tuu‘u bunsmb but 15““ 3Q .: In... APPENDIX ESTIMATES OF THE BEEF MODEL EQUATIONS USED TO COMPUTE THE ELASTI- CITY OF BEEF PRODUCTION WITH RESPECT TO EXPECTED PRICES. All beef prices are indicated by P; for the definition of the other variables refer to table 11, p. 145 of Chapter V. Variables not affected by a change in price are grouped in the constant term (cst). The choice of the most probable value of these parameters is discussed in the presentation of the results equation by equation (pp. 149 to 174) PC = cst + .30 P + .75 TC E HP = cst + .25 P + 1.0 TC ( Lab =cst + .1 P + .45 TC Variables E Output = cst + .12 PC + .15 HP + .45 Lab + .40 TC in l°g ( v0 = cst + 1.0 [ct-1 + 1/2 maul] E 'Vr = cst + l'OVt-l + .21P E v8 = cst + 3.66 vb - 2.3 vt_1 - .70P E Ht = cst + .82 vt_1 + .35P Natural ( A St = .47 AVt-1 - .57ASt-1 + .53 1.3.2.. values ( St -§ P 37:32:19,532 A Ct: = 1.01)“ —1 - .24 Act-1 + .20 A}: ( Ct '2? P Vt = vt_1+vb -vr-vfi3 -DV TC = Vt +11t +st +Ct +13“) (3) B stands for the number of bulls. 218 219 APPENDIX (Contd.) Mean values of livestock numbers over the sample period used to convert relative changes into absolute changes and vice-versa: 6 16,810 fi = 4,727 TC 43,671 MI I 7,356 n =13,875 vb 24,055 Ed=23,950 BIBLOGRAPHY Akerman, Gustav, "The Cobweb Theorem: A Reconsideration," Quarterly Journal of Economics, Vol. 71, 1957, pp. 151-160. Basman, R.L. "The Causal Interpretation of Non Triangular Systems of Economic Relations," Econometrica, Vol. 31, No. 3, July 1963, p. 439. Bentzel, R. and Hansen, B. "On Recursiveness and Interdependency in Economic Models," Review of Economic Studies, Vol. 22, 1954- 1955. Brandow, G.E. Factors Associated With Number of Sows Farrowing in the Spring and Fall Seasons, A.B. and R.S. Bulletin 7, Pennsylvania Agricultural Experiment Station, 1955. Breimyer, H.F. Demand and Price for Meat, U.S.D.A. Technical Bulletin 1253, December 1961. Cavin, J.P. 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